OTICES OF THE

AMERICAN MATHEMATICAL SOCIETY

1989 Steele Prizes page 831

SEPTEMBER 1989, VOLUME 36, NUMBER 7 Providence, Rhode Island, USA ISSN 0002-9920 Calendar of AMS Meetings and Conferences

This calendar lists all meetings which have been approved prior to Mathematical Society in the issue corresponding to that of the Notices the date this issue of Notices was sent to the press. The summer which contains the program of the meeting. Abstracts should be sub­ and annual meetings are joint meetings of the Mathematical Associ­ mitted on special forms which are available in many departments of ation of America and the American Mathematical Society. The meet­ mathematics and from the headquarters office of the Society. Ab­ ing dates which fall rather far in the future are subject to change; this stracts of papers to be presented at the meeting must be received is particularly true of meetings to which no numbers have been as­ at the headquarters of the Society in Providence, Rhode Island, on signed. Programs of the meetings will appear in the issues indicated or before the deadline given below for the meeting. Note that the below. First and supplementary announcements of the meetings will deadline for abstracts for consideration for presentation at special have appeared in earlier issues. sessions is usually three weeks earlier than that specified below. For Abstracts of papers presented at a meeting of the Society are pub­ additional information, consult the meeting announcements and the lished in the journal Abstracts of papers presented to the American list of organizers of special sessions. Meetings

Abstract Program Meeting# Date Place Deadline Issue 851 • October 21-22, 1989 Hoboken, New Jersey August 16 October 852 • October 27-28, 1989 Muncie, Indiana August 16 October 853 • November 18-19, 1989 Los Angeles, California August 16 November 854 • January 17-20, 1990 Louisville, Kentucky October 11 December t (96th Annual Meeting) • March 16-17, 1990 Manhattan, Kansas December 12 February March 23-24, 1990 Fayetteville, Arkansas December 12 February • • April 7-8, 1990 University Park, Pennsylvania January 25 March August 8-11 , 1990 Columbus, Ohio (93rd Summer Meeting) November 2-3, 1990 Denton, Texas January 16-19, 1991 San Francisco, California (97th Annual Meeting) August 8-11, 1991 Orono, Maine (94th Summer Meeting) January 8-11, 1992 Baltimore, Maryland (98th Annual Meeting) June 29-July 1, 1992 Cambridge, England (Joint Meeting with the London Mathematical Society) January 13-16, 1993 San Antonio, Texas (99th Annual Meeting) January 5-8, 1994 Cincinnati, Ohio (100th Annual Meeting) • Please refer to page 903 for listing of special sessions. •• Please note a change in this date making it earlier than previously published. t Preregistration/Housing deadline is November 17

Conferences

June/July 1990: AMS-Siam Summer Seminar on Vortex Dynamics and Vortex Methods, location to be announced. Deadlines

November Issue December Issue January Issue February Issue Classified Ads* Oct 3, 1989 Oct 27, 1989 Nov 27, 1989 Jan 10, 1990 News Items Oct 5, 1989 Nov 2, 1989 Nov 27, 1989 Jan 2, 1990 Meeting Announcements•• Sept 26, 1989 Oct 26, 1989 Nov 22, 1989 Dec 21, 1989 • Please contact AMS Advertising Department for an Advertising Rate Card for display advertising deadlines. •• For material to appear in the Mathematical Sciences Meetings and Conferences section. OTICES OF THE

AMERICAN MATHEMATICAL SOCIETY

ARTICLES DEPARTMENTS

828 Edward James McShane (1904-1989) Wendell Fleming and Victor 827 Letters to the Editor Klee · 853 News and Announcements Edward J. McShane's life and contributions to twentieth century "mathematics are highlighted. 864 Funding Information for the Mathematical Sciences 831 1989 Steele Prizes Awarded 867 Acknowledgement of The 1989 Steele Prizes were awarded at the Society's ninety-second Contributions Summer Meeting in Boulder, Colorado to Daniel Gorenstein for 891 Meetings and Conferences expository writing, to Alberto Calderon for a fundamental paper, and to of the AMS (Listing) Irving Kaplansky for his mathematical career. 910 1989 AMS Elections Candidates Election Information 911 Mathematical Sciences Meetings and Conferences FEATURE COLUMNS 921 New AMS Publications 929 AMS Reports and 837 Computers and Mathematics Jon Barwise Communications This month's column contains two reviews, one of DERIVE and the Recent Appointments, 929 other of Calculus Calculator. Also included is a piece reporting on a Statistics on Women current controversy about the use of mathematics in showing that Mathematicians, 929 computer systems are correct. Officers, 931 942 Miscellaneous 852 Washington Outlook Kenneth M. Hoffman Personal Items, 942 This month's column, written by Hans J. Oser, provides an overview of Deaths, 942 current events on Capitol Hill of interest to Notices readers. Visiting Mathematicians (Supplement), 943 945 Backlog of Mathematics Research Journals 948 New Members of the AMS 951 Classified Advertising 965 Forms

SEPTEMBER 1989, VOLUME 36, NUMBER 7 825 Volunteer Activity

Many scientific and professional organizations are voicing concern over a changing attitude toward volunteer activity. Most evidence seems to be anec­ dotal. However, volunteer service in support of the scientific activity of the AMERICAN MATHEMATICAl. SOCIETY Society is too important to take these concerns lightly. We need to understand what changes are taking place and, if necessary, react to maintain member involvement in the scientific decision making of the Society. There are two principal issues that seem to be new to volunteer activities at EDITORIAL COMMITTEE Robert J. Blattner, Michael G. Crandall scientific and professional societies. The first issue is a difficulty in finding Robert M. Fossum (Chairman) members willing to volunteer for service to the Society and the mathematics Lucy J. Garnett, D. J. Lewis community. The second is that compensation is being sought to pay for Nancy K. Stanton, Robert E. L. Turner administrative support and released time. INTERIM MANAGING EDITOR While not as big a problem at the AMS as at some other societies, these issues James W. Maxwell are of concern. What are the attitudes that have influenced these issues? ASSOCIATE EDITORS Sociological cycles parallel certain highs and lows of interest in scientific Ronald L. Graham, Special Articles and professional organizations. However, Society membership is increasing Jeffrey C. Lagarias, Special Articles and requests for Society involvement in various scientific and professional SUBSCRIPTION INFORMATION matters are similarly increasing. I do not perceive any decline of interest Subscription prices for Volume 36 (1989) are in what the Society could, or should, be doing to serve the mathematical $1 08 list; $86 institutional member; $65 individual community. member. (The subscription price for members is included in the annual dues.) A late charge of There has been a period of extreme pressure on the profession as employ­ 10% of the subscription price will be imposed ment opportunities for research mathematicians slowed down and tenure upon orders received from nonmembers after evaluations began to dominate the business of academic departments. Such January 1 of the subscription year. Add for post­ evaluation processes often have little emphasis placed on service and almost age: Surface delivery outside the United States and lndia-$10; to lndia-$20; expedited deliv­ no emphasis placed on service outside the immediate institution doing the ery to destinations in North America-$15; else­ evaluation. Proper recognition for mathematicians who contribute valuable where-$38. Subscriptions and orders for AMS service to the profession is a matter of great importance to the Society. At publications should be addressed to the Amer­ the present, it is very difficult for members to receive proper recognition and ican Mathematical Society, P.O. Box 1571, An­ reward for taking time away from scholarly and personal activities to partic­ nex Station, Providence, Rl 02901-9930. All or­ ders must be prepaid. ipate in Society activities. The Council of the Society took action during its August meeting to provide awards and citations in recognition of public and ADVERTISING professional service. It is hoped that this action will lead to encouragement Notices publishes situations wanted and classi­ and recognition for such service. Details on these awards and citations will fied advertising, and display advertising for pub­ lishers and academic or scientific organizations. be reported in later Notices. Copyright@ 1989 by the American Mathemat­ Universities, colleges, and corporations are also undergoing a change in policy ical Society. All rights reserved. Printed in the toward volunteer activities of their employees. In the past, these institutions United States of America. have provided released time, staff support, and other needs to enable the The paper used in this journal is acid-free and falls within the guidelines established to ensure volunteer to better perform outside professional activities. These institutions permanence and durability. @ Most of this publi­ now call upon the Society for compensation and reimbursement. cation was typeset using the TeX typesetting sys­ There is another issue that has been raised in this context. Namely, some tem. question the amount of reliance on AMS staff, as opposed to membership [Notices of the American Mathematical Society is support, for carrying out the work of the Society. I believe the effectiveness published ten times a year (January, February, March, April, MayfJune, July/August, Septem­ of our volunteer activity can be enriched through staff support. However, this ber, October, November, December) by the Amer­ support should be in parallel with service from Society members. ican Mathematical Society at 201 Charles Street, The importance of the volunteers who contribute their time and service for Providence, Rl 02904. Second class postage paid at Providence, Rl and additional mailing offices. the scientific activities of the Society cannot be overestimated. We are for­ POSTMASTER: Send address change notices to tunate in the AMS to have a very conscientious and supportive volunteer Notices of the American Mathematical Society, leadership. It will be this volunteer leadership, officers as well as committee Membership and Sales Department, American members, that determines the success of the Society as we consider the many Mathematical Society, P. 0. Box 6248, Provi­ dence, Rl 02940.1 Publication here of the Soci­ complex issues facing the mathematics community. ety's street address, and the other information in The Society needs this valuable contribution from the widest possible repre­ brackets above, is a technical requirement of the sentation of its membership. U. S. Postal Service. All correspondence should be mailed to the Post Office Box, NOT the street William H. Jaco address. Executive Director

8216 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Policy on Letters to the Editor TM Letters Letters submitted for publication in Notices are reviewed by the Editorial Committee, MathSci whose task is to determine which ones are to the Editor suitable for publication. The publication schedule normally requires from two to WHEN MathSci IS ONLINE four months between receipt of the letter in MATIIEMATICS IS Providence and publication of the earliest Guidelines for Referees issue of Notices in which it could appear. ON TilE SCREEN The pamphlet "A manual for au­ Publication decisions are ultimately thors of mathematical papers" has made by majority vote of the Editorial 800,000 Entries in Seconds Committee, with ample provision for prior MathSclls the online database that finds, been very helpful to the mathemat­ discussion by committee members, by mail In a matter of seconds, any information ical community. However I think or at meetings. 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SEPTEMBER 1989, VOLUME 36, NUMBER 7 827 Edward James McShane 1904-1989

E. J. McShane was born in New Orleans and died 85 under the supervision of G. A. Bliss and L. M. Graves. years later in Charlottesville, Virginia. He was a major For the following two years he held a National Research contributor to several areas of mathematics, including the Council Fellowship, spent at Princeton, Ohio State, Har­ calculus of variations, integration theory, control theory, vard and Chicago. This was a period during which the and stochastic calculus. He had a strong concern for the calculus of variations for multiple integrals was develop­ well-being of his fellow mathematicians and contributed ing rapidly, including the problem of finding a minimal to this in many ways. He was a deeply cultured man, with surface with given boundary (Plateau's problem). The a flair for languages and a great variety of other interests. "direct methods" explained in L. Tonelli's then new book He was widely known for his warmth, generosity, and Fondamenta di Calcolo della Variazione provided a key modesty, and for his fund of humorous and interesting tool in these developments. McShane had earlier learned anecdotes. Italian in order to read opera libretti. He read Tonelli McShane was elected to the National Academy of while yet a graduate student, and soon afterward reached Sciences in 1948. He served as President of the Mathe­ the forefront of research on multiple integral problems. matical Association of America in 1953 and 1954, and President of the American Mathematical Society in 1958 and 1959. Thus he was one of only four people who have, in the past fifty years, served both the AMS and the MAA as President. He later served from 1956 to 1968 as a member of the National Science Board. These periods of service, in addition to his service on numerous committees, illustrate the breadth and the depth of his concern for the mathematical community. McShane's father was a medical doctor and his mother a former school teacher. He grew up in New Orleans, and throughout his life felt a strong attachment to that city. He graduated from Tulane University in 1925, receiving the Bachelor of Science and Bachelor of Engineering degrees simultaneously. He turned down an offer from General Electric and instead continued as a student instructor of mathematics at Tulane, receiving a Master of Science degree in 1927. He maintained an interest in the mathematics associated with engineering problems, but once remarked that he had never regretted his decision to become a mathematician rather than an engineer. He received a honorary doctorate from Tulane in 1949. In the summer of 1927, McShane entered graduate school at the University of Chicago. During 1928-1929, it was necessary for financial reasons to interrupt his studies and teach at the University of Wichita. Never­ theless, he was able by 1930 to complete his doctoral dissertation and to receive his Ph.D. degree from Chicago

828 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Edward James McShane

In 1931 he married Virginia Haun, who survives him. in various guises. He wrote three books on integration, Over the years the McShanes had an unusually warm, in addition to a number of research articles. His 1944 closely knit family life with their three children and volume Integration provided a readable introduction to later two sons-in-law, all trained in music as well as the Lebesgue theory at a time when few such books mathematics. (Later six grandchildren joined the group.) existed in English. He once remarked that any textbook McShane himself was a devoted amateur cellist who was likely to be criticized by its readers for not supplying found great pleasure in his family's musical activities. In enough details, and by experts in its field for supplying his later years, he developed a strong interest in Chinese too many details. He said that in writing the book on painting and calligraphy, and spent many happy hours in integration he had ignored the second possibility, since improving his technique. he was writing to instruct and not to impress. Many Because of the Great Depression, openings in math­ students benefited from the clarity of his exposition. ematics departments were virtually nonexistent in 1932. McShane's 1953 monograph on Order Preserving The McShanes spent 1932-1933 at Gottingen, during Maps and Integration Processes was an outgrowth of which time he translated into English the two volumes of his search for a mathematically correct setting in which Courant's Differential and Integral Calculus. They also to treat divergent integrals in quantum physics. He was saw at first hand some frightening aspects of the onset considerably bothered by what he considered pseudo­ of Nazi power in Germany. After two years ( 19 33-193 5) mathematical reasoning in the physics literature. After on the faculty at Princeton, McShane joined the Depart­ reading one such "pseudoproof'' of a result for which a ment of Mathematics at the University of Virginia as a correct proof due to von Neumann was already available, full professor in the fall of 1935. He remained there for McShane commented: "Anyone who can write such the rest of his career, except for leaves of absence spent statements has forfeited all right to be scornful of the at other institutions. woman who could 'trace her ancestry to William the In the late 1930s, McShane developed methods to Conqueror with only two gaps'." provide existence theorems and necessary conditions His interest in the mathematical foundations of quan­ for a very large class of single integral problems in tum mechanics and quantum field theory continued for the calculus of variations. He introduced the use of many years after World War II. Although his ambitious convex cones of variations, and observed that optimality program in these areas did not reach fruition, the attempt of a trajectory implies the existence of a hyperplane profoundly influenced his subsequent work on integra­ separating a certain cone and ray from each other. tion processes and stochastic calculus. This is seen, for This approach later provided the key to Pontryagin's example, in his excellent 1963 survey article on Integrals principle in control theory during the 1950s, and to later Designed for Special Purposes and in his 1974 book on developments in convex and nonsmooth analysis. Stochastic Calculus and Stochastic Models, which is the With the onset of World War II, McShane agreed definitive treatment of his approach to that subject. to head a mathematics group at the Ballistics Research Laboratory in Aberdeen, Maryland. During this period In the 1960s and 1970s, when McShane's research in­ (1942-1945) he wrote with J. L. Kelley and F. V. Reno a terests turned toward developing a stochastic differential book on Exterior Ballistics, regarded as a definitive work and integral calculus, the stochastic calculus of K. Ito on the subject. He was the AMS Colloquium Lecturer at was already in existence. It provided a convenient way the summer meeting of 1943. to represent an important class of stochastic processes, McShane was deeply offended by the injustices called Markov diffusions, as the solutions to stochas­ suffered by some of his colleagues during the anti­ tic differential equations. For a stochastic differential communist hysteria that followed the war. In response equation in the sense of Ito, the random inputs are to a question on the security form of the Aberdeen Brownian motion processes whose formal time deriva­ Proving Grounds, asking whether he had ever been tives are "white noises." However, at the time there involved with organizations that had at any time ad­ was considerable confusion in the engineering literature vocated the violent overthrow of the U.S. government, about the correct interpretation if an idealized white he replied affirmatively-that he was an employee of the noise is replaced either by a physical "wide band" noise State of Virginia. During the McCarthy era, the House or by a discrete process introduced for numerical ap­ Un-American Activities Committee "invited" him to ex­ proximation to the solution of the stochastic differential press his views, but he was not subpoenaed. He did not equation. This important issue was clarified by the work cooperate with HUAC, but wrote a letter in which he of McShane, Stratonovich, and Wong-Zakai. stated his views and backed them up with quotations In 1957, J. Kurzweil defined a modification of the from various sources. Riemann integral that turned out to be more general Over the years McShane achieved an extraordinarily than the Lebesgue integral. McShane's last book, Unified deep understanding of integration processes as they arise Integration, published in 1983, develops in a similar

SEPTEMBER 1989, VOLUME 36, NUMBER 7 829 Edward James McShane vein a theory of integrals with applications to physics, the graduate students could do their work and meet to differential equations, and probability. discuss problems of common interest. His visits to the During the 1950s and 1960s, McShane took a se­ office were often accompanied by the introduction of a rious interest in efforts then under way to revitalize new mathematical problem or by his own contribution to undergraduate mathematics in the United States. The a problem already under discussion. (One student, having MAA's Committee on the Undergraduate Program in made some progress on a problem but finding himself Mathematics was established during his term as MAA unable to solve it completely, intoned "Oh, for the President, and ever since then has been a leader in these brain of McShane!") Not only McShane himself, but his endeavors. In 1964 he received the MAA's Annual Award wife Virginia and the McShane children were extremely for Distinguished Service to Mathematics. helpful and hospitable to the graduate students. They Although AMS and MAA were the two organizations contributed greatly to fostering a sense of mathematical that benefited administratively from McShane's services camaraderie at the University of Virginia. as President, his research efforts were also of great interest A popular mathematical joke claims that mathemat­ to members of the Society for Industrial and Applied ical talent passes from the father to the son-in-law. It is Mathematics. The September 1989 issue of SIAM's true that the McShanes' sons-in-law, H. N. Ward at the Journal on Control and Optimization is dedicated to University of Virginia and R. B. Warfield at the Univer­ McShane. sity of Washington, are both research mathematicians. McShane's strong sense of fairness was exhibited in However, the McShanes' daughters, Jennifer Ward and many ways. For instance, as an editorial board member Ginger Warfield, are also mathematicians, and Ginger is he went out of his way to see that papers by young au­ a member of the UW faculty. Some of the grandchildren thors were refereed fairly and helpfully. He was extremely have also exhibited exceptional mathematical talent. popular with the graduate students at the University of Both mathematical research and the mathematics Virginia because of his clear lectures, his amusing anec­ community have been enriched by McShane's contribu­ dotes, and his willingness to think about their problems. tions and his many years of dedicated service to our During the 1940s and early 1950s, the university did not profession. provide office space for graduate students, so McShane Wendell Fleming, Brown University made his own office available as a common room where Victor Klee, University of Washington

CLASSICAL GROUPS AND RELATED TOPICS Alexander J. Hahn, Donald G. James, and Zhe-Xian Wan, Editors (Contemporary Mathematics, Volume 82)

During his lifetime, L. K. Hua played a leading role in To honor his memory, a joint China-U.S. conference on and exerted a great influence upon the development in Classical Groups and Related Topics was held at Tsinghua China of modern mathematics, both pure and applied. His University in Beijing in May 1987. This volume represents the mathematical career began in 1931 at Tsinghua University proceedings of that conference and contains both survey where he continued as a professor for many years. Hua articles and research papers focusing on classical groups and made many significant contributions to number theory, closely related topics. algebra, geometry, complex analysis, numerical analysis, and 1980 Mathematics Subject Classifications: 11E, 18F, 20C, 200, 20F, operations research. In particular, he initiated the study of 20G, 20H classical groups in China and developed new matrix methods ISBN 0-8218-5089-X, LC 88-31519 which, as applied by him as well as his followers, were ISSN 0271-4132 instrumental in the successful attack of many problems. 272 pages (softcover). January 1989 Individual member $17, List price $28, Institutional member $22 To order, please specify CONM/82NA

All prices subject to change. Shipment will be made by surface. For air delivery add, 1st book $5, each additional book $3, maximum $100. Prepayment required. Order from American Mathematical Society, P.O. Box 1571, Annex Station, Providence, RI 02901-1571, or call toll free 800-566-7774 to charge with VISA or MasterCard.

830 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY 1989 Steele Prizes Awarded at Summer Meeting in Boulder

T~ree Leroy P. Steele Prizes were awarded at the Society's Finite Simple Groups, An Introduction to their Clas­ nmety-second Summer Meeting in Boulder, Colorado. sification ( 1982); possible by a bequest to The Steele Prizes are made and his two survey articles: the Society by ~r. Steele, a graduate of Harvard College, Class of 1923, m memory of George David Birkhoff The Classification of Finite Simple Groups, and William Fogg Osgood, and William Caspar Graustein. ' Classifying the Finite Simple Groups, Bulletin of Three Steele Prizes are awarded each Summer: one the American Mathematical Society 1 ( 1979) pages for expository mathematical writing, one for a research 43-199, and 14 (1986) pages 1-98, respectively. importance, and one paper of fundamental and lasting The classification of finite simple groups was the influence extending over a in recognition of cumulative largest joint mathematical effort dedicated to the proof of doctoral students. The career, including the education of a single theorem. The first hint that such a classification current award is $4,000 for each of these categories. could be done was given by Brauer at the International The recipients of the 1989 Steele Prizes are DANIEL Congress in Amsterdam in 1954. Brauer's idea was to award; ALBERTO GORENSTEIN for the expository study centralizers of involutions. Several deep theorems of fundamental impor­ CALDERON for research work were proved in the late SO's and early 60's. Early in for the career award. tance; and IRVING KAPLANSKY the 80's the program was finished, except for the formal awarded by the Council of The Steele Prizes are writing of announced results and the checking of details. the Society, acting through a selection committee whose What happened is extremely complicated. Hundreds members at the time of these selections were Frederick of mathematicians got involved in the work, a vast Charles L. Fefferman, J. Almgren, Luis A. Caffarelli, enterprise was created, and over 10,000 journal pages Massey (Chairman), Frank A. Jun-ichi lgusa, WilliamS. appeared. During most of this period it was not at all P. Raymond, Neil J. A. Sloane, Louis Solomon, Richard clear where things were going or even whether success Stanley, and Michael E. Taylor. was possible. An uncharted universe full of too many the Committee's ci­ The text that follows contains unknown simple groups was an uncomfortable possibil­ recipients' responses to the tations for each award, the ity to the classifiers. Twenty-one previously unknown sketch of each of the award and a brief biographical sporadic groups were found in the period 1965-1980. recipients. Professors Calderon and Kaplansky were un­ It would be almost impossible for our mathematical ~ble to attend the Summer Meeting to receive the prize grandchildren to understand the achievements of the to m person. They did, however, send written responses present generation on the classification problem without the award. some guide through the tangle. This is what Gorenstein has given them in these three enthusiastic and well Expository Writing written surveys. Gorenstein was a major figure in setting the direction of the classification program. He coordinated the activi­ Daniel Gorenstein ties in the program, functioning as the "coach" to a team, with optimism, perseverance, and technical power. His expository articles and books, especially the ones we list Citation here, are beautiful accounts of this fantastic intellectual adventure. His presentation of theorems and definitions, The 1989 Steele Prize for Expository Writing is awarded as well as the flow of argument and the evolution of to DANIEL GORENSTEIN for his book: the ideas, is precise and generous and reaches out to

SEPTEMBER 1989, VOLUME 36, NUMBER 7 831 1989 Steele Prizes the reader. Again and again, he invites the reader to also served as visiting assistant professor at Cornell join in yet another episode, to share the excitement of from 1958 to 1959. In 1964, he moved to Northeastern a new idea and the frustration of coping with a deluge University. In 1968-1969, he was a member of the of difficulties. Along with the formalities, he tries to give Institute for Advanced Study, and in 1969 he became a feeling for the way the ideas work. When appropriate, a professor of mathematics at Rutgers University. He he is sketchy, yet does not talk down to the reader. was chairman of the department there from 197 5-1981, These surveys are useful references for specialists and and in 1984, he was named the Jacqueline B. Lewis are also narratives for the general mathematical public. Professor of Mathematics. Since February, 1989, he has Considering the complexity of the subject, this is a great been Director of the new National Science Foundation accomplishment. Science Technology Center in Discrete Mathematics and Gorenstein proved some of the landmark results in Theoretical Computer Science, a consortium of Rutgers the program. His numerous research papers are among and Princeton Universities, AT&T Bell Laboratories, the technically most difficult in the field. It is fortunate and Bell Communications Research. His main research for mathematics that one who was able to contribute interest is finite simple group theory. so much to the effort is also able to convey to us the Professor Gorenstein was a Guggenheim Fellow excitement of the discovery and the ultimate coherence ( 1972-1973), as well as a Fulbright Research Scholar of the classification program. (1972-1973) and a Sherman Fairchild Distinguished Scholar at the California Institute of Technology ( 1978). He was elected to the National Academy of Sciences and to the American Academy of Arts and Sciences in 1987. He has been an Associate Editor of Communications in Algebra (1975-1983) and of Annals of Mathematics (1979-1984). Professor Gorenstein presented Invited Addresses at the International Congress of Mathematicians in Nice, France ( 1970) and in Helsinki, Finland ( 1978), as well as an address at the British Mathematical Colloquium in Bangor, Wales in 1982. A member of the AMS for 45 years, Professor Gorenstein has been active in the mathematical activities of AMS-sponsored meetings. Among these are presentation of an Invited Address in New York in 1971 and organization of a special session on Classification of Finite Simple Groups in San Francisco in 1981. He also delivered the Colloquium Lectures in Anaheim in 1985.

Response

I am delighted and honored to have been awarded the Steele Prize for my writings on the classification of the finite simple groups. From the late 1950s until the early 1980s was a very exciting period in finite group theory. I had switched into the field from algebraic geometry, almost by accident in 1957, learning the basic material from Herstein while collaborating with him over the next few years. My first foray into simple group theory Daniel Gorenstein dated from the famous 1960-61 group theory year at the University of Chicago, during which Feit and Thompson Biographical Sketch settled the solvability of groups of odd order. It was there that I began a long collaboration with John Walter Daniel Gorenstein was born on January 1, 1923, in and met many of the then leaders in the field: Brauer, Boston, Massachusetts. He received his Ph.D. from Suzuki, Graham Higman, and Ito. (It was only somewhat Harvard University in 1950. later that I met Philip Hall and Wielandt.) Alperin was Professor Gorenstein's first academic position was spending the year in Chicago to write his thesis with at Clark University, where he remained until 1964. He Higman, while still a graduate student at Princeton.

832 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY 1989 Steele Prizes

Largely under the impetus of the odd order theorem, group theorists were off on the wrong track. No math­ there was an awakening interest in finite group theory. ematical theorem could require the number of pages Throughout the next decade and a half a long list these fellows were taking! Surely they were missing some of gifted young mathematicians, who were to play a geometric interpretation of the simple groups that would prominent role in the classification proof, were attracted lead to a substantially shorter classification proof. to the field. In the United States, Thompson had a string The view from the inside was quite different: all the of outstanding graduate students: Sims, Goldschmidt, moves we were making seemed to be forced. It was not Lyons, Griess. Glauberman was a student of Bruck's at perversity on our part, but the intrinsic nature of the the beginning of the period and Aschbacher near the problem that seemed to be controlling the directions of end. Ronald Solomon wrote his thesis with Feit, Seitz our efforts and shaping the techniques being developed. with Curtis, Stephen Smith (an American) with Higman Thus in writing about the classification for the general at Oxford, O'Nan with me, and Shult was essentially mathematical audience, I had a dual motivation: on the self-taught. one hand, to convey the nature of the solution as But the attraction was not limited to the United it was unfolding, both the methods involved and the States. Janko in Australia, Conway in England, and Fis­ striking results themselves, and, on the other, to attempt cher in Germany, each discovering three new sporadic to convince the larger community that the internal groups, stimulated considerable additional interest, lead­ inductive approach we were taking to the classification ing to an intensification of the search for further simple was, despite its resulting length, the only viable one for groups. Tits (entering the field somewhat earlier) had establishing the desired theorem. I hope I have achieved deepened our understanding of the Chevalley groups and this second objective and I am indeed gratified that the their Steinberg-Suzuki-Ree variations, Bender in Ger­ summaries I provided of the classification proof have many was to prove the fundamental strongly embedded been held in high regard. subgroup classification theorem, and Harada was begin­ ning his career in Japan. At the end of the period, there Fundamental Paper were a number of others: Foote from Canada working with Thompson in Cambridge, England, Geoffrey Mason from England, corning to the United States, and writing Alberto Calderon his thesis with Fong, himself a former student of Brauer, Citation and in Germany, Tirnrnesfeld and Stellmacher, students of Fischer, and Stroth, a student of Huppert, but writing The 1989 Steele Prize for a Fundamental Paper is his thesis on a problem suggested by Held, who had awarded to ALBERTO P. CALDERON for his paper: himself been a student of Janko. There were a great many other group theorists as well Uniqueness in the Cauchy Problem for Partial Differ­ who made significant contributions to the classification ential Equations, American Journal of Mathematics proof. But it was Aschbacher's entry into the field in 80 ( 1958), pages 16-36. the early 1970s that irrevocably altered the simple group Calderon's paper marks a real watershed in the theory landscape. Quickly assuming a leadership role in a single­ of singular integral operators, taking it beyond its tradi­ minded pursuit of the full classification theorem, he was tional role in the study of elliptic equations. The specific to carry the entire "team" along with him over the application is to uniqueness in the Cauchy problem, a following decade until the proof was completed. phenomenon which remains one of the most mysterious I was fortunate indeed to have interacted in one way in linear PDE. In attacking this problem, Calderon set or another during this twenty-year period with most of up an approach to energy estimates which has been of the mathematicians I have mentioned. fundamental importance in dozens of subsequent inves­ Simultaneously with this burgeoning research effort, tigations. Its specialization to hyperbolic equations alone finite simple group theory was establishing a well­ has been very significant. It has also provided a model deserved reputation for inaccessibility because of the for general investigations, into such matters as local inordinate lengths of the papers pouring out. The 255 solvability. Truly this paper was a major progenitor of page proof of the odd order theorem, filling an entire the modern theory of rnicrolocal analysis. issue of the Pacific Journal, had set the tone, but it was by far not the longest paper. Moreover, the techniques being developed, no matter how seemingly powerful for Biographical Sketch the problems at hand, appeared to have no applications outside of finite group theory. Although there was ad­ Alberto P. Calderon was born on September 14, 1920, miration within the mathematical community for the in Mendoza, Argentina. A student of Alberto Gonzalez achievements, there was also a growing feeling that finite Dominguez and Antoni Zygrnund, Professor Calderon

SEPTEMBER 1989, VOLUME 36, NUMBER 7 833 1989 Steele Prizes received his Ph.D. from the University of Chicago in of the National Academy of Sciences, the American 1950. Academy of Arts and Sciences, and the French Academy Professor Calderon began his academic career as of Sciences. a visiting associate professor at Ohio State University Professor Calderon gave an Invited Address at the (1950-1953). He was also a member of the Institute for International Congress of Mathematicians in Moscow Advanced Study ( 1955) and served as associate professor ( 1966). In addition, he presented an AMS Invited Ad­ at the Massachusetts Institute of Technology ( 1955- dress in University Park in 1957 and delivered the AMS 1959). He then moved to the University of Chicago, Colloquium Lectures on Singular Integrals in Ithaca in where he served as professor of mathematics ( 1959- 1965. He serves as associate editor of the Journal ofFunc­ 1968); Louis Block Professor (1968-1972); and chairman tional Analysis, the Journal of Differential Equations, and of the mathematics department (1970-1972). He returned Advances in Mathematics. to MIT, where he was professor of mathematics ( 1972- Professor Calderon has been a member of the AMS 1975). From 1975 to 1985, he was University Professor for 40 years. He was a Member-at-Large of the Council of Mathematics at Chicago and is currently professor ( 1965-1967) and has served on numerous committees. emeritus. Since 1975, he has simultaneously held a These include the Transactions and Memoirs Edito­ position as honorary professor at the University of rial Committee ( 1959-1964); the Nominating Commit­ Buenos Aires. tee (1968-1969); the Colloquium Editorial Committee (1971-1976); and the Publications and Communications Committee (1971-1976).

Response The Steele Prize bestows great honor on its recipients. I am most grateful for having been deemed worthy of joining their ranks. I would like to make a few remarks-some of them perhaps of still current interest-on the paper "Unique­ ness of the Cauchy Problem ... " for which I was awarded the Prize. In trying to obtain the result in the paper, and after several fruitless attempts, I was finally led to the realization that every linear differential operator with sufficiently smooth coefficients can be represented as a composition of a singular integral operator and a fractional power of the Laplacian. These singular integral operators, which were slightly more general than the ones considered up to that time, form a nice algebra and can be manipulated with relative ease. This permitted me to obtain the necessary energy estimates and to prove the desired result. It was immediately realized that the representation described above had a much wider scope of applications than just to the uniqueness of the Cauchy Problem, and other applications soon followed. Also the theory was greatly refined and extended in a certain direction through the introduction of the algebra of pseudo­ differential operators by Kohn and Nirenberg. Linear Alberto Calderon differential operators with infinitely differentiable coef­ ficients are included in this algebra, but more general Professor Calderon received the Bocher Prize of ones are not, as can be seen immediately by observing the AMS in 1978 for a paper on the Cauchy integral on that differential operators with non-infinitely differen­ Lipschitz curves. In 1989, he was awarded the Wolf Prize tiable coefficients cannot be composed freely. To deal in mathematics for his groundbreaking work on singular with such operators it is necessary to return to the rep­ integral operators and their application to important resentation described above. It is possible to construct a problems in partial differential equations. He is a member scale of algebras of singular integral operators of various

834 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY 1989 Steele Prizes degrees of refinement well suited to the treatment of As commutative algebra took on new life with the differential operators with coefficients of various degrees infusion of homological methods, he turned his interest of smoothness. The description of these algebras will once more in this direction, always trying to see past the appear in print in a not too distant future. formalism into "what was really going on." His remark­ Finally I would like to mention two problems of able success in doing so is witnessed by his publications interest that await solution. from the late fifties onward and the influence they have The first one is to decide whether it is possible to had on other writers. Meanwhile he was continuing his further refine the theory of singular integral operators diversified lecturing schedule, branching into infinite­ so as to bring within its scope the results of De Giorgi dimensional Lie algebras and Lie superalgebras, among and Nash on the regularity of weak solutions of elliptic other topics. equations with merely bounded measurable coefficients. Colleagues and students from the Chicago days report It has been known for a long time that this is possible in that one could always rely on his availability and on the case of two variables. a challenging idea or question as a result of each The second problem is to study the algebra generated conversation. His service to the University of Chicago by singular integral operators on Lipschitzian subman­ and to the AMS has been characterized by the same ifolds of Euclidean space and find out whether this unselfish spirit. The most recent evidence is offered by algebra posesses a structure similar to that of the algebra his superb leadership at MSRI. of singular integral operators in Euclidean space. If this His texts, at a range of levels, are numerous, even if were the case it would permit a systematic treatment one does not count second or later editions, or Chicago of boundary value problems for elliptic equations in Lecture Notes. Though numerous, they are certainly not domains with Lipschitzian boundaries. ponderous. He is a man of few words, writing with polished economy to get the important ideas across.

Career Award Biographical Sketch Irving Kaplansky Irving Kaplansky was born on March 22, 191 7 in Citation Toronto, Ontario. He received his Ph.D. from Harvard University in 1941. His main area of research interest The 1989 Steele Prize for cumulative influence is awarded is algebra but there was a substantial component in to IRVING KAPLANSKY for his lasting impact on mathe­ functional analysis (especially C*-algebras) during the matics, particularly mathematics in America. 1950's. Work on Lie superalgebras that began in 1975 By his energetic example, his enthusiastic exposition was inspired by mathematical physics. and his overall generosity, he has made striking changes Professor Kaplansky began his academic career as a in mathematics and has inspired generations of younger Benjamin Peirce Instructor at Harvard University ( 1941- mathematicians. His early works range over number the­ 1944). He was a research mathematician in the Applied ory, statistics, combinatorics, game theory, as well as his Mathematics Group of the National Defense Research principal interest of commutative algebra. He completed Council at Columbia University (1944-1945). At the the solution of Kurosch's problem on algebraic algebras University of Chicago, he progressed from instructor of bounded degree, where Jacobson had made a decisive to professor (1945-1969) and served as chairman of reduction, and considered numerous questions in the the mathematics department ( 1962-1967). From 1969 to area of Banach algebras, always with the algebraic view­ 1984, he was the George Herbert Mead Distinguished point. In particular, he brought the algebraist's instincts Service Professor at Chicago. Since 1984, he has been the to bear on the problem of abstract characterization of director of the Mathematical Sciences Research Institute von Neumann algebras. in Berkeley. Kaplansky has always been ready to lecture on some­ Professor Kaplansky served as President of the AMS thing new, and the new lectures have usually turned during 1985-1986. A member of the AMS for 48 years, he into monographs or papers giving us his special insights. was also elected Member-at-large of the Council (1951- (His students will testify to less obvious enrichments.) 1953) and Vice President (1975). He has also served on The monographs on infinite abelian groups and on dif­ numerous committees, including the Bulletin Editorial ferential algebra are examples of such texts that have Committee (1945-1947; 1979-1985); the Transactions attracted many students to try their hands at these fields. Editorial Committee (1947-1952); the Committee on In the early days of Lie algebras of prime characteristic Translations from Russian and other Slavic Languages he showed what ingenuity and patience could achieve ( 1949-1958); the Proceedings Editorial Committee ( 1957- regarding the structure of these troublesome systems. 1959); and the Nominating Committee ( 1977-1978). He

SEPTEMBER 1989, VOLUME 36, NUMBER 7 835 1989 Steele Prizes presented AMS Invited Addresses at Ann Arbor in 1948 Response and at Stanford in 1955. A member of the National Academy of Sciences, Pro­ The citation is flattering and I am very grateful. Indeed, fessor Kaplansky also served on the executive committee it is too flattering. for the mathematics division of the National Research Council from 1959 to 1962. In 1989 he was elected to a If, during the nineteenth century, there had been a four year term on the Council of the American Academy world wide Steele Prize for cumulative influence, most of Arts and Sciences. of the giants who come to mind would undoubtedly have He was on the Toronto team that won the first been honored. Probably some others would have been William Lowell Putnam competition and received the honored who are only dimly remembered today. Time first Putnam scholarship at Harvard. In 1948-1949 he has a way of sorting these things out. held a Guggenheim fellowship. He received two honorary The citation kindly refers to my interest in a variety degrees: Doctor of Mathematics (University of Waterloo, of subjects over the years. I hope I have helped to set a 1968) and Doctor of Science (Queen's University, 1968). good example in that respect. There have, after all, been so many instances where the key idea needed to crack a ·problem in a certain field came from a totally different field. To give just one example: it is fortunate that the mathematicians working on Lie algebras of characteristic p and those working in Lie superalgebras were aware of Cartan's infinite pseudo-groups. I am going to take this opportunity to put in print some advice that I regularly give to students: spend some time every day learning something new that is disjoint from the problem on which you are currently working (remember that the disjointness may be temporary), and read the masters. Another thing I wish to do is express my indebtedness to others. In the well worn phrase, mathematics is where it is today because we have all been standing on the shoulders of giants. I look back on the inspiration I derived from Richard Brauer at Toronto, from Saunders Mac Lane at Harvard, from colleagues and students at the University of Chicago, and during my visits to the Institute for Advanced Study. The concluding reference in the citation to my direc­ torship of MSRI is also much appreciated. Not counting conferences, more than a thousand mathematicians have been welcomed to MSRI in its first seven years. I hope that most of them enjoyed it and got a nontrivial shot of mathematical adrenalin. I am going to keep trying to make this happen.

Irving Kaplansky

836 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics

Edited by Jon Barwise

Editorial notes next week, requests which I was able to fill by simply sending the Jb.TEX file by email. I quickly got many Can computers save our libraries? useful comments on the paper which I was able to The computer was once predicted to be the death take into account in the final version. I am anxious to of printing, and so of the library as we have come repeat this experiment with a more technical paper, to know and love it. Information was going to be once I finish the one I am currently working on, to see stored only electronically. Ironically, just the reverse if the response is similar. has happened. The computer has made typesetting This particular way of distributing information so much easier that papers and books are coming does not directly address the problems with our faster than ever. And with this explosion has come libraries. But it does indicate that the computer can an explosion in the numbers of scientific journals, provide alternative ways to "publish" technical work many of them at outrageous prices, especially the whereby results can be disseminated quickly and ones published by some of the private publishers, widely to interested parties without much cost or unaffiliated with any professional organization. Their bother to anyone else. strategy is basically to make enough off of library The AMS is looking into various ways to use the subscriptions to pay for the journal. But as a result, computer to speed and ease the flow of informa­ subscription prices are playing havoc with library tion within the mathematical community. But, in the budgets. Libraries can simply no longer afford to keep meantime, I suggest that readers of this column send up with all the journals. What, if anything, can be me short suggestions, intended for publication. If I get done about it? enough of them, I will devote an issue of this column Every week or so I get a message from some to them. reader of this column suggesting ways in which the Send them to: information revolution brought about by the com­ Professor Jon Barwise puter might help solve this problem. Suggestions have Center for the Study of Language and Information included replacing hardcopy journals with electronic Ventura Hall journals or electronic bulletin boards, cheaper ways of Stanford University publishing made possible by mathematical typesetting Stanford, CA 94305 programs like TEX, and abstract services provided in email: [email protected] email newsgroups. I have tried, without success, to get someone to write a piece on this problem, one that would survey This month's column various possibilities, weighing the merits and costs of each. I also recently experimented with one suggestion This month's column contains two reviews, one of by simply posting (on the newsgroups sci.logic and DERIVE and the other of Calculus Calculator. I sci.philosophy.tech) a terse announcement of a draft of have also written a piece reporting on a current the article on program verification which appears later controversy about the use of mathematics in showing in this month's column. I restricted my announcement that computer systems are correct. In it, I summarize to the USA, for no particular reason. I was astonished the controversy and try to assimilate it to the old to get over 300 requests for the article during the question: how is applied mathematics possible?

SEPTEMBER 1989, VOLUME 36, NUMBER 7 837 Computers and Mathematics

It did not make full use of the machine resources. Reviews of Mathematical Software And it had (typewritten) documentation which was useful but which left some things to be desired. Soon a new generation of software appeared (about the time that Borland's Sidekick became available). This generation offered a far better user interface, including pop-up menus, context sensitive help, multiple (but The Menu with the College Education nested) DOS shells, easy access to all memory and Reviewed by Eric L. Grinberg* peripheral resources (especially graphics), extensive typeset documentation, and more (see for example In this article we will review Derive, the mathemat­ Borland's numerical analysis package Eureka). ical assistant, a menu driven symbolic manipulation Derive represents a partial move of muMATH in program. Derive is the successor of muMATH, a very the direction of this second generation of software. Be­ popular program introduced first for CP/M machines low I shall first summarize some features of muMATH and the Apple II and later for the MS-DOS environ­ and then contrast them with Derive. runs on most IBM-PC compatible ment. The program Although not as extensive in breadth as pack­ machines with the MS-DOS operating system version ages such as MACSYMA, muMATH did feature the 2.1 or higher. It requires a minimum of 512 kilobytes differential and integral calculus, series, some tran­ of computer memory and one floppy disk drive. It scendental functions, differential equations, vector supports a wide variety of display monitors. A special analysis, and more. Sometimes it would get "stuck" version is available for the NEC PC-980 1. Derive is doing a problem, but this could be circumvented. Its for $200 from dealers and also from its available "expert knowledge" was open for the user to view. source, Soft Warehouse Inc., 3615 Harding Avenue . , The algorithms and rules that muMATH used were Honolulu, Hawaii 96816 (Phone: (808)- Smte 505, included in the program disks in the form of a series 734-5801 ); there are volume discounts for educational of ASCII files which could be read using a text editor. Unfortunately, muMATH is no longer institutions. The algorithms were written in muSIMP, a miniature available. LISP-like environment. The files were commented and longtime muMATH enthusiast I was eager to As a included turnkey demonstrations of the new capabil­ find out how Derive was different. Thus I shall begin ities introduced by each routine. If muMATH got by discussing muMATH first. The program muMATH stuck on a problem (or if you just wanted to see how was released by the Soft Warehouse in 1979. It broke muMATH did a problem, say an integral from a calcu­ within the confines of a mere Apple new ground: lus homework assignment) you could use the built-in machine it offered mathematical symbol II or CP/M debugger and single-step through the algorithm. If manipulation, a capability until then reserved for far muMATH made a wrong decision at some step, you larger computer systems. Later muMATH was ported could add a rule which would direct muMATH to the over to the IBM PC family of machines. The MS-DOS right continuation. version of the program was clearly a direct translation of the Apple and CP/M versions. While retaining the Moreover, muMATH came with two sets of in­ very high level of ingenuity that made muMATH on teractive lessons. The first set introduced the basic these modest micros possible, the MS-DOS version calculator-like features, e.g., entering a function sym­ did not take full advantage of the added power of the bolically and then differentiating it (to differentiate PC. Indeed, it was fairly typical of the first generation tan- 1(1 +x2) type DIF(ATAN(1+xl\2) ,x); . The sec­ of PC software: it was very useful, offering capabilities ond set of lessons, also interactive, exposed the pro­ never before available to a home user. It had a fairly gramming features with which muMATH was written. primitive user interface including cryptic error control. These lessons enabled the user to write his own algo­ rithms and enhancements to muMATH and, perhaps more importantly, taught some fundamental concepts *Eric L. Grinberg is Associate Professor of Mathematics at of artificial intelligence. In some sense, this is what Temple University. He received his Ph.D. in 1983 from Harvard made muMATH so valuable: here was a complete University. Before coming to Temple he taught at the University of Michigan and visited the Institut des Hautes Etudes Scientifiques as miniature expert system with its inner workings ex­ a NATO postdoctoral fellow. His primary research interests include plained. Without any outside background one could integral geometry and geometric analysis. learn about, use, and modify an artificial intelligence

838 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics

environment, one of primary interest to mathemati­ follow up with the (far easier) task of adding a more cians. versatile user interface that many of what I called Of course, muMATH was (and, except for avail­ second generation PC programs have. In the mid ability, still is) a valuable educational tool. Calculus 1980s there were rumors about a "Son of muMATH". students can use the program to check their work Derive is the long-awaited product. As will be detailed and even trace the solution to a problem step by below, Derive fulfills some of these expectations. But step to see how it is done. Indeed, some schools we shall have to wait for future releases to fulfill the now use muMATH in their calculus sequences. Also, entire wish list. muMA TH is powerful enough to be useful in research Derive is entirely menu driven. The initial stage endeavors. Many operations of higher mathematics of the program loads a screen with menu options can be represented as compositions of basic calculus on the bottom. These include entry of new symbolic and basic algebra operations. These expressions, while expressions, building new expressions out of old ones, cumbersome and difficult to manipulate in the hands performing calculus operations on expressions, factor­ of humans, are often readily computable in muMATH. ing and expanding, solving equations, plotting (in two In particular, muMATH is especially good for genera­ or three dimensions), simplifying, saving, loading and tion of examples. The reviewer has used muMATH to deleting expressions and files, managing windows, and compute intertwining numbers for integral operators setting various system parameters such as precision. on homogeneous spaces. Context sensitive help is also available. Many of the Still, these aspects of muMATH can be found menu options lead to submenus. The area on the elsewhere: by now there are many calculus books that screen above the menu is used for displaying expres­ offer accompanying tutorial floppy disks. Such tutorial sions, graphs, and other windows. I will now discuss programs provide many of the functions that mu­ the menu choices in detail. MATH has. Also, there are several mathematical sym­ Basic expressions are entered using the author bolic manipulation programs available: MACSYMA, command. This is essentially a line-oriented editor MATHEMATICA, MAPLE, and others. One can even using mathematical notation similar to that of FOR­ get pocket calculators to perform some of these func­ TRAN or BASIC. There are special mathematical tions (see: The chip with the college education [2]). The characters available such as n which are invoked larger of these programs "know" many more concepts through the alt key. These basic expressions can of higher mathematics (e.g. curvature) and do not be combined and mixed with basic operators and need to be taught so much. muMATH can be taught functions using the highlight and build commands. about curvature, but this entails some work on the Overall, editing and moving around the menu screen part of the user, and it may require some other basic tends to be a bit cumbersome and unintuitive. I find concepts that also have to be introduced. muMATH's that I sometimes reach for the cursor arrows when I role as a direct aid to elementary teaching and research should be using the space bar or tab key. Still, Derive computations does not make it stand above the rest. tries to be so flexible and gives so many simultaneous But the package, if reintroduced, would hold a unique options that some compromise of the user interface position. might be necessary. Mouse support would certainly muMATH was fairly inexpensive, was available help, but many PC users do not have a mouse. A user for small systems, and had an open architecture: the who arranges his own hot keys using resident programs user could look inside its engine, see how it operates, such as Prokey or Superkey and builds expressions and modify it if need be. The other programs men­ using a resident editor such as Sidekick will probably tioned are often black boxes. They cannot be viewed increase his throughput. In any case, the shortcomings internally. Many require substantial memory and disk of the edit and motion functions are minor and do storage resources to run. Some are restricted to run not seriously reduce the usefulness of the program. only on top-of-the-line CPU chips such as the Intel Arithmetic is performed in user selectable preci­ 80386. muMATH runs nicely on inexpensive 8-bit ma­ sion. The available modes include Exact, Approximate, chines using the Intel 8088. One could use muMATH and Mixed . In Exact mode rational arithmetic is per­ and a low-cost laptop computer such as the Toshiba formed exactly (as long as there is sufficient memory 1000 to perform complex symbolic calculations on the available) and irrationals are stored symbolically; sim­ go. plification of irrational expressions (especially those Given that the Soft Warehouse did such a fine job involving radicals) can be attempted but is not guar­ implementing mathematical symbol manipulation on anteed to succeed. In Mixed mode rationals are still a small system it was hoped by many that they would treated exactly but irrationals are replaced by rational

SEPTEMBER 1989, VOLUME 36, NUMBER 7 839 Computers and Mathematics

approximations. Finally, Approximate mode replaces worry about how much the computation will cost. irrationals by rational approximations and rounds This is a nice reminder of how far we have come fractions involving large integers to simpler fractions. in single user software and hardware. It would have These choices provide a good balance between econ­ been nice to include a discussion of the algorithms omy of time, economy of memory, and protection used here (and in the rest of Derive for that matter). from roundoff errors. The choices of notation are A modest extension of these would probably allow commensurate with (but independent of) the choices a mini number theory environment illustrating the of precision. One thing that is missing is floating point concepts of field extensions. coprocessor support (e.g. for the 80x87 family of Derive can handle variables with restricted domains chips). This could significantly speed up calculations (these may allow more simplification than a general in the Approximate and Mixed modes, and even in domain would). It also accepts infinite values for the Exact mode if cleverly implemented. On the other variables. But the choices are limited. For instance, hand, Derive performs arithmetic quite well as it is. x can be declared Non-negative , but the condition Algebraic expressions may be entered using both Re(z) 2: 1/2 can only be specified indirectly. the Latin alphabet and a limited number of Greek The user can define constants and functions with letters (those available in the extended ASCII charac­ multi-character names using both English and (some) ter set supported by the PC environment). The user Greek letters. Expressions may be turned into equa­ can attempt to simplify complex expressions using the tions by simply inserting an = sign judiciously. Al­ multifarious command Simplify . This expression ternatively, an expression F can be treated as the means different things in different contexts. Some­ equation F = 0 or y = F, where y is a user-selectable times it means algebraic simplification and sometimes variable. Derive can be asked to solve a single (non­ it could be called Go and do what I already told linear) equation for a single variable, but it cannot you to do! . For example, if you Simplify (x+l) (x- handle simultaneous nonlinear equations. For simul­ 1)-(x+2) (x-2) you get 3. But if you Simplify taneous linear equations one can get around this by DIF (f (x)), where f (x) is a predefined expression, viewing a system as just one equation involving a then you get the derivative of f (x), presumably what vector variable and matrix notation; a new version of you intended when you Authored DIF (f (x)) but forgot Derive allows vectors of equations as an alternative to select automatic simplification. To be fair, Simplify treatment of linear equations. The equation solver usually does its job well. For example, it quickly rec­ works rather nicely when there is a solution. For ognizes that ((2/\0. 5) t\ (2/\0. 5)) t\ (2/\0. 5) is equal example, to solve ex = 5x to 20 digits of precision to 2, an identity that fooled an implementation of takes about two minutes on an Epson laptop (slightly REDUCE which I once used on a mainframe. slower than an IBM-AT); if a priori bounds are known Rational expressions in one or more variables the solution time can be reduced by restricting to a can be expanded with user-selectable ordering of the compact interval. Programs such as Borland's Eureka variables. Fractional exponents can be handled using can do this much faster (with or without a numeri­ the Branch command. A particularly nice feature is cal coprocessor), but not to arbitrary precision, and the Factor command . Expressions may be factored without the full availability of symbolic definitions. relative to one or more variables. The factorization On the other hand, Derive can spend forever looking may be done at several different levels. The most basic for a root and it is up to the user to decide when (and fastest) level adds fractions (putting them under a too much time has elapsed. This is one place where common denominator) and factors out constants and more information about the nature of the general algo­ least powers of variables. The next level, Square-free rithm, the state of the current calculation, and possible factoring extracts powers of sums (or products) modifications would help. An expansion of the Solve of different powers of sums, but you have to select command would be of great help in a numerical Rational factoring to handle x 2 - 4. Factorization analysis class. The combined use of numerical and over some algebraic field extensions of the rationals symbolic techniques (e.g. Newton's method combined in the reals is available in Radical factoring. Finally, with symbolic differentiation) has not been stressed one can attempt Complex factoring, the highest sufficiently. Derive has the potential of providing a level. I've used REDUCE on a mainframe to do good environment for this. symbolic factorization in the past. I remember cryptic A nice plus that Derive enjoys over muMATH is error messages, memory overflow, and above all, large its plotting capability. It can handle most popular charges to my account balance. In contrast, Derive's graphics displays in both text and graphics modes and Factor is a pleasure to use, and I don't need to a variety of colors (or alternatively in monochrome

840 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics

mode). There are two types of plotting windows: two­ while one could add Bessel functions and much dimensional and three-dimensional. If the user simply more to Derive on one's own, it might be better selects the Plot option, Derive decides which type of to directly use Bessel functions in an application plot is appropriate by counting the number of variables with the assistance of Derive. Of course, adding more in the expression to be plotted. Thus one cannot concepts would make Derive more memory intensive, directly view the surface in R3 defined by y = x 2 ( z and perhaps more expensive. It might also restrict it to arbitrary). Rather, one has to "fool" the program into larger machines (as has been the case with programs using the 3D plot window by introducing a redundant such as MACSYMA). A set of user selectable add­ z dependence (say y = x 2 + z- z). Another way to in modules would perhaps give the best compromise accomplish this uses the windowing capability (see between extensive knowledge and modest machine below). Besides plotting curves and surfaces which and price requirements. are graphs Derive also boasts parametric and polar plots. It would also be nice to plot surfaces which are The Calculus commands handle most operations not graphs by simply specifying points on them (say, that a calculus student is likely to encounter. Besides from a matrix). Virtual windows can be designated standard integration and differentiation, these include as algebra, 2D plot, or 3D plot. These can be split, some improper integrals, Cauchy principal values, and stacked, and overlaid. In this way, several algebraic numerical integration. Derive has some knowledge of derivations and plots can be viewed simultaneously. special integrals, but the user may be disappointed The higher the screen resolution is, the more useful with his favorite tricky integral. Thus Derive can 2 00 this feature is. Color also helps with viewing several quickly evaluate J~: e-x dx but not f0 ~~~".It does 00 drawings at once. The user is given a great deal succeed in evaluating f0 ~~~ 4 in a matter of seconds, of choice over the execution of the plot with well 00 but gives up on f0 ~~~s . Probably, it does not use chosen defaults. Hidden line removal is available. complex contour integration techniques to evaluate During my first few tries at plotting I sometimes definite integrals (a lot to ask for in a small system). found the program unresponsive and preoccupied But it should be possible to add such a package with operations that seem to have nothing to do with without too much effort. my plot. But after sufficiently many references to the manual (and the help screens, when I could get the The differentiation operation DIF cannot be com­ plot command to stop so I could ask for help) I bined with the solve feature to treat differential equa­ felt more in control of the plotting process. It would tions. Vector calculus-a standard feature of muMATH­ be helpful to have an optional pop-up window to was also missing from the review version of Derive the internal parameters of a plot process; this would but was added recently. Clearly, the former feature relieve the feeling of frustration during those moments could be added without much effort. when the computer seems to "lock up". Still, the Plot Finite and infinite sums and products can be at­ command is useful, flexible, and easy to use in most tempted. Derive uses the techniques of anti-differences instances (especially those that students are likely to and anti-quotients to solve these problems. Again, the encounter). user's favorite example may generate disappointment. There are many transcendental functions available Thus I:;;c' 2-n can be evaluated while I::o n-2 cannot for use, including those likely to come up in a be. calculus course. There are also financial and statistical Finally, Derive offers a small vector and matrix functions. On the other hand, many special functions manipulation package. This feature is most interesting are missing (one example: Bessel functions). Of course, when combined with the symbolic scalar operations one could add these functions to the system by defining (e.g. taking determinants of matrices of functions). them in some way (power series, differential equations, The purely linear-algebraic features are quite limited etc.) But the newly defined functions will probably be and do not rival those of other packages such as "weaker" than the ones already included: it will take MATLAB. For instance, one can take both positive more time and memory to manipulate them just as and negative powers of a square matrix (and hence it does in programming languages such as FORTRAN invert a nonsingular matrix), and one can evaluate the or BASIC. In contrast, languages such as FORTH characteristic polynomial of a square matrix. But one allow the introduction of new functions that can be cannot directly exponentiate such a matrix. handled just as efficiently as the standard ones. Also, Derive comes with a set of files whose name having more standard concepts already available in ends in .MTH . These files are essentially turnkey a package can make the package more useful. Thus, demonstrations (with very limited error control) of

SEPTEMBER 1989, VOLUME 36, NUMBER 7 841 Computers and Mathematics

the basic features of the program. They make it easier 2. All user input (such as the assignment of an for the user to get started and do something interesting arithmetic expression to a variable or a function soon after receiving the program. The user is offered definition) appears on the screen in a "user input options for saving various states of Derive for later window" as a log of user activity. A printed log can restart and analysis. One option allows the storage of also be maintained. expressions in FORTRAN notation. This could later 3. Information in the user input window can be be used to code numerical routines in FORTRAN (or edited on screen via cursor positioning. This makes it similar high level languages) based on results from easy to modify and reimplement any previous input. Derive. 4. The current value of as many as 15 user defined In summary, Derive provides a very useful and variables can be displayed at one time. competent mathematical assistant, albeit an underem­ 5. Graphics have a resolution of 640 x 200 pixels. ployed one. It incorporates some long awaited features 6. Error messages are provided for syntax errors to muMA TH while taking away some old ones. It is and a small help facility is available. natural to hope (expect ?) that the creators of Derive The basic format for the screen is: are hard at work on providing a full extension of mu­ MATH. Combining the best of Derive and muMATH would give an environment useful both for students - The Calculus Calculator------and researche.rs at a low cost. As it stands, Derive is ------cc a very smart symbolic calculator which is very useful I 1 for students and in some cases for researchers as I USER MENU I well. I am happy to report that the staff at the Soft I I Warehouse has been very helpful and responsive to I I ------Input------Output----- technical questions and bug reports. They are con­ stantly adding new features. Who knows, they may 1 I I I INPUT WINDOW I OUTPUT WINDOW I even accept suggestions for future enhancements! USER I I I References I I I 1. Herbert S. Wilf, The disk with the college education, I I I American Math. Monthly ( 1982), 4-8. I I I 2. Yves Nievergelt, The chip with the college education, ------Last Result------American Math. Monthly ( 1987), 895-902. 1 I I I

Calculus Calculator (CC) The user may define as many as 100 variables and 100 functions. The names of user defined variables Reviewed by Herbert L. Holden* and functions are alphanumeric. They must begin with an alphabetic character, consist of at most 8 CC is a mathematical work sheet for an IBM PC with characters, and may not be a CC reserved word. For graphics capability. Memory requirements are 384k example, A, B, C are ok but I and D are not since with CGA or Hercules graphics and 512k with EGA they denote integrals and derivatives. The names of or VGA graphics. A special version is required for the variables are not case sensitive. AT&T 6300. Arithmetic expressions which are not assigned to a CC essentially emulates a calculator with the fol­ user variable are assigned to the variable ANS. lowing added advantages. The user may define functions of one or two 1. Data is entered with a keyboard. I prefer this to variables and the usual functions intrinsic to most the keys on a calculator which are often so small they programming languages are available. can only be operated with the aid of dental tools. The processing of a line of user input occurs when the cursor is on that line and the ENTER key is pressed. *Herbert Holden is Associate Professor of Mathematics and results of a sequence of user input are shown Computer Science at Gonzaga University, Spokane, Washington The 99258. below.

842 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics

window(xmin,xmax,ymin,ymax) ------Input------Output------Scales the plot region 1 I I graph(f) - Point plot of the function f I 2+2 I ANS 4.000000000 I (600-800 x values) I A=3.2 //this is a comment I A 3.200000000 I lineg(f) - Line graph of the function f I B=a*ans I B 12. 800000000 I (600-800 x values) I f(t)=1+t+t~2 I c 4.ooooooooo I quickg(f) - lineg(f) for every 20th x value I C=f(2)-3 I E 25.000000000 I polarg(f,a,b,n) I g(x,y)=x~2+y~2+sin(x*pi) I I - Line graph of r=f(t) t=a to I E=g(3,4) I I t=b with n points I I I paramg(f,g,a,b,n) -Line graph of (f(t),g(t)) t=a to t=b with n points To redefine C as f(5)- 3 simply move the cursor diffg(f,a) -Line graph off to the 2 inC= /(2)- 3, change the 2 to a 5 and press and the tangent line at a. ENTER. The value of C will be updated in the output integ(f,a,b) -Line graph off with shaded window. region from a to b which result in undefined Arithmetic expressions If a function is defined as an integral the graph may UNDEFINED rather than values return the value take longer than 30 minutes to complete because of the terminating the program. way integration is implemented. A predictor-corrector It takes less than ten minutes to show someone fa­ algorithm would be preferable in speed and would miliar with the use of a PC the applications described probably provide the accuracy needed for graphics. so far. Students in many lower division mathematics The full width of the screen is used for graphics, courses (other than calculus) could take advantage which seems unnecessary in view of the fact that it is of even these modest capabilities with reasonable easy to rescale the window. confidence. Other noteworthy functions are: The contents of the input window and the status of all functions and variables may be saved to a disk file. table(f,a,b,n) This file may be retrieved at a later session appending - Tabulates n values of f from a to b the saved input window to the current input window solve(f,c) and adding (or updating) variables and functions. - Solve f(x)=O near c using Brent's algorithm The expression I (f, a, b) integrates the function f A sequence of statements in the input window can from a to b and the expression D(f, a) evaluates the be labelled as a block and executed as a block but no derivative off at a. Sample user input might be: area other programming is possible. = I(f, 1.0,2.5) or m = D(f,0.2). The software, manual, and related files come on one floppy disk. When the manual is printed it occupies A function may be defined as a derivative or an about 60 pages. The manual is reasonably well-written such as h(x) = I(f, 0.0, x) or integral via constructs and contains numerous examples and applications. It df(x) = D(f, x). could benefit from an index and a list of reserved In the current release (version 2.0) the differentia­ words. tion is performed numerically instead of symbolically Well, it certainly is a treat to use a software and the integration strives for full single precision ac­ package that doesn't try to do everything. What this curacy which makes these operations very slow. These means to me is that I can learn to use the software problems are to be corrected in version 3.0 which may in less than one hour and be proficient in less than be available this fall. five hours. There are so many applications on the Plotting commands clear the screen and provide a market today that are so comprehensive that it takes separate graphics page. Each graphing command adds a major commitment in time ( l00 hours) to become a a graph to the graphics page and the command ERASE proficient user. clears the graphics page. Graphics are available for CC is certainly not as comprehensive as packages user defined functions via the following constructs. like Point Five or Math CAD and lacks a video arcade

SEPTEMBER 1989, VOLUME 36, NUMBER 7 843 Computers and Mathematics

e~vironment, but it is an effective and well-designed to the controversy, and then contribute my two cents p1ece of software. Even a version of CC without worth. graphics would be a desirable package. CC is copyrighted by David Meredith and dis­ Background of the Controversy tributed by Mathematics Application Group The present debate swirls around an article called Department of Mathematics "Program Verification: The Very Idea," [6] written by San Francisco State University the philosopher James Fetzer. In this article, the author 1600 Holloway Avenue attacked a certain conception of program verification San Francisco, CA 94132 and claimed to show that the proclaimed aims of CC is shareware and the authors of the program program verification are, in principle, quite simply suggest a $25 donation to the Applied Mathematics impossible. Fund at SFSU. Further information can be obtained Program verification, theory and practice, is a big by calling (415)338-2199. business. Millions of dollars are spent on it annu­ ally. So rather predictably, there was a large, outraged response. Some of the letters accused Fetzer of mis­ representation, or of knowing nothing at all about Mathematical Proofs of program verification. Others accused the editor of Computer System Correctness publishing an "ill-informed, irresponsible, and dan­ Jon Barwise* gerous article". On the other hand, some writers found merit in Fetzer's position. One even said that it did not go nearly far enough.* But to understand this In the early years of the century, there was an exciting debate, and what it has to do with mathematics, we if acrimonious, debate about the nature of mathe: need to back up a few years. matics and its relationship to the rest of the world. I assume that the reader has an intuitive grasp The debate took place in articles, published correspon­ of notions like algorithm, program, (computing) ma­ dence, and private letters. While it sometimes seemed chine, and implementation. In the way we are using to generate less light than heat, still, when the smoke these terms an algorithm A is an abstract computa­ cleared, the situation was brighter. The debate led to tional process. A program P is a linguistic object that the careful formulation of various positions, e.g., for­ plays a causal role in a computation. In writing a pro­ malism, Platonism, logicism, and intuitionism, which gram, one typically tries to implement some (implicit capture particular aspects of mathematical activity. or explicit) algorithm. That is, one wants the program Few modern mathematicians are terribly happy with P, when run on a machine M, to carry out the algo­ any of these positions, but they do seem to have kept rithm A. A proof of program correctness would prove the wolf from the door, in that they allowed us to get that this is the case. (I reserve "computer system cor­ on with mathematics. rectness" for a stronger notion, which I define towards Today a similar controversy about the nature of the end of the article.) Program verification is the mathematics and its relation to the rest of the world business of providing proofs of program correctness. is raging out of the sight of most mathematicians C. A. R. Hoare is one of the founders of the field in the pages of CACM, the Communications of the of program verification. To see what is at issue here Association for Computing Machinery. The debate is is a famous quote from Hoare. ' almost as exciting and at least as acrimonious. The purpose of this article is to draw the reader's attention Computer programming is an exact science, in that all the properties of a program and all the consequences of executing it can, in principle, be *I would like to acknowledge many conversations with John found out from the text of the program itself by Etchemendy and Brian Smith over the years on the topic of modeling in mathematics and in computer science. I also need to acknowledge means of purely deductive reasoning. [8] the role that Alan Bush has played in my thinking on the matters discussed in this essay. Talking to him, and watching him at work convinced me that there is something very important about program * These letters can be found in the same issue of CACM as [2], verification. I would also like to thank various readers of an earlier [4] and [7]. draft of this article for comments and suggestions.

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Since the late 1960s, a great deal of effort has gone they were correct in their conclusion that program into developing program verification techniques.* In verification is impossible. spite of two decades of work in the field, Fetzer claims Fetzer's argument was summarized in a critical that the premise on which it is based is false. letter (one of the thoughtful reactions) by Bevier, There was an earlier attack on program verification. Smith, and Young, roughly as follows: In 1979, DeMilio, Lipton and Perlis [3] published a 1. The purpose of program verification is to highly critical article. Their contention was that there provide a mathematical method for guaranteeing was a crucial social difference between mathematical the performance of a program. proofs and proofs of program correctness. In mathe­ matics, proofs are subjected to public scrutiny. There 2. This is possible for algorithms, which cannot is a social process at work which ends up accepting or be executed by a machine, but not possible for rejecting a purported proof. No such process is at work programs, which can be executed by a machine. in program verification, they claim. Program verifiers do not publish their purported proofs of correctness 3. There is little to be gained and much to be lost and subject them to the test of their peers. They through fruitless efforts to guarantee the reliability can't. There are just too many programs, the programs of programs when no guarantees are to be had. are too long, the proofs of correctness too long and boring, and there are too few people interested in In responding, Fetzer calls their summary of his reading any such purported proofs. So, they argue, an position perfectly reasonable, "so long as the first all important social aspect of mathematical proofs is premise is intended as a reflection of the position unavailable in the realm of program verification. The that is - implicitly or explicitly - endorsed by the crucial social mechanism for winnowing proofs from proponents of program verification." faulty purported proofs is unavailable, so the aims of All three points bear consideration, but we will program verification are unsatisfiable. start with the second. Can one conceivably give a The DeMilio, Lipton and Perlis article sparked mathematical proof that a given program P, when run quite a controversy in its own day, as can be imag­ on a machine M, will behave properly by being an ined, but nothing like the controversy ignited by embodiment of the algorithm A? Or is it, in principle, Fetzer's more recent article. In his article Fetzer did impossible, as Fetzer claims? two things. First, he argued that DeMilio, Lipton, Fetzer's argument for (2) (as he briefly summarized and Perlis were mistaken about the nature of proofs, it in [7]) is that computers are that they conflated genuine formal proofs and "proof complex causal systems whose behavior, in prin­ sketches". Genuine proofs have certain properties that ciple, can only be known with the uncertainty proof sketches do not have. And with regard to that attends empirical knowledge as opposed to the way mathematics is practiced, he would inter­ the certainty that attends specific kinds of math­ pret DeMilio, Lipton and Perlis as saying that most ematical demonstrations. For when the domain "proofs" published in mathematics papers are simply of entities that is thereby described consists of proof sketches. The social process comes in, Fetzer purely abstract entities, conclusive absolute ver­ claimed, in determining which proof sketches are in­ ifications are possible; but when the domain of deed sketches of formal proofs. (We will return to this entities that is thereby described consists of non­ part of Fetzer's claim later.) abstract physical entities . . . only inconclusive relative verifications are possible. Fetzer's Argument Reaction to Fetzer's Argument Fetzer's second aim, and the one which has drawn a firestorm of response, is to show that while De­ Many of the charges leveled against Fetzer's article are Milio, Lipton and Perlis were wrong in their reasons, typical of encounters between practitioners of any field X and philosophers of X. The philosopher necessarily attempts to give an analysis of X as it presents itself * This article will not assume any familiarity with such techniques. to the informed outsider. The practitioner feels that However, the reader interested in a simple introduction to them the philosopher misses a (or the) main point of X. might consult Chapter 4 of [1] or Chapter 5 of [12]. For a more complete look at some of the theoretical issues behind program Out of frustration, he is all too often tempted to claim verification, see [5]. that one simply cannot understand X without doing

SEPTEMBER 1989, VOLUME 36, NUMBER 7 845 Computers and Mathematics

X. As mathematicians (let X be mathematics), we can It bears noting that none of these writers question all surely recognize the temptation. But such reactions Fetzer's claim that the aim of program verification is do not really tell against the message carried by the to say something about programs running on physical philosopher; they simply try to cast doubt or ridicule computers. Their defense is that program verification on the messenger. I will ignore these sorts of reactions is a branch of science, not mathematics. So they seem to Fetzer's article in what follows and try to get at the to be backing away from the position staked out by substance of the debate, as exemplified by some of the Hoare that got program verification underway. And, more thoughtful reactions to it. in so doing, I think they give up something important The argument hinges on a perceived discontinuity too quickly. between the world of mathematics, and the physical Mathematics and the Physical World world. It is a gap that Bevier, Smith and Young [2] are at pains to diminish. They argue that if one gives At issue is one of the oldest puzzles in the philosophy a sufficiently fine-grained analysis of software and of mathematics: How is applied mathematics possible? hardware, down to the level of logical circuitry, there On the one hand is the observed fact that mathematics is little to be made of the distinction. For example, has great efficacy in science as well as in our day-to-day they write ... coping with the physical world. On the other hand, there is the seeming divide between the empirical whereas it is true that physical gates do not facts of the physical world and the a priori nature of always behave as their mathematical counterparts the deductive method. Or, from a realist perspective ... the semantic gap is sufficiently small to render rather than a formalist, there seems to be a divide Fetzer's objections inconsequential. To deny any between the concrete physical objects that populate the relation between, say, a physical AND gate and physical world and the abstract objects about which the corresponding Boolean function is to deny we reason in mathematics. that there can be any useful mathematical model It is this problem around which Fetzer and the of reality. This is tantamount to asserting the more cogent defenders of program verification are impossibility of physical science. [2] warily circling. If there are no mathematical truths Bevier, Smith and Young also dispute point (1) about physical objects, then clearly there is a sense (and (3), of course). They view program verification in which program verification is impossible, since not as a branch of mathematics but as a physical it would certainly follow that there cannot be a science. The goal is not mathematical certainty, but mathematical proof that a given program P, when run "to make it possible to make highly accurate pre­ on a particular physical computer M, has any property dictions about the behavior of programs running on whatsoever. On the other hand, applied mathematics computers." is a fact of life. Why shouldn't program verification In response to all the mail, the editor of CACM be a branch of applied mathematics? Whatever makes invited John Dobson and Brian Randell to try to other forms of applied mathematics possible would put the situation into perspective. The result was [4]. surely make program verification possible as well. In Dobson and Randell find blame on both sides of what follows, I would like to sketch a picture of what the controversy. They find proponents of program I think is going on in general, and then apply it to verification guilty of overselling their trade. On the three issues in computer correctness. other hand, they accuse Fetzer of failing to observe At the heart of the matter, I think, is the distinction the distinction between the reasons something is so, between a given physical (or other) phenomenon and and the typically weaker reasons one has for believing a mathematical model of that phenomenon. It is this it to be so. In particular, they accuse him of mis­ distinction which is implicit in Dobson and Randell's taking proofs of program correctness as "providing "distinction between 'this is the way the world is' and explanatory reasons for program correctness" whereas 'this is a useful way of thinking of the world'." It they should be taken as providing "merely evidential is explicit in Bevier, Smith and Young's claim that reasons" for program correctness. They say that "the Fetzer would have us "deny that there can be any hypothesis 'this program will execute correctly' is one useful mathematical model of reality." that can never be proven, only falsified." They take Mathematics, both pure and applied, rests on our the proof of a program's correctness to show only that experience of the world and our ability to reason. certain kinds of errors are not possible. Some of this experience is mathematical experience

846 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics

with various sorts of abstract objects. But ultimately mathematical model is faithful to the phenomenon mathematics is grounded in our experience of the being modeled, our theorems will correspond to facts nonmathematical world. This claim is controversial, about that phenomenon. So again we have at least the and it is not crucial to the point I want to make, but it possibility of mathematics shedding light on things in does suggest an answer to the question before us. For the nonmathematical world, for example, determining if mathematics ultimately rests on our experience of physical areas or actual computational processes. the nonmathematical world, it would be odd indeed Both forms* of applied mathematics have a con­ if mathematics were in principal unable to provide us tingent element (what Fetzer calls "relativity") in their with any truths about that world. conclusions about the world. The axiomatic method There are two ways to use mathematics to un­ says that our theorems are true if our axioms are. The derstand the world. One has become codified in the modeling method says that our theorems model facts axiomatic method. We state explicitly various assump­ in the domain modeled if there is a close enough fit tions and then prove that various conclusions follow.* between the model and the domain modeled. The sad Euclidean geometry is a hackneyed example. There fact of the matter is that there is usually no way to really are things like lines and triangles. Moreover, the prove - at least in the sense of mathematical proof axioms of plane geometry are true of them, or close to - the antecedent of a conditional of either of these being true in normal circumstances. Axiomatic set the­ types. ory is another example. There really are collections of Still, this does not doom the application of math­ things. Other examples are the axiomatic approaches ematics. After all, our axioms are often true, or close to the natural or real numbers. In such cases we enough to the truth. And our mathematical models are state as axioms some principles that seem true, or often good representations of the phenomenon being perhaps idealizations of true but messier facts, and modeled. Applying mathematics does not in general prove consequences of the axioms. If our axioms are lend itself to absolute certainty, but it can carry deep true, and if the purported proof is correct, then the and justified conviction. Or, as a philosopher might conclusion must also be true. But what if our axioms say, applied mathematics may not guarantee knowl­ are not exactly true? What if they are idealizations? edge of facts about the physical world, but it can lead Well, if the world is continuous enough, and if our to the next best thing -justified true belief. axioms are close approximations to the facts, then our How can our conviction in applied mathematics conclusions will also be close to the facts. be justified? In answering this, we need to distinguish The second and more prevalent method for ap­ between what it is that makes a mathematical model plying mathematics to the nonmathematical world is (say) fit the world, and what constitutes good evidence that of mathematical modeling. We use some previ­ for believing that it does. For a model to be a good one ously established domain of abstract objects, say real there needs to be a mapping from the crucial features numbers, functions, or sets, etc., about which we have of the model to corresponding features of the physical an axiomatic theory, to build a model of the new world which is an isomorphism between the model phenomenon under study. For example, the Lebesgue and the modeled, at least in normal circumstances integral is really a mathematical model of a real where the model is to be applied. physical process for determining areas. And most of Sometimes we can have explanatory evidence that computer science uses set theory as a tool for modeling there is such a mapping. For example, we have some­ computers and other computational structures in the thing very close to a mathematical proof that the world. Lebesgue integral provides a good model of the in­ With this form of applied mathematics, there is a tuitive notion of area, in normal circumstances. And somewhat different relationship between theorem and when modeling something we have built and un­ the world. For in this case theorems are really theorems derstand reasonably well, like a particular computer, about the domain of mathematical objects used to we may be able to be reasonably certain of the fit model the physical world. These truths can shed light between our model and the thing modeled. More on the physical world, though. To the extent that our typically, though, we only get empirical, experimental evidence that our model is a good one, through the

* This is a great oversimplification of the method, of course. What we really do is to try to systematize fairly self-evident truths as axioms, provided the about the domain, selecting some to serve * Actually, these two forms of applied mathematics are just the others follow as consequences. ends of a continuum. Often there is some of each going on.

SEPTEMBER 1989, VOLUME 36, NUMBER 7 847 Computers and Mathematics

success we have in using it to predict facts in the particular physical computers running programs in domain modeled. If experience leads us to trust our real time. Where they seem to differ, then, is in how model as being a good one, then we will be justified in fatal they take the gap between the model and the trusting our theorems as corresponding with the facts domain modeled to be. Does the gap lead to Fetzer's of the world. If we are led astray, then we hope that pessimistic conclusion (3 above)? the consequences are not serious, and we revise our In principle, at least, there is no more or less model. reason to doubt the applicability of a correct proof Many controversies and errors have arisen out of a computer's correctness relative to a mathematical of what one might call the Fallacy of Identification, model than to doubt the applicability of any other the failure to distinguish between some mathematical theorem about some mathematical model of some real world phenomenon, provided we have similar model and the thing it is a model of. It is natural enough for the working mathematician to identify weight of evidence for the appropriateness of the two the two while he is trying to prove his results for models. So if there is an argument against the use intuitions about the domain modeled guide ~s in of mathematical models in program verification, it finding theorems about the mathematical model. But must involve something problematic about computers, when that final "QED" is put at the end. of the computer programs and computational activity. proof, we must step back and remember that the The one candidate for a special problem suggested identification is just that, an identification, not an by Fetzer's article stems from the fact that computer identity. Fetzer is clear enough about the difference - programs play a causal role in computation, in that at least in the case of computers. His antagonists are they actually engender the particular process that is not so clear. carried out. There are two points to be made in response. First, there is the distinction between the program as abstract object, as "type," and the program Fetzer's Argument, Revisited as part of the physical world, as an instance of the type. It is the latter that plays a causal role. Fetzer is quite There is a pervasive ambiguity within the program explicit in his determination to talk about the latter, verification literature. Are the theorems about a math­ but proofs of correctness are about the former. From a ematical model of computation? Or are they about the syntactic point of view, program instances are simple real thing? It is a bit hard to say, since the literature is enough to have very reliable abstract models about far from clear about the distinction. Workers in pro­ which we can prove results. And we can also model gram verification sometimes appear to fall prey to the the causal role these programs play in computers. At Fallacy of Identification. If pushed to decide between least it is no more problematic than any other form the two, as Fetzer forces them to do, it seems that his of causality in applied mathematics. In fact, it is rather less problematic, since we know quite well how anta~onists want their work to be about the real thing, not JUSt a model of it, as we noted earlier. They are this takes place, so we can model it quite faithfully. more willing to give up the mathematical method than Indeed, as these things go, the models of programs they are to give up their claim to be showing something and computers used in proving program correctness about physically embodied computers. On the other are in above average shape. We typically have quite hand, it seems that Hoare's program was meant to ap­ good reasons for trusting them. So if we can come up ply to mathematical models of computation, and only with a genuine proof that a program is correct, it is indirectly, via the model/modeled relation, to the real typically a pretty reliable indication that the program thing. This view is reinforced by Hoare's more recent will indeed compute the intended algorithm. principles (see [9]) that "computers are mathematical . But this brings us back to a point made by DeMilio , machines" and "computer programs are mathematical Lipton and Perlis. Real programs are typically very expressions." But whatever Hoare or others want to be long and complicated. What is the chance of getting a doing, part of what they are doing is proving theorems proof of correctness right, especially when there is so about their models of computation. little outside interest in checking the proofs? It seems to me that things are not as bad as they Once things are disambiguated, there seems to be suggest. Admittedly, today's programs are often very some agreement. Fetzer would agree that mathemat­ long and the proofs can be pretty boring. But there ical certainty can apply to the mathematical model. are some telling points on the other side. ( 1) Program The program verification community agrees that math­ language methodology is advancing to allow programs ematical certainty is not possible with regard to the to have structural features (modularity, typing, etc.)

848 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics

to aid in their verification. (2) Programs written different models of that notion. And, as Kreisel has with eventual verification in mind can make the task observed ([10]) in making much the same point, 99% simpler. (3) In my (nonempty but admittedly limited) of all mathematicians don't know the rules of even experience, it is rare for such proofs to require great one of these formal systems, but still manage to give mathematical ingenuity. If they do, then there is correct proofs. something suspicious about the program. And (4), The distinction between formal proofs and real automated proof checking might help in weeding out proofs raises the question as to the fit between our faulty purported proofs from the real thing. But here mathematical model and the real thing in a new a word of caution is in order. setting. How confident can we be of this fit in this case? We can be reasonably confident in most of the Proofs Formal Proofs and models, in one sense. We can be reasonably confident that the mathematical objects declared proofs do It Fetzer and most of the com­ seems to me that correspond, under the mapping between the model including those involved in puter science community, and the domain modeled, to real proofs, at least if we automated proof checking, stumble over a landmine set aside matters of comprehensibility and elegance. Namely, they fail left by the retreating formalists. But even here it is worth noting that it took many of formal languages and to recognize the true role attempts to get the usual rules of formal logic straight, Fetzer assumes that formal proofs in mathematics. especially regarding quantifiers and the substitution mathematical logic provides the test of a real proof, of terms containing free variables. Many published with what is usually written in journals being only versions of this model get things wrong, so that proof sketches. objects get counted as proofs (in the model) which do . . . a proof of a theorem T, say, occurs just in case not at all correspond to a valid piece of reasoning . theorem T can be shown to be the last member On the other hand, I think it is clear that current of a sequence of formulae where every member formal models of proof are severely impoverished of that sequence is either given ... or else derived since there are many perfectly good proofs that are from preceding members of that sequence (by not modeled in any direct way by a formal proof in relying upon the members of a specified set of any current deductive system. For example, consider rules of inference.) proofs where one establishes one of several cases and then observes that the others follow by symmetry con­ Here, at the risk of stepping on the toes of my siderations. This is a perfectly valid (and ubiquitous) fellow mathematical logicians, I must say that Fetzer, form of mathematical reasoning, but I know of no sys­ and many others, commit the Fallacy of Identification. tem of formal deduction that admits of such a general That is, they identify a mathematical model of the rule. They can't, because it is not, in general, some­ domain of proofs with that domain itself. thing one can determine from local, syntactic features The idea that reasoning could somehow be reduced of a proof. Which is just to say that the model of proof to syntactic form in a formal, artificially constructed accepted by Fetzer (and his opponents) suffers from language, is a relatively recent idea in the history of the very same objection as do models of computers. mathematics. It arose from Hilbert's formalist pro­ Which is not to say that it isn't useful. But still, it is gram. There were proofs for thousands of years before a model, not the real thing. And it could be that the logicians came along with the mathematizations of best proofs (in the sense of being most enlightening the notion. But these "formal proofs" are themselves or easiest to understand) of a program's correctness certain kinds of mathematical objects: sequences of will use methods, like symmetry considerations, that sentences in a formally specified artificial language, are not adequately modeled in the logician's notion sequences satisfying certain syntactic constraints on of formal proof, and so which would not be deemed their members. They certainly aren't what mathe­ correct by some automated proof checker designed maticians since the time of the ancient Greeks were around the formalist's model. constructing, for one thing. For another, no particular Moreover, identifying proofs with formal proofs system can claim to be the real notion of proof, since leads to what may be an even more serious mistake. there are endless variations, as is evident from the Of course to write down a proof that a program P fact that there are as many different deductive systems is correct for an algorithm A, we need to have some as there are textbooks in logic. They can't all be the description, representation, or "specification," of A real notion of proof. Rather, they provide somewhat itself. The formal model of proofs leads people to

SEPTEMBER 1989, VOLUME 36, NUMBER 7 849 Computers and Mathematics

suppose that the specification of the algorithm has reliable model of the computer, but also of a proof been given in the artificial language over which the of algorithm correctness, relative to a model of the proof regime is defined, usually some descendant of environment in which the system is to be placed. the first-order predicate calculus. While writing things Who really gives a damn that the program correctly out in complete logical notation can sometimes result computes the algorithm A if A is not the one needed in added clarity, all too often it merely obscures things, in the real computer system. which is why practicing mathematicians almost never The question of algorithm correctness is seldom use such a language. And, it is not uncommon for an addressed. Partly this stems from the fact that builders error to enter the picture in the translation from the of computer systems, like others, find it all too easy to English description to the formal specification. Except fall into the Fallacy of Identification, forgetting that for the hope of having proofs generated, partially there can be a gulf between their implicit model and generated, or checked by a computer, there seems the world. Partly it is because there are fewer known to be no compelling reason to specify an algorithm tools at hand to study algorithm correctness. But even in a formal language. Surely a better practice would if it is addressed, how about the question of the fit be to initially describe the algorithm clearly and between the model and the domain modeled? unambiguously in the language ordinarily used by Here things are not so rosy. Many "bugs" in mathematicians, an extension of English or some programs that make it into general use are not program other human language.* errors at all. Rather, they result from a failure to anticipate some situations in which the program is required to operate, and some uses the users put it Systems Programs and Computer to. These are mismatches between the model of the As should be clear by now, I disagree with Fetzer's computer's environment and the computer's actual highly pessimistic conclusion (3 above). I think that operating environment. program verification is an effective way of getting more Modeling the environment and the user is typically reliable programs. However, there is another problem, far more complex than modeling a computer. For if we turn from the question of program verification example, it often involves many aspects of human to the larger question of computer system correctness. psychology, to mention just one nightmare. A good Computer systems are not just physical objects that model of the user may need to model her beliefs about compute abstract algorithms. They are also embedded the program and how it operates, her likely desires, in the physical world and they interact with users. and her physical abilities. (For example, can she use They are intended to generate real world activity. a mouse quickly and accurately?) Next to modeling The starting assumption of the program verification this sort of stuff adequately, modeling the computer, task is that we are given a mathematical algorithm or the solar system, is a piece of cake. A, or perhaps some description of it, to implement. In the sort of applications of program verification But, from the point of view of correctness of the that really worry Fetzer (like air traffic control or entire system, this begs at least half the question. SDI) these problems arise with a vengeance. The The larger question of computer system correctness is unexpected situation is an ever present danger, as is not whether the machine implements A, but whether the unusual user. Such cases, being unanticipated by the machine carries out the intended real world task. the model builder, often do not fit with the model. Thus, to solve the larger problem, our mathematical There are many documented cases of such mismatches models need to include not just a reliable model ([11]). And if these mismatches take place in a critical of the computer, but also a reliable model of the computer system we may well not be able to go back environment in which it is to be placed, including the and redesign the model. For we may not be around. user (Smith [11]). In sum, I think Fetzer is correct when he points Typically, this additional modeling is implicit in to the theoretical limitations of program verification. the design of the algorithm. But if we are going But they're just the limitations implicit in any ap­ to divide things up in this way, then a full proof plied mathematics. Program verification, a branch of of computer system correctness need consist of not applied mathematics, is currently an extremely useful just a proof of program correctness, relative to a tool for improving the performance of programs, and so of real world computers. On the other hand, proofs of computer system correctness are of value only to * Another motivation for writing a "formal" specification at some stage might be as a step toward writing the desired program. the extent that we can rely on the underlying models of

850 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics

the computer and its environment. Hopefully articles [5] William M. Farmer, Dale M. Johnson, and F. critical of computer system correctness methodology, Javier Thayer, "Towards a discipline for develop­ techniques, and standards will not be drowned out, ing verified software", in: James H. Burrows and but will help to generate an improved understand­ Patrick R. Gallagher, Jr., eds., Proceedings of the 9th ing among professionals and the public of what such National Computer Security Conference, September proofs show and what they do not show about the 15-18, 1986 at the National Bureau of Standards, correctness of physical computers operating in the Gaithersburg, Maryland, pp. 91-98; republished in: the real world. For only with such an understanding Rein Turn, ed., Advances in Computer System Secu­ can those outside the computer science community rity, Vol. III, Artech House, Norwood, Massachusetts, intelligently assess the relative advantages and dangers 1988, pp. 176-183 of a given proposed use of computer systems. [6] Fetzer, James H. Program verification: The very idea, CACM 31, 9 (September 1988) 1048-1063 [7] Fetzer, James H. Author's response to various Bibliography letters about [6] CACM 32, 3 (March 1989) 377-381 [1] Bentley, J. Progamming Pearls, Addison-Wesley, [8] Hoare, C.A.R. An axiomatic basis for computer 1986 programming. CACM 12 (1969), 576-580 [2] Bevier, W.R., Smith, M.K, and Young, W.O. Letter [9] Hoare, C.A.R. Mathematics of programming, in the Technical Correspondence section of CACM 32, BYTE (August 1986), 112-149 3 (March 1989) 375-376 [10] Kreisel, G. Informal rigour and completeness [3] DeMilio, R., Lipton, R. and Perlis, A. Social pro­ proofs, Int. Colloq. Philos. Sci., 1 ( 1965) 138-186 cesses and proofs of theorems and programs. CACM [11] Smith, B.C. The Limits of Correctness, SIGCAS 22, 5 (May 1979) 271-280 Newsletter 14, 4 (December 1985) 18-26 [4] Dobson, J. and Randell, B. Program verification: [12] Wulf, W.A., Shaw, M., Hilfinger, P.N. and Public image and private reality, CACM 32, 4 (April Flon, L. Fundamental Structures of Computer Sci­ 1989) 420-422 ence, Addison-Wesley, 1981

ALGEBRAIZABLE LOGICS W. J. Blok and Don Pigozzi (Memoirs of the AMS, Number 396)

Although most of the familiar logical systems are known to 1980 Mathematics Subject Classifications: 03G99; 03B45, 03B55, have an algebraic counterpart, no general and precise notion 03B60, 03C05,08C15 of an algebraizable logic exists upon which a systematic ISBN 0-8218-2459-7, LC 88-8130 ISSN 0065-9266 investigation of the process of algebraization can be based. 88 pages (softcover). January 1989 In this work, the authors propose and begin such an Individual member $8, List price $13, investigation. Their main result is an intrinsic characterization Institutional member $10 of algebraizability in terms of the Leibniz operator Q, which To order, please specify MEM0/396NA associates to each theory T of a given deductive system S a congruence relation ilT on the formula algebra. QT identifies all formulas that cannot be distinguished from one another, on the basis of T, by any property expressible in the language of S. The characterization theorem states that a deductive system S is algebraizable if and only if n is one-to-one All prices subject to change. Shipment will be made by surface. For and order-preserving on the lattice of $-theories and also air delivery add, I st book $5, each additional book $3, maximum $100. preserves directed unions. The authors illustrate these results Prepayment required. Order from American Mathematical Society, P.O. with a large number of examples from modal and intuitionistic Box 1571, Annex Station, Providence, Rl 02901-1571, or call toll free logic, relevance logic, and classical predicate logic. 800-566-7774 to charge with VISA or MasterCard.

SEPTEMBER 1989, VOLUME 36, NUMBER 7 851 Washington Outlook

Kenneth M. Hoffman

The crunch will come when all the science budgets This month's column is written by Hans J. Oser, in NASA, NSF, and DOE bump against the ceilings who is a consultant to the Office of Governmental set by the budget committees. As this is written, the and Public Affairs of the Joint Policy Board for Senate has not taken up any of the appropriations bills Mathematics in Washington, D.C. yet, but by the time they emerge from the Senate, they will most likely be different from the House versions. This column is written during the dog days of And that means more negotiations and horse trading summer when the Nation's Capital is suffering under involving very powerful political forces whose identity the worst tropical climate in memory. The weatherman is not even known at this time. says it's all due to the Omega effect, which is just On the positive side, however, we should remember describing the curious bend in the jet stream that that the year began with some very strong statements keeps all the moisture from the Gulf of Mexico by our "education" President and the largest number of bottled up along the Eastern seaboard. Congressional Hearings devoted to science, education, Other things seem to have gotten stuck here too: and university infrastructure support in many years. Congressional preoccupation with ethics issues contin­ We have a science adviser to the President after a ues; the Supreme Court went home for the Summer long wait who, by his experience in Washington, can after two highly controversial decisions, and with be expected to be a powerful spokesman in science more surprises expected in the Fall. The House of policy matters both within the White House and in Representatives, after relentlessly lambasting the for­ the Administration's dealings with Congress. Maybe mer Secretary of Defense, Caspar Weinberger, for not he arrived too late to influence much of the fiscal year controlling a run-away budget, suddenly changed its 1990 budget debate, but he should be counted on in mind when Secretary Dick Chaney proposed actually future years. cutting two weapons systems and trimming the de­ The Federal Coordinating Council for Science, fense budget by some $30 billion over the next five Engineering and Technology (FCCSET, commonly re­ years. ferred to as "FIXIT") published its long-awaited report The National Science Foundation's budget contin­ on the future of high-speed computing and electronic ues to be the responsibility of Congressional appro­ broadband networks. Many of their recommendations priations subcommittees that have to balance NSF were anticipated by a 1987 panel chaired by Harold requests with those of NASA, the Departments of Ravece, Duncan Lawrie, and Alvin Despain. Their re­ Veterans Affairs and of Housing and Urban Develop­ port was sponsored by NSF and DOE, and published ment. The politics of the situations are awesome and by SIAM under the title "A National Computing requests are rarely judged on their merits alone. Initiative". The physicists prevailed in the House and got By the time you read this, Congress should be back a $200 million promise to get the Superconducting from the Labor Day recess. We can expect a busy Supercollider construction started. But no new money, calendar this Fall for the Congress and the executive mind you, just a clip here and there from the high branch agencies that will be defending their 1991 energy physics budget in DOE. So far, the SSC is budget proposals against OMB-we hope with full an internal family affair for the physicists, who will cooperation of the President's Science Adviser. But probably have to sacrifice some of their magnetic there could still be a surprise in relation to the 1990 fusion budget. But that situation can change very budget if the Gramm-Rudman-Hollings targets are not quickly to the disadvantage of the other sciences. being met.

852 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements

Sergei L'vovich Sobolev of solving the wave equation describ­ strides in this area with his develop­ 1908-1989 ing oscillation in an elastic medium. ment of the method of critical points The study of Sobolev function spaces, at infinity. Born in Tunisia, Bahri Sergei L'vovich Sobolev, the em­ which he introduced in the 1930s, was educated in France and received inent Soviet mathematician whose immediately became a whole area of his doctorate from the Universite de work had a substantial influence on functional analysis. Sobolev's notion Paris VI in 1981. He is currently the development of twentieth cen­ of generalized function (distribution) professor of mathematics at Rutgers tury mathematics, died on January turned out to be especially important; University. 3, 1989 in Leningrad, at the age of with further development by Laurent The citation for Ribet commended 81. Sobolev made fundamental con­ Schwartz and I. M. Gel'fand, it be­ his "contribution to number theory tributions to the theory of partial dif­ came one of the central notions of and to Fermat's Last Theorem". In ferential equations, functional anal­ mathematics. His contributions to his work in arithmetic algebraic ge­ ysis, function theory, mathematical computational mathematics are ap­ ometry, Ribet has recently focused physics, and computational mathe­ parent in his influential monograph, on modular forms and the Taniyama­ matics. Introduction to the Theory of Cuba­ Weil Conjecture. He received his Sobolev was born in St. Peters­ lure Formulas. doctorate from Harvard University burg (now Leningrad) on October 6, In 1957, Sobolev moved to Novosi­ in 1973 and is currently professor 1908. He mastered the high school birsk and became one of the orga­ of mathematics at the University of material on his own, and entered nizers of the Siberian Branch of the California at Berkeley. Leningrad University in 1925. Clearly Soviet Academy of Sciences. He was The Fermat Prize rewards the re­ a mathematical prodigy, Sobolev was also a professor at Novosibirsk Uni­ search of mathematicians working in elected Corresponding Member of versity from 1960 to 1978. areas influenced by the contributions the Soviet Academy of Sciences at Sobolev was elected to the French of Pierre de Fermat: principles of the age of 25 and elected Academi­ Academy of Sciences, the Academia variational theory, the foundations cian at 31. Nazionale dei Lincei, and many other of calculus of probabilities and of an­ From 1930 to 1931, Sobolev scientific societies. He also served as alytic geometry, and number theory. served as docent at the Leningrad chairman of the National Committee This list of areas is not restrictive, Electrotechnic Institute, and in 1932, of Soviet Mathematics. however; the spirit of the prize is to he moved to the Leningrad branch reward the research results that are of the Steklov Institute. He took a accessible to the greatest number of Ribet and Bahri position at the Moscow branch of the mathematicians. Receive Fermat Prize Steklov Institute in 1934 and became Ribet and Bahri are the first re­ director of the Institute in 1941. He cipients of the prize, which will be also taught at Moscow University for Abbas Bahri and Kenneth A. Ribet awarded every other year in Toulouse. more than 20 years. From 1952 to have received the Fermat Prize for There is also a Junior Fermat Prize, 1957, he headed the first department Research in Mathematics, awarded which was not awarded this year. of computational mathematics in the by Universite Paul Sabatier and Further information, such as the Soviet Union. Matra-Espace. The two will share rules of the contest and application Among Sobolev's most important the prize of 100,000 FF. deadlines, is available from Prix Fer­ mathematical accomplishments was Bahri was cited for "the intro­ mat de Recherche en Mathematiques, his creation, together with V. I. duction of new methods in the cal­ J. B. Hiriart-Urruty, Professeur des Smirnov, of the now classical method culus of variations". He made great Mathematiques, Universite Paul

SEPTEMBER 1989, VOLUME 36, NUMBER 7 853 News and Announcements

Sabatier, 118 route de Narbonne, ley; MEI-CHI SHAW, University of of high quality undergraduate calcu­ 31062 Toulouse Cedex, France. Notre Dame, University of Wiscon­ lus curricula. sin, Madison. The NSF received a total of 7 4 NSF Awards Visiting proposals and made 1 7 new awards. Professorships Minority Scholars In fiscal year 1989, $1.86 million will Awarded Fellowships be spent on the new grants, with the As an important part of the National remainder of the $2.3 million pro­ Science Foundation's initiative to en­ The National Research Council has gram budget going to five continuing hance the participation of women announced the names of 102 mi­ grants. Several of the new grants re­ in U.S. science and engineering re­ nority scholars who have received sulted from one-year planning grants search, the Visiting Professorships fellowships in two programs spon­ awarded in the first year of the com­ for Women program has awarded sored by the Ford Foundation, the petition. grants totalling $2.36 million to 27 Predoctoral and Dissertation Fellow­ Listed below are the names of the women scientists. In addition, the ships for Minorities program and the projects, the principal investigators host institutions have contributed Postdoctoral Fellowships for Minori­ and their institutions, the sizes and nearly $500,000 to these awards. ties program. durations of the grants, and short de­ The program enables women sci­ Only one award was made in the scriptions. (The dollar amounts given entists and engineers from industry, mathematical sciences. It went to represent the entire grant to be dis­ government, and academic institu­ Jaime L. Hernandez-Santiago, who bursed over the specified time peri­ tions to serve as visiting professors. will receive a postdoctoral fellowship ods, not the amount to be granted The visiting professors will perform for research in applied mathemat­ during 1989.) The project descrip­ research, and will be involved in lec­ ics at the School of Medicine at tions were supplied by NSF staff. turing, counseling, and other activ­ Louisiana State University. Curriculum Development Project: ities to encourage students, particu­ The fellowships provide funds for Calculus larly other women, to pursue careers research costs, stipends, and tuition David 0. Lomen, David Lovelock, in science and engineering. to help increase the presence of un­ University of Arizona The 2 7 award winners were se­ derrepresented minorities on the na­ One year, $104,806 faculties. lected on the basis of a review pro­ tion's college and university Materials are being developed fellowship cess that focused on the merit of Plans for the 1990 that complement the calculus courses. under way. the research, and on a proposed plan competitions are now Integrated supplements are being de­ application for lecturing and serving as coun­ Further information and veloped that feature labs, projects, the Fel­ selor and mentor to women enter­ materials are available from problems, and software packages. In Research ing research careers. VPW awardees lowship Office, National the labs, students perform guided Avenue, are highly regarded researchers and Council, 2101 Constitution "experiments." Projects involve the Dead­ teachers, and have made outstanding N.W., Washington, DC 20418. student discovering and conjecturing middle of contributions to their disciplines. lines will begin around the results related to calculus. Problems 1990 com­ Seven of the Visiting Professor­ November 1989 for the are challenging, realistic questions and dis­ ships were awarded to mathematical petition for the predoctoral that might require modern technol­ around the scientists. These recipients, their in­ sertation fellowships, and ogy to solve. The software packages fel­ stitutional affiliation, and the institu­ end of 1989 for the postdoctoral will supply the appropriate materi­ tions they propose to visit are: lowships. als for MS-DOS and Macintosh ma­ chines. INGRID DAUBECHIES, AT&T Bell New Calculus Grants Laboratories (NJ), University of Announced Calculus and Computers: Michigan; URSULA HAMENSTADT, Toward a Curriculum for the 1990's California Institute of Technology, The National Science Foundation Marcia Linn, University of Pennsylvania; JENNY (NSF) has announced awards in its University of California at Berkeley HARRISON, University of California, calculus curriculum development pro­ One year, $42,898 Berkeley, Yale University; JoAN P. gram. The program was begun in This award was used to fund a HUTCHINSON, Smith College, Uni­ 1988 in response to concern from conference held at U.C. Berkeley this versity of Washington; LINDA KEEN, the mathematical sciences commu­ past August. Faculty from a broad CUNY H. L. Lehman College, Prince­ nity about the declining quality of spectrum of institutions, including ton University; JoYCE R. McLAUGH­ the calculus course. The purpose of two-year colleges, learned about and LIN, Rensselaer Polytechnical Insti­ the NSF program is to provide lead­ exchanged ideas on how to use Math­ tute, University of California, Berke- ership to stimulate the development ematica in teaching calculus. The

854 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements invited speakers and the Pis have perimentation, and widely varying will use the "Rule of Three" whereby been using Mathematica and other ·applications. topics are explored graphically, nu­ integrated symbol manipulation and A Revitalization of an merically, and analytically. graphics systems in their calculus Engineering/Physical Calculus Reform in courses and described exciting possi­ Science Calculus Liberal Arts College bilities for their use. Elgin H. Johnston, A. Wayne Roberts, Iowa State University Macalester College Rapid Dissemination of Science & Technology Three years, $567,263 New Calculus Projects Four years, $210,889 A calculus curriculum is being de­ Thomas W. Tucker, A four year program is under way veloped that stresses understanding Mathematical Association of America to revitalize the calculus course taken rather than techniques, contains real­ One year, $41,540 by science, engineering, and math­ istic applications, and promotes the Detailed descriptions (syllabi, as­ ematics students. The revised cur­ ability to write coherent arguments. signments, laboratories, exams, sam­ riculum stresses the modelling and Twenty-six liberal arts colleges in ple text material, preliminary assess­ problem solving aspects of calculus the Midwest are participating in the ment) of eight to ten new calculus and teaches students to use commer­ development of five Resource Collec­ projects are being prepared for publi­ cially available symbolic and numer­ tions containing fundamental mate­ cation. Project summaries of approx­ ical software to handle the technical rials that can be used for curriculum imately 50 additional projects are aspects of the subject. development in calculus at any in­ included. Calculus with Computing: stitution. These collections are to be A National Model Course published as five separate volumes. Calculus and Mathematica Keith D. Stroyanm, Utilization of Technology J. Jerry Uhl, Horacio Porta, University of Iowa in Non-traditional Calculus University of Illinois, One year, $65,000 Wanda Dixon, Urbana-Champaign A curriculum is being developed Meridian Junior College One year, $25,000 to present calculus as the language One year, $25,000 Using live Mathematica note­ of science. The project treats begin­ The calculus curriculum is being books, this pilot project is devel­ ning calculus as a laboratory course revised to place more emphasis on oping a non-traditional, entirely new with modern computers and scien­ learning the concepts, solving realis­ course. Emphasis is placed upon in­ tific software as the laboratory equip­ tic problems, and improving estima­ dividual student use of the Mathe­ ment. This development is built on a tion skills. Materials are being devel­ matica program for instruction, com­ long history of successful use of com­ oped to utilize the HP-28S hand-held putation, and symbolic manipulation puters in a calculus laboratory and calculator. within the Mathematica notebooks. will make use of new software so that Calculus: Restructuring The goal is to motivate the students students have a serious start on their and Integration with Computing to better understand the foundations education in scientific computation. Richard H. Crowell, and enable them to execute calcula­ Core Calculus Consortium: Dartmouth College tions far beyond those expected of A Nationwide Project One year, $289,171 students in the traditional course. Andrew M. Gleason, This project integrates personal Deborah Hughes-Hallet, computers into the calculus course. A Calculus Redux Harvard University substantial body of new courseware Judith H. Morrel, Five years, $1,973,762 is being created that will enable the Butler University A national consortium of institu­ students to use a personal computer One year, $27,000 tions is developing an innovative core as a regular part of their homework to Students are finding more excite­ calculus curriculum that is practical explore, analyze, or verify the central ment and making better progress in and attractive to a multitude of insti­ concepts of the calculus. Students are calculus because of a revised curricu­ tutions. Led by Harvard University, expected to write some of their own lum that emphasizes problem solv­ the consortium consists of the Uni­ software andfor to modify existing ing, building intuition, and improv­ versity of Arizona, Colgate Univer­ software as an integral part of the ing written mathematical expression. sity, Haverford-Bryn Mawr Colleges, course. Substantial restructuring of A data base is being created con­ the University of Southern Missis­ course materials will incorporate the sisting of non-routine, open-ended, sippi, Stanford University, Suffolk advantages the computer affords. The multi-step problems and discussion Community College, and Chelmsford ultimate goal is to produce a new modules emphasizing concepts, ex- High School. The refocus of calculus computer-based calculus text.

SEPTEMBER 1989, VOLUME 36, NUMBER 7 855 News and Announcements

Collaborative Learning Students are benefiting from a face to the computer algebra system in Calculus completely restructured calculus cur­ MAPLE, and numerical computation Patricia R. Wilkinson, riculum at Duke University and the and graphical display routines. CUNY Borough Manhattan CC North Carolina School of Science The deadline for proposals for Two years, $50,000 and Mathematics. The new curricu­ next year's competition is February This collaborative learning project lum features an integrated computer 2, 1990. Although the program will be is providing students, especially those laboratory for exploration and devel­ substantially the same next year, the from minority groups, a better chance opment of intuition and emphasizes NSF has decided to fund a few pi­ to achieve success in calculus. These writing to promote student compre­ lot projects in differential equations students are working in informal hension and expression. The course and linear algebra for the first two study groups with the assistance of materials are being developed jointly years of calculus. The program an­ specially trained tutors. by members of the faculties of the nouncement and more information two schools. are available from John S. Bradley, Calculus in the Liberal Arts Calculators in the Program Director, Calculus Curricu­ Curriculum/Multidisciplinary lum Development, USEME, Room Resources for College Calculus Calculus Curriculum Thomas Dick, 639, National Science Foundation, Ronald W. Jorgensen, DC Oregon State University 1800 G Street, NW, Washington, Nazareth College of Rochester elec­ Four years, $264,106 20550; telephone 202-357-7051; Two years, $78,232 tronic mail [email protected] This joint effort involves universi­ A calculus curriculum is being de­ (Internet) or jbradley@nsf (Bitnet). veloped using the computer algebra ties, two- and four-year colleges, high and high technology indus­ system MAPLE in conjunction with schools, Call for Nominations develop and implement a new writing assignments. The courses will try to for Waterman Award be organized in diagnostic learning calculus curriculum which makes in­ tegral use of symbolic/graphical cal­ units and will require students to The National Science Foundation materials appropriate keep a journal, to be evaluated reg­ culators. Text (NSF) has called for nominations for the equivalent of three semesters ularly by the instructor. This system for the 15th annual Alan T. Water­ of calculus are being produced and of ongoing feedback between stu­ man Award. The award is intended class-tested in a variety of instruc­ dent and teacher will enhance self­ to give recognition to an outstand­ tional settings. Workshops will pro­ evaluation on the part of the student. ing young researcher in any field of vide continuing instructional support science, mathematics, or engineering The Computer Revolution in the curriculum ma­ for teachers using and to encourage further high-quality Calculus: Innovative Approaches to calcu­ terials and symbolic/graphical research. Concepts and Applications lator. The recipient receives up to William E. Boyce, The Calculus Companion: $500,000 for up to three years of Rensselaer Polytechnic Institute A Computational Environment for research or advanced study in the One year, $55,000 Exploring Mathematics mathematical, physical, medical, bi­ A new calculus course is being Edmund A. Lamagna, ological, engineering, social, or other designed that exploits the power of a Diane L. Johnson, sciences at the institution of the re­ computer as an integral part of teach­ University of Rhode Island cipient's choice. ing and learning. The course takes Three years, $161,535 Candidates must be U.S. citizens of a computer's capacity advantage The calculus curriculum is be­ or permanent residents and must to perform numerical computation, ing revised to provide students with be 35 years of age or younger, or produce sophisticated graphics, and more complex, real world problems, not more than five years beyond the carry out extensive symbolic manip­ to help them develop the skills in­ Ph.D. by December 31 of the year in ulations. Students will be provided volved in performing multi-step rea­ which the nomination is made. Can­ with powerful and versatile problem­ soning, and to help them learn to didates should have sufficient per­ solving tools and simultaneously gain express mathematical ideas precisely sonal accomplishments, outstanding a deeper understanding of the under­ and coherently. A unique compu­ capability, and exceptional promise lying mathematical concepts. tational environment is being de­ for significant future achievement. In Project CALC: Calculus veloped in which students use the addition, candidates' research should as a Laboratory Course computer as both a tutoring device exhibit quality, innovation, and po­ Lawrence C. Moore, David Smith, and a computational aid. The sys­ tential for discovery. Duke University tem, called the Calculus Compan­ The mathematical scientists who Four years, $585,756 ion, consists of a user-friendly inter- have received previous Waterman

856 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements

Awards are Charles Fefferman ( 1976) 202-357-3686 Staff at DoD Agencies and William P. Thurston (1979), Alfonso Castro both of Princeton University; Harvey Fred Howes Five agencies of the Department of Friedman of Ohio State University Computational Mathematics Defense fund research in the mathe­ (1984); and Edward Witten of the 202-357-3691 matical sciences: the Air Force Office Institute for Advanced Study ( 1986). Alvin Thaler (Acting) of Scientific Research (AFOSR), the The deadline for nominations is Army Research Office (ARO), the Statistics and Probability December 31, 1989. Nominations for Defense Advanced Research Projects 202-357-3693 the award may be submitted by indi­ Agency (DARPA), the National Se­ Mary Ellen Bock viduals, professional societies, indus­ curity Agency (NSA), and the Office Peter W. Arzberger trial companies, and by other ap­ of Naval Research (ONR). Recently propriate organizations within the Special Projects there have been a number of staff scientific and educational communi­ 202-357-3453 changes in the mathematics programs ties. A special form is necessary for Deborah F. Lockhart at the defense agencies. In order to submitting nominations. The forms Alvin Thaler facilitate contact with these agencies, and further information may be ob­ The administrative staff includes: the names, addresses, and telephone tained from Lois J. Hamaty, Exec­ Division Director numbers of the staffs are provided utive Secretary for the Alan T. Wa­ Judith S. Sunley below. terman Award Committee, National 202-357-9669 Science Foundation, 1800 G Street, Deputy Division Director AFOSR, Directorate of NW, Room 545, Washington, DC Bernard R. McDonald Mathematical Sciences 20550; telephone 202-357-7512. 202-357-9669 AFOSR/NM The award will be made in May, Administrative Officer Building 41 0 1990. The Waterman Award was es­ Tyczer Henson Bolling AFB tablished by Congress in 197 5 to 202-357-3683 Washington, DC 20332 mark the 25th anniversary of the Charles J. Holland, Director, NSF and to honor Waterman, the The permanent staff consists of 202-767-5025 first director of the Foundation. Boyle, Krause, McDonald, Ryff, and Sunley. The incoming rotators are Mathematical Optimization Staff at the NSF's Math Division Herbst, University of Virginia; Cas­ Finite Mathematics tro, University of North Texas; and Neal D. Glassman Listed below are the Program Direc­ Howes, University of California at 202-767-5026 Davis. Thaler, on the permanent staff tors for the coming academic year Applied Analysis in the Division of Mathematical Sci­ of the Foundation, is returning to the DMS after a stint in the NSF's Direc­ Mathematics of Physical, Chemical, ences (OMS) at the National Science and Biological Systems Foundation. torate for Computer and Information Science and Engineering. Arje Nachman Classical Analysis The community expresses its 202-767-4939 202-357-3455 thanks for a job well done to out­ Artificial Intelligence John V. Ryff going rotators William L. Paschke, Computer Science Modern Analysis University of Kansas; Peter W. Bates, Abraham Waksman 202-357-3697 Brigham Young University; Bart S. 202-767-5028 Ira Herbst Ng, Indiana University-Purdue Uni­ Mathematics of Signal Processing Geometric Analysis versity at Indianapolis; Raymond C. 202-357-3451 Y. Chin, Lawrence Livermore Labo­ and Communication Russell B. Walker ratories; and Elbert A. Walker, New Statistics and Probability Mexico State University. Eytan Barouch Topology and Foundations 202-767-4940 202-357-3457 All of the DMS staff can be Ralph M. Krause reached via electronic mail. To form Mathematics of Computation an individual's address, take the first Algebra and Number Theory Arje Nachman (acting) initial and last name, and append 202-767-4939 202-357-3695 @note.nsf.gov for Internet, or @nsf Ann K. Boyle for Bitnet. For example, to contact Mathematics of Dynamics and Control Jonathan D. Lubin John Ryff through Internet, use the James Crowley (acting) Applied Mathematics address [email protected]. 202-767-5025

SEPTEMBER 1989, VOLUME 36, NUMBER 7 857 News and Announcements

ARO, Mathematical Sciences Division Probability and Statistics (who had previously founded Zen­ P.O. Box 12211 Julia Abrahams tralblatt fUr Mathematik) as its edi­ Research Triangle Park, NC 27709 202-696-4320 tor. Hence it has taken just slightly 50 years for MR to reach Jagdish Chandra, Director Discrete Mathematics less than 919-549-0641 Marc Lipman this milestone. G. Bartle, the present Ex­ (all program managers may 202-696-4310 Robert be contacted at this number) ecutive Editor of MR, had the honor Numerical Analysis of stamping the first 7-digit num­ Applied Analysis and Richard Lau ber on a paper to the cheers of the Physical Mathematics 202-696-4316 MR staff which had assembled to Julian Wu Applied Analysis watch this once-in-a-lifetime event. Numerical Methods and John Lavery The staff then broke for a celebra­ Scientific Computation 202-696-4314 tion in the lunchroom of the MR Kenneth D. Clark building, which once housed a brew­ There have been several changes ery. The record shows that the one­ Probability and Statistics in the mathematics program at ONR. millionth paper is: "An extension of Gerald Andersen Neil Gerr, who had been serving as Kazhdan-Lusztig theory", by Vinay Systems, Control, Modeling, and AI acting director, is now the director. V. Deodhar of Indiana University. Jagdish Chandra Two positions that had been vacant This article appeared in a confer­ for several months have now been Special Projects ence proceedings entitled "Invariant filled. The new program managers are (Centers of Excellence) theory", published in Contemporary John Lavery, from the NASA-Lewis Jagdish Chandra Mathematics, vol. 88 ( 1989), 579- Research Center, and Marc Lipman, 583. Conferences, Symposia, from IUPU at Fort Wayne. Gerr says The fact that one million items and Workshops he is continuing to recruit for the po­ have been stamped does NOT mean Francis Dressel sition of program manager for Oper­ that MR has reviewed one million the staff ations Research. Those interested in Kenneth D. Clark joined items-yet. For one thing, the stamp­ previous more information about the position of ARO in June from his ing takes place at the front end of Northern Research. can contact him at the address and position at Bell the production line, before the re­ who re­ phone number given above. He replaced Arthur Wouk, view has been written. There are two In addition, two programs that tired this year. other reasons that one million control were established at ONR two years DARPA, Applied and Computational numbers does not mean one million ago-Boundary Value and Inverse Mathematics Program reviews: 1400 Wilson Boulevard Problems, and Calculus of Varia­ tions-have been combined into the Arlington, VA 22209 (i) it may be decided at a later stage Applied Analysis program. Louis Auslander, Program Manager, that a stamped item is in fact 202-694-3145 outside the scope of MR; NSA, Mathematical Sciences Program Mathematical Reviews (ii) some stamped items are included Attn: RMA Hits One Million in the MR data base and listed Ft. George G. Meade, MD 20755-6000 in MR indexes, but are not re­ Marvin Wunderlich, Director, Tuesday, July 25, 1989, was a big day viewed (e.g., long abstracts, or 301-859-6438 at the office of Mathematical Reviews other items that appear to be pre­ On that day, at 11:45 a.m., liminary reports of a forthcoming ONR, Mathematics Division (MR). item was stamped. Code 1111 the one-millionth paper). that MR treats is given a 800 North Quincy Street (Every item called its 1989, MR will have Arlington, VA 22217 unique acquisition number, By the end of which is stamped a total of approximately Neil Gerr, Director, "control number", published to track the reviews; it will not be until 202-696-4321 on the item and used 920,000 item as it proceeds through the MR 1991 that the one-millionth review is Signal Analysis system-from receipt to published re­ published. Neil Gerr view. On July 25 the control number The growth of the size of MR 202-696-4321 reached 1 000 000.) reflects the growth in mathemati­ Operations Research MR was founded in 1940 by cal publication during the last fifty Julia Abrahams (acting) the American Mathematical Soci­ years. The first volume of MR, in 202-696-4320 ety, with Professor Otto Neugebauer 1940, contained 2, 120 reviews in 400

858 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements pages. In 1950 there were 5,241 re­ News from the S. R. Wiggins, California Institute views in 873 pages. In 1960 there Mathematical Sciences Institute of Technology. Eighteen additional were 7,824 reviews in 1,600 pages, Cornell University short term visitors will be at Cornell but the next year there were 13,382 for a month or less. These include: S. reviews in 2,548 pages. In 1989 there Hamiltonian Systems Series Antman, University of Maryland, A. will be about 48,800 reviews in ap­ This fall, the Mathematical Sciences Bloch, Ohio State; D. David, CNLS proximately 10,000 pages (including Institute (MSI), will offer a special Los Alamos; S. Ge, MSRI; J. Har- - indexes). series on Hamiltonian Systems. Un­ nad, Ecole Polytechnique; D. Holm, Los Alamos National Laboratory; D. The most memorable (and proba­ der the overall direction of Jerrold E. Lewis, Stanford; J. H. Lu, Univer­ bly the most significant) figure is that Marsden, Berkeley and Cornell, three sity of California at Berkeley; R. S. in each decade, MR has published workshops at Cornell and an affili­ Mackay, University of Warwick; F. approximately twice as many reviews ated one at the Centre de Recherche Magri, Universita di Milano; Y. G. as it did in the preceding decade. If Mathematique in Montreal will ex­ Oh, MSRI; G. Patrick, University the present rate of growth continues, plore new advances in understanding of California, Berkeley; T. Posbergh, it is estimated that just about January systems that govern the motion of Stanford; G. Raugel, Ecole Polytech­ 1, 2000, MR will stamp the number mechanical systems in engineering, 2 000 000. physics, and chemistry. Recent ad­ nique; J. Scheurle, Universitat Ham­ vances have occurred in the areas burg, W. Shadwick, University of Waterloo; V. Rom-Kedar, University New Associate Executive of computer simulation and theory, Director for AMS and the MSI workshops will focus on of Chicago; M. Tratnick, CNLS Los both areas, with special attention to Alamos. topics such as the Block Diagonal­ Donovan H. Van Osdol has joined The semester-long series will pro­ ization Technique, a new technique vide an opportunity to fully ex­ the AMS staff in Providence as an in stability theory; chaotic dynamics plore emerging interdisciplinary con­ Associate Executive Director of the in engineering and chemical systems; Society. Formerly Professor of Math­ nections. New theoretical areas draw symbolic manipulators and symplec­ from both mathematics and engi­ ematics and Chairman of the Mathe­ tic integrators for the computer sim­ neering; for example, the mathe­ matics Department at the University ulation of mechanical systems; and matical tools used to study chaotic of New Hampshire, he began his new Berry's Phase. Many other related dynamics bridge mathematics, engi­ position on July 24, 1989. topics will be addressed. (See this neering, and chemistry. Techniques Van Osdol received his Ph.D. in section in the July I August issue of borrowed from the study of chaotic mathematics, with a minor in oper­ Notices for a complete list of topics particle trajectories in fluid mechan­ ations research, from the University and workshop organizers.) ics are being used to study chemical of Illinois in 1969. He served as as­ This series on Hamiltonian Sys­ reaction rates. The application of the sistant professor at Wilkes College tems will provide an excellent op­ concepts of chaotic trajectories in before moving to UNH in 1970. His portunity to further develop exist­ Hamiltonian Systems to chemical re­ main areas of mathematical research ing theory and computer simula­ action rates has been developed in are category theory and homological tion of mechanical systems. "Lots the last 18 months by, among others, algebra. of things are poised for discovery," G. S. Ezra and P. Holmes, Cor­ R. Since 1988, Van Osdol has been says Marsden, and a large contin­ nell, and S. Wiggins, California a co-principal investigator for a plan­ gent of the field's leading researchers Institute of Technology. Other new ning grant for calculus curriculum will be at Cornell University for applications of Hamiltonian Systems concepts have also become evident. development from the National Sci­ varying periods of time over the For example, ideas about the dynam­ ence Foundation. In addition, he has course of the semester, creating the ics of coupled rigid bodies are trans­ served since 1984 as a consultant for best possible environment for ad­ the Institute for Quality and Produc­ vances. Those expected to spend sig­ ferrable to polarization laser dynam­ ics and Berry's phase has applications tivity at UNH. nificant time at Cornell include: C. Scovel, Los Alamos National Labo­ in magnetic resonance imaging. Among the many responsibilities ratory; M. Field, Australia; R. Gross­ To attend any MSI workshop, of Van Osdol's new position, the man, University of Illinois; P. S. contact the Institute at Cornell Uni­ two most visible to the mathematical Krishnaprasad, University of Mary­ versity, 2012 Caldwell Hall, Ithaca, community are serving as Manag­ land; R. Ratiu, University of Califor­ NY 14853-2602, 607-255-8005. To ing Editor of Notices and overseeing nia, Santa Cruz; J. Sima, Stanford; attend the affiliated conference in AMS membership services. C. Stuart, Ecole Polytechnique; and Montreal on Hamiltonian Systems,

SEPTEMBER 1989, VOLUME 36, NUMBER 7 859 News and Announcements

Transformation Groups, and Spec­ During March-April, 1990 there MS 2000 Plans Curriculum tral Transform Methods, contact: J. will be a concentration on Mathe­ Conference Differential­ Harnad, Ecole Polytechnique, CP matical Physiology and The National Research Council proj­ series of lectures 6079, Succursale A, Montreal, Quebec, Delay Equations. A ect Mathematical Sciences in the and Develop­ H3C 3A7, Canada, 514-343-7487, or in Neural Networks Year 2000 (MS 2000) will sponsor the conference sectary at 514-343- mental Biology is planned. a one-day conference focusing on 2197. During April-June, 1990 the con­ the service role for mathematics and centration will be on Fluid Flow and statistics. The conference, entitled Postdoctoral Applications Sought Convection Dynamics. Turbulence in "Mathematical SCi'e~ces: Servant to Applications for 1990-1991 post doc­ Fluid Flows, Nonlinear Phenomena Other Disciplines", i part of the MS toral positions are currently being in Atmospheric and Oceanic Sciences 2000 curriculum_re iew and as such, invited. The deadline is December and Chaotic Processes in Geological will be an opportunity to gather in­ 15, 1989. Awards will be made by Sciences will be among the topics to formation concerning service courses January 31, 1990. For details see the be studied. taught by mathematical sciences de­ advertisement in the July f August No­ partments at the undergraduate and tices of the AMS or contact MSI at graduate level. The perspective will Cornell University. OMS Advisory Committee be from the client's viewpoint, since Meeting in November the invited participants will represent News from the a broad range of disciplines that rely Institute for Mathematics The Division of Mathematical Sci­ on mathematics and statistics course and Its Applications ences (DMS) of the National Sci­ offerings to support their curricula University of Minnesota ence Foundation (NSF) will hold and educate their students. Beyond its semi-annual Advisory Commit­ the factual information about what 6-7, 1989, is currently being offered, the speak­ The Institute for Mathematics and tee meeting on November in Washing­ ers will address the mathematical its Applications (IMA) program for at NSF headquarters which con­ needs of their curricula and whether 1989-1990 is "Dynamical Systems ton, DC. The committee, scientists from mathematical sciences departments and Their Applications". The pro­ sists of mathematical and industry, are fulfilling the need. gram will begin September 5 with an academia, laboratories, setting priorities The conference will be held on opening workshop that will feature advises the DMS on Friday, October 13, 9am to 4:30p.m., introductory lectures by Rutherford and formulating plans. at the University of Maryland, Col­ Aris, Shui-Nee Chow, Paul Fife, Mar­ meeting in­ The last committee lege Park Campus. There will be 8 to tin Golubitsky, John Mallet-Paret, cru­ cluded discussions of several 10 disciplines represented, including Kenneth R. Meyer, Richard Moeckel, such as cial funding priority issues, the areas of physics, chemistry, biol­ Grisha Sivashinsky, and Forman A. small the new geometry initiative, ogy, engineering, computer science, Wil- activ­ travel grants, and educational management, the social sciences, the liams. The topics of concentration Priori­ ities (see "Setting Scientific arts and the humanities. The con­ for the period September to De­ 1989, page ties," Notices, MayjJune ference will be structured in a con­ cember are Chemical Reactions and 540). gressional hearing format, with the Combustion Dynamics. The organiz­ will be open to participants making 10 to 15 minute ers include Rutherford Aris, Donald The meeting for topics of statements to the MS 2000 Commit­ Aronson, Paul Fife, Amable Linan, the public. Suggestions be made to Ju­ tee, followed by a 20 to 25 minute Harry Swinney, and Forman Williams. discussion should 202-357- question and answer period between There will be a workshop on "Pattern dith Sunley, DMS Director, the presenter and the committee. The and Dynamics in Reactive Media" 9669; Internet, [email protected]; Those wishing audience will have an opportunity to during October 16-20, 1989 and a Bitnet, jsunley@nsf. should con­ participate in the question and an­ workshop on "Dynamical Issues in to attend the meeting at the same swer period to the extent that time Combustion Theory" during Novem­ tact Trudy Sensibaugh or via Internet, permits. ber 13-17, 1989. telephone number, or Bitnet, A substantial proportion of the The winter program will concen­ [email protected] The address is Na­ teaching in the mathematical sciences trate on Hamiltonian Dynamics and tsensibaugh@nsf. Division is in this service capacity, and people Mathematical Physics; L. Kadanoff, tional Science Foundation, Room 339, both inside and outside the mathe­ R. McGehee, K. Meyer, J. Moser, C. of Mathematical Sciences, Washington, DC matical sciences are troubled by the Robinson, and E. Zehnder will be the 1800 G Street NW, effectiveness of the instruction. This organizers. 20550.

860 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements conference should be a convenient midges formed two clusters whose MCM. In addition, SIAM and ORSA means for the audience and the par­ convex hulls did not overlap. Three chose one winning team from each ticipants to gain some insight into additional midges fell between the problem category and paid the ex­ the difficulties. clusters, and the problem was to de­ penses for the team members to at­ Information about the conference cide to which species each of these tend the societies' meetings. ORSA program, directions for the Uni­ three belonged. Teams generally used chose CalPoly and Harvey Mudd, versity of Maryland campus, and a statistics approach, but one of the and SIAM selected CalTech and Har­ overnight accommodations have been winning teams applied neural nets. vey Mudd. sent to mathematical sciences depart­ The discrete problem, chosen by Ben Fusaro of Salisbury State ments. Individuals interested in at­ 118 teams, asked for a scheme for University is the founder and di­ tending the conference are asked to assigning aircaft to a runway queue. rector of the MCM. The next MCM contact the department office for de­ Relevant factors were the number will be held in February, 1990. Those tails. This information can also be of passengers on board, connections, interested in further information can requested from the MS 2000 Office, and time schedules. (A pre-contest contact Fusaro at Department of NAS 301, National Research Coun­ sampling of airlines revealed that Mathematics, Salisbury State Uni­ cil, 2101 Constitution Avenue N.W., they use a first in, first out scheme. versity, Salisbury, MD 21801. Washington, DC 20418, or by email One regional airline was experiment­ [email protected]. A registration ing with a different scheme.) The stu­ American Team fee of $30 is being charged to off­ dents' solutions ranged from assign­ Places Fifth in Olympiad set the cost of lunch, refreshments ment-type linear programming ap­ and the conference proceedings. The proaches to solutions based entirely A team of six American high school deadline for registration is October on statistics. students placed fifth in the 30th In­ 4, 1989. The judges chose as winners three ternational Mathematical Olympiad, of l 7 midge papers designated as held July 13-24 in Braunschweig, Mathematical Contest Meritorious. The schools, together West Germany, with one team mem­ in Modeling with their MCM advisers, are: Cali­ ber receiving a perfect score. Eight student teams from across the fornia Polytechnic State University, The American team scored 207 country have received awards for T. D. O'Neil; California Institute of out of a possible 252 and led the par­ their outstanding solutions to the Technology, D. B. Wales; and Wash­ ticipating western countries in a com­ Mathematical Contest in Modeling ington University, H. Mukai. petition dominated by eastern na­ (MCM), which gives teams of stu­ Also chosen as winners were five tions. Ahead of the Americans were dents the opportunity to challenge of the 22 Meritorious solutions to teams from China (237), Romania their skills in solving real-world prob­ the airport problem. The schools and (223), the U.S.S.R. (217), and East lems. The winning papers were cho­ MCM advisers are: Drake Univer­ Germany (216). There were only 3 sen from among 211 entries. sity, A. F. Kleiner; Harvey Mudd western countries among the top 13 Participation in the contest has College, R. L. Borrelli; North Car­ teams, with West Germany placing grown rapidly since it was first insti­ olina School of Science and Mathe­ 8th and France 13th. Fifty countries tuted in 1985. The number of entries matics, D. Teague; Ohio State Uni­ sent a total of 291 students to the has increased more than 40% in the versity, T. G. Railey; and the Univer­ competition. last two years. sity of Dayton, R. C. Steinlage. The The judges also awarded individ­ Each three-student team had a North Carolina School of Science ual first, second, and third prizes to weekend to produce an in-depth anal­ and Mathematics, a high school in deserving team members. Jordan El­ ysis of one of two modeling prob­ Durham, was also a winner last year, lenberg of Potomac, MD received a lems. The contest gives the teams a when it was the first precollegiate gold medal for a perfect score of choice of two problems, one "contin­ team to place in the MCM. 42, one of only l 0 perfect scores. uous" and one "discrete." This year, The MCM is sponsored and ad­ Four American team members re­ the continuous problem, chosen by ministered by the Consortium for ceived silver medals: Samuel Kutin 93 teams, was based on a paper Mathematics and its Applications, of Old Westbury, NY (32), Andrew written by two biologists in 1981. a Massachusetts-based organization Kresch of Havertown, PA (37), Jef­ They had classified, by antenna and that publishes a wide variety of inno­ frey Vanderkam of Raleigh, NC (35), wing length, two species of small vative curricular materials. The Soci­ and Samuel Vandervelde of Amherst, insects called midges. One species ety of Industrial and Applied Math­ VA (32). David Carlton of Oberlin, had six midges, the other had nine. ematics (SIAM) and the Operations OH received a bronze medal (24). When plotted as points on a graph Research Society of America (ORSA) Twenty gold, 55 silver, and 72 bronze of antenna versus wing length, the also provide financial support for the medals were awarded.

SEPTEMBER 1989, VOLUME 36, NUMBER 7 861 News and Announcements

The Olympiad teams competed of information that should be use­ package of four computer files, ob­ by working on solutions to six chal­ ful to teachers, university educators, tainable from the AMS office. Two of lenging mathematical problems in community organizations, and oth­ the files contain documentation ex­ two, 4 1 /2-hour sessions. One prob­ ers who work on specific programs to plaining how the electronic submis­ lem from the exam asked the com­ strengthen science, mathematics and sion system works. Another file con­ petitors to prove that it is possible to technology education. In addition to sists of TEX macros which allow the arrange the numbers 1, 2, 3, ... , 1989 the state supervisors of mathematics user to TEXthe abstract. The last file into 11 7 lists of 1 7 numbers each, and science, the 1989 edition in­ is essentially a "template" into which in such a way that every list has the cludes the names and addresses of the user inserts the TEX-coded text same sum. the specialists in social studies. Key of his or her abstract, together with The U.S. Olympiad activities are Congressional committees responsi­ other, non-TEX information (such as sponsored by eight national organi­ ble for science education funding and the speaker's affiliation, the place and zations in the mathematical sciences, their members, reflecting the latest date of the meeting, the type of lec­ including the Mathematical Associa­ changes in the new administration, ture, etc.) used for office-processing tion of America and the AMS. Fi­ are listed too. of the abstracts. nancial support is provided by IBM, A detailed table of contents and Once the template file is complete the Army Research Office, the Office four indices help readers quickly lo­ and has been successfully processed of Naval Research, Hewlett-Packard, cate information. with TEX, the user sends it to the and the Matilda R. Wilson Fund. For a free copy of the 180- AMS either in electronic mail or on page AAAS Science Education Direc­ an IBM or Macintosh diskette. tory 1989, write to Barbara Walthall, Requests to obtain the package of AAAS Science Education American Association for the Ad­ files may be sent electronically on In­ Directory 1989 vancement of Science, Office of Sci­ ternet to [email protected]. ence and Technology Education, 1333 Requesting the files electronically will The AAAS Science Education Direc­ H Street, N.W., Room 1139, Wash­ likely be the fastest and most con­ tory 1989, a resource for anyone who ington, DC 20005. venient way, but users may also ob­ is involved in science, mathemat­ tain the package on IBM or Mac­ ics, or technology education, is now Electronic Submission intosh diskettes, available free of available. The Directory lists key per­ of Abstracts charge, by writing to: Rosanne Gra­ sons in the nation who are respon­ natiero, American Mathematical So­ sible for science, mathematics, and In the MayfJune 1989 issue of No­ ciety, Publications Division, P.O. technology education. It contains ad­ tices, the Society announced the avail­ Box 6248, Providence, RI 02940, dresses and telephone numbers of ability of a new service for sub­ USA. principal executives, directors, ad­ mitting abstracts in electronic mail When requesting the Abstracts ministrators, and policy-makers who using the plain TEX and AMS-TEX package, users should be sure to spec­ are leaders in associations, scientific computer typesetting systems. This ify whether they want the plain TEX, academies, museums, educational re­ service has now been expanded to AMS-TEX, or ~TEX package. search centers, educational laborato­ include the ~TEX system as well. ries, and state and federal govern­ Many members have requested AMS Council Agenda ment agencies. The Directory also that the AMS allow for electronic and Minutes Subscriptions provides information about the ma­ submission of abstracts for talks jor science and mathematics educa­ given at Society meetings. Before this The Agenda and Minutes of the AMS tion activities of these organizations. service was available, speakers were Council, the governing body of the Some 1700 individuals, programs, required to send to the AMS Prov­ Society, are now available through and organizations are included. idence office paper copies of their subscription. One may receive only The 1989 edition has been re­ abstracts, which are then used for the Agenda, or the Agenda and subse­ vised and expanded. A new sec­ camera copy to produce the publica­ quent Minutes of Council meetings. tion has been added that lists more tion Abstracts. This service will prove The latter includes the open min­ than thirty national educational or­ a great convenience to the many who utes of the Executive Committee and ganizations with interests in science, use the TEX system and software Board of Trustees (ECBT). mathematics and technology educa­ packages, and will make the produc­ The Council meets three times per tion. The "Resources" section in­ tion of Abstracts faster and more year. A typical Council Agenda, to­ cludes many new listings of programs efficient. gether with attachments, runs about and activities for students and teach­ In order to submit abstracts elec­ 80 pages, with the Council Minutes ers. This section contains a variety tronically, individuals will need a somewhat shorter. The Minutes of

862 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements the ECBT, which meets twice yearly, Much of the gain in the nation's considerably higher than on research. usually comprise over 1 00 pages, in­ support for R&D during the 1980s is Much of the growth in development cluding attachments. attributable to large increases in fed­ is a result of the major increases These subscriptions are available eral defense spending. The federal in federal support for defense R&D, only to AMS individual and institu­ government, which has consistently which is about 90% development. tional members and will begin in supplied approximately one-half of Even with the recent gains in federal 1990. Individual and institutional the nation's total R&D expenditures, support for civilian R&D, which has members will have received informa­ will put an estimated 66% of its a relatively higher research compo­ tion about these subscriptions in their 1989 R&D dollars toward defense nent, defense-related R&D continues dues notices, or they may contact activities. In 1980, such defense­ to receive the majority of federal the Customer Services Department, related spending accounted for one­ R&D funds, by a two-to-one margin. AMS, P.O. Box 6248, Providence, RI half of federal R&D funding. While Slow growth in R&D is also 02940. increases in defense expenditures are seen in U.S. companies. According responsible for fully 90% of the es­ to NSF estimates, U.S. firms are timated growth in federal R&D sup­ expected to spend more than $61 of Slow Rate port since 1980, most of this growth billion for R&D in 1989, a 2% 1989 R&D Growth for took place in the first half of the constant-dollar increase over 1988 decade. levels. R&D spending increases var­ The nation's expenditures for re­ In 1989, the nation is expected to ied widely among the industries. For search and development (R&D) are spend $1 9 billion on basic research, example, the chemical industry pro­ expected this year to grow only by $27 billion on applied research, and jected a 10% increase in R&D spend­ 1% in inflation-adjusted dollars-the $86 billion on development. These ing in 1989, compared to no growth lowest rate since 1975, according to totals represent real increases from at all in the motor vehicles industry. estimates by the National Science 1988 of 3%, 1%, and 1%, respec­ The data presented in this article Foundation (NSF). The lackluster tively. Since 1985, the rate of growth come from a variety of NSF surveys. showing is attributable both to a in basic research funding has annu­ A more detailed analytical report downturn in R&D funding by in­ ally exceeded that in both applied covering these data was published dustry and to tightening federal bud­ research and development. in the spring by the Science Resource getary constraints as a result of the Studies Division of the NSF. federal deficit. Expenditures the nation is expected to Erratum Overall, 140 I spend $132 billion on R&D in 1989, 120 ~ - Curren1 dollars I 10 about 5% more than the amount esti­ • • • • • Real 1982 dollars• In the list of recent recipients of the mated for 1988 (not including R&D 100 National Science Foundation's Pres­ spending by U.S. industry). Between 80 80 idential Young Investigator Awards 1977 and 1982, real R&D expendi­ 60 (Notices, May/June 1989, page 569), the name of one of the awardees, tures increased fairly steadily at an 40 40 average rate of 4.5% per year. This Bruce Donald, was inadvertently omit­ rate jumped to 6. 9% per year be­ 20 ted. Donald is a theoretical computer 0 ~~~~~~ 0 tween 1982 and 1986, the most rapid 1974 76 78 80 82 84 86 88 89 scientist at the Mathematical Sci­ growth in any 3-year period since oe,l ences Institute at Cornell University. the 1960s. In both 1986 and 1987, 03asec an GlOP •r:lD"~': !l"Ce ~et-~IOr His research involves the use of algo­ SQ.IfiCf ~~di•Or-J Sr.oence '0~·1<1.;ho~ S~S however, this rate of growth dipped rithms in robotics. to 2% per year and is estimated at Over the past decade, however, 3% for 1988. spending on development has been

SEPTEMBER 1989, VOLUME 36, NUMBER 7 863 Funding Information for the Mathematical Sciences

Travel Grants The first announcement of the college faculty and graduate students for ICM-90, Kyoto 1990 International Congress of Math­ interested in acquiring new geomet­ ematicians appears in this issue of ric tools for use in their own re­ The American Mathematical Soci­ the Notices. search specialty. The education com­ ety has applied to several funding ponent may involve geometry ed­ agencies for funds to permit par­ NSF Solicits Proposals ucation researchers, undergraduate tial travel support for U.S. math­ for Geometry Institutes and secondary faculty, undergradu­ ematicians attending the 1990 In­ ates, andjor secondary students. ternational Congress of Mathemati­ The National Science Foundation The RGis will be based at aca­ cians in Kyoto. In anticipation of the (NSF) has announced an experi­ demic institutions, either at a single availability of funds, the Society is mental activity to involve mathe­ host campus or a regional collection preparing to administer the selection maticians and scientists of all ages of campuses. So as to promote the es­ process. in research and education involving tablishment of extended interaction new geometric concepts. The Divi­ among participants, it is desirable Mathematicians who wish to ap­ sion of Mathematical Sciences and that RGis be maintained for two or ply for travel support can find an the Directorate for Science and En­ more years. However, it is likely that application form at the back of this gineering Education invite proposals the majority of the activity will take issue. Note that the deadline for com­ for the establishment of Regional place during the summers. pleting and returning the application Geometry Institutes (RGis), where A prospective host institution will form to Providence is November 1, research mathematicians will congre­ select as the focus of the research 1989. Applications will be evaluated gate to learn new geometric tools and component a particularly active area by a panel of mathematical scien­ to interact with mathematics educa­ of mathematics that significantly in­ tists under the terms of a proposal tors and students. corporates geometric ideas. Lead re­ submitted to the National Science Plans call for between one and search figures, known to be strong Foundation by the Society. Recent three awards during the first year of expositors, will deliver plenary lec­ recipients of doctoral degrees, as well this experimental activity. Should it tures on various aspects of the spe­ as women and members of minority prove successful, additional awards cialty, designed specifically to be un­ groups, are encouraged to apply. may be made in future years. derstandable to the audience at hand. If a mathematician accepts a grant In the RGis, a critical mass of The education component should for partial support of the travel to research geometers, geometry educa­ stress geometric concepts not usually Kyoto, these travel funds may not tors and teachers, and students may emphasized in the standard geometry be supplemented by any other NSF gather for activities within a frame­ curriculum. The component will fo­ funds. It is the current intention of work that promotes individual in­ cus on activities which will improve NSF's Division of Mathematical Sci­ tellectual growth while encouraging students' and faculty members' geo­ ences to provide no additional funds interaction between these groups. metric and visual thinking and may on its other regular research grants Each RGI should incorporate both be primarily concerned with precol­ for travel to ICM in 1990. How­ an Advanced Research Component lege and/ or college level geometry. ever, an individual mathematician and a Creative Education Compo­ The deadline for proposals will who does not receive a travel grant nent and should effectively integrate likely be October 1, 1989 or Novem­ may use grant funds, subject to the the research and education objectives ber 1, 1989. Further information and usual restrictions and prior approval of both. The research components a program solicitation are requirements. are aimed primarily at university and available from Russell B. Walker,

864 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Funding Information

Program Director, Geometric Analy­ mation about guidelines and eligibil­ Postdoctoral Fellowships in Japan sis Program, Division of Mathemat­ ity, contact Margrete Klein, Program ical Sciences, Room 339, National Director, Visiting Professorships for In an effort to strengthen ties be­ Science Foundation, 1800 G. Street, Women, National Science Founda­ tween U.S. and Japanese researchers NW, Washington, D.C. 20550; tele­ tion, 1800 G Street, N.W., Washing­ in science and engineering, the Na­ phone 202-357-3451; electronic mail ton, DC 20550; telephone 202-357- tional Science Foundation (NSF) es­ [email protected] (Internet). 7734. tablished last year a "Japan Initia­ tive." The initiative includes a num­ ber of programs designed to increase Visiting Professorships the number of American researchers for Women NSF-AWM Travel Grants who can operate with ease in Japan's for Women research community and follow de­ The Visiting Professorships for velopments in the Japanese research Women program at the National Sci­ literature. ence Foundation (NSF) is designed The National Science Foundation As part of the program, the NSF to provide opportunities for women (NSF) is sponsoring a program of has established two postdoctoral fel­ in science and engineering to ad­ travel grants for women mathemati­ lowship programs. The first, spon­ vance their careers while enhancing cians, administered through the As­ sored by the Japan Society for the their visibility in these professions. sociation for Women in Mathemat­ Promotion of Science, will award 25 The program is open to women em­ ics (A WM). In providing support for fellowships to conduct research in ployed in industry, government, or women to attend research confer­ Japanese university laboratories or at academia. ences in their fields, these grants other institutions affiliated with the The program allows a woman sci­ are intended not only to advance Japanese Ministry of Education, Sci­ entist or engineer to pursue advanced women's research activities, but also ences, and Culture. The 12-month research at an academic institution. to increase awareness that women are research visits are open to U.S. citi­ In addition to her research responsi­ actively involved in mathematical re­ zens or nationals not more than 35 bilities, the visiting professor under­ search. years of age. The program provides takes lecturing, counseling, and other The travel grants will suport travel airfare for the awardee, a monthly activities to increase the visibility of and subsistence to a meeting or con­ stipend, a modest housing allowance, women in the host institution and ference in the applicant's field of medical insurance, and a language­ to provide encouragement for other specialization. There is a maximum training allowance. women to pursue careers in science of $1000 for domestic travel and Through the second program, and engineering. $2000 for foreign travel. To be eligi­ sponsored by the Japanese Science Applicants must hold a doctoral ble, an applicant must be a woman and Technology Agency, approxi­ degree (or have equivalent experi­ holding a doctorate in a field of mately 35 young American research­ ence) in a field normally supported research supported by the NSF's ers will have the opportunity to col­ by the NSF and must have inde­ Division of Mathematical Sciences laborate with Japanese colleagues at pendent research experience. The in­ (or have equivalent experience). A nonacademic research facilities in struction and other activities may woman may not be awarded more Japan. The awards may be held for be directed to the undergraduate or than one grant in any two-year pe­ 6-24 months and provide a monthly graduate levels, or to the community riod and should not have available stipend, travel, housing, medical in­ at large. Proposals will be evaluated other sources of funding (except par­ surance, and research-related ex­ on the plans for such activities, as tial institutional support). penses. The Japanese Union for Sci­ well as the scientific merit of the There will be four award periods ence and Engineering will provide proposed research. The usual award in the coming year, with applications language training for the participants will be for 12 months for a full- or due November 1, 1989, February 1, at Tsukuba Science City. To be eligi­ part-time professorship, but awards 1990, May 1, 1990, and August 1, ble, applicants must be no more than for one academic semester or for 24 1990. An application should include 35 years of age. months will be considered. a description of current research and The deadline for both programs Last year, out of a total of 25 how the proposed travel would ben­ is November 1. For more informa­ awards made in all disciplines sup­ efit the research, a curriculum vita, tion, contact: Japan Initiative, Room ported by the NSF, two went to and a budget. These materials should 1208, Division of International Pro­ women in the mathematical ~ciences. be sent to the Association for Women grams, National Science Foundation, The deadline for applications is in Mathematics, Box 178, Wellesley 1800 G Street, NW, Washington, DC November 15, 1989. For further infor- College, Wellesley, MA 02181. 20550; telephone 202-357-9558.

SEPTEMBER 1989, VOLUME 36, NUMBER 7 865 I iiiiiiiiiiiiiii I A Century of ACe of: ACen in ofMa A Century in Am of Mathematics Part I Mathematics in America Jo:dued by I' Part II wuh the as Edited by Pf'tf! Part III with I hi" assts Edited by l'eler I>un·n. wllh the asst5lanre of Rtl·hard A. Askey in America Harold M. Edwards Ol?11 Uta C. Merzb;wh VOLt OJ.?ll1 QHISTORYOF VOI.Ub MATHEMATICS AN EXCELLENT ADDITION TO VOLUME 3 YOUR UBRARY COLLECTION

PART I edited by Peter Duren with the assistance of Richard A. Askey and Uta C. Merzbach This volume brings together a variety of perspectives on the political, social, and mathematical forces that have shaped the American mathematical community in the past century. Humorous, edifYing, and poignant, this book presents the personal recollections of a number of mathematicians who have influenced the development of mathematics in this country.

ISBN 0-8218-0124-4, LC 88-22155, ISSN 0899-2428; 486 pages (hardcover), 1988 List price $57, Institutional member $46, Individual member $34, Code HMATH/lNA

PART II edited by Peter Duren with the assistance of Richard A. Askey and Uta C. Merzbach Similar in perspective to Part I but differing in organization and emphasis, this volume focuses on some key elements in the making of mathematics in America. The first section of the book deals with some of the influential mathematics departments in the United States. The second section deals with an extraordinary conference held at Princeton in 1946 to commemorate the university's bicentennial. In the last section, various aspects of America's mathematical past are explored on the political, social, and scientific levels.

ISBN 0-8218-0130-9, LC 88-22155, ISSN 0899-2428; 578 pages (hardcover), 1989 List price $70, Institutional member $56, Individual member $42, Code HMATH/2NA

PART III edited by Peter Duren with the assistance of Richard A. Askey, Harold M. Edwards, and Uta C. Merzbach The third and final volume of this collection. The theme of the second volume is continued here in articles describing the mathematics and the mathematical personalities in some of the nation's prominent departments.

ISBN 0-8218-0136-8, LC 88-22155, ISSN 0899-2428; 400 pages (hardcover), 1989 List price $75, Institutional member $60, Individual member $45, Code HMATH/3NA COMBINATION OFFERS A Century of Mathematics in America, Parts I, II, and III as a set. A Century of Mathematics in America, Parts II and III as a set. ISBN 0-8218-0138-4 ISBN 0-8218-0152-X List price $182, Institutional member $146, List price $131, Institutional member $105, Individual member $109 Individual member $79 Code HMATHSET/NA Code HMATHSET/2/SNA

Prepayment required. Order from AMS, Annex Station, P.O. Box 1571, Providence, RI 02901-1571 or ca11800-556-7774 to use VISA or MasterCard. For optional air delivery, please add $5 first book, $3 each additional, $100 maximum. Acknowledgement of Contributions

The officers and the staff of the Society acknowledge with gratitude gifts and con­ tributions received during the past year. Contributing members of the Society paid dues of $132 or more. In addition to contributions to the AMS Centennial Research Fellowship Fund, there were a number of unrestricted general contri­ butions. Some of the contributors have asked to remain anonymous. All of these gifts provide important support for the Society's programs. Also listed this year are AMS members who contributed, thru the Society, to the International Math­ ematical Union's Special Development Fund for travel grants to young math­ ematicians from developing countries. The names listed below include those whose contributions were received during the year ending March 31, 1989.

CONTRIBUTING MEMBERS

Adams, Elliott T. Eckhardt, William Kiefer, James E. Palais, Richard S. Spencer, Joel H. Agarwal, Ashok K. Ecklund, Earl F., Jr. Killeen, John Palmer, Theodore W. Stakgold, lvar Akemann, Charles A. Epstein, D. I. Knuth, Donald E. Papanicolaou, George C. Sternberg, David Amir-Moez, Ali R. Fadell, Edward R. Kopala, Conrad Partridge, Eric Dorsey Strauss, Frederick B. Andrews, George E. Farrell, Roger H. Krueger, Charles G. Pearson, Robert W. Sudler, Culbreth, Jr. Assmus, Edward F., Jr. Forbes, Stephen H. Kunen, Kenneth Perry, William L. Sullivan, Richard W. Babcock, William W. Grace, Edward E. Lemay, William H. Petro, John W. Swokowski, Earl W. Baumslag, Gilbert Graves, Robert L. Lenard, Andrew Polking, John C. Taft, Margaret W. Beechler, Barbara J. Greicar, Richard K. Lewis, Hugh L. Pratt, Vaughan R. Tarzia, Domingo Alberto Bjorklund, Peter B. Greif, Stanley J. Lieb, Elliott H. Ratliff, Louis J ., Jr. Taylor, Laurence R. Black, Robert E. Grimmer, Ronald C. Martin, Gary A. Redheffer, Raymond M. Uhlenbeck, Karen Bressoud, David M. Gromov, Mikhael Mathsen, Ronald M. Reed, David L. de Valpine, Jean E. Buianouckas, Francis R. Haddad, George F. B. Mattson, H. F., Jr. Reedy, Christopher L. Veech, William A. Carson, Robert C. Halberstam, Heini Meder, Albert E., Jr. Reese, Matthias F., III Warren, William E. Clifford, Alfred H. Hassinger, Bill, Jr. Mellender, James W. Riney, John S. Weintraub, Steven H. Cohen, Henry B. Hedlund, Gustav A. Miles, E. P., Jr. Rosenblum, Marvin White, George N., Jr. Cohn, Leslie Hemstead, Robert J. Miller, W. F. Rovnyak, James L. Whitmore, William F. Cohn, Richard M. Hironaka, Heisuke Mislin, Guido Sally, Paul J., Jr. Wilson, Robert Lee Cootz, Thomas A. Hochster, Melvin Moschovakis, Yiannis N. Samit, Jonathan Woeppel, James J. Corrigan, Thomas Carney Horrigan, Timothy J. Muhly, PaulS. Sawyer, Stanley A. Woolf, William B. Daverman, Robert J. Hunt, Richard A. Murphy, Donald P. Schori, Richard M. Wright, Robert K. De Marr, Ralph E. Hutchinson, George A. Nishiura, Togo Seligman, George B. Xenos, Philippos John DeFacio, Brian Johnson, Roy A. Nummela, Eric C. Sexauer, Norman E. Yahya, S.M. DeLeon, Morris Jack Kamp, William P. Olum, Paul Shabazz, Abdul Alim Yohe, J. Michael Demana, Franklin D. Kaplan, Wilfred Orlik, Peter P. Shelstad, Diana Frost Zharn, P. Joseph Dickerson, Charles E. Kautzmann, Frank N., III Osofsky, Barbara L. Shields, Allen L. Anonymous (5) Dinneen, Gerald P. Kelly, John B. Otermat, Scott C. Singmaster, David B.

Corporate Members and Institutional Associates

The Society also acknowledges with gratitude the support rendered by the following corporations, who held either Corporate Memberships or Institutional Associateships in the Society during the past year.

Corporate Members Institutional Associtates Aerospace Corporation Kluwer Academic Publishers AT&T Bell Laboratories Princeton University Press General Motors Corporation Springer-Verlag New York Incorporated International Business Machines Corporation Supercomputer Research Center, Institute for Defense Analyses National Security Agency

SEPTEMBER 1989, VOLUME 36, NUMBER 7 867 General Contributions

GENERAL CONTRIBUTIONS

Ablow, Clarence M. Crane, George E. Hassinger, Bill, Jr. Maeda, Hironobu Reitwiesner, George W. Adams, William W. Crowell, Jack L. Heinicke, Allan G. Mahoney, Anne Renno, James G., Jr. Aeppli, Alfred Cunningham, A. B. Heller, Dorothy M. Malafronte, Thomas A. Restrepo, Guillermo Al-Medhadi, Nora Seif Dahlin, Rolf B. Hernandez, Diego B. Marshall, David Imler Reynolds, Donald F. Amitsur, Shimshon A. Day, Mahlon M. Hernandez, Horacio Matlak, Anthony R. Rice, Henry G. Anaman, Todd M. De Marr, Ralph E. Hilbert, Stephen R. Mayor, John R. Richards, John F. Anantharaman, Rajan Dedecker, Paul Hironaka, Heisuke McAdam, Stephen J. Rickart, Charles E. Anderson, R. Lucile Deeb, Waleed M. Hodgson, Jonathan P. E. McBrien, Vincent 0. Robinson, Paul Lee Antman, Stuart S. DeFacio, Brian Hoover, D. N. McKay, Thomas G. Robinson, Raphael M. Aroian, Leo A. Defrancesco, Henry F. Hoye, Laurence G. Meisner, Morris J. Rodriguez-Exposito, Jose Bachman, George Delbaen, Freddy Huerta, Carlos Cuevas Meyer, Burnett C. Rosenthal, William E. Bajusair, Mohamed S. Deprima, Charles R. Huff, Charles W. Meyer, Herman Ross, Kenneth A. Baker, Edward D. Deutz, Andre H. Hughes, Ruth L. Mielke, Paul T. Royden, Halsey L. Baldwin, John T. Donovan, Peter Humphreys, M. Gweneth Mills, Harlan D. Ruzicka, John F. Ball, N. Hansen Dou, Alberto M. Hunzeker, Hubert L. Min-oo, Maung Sahab, Salem M. Balser, Arienne S. Douglis, Avron Iha, Franklin T. Mishra, Sudhakara Samelson, Hans Barner, Klaus Duren, William L., Jr. Ihara, Yasutaka Moller, Raymond W. Sarason, Donald E. Baron, John J. Durfee, William H. Ishimoto, Hiroyasu Mooney, John J. Schauer, Richard L. Baron, Simson Dutton, Charles Everett Ito, Kiyosi Moore, Richard A. Schlesinger, Ernest C. Barreca, J. R. Eachus, J. J. Ito, Ryuichi Mostow, George Daniel Schraut, K. C. Bartick, Philip R. Eberlein, Patrick Barry Iwata, Koichi Murakami, Shingo Schreiner, Erik A. Bartle, Robert G. Ecklund, Earl F., Jr. Jackson, Stanley B. Muto, Yosio Seligman, Mark L. Baur, Lynne A. Eisman, Sylvan H. Jacob, Niels Myers, Earle F. Sharp, Henry, Jr. Bayo, Enrique El-Helaly, Sherif Taha Jockusch, Carl G., Jr. Nagase, Michihiro Shields, Allen L. Beard, Helen P. Emery, Carol J. Reinhard Johnson, D. Randolph, Jr. Nashed, M. Zuhair Shiraiwa, Kenichi Bell, Raymond F. Enomoto, Kazuyuki Johnson, Donald G. Nesbitt, Cecil J. Shorter, William Ivan Bencsath, Katalin A. Fass, Arnold L. Jonah, David W. Nevai, Paul Silberger, Allan J. Bengtson, Thomas E. Faulkner, Frank D. Jones, Carl Hilton Newman, Morris Singh, Kanhaya L. Bennett, Fredricka T. Fegan, H. D. Jorgensen, P. E. T. Nichols, Edward Sinkov, Abraham Bishop, Richard L. Fenley, John C. Justice, James H. Nishiura, Togo Slater, John B. Blanc, M. L. Ferrari, Carlo Kakihara, Yuichiro Niven, Ivan Slook, Thomas H. Blum, Lenore Finch, John V. Kalia, R.N. Nordhaus, Edward A. Small, Lance W. Bock, Mary E. Foias, Ciprian Ilie Kanno, Tsuneo Nummela, Eric C. Smith, George Rowan Boos, William Folk, Thomas F. Karle, Jerome Obata, Morio Smith, Roland F. Bramsen, John D. Fragoso, Marcelo D. Kaufman, William E. Oguchi, Kunio Solomon, Louis Brauer, Fred Freedman, Allen R. Kempachiro, Ohashi Oharu, Shinnosuke Sontag, Alexia Henderson Breves Filho, J. A. Frohlich, Jurg M. Kennedy, Edward S. Okuyama, Akihiro Sparnroft, Conrad H. Brown, Arthur B. Fuchs, Wolfgang H. Kent, George A. Oliver, Henry W. Stackelberg, Olaf P. Bryn, Milo F. Fujiwara, Daisuke Kernast, John C. Onishi, Hironori Starr, Norton Buckley, Joseph T. Furutani, Kenro Keyfitz, Barbara L. Orlik, Peter P. Stegeman, Jan D. Buianouckas, Francis R. Galbraith, A. S. Kiefer, James E. Orr, Martin Steinberg, Robert Burkholder, Donald L. Gantos, Richard L. Kim, Wan Se Otermat, Scott C. Sunouchi, Haruo Byrnes, James S. Gerlach, Jacob H. Kirby, Andrew R. Paciorek, Joseph W. Sunseri, Mary V. Caldwell, Roderick P. C. Glass, Michael S. Kita, Hiroo Paisner, Helen L. Susskind, Perry D. Cap, Clemens Heinrich Gleason, Andrew M. Kittaneh, Fuad A. Palmer, Theodore W. Swaminathan, Srinivasa Carlson, Bengt G. Glenn, Paul G. Klass, Michael J. Parker, Francis D. Sweeney, Orval L. Carmichael, Richard D. Goddyn, Luis A. Klatman, David S. Paskewitz, Charles W. Taam, Choy-Tak Cato, Benjamin R., Jr. Goldbeck, Helen L. Kolodner, Ignace I. Patterson, Larry A. Takahashi, Shuichi Chandarana, Sharad Goldberg, Seth I. Kossack, C. R. Patton, Charles M. Tam, Bit-Shun Cheng, Cheng Goldman, William Mark Krumpholz, Gary R. Peabody, Mary K. Tatevossian, Leon H. Chihara, Theodore S. Goodman, Roe W. Kurshan, Robert P. Porte, Jean Tennant, Raymond Frederick Chinn, William G. Goss, Robert N. Kurss, Herbert Powls, Keith W. Thiele, Ernst-Jochen Choksi, Jal R. Goto, Hideo Kurtzke, John F., Jr. Price, Charles M. Thomas, George B., Jr. Churchill, Richard C. Greville, Thomas N. E. Lackey, Jackson B. Protter, Philip E. Thomas, Janet D. Cohen, Daniel I. A. Griess, Robert Louis, Jr. Lander, Felix I. Quinn, Frank S., III Thomas, Lawrence E. Cohn, Richard M. Griffin, E. L., Jr. Laning, J. H. Radjavi, Heydar Thomas, Marc Phillip Cole, Paul Dana Griffiths, H. Brian Lanzano, Paolo Ralston, James V. Thomas, P. Emery Coleman, A. John Grubb, Gerd Larson, Richard G. Raney, George N. Thron, Wolfgang J. Colson, Henry D. Guillot, J. C. Lawson, Walter R. Reade, Maxwell 0. Toll, Kathryn B. Comenetz, Daniel Gurney, Margaret Lee, Jyh-Hao Reed, David L. Traina, Charles R. Cootz, Thomas A. Hale, David R. Leger, George F. Reid, James D. Tsuji, Kazo Copeland, Arthur H., Jr. Hall, Marshall, Jr. Lehrer, Gustav I. Reiner, Irma M. Tucker, Albert W. Cornelius, Thomas A. Harrold, Gladys B. Lewis, John A. Reissner, Eric Tugue, Tosiyuki Li, Bingxi Lindstrom, Wendell D. Lloyd, Stuart P. GENERAL CONTRIBUTION Lombardo, Charles J. GENERAL CONTRIBUTION IN MEMORY OF Louhivaara, Ilppo Simo IN MEMORY OF BEN T. GOLDBECK, JR. Macphail, Moray S. ORVILLE G. HARROLD, JR. Madow, William G. Helen L. Goldbeck Gladys B. Harrold

868 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS Centennial Research Fellowship Fund

Uchiyama, Akihito Wage, Michael L. Weinberg, Stephen L. Wilson, Robert Lee Yasuhara, Ann Uhlenbeck, Karen Wagner, R. W. Weinstein, Alan D. Wolpert, Scott A. Yasuhara, Mitsuru Unai, Yasushi Unai Wang, Derming Wene, Gregory P. Wong, Sherman K. Yokoi, Hideo de Valpine, Jean E. Ware, Buck West, Donald C. Woythaler, Joseph William Young, Paul M. Van Alstyne, John P. Warren, Bette L. Westbury, Christopher Grey Wright, David J. Ziebur, Allen D. Van Casteren, Johannes A. Warren, William E. White, Denis A. Wu, T. C. Zierler, Neal Van Daalen, Diederik T. Warschawski, Stefan E. Whittlesey, Emmet F. Yachter, Morris Zilmer, Delbert E. Veech, William A. Weaver, John C. Williams, Frederick C. Yamasaki, Masayuki Anonymous (75)

AMS CENTENNIAL RESEARCH FELLOWSHIP FUND IMU SPECIAL DEVELOPMENT FUND

The following list consists of contributors to the AMS Centennial Research Fellowship Fund and/or the IMU Special Development Fund. The* indicates a contribution to the AMS Centennial Research Fellowship Fund. The • indicates a contribution to the IMU Special Development Fund. A listing with neither symbol indicates a contribution to both.

Aarts, Johannes M. Agosto Torres, Francis AI-Khafaji, Mahmoud Anantharaman, Rajan Anick, David Jay Abatangelo, L. Maria Agoston, Max K. •AI-Khayyal, Faiz A. Anastasio, Salvatore Anselone, Philip M. Abbott, Catherine Ann Agrawal, Om Prakash Allan, James A. Ancel, Fredric Davis Anshel, Michael Abbott, H. L. Aguilar, Marcelo Alberto Allan, Robert Boyd •Andersen, Kurt Munk Ansorge, Rainer Abbott, James H. Aharoni, Israel Allard, William K. Andersen, Robert Nels Anspach, Peter H. *Abdel-Megied, Mohamed Aharonov, D. Allday, Christopher J. Anderson, Allan G. •Antliff, W. Bruce Abe, Eiichi Ahlbrandt, Gisela Allegra, Maria Anderson, Bertil Anton, Jose Manuel Abellanas, Pedro Ahmad, Hamid K. Allegretto, Walter Anderson, Bruce A. Antoniadis, Anestis A. Abernathy, Robert 0. •Ahmed, N. U. Allen, Howard Anderson, Chris R. Appell, Jurgen •Abikoff, William Ahrens, James Dwight Allen, Joseph N. Anderson, Donald W. Applebaum, Joseph A. Ablow, Clarence M. •Ahuja, 0. P. Allen, Randal Thomas •Anderson, Douglas R. Appleson, Robert R. Abrahamson, Brian Aidoo, Emmanuel B. •Allison, Bruce N. Anderson, Eugene R. Appling, William D. L. Abram, Thomas Joseph Aikele, M. Holbrook Alliston, R. Michael Anderson, Florence R. •Apter, Arthur William •Abramovich, Yuri A. Aimar, Hugo Alltop, William 0. •Anderson, Glen D. Arad, Zvi *Abramovici, Flavian Airault, Helene AI-Medhadi, Nora Seif Anderson, Joel H. Arai, Hitoshi Abrams, Gene D. Aissen, Michael I. Almgren, Frederick J., Jr. Anderson, John T. Araki, Shoro •Abrams, William P. Aizenman, Michael •Almeida, Jorge M. M. G. Anderson, Marlow E. Arapostathis, Aristotle Abramson, Lawrence Aizicovici, Sergiu Alonso, Agustin Anderson, Michael T. Arason, Jon Kr A'Campo, Norbert Akagi, Hatsue Alonso, James Anderson, R. Lucile *Arbarello, Enrico Acar, Robert Akbari, Gholamreza Alonso, Juan M. •Anderson, Robert Joseph •Archbold, Robert J. Accola, Robert D. M. Akin, Ethan J. Alpay, Daniel A. Anderson, Ronald M. Archdeacon, Dan Achmatowicz, Richard L. Aksoy, Asuman G. Alperin, Jonathan L. Anderson, Sabra S. Archer, Myla M. de Acosta, Alejandro Akyildiz, Ersan Alperin, Roger C. Anderson, Stuart N. •Arena, Orazio Adachi, Masahisa Akylas, Triantaphyllos R. Alpern, Steven Andersson, Lars Arenberg, C. Arne Adair, Celia L. Aladro, Gerardo Alsholm, Preben Andersson, Stig I. Arenstorf, Richard F. Adams, Colin C. •AI-Amiri, Hassoon S. Alsina, Claudi •Andima, Susan Aribaud, F. Adams, David D. •Alavi, Yousef Alspach, Brian R. Ando, Shiro Arima, Satoshi Adams, Elliott T. Al-Bassam, Mohammed Alspach, Dale E. Ando, Tsuyoshi Arino, Miguel A. Adams, J. Frank AliA. Althoen, Steven C. Andre, Peter P. Arisaka, Nakaaki Adams, M. E. Albers, Donald J. •AI-Thukair, Fawzi Ahmed Andreadakis, Stylianos Arkin, Joseph Adams, Malcolm R. Albert, John P. •Altman, Allen B. Andreassian, Agnes Arkowitz, Martin A. Adams, Scot Robert Albertson, Michael 0. Altomare, Francesco Andreoli, Dorothy W. *Arlinghaus, Sandra L. Adams, William W. Albrecht, Felix R. Aluffi, Paolo Andriamanalimanana, Bruno Arlinghaus, William C. Adamson, lain T. A. C. Albright, Hugh N. •Alvarez, Josefina Andrus, Jan F. Armbrust, Manfred K. •Addington, Susan L. Alcorn, David P. •Amann, Herbert Angad-Gaur, Hendrik W. K. Armentrout, Steve Adem, Alejandro Alder, H. L. Amberg, Bernhard *Angell, Thomas S. Armitage, John V. Adem, Jose *Alder, Hermann C. •Ambos-Spies, Klaus Angelos, James Roy *Armon, Mary Vlastink Adler, Alfred Aldous, David J. *Ames, Karen A. Angenent, Sigurd B. Arms, Judith M. Adler, George Alessandrini, Giovanni Amick, Charles James Anger, Frank D. Armstrong, Gerald M. Adler, Irving Alexander, Elaine E. Amir, Dan Anichini, Giuseppe Armstrong, Mark Anthony Adler, Robert J. Alexander, Herbert J. Amiran, Edoh Y. Anichini, Giuseppe Armstrong, Thomas E. Adluri, lndrasena Alexander, John R., Jr. Amis, Martha Lynn Adney, Joseph E., Jr. Alexander, Kenneth S. Amitsur, Shimshon A. Adolphson, Alan C. Alexander, Ronald C. Ammar, Gregory S. Aeppli, Alfred Alexander, Stephanie B. *Amrine, Brian AMS CENTENNIAL RESEARCH Afghahi, Mohammad H. Alexanderson, Gerald L. Amsbury, Wayne P. FELLOWSHIP CONTRIBUTION *Afilwap¢, A. Uyi Alfonso, Fermin Jorge Anacker, Steven E. FROM Agard, Egbert Ali, M. Kursheed Anaman, Todd M. Agarwal, Ashok K. Alif, Metod Anantharam, Venkatachalam ASSOCIATION FOR WOMEN IN MATHEMATICS

SEPTEMBER 1989, VOLUME 36, NUMBER 7 869 AMS Centennial Research Fellowship Fund

Amberg, Robert L. Bae, Jong Sook •Barlow, Martin Thomas Bechtell, Homer F. Berger, Marcel Arnold, David M. Bae, Soon-Sook Barnard, Roger W. Beck, William A. Berger, Marsha J. Arnold, Douglas N. Baer, Robert M. Barnard, Russell I. Beckenstein, Edward Berger, Neil E. Arnold, Leslie K. Baemstein, Albert, II Barner, Klaus Becker, David S. Berger, Robert W. Arnold, Timothy K. Bagby, Richard J. Barner, Martin Becker, Eberhard Berger, Ruth I. Amoux, Pierre Bagby, S. Thomas Barnes, David C. Becker, Howard S. •Berger, Thomas R. Aroian, Leo A. Baginski, Frank E. Barnes, Ward C. Becker, James C. Berglund, John F. •Aron, Richard M. Bahri, Anthony Peter Barnet, Frank Becker, Michael Bergman, George M. •Aronson, Donald G. •Baider, Alberto Baron, John J. •Becker, Ronald I. •Bergmann, Arthur •Aronsson, Gunnar Bailey, Evelyn C. Baron, Simson Becker, Thomas Bergmann, Peter G. •Arosio, Alberto Bailey, G. H. Barrar, Richard B. Beckman, Frank S. Bergstrand, Deborah J. •Arsenovic, Milos Bailey, Robert E. Barreca, J. R. Beckmann, William H. Bergstrom, Roy C. Arthur, James G. •Baillieul, John B. •Barrett, David E. •Beckner, William Bergum, Gerald E. Artin, Michael Bailyn, Paul M. Barrett, Lida K. Bedard, Robert Bergweiler, Walter Artola, Michel Bain, Osias Barrett, Terence W. Bedford, Eric D. Berin, Alec Artzrouni, Marc Bajusair, Mohamed S. Barros-Neto, Jose Beebe, Alfred S. Beringer, Alfred Arveson, William B. Bakelman, Ilya •Barry, Michael James Beechler, Barbara J. Berkovitz, Leonard D. Arzberger, Peter W. Bakenh us, Fred Barsky, Daniel Beekman, John A. Berkowitz, Harry W. Asadulla, Syed Baker, Alan • Barsotti, Leo •Beekmann, Wolfgang Berlekamp, Elwyn R. Asano, Kouhei •Baker, Andrew James Bart, H. Beem, John Kelly Berman, David R. Asano, Shigemoto Baker, Blanche J. Bartelt, Martin W. Beesley, E. Maurice Berman, J. Michael Aschbacher, Michael Baker, Charles R. Barth, Karl F. •Beeson, Michael J. Berman, Stephen Asensio Mayor, Jose Baker, Edward D. Bartick, Philip R. Behnke, K. Bermond, J-C •Ashbaugh, Mark S. Baker, Edward G. Bartle, Robert G. Beig, Robert BermUdez, Alfredo Askey, Richard A. Baker, George A. Sr •Bartnik, Robert A. •Beineke, Lowell W. Bernardi, Salvatore D. Aspenleiter, Stephen W. Baker, Kirby A. de Bartolomeis, Paolo •Bekken, Otto Borger •Berndt, Bruce C. Asprey, Winifred A. •Baker, Peter Fritz Barton, Thomas J. Belair, Luc Bernfeld, Stephen R. Assmann, Susan F. Baksa, Dennis John Bartsch, Thomas J. Belak, Diane M. Berni, Betty Assmus, Edward F., Jr. •Bakshi, Jagjit •Baruch, Herbert M., Jr. Belfi, Victor A. Bemis, Francisco Atalla, Robert E. Bal, Kenan Y. Baruch, Herbert Mark, III Bell, Allen D. Berresford, Geoffrey C. Atiyah, Michael F. Balbes, Raymond Baruch, Marjory Jean Bell, Howard E. Berstein, Israel Atkin, Joy H. Baldi, Paolo • Baruss, Imants Bell, James M. Berterman, John E. Atkinson, Frederick V. Baldwin, John T. •Barzilai, Jonathan Bell, Murray Gordon Bertin, Emile M. Atkinson, H. R. Bales, John W. • Basor, Estelle •Bell, Stoughton Bertolini, Giovanni Atkinson, Stuart L. •Balibrea, Francisco Bass, Hyman Bellamy, David P. Berton, John A. Atsuji, Masahiko Balkanyi, Leslie R. Bass, Robert James Belley, J. M. •Berzsenyi, George •Au, C. H. E. Balkema, A. A. •Bassan, Bruno •Bellin, Gianluigi Beschler, Edwin F. Auer, Jan W. •Ball, John M. Bateman, Paul T. Bellissard, Jean V. Bessenrodt, Christine •Aull, Charles E. Ball, Joseph A. •Bator, Elizabeth Mary Bellomo, Nicola Betancourt, Carlos M. Ault, J. C. Ball, Keith Batt, Jiirgen 0. •Bellout, Hamid Betsch, Gerhard Auslander, Bernice L. Ball, N. Hansen Batten, Lynn Margaret Belpaire, Gerald Betz, Ebon E. •Auslander, Joseph Ball, Richard Neal Batterson, Steven L. Bemelmans, Josef •Beyl, F. Rudolf Auslander, Louis Ball, Richard W. Batty, Charles J. K. Benardete, Diego Beylkin, Gregory Auslander, Maurice Ballantyne, Rob S. Bauer, Carole Ann Ben-Artzi, Matania Bezdek, Andras Aust, Catherine C. Ballard, William R. Bauldry, William C. Bence, James Kenyard •Bezuidenhout, Carol E. Au-Yeung, Yik-Hoi Ballou, Donald H. •Baum, Paul F. •Bencsath, Katalin A. Bhaskaran, M. •Avdispahic, Muharem Husein •Balmaceda, Jose Maria P. Baumann, Volker H. Bendat, Julius S. Bhatnagar, R. K. Avelsgaard, Roger A. Baloglou, George Baumeister, Johann Benedetto, John J. Bhattacharya, Rabi N. Aversa, Vincenzo L. Balser, Arienne S. Baumgartner, Gerald B., Jr. Benes, Vaclav E. Bialek, Paul R. •Avioli, John J. Balslev, Erik Baumgartner, James E. Benham, James W. Bialostocki, Arie eAvrin, Joel D. Banchoff, Thomas F. Baumslag, Gilbert Ben-Israel, Adi Bianco, Anthony J. Avrunin, GeorgeS. Bandle, Catherine Baur, Lynne A. Benitez, Carlos Bianco, Lucio Ayers, Kathleen L. Bandler, Wyllis Bautista, Maurino P. Benkart, Georgia M. •Bickel, Marilyn S. Ayoub, Christine W. Banerjee, Utpal Bavinck, Herman Bennett, Andrew G. Bierstedt, Klaus D. Ayoub, Raymond G. Bang, Seung Jin Baxendale, Peter H. Bennett, Fredricka T. Bierstone, Edward Azoff, Edward A. Bankston, Paul J. •Bayer, Margaret M. Bennett, Larry F. Biles, Charles M. Azpeitia, Alfonso G. Bannai, Eiichi Bayer-Fiuckiger, Eva M. •Bennhold, Cornelius Billera, Louis J. Azumaya, Goro Baouendi, M. Salah Bayo, Enrique Benson, Dave Billigheimer, Claude E. Azzam, Ali Baranow, Michael D. Bazinet, Jacques Benson, David Bernard Billik, Martin Baas, Nils Andreas Baras, John S. Beadle, Allen Jay Benson, Donald C. Bilodeau, Gerald G. Baayen, Pieter C. Barbeau, Edward J., Jr. Beale, J. Thomas Benson, F. Chal Bindschadler, David E. Babcock, William W. Barber, S. F. Beals, R. Michael Benson, Steven R. Bing, Kurt >~

870 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS Centennial Research Fellowship Fund

Bisztriczky, Tibor Borel, Armand Brennan, Joseph P. Bryant, Billy F. Byrnes, Christopher I. Bjorklund, Peter B. *Borelli, Mario Brenner, Philip Bryant, John G. Byrnes, James S. • Bjiirner, Anders Biirgers, Christoph Brent, Richard P. Bryant, Robert L. Byrnes, Raymond Albert, Jr. Black, David L. Borrelli, Robert L. Brenti, Francesco Bryce, Gerald M. Cable, Charles A. Blackall, Clair J. Borucki, Leonard John Bressler, David W. Brydges, David C. Caccianotti, Luciano Blackmore, Denis L. Borwein, David Bresson, Maurice J. Brylawski, Thomas H. •Cacioppo, Robert Joseph Blackwood, Philip D. Bosch, Carlos Giral Bressoud, David M. Brylinski, Jean-Luc Cadogan, Charles C. Blad, Michael C. Bosch, William W. Bressoud, Thomas C. Brylinski, Ranee Kathryn de Caen, D. Blair, William D. Bose, N. K. Breuer, Shlomo Bryn, Milo F. Callisch, Russel Blais, J. A. R. Bossavit, A. Breves Filho, J. A. *Brzenk, Ronald M. Cagnac, Francis Blakemore, Carroll F. Boswell, Rupert D., Jr. Brewer, James W. Brzezinski, Juliusz Cain, Bryan E. Blanch, Gertrude Botelho, Fernanda Brewer, Linda K. Bshouty, Daoud *Cain, George L., Jr. Blanche, Ernest E. Batt, Raoul H. •Brezin, Jonathan P. Bube, Kenneth P. Caines, Peter E. Blanchet-Sadri, Francine •Bottazzini, Umberto Brickell, Ernest F. Buccino, Alphonse Cairoli, R. Blankinship, William A. Bottema, Murk J. Brierley, William L. Buchanan, Thomas Calabi, Eugenio Blatter, Christian Bouchet, Andre Brieske, Thomas J. *Buck, Marshall W. Calderbank, Robert Blatter, Jorg Boules, Adel N. Brigham, Robert C. •Bucki, Andrzej J. Calderer, M. Carme Blattner, Robert J. Boulet, Genevieve Brin, Matthew G. Buckley, Joseph T. Caldwell, Gordon R. Bledsoe, Woodrow W. Boultbee, Nan Brin, Michael I. Buckley, Stephen M. Caldwell, Roderick P. C. •Blei, Ron C. Bourgeois, Brian A. Brinkmann, Hans-Berndt Bucy, Richard S. Caldwell, William V. *Bieick, Willard E. • Bourgeois, Sister Denise Britton, John L. Buddrus, Lee Edward Callahan, James J. Bleiler, Steven A. Bourgin, Richard D. Brobeck, Barbara Caldwell Budnik, Paul, Jr. Callegari, Andrew J. Blij, Frederik Van Der Bourland, David •Broline, Duane M. Buechler, Steven Allen Calvert, Bruce D. *Blizard, Wayne D. Bousfield, Aldridge K. Bromberg, Eleazer Buehler, Royce E. Calvert, James E. Bloch, Ethan D. *Bousquet, Michel Bromley, Darwin P. Buekenhout, F. Calvis, David T. Bloch, William L. Boutin, Pierre Brommundt, Eberhard W. Buhler, Joe P. Camacho, James, Jr. Blomstrom, Carol A. Bouwsma, Ward D. Brons, Hans Buianouckas, Francis R. Camarena, Vicente •Biondel, Corinne Bovier, Anton Brons, Kenneth A. Bula, Witold Cameron, Douglas E. Bloom, David S. Bower, Julia W. Brons, Morten *Bulger, Leonard L. Cameron, Edward A. Bloom, Frederick Bowers, Philip Lee Brooks, Burrow P. Bulirsch, Roland Zdenek •Camillo, Victor P. •Bloom, Thomas Bowie, Harold E. Brooks, Robert Bullen, Peter Camina, A. R. •Bloom, Walter R. Boyack, Stephen W. *Brosamler, Gunnar A. Bullivant, David P. Campanino, Massimo *Blows, T. R. Boyce, Elsa K. Brosowski, Bruno H. Bulman-Fleming, Sydney D. Campbell, Harold E. A. Bluher, Grigory Boyce, William E. Brothers, John E. Bump, Daniel Willis Campbell, L. Andrew Blum, Dorothee Jane Boyd, John P. Broue, Michel Bungart, Lutz *Campbell, Neville Ray Blum, llya Eugene Boyd, William S. Browder, William Bunge, Marta C. Campbell, Paul J. Blum, Joseph Boyle, Ann K. Brown, Anne E. •Buntinas, Martin G. •campbell, R. B. *Blum, Lenore Boyle, Jeffrey *Brown, Arthur A. Buoncristiani, John F. Campillo, Antonio Blumenthal, Robert A. Boyle, Mike Brown, Arthur B. Burchard, Hermann G. Campiti, Michele Blyth Rentzsch, Barbara J. Bozonis, Petros Brown, Edgar H., Jr. Burckel, Robert B. Campos, L. M. B. C. Boardman, John M. Braaksma, B. L. J. Brown, Gayle M. Burgess, C. Edmund •Candiotti, Alan Boas, Ralph P. Braam, Peter J. Brown, George B. Burgess, Richard Dennis Candy, Gregory T. Bobisud, Larry E. Brachman, Malcolm K. Brown, Gerald D. Burgess, Walter D. •Canfield, E. Rodney Bobonis, Augusto Brackx, Freddy F. Brown, Gerald L. Burkhart, Richard H. Cannon, James W. Bodnar, Istvan Bradford, Giles Edward, III Brown, Howard H. Burkholder, Donald L. Cannon, John R. Bodnarescu, M. V. Bradford, Phillip G. Brown, Kenneth S. Burkholder, Douglas G. Cantoni, Vittorio Bodvarsson, Gunnar Bradley, John S. Brown, Patrick J. Burkill, John C. Cantor, Robert M. •Boe, Brian D. Bradley, Richard C. Brown, Richard L. Burnap, Charles A. Cantrell, James C. Bolli, Giandomenico *Brady, Wray G. Brown, Robert Dillon Bums, Anne M. Cap, Clemens Heinrich Bogart, Kenneth P. Bragg, Arthur E. Brown, Robert E. Bums, Daniel M., Jr. •Capasso, Vincenzo Bohnke, G. C. •Brahana, Thomas R. •Brown, Robert Freeman Bums, Keith H. Capozzi, Alberto Boisvert, Robert E. Brakke, Kenneth A. Brown, Robert Gregory Burr, Stefan A. Cappell, Sylvain E. Boivin, Andre •Bralver, Peter Jeffrey *Brown, Scott W. Burris, Stanley N. Capuzzo Dolcetta, !tala Boivin, Daniel E. Bramble, James H. Brown, Sharan Inez Burstall, Francis E. Caranti, A. E. Bojanic, Ranko Bramsen, John D. Brown, William G. Burton, Leonard P. Carbery, Anthony Bojars, Juris A. Brandal, Willy Browne, H. Nelson, Jr. Busemann, Herbert *Cardenas, Humberto T. Boley, David B. Brandenburg, Harald Browne, Patrick J. •Dusenberg, Stavros N. Cardona, Ivan Balker, Ethan D. Brandstrom, Hugo F. K. Browning, David S. Buser, Peter J. Caricato, Gaetano Bailey, Don S. Brandt, Dennis E. Brualdi, Richard A. Businger, Walter A. Carini, Luisa Bollinger, Robert A. Branner, Bodil Brubaker, Matthew A. Buss, Samuel R. Carleson, Lennart A. E. Bollman, D. A. Branton, Michael G. Bruck, Ronald E., Jr. Butchart, John H. Carlson, Bengt G. •Boman, Jan Bratholdt, J. Stuart Brucks, Karen M. Butcher, John C. •Carlson, David H. Bond, David B. Brattstriim, Gudrun B. Bruckstein, Alfred M. Butcher, Ralph Stevens Carlson, James A. •BonDurant, Bill Brauer, Fred Brueggemann, Wolfgang Butler, John B., Jr. Carlson, James W. Bonet, Jose Brauer, George U. Bruen, Aiden A. Butler, Lynne M. Carlson, John R. Bonin, Joseph E. Braun, Willard J. Bruggeman, Roelof W. Butnariu, Dan Carlson, John W. Bonner, Richard F. Bravo, Raul Brumer, Armand Buttke, Thomas F. Carlson, Jon F. Boo, Per-Anders Breaux, Gary R. *Brumfiel, Gregory W. Butts, Thomas R. Carlson, Kermit H. Booker, Andrew J. Brechner, Beverly L. Bruner, Robert R. •Buys, Mutiara Carlson, Robert C. Booker, T. Hoy Breckenridge, John C. Brunet, Richard M. Buzano, Ernesto Carlsson, Renate *de Boor, Carl Breen, Lawrence S. *Brunner, Hermann Byerly, Robert E. Carmichael, Richard D. Boos, William Breen, Stephen Bruns, Winfried Byrd, Kenneth A. do Carma, Manfredo P. Boothby, William M. Breidbart, Seth I. •Brunson, Barry W. Byrne, Catriona M. Carr, Donna M. Borchers, Hans-Jurgen Brender, Melvin Brunswick, Natascha A. Byrne, Charles L. Carroll, Edward M.

SEPTEMBER 1989, VOLUME 36, NUMBER 7 871 AMS Centennial Research Fellowship Fund

Carroll, Michael P. Chang, Shao-Chien Chouteau, Charles C. Cohen, Teresa Corduneanu, Constantin •Carroll, Timothy B. Chang, Sun-Yung Alice Chover, Joshua Cohn, Donald L. Corlette, Kevin David Carruth, James H. Chang, Yu •Chow, Pak S. Cohn, George I. Cornell, Gary Carson, Andrew B. Chanillo, Sagun Chrestenson, Hubert E. Cohn, Harvey Cornette, James L. •Carstens, Allan M. Chantala, Diane Kim Christensen, Chris Cohn, Leslie •Correa, Nelson L. Cartan, Henri Chao, J. A. Christy, Joe Cohn, Richard M. Corrigan, Thomas Carney Carter, David W. Chaperon, Marc •Chu, Chinku Cohn, Stephen Edward Corson, Jon M. Carter, James E. Chapin, Steven Arthur •Chu, Tienchen Cohn, William S. Cortzen, Barbara Carter, Thomas J. •Charalambous, Michael Chuang, Pi-Chun Colbourn, Charles Joseph •Corwin, Stephen P. Cartier, Pierre Georgiou •Chuaqui, Rolando B. Colby, Robert R. Cosner, George C. Carton-Lebrun, C. Charles, Josette •Church, Alonzo •Cole, Brian J. Costa, David G. •caruso, J. L. Charney, Ruth M. Church, Philip T. Cole, Charles A. Costenoble, Steven R. •Carver, George E. Chatterji, Srishti D. Churchill, Edmund Cole, Herman D. •Cote, Louis J. Casazza, Peter G. Chauvin, Andre Churchill, Richard C. •Cole, Nancy *Cotsaftis, Michel Case, Bettye Anne Chee, Pak Soong Ciarlet, Philippe G. Cole, Paul Dana Cotter, Christopher S. Casey, Robert Francis Cheeger, Jeff •Cifuentes, Patricio Cole, Randal H. Cotton, Robert M. Casey, Stephen D. Cheifetz, Steven Todd •Cima, Joseph A. Coleman, A. John Couch, W. Eugene Casian, Luis Guillermo Chein, Orin N. Cincotta, Dominick Anthony Coleman, Courtney S. Coulter, Malcolm A. Casler, Burtis G. Chen, Concordia C. Cinlar, Erhan Coleman, Robert Countryman, William Mark •Cassels, J. W. S. Chen, Daniel K. C. Cipriani, Fabio Coleman, Thomas F. Coury, Nicholas J. Cassidy, Phyllis J. Chen, Dayue Cirina, Marco Coleman, William •Couty, R. Cassity, C. Ronald •Chen, Etang Civin, Paul Collet, Pierre Covington, Thomas E. Castagnoli, Erio A. •Chen, Kwan-Wei •Clapp, Robert E. •Colley, Susan Jane •Cowen, Carl C., Jr. •Castelfranco, Ann M. Chen, Li-Chen Clapsadle, Raymond A. Collier, Jarrell D. Cowan, Jack D. Castillo-Chavez, Carlos Chen, Louis H. Y. Clare, Loren Paul Collier, William G., Jr. •Cowan, Richard E. Castore, Glen M. Chen, Peili Clark, Bradd Evans Collins, Dennis G. Cowens, J. Wayne Catanese, Fabrizio M. E. Chen, Shuxing Clark, Cathy Ann Collins, Ken Cowles, John R. Catanzano, Sheri Chen, W. W. L. Clark, Charles L. Colonius, Fritz Cowling, Michael G. Cateforis, Vasily C. Chen, Wanxi Clark, Curtis Colonna, Flavia Cox, Gregory V. Cater, Frank S. Chen, Wenxiong Clark, Katherine A. Colquitt, Landon A. •Cox, Lawrence H. •Cato, Benjamin R., Jr. Chen, Y. W. Clark, Kenneth D. Colson, Henry D. Cox, Raymond H. Cattabriga, L. Chen, Yongzhuo Clark, Robert A. Comellas, Francese •Cox, S. H., Jr. Causey, William M. •Chen, Zhibo •Clark, W. Edwin Comenetz, Daniel •Cox, Samuel H. Cauvi, Roberto Jose Cheney, E. W. •Clarke, Francis •Comerford, Leo P., Jr. Cox, Stephen E. Cavender, James A. Cheng, Benny N. Clarke, Graham Thomas Comez, Dogan Coxeter, H. S. MacDonald Caveny, Deanna Marie Cheng, Cheng Clarkson, Helen E. Comfort, Edwin H. Cozzens, Margaret Barry Cawley, Robert Cheng, Jih-Hsin Clarkson, Peter A. •Comfort, W. Wistar Crabtree, J. B. Cazzaniga, Franco Cheng, Kuo-Shung Clary, Stuart Conlon, Joseph G. Craggs, Robert F. Cebollero, Blanca S. Cheng, Raymond S. Claus, Elly Conlon, Lawrence W. Craig, Jessica Marguerite Cecil, Thomas E. Cheon, Seok-Hyeon •Clausing, Achim Conlon, Samuel B. Crandall, Michael G. •Cegrell, Urban Cherniavsky, John C. Cleaver, Charles E. Conn, Jack Frederick Crane, George E. •Cehelsky, Priscilla Chernoff, Herman Clee, William A. Connelly, Robert Crane, Jane P. Cerda, Joan Chernoff, Paul R. Clemens, Charles Herbert Connolly, Mary V. Cranston, Michael Craig Cerruti, Umberto Cherny, Julius Clements, George F. •Connor, Frank F. Crapo, Henry H. Certain, Melinda W. Cheung, B. K. S. Clifford, Alfred H. Connor, Jeffery S. Crauder, Bruce C. deCesare, Kenneth M. Cheung, Chi-Keung Clifford, Jane E. Connors, Edward A. Craven, Bruce D. Cesari, Lamberto Cheung, Maria L. Clifton, Larry M. Conrad, Bruce P. Crawford, James P. Chabert, J. L. Cheung, Wing-Sum Cline, Edward T. Conrad, Joseph F. Crawford, John David Chacon, Paul R. Chiarenza, Filippo Clivio, Andrea Giovanni Constantin, Peter S. Creede, Geoffrey D. Chae, Dongho Chicks, Charles H. Clover, William J., Jr. Constantinescu, Corneliu Creese, Thomas M. Chaffee, James W. Chicone, Carmen C. •Coar, David R. •Conway, John B. Criscenti, Jacqueline P. •Chaiken, Seth D. Chidambaraswamy, Jayanthi •Cobham, Alan •Cook, Edith A. Crittenden, Richard J. Chakerian, Gulbank D. •Chihara, Theodore S. Cochran, Douglas Cook, Joseph M. Crone, Lawrence J. Chakravarty, Subinoy Chikwendu, Sunday C. Cochran, James A. *Cook, Larry T. Cronin, Bernard Chalmers, Bruce L. Childs, Lindsay N. Cochran, Tim D. Cooke, Roger Lee Cross, James J. Chalmers, Graham D. Chillag, David Cochrane, Todd E. Cooley, Clifford R. Cross, Ronald W. Chambers, Daniel Warren Chillak, Edward W. Cockburn, Julio Bernardo Coolsaet, Arnold A. Crothers, Derrick S. F. Champagne, Carol Z. eChillingworth, David R. J. Cockburn, Sally Patricia Coonen, Jerome T. •Crow, Edwin L. Chan, Jack-Kang Chinburg, Ted C. Coddington, Earl A. Cooper, E. D. •Crowe, John A. Chan, Jean B. Ching, Wai-Sin Coen, Salvatore Cooper, Hilda L. Crowell, Richard H. Chan, Tony F. Chinn, William G. Coffey, John Cooper, Jeffery M. Crumb, Cyndi A. •Chandarana, Sharad Chiswell, Ian M. Coffman, Robert L. Cooper, Mark A. Crumley, George L. Chandler, Michael Paul Cho, Choong Yun Cogburn, Robert F. Cootz, Thomas A. Cruthirds, John E. Chang, Bomshik Cho, Min-Hyung Cogdell, James Wesley Copeland, Arthur H., Jr. Cude, Joe E. Chang, Chao P. Choe, Geon Ho Cohen, Arjeh M. Copeland, Terry S. Cudia, Dennis F. Chang, Chienming A. Choe, Young Han Cohen, Daniel I. A. •Copper, Mark L. Culbertson, James T. Chang, Chin-Huei Choi, Kwok-Pui Cohen, Frederick R. Coppotelli, Fred Cummings, James Chang, Der-Chen Edward Choi, Un Haing Cohen, Henry B. Coram, Donald S. Cunkle, Charles H. Chang, Eugene J. Choi, Yun Sung Cohen, Leon W. •Coray, Daniel *Cunningham, A. B. Chang, Gerard J. Choksi, Jal R. Cohen, Marshall M. Corazza, Paul J. Cunningham, Frederic, Jr. •Chang, !-Chen Chong, Chi Tat Cohen, Martin J. Corbett, John V. Cunningham, Richard J. Chang, 1-Lok Choquet, Gustave Cohen, Michael P. Cordero, Luis A. Cuoco, Albert A. Chang, Kun Soo •Choudhary, Yogendra K. Cohen, Moses E. •Cordes, Craig M. Curjel, Caspar R. Chang, Ping-Tung •Choudhury, Bejoy K. Cohen, Ralph L. Cordes, Heinz 0. •Currie, Melvin R.

872 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS Centennial Research Fellowship Fund

Currier, Albert W. Davis, Robert D. Deprima, Charles R. Dominijanni, Roberto Dunwoody, Martin John Currier, Robert J. Davis, Stephen F. Depue, Bill Earl Domino, Laurence E. Dupont, Johan L. Curry, James H. Davitt, Harold H. Deriggi, Dennis F. Domokos, Gabor Duran, Wilfred 0. Curtis, Charles W. Dawes, A.M. Derr, Leroy J. •Donald, Matthew James Durand, Loyal Curtis, Herbert J. Dawson, Donald A. Deruaz, Marcel A. F. Donaly, James P. Durbin, John R. Curtis, Morton L. •Dawson, John W., Jr. Desarmenien, Jacques •Doner, John E. Duren, Peter L. Curtis, Philip C., Jr. Day, B. J. Desoer, Charles A. Donoho, David Leigh Durfee, Alan H. Curto, Rauul E. Day, Mabton M. Desolneux-Moulis, Nicole Donovan, Peter Durfee, William H. Cushing, Jim M. •Day, Martin V. Desquith, Etienne Doob, Joseph L. Durham, Stacey S. *Cushman, John H. Day, Wayne Detlefsen, Michael E. Doob, Michael •Durnota, Bohdan P. Cushman, Richard H. Dayawansa, W. P. •Detofoli, Rino Dooley, Thomas J. Durst, Lincoln K. Cusick, David A. Daybell, Dorothy A. DeTurck, Dennis Doppel, Karl Durumeric, Oguz C. Cusick, Thomas W. Daykin, Donald R. Deuber, Walter Alfred Doran, Robert S. Durusau, Patrick L. Cuthill, Elizabeth H. Dayton, Barry H. Deumens, Erik •D'Orazio, Silvana Duskin, John W., Jr. •Cutler, Doyle 0. De Bruin, Marcel G. •Deutsch, Daniel H. Dordal, Peter L. Duszynski, Martin, Jr. Cutler, Janice Z. De Cannii:re, Jean Deutz, Andre H. Dorfmeister, Josef F. Dutt, J. E. Cutrer, M. Wayne De Figueiredo, Djairo G. Devaney, Robert L. Dorlas, Tony C. Dutta, Sankar Prasad Cuttle, Yvonne H. De Iongh, Johan J. Deveney, James K. Dorroh, James R. Dutton, Charles Everett Cvetkovic, Dragan S. De La Penha, Guilherme M. •Devlin, Keith J. Dorsett, Charles I. Dwork, Bernard M. Cwikel, Michael De La Rica, Mariano Dewallens, Jean H. *Dostal, Milos A. Dwyer, William G. Da Costa, Fernando Pestana Hermida •Dewilde, Philippe Dotzel, Ronald M. Dydak, Jerzy Dabrowski, Romuald De La Sen, Manuel Dhooghe, Paul F. J. Dou, Alberto M. Dye, John M. Dade, Everett C. •De Luca, Aldo Di Concilio, Anna Dou, Ze Li Dye, Judy E. Dadok, Jiri De Marr, Ralph E. Di Maio, Giuseppe Dougherty, Robert P. *Dyer, Micheal N. •Daepp, Ulrich De Meersman, Roger DiPaola, Jane W. Douglas, Jim, Jr. Dynin, Alexander Dahl, Erlend De Snoo, Hendrik S. V. Diamond, Fred I. Douglas, Ronald G. Dyson, Verena H. Dahlin, Rolf B. De Villiers, Raoul A. Diamond, Jack *Douglis, Avron Eachus, J. J. *Dai, Taen-Yu *De Vries, Hendrik Dias DaSilva, J. A. •Doust, Ian R. *Ealy, Clifton E., Jr. Dalang, Robert C. Dean, Carolyn A. Dibner, Steve Dovermann, Karl Heinz *Earle, Clifford J., Jr. Dale, Knut T. Dean, Charmaine B. Dickenstein, Alicia M. Dow, Alan *Eaton, Timothy R. Dale, Richard H. Dean, Richard A. Dickerson, Charles E. Dowd, Robert E. Eaves, Edgar D. Dales, H. Garth DeBlassie, Richard Dante Diederich, Klas Dowds, Richard E. *Ebel, David J. D'Alotto, Louis A. Debrunner, Hans E. Diener, Karl-Heinz Dowlen, Mary M. Eberlein, Patrick Barry •Daly, James E. Dechene, Lucy I. Dietz, David Dowling, Michael L. Ebey, Sherwood F. Daly, John F. Deckert, Kenneth L. Dietz, Klaus Dowling, Thomas A. Ebiefung, Aniekan Asukwo Daly, John T. Deeb, Waleed M. Dieudonne, Jean A. Downey, Rodney G. Eccles, Peter J. D'Ambrosio, Ubiratan Deeter, Charles R. Dijksma, Aalt *Doyle, John C. Echenique, Marcial Luis Damiano, David B. DeFacio, Brian Dikshit, G. D. Doyle, Jon Eck, David J. Damkohler, Wilhelm L. Defrancesco, Henry F. Dilcher, Karl H. •Doyle, Peter G. Eckhardt, William Damon, James Norman • Dehesa, Jesus Sanchez •Dillon, Meighan Irene Drager, Lance D. Ecklund, Earl F., Jr. Dana, Martin P. Deift, Percy Alec Dillon, Richard T. Dragt, Alex J. Eckmann, Beno Dancis, Jerome Deiter, Daphne D. Dimsdale, Bernard Drake, Frank R. •Eckmann, J. P. Daney, Charles G. Dejter, ltalo J. •Dinitz, Jeffrey Howard Draper, Richard N. Edelson, Allan L. Dangello, Frank Ralph Dekker, Jacob C. E. Dinneen, Gerald P. •Drasin, David Edelstein, Michael D'Angelo, John P. Dekleine, Herbert A. Dian, Gloria S. Dray, Tevian Edelstein-Keshet, Leah Daniel, James W. DeKoninck, Jean Marie Dionne, Benoit Drazin, Michael P. *Edet, Silas B. Daniels, M. Peg M. Dekster, B. V. Dionne, Philippe A. Dreben, Burton S. Edgar, Hugh Maxwell Wallace *Dankel, Thaddeus G., Jr. Del Riego de Del Castillo, L. DiPerna, Ronald J. Dressel, Francis G. Edmonds, Allan L. D'Antona, Ottavio Del Taro, Guillermo Dipper, Richard T. Drew, Gerald C. Edmondson, Don E. D'Aprile, Margherita Delahunty, Michael D. Diute Snyder, Patricia J. Dreyer, Thomas P. *Edmundson, H. P. D'Aristotle, Anthony J. Delaney, Matthew S. Divis-Poracka, Zita M. Dribin, Daniel M. Edrei, Albert Dark, R. S. Delanoe, Philippe Dixon, Crist D. Driscoll, Mark J. Edwards, C. M. Darling, Donald A. Delbaen, Freddy •Dixon, John D. Driver, Bruce K. Edwards, Charles H., Jr. •Darling, R. W. R. Delchamps, David F. Dlab, Vlastimil •Drams, Carl G. Edwards, David Albert Darnel, Michael R. Deleanu, Aristide Dobbins, Robert R. Dshalalow, Jewgeni •Edwards, Harold M. Das, Anadijiban *Delges, H. Wolfgang Dodds, Peter G. •D'Souza, Harry J. Edwards, Kathleen R. D'Atri, Joseph E. DeLillo, Thomas K. Dodds, Theresa K. •Du Cloux, Fokko Edwards, Robert D. Datskovsky, Boris A. Dell'Antonio, Gianfausto Dodson, Christopher T. J. Dubisch, Roy Edwards, Wallace B., Jr. Dauxois, J. DellaPietra, Vincent J. Dodziuk, Jozef Dubson, Alberto S. Eells, James Daverman, Robert J. •DeLong, R. Peter Doerfler, Willibald Duchamp, Thomas E. Eenigenburg, Paul J. Davey, Brian A. Delporte, Jean Doering, Bora Dudley, Richard M. Ehlers, F. Edward David, Daniel Delver, Robert Doerr, Thomas A. Dudziak, James J. Ehren, David L. David, Karl Demana, Franklin D. Doherty, Patricia Ann Duff, George F. D. Ehrlich, Karel David, Nancy A. Demeyer, Frank R. Dokken, Douglas Paul Duggal, Krishan La! Ehrlich, Paul Ewing •Davidson, Kenneth R. Deming, Robert W. Dolan, James M. Duke, Richard A. *Eiardi, Anthony J. Davis, Burgess J. *Demko, Stephen Dolan, Peter C. Duke, William D. Eifrig, Bernd Davis, Chandler Demmel, James W. Dolbeault, Pierre E. Dukelow, James S., Jr. Eigel, Edwin G., Jr. Davis, Gregory J. Dencker, Nils Dold, Albrecht E. Dunbar, William Dart, Jr. Eigen, Stanley J. Davis, James F. •Dennin, Joseph B. Dolgachev, Igor Duncan, Cecil E. Eilenberg, Samuel Davis, James H. Denny, Diane L. Dollard, John D. Duncan, Richard D. Einthoven, Isabella H. •Davis, Linda M. Dent, Elliod Dombroski, Michael *Duncan, T. E. •Einwohner, Theodore H. Davis, Martin D. *Deo, Sadashiv G. Dombrowski, Joanne M. Dunham, Douglas J. Eirola, Timo J. *Davis, Paul W. Deodhar, Vinay Vithal Domic, Antun Dunion, Thomas J. Eisenbud, David Davis, Richard L. DePagter, Bernardus Dominguez, J. M. Duntsch, lvo Eisenstadt, B. J.

SEPTEMBER 1989, VOLUME 36, NUMBER 7 873 AMS Centennial Research Fellowship Fund

*Eisenstat, Stanley C. *Erber, Friedrich M. Federbush, Paul Fitzpatrick, Ben G. Francis, Theresa A. Eisman, Sylvan H. Erdelyi, Ivan N. Feehan, Paul Matthew Niall Fitzpatrick, Ben, Jr. *Franco, Salvatore S. Eisner, Elmer Erdman, John M. •Feeman, George F. Fitzsimmons, Patrick J. •Francoise, J. P. *Eiss, Joseph J. Erdos, Paul •Feeman, Timothy G. *Fixman, Uri Frank, Ove Ekeland, lvar Erickson, Roger P. Feferman, Solomon •Fjelstad, Paul T. Frankel, Theodore T. *Eklund, Anthony D. Erkama, Timo Fegan, H. D. •Flagg, Bob Fransen, Arne Eklund, Hans G. Erkiletian, Dickran H., Jr. Fegreus, John F. Flaherty, Francis J. Frantz, Henry W., III Ekman, Kenneth E. Erlander, Sven Feigenbaum, Joan Flahive, Mary Elizabeth Frappier, Clement El Kacimi Alaoui, Aziz Erlandsson, Thomas Feighn, Mark E. Flajolet, Philippe Frawley, William J. Eldridge, Klaus E. •Erie, Dieter H. Fein, Burton I. Flaminio, Livio Frazier, Michael W. Elhadad, Jimmy H. Eron, Mary B. Feingold, Alex J. Flanders, Harley Frech, Bruce El-Helaly, Sherif Taha Errico, Thomas G. Feingold, David Flanigan, Francis J. Frederickson, Paul 0. El-Hodiri, Mohamed Ervynck, Gontran J. 0. H. Feinsilver, Philip •Flath, Dan •Fredricks, Gregory A. Elia, Michele •Eschenbach, Carolyn A. Feit, Paul Fleckinger, J. Fredricksen, Harold M. Eliahou, Shalom Eschenbach, Dieter Feit, Walter Fleming, Charles G. *Fredrickson, Elvy L. Elias, Uri Escobales, Richard H., Jr. •Feldman, Alexander Fleming, Daniel J. Free, Norman S. Elias, Walter, Jr. Eskew, Thomas Eugene Feldman, Arnold D. Fleming, Wendell H. Freed, Daniel S. Eliason, Stanley B. Eskin, Gregory ·Feldman, Chester Flensted-Jensen, Mogens Freedman, Allen R. Eliasson, Halldor I. Eslinger, Robert C. Feldman, David Victor Fletcher, Evan Martin •Freedman, Marvin I. Elko, Constance B. *Espino-Santana, Victor M. Feldman, Edgar A. Florence, John B. Freedman, Michael H. Ellers, Erich W. Essen, Matts R. Feldman, Jacob Floret, Klaus Freeland, Mark S. Ellingham, Mark N. Esser, Anne-Marie Simon •Feldman, Marcus B. Flosser, H. 0. Freeman, Edmund E. Elliott, David •Esteban, Maria J. Feldman, Norman Floyd, Denis R. Freeman, Robert S. Elliott, George A. Estep, Donald J. Fell, James M.G. Floyd, Edwin E. Frei, Mark G. Elliott, Herbert E., Jr. Estrada, Luis Felland, Michael E. Flynn, Daniel Joseph, Jr. Freidlin, Mark Elliott, Joanne Etemadi, Nasrollah Fellers, Norman V., Jr. Flynn, David E. *Freije, Margaret Napolitano *Elliott, P. D. T. A. Etgen, Garret J. Fellman, Johan Flynn, Lawrence E. *Freiman, Gregory A. Elliott, Sheldon E. Etheridge, William L. Fellows, Michael Ralph Flynn, Robert Freimanis, Mary Louise Ellis, Alan J. *Evanovich, Peter J. *Fendrich, John W. *Fogelson, Aaron L. Freire Nistal, J. L. Ellis, James W. Evans, Steven Neil Fenley, John C. Foglio Susana, F. L. de Freitag, Herta T. Ellis, Kathryn P. Evans, Trevor Fenley, Sergio Roberto-­ Foias, Ciprian llie- *French, Donald A. Ellis, Richard S. Evens, Leonard Fenske, Christian •Fokas, Athanassios S. Frey, Regina F. Ellis, Robert Everitt, W. Norrie Fenstad, Jens E. Foley, Daniel M., Jr. Freyd, Peter J. Ellis, Robert L. Every, Jennifer B. *Ferguson, David R. Folk, Thomas F. Fridman, Burna L. Ellison, Robert J. Evyatar, Asriel Ferguson, Pamela A. Folland, Gerald B. *Fridy, John A. •Ellner, Stephen P. Ewacha, Kevin Fernandez, Emely Fong, Che-Kao Fried, David •Elmendorf, Anthony D. Ewbank, Edye Marie *Fernandez-Rodriguez, Fong, Kirby W. •Friedberg, Solomon Eloe, Paul W. *Ewer, J. Patrick Maria L. •Fong, Paul Friedberg, Stephen H. El-Sabbagh, Mostafa F. A. Ewing, George M. Ferrari, Carlo Fontaine, Marc F. *Friedland, Shmuel •Elson, Constance McMillan Ewing, Richard E. Ferreira, Andrew P. Fontenot, Robert A. Friedlander, Richard J. •Elton, John H. Ewy, Daniel J. Ferreira, Fernando J. Foran, James Friedman, Barbara Bernstein Elwood, David M. Eymard, Pierre Henri Ferreyra, Guillermo Segundo Forbes, Stephen H. Friedman, Jane E. •Emamirad, Hassan Ezeilo, James 0. C. Ferri, Massimo Ford, Benjamin J. Friedman, Joel Emch, Gerard G. Fabec, Raymond C. Ferris, Ian M. •Ford, Charles Edwin Friedman, Joyce B. Emmanuele, Giovanni Fabes, Eugene B. Ferro, Alfredo Ford, David Friedman, Merwyn M. Emmer, Michele Fabrega, Enfedaque Albert Ferro, Ruggero Ford, David A. Friedman, Nathaniel A. Emran, Obidullah AI Fabrykowski, Jacek W. Feser, Victor G. Ford, David James Friedman, Robert David •Enayat, Ali Fadell, Albert G. Field, Michael J. *Ford, Ralph M. Friesen, Donald K. Endo, Youichi Fadell, Edward R. Fife, James H. Foreman, Matthew D. Fritsch, Rudolf Endsley, Neil H. Faierman, Melvin Figueiredo, Ana Maria Forman, John W. Fritsche, Richard T. •Engber, Michael *Fair, Wyman G. Fillmore, Jay P. Forman, Robin Froese, Richard G. Engeler, Erwin Fairgrieve, Thomas F. Finch, David V. Forster, Klaus-Jurgen Frohardt, Daniel E. Engenes, Hans Faith, Carl Finch, John V. Forsythe, Keith W. Frohlich, Jurg M. Engesser, Hermann Falbo, Clement E. Finch, Steven Richard •Forsythe, W. L. Frohliger, John A. Engle, Jessie Ann Falcone, Maurizio *Fine, Benjamin Forte, Bruno Frohman, Charles D. Engler, Hans P. Falconer, Etta Z. Fingerman, Joel Fossum, Robert M. •Friichtenicht, Wiebke Engquist, Bjorn Falkner, Neil F. Finkelstein, Leib Foster, Andrew Fry, David S. Enneking, Marjorie M. Fall, Thomas C. Finkelstein, Louis D. Fotiadis, Dimitrios I. Fryer, S. Harvey *Enns, Theodore C. Failings, Kai Finlayson, Henry C. Foulis, David J. Fu, Yen-Tzu Enomoto, Kazuyuki Famoye, Kiya Felix Fino!, Carlos E. Foulser, David A. Fuad, Simonthy Renaldin Enomoto, Masatoshi Fan, Ky •Finston, David R. Fournelle, Thomas A. Fuchs, Laszlo Enqvist, Arne Fanney, Thomas R. Firey, William Fowler, Franklin H., Jr. Fuchs, Peter Rudolf Ensey, Ronald J. Faran, James J. Fischer, Arthur E. Fowler, Frederick C. Fuchs, Wolfgang H. Epp, Susanna S. Farber, Martin *Fischer, Carl H. Fox, Jeffrey Stephen Fuchssteiner, Benno Epperson, James F. Farber, Michael Fischer, H. Fox, John Michael Fuglede, Bent Epperson, Jay B. Farmer, Thomas A. Fischer, Ismor Fox, Ralph •Fuhrken, E. Gebhard Epstein, Bernard Farmer, William Michael Fishback, William T. *Foxby, Hans-Bjorn Fuji-Hara, Ryoh Epstein, Charles L. Farnsteiner, Rolf Fisher, Matthew P. Fraga, Robert J. •Fujimagari, Tetsuo *Epstein, D. I. Farrell, Roger H. Fisher, Stephen D. Fragoso, Marcelo D. Fujisaki, Rieko Epstein, David B. A. Fass, Arnold L. Fishman, Louis Fraleigh, J. B. Fujiwara, Daisuke *Epstein, Henry Fathi, Albert Fisk, Steve Frame, Michael Lee Fujiwara, Hidenori Epstein, Raisa Faucett, William M. Fitzgerald, Eugenia E. France!, Margaret Ann Fujiwara, Masahiko Erban, Daniel Faulkner, Frank D. Fitz-Gerald, Gary F. Francis, Bruce A. Fukuda, Komei Erbe, Lynn H. Faurre, Pierre L. Fitzgibbon, William E. Francis, Eugene A. Fukui, Seiichi

874 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS Centennial Research Fellowship Fund

Fukushima, Masatoshi •Gau, Yihnan David Gingrich, Ross B. Gopalsamy, Kondalsamy Greene, Curtis Fukushima, Mitsuo Gauchman, Hillel Gioia, Anthony A. Gopinath, Bhaskarpillai Greenfield, Gary R. •Fuller, Kent R. Gaudefroy, Alain Giordano, George Gordh, George R., Jr. Greenhall, Charles A. Fuller, Leonard E. Gautschi, Walter Girela, Daniel Gordon, B. Brent *Greenleaf, Allan T. Fuller, Luther B. Gebauer, Ruediger J. Giller, Samuel Gordon, C. M. Greenleaf, Frederick P. Fuller, Robert Arthur *Geddie, Peggy Emmons •Gladue, Earl C. Gordon, Jonathan Greenleaf, Newcomb Fuller, William R. Gehring, Frederick W. Glass, Michael S. Gordon, Robert Greenspan, Bernard D. Fuller, William R. Geissinger, Ladnor D. Glauberman, George Gorenflo, Rudolf Greenwood, Robert E. Fulton, Curtis M. Gelbart, Abe Glaz, Sarah Gorenstein, Daniel Gregg, Joe N. Fulton, William Gelbart, Stephen S. Glazebrook, James F. •Gorkin, Pamela B. Gregory, David A. Funk, William F. •Geller, Susan C. *Gleason, Andrew M. Gorlich, Ernest Gregory, John Fuqua, Jeffry B. Geman, Helyette E. Glenn, Paul G. Gormley, Michael J. Gregory, Thomas Bradford • Fiirer, Martin Geman, Stuart Alan Glickfield, Dianne Steele Goss, Robert N. Greicar, Richard K. Furutani, Kenro Genensky, Samuel M. Glimm, James G. Gosselin, John A. Greif, Anthony David Futia, Carl A. Genet, Jean Raymond Glover, Henry H. *Gosselin, Richard P. Greif, Stanley J. Fwu, Chihchy Gentili, Graziano Glover, Robert A. •Gossett, Eric James •Greim, P. Gaal, Lisl Novak Geoghegan, Ross Gluck, Herman R. Goto, Hideo Greiner, Peter C. Gabardo, Jean-Pierre George, John Clay Glynn, John J. •Goto, Midori S. •Greller, Larry David Gabay, Jacques Georgiady, MichaelS. Goblirsch, Richard P. Goto, Shiro Greville, Thomas N. E. Gabriel, Richard F. Georgiou, D. A. Godbey, Kevin S. Gottlieb, Daniel H. Griess, Robert Louis, Jr. Gacs, Peter Geramita, Anthony V. Goddard, J. D. Gouvea, Fernando Quadros •Griffeath, David S. Gadella, Manuel Geramita, Joan M. Goddyn, Luis A. Gover, Eugene H. Griffin, E. L., Jr. Gadia, Shashi Kumar Geremia, Raymond S., Jr. Godfrey, Colin Gow, Roderick I. Griffin, William Gerald •Gage, Michael E. *Gerhardt, C. Godin, Paul J. Graber, James S. Griffing, Gary R. Gaier, Dieter Gerig, Stephen R. Goebel, K. •Grabiel, Federico Griffiths, H. Brian Gaillard, Pierre Yves Gerisch, Wolfgang Goerss, Paul G. Grabiner, Sandy Griffiths, Phillip A. Gaito, Stephen T. Gerlach, Eberhard G. P. Goethals, J. M. E. Grabner, Elise M. Griggs, T. S. Galbraith, A. S. Gerlach, Jacob H. Goetz, Abraham Grabner, Gary Clem •Grillakis, Manoussos Gale, Carolyn Spencer Germain, Paul Gokhale, Sudhir Bhaskar •Grace, Edward E. Grilliot, Thomas J. Gallagher, Patrick X. Gershenson, Hillel H. Golan, Jonathan S. •Gracia-Bondia, Jose M. •Grimmett, Geoffrey R. Gallavotti, Giovanni •Gerstein, Larry J. Golber, David L. Graf, Siegfried Grimson, W. Eric L. Gallier, Jean H. Gersten, S. M. Goldberg, David M. Graffi, Dario Grinstead, Dana L. Gambaudo, Jean-Marc Gerstenhaber, Murray •Goldberg, Donald Y. Grah, Jacques •Gripenberg, Gustaf Gambi, Jose Maria Gerszonowicz, Jorge A. Goldberg, Moshe Graham, Aly Gritzmann, Peter Gamelin, Theodore W. Gervais, Jean Jacques Goldberg, Richard R. *Graham, Colin C. Grivel, Pierre P. •Gamst, Andreas Gerver, Joseph L. Goldberg, Seth I. Graham, George Grobler, Jacobus J. •Gamst, Jens Gessaman, Margaret P. Goldberg, Seymour Graham, George P. •Groemer, Helmut Ganelius, Tord H. Gessel, Ira M. •Goldblatt, Robert I. Graham, Ian Grognard, Rene J. M. Gangolli, Ramesh A. Getu, Seyoum Golden, Kenneth M. Graham, Victor W. •Groisser, David Gani, Joseph M. Geue, Andrew S. Goldfeld, Dorian Grainger, Arthur D. Gromoll, Detlef Ganser, Carl C. Gevirtz, Julian Goldhaber, J. K. Gramsch, Bernhard Gromov, Mikhael Ganster, Maximilian Gewirtz, Stephen J. •Goldman, Jay R. Grannell, Michael John Grone, Bob Gantner, Thomas E. •Ghatage, Pratibha Goldman, Jerry Grant, David R. Gropp, William D. Gantos, Richard L. *Ghent, K. S. Goldman, William Mark Grant, Nancy K. Gross, Daniel Joseph Garaizar, F. Javier Ghidaglia, Jean-Michel Goldsmith, Gineane J. Grantham, Stephen B. Gross, Fletcher I. Garcia, Mariano, Jr. Ghoniem, Ahmed Fouad Goldsmith, Judy A. Granville, Andrew J. •Gross, Kenneth I. Garcia, Octavio C. •Ghosh, Parimal K. Goldstein, Larry J. Grasse, Kevin A. Gross, Leonard Garcia-Loygorri, Cristobal *Gieringer, John D. Goldstine, Herman H. Grasser, Horst-Siegfried Grossman, Edward H. •Gard, Thomas C. *Gierz, Gerhard Goldston, Daniel A. Gratiaa, Marceline C. *Grossman, Marvin W. Gardiner, Christopher J. Giga, Yoshikazu Goldstone, Richard J. Gratzer, George A. Grosswald, Emil Gardiner, Cyril F. Gilat, David Gomez Pardo, Jose Luis Gravel, Pierre Grove, Edward A. *Gardner, Merritt P. Gilbarg, David Gomez-Ruiz, Francisco Graver, Jack E. Grove, John W. Gardner, Robert A. Gilbert, Angela Marie Gomi, Kunio Graves, Glenn W. •Grove, K. Gardner, William Allen Gilbert, Freeman Gompf, Robert E. Graves, Larry K. Grove, Larry C. Garfinkle, Devra Gilbert, Michael D. Gondard-Cozette, Daniell J. Graves, Robert L. •Groves, J. R. J. Garner, Lynn E. Gilbert, William J. Gonshor, Harry Graves, William H. Grow, David E. Garrett, John W. Gilchrist, Martin P. eGonska, Heinz H. Gravesen, Jens Growney, Wallace J. Garrett, Paul B. Gildenhuys, Dion Gonzalez Escobar, Rudy Gray, Alfred •Grubb, Gerd Garrido, Jose •Giles, John R. Fernando Gray, Jeremy John von Grudzinski, Olaf Garrison, Betty B. Gilewicz, Jacek •Gonzalez, Fulton Beltran Gray, John W. Gruenhage, Gary F. Garrity, Thomas A. Gill, Tepper L. •Gonzalez, Raul Ernesto Gray, Mary W. •Grundhofer, Theo Garsia, Adriano M. Gillard, Roland D. •Good, Irving John Gray, Robert E. Gruter, Michael Garst, Peter Gillespie, James R., Jr. Goodearl, Kenneth R. Gray, Samuel Hutchison Grzybowski, Pamela Marples Gartland, Eugene C., Jr. Gillespie, Robert G. Goodman, A. W. Grayson, Daniel Richard Gualtierotti, A. F. Garvan, Frank G. Gillman, Daniel W. *Goodman, Frederick M. Greaves, G. Guelzow, Andreas Juergen Gary, James D. Gillman, David S. Goodman, Jacob Eli Grecos, Alkis Guenard, Francois Garzon, Maximiliano Gillman, David W. Goodman, James Thomas •Green, Gary Brian Guerin, Esther E. Gasca, Mariano Gilman, Jane P. Goodman, Roe W. Green, James A. Guetti, Joan F. Gasper, George, Jr. Gilman, Robert Goodman, Sue E. Green, Mark L. •Giiichal, Edgardo N. Gass, Clinton B. •Gilmer, Gloria •Goodman, Victor *Green, Roderick M. Guilbault, Craig R. Gass, Norbert Gilmer, Patrick M. Goodner, D. B. Green, Simon Guillemin, Victor W. Gatica-Perez, Gabriel N. •Gilmore, Maurice E. *Goodrich, Suzanne Dinga Green, William L. Guillot, J. C. Gatterdam, Ronald W. Gilmour, Grant James •Goodson, Geoffrey Ross Greenbaun, Nicholas N. Gulbenkian, Garabed Gatteschi, Luigi Gilsdorf, Thomas E. Gopal, Mangalam R. •Greenberg, Peter A. Gulden, S. L.

SEPTEMBER 1989, VOLUME 36, NUMBER 7 875 AMS Centennial Research Fellowship Fund

Gulick, Denny Hamrick, Gary C. Haskell, Peter E. Hellerman, Leo Hicks, Darrell Lee Gulliver, Robert D., II Hamstrom, Mary-Elizabeth Haslach, Henry W., Jr. Hellerstein, Simon Hida, Haruzo Gundersen, Gary G. Han, Chong-Kyu • Haslinger, Friedrich Helmer, Gary A. Hida, Takeyuki Gundy, Richard F. Han, Jin Kyu Hass, Joel *Helminck, Aloysius G. Higgins, John A. *Gunnarsson, Thomas E. W. Han, Jongsook Hassinger, Bill, Jr. Helminck, Gerard Franciscos Higgins, John R. Gunter, Elsa L. Handler, Ivan Arthur Hastad, Johan Helson, Henry Higman, Donald G. Gupta, Dharma P. Handwerker, A. M. Hastings, Harold M. Helton, Burrell W. Higuchi, Yasunari •Gupta, Shanti S. Hanes, Kit Hastings, Stuart P. Helton, Frances J. •Hijazi, Oussama •Gurarie, David E. Hanlon, Philip J. Hasumi, Morisuke Helton, J. William Hilbert, Stephen R. Gurney, Margaret Hanna, J. Ray Hatori, Osamu Helwig, Karl-Heinz Hilgers, John W. Guseman, Lawrence F., Jr. •Hannah, John Hattori, Akio Hemasinha, Rohan •Hill, C. Denson Gustafson, Richard F. Hannan, Edward J. Hatvany, Adalbert Csaba Hemmingsen, Erik Hill, David G. B. Gustafson, Robert A. Hano, Jun-Ichi •Haughton, Dominique M.A. Hempel, J. A. •Hill, Donald M. Gustafson, Sven-Ake Hansen, Carsten Hausmann, Jean-Claude Hempel, John P. Hill, E. Stamford, II Gutek, Andrzej S. Hansen, Idar Hausner, Melvin Hemstead, Robert J. Hill, Gregory Mark Guterman, Martin M. Hansen, R. 0. Haver, William E. Henderson, David W. Hill, James •Gutierrez, Cristian E. Hansen, Vagn Lundsgaard Havermann, Hans Henderson, Francis McVey Hill, Ned W., Jr. Gutknecht, Martin H. Hanson, Stanley C. •Hawkins, Jane M. Henderson, James P. Hill, Shirley A. Guy, Richard K. Harada, Shigeharu *Hawkins, William •Hendricks, Walter J. Hillman, Abraham P. Guy, Wynne Alexander Haralambous, Yannis Anthony, Jr. •Hendy, Michael D. Hillman, Jonathan Arthur •Guzman, Fernando Haralampidou, M. Marina Hayashi, Elmer K. •Henkin, Douglas W. Hilt, Sandra N. •Guzman, Miguel de Harbater, David Hayashi, Eric *Henkin, Leon A. Hilton, Peter J. Gwyn, Douglas A. *Harborth, Heiko Hayashi, Kazumichi Hennequin, Paul-Louis Himonas, Alexandrou A. Ha, Young-Hwa Harbourne, Brian Hayashi, Mikihiro Henniart, Guy M. Hinder, Rainer •Haas, Ruth Hardarson, Askell Hayden, John L. Henniger, J. P. Hindley, James Roger Habetha, Klaus Hardt, Robert M. Haydon, Richard G. Henrich, Christopher J. Hindman, Neil B. Hackborn, William W. Hardy, Dare! W. Hayek, Nacere Henriksen, Melvin Hingston, Nancy Hackenbroch, Wolfgang Hardy, John T., Jr. Hayes, Catherine Cummins Henry, Myron S. *Hinkkanen, Aimo Hackler, Donald B. •Hardy, John W., Jr. Hayes, David F. Hensel, Robin Ann Morgan Hinman, Peter G. Haddad, George F. B. Hargraves, Beverly Bailey Hayes, David R. Hensley, Elmer L. Hinojosa-Berrones, J. A. Haddad, Hadi M. Harinath, K. S. Hayne, Roger M. Henstock, Ralph Hinson, Edward K. Haddock, A. Glen Raring-Smith, Robert H. *Haynes, Nola A. Hepp, Klaus Hinthorne, Stephen G. Hadid, Samir Bashir Harker, Patrick T. Haynes, Tyler H., Jr. Herbst, Albert F. Hintzman, William R. Haeberly, Jean-Pierre A. Harmand, Peter Hays, M. M. R. Herbst, B. M. Hirano, Tetsutaro Haebich, William Harmelin, Reuven Hazewinkel, Michie! Herfort, Wolfgang Norbert Hironaka, Heisuke Haefner, Jeremy A. *Hamad, John P. Hazlewood, Donald G. •Herman, Eugene A. Hirsch, Morris W. Haemmerlin, Guenther Harnett, Gerald P. He, Tian-Xiao Herman, Franklin B. Hirschfelder, John J. Hafner, James L. Harpe, Pierre de Ia Head, Thomas J. Herman, Michael Hirschfelder, Rosemary Hag, Per Harper, James D. Headley, Velmer B. Hermann, Margaret A. Hirzebruch, F. E. P. Hagan, Robert M., Jr. Harper, Lawrence H. Heard, Melvin L. Hermann, Robert Hirzebruch, Ulrich Hager, Anthony W. •Harrell, Andrew William Heath-Brown, Roger Hernandez, Diego B. Hisao, Kato Haggerty, Gerald B. Harrell, Ronald E. Hebert, Michel Hernandez, Eugenio Hislop, Peter David Hagis, Peter, Jr. *Harris, Bruno Hechler, Stephen H. Hernandez, Gaston E. Hitchin, Nigel J. Hagler, James N. Harris, David Carter Hecht, Henryk Hernandez, Rafael Hitotsuyanagi, Nobuo Hahn, Christopher Kenneth Harris, Gary A. Hecht, James E. • Hernandez, Rene A. Hlavac, Paul P. Hahn, Gena Harris, Joe Hecker, David A. Hernandez Ruiperez, Daniel Hlavka, James L. Hahn, Marjorie G. Harris, John C. •Hedayat, GholamAli • Herrera, Ismael Ho, Chung-Wu Hahne, Gerhard E. Harris, Michael H. Hedberg, Lars I. Herod, James V. •Hobart, Sylvia A. Haight, John A. Harris, Morton E. Hedlund, Gustav A. Herod, Scott A. Hobbs, Arthur M. •Hailat, Mohammad Q. Harrison, David K. Hedlund, James H. •Herron, David A. Hochschild, Gerhard P. •Haile, Darrell E. Harrison, Monica L. *Hedstrom, Gerald W. *Herrera, R. B. Hochstadt, Harry Hailperin, Ruth M. Harrop, Fred F. Heifetz, Daniel B. Herreshoff, James B. Hochster, Melvin Hailperin, Theodore Hart, Garry D. Heigho, George W. Herriot, John G. Hochwald, Scott H. Raimo, Deborah Tepper Hart, Klaas Pieter Heijmans, Johannes G. Herrmann, Joseph M. Hockett, Kevin G. Rain, Richard Martin Hart, Susan 0. Heil, Christopher E. •Herz, CarlS. •Hodel, Richard E. Hale, David R. Hart, Therese A. •Heil, Erhard Herschorn, Michael Hodges, Lucille M. Hale, Douglas F. Hartig, Donald Heineken, Hermann Herve, Michel Hodges, Wilfrid A. Hales, Alfred W. Hartl, Johann Heinicke, Allan G. Herwitz, Paul S. Hodgson, Jonathan P. E. Hales, R. Stanton, Jr. Hartman, James L. Heinig, Hans P. Herzog, Emil R. Hoeffding, Wassily Hall, Glen Richard Hartmann, Frederick W. *Heinold, Robert D. Hess, Jacob J. Hofer, Helmut H. W. Hall, Mark Edwin Hartshorne, Robin Heinonen, Juha M. Hesselink, Wim H. Hofer, Robert D. Hall, Marshall, Jr. Hartzler, H. Harold Heinrich, Katherine Hestenes, Magnus R. Hoffman, James A. Hall, Robert B. Haruki, Hiroshi Heins, Albert E. Hestenes, Marshall D. Hoffman, Jerome William Haller, Thomas Haruki, Shigeru Heins, Maurice H. Hetherington, Richard G. Hoffman, Kenneth R. Halpern, Herbert Harvey, Charles M. • Heintze, Ernst Hettling, Karl F. Hoffman, Michael E. Halvorsen, S. G. Harvey, F. Reese Heinze, Joachim Hetzer, Georg Hoffman, Michael J. Hamana, Masamichi Harvey, William J. Heitsch, James L. Heuer, Gerald A. Hoffman, William C. •Hamill, William A. Harvill, Jane Lea Hejtmanek, Johann Hans Heuvers, Konrad John Hoffmann-Jorgensen, Jorgen *Hamilton, Howard B. Haschke, Rebecca A. Heldermann, Norbert Hewett, Thomas James Hofmann, Karl H. Hamilton, Phillip M. Hasenfus, Harold J. Helgason, Sigurdur Heyer, Herbert K. Hofmann, Steve C. *Hamlett, Troy R. Hasenjaeger, Gisbert F. R. Hellberg, H. Stefan Hiai, Fumio Hoft, Hartmut Hammer, F. David Hashimoto, Kazuo Augustine Hellen, Gregory R. Hickernell, Fred J. Haft, Margret H. Hammer, Peter L. Hashimoto, Ki-ichiro Heller, Alex Hickey, Timothy J. Hogbe-Nlend, Henri Hammond, William F. *Haskell, Deirdre Heller, Dorothy M. Hickling, Fred Hogesteeger, F. W.

876 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS Centennial Research Fellowship Fund

Hogniis, Goran Hoyt, Gaylord M. Hutches, David J. Jackson, Stanley B. Johnson, Ben Hohs, Stephen M. Hoyt, W. L. Hutchinson, George A. Jackson, William D. Johnson, Bradford W. Holbenon, John V. Hratz, Joseph A. •Hutchinson, Joan P. Jaco, William H. Johnson, Charles N. Holbrook, John A. Hrbacek, Karel Hutton, Edward L. Jacob, Henry G. Johnson, Charles R. •Holden, Helge Hsia, J. S. Hveberg, Steinar Magne Jacob, Niels Johnson, D. Randolph, Jr. Holder, L. I. •Hsiang, Wu-Chung •Hvidsten, Michael D. *Jacob, William Burkley •Johnson, Dale Martin Holenweg, Werner Hsiao, L. Hwang, Jang C. Jacobs, Elliott Johnson, Daniel P. •Holland, DanielL. Hsieh, Simon C. Hwang, John Jew-Chen Jacobs, Felix J. Johnson, David Copeland Holland, Finbarr Hsieh, Wan-Chen Hyers, Donald H. Jacobs, Glenn K. Johnson, David H. Holland, Manin P. •Hsu, Guan-Hsong Hyllengren, Anders R. Jacobs, Harold Johnson, David L. Holland, Samuel S., Jr. Hu, K. Y. Hyvonen, Jaakko P. Jacobs, Jonathan M. Johnson, Diane M. Holland, W. Charles Hu, S. T. larrobino, Anthony A., Jr. Jacobs, Marc Q. Johnson, Donald G. Holley, Frieda K. Huang, Huaxiong Ibrahim, A. Shawky *Jacobs, Wanda Johnson, Gene Douglas Holley, Richard Andrew Huang, Tayuan lei, Yutaka Jacobsen, Lisa Johnson, Gerald W. Hollister, Lindsay Huang, Xun-Cheng Igarashi, Akira Jacobsen, Manin Johnson, Guy, Jr. Holman, Wayne James, III Huard, James G. Igarashi, Masao Jacquet, Herve M. Johnson, James E. Holmann, Harald R. A. Huber, Alfred 0. lgari, Satoru Jaffa, Roben E. Johnson, Jean T. Holme, Audun *Huber, Manin lgodt, Paul G. Jaffe, David B. Johnson, Jon L. Holmes, Dave R. Huckaba, James A. lha, Franklin T. Jaffe, Manha A. Johnson, Joseph F. Holmes, Ernest J. Hudson, Anne L. lhara, Yasutaka Jaffe, William J. Johnson, Joseph L., Jr. Holmes, James Samuel, Jr. *Hudson, Dennis Monroe lino, Riichi Jager, H. Johnson, Kenneth D. Holmes, John P. Hudson, Steven M. lio, Tutomu Jagy, William C. Johnson, Kenneth Walter Holmes, Philip John Huebschmann, Johannes ljjasz Vasquez, Ede J. •Jahren, Bjorn *Johnson, Peter A. Holmes, Randall Reed Huena, Carlos Cuevas lkebe, Teruo Jain, M. K. Johnson, Peter D., Jr. Holmes, Richard B. Huet, Denise Ikeda, Kazumasa Jain, Naresh C. Johnson, Peter M. Holmstrom, Lasse L. *Huff, Gerald B. •lllman, Soren A. Jain, P. K. Johnson, Peter M. Holton, Derek A. Huff, W. N. llmanen, Tom Jakel, David W. *Johnson, Roben A. Homer, William D. Hughan, Stanley P. lm Hof, Hans Christoph •James, David M. Johnson, Roben L. Honda, Kin-Ya Hughes, Anne lmai, Hideo James, Douglas Johnson, Roben Shepard Honda, Koji Hughes, Anthony lmayoshi, Yoichi James, Matthew R. Johnson, Robena F. Hong, Sungpyo Hughes, C. Bruce •Immerman, Neil James, Roben C. Johnson, Rodney W. Honig, Chaim Samuel Hughes, Cephas D. lmrich, Wilfried Jamieson, Michael W. Johnson, Roy A. Hoobler, Raymond T. Hughes, Joseph A. lnaba, Hiroshi Janicki, Ryszard Johnson, Russell A. •Hook, Edward C. Hughes, Mark P. lndlekofer, K. H. Jankins, Mark *Johnson, Steven Darrel *Hooton, James G. Hughes, Rhonda J. •Infante, Ettore Jannsen, U. Johnstone, P. T. Hoover, Thomas B. Hughes, Richard P., Jr. Ingraham, Edward C. Jansen, Willem G. Jonah, David W. *Hopkins, Mike Hughes, Ruth L. Ingram, Nancy Jane •Janson, Svante *Jones, Ben J. Hormander, Lars V. Huh, Won lnnami, Nobuhiro Jantosciak, James S. Jones, Carl Hilton Horn, Alfred Huibregtse, Mark E. loakimidis, N. I. Jantzen, Jens Carsten Jones, Christopher K. R. T. Horn, Jean MacGregor Huilgol, Raja R. lonescu, Dan Janusz, Gerald J. Jones, Earl P. Hornback, Joseph H. Huisken, Gerhard Iorio, Rafael J ., Jr. Jara Maninez, Pascual *Jones, F. Bunon Horne, J. G., Jr. Hukle, George W. lpina, Lynne Kamstra •Jarchow, Hans Jones, G. A. Horner, Mary Lynn Hulben, Guy William •Irving, Ronald S. Jardine, John Frederick Jones, Gordon C. Horner, T. S. *Hulkower, Neal D. Isaacs, Godfrey L. Jareb, Anthony Jones, Harold T. *Hornor, William E. *Hull, Richard B. Isaacs, I. Manin Jarratt, Mary K. Jones, James P. •Hornung, Ulrich Hulsbergen, Wilfred W. J. Isaacson, Eugene Jarvi, Pentti K. Jones, Jason Andrew Horrigan, Timothy J. Hume, Leigh R. Isaak, Ganh T. Jarvis, Trevor M. Jones, Jeffrey P. Horrobin, Elizabeth Ann Humphreys, James E. Isbell, John R. Jaworowski, Jan W. Jones, Kathryn A. Horrocks, Geoffrey •Humphreys, John F. eiseki, Kiyoshi Jea, Hae-Pyng •Jones, Peter R. Horsfield, Christopher H. Humphreys, M. Gweneth Isenberg, J. Jean, Michel Jones, Theodore W. Horsley, Anthony Huneke, Craig L. Ishihara, Toru Jefferies, Nigel Jones, Vaughan F. R. Horstmann, Cay S. Hung, Henry Hin-Lai Ishii, Jyun Jeffrey, Alan •Jones, William B. Horvath, Charles Daniel Hunkins, Dalton R. Ishikawa, Hirofumi Jeffs, Janice Jones, William R. Horvath, John M. Hunsberger, L. Gerald lshimoto, Hiroyasu • J eggle, Hansgeorg Jongen, Hubenus Th Horvath, Jozsef Hunt, Louis Robens Ismail, Mourad El-Houssieny Jekel, Solomon M. Jonker, Leo B. Horwitz, Alan L. Hunt, Richard A. Ito, Hiroshi Jenkins, Joe Wiley Jonsdottir, Kristin Halla Hosack, John M. Hunt, Walker E. Ito, Kiyosi Jensen, Arne Jonsson, Bjarni Hoste, Jim E. Hunte, Beryl E. Ito, Noboru Jerison, David Jonsson, Thordur Hotta, Ryoshi Hunter, Maxwell Norman Ito, Ryuichi Jerome, Carlos Jordan, G. Samuel Hotzel, Eckehan Hunter, Norma Gerkens •Ito, Seizo Jerrard, Richard P. Jordan, Kirk E. Householder, James E. Hunzeker, Huben L. •Ito, Yuji Jessen, Borge Jordan, Steven L. Houston, Evan G. Huotari, Roben Heikki ltoh, Mitsuhiro •Jessup, B. J. Jorgensen, P. E. T. Houston, Raymond S. Hurd, Spencer Peyton ltokawa, Yoe Jha, V. Josephson, William Allen Howard, David R. Hurder, Steven E. lves, Roben T. Ji, Ronghui Joshi, Nalini Howard, Edgar J. Hurley, Charles Rory lwanaga, Yasuo Jian, Alan S. eJost, Juergen Karl Howard, Fredric T. Hurley, Donal J. lwaniec, Henryk Jimenez, Jose Alfredo Jouanolou, Jean-Pierre Howard, Louis N. Hurley, James F. Iwasaki, F. Shigeo Job, Vanessa R. •Joyce, David E. Howard, Paul E. Hurley, Michael G. !washita, Yuichi Jockusch, Carl G., Jr. Joyner, W. David Howard, Ralph E. Hurley, Susan E. Iwata, Koichi Johann, Patricia Juberg, Richard K. Howard, William A. Hurst, C. A. lze, Jorge A. Johannson, Klaus Jubran, !sa S. Howell, Kenneth Hunubise, Jacques C. lzuchi, Keiji Johansson, Bo lngvar Jumper, Gregory S. Howes, Frederick A. Hurwitz, Solomon Izumi, Shin-lchi John, David J. Jun, Kil Woung Hoye, Laurence G. Husain, Taqdir lzumiya, Shyuichi Johnsen, Eugene C. Junghenn, Hugo D. Hoyle, Hughes B., III Hustin, Deborah L. Jackson, Lloyd K. Johnsen, Ronald L. eJungnickel, Dieter

SEPTEMBER 1989, VOLUME 36, NUMBER 7 877 AMS Centennial Research Fellowship Fund

Jurca, Dan Katz, Andrew Kestenband, Barbu C. Kirk, William A. Koethe, Gottfried M. •Jurca, Louis J., Jr. Katz, Sheldon Kettler, Paul C. Kirkman, Ellen E. Kogelman, Stanley JUrgensen, Helmut Katz, Talbot Michael Kevorkian, Aram K. Kirley, Paul 0. Koh, Kwangil Justice, James H. Katz, Victor J. Kevorkian, Aram K. Kirmser, P. G. Kohler, Peter Kaashoek, Marinus A. Katznelson, Y. Key, Eric Stephen Kirsch, Werner Kohler, William Joseph Kac, Victor Kauffman, Louis H. Keyfitz, Barbara L. Kirwan, Frances C. Kohn, Joseph J. •Kaczynski, Tomasz Kauffman, Robert M. Keys, Charles David Kirwan, William E., II Koivisto, Pertti T. Kadlecek, David Kaufman, Arthur Kezlan, Thomas P. Kiselman, Christer 0. Kojima, Sadayoshi Kahan, William M. Kaufman, William E. Khajah, H. G. Kishi, Masanori Kokoska, Stephen M. Kahane, Jean-Pierre Kaul, S. K. Khaleelulla, S. M. Kishore, Masao Kolaitis, Phokion G. Kahn, Donald W. Kaup, David J. Khalifah, M. F. Kister, Jane Ktilbig, Kurt Siegfried Kahn, Jeff N. *Kaup, Wilhelm Khalimsky, Efim Davidovich Kita, Hiroo Kolchin, E. R. Kahn, Peter J. •Kautzmann, Frank N., III Khan, Mohammad Ahmad Kitada, Hitoshi Kolesar, R. J. *Kaijser, Thomas Olof Kavanagh, John P. Khiyal, Sikander Hayat Kitano, Koh-lchi •Kolk, Johan A. C. Kailath, Thomas Kawamoto, Shunji *Khoshkam, Mahmood •Kittaneh, Fuad A. Kolmus, Peter A. Kajiwara, Joji Kawasaki, Tetsuro *Khosrovshahi, Golamreza B. Kittel, Phyllis M. Kolodner, Ignace I. Kakihara, Yuichiro Kay, Irvin W. Khouri, Khalid Subhi Kiyek, K. Komanska, Henryka Kakiichi, Yoshiaki Kazamaki, Norihiko Kibler, Robert E. Kiyohara, Mineo Krystyna Kalia, R.N. •Kazarinoff, Nicholas D. Kichenassamy, Satyanad *Klambauer, Gabriel Komatsu, Hikosaburo Kalisch, Gerhard K. •Kazdan, Jerry L. Kiefer, James E. Klass, Michael J. Komatu, Yusaku Kaliszewski, Steven Paul Keane, M.S. Kiessler, Peter C. Klatman, David S. Komiya, Yurin Kall, Peter Keane, Michael K. Kieval, Harry S. Klauder, John R. Komura, Takako Kallman, Ralph A. Kearton, Cherry •Kilambi, Srinivasacharyulu •Kiawe, Maria Margaret Kon, Mark Andrew Kallstrom, Anders Keating, Kevin P. Kilgour, D. Marc Klay, Matthias P. Konhauser, Joseph D. E. Kalman, Dan Kechagias, Epaminondas N. Kilhefner, Dale Z. Kleiman, Steven L. Konig, Heinz J. Kalmbach, Gudrun Keeler, Stephen P. Killeen, John *Klein, Abraham de Koning, Jan Kalton, N.J. •Keen, Linda Killgrove, Raymond B. •Klein, David M. Koo, Hyeng Keun Kaman, Charles H. Keenan, Daniel Macrae Kilpelainen, Tero Kleiner, Alexander F., Jr. Koo, Ja-Kyung •Kambayashi, T. Keeping, Anthony J. *Kim, Chul Kleiner, Bruce A. Koo, Reginald Kamejima, Kohji Kegel, Otto H. Kim, Dong-Gyom Kleiner, Mark Koornwinder, Tom H. Kamin, Shoshana *Kehayopulu, Niovi •Kim, Donggyun •Kleinman, Ralph E. Kopacek, Hal W. Kaminker, Jerry Keiding, Hans Kim, Hayon Kleisli, H. Kopperman, Ralph D. Kaminski, David 0. Keigher, William F. Kim, Hong Jong Kleitman, Daniel J. Koninyi, Adam Kamishima, Yoshinobu Keinert, Fritz •Kim, Hyuk Kletzing, Dennis R. Korenblum, Boris Kammler, David W. Keisler, James E. Kim, lhn Sue Kliemann, Wolfgang H. *Korman, Philip L. Kamowitz, Herbert M. Keisler, Michael Kim, In Su Klingen, Helmut Kortanek, Kenneth 0. Kamran, Niky Kelingos, John A. Kim, JeongSook Lee • Klingler, Lee Charles •Korzan, Dale M., Jr. Kanai, Masahiko *Keller, Charles Lewis Kim, Jong-Chul Klingsberg, Paul R. Koschorke, Ulrich Kanamori, Akihiro Keller, Wilfrid •Kim, Kyung Hwa •Knapp, Wolfgang D. Kosinski, Antoni A. Kanda, Mamoru Kelley, Robert L. Kim, Seong-A Knaus!, Helmut Kosier, Karl Andrew Kaneko, Akira Kellogg, Bruce *Kim, Soon-Kyu Knight, Julia Koslowski, Jiirgen Kanemitsu, Shigeru Kellogg, Charles N. Kim, Wan Se *Knight, Karl • Kosmann-Schwarzbach, Kanenobu, Taizo Kelly, David Kim, Woo Jong Knill, Ronald J. Yvette Kang, Ming-Chang Kelly, David C. Kim, Young-Kook Knisley, Jeff Randell Kossack, C. R. Kaniuth, Eberhard Kelly, G. Maxwell Kimber, John E., Jr. •Knoebel, Arthur *Kostenbauder, Adnah G. Kanjin, Yuichi Kelly, John B. Kime, Katherine A. Knoerr, Alan P. Kostlan, Eric James Kann, Edgar D. Kelly, John F. Kimmel, John Edward Knopp, Marvin I. Kotiuga, P. Robert Kanno, Tsuneo Kelly, Theresa D. Kimura, Tatsuo Knorr, K. R. K. •Kotter, Manfred *Kano, Takeshi Kemeny, John G. Kincaid, Wilfred M. Knorrer, Horst Kotzen, Marshall J. Kanold, Hans-Joachim Kempachiro, Ohashi Kindler, Philippe Knowles, J. David •Kourouniotis, Christos Kaper, Hans G. Kendall, Richard P. King, Brian S. Knox, Nathaniel Kovarik, Zdislav V. Kaplan, Stanley Kenelly, John W. King, Christopher K. Knudsen, John R. *Kovesi-Domokos, S. Kaplan, Wilfred Kenku, Monsur Akangbe King, Donald R. Knuth, Donald E. Kowalik, Virgil C. Karal, Frank C., Jr. Kennedy, Edward S. King, James A. Knutson, Donald I. Kozin, Frank Karamatsu, Yoshikazu Kennedy, Gary P. King, James R. Ko, Bongsoo Kra, Irwin Karel, Martin Lewis Kennedy, Judy Anita King, L. Richardson Ko, Hai-Ping Kracht, Manfred Karle, Jerome Kenner, Paul M. King, Larry Ko, Ki Hyoung •Krafft, Olaf W. Karlovitz, Les A. Kennison, John F. King, Paul Everson Ko, Youngso Kraft, Hanspeter Karlsson, Johan Kenschaft, Patricia Clark King, Randall R. Kobayashi, Shoshichi Kraft, Jiirgen •Karlsson, Per W. •Kent, Darrell C. King, Stephen C. Kobayashi, Yuji Kraines, David P. Karpilovsky, G. Kent, George A. •Kinoshita, Shinichi *Kober, Wolfgang Krakowski, Fred Karpishpan, Yakov Kent, Joseph F. •Kinsey, David W. • Koc, Cetin K. Kramer, Earl S. Karr, Alan F. •Kent, Mark D. Kinukawa, Masakiti Kocan, Daniel Kramer, Jurg Karrass, Abraham Kent, Steven L. Kinyon, Michael Kenneth Koch, Charles F. Kramer, Raymond F., Jr. Karreman, Herman F. Kenyon, Richard W. Kipps, Thomas C. Koch, Hans A. Kramer, Thomas R. Karrenberg, Frederick G. Keown, Nancy A. Kiraly, Emery Koch, Richard M. Kranjc, Marko Karrer, Guido Kernast, John C. Kirane, Mokhtar Kochman, Fred Krasny, Robert *Karube, Takashi Kerr, Eldon R. Kirby, Robion C. Kochman, Stanley Oscar Kraus, Gerald A. Kasriel, Robert H. Kerr, Sandria N. Kirch, Allan M. Koditschek, Daniel Eliezar Kraus, Jon E. Kast, David H. Kersting, Gary Steven Kirchbraber, Urs Koditz, Helmut Krause, Ralph M. Kates, Louis K. Kerzman, Norberto L. Kirchgassner, Klaus W. Koebbe,Joseph V. •Krause, Ulrich Kato, Takao Keshishyan, Joseph Kirchherr, Walter W. Koehler, Anne B. Kraut, Gertrud L. Katok, Svetlana R. Kessel, Catherine B. Kirk, David B. Koehler, T. L. Krauter, Arnold R. Katsura, Toshiyuki Kesten, Harry Kirk, Joe E., Jr. Koestner, Alfred Kravitsky, Naftali

878 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS Centennial Research Fellowship Fund

Kravvaritis, D. Kyner, Walter T. Larson, Edward H. Leeb, Klaus •Levy, Lawrence S. Krebs, Neil E. Kyrouz, Thomas J. Larson, Lee M. Leemans, H. W. Levy, Paul *Kree, Paul Kythe, Prem K. Larson, Richard G. Leep, David B. Lewan, Douglas Kreith, Kurt Kyuno, Shoji Larson, Roland E. Lefebvre, Jean E. Lewin, Jacques Krener, Arthur J. • Labelle, Gilbert Larson, Suzanne Lynne *Lefkovitch, Leonard P. Lewin, Mordechai •Kreuzman, Mary Joan Labelle, Jacques Larusson, Finnur Lefton, Lew E. Lewis, Charles J. Kreyszig, Erwin 0. LaBerge, Timothy J. LaSalle, Margaret M. Leger, George F. •Lewis, David W. Krieger, Henry A. Labesse, J. P. Lashof, Richard K. •Leggett, Anne M. Lewis, George M. Kriegsman, Helen F. Labouriau, Isabel Salgado *Laska, Michael Leggett, Robert N., Jr. *Lewis, John A. Kriegsmann, Gregory A. Labrousse, Jean-Philippe Lassettre, Edwin R. Lehman, J. Larry Lewis, L. Gaunce, Jr. Krinik, Alan C. LaBudde, Christian D. Lassiter, Julie B. Lehner, Joseph Lewis, Roger T. •Krishnapriyan, H. K. •Laca, Marcelo E. Latch, Dana May Lehrer, Gustav I. Lewis, William James Kristensen, Soren Lacampagne, Carole B. Lauchli, Hans Lehrer-Hamed, Y. L'heureux, James E. Kristiansen, Gundorph K. Lachance, Michael Anthony Laudenbach, Francois Lehtinen, Matti T. Li, Bingxi Krompart, Lucia Beth Lachlan, Alistair H. Lauer, Mark D. •Lehto, OlliE. *Li, Lide Kronheimer, P. B. Lackey, Jackson B. Lauer, Norma Fay Lehtonen, Ari Taavi Einari Li, Lige Kronstein, Karl M. •Lacomba, Ernesto A. Laufer, Henry B. Leib, James H. Li, Luen-Chau Krueger, Charles G. Lada, Thomas J. Lauria, Francesco E. Leibnitz, Edward A. Li, Ming-Sun Krug, Don K. Ladas, Gerasimos Lauritzen, Steffen L. Leichtweiss, Kurt Li, Tien-Yien Krumpholz, Gary R. Laderman, Julian David •Lausch, Hans Leighton, Frank Thomson Liang, Jaung Kruskal, Joseph B. Laduke, Jeanne Laush, George Leinbach, L. Carl *Liang, Joseph J. Ku, Hsu-Tung •Ladwig, John A. Lavalle, Irving H. Leipnik, Roy B. Libby, Richard Allan Kubo, Fumio •Laffey, Thomas J. Laverell, W. David Leith, Cecil E., Jr. Liberman, Zvie Kubo, Tadao Lafontane, Jacques Lavine, David Leitner, Michael P. Libgober, Anatoly S. Kubokawa, Yoshihiro Lagarias, Jeffrey C. Lavine, Richard B. Leitzel, James R. C. Lichtenbaum, Stephen Kucera, Thomas Glen Lagnese, John E. Law, Peter R. Leitzel, Joan P. Lichtin, Benjamin L. Kudla, Stephen S. Lai, Tony W. Lawlor, Gary R. Lelek, Andrzej Lichtman, Alexander Kudo, Tatsuji Laidacker, Michael A. •Lawniczak, AnnaT. Lelong, P. J. Lick, Dale W. Kuebler, Roy R., Jr. Lakos, Nela Lawrence, Anthony Lee Lemaire, Luc •Lieb, Elliott H. Kuenzi, Norbert J. Lakshmanan, Neela Lawrence, Carol Jean *Lemay, William H. Lieberman, David I. *Kuga, Michio Lalli, Bikkar S. Lawrence, John W. Lemei, Han Lieberman, Gary M. Kugler, Lawrence D. Lam, Kee Y. Laws, Zane John LeMesurier, Brenton John Liggett, Thomas M. Kuhlmann, Norbert Lam, Tsit-Yuen Lawson, David F. Lempp, Steffen Lightbourne, James H., III Kuhn, Nicholas J. Lambert, Howard W. Lawson, H. Blaine, Jr. Lengyel, Bela A. Ligouras, Panagiotis K. Kiihnel, Wolfgang Lambert, John Patrick Lawson, Walter R. *Lenhart, Suzanne Marie Lim, Chong-Keang Kuiper, Nicolaas H. Lampe, William A. Lawvere, F. William •Lenihan, Stanley R. Lima, Asvald Kulenovic, Mustafa R. Lampert, David S. Lax, Anneli Lenstra, H. W., Jr. Lima-Filho, Paulo Kulisch, Ulrich Lamperti, John W. Lax, Peter D. *Leon, Jeffrey S. Lin, Charles S. C. *Kulkarni, Devadatta M. *lancaster, Kirk E. Lax, Robert F. Leonard, Henry S., Jr. Lin, Charlotte Kulp, Daniel Teibi Lancaster, Peter Laywine, Charles F. Leonard, Philip A. Lin, Jindra Kumagai, Donna J. Lance, Timothy L. Lazarov, Connor Lepisto, Timo Vatter Lin, Shen Kumahara, Keisaku Lander, Felix I. * Lazarsfeld, Robert K. Lepowsky, James I. Lin, Wen-Hsiung Kumar, A. Anil Lander, Julian Charles •Lazerson, Earl E. Leray, Jean Lind, David W. Kumasawa, Nin *Landesman, Edward M. Lazzari, Claudio Lerche, Kenneth D. Lind, Douglas A. Kumjian, Alexander A. Landin, Joseph Le Cam, L. M. Leschen, John G. Lindberg, John A., Jr. Kunen, Kenneth Landman, Michael J. U\, Diing Trang Lesieur, Leonce *Lindemann, Willi Kunle, Heinz *Lando, Clifton A. Lea, James D. Leslie, Arthur S. •Linden, Carl N. Kunoff, Sharon •Landraitis, Charles K. Leach, Ernest B. Lesmes, Jaime Lindenstrauss, Joram Kunze, Ray A. Landrock, Peter Leader, Jeffery J. Lesniak, Linda Lindgren, Georg Kiinzle, Hans Peter •Landstad, Magnus B. Leader, Solomon Lett, G. Scott Lindgren, John E. Kuo, Tzee Char Landweber, Peter S. Leahy, John V. Letzter, Gail R. •Lindsay, J. Martin *Kupferwasser, Marcelo Lanford, Oscar E., III Leavitt, William G. •Leung, Anthony W. Lindstrom, Ingrid Kupka, Ivan •Lang, George E. LeBlanc, Michele K. Leung, Denny Ho-Hon Lindstrom, Mikael Kurata, Yoshiki Lang, Serge Lebow, Arnold Leung, Tat-Wing Lindstrom, Tom L. Kuroda, S. T. Lange, Charles G. Lebowitz, Joel L. Levaro, Richard A. Lindstrom, Wendell D. Kurshan, Robert P. Lange, Ridgley *LeBrun, Claude R. Levatin, JoAnne Lee Ling, William Halstead Kurss, Herbert Langebartel, Ray G. Leduc, Robert E. *Leveille, Michel Linnell, P. A. Kurtz, David C. Langenhop, Carl E. Lee, Carl W. Levenberg, Norman Lions, J. L. •Kurtz, DouglasS. •Langford, William F. Lee, Cheng-Ming Levermore, Charles David Lions, Pierre Louis Kurtz, Stuart A. Langlands, Robert P. Lee, Dong Hoon Levi, Howard Lipkin, Leonard J. •Kurtz, Thomas G. Langsam, Joseph A. Lee, Dong-Sao Levin, Jacob J. Lipschutz, Seymour Kurtzke, John F., Jr. Langston, Michael David Lee, D6-Won Levin, Richard G. Lipshutz, Robert J. Kushner, Harvey Laning, J. H. •Lee, Hung-Mou Levine, Daniel S. Lipton, R. J. •Kusuda, Masaharu •Lansdon, Robert Steven Lee, John M. Levine, Eugene Litchfield, Kay P. Kusunoki, Yukio Lanski, Charles P. Lee, Jyh-Hao Levine, Harold I. *Litherland, Rick Kutzko, Philip C. Lanteri, Antonio Lee, Ke-Seung Levine, Howard A. Little, Charles H. C. •Kwak, Hyo Chul •Lantz, David C. Lee, Kotik K. Levine, Jack Little, John B. Kwak, Jin Ho Lanza de Cristoforis, M. Lee, Peng-Yee Levine, Jerome P. Littman, Walter Kwak, Nosup Lanzano, Paolo Lee, Ronnie Levitt, Norman J. Liu, Hsi-Ching Kwasik, Slawomir Lapidus, Arnold Lee, Sa-Ge •Levitt, Tad S. Liu, Jong-Diing Kwee, Xenia M. Lappan, Peter A., Jr. Lee, Shyling Levko, John J. Liu, Li-Qian *Kwon, Kit H. Larkin, Martha A. •Lee, Tzong-Yow Levy, Azriel Liu, Shih-Chao •Kye, Seung-Hyeok Larrazabal, J. M. Lee, Wen-Chien Levy, Gene Liu, Shih-Hua Kymala, Earl E. Larson, Bruce R. Lee, WillY. •Levy, Joel Liu, Wei-Nung

SEPTEMBER 1989, VOLUME 36, NUMBER 7 879 AMS Centennial Research Fellowship Fund

Livingston, Albert E. Lozano, Maria Teresa •Maclachlan, Colin Marion, Jean Albert Matsushita, Yasuo *Livingston, Marilynn L. Lu, Chin-Pi Macphail, Moray S. Markel, Scott A. Matti, Joseph T. Livingston, William Robert Lu, Kau-Un •Macpherson, Robert D. Marker, David E. Mattson, Leroy T. Llave, Rafael de Ia Lubin, Clarence I. Macwilliams, F. Jessie Markert, Matthew J. Mattuck, Arthur P. Llewellyn, James Lucas, Billy J. Madden, James Joseph Markot, Robert P. Mauceri, G. C. Llibre, Jaume Lucas, Thomas G. •Maddocks, John H. Markvorsen, Steen *Mauduit, Christian Llosa, Joseph Luce, R. Duncan Maddux, Roger D. Marie, Charles Michael Maumary, Serge Lloyd, Noel G. Luchins, Edith H. Mader, Adolf Marotto, Frederick R. Maurer, Donald E. Lloyd, Stuart P. Ludden, Gerald D. Madison, Bernard L. Marsden, Jerrold E. Maurer, Stephen B. Lluis, Emilio R. •Ludwig, Garry Madow, William G. Marsh, Marcus M. Mawata, Christopher P. Lo, Tzee-Nan Kuo Luecking, Daniel H. Madsen, Ib H. Marshall, David Imler Mawyer, Farley Lockhart, Deborah Frank Lueneburg, E. •Maeda, Fumi-Yuki •Marshall, Donald E. Maxfield, John E. •Lockhart, Jody Meyer Luh, Jiang Maeda, Hironobu Marshall, Hunter H. Maxson, Carlton J. Loeb, Peter A. •Lui, Roger Y. Maeder, Roman E. Marshall, Murray Angus Maxwell, James W. Loeser, Francois Lui, Shiu-Hong Maehara, Kazuhisa Marsiliano, Judy May, E. Lee, Jr. •Lofquist, George W. •Luk, Hing-Sun Magenes, Enrico Marstrand, John M. May, Edward T. Loftin, John C. *Lumer, Gunter Magill, Kenneth D., Jr. Martelli, Mario Umberto May, Eleanor Lolli, Gabriele Luna, Eduardo A. Magnus, Arne Martens, Henrik H. · May, J. Peter Lombardo, Charles J. Lundgren, J. R. Magnuson, Alan William Marti, Jurg T. May, Michael K. Lomonaco, S. J., Jr. *Lundy, Thomas James Magruder, Richard B. Martin, Corindo I. May, Warren L. Loncaric, Josip Lunsford, Matt David Mahdavi, Kazem Martin, Donald A. May, William London, David Lustig, Martin Maheshwari, Sandeep Martin, E. Dale Mayberry, John P. Long, David Darren Luther, C. F. Mahoney, Anne Martin, Gary A. Mayer, John Clyde Long, Ding-Gwo Luther, Norman Y. Mahrous, Mohamed-Amin A. Martin, Geoffrey K. Mayer, Raymond A., Jr. Long, John M. •Lutoborski, Adam Maiellaro, Michele Martin, George E. Mayer-Wolf, Eddy Longley, James Wildon Lutterodt, Clement Henry Maier, Franz W. Martin, John R. Mayor, John R. •Longo, Roberto Lutzer, David J. Maier, Mary A. Martin, John R. Mayorga, Jose B. Loo, Joseph C. Luvisetto, Maria Luisa Mairhuber, John C. Martin, Margaret A. Maziarz, E. A. Loomis, L. H. Luxemburg, Wilhelmus A. J. Maj, Mercede Martin, Nathaniel F. G. Mazorow, Moya Michelle Lopez, Amparo *Lyford, William C. Makar-Limanov, L. G. Martin, Nigel Mazumdiir, Tapas •Lopez Lagomasino, Lynch, Robert E. Makepeace, Coline M. Martin, Norman M. Mazur, Martin Alois Guillermo Lynch, William C. Makovoz, Yuly Martin, Robert H., Jr. Mazzeo, Rafe R. Lopez-Carmona, Antonio Lyon, Herbert C. Malafronte, Thomas A. Martindale, Wallace S., III McAdam, Stephen J. L6pez-Escobar, Edgar G. K. *Lyons, Carter G. Maleki, Amir Martinez, Rafael A. McArthur, C. W. •Lorch, Lee Lyons, Jeremiah J. Malkevitch, Joseph Martino, James R. McAsey, Michael J. Lorentz, George G. Lyons, Russell D. Maim, Dennis R. Martin-Reyes, Francisco McCarthy, Charles A. Lorenz, Dan H. Lysko, Janusz M. Malon, David M. Javier McCarthy, Donald J. Lorenz, Martin Lytle, Raymond A. Maloney, James J. Martins, Joyce A. McCarthy, John •Lorenzini, Dino J. Lyubeznik, Gennady M. Maloof, Giles W. •Martsinkovsky, Alex McCarthy, John David Lorimer, Joseph Wilson Ma, Daowei Maltese, George J. Marumoto, Yoshihiko McCarthy, Paul J. Loring, Terry A. *Ma, Frank T. Malyshev, Igor G. Maruyama, Toru McClanahan, Ray A. Lotan, Moshe •Mac Lane, Saunders •Manaster, Alfred B. Marvin, John W. McCleary, John H. •Lotto, Benjamin A. Macbeath, A. M. Mandelbrot, Benoit B. Mascioni, Vania D. McClenahan, Maurice D. •Lotto, Edith N. S. MacCamy, Richard C. Manders, Kenneth L. *Maserick, Peter H. •McClure, Donald E. Lou, You-Shi Macdonald, I. G. Manderscheid, David C. Maskit, Bernard McColm, Gregory Loren Loud, Warren S. Macdonald, Ian D. Manfredi, Juan J. •Maslowski, Henryka McConnell, John C. Louhivaara, Ilppo Simo MacDonnell, John J. Manis, Merle E. Mason, Geoffrey McConnell, Robert K. Loustau, John A. Macfarlane, Andrew Ian *Manitius, Andre Z. *Mason, Robert M. McConnell, Terry R. Louton, Tom Macgibbon, Brenda Manjarrez, Victor M. Massam, Helene McConnell, Thomas Lovell, John R. MacGillivray, A. Dean Mann, Benjamin M. *Massey, Fred A. •McCool, Kenneth Lovett, Jane T. MacGregor, Thomas H. Mann, Henry B. Massey, William A. McCormick, Ferris E. Lovric, Miroslav Machado, Armando Mannur, Narasimha Reddy •Massey, WilliamS. McCoy, Dorothy Low, Emmet F., Jr. Machedon, Matei Manoly, Bruce E. Masson, David R. *McCoy, Peter A. Low, Marc E. Machover, Maurice Mansfield, Maynard J. Massoni, Daniel McCoy, Robert A. Lowe, Bruce D. Mack, John E. Mansfield, Ralph *Masten, J elf P. McCoy, Thomas L. Lowe, Peter G. Mack, John Michael Mantel, Harold John Masters, Harold U. McCray, Patrick D. Lowengrub, Morton Mackenzie, Kirill C. H. •Mantini, Lisa Masterson, John T. McCrea, Michael M. Loxton, John Harold MacKenzie, Robert E. Marble, Robert P. Masumoto, Makoto McCready, Robert R. •Loy, Richard J. Mackey, Michael C. Marcati, Pierangelo A. Masunaga, David K. McCreary, Paul R. Marchand, Margaret 0. •Matala-aho, Tapani McCulloh, Leon R. Marchesin, Dan Matchett, Andrew J. McCullough, Darryl Mather, Bertha W. McCurley, Kevin Snow AMS CENTENNIAL RESEARCH Marchiafava, Stefano Marcus, Brian Harry Mathews, John H. McDaniel, Andrew FELLOWSHIP CONTRIBUTION Marcus, David J. Mathis, Frank H. McDonald, Janet IN MEMORY OF Marcus, Leo G. Mathsen, Ronald M. *McDonald, John N. ROGER C. LYNDON Marcus, Michael B. Matijevic, Jacob R. McDonough, J. M. Anthony R. McGarry, Dorothy Leo P. Comerford, Jr. Marcus, Morel Moshe Matlak, Marcus, Steven I. Matovsky, John-Anton McDonough, Joseph Michael Peter L. Duren Margerum, Eugene A. Charles McDuff, Dusa Carl H. Fischer Margosian, Zaven Matsko, Vincent J. •McGarry, Dorothy Jim and Jane Kister Margulies, William Matsuda, Shigeo McGavran, Dennis R. Cecil J. Nesbitt Marhuenda, Francisco Matsumoto, Yukio McGee, Robert I. B. A. Taylor Maria, May H. Matsumura, Hideyuki McGehee, 0. Carruth Matsunaga, Teru *McGehee, Richard P. Leon P. Zukowski Marin, Irwin C.

880 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS Centennial Research Fellowship Fund

McGibbon, Charles A. Meserve, Bruce E. Miller, William David Monk, J. Donald eMuder, Douglas J. McGill, Suzanne Mess, Geoffrey Miller, William V. Monleon-Pradas, Manuel Mueller, Bruno J. W. McGonigle, Timothy P. Metas, Nick Miller, Zevi Monroe, Ted R. Mueller, James R. McGovern, Richard J. *Metivier, Michel Millett, Kenneth C. Montaldi, James A. Mugele, Raymond A. McGowan, Jeffrey K. Metropolis, Nicholas C. Mills, Janet E. Montanari, Daniele •Mulase, Motohico McGuinness, Francis Oisin Metzen, Gerhard Mills, Stuart E. Montgomery, Deane Mulder, Henry Martyn Mcintosh, William D. Metzler, Richard C. Mills, Susan Rose Montgomery, Hugh L. •Muldoon, Martin E. Mciver, Jeffrey L. Meuser, Diane Mae Milman, Mario *Montgomery, M. Susan *Muldowney, James S. •McKay, Brendan D. •Mewing, Robert •Milne, J. S. Montgomery, Peter L. Muller, D. E. McKay, James H. Meyer, Burnett C. •Milne, Stephen C. •Montgomery, Philip R. *Muller, George M. McKay, Thomas G. Meyer, Donald V. Milner, Eric C. Montgomery, Richard W. Muller, Gert H. McKean, Henry P., Jr. Meyer, Herman •Milner, Fabio A. Montgomery, W. Duane Mullikin, Thomas W. McKenzie, Martin J. Meyer, Jean-Pierre G. Milnor, John W. Monticone, Leone C. Mullin, Albert A. McKenzie, Ralph N. Meyer, Kenneth R. •Mimar, Arman Moon, Kyung-Ho *Mullis, James W., Jr. McKinney, Richard L. •Meyer, N. Christian, Jr. Mims, Edgar H. Moon, Myung-Suk Mullis, Robert Harvey, Jr. McLarnan, Timothy J. Meyer, Paul R. Mimura, Mamoru Mooney, John J. *Mulry, Mary H. *McLaughlin, Harry W. *Meyer, W. Weston Minac, Jan Moons, Theodoor M. Mundt, Marlon P. McLaughlin, Jack E. Meyerhoff, Robert *Minagawa, Takizo Moore, C. Edward Munemasa, Akihiro McLaughlin, Joyce R. Mez, Hans-Christian Minda, C. David Moore, Charles Nelson Munkholm, Hans J. McLaughlin, Renate •Miamee, Abolghassem Minehart, Deborah Fairley Moore, Danny J. Munoz, Edgar McLean, Jeffery Thomas Miao, Lung-Chi Minemura, Katsuhiro Moore, James Andrew Munoz, Miguel-C McLeod, Edward B., Jr. Michael, Ernest A. Mines, Ray •Moore, Omar K. Munoz-Porras, Jose M. McLeod, Robert M. •Michael, Mark Ming, Ronald W. Moore, Richard A. Munroe, M. Evans McMillan, Audrey W. Michael, T. S. Min-oo, Maung Moore, Robert H. Murakami, Shingo McMillan, Brockway Michael, William A. Minsker, Steven Moore, Robert Laurens Murata, Hiroshi McMillan, Daniel R., Jr. Michaux, Christian Min tel, Ernest J. •Moore, Robert T. Murdoch, David C. McMillan, Evelyn R. de-Michele, Leonede Minton, Roland B. Moore, Rufus A. Murphy, Donald P. McMillen, William Robert Michiaki, Watanabe *Miranda, Rick Moore, William E. Murphy, Grattan P. McMinn, Trevor J. Michler, G. Mirchandaney, Arjan Sobhraj *Mora, Xavier Murphy, Katherine Adele McMurtrie, Kenneth A. •Michor, Peter Mirelli, Vincent Moran, Charles W. Murphy, Paul F. McNeill, Robert B. Mickens, Ronald E. Mirkovic, Ivan Moran, William Murphy, R. B. McNulty, George F. •Middleton, David Mirsky, Norman D. Morawetz, Cathleen S. Murphy, Thomas N. McNulty, Nieves Austria Miekisz, Jacek Mishra, Sudhakara Mordeson, John N. Murphy, Timothy Sean McOwen, Robert C. Mielke, Marvin V. Mislin, Guido Moretz, Marjorie A. Murray, Francis J. McQueen, E. Tye Mielke, Paul T. Misra, A. K. Morgan, Christopher L. Murray, G. Graham McRae, Vincent V. *Mielke, Steven L. Misra, Prabudh Ram Morgan, Frank Murray, Margaret A. M. McShane, Edward J. •Mientka, Walter E. Mitchell, A. Richard *Morgan, John W. Murre, Jacob P. Meacham, Robert C. Miesner, Walter Mitchell, Alan R. Morimoto, Akihiko Muto, Hideo Mead, David G. •Migliore, Juan C. Mitchell, James C. Moriy6n, Roberto Muto, Yosio Meadows, Douglas Shelby Mignot, Fulbert Mitchell, Josephine M. Morley, Larry J. Myers, Dale W. Meadows, Lawrence F. Mihalik, Michael L. Mitchell, Stephen Ames Morrel, Bernard B. Myers, Donald E. Meagher, Jack R. Miklavcic, Milan Mitchell, Stephen G. •Morris, Alun 0. Myers, Earle F. Meakin, John C. *Mikolajczak, Boleslaw Mitchem, John A. Morris, L. E. Myers, John R. •Meaney, Christopher Mikolic-Torreira, Igor •Mitro, Joanna B. Morris, Peter C. Myers, Russell W. Mears, Florence M. •Milcetich, John G. *Mittal, D. M. Morrison, David R. Myerson, Gerald Meder, Albert E., Jr. Miles, E. P., Jr. Mityagin, Boris Morrison, Evelyn J. •Mylvaganam, Kanaga Medhin, Negash G. *Miles, Philip E. Miura, Robert M. •Morrison, Ian L. Sabapathy Meeker, Loren David Miles, Thomas J. Miyadera, !sao Morrison, John A. Myrvold, Wendy J. Meilan, Gerard Miletta, Peter D. Miyahara, Yoshio • Morrison, Kent E. •Naatanen, Marjatta Meir, Amram Milici<\ Dragan Miyakawa, Tetsuro Morrison, Michael A. Nachman, Louis J. Meisner, Morris J. Milin, Lazar Miyazaki, Ken-Ichi Morrison, Sally D. *Nadel, Mark E. Meister, Erhard V. Millar, Robert F. *Mizel, Victor J. Morse, Burt J. Nagahara, Takasi Meixner, Th Millar, T. S. Mizumoto, Hisao Mortensen, Jeffrey W. Nagai, Osamu Mejia, Raymond Miller, D. D. Mizuno, Hirobumi Moschovakis, Joan Rand Nagano, Tadashi Mejlbo, Lars C. Miller, Dale A. Mlitz, Rainer Moschovakis, Yiannis N. Nagao, Hirosi •Mekler, Alan H. Miller, David E. Mochizuki, Horace Y. Moscovici, Henri Nagasaka, Kenji Melin, Anders E. Miller, Donald S. Modica, Luciano Moscovitz, Hanna Nagase, Michihiro •Melrose, Gordon Miller, Erik A. Moen, Courtney H. Moser, Joseph G. •Nagata, K. Wayne Melrose, Richard B. Miller, Forrest R. *Moena, Ricardo Moser, Jiirgen K. Nagel, Alexander J. Melvin, Paul M. Miller, Haynes R. Moerdyk, !eke Moser, Lucy I. *Nagel, Bengt C. H. Melzi, Giovanni Miller, Hugh D. B. Moghaddam, Mohammad Moser, William 0. J. Nagle, R. Kent Memory, Margaret C. Miller, Jack M. Reza R. Mosher, Lee D. Nagurney, Anna B. Menconi, Mario Miller, James Curtis Mohamed, I. J. Mosier, Ronald G. Naiman, Daniel Q. Mendelsohn, Eric Miller, John G. Mohamed, Saad Moss, Kenneth N. Naimpally, Somashekhar A. Mendelssohn, Roy •Miller, John J. Mohanty, Radhagobinda Moss, Lawrence Stuart Nairn, Dean C. Mendoza, Gerardo A. Miller, Kenneth S. Mohapeloa, Khomo T. S. Mostow, George Daniel Najarian, John P. Menezes, Lucia S. Miller, Matthew •Mohar, Bojan Motegi, Masanori Nakagawa, Kiyokazu Menninga, Nadine L. Miller, Michael J. Mohler, Lee K. Motto, Michael H. Nakagawa, Yoko Merindol, Jean-Yves Miller, Nicholas S. Moise, Edwin E. de Mottoni, Piero L. Nakamura, Masahiro *Merkel, Rudolph B. Miller, Richard Alan Moller, Raymond W. •Moulden, Trevor H. Nakamura, Riichiro Merriell, David M. *Miller, Robert N. Molzon, Robert E. Mount, Kenneth R. Nakamura, Yoshimasa Merrien, Jean Miller, Stephen S. Mond, Bertram Moy, Allen Nakanishi, Yasutaka Merryfield, Kent G. Miller, Timothy L. Mong, Christopher Chsiu Moyls, Benjamin N. Nakano, Kazumi Mertens, John R., Jr. Miller, Willard, Jr. Monheit, Lilly A. Mozes, Shahar Nakata, Masaomi

SEPTEMBER 1989, VOLUME 36, NUMBER 7 881 AMS Centennial Research Fellowship Fund

Nakata, Mie eNg, Sze-Kui Oberg, Edwin N. Oodaira, Hiroshi Panchapagesan, T.V. Namba, Kanji Ng Wong Hing, John Dilwyn Oberguggenberger, Michael B. Oohashi, Tsunemichi Pandit, Onkar Nath Namioka, Isaac Nguyen, Bao Gia Obermayer, Judith H. Ooms, Alfons I. •Pankin, Mark D. Namkoong, Kyu-Oh Nguyen, Diing X. Oberschelp, Walter Oono, Yoshitsugu •Pantie, Drazen Nance, Dana W. Nguyen, Hung Trung de las Obras, Carmen •Opfer, Gerhard H. •Paolucci, Michael J. •Nandakumar, N. R. Nichols, Edward Ochanine, Serge Oppenheim, Joseph H. Papageorgiou, Nikolaos S. Narang, Deborah Lynn Nichols, Eugene D. Ochiai, Takushiro Oppenheimer, Seth F. Papangelou, Fredos Narang, Kamal •Nicholson, W. Keith Ochs, Robert L., Jr. Oprea, John F. Papanicolaou, George C. Narayanaswami, P. P. N[ Chuiv, Nora Ocken, Stanley Orellana, Chacin Mauricio Papantonopoulou, Aigli Narcowich, Francis J. Nickel, James A. Ocneanu, Adrian Orey, Steven Helen Narushima, Hiroshi Nickerson, Helen K. Ocone, Daniel L. Orihuela, Jose Papas, Theodore Thomas Nash, Peter Nico, William R. Oda, Tadao Orlik, Peter P. Papistas, Athanassios Nash, Stephen G. Nicodemi, Olympia E. O'Dea, Paul J. O'Rourke, Joseph Pappas, Peter C. Nashed, M. Zuhair Nicol, Sherrie Jean Odencrantz, Kristiana Orr, Martin Pappas, Richard C. Nash-Williams, *Nicolaenko, Basil Odlyzko, Andrew M. Orr, Richard J. Parchment, Osborne C. Crispin St J. A. Nicolas, Jean-Louis •Odom, Earl T., Jr. Orsted, Bent Pardee, Otway O'M •Nastold, Hans-Joachim Niederhausen, Heinrich Odoni, R. W. K. Oruc-Yaman, Melda •Pareek, Chandra Mohan Nataro, Dean C. Niedzwecki, G. P. Oehmke, Robert H. Osborn, J. Marshall •Pareja-Heredia, Diego Nath, Radha G. •Niefield, Susan B. •Oeljeklaus, E. *Osborn, John E. Parish, James L. Nathanson, Melvyn B. •Niemeyer, Horst F. Oertel, Ulrich •Osborn, T. A. Park, Chull Nation, James B. Nievergelt, Yves •O'Farrell, Anthony G. Osborne, Mason S. Park, Hong-Suh Naugle, Norman Wakefield Niino, Kiyoshi Ogawa, Hajimu Osborne, Michael Robert Park, Jae Keol Navarro, Francisco J. Nirenberg, Louis Ogg, Andrew P. *Osborne, Richard P. Park, Jong Geun Naveira, Antonio Martinez Nishida, Takaaki Ogielski, Andrew T. Osgood, Brad G. Park, Kwang S. Navot, Israel Nishikawa, Seiki Ogle, Crichton •Osgood, Charles F. Park, Sehie •Nayak, M. K. Nishiura, Togo Oguchi, Kunio O'Shea, Donal B. Park, Young Soo Nayar, Bhamini M. •Nishiwada, Kimimasa Ogus, Arthur Oslon, Steve G. Parker, David W. Nayar, Brij M. Nisnevich, Yevsey A. Oh, Hi-Jun Osofsky, Barbara L. Parker, Ellen Maycock Nduka, A. Nissim, Leonard J. •Oh, Yong-Geun Osserman, Robert Parker, Elwood G. Neeb, Donna M. Nitecki, Zbigniew H. Oharu, Shinnosuke Osterburg, James Parker, Francis D. Neggers, Joseph Nitsche, Johannes C. C. Ohwaki, Shin-lchi Osterwalder, Konrad Parker, George D. Negishi, Norio Nitzberg, Mark J. Oikawa, Kotaro Ostrom, T. G. Parker, S. Thomas Negrepontis, Stylianos *Nivat, Maurice P. •Oka, Shinpei Oswald, Urs Parker, Thomas H. Negro, Angelo L. Niven, Ivan Okada, Ikutaro •Ota, Clem Z. Parker, Willard A. Negron, Pablo Victor Njastad, Olav Okada, Masami 6ta, Schoichi Parks, Harold R. •Neher, Erhard Nkashama, Mubenga Ngandu •Okada, Mitsuhiro Otal, Javier Parks, Teresa A. Nehs, Robert M. Noakes, J. L. Okada, Susumu Otermat, Scott C. Parr, James T. Neidhardt, Arnold L. Nobusawa, Nobuo *Okamoto, Kiyosato Otero, Maria Carmen Parrott, David Neidinger, Richard Dean *Nocilla, S. Okayasu, Takateru Otsu, Yukio *Parry, Walter R. Nel, Louis D. Noel, Guy G. J. Okoh, Frank Otsuki, Nobukazu Parry, William •Nelson, Carla A. Noguchi, Hiroshi Okuyama, Akihiro Otway, Thomas H. Parsons, Charles D. Nelson, David •Noguchi, Junjiro Olafsson, Gestur Oursler, C. C. Parsons, John D. Nelson, Edward Noguchi, Mitsunori Oldham, Frank Ernest Overton, Steve Randall *Parter, Seymour V. •Nelson, George C. Nogura, Tsugunori *Oler, Norman Owen, David R. Pascali, Dan D. •Nelson, Paul, Jr. Nohel, John A. Olesen, Mogens Norgaard Owings, James C., Jr. Paschke, William L. Nelson, Robert R. Nolan, John P. Oliger, Joseph E. Oxley, Theron D., Jr. Pascual-Gainza, Pere Nelson, William Nold, Annett Olin, Robert F. Oyabu, Takashi Pascuas, Daniel Nemethi, Csaba Noll, Landon Curt *Oliver, Fatma Ozaki, lsao Pascucci, Richard S. •Neri, Umberto *Noonburg, Virginia A. •Oliver, Henry W. Ozsvath, Istvan •Pasik-Duncan, Bozenna J. Nerode, Anil Noor, Khalida Inayat •Oliver, Robert A. Pacella, Filomena •Pasini, Antonio Nesbitt, Cecil J. •Norden, Jeffrey S. Olivier, Reinhard M. Pacheco-Castelao, Jose M. Paskewitz, Charles W. Nesin, Ali H. Nordgren, Eric A. Olmstead, P. S. •Paciorek, Joseph W. Passerini, Henry J. Neubauer, Gerhard J. Nordhaus, Edward A. Olmsted, John M. H. Packer, Judith A. Passman, Donald S. •Neuberger, John W. Norman, Francis Alexander Olsen, Martin Pade, Offer Passty, Gregory B. Neugebauer, Christoph J. Norman, R. Daniel Olshen, A. C. Padma, Narasimhachari •Pastijn, Francis J. Neumann, Bernhard H. Northcutt, Robert A. Olson, Dwight M. Pagano, Miriam E. Pastro, Pier-Ivan Neumann, Michael M. Norton, Alec Olson, Loren D. Page, Stanley S. Pathak, Vijay Damodar Neumann, Peter M. Notarnicola, Filippo Olver, Peter J. Paige, Eugene C., Jr. Patil, Dattatraya J. •Neumann, Walter David N ottrot, Roel Oman, John Arthur Paige, Lowell J. *Patterson, Larry A. Neuwirth, Lee P. Novikoff, Albert B. O'Meara, Kevin C. Paisner, Helen L. Patterson, Nick J. Nevai, Paul •Nowell, William 0., Jr. O'Meara, 0. Timothy Pak, Jingyal Patterson, Samuel E. •Neves, Vitor M. C. Nucci, Maria-Clara Omori, Hideki •Palagallo, Judith A. Patton, Charles M. Neveu, Jacques Nulton, James D. Onat, Emin T. Palais, Eleanor G. Patty, C. Wayne Neveu, Lawrence V. Nummela, Eric C. Ondarza, Nelson R. Palka, Bruce P. •Paulling, John M. B. Newberger, Stuart M. Nunke, Ronald J. O'Neil, Philip J. Pallara, Diego Massimo •Paulowich, David G. Newcomb, Lynn T. Nunley, Charles L. O'Neill, Anne F. Pallaschke, Diethard •Paur, Sandra 0. Newlander, August, Jr. Nussbaum, Roger D. O'Neill, Barrett Palm, Andrew C. •Pavlicek, Glenn H. Newman, Morris Nusse, Helena E. O'Neill, Bernard V., Jr. Palm, Mark A. *Pavlopoulos, Haralabos Newstead, Peter E. Nutt, Michael D. Ong, Boon-Hua Palmer, Edgar M. Pawelke, Siegfried H. R. Newton, Mervin E. •Nyman, Philip D. Onieva, Victor M. Palmer, John Bergin Payne, Lawrence E. Ng, BartS. Oakland, David 0. Onishi, Hironori Palmer, John N. Payne, Stanley E. eNg, Boon-Yian Oates-Williams, Sheila Ono, Takashi Palmer, Theodore W. Pazy, Amnon J. eNg, Eugene Kwan Sang Obaid, Samih A. Onose, Hiroshi Pan, Kuo Chen Peabody, Mary K. Ng, Ho Kuen Obata, Morio Onstott, Edward D. Pan, Ting K. Pearce, Kent

882 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS Centennial Research Fellowship Fund

Pearcy, Carl M. *Petulante, Nelson R. Pohst, Michael E. Promel, Hans Jurgen Rassias, Themistocles Pears, Alan R. Peyerimhoff, Alexander Polachek, Harry • Propes, J. C. Michael Pearson, Robert W. Peyrovian, Reza Polemarchakis, H. Protas, David S. *Rathbun, Ethel Pearson, Stephen C. Pfeffer, Washek F. Polimeni, Albert D. Protopopescu, V. Ratiu, Tudor Stefan *Peart, Paul B. Pfeiffer, Paul E. *Polites, George W. Protter, Murray H. Ratliff, Louis J., Jr. Peccati, Lorenzo Pflaum, C. W. •Polking, John C. Protter, Philip E. Ratner, David A. Peck, Emily Mann Pflug, Peter Pollack, Richard •Proulx, Viera Kriianova Riitz, Jiirg J. Peck, N. Tenney Pfluger, Albert Pollatsek, Harriet S. Provencher, Normand Rausen, John Peck, Paul S. Pham, Tuan Dinh Pollingher, Adolf Pruitt, William E. Raussen, Martin Peck, Vincent Christopher Phan, Kok W. Polonsky, Ivan P. Pruss, Jan Rave, Werner J. Peckham, Bruce B. Phanord, Dieudonne D. Ponce, Gustavo Alberto Prussner, Laird Drew Ravenel, Douglas C. Pedersen, Edward A. Pheidas, Athanasios C. •Ponomarev, Paul Przytycki, Jozef H. Rawnsley, John H. Pedersen, Franklin D. Phelps, Robert R. Pons, Montserrat Pucci, Patrizia Rawsthorne, Daniel A. Pedersen, Henrik Phili, Christine Melle Ponthieux, Delores Marie Puerta, Fernando Rayburn, Marlon C. •Pedersen, John F. •Phillips, Anthony V. Pool, James C. T. Puigbo, Jaume Vila Read, Dwight Pedersen, Katherine L. Phillips, Ralph S. Poole, George D. •Puppe, Dieter •Read, Thomas T. Peek, James M. Phillips, Richard E. Poon, Yat Sun Pursell, Lyle E. Reade, Maxwell 0. Pego, Robert L. Piacentini, Giulia Maria Poorman, Alan G. Putnam, Alfred L. Reardon, Philip C. Peiffer, Barry L. •Piacenza, Robert John van der Poorten, Alfred J. *Puttaswamy, T. K. •Rebarber, Richard L. Peitgen, Heinz 0. Pianzola, Arturo J. Pop-Stojanovic, Zoran R. Pym, JohnS. Reber, Douglas C. Peixoto, Mauricio M. Piatetski-Shapiro, I. Poris, Michael J. Quan, Loi T. *Rechard, Ottis W. Peleg, Bezalel Piazza, Barry L. Poritz, Alan B. *Quigley, Frank D. Reddy, William L. Peletier, Lambertus A. Picard, Rainer H. Port, Sidney C. Quinn, Declan P. F. Redfield, Robert H. •Peligrad, Coste! •Piccinini, Renzo A. Porte, Jean Quinn, Frank S., III Redheffer, Raymond M. •Peligrad, Magda Piccinni, Paolo • Porter, Gerald J. Quinn, Grace S. Redlin, Lothar H. •Pelletier, Donald H. Pichaud, Joelle •Porter, James F. Quinn, Joseph E. Redmond, Don *Pellikaan, Ruud Pichet, Claude Porter, Kathryn Frost Quinn, Michael Paul Redner, Richard A. Pence, Dennis D. Pickel, Paul Frederick Porter, Richard D. Quint, Richard A. Reed, David L. •Pengelley, David John •Picken, David Paul Porter, Willis B. Quintana, Ricardo B., Jr. Reed, Robert E. Pennell, Stephen A. Picoult-Hart, Darri C. Portinari, Joao C. •Quinto, Eric Todd Reedy, Christopher L. Penner, Robert Clark •Piene, Ragni Poschel, Jurgen Quiring, Donald K. Rees, Elmer Penney, Carol W. Pierce, John Festus Posey, Eldon E. Rabau, Patrick F. Rees, Mina S. Penney, David E. Pierce, Richard S. Post, Karel A. Rabier, Patrick J. Rees, P. K. Pennisten, John W. Pierce, Stephen J. Pothen, Alex Rabinovitch, Peter Reese, Matthias F. Pepin, Jacinthe C. *Pietrowski, Alfred Potter, Amy M. Rabinowitz, Paul H. Reese, Matthias F., III Pepper, Paul M. Pigozzi, Don L. Potter, Walter M. Radjabalipour, Mehdi Reese, Richard H. Perel, William M. Piirila, Olli-Pekka Potts, Donald H. Radkowski, Alfred F. Reese, Sylvester Perelli, Alberto Pila, Jonathan S. Poulin, Bernard Radulescu, Nicholas Andrew Reetz, Dieter A. Perera, Shelton Pillay, Anand Poulsen, Ebbe T. Radzikowski, Marek J. Reeves-Hicks, Ernestine Perera, Shelton Pilz, Gunter Pourciau, Bruce Hunter Radzikowski, Pawel *Regan, Francis *Pericak-Spector, Kathleen A. Pimbley, George H., Jr. Pour-El, Marian B. *Rager, John E. Rehmann, Ulf Perkel, Manley Pinero, Alfredo Pouzet, Maurice Raggio, Guido A. •Reich, Daniel Perkins, Peter Pinkus, Allan M. Powell, C. Spencer •Rahman, Mizanur Reichaw, Meir Perlis, Robert V. Pinney, Karen R. *Powell, Russell E. Raisbeck, James G. •Reichel, Lothar Perlman, Sanford Pinsky, Mark A. Power, Stephen Charles •Rajca, John F. Reid, James D. Pernice, Michael Pinsky, Ross George Powers, Morris Walton Rajnak, Stanley L. Reid, K. Brooks Perovic, Miodrag Pippert, Raymond E. Powers, Robert T. Rakesh Reid, Les Perrine, Serge Piranian, George •Powers, Victoria Ann Rail, Louis B. •Reid, Talmage James Perry, Peter Anton •Pirraglia, Joseph A. Powls, Keith W. Ralph, William J. Reid, William H. Perry, William L. Pisanski, Tomaz Pradines, Jean Ralston, James V. Reilly, Ivan L. Persek, Stephen C. Pistone, Giovanni • Praeger, Cheryl E. Ram, Ram Bachan Reilly, Norman Raymond Persson, Ulf Pitcairn, Joel Prakash, Deepak *Ramachandran, Doraiswamy Reineck, James F. Persson, Ulf Pitcher, Everett Prakash, Jagdish Ramaley, James F. Reiner, Irma M. Pertica, Horacio N. Pitt, Loren D. Pratt, Vaughan R. *Ramalho, Margarita Reinhardt, Elsi A. Pervin, William J. Pittnauer, Franz Preiss, Mitchell Paul Ramanujan, Melapalayam S. Reinhardt, William N. Pesotan, Hoshang Pitts, Andrew M. Preissendorfer, Manfred W. Ramaroson, Francois Reise!, Robert B. Pestana, Dinis Duarte Pitts, David R. Preston, Gordon B. Ramirez, Arturo Flores Reissner, Eric Petermann, G. E. Pixley, Carl P. Presutti, Errico Ramm, Alexander G. Reitwiesner, George W. Peters, Craig Steven Pixton, Dennis G. *Prevots, Claude Ramsay, Bruce E. Rejto, Peter A. Peters, James Vincent Pizer, Arnold K. Price, Charles M. Ramsay, Keith A. Rembis, Frederick C. Peters, John E. •Plachky, Detlef Price, G. Baley Ran, Andre C. M. Rempel, Richard S. Peters, Klaus Plank, Donald L. Price, John F. •Randall, A. Duane Remus, Dieter Petersen, Bent E. Plano, Richard A. Price, Justin J. Randol, Burton S. Renardy, Michael Petersen, Peter Plante, Joseph F. Price, Roderick A. Raney, George N. •Renault, Jean N. Petersen, Troels Platek, Richard A. Price, Thomas E., Jr. •Rangaswamy, K. M. •Renegar, James M. Petersen, Wesley P. Pless, Vera S. Price, Thomas M. Range, R. Michael Renner, Lex E. Peterson, Allan C. *Plohr, Bradley J. •Priestley, Hilary A. •Rankin, R. A. Renno, James G., Jr. Peterson, Charles L. Plotnick, Daniel H. •Prill, David D. Rankin, Samuel Murray Renshaw, James H. Peterson, Gary L. Plumeri, Charles John Prime, Mirko Rankin, Stuart A. •Repka, Joe Peterson, William C. Plymen, Roger J. Primer, Jeremy D. Rao, Ranga R. Resch, Richard I. Petro, John W. Podber, David P. Prince, Geoffrey Eamonn *Rao, Veldanda V. Restrepo, Guillermo Pettet, Martin R. Podio-Guidugli, Paolo Prindle, John C. •Raphael, Louise A. *Retherford, James R. Petticrew, James W. Poe!, Mannes Proctor, C. Wayne Rapp, P. E. Retnam, P. Xavier Raja Petty, Clinton M. Pogu, Marc •Proctor, Robert A. Rascle, Michel Revesz, Michael Bela

SEPTEMBER 1989, VOLUME 36, NUMBER 7 883 AMS Centennial Research Fellowship Fund

Reyes, Edgar N. Roberts, Charles E., Jr. Rosati, Mario Rubin, Jean E. Salamanca-Riba, Susana Reyes, Francisco G. Roberts, Dorothy K. Rose, Donald J. Rubin, Karl Alicia Reynolds, David W. Roberts, Howard M. •Rose, Harvey E. Rubin, Robert J. Salamin, Eugene Reynolds, Donald F. Roberts, Jean E. Rose, N.J. Rubinstein, Joachim H. •Salamon, Dietmar A. Reynolds, Robert J. Roberts, Joel L. Roselle, David P. Rubinstein, Robert Saleem, Mohammad Reynolds, William F. Roberts, Joseph B. Roseman, Joseph J. Rudin, Bernard D. Salehi, Ebrahim •Reznick, Bruce A. Roberts, Lawrence Gordon Rosen, Lon M. •Rudin, Mary E. Salisbury, Thomas S. Rhai, Tong-Shieng •Roberts, Leslie G. Rosen, Michael I. Rudnick, Karl Salkind, William Rhee, Choon Jai Roberts, Mark Rosen, Ned Ira Rudolph, Daniel Jay Sallee, G. Thomas Rhodes, Frank Roberts, Richard C. Rosen, William G. Rudolph, Lee N. •Sallee, John F. Rhodes, Patricia V. Roberts, Stephen G. Rosenbaum, Robert A. Ruelle, David P. Salles, Maurice Riaza, Roman Robertson, Alexander P. Rosenberg, Burton J. Ruess, W. Saltiel, Leon Riazi-Kermani, Mohammad •Robertson, James B. Rosenberg, David Ruh, Ernst A. Saltman, David J. Ribes, Luis Robertson, Malcolm S. Rosenberg, Ivo G. Ruijsenaars, Simon Norbert Salvadori, Anna Rica DaSilva, Amaro J. Robinson, Clark Rosenberg, Milton Ruiz, Alberto Salzberg, Pablo M. Ricci, Fulvio Robinson, Daniel A. Rosenberg, Steven Ruiz, Ceferino Samelson, Christopher L. Ricci, Michael G. Robinson, Derek J. S. Rosenblatt, Joseph Max Rulla, James L. Samelson, Hans Ricci, Stephen J. Robinson, Donald W. Rosenblum, Marvin Rumbos, Adolfo J. Sampson, Gary Rice, Henry G. Robinson, E. Arthur, Jr. Rosenfeld, Gerald Rumely, Robert S. •Sampson, Gilbert L. Rice, John William Robinson, G. de B. Rosenfeld, Norman S. Rumsey, Howard C., Jr. Samuel, Pierre •Rich, Andrew Robinson, Geoffrey Raymond Rosenfeld, Ronald L. Runck, Paul Otto Sanchez-Vazquez, Gonzalo Richard, B. K. •Robinson, Helen Drummond Rosengard, Douglas J. Rupp, Russell D. •Sand, Mark P. *Richards, Donald St P. •Robinson, Karl H. Rosenlicht, Maxwell A. •Ruscheweyh, Stephan Sanders, B. L. Richards, Franklin B. Robinson, Paul Lee Rosenstein, George M., Jr. Rush, David Eugene Sanders, Georgia E. Richards, John F. Robinson, Raphael M. Rosenthal, Arthur J. •Rushanan, Joseph J. Sanders, Jan A. Richards, Pamela C. Robinson, Sam L. *Rosenthal, David S. Ruskai, M. Beth Sanders, Marc D. Richardson, Henry R. Robinson, Stanley A. Rosenthal, Eric S. Russell, David Martin Sanders, Robert W. •Richardson, Roger W., Jr. Robinson, Susan D. Rosenthal, Erik J. •Russell, Dennis C. Sanderson, Brian J. Richert, Hans-Egon Robkin, Eugene E. Rosenthal, Haskell P. Russell, Gary L. Sanderson, Donald E. Richert, Norman J. Rocha, Luiz F. •Rosenthal, Kimmo I. Russo, Dominick A. Sanderson, John M. Richmond, Glayvera Rochberg, Richard H. Rosenthal, Peter Russo, Paula A. Sandomierski, Frank L. Richmond, Lawrence B. Rochon, Donna F. Rosenthal, Steven M. Rutland, Leon W., Jr. Sands, Jonathan Winslow Richter, Guenther E. Rockett, Andrew M. Rosenthal, William E. Rutledge, Dorothy S. Sangren, Ward C. Richter, Horst P. Rod, David L. Rosier, Ronald C. Rutschman, David H. Sangwine-Yager, Jane Richter, Linda Jean C. Rodman, Leiba Ross, Bertram Rutter, J. W. Rosamund Richter, Michael M. • Rodrigues, J. F. Ross, David A. Ruttimann, Gottfried T. Sant, Lino Richter, Stefan Rodriguez, Gilmar Ross, J. Andrew Ruymgaart, Peter A. Santalo, L. A. Richtmyer, Robert D. Rodriguez, Mauro Efrain C. Ross, Kenneth A. Ruzicka, John F. •Santana, Victor Espino Rickart, Charles E. •Rodriguez, RubiE. Ross, Paul Ryan, Donald E. Santos Filho, Jose Rickey, V. Frederick Rodriguez, Sanjurjo Jose Rossa, Robert F. Ryan, Frank B. Ruidival S. D. Rickman, B. Rodriguez-Exposito, Jose Rossi, Guido A. Ryan, Kevin M. Sanz-Serna, J. M. Riddle, Malcolm Lee •Rodriguez-Anger, Rita V. Rossi, Hugo Ryan, Michael D. Sanz-Sole, Marta *Ridolfo, Anthony S. Roe, John Rossler, Otto E. Ryan, Patrick J. Saphar, Pierre David Rieffel, Marc A. *Roe, Robert P. Rosson, John Ryan, Peter M. Sarason, Donald E. Rieger, Georg J. Roels, Jacques Albert van Rossum-Wijsmuller, Rychlik, M. Sarason, Leonard Riemen, William P. Rofman, Edmundo Marijke Rydeen, Clarence F. Sarian, Edward Riemenschneider, Oswald Rogawski, Jonathan David Rost, Markus Ryeburn, David Sario, Leo Riesel, Hans I. Rogers, Jack W., Jr. Rota, Gian-Carlo Rykken, Charles John Sarrat, Charles F. Rigdon, Robert D. Roggenkamp, Klaus W. Roth, Richard L. Sabbagh, Gabriel Sasaki, Takeshi •Riihentaus, Leo Juhani Rognes, John Roth, Rodney J. Sabharwal, Ranjit S. Sastri, Chelluri C. A. •Rijnks, H. Rogowski, Paul B. Rothaus, Oscar S. Saccoman, John J. Satake, lchiro Rike, Thomas A. Rohatgi, Vijay K. Rothberger, Fritz Sachs, Jeffrey R. Sathaye, Avinash *Riley, Geoffrey William Rohl, Frank D. Rothman, Neal J. Sachs, Robert L. Sato, Hiroki Rinaman, William C. Rohlfs, J iirgen Rothschild, Bruce L. Sacks, Paul E. Sato, Ken-iti Ringeisen, Richard D. Rohm, Dale M. Rothschild, Linda Preiss Sacksteder, Richard C. Sato, Shizuka Ringel, Gerhard Rohrlich, David E. Rottenberg, Reuven R. •Sadosky, Cora S. Sattinger, David H. Ringseth, Paul F. Roitman, Judith Rotthaus, Christel Sadun, Lorenzo A. Sauder, Dean L. •Rinne, Dan C. Rolf, Howard L. Rouche, Nicolas Saeki, Sadahiro Saul, Jean Claude Rio, Jose *Rolin, Jean-Marie Gerard Roush, Fred Saff, Edward B. Savariraj, G. A. Rio, Sheldon T. Roller, Towanna A. Rousseau, Cecil C. Sagan, Bruce E. Sawada, Hideki Rishel, Thomas W. Romanelli, S. Rousseau, Christiane •Sagong, Seok Sawyer, Eric T. Risnes, Martin Romanyuk, Leonid *Roussou, Athina Sah, Chih-Han Sawyer, Stanley A. Rittenhouse, Jean M. Romero-Fuster, Maria Rouys, Robert L. Sahab, Salem M. Saxton, Ralph Arthur Ritter, David L. Carmen •Rovnyak, James L. Sahoo, Prasanna Sayeki, Hidemitsu *Rivet, Roger Ronga, Felice L. L. •Rovnyak, Virginia G. Saigusa, Youichi Scalzo, Richard C. •Rizvi, Syed Mohammad Ronveaux, Andre Rowe, Niles W. Saito, Kazuyuki Scanlon, Jane Cronin Tariq Rood, John J. •Rowen, Louis Halle Saito, Kichi-Suke Scaramuzzi, Roberto Rno, Jung-Sik Roohan, James T. Roxin, Emilio 0. Saito, Shiroshi Scarborough, Steve Douglas Roach, Michael D. Rooney, Gerald E., Jr. Roy, Charles L. Saito, Yoshimi Scarpellini, Bruno J. Robacker, John T. Rooney, Paul G. Royden, Halsey L. Saitoh, Saburou Scarpi, Giambattista Robbins, David P. Roos, Bernard W. Royer, James Samuel Sakai, Fumio Scarsini, Marco *Robbins, Leon C., Jr. Roos, Guy Royster, Wimberly C. Sakai, Katsuro Schaal, Werner G. H. •Robert, Alain Roosenraad, Cris T. Ruben, Flores Espinoza Sakai, Makoto Schacher, Murray M. •Roberts, Anne Drinkwater Rosa, Alexander Ruberman, Daniel Sakuma, Motoyoshi Schachermayer, W.

884 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS Centennial Research Fellowship Fund

Schaefer, Paul T. Schoenenberger-Deuel, Seebeck, Charles L., III Shapley, L. S. Shultz, Frederic W. Schaeffer, John M. Johanna Seeley, Robert T. Sharma, P. L. Shultz, Harris S. Schaettler, Heinz M. Schoenfeld, Lowell Segal, Kevin Sharp, Henry, Jr. Shutt, Elsie G. *Schafer, Alice T. •Schoenwaelder, Ulrich F. *Segal, Sanford L. Sharp, Jack Carroll, Jr. Shwartz, Adam *Schafer, Richard D. Scholl, Anthony J. Segert, Jan Sharpe, Michael J. Sibille, E. Schaffer, Juan Jorge Scholz, E. •Sehgal, Sudarshan K. Sharpe, Richard W. Sibley, Thomas Q. *Schaffer, Steven Schon, Rolf Sehgal, Surinder Sharpton, John T. Sibner, Lesley M. Schafke, R. •Schonbek, Maria Elena *Sehgal, Virindra M. Shatz, Stephen S. Sibner, Robert J. Schapiro, Philip J. Schoof, Rene Sehnert, James Ellis Shaw, Guy B. Sichler, J. Schaps, Maika Elisheva Schori, Richard M. *Seid, Howard A. Shawcroft, Paul H. Siddiqi, Rafat N. Scharlau, Rudolf M. E. •Schottenloher, R. Martin Seidel, Eric Shea, Patrick J. Sidek, Halim Scharlemann, Martin G. •Schrauf, Geza H. •Seidel, J. J. Shearer, James W. Sidney, Stuart J. Schattschneider, Doris W. Schreiber, Bert M. Seidel, Johan J. Shearer, Michael Siegel, Alan Schatz, James R. Schreiner, Erik A. Seiden, Esther Sheehan, George •Siegel, Eli A. Schatzman, James Carl Schremmer, Fran~oise Seidman, Thomas I. Sheffer, lsador M. *Siegel, Paul H. Schatzman, Michelle Schrijver, Alexander Seifert, George Sheii-Small, Terence Brian Siegrist, Kyle T. Schauer, Richard L. Schroder, M. Seifter, Norbert eSheingorn, Mark Siemon, Helmut Schaumberger, Norman Schroeck, Franklin E., Jr. Seikkala, Seppo A. Shelburne, Brian J. Siemons, Johannes Schay, Geza Schroeder, Carolyn L. •Seiler, Wolfgang K. Shelly, Eugene P. Siersma, Dirk •Schechtman, Gideon •Schryer, Norman L. Sein, Hla Hla Shelly, Maynard W. •Sigal, Israel Michael •Schecter, Stephen Schubert, Cedric F. Sekigawa, Hisao Shelupsky, David I. Sigman, Karl Scheffer, Carel L. Schubert, David C., Jr. Sekino, Kaoru Shemanske, Thomas R. Sigrist, Francois Scheffer, Vladimir •Schue, John •Selby, Michael J.P. *Shen, Mei-Chang Sigurdsson, Gunnar Scheier, M. A. Schueller, George W. Seldin, Jonathan P. Shen, Yuan-Yuan Sigurdsson, Ragnar Scheim, David E. Schuett, Werner Seligman, George B. Shene, Ching-Kuang Sikorav, Jean-Claude Scheinberg, Stephen Schultz, Phillip Seligman, Mark L. Shepherd, J. C. Silberger, Allan J. Scheinerman, Edward R. Schulz, Friedmar J. *Seligson, Stuart A. Shepherdson,JohnC. Silberger, Donald Morison Schell, Emil D. •Schulze-Pillot, R. Selman, Alan L. Sherif, Nagwa *Silbert, Gary Allen *Scherkoske, Kenneth D. Schumacher, Carol S. Selmer, Ernst S. Sherk, F. A. Silver, Daniel S. •Scheurle, Jurgen K. Schumacher, Georg B. •Seltzer, Stanley E. Sherlock, Philip Thomas Silverman, Herb Schibell, Stephen T. Schumacher, Scott •Semadeni, Zbigniew W. Sherman, Clayton C. Silverman, Joseph H. Schiffer, Max M. Schumaker, John A. Sember, John J. Sherman, Gary J. *Silverman, Robert David Schiller, Ilya Schumaker, Larry Lee Semmes, Stephen William Sherman, Glen A. Silverstein, Martin L. Schiller, Ilya Schumitzky, Alan Sempi, Carlo E. Sherr, Joseph S. Silvia, Evelyn Marie Schiller, John J. Schunck, Brian G. Sen, R.N. Shi, Sheng G. Simas, David Schilling, R. J. Schupp, Paul E. Senechal, Lester J. Shiba, Masakazu *Simen, David C. Schillo, Paul J. Schurrer, Augusta L. Senechal, Marjorie Shibata, Masanori K. •Simion, Rodica E. Schirmeier, Horst Schuster, Seymour Senge, George Shibata, Yukio Simkani, Mehrdad Schleifer, Louis M. •Schutt, lngo Senger, Steven 0. Shibuya, Yhuji •simmons, Harold Schlesinger, Ernest C. Schwalbe, Daniel A. *Seppala, Mika Kristian •Shick, PaulL. Simms, David J. Schlessinger *Schwartz, Charles Freund Seppala-Holtzman, David *Shiffman, Bernard Sim6, Carles •Schlichenmaier, Martin Schwartz, Jacob T. •Sepulveda, Eric Shiffman, Max Simoes-Pereira, J. M. S. Schlick, Tamar Schwartz, Laurent Serapioni, Raul Shiflett, Ray C. Simon, Irnre Schlingmann, Dirk *Schwartz, Lionel Serbyn, William D. •Shifrin, Theodore Simon, Robert Schlipf, John S. Schwarz, Binyamin Serfling, Robert J. Shiga, Koji Simons, Lloyd D. Schmeelk, John F. Schwarz, Gerald W. Serizawa, Shozo Shih, Kuang-Yen Simons, Stephen Schmerl, James H. Schwarz, Thomas Serre, Jean-Pierre Shilling, Geoffrey B. Simpson, Henry Clark Schmets, Jean F. Schweiger, Fritz *Serrell, Robert Shimada, Nobuo Sims, Charles C. Schmetterer, Leopold K. Schweitzer, Eric Servatius, Brigitte Shimamoto, Don H. Sinclair, George Edward Schmickler-Hirzebruch, Schweizer, Berthold Servedio, Frank J. Shimizuike, Yuzi Singer, Isadore M. Ulrike Schweppe, Earl J. Sethian, James A. Shimura, Goro •Singer, Michael F. Schmid, Josef Schwietzer, Michael J. Sethuraman, J. Shin, Dong Sun Singer, Phyllis E. Schmid, Jurg Scoppola, Carlo M. Sevenster, Arjen Shin, Yong-Tae *Singer, Seymour *Schmid, Rudolf Scott, Damon Sever, Michael Shinohara, Yaichi Singer, William M. Schmid, Wilfried Scott, Leonard L., Jr. Sexauer, Norman E. Shiohara, Hiroshi Singerman, David *Schmidt, Dieter S. Scott, Paul James Sexton, Harlan B. Shiota, Takahiro Singh, Harpreet Schmidt, Henry J., Jr. Scott, Peter Seydel, Robert E., Jr. Shipp, R. Dale Singh, Jagraj Schmidt, Kenneth C. Scott, Ridgway Sgro, Joseph A. Shiraiwa, Kenichi Singh, Kanhaya L. Schmidt, Klaus D. Scott, Warner Henry *Shabazz, Abdul Alim Shiratani, Katsumi Singmaster, David B. Schmidt, Ralph 0. Harvey, III •Shabazz, Abdulalim Shochat, David D. Sink, Ann M. Schmidt, Roland Scott-Thomas, John F. Shafer, John Sholander, Marlow C. Sinkala, Zachariah Schmidt, Wolfgang M. Scourfield, Eira J. Shaftman, David H. Shor, S. W. Williston Sinke, Carl J. Schmitt, Klaus Scoville, Richard Shaharir Shore, Terence R. Sinkiewicz, Gerald P. Schnabel, Dan Scriba, Christoph J. Shahin, Mazen Mohammed Short, Hamish B. •Sipe, Patricia Lilaine Schneebeli, H. R. •Scroggs, James E. Shahshahani, Mehrdad M. Shorter, William Ivan Sitaraman, Yegnaseshan Schneider, Dennis M. Scull, Sidney C. *Shaio, Jack Shreve, David C. Sitia, Candido Schneider, Hans Seal, Charles Edwin Shallit, Jeffrey Outlaw Shreve, Warren E. Siu, Man-Keung Schneider, Victor P. Searl, James E. Shand, Sherman M. Shrikhande, Mohan Sharad Sivera, Rafael Schnitzer, Franz J. Sears, Michael Shannon, Gary P. Shubsda, Stanley R., Jr. Sizer, Walter S. Schnyder, Walter A. Secunda, Jeanne Shapiro, Daniel B. Shuchat, Alan H. •Sjodin, Tord J. Schochet, Claude L. Sedory, Stephen A. Shapiro, Dawn M. Shucker, David S. eSjolin, Per •Schochet, Steven H. Sedwick, Jackson L. Shapiro, George S. *Shukla, Pradeep K. Skaff, Michael S. Schoenberg, Isaac J. See, Richard •Shapiro, Joel H. Shulberg, Gary W. Skiffington, John Joseph, III Seebach, J. Arthur Shapiro, Victor L. Shult, Ernest E. Sklar, David

SEPTEMBER 1989, VOLUME 36, NUMBER 7 885 AMS Centennial Research Fellowship Fund

Skora, Richard Kevin *Sobel, Bernard A. Stachniak, Zbigniew Stell, John Greenwood eStray, Arne Skoug, David L. Soedirman, Massy Stackelberg, Olaf P. *Stelzer, Joerg M. Streater, David Neil Skrzeczkowski, Gwen Anne Sohmer, Bernard Staffeld!, Ross E. Stembridge, John R. Strebel, Kurt Slack, Michael D. Sol, Ton Gei Stafford, J. T. Stenger, Frank Strebel, Ralph Slade, Gordon D. Solakiewicz, Richard J. Stafford, Jonathan Stenger, William •Stredulinsky, Edward W. Slaman, Ted Soldate, Albert M., Jr. Stafford, Matthew W. Stengle, Gilbert A. Street, Ross H. Slater, John B. Sole, Patrick Stafney, James D. Stenson, David L. Streitman, Max Slater, Michael •Solian, Alexandru Stahel, Andreas Stenson, Ellen M. Strelitz, Shlomo •Slattery, Michael Solin, Robert N. Stahl, Saul Stenzel, Matthew B. Strikwerda, John C. Sleeman, Brian D. Solitar, Donald Stahmer, Karl Pangburn Stephens, Clarence F. Stroeker, R. J. Sliwa, Jan Solomon, Bruce Stakgold, Ivar *Stephens, Stanley L. Stroethoff, Karel M. Slook, Thomas H. *Solomon, Daniel L. Staknis, Victor R. Sterba-Boatwright, Blair D. Strogatz, Steven H. •Slowikowski, Wojciech Solomon, Jimmy L. •Stallings, John R. Sterling, Theodor D. Strohl, G. Ralph, Jr. Sluchin, Benny Solomon, Louis Stallmann, Friedemann W. Stern, Alan Spector •Strohmer, Gerhard 0. Slye, John M. Solomon, Ronald M. Stamey, William L. Stern, Andre Strom, Arne •Small, Kenneth A. •Somer, Lawrence E. Stammbach, Urs Stern, Mark A. Stromberg, Marc R. Small, Lance W. Song, Sung-Yell *Stamp, Mark Stern, Robert B. Stroomer, Jeffrey Dean Small, Lynne Barnes •Soni, Kusum K. Stampfli, Joseph G. Stern, Ronald J. Stroth, Gernot H. W. Smart, John R. Sonneborn, Lee M. * Stanai tis, Otonas E. Sternberg, David Stroud, Eric G. Smiley, Leonard Sonner, Johann Stand, Donald L. Sterrett, Andrew, Jr. Struwe, M. •Smiley, Michael W. Sonnesso, Geraldine Stand, Mildred L. Stetkaer, Henrik Stryker, Judson P. Smillie, John Sonntag, Rolf U. Stanek, Peter F. G. Stevens, Damon R. *Stuart, Donna J. Smith, Alexander John Sons, Linda R. Stanford, Ted •Stevens, Deborah Stuckwisch, Stephen E. Smith, Barry F. Sontag, Alexia Henderson Stanford, William G. Stevens, Glenn Howard Stueckle, Samuel K. *Smith, Cory B. Sontz, Stephen Bruce Stanley, Lee James Stevens, Randy S. *Stufken, John Smith, David A. Sorenson, John R. Stanley, Richard P. Stevens, Richard S. •Stummel, Friedrich *Smith, Douglas D. Sorgo, Teodoro G. Stanton, Charles S. Stevens, T. Christine Sturm, Teo Smith, Edgar C., Jr. •Soria, Fernando Stanton, Dennis W. Stewart, Ian Sturnfield, James F. Smith, F. R. Sormani, Michael J. •Stanton, Nancy K. Stewart, Robert C. Styan, George P. H. Smith, Frank D., Jr. Sorvali, Tuomas Staples, Edmund Beauderc, Stiles, Joseph L. •Styer, Robert A. Smith, Fredrick L. Soto, Ricardo L. III *Stob, Michael Suarez, Pedro A. Smith, George Rowan *Souganidis, Panagiotis E. Staples, John C. Stock, John R. Suchanek, Ana M. •Smith, Hal L. •Sousa Ramos, Jose Staples, Susan G. Stocker, Harold Edward •Sudderth, William D. Smith, Harold Robert, Jr. Southgate, Theodore J. Starbird, Michael Stockmeyer, Paul K. Sueiro-Bal, Juan *Smith, Harvey A. Spaltenstein, Nicolas Starbird, Thomas W. Stoddard, James H. Sueyoshi, Yutaka Smith, Herman J., Jr. Spanier, Jerome *Stark, Harold M. Stohs, Stephen M. *Sugar, Olive K. •Smith, John Howard Sparnroft, Conrad H. Stark, Sheldon H., Jr. Stoker, James R. Sugawara, Masahiro Smith, John M. Sparr, Gunnar *Starr, David W. Stokes, H. Christine B. *Sugiyama, Linda E. Smith, Justin R. Spatz, Ian N. •Starr, Norton Stokes, Russell A. Suita, Nobuyuki •Smith, Kenneth Woodward Spatzier, Ralf J. State, Emile Y. Stokes, William G. *Sulanke, Robert A. Smith, Kirby C. Specht, Edward J. •Staton, William A., III Stolarsky, Kenneth B. Sulis, William H. Smith, Laurie Melany •Speh, Birgit Staude, Ulrich B. C. Stolberg, Harold J. Sullivan, Dennis P. Smith, Lois E. B. Speiser, Robert Stavroudis, Orestes N. Stoll, Wilhelm F. •Sullivan, Frederick J. Smith, Mark D. Spellman, David Laurance Stearns, Joseph E., Jr. Stoltenberg-Hansen, Viggo Sullivan, Richard W. Smith, Michael G. Spellman, Dennis •Stecher, Michael J. Stoltzfus, Neal W. Sullivan, Wayne G. Smith, Richard Allan *Spencer, Domina E. Steel, Thomas B., Jr. Stolz, Stephan A. *Sulski, Leonard C. Smith, Robert Colman Spencer, Guilford L., II Steele, Alfred T. Stone, Alexander P. Summerhill, R. Richard *Smith, Roger R. •Spencer, Joel H. Steelman, John Henry •Stone, Arthur H. Summers, Arthur R. •Smith, Roland F. Spencer, Philip H. *Steen, F. H. *Stone, Arthur L. Summers, John W. Smith, Stephen B. Spencer, Thomas Crawford Steenbrink, J. Stone, Charles J. Summers, Stephen J. Smith, Stephen D. Sperry, Marvin G. •Steer, Brian F. Stone, David A. Summers, Timothy W. Smith, Tara L. Spiegel, W. Stefani, Stefano T. Stone, David R. Sun, Hugo Sui-Hwan Smith, Thomas J. •Spielberg, Jack Stegeman, Jan D. Stone, Eugene A. Sun, Kang *Smith, Wayne Stewart Spiro, Andrea Stegenga, David A. •Stone, John David Sun, Tien-Yu Smith, William K. Spivack, Mark Steger, Arthur Stone, Lawrence D. Sun, Ziqi *Smithers, Paul G. Sprecher, David A. Steger, Tim J. Stone, Michael G. Sundar, P. •Smithies, Frank eSpring, David H. Stegun, Irene A. Stong, Richard A. Sundararaman, D. Smolarski, Dennis C. Springer, Tonny A. Stehle, S. P. *Store, Lise Sundaresan, Kondagunta Smaller, Joel A. Spruck, Joel Steif, Jeffrey Edward Storey, Albert J. Sunderland, Benjamin B., Jr. Smyth, William F. •Spurr, Michael J. Stein, Alan H. Storrer, Hans H. Sundt, Mitchell E. Snaith, Victor P. eSquires, William A. *Stein, Marvin L. Stortz, Clarence B. Sung, Li-yeng Sniatycki, Jedrzej Srinivasan, Bhama Stein, Michael C. Stout, Edgar Lee •Sungyun, Lee Snover, James E. Sritharan, Sivaguru Steinberg, Leon Stout, Quentin F. Sunley, Judith S. •Snyder, Timothy Law Srivastav, RamP. Steinberg, Maria W. Stowe, Dennis C. Sunouchi, Gen-ichiro Snyder, William Merritt, Jr. St John, Katherine Ann Steinberg, Paraskevi •Straflin, Philip D., Jr. Sunouchi, Haruo Soare, Robert I. Stacey, Peter John Steinberg, Robert Stralka, Albert R. Sunseri, Mary V. Steiner, Anne K. Strang, Gilbert Suppes, Patrick Steiner, Donald D. Strassberg, Helen A. *Surbat, John AMS CENTENNIAL RESEARCH Steiner, Gilbert *Strassen, Volker Suri, Manil Steiner, Ray Phillip •Straube, Emil J. Suryanarayan, E. R. FELLOWSHIP CO~IRIBUTION Steinert, Leon A. Straubing, Howard Sussman, Myron M. IN MEMORY OF Steinhardt, Fritz Strauss, Leon •Sutner, Klaus ALVIN C. SUGAR Steinborn, Charles I. Strauss, N. C. Sutton, Charles S. Olive K. Sugar Steketee, Jakob A. Strauss, Walter A. Sutton, Michael D.

886 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS Centennial Research Fellowship Fund

Suttorp, L. G. Tancreto, Daniel Louis Thompson, Abigail A. Trench, William F. Turquette, Atwell R. Suzuki, Haruo Tang, Alfred S. •Thompson, Christopher L. Tretter, Marietta J. Turrittin, Hugh L. Suzuki, Michio Tang, Betty M. Thompson, David John Treves, Francois Turull, Alexandre Suzuki, Naoyoshi Tang, Hwa Tsang Thompson, Jon H. Treybig, L. Bruce Tutte, W. T. Suzuki, Shinichi *Tang, Tong Gao Thompson, Layton 0. •Trias Pair6, Joan Tuvell, Walter E. Sverdlove, Ronald •Tang, Wai-Shing Thompson, Lee D. Tribbey, William P. *Twombly, Evan E. *Swaminathan, Srinivasa •Tangora, Martin C. Thompson, Mary E. Tricerri, Franco Tymchatyn, Edward D. Swamy, Srikanta M. N. Tanimoto, Tatfee T. Thompson, Robert C. Trigiante, Donato Tysk, Johan Swan, Richard G. •Tannenbaum, Peter Thompson, Russell C. Trimble, Selden Y. Tzavaras, Athanassios E. *Swanberg, Katherine Tao, Yoko Thomson, Brian S. Tripp, John C. Uchiyama, Akihito Swanek, James J. Tartakotf, David S. Thorbergsson, Gudlaugur Trivieri, Lawrence A. Uchiyama, Saburo *Swanson, David L. Tashiro, Yoshihiro Thorne, John Farley, III Troger, Hans Uebelacker, James W. Swanson, Ellen E. Tashjian, Gloria J. Thornton, John Richard Trojanowski, Douglas A. Ueno, Kazushige •swanson, Laif Tatevossian, Leon H. Thrall, Robert M. Tromba, A. J. Ueno, Yoshiaki Sward, Marcia P. Taussky, Olga Thrash, Joe B. Trombi, Peter C. Uhl, J. Jerry, Jr. *Swardson, Mary Anne Tavantzis, John Thron, Wolfgang J. Tronel, Gerard Uhlenbeck, Karen Swart, Pieter J. •Tavares, Geovan Throop, T. Tronzo, Mark D. Uhlmann, Werner Swartz, Joseph H. Tavernini, Lucio Tickamyer, Cecil H., II Trotman, David J. A. Ukegawa, Takasaburo Swearingen, Daniel B. Taylor, Angus E. Tierney, John A. Trotter, Hale F. Ullery, William D. Sweeney, Edward T. *Taylor, B. A. •Tijdeman, Robert Trotter, P. G. Ullman, Daniel Sweeney, Orval L. Taylor, Donald E. Tilidetzke, Robert James Troubetzkoy, Serge Ullman, Joseph L. Sweeney, William J. *Taylor, Gladys Gillman Tillmann, Heinz G. Troue, Jacques Ulrich, Bernd Sweet, Melvin M. Taylor, Laurence R. Tilson, Bret R. Troy, Alan Ulrich, Klaus Swick, Kenneth E. Taylor, Lee A. •Timourian, James G. Troyanov, Marc Umble, Ronald N. Swift, William C. Taylor, Michael D. Tinkelman, Robert P. Troyer, Stephanie F. Umeda, Takato Swokowski, Earl W. Taylor, S. James Tinsley, Frederick C. •Trubek, Jeanne Umeda, Tomio Sylvester, John Taylor, Thomas J. Tintarev, Kyril *Trucano, Timothy Guy Umegaki, Hisaharu Syrotiuk, Violet R. Taylor, William W. Tischler, David C. Trudinger, Neil S. Unai, Yasushi Unai Szabo, Manfred Egon Tee, Garry J. Titani, Satoko Trueman, D. C. Unal, Aysenur Szalajka, Walter S. Teirlinck, Luc M. •Titi, Edriss Saleh Trussell, Carl Eugene Underwood, Douglas H. Szczarba, Robert H. Teissier, Bernard *Tjiok, Mouw-Ching Trytten, George N. Ungar, Abraham Sze, Alexander Teleman, Nicolae Tobias, Richard J. *Tsai, Long-Yi Ungar, Peter Szego, Peter A. Teleman, Silviu Toby, Ellen H. Tsai, Tian-Yue Uno, Katsuhiro Szekeres, George Temam, Roger Todd, John Tsai, Yen-Shung Upatisringa, Visutdhi Szeto, Mabel •Temme, Nico M. *Todd, Philip Hamish Tsang, Kai-Man Upmeier, Harald Sznitman, Alain-Sol Tena, Juan Todor, Fabian Tsao, Liang-Chi Upton, John A. W. Sziics, Joseph M. *Teng, Tsing-Houa Tokuyama, Takeshi Tsatsomeros, Michael J. Urda, Michael Szulkin, Andrzej Tennant, Raymond Frederick Toledo, Domingo Tsau, Chichen Michael *Urenko, John B. *Szymanski, Andrzej Teply, Mark L. Toll, Kathryn B. Tschantz, Steven T. *Uribe, Alejandro Taam, Choy-Tak Terao, Hiroaki *Tolle, Louis F. •Tsing, Nam-Kiu Ursini, Aldo Tadic, Marko Terman, David Tolosa, Juan Tsuchikura, Tamotsu Usmani, Riaz A. Tadmor, Eitan Terras, Riho Tomczak-Jaegermann, N. Tsuchiya, Morimasa van der Vaart, H. Robert Taft, Earl J. Terrier, Jean Marc Tomer, Eugene R. Tsuchiya, Takuya •Vachuska, Colleen A. Tagawa, Masa-Yoshi Terzuoli, Andrew J. Tominaga, Hisao Tsui, Sze-Kai Jack Vagi, Stephen Taggart, Marcia D. Tesei, Alberto Tomita, Yoshihito Tsuji, Kazo •Vahey, John T. Taiani, Geraldine Testerman, Donna M. Tomiyama, Jun •Tsuji, Mikio Vaillancourt, Jean Taibleson, Mitchell H. Tewfick, Ahmed Hisham Tomsky, Jack Tsujishita, Toru Vainio, Reino Johan Taira, Kazuaki •Tews, Melvin C. *Tondra, Richard J. Tsukada, Makoto Valle, Antonio Takacs, Lajos F. Textorius, Bjorn 0. B. *Tonga, Marcel Tsukiyama, Kouzou de Valpine, Jean E. •Takahashi, Joji Theilheimer, Feodor •Tonge, Andrew M. Tsukui, Yasuyuki Vamanamurthy, Mavina K. Takahashi, Reiji Theodorescu, Radu •Ton-That, Tuong Tsutsumi, Massayoshi Van Alstyne, John P. Takahashi, Shuichi *Theohari-Apostolidi, Topsoe, Flemming Tu, Yih-0 Van Assche, Walter J. Takahashi, Wataru Theodora Torgerson, Norman Wesley Tubaro, Luciano Van Bendegem, Jean Paul Takeda, Ziro Theusch, Colleen J. Torre, Nicolo Goodrich •Tubbs, Robert Earl *Van Casteren, Johannes A. Takesaki, Masamichi Thickstun, W. R., Jr. Torrecillas, Bias Tucci, Ralph P. Van Daalen, Diederik T. Takeuchi, Kisao *Thiele, Ernst-Jochen Torres, M. Tucker, Alan C. Van de Wetering, R. Lee Takeuchi, Masaru •Thieler, Peter Torres, Waldo A. Tucker, Albert W. Van Den Ban, Erik P. Takeuti, Gaisi Thistlethwaite, Morwen B. Toshi, !ida Tucker, Howard G. Van der Geer, Gerard Takizawa, Kiyoshi Thoele, Edward C. Totaro, Burt J. Tuckerman, Bryant Van Der Kallen, Wilberd Talenti, Giorgio G. Tholen, Walter P. Toth, Gabor Tugue, Tosiyuki VanDer Mee, Cornelis V. Talge, Gordon J., III Thoma, Elmar H. Tousley, Horace W. Tulipani, Sauro evan Der Meer, Jan-Cees Talmadge, Richard B. Thomas, Alan T. Townsend, James T. Tull, Jack P. Van Der Waerden, B. L. Talman, Louis A. •Thomas, Charles B. *Toyoshima, Tetsunosuke Tuller, Annita Van Dulst, Dick Tam, Bit-Shun Thomas, Clayton J. Trace, Bruce S. Tuncel, Selim Van Eck, H. N. Tamura, Takayuki Thomas, George B., Jr. Traina, Charles R. Tung, Shih-Hsiung Van Eerdewegh, Paul Tan, Henry K. Thomas, Janet D. Tran, Hung Viet *Turcotte, Daniel M. C. L. Tan, Ruo Yang Thomas, Ken E. Transue, William R. Turgeon, Jean M. evan Emde Boas, Peter Tanabe, Hiroki Thomas, Lawrence E. •Transue, William R. R. Turiel, F. J. Van Engelen, F. Tanaka, Hisao Thomas, Marc Phillip Trautman, David A. Turisco, Joann Stephanie Van Geemen, Bert Tanaka, Jun-Ichi Thomas, Mark A. Trebels, Walter •Turley, Jennifer Van Keppel, Marilyn J. Tanaka, Katsumi Thomas, P. Emery *Treger, Robert Turner, Edward C. Van Lint, Jacobus H. Tanaka, Minoru Thomas, Pascal J. Treibergs, Andrejs E. Turner, Jim M. Van Meter, Robert G. *Tanaka, Toshie •Thomason, Steven K. •Treibich, Armando Turner, Peter R. Van Mulbregt, Paul A. Tancredi, Alessandro Thomee, Vidar Tremain, Janet C. Turner, T. Rolf *VanRossum, Herman

SEPTEMBER 1989, VOLUME 36, NUMBER 7 887 AMS Centennial Research Fellowship Fund

H. Van Stone, Kathryn L. Voiculescu, Dan Wang, Hsiao-Lan eWeis, Dennis G. *Wicke, Howard Mladen Victor Van Tuyl, A. H. Voigt, Paul S. Wang, Hwai-Chiuan Weis, Lutz Wickerhauser, Douglas H. Van Veldhuizen, M. Vojta, Paul A. Wang, Kwang-Shang Weisgram, Thomas P. Wiedemann, Roger A. Van Vleck, Fred S. Volkmann, Bodo •Wang, Paul K. C. Weiss, Guido L. Wiegand, Sylvia Margaret Vance, Elbridge P. Volkmer, Hans W. Wang, Stuart Sui-Sheng •Weiss, John Wiegand, Klaus Werner Vance, James T., Jr. Voreadou, Rodiani Wang, Ying Hsiung Weiss, Norman J. Wiegmann, Norbert J. Vanden Boss, Eugene L. Vrbik, Jan Wantland, Evelyn K. Weiss, Randall H. Wielenberg, Wiener, Howard W. Vanderbauwhede, A. L. Vuignier, Diane J. Wanzong, Robert C. Weiss, Richard M. Wieschenberg, Agnes J. Vanderbei, Robert Vukomanovic, Djordje V. Warchall, Henry A. Weissler, Frederic B. Arthur S. Vandervelde, Richard A. Vulakh, L. Ya Ward, Doug E. •Weitkamp, Galen L. Wightman, Wihstutz, Volker Vandevelde, J. Richard evuorinen, Matti Ward, Harold N. Welch, Lloyd R. G. Vanstone, James R. Wacker, Paul F. •Ward, James Norman Weld, Kathryn C. Wiid, Frans Vaquie, Michel Wackwitz, Maynell H. •ward, Josephine A. Wellner, Jon A. Wik, Anders L. Varadarajan, Kalathoor Wada, Hidekazu Wardle, Robin W. Wells, Charles F. Wik, Ingemar Kenneth R. evaradarajan, V. S. Wada, Junzo Ware, Buck Wells, David M. Wildenhain, S. Varadhan, Srinivasa S. R. Wada, Masaaki Ware, Roger P. Wells, R. 0., Jr. Wilf, Herbert David L. Varadi, Ferenc Wada, Toshimasa Warfield, Diane Crockett Welters, G. E. Wilkens, Wilker, John B. •Varga, Richard S. *Wadhwa, Bhushan La! Warfield, Robert B., Jr. Wendel, James G. Wilkins, David A. Vargas, John David Wadsworth, Adrian R. Warhola, Gregory T. Wendland, Wolfgang L. Steven V. Vasak, Janet Trzcinski Wage, Michael L. *Warne, Ronson J. Wendt, Dieter W. F. Wilkinson, Stuart A. Vasavada, Mahavirendra H. Wagener, Raymond Warnecke, Gerald Wene, Gregory P. *Wilkinson, Williams, Alice T. Vasconcelos, Wolmer V. Wagner, David H. •Warner, C. Robert Wenger, John C. Bennie B. *Vasquez, Alphonse T. *Wagner, Diane M. Warner, Frank W., III Wente, Henry C. Williams, *Williams, Charles W. Vassiliou, Efstathios Wagner, Gretchen B. Warren, Bette L. Wermer, John Williams, Dana P. Vaughn, James M., Jr. Wagner, R. W. Warren, William E. Werner, Dirk David A. eveech, William A. *Wagner, Richard C. Warrinnier, Alfred E. Werner, Peter Williams, Williams, David E. •Vega, Jose Manuel Wagoner, John B. Warschawski, Stefan E. Wernick, Robert J. Williams, David Neil *Vega de Prada, Jose Manuel Wagreich, Philip D. Washburn, Robert B., Jr. Wessel, W. Roy E. Bruce Velasco-Hernandez, Jorge X. Wagstaff, Samuel S., Jr. Washington, Lawrence C. West, Donald C. Williams, Gareth Veldman, Willem H. Wahba, Grace G. Wasserman, Arthur G. West, James E. Williams, Williams, George K. Vella, David C. Wahl, Jonathan M. Wasserman, Richard S. Westbrook, Edwin P. Williams, Gerald W., Jr. Velleman, Daniel Wahlbin, Lars B. Watanabe, Shoji Westbury, Christopher Grey Williams, Gregory P. * Venkataraman, Rangachari Wainger, Stephen Watatani, Yasuo Western, D. W. Williams, Hugh M. •Ventura, Belisario Augusto Wainwright, John *Waterhouse, William C. Westlund, Eric R. John K. Venzi, P. Waiveris, Charles F. Watkins, David S. Westman, Joel J. •Williams, Joyce W. Venzke, Paul B. Wajnryb, Bronislaw Watkins, Joseph C. •Weston, Jeffrey D. Williams, Kenneth S. Vera, Gabriel Wakae, Masami Watkins, Mark E. Westphal-Schmidt, U. Williams, Williams, Lawrence R. • Verde Star, Luis Wakana, Kaoru Watnick, Richard M. Westwood, Derek J. Lynn R. Verdier, Jean-Louis Wake, Robert Alan Watson, James D. ewette, E. W. *Williams, Mark •Verhulst, Ferdinand Walcher, Sebastian Watson, Mark J. Wetzel, John E. *Williams, •Williams, Neil H. *Verlinden, John P. Walde, Ralph E. Watson, Martha F. *Wetzel, Marion D. Williams, Peter David Verma, Ghasi R. Waldinger, Hermann V. •Watt, Stephen B. Wexler, D. Robert F. Vermeer, Johannes *Wales, David B. Wattenberg, Frank A. Wheeler, Charles H., III Williams, Williams, Ronald 0. Vermes, Robert Walker, Carol L. Wayment, Stanley G. Wheeler, Robert F. Williams, Stanley C. Veron, Laurent Walker, Homer F. Waymire, Edward C. White, Alvin M. Williams, Susan Gayle Verriest, Erik I. Walker, James S. Wayne, Alan White, Arthur T. Charles K. Verrios, Katherine G. D. •Walker, James W. Wayne, David Scott White, Benjamin S. *Williamson, Williamson, Frank, Jr. Vervaat, Wim Walker, Kevin Weaver, George E. White, Brian Cabell Williamson, Jack Vesentini, Edoardo *Walker, Larry R. Weaver, John C. White, Denis A. Richard E. Vestal, Sally D. Wall, Charles T. C. Weaver, Martha E. White, George N., Jr. *Williamson, Williamson, Susan Vetter, Udo Wall, Curtiss E. Weaver, Robert Wooddell White, Gregory B. M. Videla, Carlos Rodolfo Wall, G. E. Webb, David L. White, Janis E. Wills, Jorg Stephen J. Vietsch, W. Karel Wallace, David A. R. Webb, Glenn F. White, John T. •Willson, Wilson, David Barrett eVila-Freyer, Ricardo Wallace, David Robert Webster, Sidney M. White, Lee Wayne Wilson, David L. Francisco Wallen, C. J. Wechsler, Martin T. White, Neil L. Wilson, Edward N. Vilcius, AI R. Wallen, Lawrence J. Wedel, Arnold M. White, Stevan Russell James A. Vincenzi, Antonio Walschap, Gerard E. Wehlau, David L. White, Warren H. •Wilson, Wilson, John H. eVinsonhaler, Charles I. *Walsh, John B. Wehlen, Joseph A., Jr. White, WmA. Leslie Charles Viola, Carlo *Walsh, John J. •Weibel, Charles A. Whitehart, F. E. Wilson, Wilson, Raj eVirsik, George Walsh, John Thomas Wei!, Clifford E. Whitehead, George W. Raymond B. Vitale, Joseph N. Walster, G. William Weiler, Fred W. Whitehead, Kathleen B. Wilson, Wilson, Richard Vitale, Richard A. Walter, Charles N. Weiler, Jerome T. Whitfield, John H. M. Wilson, Robert Lee Vitale, Vincent G. Walter, John H. Weill, Lawrence R. •Whitley, Robert J. Wilson, Ruiz Torres Viterbo, Claude Walter, Leslie J. Weiner, Jerome H. Whitley, W. Thurmon Wingate, John W. Vitter, Albert L., III Walters, Peter Weiner, Joel L. Whitman, Andrew P. Wingler, Eric J. Viviente, Jose L. Walters, Randall K. *Weiner, Louis M. Whitman, Philip M. Steven K. Vodola, Paul A. Waltman, Paul *Weinert, Hanns Joachim Whitney, D. Ransom Winker, Winkler, Jorg H. Voelker, Dietrich H. Walton, Jay R. Weinitschke, Hubertus J. Whitney, Hassler Winslow, Dennis N. Vogan, David A., Jr. Walus, Herwig Weinkam, James J. Whitney, Ronald F. Winston, Kenneth Vogel, Thomas I. Wan, Frederic Y. M. Weinstein, Alan D. Whitt, Lee B. *Winter, Eva P. •Vogelius, Michael Steenstrup Wanby, Goran Weinstein, Jack Whittaker, James V. Wintrobe, F. Vogt, E. Wang, Cecilia Y. Weinstein, Michael I. Whitten, Wilbur Wirth, Andrew Vogtmann, Karen Wang, Derming Weinstein, Stephen T. Whittlesey, Emmet F. Lamar Voichick, Michael Wang, Edward T. H. Weintraub, Steven H. Whyburn, Lucille E. Wise, Gary

888 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS Centennial Research Fellowship Fund

Wiskott, Bettina Woodruff, William M. Yamaguchi, Keizo •Younce, Matthew B. •Zhang, Jiaxiang John Wissner, Heinz-Wolfgang Woods, Alan C. Yamaguchi, Seiichi •Young, Anne L. Zhang, Ning Witsch, K. J. Woods, Dale Yamakawa, Mineo Young, Barry H. *Zhang, Xianke Witsenhausen, Hans S. Woods, R. Grant Yamaki, Hiroyoshi Young, David M., Jr. Zhao, Zhi-Yong Witten, Edward Woolf, William B. Yamamoto, Koichi Young, Donald F. Zharn, P. Joseph •Wittman, Richard H. •Woolford, Thomas L. Yamanoshita, Tsuneyo Young, Eutiquio C. •Zhou, Zhiming Wittner, Ben Scott Wooster, Kenneth Yamaoka, Kenya Young, LaeiM. ezhu, Jianchao Woan, Wen-Jin Woyczyr\ski, Wojbor A. Yamasaki, Masayuki *Young, MacDonald Burritt Zia, Lee L. Woess, Wolfgang Woythaler, Joseph William Yanagawa, Minoru Young, Paul M. Ziebarth, Steven W. Wogen, Warren R. Wright, Charles R. B. Yanagi, Kenjiro Young, Sam Wayne Ziegler, John Alan Woldar, Andrew J. Wright, David Yang, Chung-Tao Younger, Daniel H. •Ziegler, Lynn Wolf, Edwin M. Wright, David G. Yang, Deane Younis, Rahman Mahmoud Ziegler, Zvi Wolf, Herbert S. Wright, David J. Yang, Jae-Hyun Yovanovich, M. Michael Ziemer, William P. •Wolf, Joseph A. Wright, Jeffrey Allen Yang, Jeong Sheng Ypma, Tjalling J. Zierau, Roger Craig •Wolf, Michael Wright, Jill D. •Yang, Kichoon Yu, Jing Zierler, Neal Wolfe, Carvel S. Wright, Marcus W. Yang, Kung-Wei Yu, Lucille Chich Ziller, Wolfgang Wolfe, Michael David Wright, Mary H. Yang, Paul C. Yu, Xiaokang Zilmer, Delbert E. *Wolff, Thomas H. Wright, Otis C. Yang, Wei-Shih Yuen, David S. Zimmer, J. W. •Wolffhardt, Klaus R. A. Wright, Thomas Perrin, Jr. Yanik, Elizabeth G. Yui, Noriko Zimmerman, Donald W. Wolfskill, John Wrobleski, William J. Yanik, Joe Yung, Mordechai M. Zimmerman, Jay J. Wolfson, Kenneth G. Wschebor, Mario Yano, Kentaro Yung, Tin-Gun Zimmermann, B. •Wolfson, Paul R. Wu, Ching-mu Yanowitch, Michael Zaballa, Ion Zimmermann-Huisgen, Wolkowicz, Gail S. K. Wu, Hung-Hsi •Yap, H. P. Zachariah, Thomas M. Birge K. Wollman, Stephen Wu, Ling-Er! Eileen T. Yaqub, Fawzi M. Zacks, Shelemyahu Zinn, J. *Wolper, James S. Wu, T. C. Yaqub, Jill S. Zadeh, Lotfi A. Zippo, Siro Wolpert, Scott A. Wulf, Leo M. Yasue, Kunio Zafrullah, Muhammad Zipse, Philip W. *Woltermann, Michael L. •Wurfel, Tilmann Yasuhara, Ann •Zahid, Muhammad Ishaq Zirilli, Francesco Womble, David E. Wylie, Clarence R., Jr. Yasuhara, Mitsuru Zahreddine, Ziad Zitarelli, David E. Wong, Alex Cheuk W. Wyman, Bostwick F. Yates, George R., Jr. Zajac, Edward E. Zitron, Norman R. *Wong, Edward T. Wyss, Walter Yau, Shing-Tung Zalik, R. A. Zizler, Vaclav Wong, James S. W. *Xambo, S. •Yebra, Jose Luis Andres Zama, Nobuo Zlatev, Zahari *Wong, Kwok Chi Xenos, Philippos John Yeh, Rui Zong Zambrini, Jean-Claude Zo, Felipe J. Wong, Maurice K. F. Xia, Daoxing Yen, David H. Y. *Zame, Alan Zoch, Richmond T. Wong, Paul W. T. Xu, Geng Yhap, Ernesto Franklin Zamfirescu, Christina M. Zoreda-Lozano, Juan J. Wong, Philip Pit-Wang *Xue, Weimin Yin, Hong-Ming •Zamfirescu, Tudor Zorn, M.A. *Wong, Pit-Mann Yachter, Morris Yiu, Paul Y. H. Zanolin, Fabio Zorn, Paul Wong, Raymond Y. Yackel, James W. Yocom, Kenneth L. •Zaslavsky, Alan M. Zoroa, P. Wong, Roman Woon-Ching Yadin, Micha Yohe, J. Michael Zaslavsky, Thomas Zorzitto, Frank A. Wong, Sherman K. Yahya, S.M. Yokoi, Hideo *Zaslove, Barry L. Zouyousefain, Mohammad S. Wong, Shiu-Chun Yajima, Kenji Yokota, Hisashi Zedek, Mishael Zsid6, Laszlo Wong, Yung-Chow Yajima, Yukinobu Yoneda, Kaoru Zeheb, Ezra Zucker, Steven M. •Wood, Carol Yaku, Takeo Yoneguchi, Hajimu Zehnder, Eduard J. Zuckerman, Gregg J. Wood, Geoffrey V. Yamada, Hiromichi Yood, Bertram Zelinsky, David S. Zuckerman, Martin M. Wood, Jay A. Yamada, Naoki Yorke, James A. Zelle, Joseph *Zukowski, Leon P. Wood, John C. Yamada, Shinichi Yoshida, Norihiro •Zeller, Mike Zweibel, John A. Wood, John W. Yamada, Toshihiko Yoshino, Genji Zemmer, Joseph L., Jr. Anonymous ( 102) Woodroofe, Michael B. Yamaguchi, ltaru *Yoshino, Takashi Zero, Jose Rodolfo Woodrow, Robert Edward Yamaguchi, Jinsei Yoshizawa, Taro Zhang, Jian

SEPTEMBER 1989, VOLUME 36, NUMBER 7 889 JOURNAL OF THE

AMERICAN MATHEMATICAL SOCIETY

The Journal of the American Mathematical Society is a quarterly journal containing research articles of the highest quality in all areas of pure and applied mathematics.

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Michael Artin H. Blaine Lawson, Jr. Richard Melrose Wilfried Schmid Robert E. Tarjan

ISSN 0894-0347 Quarterly, Volume 3, 1990 Code 90JAMS/NA 1990 Subscription Prices: List $116*, Institutional Member $93*, Individual Member $70*

* Add for postage: Surface delivery to destinations outside the U.S. and India-- $8; to India-­ $18. Expedited delivery to destinations in North America $12; elsewhere -- $25.

Note: Subscriptions to AMS journals are sold only on a calender year basis (January-December); split year and multiple year subscription orders are not accepted. Subscription orders received from nonmember institutions and organizations after January I of the subscription year will be sold at list price plus a I 0% late charge (rounded); the maximum late charge for any subscrip­ tion is $200. Subscription cancellations from nonmembers will not be accepted after March I of the subscription year. Cancella­ tion refunds are computed by deducting an $8 cancellation fee, and the price of each issue already shipped, from the price paid.

To order: Prepayment required in U.S. funds. Mail to AMS, Annex Station, P. 0. Box 1571, Providence, Rhode Island 02901-1571 U.S.A. or ca11800-556-7774 in the continental U.S. to use VISA or MasterCard. Meetings and Conferences of the AMS

FUTURE MEETINGS

Hoboken, New Jersey October 21-22 893

Muncie, Indiana October 27-28 896

Los Angeles, California November 18-19 900

Invited Speakers and Special Sessions 903

MAA Contributed Paper Sessions at Louisville 906

SEPTEMBER 1989, VOLUME 36, NUMBER 7 891 Coming Events

The First Announcement of the 1990 International Congress of Mathematicians to be held in Kyoto, Japan, August 21-29 appears at the end of this section. Interested parties should read this information and then complete and mail the form which appears at the back of this issue in order to receive the Second Announcement, which will contain details on the scientific program, preregistration and accommodations. Elsewhere in this issue is an article regarding the possibility of travel grants to mathematicians wishing to attend the Congress, should funds become available. Louisville Meetings

Louisville, Kentucky, a city perhaps best known for the Kentucky Derby, is the site for the upcoming Joint Mathematics Meetings, to be held January 17-20, 1990. This unique city offers much more than horse races and mint juleps: as the gateway to America's westward expansion, a focal point for innovative research in medical technology, and a bastion of southern charm, Louisville is a rich blend of the past, present, and future.

This remarkable city will provide a pleasant backdrop for the rich mathematical program at the Joint Meetings. AMS activities begin with the Short Course on Mathematical Questions in Robotics, organized by RoGER BROCKETT. This Short Course will explore the mathematics of robot kinematics and dynamics, with a focus on both the physical and computational struc­ tures. The speakers, in addition to Brockett, will be JOHN B. BAILLIEUL, BRUCE R. DoNALD, MADHUSUDAN RAGHAVAN, and SHANKAR SASTRY.

The tradition of excellence in expository lectures will continue with the AMS-MAA Joint In­ vited Address series, featuring BARRY SIMON (speaking on eigenvalue perturbation theory), CHARLES W. CuRTIS (on representation theory of finite groups), and JoN BARWISE (on non­ wellfounded sets). GEORGE B. DANTZIG, holding the honor of Gibbs Lecturer, will speak on The world of pure math which goes by other names. The prestigious Colloquium lectures will be presented by SHLOMO STERNBERG.

The MAA program will include LEONARD GILLMAN's Retiring Presidential Address, which will be on innovative teaching methods with attention to minorities. Other MAA Invited Ad­ dresses are by JANOS D. AcZEL speaking on work on the second part of Hilbert's Fifth Prob­ lem, MICHAEL BARNSLEY speaking on fractal geometry and its applications, THOMAS KAlLA TH speaking on displacement structure of matrices and some applications, JuDITH D. SALLY speak­ ing on a topic to be announced later, and PETER WINKLER speaking on the (sometimes) strange behavior of large random things. This talk is about 0, 1-limit laws in probability theory and the interesting situations in which they do not hold.

The deadline for abstracts of papers submitted for consideration for AMS contributed paper sessions is October 11, 1989. The deadline for submission of papers for consideration for presentation at an AMS special session is September 20, 1989, three weeks earlier than the deadline for contributed papers. Information on MAA contributed paper sessions can be found elsewhere in this issue.

So, Louisville will be the place for mathematics this January! Mark your calendars now, and be sure not to miss the November 17 deadline for preregistration and housing. A full announce­ ment for the Louisville meeting, including the Preregistration/Housing Form, will appear in the next issue of Notices.

892 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Hoboken, New Jersey Stevens Institute of Technology October 21-22 Second Announcement

The eight-hundred-and-fifty-first meeting of the Ameri­ Computational algebra, CHARLES C. SIMS, Rutgers can Mathematical Society will be held at Stevens Institute University, New Brunswick. of Technology in Hoboken, New Jersey on Saturday, Oc­ Algebraic geometry, p-adic aspects, MARVIN D. tober 21, and Sunday, October 22, 1989. TRETKOFF, Stevens Institute of Technology.

Invited Addresses Contributed Papers By invitation of the Eastern Section Program Commit­ There will also be sessions for contributed ten-minute tee, there will be four invited one-hour addresses. The papers. Late papers will not be accommodated. speakers, their affiliations, the titles of their talks, and the scheduled times of presentation are: Registration RussEL CAFLISCH, Courant Institute of Mathematical The meeting registration desk will be located in the lobby Sciences and the University of California, Los Angeles, of the Stevens Center and will be open from 8:00 a.m. to Mathematical analysis ofvortex sheets, 1:30 p.m. Sunday. 5:00p.m. on Saturday, October 21, and from 8:00a.m. BRUCE KITCHENS, IBM Thomas J. Watson Research to 12:00 noon on Sunday, October 22. Center, Yorktown Heights, Symbolic dynamics, 11:00 The registration fees are $30 for members of the a.m. Sunday. AMS, $45 for nonmembers, and $10 for students or FANG HuA LIN, Institute for Advanced Study and unemployed mathematicians. University of Chicago, Level sets of solutions of elliptic and parabolic equations, 11:00 a.m. Saturday. Social Event SHELDON E. NEWHOUSE, University of North Car­ olina, Chapel Hill, The dynamics of two-dimensional A special reception and dinner will be held Saturday di.ffeomorphisms, 1:30 p.m. Saturday. evening, October 21, in the S. W. Williams Library. The event will include cocktails and a buffet dinner Special Sessions appropriate to the harvest season. Participants can make reservations by sending a check for $25 per person to By invitation of the same committee, there will be eight Denise Ryan, Department of Mathematics, Stevens In­ special sessions of selected twenty-minute papers. The stitute of Technology, Hoboken, NJ 07030. Reservations topics, and the names and affiliations of the organizers, should be made by the first week in October. Participants are as follows: having any questions regarding the dinner should call PRABIR BHAT­ Geometry related to computer vision, Ms. Ryan at 201-420-5448. TACHARYA, University of Nebraska, Lincoln, and RoBERT A. MELTER, Long Island University. Petition Table Algebraic semantics, STEPHEN L. BLOOM, Stevens In­ stitute of Technology. A petition table will be set up in the registration area. Mathematical fluid dynamics, RUSSEL CAFLISCH. Additional information about petition tables can be Low-dimensional topology, MARK E. FEIGHN, LEE found in a box in the Boulder meeting announcement on D. MosHER, AND ULRICH OERTEL, Rutgers University, page 457 of the April 1989 issue of Notices. Newark. Smooth dynamical systems, BRUCE P. KITCHENS AND Accommodations SHELDON E. NEWHOUSE. A block of rooms has been reserved at the Holiday Inn Finite groups, RICHARD N. LYONS AND RICHARD Harmon Meadow for Friday, October 20, and Saturday, O'NAN, Rutgers University, New Brunswick.

SEPTEMBER 1989, VOLUME 36, NUMBER 7 893 C» !

Stevens Institute of Technology

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October 21, at a special rate of $69 per night for a left onto 9th Street. Go two blocks to Castle Point Terrace, turn single or double. The special rate may be available for right and park in the 8th Street Lot directly ahead. Sunday, October 22, but this is not guaranteed. The To Stevens from the north: Take the New York State Thruway rooms will be held until October 7, 1989. To reserve to the Garden State Parkway south. Take Exit 153 to Route a room at this special rate, individuals must call the 3 east toward the Lincoln Tunnel. Exit to the right at a sign Holiday Inn Harmon Meadow at 201-348-2000, ask for marked Last Exit in New Jersey and turn right at the second the sales office, and identify themselves as participants traffic light. Proceed south over the viaduct as above. of the AMS meeting at Stevens Institute of Technology. To Stevens from the south and west: Take the New Jersey The Holiday Inn provides free return transportation Turnpike to Exit l6E and follow signs toward the Lincoln Tun­ to Newark Airport or Penn Station in Newark. Par­ nel. Exit to the right at a sign marked Last Exit in New Jersey ticipants must ask for this service when making room and turn right at the second traffic light. Proceed south over the reservations. viaduct as above. The Holiday Inn is located in a pleasant outdoor mall To the Holiday Inn from New York City: Take the Lincoln with several stores and restaurants and 14 movie theaters. Tunnel. Follow I-495 west to Route 3 west. Follow the signs It is approximately four miles from the Stevens campus for Harmon Meadow Boulevard, and make the second right to the mall and the Holiday Inn provides free shuttle (immediately before an EXXON station). Continue around the service. The Holiday Inn has an exercise room and a car complex and make a right at the first stop sign. Make a left at rental agency which offers cars for approximately $30 the next stop sign. The entrance to the Holiday Inn is one half per day. block ahead on the right. To the Holiday Inn from the north: From Routes 80 and 95 Travel or the George Washington Bridge take the New Jersey Turnpike south; where the turnpike divides take the eastern spur (toward From Newark Airport the Lincoln Tunnel). Leave the turnpike at Exit 17. After the The Newark Airport is located about ten miles from toll stay right and follow the service road marked by a sign for both the Stevens campus and the Holiday Inn Harmon Route 3-Secaucus straight through the first light and turn right Meadow. Taxi service is available to both the Stevens at the first stop sign. The entrance to the Holiday Inn is one campus and the Holiday Inn for approximately $25- half block ahead on the right. $30. By bus, participants should take the #300 New To the Holiday Inn from the south and Newark Airport: Take Jersey Transit Airport Express to the Port Authority Bus the New Jesey Turnpike north; where the turnpike divides take Terminal in Manhattan at a cost of $7. This service runs the eastern spur (toward the Lincoln Tunnel). Leave the turn­ every ten to fifteen minutes and takes approximately pike at Exit l6E. After the toll follow the service road marked thirty minutes depending on the traffic. From the Port by a sign for Secaucus straight through the first light and turn Authority Bus Terminal take the #126 New Jersey Transit right at the first stop sign. The entrance to the Holiday Inn is bus to Hoboken ($1. 70), or the #320 New Jersey Transit one half block ahead on the right. bus to Harmon Meadow ($2.15), with service every hour To the Holiday Inn from the west: Take Route 3 east and exit beginning at 8:20 a.m. until 9:20 p.m. onto a service road at the sign marked Secaucus-N.J.Turnpike­ From Penn Station Manhattan Exit Only. Follow the service road and turn right onto Harmon Go to the Port Authority Bus Terminal at 8th Avenue Meadow Boulevard immediately after passing under the New and 42nd Street and proceed as above, or take a PATH Jersey Turnpike. Continue through a traffic light and turn right train from 6th Avenue and 33rd Street to Hoboken ($1 at the first stop sign. The entrance to the Holiday Inn is one half block ahead on the right. exact fare in bill or coins required). From the Hoboken terminal it is a walk of approximately one-half mile to Parking the Stevens Center. The taxi fare to Stevens Center is $2.75. Free parking is available in the 8th Street and 6th Street By Car parking lots. (Please refer to the campus map). Hoboken is located on the Hudson river across from Manhattan between the Lincoln and Holland Tunnels. Weather The Holiday Inn Harmon Meadow is located off Route October weather is usually pleasant in the Hoboken area. #3 approximately three miles west of the Lincoln Tunnel. Meteorological averages for the month are 57°F and 3.1 To Stevens from New York City: Take the Lincoln Tunnel. At inches of rain. the tunnel exit bear to the extreme right through the underpass W. Wistar Comfort marked Hoboken. Proceed south over a viaduct and turn left Associate Secretary onto 14th Street. Go about four blocks to Washington Street and turn right. Take Washington Street for five blocks and turn Middletown, Connecticut

SEPTEMBER 1989, VOLUME 36, NUMBER 7 895 Muncie, Indiana Ball State University October 27-28

Second Announcement

The eight-hundred-and-fifty-second meeting of the Amer­ Number theory and algebraic geometry, ALAN ican Mathematical Society will be held at Ball State ADOLPHSON, Oklahoma State University, and STEVEN University in Muncie, Indiana on Friday, October 27, SPERBER. and Saturday, October 28, 1989. This meeting will be Statistics and probability, M. MAsooM ALI, Ball State held in conjunction with the Indiana Section of the University. Mathematical Association of America. Complex analysis, DAVID E. BARRETT, University of Michigan, Ann Arbor, and LASZLO LEMPERT. Extrema/ly disconnected spaces and their applications, Invited Addresses Joint ANANDA GUBBI, Southwest Missouri State University. By invitation of the Central Section Prbgram Committee, Noncommutative algebra in geometry and arithmetic, and the Mathematical Association of America, there will DARRELL E. HAILE, Indiana University. be one joint invited address as follows: Triangular operator algebras, DAVID R. LARSON, Texas SHELDON AXLER, Michigan State University, Writing A&M University. mathematics. Function spaces and topology, KATHRYN FRosT PoRTER, Ball State University. Differential equations, JoHN F. PoRTER and T. K. Addresses Invited PUTTASWAMY, Ball State University. By invitation of the Central Section Program Commit­ tee, there will be four invited one-hour addresses. The Contributed Papers speakers, their affiliations, and the titles of their talks are: There will also be sessions for contributed ten-minute LASZLO LEMPERT, Purdue University, Imbedding pseu­ papers. Late papers will not be accommodated. doconvex domains into a ball, scheduled time to be announced. MAA Program KENNETH R. MEYER, University of Cincinnati, Sta­ bility and chaos in almost periodic systems, scheduled The MAA program will begin on Saturday, October 28, at time to be announced. 9:00 a.m. The MAA Business Meeting will begin at 3:05 PAULS. MuHLY, University ~wa, Iowa City, Some p.m. In addition to the jointly sponsored Invited Address, recent advances in operator alge~cheduled time to be the following MAA Invited Addresses are scheduled: announced. GERALD ALEXANDERSON, Santa Clara University, STEVEN SPERBER, University of Minnesota, Min­ Gaussian binomial coefficients. neapolis, p-adic analysis and exponential sums, scheduled DANIEL GoTTLIEB, Purdue University, Topology and time to be announced. the robot arm. RoBERT LoPEZ, Rose-Hulman Institute of Technol­ ogy, Teaching calculus and differential equations with the Special Sessions computer algebra system MAPLE. By invitation of the same committee, there will be eight GLORIA OLIVE, Anderson University and the Univer­ special sessions of selected twenty-minute papers. The sity of Otago, Does Rudolf Steiner have the answer? topics, and the names and affiliations of the organizers, GARY SHERMAN, Rose-Hulman Institute of Technol­ are as follows: ogy, REV students get results in group theory.

896 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings MUNCIE, INDIANA

TO GASTON II DELAWARE COUNTY AIRPORT

RIGGIN ROAD

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TO WINCHESTER JACKSON

BY-PASS

TO COWAN TO NEW CASTLE TOI-70 TO ANDERSON

1. BALL STATE UNIVERSITY CAMPUS SCALE 2. STUDENT CENTER AND PITTENGER HOTEL 2.25 em. = 1 mile 3.DAYSINN 4. LEES INN 5. MUNCIE INN 6. RADISSON HOTEL [£]-STATE IDGHWAYS 7. SIGNATURE INN 8. SUPER 8 MOTEL

SEPTEMBER 1989, VOLUME 36, NUMBER 7 897 Meetings

Registration 1-2 persons $42 3-4 persons $48 Includes buffet breakfast and two cocktails meeting registration desk will be located in the The per occupant per evening. east end of the second floor corridor of the Pittenger Student Center on the Ball State University campus. The Signature Inn (two-and-one-half miles) campus is located at the corner of University Avenue 3400 Chadam Lane, Muncie, IN 47305 and McKinley Avenue. All sessions will be held in the Telephone: 317-284-4200 Toll Free: 1-800-822-5252 Student Center. The meeting registration desk will be Single $43 Each additional occupant $6 open from 8:00a.m. to 5:00p.m. on Friday, October 27, Includes continental breakfast. and from 8:00 a.m. to noon on Saturday, October 28. The registration fees are $30 for members of the Student Center Pittenger Hotel AMS, $45 for nonmembers, and $10 for students and Ball State University, Muncie, IN 47306 unemployed mathematicians. Telephone: 317-285-1555 Use SUVON from Indiana campuses. Petition Table Single $33 Double $38 A petition table will be set up in the registration area. Each additional occupant $4 Additional information about petition tables can be Located on the Ball State University campus. found in a box in the Boulder meeting announcement on Super 8 Motel (two-and-one-half miles) page 716 of the July/August 1989 issue of Notices. 3601 West Foxridge Lane, Muncie, IN 47304 Telephone: 317-286-4333 Toll Free: 1-800-843-1991 Accommodations One person/one bed $30.88 Blocks of rooms have been set aside in several area Two persons/one bed $34.88 motels and hotels. Participants should make their own Two persons/two beds $37.88 reservations directly with the hotel or motel of their Each additional occupant: $3 choice, and identify themselves as AMS members in order to obtain the special rates given below. Reservations Food Service should be made no later than September 27, 1989. After that date reservations will be accepted on a space­ There are a number of restaurants on campus and in available basis. The rates are subject to a ten percent tax. the surrounding area. Complete listings will be available Distances given below are driving distances measured at the meeting registration desk. There will be several from the Student Center. hundred visitors on campus on Friday, October 27, and it is anticipated that campus area dining facilities will Days Inn (three miles) be used to their capacities during the noon hour only. 2000 North Broadway, Muncie, IN 47303 A buffet lunch will be served for participants and their Telephone: 317-288-9953 Toll Free: 1-800-325-2525 guests in the Student Center at noon on Friday, October Single $30 Double $37 27, and Saturday, October 28. It is recommended that participants have lunch at these buffets due to the tight Lees Inn (two-and-one-half miles) schedule. There are no formal evening meals planned. 3302 North Everbrook Lane, Muncie, IN 47304 Telephone: 317-282-7557 Toll Free: 1-800-733-5337 Travel Single $43 Each additional occupant: $6 Please note: Eastern Standard Time is in effect in Indi­ Includes continental breakfast. ana all year. Muncie is located approximately 60 miles Muncie Inn (one-and-one-half miles) northeast of downtown Indianapolis, and 75 miles from 414 North Madison Street, Muncie, IN 47305 Indianapolis International Airport. A number of major Telephone: 317-282-5981 airlines and several regional airlines serve Indianapo­ lis. The American Eagle Commuter Airline flies twice Single $25 Double $34 Waterbed $35 daily each way between Chicago and the Muncie Air­ Includes morning coffee. port, which is approximately four miles from campus. Radisson Hotel (one-and-one-half miles) Interstate I-69 is approximately eight miles west of the 420 South High Street, Muncie, IN 47305 campus and runs north from Indianapolis into Michigan. Telephone: 317-741-7777 Toll Free: 1-800-333-3333 The shortest route from I-69 to the campus is from the exit at State Road #332.

898 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings

There is direct bus service from the Indianapolis at the northeast corner of Bethel and Tillotson Avenues, Airport to Muncie. Three buses per day are scheduled, and is accessible from either east or west via McGalliard leaving the airport at 11:20 a.m., 5:30 p.m., and 9:15 Road. From the west, McGalliard Road is also State p.m., arriving in Muncie at 1:50 p.m., 7:35 p.m., and Road 332 connecting with I-69. 11:20 p.m. respectively. The bus will be marked either On Saturday, October 28, there should be no difficulty "ABC" or "Summit". A university van will meet all three parking near the Student Center. There is a parking bus arrivals on Thursday, October 26, at the Muncie structure south of the building, and a parking lot west bus station. Those arriving by bus on other days should of the building. Additional university lots are a block inform the Department of Mathematical Sciences, Ball further south. State University, Muncie, Indiana, 47306, or call 317- 285-8640 to make arrangements for service. The van will Weather also meet the American Eagle flights from Chicago to the Muncie Airport on Thursday, October 26. Autumn weather in Muncie is likely to be clear, with cool days and crisp nights. The average daily maximum temperature at this time is 60°F, and the average daily Parking minimum temperature is 38°F. The average rainfall for the month of October is 2.56 inches. Parking near the Student Center on Friday, October 27, will be limited. Vans marked "AMS" will make stops at Andy Roy Magid the hotel, motels, and Stadium Parking Lot starting on Associate Secretary Friday morning at 7:45 a.m. The Stadium Parking Lot is Norman, Oklahoma west of the Ball State Stadium. The stadium is located

...•...... •.....••...... •.....•...

ALGEBRAIC K-THEORY AND ALGEBRAIC BANACH SPACE THEORY NUMBER THEORY Bor-Luh Lin, Editor Michael R. Stein and R. Keith Dennis, Editors (Contemporary Mathematics, Volume 85) (Contemporary Mathematics, Volume 83) This volume contains the proceedings from a Research This volume contains the proceedings of a seminar on Workshop on Banach Space Theory held at the University Algebraic K-theory and Algebraic Number Theory, held at the of Iowa in Iowa City in July 1987. The workshop provided East-West Center in Honolulu in January 1987. The seminar, participants with a collaborative working atmosphere in which which hosted nearly 40 experts from the U.S. and Japan, ideas could be exchanged informally. Several papers were was motivated by the wide range of connections between the initiated during the workshop and are presented here in two topics, as exemplified in the work of Merkurjev, Suslin, their final form. Also included are contributions from several Beilinson, Bloch, Ramakrishnan, Kato, Saito, Lichtenbaum, experts who were unable to attend the workshop. None of Thomason, and lhara. As is evident from the diversity of topics the papers will be published elsewhere. During the workshop, represented in these proceedings, the seminar provided an two hours each day were devoted to seminars on current opportunity for mathematicians from both areas to initiate problems in such areas as weak Hilbert spaces, zonoids, further interactions between these two areas. analytic martingales, and operator theory, and these topics are reflected in some of the papers in the collection.

1980 Mathematics Subject Classifications: 46-06, 46B10, 46B20, 46B22, 46B25 ISBN 0-8218-5092-X, LC 88-38106 ISSN 0271-4132 536 pages (softcover), January 1989 Individual member $29, List price $48, Institutional member $38 All prices subject to change. Shipment will be made by surface. For To order, please specify CONM/85 NA $100. air delivery add, I st book $5, each additional book $3, maximum All prices subject to change. Shipment will be made by surface. For Mathematical Society, P.O. Prepayment required. Order from American air delivery add, 1st book $5, each additional book $3, maximum $100. or call toll free Box 1571, Annex Station, Providence, RI 02901-1571, Prepayment required. Order from American Mathematical Society, P.O. 800-566-7774 to charge with VISA or MasterCard. Box 1571, Annex Station, Providence, RI 02901-1571, or call toll free .•...... •..••••..•••.••••...... •.....800-566-7774 to charge with VISA or MasterCard .

SEPTEMBER 1989, VOLUME 36, NUMBER 7 899 Los Angeles, California University of California, Los Angeles November 18-19

First Announcement

The eight-hundred-and-fifty-third meeting of the Ameri­ and Conferences and in the Invited Speakers and Special can Mathematical Society will be held at the University Sessions section of the Notices. of California, Los Angeles on Saturday, November 18, and Sunday, November 19, 1989. This meeting will be Contributed Papers held in conjunction with the Southern California Section of the Mathematical Association of America. All sessions There will also be sessions for contributed ten-minute will take place in the Mathematical Sciences Building on papers. the UCLA campus. Abstracts for these sessions should have been sub­ mitted by the August 16 deadline. This deadline was Invited Addresses previously published in the Calendar of AMS Meetings and Conferences and the Invited Speakers and Special By invitation of the Far Western Section Program Com­ Sessions section of the Notices. mittee, there will be four invited one-hour addresses. The speakers and their affiliations are: Electronic Submission of Abstracts BURTON I. FEIN, Oregon State University This service is now available to those who use the STEPHEN M. GERSTEN, University of Utah, Salt Lake TEX typesetting system and can be used with abstracts City of papers to be presented at the autumn sectional NICOLAS SPALTENSTEIN, University of Oregon, Eu­ meetings of the AMS. Requests to obtain the package gene of files may be sent electronically on the Internet to THOMAS H. WOLFF, California Institute of Technol­ [email protected]. Requesting the files elec­ ogy tronically will likely be the fastest and most convenient way, but users may also obtain the package on IBM or Macintosh diskettes, available free of charge by writing Special Sessions to: Rosanne Granatiero, American Mathematical Soci­ By invitation of the same committee, there will be four ety, Publications Division, P.O. Box 6248, Providence, special sessions of selected twenty-minute papers. The RI 02940, USA. When requesting the Abstracts package, topics, and the names and affiliations of the organizers, users should be sure to specify whether they want the are as follows: plain TEX, J!.M,S-TEX, or the IH:EX package. Geometric methods in combinatorial group theory, MAA Program ROGER C. ALPERIN, San Jose State University, and KAREN VOGTMANN, Cornell University. The Southern California Section of MAA will meet on Algebraic topology, JAMES P. LIN, University of Cali­ Saturday, November 18. Program information will be fornia, San Diego. announced later. Quadratic forms and simple algebras, DAVID J. SALT­ MAN, University of Texas, Austin, and MuRRAY M. Registration ScHACHER, University of California, Los Angeles. Harmonic analysis, THOMAS H. WoLFF. The meeting registration desk will be located in the Abstracts for these sessions should have been sub­ Faculty Lounge in the Mathematical Sciences Building. mitted by the July 26 deadline or three weeks before The desk will be open from 8:00 a.m. until 4:00 p.m. on the deadline for contributed papers. This deadline was Saturday, and from 8:30 a.m. to noon on Sunday. The previously published in the Calendar of AMS Meetings registration fees are $30 for members of the AMS, $45

900 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings

0 INFORMATION 0 ENTRANCE * EMERGENCY REPORTING ... SYSTEM(ERS)BOOTHS ACCESSIBLE TO N THE DISABLED

SEPTEMBER 1989, VOLUME 36, NUMBER 7 901 Meetings for nonmembers, and $10 for students and unemployed Travel mathematicians. There is a special one-day $15 fee for The UCLA campus is located approximately 12 miles MAA members on Saturday only. north of Los Angeles International Airport (LAX), which is served by all of the major airlines. The taxi fare Petition Table from the airport to the UCLA campus is approximately $20 plus tip. There is no extra charge for additional A petition table will be set up in the registration area. passengers going to the same destination .. The Super Additional information about petition tables can be Shuttle, which provides door-to-door servtce, can be found in a box in the Boulder meeting announcement on summoned by dialing number 35 from the courtesy page 716 of the July August 1989 issue of Notices. I phones in the baggage claim area. The bus should arrive within 15 minutes; the fare is $12 for one P.assenger Accommodations plus tip. For information or advance reservatiOns call 213-777-8000. From courtesy phones dial number 35. Blocks of rooms are being held until October 17 at The most economical transportation is via public the following locations. Participants should make their bus from the LAX Transit Center at 96th Street and own arrangements directly with the hotel of their choice Vicksburg Avenue ( 1I 4 mile northeast of the main airport and be sure to mention the joint AMS-MAA meeting exit). To reach the Transit Center from the termmal, at UCLA. Note that the rates do not include applicable wait next to the lower level roadway under a SHUTTLE taxes. The Claremont and Royal Palace hotels are located BUS sign, which lists buses as A, B, C, etc: Board t?e in Westwood Village within walking distance, adjacent free Cor Lot C bus and exit the airport, gettmg off at lts to the south side of campus. The UCLA Guest House is first stop outside of the airport just after it enters Parking on the campus. Lot C. Walk 100 yards east to the LAX Transit Center. Participants must refer to AMS-MAA meeting when The fastest and most frequent service to UCLA is by the making reservations at the following hotels. RTD #560 bus, which takes approximately 30 minutes costs $1.20. (NOTE: Exact Claremont Hotel to reach the campus and in coins is required; no bills accepted!) D~rect 1044 Tiverton Avenue, Westwood 90024 change to UCLA is also available Monday through Fnday Telephone: 213-208-5957 service on the Culver City #6 bus, which takes approximately Single $35.50 Double $37.50 50 minutes; the fare is 50 cents. All buses approach Twins $41.50 the campus from the south, up Westwood Boulevard, turning right (east) at LeConte Avenue. Exit the bus at the Royal Palace Westwood corner and walk north up Westwood to the Mathematical 1052 Tiverton Avenue, Westwood 90024 Sciences Building (Boelter Hall, approximately 3I 4 mile Telephone: 213-208-6677 or 800-248-6955 (Califor­ on the right, beyond parking structure #9.) Participants nia) or 800-631-0100 (Outside California) planning to stay at the UCLA Guest House should stay Single $67 Double $73 on the bus to the end of the line. All rooms have kitchenettes. Participants must refer to Reference #2905 when making Parking reservations at the following hotel. Permits costing $4 per day are required for any cars UCLA Guest House parking on campus between the hours of 7:00a.m. and (on UCLA campus) 9:00 p.m. daily and may be obtained at any of the several Telephone: 213-825-2923 parking kiosks around the campus. Visitors with permits from other University of California campuses may use Queen bed $71 these to park at UCLA, but must check in at a kiosk. Two twin beds $71 The parking area closest to the Mathematical Scien~es Parlor room (sofa sleeper and kitchenette) $66 Building is Structure #9 on Westwood Boulevard; tts Two room suite (kitchenette, queen kiosk is in the center of the Boulevard. and sofa sleeper) $99 Lance W. Small Food Service Associate Secretary La Jolla, California Information will be provided at the meeting registration desk regarding availability of food service within walking distance.

902 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Invited Speakers and Special Sessions

Invited Speakers Denton, TX, November 1990 at AMS Meetings Avner D. Ash The individuals listed below have accepted invitations Organizers and Topics to address the Society at the times and places in­ of Special Sessions dicated. For some meetings, the list of speakers is incomplete. The list below contains all the information about Special Sessions at meetings of the Society available at the time this issue of Notices went to the printer. Hoboken, NJ, October 1989 The section below entitled Information for Organizers Russel Caflisch Bruce P. Kitchens describes the timetable for announcing the existence Fang Hua Lin Sheldon E. Newhouse of Special Sessions. Muncie, IN, October 1989 Laszlo Lempert PaulS. Muhly October 1989 Meeting in Hoboken, New Jersey Kenneth R. Meyer Steven Sperber Eastern Section Associate Secretary: W. Wistar Comfort Los Angeles, CA, November 1989 Deadline for organizers: Expired Burton I. Fein Nicolas Spaltenstein Deadline for consideration: Expired Stephen M. Gersten Thomas H. Wolff Prabir Bhattacharya and Robert A. Melter, Geometry Louisville, KY, January 1990 related to computer vision Jon Barwise (AMS-MAA) Henryk Iwaniec Stephen L. Bloom, Algebraic semantics Sun-Yung Alice Chang Janos Kollar Russel Caflisch, Mathematical fluid dynamics Charles W. Curtis Israel M. Sigal Mark E. Feighn, Lee D. Mosher and Ulrich Oertel, (AMS-MAA) Barry Simon (AMS-MAA) Low-dimensional topology George B. Dantzig Shlomo Sternberg Bruce P. Kitchens and Sheldon E. Newhouse, Smooth (Gibbs Lecture) (Colloquium Lectures) dynamical systems Israel C. Gohberg Nolan R. Wallach Richard N. Lyons and Richard O'Nan, Finite groups Mike Hopkins (AMS-MAA) Charles C. Sims, Computational algebra Fayetteville, AK, March 1990 Marvin D. Tretkoff, Algebraic geometry, p-adic aspects Marcel F. Neuts Mark A. Stern (AMS-SIAM) Jonathan M. Wahl October 1989 Meeting in Muncie, Indiana Vladimir I. Oliker Central Section Associate Manhattan, KS, March 1990 Secretary: Andy Roy Magid Deadline for organizers: Expired J. Brian Conrey Jean-Pierre Rosay Deadline for consideration: Expired Stewart B. Priddy Jang-Mei Wu Alan Adolphson and Steven Sperber, Number theory University Park, PA, April1990 and algebraic geometry Robert T. Glassey Lowell Jones M. Masoom Ali, Statistics and probability Carsten Grove Gang Tian David E. Barrett and Laszlo Lempert, Complex anal­ Columbus, OH, August 1990 ysis Michael G. Crandall Ananda Gubbi, Extremally disconnected spaces and (Progress in Mathematics Lecture) their applications

SEPTEMBER 1989, VOLUME 36, NUMBER 7 903 Invited Speakers and Special Sessions

Darrell E. Haile, Noncommutative algebra in geometry Lynn McLinden and Jay S. Treiman, Optimization and arithmetic and nonlinear analysis David R. Larson, Triangular operator algebras Hugh L. Montgomery, Analytic number theory Kathryn Frost Porter, Function spaces and topology Peter A. Perry, Geometric spectral and inverse spectral John F. Porter and T. K. Puttaswamy, Differential problems equations Philip E. Protter, Markov processes and stochastic analysis

November 1989 Meeting in Los Angeles, California Far Western Section March 1990 Meeting in Fayetteville, Arkansas Associate Secretary: Lance W. Small Southeast Section Deadline for organizers: Expired Associate Secretary: Joseph A. Cima Deadline for consideration: Expired Deadline for organizers: Expired Roger C. Alperin and Karen Vogtmann, Geometric Deadline for consideration: November 21, 1989 Banach algebras methods in combinatorial group theory J. Duncan and A. L. T. Patterson, Colm A. O'Cinneide and ltrel E. Monroe, Probability James P. Lin, Algebraic topology distributions of phase-type and applications David J. Saltman and Murray M. Schacher, Quadratic H. Hofmann and Jimmie D. Lawson, Semi-groups forms and simple algebras Karl in geometry and analysis Thomas H. Wolff, Harmonic analysis Dima Khavinson, On complex function theory of one and several complex variables January 1990 Meeting in Louisville, Kentucky Associate Secretary: Joseph A. Cima Vladimir I. Oliker and Andrejs E. Treibergs, to be Deadline for organizers: Expired announced Deadline for consideration: Expired Joseph A. Ball and Israel C. Gohberg, Linear operators, March 1990 Meeting in Manhattan, Kansas matrix functions and control Central Section Joseph G. Conlon, The Schrodinger equation Associate Secretary: Andy Roy Magid Raul E. Curto and Paul S. Muhly, Multivariable Deadline for organizers: Expired Deadline for consideration: November 21, 1989 operator theory Andrew G. Bennett, Harmonic analysis and probability Ethan S. Devinatz and Mike Hopkins, Homotopy theory theory David J. Foulis and Richard J. Greechie, Orthostruc­ Robert S. Doran, Group representations and operator tures algebras David H. Hamilton and John F. Rossi, Geometric Bruce R. Ebanks, Functional equations and their ap­ function theory plications Lige Li, Partial differential equations Florence D. Fasanelli and Victor J. Katz, History of Satyagopol Mandai, Commutative algebra mathematics Alexander G. Ramm, Inverse problems and scattering Robert E. Fennell and Suzanne Marie Lenhart, Control theory of infinite dimensional systems Joseph M. Rosenblatt, Ergodic theory Naomi Fisher, Harvey B. Keynes and Philip D. Richard H. Schelp, Graph theory Wagreich, Mathematics and education reform George E. Strecker, Applications of category theory (AMS-MAA Session) Carl H. FitzGerald and Ted J. Suffridge, Geometric April1990 Meeting in University Park, Pennsylvania function theory in one and several complex variables Eastern Section Gary D. Jones, Oscillation theory in ordinary differen­ Associate Secretary: W. Wistar Comfort tial equations Deadline for organizers: Expired Janos Kollar, Algebraic geometry Deadline for consideration: January 4, /990 Efim D. Khalimsky, Yung Kong and Ralph D. Donald M. Davis, Algebraic topology Kopperman, Topology in computer graphics and image processing August 1990 Meeting in Columbus, Ohio Inessa Levi and W. Wiley Williams, Semigroup theory Associate Secretary: W. Wistar Comfort Deadline for organizers: November 15, 1989 Peter A. McCoy, Function theoretic methods in differ­ Deadline for consideration: April 27, 1990 ential equations

904 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Invited Speakers and Special Sessions

November 1990 Meeting in Denton, Texas Special Sessions are very effective at Sectional Central Section Meetings and can usually be accommodated. They are Associate Secretary: Andy Roy Magid selected by the Section Program Committee. The pro­ Deadline for organizers: February 15, 1990 cessing of proposals for Special Sessions for Sectional Deadline for consideration: July 16, 1990 Meetings is handled by the Associate Secretary for the Section, who then forwards the proposals to the Information for Organizers Section Program Committee, which makes the final selection of the proposals. Each Invited Speaker at Special Sessions at Annual and Summer Meetings are a Sectional Meeting is invited to organize a Special held under the supervision of the Program Committee Session. Just as for national meetings, no Special for National Meetings (PCNM). They are adminis­ Session at a Sectional Meeting may be approved so tered by the Associate Secretary in charge of that late that its announcement appears past the deadline meeting with staff assistance from the Meetings and after which members can no longer send abstracts for Editorial Departments in the Society office in Provi­ consideration for presentation in that Special Session. dence. The Society reserves the right of first refusal for According to the "Rules for Special Sessions" of the publication of proceedings of any Special Ses­ the Society, Special Sessions are selected by the PCNM sion. These proceedings appear in the book series from a list of proposed Special Sessions in essentially Contemporary Mathematics. the same manner as Invited Speakers are selected. The More precise details concerning proposals for and number of Special Sessions at a Summer or Annual organizing of Special Sessions may be found in the Meeting is limited. The algorithm that determines the "Rules for Special Sessions" or may be obtained from of Sp~cial Sessions allowed at a given meeting, nu~be~ any Associate Secretary. whlle simple, IS not repeated here, but can be found in "Rules for Special Sessions" on page 614 in the April Send Proposals for Special Sessions to the issue of Notices. 1988 Associate Secretaries a Spe­ Each Invited Speaker is invited to generate The programs of sectional meetings are arranged by the Associate cial Session, either by personally organizing one or Secretary for the section in question: by having a Special Session organized by others. Pro­ Far Western Section (Pacific and Mountain) posals to organize a Special Session are sometimes Lance W. Small, Associate Secretary requested either by the PCNM or by the Associate Department of Mathematics Secretary. Other proposals to organize a Special Ses­ University of California, San Diego sion may be submitted to the Associate Secretary in La Jolla, CA 92093 meeting (who is an ex-officio member e-mail: [email protected] charge of that (Telephone 619-534- 3590) and whose address may be found of the committee Central Section must be in the hands of the below). These proposals Andy Roy Magid, Associate Secretary PCNM well in advance of the meeting and, in any Department of Mathematics case, at least nine (9) months prior to the meeting at University of Oklahoma which the Special Session is to be held in order that 601 Elm PHSC 423 the committee may consider all the proposals for Spe­ Norman, OK 73019 Proposals that are sent e-mail: [email protected] cial Sessions simultaneously. (Telephone 405-325-2052) of the Society, to Notices, or t~ the Providence office Eastern Section than the Associate Secretary di_rected to anyone other W. Wistar Comfort, Associate Secretary Will have to be forwarded and may not be received in Department of Mathematics time to be considered for acceptance. Wesleyan University It should be noted that Special Sessions must Middletown, CT 06457 be announced in Notices in such a timely fashion e-mail: [email protected] (Telephone 203-347-9411) that ~ny member of the Society who so wishes may submit an abstract for consideration for presentation in the Special Session before the deadline for such consideration. This deadline is usually three (3) weeks before the Deadline for Abstracts for the meeting in question.

SEPTEMBER 1989, VOLUME 36, NUMBER 7 905 Invited Speakers and Special Sessions

Southeastern Section for contributed papers for the same meeting. The Joseph A. Cima, Associate Secretary Council has decreed that no paper, whether invited or Department of Mathematics contributed, may be listed in the program of a meeting University of North Carolina, Chapel Hill of the Society unless an abstract of the paper has been Chapel Hill, NC 27599-3902 e-mail: [email protected] received in Providence prior to the deadline. (Telephone 919- 962- I 050) Electronic submission of abstracts is now available As a general rule, members who anticipate organizing Special to those who use the TEX typesetting system. Requests Sessions at AMS meetings are advised to seek approval at least to obtain the package of files may be sent electron­ nine months prior to the scheduled date of the meeting. No Special ically via the Internet to [email protected]. Sessions can be approved too late to provide adequate advance Requesting the files electronically will likely be the notice to members who wish to participate. fastest and most convenient way, but users may also obtain the package on IBM or Macintosh diskettes, Information for Speakers available free of charge by writing to: Rosanne Gra­ natiero, American Mathematical Society, Publications A great many of the papers presented in Special Ses­ Division, P.O. Box 6248, Providence, RI 02940, USA. sions at meetings of the Society are invited papers, but When requesting the Abstracts package, users should any member of the Society who wishes to do so may be sure to specify whether they want the plain TEX, submit an abstract for consideration for presentation A.MS-TEX, or the ~TEX package. in a Special Session, provided it is received in Prov­ idence prior to the special early deadline announced above and in the announcements of the meeting at Number of Papers Presented which the Special Session has been scheduled. Con­ Joint Authorship tributors should know that there is a limitation in Although an individual may present only one ten­ size of a single special session, so that it is sometimes minute contributed paper at a meeting, any combina­ true that all places are filled by invitation. Papers tion of joint authorship may be accepted, provided not accepted for a Special Session are considered as no individual speaks more than once. An author can ten-minute contributed papers. speak by invitation in more than one Special Session Abstracts of papers submitted for consideration for at the same meeting. presentation at a Special Session must be received by An individual may contribute only one abstract by the Providence office (Editorial Department, American title in any one issue of Abstracts, but joint authors Mathematical Society, P. 0. Box 6248, Providence, are treated as a separate category. Thus, in addition RI 02940) by the special deadline for Special Sessions, to abstracts from two individual authors, one joint which is usually three weeks earlier than the deadline abstract by them may also be accepted for an issue.

MAA Contributed Paper Sessions at Louisville This early preliminary announcement of the Louisville meeting is made to encourage members' participation and to provide lead-time for organizing the sessions on contributed papers. The meeting will be held January 17-20 (Wednesday- Saturday), 1990. Past President Leonard Gillman will give his Retiring Presidential Address at this meeting. In addition, there will be other invited addresses, Joint AMS-MAA addresses, minicourses and various panel discussions. Contributed papers are being accepted on several topics in collegiate mathematics. The topics, organizers, their affiliations, and the days they will meet are: • Prognostic and diagnostic testing: Helping high school students get ready for college-level mathematics, sponsored by the Committee on Placement Examinations-BERT K. WAITS, Ohio State University. Wednesday andjor Thursday. Papers are invited that describe local, regional, or statewide projects that give college mathematics placement tests to high school students (like the Ohio Early College Mathematics Placement Testing Program-EMPT), or projects that give high school students diagnostic tests to help them prepare for college-level mathematics (like the California Mathematics Diagnostic Testing Project), or other programs or projects designed to improve the mathematics articulation from high school to college.

906 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY MAA Contributed Paper Sessions

• Recent developments in placement- ELIZABETH J. TELES, Montgomery College, Maryland, RAY E. COLLINGS, Tri-County Technical College, South Carolina, and JoHN W. KENELLY, Clemson University, Friday and/or Saturday. Papers are sought describing placement procedures in colleges and universities for entry level mathematics courses beyond local efforts. The focus of the session will be on regional, state, and national initiatives. • Discrete mathematics: Has the bubble burst?-MARTHA J. SIEGEL, Towson State University, Maryland, Wednesday and/or Thursday. Presentations on the teaching of discrete mathematics in the first two years are welcome. Special consideration will be given to papers which emphasize innovative and successful courses for freshman or sophomore mathematics and computer science majors. Curricula integrating the discrete component into the calculus sequence or courses emphasizing discrete models are of special interest. The organizers will aim for diversity in choosing the program. • Classic classroom calculus problems-ANTHONY BARCELLos, American River College, California, Friday and/or Saturday. Every calculus teacher has favorite examples that he or she manages to present in an interesting way. We invite you to share your examples and insights with us. • A core in mathematics-KAY B. SoMERS, Moravian College, Pennsylvania, Friday and/ or Saturday. This session will focus on approaches taken to provide a base in mathematics for college undergraduates. Information on particular courses and ways to present specific topics are encouraged. Topics to be discussed can include, but are not limited to, the following: quantitative problem solving, interdisciplinary courses incorporating mathematics, introductory mathematical modeling, historical perspectives in mathematics, graphical presentations across disciplines, the role of data analysis in a mathematics core. Presentations are normally limited to ten minutes, although selected contributors may be given up to twenty minutes. Individuals wishing to submit papers for any of these sessions should send the following information to the MAA Washington office at 1529 Eighteenth Street, NW, Washington, DC 20036 by September 28: 1. Title 2. Intended session 3. A one-paragraph abstract (for distribution at the meeting) 4. A one-page outline of the presentation. Rooms where sessions of contributed papers will be held are equipped with overhead projector and screen. Blackboards are not available. Persons having other equipment needs should contact the secretary (Kenneth A. Ross, Department of Mathematics, University of Oregon, Eugene, OR 97403) as soon as possible, but in any case prior to November 1. Upon request, the following will be made available: one additional overhead projector/screen, 35mm carousel slide projector, 16mm film projector, or VHS video cassette recorder with one color monitor. Special Computer Session of Contributed Papers Computers in the Classroom: The time is right is being organized by DAVID P. KRAINES, Duke University, and VIVIAN Y. KRAINES, Meredith College. Presentations are invited on the use of microcomputers to enhance undergraduate mathematics classroom instruction. Proposals for the fifteen minute presentations should include ( 1) title, (2) a one-paragraph abstract (for distribution at the meeting), ( 3) a one-page outline of the presentation and (4) a list of the software and computer to be used. Also indicate if a color projection system is required and list any other special equipment needed. If noncommercial software is to be used, please include a copy. Submissions should be sent to Vivian Y. Kraines, Department of Mathematics and Computer Science, Meredith College, Raleigh, NC 27607-5298 by October 20. Participants will be notified by November 3 whether their submission has been accepted.

SEPTEMBER 1989, VOLUME 36, NUMBER 7 907 1:11 INTERNATIONAL CONGRESS OF ICM-90 MATHEMATICIANS International Congress of Kyoto, JAPAN August 21-29, 1990 ""Mathematicians KYOTO FIRST ANNOUNCEMENT

The Organizing Committee is pleased to announce that the next International Congress of Mathematicians will be held at the Kyoto International Conference Hall, from Tuesday, August 21 through Wednesday, August 29, 1990. It will be held under the auspices of the International Mathematical Union and under the sponsorship of the Science Council of Japan, the Mathematical Society of Japan, the Japan Society of Mathematical Education, The History of Science Society of Japan, The Institute of Actuaries of Japan, the Japan Society for Software Science and Technology, The Japan Statistical Society, and The Operations Research Society of Japan. Mathematical Program There will be about 16 invited one-hour expository addresses covering recent developments in major areas of mathe­ matics, and approximately 140 invited 45-minute lectures divided into the following 18 sections:

1. Mathematical logic and foun- 9. Operator algebras and functional 15. Mathematical aspects of computer dations analysis science 2. Algebra 1 0. Probability theory and 16. Computational methods 3. Number theory mathematical statistics 17. Applications of mathematics to the 4. Geometry 11. Partial differential equations sciences 5. Topology 12. Ordinary differential equations 18. History, teaching and the nature of 6. Algebraic geometry and dynamical systems mathematics 7. Lie groups and representations 13. Mathematical physics 8. Real and complex analysis 14. Combinatorics

The International Commission on Mathematical Instruction will have several invited lectures. All Ordinary Members of the Congress will have an opportunity to present ten-minute short communications; informal mathematical seminars may be organized on participant's initiative. All invited lectures will be published in the Proceedings of ICM-90. A complimentary copy will be sent to each Ordinary Member after the Congress. Abstracts of the short communications will be distributed to Ordinary Members at the Congress free of charge. English, French, German and Russian will be the official languages of the Congress. Social Events The Organizing Committee will arrange a reception on Tuesday, August 21; a traditional art performance theater in the late afternoon of Saturday, August 25; and a banquet on Wednesday, August 29. These events will be free to all registered Ordinary and Accompanying Members. Excursions and (pre- and post-Congress) tours will be arranged by Japan Travel Bureau, Inc. Sunday, August 26 will be set aside for optional excursions and no lectures will be scheduled on this day. Further details concerning these activities will appear in the Second Announcement. Location of the Conference The Kyoto International Conference Hall is located in the northern part of Kyoto City. The closest airport to Kyoto is Osaka International Airport, which is about 55 minutes from Kyoto by the limousine bus service. The buses leave the airport every 20 minutes between the hours of 7:55a.m. to 9:30p.m. Kyoto is located 500km west of Tokyo. A rapid train service (Shinkansen) from Tokyo to Kyoto is available with about a 10 - 30 minutes interval between each train from the hours of 6 a.m. to 9 p.m. It takes about 2 hours and 45 minutes, and the current price is ¥12,970 one way. Kyoto, surrounded by gracefully wooded hills, was the capital of Japan from 794 A.D. to 1868 A.D. Besides two magnificient Imperial Villas, Kyoto has about 400 Shinto shrines and 1 ,650 Buddhist temples which dot the entire city. Kyoto offers the innumerable cultural treasures and traditional crafts and attracts visitors from throughout the world as well as from within Japan. The city of Nara, which is an ancient capital and another renowned sightseeing center of old Japanese culture, can be reached within 30 minutes from Kyoto by an express train and makes an excel­ lent one-day excursion.

908 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY The Official Carrier Japan Air Lines (JAL) is the official carrier for the Congress. Please contact the nearest JAL overseas office for the appropriate air schedules.

The Official Travel Agent (Group Flights) Japan Travel Bureau, Inc. (JTB) Kyoto Office has been appointed as the official travel agent for the Congress and will handle all travel arrangements related to the Congress including hotel accommodations and group flights. All inquiries should be addressed to the following: Japan Travel Bureau, Inc. Tel: (075) 361-7241 Kyoto Office Fax: (075) 341-1028 Convention Dept. Telex: J24418TOURIST (attn. KYOTO) Higashi-shiokoji-cho, Shimogyo-ku Kyoto 600, JAPAN Accommodations For participants and their accompanying members, a sufficient number of rooms have been reserved in Kyoto at various prices by Japan Travel Bureau, Inc., Kyoto. More precise information along with the hotel reservation form will be included in the Second Announcement. Hotels in Kyoto The specially discounted room rates (in yen), which includes the tax and service charges (but no meals), are as follows:

Class Single with bath Twin with bath A ¥9,000- ¥20,000 ¥13,000- ¥22,000 B ¥7,000 -- ¥8,000 ¥11,000-¥13,000 ------f------··------·--- -- c ¥5,500- ¥7,000 ¥9,000- ¥11,000 ·------D ¥4,000- ¥5,500 ¥7,000- ¥9,000

4 beds in 1 room without bath *E ¥2,500- ¥4,000/person 4-8 beds in 1 room without bath Youth Hostel ¥2,100- ¥2,450/person *If you wish to book a room of Class E, please find 3 other people with whom you can share a room, and include their names on the application form in the Second Announcement. Climate and Clothing In late August, the average temperature in Kyoto is approximately 28°C (82°F) and the humidity is somewhat high. Light summer clothing is recommended. The Congress Hall and hotels are all well air-conditioned. No formal dress will be required on any occasion during the congress.

Second Announcement The Second Announcement of ICM-90 will describe all the activities of the Congress in detail and provide instructions on how to complete the pre-registration process and obtain accommodations. It will provide more, although not com­ plete, information on the scientific program, and give instructions regarding the submission of abstracts of short com­ munications and the organization of informal seminars. The Second Announcement will also include advice on how to reach Kyoto and will be accompanied by a brochure describing the day trips and tours organized by Japan Travel Bureau.

If you wish to receive the Second Announcement, please complete the special form provided in the back of this issue of Notices.

The form must be received by ICM-90 in Kyoto no later than October 15, 1989. The Second Announcement will be mailed to you by ICM-90 before the end of 1989.

SEPTEMBER 1989, VOLUME 36, NUMBER 7 909 1989 AMS Elections

Candidates Reports and Communications section of this issue for the list of cur­ OFFICERS rent members of the Council and Board of Trustees. Members are President Elect* requested to write their suggestions for such candidates in the ap­ Michael Artin propriate spaces below. REPLACEMENT BALLOTS Vice President (two to be elected) James G. Arthur James B. Serrin This year ballots for the AMS election will be mailed September I 0, Lenore Blum Dennis P. Sullivan 1989, or within a day or two thereafter. The deadline for receipt of Phillip A. Griffiths ballots in Providence is November 10, 1989. There has been a small but recurring and distressing problem concerning members who state that they have not received ballots Associate Secretaries* Andy Roy Magid Lance W. Small in the annual election. It occurs for several reasons, including fail­ (Central) (Far Western) ure of local delivery systems on university or corporate properties, failure of members to give timely notice of changes of address to the Providence office, failures of postal services, and other human Member-at-Large of the Council (five to be elected) errors. Sheldon Axler Charles Herbert Clemens To help alleviate this problem, the following replacement proce­ Joan S. Birman Amassa G. Fauntleroy dure has been devised: A member who has not received a ballot by Edwin E. Floyd James W. Cannon October 10, 1989, or who has received a ballot but has accidentally Alexandre J. Chorin Carl Pomerance spoiled it, may write after that date to the Secretary of the AMS, Post Shing-Tung Yau Frank H. Clarke Office Box 6248, Providence, RI 02940, asking for a second ballot. The request should include the individual's member code and the Board of Trustees (one to be elected) address to which the replacement ballot should be sent. Immediately Ramesh A. Gangolli John C. Polking upon receipt of the request in the Providence office, a second ballot, which will be indistinguishable from the original, will be sent by first NOMINATING COMMITTEE FOR 1990 class or air mail. It must be returned in an inner envelope, which (Preferential Ballot, three to be elected) will be supplied, on the outside of which is the following statement Sylvain E. Cappell Ray A. Kunze to be signed by the member: Robert M. Hardt Paul C. Roberts The ballot in this envelope is the only ballot that I am submitting Barbara Lee Keyfitz Robert F. Williams in this election. I understand that if this statement is not correct then no ballot of mine will be counted. EDITORIAL BOARDS COMMITTEE FOR 1990 (Preferential Ballot, two to be elected) signature Linda Keen Andrew M. Odlyzko Carlos E. Kenig Barry Simon Although a second ballot will be supplied on request and will be sent *Uncontested offices by first class or air mail, the deadline for receipt of ballots will not be extended to accommodate these special cases. SUGGESTIONS FOR 1990 NOMINATIONS Election Information Council and Board of Trustees

The ballots for election of members of the Council and Board of Vice President (I) Trustees of the Society for 1990 will be mailed on or shortly after September 10, in order for members to receive their ballots well in advance of the November I 0 deadline. Prior to casting their ballots Associate Secretaries (2) members are urged to consult the following articles and sections of the Bylaws of the Society: article I, section I; article II, sections I, 2; article III, sections I, 2, 3; article IV, sections I, 2, 4; article VII, sections I, 2, 5. The complete text of the Bylaws appears on pages Members-at-large of the Council (5) 1155-1160 of the November 1987 issue of Notices. A list of the members of the Council and Board of Trustees serving terms during 1989 appears in the AMS Reports and Communications section of this issue.

SUGGESTIONS FOR 1990 NOMINATIONS Each year the members of the Society are given the opportunity to Member of the Board of Trustees (I) propose for nomination the names of those individuals they deem both qualified and responsive to their views and needs as part of the mathematical community. Candidates will be nominated by the The completed form should be addressed to AMS Nominating Com­ Council to fill positions on the Council and Board of Trustees to mittee, Post Office Box 6248, Providence, RI 02940, to arrive no replace those whose terms expire December 31, 1990. See the AMS later than November 10, 1989.

910 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY 1988-1989. Academic Year Devoted to Mathematical Sciences Operator Algebras, Mittag-Leffler Insti­ tute, Djursholm, Sweden. (Feb. 1988, Meetings and Conferences p. 307) I 9 89. 40th Anniversary of Kansas Gamma of Pi Mu Epsilon, Wichita State Univer­ sity, Wichita, KS. (Jan. 1989, p. 63) 1989. Concentration Year on Fluid Dy­ namical Aspects of Combustion Theory, Instituto Per Le Applicazioni Del Cal­ colo, Rome, Italy. (Jan. 1989, p. 63) 1989-1990. Academic Year Devoted to Hyperbolic Geometry and Quasiconformal Mappings, Mittag-Leffler Institute, Djur­ of meetings and conferences of interest to sholm, Sweden. (Dec. 1988, p. 1584) THIS SECTION contains announcements some segment of the mathematical public, including ad hoc, local, or regional meetings, January !-December 23, 1989. Math­ and meetings or symposia devoted to specialized topics, as well as announcements ematisches Forschungsinstitut Oberwol­ of regularly scheduled meetings of national or international mathematical organizations. fach (Weekly Conferences), Federal Re­ (Information on meetings of the Society, and on meetings sponsored by the Society, will public of Germany. (Apr. 1988, p. 629 be found inside the front cover.) and Nov. 1988, p. 1381) AN ANNOUNCEMENT will be published in Notices if it contains a call for papers, and specifies the place, date, subject (when applicable), and the speakers; a second full announcement will be published only if there are changes or necessary additional September 1989 information. Once an announcement has appeared, the event will be briefly noted in each issue until it has been held and a reference will be given in parentheses to the month, 8-14. COSMEX '89: International Con­ year, and page of the issue in which the complete information appeared. Asterisks (*) ference on Stochastic Methods in Experi­ mark those announcements containing new or revised information. mental Sciences, Technical University of IN GENERAL, announcements of meetings and conferences held in North America carry Wroclaw, Poland. (Nov. 1988, p. 1388) only date, title of meeting, place of meeting, names of speakers (or sometimes a general program), deadlines for abstracts or contributed papers, and source Ober­ statement on the l 0-16. Transformationsgruppen, of further information. Meetings held outside the North American area may carry more wolfach, Federal Republic of Germany. detailed information. In any case, if there is any application deadline with respect to (Jul./ Aug. 1989, p. 762) participation in the meeting, this fact should be noted. All communications on meetings ll-13. Supercomputers: Emerging Appli­ and conferences in the mathematical sciences should be sent to the Editor of Notices, cations in Manufacturing, Minneapolis, care of the American Mathematical Society in Providence. MN. (Mar. 1989, p. 312) DEADLINES for entries in this section are listed on the inside front cover of each issue. In order to allow participants to arrange their travel plans, organizers of meetings are urged des Donnes, Antibes, ll-14. Analyse to submit information for these listings early enough to allow them to appear in more than France. (Mar. 1989, p. 312) one issue of Notices prior to the meeting in question. To achieve this, listings should be ll-14. Calculus of Variations and Re­ received in Providence SIX MONTHS prior to the scheduled date of the meeting. lated Topics, Research Institute for Math­ ematical Sciences, Kyoto University, Japan. (Jul./ Aug. 1989, p. 762) 15-20. Sino-French Colloquium on Prob­ 18-21. Traffic Theories for New Telecom­ ll-15. Journees de Probabilites, Mar­ ability and Statistics, Centre sino-fran~ais munications Services, Adelaide, Australia. seille, France. (Mar. 1989, p. 312) de Mathematiques et d'Informatique, (Nov. 1988, p. 1388) l l-15. Fifth International Conference on Universite de Wuhan, 430072 Wuhan, 18-21. SIAM Conference on Mathe­ Numerical Methods in Engineering, Lau­ People's Republic of China. (MayfJun. matics of Geophysical Sciences, Houston, sanne, Switzerland. (Nov. 1988, p. 1388) 1989, p. 598) TX. (Nov. 1988, p. 1388) ll-16. Trends in Functional Analysis and 16-0ctober 20. Sixth World Congress 18-22. Bifurcations et Orbites Peri­ Approximation Theory, Acqua Fredda di on Medical Information, Beijing, China. odiques des Champs de Vecteurs du Plan, Maratea (Potenza), Italy. (Feb. 1989, (Apr. 1988, p. 639) Marseille, France. (Mar. 1989, p. 312) p. 182) 17-22. The ICME Conference on the 18-23. Conference on Integral Equations ll-17. Conference on Foliations (in mem­ Popularization of Mathematics, Leeds, and Inverse Problems, Varna, Bulgaria. ory of Bruce L. Reinhart), University of England. (Jan. 1989, p. 70) (Nov. 1988, p. 1388) Maryland, College Park, MD. (Jul./ Aug. 17-22. Twelfth Osterreichischer Math­ 19-23. 1830-1930: A Century of Geom­ 1989, p. 762) ematikerkongress, Wien, Austria. (Jul./ etry, from C. F. Gauss and B. Riemann 12-15. National Computer Graphics As­ Aug. 1989, p. 762) to H. Poincare and E. Cartan; Episte­ sociation Conference on CAD/CAM/­ 17-23. Effiziente Algorithmen, Ober­ mology, History, and Mathematics, Insti­ CAE/CIM Aerospace and Electronics, wolfach, Federal Republic of Germany. tut Henri Poincare, Paris, France. (Apr. Santa Clara, CA. (Apr. 1989, p. 494) (Jul./ Aug. 1989, p. 762) 1989, p. 494)

SEPTEMBER 1989, VOLUME 36, NUMBER 7 911 Meetings and Conferences

21-22. Mathematics in the Car Industry, ORGANIZERS: J. B. Bednar, Amerada Validating Numerical Methods, Univer­ Warwick, England. (Nov. 1988, p. 1388) Hess Corporation, Tulsa. sity of Basel, Basel, Switzerland. (Mar. * 24-27. Annual Conference MANSW, INFORMATION: SIAM Conference Co­ 1989, p. 313) Taking Maths into the 1990's, Mudgee, ordinator, 3600 University City Sci­ 2-6. Geometrie Algebrique Reelle, Mar­ NSW, Australia. ence Center, Philadelphia, P A 19104- seille, France. (Jul./ Aug. 1989, p. 763) 2688;Phone:215-382-9800;Fax:215- 2-6. Third Workshop on Computer Sci­ INFORMATION: Annual Conference Or­ 386-7999. ganizer, P.O. Box 536, Darlinghurst, ence Logic, Kaiserslautern, West Ger­ NSW 20 I 0, Australia. * 27-0ctober 5. International School on many. (Apr. 1989, p. 494) Lyapunov Functions Methodflrkutsk'89, 2-6. Symposium on Applied and Indus­ 24-30. Kryptographie, Oberwolfach, Fed­ Irkutsk, USSR. trial Mathematics, Island of San Servolo, eral Republic of Germany. (Mar. 1989, Venice, Italy. (Apr. 1989, p. 494) SPONSOR: International Association p. 312) 4-6. Geometry and Mathematical Physics: for Mathematics and Computers in 24-0ctober 6. Extrapolation et Approxi­ John H. Barrett Memorial Lectures, The Simulation (IMACS). mation Rationelle, Marseille, France. University of Tennessee, Knoxville, TN. CONFERENCE TOPICS: Mathematical (Mar. 1989, p. 312) (Mar. 1989, p. 313) problems of the method of Lyapunov Con­ 25-27. SSA-IMACS 1989 Biennial functions; elaboration of techniques 4-6. First European Workshop on Hyper­ ference on Modelling and Simulation, and algorithms of construction of cube and Distributed Computers, Rennes, p. 312) Canberra, Australia. (Mar. 1989, Lyapunov functions and comparison France. (Jul./ Aug. 1989, p. 763) 25-28. SIAM Conference on Mathemati­ systems; development of stability the­ 6-7. Conference on Issues in the Teaching cal and Computational Issues in Geophys­ ory for differential and integrodiffer­ of Calculus, Miami University, Oxford, ical Fluid and Solid Mechanics, Houston, ential equations with partial deriva­ OH. (Apr. 1989, p. 494) TX. (Mar. 1989, p. 312) tives; application of the method of 8-14. Arbeitsgemeinschaft Geyer-Harder, 25-29. Third International Conference Lyapunov functions to investigation Oberwolfach, Federal Republic of Ger­ on the Theory of Groups and Related of diverse-type systems. many. (Jul./ Aug. 1989, p. 763) Topics, Australian National University, INFORMATION: V. M. Matrosov, Di­ 9-13. Workshop on Geometric Phases in Canberra. (May/June 1988, p. 732) rector of the Irkutsk Computing Cen­ Geometric Phases in Mechanics, Mathe­ 25-29. Extrapolation et Approximation ter, Siberian Branch, USSR Academy matical Sciences Institute, Cornell Uni­ Rationelle, Marseille, France. (Jul./ Aug. of Sciences, Lermontov Str. 134, versity, Ithaca, NY. (MayfJun. 1989, 1989, p. 762) 664033 Irkutsk, USSR. p. 599) * 25-30. Workshop: Quantum Groups, Op­ * 28-29. International Conference on Math­ 12-14. Second Interdisciplinary Confer­ erator Algebras and Duality and Their ematics in Transport Planning and Con­ ence on Natural Resource Modeling and Applications to Physics, Cortona, Italy. trol, Cardiff, Wales. Analysis, Florida State University, Talla­ INVITED SPEAKERS: L. Bonora, A. hassee, FL. (Apr. 1989, p. 494) INFORMATION: S. Wardle, Conference 13-14. Ninth Annual Southeastern­ Connes, R. Cotta, C. D'Antoni, G. Officer, The Institute of Mathematics Dell' Antoni, F. Eidaleo, K. Freden­ Atlantic Regional Conference on Differ­ and its Applications, Maitland House, ential Equations, University of North hagen, J. Frohlich, F. Goodman, R. Es­ Warrior House, Southend-on-Sea, Carolina at Charlotte, Charlotte, NC. Herman, M. B. Landstad, R. Longo, sex SS l 2JY, England. Y. Nakagami, A. Ocneanu, M. Rosso, (MayfJun. 1989, p. 599) B. Schroer, G. Skandalis, M. Spera, F. 29-30. Midwest Noncommutative Ring 15-18. Fourth International Workshop on Strocchi, M. Takesaki, I. T. Todorov, Theory, Ohio University, Athens, OH. High-Level Synthesis, Kennebunkport, A. Wasserman, H. Wenzl, S. L. (Jul./ Aug. 1989, p. 763) ME. (Dec. 1988, p. 1590) Woronowicz. 29-0ctober 1. Sixth IFAC/IFIP/IFORS 15-21. Geometrie, Oberwolfach, Federal INFORMATION: S. Doplicher, Dipar­ /IMACS Symposium on Information Con­ Republic of Germany. (Jul./ Aug. 1989, timento di Matematica, Universita trol Problems in Manufacturing Technol­ p. 763) di Roma "La Sapienza", Citta Uni­ ogy, Madrid, Spain. (Mar. 1989, p. 313) 16-18. Second International Conference versitaria, 00185 Roma, Italy; Email: on Data and Knowledge Systems for Man­ [email protected]. ufacturing and Engineering, National In­ October 1989 26-28. Third International Workshop stitute of Standards and Technology, on Distributed Algorithms, La Colle-sur­ l-7. Topologische Methoden in der Grup­ Gaithersburg, MD. (Apr. 1989, p. 495) Loup, France. (Feb. 1989, p. 182) pentheorie, Oberwolfach, Federal Repub­ 16-20. Workshop on Set Theory and the 27-29. Eighth Gamm Conference on lic of Germany. (Jul./ Aug. 1989, p. 763) Continuum, Mathematical Sciences Re­ Numerical Methods of Fluid Mechanics, 2-4. Topics in Univalent Functions and search Institute, Berkeley, CA. (MayjJun. Delft, The Netherlands. (Jul./ Aug. ( 1989, Its Applications, Research Institute for 1989, p. 599) p. 763) Mathematical Sciences, Kyoto Univer­ 16-20. Sixth World Congress on Medical * 27-29. SIAM Workshop on Geophysical sity, Japan. (Jul./ Aug. 1989, p. 763) Informatics, Beijing, China. (Feb. 1989, Inversion, Houston, TX. 2-6. IMACS-GAMM International Sym­ p. 182) posium on Computer Arithmetic and Self-

912 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences

16-20. Workshop: Patterns and Dynam­ * 27-28. Fourth Annual Pi Mu Epsilon Re­ 5-11. Fastringe und Fastkorper, Ober­ ics in Reactive Media, Institute for Math­ gional Undergraduate Mathematics Con­ wolfach, Federal Republic of Germany. ematics and its Applications, Minneapo­ ference, De Pere, WI. (Jul./ Aug. 1989, p. 764) lis, MN. (Feb. 1989, p. 182) of Solutions to INVITED SPEAKER: J. S. Frame, Michi­ 6-8. On the Structure Equations, Research 17-20. Hyperfunctions and Differential gan State University. Partial Differential Ky­ Equation, Research Institute for Mathe­ INFORMATION: R. Poss, St. Norbert Institute for Mathematical Sciences, 1989, matical Sciences, Kyoto University, Japan. College, De Pere, WI 54115; 414-337- oto University, Japan. (Jul./ Aug. (Jul./ Aug. 1989, p. 763) 3198. p. 764) 19-20. Workshop on Large-Scale Numer­ 6-9. International Conference on ical Optimization, Mathematical Sciences 29-November 4. Computational Methods Computer-Aided Design, Santa Clara, CA. Institute, Cornell University, Ithaca, NY. in Solid Mechanics, Oberwolfach, Fed­ (Apr. 1989, p. 495) (May/ Jun. 1989, p. 599) eral Republic of Germany. (Mar. 1989, 6-10. SIAM Conference on Applied Ge­ 19-21. Journees Mathematiquesjlnforma­ p. 313) ometry, Tempe, AZ. (Nov. 1988, p. 1388) tique, Marseille, France. (Jul./ Aug. 1989, * 30-November I. Thirtieth Foundations 6-10. SIAM Conference on Geometric p. 763) of Computer Science (FOCS), Research Design, Tempe, AZ. (Mar. 1989, p. 314) Park, NC. 20-26. Hamiltonian Systems, Trans­ 8-10. Conference for Mathematics in formation Groups and Special Trans­ SPONSORs: IEEE Computer Society. Chemistry, College Station, TX. (Jul./ Aug. form Methods, Centre de Recherches INFORMATION: C. Papadimitriou, 1989, p. 764) Mathematiques (CRM) Universite de Dept. of Computer Science, Univ. I 0-11. Eighteenth Midwest Differential Montreal. (Please note date change from of California, San Diego, La Jolla, Equations Conference, Southern Illinois Jan. 1989, p. 70) CA 92093; Phone: 619-534-2086. University, Carbondale, IL. (Apr. 1989, 21-22. Eastern Section Meeting of the p. 495) 2. Workshop on Ho­ AMS, Stevens Institute of Technology, 30-November Mathematical Sciences I 0-11. Conference on Women in Mathe­ Hoboken, NJ. motopy Theory, Research Institute, Berkeley, CA. (Mar. matics and the Sciences, St. Cloud State INFORMATION: W. Drady, AMS, P.O. 1989, p. 313) University, St. Cloud, MN. (Jul./ Aug. 1989, p. 764) Box 6248, Providence, RI 02940. 30-November 2. Differential Analysis Differential Topology, Research In­ 12-15. National Computer Graphics As­ 22-28. Linear Operators and Applica­ and for Mathematical Sciences, Ky­ sociation Mapping and Geographic Infor­ tions, Oberwolfach, Federal Republic of stitute University, Japan. (Jul./ Aug. 1989, mation Systems, Los Angeles, CA. (Apr. Germany. (Jul./ Aug. 1989, p. 763) oto p. 764) 1989, p. 494) 22-28. Second Osterreichisches Sym­ I. College on Differen­ 13-17. Workshop on Logic Related to posium Zur Geschichte der Mathematik, 30-December tial Geometry, Trieste, Italy. (Mar. 1989, Computer Science and Programming Lan­ Neuhofen a.d. Ybbs, Austria. (Jul./ Aug. p. 313) guage Theory, Mathematical Sciences Re­ 1989, p. 763) search Institute, Berkeley, CA. (May I Jun. 23-26. Beijing International Confer­ 1989, p. 600) ence on System Simulation and Scientific November 1989 13-1 7. Workshop: Dynamical Issues in Computing, Beijing, China. (Mar. 1989, Conference on Tech­ Combustion Theory, Institute for Mathe­ p. 313) 2-4. Second Annual nology in Collegiate Mathematics, Ohio matics and its Applications, Minneapolis, Appli­ 25-27. Evolution Equations and State University, Columbus, OH. (Mar. MN. (Dec. 1988, p. 1591) Problems, Research cations to Nonlinear 1989, p. 313) 13-17. Supercomputing '89, Reno, NV. Institute for Mathematical Sciences, Ky­ Third International Conference on (Jul./Aug. 1989, p. 764) oto University, Japan. (Jul./ Aug. 1989, 2-5. in Law, Florence, Italy. 15-17. Geometry of Manifolds, Research p. 764) Expert Systems (May /Jun. 1989, p. 599) Institute for Mathematical Sciences, Ky­ 25-28. Workshop on Numerical Meth­ oto University, Japan. (Jul./ Aug. 1989, ods for Elliptic Systems, Espoo, Finland. * 3-5. Conference on Low Dimensional Topology and Combinatorial Group The­ p. 764) (May /Jun. 1989, p. 599) ory, SUNYA, Albany, NY. 17-20. Workshop on Classical and Quan­ 26-28. The Riccati Equation In Control, tum Transport in Hamiltonian Systems, Systems and Signals, Villa Gallia, Como, INVITED SPEAKERS: K. Brown, J. Can­ Mathematical Sciences Institute, Cornell Italy. (Jan. 1989, p. 70) non, M. Handel, W. Metzler, J. Mor­ University, Ithaca, NY. (MayjJun. 1989, 27-28. Central Section Meeting of the gan, P. Scott, P. Shalen. p. 600) INFORMATION: E. C. Turner, Dept. of AMS, Ball State University, Muncie, IN. 18-19. Far Western Section Meeting of Math. and Stat., SUNYA, Albany, NY (May/ June 1988, p. 732) the AMS, University of California, Los 12222. INFORMATION: W. Drady, AMS, P.O. Angeles, CA. Box 6248, Providence, RI 02940. 4-8. Workshop on Geometric and Alge­ INFORMATION: W. Drady, AMS, P.O. braic Integration Algorithms, Mathemati­ Box 6248, Providence, RI 02940. cal Sciences Institute, Cornell University, Ithaca, NY. (MayjJun. 1989, p. 599)

SEPTEMBER 1989, VOLUME 36, NUMBER 7 913 Meetings and Conferences

19-25. Random Partial Differential Equa­ 10-16. Asymptotic Methods for tions, Oberwolfach, Federal Republic of Computer-Intensive Procedures in Statis­ January 1990 Germany. (Jul./ Aug. 1989, p. 764) tics, Oberwolfach, Federal Republic of 20-24. Seminaire Sud-Rhodanien de Ge­ Germany. (Mar. 1989, p. 314) 1-6. Zeitreihenanalyse, Oberwolfach, ometrie Differentielle, Marseille, France. 11-13. Fourth SIAM Conference on Par­ Federal Republic of Germany. (Mar. (Jul./ Aug. 1989, p. 764) allel Processing for Scientific Computing, 1989, p. 314) 26-December 2. Methoden und Ver­ Chicago, IL. (Mar. 1989, p. 314) 7-13. Mathematische Optimierung, Ober­ fahren der Mathematischen Physik, Ober­ 11-14. Number Theory- Studies Related wolfach, Federal Republic of Germany. wolfach, Federal Republic of Germany. to Automorphic Forms, Research Institute (Mar. 1989, p. 314) (Jul./ Aug. 1989, p. 764) for Mathematical Sciences, Kyoto Uni­ * 8-13. Workshop on Variational Meth­ 27-29. Computer Algebra and Its Ap­ versity, Japan. (Jul./ Aug. 1989, p. 765) ods in Hamiltonian Systems and Elliptic plication to Investigations for Mathemat­ * 12-14. Second Australian Supercomputer Equations, L' Aquila, Italy. ics, Research Institute for Mathemati­ Conference, University of Wollongong, INVITED SPEAKERS: A. Ambrosetti, A. cal Sciences, Kyoto University, Japan. NSW, Australia. Bahri, V. Benci, H. Berestycki, H. 764) (Jul./Aug. 1989, p. INFORMATION: J. Barry, Australian Brezis, G. Deii'Antonio, I. Ekeland, 27-29. The Recent Developments of High Nuclear Science and Technology Or­ D. Fortunato, M. R. Herman, H. Technology and Mathematical Science ganisation, Private Mail Bag I, Menai, Hofer, P. L. Lions, A. Marino, L. (II), Research Institute for Mathemat­ NSW 2234, Australia. Modica, K. R. Meyer, J. Moser, L. ical Sciences, Kyoto University, Japan. Nirenberg, S. P. Novikov, P. H. Ra­ (Jul./ Aug. 1989, p. 765) 17-23. Theory and Numerical Meth­ binowitz, M. Willem. 29-December I. Numerical Analysis and ods for Initial-Boundary Value Problems, INFORMATION: M. Girardi or M. Scientific Computing, Research Institute Oberwolfach, Federal Republic of Ger­ Matzeu, Dipartimento di Matemat­ for Mathematical Sciences, Kyoto Uni­ many. (Mar. 1989, p. 314) ica Pura e Applicata-Universita di versity, Japan. (Jul./ Aug. 1989, p. 765) * 27-31. Holiday Symposium on Braids L'Aquila- Via Roma Pal. Del Tosto - and Knots, New Mexico State University, 67100 L'Aquila-Italy; or to F. Pacella, Las Cruces, NM. Dipartimento di Matematica, Uni­ December 1989 versita di Roma, La Sapienza, P.le is PROGRAM: This year's symposium A.moro 2, 00185 Roma, Italy; Email: 3-9. Wiener-Hopf-Probleme, Topelitz­ There focused on braids and knots. pacella@irmunisa (bitnet). Operatoren und Anwendungen, Oberwol­ will be a series of ten lectures, two fach, Federal Republic of Germany. each day, by Professor J. Birman of * 10-13. International Conference on Dif­ (Jul./ Aug. 1989, p. 765) Columbia University. There will be ferential Equations and Applications to 4-6. 1989 Winter Simulation Confer­ additional sessions for contributed pa­ Biology and Population Dynamics, Har­ ence, Washington, DC. (May /Jun. 1989, pers, research ideas, and discussion. vey Mudd College, Claremont, CA. p. 600) Some support may be available for a CONFERENCE TOPICS: Delay differen­ Decision Theory and limited number of participants. 4-6. Studies on tial equations, difference equations, Related Topics, Research Institute INFORMATION: R. J. Wisner, Braids Their functional differential equations, infi­ Sciences, Kyoto Uni­ and Knots Symposium, Dept. of Math­ for Mathematical nite dimensional dynamical systems, p. 765) ematical Sciences, New Mexico State versity, Japan. (Jul./ Aug. 1989, models, physiological mod­ University, Box 30001, Las Cruces, epidemic 4-7. Research on Complex Analytic Ge­ els. NM 88003-0001; 505-646-3901. ometry and Related Topics, Research In­ INVITED SPEAKERS: K. Cooke, K. stitute for Mathematical Sciences, Ky­ Hadeler, J. Hale, M. Iannelli, S. Levin, oto University, Japan. (Jul./ Aug. 1989, J. Mawhin, G. Sell, P. Waltman. p. 765) * 1990. IMACS International Workshop ORGANIZING COMMITTEE: S. Busen­ 4-8. Fifth Aerospace Computer Secu­ on Massively Parallel Methods in Com­ berg, Harvey Mudd College; R. El­ rity Applications Conference, Tucson, AZ. putational Physics, Boulder, Colorado. dekin, Pomona College; M. Martelli, (May /Jun. 1989, p. 600) California State University Fullerton. INFORMATION: K. E. Gustafson, Dept. 6-9. Algebraic Number Theory, Research INFORMATION: Differential Equations of Mathematics, Box 426, Univ. of Institute for Mathematical Sciences, Ky­ Conference, Mathematics Department, Colorado, Boulder, CO 80309, USA. oto University, Japan. (Jul./ Aug. 1989, Harvey Mudd College, Claremont, CA p. 765) * 1990. IMACS Conference on Computer 91711. * 9. Boston Celebration of the ASAISO Aided Design, Yugoslavia. 14-20. Nonlinear Evolution Equations, Sesquicentennial, Boston, MA. INFORMATION: L. T. Grujic, Faculty Solitons and the Inverse Scattering Trans­ INFORMATION: J. Efird, Dept. of of Mechanical Engineering, Belgrade form, Oberwolfach, Federal Republic of Health Policy & Mgmt, Harvard Univ., P.O.Box 174, 11001, Belgrade, Germany. (Mar. 1989, p. 314) Univ., 677 Huntington Ave, Boston, Yugoslavia. 15-26. Workshop on Composite Me­ MA 02115; 617-732-2291. dia and Homogenization Theory, Inter-

914 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences

national Centre for Theoretical Physics, * 11-15. The Twenty-sixth Australian Ap­ ferman, Stanford University; J. A. Trieste, Italy. (May/ Jun. 1989, p. 600) plied Mathematics Conference, Coolan­ Goguen, Oxford University; G. H. 16-1 7. AMS Short Course on Mathe­ gatta, Queensland, Australia. Gonnet, University of Waterloo; D. Hare!, The Weizmann Institute of Sci­ matical Questions in Robotics, Louisville, V. G. Hart, Dept. of INFORMATION: ence; G. Longo, Universita di Pisa; R. KY. University of Queens­ Mathematics, Milner, Edinburgh University; M. M. 406 7, INFORMATION: M. Foulkes, AMS, P.O. land, St. Lucia, Queensland Richter, U niversitat Kaiserslautern; Box 6248, Providence, RI 02940. Australia. D. Scott, Carnegie-Mellon University; J. C. Shepherdson, University of Bris­ 17-20. Joint Mathematics Meetings, 11-17. Funktiontheorie, Oberwolfach, tol. Louisville, KY. (Including the annual Federal Republic of Germany. (Mar. ORGANIZING COMMITTEE: G. Jager, meetings of the AMS, AWM, MAA and 1989, p. 315) H. Lauchli, U. Stammbach, N. Wirth. NAM). * 15-20. American Association for the INFORMATION: H. Lauchli, Sympo­ Advancement of Science Annual Meeting, INFORMATION: H. Daly, AMS, P.O. sium on Symbolic Computation, Math­ New Orleans, LA. Box 6248, Providence, RI 02940. ematik, HG G 62.3, ETH-Zentrum, INFORMATION: AAAS, 1333 H St., CH-8092 ZUrich, Phone 01 256 34 21-27. Modelltheorie, Oberwolfach, Fed­ N.W., Washington, DC 20005; 202- 25. eral Republic of Germany. (Mar. 1989, 326-6640. p. 314) 11-17. Mathematische Stochastik, Ober­ * 22-24. ACM/SIAM Symposium on Dis- 18-24. Mathematische Modelle in Der wolfach, Federal Republic of Germany. crete Algorithms, San Francisco, CA. Biologie, Oberwolfach, Federal Republic (Mar. 1989, p. 315) of Germany. (Mar. 1989, p. 315) 13-16. Twenty-first Annual Iranian Math­ ORGANIZERS: F.R.K. Chung, Bell Com­ 20-22. Association for Computing Ma­ ematics Conference, University of Isfa­ munications Research, Inc.; D. John­ chinery 1990 Computer Science Confer­ han, Iran. (Jul./ Aug. 1989, p. 766) son, AT&T Bell Laboratories. ence, Washington, D.C. (May/ Jun. 1989, INFORMATION: SIAM Conference Co­ 14-19. East European Category Semi­ p. 60 I) ordinator, 3600 University City Sci­ nar, Predela, Bulgaria. (MayfJun. 1989, Technical ence Center, Philadelphia, PA 19104- 22-23. Twenty-first SIGCSE p. 60 I) 2688; Phone: 215-382-9800; Fax: 215- Symposium, Washington, D.C. (May/ Jun. 16-1 7. Central Section Meeting of the 386-7999. 1989, p. 601) AMS, Kansas State University, Manhat­ 25-March 3. Eigenwertaufgaben In Natur tan, KS. 22-26. Workshop on Applications of Al­ Und Ingenieurwissensachaften Und Ihre INFORMATION: W. Drady, AMS, P.O. gebraic Topology to Geometry and Analy­ Numerische Behandlung, Oberwolfach, Box 6248, Providence, RI 02940. sis Mathematical Sciences Research In­ Federal Republic of Germany. (Mar. sti~ute, Berkeley, CA. (May/ Jun. 1989, 1989, p. 315) 18-24. Masstheorie, Oberwolfach, Fed­ p. 600) * 26-March 2. IEEE Computer Society eral Republic of Germany. (Mar. 1989, 28-February 3. Regelungstheorie, Ober­ COMPCON Spring '90, San Francisco, p. 315) wolfach, Federal Republic of Germany. CA. 18-24. Third Centenary Celebration of (Mar. 1989, p. 314) INFORMATION: COMPCON Spring'90, the Mathematische Gesellschaft in Ham­ 16. Second College on Vari­ 29-February Computer Society of the IEEE, 1730 burg, BundesstraBe, Hamburg. (Jan. 1989, ational Problems in Analysis, Interna­ Massachusetts Ave., N.W., Washing­ p. 71) tional Centre for Theoretical Physics, ton, DC 20036-1903; 202-371-10 13; 19-22. Eleventh Annual National Graph­ Jun. 1989, p. 600) Trieste, Italy. (May/ Telex 7082500437 IEEECOMPSO. ics Association Conference and Expo­ sition, Anaheim, CA. (Jul./ Aug. 1989, p. 766) February 1990 March 1990 19-24. US-USSR Approximation Theory 4-10. Funktiontheoretische Methoden 4-10. Interval Methods for Numerical Conference, University of South Florida, Dei Partiellen Differential Und Integral­ Computation, Oberwolfach, Federal Re­ Tampa, FL. (Jul./ Aug. 1989, p. 766) gleichungen, Oberwolfach, Federal Re­ public of Germany. (Mar. 1989, p. 315) 20-23. Directions in Matrix Theory, public of Germany. (Mar. 1989, p. 314) 5-7. SIAM Conference on Applied Prob­ Auburn, AL. (May/Jun. 1989, p. 601) 4-10. Nukleare Frechet-Raume, Ober­ ability in Science and Engineering, New 23-24. Southeast Section Meeting of wolfach, Federal Republic of Germany. Orleans, LA. (Nov. 1988, p. 1389) the AMS, University of Arkansas, Fayet­ (Mar. 1989, p. 314) * 5-7. Symposium on Symbolic Computa­ teville, AR. 5-l 0. Eighth International Seminar on tion (on the occasion of the sixtieth birth­ AMS, P.O. Model Optimization in Exploration Geo­ day of Erwin Engeler), ZUrich, Switzer­ INFORMATION: W. Drady, Providence, RI 0240. physics, with a Workshop on Geophysical land. Box 6248, Data Inversion in Environmental Research 25-31. Kontinuumsmechanik der Festen and Planning, Berlin-West, Free Univer­ INVITED SPEAKERS: B. Buchberger, Korper, Oberwolfach, Federal Republic sity of Berlin, Federal Republic of Ger­ Johannes Kepler Universitat; J. C. of Germany. (Mar. 1989, p. 315) many. (Jul./ Aug. 1989, p. 765) Davenport, University of Bath; S. Fe-

SEPTEMBER 1969, VOLUME 36, NUMBER 7 915 Meetings and Conferences

* 26-29. Workshop on Number Theory and 18-21. Sixty-eighth Annual Meeting of 6-12. Geschichte der Mathematik, Ober­ Algorithms, Berkeley, CA. the National Council of Teachers of Math­ wolfach, Federal Republic of Germany. ematics, Salt Lake City, UT. (Jul./Aug. (Jul./ Aug. 1989, p. 766) ORGANIZER: H. Lenstra. 1989, p. 766) INFORMATION: I. Kaplansky, Direc­ * 7-10. SIAM Conference on Applications tor, Mathematical Sciences Research 21-22. Northeast Section Meeting of of Dynamical Systems, Orlando, FL. the AMS, Pennsylvania State University, Institute, lOOO Centennial Dr., Berke­ SPONSOR: SIAM Activity Group on University Park, PA. ley, CA 94720. Dynamical Systems INFORMATION: W. Drady, AMS, P.O. ORGANIZER: Shui-Nee Chow, Michi­ 26-April 6. Workshop on Group Theory Box 6248, Providence, RI 02940. gan State University. from a Geometrical Viewpoint, Interna­ CALL FOR PAPERs: Abstract Deadline: tional Centre for Theoretical Physics, 22-28. Einhollende Algebren und Ringe November 28, 1989. Trieste, Italy. (MayjJun. 1989, p. 601) Von Differentialoperatoren, Oberwolfach, INFORMATION: Siam Conference Co­ 29-31. Mathematical Sciences Insti­ Federal Republic of Germany. (Jul./ Aug. ordinator, 3600 University City Sci­ tute Symposium on Mathematics as Art, 1989, p. 766) ence Center, Philadelphia, P A 19104- Mathematics as a Consumer Good, Cor­ 29-May 5. Gruppentheorie (Pro-Endliche 2688;Phone:215-382-9800;Fax:215- nell University, Ithaca, NY. (Jul./ Aug. Gruppen), Oberwolfach, Federal Repub­ 386-7999. 1989, p. 766) lic of Germany. (Jul./ Aug. 1989, p. 766) 7-June l. College on Recent Develop­ ments and Applications in Mathematics April1990 May 1990 and Computer Science, International Cen­ Italy. 1-4. ENAR Spring Meeting, Baltimore, * 3-4. Twenty-first Annual Pittsburgh Con­ tre for Theoretical Physics, Trieste, MD. (Jul./ Aug. 1989, p. 766) ference on Modeling and Simulation, Uni­ (MayjJun. 1989, p. 601) l-7. Design and Codes, Oberwolfach, versity of Pittsburgh, Pittsburgh, PA. 13-19. Abstrakte Konvexe Analysis, Federal Republic of Germany. (Jul./ Aug. Oberwolfach, Federal Republic of Ger­ CONFERENCE TOPICS: Emphasis for 1989, p. 766) many. (Jul./ Aug. 1989, p. 766) the conference will be microproces­ 14-18. Conference on Nonlinear Anal­ * l-14. NATO Advanced Study Institute applications sors, personal computer ysis and Partial Differential Equations, on "Generators and Relations in Groups and software, artificial intelligence, Rutgers University, New Brunswick, NJ. and Geometries", Castelvecchio Pascoli expert systems, robotics and all as­ (Jul./ Aug. 1989, p. 767) (Lucca), Italy. pects of control theory and applica­ * 17-19. Interface '90 (formerly Computer INVITED SPEAKERs: A. Caranti, Trento; tions, as well as social, economic, ge­ ography, regional science, and global Science and Statistics: Symposium on In­ A. M. Cohen, Amsterdam; L. Di Mar­ terface), East Lansing, MI. tino, Milano; E. W. Ellers, Toronto; modeling and simulation. M. Gotzky, Kiel; H. Ishibashi, Sakado; SPoNsoRs: School of Engineering, Uni­ SPONSORS: AMS, ASA, IASC, IMS, M. Jarden, Tel Aviv; F. Kniippel, versity of Pittsburgh; The Institute of NCGA, ORA, SIAM. Kiel; T. J. Laffey, Dublin; H. Lausch, Electrical and Electronic Engineers; INFORMATION: R. LePage, Dept. of Wiirzburg; P. Plaumann, Erlangen; The Systems, Man and Cybernetics Stat. & Probability, Michigan State T. A. Springer, Utrecht; B. Zimmer­ Society; The Instrument Society of Univ., East Lansing, MI 48824-1024. mann, Trieste. America; The Society for Computer INFORMATION: Organizing Commit­ Simulation; The International Associ­ 20-26. The Schrodinger Equation and tee of the NATO ASI meeting cjo ation for Mathematics and Computers Its Classical Counterparts, Oberwolfach, K.Strambach, Universitat Erlangen­ in Simulation. Federal Republic of Germany. (Jul./ Aug. Niirnberg, Mathematisches Institut, CALL FOR PAPERS: Two copies of ti­ 1989, p. 767) Bismarckstr. l l /2, D-8520 Erlangen, tles, authors, all author's addresses, * 21-24. The Simulation of Random Pro­ Federal Republic of Germany. abstracts and summaries should be cesses and Fields - Mathematics and submitted by January 31, 1990. The Applications, Portofino, Italy. 4-7. Symposium on Distributions with abstract should be approximately 50 CONFERENCE TOPICS: Topics to be Given Marginals (In Memory of Giuseppe words in length and the summary covered include mathematical ques­ Pompilj), Rome, Italy. (May j Jun. 1989, should be of sufficient length and de­ tions and actual applications of com­ p. 601) tail to permit careful evaluation. Only puter simulations in various fields. papers not published previously will 8-14. Arbeitsgemeinschaft Mit Aktuellem INVITED SPEAKERs: G. K. Ackers, A. be considered. Identify one author as Thema (wird in den Mitteilungen der Benveniste, M. Eigen, D. Griffeath, the correspondent for the paper. DMV Heft 1/1990 bekanntgegeben), Ober­ R. Holley, J. Hopfield, R. Kapral, INFORMATION: W. G. Vogt or M. wolfach, Federal Republic of Germany. R. May, A. Sokal, D. Stroock, A. T. p. 766) H. Mickle, Modeling and Simulation (Jul./Aug. 1989, Winfree. Conference, 348 Benedum Engineer­ 15-21. Mathematical Concepts of De­ INFORMATION: F. Marchetti, Univer­ ing Hall, University of Pittsburgh, pendable Systems, Oberwolfach, Federal sita di Genova, Dipartimento di Mat­ Pittsburgh, PA 15261. Republic of Germany. (Jul./ Aug. 1989, ematica, v. L. B. Alberti 4, 1-16132 p. 766) Genova, Italy; Phone: (+39-10) 353-

916 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences

8717; Fax: (+39-10) 353-8769; Email CALL FOR PAPERS: The deadline for INFORMATION: J. C. Mitchell, LICS marketti@igecuniv (earn/bitnet). short communications is November Program Chair, Dept. of Computer 30, 1989. The deadline for registra­ Science, Stanford University, Stan­ 21-25. Eleventh United States National tion is March I, 1990. ford, CA 94305, USA; Internet: Congress of Applied Mechanics, Tucson, INFORMATION: L. Rodono or L. [email protected]. AZ. (Nov. 1988, p. 1389) Michelucci, Dipartimento di Mate­ * 4-8. Workshop on Model Theory, Berke- 23-25. 1990 International Symposium matica e Applicazioni, Universita di CA. on Multiple-Valued Logic, Charlotte, NC. Palermo, Via Archirafi 34, 1-90123 ley, (Apr. 1989, p. 496) Palermo, Italy; Phone: 39-91-6162824. PROGRAM: This is the last of three 25-31. Tenth International Conference workshops planned as part of the * 3-6. 1990 Annual Meeting of the Sta­ on Pattern Recognition, Resorts Hotel, Mathematical Sciences Research In­ tistical Society of Canada, St. John's, Atlantic City, NJ. (Mar. 1988, p. 466) stitute's yearlong 1989-1990 program Newfoundland, Canada. 27-June 2. Lyapunov-Exponents, Ober­ on logic. wolfach, Federal Republic of Germany. INFORMATION: C. A. Field, Program ORGANIZER: E. Hrushovski. (Jul./Aug. 1989, p. 767) Chairperson, Dept. of Mathematics, INFORMATION: I. Kaplansky, Direc­ Statistics and Computing Science, Dal­ tor, Mathematical Sciences Research housie University, Halifax, Nova Sco­ Institute, 1000 Centennial Dr., Berke­ June 1990 tia B3H 4H8, Canada; or B. Sutrad­ ley, CA 94720. har, Local Arrangements Chairperson, June 1990. AMS-SIAM Summer Sem­ Fifth Annual Conference of the Dept. of Mathematics and Statistics, 6-9. inar on Vortex Dynamics and Vortex Consortium for Mathematics Memorial University of Newfound­ European Methods, Location on the west coast in Industry, Lahti, Finland. (Apr. 1989, land, St. John's, Newfoundland AIC to be announced. 496) 5S7, Canada. p. INFORMATION: B. Verducci, AMS, P.O. 6-12. 1990 Barcelona Conference on Box 6248, Providence, RI 02940. 3-9. Graphentheorie, Oberwolfach, Fed­ Algebraic Topology, Centre de Recerca eral Republic of Germany. (Jul./ Aug. Matematica, Barcelona, Spain. (Sept. *June/ July 1990. International IMACS 1989, p. 767) 1988, p. 1060) Modelling Conference on Mathematical * 4-7. Fifth Annual IEEE Symposium on 10-16. Reelle Algebraische Geometrie, Vilnius, USSR. and Applied Mathematics, Logic in Computer Science, Philadelphia, Oberwolfach, Federal Republic of Ger­ ORGANIZERS: USSR Academy of Sci­ PA. many. (Jul./ Aug. 1989, p. 76 7) ences, Keldysh Institute of Applied PuRPOSE: The symposium aims for 11-14. Fourteenth Rolf Nevanlinna Col­ Mathematics, Lithuanian SSR Acad­ wide coverage of theoretical and prac­ loquium, University of Helsinki, Helsinki, emy of Science, Institute of Math­ tical issues in computer science that Finland. (Jul./ Aug. 1989, p. 767) ematics and Cybernetics. relate to logic in a broad sense, includ­ 11-14. World Organization of Systems INFORMATION: A. A. Samarskii, Kel­ ing algebraic, categorical and topolog­ and Cybernetics Eighth International Con­ dysh Institute of Applied Mathemat­ ical approaches. gress, New York, NY. (Mar. 1989, p. 315) ics, ORGANIZING CoMMITTEE: M. Abadi, * 11-14. Fifth SIAM Conference on Dis- Academy of Sciences, Miuss­ USSR J. Barwise, A. Chandra, E. Engeler, crete Mathematics, Atlanta, GA. kaya pl.4, 125047 Moscow, USSR. J. Gallier, J. Goguen, D. Gries, Y. Kozen, Z. SPONSOR: Siam Activity Group on * 1-8. Third International IMACS Sym­ Gurevich, D. Johnson, D. J. Mitchell, Discrete Mathematics. posium on Orthogonal Polynomials and Manna, A. Meyer (chair), Parikh, G. ORGANIZER: P. Winkler, Emory Uni­ Their Applications, Erice-Trapani (Sicily), C. Papadimitriou, R. Plotkin, D. Scott. versity. Italy. Abstract Deadline: SPONSORS: IEEE Technical Commit­ CALL FOR PAPERS: PROGRAM: Invited talks and short tee on Mathematical Foundations of January 5, 1990. SIAM Conference Co­ communications. Computing, Association for Symbolic INFORMATION: 3600 University City Sci­ ORGANIZING COMMITTEE: C. Brezin­ Logic, European Association of The­ ordinator, Philadelphia, PA 19104- ski, Lille; L. Gori Nicolo-Amati, oretical Computer Science. ence Center, 215-382-9800; Fax: 215- Rome; A. Laforgia, Palermo; G. CALL FOR PAPERS: Fifteen ( 15) copies 2688; Phone: Mastroianni, Potenza; G. Monegato, of a detailed abstract-not a full 386-7999. Turin; paper-should be received by De­ 11-15. Third International Conference on Nevai, Columbus; A. Ronveaux, P. G. cember 1, 1989. The entire extended Hyperbolic Problems, Uppsala, Sweden. Namur. abstract should not exceed ten (I 0) (Jul./ Aug. 1989, p. 767) INVITED SPEAKERS: R. Askey, T. S. standard front doubled-spaced pages 11-15. Rigorous Results in Quantum Dy­ Chihara, L. Gatteschi, W. Gautschi, (2500 words). The title page of the namics, Liblice Castle, Czechoslovakia. T. H. Koornwinder, D. S. Lubinsky, submission should include a brief (MayfJun. 1989, p. 602) A. Magnus, F. Marcellan, P. Maroni, synopsis and author's name, address, E. B. Saff, H. Stahl, S. K. Suslov, V. phone number, and email address if Totik, W. Van Assche. available.

SEPTEMBER 1989, VOLUME 36, NUMBER 7 917 Meetings and Conferences

13-15. Seventh Annual Quality and Pro­ PROGRAM: The program will consist and Applications, University of Madras, ductivity Research Conference, Madison, of invited talks and contributed pa­ Madras, India. pers. WI. (Mar. 1989, p. 315) INVITED SPEAKERS: H. M. Srivastava, INFORMATION: A. Pixley, Dept. of 13-22. Free Boundary Problems: Theory Canada; R. Srivastava, Canada; M. A. Mathematics, Harvey Mudd College, and Applications, Centre de Recherches Nasr, Egypt; S. Ruscheweyh, FRG; 0. Mathematiques, Universite de Montreal, Claremont, CA 91711; Ch. Herrmann, Tammi, Finland; S. Owa, Japan; R. FB4 AG I, Technische Hochschule Canada. (Jul./ Aug. 1989, p. 767) M. Porter, Mexico; J. Krzyz, Poland; Darmstadt, D-61 00 Darmstadt, West 17-23. Partial Differential Equations in J. M. Anderson, U.K.; D. K. Thomas, Germany. Complex Analysis, Oberwolfach, Federal U.K.; C. H. Fitzgerald, USA; W. H. Republic of Germany. (Jul./ Aug. 1989, * 3-6. Eleventh Dundee Conference on Or­ Fuchs, USA; A. W. Goodman, USA; p. 767) dinary and Partial Differential Equations, E. P.Merkes, USA; S. S. Miller, USA; 18-20. Joint WNAR-IMS Regional Meet­ Dundee, Scotland. C. D. Minda, USA; M. 0. Reade, ing, Montana State University, Bozeman, USA; D. Sarason, USA; S. M. Shah, MT. (Mar. 1989, p. 315) PuRPOSE: The conference will bring USA; H. Silverman, USA; E. M. Sil­ together research workers with a com­ in der via, USA; D. Sundararaman, USA. 24-30. Mathematische Probleme mon interest in differential equations Nichtlinearen Elastizitiit, Oberwolfach, INFORMATION: R. Parvatham, Con­ and their applications. Particular at­ vener, International Conference - Ge­ Federal Republic of Germany. (Jul./ Aug. tention will be focused on recent de­ 1989, p. 767) ometric Function Theory, Ramanu­ velopments in the theory of nonlinear jan Institute for Advanced Study in 27-30. Fourth International Congress differential equations and their ap­ Mathematics, University of Madras, on Algebraic Hyperstructures and Ap­ plications to biological phenomena, Madras-600 005, India. plications, Xanthi, Greece. (Apr. 1989, wave propagation and dynamical sys­ p. 496) tems. 29-August 4. Mechanik Und Algebrais­ INVITED SPEAKERS: J. M. Ball, P. che Geometrie, Oberwolfach, Federal Re­ Diekmann, I. Ekeland, public of Germany. (Apr. 1989, p. 497) July 1990 Binding, 0. P. J. Holmes, G. Kreigsman, M. C. 1-7. Modulfunktionen In Mehreren Vari­ Mackey, R. E. Meyer, D. H. Sattinger, ablen, Oberwolfach, Federal Republic of L. Tartar. August 1990 Germany. (Apr. 1989, p. 497) INFORMATION: R. J. Jarvis, Depart­ 5-11. Mathematical Methods in Tomog­ * l-15. International Symposium on Alge­ ment of Mathematics & Computer raphy, Oberwolfach, Federal Republic of braic Topology - Adams Memorial Sympo­ Science, The University, Dundee DDI Germany. (Apr. 1989, p. 497) sium, University of Manchester, England. 4HN, Scotland, U.K. 6-9. 1990 Joint Statistical Meetings, PuRPOSE: This symposium will com­ 8-14. Variationsrechnung, Oberwolfach, Anaheim, CA. (Mar. 1988, p. 466) memorate the life and work of Frank Federal Republic of Germany. (Apr. 8-ll. Joint Mathematics Meetings, Ohio Adams, who held the Fielden chair of 1989, p. 497) State University, Columbus, OH. (includ­ pure mathematics at Manchester from 9-11. "Universita'di Genova- The Ohio ing the summer meetings of the AMS, 1964 to 1971, and will be centered on State University Joint Conference" on AWM, MAA and PME). This is the 75th stable homotopy theory. New Trends in Systems Theory, Genoa, Anniversary of the MAA. SPONSOR: SERC. Italy. (Jul./ Aug. 1989, p. 768) INFORMATION: H. Daly, AMS, P.O. INFORMATION: J. Minshull, Dept. of 9-20. Geometry and Topology of Four­ Box 6248, Providence, RI 02940. Mathematics, Univ. of Manchester, Manifolds, McMaster University, Hamil­ Manchester M 13 9PL; (Email: ton, Ontario, Canada. (May I Jun. 1989, 12-18. Algebraische Zahlentheorie, Ober­ [email protected]). p. 602) wolfach, Federal Republic of Germany. (Apr. 1989, p. 497) 1-18. Twentieth Summer Session on 15-21. Stochastic Image Models and Al­ 12-18. Pre-Congress Topology Confer­ Probability Theory, Saint-Flour (Cantal), gorithms, Oberwolfach, Federal Republic ence, University of Hawaii, Honolulu, France. (Mar. 1989, p. 315) of Germany. (Apr. 1989, p. 497) HI. (Feb. 1989, p. 183) 2-6. Tenth Australian Statistical Con­ 15-23. Colloquium in Honor of Roland 13-l 7. Fifth International Conference ference/Second Pacific Statistical Con­ Fraisse, Centre International de Recon­ and Nonpoten­ gress, Sydney, Australia. (Jul./ Aug. 1989, tres Mathematiques, Luminy, France. on Hadronic Mechanics p. 768) (MayjJun. 1989, p. 602) tial Interactions, University of Northern Iowa, Cedar Falls, Iowa. (Jul./ Aug. 1989, 16-20. SIAM Annual Meeting, Chicago, * 2-6. The Jonsson Symposium, Laugar- p. 768) vatn, Iceland. IL. (Nov. 1988, p. 1389) * 13-17. Eleventh IFAC World Congress, 22-28. Konvexgeometrie, Oberwolfach, PuRPOSE: This international confer­ Tallin, USSR. (Apr. ence honoring Bjarni Jonsson will Federal Republic of Germany. IFAC Secretariat, survey the current state of research 1989, p. 497) INFORMATION: Schlossplatz 12, A-2361 Laxenburg, in universal algebra, lattice theory, * 26-29. International Conference on New algebraic logic, and related fields. Trends in Geometric Function Theory Austria.

918 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences

* 13-1 7. Algebraic Geometry and Analytic 19-25. Mathematische Methoden Des mechanics, electrotechnics, electron­ Geometry, Tokyo, Japan. VLSI-Entwurfs Und Des Distributed Com­ ics/biological, chemical, biomechani­ putings, Oberwolfach, Federal Republic cal and others. PURPOSE: The conference is intended of Germany. (Apr. 1989, p. 497) ORGANIZERS: J. Niziol, S. Marcyzk, an overview of recent de­ to provide K. Arczewski, A. Bar, A. Chodacki, velopments in algebraic, analytic and 21-2 9. The International Congress of K. Gajewski, S. Michalowski, R. Palej, arithmetic geometry. Mathematicians 1990, Kyoto, Japan. M. Pracik. TOPICS: BirationaJ ge­ (Nov. 1988, p. 1389) CONFERENCE INFORMATION: S. Marczyk, Twelfth classification theory, ge­ 26-September I. Komplexe Analysis, ometry and ICNO Secretariat, Cracow University and mixed char­ Oberwolfach, Federal Republic of Ger­ ometry in positive of Technology, Institute of Mechan­ analytic and many. (Apr. 1989, p. 497) acteristics, singularities, ics and Machine Design, AI. Planu 6- differential-geometric methods, vector European Simulation 28-30. IMACS Letniego 19A, 31-864 Cracow, Poland. bundles. Meeting on Problem Solving by Simula­ ORGANIZERS: K. Kato, T. Katsura, tion, Esztergom, Hungary. (Mar. 1989, 2-8. Topologie, Oberwolfach, Federal Y. Miyaoka, S. Mori, K. Saito, N. p. 316) Republic of Germany. (Apr. 1989, p. 497) Sasakura. 28-31. Operations Research 1990, Inter­ 3-6. Fourth Asian Logic Conference, INVITED SPEAKERs: P. Berthellot, S. national Conference Operations Research, Tokyo, Japan. (Mar. 1989, p. 316) Bloch, J. Carlson, H. Clemens, T. Vienna, Austria. (Jul./ Aug. 1989, p. 768) 3-7. IMACS Symposium on Intelligent Ekedahl, T. Fujita, K. Hulek, Y. 30-September 4. International Confer­ Models in Systems Simulation, Brussels, Kawamata, J. Kollar, LC Dung Trang, ence on Potential Theory, Nagoya, Japan. Belgium. (Mar. 1989, p. 316) Mukai, C. B. Mazur, N. Mok, S. (May /Jun. 1989, p. 602) Okonek, M. Reid, C.S. Seshadri, Y.­ 3-7. Representation des Groupes et Anal­ T. Siu, C. Soule, J.H.M. Steenbrink, yse Complexe, Marseille, France. Aug. 1989, p. 768) P.M.H. Wilson, D. Zagier. September 1990 (Jul./ INFORMATION: Y. Miyaoka, Dept. of 8-12. Neuronet-90: IMACS International 1990. IMACS- Mathematics, Tokyo Metropolitan Uni­ *September /October Symposium on Neural Nets and Neu­ Arith­ versity, Fukazawa, Setagaya, Tokyo GAMM Conference on Computer ral Computers, Prague, Czechoslovakia. 158, Japan. metic, Scientific Computation and (Please note change from May/ Jun. 1989, Mathematical Modelling, Bulgaria. p. 602) of Mathematical Statis­ * 13-18. Institute ORGANIZER: Bulgarian Academy of 9-15. Surgery and L-Theory, Oberwol­ Annual Meeting(jointly tics Fifty-third Sciences. fach, Federal Republic of Germany. (Apr. World Congress of the with the Second INFORMATION: U. Kulisch, Universi­ 1989, p. 498) Bernoulli Society), Uppsala, Sweden. tat Karlsruhe, Institut fur Angewandte I 0-0ctober 5. School on Qualitative INFORMATION: L. Billard, Dept. of Mathematik, Kaiserstrasse 12, Post­ Aspects and Applications of Nonlinear Statistics, Univ. of Georgia, Athens, fach 6980, D-7500 Karlsruhe I, Ger­ Evolution Equations, International Centre GA 30602; 404-542-5232. many. for Theoretical Physics, Trieste, Italy. (May/ Jun. 1989, p. 602) * 14-18. The Asian Mathematical Confer- IMACS Symposium on Modelling and 10-14. Mathematiker-Kongress, Dres­ ence 1990, Hong Kong, China. Simulation of Electrical Machines, EN­ Democratic Republic. SEM - Nancy, France. (May/ Jun. 1989, den, German Algebra and CONFERENCE TOPICS: p. 602) (Jul./ Aug. 1989, p. 769) logic, analysis, geometry, applicable Fed­ * 2-7. Twelfth International Conference on 16-22. Risikotheorie, Oberwolfach, and discrete mathematics, probability of Germany. (Apr. 1989, Nonlinear Oscillations, Cracow, Poland. eral Republic and statistics. p. 498) ORGANIZING CoMMIITTEE: K. Y. SPONSORs: Polish Academy of Sci­ 17-22. DMV-Jahrestagung 1990, Bre­ Chan, (HKU) (Chairman); K. P. ences and Cracow University of Tech­ men, Federal Republic of Germany. Shum, (CUHK); R. F. Turner-Smith nology. (Jul./ Aug. 1989, p. 769) (HK Polytechnic); H. K. Chow, (HK PuRPOSE: The aim of the conference 23-29. Random Graphs and Combinator­ Polytechnic); T. H. Yao, (HKU). is to present the most recent advances ical Structures, Oberwolfach, Federal Re­ INFORMATION: H. K. Chow, Assistant in the field of nonlinear oscillations public of Germany. (Apr. 1989, p. 498) Secretary, Asian Mathematical Con­ concerning mathematical methods of ference 1990, Dept. of Mathemati­ analysis, synthesis, optimization and 24-28. International Symposium on Math­ cal Studies, The Hong Kong Poly­ the applications in the field of physics, ematical Theories, San Sebastian, Spain. technic, Hung Hom, Kowloon, Hong structural mechanics, electrotechnics, (Jul./ Aug. 1989, p. 769) Kong; Telex: 38964 POLYX HK; Fax: electronics, biomechanics, chemistry 30-0ctober 6. Diophantische Approxi­ (852)3-7643374. and others. mationen, Oberwolfach, Federal Republic CONFERENCE TOPICS: Analytical meth­ of Germany. (Apr. 1989, p. 498) on Knot 15-19. International Conference ods, qualitative methods, numerical Theory and Related Topics, International methods, experimental techniques, (Apr. 1989, p. 497) House, Osaka, Japan. physical and technical applications/

SEPTEMBER 1989, VOLUME 36, NUMBER 7 919 Meetings and Conferences

18-24. Komplexitiitstheorie, Oberwol­ fach, Federal Republic of Germany. (Apr. October 1990 August 1991 1989, p. 498) 7-13. Arbeitsgemeinschaft Mit Aktuellem 25-December I. Stochastische Approx­ 8-11. Joint Mathematics Meetings, Uni­ Thema, Oberwolfach, Federal Republic imation Und Optimierungsprobleme In versity of Maine, Orono, ME. (including of Germany. (Apr. 1989, p. 498) Der Statistik, Oberwolfach, Federal Re­ the summer meetings of the AMS, AWM, 14-20. Geometrie, Oberwolfach, Fed­ public of Germany. (Apr. 1989, p. 498) MAA, and PME) eral Republic of Germany. (Apr. 1989, 25-December I. Lineare Modelle und INFORMATION: H. Daly, AMS, P.O. p. 498) Multivariate Statistische Verfahren, Ober­ Box 6248, Providence, RI 02940. 21-27. Mathematische Methoden In Der wolfach, Federal Republic of Germany. Robotik, Oberwolfach, Federal Republic (Jul./ Aug. 1989, p. 769) 19-22. 1991 Joint Statistical Meetings, of Germany. (Apr. 1989, p. 498) Atlanta, GA. (Mar. 1988, p. 466) 28-November 3. Mathematical Eco­ December 1990 nomics, Oberwolfach, Federal Republic January 1992 of Germany. (Apr. 1989, p. 498) 2-8. Multigrid Methods, Oberwolfach, Federal Republic of Germany. (Apr. 8-11. Joint Mathematics Meetings, Bal­ 1989, p. 498) timore, MD. (including the annual meet­ November 1990 3-7. 1990 Australasian Conference on ings of the AMS, AWM, MAA and NAM) 2-3. Central Section Meeting of the Combinatorial Mathematics and Comput­ INFORMATION: H. Daly, AMS, P.O. AMS, University of North Texas, Den­ ing, Palmerston North, New Zealand. Box 6248, Providence, Rl 02940. ton, TX. (Feb. 1989, p. 183) 9-15. Allgemeine Ungleichungen, Ober­ INFORMATION: W. Drady, AMS, P.O. June 1992 Box 6248, Providence, RI 02940. wolfach, Federal Republic of Germany. (Apr. 1989, p. 498) 29-July 1. Joint Meeting with the Lon­ * 5-7. Second SIAM Confernce on Linear 16-22. Mathematische Logik, Oberwol­ don Mathematical Society, Cambridge, Algebra in Signals, Systems & Controls, fach, Federal Republic of Germany. (Apr. England. (Mar. 1989, p. 316) San Francisco, CA. 1989, p. 498) SPONSOR: SIAM Activity Group on 25-January 1. Lineare Modelle Und Mul­ January 1993 Linear Algebra. tivariate Statistische Verfahren, Oberwol­ ORGANIZERS: B. Datta, Northern Illi­ fach, Federal Republic of Germany. (Apr. 13-16. Joint Mathematics Meetings, San nois University; D. Carlson, San Diego 1989, p. 498) Antonio, TX. (including the annual meet­ State University. ings of the AMS, AWM, MAA, and CALL FOR PAPERS: Abstract Deadline: NAM) January 1991 May 16, 1990. INFORMATION: W. Drady, AMS, P.O. INFORMATION: SIAM Conference Co­ 16-19. Joint Mathematics Meetings, Box 6248, Providence, RI 02940. ordinator, 3600 University City Sci­ San Francisco, CA. (including the an­ ence Center, Philadelphia, P A 191 04- nual meetings of the AMS, AWM, MAA, 2688; Phone: 215-382-9800; Fax: 215- and NAM) January 1994 386-7999. INFORMATION: H. Daly, AMS, P.O. 5-8. Joint Mathematics Meetings, Cincin­ * 12-16. Supercomputing '90, New York, Box 6248, Providence, Rl 02940. nati, OH. (including the annual meetings NY. of the AMS, AWM, MAA, and NAM) SPONSORS: IEEE Computer Society, July 1991 INFORMATION: H. Daly, AMS, P.O. ACM. Box 6248, Providence, RI 02940. 8-12. Second International Conference INFORMATION: Supercomputing '90, on Industrial and Applied Mathematics, IEEE Computer Society, 1730 Mas­ Washington, DC. (Nov. 1988, p. 1389) sachusetts Ave.,N.W., Washington, DC 20036-1903; Phone: 202-3 71- 22-26. Thirteenth IMACS World Con­ 1013; TWX 7082500437 gress on Computing and Applied Math­ IEEECOMPSO. ematics, Trinity College, Dublin Univer­ sity, Dublin, Ireland. (Mar. 1989, p. 316)

920 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY New AMS Publications

J. R. Harper, A proof of Gray's conjecture ALGEBRAIC TOPOLOGY H.-W. Henn, J. Lannes and L. Schwartz, Analytic functors, Mark Mahowald and Stewart Priddy unstable algebras and cohomology of classifying spaces L. Kauffman, Statistical mechanics and the Alexander (Contemporary Mathematics, Volume 96) polynomial J. Kulich, A quotient of the iterated Singer construction This book will provide readers with an overview of some of the R. Lee and S. H. Weintraub, A generalization of a theorem of major developments in current research in algebraic topology. Heeke to the Siegel space of degree two Representing some of the leading researchers in the field, the W.-H. Lin, A Koszu/ algebra whose cohomology is the E3-term book contains the proceedings of the International Conference of the May spectral sequence for the Steenrod algebra on Algebraic Topology, held at Northwestern University in M. Mahowald and R. Thompson, K -theory and unstable March, 1988. Several of the lectures at the conference were homotopy groups expository and will therefore appeal to topologists in a broad H. Miller, The elliptic character and the Witten genus range of areas. G. Mislin, On the characteristic ring of flat bundles defined over a number field The primary emphasis of the book is on homotopy theory N. Ray, Loops on the 3-sphere and umbra/ calculus and its applications. The topics covered include elliptic C. B. Thomas, Characteristic classes and 2-modu/ar cohomology, stable and unstable homotopy theory, classifying representations of some sporadic simple groups spaces, and equivariant homotopy and cohomology. T. Tsuboi, On the connectivity of the classifying spaces for Geometric topics-such as knot theory, divisors and foliations configurations on surfaces, foliations, and Siegel spaces-are J. A. Wood, Maximal abelian subgroups of Spinor groups and also discussed. Researchers wishing to follow current trends error-correcting codes in algebraic topology will find this book a valuable resource. 1980 Mathematics Subject Classifications: 55-06; 55P42, 55P45, Contents 55R45,55T15, 18F25 A. Adem, R. L. Cohen and W. G. Dwyer, Generalized Tate ISBN 0-8218-5102-0, LC 89-15023 ISSN 0271-4132 homology, homotopy fixed points and the transfer 368 pages (softcover), August 1989 David J. Anick, On the homogeneous invariants of a tensor Individual member $25, List price $41, algebra Institutional member $33 A. Bahri, M. Bendersky and P. Gilkey, The relationship To order, please specify CONM/96N between complex bordism and K -theory for groups with periodic cohomology A. Baker, Elliptic cohomology, p-adic modular forms and DYNAMICS AND CONTROL OF MULTIBODY Atkin's operator Up SYSTEMS R. Brown, Triadic Van Kampen theorems and Hurewicz theorem D. Burghelea, The free-loop space J. E. Marsden, P. S. Krishnaprasad, and D. P. Carlisle and N. J. Kuhn, Smash products of summands J. C. Simo of B(lfp)"+ (Contemporary Mathematics, Volume 97) F. R. Cohen, R. L. Cohen, B. Mann and R. J. Milgram, Divisors and configuration on a surface The study of complex, interconnected mechanical systems M. C. Crabb, Periodicity in l/4-equivariant stable homotopy with rigid and flexible articulated components is of growing theory interest to both engineers and mathematicians. Recent E. B. Curtis and M. Mahowald, The unstable Adams spectral work in this area reveals a rich geometry underlying the sequence for s3 mathematical models used in this context. In particular, Lie D. H. Gottlieb, Zeroes of pullback vector fields and fixed point groups of symmetries, reduction, and Poisson structures play theory for bodies a significant role in explicating the qualitative properties of B. Gray, Homotopy commutativity and the EHP sequence multibody systems. In engineering applications, it is important

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SEPTEMBER 1989, VOLUME 36, NUMBER 7 921 New AMS Publications

to exploit the special structures of mechanical systems. For Jerrold E. Marsden, Juan C. Simo, Debra Lewis, and Thomas example, certain mechanical problems involving control of A. Posbergh, Block diagonalization and the energy-momentum interconnected rigid bodies can be formulated as Lie-Poisson method systems. The dynamics and control of robotic, aeronautic, and George Patrick, The dynamics of two coupled rigid bodies in space structures involve difficulties in modeling, mathematical three space analysis, and numerical implementation. For example, a new E. Polak, Nonsmooth optimization algorithms for the design of generation of spacecraft with large, flexible components controlled flexible structures are presenting new challenges to the accurate modeling T. A. Posbergh, J. C. Simo, and J. E. Marsden, Stability and prediction of the dynamic behavior of such structures. analysis of a rigid body with attached geometrically nonlinear Recent developments in Hamiltonian dynamics and coupling rod by the energy-momentum method of systems with symmetries has shed new light on some of Gloria Sanchez de Alvarez, Controllability of Poisson control these issues, while engineering questions have suggested systems with symmetries new mathematical structures. JUrgen Scheurle, Chaos in a rapidly forced pendulum equation N. Sreenath, Accurate time critical control of many body These kinds of considerations motivated the organization systems of the AMS-IMS-SIAM Joint Summer Research Conference A. J. van der Schaft, Hamiltonian control systems: on Control Theory and Multibody Systems, held at Bowdoin decomposition and clamped dynamics College in August, 1988. This volume contains the proceedings Jens Wittenburg, Graph-theoretical methods in multibody of that conference. The papers presented here cover a range dynamics of topics, all of which could be viewed as applications of 70QXX geometrical methods to problems arising in dynamics and 1980 Mathematics Subject Classifications: 55FXX, 70HXX, ISBN 0-8218-5104-7, LC 89-15019 control. The volume contains contributions from some of the ISSN 0271-4132 top researchers and provides an excellent overview of the 488 pages ( softcover), August 1989 frontiers of research in this burgeoning area. Individual member $28, List price $46, Institutional member $37 Contents To order, please specify CONM/97N John Baillieul, An enumerative theory of equilibrium rotations for planar kinematic chains Anthony M. Bloch and Robert R. Ryan, Stability and stiffening of driven and free planar rotating beams SOME MATHEMATICAL QUESTIONS IN P. E. Crouch and A. Van der Shaft, Characterization of BIOLOGY:MODELS IN POPULATION Hamiltonian input-output systems BIOLOGY Ruth F. Curtain, Robustness of distributed parameter systems Alan Hastings, Editor On the relationship C. J. Damaren and G. M. T. D'Eieuterio, (Lectures on Mathematics in the Life Sciences, Volume 20) between discrete-time optimal control and recursive dynamics for elastic multibody chains Population biology has had a long history of mathematical T. E. Duncan, Some solvable stochastic control problems in modeling. The 1920s and 1930s saw major strides with compact symmetric spaces of rank one the work of Latka and Volterra in ecology and Fisher, T. A. W. Dwyer, Ill, Slew-induced deformation shaping on slow Haldane, and Wright in genetics. In recent years, much more integral manifolds sophisticated mathematical techniques have been brought B. Gardner, W. F. Shadwick, and G. R. Wilkens, Feedback to bear on questions in population biology. Simultaneously, equivalence and symmetries of Brunowski normal forms advances in experimental and field work have produced a Daniel E. Koditschek, The application of total energy as a wealth of new data. While this growth has tended to fragment Lyapunov function for mechanical control systems the field, one unifying theme is that similar mathematical Jair Koiller, Classical adiabatic angles for slowly moving questions arise in a range of biological contexts. mechanical systems P. S. Krishnaprasad, Eulerian many-body problems This volume contains the proceedings of a symposium on Mark Levi, Morse theory for a model space structure Some Mathematical Questions in Biology, held in Chicago in Zexiang Li and Shankar Sastry, A unified approach for the 1987. The papers all deal with different aspects of population control of multifingered robot hands biology, but there are overlaps in the mathematical techniques D.-C. Liaw and E. H. Abed, Tethered satellite system stability used; for example, dynamics of nonlinear differential and E. B. Lin, Quantum control theory I difference equations form a common theme. The topics J. E. Marsden, R. Montgomery, and T. Ratiu, Cartan-Hannay­ covered are cultural evolution, multilocus population genetics, Berry Phases and symmetry spatially structured population genetics, chaos and the

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922 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY New AMS Publications

dynamics of epidemics, and the dynamics of ecological Frank D. Grosshans, Finitely generated rings of invariants communities. having rational singularities Contents Jozsef Horvath, Bruhat decomposition in unipotent actions Jurkiewicz, On some reductive group actions on affine Peter J. Richerson and Robert Boyd, Social learning as an Jerry adaptation space Konarski, Some examples of cohomological projective Alan Hastings, Deterministic multilocus population genetics: Jerzy An overview spaces, via c+ -actions R. Kempf, Equations of isotropy Thomas Nagylaki, The diffusion model for migration and George On linearizing "Good" selection Mariusz Koras and Pete Russell, 3 G. L. Truty and W. M. Schaffer, Chaos versus noise-driven C* -actions on C dynamics Mariusz Koras and Peter Russell, Codimension 2 torus Peter L. Chesson, A general model of the role of environmental actions on affine n-space variability in communities of competing species Hanspeter Kraft, G-vector bundles and the linearization problem 1980 Mathematics Subject Classifications: 92A 10, 92A 15 Hanspeter Kraft and Gerald W. Schwarz, Reductive group ISBN 0-8218-1170-3, LC 89-15119 ISSN 0075-8523 actions on affine space with one-dimensional quotient 136 pages (softcover), September 1989 Andy Magid, Equivariant completions and tensor products Individual member $17, List price $28, Tetsuo Nakano, Regular actions of semisimple algebraic Institutional member $22 groups on projective threefolds, especially SL(2) To order, please specify LLSCI/20N Vladimir L. Popov, Some applications of algebra of functions on G/U Mohan S. Putcha, Linear algebraic monoids and GI H GROUP ACTIONS AND INVARIANT THEORY embeddings A. Bialynicki-Birula, J. Carrell, P. Russell, and Lex E. Renner, Reductive embeddings Dennis M. Snow, Homogeneous vector bundles D. Snow, Editors Lin Tan, Some recent developments in the Popov-Pommerening (Conference Proceedings, Canadian Mathematical Society, conjecture Volume 10) David L. Wehlau, Some recent results on the Popov conjecture Subject Classifications: 14-02, 14L30, 1406, 2006; This volume contains the proceedings of a conference, 1980 Mathematics 20G05, 14025 sponsored by the Canadian Mathematical Society, on ISBN 0-8218-6015-1, LC 89-17605 Group Actions and Invariant Theory, held in August, 1988 in ISSN 0731-1036 Montreal. The conference was the third in a series bringing 240 pages (softcover), September 1989 together researchers from North America and Europe Individual member $20, List price $33, Institutional member $26 The papers collected here will provide (particularly Poland). To order, please specify CMSAMS/10N an overview of the state of the art of research in this area. The conference was primarily concerned with the geometric side of invariant theory, including explorations of the linearization problem for reductive group actions on affine spaces (with THE METAPLECTIC REPRESENTATION, MPc a counterexample given recently by J. Schwarz), spherical STRUCTURES AND GEOMETRIC and complete symmetric varieties, reductive quotients, QUANTIZATION automorphisms of affine varieties, and homogeneous vector P. L. Robinson and J. H. Rawnsley bundles. (Memoirs of the AMS, Number 410) Contents Shreeram S. Abhyankar and Sanjeevani B. Joshi, Generalized This work presents a detailed and unified account of the codeletion and standard multitableaux metaplectic representation and symplectic spinors, based on A. Bialynicki-Birula and J. Swiecicka, On exotic orbit spaces the Bargmann-Segal model of the canonical commutation of tori acting on projective varieties relations. Though the standard Schrodinger model is Michel Brion (after D. Ahiezer, A. Huckleberry and D. Snow), customarily used in this context, the present approach On spherical varieties of rank one enables the authors to explicitly describe the structure and Piotr Blass, K. J. Horodam, Peter B. Kleidman and A. J. E. pairing of vacuum states for positive polarizations. They Ryba, A new doubly-infinite class of factorial rings develop a scheme for the geometric quantization of symplectic A. Fauntleroy, G./. T. for general algebraic groups manifolds that involve half-forms defined by symplectic spinors

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and that, following Hess, use Mpc structures in place of the determining which covers of compact 3-manifolds are missing standard metaplectic structures. This scheme extends the boundary manifolds. standard scheme due to Kostant and Souriau and is applied Contents to complex projective spaces and linear symplectic manifolds. Statements, definitions, examples and discussion Contents Handles, handle procedures, reductions and end reductions Pr_eliminary topics Elementary consequences of end 1-movability Th~),etaplectic representation . J The eventually end irreducible case Positive polarizations End 1-movability of interiors Isotropic reduction The irreducible ease-l: Basic structure Derived representations The irreducible case-11: Missing boundary Mpc structures The irreducible case-Ill: Isolated ends Prequantization The final analysis-the simply connected case Quantization 1980 Mathematics Subject Classifications: 57N10; 57M10, 57N65 Complex projective spaces ISBN 0-8218-2474-0, LC 89-15146 Linear symplectic manifolds ISSN 0065-9266 73 pages (softcover), September 1989 1980 Mathematics Subject Classifications: 22E70, 53C10, 53C57, Individual member $9, List price $15, 58F06,81007 Institutional member $12 ISBN 0-8218-2473-2, LC 89-15191 To order, please specify MEM0/411N ISSN 0065-9266 93 pages (softcover), September 1989 Individual member $10, List price $16, Institutional member $13 RINGS OF DIFFERENTIAL OPERATORS ON To order, please specify MEM0/410N CLASSICAL RINGS OF INVARIANTS T. Levasseur and J. T. Stafford (Memoirs of the AMS, Number 412) 3-MANIFOLDS WHICH ARE END 1-MOVABLE Matthew G. Brin and T. L. Thickstun This book will provide readers with an understanding of (Memoirs of the AMS, Number 411) the interrelationship between differential operators, invariant theory, and the primitive ideal theory of semisimple Lie While requiring only the basics of 3-manifold topology as algebras. The main topic concerns a study of rings of background, this book introduces recent techniques that will differential operators on classical rings of invariants, in the certainly find further application and brings readers to the sense of Weyl's book, The Classical Groups. The authors frontiers of the topology of noncompact 3-manifolds. consider three different classes of rings of invariants and show that, for each of these cases, the ring of differential Traditional techniques for analyzing noncompact 3-manifolds operators is a simple factor ring of a certain enveloping involve study of its compact subsets. By contrast, this work algebra. In particular, the ring of differential operators is a utilizes certain open subsets called end reductions, which simple Noetherian ring. They also demonstrate that, if SO(k) are ''simple'' approximations to a noncompact manifold that acts in the natural way on the ring of complex polynomials in inherit many of the manifold's properties. In this work, the kn variables, then, for k :::; n, the ring of differential operators authors further their development of the concept of end on C[X]50(klis finitely generated as a module of a certain reduction and use it to analyze all orientable, noncompact enveloping algebra. 3-manifolds in which loops near infinity homotop to infinity Contents while staying near infinity (this is the proper homotopy condition "end 1-movable" of the title). Reductive dual pairs and the Howe correspondence The class of manifolds examined here also includes the Classical reductive dual pairs: explicit calculations "missing boundary" manifolds. The authors provide a new Differential operators on classical rings of invariants characterization of orientable, missing boundary 3-manifolds and contribute some information about the open question of The maximality of J(k) and the simplicity of D(xk)

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Differential operators on the ring of SO(k)-invariants 1980 Mathematics Subject Classifications: 05A20; 05A 15, 05A 10, 05C20,06A10, 11B73, 15A04,26C10,30C15 Appendix. Gabber's Lemma ISBN 0-8218-2476-7, LC 89-15137 ISSN 0065-9266 1980 Mathematics Subject Classifications: 17B35, 13N05, 14L30, 106 pages (softcover), September 1989 14M12, 17B20, 16A19, 16A33 Individual member $10, List price $17, ISBN 0-8218-2475-9, LC 89-15147 Institutional member $14 ISSN 0065-9266 To order, please specify MEM0/413N 117 pages ( softcover), September 1989 Individual member $11, List price $19, Institutional member $15 MEM0/412N To order, please specify ACTIONS OF LINEARLY REDUCTIVE GROUPS ON AFFINE PI-ALGEBRAS Nikolaus Vonessen UNIMODAL LOG-CONVAVE AND POLYA (Memoirs of the AMS, Number 414) FREQUENCY SEQUENCES IN COMBINATORICS Francesco Brenti Aimed at researchers and advanced graduate students (Memoirs of the AMS, Number 413) interested in ring theory and invariant theory, this book introduces readers to a new and quite beautiful area of In recent years, considerable research has focused on noncommutative invariant theory. unimodal or log-concave sequences that are of combinatorial interest. Although these two properties have simple definitions, The author examines this subject in the setting of affine proving that a sequence is unimodal or log-concave is often a PI-algebras, extending both the theory of actions of finite difficult task requiring refined and sophisticated mathematical groups on noncommutative rings and commutative invariant tools from such areas as representation theory, algebraic theory. The work focuses the action of a linearly reductive geometry, or classical analysis. group G on a finitely generated PI-algebra R. One of the book's major results is that the fixed ring RG is finitely The main purpose of this book is to show the theory of total generated, provided that R is Noetherian. Other topics positivity can be very useful in studying this area. In the explored here include localization, the behavior of prime first part of the book, after discussing some combinatorial ideals in the ring extension RG c R, and actions by inner motivations, the author studies some of the fundamental automorphisms. The author also shows that many of the linear transformations that preserve the log-concavity or P61ya results obtained actually characterize linearly reductive frequency properties of a sequence. This part forms the groups, for some results are false in prime characteristic if the theoretical core of the work and may be read independently acting group is reductive rather than linearly reductive. This from the rest. In fact, this rich and powerful theory can be situation contrasts with commutative invariant theory, where, applied to any situation in which log-concavity and unimodality in prime characteristic, most results can also be proven for questions arise. The second part of the book is devoted to reductive groups. applications to several combinatorial situations, yielding many new results and solutions to some problems that had resisted Contents attack with other techniques. Both parts of the book point to many conjectures, open problems, and directions for further study. The trace ring Contents Affine fixed rings The Poset conjecture Borha thoery A general theory The correspondence : Spec R - o Spec RG Ramifications of the general theory Lying over Polynomials in P F [ (x+~-i)] Characterizations of linearly reductive groups through actions Applications to the Poset conjecture on affine Pi-algebras Applications to enumerative combinatorics Actions by inner automorphisms P61ya frequency digraphs

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SEPTEMBER 1989, VOLUME 36, NUMBER 7 925 New AMS Publications

1980 Mathematics Subject Classifications: 16A7 4; 16A38, 16A33, 1980 Mathematics Subject Classifications: 32E10, 14J15, 32J15, 16A 16, 20G99 32C35 ISBN 0-8218-2477-5, LC 89-15148 ISBN 0-8218-2478-3, LC 89-15176 ISSN 0065-9266 ISSN 0065-9266 106 pages (softcover), September 1989 123 pages (softcover), September 1989 Individual member $10, List price $17, Individual member $11, List price $19, Institutional member $14 Institutional member $15 To order, please specify MEM0/414N To order, please specify MEM0/415N

UEDA THEORY: THEOREMS AND PROBLEMS BOUNDARY VALUE PROBLEMS OF Amnon Neeman MATHEMATICAL PHYSICS. XIII (Memoirs of the AMS, Number 415) 0. A. Ladyzhenskaya, Editor (Proceedings of the Steklov Institute, Volume 179) Ueda explored the question of which algebraic varieties over the complex numbers give rise to Stein manifolds. Affines This book brings together eleven papers by leading Soviet are one obvious example, but there are others. In 1983, experts in the area of mathematical physics. The main topics Ueda defined an invariant that "measures" the Steinness covered fall into two general areas: the theory of nonlinear of a Zariski open subset of a compact complex surface. problems for partial differential equations, and the study of The purpose of this book is to study this fascinating and spectral and other properties of linear differential operators mysterious homological invariant by exploring its functoriality generated by various problems of mathematical physics. properties, variational properties, and higher dimensional generalizations. The author sets Ueda's invariant in the right Papers in the first area cover such topics as sharp estimates formal framework, permitting formulation of many problems of Holder norms for V' u on the boundary for functions and conjectures indicating that further study might reveal truly satisfying quasilinear inequalities of elliptic or parabolic type; surprising and interesting phenomena. Aimed at researchers problems of hydrodynamics; and the existence of nontrivial in several complex variables and in algebraic geometry, the dynamics on the entire infinite-dimensional phase space for book requires familiarity with coherent analytic sheaves and a certain class of systems of classical dynamics. Among the the solution of the Levi problem, as well as some basic topics in the second area are the Maxwell system in domains knowledge of algebraic geometry. with boundary, and the investigation of scattering data for the Schrodinger operator for large values of the wave number Contents and coupling constant. Geometric consequences of Ueda's results Contents The Ueda class Variation of the Ueda class Forward The Ueda class and plurisubharmonic functions A. A. Arkhipova and N. N. Ural'tseva, Regularity of the solution The proofs of Lemma 3.2 and Lemma 3.4 of a problem with a two-sided constraint on the boundary for The Ueda class of curves on projective surfaces elliptic and parabolic equations The case of elliptic curves M. Sh. Birman, The Maxwell operator for a periodic resonator Sections of IP 1-bundles with inward edges Sharp asymptotics of the The functoriality of the Ueda class T. E. Gureev and Yu. G. Safarov, on a manifold with periodic Ueda classes of high type spectrum of the Laplace operator A different example geodesics A. V. Ivanov, On classical solvability of the Dirichlet problem Problems in Ueda theory for nonlinear, nonuniformly elliptic equations Infinitesimal connections E. M. ll'in, Scattering by unbounded obstacles for elliptic Lifting infinitesimal connections operators of second order The Ueda class 0. A. Ladyzhenskaya and N. N. Ural'tsev, Estimates on the Variation of the Ueda class boundary of a domain for the first derivatives of functions The Ueda class of M c X with a torsion normal bundle satisfying an elliptic or parabolic inequality Classification A. P. Oskolkov, Initial-boundary value problems for the Higher dimensions equations of motion of Kelvin-Voigt fluids and Oldroyd fluids Computations of some Ueda classes V. G. Osmolovskii, Rigidity of a surface relative to deformations Elliptic curves M c X with u(M, X) i- 0 satisfying nonlinear differential equations of first order

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926 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY New AMS Publications

V. A. Solonnikov, Solvability of the problem of effluence of a Stability. Linear systems viscous incompressible fluid into an infinite open basin Stability of sample paths of homogeneous Markov V. I. Shubov, On the dynamics of infinite classical anharmonic processes systems with constraints Linear equations in Rd and the stochastic semigroups D. R. Yafaev, The eikonal approximation for the Schrodinger connected with them. Stability equation Stability of solutions of stochastic differential equations 1980 Mathematics Subject Classifications: 35845, 35865, 35J05, Linear stochastic equations in Hilbert space/Stochastic 35J10, 35J25,35J60, 35K20, 35P20, 35P25, 47F05, 53A05, 76A10, semigroups. Stability 76005, 78A99,82A05, 82A60 ISBN 0-8218-3127-5, LC 67-6187 Linear equations with bounded coefficients ISSN 0081-5438 Strong stochastic semigroups with second moments 266 pages (hardcover), September 1989 Stability Individual member $77, List price $128, Institutional member $102 1980 Mathematics Subject Classifications: 60-02, 60H10, 60J60; To order, please specify STEKL0/179N 60H15,60J25,28010,34F05,47007,47A35,60J75,35R60,34K20 ISBN 0-8218-4531-4, LC 89-17698 ISSN 0065-9282 328 pages (hardcover), September 1989 ASYMPTOTIC METHODS OF THE THEORY Individual member $71, List price $119, OF STOCHASTIC DIFFERENTIAL Institutional member $95 To order, please specify MMON0/78N EQUATIONS A. V. Skorokhod (Translations of Mathematical Monographs, Volume 78) ARITHMETIC PROGRESSION: FROM Written by one of the foremost Soviet experts in the field, HILBERT TO SHELAH this book is intended for specialists in the theory of random Ronald L. Graham processes and its applications. The author's 1982 monograph on stochastic differential equations, written with losif ll'ich In this lively and absorbing videotaped lecture, Graham Gikhman, did not include a number of topics important explores connections between arithmetic progressions and to applications. The present work begins to fill this gap combinatorics over the past century. Arithmetic progressions by investigating the asymptotic behavior of stochastic are among the most basic structures in number theory, differential equations. The main topics are ergodic theory for and their combinatorial properties now form an important Markov processes and for solutions of stochastic differential branch of combinatorics. The starting point for the talk is a equations, stochastic differential equations containing a small 1927 theorem of van der Waerden connecting partitions of parameter, and stability theory for solutions of systems of the integers and finite arithmetic progressions, and Graham stochastic differential equations. shows how this theorem is related to a purely combinatorial result of Hales and Jewett. The work of Schur, Rado, Contents Ramsey, Szemeredi, and Furstenberg come into play as Ergodic theorems Graham shows how different combinatorial areas interact. A General ergodic theorems surprising connection is drawn between Hilbert's "irreducibility Densities for transition probabilities and resolvents for theorem" of 1892 and Shelah's 1988 result, which gives a Markov solutions of stochastic differential equations new bound on van der Waerden's theorem. Sprinkling the Ergodic theorems for one-dimensional stochastic equations talk with intriguing problems and $1000 conjectures, Graham Ergodic theorems for solutions of stochastic equations in brings his impressive command of contemporary research in Rd combinatorics together with a historical perspective and talent for clarity of exposition to make this an especially appealing Asymptotic behavior of systems of stochastic equations and accessible lecture. containing a small parameter Equations with a small right-hand side 1980 Mathematics Subject Classification: 05 Processes with rapid switching VHS format, approx. one hour, September 1989 Averaging over variables for systems of stochastic Price $59 differential equations To order, please specify VIDGRAHAM/N

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SEPTEMBER 1989, VOLUME 36, NUMBER 7 927 New AMS Publications

TRANSONIC FLOW AND MIXED EQUATIONS SOCIETE MATHEMATIQUE DE FRANCE, ASTERISQUE Cathleen S. Morawetz The AMS distributes Asterisque only in the U.S., Canada, and Mexico. In this videotaped lecture, Cathleen Morawetz brings a wealth Orders from other countries should be sent to the SMF, B.P. 126-05, of distinguished research experience to bear on recent 75226 Paris Cedex 05, France, or to OFFILIB, 48 rue Gay-Lussac, members of either AMS or developments in the area of transonic flow and the associated 75240 Paris Cedex 05, France. Individual SMF are entitled to the member price. (ISSN 0303-1179) differential equations. The talk begins with a short review of mixed equations (for many cases, including transonic flight, flow is governed partly by elliptic and partly by hyperbolic equations) and moves on to a discussion of compressible HIGHER DIMENSIONAL COMPLEX flow. Morawetz vividly illustrates the phenomenon of shocks GEOMETRY in transonic flow and describes computations made in the Herbert Clemens, Janos Kollar, and 1970s that showed that these shocks could be smoothed by clever design. Though there is still no full mathematical theory Shizefumi Mori for solutions with small shocks, Morawetz describes the (Asterisque, Number 166) DiPerna-Tartar-Murat method of compensated compactness, This work consists of the twenty-four lectures which which has proved a fruitful tool. In addition, she discusses comprised a summer seminar in higher dimensional complex some new bounds that have been deduced for transonic flow. geometry. The seminar took place during the months of July 1980 Mathematics Subject Classifications: 35M05, 76H05, 35G30, and August, 1987, at the University of Utah. The first sixteen 76G99 lectures give an introduction to Mori's program for finding VHS format, approx. one hour, minimal models of complex projective manifolds of dimension September 1989 three or more. The central theme is the investigation of Price $59 To order, please specify VIDMORAWETZ/N varieties on which the canonical class is not numerically effective. Lectures seventeen to twenty examine the geometry of the period mapping and, more generally, harmonic mappings from compact Kahler manifolds to a large class of COMBINED MEMBERSHIP LIST symmetric spaces. The last four lectures consist in a study of the existence and behavior of curves of low genus on generic This CML is a comprehensive directory of the membership projective manifolds with sufficiently ample canonical class. of the AMS, the Mathematical Association of America, and the Society for Industrial and Applied Mathematics. The list is ISSN 0303-1179 144 pages (softcover), September 1989 membership to AMS members in distributed as a privilege of Individual AMS or SMF member $12, List price $17 even-numbered years and the MAA members in odd-numbered To order, please specify AST /166N years. The CML is an invaluable reference for keeping in touch with colleagues and for making connections in the mathematical sciences community in the U.S. and abroad. MOUVEMENT BROWNIEN A PLUSIEURS There are two lists of individual members. The first is PARAMETRES: MESURE DE HAUSDORFF a complete alphabetical list of all members in all three DES TRAJECTOIRES organizations. For each member, the CML provides his or her address, title, department, institution, and telephone number (if A. Goldman available), electronic address (if indicated), and also indicates (Asterisque, Number 167) the mathematical organizations to which the individual belongs. The function ¢>(x) = x 2P log log(1 jx) is shown to be exact The second lists individual members according to their Hausdorff measure function for the range of a transient locations. In addition, the CML lists all academic geographic Levy Brownian motion with p-dimensional time; this result and institutional members and provides addresses and settles a question asked by P. Levy. In connexion with this telephone numbers of mathematical sciences departments. problem, some prediction estimates and an evaluation of the 1980 Mathematics Subject Classification: 00 distribution of the absolute maximum are obtained. ISBN 0-8218-0140-6 400 pages (softcover), September 1989 ISSN 0303-1179 Individual member $22, List price $36, 106 pages (softcover), September 1989 Institutional member $29 Individual AMS or SMF member $9, List price $13 To order, please specify CML/89/90N To order, please specify AST/167N

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928 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS Reports and Communications

Recent Appointments Local Arrangements for the Colum­ collected using the AMS-MAA An­ bus Meeting August 8-11, 1990. nual Survey. Since name identifi­ Professor Leitzel will serve as chair­ cation was used, the information Committee members' terms of man. for some categories necessitated office on standing committees Donna L. Beers (AMS, 1991) the use of four classifications: has been appointed by President expire on December 31 of the Male: names that were obvi­ William Browder to the AMS­ year given in parentheses fol­ ously male; MAA Committee on Employment lowing their names, unless oth­ Female: names that were obvi­ and Educational Policy. Contin­ erwise specified. ously female; uing members of the committee Unknown: names that could are Morton Brown (MAA, 1989), not be identified as clearly male or Vladislav V. Goldberg has been Stefan A. Burr (AMS, 1989), Ed­ female (e.g., only initials given); appointed to the Advisory Com­ ward A. Connors (AMS, 1991), and mittee for the Russian-English Dic­ chairman, Philip C. Curtis, Jr. Foreign: foreign names that tionary by President William Brow­ (MAA, 1990), David J. Lutzer could not be identified as clearly der. Other members of the com­ (MAA, 1989), James W. Maxwell male or female. mittee are Joseph N. Bernstein, (ex officio), and James J. Tattersall Ralph P. Boas, chairman, James (MAA, 1990). The following is the fourth re­ R. Bunch, Courtney S. Coleman, Cathleen S. Morawetz was ap­ porting of this information. Up­ Joseph L. Doob, Bogdan Dudzik, pointed by then President G. D. dated reports will appear annually Eugene Dynkin, Mark I. Freidlin, Mostow as representative to Sec­ in Notices. Paul R. Halmos, Edwin Hewitt, tion A of the American Association John R. Isbell, Anatole Katok, for the Advancement of Science. George Mackey, John McCarthy, The term expires on February 12, Members of the AMS Boris Mityagin, Eric John Fyfe 1992. Primrose, Boris Schein, Lawrence Residing in the U.S. A. Shepp, Ben Silver (ex officio), Male: 12,935 72% and Smilka Zdrakovska. Statistics on Women Female: 2,615 15% Unknown: 1,395 8% Nancy Anderson, Richard A. Mathematicians Compiled Foreign: 960 5% Askey, Robert S. Doran, Dorothy by the AMS Total checked: 17,905 McGarry, James Rovnyak, George Seligman, Mary Ann Southern, At its August 1985 meeting, the Invited Hour Address Speakers and Jack Weigel have been ap­ Council of the AMS approved a at AMS Meetings (1979-1988) pointed by President William Brow­ motion to regularly assemble and Male: 360 92% der to an ad hoc Library Commit­ report in Notices information on Female: 29 7% tee. Professor Rovnyak will serve the relative numbers of men ver­ Unknown: 1 1% as chairman. sus women in at least the follow­ Foreign: 0 0% Robert M. Thrall and Daniel ing categories: membership in the Total checked: 391 AMS; invited hour addresses at H. Wagner were appointed to a Speakers at Special Sessions Committee on Cooperative Sym­ AMS meetings; speakers at special at AMS Meetings (1984-1988) posia by then President, G. D. sessions at AMS meetings; and Male: 2,873 80% Mostow. members of editorial boards of Female: 227 6% Frank Carroll, W. Wistar Com­ AMS journals. Unknown: 287 8% fort (ex officio), Joseph C. Ferrar, It was subsequently decided Foreign: 204 6% William J. Friel, William H. Jaco that this information would be Total checked: 3,591 (ex officio), James R. Leitzel, Car­ gathered by determining the sex olyn Mahoney, Kenneth A. Ross of the individuals in the above Trustees and Council Members (ex officio), and Andrew Sterrett categories based on name identi­ ------1988 1987 1986 1985 have been appointed by William fication and that additional infor­ Total: 56 65 65 71 Browder (AMS), and Lida K. Bar­ mation on the number of Ph.D.'s Male: 46 82%52 80%56 86%61 86% rett (MAA) to the Committee on granted to women would also be Female: 10 18% 13 20% 9 14%10 14%

SEPTEMBER 1989, VOLUME 36, NUMBER 7 929 AMS Reports and Communications

Members of Editorial Boards of AMS Journals 1988 1987 1986 1985 1984 1983 1982 1981 1980 1979 Total: 161 133 109 102 93 90 83 85 82 82 Male: 148 92% 125 94% 104 95% 94 92% 85 91% 84 93% 77 93% 79 93% 77 94% 78 95% Female: 13 8% 8 6% 5 5% 8 8% 8 9% 6 7% 6 7% 6 7% 5 6% 4 5%

Ph.D.'s Granted to U.S. Citizens 1988 1987 1986 1985 1984 1983 1982 1981 1980 1979 Total: 363 362 386 396 433 455 519 567 578 596 Male: 287 79% 289 80% 304 79% 315 80% 346 80% 366 80% 431 83% 465 82% 491 85% 503 84% Female: 76 21% 73 20% 82 21% 81 20% 87 20% 89 20% 88 17% 102 18% 87 15% 93 16%

reviews in GLOBAL ANALYSIS Introduction by 1980-86 Anthony J. Tromba

The term "global analysis" refers to the These five volumes contain the more 1980 Mathematics Subject Classification: 58 general area of analysis on manifolds, in than 18,000 reviews that appeared ISBN 0-8218-0104-X, LC 88-10565 which the methods of modern algebra, in Mathematical Reviews from 1980 5 volumes, _4060 pages (softcover}, August 1988 analysis, geometry, and topology are through 1986 and have a primary or List price $307 , Institutional member $246, blended. Although the beginnings of a secondary classification in Global Individual member $184, Reviewer $154 these ideas can be traced to the 17th Analysis (classification number 58). To order, please specify REVGL0/86PNA century, major contributions in this Relevant cross-references are provided direction were made by Lie, Riemann, with each review. The fifth volume and Poincare toward the end of the of this set contains author and key Combination offer. Reviews in Partial last century, followed by the work indexes, making it very easy to locate Differential Equations, 1980-86, and of G. D. Birkhoff, E. Cartan, and items written by a specific author or Reviews in Global Analysis, 1980-86 Morse in the early part of this century. to get information about collections or (REVPDE/86 and REVGL0/86). However, it is only in recent years that conference proceedings dealing with List $491, Institutional member $393, the subject has attained its present global analysis. Individual member $295, Reviewer $246 . central position in mathematics. The To order, Please specify subject has many rich applications to Contents: REVPGL/86NA fields outside mathematics--such as Volume 1: Global analysis, analysis on mechanics, quantum physics, and general manifolds; General theory of differentiable relativity-as well as within mathematics manifolds; Infinite-dimensional manifolds; All prices subject to change. Shipment will itself. Calculus on manifolds; nonlinear operators; be made by surface. For air delivery add, Spaces and manifolds of mappings; 1st book $5, each additional book $3, maxi­ Today, this vital and active field is Volume 2: Variational problems in infinite­ mum $100. Prepayment required. Order from American Mathematical Society, P.O. Box undergoing a virtual explosion of new dimensional spaces; Ordinary differential 1571, Annex Station, Providence, RI 02901- and important results. Reviews in equations on manifolds; dynamical systems; 15 71, or call toll free 800-566-777 4 to charge Global Analysis makes information about Volume 3: Ordinary differential equations with VISA or MasterCard. the most recent contributions to this on manifolds; dynamical systems; Volume 4: rapidly growing field accessible both to Partial differential equations on manifolds; specialists working in global analysis, differential operators; Pseudogroups and and to those in other areas of pure and general structures on manifolds; Volume 5: applied mathematics. Series contents; Author index; Key index.

930 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Officers and Committee Members

Numbers to the left of headings are used as points of reference in Vice-Presidents Sun-Yung Alice Chang 1990 a index to AMS committees which follows this listing. Primary and Barry Simon 1989 secondary headings are: William P. Thurston 1989 Secretary Robert M. Fossum 1990 Officers Former Secretary Everett Pitcher 1990 1.1 Liaison Committee Associate 2 Council Secretaries* Joseph A. Cima 1990 2.1 Executive Committee of the Council W. Wistar Comfort 1990 3 Board of Trustees Andy Roy Magid 1989 4 Committees Lance W. Small 1989 4.1 Editorial and Communications Committees Treasurer Franklin P. Peterson 1990 4.2 Committees of the Board of Trustees Associate 4.3 Internal Organization of the AMS Treasurer Steve Armentrout 1990 4.4 Program and Meetings 4.5 Status of the Profession 4.6 Prizes and Awards 2.0.2. Representatives of Committees 4. 7 Institutes and Symposia American Journal of 4.8 Joint Committees Mathematics M. Salah Baouendi 1989 5 Representatives Bulletin Roger E. Howe 1990 6 Index Colloquium Raoul H. Bott 1990 Terms of members expire on December 31 of the year given unless Journal of the AMS Michael Artin 1991 otherwise specified. Committee to Monitor Problems in Communication Richard S. Palais 1990 1. Officers------Mathematical Reviews Melvin Hochster 1989 Mathematical Surveys and President William Browder 1990 Monographs M. Susan Montgomery 1990 Ex-President G. D. Mostow 1989 Mathematics of Vice-Presidents Sun-Yung Alice Chang 1990 Computation Walter Gautschi 1989 Barry Simon 1989 Proceedings William J. Davis 1991 William P. Thurston 1989 Andrew M. Odlyzko 1989 Secretary Robert M. Fossum 1990 Science Policy Committee Former Secretary Everett Pitcher 1990 Ronald G. Douglas 1989 Associate Transactions and Memoirs Secretaries Joseph A. Cima 1990 Ronald L. Graham 1989 W. Wistar Comfort 1990 Andy Roy Magid 1989 2.o.J. Members-at-Large Lance W. Small 1989 Treasurer Franklin P. Peterson 1990 Jonathan L. Alperin 1991 Yiannis N. Moschovakis 1989 Associate Fan R. K. Chung 1991 Linda A. Ness 1989 Treasurer Steve Armentrout 1990 Lawrence J. Corwin 1991 Michael C. Reed 1991 Richard K. Guy 1990 Marc A. Rieffel 1989 1.1. Liaison Committee Rhonda J. Hughes 1990 Hugo Rossi 1991 Robion C. Kirby 1990 Harold M. Stark 1990 All members of this committee serve ex officio. Irwin Kra 1990 William A. Veech 1989 Chairman William Browder H. Blaine Lawson, Jr. 1989 Carol S. Wood 1989 Robert M. Fossum Albert Marden 1990 Franklin P. Peterson * Only one Associate Secretary at a time is a voting member of the Council, namely the cognizant Associate Secretary for the scientific 2. Council------sessions.

2.0.1. Officers of the AMS President William Browder 1990 Ex-President G. D. Mostow 1989

SEPTEMBER 1989, VOLUME 36, NUMBER 7 931 Officers and Committee Members

2.1. Executive Committee of the Council Associate Editors for Research Announcements Chairman William Browder ex officio William B. Arveson 1990 Ronald L. Graham 1990 Robert M. Fossum ex officio Spencer Bloch 1990 Victor W. Guillemin 1990 Irwin Kra 1990 Gergory L. Cherlin 1989 Frank S. Quinn III 1990 G. D. Mostow ex officio Percy Alec Deift 1990 Peter B. Shalen 1990 Hugo Rossi 1992 Michael D. Fried 1990 Nolan R. Wallach 1990 William P. Thurston 1991 Expository Articles William A. Veech 1989 Associate Editors for Research- Lenore Blum 1989 David A. Vogan, Jr. 1989 Barry Mazur 1989 Alan D. Weinstein 1989 3. Board of Trustees------Richard S. Palais 1990 Guido L. Weiss 1990

Steve Armentrout ex officio 4.2.4. Colloquium William Browder ex officio Chairman Raoul H. Bott 1990 Ramesh A. Gangolli 1989 Charles L. Fefferman 1991 Secretary Frederick W. Gehring 1992 H. Jerome Keisler 1989 Ronald L. Graham 1991 Chairman M. Susan Montgomery 1990 4.2.s. Committee to Monitor Problems Franklin P. Peterson ex officio in Communication Paul J. Sally, Jr. 1993 Sheldon Axler 1989 Consultant Nancy Gubman Arthur M. Jaffe 1991 4. Committees------Richard G. Larson 1990 William H. Jaco ex officio Paul G. Nevai 1991 4.1. Committee of the Council Chairman Richard S. Palais 1990 Marian B. Pour-El 1989 Ad Hoc Committee 4.2.6. Contemporary Mathematics Richard W. Beals 1991 4.1.1. Commmittee to Review the Procedures of the Chairman Daniel M. Burns, Jr. 1989 Council in Considering Issues Sylvain E. Cappell 1991 Robert M. Fossum David Eisenbud 1989 Albert Marden Jonathan Goodman 1990 Chairman Marian B. Pour-EI Gerald J. Janusz 1989 Harold M. Stark Jan Mycielski 1990 Michael E. Taylor 1991 4.2. Editorial and Communications 4.2.7. Journal of the AMS Committees Chairman Michael Artin 1992 H. Blaine Lawson, Jr. 1991 4.2.1. Abstracts Editorial Committee Richard B. Melrose 1990 All members of this committee serve ex officio. Wilfried Schmid 1990 Robert E. Tarjan 1992 Joseph A. Cima W. Wistar Comfort Associate Editors Chairman Robert M. Fossum Andy Roy Magid James G. Arthur 1992 Joe Harris 1990 Lance W. Small Peter Bickel 1990 Hendrik W. Lenstra, Jr. 1991 Gerd Faltings 1991 Andrew Majda 1992 4.2.2. American Journal of Mathematics, Charles L. Fefferman 1992 Hugh L. Montgomery 1990 Society's Representatives Michael H. Freedman 1990 Paul H. Rabinowitz 1991 Daniel Friedan 1991 Karen Uhlenbeck 1992 Chairman M. Salah Baouendi 1989 Ronald L. Graham 1992 W. Hugh Woodin 1990 David Gieseker 1991 4.2.8. Mathematical Reviews 4.2.3. Bulletin (New Series) Leonard D. Berkovitz 1991 Morris W. Hirsch 1989 Chairman Melvin Hochster 1989 Chairman Roger E. Howe 1990 John L. Selfridge 1991 Murray H. Protter 1991 Hans F. Weinberger 1990

932 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Officers and Committee Members

4.2.9. Mathematical Surveys and Monographs 4.2.13. Proceedings of Symposia in Applied Victor W. Guillemin 1989 Mathematics David S. Kinderlehrer 1991 Giles Auchmuty 1989 Chairman M. Susan Montgomery 1990 Alexandre Chorin 1991 1991 Bjorn E. J. Dahlberg 1991

4.2.1o. Mathematics of Computation 4.2.14. Transactions and Memoirs Chairman Walter Gautschi 1989 James E. Baumgartner 1991 Donald Goldfarb 1990 James W. Cannon 1989 Andrew M. Odlyzko 1991 Ralph L. Cohen 1990 John E. Osborn 1989 Eugene B. Fabes 1992 L. Graham 1989 Associate Editors Chairman Ronald Jerry L. Kazdan 1990 James Bramble 1989 Rene Schoof 1989 Roger D. Nussbaum 1991 Bille C. Carlson 1989 Larry L. Schumaker 1991 Carl Pomerance 1991 James W. Demmel 1991 Ridgway Scott 1989 David J. Saltman 1990 Eugene Isaacson 1989 Daniel Shanks 1990 Masamichi Takesaki 1989 Heinz-Otto Kreiss 1990 Frank Stenger 1989 Audrey A. Terras 1991 James N. Lyness 1989 Hans J. Stetter 1991 Robert J. Zimmer 1990 Niederreiter G. W. Stewart 1989 Harald 1990 Associate Editor Syvert P. Norsett 1990 Vidar C. Thomee 1989 Frank W. J. Olver 1989 Lars B. Wahlbin 1989 Burgess Davis 1989 Stanley J. Osher 1989 Hugh C. Williams 1991 Carl Pomerance 1989 John W. Wrench, Jr. 1990 4.2.15. Translation from Chinese Sun-Yung Alice Chang 4.2.11. Notices S.-Y. Cheng Robert J. Blattner 1990 Chairman Tsit-Yuen Lam Michael C. Crandall 1992 Tai-Ping Liu Chairman Robert M. Fossum ex officio Chung-Chun Yang Lucy J. Garnett 1990 D. J. Lewis 1992 4.2.16. Translation from Japanese Nancy K. Stanton 1990 Shoshichi Kobayashi Robert E. L. Turner 1992 Chairman Katsumi Nomizu Donovan Van Osdol ex officio Standing Committees Associate Editors

Special Articles Ronald L. Graham 4.2.17. Advisory Committee for the Russian-English Jeffrey C. Lagarias Dictionary Joseph N. Bernstein 4.2.12. Proceedings Chairman Ralph P. Boas William W. Adams 1992 James R. Bunch J. Marshall Ash 1992 Courtney S. Coleman Maurice Auslander 1992 Joseph L. Doob Andreas Blass 1992 Bogdan Dudzik Thomas H. Brylawski 1989 Eugene Dynkin Dennis Burke 1989 Mark I. Freidlin Frederick R. Cohen 1991 Vladislav V. Goldberg Chairman William J. Davis 1991 Paul R. Halmos Clifford J. Earle, Jr. 1992 Edwin Hewitt Palle E. T. Jorgensen 1992 John R. Isbell Barbara Lee Keyfitz 1991 Anatole Katok R. Daniel Mauldin 1989 George Mackey Kenneth R. Meyer 1991 John McCarthy Paul S. Muhly 1990 Boris Mityagin Andrew M. Odlyzko 1989 Eric John Fyfe Primrose George C. Papanicolaou 1991 Boris Schein Louis J. Ratliff, Jr. 1991 Lawrence A. Shepp Jonathan M. Rosenberg 1991 Ben Silver ex officio William D. Sudderth 1991 Smilka Zdrakovska James E. West 1991 Warren J. Wong 1991

SEPTEMBER 1989, VOLUME 36, NUMBER 7 933 Officers and Committee Members

4.2.18. Editorial Boards 4.3.3. Audit Carlos E. Kenig 1989 Paul J. Sally, Jr. 1989 Haynes R. Miller 1990 M. Susan Montgomery 1990 Richard M. Schoen 1990 4.3.4. Operations and Facilities, Barry Simon 1989 Computer Chairman Daniel Zelinsky 1991 Visiting Committee on Jill P. Mesirov 1991 4.2.19. History of Mathematics Chairman S. Tucker Taft 1989 Richard A. Askey 1991 Peter J. Weinberger 1990 Chairman Peter L. Duren 1990 Harold M. Edwards 1991 4.3.s. Corporate Relations Uta C. Merzbach 1989 Chairman Ramesh A. Gangolli Maria M. K.lawe 4.2.20. Subcommittee on Russian Mathematical Oscar S. Rothaus History 4.3.6. Endowment V.I. Arnol'd Andrew M. Gleason A. Askey Richard Chairman W. Ted Martin S. G. Gindikin Cathleen S. Morawetz Igor Dolgachev N. K. Nikol'skii 4.3.7. Investment Chairman Allen Shields Steve Armentrout . ex officio Ramesh A. Gangolli 1989 4.2.21. Reprinted Books Chairman Franklin P. Peterson ex officio Eugenio Calabi Charles W. Curtis 4.3.8. Legal Aid Chairman Oscar S. Rothaus Steve Armentrout Todd Dupont 4.2.22. University Lecture Series Murray Gerstenhaber Theodore W. Gamelin Donald S. Ornstein Chairman Hugo Rossi 4.3.9. Liaison Committee Leonard L. Scott All members of this committee serve ex officio. Ad Hoc Committee Chairman William Browder Robert M. Fossum Franklin P. Peterson 4.2.23. AMS Publications in Applied Mathematics Steve Armentrout 4.3.10. Long Range Planning Ramesh A. Gangolli All members of this committee serve ex officio. Hans F. Weinberger Robert M. Fossum 4.3. Committees of the Board of Trustees William H. Jaco Chairman Irwin Kra M. Susan Montgomery 4.3.1. Agenda and Budget Franklin P. Peterson All members of this committee serve ex officio. William P. Thurston Steve Armentrout 4.3.11. Membership William Browder 1990 M. Fossum Chairman Frederick W. Gehring Robert 1990 M. Susan Montgomery Melvin Henriksen 1990 Franklin P. Peterson Irwin Kra 1989 William A. Veech Jill P. Mesirov Hugo Rossi 1991 4.3.2. Appeals Committee on Discounted Subscriptions 4.3.12. The Publication Program Blackwood Consultant Carol-Ann 1990 Hochster Steve Armentrout Consultant Melvin 1989 William H. Jaco ex officio Chairman Peter L. Duren ex officio Lowengrub Robert M. Fossum Chairman Morton 1989 Franklin P. Peterson Ramesh A. Gangolli ex officio Paul J. Sally, Jr. William H. Jaco Consultant Mary C. Lane Cathleen S. Morawetz 1991 Andrew M. Odlyzko 1989

934 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Officers and Committee Members

Hugo Rossi 1989 4.4.5. Electronic Exchange of Information (CEEI) Paul J. Sally, Jr. 1989 Joe P. Buhler William H. Jaco 4.3.13. Salaries Maria M. Klawc Steve Armentrout ex officio Richard G. Larson Chairman Ronald L. Graham Andrew M. Odlyzko M. Susan Montgomery ex officio Chairman Richard S. Palais Franklin P. Peterson ex officio 4.4.6. Library Committee 4.3.14. Staff and Services Nancy Anderson Chairman Steve Armentrout ex officio Richard A. Askey Franklin P. Peterson ex officio Robert S. Doran Paul J. Sally, Jr. Dorothy McGarry Chairman James Rovnyak Ad Hoc Committee George Seligman Mary Ann Southern 4.3.15. Institutional Membership Jack Weigel Consultant Carol-Ann Blackwood 4.4.7. Vending Software Ramesh A. Gangolli Chairman Frederick W. Gehring Peter Doyle William A. Veech Sidnie Feit Chairman Robert M. Fossum Barry Simon 4.4. Internal Organization ofthe American Mathematical Society 4.4.8. 1988 Election Tellers Lawrence H. Riddle Standing Committees Peter M. Winkler

4.5. 4.4.1. Archives Program and Meetings Andrew M. Gleason Franklin P. Peterson Standing Committees Chairman Everett Pitcher 4.5.1. Program Committee for National Meetings 4.4.2. Committee on Committees James G. Arthur 1991 M. Salah Baouendi 1990 ex officio William Browder ex officio Robert M. Fossum 1990 Robert M. Fossum ex officio Peter B. Gilkey George A. Hagedorn 1990 Morris W. Hirsch 1990 Hugh L. Montgomery 1989 Rhonda J. Hughes 1990 Chairman Peter Sarnak 1991 Irwin Kra 1990 Jean E. Taylor 1991 Philip Kutzko 1990 Chairman Julius L. Shaneson 1990 4.5.2. Central Section Program Committee 4.4.3. Nominating Committee David Drasin 1989 Dennis A. Hejhal 1990 Roger C. Alperin 1989 Andy Roy Magid ex officio Joan S. Birman 1990 Mark Mahowald 1990 Ronald DeVore 1989 1989 Chairman Jane P. Gilman 1989 Chairman Robert J. Zimmer James E. Humphreys 1990 4.5.3. Far Western Section Program Committee Victor L. K.lee, Jr. 1990 Sun-Yung Alice Chang 1990 Leonard L. Scott 1989 Ronald J. DiPerna 1989 Alan D. Weinstein 1990 Chairman William M. Kantor 1989 Ad Hoc Committees John R. Stallings 1990 Lance W. Small ex officio

4.4.4. Election Scheduling 4.5.4. Northeastern Section Program Committee Jane P. Gilman Chairman Ruth M. Charney 1989 Irwin Kra W. Wistar Comfort ex officio Chairman William P. Thurston Detlef Gromoll 1990 William A. Veech Jerry L. Kazdan 1990 James A. Voytuk Walter A. Strauss 1990

SEPTEMBER 1989, VOLUME 36, NUMBER 7 935 Officers and Committee Members

4.5.5. Southeastern Section Program Committee 4.6.4. Liaison Committee on Education in Mathematics Joseph A. Cima ex officio John A. Dossey Chairman Patrick B. Eberlein 1989 Melvin Hochster Ronald F. Gariepy 1989 Rogers J. Newman Ray A. Kunze 1990 Louise A. Raphael William Pardon 1990 Chairman Paul J. Sally, Jr. James D. Stashetf 4.5.6. Agenda for Business Meetings Lynn A. Steen M. Salah Baouendi 1990 Chairman Robert M. Fossum 4.6.5. Professional Ethics Carol L. Walker 1990 C. Edmund Burgess 1990 Harold M. Edwards 1991 4.5.7. Gibbs Lecturers for 1989 and 1990, Frank L. Gilfeather 1990 Committee to Select Chairman Linda Keen 1989 Jane Cronin Scanlon George B. Seligman 1991 Chairman Thomas Crawford Spencer Shmuel Winograd 4.6.6. Science Policy Hyman Bass 1990 4.5.8. Progress in Mathematics William Browder ex officio Chairman Armand Borel 1991 Chairman Ronald G. Douglas 1989 Paul H. Rabinowitz 1990 Frank L. Gilfeather 1990 Hugo Rossi 1990 James G. Glimm 1989 John T. Tate 1989 William H. Jaco ex officio Alan D. Weinstein 1991 Ronald L. Lipsman 1989 Jerrold E. Marsden 1991 Cathleen S. Morawetz 1991 4.6. Status of the Profession John C. Polking 1990 Oscar S. Rothaus 1991 Standing Committees David A. Sanchez 1989 William P. Thurston 1989 4.6.1. Academic Freedom, Tenure, and William A. Veech 1989 Employment Security David A. Vogan, Jr. 1991 Jerome A. Goldstein 1989 4.6.7. Service to Mathematicians Thomas G. Kurtz 1990 in Developing Countries Chairman Barbara L. Osofsky 1990 Robert R. Phelps 1989 Chairman Raymond G. Ayoub Charles E. Rickart 1991 James A. Donaldson Gail S. Young 1989 James Eells Donald M. Hill 4.6.2. Academic Review Frederick W. Gehring Ad Hoc Committees Frank L. Gilfeather Andrew M. Gleason Chairman J. K. Goldhaber 4.6.8. Applied Mathematics David A. Sanchez Constantine M. Dafermos David S. Kinderleher 4.6.3. Human Rights of Mathematicians Eduardo Daniel Sontag Michael I. Brin 1990 Chairman Jean E. Taylor Bettye Anne Case 1989 Patrick X. Gallagher 1989 4.6.9. Cooperation with the Chinese Herman R. Gluck 1989 S.-Y. Cheng Leon A. Henkin 1988 Ronald L. Graham Neal I. Koblitz 1988 Chairman Richard S. Palais Joel L. Lebowitz 1990 Chairman Alice T. Schafer 1990 4.6.to. Coordinating Committee for the Doctoral Program in Mathematics Chairman R. Creighton Buck Franklin P. Peterson Murray H. Protter

936 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Officers and Committee Members

4.6.11. Fellowship Policy Ad Hoc Committees George E. Andrews Kenneth Millet 4.7.5. Automatic Theorem Proving, Committee Chairman M. Susan Montgomery to Recommend Winners of Prizes for M. Beth Ruskai Chairman David Mumford Paul J. Sally Jr. Jacob T. Schwartz John L. Selfridge 4.6.12. NCTM Standards William Browder 4.7.6. Bocher Prize for 1989, Committee to Select the Chairman Edward A. Connors Winner of Robert M. Fossum Paul J. Cohen Harvey B. Keynes Chairman Richard B. Melrose Jean E. Taylor Louis Nirenberg William P. Thurston Philip D. Wagreich 4.8. Institutes and Symposia

4.7. Prizes and Awards Standing Committee Standing Committees 4.8.1. Cooperative Symposia

4.7.1. Centennial Fellowships Robert M. Thrall Daniel H. Wagner Terms expire on June 30 Chairman Frederick J. Almgren, Jr. 1989 4.8.2. Liaison Committee with AAAS David Eisenbud 1990 Hyman Bass Lawrence Craig Evans 1990 James McKenna Dorian Goldfeld 1989 Cathleen S. Morawetz Victor L. Klee, Jr. 1990 Warren Page John W. Morgan 1989 Gian-Carlo Rota Karen Vogtmann 1990 Alan D. Weinstein

4.7.2. National Awards and Public Representation 4.8.3. Summer Institutes and Special Symposia Chairman William Browder ex officio Terms expire on February 28 Robert M. Fossum ex officio Chairman Steven L. Kleiman 1990 G. D. Mostow ex officio Haynes R. Miller 1991 David Mumford 1989 Raghavan Narasimhan 1991 Rabinowitz 1989 4.7.3. Subcommittee on Appointments of the Paul H. 1990 Committee on National Awards and Public Thomas Crawford Spencer Robert B. Warfield, Jr. 1989 Representation

Robert M. Fossum ex officio 4.9. Joint Committees Chairman Irwin Kra John C. Polking 4.9.1. AMS-AAAS-MAA Committee 4.7.4. Steele Prizes on Opportunities in Mathematics Terms expire on June 30 for Underrepresented Minorities Manuel P. Berriozabal 1989 Jr. 1989 Frederick J. Almgren, Sylvia T. Bozeman 1989 1990 Luis A. Caffarelli James A. Donaldson 1989 Charles L. Fefferman 1991 Chairman Gloria F. Gilmer 1989 1991 Jun-ichi Igusa Shirley Malcom ex officio 1989 Chairman William S. Massey Rogers J. Newman 1989 1989 Frank A. Raymond Clarence E. Stephens 1989 Neil J. A. Sloane 1990 Consultant Argelia Veh!z-Rodriguez Louis Solomon 1989 Richard P. Stanley 1989 Michael E. Taylor 1990

SEPTEMBER 1989, VOLUME 36, NUMBER 7 937 Officers and Committee Members

4.9.2. AMS-ASA-IMS-MAA-NCTM-SIAM William B. Arveson (AMS) 1989 Committee on Women in the John A. Burns (SIAM) 1990 Mathematical Sciences Martin Golubitsky (SIAM) 1990 Daniel J. Kleitman (AMS) 1989 NCTM members' terms expire April I of the year given. Anthony W. Knapp (AMS) 1992 Grace M. Burton (NCTM) 1990 Chairman Ingram Olkin (IMS) 1990 Marjorie M. Enneking (NCTM) 1989 Emanuel Parzen (IMS) 1991 Chairman Susan Geller (AMS) 1991 Mary Ellen Rudin (AMS) 1989 Marjorie G. Hahn (IMS) Stephen G. Simpson (AMS) 1990 Mary Hesselgrave (MAA) 1991 Gregg J. Zuckerman (AMS) 1992 Jeanne W. Kerr (AMS) 1989 ___,(AMS) 1990 Patricia Kenschaft (A WM) 4.9.s. AMS-MAA Arrangements Committee for the Jeanne LaDuke (MAA) 1989 Suzanne Marie Lenhart (AMS) 1989 Louisville Meeting Betty K. Lichtenberg (NCTM) 1989 Januaryl7-20,1990 Edith Luchins (MAA) 1991 Martin Brown Joyce R. McLaughlin (SIAM) 1990 Joseph A. Cima ex officio Ingram Olkin (IMS) William Fenton Anne Parkhurst (ASA) Leon Harkleroad Janet Peterson (SIAM) 1988 William H. Jaco ex officio Linda Petzold (SIAM) 1989 Chairman John Oppelt Alice T. Schafer (MAA) 1988 Kenneth A. Ross ex officio Bhama Srinivasan (AMS) 1989 Carol Russell Elaine Salvo 4.9.3. AMS-ASL-IMS-SIAM Committee on Sandy Spears Translations from Russian and Other Slavic Wiley Williams Languages Jeffrey Allen Wright Chairman Peter Landweber (AMS) 1989 4.9.6. AMS-MAA Joint Program Committee for the AMS Subcommittee Members Louisville Meeting Consultant V.I. Arnol'd Hugh L. Montgomery (AMS) Joseph N. Bernstein 1990 David P. Roselle (MAA) Charles V. Coffman 1988 Mary Ellen Rudin (MAA) Allen Devinatz 1988 Chairman Peter Sarnak (AMS) Consultant S. G. Gindikin 4.9.7. AMS-MAA Arrangements Committee for the Vladislav V. Goldberg 1988 John R. Isbell 1988 Columbus Meeting Anatole Katok 1990 August 8-11, 1990 Consultant Askol'd Georgievic Khovanskii Frank Carroll Chairman Peter Landweber (AMS) 1989 W. Wistar Comfort ex officio L. G. Makar-Limanov 1989 Joseph C. Ferrar Paul G. Nevai 1989 William J. Friel Consultant N. K. Nikol'skii William H. Jaco ex officio Acquisition Editor Smilka Zdravkovska Chairman James R. Leitzel ASL Subcommittee Members Carolyn Mahoney Kenneth A. Ross ex officio Vladimir Lifschitz 1990 Andrew Sterrett Chairman Elliott Mendelson 1989 Gregory Mine 1990 4.9.s. AMS-MAA Joint Meetings Committee B. F. Wells 1989 All members of this committee serve ex officio. IMS Subcommittee Members Consultant H. Hope Daly Robert M. Fossum Chairman M. I. Freidlin Chairman William H. Jaco B. Pittel Kenneth A. Ross A. Rukhin Alfred B. Willcox W. J. Studden 4.9.9. AMS-MAA Committee on Employment and 4.9.4. AMS-IMS-SIAM Committee on Joint Summer Research Conferences in the Educational Policy Mathematical Sciences Donna L. Beers (AMS) 1991 Morton Brown (MAA) 1989 Terms expire on June 30 Stefan A. Burr (AMS) 1989

938 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Officers and Committee Members

Chairman Edward A. Connors (AMS) 1991 4.9.16. AMS-MAA-SIAM Joint Policy Board Philip C. Curtis, Jr. (MAA) 1990 for Mathematics (see 1989 Mathematical Sciences David J. Lutzer (MAA) 1989 Professional Directory, page 26) James W. Maxwell ex officio James J. Tattersall (MAA) 1990 4.9.17. AMS-SIAM Committee on Applied Mathematics 4.9.10. Data Subcommittee Constantine M. Dafermos 1989 Chairman Edward A. Connors 1990 James M. Hyman 1990 Consultant Lincoln K. Durst Chairman George C. Papanicolaou 1989 John D. Fulton 1991 Lawrence A. Shepp 1991 James F. Hurley 1991 Gilbert Strang 1991 Charlotte Lin 1989 Robert F. Warming 1990 Don 0. Loftsgaarden 1990 David J. Lutzer 1990 4.9.18. AMS-SIAM Committee to Screen Applicants for James W. Maxwell ex officio Graduate Study from the People's Republic of Donald E. McClure 1990 China Donald C. Rung 1989 David Benney 4.9.11. Employment Concerns Subcommittee Robert Bryant

Morton Brown 1989 4.9.19. AMS-SIAM Committee to Select the Winner of Chairman Barnet M. Weinstock 1989 the Wiener Prize of 1990

4.9.12. Short Course Subcommittee Elliott H. Lieb Chairman I. M. Singer Chairman Stefan A. Burr 1989 Stephen Smale R. Peter DeLong 1991 Lisl Novak Gaal 1989 4.9.2o. AMS-SIAM-SMB Committee on Robert P. Kurshan 1990 Mathematics in the Life Sciences Barbara L. Osofsky 1991 Jack D. Cowan 1991 Marjorie L. Stein 1990 Michael C. Mackey 1989 James J. Tattersall 1990 Marc Mangel 1992 James Murray 1992 4.9.13. AMS-MAA Committee on Teaching Assistants Hans G. Othmer 1988 Instructors (TA/PTI) and Part Time Chairman Richard E. Plant 1988 Thomas F. Banchoff John M. Rinzel 1989 Chairman Bettye Anne Case John P. Huneke David Kraines Thomas T. Read Robert H. Szczarba s. Representatives ------

4.9.14. AMS-MAA-SIAM Joint Committee on 5.o.l. Advisory Board of the National Translations Employment Opportunities Center of the John Crerar Library Chairman Ronald M. Davis (MAA) 1990 Ralph P. Boas James W. Maxwell ex officio Brian J. McCartin (SIAM) 1989 5.o.2. American Association for the Advancement of S. Brent Morris (AMS) 1991 Science Marc A. Rieffel (MAA) 1991 Section A Cathleen S. Morawetz February 12, 1992 Donald C. Rung (AMS) 1990 Section L Richard A. Askey February 12, 1992 Leon H. Seitelman (SIAM) 1991 Section Q Jerry L. Bona February 12, 1992 Section T Martin D. Davis February 12, 1992 4.9.1s. AMS-MAA-SIAM Joint Administrative Committee 5.o.3. Commission on Professionals in Science and All members of this committee serve ex officio. Technology Edward A. Connors Lida K. Barrett (MAA) I. Edward Block (SIAM) 5.0.4. Committee on the American Mathematics James W. Daniel (SIAM) Competition Chairman Robert M. Fossum (AMS) 30 William H. Jaco (AMS) Term expires on June Franklin P. Peterson (AMS) Guido L. Weiss 1990 Kenneth A. Ross (MAA) Alfred B. Willcox (MAA) Shmuel Winograd (SIAM)

SEPTEMBER 1989, VOLUME 36, NUMBER 7 939 Officers and Committee Members

S.O.S. Conference Board of the Mathematical Sciences Applied Mathematics, AMS Publications in . . . . . 4.2.23 William Browder 1990 Applied Mathematics, AMS-SIAM Committee on . 4.9.17 Archives ...... 4.4.1 S.0.6. Fulkerson Prize Committee Arrangements Committee for the Columbus Meeting 4.9.7 Alan J. Hoffman Arrangements Committee for the Louisville Meeting . 4.9.5 Audit ...... 4.3.3 s.o.1. U.S. National Committee on Theoretical and Automatic Theorem Proving, Committee to Recommend Applied Mechanics Winners of Prizes for ...... 4.7.5 Term expires on October 31 Board of Trustees ...... 3 Bulletin (New Series) ...... 4.2.3 Constantine M. Dafermos 1992 Bacher Prize for 1989, Committee to Select the Winner of . 4.7.6 CAFTES . 4.6.1 CBMS ...... 5.0.5 6. Index------CEEP ...... 4.9.9 1988 Election Tellers 4.4.8 Centennial Fellowships . 4.7.1 ABC Committee . . . 4.3.1 Central Section Program Committee 4.5.2 AMS Publications in Applied Mathematics ...... 4.2.23 Chinese, Cooperation with 4.6.9 AMS-AAAS-MAA Committee on Opportunities in Chinese, Translation from . . 4.2.15 Mathematics for Underrepresented Minorities . . . . 4.9.1 Colloquium ...... 4.2.4 AMS-ASA-IMS-MAA-NCTM-SIAM Committee on Women in Comm-Comm ...... 4.2.5 the Mathematical Sciences ...... 4.9.2 Commission on Professionals in Science and Technology 5.0.3 AMS-ASL-IMS-SIAM Committee on Translations from Committee of the Council ...... 4.1 Russian and Other Slavic Languages ...... 4.9.3 Committee on Committees ...... 4.4.2 AMS-IMS-SIAM Committee on Joint Summer Research Committee on the American Mathematics Competition 5.0.4 Conferences in the Mathematical Sciences ...... 4.9.4 Committee to Monitor Problems in Communication . 4.2.5 AMS-MAA Arrangements Committee for the Columbus Committees ...... 4 Meeting August 8-11, 1990...... 4.9.7 Committees of the Board of Trustees ...... 4.3 AMS-MAA Arrangements Committee for the Louisville Commmittee to Review the Procedures of the Council in Meeting January 17-20, 1990 ...... 4.9.5 Considering Issues ...... 4.1.1 AMS-MAA Committee on Employment and Educational Communication, Committee to Monitor Problems in . . .. 4.2.5 Policy ...... 4.9.9 Computer Operations and Facilities, Visiting Committee on 4.3.4 AMS-MAA Committee on Teaching Assistants and Part Time Conference Board of the Mathematical Sciences . . 5.0.5 Instructors (TA/PTI) ...... 4.9.13 Contemporary Mathematics . 4.2.6 AMS-MAA Joint Meetings Committee ...... 4.9.8 Cooperation with the Chinese ...... 4.6.9 AMS-MAA Joint Program Committee for the Louisville Cooperative Symposia ...... 4.8.1 Meeting ...... 4.9.6 Coordinating Committee for the Doctoral Program in AMS-MAA-SIAM Joint Administrative Committee ...... 4.9.15 Mathematics ...... 4.6.10 AMS-MAA-SIAM Joint Committee on Employment Corporate Relations . . 4.3.5 Opportunities ...... 4.9.14 Council ...... 2 AMS-MAA-SIAM Joint Policy Board for Mathematics (see Data Subcommittee .. 4.9.10 1989 Mathematical Sciences Professional Directory, Developing Countries . 4.6.7 page 26) ...... Discounted Subscriptions . 4.3.2 AMS-SIAM Committee on Applied Mathematics ...... 4.9.17 Doctoral Program in Mathematics, Coordinating Committee AMS-SIAM Committee to Screen Applicants for Graduate for ...... 4.6.10 Study from the People's Republic of China ...... 4.9.18 EC ...... 2.1 AMS-SIAM Committee to Select the Winner of the Wiener Editorial Boards ...... 4.2.18 Prize of 1990 ...... 4.9.19 Editorial and Communications Committees 4.2 AMS-SIAM-SMB Committee on Mathematics in the Life Election Scheduling ...... 4.4.4 Sciences ...... 4.9.20 Electronic Exchange of Information (CEEI) 4.4.5 Abstracts Editorial Committee ...... 4.2.1 Employment Concerns Subcommittee . 4.9.11 Academic Freedom, Tenure, and Employment Security 4.6.1 Employment Opportunities . . . . . 4.9.14 Academic Review ...... 4.6.2 Employment and Educational Policy 4.9.9 Administrative Committee ...... 4.9.15 Endowment ...... 4.3.6 Advisory Board of the National Translations Center of the Ethics ...... 4.6.5 John Crerar Library ...... 5.0.1 Executive Committee of the Council 2.1 Advisory Committee for the Russian-English Dictionary .. 4.2.17 Far Western Section Program Committee . 4.5.3 Agenda and Budget ...... 4.3.1 Fellowship Policy ...... 4.6.11 Agenda for Business Meetings ...... 4.5.6 Fulkerson Prize Committee ...... 5.0.6 American Association for the Advancement of Science ... 5.0.2 Gibbs Lecturers for 1989 and 1990, Committee to Select 4.5.7 American Journal of Mathematics, Society's Representatives 4.2.2 History of Mathematics ...... 4.2.19 American Mathematics Competition, Committee on . . . . . 5.0.4 Human Rights of Mathematicians . . . 4.6.3 Appeals Committee on Discounted Subscriptions . 4.3.2 Institutes and Symposia . 4.8 Applied Mathematics ...... 4.6.8 Institutional Membership ...... 4.3.15

940 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Officers and Committee Members

Internal Organization of the American Mathematical Society 4.4 Program and Meetings . 4.5 Investment ...... 4.3.7 Progress in Mathematics 4.5.8 JCEO ...... 4.9.14 Publication Program . . 4.3.12 JPBM (see 1989 Mathematical Sciences Professional Representatives . . . . . 5 Directory, page 26) ...... Representatives of Committees 2.0.2 Japanese, Translation from . . . . 4.2.16 Reprinted Books ...... 4.2.21 Joint Administrative Committee 4.9.15 Russian Mathematical History, Subcommittee on. 4.2.20 Joint Committees ...... 4.9 Russian and Other Slavic Languages, Translations from . 4.9.3 Joint Meetings Committee . . . . 4.9.8 Russian-English Dictionary, Advisory Committee for the 4.2.17 Joint Policy Board (see 1989 Mathematical Sciences Salaries ...... 4.3.13 Professional Directory, page 26) ...... Science Policy ...... 4.6.6 Joint Summer Research Conferences 4.9.4 Service to Mathematicians in Developing Countries 4.6.7 Journal of the AMS 4.2.7 Short Course Subcommittee ...... 4.9.12 LRP ...... 4.3.10 Southeastern Section Program Committee 4.5.5 Legal Aid ...... 4.3.8 Special Symposia 4.8.3 Liaison Committee I. I, 4.3.9 Staff Salaries ...... 4.3.13 Liaison Committee on Education in Mathematics 4.6.4 Staff and Services . . . . 4.3.14 Liaison Committee with AAAS 4.8.2 Status of the Profession 4.6 Library Committee . 4.4.6 Steele Prizes ...... 4.7.4 Life Sciences ...... 4.9.20 Subcommittee on Appointments of the Committee on Long Range Planning . 4.3.10 National Awards and Public Representation ...... 4.7.3 Mathematical Reviews 4.2.8 Subcommittee on Russian Mathematical History 4.2.20 Mathematical Surveys and Monographs 4.2.9 Subscriptions ...... 4.3.2 Mathematics in the Life Sciences 4.9.20 Summer Institutes and Special Symposia . 4.8.3 Mathematics of Computation 4.2.10 Summer Research Conferences 4.9.4 Members-at-Large 2.0.3 Tellers, 1988 Election ...... 4.4.8 Membership 4.3.11 The Publication Program ...... 4.3.12 Memoirs ..... 4.2.14 Theoretical and Applied Mechanics . 5.0.7 Monographs . . . 4.2.9 Transactions ...... 4.2.14 NCTM Standards 4.6.12 Transactions and Memoirs . 4.2.14 National Awards and Public Representation . 4.7.2 Translations: National Meetings ...... 4.5.1 Chinese ...... 4.2.15 National Translations Center of the John Crerar Library, Japanese ...... 4.2.16 Advisory Board of the ...... 5.0.1 Russian and other Slavic Languages . 4.9.3 Nominating Committee ...... 4.4.3 U.S. National Committee on Theoretical and Applied Northeastern Section Program Committee . 4.5.4 Mechanics ...... 5.0.7 Notices ...... 4.2.11 Underrepresented Minorities . 4.9.1 Officers ...... I, 2.0.1 University Lecture Series ...... 4.2.22 Opportunities in Mathematics for Underrepresented Vending Software ...... 4.4.7 Minorities ...... 4.9.1 Wiener Prize of 1990, AMS-SIAM Committee to Select the PSAM ...... 4.2.13 Winner of ...... 4.9.19 Prizes and Awards ...... 4.7 Women in the Mathematical Sciences ...... 4.9.2 Proceedings ...... 4.2.12 Proceedings of Symposia in Applied Mathematics 4.2.13 Professional Ethics ...... 4.6.5 Professionals in Science and Technology, Commission on . 5.0.3 Program Committee: National Meetings 4.5.1 Central ... 4.5.2 Far Western 4.5.3 Northeastern 4.5.4 Southeastern 4.5.5

SEPTEMBER 1989, VOLUME 36, NUMBER 7 941 Miscellaneous

Personal Items Colony Life Insurance Company Robert W. Hafner, of IBM, in Lynchburg, Virginia. Rolling Meadows, Illinois, died on Theodore W. Anderson, professor June 1, 1989, at the age of 59. He emeritus of statistics and eco­ Deaths was a member of the Society for nomics at Stanford University, one year. received an honorary Doctor of Gunnar Bodvarsson, of Co~allis, Science degree from Northwestern Oregon, died on May 9, 1989, at Franklin Wesley Kokomoor, Pro­ University at the commencement the age of 72. He was a member fessor Emeritus of the University ceremonies in June, 1989. of the Society for 36 years. of Florida, died on April 30, 1989, James Coykendall IV, of the Jewell Hughes Bushey, Profes­ at the age of 98. He was a member California Institute of Technology, sor Emeritus of Hunter College, of the Society for 60 years. received that institution's E. T. died on May 5, 1989, at the age Howard R. Siepman, of the Bell Undergraduate Mathematics of 93. She was a member of the Baxter Healthcare Corporation, Research Prize for a paper on Society for 69 years. Rould Lake, Illinois, died on April Picard groups of polynomial rings. Robert Cameron, Professor 24, 1989, at the age of 30. He Howard A. Levine, of Iowa Emeritus of the University of Min­ was a member of the Society for 7 State University, has been ap­ nesota, died on June 17, 1989, at years. pointed chairman of the mathe­ the age of 81. He was a member Sergei L. Sobolev, of the Novo­ matics department at that institu­ of the Society for 59 years. sibirsk Academy of Sciences, died tion. Robin W. Chaney, of Western on January 3, 1989, at the age of Russell Manning, of the Cali­ Washington University, died on 80. He was a member of the Soci­ fornia Institute of Technology, re­ March 3, 1989, at the age of 50. ety for 17 years. (See the News and ceived that institution's Morgan He was a member of the Society Announcements section of this is­ Ward Prize in recognition of a pa­ for 28 years. sue of Notices. per giving a recursive development Myrle V. Cross, Jr., of Costa Avgustin Tuzhilin, of the Col­ of the Catalan number formula. Mesa, California, died on April lege of Staten Island (CUNY), Ellen Torrance has been pro­ 27, 1989, at the age of61. He was died on September 24, 1988, at moted to Assistant Vice-President a member of the Society for 18 the age of 54. He was a member and Associate Actuary at First years. of the Society for 8 years.

942 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Visiting Mathematicians (Supplementary List)

The list of visiting mathematicians includes both foreign mathematicians visiting in the United States and Canada, and Americans visiting abroad. Note that there are two separate lists.

American Mathematicians Visiting Abroad Name and Home Country Host Institution Field of Special Interest Period of Visit Hinkley, David V. (U.S.A.) University of Oxford Statistics 9/89- 5/90 Palka, Bruce P. (U.S.A.) Mittag-Leffler Institute Complex Analysis 9/89- 5/90

Visiting Foreign Mathematicians Amitsur, Shimshon (Israel) University of Texas, Austin Algebra 9/89- 1/90 Arazy, Jonathan (Israel) University of Kansas Functional Analysis 8/89- 1/90 Beiglbock, Wolf D. (West University of Texas, Austin Theoretical Physics 9/89- 1/90 Germany) Belaga, Schlomo E. (France) Universite du Quebec a Montreal 8/89- 6/90 Boyadzhiev, Khristo Ohio University Operator Theory 1/90- 6/90 (Bulgaria) Cassandra, Marzio (Italy) University of Texas, Austin Mathematical Physics 9/89- 1/90 Cohen, Arjeh M. (The University of Michigan Representation Theory 9/89- 12/89 Netherlands) Engelking, Ryszard (Poland) Ohio University Topology 9/89- 12/89 Globevnik, Josip University of Washington Complex Analysis 8/89- 6/90 (Yugoslavia) Gritzman, Peter (West University of Washington Combinatorial Geometry 9/89- 3/90 Germany) Hari, Vjeran (Yugoslavia) University of Kansas Numerical Analysis 8/89- 1/90 Hogan, Jeffrey A. (Australia) University of Texas, Austin Harmonic Analysis 9/89- 5/90 Horak, Peter University of Nebraska-Lincoln Combinatorics 9/89- 5/90 (Czechoslovakia) Hurri, Ritva (Finland) University of Texas, Austin Complex Analysis 1/90- 5/90 Kanev, Vassill. (Bulgaria) University of Michigan Algebraic Geometry 1/90- 5/90 Kondo, Shigayuki (Japan) University of Michigan Algebraic Geometry 9/89- 12/89 Liao, Ming (People's University of Michigan Probability 9/89- 5/90 Republic of China) Lickorish, W.B. Raymond University of Texas, Austin Geometric Topology 9/89- 1/90 (United Kingdom) Lu, Chunqing (People's SUNY at Buffalo Applied Mathematics 8/89- 6/90 Republic of China) Lu, Kun-Liang (China) University of Nebraska-Lincoln Statistics 9/89- 5/90 Macdonald, Ian G. University of Michigan Representation Theory and 9/89- 12/89 (England) Combinatorics Mendoza, Geraldo University of Washington Partial Differential Equations 1/90- 6/90 (Venezuela) Muleshkov, Angel (Bulgaria) University of Texas, Austin Applied Mathematics 9/89- 1/90

SEPTEMBER 1989, VOLUME 36, NUMBER 7 943 Visiting Mathematicians

Name and Home Countn: Host Institution Field of SQecial Interest Period of Visit Necas, J. (Czechoslovakia) Northern Illinois University Partial Differential Equations 8/89- 12/89 Necasova, z. Northern Illinois University Operations Research 8/89- 12/89 (Czechoslovakia) Prasad, Gopal (India) University of Michigan Representation Theory 9/89- 12/89 Peretz, Ronen (Israel) University of Michigan Analysis 9/89- 6/90 Qi, Duan (People's Republic University of Arkansas Spline Theory 9/89- 8/90 of China) Ruess, Wolfgang (West University of Arkansas Functional Analysis 7/89- 9/89 Germany) Shephard, Geoffery University of Washington Geometry 9/89- 12/89 (England) Spiez, Stanislaw (Poland) University of Washington Topology 3/90- 6/90 Syrjanen, Ritva (Finland) University of Michigan Complex Analysis 9/89- 12/89 Takai, Hiroshi (Japan) SUNY at Buffalo Functional Analysis 8/89- 6/90 Terdik, Gyorgy (Hungary) University of Arkansas Time Series 8/89- 6/90 Ulger, Ali (Turkey) University of Arkansas Banach Algebras 8/89- 6/90 Zhou, Hao-Xuan (People's SUNY at Buffalo Topology 8/89- 6/90 Republic of China)

A Century of Mathematics in America - Part II Peter L. Duren, Editor with the assistance of Richard A. Askey and Uta C. Merzbach (History of Mathematics, Volume 2) This volume is the second in the History of Mathematics glimpse into the mathematical world of 1946, the discussions series, initiated in 1988 to commemorate the Centennial are put into a contemporary context with commentary by of the Society. The inaugural volume, Part I of A Century current leaders in these areas. of Mathematics in America, presented a collection of In the last section, various aspects of America's mathematical autobiographically oriented historical articles by senior past are explored on the political, social, and scientific American mathematicians. Similar in perspective to Part I but levels. The influence of women in American mathematics, differing in organization and emphasis, the present volume the burgeoning of differential geometry in the last 50 years, focuses on some key elements in the making of mathematics and discussions of the work of von Karman and Wiener are in America. among the topics covered. The first section of the book deals with some of the influential Also included are the Joint AMS-MAA Invited Addresses mathematics departments in the United States. Functioning presented at the AMS Centennial Celebration. as centers of research and training, these departments played a major role in shaping the mathematical life in this Mathematicians, historians of science, and students alike will country. The section is organized around seven departments: find this book illuminating and rewarding, and it would make Harvard, Yale, Chicago, Princeton, Stanford, Berkeley, and an excellent addition to any library collection. That the lessons NYU. Several of the articles are primary accounts, and most of the past can guide the resolution of future problems makes of these are supplemented by other recent articles. this book important reading for all who are concerned with the development of mathematics. The second section deals with an extraordinary conference held at Princeton in 1946 to commemorate the university's 1980 Mathematics Subject Classification: 00 bicentennial. The war had just ended, mathematicians had ISBN 0-8218-0130-9 returned to their university positions, and a large number ISSN 0899-2428 578 pages (hardcover), January 1989 of veterans were beginning or resuming graduate work. Individual member $42, List price $70, The conference brought together many of the leading Institutional member $56 mathematicians of that era to take stock of open problems To order, please specify HMATH/2NA and to try to chart the future course of research in nine broad All prices subject to change. Shipment will be made by surface. For areas. Reprinted here are written versions of the discussions air delivery add, 1st book $5, each additional book $3, maximum $100. in which von Neumann, Weyl, Whitehead, Hopf, Courant, Prepayment required. Order from American Mathematical Society, P.O. Zariski, Godel, and many others pondered the present and Box 1571, Annex Station, Providence, Rl 02901-1571, or call toll free future of mathematical research. Providing a fascinating 800-566-7774 to charge with VISA or MasterCard.

944 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Backlog of Mathematics Research Journals

Backlog. Information on the backlog of papers for revision and its publication may be much shorter than research journals, primarily those published in North is the case otherwise, so these figures are low to that America, is reported to the Providence Office by those extent. editorial boards which elect to participate. The fig­ The observations are made from the latest issue ures are an estimate of the number of printed pages published, before the deadline for this issue of Notices, which have been accepted, but are in excess of the from journals that have actually been received by number required to maintain copy editing and printing a subscriber in the Providence, Rhode Island, area; schedules. in some cases this may be two months later than Observed Waiting Time. The quartiles give a measure publication abroad. If the waiting time as defined above of normal dispersion. They do not include extremes is not given in the journal, if no new issue has been which may be misleading. Waiting times are measured received since the last survey, or if the latest issue is in months from receipt of manuscript in final form to for some reason obviously not typical, no times are publication of the issue. When a paper is revised, the given in this report and such cases are marked NA (not waiting time between an editor's receipt of the final available or not applicable).

Editor's Estimated Observed Waiting Approximate Time for Paper Time in Latest Number Number Backlog of Submitted Currently Published Issue Issues Pages Printed Pages to be Published (in Months) Journal per Year per Year 6/30/89 12/31/88 (in Months) a1 M 03

Acta Inform. 8 800 0 0 5 5 6 8 Aequationes Math. 4 640 100 0 9 6 11 15 Alg. Groups Geom. 4 600 0 0 6 8 9 10 Algorithmica 4 576 120 432 12 9 12 12 Amer. J. Math. 6 1200 0 0 8-12 14 15 20 Ann. of Math. 6 1320 700 600 12 13 16 17 Ann. Probab. 4 1600 300 250 12 10 11 12 Ann. Sci. Ecole Norm. Sup. 4 648 47 0 13 7 7 9 Ann. Statist. 4 1750 225 180 10 10 12 14 Appl. Math. Letters 4* 400 0 50 3 NA Appl. Math. Optim. 6 672 180 185 12 9 12** 14 Arch. Hist. Exact Scis. 8 800 0 0 11 10 NA 13 Arch. Math. Logic 3 200 0 0 8 6 8 9 Arch. Rational Mech. Anal. 16 1600 0 0 10 9 9 11 Bull. Austral. Math. Soc. 6 1000 400 200 12 12 13 14 Canad. J. Math. 6 1152 0 0 8-10 10 12 19 Canad. Math. Bull. 4 512 640 288 21 14 16 21 Circuits Systems Signal Proc. 4 512 0 0 4 8 11 13 Comm. Algebra 12 3000 1602 2220 12 11 14 17 Comm. Math. Phys. 24 5184 0 0 8 8 9 11 Comm. Partial Diff. Equations 12 1600 200 0 10 6 8 10 Comp. Math. Appl. 24 2400 1000 1200 10 8 9 10 Computing 8 720 280 180 9 8 14 15 Constr. Approx. 4 448 100 112 8 12 16 18

SEPTEMBER 1989, VOLUME 36, NUMBER 7 945 Research Journals Backlog

Editor's Estimated Observed Waiting Approximate Time for Paper Time in Latest Number Number Backlog of Submitted Currently Published Issue Issues Pages Printed Pages to be Published (in Months) Journal per Year per Year 6/30/89 12/31/88 (in Months) 01 M 03

Discrete Comput. Geom. 6 600 375 370 15 15 18 22 Duke Math. J. 6 1800 150 150 9 7 8 10 Houston J. Math. 4 600 600 500 18 *** Illinois J. Math. 4 704 897 858 26 26 27 28 IMA J. Appl. Math. 6 510 0 0 12 6 9 12 IMA J. Math. Appl. Med. Bioi. 4 350 NR 80 NR NA IMA J. Math. Control Inform. 4 350-400 NR NR NR 11 11 12 IMA J. Numer. Anal. 4 600 100 0 14 10 11 21 Indiana Univ. Math. J. 4 1000 80 NR 9.5 7 9 14 lnst. Hautes Etudes Sci. Publ. Math. 2 400 0 0 15 13 19 22 lnternat. J. Math. Math. Sci. 4 832 100 125 NR 9 18 21 Invent. Math. 12 2700 0 0 8 11 13 14 Israel J. Math. 12 1500 350 700 8 9 10 14 J. Algorithms 4 NR NR NR NR 13 13** 14 J. Amer. Math. Soc. 4 1000 0 0 NA 9 11 15 J. Appl. Math. Simulation 4 340 180 100 4 NA J. Assoc. Comput. Mach. 4 1000 300 250 12 8 9 9 J. Austral. Math. Soc. Ser. A 6 1100 600 600 22 16 20 24 J. Austral. Math. Soc. Ser. B 4 512 256 0 15 7 9 10 J. Classification 2 300 0 0 6 NA J. Comput. System Sci. 6 950 200 800 12-14 NA J. Differential Geom. 6 1500 1300 1200 10 12 15 18 J. Integral Equations Appl. 4 700 0 0 8 NA J. Math. Bioi. 6 720 0 0 6.5 5 6 7 J. Math. Phys. 12 3000 0 0 5 4 5** 5 J. Nigerian Math. Soc. 1 100 NR 0 NR NA J. Operator Theory 4 800 0 NR 12 13 15 19 J. Symbolic Logic 3t 1350t 100 tt 16 17 18 20 Linear Algebra Appl. 16 4800 600 600 10-12 8 9** 9 Manuscripta Math. 12 1536 0 0 6 4 5 5 Math. Ann. 16 2816 0 0 15-17 8 12 15 Math. Comput. Modelling 16 1600 500 900 10 8 9** 9 Math. Comp. 4 1500 260 50 12 10 12 14 Math. Control Signals Sys. 4 400 1000 400 NA NA Math. Oper. Res. 4 724 360 400 18 17 17 19 Math. Programming Ser. A 6 720 240 166 15 14 16 19 Math. Social Sci. 6 600 180 90 12 12 12 17 Math. Systems Theory 4 256 0 0 6 5 6 7 Math. z. 12 2016 0 0 13-14 12 19 24 Mem. Amer. Math. Soc. 6 2800 0 0 2 10 15 33 Michigan Math. J. 3 480 130 130 15 7 9 10 Monatsh. Math. 8 704 0 0 9 8 10 10 Numer. Funct. Anal. Optim. 12 1300 0 0 5 5 8 8 Numer. Math. 12 1488 0 0 5 5 6 9 Oper. Res. 6 1008 420 315 10-15 17 19 23 Pacific J. Math. 10 2000 NR NR 12 13 15 18 Probab. Theor. Relat. Fields 12 1680 0 0 12 10 17 24 Proc. Amer. Math. Soc. 12 3200 572 0 12 10 11 14 Proc. London Math. Soc. 6 NR NR NR NR 13 16 20 Quart. Appl. Math. 4 800 200 200 12 10 13 16

946 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Research Journals Backlog

Editor's Estimated Observed Waiting Approximate Time for Paper Time in Latest Number Number Backlog of Submitted Currently Published Issue Issues Pages Printed Pages to be Published (in Months) Journal per Year per Year 6/30/89 12/31/88 (in Months) Ql M Q3

Quart. J. Math. Oxford Ser. (2) 4 512 96 64 12-18 15 17 20 Quart. J. Mech. Appl. Math. 4 640 0 NA 13 13 16 19 Results Math. 4 768 0 0 6 7 9 12 Rocky Mountain J. Math. 4 1000 2000 2000 20 *** Semigroup Forum 6 768 200 128 5 10 11 12 SIAM J. Appl. Math. 6 1800 500 556 22 11 12** 13 SIAM J. Comput. 6 1350 200 270 18 10 10** 12 SIAM J. Control Optim. 6 1500 350 215 20 8 8** 10 SIAM J. Discrete Math. 4 600 50 0 9 6 7** 7 SIAM J. Math. Anal. 6 1650 430 388 22 9 9** 12 SIAM J. Matrix Anal. Appl. 4 680 150 30 9 7 7** 10 SIAM J. Numer. Anal. 6 1650 550 639 22 12 14** 15 SIAM J. Sci. Statist. Comput. 6 1200 400 400 20 9 9** 11 SIAM Rev. 4 680 0 50 6-9 5 7** 9 Topology Appl. 9ttt 1000ttt 500 1100 14 15 18 19 Trans. Amer. Math. Soc. 12 5000 200 200 16 18 18 22

NR means no response received. NA means not available or not applicable. * The frequency of this journal will increase according to demand (number of papers accepted) to maintain: a zero backlog, a within three month publication schedule, and TEX typeset quality. ** From date accepted. *** This journal recently ended a moratorium on the acceptance of new papers; latest issue consists of pre-moratorium papers. t Usually four issues per year, however the December 1990 issue will be a 30-year index. Its pages are not counted in the 1350 page estimate for the other three issues. tt The publishers of this journal have authorized publication of extra pages as needed to reduce backlog to zero at the end of the 1989 volume. ttt For 1990: Twelve issues and 1320 pages per year.

PARTITION PROBLEMS IN TOPOLOGY Stevo Todorcevic (Contemporary Mathematics, Volume 84)

This book presents results on the case of the Ramsey problem 1980 Mathematics Subject Classifications: 04-02, 03E05, 03E50; 50-02, for the uncountable: When does a partition of a square of 54A25 an uncountable set have an uncountable homogeneous set? ISBN 0-8218-5091-1, LC 88-39032 ISSN 0271-4132 This problem most frequently appears in areas of general 130 pages (softcover), January 1989 topology, measure theory, and functional analysis. Building on Individual member $13, List price $22, his solution of one of the two most basic partition probl~ms Institutional member $18 in general topology, the ··s-space problem, .. the author To order, please specify CONM/84NA has unified most of the existing results on the subject and made many improvements and simplifications. The first eight sections of the book require basic knowldege of naive set All prices subject to change. Shipment will be made by surface. theory at the level of a first year graduate or advanced For air delivery add, 1st book $5, each additional book $3, undergraduate student. The book may also be of interest maximum $100. Prepayment required. Order from American to the exclusively set-theoretic reader, for it provides an Mathematical Society, P.O. Box 1571, Annex Station, Provi­ excellent introduction to the subject of forcing axioms of set dence, RI 02901-1571, or call toll free 800-566-7774 to charge theory, such as Martin's axiom and the Proper forcing axiom. with VISA or MasterCard.

SEPTEMBER 1989, VOLUME 36, NUMBER 7 947 New Members of the AMS

ORDINARY MEMBERS Shirley M Frye, Scottsdale School Dist, Robert D Little, Univ of Hawaii, Dumitru I Acu, Sibiu, Romania Phoenix, AZ Honolulu Winfred P Adams, Farmington, NM Zhiyong L Gao, Rice Univ, Houston, TX Lai Fu Liu, Beijing Normal Univ, Lateef A Adelani, St Louis, MO Sidney C Garrison, Tempe, Arizona People's Republic of China Jawad Yusuf Al-Khal, Washington, DC Alan C Genz, Washington State Univ, Ramon Lopez, Florida, PR Jusuf Alajbegovic, Swinburne Inst of Pullman Zhiqi Lu, McMaster Univ, Hamilton, Tech, Melbourne, Australia Lyenatte S Goff, Glendale Community Ontario, Canada Anne H Allen, Bennington, VT College, AZ Zhu Jia Lu, Academia Sinica, Beijing, Julius A Archibald, SUNY, Plattsburgh Piotr Grabowski, Acad of Mining & People's Republic of China N S Asaithambi, Mississippi State Univ, Metallurgy, Cracow, Poland Nina I Luft-Whelton, Calverton, MD Mississippi State Richard M Grassl, Muhlenberg College, Gregory Lupton, Dartmouth College, Jonathan James Ashley, Univ of Allentown, PA Hanover, NH Washington, Seattle Michael P Greeley, Univ of Neal J MacMillan, Brookline, MA Christopher Eugene Barat, Providence, RI Massachusetts at Boston Eugene W Madison, Univ of Iowa, Iowa Susan Barton, Pennsylvania State Univ, Patricia Griswold, Iowa City, lA City Media Richard Webster Griswold, Iowa City, lA Raul Manasevich, Univ de Chile, Santiago Marcelle Bessman, Frostburg, MD Thomas E Hansen, Las Vegas, NV Josef Mattes, Wien, Austria Marvin L Bittinger, Carmel, IN Timothy B Hansen, Madison, WI David M McCahon, Chagrin Falls, OH Doug J Blount, Univ of Utah, Salt Lake Mark Blondeau Hedrick, Georgia State Gael T Mericle, Mankato State Univ, MN City College, Statesboro Michael Thomas Meuleners, Fort Glen A Bookhout, Broomfield, CO Nancy G Henry, Indiana Univ, Kokomo, Washington, P A Branislav Boricic, Belgrade, Yugoslavia IN John S Meyer, Muhlenberg College, Margaret L Brandeau, Stanford Univ, CA Dale T Hoffman, Bellevue Community Allentown, P A Erwin A BrUning, Princeton Univ, NJ College, WA Shu Mei Miao, Jilin Univ, People's G Binthan Burah, London, England Douglas Vincent Horacek, St Louis, MO Republic of China John C Burkhart, Toledo, OH Min Qiang Huang, China Univ of Science C Jonathan Mitschele, St Joseph's College, Jan 0 Case, Samford Univ, Birmingham, & Tech, Beijing, People's Republic of Windham, ME AL China James John Moloney, Huntington, WV Su-Han Chan, Nepean, Ontario Canada William E Huggins, Baltimore, MD Damaso Muniz Jr, Bayamon, PR Yi-Ying Chen, California State Univ San John R Hunt, Menomonie, WI Shoukry I M Nada, Menoufia Univ, Bernardino Michael Bee Jackson, Earlham College, Shebeen El Kohom, Egypt David W Cribb, USAF Academy, CO Richmond, IN Reema Nayar, Brown Univ, Providence, Joseph D Cron, Fairfield, CT Thomas E Johnson III, Newark, DE RI Jack L Crowell, Delta College, University Irena H Kageorgis, Santa Monica, CA Harald M Ness, Univ of Wisconsin Center, MI Shriniwas K Katti, Univ of Missouri, Ctrs-Fond duLac George Tinsley Davies, St Petersburg, FL Columbia Rosalie S Nichols, Salina, KS Kenrick L Dillah, New York, NY Rasul A Khan, Smith College, Frank W Nijhoff, Clarkson Univ, Miao Ding, Shanghai Jiaotong Univ, Northampton, MA Potsdam, NY People's Republic of China Seshavadhani Kumar, Univ of North Eleanor H Ninestein, Fayetteville, NC Jack Edmonds, Univ of Waterloo, Ontario Carolina, Charlotte John P Nordlund, Brooklyn, NY Canada George Labahn, Univ of Waterloo, Penelope E Nordlund, Brooklyn, NY Wade Ellis Jr, San Jose, California Ontario, Canada Chris Oliwa, Liverpool, Australia Alain Escassut, Univ Blaise Pascal, Derek Lane, Univ of Alabama, Carmen A Ortiz-Quinones, Humacao, PR Aubiere, France Tuscaloosa Mina E Ossiander, Oregon State Univ, Leigh A Fiedler, Moline, IL Laszlo Lempert, Purdue Univ, West Corvallis Christopher P Foley, Chicago, IL Lafayette, IN Deborah Ann Pace, Tyler, TX John Erik Fornaess, Princeton Univ, NJ Nicolas Lerner, Purdue Univ, West David F Pallai, Addison-Wesley Publ, Norman A Frechette, New Bedford, MA Lafayette, IN Reading, MA

948 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY New Members of the AMS

Edward C Phillips, Chappaqua, NY Yun Min Zhu, Academia Sinica, Sichuan, Misrak Gezmu Andre S Picard, Montreal, Quebec, People's Republic of China Behzad Jalali-Shirazi Canada Euripides Kondelis Edward J Piston, Liverpool, NY Wenpu Li Ilie Popescu, Bucharest, Romania RECIPROCITY MEMBERS Yong Li Marie H Postner, Yonkers, NY Australian Mathematical Society Charles B Pierre Michael John Pratts, NBC Merchandise Jacinta Ann Covington June F Winter Mart, Chicago, IL David G Glynn Chongqing Yan Hans Primas, Eidgen Tech Hochschule, Deutsche Mathematiker- Vereinigung e. v. Jen-Jue Yeh Zurich, Switzerland Johann Boos Boston University Ziv Ran, Univ of California, Riverside Gesellschaft fiir Angewandte Mathematics Renata M Cioczek Sujukta Rath-Hota, Madison, TN und Mechanik Timothy J Raczkowski Joseph M Sabol, San Luis Obispo, CA Martin Costabel California State University Fullerton Scott M Sampson, Bloomington, IN Jurgen Garloff William D VanLear Wallace M Scheier, Sepulveda, CA Israel Mathematical Union California State University Northridge William D Schwartz, Denver, CO Joram Hirshfeld Greg Lewis Patricia G Shelton, North Carolina London Mathematical Society City College (CUNY) Agricultural & Technical State Univ, Graham R Allan Peter Paul Arnez Greensboro, NC Philip Holgate Ariel Colin Linda B Shields, Columbia, MD Mathematical Society of Japan Junior Mota Melo James Lindsey Short II, El Dorado, AR Huzihiro Araki Lavoizier Saint Jean Naomi B Sinnreich, New York, NY Hiroshi Inoue Claremont Graduate School Tom J Slusher, Tennessee Colony, TX Ruishi Kuwabara Gnanamanikam Mahinthakumar Alice F Snodgrass, John Burroughs Yasuichiro Nishimura Jerry E Purcell School, St Louis, MO Ken-lchi Yoshihara Gustavus Adolphus College Dhiraj Kumar Soni, Davis, CA Polskie Towarzystwo Matematyczne Fereja M Tahir Pari D Spolter, Granada Hills, CA Anna Kaminska Indiana State University Joseph J Sroka, Valdosta, GA Societe Mathematique Suisse Rakesh Kumar Chadha Radomir S Stankovic, Nis, Yugoslavia Christian Schindler Damodaran Chittibabu Gregory C Stein, New York, NY Societe Mathematique de France Michael A Demerly Leonid Stern, Towson State Univ, AI Ayham A AI Assaad Melinda Jill Fox Baltimore, MD Nicolas Boulean Indiana University at South Bend Stanislaw S Swierczkowski, Sultan Qaboos Georges Alexandre Bray Jodell A Petty Univ, Al-Khod, Oman Guy Chasse Inst for Advanced Study Zoltan I Szabo, Univ of Zimbabwe, Paul Deheuvels Thomas W Hawkins Harare Daniel G Ferrand Shrawan Kumar B P Szane, Worcester Polytech lnst, MA Gerard Laumon Jian Yi Shi Serge Tabachnikov, Moscow State Univ, Gerard Lebourg Grzegorz Swiatek USSR Alain Louveau Francisco P Thaine Robert K Tamaki, San Marino, CA Alexis Marin Thomas F Zink Folkert M Tangerman, Brooklyn, NY Jean C Michel Lock Haven University of Pa Todor D Todorov, Univ of California, Frederic Paulin Dean R Wagner Santa Barbara Genevieve Pourcin Marshall University Kenneth V Towson, Capilano College, Valerie Tardive! Jian Chang North Vancouver, British Columbia, Gerald Tenenbaum Lihua Yang Canada Brigitte Vallee Memphis State University Zvonimir Tutek, Univ of Zagreb, Societal Catalana de Ciencies Fisiques Rajiv R Doshi Yugoslavia Quimiques i Matematiques Maria A Economov A M Vershik, Leningrad State Univ, Claudi Busque David G Kilman USSR Svenska Matematikersamfundet Shinko Kojima Bert K Waits, Ohio State Univ, Columbus Klas V Forsman John Z Lin Jack V Wales Jr, Ojai, CA Unione Matematica Italiana Sudha Rangan Russell C Walker, Carnegie Mellon Univ, Francesco Barbieri Jerry A Riepe Pittsburgh, PA Wiskundig Genootschap Barry G Schultz S P Wang, Purdue Univ, Lafayette, IN Leo Egghe Meenakshi Sivaram David C Wetlesen, USAF Academy, CO Mark A Stevens Bonnie Z Xiong, Univ of Scranton, PA Si Chin Tang Hong Kun Xu, East China lnst of Chern NOMINEE MEMBERS Gweihung Herb Tsai Tech, Shanghai, People's Republic of American University Zin M Young China Gregory E Alexander Xiaofei Zhu Richard K Zack, Vienna, Austria Nihaya Awartani Michigan State University John M Zerzan, BP Exploration, Serapio Byekwaso Colin G Mackinnon Anchorage, AK Ling Chen Kara L Walcher

SEPTEMBER 1989, VOLUME 36, NUMBER 7 949 New Members of the AMS

Montclair State College University ofAlabama-Huntsville Prabir Majumder Betsy J Beck Donna M Nicastro Kathleen M Perron Richard A Kugel University ofArizona Gretchen M Scheuer James Laux Elizabeth A Palmer Scott D Skansberg John G Sterling Francisco Javier Solis Yanhua Sun Mount Holyoke College University of Calgary Steven John Winters Katherine F Stevenson Mark W Campbell University ofMissouri, Columbia New Jersey lnst of Tech Sylvie G Desjardins Ali A Nayeb-Hashemi Sunill Paek David S Gunderson Reza Shirkhorshidi Rajeev K Vaid Indy Lagu University of Nebraska at Lincoln North Carolina State University Ann I McKenna Byung Moo Ahn Andy Eduardo Ravenna Zhaiyu Mo James Allen Boeve Northeastern University Chi Chuen So Daniel Richard Evenson Jorge E Navarro Hong Wang Linda Sue Fosnaugh Ranjit Vohra University of California, Davis Deena M Parker Northern Michigan University Ali Ali El-Ekh tiar Robert L Ruyle Lisa M Mansfield Kathleen Marie Hann Matt L Stiegert Bonnie J Orr Donald P Johnson Qiu-rong Wu Cheryl Ann Royea Wei Kang University of Nebraska at Omaha Oakland University Aaron David Klebanoff Monica Marie Brogan Nancy A Ernst Roberto E Lucchetti University of Pennsylvania Lisa Marie Jokubaitis Nam D Nguyen SarahB Nemeth Linda K Lester Adrian Riskiu University of South Carolina, Aiken Titus G Sfirlea Yi Zhu Janie Hightower Key Kenneth M Williams University of Colorado, Boulder University of Texas at San Antonio Portland State University Robert G Walsh Richard Paul Proft Marcia Lynne Burdon University of Connecticut, Storrs Timothy Mark Schmidi Rollins College Chris Koutsoukos Robin W Schulze Gloria A Child University of Florida University of Tulsa SUNY at Binghamton Nathalie C Millot Charles L Bottoms James Scott Babb University of Illinois at Chicago James L Day Mark Anthony Bianchi Ruby Q Tan James G Frost Leslie Ann Eisen University of Illinois at Urbana- Jared Fults David M Harris Champaign Bhuvaneswari Jayaraman John Watkins Harrison Myung Sook Chung Mary Lou Moss Mile P Krajcevski University of Louisville University of Waterloo Michael J Reedy Kenneth Robert Singleton Charles L A Clarke Mark Jon Rhodes University of Maine, Orono University of the West Indies LeonardA VanWyk Ronald C Currier Jr Sieudial Baball David H Wasilewski Ranga R Pattipati Balswaroop Bhatt Daryll A Weatherly Andrzej Pospiech Jeanine L Hendy SUNY, College at Plattsburgh University of Manitoba Savitri Maharaj Melissa Frenyea Issie K C Leung Marlon M Raghunanan Thomas R Hinsch Vladimir Tasic Shanaz Ansari Wahid Edward A Marcy Mirna Ungar Valdosta State College Sacred Heart University University of Michigan, Dearborn Thomas M Dart Rose Marie B Kinik Debra M Nelson Mary Suzanne Hopper Tennessee Tech University C Barbara Riehl John W Schleusner Vesna Cavka William A Smyth Washington State University Mohamad Diab John F Stapel Shun-Hwa Wang Dollena Hawkins University of Minnesota-Duluth Weiyi Wang Robert L Hebble Phyllis A Carlson Worcester Polytechnic Inst University Nac Autonoma de Mexico Steven D Copas Hongxiang Chen Montano Bermudez Gustavo Brant Douglas Deppa Sheila M Finnegan Laura Hidalgo-Solis Sandor F Felho Ulrich J Gerhausser Martha Takane-Imay Jeffery M Franke Lucia M Kimball University ofAkron Michael P Hanratty Thomas Krischke Robert Carnahan Keith M Hill Timothy Patrick Mavor Brian Gilby David D Kingsley Gregory John Toland Jennifer Mowrey Chi-Cheng Lin York College, CUNY Richard Slocum Hui-Liang Low Li-Mei Chen

950 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements

SUGGESTED USES for classified advertising are positions available: books .or lecture notes UNIVERSITY OF CALIFORNIA for sale, books being sought, exchange or rental of houses, and t~p1ng s.e':"1ces. LOS ANGELES THE 1989 RATE IS $42.50 per inch on a single column (one-mch m1mmum), calculated Department of Mathematics from the top of the type; $18 for each additional 1/2 inch or fraction th~~eof. No discounts for multiple ads or the same ad in consecutive issues. For an add1t1onal $10 charge, TEMPORARY POSITIONS announcements can be placed anonymously. Correspondence will be forward~d. . . (1) Two E. R. Hedrick Assistant Pro­ Advertisements in the "Positions Available" classified section will be set w1th a m1~1~um fessorships. Applicants must show very name above body copy, unless add1t1?~al one-line headline, consisting of the institution strong promise in research and teaching. headline copy is specified by the advertiser. Advertis~men~s in other ~ection_s of the class1f1~d Salary $37,000. Three year appointment. pages will be set according to the advertisement 1nsert1on. Headlines w1ll b~ cente~ed 1n boldface at no extra charge. Classified rates are calculated from top of ty~e 1n headli~e to Teaching load: four quarter courses per bottom of type in body copy, including lines and spaces within: Any_ fractional text w~ll be year, which may include one advanced charged at the next 1/2 inch rate. Ads will appear in the l~ng~ag~ 1n which they are submitted. course in the candidate's field. Pref­ Prepayment is required of individuals but not of 1nst1tUt1ons. There are no me~ber erence will be given to applications discounts for classified ads. Dictation over the telephone will not be accepted for classified completed by January 1, 1990. advertising. . (2) Two or three Research Assistant DEADLINES are listed on the inside front cover or may be obtamed from the AMS Professorships in Computational and Advertising Department. . Applied Mathematics. Applicants must se~, race, u. s. LAWS PROHIBIT discrimination in employment on the bas1s ~f c~lor: age, show very strong promise in research religion or national origin. "Positions Available" advertisements from 1nst1tut1ons o~ts1~e ~he and teaching. Salary $37,000. Three year u. s. cannot be published unless they are accompanied by a statement that the 1nst1tut1~n does not discriminate on these grounds whether or not it is subject to _u. S. laws. Deta11s appointment. Teaching load: four quarter and specific wording may be found near the Classified Advertisements 1n the January and courses per year, which may include one July/August issues of the Notices. . . advanced course in the candidate's field. SITUATIONS WANTED ADVERTISEMENTS from involuntarily unemployed mathematiCians Preference will be given to applications are accepted under certain conditions for free publication. Call toll-free 800-556-7774 and completed by January 1, 1990. speak to Paula Montella for further information. (3) One or two Assistant Profes­ SEND AD AND CHECK TO: Advertising Department, Attn: Paula Mo_ntella, AMS, P. C?· Box sorships in the Program in Comput­ 6248, Providence, Rhode Island 02940. AMS location for express delivery pack~ges IS 201 ing (PIC). Applicants must show very Individuals are requested to pay m advance, Charles Street, Providence, Rhode Island 02904. strong promise in teaching and research, institutions are not required to do so. AMS FAX 401-331-3842. preferably in the general area of Logic, Language and Computation. Teaching load: four quarter programming courses POSITIONS AVAILABLE UNIVERSITY OF VIRGINIA and an advanced quarter course of the candidate's choice per year. Two year BROWN UNIVERSITY The Department of Applied Mathemat­ appointment, possibly renewable once ics at the University of Virginia seeks or twice. Salary range: $37,000-$44,000. BROWN UNIVERSITY, Providence, Rl a numerical analyst with a strong in­ 02912. Two professorships at the As­ Preference will be given to applications terest in partial differential equations completed by January 1, 1990. sociate Professor level or above, with and their physical applications. The De­ tenure, to begin July 1, 1990. Salary to (4) One or two Lectureships in the partment, which cooperates closely with Program in Computing (PIC). Applicants be negotiated. Preference to be given other departments within the School of to applicants with research interests must show very strong promise in the Engineering and Applied Science where teaching of programming. Teaching load: consonant with those of the present it is located and with the Mathematics members of the Department. For one of five quarter programming courses per Department in the College of Arts and year. One year appointment, possibly the positions preference will be given to Science, has active research progams those with research interest in Algebraic renewable up to four times. Salary de­ in continuum mechanics, control theory, pends on experience, begins at $31,200. Geometry, Differential Geometry, or re­ and numerical analysis/scientific com­ lated fields. Candidates should have (5) Subject to administrative approval, puting. The successful candidate will be a few adjunct assistant professorships. a distinguished research record and a able to support and direct doctoral stu­ strong commitment to teaching. Qual­ Two year appointments. Strong re­ dents in this latter area, to collaborate search and teaching background re­ ified individuals are invited to send a with faculty, and to teach a range of vita and at least three letters of rec­ quired. Salary $32,400-$36,500 per year. applied mathematics courses. EOE/ AA. Teaching load: five quarter courses per ommendation, no later than November Applications should be sent to 1, 1989, to Professor Robert Accola, year. James G. Simmonds, Chair (6) Several positions for visitors and Executive Officer, Department of Math­ Department of Applied ematics, Brown University, Providence, lecturers. To apply, write to Alfred W. Mathematics Hales, Chair, Department of Mathemat­ Rl 02912. Brown University is an Equal Thornton Hall Opportunity1 Affirmative Action employer. ics, University of California, Los Angeles, University of Virginia CA 90024-1555. Attn: Staff Search. Charlottesville, VA 22903 UCLA is an equal opportunity/affirm­ ative action employer.

SEPTEMBER 1989, VOLUME 36, NUMBER 7 951 Classified Advertisements

AVAILABLE POSITIONS THE AIR FORCE FLIGHT tory, the use of modern computers, and DYNAMICS LABORATORY other service support will be provided for UNIVERSITY OF UTAH and the visiting professor and may include Department of Mathematics THE AIR FORCE INSTITUTE support for a limited number of visiting invites applications for the OF TECHNOLOGY professor's doctoral students. following positions: announce the PERIOD OF APPOINTMENT AND SALARY 1990-1991 The initial period of appointment is 1. At least four full time tenure track FLIGHT CONTROL period and appointments on any of the professorial DISTINGUISHED VISITING for one full year. A shorter levels. The Department is particularly in­ PROFESSOR PROGRAM the starting date are negotiable, but terested in applicants who work in the should be prior to October 1, 1990. areas of geometry, algebra, topology, The Air Force Institute of Technology Extension for a second year may be group representation theory, applied (AFIT) at Wright-Patterson Air Force possible. Salary is commensurate with mathematics, and scientific computing. Base, Dayton, Ohio announces the op­ qualifications. A per diem allowance is Selection will be based on research ex­ portunity to join the AFIT graduate fac­ also paid. pertise and teaching ability. Applications ulty as a Distinguished Visiting Profes­ APPLICATION will be accepted until January 31, 1990 sor in the Department of Electrical and A resume of qualifications and ex­ or until the positions are filled. Computer Engineering in the School of perience, including a list of significant 2. Two or more nonrenewable three­ Engineering. publications and any need for support of year Instructorships. Persons of any age RESPONSIBILITIES Ph.D students can be submitted anytime receiving Ph.D. degrees in 1989 or 1990 The responsibilities of the AFIT Distin­ prior to February 28, 1990 to: are eligible. Applicants will be selected guished Visiting Professor include pro­ Capt. RANDALL N. PASCHALL on the basis of ability and potential in viding academic leadership in teaching Department of Electrical and teaching and research. Starting salary and research in association with AFIT Computer Engineering this academic year is $29,500; cost of faculty and students, and initiating and Air Force Institute of Technology living increases are contingent on action conducting research and consultation (AFIT/ENG) by the State Legislature. Duties consist with the Flight Dynamics Laboratory, Air Wright-Patterson AFB, Ohio of teaching five courses during the three Force Wright Research and Development 45433-6583 quarter academic year. Applications will Center. Phone:(513) 255-3576 be accepted until December 31, 1989 or QUALIFICATIONS The Flight Control Distinguished Visit­ until the positions are filled. The person appointed as Distin­ ing Professor Program is made possible 3. One or more visiting positions of one guished Visiting Professor should be an through a grant from the Air Force year or less. Selection criteria are teach­ eminent faculty member at a prestigious Wright Research and Development Cen­ ing ability and potential contribution to university. Selection will be based upon ter's Flight Dynamics Laboratory. our research environment. Applications the individual's experience, proposed AFIT is an Equal Opportunity and will be accepted until January 31, 1990 teaching program and research areas. Affirmative Action Employer. or until the positions are filled. Areas of special interest and activity at Applications must include curriculum AFIT are: Flight Control Systems, Con­ vitae, bibliography and three letters of trol Systems for Reconfigurable Aircraft, THE CITY UNIVERSITY OF NEW YORK reference. (Instructorship applications Design of Robust Multivariable Control John Jay College of Criminal Justice must also include an abstract of the Systems, Quantitative Feedback Theory Department of Mathematics Design, Output Digital Feedback De­ thesis and either a list of graduate Professor, tenure-track posi­ sign Technique for Multivariable Track­ Assistant courses completed or a transcript of 1990. Requirements: Ph.D.; ing Systems, Hoo Control Theory, and tion, January graduate work.) demonstrated potential for research; Adaptive Control and Estimation. Appli­ Please send your application to: commitment to teaching. Com­ cants are expected to have a Ph.D and strong COMMITTEE ON STAFFING numerical analysis or op­ be a professional contributor in the area puter science, DEPARTMENT OF erations research background preferred. of flight control. Consideration will be MATHEMATICS John Jay College of Criminal Justice, given to applicants who have extensive UNIVERSITY OF UTAH in Manhattan, is a senior col­ flight control experience within industry located 233JWB CUNY. Send resume, graduate and government. lege in SALT LAKE CITY, UTAH 84112 relevant reprints, dissertation RESEARCH SUPPORT transcript, The University of Utah is an equal of reference to Two powerful hybrid computers (EAI abstract and three letters opportunity-affirmative action employer. Graff, Chairperson, Department SIMSTARS) are the heart of AFIT's Samuel John Jay College of flight control laboratory. A high fidelity, of Mathematics, 445 West 59 Street, full flight envelope, real-time aircraft sim­ Criminal Justice, NY 10019 by December 1, ulator is developed for academic and New York, and women are encour­ research use. Overall, AFIT's computer 1989. Minorities apply. AA/EOE Employer. resources equal or exceed those found aged to at other universities. An office, labora-

952 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements

POSITIONS AVAILABLE THE UNIVERSITY OF THE UNIVERSITY OF FLORIDA WESTERN ONTARIO Department of Mathematics UNIVERSITY OF BRITISH COLUMBIA Department of Mathematics Mathematics, Dept., Room 121 In each of the next several years, the 1984 Mathematics Road Applications are invited for a tenure track Department of Mathematics intends to Vancouver, B.C., appointment at the Assistant or Asso­ fill a substantial number of tenure-track Canada, V6T 1 Y 4 ciate Professor level. Preference will be faculty positions with mathematicians of given to candidates in algebra whose The Mathematics Department is seeking exceptional caliber. Outstanding candi­ research has strong connections to one an outstanding candidate for a tenure dates from all academic ranks and all of the following areas: algebraic geome­ track Assistant Professorship to begin areas of pure and applied mathematics try, algebraic number theory, Lie theory, 1 July 1990. Our highest priority is for are invited to apply for these positions. representation theory of finite groups. a candidate in differential geometry. If Applications from junior candidates with A solid research and publication record there is no suitable applicant in this field, post-doctoral experience are especially is expected. The successful candidate we will also consider candidates in the welcome. will be expected to contribute to the de­ field of Lie algebras. For an exception­ First preference will be given to can­ partment's research programme and, in ally well-qualified candidate, this position didates who will facilitate Department particular, supervise graduate students. may be upgraded to a junior Associate goals of establishing strong working In addition, the candidate should have Professorship. Applicants should have a groups in partial differential equations, commitment to and aptitude for teaching proven research record of high quality algebraic geometry and number theory. undergraduate and graduate courses. and have demonstrated interest and abil­ Secondary preference will be given to The appointment, which is subject to ity in teaching. Preference will be given candidates who will fit well into currently the availability of funds, is scheduled to to candidates who have one or more functioning groups. In particular, it is begin on July 1, 1990. Applicants should years of postdoctoral experience. This likely that one position will be filled this forward a curriculum vitae and names of position is subject to final budgetary ap­ year by an algebraist. at least three referees to proval. The salary will be commensurate Senior candidates should have dis­ Dr. Richard Kane, Chairman with experience and research record. tinguished research records, and junior Department of Mathematics, Applicants should send a C.V. including candidates are expected to have made Middlesex College list of publications, statement of research significant research contributions. Every The University of Western Ontario and teaching interests and arrange for candidate is expected to possess a London, Ontario N6A 587 three letters of recommendation to be strong commitment to teaching. Candi­ Canada sent directly to: The Head, Department dates should forward a resume (includ­ The closing date for application is De­ of Mathematics, University of British ing a list of publications) and should cember 1, 1989. In accordance with Columbia, Vancouver, B.C. Canada V6T arrange for at least four letters of rec­ Canadian Immigration requirements, this 1Y4. Applications must be received be­ ommendation to be sent to: advertisement is directed to Canadian fore January 1, 1990. In accordance with David A. Drake, Chair citizens and permanent residents of Canadian immigration requirements, pri­ Department of Mathematics Canada. ority will be given to Canadian citizens University of Florida ""An Equal Opportunity Employer"" and permanent residents of Canada. 201 Walker Hall Gainesville, Florida 32611 All applications for the academic year 1990-1991 should be complete by De­ cember 31, 1989. The University of Florida is an equal opportunity employer and energetically solicits applications from women and minority candidates.

SEPTEMBER 1989, VOLUME 36, NUMBER 7 953 Classified Advertisements

POSITIONS AVAILABLE TRINITY UNIVERSITY WAKE FOREST UNIVERSITY Position Announcement The Z. Smith Reynolds DARTMOUTH COLLEGE Professorship in Mathematics Trinity University invites applications and Senior Position in Mathematics. Asso­ nominations for a tenure-track position Wake Forest University announces the ciate or Full Professor position avail­ in mathematics, appointment beginning establishment of a distinguished profes­ able beginning in 1990-91. Candidates August, 1990. The appointment will be sorship made possible by the Z. Smith should have established and recognized made at the rank of Assistant Professor. Reynolds Foundation. The scholar se­ research program, proven ability to at­ Responsibilities include teaching nine lected to fill this position must have an tract external research support, and credit hours per semester, continuing established record of recognized schol­ interest in building and leading a strong scholarly activity, assisting in curriculum arship and a commitment to teaching research group. Appointee will partici­ development, advising, and committee and research in a university setting. pate in the recruitment for several junior service. Minimum qualifications are the Duties include teaching, continuing a positions. Proven record of excellence Ph.D. in Mathematics with excellence in program of research, contributing to in teaching at both the undergraduate and strong commitment to teaching. the intellectual life of the Department and graduate levels and committment Founded in 1869, Trinity University of Mathematics and Computer Science, to professional interaction with faculty occupies a modern campus overlook­ and fostering the mathematical growth and Ph.D. students required. Applica­ ing the San Antonio skyline. Purposely of gifted undergraduates. The position, tions are welcome in all fields of math­ small and selective, with about 2500 which carries both tenure and the rank ematics. Department has special inter­ students, Trinity stresses a high quality, of professor, could be filled as early as ests in algebra, combinatorics, geom­ undergraduate liberal arts and science the fall semester of 1990. etry /topology, and probability /statistics. program; in particular, the Mathemat­ Wake Forest University is a compre­ Dartmouth provides grants to new fac­ ics Department does not offer graduate hensive university with 5000 students, ulty members for research-related ex­ courses. San Antonio is a city of ap­ 3500 of whom are in the undergraduate penses, a generous sabbatical program, proximately 850,000 people situated in a college. The Department of Mathematics and moderate teaching loads. The review metropolitan area of 1.2 million. and Computer Science has 17 per­ of applications will begin on January 1, Closing date for applications is De­ manent positions, 13 of which are in 1990. Send a letter of application, a cember 29, 1989. Send vita, graduate mathematics, and offers majors in math­ curriculum vitae, the names of four peo­ transcripts and three letters of reference ematics and computer science and an ple who have agreed to write letters to: MA in mathematics. of recommendation, and a description Professor William F. Trench Inquiries, nominations, and applica­ of research interests to: Mathematics Department of Mathematics tions should be directed to: Senior Search Committee Chair, De­ Trinity University Professor Richard Carmichael, partment of Mathematics and Computer 715 Stadium Drive Chair Science, Bradley Hall, Dartmouth Col­ San Antonio, Texas 78212 Department of Mathematics and lege, Hanover, NH 03755. Dartmouth is Trinity University is an equal opportunity Computer Science firmly committed to Affirmative Action affirmative action employer. P.O. Box 7311 and strongly encourages applications Wake Forest University from minorities and women. Winston-Salem, NC 27109 USA Evaluation of applicants will begin in late THE OHIO STATE UNIVERSITY winter and will continue until the position Department of Mathematics TEXAS CHRISTIAN UNIVERSITY Research Instructorships in is filled. AA/EO employer. Mathematics The Dept. of Mathematics invites appli­ cations for two tenure track positions at Applications are invited for the position WILLIAMS COLLEGE the Assistant Professor rank beginning of research instructor in mathematics for Department of Mathematics August, 1990. The Ph.D. degree in a the academic year 1990-91. Candidates Williamstown, Massachusetts 01267 core area of mathematics is required. should hold a Ph.D. (or equivalent) in Duties include teaching (approx. 9 hrs. mathematics and show strong research Three anticipated positions, probably at per semester) and the active pursuit promise. the rank of assistant professor, for of a research program. Salary will be Please send credentials and have Fall 1990. Strong Commitment to both commensurate with qualifications. Send letters of recommendation sent to Pro­ teaching and scholarship is essential. letter of application, resume, and three fessor Joseph Ferrar, Department of Please have a vita and three letters letters of reference to: Victor A. Belfi, Mathematics, The Ohio State Univer­ of recommendation on teaching and Chairman, Dept. of Mathematics, P.O. sity, 231 W. 18th Avenue, Columbus, research sent to Frank Morgan, Chair. Box 32903, TCU, Fort Worth, TX 76129. Ohio 43210. The Ohio State University is Evaluation of applications will continue Deadline for applications December 15, an Equal Opportunity 1Affirmative Action until positions are filled. 1990. TCU is an AA/EOE. Employer. AA/EOE

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POSITIONS AVAILABLE UNIVERSITY OF CALIFORNIA AT UNIVERSITY OF CALIFORNIA BERKELEY SANTA CRUZ OREGON STATE UNIVERSITY Department of Mathematics Berkeley, CA 94720 The Mathematics Department at the The Andreotti Assistant Professor posi­ TENURED POSITION University of California, Santa Cruz is tion in mathematics will become available recruiting for a position in algebra or September 16, 1990. Salary depends on We invite applications for one or more number theory. The teaching load is qualifications. Closing date is December positions effective July 1, 1990, at tenure 4 one-quarter courses per year. Rank: 15, 1989. Write to: level {Associate or full Professor), sub­ Assistant Professor 1-111. Minimum Quali­ Professor Bent Petersen, Chair ject to budgetary approval, in the ar­ fications: Ph.D. in Mathematics. Demon­ Andreotti Professorship Selection eas of algebra, analysis, applied math­ strated achievements in, or potential Committee ematics, foundations, or geometry and for, research, teaching and professional Department of Mathematics topology. Demonstrated leadership in re­ service, commensurate with experience. Oregon State University search is expected of applicants. Appli­ Salary: $32,400-$34,900. Effective: July Corvallis, Oregon 97331-4605 cants should send a curriculum vitae, list 1, 1990. Applicants should send vi­ Oregon State University is an Affirma­ of publications, a few selected reprints tae, information about their research tive Action/Equal Opportunity Employer or preprints, and the names of three ref­ and teaching experience and four let­ and complies with Section 504 of the erences to Andrew J. Casson, Vice Chair ters of recommendation commenting Rehabilitation Act of 1973. OSU has a for Faculty Affairs at the above address. on their teaching and research, to­ policy of being responsive to the needs We should receive this material no later Recruitment Committee, Mathemtics De­ of dual-career couples. than October 1, 1989. The University partment, University of California, Santa STAFF SELECTION COMMITTEE of California is an Equal Opportunity, Cruz, CA 95064. Closing Date: Decem­ B. E. Petersen, Chair Affirmative Action Employer. ber 31, 1989. Please refer to #190-890 in B. I. Fein your reply. UCSC IS AN EEO/AA/IRCA R. Higdon EMPLOYER R. M. Schori

OREGON STATE UNIVERSITY RUTGERS UNIVERSITY-NEWARK UNIVERSITY OF OTTAWA Professor of Mathematics Assistant Professor positions in Alge­ The Department of Mathematics will bra/Number Theory, Numerical Analysis, The Department of Mathematics and have two or three tenure-track open­ Geometric-Topology /Dynamical Systems, Computer Science anticipates an open­ ings at the assistant or asociate level and Differential Geometry will become ing at the Rank of Professor I or Profes­ starting July 1, 1990. Applicants in all available September 16, 1990. Salary sor II beginning Fall 1990. Candidates branches of mathematics and statistics depends on qualifications. Closing date should exhibit outstanding research ac­ who hold a doctorate and have demon­ December 15, 1989. Write to: complishments. Salary and teaching load strated research potential are invited. Professor Bent Petersen are negotiable. Applicants from all fields The teaching attached to one of the Staff Selection Committee are invited. Areas of research inter­ posts will be in French. For the other(s), Department of Mathematics est in the department include number ability to teach in English and French Oregon State University theory, representation theory and auto­ is required for tenure but one language Corvallis, Oregon 97331-4605 morphic forms, Lie algebras, transfor­ suffices for the initial appointment. In Oregon State University is an Affirma­ mation groups, low dimensional topol­ accordance with Canadian immigration tive Action/Equal Opportunity Employer ogy and Teichmuller theory. Nominations requirements, priority will be given to and complies with Section 504 of the and applications should be sent to: Jane Canadian citizens and permanent resi­ Rehabilitation Act of 1973. OSU has a Gilman, Chair, Department of Mathemat­ dents of Canada. Applicants should send policy of being responsive to the needs ics, Rutgers University, Newark, New a resume and have at least three let­ of dual-career couples. Jersey 07102. The closing date for appli­ ters of recommendation sent directly to: STAFF SELECTION COMMITTEE cations is 1/15/90 but applications will W. D. Burgess, Dept. Math., University B. E. Petersen, Chair be considered until the position is filled. of Ottawa, Ottawa, CANADA K1 N 6N5. B. I. Fein AA/EOE. Deadline: December 15, 1989. R. Higdon R. M. Schori

SEPTEMBER 1989, VOLUME 36, NUMBER 7 955 Classified Advertisements

POSITIONS AVAILABLE UNIVERSITY COLLEGE LONDON BAYLOR UNIVERSITY Endowed Chair of Mathematics BRYN MAWR COLLEGE The College is exploring the possibility of filling the Astor Chair in Pure Math­ The Mathematics Department is accept­ Applications are invited for two posi­ ematics. The last three holders of the ing applications for the Ralph and Jean tions in Mathematics, to start September chair have been Professor H. Davenport Storm Chair for research in mathemat­ 1990, one open as to rank and tenured F.R.S., Professor C. A. Rogers F.R.S. ics. We are seeking a mathematician or tenure-track, and one at Assistant and Professor P. M. Cohn F.R.S. Nom­ with an established record of excel­ Professor rank, tenure-track. One of the inations and enquiries are invited. The lence in research and a strong interest positions must be filled with a person college is looking for a mathematician in teaching. The teaching load is three taking responsibility in the joint com­ with an excellent record in one of the hours per semester. The starting date is puter science program with Haverford main stream branches of pure math­ negotiable. College. Preferred specialties: geometry, ematics. It would especially welcome The Department offers the BA, BS, algebra, applied mathematics, or com­ nominations of distinguished mathemati­ and MS degrees. The department has puter science. Strong research record cians in number theory or analysis of an enrollment of 2500 students and the and excellence in teaching expected. any related field. University has 11 ,000 students. Baylor Women and minority candidates are es­ A vacant lectureship is available so is located in Waco, Texas, which is 100 pecially encouraged to apply. Please that an incoming Astor Professor could miles from Dallas and 100 miles from direct application and three letters of help in appointing a suitable candidate Austin. Baylor University is an Affirma­ recommendation to: F. Cunningham, Jr., in his/her field. tive Action/Equal Opportunity Employer Faculty Search, Department of Mathe­ Please contact: and is under the patronage and general matics, Bryn Mawr College, Bryn Mawr, Dr. D. H. Roberts F.R.S. direction of the Baptist General Conven­ PA 19010. Closing date January 1, 1990. Provost tion of Texas. Send vita to Howard L. Bryn Mawr College is an EO/AA em­ University College London Rolf, B.U. Box 7328, Baylor University, ployer. Gower Street Waco TX 76798-7328. London WC1 E 6BT England CALIFORNIA STATE UNIVERSITY OF CALIFORNIA UNIVERSITY, NORTHRIDGE LOS ANGELES Department of Mathematics Applications are invited for four tenure UNIVERSITY OF MIAMI track positions for the Fall of 1990. Three Chairperson REGULAR POSITIONS IN Department of Mathematics and at the assistant professor level AND APPLIED MATHEMATICS positions Computer Science PURE in areas of interest to the faculty and Four to six regular positions in pure and possibly one at the associate profes­ We are seeking a distinguished mathe­ applied mathematics. Areas of specific sor level, will be available. A Ph.D. by matician with a strong record in research. interest include logic; algebra, algebraic the Fall of 1990 is required. Candidates The department is firmly committed to geometry, number theory and combi­ in Mathematics Education and Applied excellence in research and teaching, has natorics; geometry and topology; anal­ mathematics (especially with experience enjoyed substantially increased outside ysis, functional analysis, mathematical in industry) are encouraged to apply, but funding in recent years, and anticipates physics and dynamical systems; prob­ candidates in all areas of mathematics several new faculty appointments in the ability, statistics and game theory; lin­ with a commitment to both teaching and near future. The new chairperson would ear and non-linear differential equations; research will be considered. Responsi­ play a major role in the further develop­ applied mathematics, numerical analy­ bilities include teaching 9-12 hours, de­ ment and enhancement of our program. sis and mathematical computer science. pending on research and/or other con­ Applicants should submit curriculum Very strong promise in research and tributions. Send vita and three letters of vitae and the names and addresses of teaching required. Positions initially bud­ recommendation to Jerry Rosen, Hiring four references to: Prof. Chris Cosner, geted at the assistant professor level. Committee Chair, Dept. of Mathematics, Chair, Search Committee, Department Sufficiently outstanding candidates at California State University, Northridge, of Mathematics and Computer Science, higher levels will also be considered. CA 91330 by Feb. 15 for full con­ P.O. Box 249085, University of Miami, Teaching load: Averaging 1.5 courses sideration. Women and minorities are Coral Gables, FL 33124. The appoint­ per Quarter, or 4.5 Quarter courses per especially encouraged to apply. CSUN ment could be effective as early as year. is located in a Northwestern suburb of Spring 1990, so immediate applications To apply, write to Alfred W. Hales, Los Angeles and is in close proximity are encouraged. However, applications Chair, Department of Mathematics, Uni­ to Cal. Tech., U.S.C., and U.C.L.A. (15 will be accepted until the position is versity of California, Los Angeles, CA mins. away). filled. 90024-1555. Attn: Staff Search. UCLA is AFFIRMATIVE ACTION/EQUAL OP­ The University of Miami is an Equal an equal opportunity1 affirmative action PORTUNITY EMPLOYER Opportunity1 Affirmative Action Employer. employer.

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POSITIONS AVAILABLE PUBLICATIONS MATH SCI PRESS, 53 Jordan Rd., UNIVERSITY Brookline, MA 02146, 617-738-0307, THE OHIO STATE Curvature Geometry Workshop, Lan­ Department of Mathematics TOPICS IN PHYSICAL GEOMETRY, by caster 1989 R. Hermann, $80. In Preparation: Geo­ The Department of Mathematics of The Proceedings, Edited by C. T. J. Dodson metric Aspects of Computer Science. Ohio State University hopes to fill several Contains papers presented by positions, both visiting and permanent, L. Vanhecke, F. Tricerri, C. T. J. Dodson, effective Autumn Quarter 1990. Candi­ S. M. Salamon, M. Fernandez, L. A. FOR SALE dates in all areas of applied and pure Cordero, C. M. Wood, A. F. Swann, mathematics are invited to apply. Sig­ P. Bueken. AMS Subject Classifications: BOOKS URGENTLY NEEDED nificant research accomplishments or 53B 53C 55R 57R BOOKS FOR SALE In !.!\TEX. Softcover, 195 pages ISBN 0 exceptional research promise, and evi­ J. F. Ptak Science Books stocks roughly 901272 66 3 dence of good teaching ability, will be 15000 uncommon and out-of-print books ULDM Publications, Mathematics De­ expected of successful applicants. in the physical sciences and history of partment, Lancaster University, Lan­ Please send credentials and have science as well as 100+ (better) journals caster LA1 4YF, England. Fax 0524 letters of recommendation sent to Pro­ in physics and math. 381707 fessor Joseph Ferrar, Department of We buy single titles and libraries email [email protected]. Mathematics, The Ohio State University, Catalogs Issued Price Postfree, Prepaid £12 Europe, 231 W. 18th Avenue, Columbus, Ohio Write or call: J. F. Ptak Science Books, US$ 25 elsewhere. Cheques payable 43210. Review of resumes will begin 3236 P St., NW Wash. DC 20007 202- to Lancaster University. immediately. 337-2878. The Ohio State University is an Equal Opportunity I Affirmative Action Employer.

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SEPTEMBER 1989, VOLUME 36, NUMBER 7 957 Part II of this highly-acclaimed reference book and widely-adopted text by Yvonne Choquet-Bruhat and Cecile DeWitt-Morette: Analysis, Manifolds and Physics Part II: 92 Applications

This second, companion volume contains 92 applications developing concepts and theorems presented or mentioned in the first volume. Introductions to and applications in several areas not previously covered are also included such as graded algebras with applications to Clifford algebras and (S)pin groups, Weyl Spinors, Majorana pinors, homotopy, supersmooth mappings and Berezin integration, Noether's theorems, homogeneous spaces with applications to Stiefel and Grassmann manifolds, cohomology with applications to (S)pin structures, Backlund transformations, Poisson manifolds, conformal transformations, Kaluza-Klein theories, Calabi-Yau spaces, universal bundles, bundle reduction and symmetry breaking, Euler-Poincare characteristics, Chem-Simons classes, anomalies, Sobolev embedding, Sobolev inequalities, Wightman distributions and Schwinger functions.

The material included covers an unusually broad area and the choice of problems is guided by recent applications of differential geometry to fundamental problems of physics as well as by the authors' personal interests. Many mathematical tools of interest to physicists are presented in a self-contained manner, or are complementary to material already presented in part I.

All the applications are presented in the form of problems with solutions in order to stress the questions the authors wished to answer and the fundamental ideas underlying applications. The answers to the solutions are explicitly worked out, with the rigor necessary for a correct usage of the concepts and theorems used in the book. This approach also makes part I accessible to a much larger audience.

CONTENTS: I. Review of fundamental notions of analysis. II. Differential calculus on Banach spaces. III. Differentiable manifolds. IV. Integration on manifolds. V. Riemannian manifolds. IGUllerian manifolds. V his. Connections on a principal fibre bundle. VI. Distributions. Subject Index.

1989 452 pages Price: US $40.00/Dfl.120.00 ISBN 0-444-87071-7

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NORTH-HOLLAND In the USA & Canada: Elsevier Science Publishers Elsevier Science Publishing Co., Inc. P.O. Box 211, 1000 AE Amsterdam P.O. Box 882, Madison Square Station The Netherlands New York, NY 10159, USA US S prices are valid only in the USA and Canada. In all other countries, the Dutch Guilder price is definMive. Customers in The Netherlands, please add 6% BTW. In N-York State, applicable sales tax should be added. AU prioes are subject to change wMhout prior notice. 404/B/344 Then, introduce yourself to the over­ Plus, your very own HP-288 cal­ head display for the HP-288. It allows culator free. (A $235 retail value.) you to project your calculations on an HP-288 for everyone in the class­ To learn more, and get free curric­ room to see. ulum materials, call ( 503) 757-2004 between 8am and 3pm, PT. Offer Now there's a better way to teach A scholastic offer for you. ends October 31, 1989. algebra and calculus in the class­ room. In fact, two ways. If your department or students There is a better way. purchase a total of 30 HP-288 cal­ First, introduce your students to the culators, we'll give you a classroom HP-288. It's the only calculator that overhead display for the HP-288 FJ/~ HEWLETT offers symbolic algebra and calculus. absolutely free. (A $500 retail value.) ~~PACKARD

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Computability: Computable Functions, Logic, and the Foundations of Mathematics by Richard L. Epstein and Walter A. Carnielli Introduction to the mathematics of computable functions and logic using readings from Hilbert, Godel, Turing, Post, Church, and many others. Contents: Part I: The Fundamentals 1. Some Paradoxes 2. What do the Paradoxes Mean? 3. Whole Numbers 4. Functions 5. Proofs 6. Infinite Collections? 7. Hilbert: On the Infinite Part II: Computable Functions 8. Computability 9. Turing Machines 10. The Most Amazing Fact and Church's Thesis 11. Primitive Recursive Functions 12. The Grzegorczyk Hierarchy 13. Multiple Recursion 14. The Least Search Operator 15. Partial Recursive Functions 16. Numbering the Partial Recursive Functions 17. Listability 18. Turing Machine Computable =Partial Recursive Part III Logic and Arithmetic 19. Propositional Logic 20. An Overview of First-Order Logic and Godel's Theorems 21. First-Order Arithmetic 22. Functions Representable in Formal Arithmetic 23. The Undecidability of Arithmetic 24. The Unprovability of Consistency Part IV Church's Thesis and Constructive Mathematics 25. Church's Thesis 26. Constructivist Views of Mathematics 1989. 297 pp. Cloth. ISBN 0-534-10356-1.

Bolomorphic Hilbert Modular Forms by Paul B. Garrett Self-contained introduction to a substantial part of the theory of holomorphic Hilbert modular forms, associated L-functions, and their arithmetic. Contents: 1. Classical Theory of Hilbert Modular Forms. 2. Automorphic Forms on GL(2,A) 3. Comparison of Classical and Adelic Viewpoints. 4. Eisenstein Series. 5. Theta Series. 6. Arithmetic of Hilbert Modular Forms. 7. Proof of the Arithmetic Structure Theorem. 1989. 304 pp. Cloth. ISBN 0-534-10344-8.

Finite Difference Schemes and Partial Differential Equations by John C. Strikwerda Graduate text for students in applied mathematics, engineering, and the sciences. Contents: 1. Hyperbolic Partial Differential Equations and Finite Difference Schemes. 2. Analysis of Finite Difference Schemes. 3. Accuracy of Finite Difference Schemes. 4. Multistep Finite Difference Schemes. 5. Dissipation and Dispersion. 6. Parabolic Partial Differential Equations. 7. Systems of Partial Differential Equations in Higher Dimensions. 8. Second-Order Equations. 9. Analysis of Well-Posed and Stable Problems. 10. Convergence Estimates for Initial Value Problems. 11. Initial Boundary Value Problems. 12. Elliptic Partial Differential Equations. 13. Linear Iterative Methods. 14. The Method of Steepest Descent and the Conjungate Gradient Methods. 1989. Cloth. 386 pp. ISBN 0-534-09984-X.

Partial Differential Equations: Analytical Solutions Techniques by J. Kevorkian Graduate text for students in applied mathematics, engineering, and the sciences. Contents: 1. The Diffusion Equation 2. Laplace's Equation 3. The Wave Equation 4. Linear Second­ Order Equations with Two Independent Variables. 5. Quasi-linear First-Order Equations 6. Nonlinear First-Order Equations 7. Quasi-linear Hyperbolic Equations 8. Perturbation Solutions January 1990. 600 pp. (est.) Cloth. ISBN 0-534-12216-7.

Wadsworth & Brooks/Cole Advanced Books & Software Department JMA004 511 Forest Lodge Rd. Pacific Grove, CA 93950 Now available in f!.ap_erback Benefits and Risks of Now in a new edition Computer Simulation of Knowledge-Based Systems Fortran 8x Explained Council for Science and Society Revised Edition liquids MICHAEL METCALF and J.K. REID M.P. ALLEN and D.J. TILDESLEY Provides a unique treatment of the many benefits, as well as the potential dangers, of "Well-written .... many useful exercises and Discusses the latest simulation techniques the new advice-giving computer systems. example programs. Fascinating and infor­ of molecular dynamics and the Monte Carlo 1989 86 pp. paper $14.95 mative."-Personal Computer World methods as well as how to avoid program­ 1989 320 pp.; illus. paper $29.95 ming pitfalls. 1988 408 pp.; 68 ill us. paper $42.50 Now in f!.ap_erback Direct Methods for Sparse Parallel Algorithms and Matrix Computation A First Course in Matrices JAGDISH J. MODI I.S. DUFF, A.M. ERISMAN, and J.K. REID Combinatorial Mathematics One of the first textbooks on the topic. Re­ Second Edition Provides practical approaches to the effi­ views fundamental concepts in parallel IAN ANDERSON cient use of sparcity. computing. $27.95 "Excellent introductory text."-Times Higher 1987 360 pp. cloth $45.00, paper 1989 272 pp., illus. Education Supplement cloth $75.00, paper $24.95 1989 144 pp.; illus. Now in f!.ap_erback cloth $56.50, paper $21.95 GLIM An Introduction Numerical Methods for M.J.R. HEALY Fluid Dynamics III Now available in f!.ap_erback A thorough introduction to one of the most Edited by K.W MORTON and M.J. BAINES widely used and powerful computer Image ~estoration and Reviews recent advances in mathematical packages. and computational techniques for model­ Reconstruction 1988 144 pp.; 15 illus. ling fluid flows. R.H.T. BATES and M.J. McDONNELL cloth $39.95, paper $22.50 1989 552 pp.; 284 illus. $95.00 "Essential reading for anyone with a serious interest in restoration and reconstruction." Discrete Relaxation -Applied Optics Intelligent Systems in a 1986 304 pp.; 40 illus. Techniques Human Context paper $45.00, cloth $70.00 THOMAS C. HENDERSON Development, Implications, and Provides a firm foundation in relaxation Applications techniques and their applications. Edited by LINDA A. MURRAY and Cryptography and Coding May 1989 256 pp.; 60 ill us. $29.95 JOHN T.E. RICHARDSON Edited by HENRY J. BEKER Explores the relationship between user and and EC. PIPER Software Development machine, and the organizational context in A state-of-the-art account that will help read­ Fashioning the Baroque which intelligent systems are deployed. and store information effi­ $39.95 ers to produce, DARRELINCE 1989 192 pp.; 2 illus. ciently, securely, and cost -effectively. Explains why software is difficult to develop 1989 312 pp.; illus. $75.00 and discusses some of the solutions. Smooth Tests of Goodness 1989 176 pp.; illus. of Fit Introduction to Computing cloth $39.95, paper $17.95 J.C.W RAYNER and D.J. BEST with Pascal An introductory reference work that should the appeal to all professionals involved in statis­ NORMAN L. BIGGS Power Electronics for tical modelling. suited Microprocessor Age Unique introduction to Pascal; well 1989 224 pp.; 28 ill us. $45.00 for an introductory programming course. TAKASHI KENJO 1989 224 pp.; 20 i!lus. Explores the aspects and applications of mi­ cloth $45.00, paper $19.95 croprocessor-controlled electronic drives. Computer Engineering November 1989 320 pp.; 294 illus. $75.00 Circuits, Programs, and Data PETER P. SILVESTER and Project Universe DAVID A. LOWTHER An Experiment in High-Speed Functional Analysis, This introductory text includes software Computer Networking Optimization, and which allows students to test logic circuits J.W BURREN and C.S. COOPER Mathematical Economics and designs, and to examine the operation the design, construction, and test­ of a simple C.P.U. Describes LEV J. LEIFMAN ing of the experimental UNIVERSE informa­ 1989 416 pp.; 142 illus. $37.50 Examines the work of Leonid Kantorovich in tion technology network. the fields of optimization and mathematical 1989 304 pp.; 51 i!lus. $49.95 economics. To order, or for more information, please December 1989 288 pp.; 16 illus. $70.00 write: Biomolecular Data A Resource in Transition Machine Translation OXFORD Edited by RITA COLWELL How Far Can It Go? UNIVERSITY PRESS Examines both the strengths and shortcom­ MAKOTO NAGAO 200 MADISON AVENUE ings of today's databases, and explores a Translated by Norman D. Cook NEW YORK, NY 10016 variety of future proposals. A lucid, up-to-date account of the process of Attn: Marketing Director for Science and 1989 384 pp.; 26 illus. $64.00 machine translation systems. Medical Books 1989 168 pp.; 22 ill us. $35.00 Prices and publication dotes are subject to change. WILEY MATHEMATICS from THEORY to PRACTICE Examine any title free for 15 days!

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ELEMENTS OF COMPUTER ALGEBRA WITH APPLICATIONS A.G. Akritas, University of Kansas 1-61163-8 425pp March 1989 $46.95 INTRODUCTION TO THE INTRODUCTION TO MODERN THEORY OF ERROR­ SET THEORY FRACTAL GEOMETRY: CORRECTING CODES, 2nd Ed. Judith Roitman, University of Kansas Mathematical Foundations and 1-63519-7 250pp Aug. 1989 $39.95(tent) Applications Vera Pless, University of Dlinois - Chicago K.J. Falconer, University of Bristol, U.K. 1-61884-5 200pp Aug. 1989 $34.95 1-92287-0 224pp Dec. 1989 $33.95 THE FINITENESS PARTIAL DIFFERENTIAL OBSTRUCTION OF C.T.C. WALL K. Varadarajan, University of Calgary TOPOLOGY EQUATIONS OF APPLIED 1-62306-7 300pp Mar. 1989 $46.95 A Geometric Account of General MATHEMATICS, 2nd Ed. Topology, Homotopy Types and the Erich Zauderer, Polytechnic University Fundamental Groupoid 1-61298-7 89lpp June 1989 $64.95 ALGEBRA Ronald Brown, Univ. College of North Wales 2nd Ed., Volume II 0-21217-9 460pp Dec. 1988 $59.95 PRIMES OF THE FORM 2 + ny2 P.M. Cohn, University College London x 1-92234-X 428pp June 1989 $54.95 Fermat, Class Field Theory and ELLIPTIC SYSTEMS AND Complex Multiplication QUASICONFORMAL David A. Cox, Amherst College ABS PROJECTION 1-50654-0 256pp Oct. 1989 $42.95 MAPPINGS ALGORITHMS: H. Renelt, Martin Luther University, GDR Mathematical Techniques for Linear and 1-91731-1 146pp June 1989 $33.95 Nonlinear Equations MATHEMATICAL METHODS J. Abaffy, Karl Marx Univ. of Economics, Budapest FOR ENGINEERS E. Spedicato, Univ. of Bergamo, Italy LARGE ORDER R.K. Livesley, University of Cambridge, UK 0-21507-0 220pp Aug. 1989 $59.95 STRUCTURAL 0-21468-6 462pp Aug. 1989 $74.95 EIGENANAL YSIS FOUNDATIONS OF DISCRETE TECHNIQUES FIBONACCI AND LUCAS MATHEMATICS Algorithms for Finite Element Systems NUMBERS AND THE GOLDEN K.D. Joshi, Indian Institute of Technology N.S. Sehmi, Univeristy of Bristol 0-21152-0 748pp July 1989 $34.95 0-21497-X 223pp Aug. 1989 $84.95 SECTION: Theory and Applications S. Vajda, University of Sussex 0-21508-9 189pp July 1989 $64.95

Now in paperback! To order, write: JOHN WILEY & SONS, INC. U 605 Third Avenue, New York, NY 10158 DECISION THEORY Attn: Sharon Nelson, 5th Hoor An Introduction to the Mathematics WILEY of Rationality Simon French, University of Manchester To order by phone: Call TOLL-FREE: 1-800-526-5368 0-21090-7 448pp July 1988 $37.95(pb) All other inquiries, call: 212-850-6418 Prices subject to cfulnge without notice & higher in Canada ~------CambridgeUnwe~UyPress------The Theory and Applications of Harmonic Integrals !-Knots and Their Groups W. V. D. Hodge J.A. Hillman This book details the geometry of manifolds and the properties of integrals on The author draws on a variety of techniques, focusing on knots in 54, whose manifolds. It also examines the application of the theory of harmonic integrals fundamental groups contain abelian normal subgroups in order to attack certain to other branches of mathematics. problems in 4-dimensional knot theory. Cambridge Mathematical Ubrary Australian Mathematical Society Lecture Series 19891281 pp./35881-7/Paper $22.95 19891200 pp./37812-5/Paper $19.95 Functional Equations in Several Variables The Theory of Evolution and Dynamical Systems J. Aczel and J. Dhombres Mathematical Aspects of Selection This treatise deals with modern theory of functional equations in several vari­ J. Hofbauer and K. Sigmund ables and their applications to mathematics, information theory, and the natural, This textbook is an introduction to dynamical systems and its applications to behavioral and social sciences. evolutionary game theory, mathematical ecology, prebiotic evolution, and Encyclopedia of Mathematics and Its Applications population genetics. 1989/500 pp./35276-2/Hardca.~er $89.50 London Mathematical Sodety Student Texts 19881352 pp 135288-6/Hardcover $65.00 Fibrewise Topology 35838-8/Paper S19. 95 I.M.Jamtts This book will provide a solid and invigorating foundation for the increasing Volume 2: Analysis in Abstract Spaces research interest in fibrewise topology. Edited by E. Berkson and T. Peck Cambridge Tracts in Mathematics 91 London Mathematical Sodety Lecture Note Series $34.50 19891224 pp./36090-0/Hardca.~er $49.50 19891368 pp./36437-X/Paper Topology via Logic Now in paperback ••• StttYttn Vickers Commutative Ring Theory This advanced textbook on topology for computer scientists provides a more H. Matsumura direct approach than the traditional one based on abstracting properties of Cambridge Studies in Advanced Mathematics open sets in the real Iine. 79891330 pp./36764-6/Paper Si!4. 95 Cambridge Tracts in Theoretical Computer Science 19891120 pp./36062-5/Hardca.~er $39.50 Regular Variation N.H. Bingham, C.M. Goldie and J.L. Tcugcls Proofs and TYPes Encyclopedia of Mathematics and Its Applications J.-Y. Girard, Y. Lafont and P. Taylor 7989/572 pp./37943-7/Paper $34.50 This text deals with the mathematical background of the application to At bookstores or order from computer science of aspects of logic (namely the correspondence between proposition and types). Cambridge University Press Cambridge Tracts in Theoretical Computer Science 40 West 20th Street, NY. NY10011. Call toll-free, 800-872-7423, outsioe NY State. 800-227-0247, 19891250 pp./37181-3/Hardca.~er S34.50 NY State only MasterCard & VISA accepted. Prices subject to change.

REPRESENTATION THEORY AND NUMBER This volume contains the proceedings of the conference THEORY IN CONNECTION WITH THE LOCAL ""Representation Theory and Number Theory in Connection LANGLANDS CONJECTURE with the Local Langlands Conjecture," held in December 1985 at the University of Augsburg. The program of the J. Ritter, Editor conference was divided into two parts: (i) the representation (Contemporary Mathematics, Volume 86) theory of local division algebras and local Galois groups, The Langlands Program summarizes those parts of and the Langlands conjecture in the tame case: and (ii) new mathematical research belonging to the representation theory results, such as the case n = p, the matching theorem, of reductive groups and to class field theory. These two principal orders, tame Deligne representations, classification topics are connected by the vision that, roughly speaking, the of representations of GL(n), and the numerical Langlands irreducible representations of the general linear group may conjecture. The collection of papers in this volume provides an well serve as parameters for the description of all number excellent account of the current state of the local Langlands fields. In the local case, the base field is a given p-adic field Program. K and the extension theory of K is seen as determined by the irreducible representations of the absolute Galois group 1980 Mathematics Subject Classifications: 11537, 11540, 11545, GK of K. Great progress has been made in establishing 20G25, 22E50 correspondence between the supercuspidal representations ISBN 0-8218-5093-8, LC 88-39030 of GL(n, K) and those irreducible representations of GK ISSN 0271-4132 280 pages ( softcover), January 1989 whose degrees divide n. Despite these advances, no book Individual member $17, List price $28, or paper has presented the different methods used or even Institutional member $22 collected known results. To order, please specify CONM/86NA All prices subject to change. Shipment will be made by surface. For air delivery add, 1st book $5, each additional book $3, maximum $100. Prepayment required. Order from American Mathematical Society, P.O. Box 1571, Annex Station, Providence, RI 02901-1571, or call toll free 800-566-7774 to charge with VISA or MasterCard. DEAN Chairperson: College of Science Department The University of Texas at Arlington of Mathematics

The University of Texas at Arlington invites applicants and nominations for Dean of the College of Science. UTA is a major university NJIT seeks applications for chairperson of mathematics. The (enrollment 24,000) located in the center of the Dallas/Ft. Worth metropolitan area (three million population). The university is a member department offers: B.S. degrees in applied mathematics and of the University Research Associates consortium. The College of Science in statistics and actuarial science; M.S. degree in applied consists of the departments of Biology, Chemistry, Geology, Mathematics, mathematics; courses which support other university Physics, and Psychology and offers a wide range of bachelors, masters and doctoral degrees. The college currently has 120 faculty, 550 graduate curriculum. Qualifications: earned doctorate in mathematics students and 2150 undergraduates. or closely related field; documented teaching, research, Applicants should have an earned doctorate and credentials suitable for a administrative and leadership experience. tenured faculty appointment in one of the departments in the college. The successful applicant will be expected to lead a strong research and New Jersey Institute of Technology is a comprehensive educational program, and should possess exceptional qualities of leadership technological university with approximately 7, 700 students and technical strength as well as demonstrated communication and managerial skills. The new dean should be prepared for a unique enrolled in baccalaureate through doctoral programs within opportunity to lead a significant expansion in personnel and facilities due to Newark College of Engineering, the College of Science and the needs of the rapidly developing North Texas area, including the Liberal Arts, the School of Architecture and the School of anticipated establishment of the nearby superconducting supercollider. Inquiries and letters of application, accompanied by a curriculum vita, Industrial Management. should be sent to: NJIT does not discriminate on the basis of sex, race, color, Prof. Robert Mitchell Dean of Science Search Committee handicap, religion, national or ethnic origin or age in employment. Box 19016 University of Texas at Arlington Send resume by Nov. 30, 1989 to: Personnel Box M. Arlington, Texas 76019 (telephone: 817-273-3472; fax: 817-273-2548).

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THE BASIC THEORY OF Bei der Technischen Universitat Berlin ist fol­ REAL CLOSED SPACE gende Stelle zu besetzen: Niels Schwartz (Memoirs of the AMS, Number 397) Universitiitsprofessorf-professorin- BesGr. C 4- Through Grothendieck's Elements de geometrie algebrique, f.d. Fachgebiet "Mathematik" classical algebraic geometry became part of the theory of schemes. Informally speaking, this book seeks to establish Fachbereich 3 - Mathematik that a similar embedding of semialgebraic geometry into a more general theory should also be possible. The author Kennziffer: 3 - 505 (Bewerbungsfristende 15.1 0.89) generalizes locally semialgebraic spaces by real closed Aufgabengebiet: Wahrnehmung von Forschung und Lehre spaces, a class of locally ringed spaces. The underlying auf dem Gebiet der Mathematik, insbes. Lehre in Algebra spaces of affine real closed spaces are real spectra of rings, fiir Studenten im Hauptstudium; Beteiligung an der Lehre and the structure sheaves are called real closed sheaves. The fiir andere Studiengange author shows that there is a natural functor from the category of semialgebraic spaces to the category of real closed spaces. Anforderungen: Erfiillung der Berufungsvoraussetzungen gem. In this way, functorial properties of semialgebraic spaces and §100 Ber!HG (Merkblatt wird auf Wunsch zugesandt); die their corresponding real closed spaces can be compared. Arbeitsrichtung des kiinftigen Stelleninhabers soli im Be­ 1980 Mathematics Subject Classifications: 14G30; 14A04, 14A15, reich AlgebrafZahlentheorie unter Einbeziehung computer­ 12J15, 13J25, 06F25 gestiitzter Methoden liegen; die Zusammenarbeit mit an­ ISBN 0-8218-2460-0, LC 88-8168 deren Fachgebieten wird erwartet. ISSN 0065-9266 132 pages (softcover), January 1989 Individual member $10, List price $16, Schwerbehinderte werden bei gleicher Qualifikation bevorzugt. Institutional member $13 To order, please specify MEM0/397NA Ihre schriftliche Bewerbung richten Sie bitte unter Angabe der Kennziffer mit den iiblichen Unterlagen an den Prasidenten All prices subject to change. Shipment will be made by surface. For der Technischen Universitat Berlin - II A 13 - StraBe des air delivery add, 1st book $5, each additional book $3, maximum $100. 17. Juni 135, 1000 Berlin 12. Prepayment required. Order from American Mathematical Society, P.O. Box 1571, Annex Station, Providence, RI 02901-1571, or call toll free 800-566-7774 to charge with VISA or MasterCard. t..;.;.; .... •:·:·:·:·:·.·.·.•,•,·.·.·:·:·:·:·.·:·:·:·:·:·:·:·:·:·:·:·.·:·:·:·:·:·:·:·.·:·:·.·:·:·:·:·:·:·.·:·:·:·:·:·:·:·:·:·:·:·:·:·:·:·:·:·:·:·:·:·:·:·:·:·:·:·.·:·:·:·:·:·:·:·:·:·:·:·:·:·:·:·.·=·.·.·=·=·=·:·:·:·:·:·:·:·.·:·:·:·:·:·:·:·:·:·:·:·:·:·:·.·:·:·.·:·.·.J ICM-90 SPECIAL FORM REQUEST FOR SECOND ANNOUNCEMENT

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Topics in Field Theory Topological Fields by G. Karpilovsky byS. Warner

(North-Holland Mathematics Studies, 155) (North-Holland Mathematics Studies, 157)

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This monograph gives a systematic account of certain Aimed at those acquainted with basic point-set topology important topics pertaining to field theory, including the and algebra, this text goes up to the frontiers of current central ideas, basic results and fundamental methods. research in topological fields (more precisely, topological rings that algebraically are fields). The reader is given Avoiding excessive technical detail, the book is intended for enough background to tackle the current literature without the student who has completed the equivalent of a undue additional preparation. Many results not in the text standard first-year graduate algebra course. Thus it is (and many illustrations by example of theorems in the text) assumed that the reader is familiar with basic ring-theoretic are included among the exercises. Sufficient hints for the and group-theoretic concepts. A chapter on algebraic solution of the exercises are offered so that solving them preliminaries is included, as well as a fairly large does not become a major research effort for the reader. bibliography of works which are either directly relevant to A comprehensive bibliography completes the volume. the text or offer supplementary material of interest.

Contents: Algebraic Preliminaries. Separable Algebraic Extensions. Transcendental Extensions. Derivations. Purely Graph Colouring and Variations Inseparable Extensions. Galois Theory. Abelian Extensions. Radical Extensions. Bibliography. Index. edited by D. de Werra and A. Hertz

Reprinted from the journal Discrete Mathematics, Vol. 74, Clifford Theory for Group Nos. 1-2

Representations (Annals of Discrete Mathematics, 39) by G. Karpilovsky 1989 vi + 262 pages Price: US $92.00/Dfl. 175.00 (North-Holland Mathematics Studies, 156) ISBN 0-444-70533-3

Graph colouring has been an attractive field for some years, 1989 viii + 364 pages with many papers dealing with the study of chromatic Price: US $110.50/Dfl. 210.00 properties of graphs. As people were becoming used to ISBN 0-444-873n-5 applying the tools of graph theory to the solution of real-life organizational problems, chromatic models appeared as a Let N be a normal subgroup of a finite group G and let F be natural way of tackling many situations. Contributions by a field. An important method for constructing irreducible leading researchers in the area of graph colouring have FG-modules consists of the application (perhaps repeated) been collected in this volume. These include many of three basic operations: extensions of results which are scattered over various areas. (I) restriction to FN. Such variations and extensions provide interesting models (li) extension from FN. for a large collection of combinatorial problems in areas (iii) induction from FN. such as scheduling, cluster analysis, production, and flexible manufacturing systems. This is the 'Oifford Theory' developed by Clifford in 1937. In the past twenty years, the theory has enjoyed a period of vigorous development. The foundations have been strengthened and reorganized from new points of view, especially from the viewpoint of graded rings and crossed products. NORTH-HOLLAND The purpose of this monograph is to tie together various In the USA and Canada: threads of the development in order to give a Elsevier Science Publishing Co. Inc. comprehensive picture of the current state of the subject. P.O. Box 886, Madison Square Station, New York, NY 10159, USA It is assumed that the reader has had the equivalent of a standard first-year graduate algebra course, i.e. familiarity For all other countries: with basic ring-theoretic, number-theoretic and Elsevier Science Publishers group-theoretic concepts, and an understanding of Book Order Department, elementary properties of modules, tensor products and P.O. Box 211, 1000 AE Amsterdam, fields. The Netherlands

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G.E.Sacks Y.lhara, K. Ribet and J.-P. Serre (Eds.) Higher Recursion Theory Galois Groups Over Q Hyperarithmetical theory is developed at length and used to Contains key original papers by experts in the field, and treats list classical recursion theory from integers to recursive a variety of questions in arithmetical algebraic geometry. A ordinals (metarecursion). Two further liftings are then made, number of the contributions discuss Galois actions on fun­ first ordinals (a-recursion) and then to sets (E-recursion). damental groups, and associated topics: these include Fermat Techniques such as finite and infinite injury, forcing and fine curves, Gauss sums, cyclotomic units, and motivic questions. structure are extended and combined. Dynamic and syntacti­ Other themes which reoccur include semistable reduction of cal methods are contrasted. Several notions of reducibility algebraic varieties, deformations of Galois representations, and computation are compared. Post's problem is answered and connections between Galois representations and modular affirmatively in all three settings. forms. 1989/352 pp./Hardcover $89.00/ISBN 0-387-19305-7 1989/449 pp., II illus./Hardcover $45.00/ISBN 0-387-97031-2 Perspectives in Mathematical Logic Mathematical Sciences Research lnstittlle Pul>lications. Volume 16

D.M. Bressoud I.R. Shafarevich Factorization and Primality Testing Collected Mathematical Papers This self-contained book is about how to factor or prove This collection, which contains almost all of Shafarevich's primality for large numbers; it is also an introduction to the papers, reflects his broad mathematical interest. Included are theory of numbers. Intended for upper-level undergraduates topics such as the proof of the general reciprocity law, the in mathematics and computer science, the book aims to intro­ realization of groups as Galois groups of number fields, class duce current research, give an appreciation for the results that field towers, algebraic surfaces (in particular K3 surfaces), have tx;,en produced throughout the history of number theory, elliptic curves, and finiteness results on abelian varieties, and get students using the computer to factor and prove algebraic curves over number fields and Lie algebras. Notes primality. Currently, no introduction to this area is as up-to­ by Shafarevich at the end of the volume contain corrections date or as accessible to the non-specialist. and remarks on the subsequent development of the subjects 1989/app. 272 pp., 2 illus.!Hardcover $45.00/ISBN 0-387-97040-1 considered in the papers. Undergraduate Texts in Mathematics 1989/769 pp./Hardcover $99.00/ISBN 0-387-13618-5

I.L. Kantor and A.S. Solodovnikov G.W. Bluman and S. Kumei Hypercomplex Numbers Symmetries and Differential An Elementary Introduction to Algebras Equations translated from the Russian by A. Shenitzer Provides a comprehensive treatment of Lie groups of trans­ Organized in three parts, this book is a basic core introduc­ formations and thorough discussions of basic symmetry tion to algebras. The first of its three parts familiarizes the methods for solving ordinary and partial differential equa­ reader with examples of algebras, including the quatemions tions. Emphasis is placed on explicit computational algo­ and the Cayley numbers. The second part is an elementary rithms to discover symmetries admitted by differential exposition of the fundamental concepts of linear algebra and equations and to construct solutions resulting from sym­ is of an auxiliary nature. The third part explains the unique metries. Concrete examples are taken from physical and role of the complex numbers, the quatemions and the Cayley engineering problems including many concerned with wave numbers as the only real division algebras (other than the propagation, heat conduction, and fluid flows. reals themselves). 1989/412 pp., 21 illus.!Hardcover $54.00/ISBN 0-381-96996-9 1989/169 pp.!Hardcover $39.80/ISBN 0-387-96980-2 Applied Mathematical Sciences. Volume 81

D.A. Buell Ordering Information: Call Toll-Free: 1-800-SPRINGER (In NJ call 201-348-4033) Or $end Binary Quadratic Forms FAX: 201-348-4505. For mail orders, send payment plus $2.50 f.:>r Classical Theory and Modem Computations postage and handling to: Springer-Verlag New York, Inc., Attn: S. Klarnkin - Dept. S308, 175 Fifth Avenue, New York, NY Covers the basic theory of binary quadratic forms, emphasiz­ 10010. We accept Visa, MC, and Amex charges (with signature and ing computational and algorithmic aspects, and summarizes exp. date noted) as well as personal checks and money orders. NY. ongoing computations with forms, including both applica­ NJ and CA please include state sales tax. tions and the as-yet-unproved heuristics gained from the extensive computations of the last few years. Some number theory is required as a prerequisite including the usual material on congruences, quadratic residues, and the reciprocity laws. This book is intended to be understandable Springer-Verlag by advanced undergraduates in mathematics or computer New York Berlin Heidelberg Vienna science. London Paris Tokyo Hong Kong 1989/243 pp.!Hardcover $35.00/ISBN 0-387-97037 -I