Calendar of AMS Meetings and Conferences
Providence, Rhode Island, USA ISSN 0002-9920 Calendar of AMS Meetings and Conferences
This calendar lists all meetings and conferences approved prior to the date this insofar as is possible. Abstracts should be submitted on special forms which are issue went to press. The summer and annual meetings are joint meetings of the available in many departments of mathematics and from the headquarters office of Mathematical Association of America and the American Mathematical Society. The the Society. Abstracts of papers to be presented at the meeting must be received meeting dates which fall rather far in the future are subject to change; this is par at the headquarters of the Society in Providence, Rhode Island, on or before the ticularly true of meetings to which no numbers have been assigned. Programs of deadline given below for the meeting. The abstract deadlines listed below should the meetings will appear in the issues indicated below. First and supplementary be carefully reviewed since an abstract deadline may expire before publication of announcements of the meetings will have appeared in earlier issues. Abstracts a first announcement. Note that the deadline for abstracts for consideration for of papers presented at a meeting of the Society are published in the journal Ab presentation at special sessions is usually three weeks earlier than that specified stracts of papers presented to the American Mathematical Society in the issue below. For additional information, consult the meeting announcements and the list corresponding to that of the Notices which contains the program of the meeting, of special sessions. Meetings
Abstract Program Meeting# Date Place Deadline Issue 876 • October 30-November 1, 1992 Dayton, Ohio Expired October 877 • November 7-8, 1992 Los Angeles,California Expired October 878 • January 13-16, 1993 San Antonio, Texas October 8 December (99th Annual Meeting) 879 • March 26-27, 1993 Knoxville, Tennessee January 5 March 880 • April9-10, 1993 Salt Lake City, Utah January 29 April 881 • April17-18, 1993 Washington, D.C. January 29 April 882 • May 21-22, 1993 DeKalb, Illinois February 26 May-June 883 • August15-19, 1993 Vancouver, British Columbia May 18 July-August (96th Summer Meeting) (Joint Meeting with the Canadian Mathematical Society) 884 • September 18-19, 1993 Syracuse, New York May 18 September 885 * October 1-3, 1993 Heidelberg, Germany (Joint Meeting with the Deutsche Mathematiker-Vereinigung e.V.) October 22-23, 1993 College Station, Texas January 12-15, 1994 Cincinnati, Ohio (1 OOth Annual Meeting) March 18-19, 1994 Lexington, Kentucky March 25-26, 1994 Manhattan, Kansas June 16-18, 1994 Eugene, Oregon October 28-29, 1994 Stillwater, Oklahoma January 25-28, 1995 Denver, Colorado (1 01 st Annual Meeting) March 24-25, 1995 Chicago, Illinois January 10-13, 1996 Orlando, Florida (1 02nd Annual Meeting) March 22-23, 1996 Iowa City, Iowa * Please refer to page 760 for listing of Special Sessions. Conferences
January 11-12, 1993: AMS Short Course on Wavelets and Applications, San Antonio, Texas. Deadlines
November Issue December Issue January Issue February Issue Classified Ads* October 1 , 1992 November 13, 1992 December 10, 1992 January 7, 1993 News Items September 21, 1992 October 29, 1992 December 2, 1992 December 24, 1992 Meeting Announcements** September 21, 1992 October 29, 1992 December 2, 1992 December 24, 1992 • 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
DEPARTMENTS ARTICLES 683 Letters to the Editor 694 Forum 684 Deane Montgomery (1909-1992) Armand Borel 715 News and Announcements This article pays tribute to the life and career of former AMS President 724 Funding Information for the Deane Montgomery, a distinguished topologist and longtime member of the Mathematical Sciences Institute for Advanced Study. 725 Acknowledgment of Contributions 688 Sloan Foundation Joins AMS to Aid Mathematics in the former Soviet Union 745 1992 AMS Elections Biographies of Candidates, 746 The Sloan Foundation has awarded the Society a $30,000 challenge grant to support the AMS program to assist mathematics in the former 755 Meetings and Conferences of Soviet Union. Allyn Jackson describes the assistance program, and an the AMS accompanying announcement provides information on how to contribute to Dayton, OH this important effort. Ocrober3G-November1, 755 Los Angeles, CA 689 European Meetings Bring Mathematicians Together November 7-8, 758 Invited Speakers, 760 A number of historic ''firsts" took place in Europe this summer-the joint 1992 Symposium on Some AMS meeting with the London Mathematical Society in Cambridge, England; Mathematical Questions the opening of the Isaac Newton Institute in Cambridge; and the first in Biology, 764 European Congress of Mathematics, held in Paris. Allyn Jackson reports on San Antonio, TX these events. January 13-16, 765 767 Mathematical Sciences Meetings FEATURE COLUMNS and Conferences 776 New Publications Offered by the 696 Computers and Mathematics Keith Devlin AMS Andrew Granville writes an expository article based on his paper There are 781 AMS Reports and infinitely many Carmichael numbers, cowritten with Red Alford and Carl Communications Pomerance. Following Granville's piece, Barry Simon presents the results Statistics on Women, 781 of a series of benchmark tests he has run on a number of computer Officers and Committee Members, mathematics systems. 782 783 Miscellaneous 711 Inside ~he AMS Personal Items, 793 Alice Schafer, Chair of the AMS Committee on Human Rights of Deaths, 793 Mathematicians, reports on the Committee's activities and accomplishments 794 Classified Advertising over the past two years. 809 Forms 712 Washington Outlook Lisa Thompson discusses how the government allocates resources among the various elements of the scientific enterprise.
SEPTEMBER 1992, VOLUME 39, NUMBER 7 681 ------·········· ......
From the Executive Director ...
RESOURCES FOR EXCELLENCE
AMERICAN MATHEMATICAL SOCIETY There have been numerous national reports pointing out the need for the renewal of academic mathematical sciences departments. The reports call upon the departments to maintain the tradition of first class research; reform mathematics education at all levels; revise the curriculum to introduce experimental classes, varied instructional approaches, and new technologies; become involved in teacher enhancement and preparation; en EDITORIAL COMMITIEE gage in interdisciplinary activity and university service; increase the participation of Michael G. Crandall underrepresented minorities and women; and contribute to economic competitiveness. Amassa Fauntleroy This is only a partial list. Information is available, in varying degrees of detail and Robert M. Fossum (Chairman) clarity, as to how to go about doing all these things. Carolyn S. Gordon (Forum Editor) D. J. Lewis These reports have been useful in providing a springboard for debate, in distributing L. Ridgway Scott (Letters Editor) important information, and in outlining means for change. However, it is time to move Robert E. L. Turner beyond the reports and into action, and mathematical sciences departments are the natural institutions to take actions to bring about substantial, long-term change within MANAGING EDITOR the community. There is general agreement on what needs to be done, and there are John S. Bradley laudable examples of activities of individuals, groups, and departments that are doing ASSOCIATE EDITORS exciting things. But, is the academic mathematical sciences community positioned to Ronald L. Graham, Special Articles respond? Does this community have the resources (or the political sophistication to get Jeffrey C. Lagarias, Special Articles them) necessary to meet these challenges and opportunities?
SUBSCRIPTION INFORMATION Mathematical sciences departments, on the whole, are not viewed as major players Subscription prices for Volume 39 (1992) are in acquiring academic resources. There is a history of little attention being paid to the $131 list; $105 institutional member; $79 individ political avenues by which mathematical sciences departments might position them ual member. (The subscription price for members selves more favorably. The current challenges and opportunities come at a time when is included in the annual dues.) A late charge of there is a shortage of federal research funds and there is a depressed economy that is af 10% of the subscription price will be imposed upon fecting academic finances. Indeed, department resources are vulnerable to serious cuts. orders received from nonmembers after January 1 Distressed departments cannot respond adequately to the new challenges confronting of the subscription year. Add for postage: Surface them. Faculty, staff (including technical assistance), appropriate space, computers and delivery outside the United States and lndia-$15; networking, libraries, instructional labs, and research and travel funds are just some of to lndia-$28; expedited delivery to destinations in for departments to respond to the recommendations that are North America-$32; elsewhere-$67. Subscrip the resources necessary tions and orders for AMS publications should be being made. How can we make the case for adequate academic resources for mathemat addressed to the American Mathematical Society, ics? How does a department determine what will work or, recognizing the limitations P.O. Box 1571, Annex Station, Providence, Rl on its resources, what resources are needed to be successful in meeting the challenges? 02901-1571. All orders must be prepaid. These are issues that the reports leave unanswered.
ADVERTISING The mathematical sciences are generally seen as important to education, research, Notices publishes situations wanted and classified and the mission of the university. In addition, there is widespread concern over low advertising, and display advertising for publishers student retention in entry-level mathematics courses because it affects not only science and academic or scientific organizations. and engineering career paths, but also overall retention at the university. However, Copyright@ 1992 by the American Mathematical these points will not suffice to make the case for improving resources for mathematical Society. All rights reserved. Printed in the United sciences departments. We need solid evidence with data and arguments about what States of America. works and what does not work. We need to set forth measurable expectations and The paper used in this journal is acid-free and falls articulate the case that changes will result from increased resources. within the guidelines established to ensure perma The Society is engaged in an intense examination of how it might be able to help nence and durability. § Most of this publication was typeset using the TEX typesetting system. the academic mathematical sciences community confront these issues. Can we provide information and assistance to academic departments in planning and in articulating the [Notices of the American Mathematical Society is published monthly except bimonthly in May, June, case for necessary resources? July, and August by the American Mathematical So An AMS Task Force is being formed to address these questions and to try to Rl 02904- ciety at 201 Charles Street, Providence, provide academic departments with a description of what activities are finding success 2213. Second class postage paid at Providence, departments face. It is expected Rl and additional mailing offices. POSTMASTER: and what resources are necessary to meet the challenges Send address change notices to Notices of the that usable data will be part of the outcome of this work. The Task Force will be working American Mathematical Society, Customer Service with other organizations in order to coordinate related activities. Continued coverage Department, American Mathematical Society, P. 0. of the work of the Task Force will be in the Notices. The community's advice and Box 6248, Providence, Rl 02940-6248.] Publica comments are needed and welcome. tion here of the Society's street address, and the other information in brackets above, is a technical requirement of the U. S. Postal Service. All corre spondence should be mailed to the Post Office Box, William Jaco NOT the street address. Tel: 401-455-4000.
682 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY left deliberately vague just as the ac Again it is very much like the letters to Letters cusation in "anti-sovietism" so familiar Sakharov in USSR; "I have not read this to me. Still you do not try to make slander but I despise it ..." to the Editor your accusations precise. Change "anti My last question is to the people semitism" to "anti-sovietism" and your who signed the letter and whom I knew letter will become one of those hatred 15 or 20 years ago as soviet mathemati letters in our country 20 years ago. cians. Living in USSR they witnessed Shafarevich Responds You predict the effect of my paper the deportation of Solzhenitzin, exile of to Open Letter on my interactions with other mathe Sakharov, persecution of religion, deten Editor's Note: The following is are maticians. Are you authorized by them tion of sane persons in psychiatric hos sponse to the Open Letter to I. R. Sha to express their feelings? In those letters pitals for political reasons. We haven't farevich which appeared in the adver in our country the authors also usually heard their protests against it then. Do tisements section of the March 1992 is used to speak on behalf of "Progres they really believe that my paper is more sue of the Notices. Both the Open Letter sive mankind" or at least "All soviet dangerous? and the response below refer to Sha scientists" Respectfully yours, farevich's workRussophobia [published Without burdening yourself with ar I. R. Shafarevich by the Russischer Nationaler Verein, guments, you demand my public dis Mathematical Institute of the Miinchen, Germany, 1989; the latest ver claimer of my views (which you call Russian Academy of Sciences sion was published by Sovietskii Pisatel, "anti-semitic polemic")-that is the pro (Received July 20, 1992) Moscow, 1991] cedure that was so common during the Dear Colleagues, purges under the communist regime in Letters to the Editor I was deeply upset by your letter. the USSR. Letters submitted for publication in the Notices In the years of our dissident struggle You attribute to me the "conspira are reviewed by the Editorial Committee. do not The Notices does not ordinarily publish com in the USSR, many of us looked at the torial theory" which I certainly plaints about reviews of books or articles, al U.S. as a kind of "Existenzbeweis"-a share (if only you do not broaden the though rebuttals and correspondence concerning proof of existence of solution of the notion of "conspiracy" in such a way reviews in Bulletin ofthe American Mathematical problem we aimed to solve: to establish as to consider e.g.; the annihilation of Society will be considered for publication. Letters should be typed and in legible form or a society where speech and thought North American Indians to be a conspir they will be returned to the sender, possibly re are free. Unfortunately this letter of acy of English settlers). You certainly sulting in a delay of publication. All published let yours reminds me of numerous letters could see it from my paper, should you ters must include the name of the author. Letters in our country to Solzhenitzin, read it. But I have serious doubts about which have been, or may be, published elsewhere addressed will be considered, but the Managing Editor of the Pasternak, and Sakharov at that time. many .of you having read it. I know Notices should be informed of this fact when the Not that I compare myself with one of personally many of those signed the letter is submitted. those people, but the whole spirit of the letter who do not read Russian. While The committee reserves the right to edit let ters. letter is the same. there is only a pirate English translation Letters should be mailed to the Editor of the For instance you allude to "anti of the paper-without my authorization Notices, American Mathematical Society, P. 0. semitic" sentiment in my paper. In and supervision, I leave it to you to de Box 6248, Providence, RI 02940, or sent by email this paper I tried to show that "anti cide about the legal and moral character to [email protected], and will be acknowl edged on receipt. semitism" is an empty political slogan of such edition and about references to it.
SEPTEMBER 1992, VOLUME 39, NUMBER 7 683 Deane Montgomery 1909-1992
Deane Montgomery was born on September 2, 1909, in His thesis adviser had been E. W. Chittenden, and he Weaver, Minnesota. He received a B.A. from Hamline Uni had a solid background in real analysis and point set topol versity in 1929, a M.S. in 1930 and a Ph.D. in 1933 from the ogy. His initial research interests focused on the latter, to University of Iowa. which he devoted his first four papers. In the tradition of After having held various fellowships at Harvard Uni L. E. J. Brouwer and "Polish topology", they already show versity, Princeton University, and the Institute for Advanced considerable technical strength and expertise. As soon as he Study, he went to Smith College, where he was successively came to Harvard and Princeton, he broadened his interests, assistant professor (1935-1938), associate professor (1938- first to algebraic or geometric topology (initially on his own 1941), and professor (1941-1946). During that period, he and in a private study group including N. Steenrod and Garrett was also a Guggenheim fellow at the Institute and a visiting Birkhoft), and then gradually to transformation groups, which associate professor at Princeton University. After two years became his major interest for the rest of his career. at Yale University as an associate professor (1946-1948), he His first papers in that area, many written in collaboration came to the Institute, where he was a permanent member from with Leo Zippin, were in part in the spirit of earlier work of 1948 to 1951 and a professor from 1951 to 1980, at which Brouwer and Kerejarkto, aiming at characterizing groups of time he became emeritus. familiar euclidean motions such as translations or rotations by topological conditions. They were motivated by questions on the foundations of geometry and, foremost, by Hilbert's fifth problem. In the broad sense, the latter asks, given a locally euclidean topological group acting effectively (i.e., no element =11 acts trivially) on an analytic manifold, whether coordinates can be introduced to make the group and the operation analytic (the answer is no). In its narrow sense, it asks whether a locally euclidean topological group is, after a suitable change of coordinates, a(n analytic) Lie group. Variants of the first problem and the second one became points of major interest in the next fifteen years or so, but not of sole interest, though. Among Deane's contributions to the first question, let me mention the following results pertaining to a (separable metric) locally compact group G acting effectively on a manifold M: (i) If G is compact, M analytic, and each transformation is analytic, then G is a Lie group (1945); (ii) (with S. Bochner, 1946). If M is CJl and every transformation is 0 2, and no element =11 leaves pointwise fixed a nonempty open subset, then G is a Lie group; (iii) (with S. Bochner, 1947). If M is a compact complex analytic manifold and G the group of automorphisms of M, then G is a complex Lie group acting holomorphically. On the fifth problem proper, after a series of papers with L. Zippin, Deane gave a positive solution in dimension three (1948). Then came shortly afterwards the decisive results proved jointly with L. Zippin: The existence of a closed subgroup isomorphic to IR in a locally compact, noncompact, connected, separable metric group of strictly
684 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ·-·-···--·-·--··--·-··--····... ··-··-···---··-··-···--·············-····--·--·······-······ ························~:11111111171111111111111111-1111111111111111-IIIIIIIIIIIIIIIIIIJ!lilMIIIIIilll!llill;7t-mmE······ ...... Deane Montgomery positive finite dimension (1951) (also established by A. kept up with the great advances of differential topology and Gleason) and then the reduction to groups without small soon veered more and more to differentiable actions, adapting subgroups (1952). Since A. Gleason had just proved that such techniques and points of view of differential topology. This a group is a Lie group, that gave a positive answer to Hilbert's led to his last major effort, a long series of joint papers with C. fifth problem. In fact, the whole investigation had been carried T. Yang on free or semi-free (i.e., free outside the fixed point out for separable metric finite-dimensional locally compact set) actions of the circle group on homotopy 7-spheres, which groups and it was shown more generally that such a group is a produced notably many interesting examples of homotopy "generalized Lie group", i.e., possesses an open subgroup that complex projective 3-spaces (1966-1973). is a projective limit of Lie groups, hence is a Lie group if it During his tenure as a professor at the Institute, Deane is locally connected. The assumption of finite dimensionality was at the center of activity in topology (algebraic, geometric, was soon removed by H. Yamabe, who was Deane's assistant differential), one of the highlights in the life of the School, at the time. first by his seminar, a perennial feature and a meeting ground This was the climax of a major effort and, as I remember for topologists in the Princeton community, but also in more it, some people were mildly curious to see where Deane would informal ways. He frequently organized seminars in his turn, now that this big problem had been solved. But he did not office, usually with some younger members with whom he have to look around at all. Apart from writing with L. Zippin would go through some recent developments. He was always a systematic exposition of the work on the fifth problem seeking out and encouraging young mathematicians. He and (1955), he just went back full time to what was really his main his wife Kay would regularly and very warmly receive the interest (and is already the subject matter of the last chapter visiting members at their home. Maybe remembering his own of that book): Lie groups (especially compact Lie groups) of beginnings in an out of the way place, he had a special transformations on manifolds, so that, in the context of his interest, and talent, in finding out people with considerable whole work, the contributions of the fifth problem appear potential among some applicants from rather isolated places almost as a digression, albeit a most important one. about whom not much information was available. Even during that hot pursuit, Lie transformation groups His concern for the Institute went far beyond his immediate were very much on his mind, and he brought a number of scientific interests and was all encompassing. He had a very interesting contributions, in particular in joint works with L. high view of the role the Institute should play and served Zippin and with H. Samelson. In fact, two papers with H. this ideal with unwavering and thoroughly unselfish loyalty. Samelson on compact Lie groups transitive on spheres or tori In day to day contacts, he was very kind, informal, full of (1943) have a special place in my memory: When I was an understanding, always ready to help, and struck one as a very assistant in ZUrich, H. Hopf once gave me copies of them, mild person, but deceptively so for anyone who, in his eyes, and I could generalize and sharpen some of their results. This would threaten the Institute's standards, and who would then led to my first single author paper, which I submitted for soon see rising an iron-willed and formidable opponent. His publication in the Proceedings of the AMS to Deane, then an care for the highest standards at the Institute, later gratefully editor; my first contact with him. acknowledged in citations by the Trustees, was not always The general problem in transformation groups is, roughly, universally understood or shared at the time, so that he and to relate the structures of the group G, the manifold M like-minded colleagues had to weather some rather stormy operated upon, the orbits, fixed points, and the quotient space. moments, during which he was totally unshakable. At the time, there was one body of special, but deep, work, His abiding interest in the welfare of mathematics also led that of P. A. Smith on homeomorphisms of prime power order him to accept a number of official positions. In particular, he of homology spheres or acyclic spaces. Very little was known was Vice President (1952-1953), elected Trustee (1955-1961) otherwise, and Deane was a prime mover in the development and President (1960-1963, includes terms as President-Elect of a general theory, which he pushed in many directions. He and Ex-President) of the AMS, where he also served on a and various collaborators proved a number of foundational number of committees, and President of the International results, as well as more special ones, which often opened up Mathematical Union (1974-1978). fruitful directions for others. A survey of these contributions Honors, too, came his way: Honorary Doctor of Science and of work they led to is given by F. Raymond and R. Schultz from Hamline University (1954), Yeshiva University (1961), in the Proceedings of a Conference honoring Deane on his the University of lllinois (1977), and the University of 75th birthday (Contemporary Mathematics, vol. 36 (1983)), Michigan (1986), as well as a Doctor of Laws degree from and I shall not try to duplicate it. It ranges from basic results Tulane University (1967); election to the National Academy such as the existence of a slice (with C. T. Yang, 1957), of Sciences in 1955, to the American Academy of Arts and a powerful tool to study a group action near an orbit, the Sciences, and the American Philosophical Society in 1958; existence of a principal type of orbits (with C. T. Yang, 1958), and receipt of the Steele Prize of the AMS in 1988. to more special ones, such as actions on euclidean space or Deane was an early riser and it was a rare event for anyone spheres with orbits of small codimension or the existence to be at the Institute before him. Being very gregarious, he of smooth actions of 803 on euclidean space without fixed talked to practically everybody working in any capacity at the points (with P. E. Conner, 1962). In a first phase, the emphasis Institute, which won him the respect and affection of members was on continuity, i.e., on topological properties, but Deane and staff alike and gave him an exhaustive knowledge of the
SEPTEMBER 1992, VOLUME 39, NUMBER 7 685 ···········--·----····-·---·-·····-····---·····-·-·······-·····-·.. ·········-·········· ...... _...... ______...... _...... ______...... ··················--·-······ .. ······· Deane Montgomery
Institute. Through 0. Veblen, to whom he had been very close knocking at his door, sure to find him, to have a chat, mostly during the latter's late years, it reached to the very beginnings about mathematics, mathematicians, and Institute affairs. That of the Institute so that he was a walking encyclopedia on all I have not been able to do so after his departure has left for aspects of the Institute's history and operations. me a void which could not be filled. In 1988, he and Kay moved to Chapel Hill, NC to be Deane died in his sleep in Chapel Hill, on March 15, 1992. close to their daughter and granddaughters. That prospect did He is survived by his wife, his daughter Mary Heck, and two not fully compensate for the severance of the ties with an granddaughters. institution which had meant and still meant so much to him, and it was altogether a rather sad occasion, the sadness of Armand Borel which was hardly mitigated by promises to keep in touch. Institute for Advanced Study Being myself a fairly early riser, I often started my day by
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operations Analysis "His straightforward narrative lets the story tell itself and the chips fall in the U.s. ArmY where they may. The individual accounts let us hear the voices of the Eighth Air Force characters. Tragic anecdotes emerge. Personality conflicts over strategy in world warn resulted in lost lives. Errors in judgement are made. Politics sometimes CharleS W. McArthur prevailed over strategy. Inspirational stories are there too, of those whose contribution to the war was their intelligence, honesty and perseverance. Good ideas did not become strategy by themselves .... This fascinating book is not of math, but of men." -Jerome Stem, Tallahassee Democrat Published jointly with the London Mathematical Society, McArthur's book offers a careful, readable study of an important slice of history on both World War II and operations analysis one you won't find anywhere else.
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SEPTEMBER 1992, VOLUME 39, NUMBER 7 687 Sloan Foundation Joins AMS to Aid Mathematics in the Former Soviet Union
As reported in the July/August 1992 issue of the Notices (pages Institute is a gathering place for researchers and students in 557-558), the Society has launched the AMS fSU Aid Fund to the mathematical sciences. On the governing board are Pierre provide assistance to the mathematical sciences community of Deligne of the Institute for Advanced Study, Vladimir Drinfeld the former Soviet Union. Because of political and economic of the Institute of Low-Temperature Physics in Kharkov, crises in the former Soviet Union and Eastern Europe, Ukraine, and Alexander Beilinson and Robert MacPherson the distinctive traditions and future promise of this prolific of the Massachusetts Institute of Technology. Its staff will community could all but disappear without international be comprised of a few permanent members, some three-year assistance. There have been a number of developments since appointees, and visitors from abroad. The AMS fSU Aid Fund the appearance of the previous Notices article. will help support this important institute. The Sloan Foundation has awarded the AMS a "challenge • Libraries. An AMS Rel!.ding Room, with copies of grant", which will match individual contributions to the AMS books and journals and MathSci in CD-ROM, is the Fund up to a total of $30,000, to support the small grants centerpiece of this effort. In addition, the AMS plans to component of the assistance program. Since the appearance identify libraries in the former Soviet Union to receive free of the call for contributions in the July/August Notices, the subscriptions to Society journals. Society has already received a number of contributions. If • Independent groups and other needs. Plans are also being the fundraising effort goes well, the Sloan Foundation has made to support a variety of independent group efforts that indicated it will consider making a second challenge grant. have arisen in a number of locations to support and revitalize The American Physical Society, for example, has received a mathematical sciences research and scholarship. One notable $100,000 challenge grant from Sloan. example is the Mathematics Department at the Independent In addition, the Advisory Committee for the program University of Moscow, headed by V. I. Arnold. Other efforts has now been appointed. The members of the Committee are under way in St. Petersburg, Novosibirsk, Kharkov, Kiev, are: Michael Artin, AMS President, Massachusetts Institute and other cities. In addition, the AMS is looking into other of Technology; William H. Jaco, AMS Executive Director; needs, such as workshops, conferences, and exchanges. Robert D. MacPherson, MIT; Cathleen Morawetz, Courant In At present, the political and economic climate of the stitute of Mathematical Sciences; Robert O'Malley, President former Soviet Union is quite uncertain. The AMS and the of the Society for Industrial and Applied Mathematics, Uni Advisory Committee are monitoring the situation and will versity of Washington; John C. Polking, AMS Trustee, Rice make every effort to obtain reliable information from a variety University; Linda Preiss Rothschild, University of California of sources inside and outside the former Soviet Union to at San Diego; and Daniel Stroock, MIT. The Committee will insure that the AMS fSU Aid Fund is put to the best possible . use. The goal is to provide short-term support to bring a also benefit from the advice of a group of consultants in the measure of stability to the mathematical sciences community former Soviet Union and elsewhere. and sustain its intellectual activity during these difficult times. Some aspects of the program have evolved since the The AMS calls upon the international mathematical sci previous Notices article. The four primary activities, described ences community to contribute toward this important effort to below, will comprise all areas of the mathematical sciences, help keep alive mathematical sciences research and scholar including applied areas, statistics, and probability. ship in the former Soviet Union. Please see the accompanying • Small Grants. These grants will be made directly advertisement on the previous page for information on how to to individuals, with a focus on graduate students, young make a contribution. Questions about the AMS fSU Aid Fund mathematicians, and established scholars. Recommendations may be directed to Timothy J. Goggins, AMS Development for grantees will be made by a panel of mathematical scientists Officer, 401-455-4110; electronic mail [email protected]. in the former Soviet Union. The Sloan Foundation funds will support this activity. • Moscow Mathematics Institute. Directed by Askold Allyn Jackson Khovanski and established in 1991, the Moscow Mathematics Staff Writer
688 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY European Meetings Bring Mathematicians Together Historic "Firsts" in Cambridge and Paris
This summer, two back-to-hack meetings in Cambridge and "We were very fortunate to get together such a strong group Paris brought the U.S., Europe, and the former Soviet Union of speakers from both sides of the Atlantic," commented Sir a little closer together. The joint meeting with the London John Kingman, President of the London Mathematical Society. Mathematical Society (LMS), held June 29 to July 2 in "This was partly due to the attraction of Cambridge, but also Cambridge, England, marked the first AMS international due to the fact that the program committee had put together meeting, and its first joint meeting with the LMS. The a very interesting program." One participant remarked that following week, the first European Congress of Mathematics this was a very good "working meeting", unlike many general brought together mathematicians from all over Europe and the conferences of this type. former Soviet Union to participate in a wide-ranging program. "The impressions I got from talking to quite a few of the In between these two events was the inaugural opening of participants at the AMS-LMS meeting were very positive," the Isaac Newton Institute, headed by Sir Michael Atiyah of noted Ronald Graham, AMS President-Elect. "They were Trinity College, Cambridge University. very happy with the number and quality of the talks and with the substantial attendance. In fact, many people thought The AMS-LMS Meeting that it would have been better to spread the meeting over The Joint AMS-LMS Meeting began on a warm Mon three days because it was packed pretty tightly in the two day evening, when John M. Ball of Heriot-Watt Univer days scheduled." (Despite the intensity of the schedule, some sity presented an intriguing talk about the mathematics of participants managed to find spare time to punt on the River microstructure-an unusual physical phenomenon in that Cam or quaff beer on the bridges arching over the river.) certain energy functions associated with microstructure do not attain a minimum. The plenary lectures were, on the whole, expository and accessible to a general mathematical audience. Spanning a range of areas, the list of speakers in cluded Lawrence Craig Evans of the University of California at Berkeley, Benedict Gross of Harvard University, Nigel Hitchen of the University of Warwick, and Edward Witten of the Institute for Advanced Study.
Paul Halmos at a reception during the AMS-LMS meeting. A total of 477 people registered, with 162 from the United Kingdom, 220 from the U.S., and 95 from other countries. Ten publishers hawked their wares, some of them in rather steamy conditions in the Mill Lane Lecture building, which, like most buildings in Cambridge, had no air conditioning. Despite the The book exhibit at the AMS-LMS meeting. humidity, the hospitality of the LMS was evident through the
SEPTEMBER 1992, VOLUME 39, NUMBER 7 689 ______...... European Meetings efforts of staff members Susan Oakes and Harvinder Lotay, that brings in light and encourages discussion and interaction. who, together with AMS housing and registration coordinator Architect Duncan Annand explains that one can see from Penny Pina, made sure everything ran smoothly. anywhere in the building what's going on in the common The social activities of the conference were particularly areas. There is a library and two seminar rooms, one of which well attended and jovial. A reception held the first evening of holds about 120 people. "We wanted space where people the meeting attracted a crowd of more than five hundred and could interact, so [Annand] came up with this design, and then included a sculpture exhibit of the work of Gabriella Bollobas. we commented on it," notes Sir Michael. "We're very pleased The most commanding piece was a full-size sculpture of with it, it worked out exceptionally well ... 'Architects are Newton and Dirac talking together (at one point, someone more often interested in what the outside looks like, they're had placed an apple in Newton's outstretched palm). The not too worried about the inside, whereas people are using the following evening, nearly 300 people attended the conference inside, that's what's important. So we're very pleased here, dinner, the highlights of which were the excellence of the food he's put a lot of thought into it." Annand came to understand and service and an eloquent speech by Sir John. at least a few things about what mathematicians are like: there are chalkboards everywhere, even in the bathrooms--even in the elevator.
Sir John Kingman (left), President of the LMS, and Ronald Graham, President Elect of the AMS. This was a historic venture for the AMS and LMS, in The Isaac Newton Institute more ways than one. "I think it got the staffs of the two The Newton Institute does not have a permanent staff, societies to get to know one another better and to work except for Sir Michael, Deputy Director Peter Goddard, a together," commented Sir John. "We've always had a close theoretical physicist at Cambridge, and the administrative relationship, but at distance, in the sense that we've talked staff. Rather, the Institute will bring in a rotating staff of on the telephone and written, but not worked together face to visitors. The scientific aim of the Institute is to cover a broad face." In addition, it was an important event for the British area of mathematics and its connections with other areas mathematical community, which does not often host meetings of science. "We're going to definitely have a lot of things of this size. "The significant thing was to get so many North which spread over from mathematics into all sorts of other American mathematicians visiting at one time," said Sir John. disciplines-biology, economics, physics, computer science," "Often we have visitors from the U.S. and Canada, but not as says Sir Michael. "I think the view is at the present time that a group at one time, and this was an event we welcomed." a lot of the future development of mathematics probably will be to use more advanced mathematics in related fields and The Isaac Newton Institute to bring problems from other fields into mathematics. So our During the AMS-LMS meeting, workers were rushing to put aim is really to bridge the gap by bringing people together." In the finishing touches on the Isaac Newton Institute-rolling addition, while the Institute is intended to be an international out stretches of lawn, polishing the bannisters, arranging center for research, "we hope it will have a major impact on the furniture, and hanging a portrait of Sir Isaac Newton. Btjtish mathematics. Cambridge is obviously a good center For a visitor arriving on Tuesday June 30, it was a little from that point of view, there's a lot of mathematics here difficult to believe that everything would be ready for the already ... And I think we were very fortunate that we were inaugural opening the following Friday. But Friday came, and able to time it so that we could start off just at the time of [the everything was in readiness for the opening events. AMS-LMS] joint meeting". Light, airy, and elegant without being formal, the Institute Every six months, the Newton Institute will run two building was designed with mathematics in mind. Thirty concurrent programs in different areas. From July to December offices on the second and third levels circle a central open area 1992, there are programs on low-dimensional topology and
690 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ______...... European Meetings quantum field theory and on dynamo theory, and from January of the main results in the development of knot invariants, to June 1993, the focus will be on £-functions and arithmetic Jones wound up the lecture by touching on some of the recent and on epidemic models. Next year, there will be programs in connections between knot theory and statistical mechanics, computer vision; random spatial processes; cellular automata, quantum field theory, and von Neumann algebras. The other aggregation, and growth; and geometry and gravity. speakers included Sir Peter Swinnerton-Dyer, Senior Fellow at the Newton Institute, who spoke on arithmetic; Keith Moffatt, Cambridge University, who spoke on flow; Roy Anderson, Imperial College, a biologist who discussed epidemics; and Allan Chapman, Oxford University, who presented a historical perspective on Newton and his work. Sir Michael closed the day's activities with a short talk about the Newton Institute. Given his responsibilities as President of the Royal Society of London and Master of Trinity College, Sir Michael says he can devote only limited time to the Newton Institute. He acknowledges the efforts of Deputy Director Goddard, who has been involved in the Institute from the early planning stages right through the construction of the building and the appointment of staff. "Goddard is the person who really worked enormously long hours to get things going," says Sir Michael. "I have limited time, so I just help and advise on policy, the scientific mission, things like that . . . I hope I have some time to come in. I won't really work here; I have One of the common areas at the Newton institute. offices elsewhere." But maybe he'll come in to do a little Sir Michael says the Institute will consider nearly any mathematics? "Absolutely ... " scientific area for a program, provided there is some serious mathematics involved. "Also, it ought to be an area which is going through an exciting stage ... And it probably ought to be The European Congress of Mathematics one which brings people together from different backgrounds, Following on the heels of the AMS-LMS meeting and the different disciplines, or makes a new contribution. So, we opening of the Newton Institute was yet another historic event: don't go in for orthodox, conventional type meetings, of which the first European Congress of Mathematics (ECM), held in there are plenty already. We'll try to do something new." Paris, July 7-11. Centered at the Sorbonne University in the St. John's College, Cambridge constructed the new build lively Latin Quarter, the ECM combined French sensibility for ing and also provided £750,000 to cover most of the first the good life with an ambitious vision for the Congress, which five years' rent. In addition, Trinity College, Cambridge has included some serious and successful efforts to go beyond the established the Newton Trust, which is providing £1 million usual presentation of mathematical lectures and reach out to a for other expenses during that period, and other Cambridge broader audience of nonmathematicians and young people. colleges have given grants. There are also many donors from Credit for the idea of a European Congress generally goes outside Cambridge, including the London Mathematical So to Max Karoubi of the University of Paris V who was named ciety, and from outside the U.K. In additi'on, the Science and Founder of the Congress. Together with the efforts of Rudolph Engineering Research Council of the U.K. has awarded the In Rentschler at the University of Paris VI, who joined Karoubi stitute over £1.5 million over the coming four years. Presently, early on in the project, Karoubi began working on preparations the total funding for the Institute stands at over £5 million. for the ECM in mid-1989 and was able to secure funding for Sun Microsystems and Apple U.K. donated workstations for the ECM from European Community sources in Brussels and computing, word-processing, and email. the French government. As the project proceeded, the Societe The inaugural activities for the Newton Institute included Mathematique de France and the Societe des Mathematiques talks on pure and applied topics reflecting the diversity Appliquees et Industrielles agreed to sponsor the Congress, of topics in the coming two years of activities. Vaughan and various committees were appointed to bring the idea to Jones of the University of California at Berkeley presented fruition. Among the key players were Fulbert Mignot of Paris a lucid and entertaining lecture on knots that would have VI and Paris XI, chair of the Organizing Committee, and been understandable to a high school student. At one point. Fran~ois Murat of Paris VI, who served as treasurer; Hans Jones broke the "No Smoking" rule of the Institute and lit Follmer of the University of Bonn, chair of the Scientific a cigar to demonstrate the origins of knot theory. "This, Committee; and Henri Cartan, member of the Academie des believe it or not, is what happened," said Jones: In the Sciences de Paris and professor emeritus at the University of 1860s, Lord Kelvin became interested in the idea of knotted Paris XI (Orsay), chair of the Steering Committee. Together vortices when Tait blew some smoke rings during a lecture with the organizers of the Round Tables, there were nearly in Edinburgh. Jones says he's been trying for years to blow a one hundred people involved in planning and executing the trefoil smoke ring, but without success. After surveying some ECM.
SEPTEMBER 1992, VOLUME 39, NUMBER 7 691 mmm Wili!i -ili!*ili!~ili!'Mili!'•••*111!·-··111!1111! ______European Meetings
the various embassies in Paris invited participants from their countries to receptions. One of the largest, with over 200 people, was given by the German Embassy, where, on the occasion of his 88th birthday, Cartan was presented with a bouquet of flowers by the German ambassador. In addition to his mathematical distinctions and his work on the ECM, Cartan has been politically active in advocating for a united Europe. Perhaps the most important reception, though, was held at the Hotel de Ville, where Jacques Chirac, Mayor of Paris and former Prime Minister of France, presented prizes sponsored by the city of Paris on the occasion of the ECM. The prizes were awarded to ten mathematicians under the age of thirty-two: Richard Borcherds, Jens Franke, Alexander Goncharov, Maxim Kontsevich, Franc;ois Labourie, Tomasz Luczak, Stefan Muller, Vladimir Sverak, Gabor Tardos, and Claire Voisin. Kontsevich and Borcherds presented parallel The chapel of the Sorbonne session talks during the ECM. In addition, the prize committee paid an eloquent tribute to Andreas Floer, who died last year under tragic circumstances at the age of thirty-four. The plenary speakers at the ECM spanned a wide range The Congress attracted the attention of the media and of areas and perspectives. One participant commented that resulted in a number of newspaper articles on mathematics the Scientific Committee must have impressed upon the in French papers and magazines, as well as periodicals in speakers the need to make their talks accessible to a general other countries. The high level of interest the Congress mathematical audience, because most were expository with a drew was also evident in the speech by Hubert Curien, good balance of technical details. In particular, the lecture by the French Research Minister, at the Opening Ceremonies. Laszlo Babai of the University of Chicago and Lorand Eotvos Also presenting a speech was Friedrich Hirzebruch, director University about recent work on transparent proofs seemed of the Max Planck Institute and president of the European to be a favorite among the participants, as it touched on the Mathematical Society (EMS). Founded in Poland in October foundations of mathematics and what is meant by the notion 1990, the EMS is intended to serve as an advocate for of "proof". David Mumford of Harvard University presented mathematics on issues that reach beyond national borders. a fascinating survey lecture about the tough mathematical More than thirty mathematical societies belong to EMS, and problems posed by computer vision. V. I. Arnold of the there are also about 1100 individual members, who have the Steklov Mathematical Institute was the final speaker on option of joining through their local mathematical societies. the program, and his lecture on Vassiliev's knot invariants One of the concerns that prompted the formation of the demonstrated that mathematical research continues to flourish EMS was the situation for mathematicians in Eastern Europe in the former Soviet Union. Two days. of the Congress were and the former Soviet Union. Although travel restrictions devoted to parallel sessions that comprised forty lectures, and have eased considerably in recent years, economic problems these featured some of the top mathematicians in Europe. In make travel to conferences effectively impossible for many addition, there were about fifteen more specialized "satellite" mathematicians. Moreover, many have had problems obtain conferences that took place before and after the ECM that ing visas to visit other countries. For this reason, the Congress drew many participants. organizers raised funds specifically to cover the living ex Perhaps the most unusual aspect of the ECM, and probably penses and registration fees for needy participants from the the most difficult to pull off, were the sixteen Round Tables former Soviet Union and Eastern Europe. Although some still that examined the relations between mathematics and society could not attend because getting to Paris was prohibitively and connections between mathematics and other areas of expensive, the ECM was quite successful in bringing a large science. Given the complexity of the problems they addressed, contingent from that region: out of a total of 1300 participants, and the fact that their inclusion in such a conference has there were about forty registered participants from Russia (the almost no precedent, they can be counted as a success. same number as from the U.S.), another forty or so from other One of the liveliest discussions took place at the Women states in the former Soviet Union, and nearly two hundred and Mathematics Round Table, organized by Eva Bayer of from other countries in Eastern Europe. Centre National des Recherches Scientifiques, Besanc;on. The Several lavish social events heightened the celebratory panel, which included women mathematicians from Italy, spirit of the Congress. The opening reception at the Palais Germany, Poland, the U.S., and France, brought out some de la Decouverte, a science museum, attracted a substantial differences among various countries' representation of women fraction of the Congress participants, who feasted on hors in mathematics. For example, figures presented at the session d'oeuvres, petit fours, and champagne. On another evening, show that women currently comprise about 35% of the
692 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY European Meetings mathematicians in Italy while in 1987 there were only 3% Many have said that Russian mathematics could all but women among mathematicians in West Germany. disappear in ten to fifteen years; Sossinsky stated that the only source of optimism is these kinds of educational programs, though even their fate is uncertain at this time. (Please see the article on p. 688 in this issue for information on the AMS program to assist mathematics in the former Soviet Union.) There were other unusual features of the Congress that made it clear that mathematics doesn't just consist of a bunch of experts sitting and talking only to each other. One example was the "Junior Congress", a three-day event for high school students that kicked off on the second day of the ECM with an afternoon and evening program for high school students featuring talks by mathematicians and by the stu dents themselves. There was also an exhibit called Horizons Mathematiques, which was open to the public and which illus trated various mathematical concepts through manipulatives, puzzles, drawings, soap bubbles, and so on. In addition, David Singmaster of South Bank University in London assembled an extensive exhibit of puzzles containing mathematical content, and there was a program of mathematical films and videotapes I. M. Gelfand (left) and V. I. Arnold. Photo courtesy of Leon Betute. shown on three afternoons, as well as a number of musical At the Round Table on Mathematics and the General presentations. Public, Alexei Sossinsky of Moscow described some of the The plan is to hold a European Congress every four programs that mathematicians in the former Soviet Union years, between the International Congresses. The next ECM, have developed to cultivate an interest in mathematics among scheduled for Budapest in 1996, will have a tough act to young people. As the former editor of Kvant, a mathematics follow to surpass the lively and varied events and the high and science magazine for young people, Sossinsky has had ex scientific quality of the Paris conference. But most likely the tensive experience in this area. He described problem-solving Budapest Congress will have a flavor all its own, so Vive Ia seminars, popular mathematics books, olympiads, summer difference. schools, Gelfand's mathematics correspondence school, and other efforts that have contributed to the distinctive Russian Allyn Jackson tradition of inspiring mathematical interest in young people. Staff Writer
Why the Boundary of a Round Drop Becomes a Curve of Order Four University Lecture Series, Volume 3 • A. N. Varchenko and P. I. Etingof
This monograph concerns the problem of evolution of a round oil spot surrounded by water when oil is extracted from a well inside the spot. Varchenko and Etingof discuss this topic and other recent work in the theory of fluid flows with a moving boundary. Problems are included at the end of each chapter, and there is a list of open questions at the end of the book. Contents Mathematical model; First integrals of boundary motion; Algebraic solutions; Contraction of a gas bubble; Evolution of a multiply connected domain; Evolution with topological transformations; Contraction problem on surfaces.
1991 Mathematics Subject Classification: 58, 76, 31, 30 ISBN 0-8218-7002-5, 72 pages (softcover), August 1992 Individual member $23, List price $38, Institutional member $30 Your ordering code is ULECT/3NA All prices subject to change. Free shipment by surface: for air delivery, please add $6.50 per title. Prepayment required. Order from: American Mathematical Society, P.O. Box 1571, Annex Station, Providence, RI 02901-1571, or call toll free 800-321-4AMS (321-4267) in the U.S. and Canada to charge with VISA or MasterCard. Residents of Canada, please include 7% GST.
SEPTEMBER 1992, VOLUME 39, NUMBER 7 693 Forum
mathematicians at a similar stage of development are espe cially influential. Students should be advised that letters from short articles on issues that are of interest The Forum section publishes scientists other than mathematicians tend to carry less weight to the mathematical conimunity. Articles should be between 1000 and 2500 words long. Readers are invited to submit articles for possible and letters from nonscientists carry virtually no weight at all. inclusion in Forum to: IV. The mathematics panel found research experience Notices Forum Editor desirable but did not consider it essential to a successful American Mathematical Society application. Many of the applicants have been through one P.O. Box 6248 of the Research Experiences for Undergraduates programs Providence, Rl 02940 sponsored by the NSF; several have even published papers. or electronically to [email protected] The panelists viewed rambling and unfocused statements (under career goals, research experience) as detrimental. It is best to be concise and to the point. Panelists must review many NSF Graduate Fellowship Program applications in a short time, and information buried in long NSF Graduate Fellowship Panel winded statements will most likely be overlooked. Applicants should play to their strengths; all relevant experiences should Chair Sylvia Wiegand, be mentioned. just served on the panel that awards National Science We have V. First-year graduate students may apply, as well as Foundation (NSF) Graduate Fellowships in mathematics. Part senior undergraduates. There are fewer of the former than of the purpose of this letter is to explain the selection might be expected-just sixty-four this year, and seven of process to the mathematics community, especially to potential them received awards. Possibly the graduate students have applicants, advisors, and writers of letters of recommendation. difficulty finding letter writers at their new institutions. It may I. The mathematics panel reviewed 257 applications be that the fellowships should be better advertised to this for twenty-six awards. The number of awards in a given faculty should be encouraged to bring the fellowships discipline is roughly proportional to the number of competitive group; their advisees/students. applications in that discipline. In other words, to a certain to the attention of the competition, the NSF extent, we would have more awards in mathematics if more VI. In its announcement of groups, students applied. Physics and chemistry each had almost twice encourages applications from members of minority as many applications as mathematics, with a correspondingly women, and persons with disabilities, although the panelists greater number of awards; there were 7, 723 applications in are expected to disregard race, sex, and handicap in their delib all fields. erations. There is a separate program for minority fellowships. II. In view of the large number of highly qualified (Ma,ny students compete in both.) There is a separate program candidates and the small number of fellowships, the award for women in engineering. There is also additional financing of "honorable mention" should be viewed as a competitive for persons with handicaps who are successful (defined to recognition of significant achievement. include honorable mention) in the initial competition. As an illustration of the quality of the applicants for However, there is no special program for outstanding mathematics, fifteen percent had perfect GRE subject test women in mathematics. The panel wondered if such a program scores and three and a half percent (nine) had perfect scores might be initiated for women in mathematics, because ( 1) on all four parts of the GRE. (Scores on these exams are there are still various barriers that put women at a disadvantage just one consideration; letters of recommendation, grades, and in this competition and (2) we feel that additional incentives individual student statements are also very important.) for women would inspire more women to pursue mathematics. III. Carefully written and appropriate letters of recom The panel has noticed that women may not do as well in mendation are extremely helpful in the evaluation process. our evaluation process due to a number of factors: perhaps they In particular, comparisons between two or more applicants have had a harder time finding mentors for research projects; make the panel's job easier, and comparisons to successful women often score lower than men on tests (although they
694 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Forum may have better grades than men); and references may be months it will be M. Kent Wilson on an acting basis; after written with a bias towards men. The panelists are sensitive that, another individual will be named to the position.) to these problems, but have not felt that women's applications VII. The panelists present the NSF with three unordered, should be evaluated differently from men's. The panelists alphabetized lists. All the applicants in the first list and half would like to see extra fellowships set aside specifically the applicants in the second receive awards. The awardees for women. We need more highly qualified women graduate in the second group are chosen by the National Science students, more women writing excellent Ph.D. theses, and Foundation, based on geographical and other considerations. more women with outstanding careers in mathematics. This year the first two lists comprised six and eight percent There were fewer female applicants this year (eighty of the applicants respectively. The third list is for those who three) than last year (ninety), although overall the number will receive honorable mention along with those in group two of applicants went up (257 applicants this year versus 222 who don't get awards. last year). This year only three fellowships were awarded to VIII. In giving these details, we are concerned that math women in mathematics; last year ten were awarded to women. ematics faculties should not discourage good mathematics (Last year there were thirty-two awards in all, whereas this students from applying for an NSF Graduate Fellowship. We year there were only twenty-six.) The picture in computer submit that it is beneficial for our profession and for students science and in applied mathematics is equally bleak-last year to go through the process of applying, even if the application five fellowships went to women in computer science, this year, does not result in an award. We hope faculty will explicitly two; last year four went to women in applied mathematics, encourage students who are considering graduate school to this year, three. apply. This would yield: an early opportunity to think about Note: If mathematicians and others are interested in an graduate school; an early opportunity to refine thinking about extra program for women, they should write to Dr. Terry what one wants to accomplish in graduate school; and experi Porter, Division Director for Research Career Development, ence in writing about oneself and one's goals with respect to and to the Division Director for Mathematical Sciences. mathematics. (Presently that director is Dr. Judith Sunley; for the next few
Translations of Mathematical Monographs
Multidimensional Residues and Their Applications A. K. Tsikh Volume 103 Tsikh's book presents a systematic account of residues associated with holomorphic mappings and indicates many applications. The book begins with preliminaries from the theory of analytic sets, together with material from algebraic topology that is necessary for the integration of differential forms over chains. Tsikh then presents a detailed study of residues associated with mappings that preserve dimension (local residues). There is also a treatment of residues associated with mappings that reduce dimension-that is, residues of semimeromorphic forms, connected with integration over tubes around nondiscrete analytic sets.
1991 Mathematics Subject Classification: 32 ISBN 0-8218-4560-8, 188 pages (hardcover}, July 1992 Individual member $71, List price $119, Institutional member $95 Your ordering code is MMON0/103NA
American Mathematical Society. All prices subject to change. Free shipment by surface: for air delivery, please add $6.50 per title. Prepayment required~ Order from: American Mathematical Society, P. 0. Box 1571, Anriex Station, Providence, RI 02901-1571, or call toll free 800-321-4AMS in the U.S. and Canada to charge with VISA or Master Card. Residents of Canada, please include 7% GST.
SEPTEMBER 1992, VOLUME 39, NUMBER 7 695 Computers and Mathematics
Edited by Keith Devlin
This month's column ______...... Primality testing and related computational pastimes frequently put mathematics onto the pages of the national press. I suspect that the Primality Testing general impression created in the public mind by such publicity is that computers will, one day soon, put most mathematicians out of a job. Of and Carmichael Numbers course, the reality is-as it is in almost all areas where the computer has had a significant impact-that the computer revolution has certainly Andrew Granville* changed the nature of what many mathematicians do, and the way they do it, but, if anything, has created more need for mathematicians, not The problem ofdistinguishing prime numbers from composite decreased it. I myself fall into the camp of those who think that almost numbers is one of the most fundamental and important in any publicity is good publicity, and pure mathematicians need publicity arithmetic. It has remained as a central question in our subject just as much as any other group, and perhaps more so given our al 1 most invisible profile until recently. But I know that there are many who from ancient times to this day , and yet still fascinates and disagree with this view. frustrates us all. From the very definition of primality, that an Still, I think we probably all agree that, publicity or not, compu integer tational investigations, even in areas of mathematics that are of the n is prime if it has no divisor between 2 and .fii, "recreational" variety' that appeal to journalists, can lead to interesting, one can evolve a simple test for primality: Just check whether nontrivial, and worthwhile mathematical results. Such is the case with any integer d between 2 and y'n actually divides n. This is an Carmichael numbers. Earlier this year, Red Alford, Andrew Granville, and Carl Pomerance of the University of Georgia proved that the set of easily implemented test for, say, n = 107 or n = 11035, but Carmichael numbers is infinite, thereby solving a problem that has been how about for n = 123456789012345677? This requires over around for some 80 years or so. a billion test divides, and if one were to try to verify that a Their joint paper There are infinitely many Carmichael numbers given 100 digit integer n is prime in this way it would take presently exists only in preprint form, but I asked Granville to write an longer than the remaining lifespan of our universe, even on an expository article on the work for this column. The result constitutes this impossibly fast computer! month's lead article. a more sophisticated approach to handle Following on from Granville's piece, Barry Simon presents the re One thus needs sults of a series of benchmark tests he has run on a number of com large numbers. Perhaps a different definition of prime numbers puter mathematics systems. The format is much the same as in Simon's will furnish us with a quicker method? One such definition previous benchmark evaluation, which he reported in this column in follows from Wilson's Theorem (1770): September 1990 (Notices, Volume 37, Number 7, pp. 861-868). n is prime if and only if n divides (n- 1)! + 1. Finally, if any readers are interested in reviewing software for this So, to find out whether n is prime, we multiply together all column, please let me know. The information I need is the equipment integers less than n, add 1, and see whether the resulting at your disposal and the kinds of software you would be interested in reviewing. I currently have more volunteers than I need for trying out number is divisible by n. However, this requires multiplying NeXT software, but need more people prepared to review software for n - 3 pairs of numbers together, as opposed to y'n test divides Macs orPCs. earlier, so it takes even longer than our previous method. The ancient Chinese made the startling discovery that Editor's address: If n is prime then n divides 2n - 2, Professor Keith Devlin which implies that Department of Mathematics and Computer Science (1) If n does not divide 2n - 2 then n is composite (that is, Colby College not prime). Waterville, Maine 04901 So we now have a new, and quite different, criterion, which Correspondence by electronic mail is preferred, to: will tell us that certain numbers n are composite. However, if kjdevlin @colby.edu. 1from Article 329 of Gauss's Disquisitiones Arithmeticae (1801) *Andrew Granville is an Assistant Professor of Mathematics at the Uni versity of Georgia in Athens, Georgia. He can be reached by email at: [email protected].
696 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics a number fails this criterion (that is, if n does divide 2n - 2), such a number, then so is n' = 2n - 1. 3 This is proved by then it doesn't, a priori, tell us that n is prime; but let's check observing that, since a divides n which divides n'- 1, thus it out: Xa- 1 divides Xn- 1, which divides x(xn'-1 - 1) = xn'- X, and so, in particular with x = 2, we get that 2a - 1 divides 2 divides 22 - 2 = 2 2n - 1 =n' which divides 2n' - 2. 3 divides 23 - 2 =6 101 divides 2101 - 2 obtaining a complete list of base 2 pseu 4 doesn't divide 24 - 2 = 14 103 divides 2103 - 2 Our hope of 5 divides 25 - 2 = 30 105 doesn't divide 2105 - 2 doprimes is thus doomed, but we might still find all base 2 6 doesn't divide 26 - 2 =62 107 divides 2107 - 2 pseudoprimes up to some large number x. However, in 1982, 7 divides 27 - 2 = 126 109 divides 2109 - 2 Pomerance showed that there are more than e<1og x)c base 2 8 doesn't divide 28 - 2 = 254 111 doesn't divide 2m-2 pseudoprimes ~ x, for some constant c, 0 < c < 1, once xis 9 doesn't divide 29 - 2 = 510 etc. sufficiently large.4 This is quite a fast-growing function of x and shows that our hoped for, easy and quick primality test In all of these examples we observe that n is prime exactly would not be practical for large values of x. So what else can when n divides 2n - 2, and is composite otherwise. According we do? to E. T. Bell, the ancient Chinese thought that this is always On October 18th, 1640 Fermat wrote, in a letter to 2, However, the true as did Leibniz many centuries later. his confidante Frenicle, that the fact that n divides 2n - 2 (smallest such) example, n = 341, refutes this belief since whenever n is prime is not an isolated phenomenon. Indeed 341 341 = 11 x 31 is composite, yet 341 divides 2 - 2. that, if n is prime then Further computation shows that such composite n seem (2) n divides an - a for all integers a; to be rare and so we define a composite number n to be a which implies that base 2 pseudoprime if n divides 2n - 2. To exhibit quite If n doesn't divide an - a for some integer a how rare these are, note that up to 1010 there are around then n is composite. 450 million primes, but only about fifteen thousand such So instead of considering pseudoprimes to base 2, we can base 2 pseudoprimes, while up to 2.5 x 1010 there are over consider pseudoprimes to any base a: it turns out that such a billion primes, and yet fewer than 22 thousand base 2 pseudoprimes are rare, though some do exist. However, since pseudoprimes. So, if you were to choose a random number base 2 pseudoprimes are rare, and base 3 pseudoprimes are n < 2.5 x 1010 for which n divides 2n - 2 then there would also rare, one would guess that numbers that are both base be a less than one-in-fifty-thousand chance that your number 2 and base 3 pseudoprimes must be extremely rare; perhaps would be composite. none exist at all? Unfortunately some do exist, such as 2701, Testing whether 2n-l = 1 mod n is easily implemented which divides both 22701 - 2 and 32701 - 3, yet 2701 = 37 x 73 on a computer, as follows: is composite. Numbers that are pseudoprimes to bases 2, 3, (i) Write n - 1 in base 2, say n - 1 = 2ak + 2ak-l + ... + 2a1 and 5 simultaneously should be even rarer, but again do exist, where ak > ak-1 > · · · > a1 for instance n = 181 x 361; and, indeed, there are examples for any finite set of bases. So maybe we should ask whether (ii) Compute ri 22; mod n for 0 ~ j ~ ak, by taking r0 =2 = there are any composite numbers n that are pseudoprime for and ri+l = r] mod n for each j 2: 0 every base a, that is, for which (2) holds. Such a number n (iii) Finally, since 2n-1 22"k • 22"k-l · · · 22"1, we have 2n-1 = = would have to have certain extraordinary properties: Takrak-l · · · Ta 1 (mod n). (i) n must be squarefree, else if r divides n then p2 divides This algoritlun requires no more than 20 log3 n operations n divides pn - p which is false. so that, for a 40 digit number n, this "pseudoprime test" takes (ii) If prime p divides n then p- 1 must divide n- 1, for if a few million operations (a few seconds on a PC) whereas a is a primitive root mod p then a has order p - 1 mod p, test division takes more than a billion billion operations (over but an-1 = 1 (mod p) by (2). a thousand years on a PC). It has been suggested that one In 1899 Korselt5 observed that these two conditions imply might obtain a practical primality test by writing down a list that (2) holds (which the reader may verify-hint: use the of all base 2 pseudoprimes, and then, if n divides 2n - 2 but Chinese Remainder Theorem). We thus state is not on the list, one knows that n is a prime. Since there are Korselt' s criterion: n divides an - a for all integers a if less than 22 thousand base 2 pseudoprimes up to 2.5 x 1010 , and only if n is squarefree and p - 1 divides n - 1 for all this method works well in this range, and will continue to primes p dividing n. work well as long as the base 2 pseudoprimes remain so So now, to determine whether (2) holds for n, we need only scarce. However, this won't always be so since Malo proved, 3 2n_1 22n_1 1 in 1903, that there are infinitely many odd composite base 2 Thenwegetthesequencen, 2n -1, 2 -1, 2 _ -1, ... ofbase2 pseudoprimes by iterating this observation. pseudoprimes by showing that if n = ab (with a, b > 1) is 4For those readers not accustomed to such "estimates", we note that, e SEPTEMBER 1992, VOLUME 39, NUMBER 7 697 -····················-·········································· ...... -·-··········-·-····-·················-···-········-······------····························-·······-·········-··········-·-···························-············· ...... Computers and Mathematics verify a few simple properties of its prime factors. Korselt forintegers k ;::: 1, giving L = 36k. Since pqr-1 = 36k(36k2+ did not exhibit an example of such an integer n, and he 11k + 1), Korselt's criterion tells us that pqr is a Carmichael might have thought that no such n exist. However, such n do number provided each of p, q, and r are prime. It is easy exist, as was discovered by Carmichael in 1910, the smallest to find many values of k for which the three numbers in (3) being 561 = 3 x 11 x 17. These numbers are now known as are simultaneously prime, but can we prove that there are Carmichael numbers, but surely would have been known as infinitely many such k? This is considered an outstandingly ·Korselt numbers had he just done a few computations! difficult open problem in analytic number theory, and although The first few Carmichael numbers are experts are certain that infinitely many such k do exist, there have been no plausible ideas as to how to prove such a result. 561 = 3 X 11 X 17 One can obtain other sequences in which one expects infinitely many prime triplets or quadruplets or quintuplets, 1105=5 X 13 X 17 which would give rise to infinitely many Carmichael numbers, 1729* =7 X 13 X 19 for instance 2465 = 5 X 17 X 29 (12k + 5)(36k + 13)(48k + 17), (6k + 7)(12k + 13)(18k + 19), 2821 = 7 X 13 X 31 (28k + 5)(112k + 17)(196k + 29), (30k + 7)(60k + 13)(150k + 31), Notice how they all have three prime factors. To obtain one (180k + 7)(300k + 11)(360k + 13)(1200k + 41); with four prime factors we must go out to but it seems unlikely that this approach will lead to a proof 41041 = 7 X 11 X 13 X 41 that there are infinitely many Carmichael numbers in the foreseeable future. and for five prime factors to Let C(x) be the number of Carmichael numbers up to x. The following table gives the number of Carmichael numbers 825265 = 5 X 7 X 17 X 19 X 73. up to various values of x: x C(x) Year Discoverer(s) Carmichael computed fifteen such numbers in his 1912 1o3 1 1910 Carmichael paper and stated that "this list might be indefinitely extendecf'. 104 7 1912 Carmichael 5 However, it soon became apparent that it was going to be 10 16 106 43 difficult to prove that his list could be so lengthened, and this 107 1Q5 statement has since been considered an open problem.6 · 108 255 1938 Poulet Korselt's criterion may be rewritten as follows: 109 646 1975 Swift n = P1P2 · · · Pk is a Carmichael number if and only if the 1010 1547 p/s are distinct and L = LCM[pr- 1,p2- 1, ... ,pk- 1] 2.5 X 1010 21(i3 1980 Pomerance, Selfridge, Wagstaff divides n - 1. 1011 3605 12 So, to verify that those numbers listed above are in 10 8241 1990 Jaeschke 1013 19279 deed Carmichael numbers, we only need check that L = 1014 44706 80 =LCM[2, 10, 16] divides 560, that L = 48 divides 1104, 1015 105212 1992 Pinch that L = 36 divides 1728, that L = 112 divides 2464, that L = 60 divides 2820, that L = 120 divides 41040, and finally This data suggests that there must indeed be infinitely many that L = 144 divides 825264. Notice that Lis extremely small Carmichael numbers, even though they remain fairly scarce 15 compared to n - 1 in each example, which gives us a hint all the way up to 10 • In 1949 Paul Erd6s showed quite how as to how to find more Carmichael numbers: Let's try to scarce Carmichael numbers are, by proving that the sums of find a set of primes where these primes minus one have a their reciprocals converge7 ; it has since been proved that surprisingly small common multiple. For example, since the (4)t C(x) ~ xl-{l+oO>}Iogiogiogx/loglogx prime divisors of 1729 are p = 6 + 1, q = 12 + 1, r = 18 + 1 giving L = 36, we can generalize this to (3) p = 6k + 1, q = 12k + 1, r = 18k + 1, In 1956 Erd6s took a radically different approach to constructing Carmichael numbers. Earlier we noted that L = *1729 is best known from the story of when Hardy visited Ramanujan in LCM[p1 - 1, ... , Pk - 1] is much smaller than n- 1 for most the hospital, and pronounced his taxicab number, 1729, to be a dull number. Carmichael numbers n = p 1 • • • Pk· However, for a typical set Ramanujan refuted this by noting that it is the smallest number that is the sum of primes, {p1, ... , Pk}, there is no particular reason to expect of two cubes in two different ways. However, Ramanujan didn't say that 1729 is this to happen; indeed we'd expect L to be just a bit smaller also interesting as being the third smallest Carmichael number! Carl Pomerance further observes that the second smallest Carmichael number, 1105, is the sum of two squares in more ways than any preceding number. We leave it to the reader 7Unlike the primes, whose sums of reciprocals diverge. to come up with the analogous remark for 561, the smallest Carmichael number! tFor those not accustomed to such estimates, this is larger than x 1-• for 6See Alford's forthcoming paper Chasing Carmichael numbers for a revealing any fixed e > 0, but smaller than any given positive constant times x, once x is discussion of Carmichael's paper. sufficiently large. 698 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics than n - 1. So to construct Carmichael numbers we must find year, there were fewer than ten thousand Carmichael numbers some way of forcing L to be small. In our constructions above known, and it seemed to be a very difficult task to find many (like (3)), we selected our primes p to have certain special more. Then, suddenly on January 21, "Red" Alford announced forms: this guaranteed that the p - 1 had large common that he had proven the existence of at least 2128 Carmichael divisors, forcing L to be small compared to n - 1. Erdos numbers! Unlike previous computations, which had sought approached this problem from the other direction. Instead of all the Carmichael numbers up to some pre-assigned limit, or choosing primes in special ways so as to force L to be small, had found many in certain sequences (such as in that given he chose L so that there are many primes p for which p - 1 by (3)), Alford modified Erdos's construction so as to make divides L. Once this is done, one need only find a subset of it computationally practical: As we've already discussed, it is these primes, say PI, Pz, . .. , Pk. for which n =P1P2 · · · Pk = 1 easy (computationally) to implement steps (i) and (ii) above, (mod L), to obtain the Carmichael number n-one sees that but how can we find subsets of the primes in (ii) whose n is a Carmichael number, by using Korselt's criterion, since product is= 1 mod L? Here's Alford's idea: n is squarefree, and each Pi - 1 divides L, which divides n - 1. Let's review. (iiia) Find a subset P of the primes in (ii), such that for every a, 1 :::; a :::; L with gcd(a, L) = 1, there is a subset Erdos's construction of Carmichael numbers p,, ... ,pk of P for which P1P2 · · · Pk =a (mod L); (i) Select integer L; (iiib) Let Q be the primes found in (ii), excluding those (ii) Determine primes p for which p- 1 divides L, but p does belonging toP. For any subset q1, •.. , qr of these primes, not divide L; let a be that integer, 1 :::; a :::; L, that is = (q,q2 • • • qr)-1 (iii) Find a subset of the primes obtained in (ii) whose product (mod L ). From (iiia) we know that there is a subset is = 1 (mod L). Ph ... ,pk of P for which PI··· Pk = a = (q, · · · qr)-1 This product is a Carmichael number. (mod L), and so p 1 • · • pkq1 · · · qr = 1 (mod L). Therefore, by Erdos's construction, p1 · · · pkq! · · · qr is a Carmichael As an example, let's try (i) L = 120. The primes p that do not number. · divide 120, but for which p- 1 does divide 120, are (ii) 7, 11, 13, 31, 41, 61. Checking through all subsets of these primes Thus, for each different nontrivial subset of Q we've con we find that (iii) 41041 = 7 x 11 x 13 x 41 = 1 mod 120, structed a different Carmichael number, providing a total of and 172081 = 7 x 13 x 31 x 61 =: 1 mod 120, and 852841 = at least 21QI - 1 Carmichael numbers. This method is very 11 x 31 x 41 x 61 = 1 mod 120, so that 41041, 172081, and practical, since we don't need to explicitly write down the 852841 are all Carmichael numbers. Carmichael numbers constructed in (iiib) to be guaranteed of With bigger, highly composite, values of L, we expect to their existence; all we need know is that there is some product find many more Carmichael numbers. Indeed, if we obtain of the primes in P in the congruence class (q,q2 · • • qr)-1 r different primes in step (ii) above, then there are 2r - 1 (mod L) corresponding to each subset q1, ..• , qr of Q. distinct products of nontrivial subsets of these primes. It It remains to find a suitable set P in (iiia). To do this, seems plausible that roughly 1I L of these products are suppose that the primes found in (ii) were PI < P2 < · · · < Pm. = 1 (mod L ), and so we would have approximately 2r I L and define Ri to be the set of products (mod L) of the subsets Carmichael numbers so formed. It can be shown that if of p1,p2, ••• ,Pi· We easily obtain Rj+I from Ri by observing L is the product of all the primes up to some sufficiently that Rj+I = Rj U {rPi+! (mod L) : r E Ri}· Once we find j large point, then we can obtain more than 2log3 L primes in for which Rj is the set of all residue classes a (mod L) with (ii), and so we'd expect more than L 10g2 L such Carmichael 1 :::; a :::; Land (a, L) = 1, then we can take P =Rj and we're numbers. Erdos gave a similarly reasoned argument to justify done. 6 3 2 2 his conjecture that for any fixed E > 0, there are more than Alford worked with the example (i) L = 2 .3 . 5 .7 . 11, x 1-e Carmichael numbers up to x, once xis large enough.8 and found that there are (ii) 155 primes p ;::: 13 such that However, we see from our table above that the Carmichael p- 1 divides L. By computing R 1, R 2 , ••• as above he got numbers remain scarce all the way up to 1015, which is (iiia) P = R21 , that is, that every residue class a (mod L) surprising if Erdos's conjecture is to be believed. Indeed, Dan with (a, L) = 1 is given by the product of some subset of the Shanks, in his book Solved and Unsolved Problems in Number smallest 27 primes found in (ii). Thus if Q is the set of the Theory, challenged those who believe Erdos's conjecture to largest 128 (= 155-27) primes found in (ii) then, as described produce a value of x for which there are more than x 112 above, each subset of Q corresponds to a Carmichael number, Carmichael numbers up to x. (Note that up to x = 1015, there and we've proved the existence of at least 2128 - 1 Carmichael are only a few more than x 113 Carmichael numbers.) numbers. · It is important to note that Erdos's construction is imprac So, in an afternoon's work, Alford increased the number tical, both theoretically and computationally, if one doesn't of Carmichael numbers known from fewer than 214 , to more know how to find products, of the primes produced in (ii), that than 2128 • Certain faculty members, here at the University of are = 1 (mod L ), as required for (iii). At the beginning of this Georgia, taunted the number theory group that there cannot be interesting finite sets that contain more than 2128 elements, and 8Taking his argument to its limit, one expects C(x} to be approximately the that surely Alford's idea should provide sufficient impetus size of the function in (4). to finally prove that there are infinitely many Carmichael SEPTEMBER 1992, VOLUME 39, NUMBER 7 699 ______...... _...... Computers and Mathematics numbers. And indeed it did. The theorem that we eventually which C(x) > x 112, one can extrapolate our tabulated values proved is of logC(x)/logx to guess that one needs x to be around Theorem. (Alford, Granville, Pomerance- 1992): There are 1060-it wouldn't be feasible to write down all the Carmichael more than x 217 Carmichael numbers up to x, once x is numbers up to this point!! sufficiently large. So what does all this tell us about primality tests? Although To make Erdos's construction theoretically practical, one there are various methods known that will verify that a given evidently needs a result which guarantees that, given enough number is prime in a "small" number of steps (thanks to Miller, primes satisfying (ii), there is some subset whose product is Goldwasser and Killian, Adleman and Huang, and others), = 1 (mod L ). A theorem of van Emde Boas and Kruyswijk they all consist of checking a large number of conditions implies that if m > 2 is the largest order of an element of (polynomial in the number of digits of n). It would be more the multiplicative group modulo L, then such a subset exists elegant if one only needed to check a finite number of such provided there are more than m log L primes satisfying (ii). A conditions, but it now seems unlikely that any such method theorem of Prachar guarantees the existence of integers L for proposed thus far will work. which there are more than LcfiogiogL primes p satisfying (ii); In particular, there are various widely-used software however, this quantity is usually a lot smaller than m log L. packages that assert that a given integer is prime if it is To avoid this difficulty one wishes to select L so that m is a "strong pseudoprime" for some given finite set of bases. very small, but Prachar's construction doesn't allow this. So However, we can prove that, for any given finite set of bases, instead we showed the existence of integers L of the form there are infinitely many Carmichael numbers that are "strong L'k with (L',k) = 1, where the maximal order m' of an pseudoprimes" to all the bases in that set. Such numbers would element modulo L' is extremely small, and there are more be falsely identified as prime by such software packages, so than m' log L primes p satisfying (ii), each with the additional reader, beware! property that p = 1 (mod k). The result of van Emde Boas and Kruyswijk then guarantees the existence of a subset of these primes whose product is 1 (mod L )') and, since any such product is 1 (mod k) (as each such prime is 1 (mod k)), thus this product is 1 (mod L ), and so a Carmichael number, from Erdos's construction. Filling in the details of this outline involves some deep Comparative CAS Reviews tools from analytic number theory, as well as combinatorial techniques involving groups and sets. This will all be described Barry Simon* in detail in a forthcoming journal article. One ingredient needed for the proof is a lower bound for the number of primes in certain arithmetic progressions: As is well known, there are asymptotically x /log x primes Symbolic Math: Problems and Solutions up to x, and we expect these to be more-or-less equally I've recently written a review for PC Magazine of five sym distributed amongst the arithmetic progressions a (mod d) bolic math packages (Derive, Maple, Mathematica for DOS, with (a, d)= 1, provided dis a little smaller than x. Currently, Mathematica for Windows, and Reduce)-it is scheduled for it is only known how to prove such a result if dis considerably issue #14 of 1992 and should be out by the time this appears. smaller than x, in fact smaller than a fixed power of log x. As in PC Magazine's last round up in 1990, part of However, for our purposes, we proved the test procedure was to supply the vendor with a list of twenty problems to solve with their software. We'll present Fix E > 0. If x is sufficiently large then for all, but a the problems and solutions here. few9, integers d ~ x5/i2-€ there are more than x/2dlog x Macsyma was not included in this review because there primes ~ x in the arithmetic progression 1 (mod d). hasn't been a significant upgrade since it was reviewed in It is widely believed that such a result holds for any d ~ xi-€. 1990; the vendor plans a new release later this year. MathCAD If true this implies Erdos's conjecture, for we also proved 3.0 includes some symbolics licensed from Maple, but it's a Theorem. (Alford, Granville, Pomerance- 1992): FixE > 0. small subset and doesn't change MathCAD's focus on quick Assume that, for sufficiently large x, the arithmetic progres and dirty calculations rather than medium/large projects. sion 1 (mod d) contains more than xj2dlogx primes up Some comments on the problems and results before turning to x provided d ~ xi-€. Then there are more than xi-2€ to the specifics (these are my opinions and not necessarily Carmichael numbers up to x, once xis sufficiently large. those of PC Magazine!): This theorem seems to guarantee that Erdos's conjecture • Reduce and Derive will post the solutions on their is correct. So, in answer to Shanks's challenge to find an x for electronic BBS. For Reduce, that's the internet address reduce-netlib @rand.org 9 A precise description of "but a few" is: There exists an integer c (depending only on €) such that there is a set B of no more than c integers, each > log x, such *Barry Simon is a Professor of Mathematics at Caltech. He can be reached that we must miss out all those d above that are divisible by an element of B. by email at: [email protected]. 700 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ~--~~~-~~~··.,~~-·-~·-·~~., ..,,.,,.~,.,~~-·~"~"""~-··""~~~ lillJU~~J £----···-·- ,,,,,._.,, _____ ,~-·--·-·-·--~····-····-·········-········· Computers and Mathematics while for Derive it is 217-337-0926. give it a run for the money on interface. • This round of tests included some medium length • Mathematica's graphics are special. You get program projects (17, 20, and, to a lesser extent, 18 and 19) as well matic control of the graphics, links to standard graphics file as short problems. But for many users, the true test is a long types for import to desktop publishing programs, and more project, which just can't be reasonably simulated under the primitives. But its kernel is weak in the area of integration. time scales and circumstances of this review. You can get • I had a dramatic indication that how you code solutions a feet for somewhat larger projects by looking at some of can make a big difference. One vendor, who shall remain the books out on these programs-! especially recommend nameless, initially submitted a solution of problem 9 that took Gray and Glynn's Exploring Mathematics with Mathematica over 35 minutes to run. I expressed surprise at the time and (Addison Wesley, ISBN 0-201-52818-5, $31.95 PB, $42.95 that the solution was different from what I'd expected, which HC). was just a set of rules. What I got by return email was a second • Timing tests were done on the short problems on a solution that ran in under 2 sees!! 386/25 with 15 MB of RAM for all the products (since the • Mathematica has added copy protection! It's worse common kernel was involved, we only tested Mathematica than merely having to type in your name and having the for DOS). They are reported in Figure 1. The differences are software branded because the program records hardware much less significant than they were in 1990, enough so that I information. As happens so often with copy protection, there don't regard them as important any more. are glitches that burn users-I was unable to run QEMM with • To me, the biggest surprise is that neither Mathematica Mathematica without getting a four-question inquisition after nor Maple would simplify Sqrt(4+2 Sqrt(3)) and that both got EACH command as the copy protection kicked in. American the wrong answer on the gravitational potential problem (3c)! business users rebelled against copy protection roughly five • All programs but Derive require a 386 or better. All but years ago and forced companies to drop it. Should. scientists Derive recommend a coprocessor. Derive doesn't need (or do less? use) more than 640K of RAM. The others recommend at least 2 M of RAM, and Mathematica will perform poorly without 6or8MB. • Reduce is not yet a mature product (ironic since it is by far the "oldest" of these products). It is just starting to make Figure 1 the transition from hacker's cult to commercial product. It Mathematica Reduce has a solid core, an eclectic collection of library functions, no Problem Derive Maple graphics, and a terrible interface. But that solid core language la Sls 2m 15s lm 55s 2m3s is critical and means that a competitive product could be out lc Sls 2m40s 25s 18m 47s 6s based on Reduce before long. They are already pushing to 2a ls 6s NA 2b ls ls ls ls Windows with graphics and a better interface. 2c ls ls ls ls • Derive is little changed from 1990. There has been 2d 2s ls ls 17s a key addition of an IF command that accepts iterative 3a ls ls ls ls constructions. This let them solve virtually all our problems, 3b NA Sls NA 3s although the code was often convoluted. Derive's virtue was 3c 2s NA NA BH its low resource usage, which is important in a world of 4a 4s 2s Ss 6s XTs. But over 60% of the PC compatibles sold in 1991 were 4b ls 2s Ss BH 386s and that trend is only accelerating with 386 machines 5 7m22s 15s lm 12s 2m lOs available with VGA and hard disk for under $1000! Derive 6 14s 2s 38s 2m48s makes no use of any hardware beyond an XT, and its graphics 7a ls 15s 59s 2s and interface are getting dated. The program is in need of a 7b ls 4s ls ls major overhaul if it is to survive. 8a ls 2s ls BH • Robert Cringley, in his fun book Accidental Empires, 8b ls 2s ls ls states the 70/30 rule that most markets have a market leader 8c ls ls 43s ls Ss 33s with 70% of the market and a second company with the lOa 3s ls lOb 2m46s Ss Ss 13s bulk of the remainder. While I've no idea of precise sales lOc BH 2ls ls 15s figures, it appears that Mathematica/Maple fit this pattern 11 7s (per sol) 25s 2s (1 sol) lm 20s (1 sol) Mathematica is the market leader in terms of perception, and 12a ls 6s 9s 43s Maple has the bulk of the rest. 12b BH 3s NA lm36s • Maple's DOS interface with the possibility of calling 12c ls 2s 3s 17s previous commands into a full screen editor and customizable menus is by far the slickest DOS interface. Mathematica for Times are rounded, except any time less than ls is listed as ls. Windows' notebook interface with some word processing and BH: The problem was done by hand in multiple steps so no timing is outlining features lets you produce live documents and is also possible. impressive. Maple for Windows, due out later this year, could NA: Couldn't do problem. SEPTEMBER 1992, VOLUME 39, NUMBER 7 701 ··------·-···-----·--··--... -...... _...... __ ._._. __ .. _...... __ ...... ______...... _, ...... Computers and Mathematics Vendor Information (b) Then provide a way to estimate the number of decimal Note: These products have academic and/or site license places needed to be sure ihat M*MA( -1) is the identity to one discounts. part in 1OA6 and Derive, Version 2.10 (c) provide the numerical inverse for this accuracy. Soft Warehouse Note: M has elements of order 10A42 so 50 place accuracy 3660 Walalae Ave., Suite 304 was used for 1c. Honolulu, HI 96818 Derive Problem 1a: 808-734-5801 HILBERT(n):=VECTOR(VECTOR(1/(i+j-1 ),j, 1,n),i, 1,n) Price: $250; $289 for an HP 95LX Rom card HILBERT(30rc-1) Student Edition: Available from Addison-Wesley, Then choose Simplify from the menu. 800-527-5210, $50 Note: While I could do the calculation, I was unable Maple V, Version 1.1 to examine the answer or continue (except to exit) without Waterloo Maple Software getting an out-of-memory error. 160 Columbia St. West Derive Problem 1c: Waterloo, Ontario, Canada N2L 3L3 Same as 1a, only choose Options Precision Exact 50, 519-747-2373 then Options Notation Decimal, then use Approx rather than Price: $695 Simplify. Actually, you run out of memory if you ask for the Student Edition: Available from full inverse but you can ask for something like the maximum Brooks/Cole, 408-373-0728, $99 element (which is where the time comes from). The vendor Mathematica for DOS, Version 2.0 remarks that even though the matrix elements are of order Mathematica for Windows, Version 2.0 10A42, taking 42 place accuracy suffices in Derive because of 100 Trade Center Drive the method of rational approximation of decimals that is used! Champaign, Ill. 61820 800-441-6284 Maple Problem 1a: with(linalg): 217-398-0700 h:=hilbert(30): Price: $995 for Windows version; ih:=inverse(h): $895 for enhanced DOS "With" loads an external library (coprocessor) version; Maple Problem 1c: digits = 50 $595 for standard DOS (won't use a fh:=map( evalf,eval(h) ): coprocessor) version. ifh:=inverse(fh): Student price for standard DOS version: $175 The map function says to apply evalf to each element cif Reduce, Version 3.4 the matrix and evalf forces rational numbers to be floating Calcode Systems point. 1057 Amoroso Place Mathematica Problem 1a, c: Venice, CA 90291 HilbertMatrix[n_] := Table[1/(i + j- 1), {i,n},{j,n}] 310-399-7612 matrix = HilbertMatrix[30]; Price: $495 inverse= Inverse[matrix]; In the UK: Codemist Ltd, t = SetPrecision[matrix,50]; "Alta", Horsecombe Vale, inverse= Inverse[t]; Combe Down, Bath BA2 5QR, UK +44-225-837-430 In Germany: Konrad-Zuse-Zentrum Reduce general remark: Expressions in the language end fuer Informationstechnik Berlin, in; (answer displayed) or$ (answer not displayed). Comments Attn: Herbert Melenk, start with%. Heilbronner Str. 10, D 1000 Berlin 31, GERMANY, Reduce Problem 1a: matrix m(30,30): +49-30-89604-195 for i:=1:30 do for j:= 1:30 do m(i,j):= 1/(i+j-1); lim; The Problems and Solutions Reduce Problem 1c: Given the definition of m: on rounded; {Note: Problems 2a, 2b, 3c, 4a, and 4b are suggested by precision 50; 1/m; Kahane. Problem 12 is unchanged from last time.} off rounded; 1. Hilbert Matrices: Invert a 30 x 30 Hilbert matrix-this is a matrix whose iJ element (with elements starting at 2. Simplifications 1,1) is (a) Simplify {4 + 2 C3n1t2)} A(l/2) (lli+j-1). (b) Simplify (3+4Irc112) {Here I=sqrt of -1} (a) First use exact rational arithmetic. (c) Expand Tan (X+Y) 702 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ····.-··········-·-·· .. ··········· ...... -...... _f •. ·------~~.--·-·-····--••··-- ...... Computers and Mathematics (d) Compute to 6 digit accuracy (at least) tan(10A100) Mathematica Problem 2c: Needs["Algebra 'Trigonometry' "] Derive Problems 2a, b: Type in and choose Simplify; TrigReduce[Tan[x + y]] worked fine. gave the right answer. The Needs command loads an external Derive Problem 2c: Type in Manage Trigonometry Ex library. pand from the menu and then Simplify. Gives answer in terms Mathematica Problem 2d: of sin/cos; not tan. N[Tan[10Al00],110] Derive Problem 2d: Options Precision Exact N with N at says to work to 110 place accuracy. least 107 (we used 200) and Reduce Problem 2a: Here's the solution-had to be then Author and type in tan(lOAlOO). Approx will give worked out "by hand": answer which is %The standard REDUCE simplifier doesn't handle either 0.40123196199081435418575434365329495832387 ... of these cases Maple Problem 2a: Such simplifications are not built in! % directly, so we solve them as factorization problems. q2a := (4+2*3A(l/2)t(l/2); load_package arnum; t := convert(q2a,Root0f): defpoly sqrt3**2- 3; tl := traperror(evala(Normal(t))): factorize(x**2- (4+2*sqrt3)); %Factoring over algebraic if t1 = lasterror then domain sqrt(3). tl := map(rhs, t1[2]); % So {4 + 2 (3t(l/2)} A(l/2) is one of the expressions: t1 := select(proc(x) evalb( evalf(x, 1O)=evalf( q2a, 10)) for each j in ws collect -sub(x=O,j); end, tl); offarnum; a2a := convert(op(tl),radical): Note: ws =workspace else Reduce Problem 2b: Similar solution to 2a a2a := convert(tl,radical); fi; Reduce Problem 2c: Not built in but % We show this solution to demonstrate REDUCE's Maple Problem 2b: This is built in! pattern matching. a2b := sqrt(3+4*I): (tan(x+y) where {tan(rvx)=sin(x)/cos(x), Maple Problem 2c: cos( rvx +rvy )=cos(x)*cos(y)-sin(x)*sin(y ), q2c := tan(x+y); sin(rvx+rvy)=sin(x)*cos(y)+cos(x)*sin(y)}) a2c := expand(q2c): where sin( rvX)=COS(x)*tan(x); #optional: express in terms of tan(x) and tan(y) Reduce Problem 2d: normal(eval(subs(sin=(a~ tan(a)*cos(a)),a2c))); on rounded; Maple Problem 2d: precision 120; q2d := tan(10A100) prinLprecision 20; a2d := evalf(evalf(q2d,106),6) tan(10A100); precision 12; Mathematica Problem 2a: off rounded; expr := (4 + 2 (3t(l/2)r(ll2) Expand[expr] 3. Symbolic Integration and Differentiation: The answer given though was Sqrt[2J Sqrt[2 + Sqrt[3]], (a) Take the derivative ofxA10 * (cos (xA5 * 1n (x)) t(l/2) NOT the expected l+Sqrt[3]. And trying Solve[xA2-4-2 (b) Symbolically integrate the derivative computed in 2(a) Sqrt[3]==0,x] didn't yield the simplified answer (although (c) Compute the gravitational potential of a sphere in such a solve command did coax the answer from Maple spherical coordinates-explicitly as a function of x compute and Reduce). However, one can use Mathematica's ability the double integral in r, t for O SEPTEMBER 1992, VOLUME 39, NUMBER 7 703 Computers and Mathematics 2*x*r*COS(theta)),theta,O,pi),r,0,1) Maple Problem 4b: q4b := 1/(exp(x) - exp(x-1/xA2)); and choose Simplify from the menu. The form of the answer a4b:=limit(expand( q4b ),x=infinity); given was (xA2+x-2)* ABS(x-1)/(6*x)-(xA2-x-2)* ABS(x+ 1)/ The answer is 0. (6*x). This was the only automated correct solution! Mathematica Problem 4a: Maple Problem 3a: Limit[Log[x- a]/((a-b)(a-c)) + q3a := xAlO * ( cos (xA5 * ln (x) ) r<112); Logf2 (x- b)]/((b-c)(b-a)) + a3a := diff(q3a,x); Log[x-c]/((c-a)(c-b)), X--t Infinity] provided the right answer. Maple Problem 3b: a3b := int(a3a,x); Mathematica Problem 4b: The answer came out in a complicated rewriting of the Needs["Calculus 'Limit' "] original function, to whit: Limit[l/(EAx- EA(x-xA(-2))), x--t Infinity] 112 sqrt(2) *(alb+ c/b) where a,b,c were written out with (here d = I xA5) Reduce Problem 4a: b = sqrt (xA(2d)+1) limit(log(x-a)/( (a-b)*( a-c)) + log(2(x-b) )/((b-e )*(b-a)) a = xA(3/2 d + 10) c = xA(-1/2 d + 10). + Iog(x-c )/((c-a)*(c-b )),x,infinity); Maple Problem 3c: "Maple getint(int(q3c,t=O .. Pi),r=0 .. 1) Reduce Problem 4b: Can't be handled directly so the = 1, which is wrong." (!! !). A way of doing the integral in expression is simplified (by hand!) and l'Hopital's rule is steps fixing the signs by hand was provided. used. (Hardly counts as a solution). Mathematica Problems 3a,b: deriv = D[xAlO (Cos[xA5] Log[x]r<112),x] worked but Integrate[deriv,x] did not return a completely 5. Symbolic Sums and Factoring Polynomials integrated expression. Factor over the rationals, the sum from 1 to N of f40 as a function of N. Mathematica Problem 3c: Integrate[rA2 Sin[th]/(xA2 + rA2- 2 x r Derive Problem 5: Use Calculus Sum to enter the sum Cos[th]r<112),{r,0,1 },{th,O,Pi}] and then Simplify. returned Maple Problem 5: a5a:=sum((40,j=l..N): (2- 3x)Sqrt[(1 - x)2] Sqrt[(1 + x)2](2 + 3x) a5b:=factor(a5a); -----,,--=------,---::-----'--- + --=-----'---,-----'-,.....-7----'- -6x + 6x2 6x + 6x2 Mathematica Problem 5: Needs["Algebra'SymbolicSum' "] which is the wrong answer for x < 1 (but correct if x> l ). sum= SymbolicSum[(40,{j,l,n} ]; Reduce Problems 3a, b: Factor[ sum] df(xA10*( cos (xA5 *log (x)) r<112),x); Reduce Problem 5: int(ws,x); sum((40,j,1,n)$ Reduce Problem 3c: Reduce doesn't do definite integrals. on factor; So a solution by hand was provided where, at a critical point, ws; the sign of a square root was flipped! off factor; 4. Limits (a) Compute the limit as x goes to infinity of 6. Prime Testing Find the next prime after 1OA80 log(x- a) log(2 * (x - b)) log(x- c) -:--....:::..:-~___:_--:- + + -,--_.::._.,-,-----,::-:- Derive Problem 6: Enter NEXLPRIME(10A80) and (a- b)(a- c) (b- c)(b- a) (c- a)(c- b) Choose Simplify from the menu. The answer is 10A80+ 129. All these programs use a probabilistic approach so it is (b) Compute the limit as x goes to infinity of the inverse guaranteed this is a prime but it surely is. 1/[exp(x)- exp {x- (xA(-2))}] Maple Problem 6: a6:=nextprime(10A80); Derive Problem 4a,b: Enter the function in author mode and then choose Calculus Limit from the menus; infinity is Mathematica Problem 6: entered as "inf". Needs["NumberTheory'NumberTheoryFunctions' "] NextPrime[10A80] Maple Problem 4a: a4a:=limit(q4a,x=infinity) with q4a the obvious input. The answer is -ln(2) I (b- c)(a- b) Reduce Problem 6: nextprime(10A80); 704 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ------····----·-··--·····-···--·-········Computers and Mathematics ·····················•············· 7. Integer Factoring 8. Infinite Sums and Integrals (a) Factor 98765432123456789 over the integers. (a) Compute the sum off(-6) for j from 1 to infinity. (b) Factor 13 over the Gaussian integers. (Gaussian inte (b) Compute the integral from 0 to infinity of xA(7/2) * gers are of the form a+bl with a,b integers; note factorization exp(-xA3). is NOT unique; you should try to find ALL factorizations into (c) Compute the integral from 0 to infinity of xA(7) * Gaussian primes.) exp(-xA3). If possible see if the answer has an exact answer in terms Derive Problem 7a: Enter the number and choose Factor of pi, etc. from the menu. Derive Problem Enter the sum, integral via the Calculus The answer is 449 494927 444444443. 8: submenu and Simplify. The answers are Derive Problem 7b: An expression \\'aS provided for piA6/945, Sqrt(pi)/6 and 5/9*(Gamma(5/3))=0.501525 primes that gave their Gaussian factors explicitly (depending Maple Problem 8: a8a:=sum(l/f6,j=l..infinity); on whether pis congruent to 1 or 3 mod 4). The prescription a8b:=int(xA(7 /2)*exp( -xA3),x=O .. infinity); is to factor and then apply this function to each prime. a8c:=int(xA7*exp( -xA3),x=O .. infinity); Maple Problem 7a: a7a:=ifactor(98765432123456789); Mathematica Problem 8: Maple Problem 7b: Gaussian factorization will be in the Sum[r<-6),{j,1,Infinity}] next release of Maple but for now the solution is via knowing Integrate[xA(7/2) Exp[-xA3],{x,O,Infinity}] the way Gaussian factorization takes place-namely solving Integrate[x/ Exp[ -xA3],{x,O,Infinity}] a Diophantine equation: Reduce doesn't do definite integrals per se, but solutions t := {isolve(aA2+bA2=13)}: of sorts were provided: a7b := map(proc(x) subs(x,a+l*b); "*evalc(13/") end,t): Reduce Problem Sa: Solved using residue calculus knowl- edge; hardly counts as a solution: Mathematica Problem 7: load_package taylor; Factorlnteger[98765432123456789] resid := coeffn(taylortostandard taylor(z/tan(pi *z),z,0,6),z,6)$ Factorlnteger[ 13, Gaussianlntegers--? True] Currently, the only package that offers built-in support for Reduce Problem Sb,c: Loaded Laplace Transform pack- Gaussian integers. age and did change of variable by hand. Reduce Problem 7a: (typical of mode turning on/off) 9. Rule Based Algebra on ifactor; Consider the Clifford algebra in 10 variables, that is, the factorize 98765432123456789; complex algebra with ten generators, s0, ... ,s9 obeying off ifactor; si sj + sj si = 0 if i is different from j Reduce Problem 7b: Custom code si si = 1 That is, multiplication is NOT commutative (but is as procedure try JacLsquares n; sumed associative). Compute % See if the prime (over integers) n is the sum of two (sO+sl+ .... +s9t5 positive squares. NOTE: This must be done with general methods-it is begin cheating to use the invariance of the Clifford algebra under scalar j; orthogonal transformations. j := 1; top: Derive Problem 9: A solution was provided with 55 lines m := sqrt(n-j*j); of function definition of which the following is typical: if m*m+j*j = n then return list ((m+i*j),(m-i*j)); ADD_A.UX(u,v,j,k):="' j:=j+1;. IF(j=O,HEAD(v,k),"' IF(k=O,HEAD(u,j),"' if j*j< n/2 then goto top; IF(SIMILAR(ELEMENT(u,j),ELEMENT(v,k)),"' return list n; APPEND(ADD_A.UX(u,v,j-l,k-1),"' end; ADDSIMILAR(ELEMENT(ELEMENT(u,j),l)+ procedure factorJ.nteger_over_complex n; ELEMENT(ELEMENT(v,k), l),ELEMENT(u,j))),"' begin IF(BEFORE(ELEMENT(u,j),ELEMENT( v,k) ),"' scalar facts; APPEND(ADD_A.UX(u,v,j,k-l),[ELEMENT(v,k)]),"' on ifactor; APPEND(ADD_A.UX(u,v,j-1,k),[ELEMENT(u,j)]))))) facts := factorize n; Anyone who thinks you can't program with just an IF return for each k in facts join try _facLsquares k; statement should look at this. It's awkward but certainly end; doable! The answer, by the way, is 100 times the sum of the factor J.nteger _over _complex 13; sigmas. SEPTEMBER 1992, VOLUME 39, NUMBER 7 705 ...... ·-·····------······················································· Computers and Mathematics ... ··················-··································· Maple Problem 9: Here's the code to set up the rule based Derive Problem lOb: Choose Factor Rational algebra: Derive Problem tOe: The solution suggested was to s.(0 .. 9): factor over the complexes and by hand pick out the factors readlib( commutat): that combine to give factors over the complex numbers. fori from 0 to 9 do for j from i+1 to 9 do Maple Problem lOa: Expand((x+y+zr20); &*(s.j,s.i) := -&*(s.i,s.j); By default, the ordering of terms in the output of such od; expansions appears to be random and certainly isn't organized &*(s.i,s.i) := 1; in a useful way. od: Maple Problem lOb: a10b := factor(alOa); &A := proc(a,n) local t; t := 1; Maple Problem tOe: ton do "It is unfortunate that you ask this question at this time. if type(t,constant) then t := t*a Maple 5.1 has multivariate polynomial factorization over else t := expand(t&*a) algebraic number fields and also algebraic function fields built fi in. Maple 5.0 can factor UNIVARIATE polynomials over od; ANY algebraic number field though." A twelve line program t was provided instead. end: q9 := sum('s.k' ,k=0 .. 9); Mathematica Problem 10: a9:=q9&A5; poly= Expand[(x + y + zr20]; Factor[poly] Mathematica Problem 9: Factor[xA4 + yA4, Gaussianlntegers--+ True] (* rulesfor Clifford algebra *) ncm[s[L],s[j_]] := -ncm[s[j], s[i]]/;i > j Reduce Problem 10a,b: ncm[s[L], s[L]] := 1 (x+y+zr2o; (* rules for noncommutative multiplication *) on factor; ws; (* - behavior .of multiplication of integers *) Reduce. Problem tOe: ncm[a_?Nuril.berQ, b_?NumberQ, c ___ ] := ncm[a b, c] on complex, factor; (* - distributivity of addition *) x**4 + y**4; ncm[m___ , a_plus,b_plus, n ___ ] := off complex,factor; ncm[m, Distribute[tmp[a,b],Plus]/.tmp--+ ncm, n] (* - associativity *) ncm[a ___ , ncm[r_ __], b ___] := ncm[a, r, b] 11. Solve Numerically the Triple of Nonlinear Equations (*here's the expression*) (Real OR Complex Solutions): expr =Plus @@ Map[s, Range[1,9]] sin (x) + yA2 + ln(z) = 7 (* and here's the power. Note the output form involves 3*x + 2Ay - zA3 = -1 nero; this could be formatted to look cleaner for one's xA2 + yA2 + zA3 = 5 individual purposes. *) exprA5/. x_An_ :> Fold[ncm, x, Table[x, {n- 1}]] Derive Problem 11: Six approximate complex solutions were found for Reduce Problem 9: Shows simple elegance of the Reduce Example. x = -2.46556- 1.69474 i, y = -2.89745 language. + 0.573737 i and z = 0.58869 + 1.91505 i. This is done operators; by using the Newton's method code from the supplied file noncoms; Solve.Mth guessing various starting points. Each solution for all i,j such that i>j let s(i)*sG)=-sG)*s(i); took about 7 seconds to find once typed in. There are no real for all i let s(i)*s(i) = 1; solutions. xxx :=for i:=0:9 sum s(i); xxxA2; Maple Problem 11: A thirty line program implementing a xxx*wsA2; complex Newton's method was provided; it is not built in. Mathematica Problem 11: eq1 = Sin[x] + yA2 + Log[z] == 7; 10. Polynomials in Several Variables eq2 = 3x + 2Ay- zA3 == -1; (a) Expand (x+y+zr2o. eq3 = xA2 + yA2 + zA3 == 5; (b) Now factor the polynomial in (a) over the rationals. FindRoot[Evaluate[{ eq 1,eq2,eq3} ], (c) Factor xA4 + yA4 over the Gaussian integers. {x,1 + l},{y,1 + I},{z,l +I}] found the root Derive Problem lOa: Enter Expression and Choose Ex {x--+ 0.339961 + 2.36119 I, y--+ 2.39276- 1.0728 I, pand z --+ 1.86956 + 0.34026 I} 706 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Computers and Mathematics Taking random starting points found another 11 roots; Maple Problems 12a,b: here's the code including code for removing duplicates from q12a := diff(y(x),x$2) + y(x)=cos(x); a list: a12a := dsolve(q12a,y(x)); FindRoot[Evaluate[{ eq 1,eq2,eq3}], { x, 1 + 12b is virtually identical in syntax I},{y,1 + l},{z,1 +I}] fr =Table[ Maple Problem 12c: FindRoot[Evaluate[{eq1, eq2, eq3}], {x,#l}, q 12c := { s(n)=3*s(n-1)-2*s(n-2),s(1)=1,s(2)=1 }; {y,#2},{z,#3}]& @@ a12c := rsolve(q12c,s(n)); Table[Random[Complex, Mathematica Problem 12a,b: {-7 -7 I, 7 + 7 1}],{3}], {30}]; DSolve[y"[x] + y[x] == Cos[x], y[x],x] fr = Select[fr,(({ eq1, eq2, eq3}/.#) ==={True, yielded a solution but True, True})&]; DSolve[xA2 + y'[x] + 2 x y[x] -y[xr3 == 0, y[x], x] removedups[{}] := {} did not (although NDSolve provided a numeric solution). removedups[lisL] := Join[{First[list]}, Mathematica Problem 12c: removedups[Select[Rest[list], Needs ["DiscreteMath 'RSolve' "] (Chop[First[list] -#,lOA -8] =!= {0,0,0}) &]] RSolve[{ s[n] == 3 s[n- 1] - 2 s[n- 2], ] s[l] == 1, s[2] == 1}, removedups[{ x,y,z }/.fr] s[n], n] Reduce Problem 11: (This requires a package not included Reduce Problem 12a: with Reduce but available via internet from Rand); load_package odesolve; load_package numeric; depend y,x;· % This system has no real solution. odesolve(df(y,x,2)+y=cos(x),y,x); % looking for complex solutions: . sys :={sin (x) + yA2 + log(z) = 7, Reduce Problem 12b: (Notice how much easier this is 3*x + 2Ay- zA3 = -1, than Derive): odesolve(xA2*df(y,x)+2x*y=yA3,y,x); xA2 + yA2 + zA3 = 5}; on rounded,complex; Reduce Problem 12c: Provided a 24 line general procedure for solving recursion soil := num_solve(sys,x=l +i,y=1 +i,z=1 +i); % Found three solutions by this method relations! procedure solve_lin_rec(rec,ic); % solves homogenous linear recursion relation REC which 12. ODE's and Recursion Relations % has to have the form s(n)= ... with initial conditions (a) Solve y" + y = cos(x) % IC in the form of list { s(1)=?,s(2)= ... } (b) Solve xA2 * (dy/dx) + 2 x*y- yA3 = 0 % the method used - substitution s(n)=xAn % like eA(lambda*x) in linear homogeneous ODE. (c) Solve the recursion relation s(n) = 3 * s(n-1)- 2* s(n-2) % Of course some checking should be added. s(l) = 1 s(2) = 1 begin scalar lrec,sol,msol,gsol,j; Note: Unfortunately, I copied this problem from the last for all n let s(n)=xAn; Notices article which had dropped a minus sign in the initial condition for s(2) so the answer is identically 1! lrec:=lhs rec; rec:=rhs rec; Derive Problem 12a: Use routines from ode2new.mth. for all n clear s(n); Need to load that and type in LIN2_GEN(0,1,COS(x)) and rec:=num( (lrec-rec )llrec); use Simplify. j:=1; for each a in solve(rec,x) do Derive Problem 12b: Depends on realizing it has Bernoulli < SEPTEMBER 1992, VOLUME 39, NUMBER 7 707 ·····--····· ... ··--······- ...... ····················-············-··--··-~!:II.. ~!IIIIIIIL&IIIIill££11£1!11111 illllllllll'llllllll-11111111-111121111'11 Computers and Mathematics sol:=solve(for each a in ic collect sub(n=part(lhs a,l),gsol) Maple Problem 14b: =rhs a, al4b := plot3d(sin(x+sin(y)),x=0 . .4*Pi,y=0. .4*Pi, for i:=l:length ic collect c(i)); grid=[36,36],axes=BOXED,scaling=CONSTRAINED); %If some c(i) remains it can be arbitrary real. Maple Problem 14c: Explicit coordinates for the vertices let sol; of the Icosahedron were provided and could be used via the gsol:=gsol; clearrules sol; grid command to plot the figure. The points were generated return gsol with a little program. end; Maple Problem 14d: solveJin...rec(s(n)=3*s(n-1)-2*s(n-2),{ s(l)=l,s(2)=1} ); Maple V cannot in general draw contour surfaces, but it is possible to do it in this case. Special code based on the particular example was pro 13. External Conversions. Consider the function f(x) := vided. exp{-xA(-1/2)} I {sin(x) + xA7} Maple Problem 14e: If you have Maple try this lovely (a) Translate into 'lEX format. graphic: (b) Translate into a C program. Spiral Tube Around a Torus Derive can do (b) but not (a); the other three can do both. with(plots): N:=lO: a14e := tubeplot( {[lO*cos(t),lO*sin(t),O, 14. Graphing t=0 .. 2*Pi,radius=2,numpoints=10*N,tubepoints=2*N] (a) Graph the parametric curve: ,[cos(t)*(10+4*sin(9*t)),sin(t)*(10+4*sin(9*t)),4*cos(9*t), x = cos(3t) y = 3 sin(5t) t=0 .. 2 *Pi,radius=l ,numpoints=trunc(37 .5*N),tubepoints=N]}, fort from 0 to 2*pi scaling=CONSTRAINED,orientation=[76,40]): (b) Graph the surface sin[x + sin(y)] Mathematica Problem 14: with x,y running from 0 to 4*pi a) ParametricPlot[{Cos[3 t], 3 Sin[5 tl},{t,0,2 Pi}] (c) Draw an Icosahedron. b) Plot3D[Sin[x + Sin[y]], {x,0,4 Pi}, {y,0,4 Pi}, Plot (d) Draw the contour surfaces of y * Sqrt [9- xA2] where Points -+ 30] x andy run from -3 to 3. c) Needs["Graphics 'Polyhedra' "] Show[Polyhedron [Icosa (e) Provide an additional graphical example that you think hedron]] shows off your product. d) ContourPlot[ y Sqrt[9- xA2], {x,-3,3}, {y,-3,3}] e) Five extra graphics were provided (graphics is Mathe- Derive Problems 14a/b: Simple applications. Define the matica's strong suit!) including function. Show[Polyhedron[Greatlcosahed.ron]] Go to the Windows menu and split the window, set the and larger window to 2D or 3D graphics, set some parameters Needs ["Miscellaneous 'WorldPlot' "] for optimal display (requires some experimentation) and pick WorldPlot[ {World,RandomColors }, "plot". WorldProjection -+ Sinusoidal] Derive Problem 14c: The vendor used the vertices of the Reduce has no graphics! Icosahedron as found in Mathematica's library(!) and entered them as a complicated data set and used the vector command. Derive Problem 14d: You can define contours as a vector and plot the values of a vector. Color coding by height is NOT 15. For each of the graphs you could draw in problem 14, possible. do the following: (a) Print it out on a laser jet. Derive Problem 14e: The vendor points out that "Un (b) Save it as a vector graphic file - EPS or CGM or ... like many packages, most discontinuities such as tan(x) or (c) Save it as a bitmap file- PCX or TIFF or ... sign(x) are not bridged, and false transformations such as arc Reduce has no graphics; Derive has no explicit support for tan(tan(x)) -+ x are avoided", and provides a graphic sample printing graphs or saving to a file but expects you to use third to illustrate this. party print screen products which capture the graphic and Maple Problem 14a: unfortunately the on screen menu (some third party products aspecLratio := 1.45; #This depends on your monitor. will let you crop this menu out). Maple has support for many w := aspecLratio*3: printers- you can print to a file and so capture an HPGL file. a14a := plot([cos(3*t),3*sin(5*t),t=0 .. 2*Pi],x=-w.. w,y=- Mathematica has strong support for printers; the DOS version 3 .. 3, resolution=1024,style=LINE); can send to a file in EPS format. The Windows version adds Once plotted, a small menu can be popped up with FlO. BMP and WMF to EPS. 708 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ffi!lllllllffi!lllllllffi!lllllllffi!lllllllffi!lllllllffi!lllllllffi!lllllllffi!IIIIIII-'KT~'\\U2~lffi!lllllll Computers and Mathematics 16. Provide a program to draw the Koch snowflake (this e:=f; f:=iquo(f,4); is a two-dimensional "curve" obtained as a limit by od; the following iterative process. Start with an equilateral end: triangle. At each stage go to the next by adding to each al6 := Koch(6); side an equilateral triangle pointing outwards of side 1/3 Mathematica Problem 16: the size of the current edges, centered on the edge; Contact KochSnowfl.ake[n_lnteger?NonNegative] := me if you aren't familiar with this object already). Show[Graphics[FixedPoint[ Clearly you'll need to end the iteration after finitely many (#1/.Line[ { starL,finish_}] steps. That should be a parameter in the program. :> doline[start,finish]) &, Derive Problem 16: A use of IF allows a recursive {Line[{ {0,0},{ l/2,Sqrt[3]/2}} ], definition of the Koch snowflake (Note: multiple lines in Line[ { {112, Sqrt[3]/2},{1,0}} ], Derive require a"' continuation character, not shown here): Line[ { {1,0},{0,0}} ]}, s:=3*TAN(pi/6) n 11. EDGE(a,b,c,n):=IF(n=O,[a,b], AspectRatio -t Automatic, PlotRange -tAll] [EDGE(a,(2*a+b)/3,(2*a+c)/3,n-1), doline[start_,finish_] := EDGE((2*a+b)/3,(a+b+c)/3,(2*a+c)/3,n-1), Module[ {vee, normal}, EDGE((a+b+c )/3,(a+2*b )/3, (2*b+c )/3,n-1), vee = finish - start; EDGE((a+2*b )/3,b,(2*b+c)/3,n-1)]) normal= Reverse[ vee] {-1,1} Sqrt[3]/6; STAR(n):=[EDGE([-s,-1],[s,-1],[0,-4],n), {Line[{start, start+ vec/3} ], EDGE([s,-1],[0,2],[2*s,2],n), Line[ {start+ vec/3, start+ vec/2 +normal}], EDGE([0,2],[ -s,-1],[ -2*s,2],n)] Line[ {start + vec/2 + normal, start+ 2 vec/3} ], With these definitions STAR(n) is an nth order iterate Line[ {start + 2 vec/3, finish}] stating on the star for n=l. } J Maple Problem 16: KochSnowfl.ake[ 4] aspecLratio := 1.45; #This depends on your monitor. Reduce has no graphics. Koch:= proc(n) local n1,d,x,y,p,i,h,v; if type(n,integer) and O SEPTEMBER 1992, VOLUME 39, NUMBER 7 709 y ..y··..,,·.. ~,,·~.w y·••••• ••••.. • ••••••••••••••• •••••••••• • ..••• ·.··w~w..•••A" w w yy ItI~..~ ., I11 ··· ·· ·' N·..•' . Computers and Mathematics Derive Problem 18: Here it is in one line!! Maple Problem 19: F(n):=VECTOR(VECTOR(VECTOR plist := proc(a,b) ([k,m,h],m,MAX(k,2*(h-k)),h),k,h,rv local p,i,t,j; MAX(I,hl2),-I),h,n-l) p := nextprime(a); for i do Maple Problem 18: t[i] := p; triple :=proc(n) p := nextprime(p); local i,j,k,c,t; if p>b then break fi; c :=0; od: for i from 3 to n-2 do [seq(t[j],j=1..i)] for j from i+1 to n-l do end: for k from j+1 to n while 2*(k-i)<=j do c:=c+1; t[c]:=[i,j,k]; Mathematica Problem 19: od PrimesBetween[nl_, n2_] := od Table[Prime[t], {t,PrimePi[nl] od; + 1, PrimePi[n2]}] [seq(t[i],i=I ..c)] PrimesBetween[100000,101000] end: Reduce Problem 19: Mathematica Problem 18: for i:=100000:101000 join ifprimep i then {i} else {}; Needs["DiscreteMath'Combinatorica' "] myTriples[njnteger?Positive] := Select[KSubsets[Range[n - 1],3], 20. Write a program to find the GCD of two polynomials ((#[[3]] - #[[1]]) <= #[[2]]/2) &] over the field oforder 27. allmyTriples[n_] := Derive Problem 20: A 26 line program was provided. Join[Flatten[Map[Permutations, myTriples[n]],I], Map[{#,#,#}&,Range[n-l]] ] Maple Problem 20: A solution was even provided for multivariate polynomials. Here is one for single variable Reduce Problem 18: polynomials: procedure gentriple n; Given a and b in GF(p~k)[x] compute their gcd using the for il :=1 :n-l join Euclidean Algorithm. for i3:=il:n-l join GcdUniGFq := proc(a,b,x,p) local c,d,r; if i3<2*(i3-il) then {} c := Expand(a) mod p; else for i2:=max(il,2*(i3-il)):i3 d := Expand(b) mod p; join {{il,i2,i3}}; while d <> ado r := Rem(c,d,x) mod p; c := d; d := rod; Expand(cllcoeff(c,x)) mod p # Make the Gcd monic 19. Write a program to generate a list of primes between end: 100,000 and 101,000. Mathematica Problem 20: A 50 line program was pro Derive Problem 19: It's two lines of general code: vided. PRIME_COUNT(m,n):=IF(NEXT-PRIME(m»n,O,1 +PRIME_COUNT(NEXT-PRIME(m),n)) Reduce Problem 20: No general code for finite fields PRIME..LIST(m,n):=ITERATES(NEXT-PRIME(k),k, but there is for modulo arithmetic so it wasn't hard to set NEXT-PRIME(m),PRIME_COUNT(m,n)-I) everything up although there were more than 50 lines of PRIME..LIST(100000,101000) code. Uses the fact that the field of 27 elements is gotten by There are 81 primes in the list. adjoining an element of order 3 to Z3. 710 NOTICES OF THE AM~RICAN MATHEMATICAL SOCIETY Inside the AMS Committee on Human Rights colleges open. A resolution was submitted to the Council at of Mathematicians its meeting in Orono in August 1991. That resolution was tabled. A second resolution was submitted to the Council for Alice T. Schafer, Chair consideration at its meeting in Baltimore in January 1992. In the two years since a report from this Committee appeared That resolution was defeated by a vote of 12 to 11. * At in the Notices, the Committee has considered cases of the time of the writing of this report, the Israeli Embassy in human rights violations of mathematicians in Russia, Somalia, Washington reports that all universities and colleges in the Tunisia, and the United States. Three of the cases have been West Bank and Gaza are open. settled somewhat satisfactorily but not ideally. The last of the Richard Dicker, Director of the New York based Commit Russian mathematicians on whose behalf the Committee had tee to End the Chinese Gulag, met with this Committee at the worked for some time has been allowed to emigrate and is Joint Mathematics Meetings in Baltimore in January 1992. living in this country, but the latest information from him is The Committee to End the Chinese Gulag was formed in 1991 that he has been unable to locate a position. The Somalian and numbers among its members the astrophysicist Fang Lizhi mathematician has been freed from prison and allowed to and the physicist Yuri Orlov. The Committee has written a leave the country. (His family had been allowed to leave pamphlet giving suggestions for actions that scientists might somewhat earlier.) They are now living in the United States take when they attend scientific conferences in China. (For where he has a university position. Unfortunately, the Tunisian additional information, the Committee may be contacted at mathematician on whose behalf this Committee, as well as 485 Fifth Avenue, New York, NY 10017.) other human rights groups, has worked diligently for several The Committee wishes to express its appreciation to years is still in prison under a sentence to run through May the following groups for sharing information on human 1993. (For a more complete report on this case see the report rights violations of individual mathematicians: Committee from this Committee in the July/August 1990 issue of the of Concerned Scientists (New York), the Human Rights Notices.) Committees of the American Association for the Advancement The case in the United States concerned Professor Ethel of Science (AAAS) and of theNational Academy of Sciences, bert N. Chukwu of North Carolina State University. The and the Chicago Action for Soviet Jewry. I would like Immigration and Naturalization Service (INS) was attempting to thank personally those members who have retired from to deport him on grounds that this Committee, and many the Committee in the last two years for their invaluable other individuals as well, felt were unjustified. The INS even contributions to the work of the Committee: Raymond Ayoub, tually brought him to trial and he won. His text, Stability Joan S. Birman, Michael I. Brin, Chandler Davis, and Joel L. and Time-Optimal Control of Hereditary Systems, has just Lebowitz. been published (by Academic Press). Professor Chukwu has dedicated that text to " . . . the good and courageous men *The resolution presented at the Baltimore meeting read as follows: "The and women whose faith in my family sustained us through Council of the AMS takes note of the historical fact that the universities in our recent difficulties ...". Among those mentioned are some the West Bank and Gaza came into existence after the 1967 war under Israeli occupation as a result of the initiatives taken by residents of the territories. These members of this Committee and William Browder, AMS initiatives had been ignored by former regimes there. The Council, with this President at the time of Professor Chukwu' s trial. history in mind, deplores the frequent closings of the colleges and universities In addition to its efforts on behalf of the mathematicians in the territories. These closings have hurt students and faculty in all fields, in the above cases, some members of the Committee felt that including mathematics, and impaired their ability to carry out normal educational activities. the AMS Council should be asked to submit to the Israeli "The Council notes that Birzeit and Al-Najah Universities have been closed authorities a resolution on behalf of the mathematicians and for over three years and that the other colleges and universities have been closed mathematics students at the universities and colleges in the for shorter periods of time. It is pleased to note that all of these institutions, with West Bank and Gaza, which had been closed from time the exception of Birzeit University, have recently been reopened. The Council calls upon the Government oflsrael to reopen Birzeit University. The Council asks to time. The resolution would urge the Israeli Government all sides to work actively to restore conditions which would permit maintaining and all parties to work together to keep the universities and normal educational and research activities of the colleges and universities." SEPTEMBER 1992, VOLUME 39, NUMBER 7 711 Washington Outlook tiatives it coordinates have added a new layer to the budget This month's column is written by Lisa A. Thompson, making process. The ''top-down" priorities imposed on basic who is the Assistant for Governmental Affairs of the Joint research by FCCSET need to be reconciled with the ''bottom Policy Board for Mathematics (JPBM). up" priorities coming from the scientific community. Once an intriguing albeit academic topic for science policy ob Research and Development servers, discussion of how the government allocates resources in the Federal Budget Process among the various elements of the scientific enterprise-that The executive branch's prioritization of federal science pro is, how it sets priorities-has received more attention from grams is implicit in its annual budget submissions, in which the science policy establishment, including Congress, in the R&D is highly compartmentalized. The numerous agencies past few years. responsible for research set their budgets independently ac The issue is not straightforward, because the R&D budget cording to their own missions and goals. While the Office is necessarily disaggregated in different ways at different of Management and Budget (OMB), in consultation with the stages of the complex federal budget process, but. Congress Office of Science and Technology Policy (OSTP) approves is increasingly concerned that funding decisions need to be agency science budgets with broad Administration goals in made more rationally. Several scientific groups, too, have mind, this cannot be construed as a prioritization of the overall formulated goals and priorities to guide federal support for R&D budget. their particular areas. In fact, federal R&D cannot be prioritized as a bloc since The severity of the federal budget crisis (discussed in most of it is done for purposes that transcend science-e.g., previous Washington outlook columns) is one reason im national defense and public health. Federal Science programs provements in the science budget-making process are so compete within these areas among not only other science important. Moreover, the political climate of the last decade programs but other spending as well. Because questions raised new demands that government be accountable to voters relating to allocation of funds among these and other national and taxpayers. needs and public goods belong to the realm of politics, the Because Congress is not well equipped to determine the political process will always be the final arbiter of the trade scientific merit of R&D proposals, it relies on advice from offs among competing public needs and, therefore, of the the science community to sort out the diverse claims on the broad structure of the science budget. R&D budget. What many see as a lack of priority-setting by In this context, Congress influences the structure of the the science community has led to some accusations that it is science budget only at the margins. In responding to the an insatiable constituency that regards all of its proposals as President's spending proposals, it divides the budget into essential. trade-off areas in different ways for each of the three different The issue is often highlighted-and muddled-by imme stages of the budget process (budget, authorization, and diate policy concerns, the most controversial of which are appropriation). While it can assign different relative values "big science" projects like the space station and the Super to defense and domestic spending, and thus influence the conducting Supercollider. While the high energy physicists research budget at broad levels, it is logistically difficult to might regard the latter project as crucial to the advancement impose an alternative priority scheme on the overall science of high energy physics, and the Office of Energy Research budget or to directly transfer funds from, say, the space station (with advice from scientific panels) decides where the project to AIDS research. fits into its goals and budget plan, Congress, facing an up or down vote, will always weigh the project in light of other Improving the Science Policy Process national needs, including deficit reduction. There is a need to consider the science budget as a whole, Furthermore, the Federal Coordinating Council for Sci however, especially since sustaining the U.S. scientific en ence, Engineering, and Technology (FCCSET) and the ini- terprise is an important national goal in itself. The House ····························································································································································································································································-··················································-·······-·························-···········································-··························-···················································································································-······························-····· 712 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Washington Outlook Committee on Science, Space, and Technology (HSST), as Several witnesses emphasized the importance of involving the one of the few mechanisms that could conceivably approach scientific community in assessing relative merits of federal assessment of the federal research enterprise, has made the science programs, some suggesting an iterative process would most progress in addressing science priorities. (The House be necessary. Budget Committee has also taken up the matter, although in the context of the big science vs. little science debate; also, a Agencies Plan for Leaner Times few Members of Congress are trying to establish a bipartisan, The federal research agencies are mindful of Congressional bicameral Science and Technology Study Conference, which frustration with the unending demands on the federal science might also choose to look at science priorities.) budget. Coupled with expectations of flat or even declining At the request of the committee, the Office of Technology budgets, several agencies have tackled, or will soon tackle, the Assessment (OTA) last year released a comprehensive report, process of setting explicit criteria for making choices among "Federally Funded Research: Decisions for a Decade," outlin competing scientific programs and projects. At the same time, ing the major issues involved in priority-setting for science. the agencies are in search of new ways to justify growing The thrust of the report is that there will always be more research budgets in a tight fiscal climate. good ideas from the scientific community than there is federal In particular, the National Science Foundation (NSF) and money to support them, and therefore, the government needs the National Institutes for Health (NIH) are responding to new to set priorities to guide funding decisions. The report then demands on their agencies with strategic goals and plans. NIH defines some of the issues arising from the installation of a Director Bernadine Healy, who is fond of saying, "This is not more rational priority-setting process. your father's NIH," is dragging the biomedical community In response to the OTA report, the staff of HSST organized through a strategic planning process to frame the agency's a task force to reexamine the assumptions and conventional budget in terms of national goals rather than numbers of wisdom of federal science policy and the criteria used in research grants. allocating resources among the elements of the scientific en NSF Director Walter Massey, too, is developing a strategic terprise. A report from this task force is expected imminently, plan for his agency. Massey intends that the result of the and it will likely focus on how the government might go strategic planning process will be an agreement with the about setting science policy goals, formulate criteria used Administration and Congress for continued NSF budget to determine which research ought to be funded, and mea growth. As does Healy, Massey realizes that NSF cannot sure progress toward those goals. (See the February 1992 keep doing business as usual. It must be a responsible, issue of the Notices for a more thorough explanation of this accountable steward of public funds. It must coordinate its exercise and the contributions of the mathematical sciences programs with those of other entities (e.g., states, other federal community.) agencies, colleges and universities) and must be responsive The objective of this exercise is to allow the committee to to overall federal R&D priorities associated with important carry out its authorization responsibilities more systematically national goals, including those initiated by Congress. Specific and, hopefully, to facilitate optimal decisions. While HSST justifications are necessary for budget increases even in basic is charged with determining appropriate funding levels for research, where level-of-effort, as opposed to goal-driven, and setting priorities within the budgets of the agencies under programs predominate and the primary criteria for funding its jurisdiction (the National Science Foundation, NASA, decisions is scientific excellence. the National Institute for Standards and Technology, and other programs at the Department of Commerce, Department of Energy research programs, and Environmental Protection Setting Goals and Priorities Agency research programs), it has no methodical procedure for Scientific Disciplines to make these decisions. At the agency program level, the scientific disciplinary com Concurrently, the committee's subcommittee on science is munities contribute greatly to the implementation of priorities holding a series of hearings to examine how priorities are set for programs associated with their respective discipline. But among research programs of different agencies and programs these programs increasingly have to be reconciled with the within those agency budgets and how those priorities are broad directives of federal R&D, as well as those of the conveyed to Congress. The frustration of the subcommittee agency budget. Reconciling "bottom-up" goals and priorities clearly stems from the fact that the Administration's sci coming from the scientific community with the "top-down" ence priorities are rarely made explicit, despite the recent goals and priorities of (in most cases) several agencies that emergence of cross-agency research programs. sponsor disciplinary research is an even greater challenge, Witnesses at these hearings generally concur that a more and leaves many feeling that science budgets are less than rational process for determining science budgets is desirable. optimal. Here, too, it was made clear that well-defined goals have to be The science subcommittee hearings also showcased sev established before priorities can be invested with meaning. The eral disciplinary scientific organizations that have undertaken subcommittee appears to be leaning toward assigning specific bottom-up goal- and priority-setting exercises for their partic responsibility for establishing priorities to some executive ular areas of science. It was noted that such statements seem branch entity; an upgraded FCCSET is a likely candidate. to be faring well in the political process; after all, consensus SEPTEMBER 1992, VOLUME 39, NUMBER 7 713 ...... ______...... _.. _ .... ___ .___ .____ ...... _._._ ...... ___ , ...... --.. Washington Outlook is politically compelling. At the same time, it is not neces linked with important socio-environmental goals, a powerful sarily a simple matter to gain the acceptance of the affected combination. The jury is still out as to whether these efforts agencies and Congress for a discipline's self-selected goals. will succeed at both of their underlying objectives: more Acceptance of goals is often a function of advocacy even influence for the discipline over federal funding decisions when the political process relies on the scientific community with regard to the discipline, and a higher priority for the to establish funding criteria. discipline relative to other elements of federal research. The astronomers, through an iterative consensus-building While declining research budgets pose a serious threat for process, put together a plan that prioritizes astronomy research the mathematical sciences community, the new emphasis on and derives from that a ranking of proposed facilities. Space science priorities provides a challenge and an opportunity to ·scientists are in the process of a similar exercise. The ecol think about how the federal government approaches support ogists recently developed and are promoting a "sustainable for the mathematical sciences and perhaps obtain more support biosphere initiative"; the goals for basic ecological science are for the legitimate needs of the discipline. American Mathematical Society TRANSLATIONS Series 2 • Volumes 148 & 150 Algebra and Analysis Spectral Theory of Operators A. D. Aleksandrov, S. G. Gindikin, Editor 0. V. Belegradek, I. A. Bokut', and Yu. L. Ershov, Editors This volume focuses on the spectral theory of differential operators. The emphasis is on This collection consists of lectures estimates of the number of negative delivered at the First Siberian Winter eigenvalues of elliptic School, "Algebra and Analysis," held differential operators and on in March 1987 at a retreat near the analysis of asymptotical Kemerovo. The school was organized distribution of eigenvalues. by Kemerovo State University and the This collection provides an Institute of Mathematics of the excellent overview of prob Siberian Branch of the Academy of lems in the field, for Gindikin Sciences of the USSR. The conference ranks among the leading drew more than 100 participants from Soviet specialists in this area of Novosibirsk, Kemerovo, Omsk, research. Moscow, St. Petersburg, and other 1991 Mathematics Subject Classification: cities. The papers concern current 34, 47; 58, ISBN 0-8218-7500-0, 176 pages research on the interface of algebra and (hardcover), March 1992 analysis. Indiv. Inenn. $67, List $112, Inst. menn. $90 Your ordering code is TRANS2/150NA 1991 Mathematics Subject Classification: 05, 14, 15, 16, 17, 22, 28, 34, 51, 53, ISBN.0-8218-3700-1, 112 pages (hardcover), February1991,lndiv.Inenn.$38,List$63,lnst.rnern.$50 Your ordering code is TRANS2/148NA All prices subject to change. Free shipinent by surface: for air delivery, please add $6.50 per title. Prepayment required. Order froiD: American Matheinatical Society, P.O. Box 1571, Annex Station, Providence, RI 02901-1571, or call toll free 800-321-4AMS in the continental U.S. and Canada to charge with VISA or MasterCard. Canada residents, please include 7% GST. 714 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements Richard S. Pierce cisive contributions to the development bility techniques. His first works, partly 1927-1992 of the theory of finite groups during the in collaboration with Bernard Maurey, Richard Scott Pierce, former AMS as past thirty years. concerned the notion of "type" and "co sociate secretary, died on March 15, The Ampere Prize of 200,000FF has type" of Banach spaces. In particular, 1992. Born on February 26, 1927, he been awarded to PIERRE-LOUIS LIONS of using martingales, Pisier has studied the received his B.S. in 1950 and his Ph.D. the University of Paris-Dauphine. This type and cotype of uniformly convex in 1952, both from the California In prize is given every year, alternately spaces. He has solved several conjec stitute of Technology. He was a Fellow in mathematics and physics. Lions is tures of Grothendieck concerning tensor of the Office of Naval Research at Yale honored for his major contributions to products of Banach spaces and nuclear University (1952-1953) and a Jewett the study of nonlinear partial differential operators. In addition, he has made im Research Fellow at Harvard University equations arising in stochastic analy portant contributions to random Fourier (1953-1955). He was at the University sis, continuum mechanics, and mathe series and harmonic analysis. His book, of Washington unti11970, when he went matical physics. His Ph.D. thesis, un Volume Inequalities in the Geometry to the University of Hawaii. In 1975, der the direction of Hai:m Brezis, was of Banach Spaces, was published by he joined the faculty at the University concerned with the Hamilton-Jacobi Cambridge University Press in 1989. of Arizona, where he remained until his Bellman equation, which he solved us There were several other prizes death. His mathematical areas were lat ing a combination of partial differential awarded by" the Academie. GILLES LE tice and ring theory, Boolean algebras, equation and probabilistic techniques. BEAU of the University of Paris-Sud re and abelian groups. Later, he introduced with Michael Cran ceived the Servant Prize (10,000FF) for In addition to serving as associate dall the notion of "viscosity solutions", his work on the propagation of singular secretary of the AMS from 1960 to which has now become a classical tool. ities and controllability. GERARD LAU 1971, Professor Pierce served on anum In 1987, Lions and Ronald DiPerna MON of Centre National des Recherches ber of Society committees, including the presented the first gen-eral existence re Scientifiques (CNRS) in Orsay received Mathematical Reviews Editorial Com sult of global weak solutions for the the E. Dechelle Prize (lO,OOOFF) for mittee ( 1968-1973) and the Publications Boltzmann equation, using ail approach his work on the geometric Fourier He was an ex Committee (1968-1970). that applies to many models of gas transform and automorphic forms. the Council from 1960 officio member of dynamics. Lions is also the inven BENOIT PERTHAME of the University of to 1969. tor of the "concentration-compactness" Orleans received the Blaise Pascal Prize method which aids the understanding (lO,OOOFF) for his work on Boltzmann Prizes of the of all possible singular behaviors of schemes. CLAUDE BARDOS of the Uni Parisian Academy sequences in problems which lack com versity of Paris VII received the E. Brun The Academie des Sciences de Paris pactness; this method has numerous ap Prize (lO,OOOFF) for his work on gas has announced a number of prizes and plications, from differential geometry to dynamics and its applications to reen awards presented to researchers in the fluid mechanics. try problems. JEAN-JACQUES RISLER of mathematical sciences. The Prix de l'Etat of 50,000FF was the University of Paris VI received the The golden medal "Henri Poincare" presented to GILLES PISIER of the Uni C. L. de Saulses de Freycinet Prize for 1992 has been awarded to JoHN versity of Paris VI. Awarded every year, (8000FF) for his work on real alge THOMPSON of Cambridge University. this prize rotates among all areas of sci braic geometry and differential analysis. This medal has been awarded only ence. Pisier is a leading expert in the ETIENNE PARDOUX of the University of on exceptional occasions. The previous geometry of Banach spaces. Strongly Provence at Marseille received the Mon two recipients were Jacques Hadamard influenced by Laurent Schwartz, he has tyon Prize (6000FF) for his work on in 1962 and Pierre Deligne in 197 4. combined in a very ingenious manner the stochastic analysis. F'RAN<;:ms LEDRAP Thompson received the medal for his de- geometry of Banach spaces with proba- PIER of CNRS at Paris VI received the SEPTEMBER 1992, VOLUME 39, NUMBER 7 715 News and Announcements Carriere Prize (4500FF) for his work on catastrophe theory, and the use of statis ematics, carries a $1000 stipend. The ergodic theory. DANIEL LEHMANN of the tics in these areas. The citation ends by prize committee also named Julie B. University of Toulouse received the V. noting, "this book is not only one by a Kerr of Washington State University Thebault Prize (4500FF) for his original mathematician, but one by a humanist as Runner-Up and selected nine other book, Initiation to Geometry. GEORGES and a writer. It is a book that makes one nominees for Honorable Mention. The SKANDALIS of the University of Paris VII understand and makes one reflect." awards were presented at the annual received the Francoeur Prize (4500FF) The other winner is the project meeting of the Society for Industrial and for his work on the K-theory of C* "Math en jeans". The idea of "Math Applied Mathematics in Los Angeles in algebras and Kasparov's theory. PIERRE en jeans" is to associate two secondary July. GRISVARD of the University of Nice and school mathematics classes with a re The prize is named in honor of Alice Institut Henri Poincare received the P. search project, under the guidance of T. Schafer of Marymount University, a D. Emile Blutet Prize (4000FF) for his a teacher and a mathematician. The former president and a founding member work on elliptic equations in irregular students (not necessarily those at the of AWM who has taken a special interest domains. JEAN-MICHEL GHIDAGLIA of top of their class in mathematics) de in supporting women at the start of theUniversite de Paris-Sud at Orsay and vote two hours per week to learning their mathematics careers. The 1992 Ecole Normale Superieure de Cachan re about such subjects as secret codes, non prize committee consisted of Schafer, ceived the d' Aumale Prize (3000FF) for Euclidean geometry, or the golden mean. Jill P. Mesirov of Thinking Machines his work on attractors of some nonlinear The group defines and explores various Corporation, and Ann K. Stehney of the evolution problems. questions that arise, and the presentation Center for Communications Research. The Parisian Academy also elected a of "seminars" allows for many fruitful The committee noted that the field of number of foreign members. LENNART exchanges. The citation notes, "This lib thirty-two candidates seemed especially CARLESON of the University of Uppsala eral and open approach to mathematics strong. In addition to their impressive and the University of California at Los has encountered unprecedented success achievements in coursework, indepen Angeles and JOHN T. TATE of the Uni among the students, to whom it offers dent study, competitions, and under versity of Texas at Austin were elected the possibility to create in a domain that graduate research programs, the nom in Mathematics, and T. BROOKE BEN had previously seemed cold and inacces inees devoted themselves to numerous JAMIN of Oxford University was elected sible. The jury of the d' Alembert prize projects on behalf of the mathematical in Mechanics. could certainly not remain insensitive life of undergraduates at their institu to the spirit of 'Math en jeans' which tions. 1992 d'Alembert Prize seems to them to be one of the best ways Awarded to bring to young people a new vision of The Societe Mathematique de France mathematics." has announced two winners of the The d' Alembert prize was presented d' Alembert Prize for 1992. Presented by Professor Hubert Curien, French every two years, the prize recognizes Minister of Research and Space, during outstanding books, articles, radio or tele a reception held at the Ministry on May vision broadcasts, films, or other projects 15, 1992, at the conclusion of a gath that promote public awareness of recent ering organized jointly by the Societe developments in mathematics. This year, Mathematique de France and the Societe the prize amount is 20,000FF. Mathematiques Appliquees et lndus IVAR EKELAND received the prize for trielles. Under the title, "Mathematiques the book Au Hasard: La Chance, La Sci au Futur," this meeting announced to ence, Le Monde (At Random: Chance, the press the launching of the World Science, and the World), published by Mathematical Year 2000 as decided by Le Seuil. Ekeland is currently presi the Executive Committee of the Interna dent of Paris Dauphine University. The tional Mathematical Union at its May 6 citation for the prize says that Eke meeting in Rio de Janeiro. land explains, in a clear, simple, and imaginative way, the great mathemati AWM Announces cal notions connected to chaos and their Schafer Prize Winner Zvezdelina E. Stankova applications to physics and economics. Zvezdelina E. Stankova of Bryn Mawr This well-written book, says the cita College has been named the recipient ZVEZDELINA E. STANKOVA, a 1992 tion, "is a dialetical fresco on order and of the third annual Alice T. Schafer graduate of Bryn Mawr College, has disorder, determinism in indeterminism, Prize, sponsored by the Association for earned wide recognition for her work and indeterminism in determinism." The Wonien in Mathematics (AWM). The and her performance in mathematical book discusses randomness, entropy, un prize, given to an undergraduate woman competitions. She participated last sum predictability, game , theory, attractors, in recognition of excellence in math- mer in the Research Experiences for 716 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY -----~~---~~·~------··---···-··-..- !... ·. Ali... ·:!ii t II-···------·· News and Announcements Undergraduates program at the Uni sponsored Mills Summer Mathematics sels. Daubechies is organizing an AMS versity of Minnesota at Duluth, where Institute, and this summer she worked in Short Course on Wavelets and Applica her research on classifying permutations computational number theory at the Re tions, to be held January 11-12, 1993, in with forbidden subsequences of length search Experiences for Undergraduates conjunction with the Joint Mathematics four was praised as impressive work on program at the Rose-Hulman Institute of Meetings in San Antonio. a difficult problem. She presented her Technology. An aspiring teacher, Kerr JOHN HOLLAND, professor of psy results at the Joint Mathematics Meet also finds time to tutor in mathematics. chology at the University of Michigan ings in Baltimore in January 1992. In The following outstanding women and a fellow at the Santa Fe Insti nominating Stankova, Rhonda Hughes students received Honorable Mention: tute, received a $369,000 grant over of Bryn Mawr wrote, "Her results are MARCIA JoYCE GEIGER ISAKSON, U.S. five years. In the early 1970s, Holland strikingly original and one is always Military Academy; CHERYL P. GROOD, created the genetic algorithm, a gen reminded that her work is that of an University of Michigan; KRisTINE eral computational algorithm that can extraordinary mathematician." A two HAUSER, Grinnell College; LAURA HE be used to discover better solutions to time silver medalist on the International GERLE, Colorado College; EUGENIE HuN problems by recombining and mutating Mathematics Olympiad team from her SICKER, Haverford College; MARY C. previous solutions. In the 1980s, he be native Bulgaria, Stankova's talents as a JoYCE, University of Massachusetts at gan to investigate how learning systems problem-solver and an expositor earned Amherst; MARTHA J. MANCEWICZ, Kala generalize, make inductions, and form her the distinction of Runner-Up for the mazoo College; JENNIFER WILLIAMS, internal representations of their envi Schafer Prize last year. She returned to Oklahoma State University; and VIR ronments. By studying how biological the Duluth program this summer before GINIA E. WRIGHT, Emory University. systems adapt and improve, Holland was beginning graduate work in mathematics able to create classifier systems, which this fall at Harvard University. MacArthur Fellowships Awarded are sets of interacting condition/action Three members of the mathematical rules. With the tool of classifier sys sciences community have received tems, he solved two practical problems· MacArthur Fellowships in this year's in artificial intelligence: how to design round of awards. The fellowships range procedures that can learn appropriate in size from $150,000 to $375,000 over behavior rather than have the behavior five years, depending on the age of the programmed in; and how to test new recipients. There are no strings attached, behaviors while avoiding system break and fellows may use the funds in any way down. He is also beginning to apply his they please. Individuals cannot apply for ideas on nonlinear adaptive systems to MacArthur Fellowships. Candidates are economics. Holland received his B.S. nominated by a group of one hundred in physics from the Massachusetts In designated nominators, and awardees stitute of Technology (1950), his M.A. are chosen by a twelve-member selec in mathematics from the University of tion committee which meets eight times Michigan (1954), and the first Ph.D. in a year. computer science (at that time called INGRID DAUBECHIES, professor of communications sciences) awarded by mathematics at Rutgers University, re Michigan (1959). ceived a $240,000 grant over five years. URI TREISMAN, professor of math Daubechies specializes in wavelet the ematics at the University of Texas at ory, a new form of Fourier analysis Austin and director of the Dana Cen Julie B. Kerr that may revolutionize the manipulation ter for Mathematics Education at the and storage of data, including voice and University of California at Berkeley, re JULIE B. KERR, Runner-Up for this image signal analysis, and data com ceived a $285,000 grant over five years. year's Schafer Prize, will graduate in De pression. In addition, wavelet theory is Treisman works on improving mathe cember from Washington State Univer finding applications in numerical analy matics instruction in high schools and sity. She received Special Recognition sis, operator theory, harmonic analysis, colleges, with an emphasis on ethnic from the 1990 Schafer Prize committee and the study of turbulence. Daubechies minority students. His research and its for her early achievements, including has also worked on Weyl quantization, applications have led to a dramatic in distinction in graduate courses as a first continuous-time regularization of coher crease in the retention and graduation of year student. In each of the last two ent state path integrals, and the extension minority students. He started the Math years, she finished in the top sixty stu of mathematical models for the stability ematics Workshop Program at Berkeley dents on the Putnam Examination for of matter to include relativistic kine in 1978, which reduced to as little as undergraduates. Following a Budapest matic effects. She earned her bachelor's 4% the failure rate in calculus of partic Semester in Mathematics as a sopho degree (1975) and doctorate (1980) in ipating minority students. Adaptations more, Kerr participated in the 1991 NSF- physics at the Free University in Brus- of the workshop have been successfully SEPTEMBER 1992, VOLUME 39, NUMBER 7 717 ...... ___ ...... _._ .. __ .. _.... _...... -.•... _.....•. _.... ____ .....•.... ___ ._ .. _...... News and Announcements used at institutions across the country. number of institutions, including Indi days, but my impression now is that they He directed an equally influential at ana University (1966), the Institute for are rare. tempt to alter the freshman year program Advanced Study in Princeton (1970- "These are some of the challenges in calculus and precalculus. He is cur 1971), and the University of Virginia which need to be addressed in the next rently working to assemble a consortium (Fall 1975). He has been on a number few years at MR, and this is why I am of 200 institutions of higher education of administrative committees at UCLA excited about my new job as executive to encourage greater representation of and also served as associate dean of the editor. I am well aware that all of the minority students in mathematics and Graduate Division: challenges must be addressed with the related fields. He advocates systemic advice and help of the excellent MR changes at all levels of educational pol staff, the MR Editorial Committee, and icy. the mathematics community at large." Minority Scholars Steen Heads MSEB Receive Fellowship Lynn Arthur Steen of St. Olaf College The National Research Council has has taken the position of executive di made one hundred awards in two Ford rector of the Mathematical Sciences Ed Foundation programs to support mi ucation Board (MSEB) of the National nority scholars. The first program sup Research Council (NRC). He succeeds ports graduate students, through Pre Ray Shifflett, who has returned to his doctoral Fellowships that provide funds faculty position at California State Poly for stipends and tuition for three years technic University at Pomona. of tenure, and through Dissertation Fel Steen, well known for his influential lowships that provide a nine- or twelve writings and his advocacy for mathe month stipend. The second program pro matics education, has had close ties with vides Postdoctoral Fellowships to allow the MSEB since the Board was estab doctoral recipients to pursue research. lished in 1985. He was a member of Among this year's recipients are the original Conference Board of the two in the mathematical sciences: F. Mathematical Sciences committee that DuBOis BoWMAN of Duke University, Donald G. Babbitt proposed the formation of a national who works in statistics, and PABLO A. board on mathematics education, and he PEREZ of the University of California "These are very challenging times in was a charter member of MSEB un at Los Angeles, who works in applied the production and delivery of mathe til June 1991. Steen has worked on a mathematics. Each received a Predoc matical databases," says Babbitt. Some number ofMSEB publications: he wrote toral Fellowship. of the challenges for MR are the ever Everybody Counts and edited Reshaping Plans for the 1993 fellowship com increasing number of mathematical pub School Mathematics, On the Shoulders petitions are now under way. For infor lications, calling for more sophisticated of Giants, and Moving Beyond Myths. mation and application materials, write search strategies for the database; space In addition, he worked last year on a to: Fellowship Office, National Re limitations of libraries; keeping MR joint effort of MSEB and the Mathe search Council, 2101 Constitution Av useful and responsive to the needs matical Association of America to begin enue, NW, Washington, DC 20418. of mathematicians; and controlling the MSEB outreach to the higher education costs of producing and delivering the community. MR database. These challenges portend "MSEB will continue to stress pol Babbitt Named changes in MR, Babbitt explains. "For icy studies in areas of importance to the Executive Editor of MR example, many experts feel that most mathematics education reform move Donald G. Babbitt of the University database publications such as MR will ment," says Steen. "Our emphasis at of California at Los Angeles has been become purely electronic in the rela the moment is on assessment-to help named executive editor of Mathematical tively near future," he notes. "In another the nation learn to measure what's im Reviews. He succeeds Gerald J. Janusz, direction, some have suggested that the portant in ways that improve childien's who served in the post for two years and MR database itself should be changed learning." In addition, he notes, MSEB has now returned to the University of so that, for example, 'seminal' papers is beginning to increase emphasis on lllinois at Urbana-Champaign. would receive in-depth special reviews. minority students and higher education. Babbitt received his Ph.D. from the These papers might be selected by a Two new program directors, J. Arthur University of Michigan in 1962 and special editorial body (this, of course, Jones and Susan Forman, are in place works in mathematical physics and dif is a tricky issue!) and the review itself to head these activities, and task forces ferential equations in the complex do would be expected to include the histor have been established. · main. Ht'has been at UCLA since 1962 ical context of the main results ... There MSEB will also be tying into an NRC and has held visiting positions at a were many reviews like this in the old effort, begun this summer, to produce the 718 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ····,'fli'~a'-.§@~ll&liiJIIIfm News and Announcements nation's first statement of standards for deplorable, but violates the principles of Most of the meeting will be open to school science. "There will be many our Academy. the public. Those interested in attend opportunities for cooperation and cre "If Russophobia represents an accu ing should contact Trudy Sensibaugh in ative curricular linkages that emerge as rate expression of your views, and if our the Division of Mathematical Sciences: the science standards join the [National information of the composition of the telephone 202-357-9669; tsensiba@ Council of Teachers of Mathematics] algebra section is a reflection of your in nsf.gov (Internet) or tsensiba@nsf mathematics standards as statements of fluence on hiring and appointment prac (Bitnet). national expectations for our schools," tices, you may wish to consider whether Steen remarks. it is appropriate for you to maintain your News from the "I am excited by the challenge of membership in the National Academy Mathematical Sciences Research MSEB, especially at this particular time of Sciences." Institute of new opportunity to make learning ef The letter is signed by Frank Press, Berkeley, California fective for all students, to cooperate on President, and James B. Wyngaarden, This fall, William Thurston will as science standards, and to move beyond Foreign Secretary, of the NAS. sume the Directorship of the Mathemat myths in higher education," Steen de The press release from the NAS said ical Sciences Research Institute (MSRI) clares. "MSEB has broken new ground that this is the first time in the Academy's upon the retirement of Irving Kaplansky. for national leadership within the Amer history that such a letter has been sent Robert Osserman will continue to serve ican tradition of decentralized educa to one of its members. Shafarevich has half-time as Deputy Director and will be tion and helped create a momentum for been at the center of a controversy in the joined by Lenore Blum who will also change that now has many partners. It international mathematical community serve as half-time Deputy Director. is a good time to improve mathematics because of Russophobia. In particular, Three programs are planned for education, and I feel fortunate to have an open letter to Shafarevich, carrying 1992-1993: a full-year program in Al the opportunity to make a contribution." about 425 signatures, was published in gebraic Geometry, a half-year program the March 1992 issue of the Notices. in the Fall in Symbolic Dynamics, and a NAS President half-year program in the Spring on Tran and Foreign Secretary scendence and Diophantine Problems. Send Letter to I.R. Shafarevich The following workshops are sched OnJuly28, 1992, the National Academy Mathematics Advisory Committee uled for 1992-1993: of Sciences (NAS) sent out in a press to Meet September 21-23, 1992, Workshop release the following letter to I. R. The Advisory Committee for the Math on Algebraic Cycles, Organizers: A. Shafarevich of the Steklov Institute in ematical Sciences for the National Sci Beilinson and W. Fulton; October 12- Moscow: ence Foundation (NSF) will meet Octo 16, 1992, Workshop on Visualization "We are writing to you, a distin ber 26-28, 1992, at NSF headquarters in of Geometric Structures, Committee: F. guished foreign member of our Academy, Washington, DC. Almgren, D. Hoffman, D. Lind, and by unanimous decision of the Council The Committee provides advice on A. Marden (chairman); November 2-6, of the National Academy of Sciences NSF policy as it relates to the mathe 1992, Workshop on Symbolic Dynam to express our strong aversion to your matical sciences. The last meeting of the ics, Committee: M. Boyle (chairman), anti-Semitic writings as contained in Committee touched on concerns raised J. Wagoner, and S. Williams; Novem Russophobia, a translation of which has within the mathematical sciences com ber 16-18, 1992, Workshop on Higher been made available to us. munity about the Foundation's budget Dimensional Complex Geometry, Orga "Moreover, we are informed that request for fiscal year 1993. In addition, nizers: J. Kollar and S. Mori; Decem there are few, if any, Jewish members there was a serious discussion of the ber 2-4, 1992, Workshop on Curves, of the Steklov Institute in Moscow, even idea of revamping the structure of math Abelian Varieties, and their Moduli, Or though many of the outstanding math ematics grants so that grant amounts are ganizers: A. Arbarello, A. Beauville, ematicians of Russia are Jewish. It is based on a tiered, flat-rate system, rather and J. Harris; March 29-April 2, 1993, difficult to avoid the conclusion that than on principal investigator salary. Workshop on Diophantine Geometry, the discriminatory practices of the well The. upcoming meeting is likely to Organizer: P. Vojta; and July 12-23, known anti-Semitic former director per center on these and other important is 1993, Conference on Universal Alge sist under present leadership. sues facing the community. In addition, bra and Category Theory, Committee: F. "The National Academy of Sciences, a new director of the Division of Mathe Linton, S. Mac Lane (cochairman), R. as an institution, holds deeply to the matical Sciences (the successor of Judith McKenzie (cochairman), G. McNulty, principle that discrimination against in Sunley, who is now executive officer of W. Taylor, and C. Wells. dividuals for reasons of race, sex, or NSF's Directorate of Mathematical and The algebraic geometry program religious beliefs is intolerable. Using Physical Sciences) will probably have will be organized around monthly themes your position to speak against Jews been chosen by the time of the meeting, as follows: because of your perception of their in making for interesting and lively discus September: Algebraic Cycles (Con fluence upon Russian society is not only sions about the future of the Division. tacts: A. Beilinson, W. Fulton); October: SEPTEMBER 1992, VOLUME 39, NUMBER 7 719 ...... ______...... _•.. ._...... _...... -..... _..•... -.... ·-·-··············-············· ·······--·-····················-·--········--·-· News and Announcements Vector Bundles (Contact: R. Lazarsfeld); riod: September - October 1993 with a three parts (corresponding to fall, win November: Higher Dimensional Geom workshop. ter, and spring quarters) although it is etry (Contacts: J. Kollar, S. Mori); De 4. Hyperbolic Geometry (Ballmann). expected that there will be considerable cember: Curves, Abelian Varieties, and Negative curvature, rigidity, geodesic fluidity between the various parts. their Moduli (Contacts: A. Beauville, J. flows, hyperbolic groups, etc. This pro (1) Fall: September 8-December 30, Harris); January: Surface Theory, Clas gram is emphasized in the Fall. High 1992, Linear and distributed parameter sical Projective Geometry (Contacts: R. activity period: October 1993. systems Friedman, J. Harris); February: Topol 5. Spectral Geometry (Gordon). !so (2) Winter: January 2-March 30, ogy of Moduli Spaces (Contact: E. Ar spectral deformations, eigenvalue prob 1993, Nonlinear systems and optimal barello); March: Enumerative and Com lems, eta invariants, etc. High activity control putational Algebraic Geometry (Con period: November 1993. Secondary ac (3) Spring: April 1-June 30, 1993, tact: W. Fulton); March: Crystalline tivity period: Spring 1994. Stochastic and adaptive systems Methods and Hodge Theory (Contacts: 6. Exterior Differential Systems The fall program was described in A. Beilinson, A. Ogus); April: (Open); (Bryant). Geometric structures, charac the July/August 1992 Notices. Here we and May: Singularity Theory and Hodge teristic classes of systems, control the provide some details about the winter Theory (Contacts: M. Green, J. Steen ory, etc. This program is emphasized in program. brink). the Fall. High activity period: December On January 25-29, 1993 there will 1993-1994 will feature a jumbo pro 1993. be a workshop on Robotics organized gram in Differential Geometry lasting 7. Low Dimensional Geometry. Ge by J. Baillieul, S. Sastry, and H.J. Suss the full year, and a half-year program ometry of 3- and 4-manifolds, gauge mann. This workshop will feature a in Dynamical Systems and Probabilistic field theory, monopoles, gravity in 2 + mathematical introduction to: 1) Kine Methods for PDE's in the Spring: Jan 1 dimensions, twistor theory, etc. High matics and Fine Motion Planning; 2) uary - June, possibly extending through activity period: February 1994. The dynamics and control of kinemat July. Note that the latter program was 8. Arakelov Theory. High activity ically redundant robot arms including referred to as "Coherent Structures" in period: Possibly November or March. snake-like robots, multi-fingered robotic preliminary announcements and also in 9. Ricci Curvature Questions. Ein hands; 3) Methods ofnonholonomic mo the application forms for 1993-1994. stein spaces and their moduli, spaces of tion planning for space robots, multifin The Differential Geometry program positive/negative Ricci curvature. High gered robot hands, and mobile robots; has been organized around a number activity period: Sometime in Fall or in and 4) New techniques in analytical of themes, running during overlapping late Spring. mechanics for writing the dynamics of periods. The final schedule has not yet For more information, write to MSRI complicated multi-body systems subject been set, but the following is a tentative at 1000 Centennial Drive, Berkeley, CA to constraints on angular momentum plan, including members of the organiz 94720. Program information and docu or other nonholonomic constraints. The ing committee associated with certain of ments, including application forms are emphasis will be on those conceptual the themes. also available on-line by sending email problems of robotics that are funda 1. Mathematical Physics and Geom to [email protected], consisting of themes mental to understanding a very tech etry (Bott). This is the main subprogram sage "index". nologically driven and interdisciplinary outside of pure geometry and, in princi Note: The Fields Institute in Wa field. The workshop will highlight the ple, it should run all year. High activity terloo, Canada, has scheduled a micro mathematical problems but the partici period: January 1994, with a workshop program in Riemannian geometry for pants will also be shown video tapes of including some other areas, for exam August 1993, in coordination with the multifingered hands, redundant robots, ple: low-dimensional geometry, moduli MSRI 1993-1994 program in Differen and nonholonomic motion planning for of Einstein spaces, elliptic genera, etc. tial Geometry. Details of the program space robots and mobile robots. Other periods of activity: February and will be announced shortly. W.S. Levine is organizing a mini periods in the Fall. symposium February 1-3 on Biological 2. Nonlinear Analysis and Geometry News from the Control of Movement. The study of the (Schoen). Harmonic maps, minimal sur Institute for Mathematics means by which animals and humans faces, Einstein spaces, scalar curvature, and its Applications perform voluntary movements presents etc. This theme is emphasized in the Fall University of Minnesota interesting and challenging mathemat and late Spring. High activity period: The Institute for Mathematics and its ical problems. The primary purpose September 1993. Applications (IMA) 1992-1993 aca of this informal workshop is to inter 3. Rauch-Gromov Theory (Grove). demic year program Control Theory est mathematicians in these problems. Positive curvature, convergence and col and its Applications is now underway, This will be done by exposing them lapse of metrics, finiteness theorems, fill led by program coordinators H.J. Suss to recent experimental results that pose ing manifolds, Alexandrov spaces and mann (Chairman), W.H. Fleming, P.P. fundamental questions about how move singular metrics, etc. This theme is em Khargonekar, P.R. Kumar, D.L. Russell, ment is controlled as well as to recent phasized in the Fall. High activity pe- and S.E. Shreve. The year is divided into theoretical results aimed at answering 720 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY News and Announcements these questions. The minisymposium alyzing, designing, and operating these Kathleen Crowe, who has been a vis will bring together some of the leading future systems. The emphasis of this iting assistant professor at UC, Davis. experimentalists, analysts, and theoreti workshop will be on the role of mathe Benjamini will continue his work on cians in this broad and deep subject. matical theory in the analysis and con Brownian motion on manifolds. Crowe, The talks and discussions will focus on trol of nonlinear dynamics in large-scale who received her degree from the Uni the current status of research and on the electric power systems. The topics to versity of Arizona, will fill a position formulation of problems of interest to be discussed will include: 1) Modeling reserved for researchers from groups both mathematicians and specialists in of large power systems using invariant underrepresented in mathematics. She the biological control of movement. and integral manifold theory; 2) Security will work on biological problems with A workshop on Nonsmooth Anal assessment and enhancement problems Carlos Castillo-Chavez. Ken Hochberg ysis and Geometric Methods in De including current research methodology from Bar-llan University will visit dur terministic Optimal Control will be for solution of these problems. Areas ing the fall semester. R. Dobrushin from held February 8-17, with V. Jurdjevic, such as direct methods, voltage stability the Institute for Problems oflnformation B.S. Mordukhovich, R.T. Rockafellar, analysis, and structural stability analy Transmission, Russia will visit during and H.J. Sussmann as organizers. The sis will be presented; and 3) Control the spring semester. purpose of this two-part meeting is to system design considerations including The Center for Symbolic Methods in concentrate on powerful mathematical measurement-based control, nonlinear Algorithmic Mathematics, directed by techniques that have been developed control, parametric robust control, and Moss Sweedler, will host visits from No in deterministic optimal control the decentralized and distributed control. colai Vorobjov and Kiyoshi Shirayanagi. ory after the basic foundations of the For more information about IMA Shirayanagi is with the NTT Communi theory (existence theorems, Maximum activities, see the Meetings and Confer cation Science Laboratory. Principle, dynamic programming, suffi ences section of this issue or contact ciency theorems for sufficiently smooth the IMA, (ima_staff~ima. umn. edu). fields of extremals) were laid out in Also, weekly IMA seminar schedules News from the Fields Institute the 1960s. These advanced techniques with titles and abstracts are available The Fields Institute Distinguished Lec make it possible to derive much more on Usenet: umn.math.dept, and 'lEX ture Series will continue this fall with detailed information about the structure files for the Newsletter and the Up lectures by Vaughan Jones, University of solutions than could be obtained in date are available via anonymous ftp (at of California, Berkeley (September 23, the past, and they support new algo ima. umn. edu). 24, and 25, 1992) on operator theory, rithmic approaches to the calculation of knots, and mathematical physics and by such solutions. In addition to the theo News from the Michael Berry, University of Bristol, retical side, there will be attention given Mathematical Sciences Institute (October 22, 23, and 24, 1992) who to applications such as recent work on Cornell University will speak on quantum and classical robotics problems, the control of chem The Army Research Office Center of asymptotics, chaology, and the Riemann ical batch processes, economic models, Mathematical Excellence, located at Cor zeros. hierarchical models, and some problems nell University's Mathematical Sciences The main focus of the Institute's ac involving uncertainty. Numerical results Institute (MSI), is preparing to welcome tivities for 1992-1993 is its program on will also be taken up. The first five a distinguished group of visiting schol Dynamical Systems and Bifurcations. days will be devoted to topics primarily ars during the late summer and early fall The first of the short courses for grad involving geometric methods, and the of 1992. uate students and faculty will be given last five to topics related to nonsmooth MSI Director Anil Nerode will host by Institute Director Jerrold E. Marsden. analysis methods. The two-day overlap Bakhadyr Khoussainov during the 1992- The course, entitled Lectures on Hamil will be be devoted to the discussion of 1993 academic year. Khoussainov has tonian Bifurcation Theory, will run from issues where both lines of research come recently been a visitor at the University September 23-26, 1992. The first work together. of Washington. Rod Downey from the shop of the Dynamical Systems year will On March 15-19 there will be a University of Wellington, New Zealand be on Conservative Systems and Quan workshop on Systems and Control is currently in residence at MSI and Pro tum Chaos (October 21-25, 1992). This Theory for Power Systems, organized fessor D. Bridges from the University workshop will focus on bifurcation and by J. Chow, P.V. Kokotovic, and R.J. ofWaikato, Hamilton, New Zealand and integrability problems in Hamiltonian Thomas. Future electric power sys Dr. Y. Tabesh from Sharif University, systems. tems will be expected to satisfy ex Iran are expected to visit. For further information about the traordinary performance and reliabil The Center for Stochastic Analysis, Institute please contact Liz Reidt at ity requirements and to tolerate pro under the direction of Richard Dur The Fields Institute for Research in nounced dynamic behavior while re rett, has filled its two postdoctoral po Mathematical Sciences, 185 Columbia maining amenable to diagnostics and sitions for academic years 1992-1994. St. West, Waterloo, Ontario Canada, maintenance. Mathematical theory is ex The Center will host Itai Benjamini from N2L 5Z5; Tel.: 519-725-0096, Fax: 519- pected to play a significant role in an- the Hebrew University of Jerusalem and 725-0704; [email protected]. SEPTEMBER 1992, VOLUME 39, NUMBER 7 721 ...... _...... ______...... ~ ...... News and Announcements For the October workshop please tary School Teachers", is unusually brief ically intended to meet the needs of email: [email protected] or the for a report on this topic, running only elementary teachers. organizers: David Goodings (goodings@ seventeen pages. As the report points Copies of the report are available physun.physic.mcmaster.ca) or David out, more detailed ideas and perspec for $4 (includes shipping and han Rod ([email protected]). tives may be found in such documents dling) from: Sheila Sconiers, Univer as Professional Standards for Teaching sity of Chicago, Department of Ed Model Programs Sought Mathematics, Curriculum, and Evalu ucation, 5835 South Kimbark Avenue, The Mathematical Association of Amer ation Standards for School Mathemat Chicago, IL 60637 -1609; telephone 312- ica (MAA) has received funding from ics, Everybody Counts, and A Call for 702-1561. the National Science Foundation to pre Change. This report makes a persuasive pare, for the mathematical community, case for the idea that there is plenty Mathematics Awareness Week descriptions of highly successful un of information on what to do--what is 1993 dergraduate mathematical sciences pro needed is the will to do it. "Mathematics and Manufacturing" grams. We are searching for programs The report's main conclusion is that April 25-May 1, 1993 that enhance recruitment and retention more attention must be paid to what Every year, Mathematics Awareness of mathematics majors; programs that kind of mathematics elementary school Week celebrates the richness and rel prepare a substantial number of stu teachers learn, how they learn it, and evance of mathematics and provides dents effectively for teaching school how they bring their knowledge to bear an excellent opportunity to convey this mathematics or for continued gradu on actual classroom practice. Among message through local events. During ate study; or programs that are partic the report's specific recommendations a week-long celebration from Sunday, ularly effective in attracting, and ad are a coordinated national effort to 25 April- Saturday, 1 May 1993, the dressing the needs of, groups tradition bring about "a complete overhaul of festivities will highlight Mathematics ally underrepresented in mathematics. the way elementary teachers are taught and Manufacturing. Mark your calen Alan Tucker, chair of MAA's Educa college mathematics", the adoption of dars now and plan to observe Mathe tion Coordinating Council, is the project a 12-semester-hour minimum for the matics Awareness Week in your area, director. MAA invites readers to nom mathematical preparation of elementary school, or organization. Look for further inate programs (including their own) school teachers, and "bridges" between information from the Joint Policy Board for possible inclusion in this case stud colleges and elementary schools for for Mathematics, national sponsor of ies project. Send your nomination letter the continued professional development Mathematics Awareness Week, in future to Professor Alan C. Tucker, Applied of elementary school teachers. Math issues of the Notices. Mathematics Department, SUNY-Stony ematics faculty don't get off easy in Brook, Stony Brook, NY 11794 (email: this report--one recommendation calls Special Reduced Rates atucker@ sbccmail. bitnet). for institutes designed to improve the for AMS Members teaching methods of college faculty As a result of negotiations between Report on Preparation who are responsible for the mathemat the American Mathematical Society and of Teachers ical preparation of teachers. The re J. C. Baltzer AG Scientific Publishing "Mathematics education in the United port also declares that "the mathematics Company, AMS members can now take States today is a vast enterprise in community-specifically the AMS and advantage of a special reduced rate on volving millions of teachers and tens the Mathematical Association of Amer the following journals: of millions of students . . . Along with ica (MAA)-must go clearly and ex • Annals of Operations Research, reading, it is the most important item plicitly on record as recognizing the im US $80 per volume on our schools' agenda. Yet by nearly portance of their critical role in prepar • Annals of Mathematics and Artifi every measure, mathematics education ing elementary school teachers to teach cial Intelligence, US $80 per volume in the United States today is a fail mathematics". • Journal of Mathematical Chem ure." So begins a report of a two-part Now that the report is out, two other istry, US $93 per volume conference held at the University of initiatives are under way. The first is • Numerical Algorithms, US $92 per Chicago. Bringing together more than a survey of all U.S. colleges gradu volume three dozen mathematicians, mathemat ating significant numbers of education • Queueing Systems, US $93 per ics educators, psychologists, college ad majors, which will gather information volume ministrators, and classroom teachers, the on the mathematics components of the • Telecommunication Systems, US conference aimed to identify specific preparation of elementary school teach $92 per volume. steps that need to be taken at the college ers. The second is a proposal submitted This offer is being made exclusively level to improve the mathematical prepa to the National Science Foundation for to individual members of the American ration of preservice elementary school a planning grant to begin laying the Mathematical Society. teachers. foundation for one of the more signifi In order to obtain this special dis The report, entitled simply "On the cant ideas in the report: the creation of count, please send your order, stating Mathematical Preparation of Elemen- a college mathematics program specif- your AMS membership code, directly 722 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ------······--············--··-··········-·······-··········--·--·--·······--·····-··-·······---·-··-·-·----·.. ···-·······---··•·""" News and Announcements to the address mentioned below. The be available for use at the upcoming San register. A full set of priorities and publisher will be happy to supply you Antonio Employment Register. The new revised guidelines for the new system with leaflets, containing all the necessary system is based on computer code being are being developed by the AMS-MAA bibliographic information. developed by J.P. Jarvis, D. R. Shier, and SIAM Joint Committee on Employment Please contact: In the United States: M. Myers of the Department of Math Opportunities. J. C. Baltzer AG, Scientific Publishing ematical Sciences, Clemson University, The October issue of the Notices Company, P.O. Box 8577, Red Bank, NJ under a contract jointly sponsored by will contain complete information on 07701-8577; from all other countries: AMSandMAA. the Sail Antonio Employment Register, J. C. Baltzer AG, Scientific Publish While maintaining the Employment including information on preregistration ing Company, Wettsteinplatz 10, CH- Register tradition of maximizing the for the register. 4058 Basel, Switzerland, Fax: +41-61- number of total interviews, the new 692 42 62. system will support assigning various levels of priority to certain classes of Erratum interview requests. One class of inter Bylines were inadvertently omitted on Enhanced Employment Register views which will be assigned top pri two articles in the July/August 1992 is Interview Scheduling System ority are mutual requests, i.e., instances sue of the Notices. "Canada's Fields In Mathematics job seekers and employers where an employer and an applicant re stitute Opens its Doors," pages 564-566, will be pleased to learn that an enhanced quest each other. Early tests indicate that and "AMS Operating Plan for 1993," interview scheduling system is under virtually all such mutual requests will pages 597-598, were both written by development by the AMS, and it should be scheduled during the two days of the AMS Staff Writer Allyn Jackson. Advances in Soviet Mathematics Properties of Global Attractors of Partial Differential Equations A. V. Babin and M. I. Vishik, Editors Volume 10 The four papers in this volume examine attractors of partial differential equations, with a focus on investigation of elements of attractors. Considered here is the dependence of attractors on singular perturbations of the equations. The theory of unbounded attractors of equations without bounded attracting sets is also covered. All of the articles are systematic and detailed, furnishing an excellent review of new approaches and techniques developed by the Moscow school. 1991 Mathematics Subject Classification: 35, 58, 76 ISBN 0-8218-4109-2, 172 pages (hardcover), July 1992 Individual member $64, List price $106, Institutional member $85 Your ordering code is ADVSOV/lONA American Mathematical Society. All prices subject to change. Free shipment by surface: for air delivery, please add $6.50 per title. Prepayment required. Order from: American Mathematical Society, P.O. Box 1571, Annex Station, Providence, RI 02901-1571, or call toll free 800-321-4AMS in the U.S. and Canada to charge with VISA or MasterCard. Residents of Canada, please include 7% GST. SEPTEMBER 1992, VOLUME 39, NUMBER 7 723 Funding Information for the Mathematical Sciences Research at Foreign Centers In recent years, mathematics faculty research environments that will have Through its program for long-term re nationwide have implemented major maximal impact on their future scientific search at foreign centers of excellence, changes in calculus instruction. While development. Awards will be made for tlie National Science Foundation (NSF) approaches have varied greatly, the em appropriate research in pure mathemat seeks to increase the presence of young phasis has been on raising student con ics, applied mathematics and operations U.S. investigators in foreign laboratories ceptual understanding, problem solving research, and statistics at an appropriate and research institutions. skills, and analytical aild transference nonprofit United States institution. Awards are made for research in skills, as well as on implementing new The fellowships will be offered only any field of science or engineering sup methods that reduce tedious calculations to persons who 1. are citizens, nationals, ported by the NSF for visits of three and place the student in the role of an or lawfully admitted permanent resident to twelve months. Appropriate foreign active learner. Some of the projects have aliens of the United States as of January science and technology centers include had NSF support, some have received 1, 1993; 2. will have earned, by the be industrial research laboratories, govern other external support, and others have ginning of their fellowship tenure, a doc ment research laboratories and centers, been developed with only institutional toral degree in one of the mathematical privately sponsored nonprofit institu support. sciences; 3. will have held the doctorate tions, and universities. Information about more than seventy for no more than five years as of January The annual deadline for submissions such projects may be found in the re 1, 1993; and 4. will not previously have is November 1. For more information, port of the Mathematical Association of held any other NSF postdoctoral fellow contact: Division of International Pro America, "Priming the Calculus Pump: ship. Subject to the availability of funds, grams, Room V-501, National Science Innovations and Resources". Additional it is expected that in FY 1993, thirty to Foundation, 1800 G Street, NW, Wash reports have appeared in issues of UME forty awards will be made. The evalua ington, DC 20550; telephone 202-653- Trends and have been presented at con tion of applicants will be based, in part, 5387. ferences and at sessions of meetings of on ability as evidenced by past research professional societies. With information work and letters of recommendation, Grants Available about successful models at hand, the likely impact on the future scientific for Calculus Projects challenge now is to include large num development of the applicant, and sci The National Science Foundation (NSF) bers of students in the renewed calculus entific quality of the research likely to funds projects to improve mathematics courses. emerge. Applicants' qualifications will curricula through its Curriculum Devel The closing date for proposals to the be evaluated by a panel of mathemati opment in Mathematics: Calculus and NSF's calculus program is December cal scientists. Women, underrepresented Bridge to Calculus Program. The pro 7, 1992. More information and pro minorities, and persons with disabili gram is managed by the Division of gram announcements may be obtained ties are strongly encouraged to submit Undergraduate Education, in coopera from the program director, James Light applications. tion with the Division of Mathematical bourne, Division of Undergraduate Ed For copies of the application brochure Sciences and the Division of Elemen ucation, Room 1210, National Science or further information, contact the Office tary, Secondary, and Informal Science Foundation, 1800 G Street, NW, Wash of Special Projects, Room 339, Divi Education. ington, DC 20550; telephone 202-357- sion ofMathernatical Sciences, National Proposals are solicited in three gen 7292; [email protected] (Internet) Science Foundation, 1800 G Street, eral categories: 1) projects to revitalize or jhlightb@nsf(Bitnet). NW, Washington, DC 20550; 202-357- calculus instruction on a large scale in 3453; email [email protected] (internet) volving students at the collegiate and/or Mathematical Sciences or msprf@nsf (bitnet) or the American secondary levels; 2) new curriculum de Postdoctoral Research Mathematical Society, 401-455-4104; velopment projects, particularly for the Fellowships email [email protected]. second year of calculus, including lin The National Science Foundation's The deadline for applications is Oc ear algebra and differential equations; (NSF) Mathematical Sciences Postdoc tober 15, 1992. Please note that this and 3) curriculum development projects toral Research Fellowship program is deadline is one month earlier than in focused on preparation for calculus. designed to permit recipients to choose the years prior to 1991. 724 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Acknowledgment 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 $156 or more. In addition to contributions to the AMS Centennial Fellowship Fund, there were a number of unrestricted general contributions. Some of the contrib utors have asked to remain anonymous. All of these gifts provide important support for the Society's programs. Also listed are AMS members who contributed, through the Society, to the International Mathematical Union's Special Development Fund for travel grants to young mathematicians from developing countries. This year, gifts to the Society's Memorial Gift Program are included in this list. The names listed below include those whose contributions were received during the year ending March 31, 1992. CONTRIBUTING MEMBERS Akemann, Charles A. Dickerson, Charles E. Howe, Roger E. Nashed, M. Zuhair Shahidi, Freydoon Al-Droubi, Akram Dinneen, Gerald P. Hufford, George A. Nishiura, Togo Shelstad, Diana Frost Amir-Moez, Ali R. Earle, Clifford J., Jr. Hunt, Richard A. Olum, Paul Singmaster, David B. Andrews, George E. Eckhardt, William Hutchinson, George A. Orlik, Peter P. Spencer, Joel H. Appleby, Bruce W. Ecklund, Earl F., Jr. Jaco, William H. Osofsky, Barbara L. Stakgold, Ivar Assmus, Edward F., Jr. Ellis, Robert L. Kamp, William P. Otermat, Scott C. Sternberg, David Babcock, William W. Fadell, Edward R. Kautzmann, Frank N., ill Palais, RichardS. Strauss, Frederick B. Bauer, Frances B. Farrell, Roger H. Kelly, John B. Palmer, Theodore W. Strichartz, Robert S. Baumslag, Gilbert Forbes, Stephen H. Kiefer, James E. Papanicolaou, George C. Sudler, Culbreth, Jr. Bjorklund, Peter B. Garnett, John B. Kopala, Conrad Pearson, Robert W. Sullivan, Richard W. Bressoud, David M. Grace, Edward E. Krause, Ralph M. Perry, William L. Swokowski, Earl W. Brown, Terrell N. Graves, Robert L. Krueger, Charles G. Petro, John W. Taft, Margaret W. Buianouckas, Francis R. Greicar, Richard K. Lemay, William H. Polking, John C. Taylor, Laurence R. Carson, Robert C. Greif, Stanley J. Mamelak, Joseph S. Pratt, Vaughan R. Uhlenbeck, Karen Chafee, Nathaniel Grimmer, Ronald C. Mandell, Arnold J. Quinn, Michael F. de Valpine, Jean E. Clifford, Alfred H. Gromov, Mikhael Martin, Gary A. Ratliff, Louis J., Jr. Veech, William A. Cohen, Henry B. Haddad, George F. B. Mathsen, Ronald M. Redheffer, Raymond M. Warren, William E. Cohn, Richard M. Haddix, George F. Mattson, H. F., Jr. Reedy, Christopher L. Weintraub, Steven H. Colon, Ivan E. Halberstam, Heini Meder, Albert E., Jr. Reese, Matthias F., ill White, Edward C., Jr. Cootz, Thomas A. Hassinger, Bill, Jr. Mellender, James W. Rosenblum, Marvin White, George N., Jr. Corrigan, Thomas Carney Haynes, Neil J. Miles, E. P., Jr. Rovnyak, James L. Whitmore, William F. Das, Anadi Jiban Hedlund, Gustav A. Miller, John E. Sally, Paul J., Jr. Wilkins, J. Ernest, Jr. Daverman, Robert J. Hemstead, Robert J. Mislin, Guido Samit, Jonathan Woeppel, James J. DeFacio, Brian Higgins, Stanley B. Morris, Robert A. Sawyer, Stanley A. Woolf, William B. DeLeon, Morris Jack Hironaka, Heisuke Moschovakis, Yiannis N. Seligman, George B. Xenos, Philippos John Demana, Franklin D. Hochster, Melvin Muhly, Paul S. Sexauer, Norman E. Yohe, J. Michael DeMarr, Ralph E. Horrigan, Timothy J. Murphy, Donald P. Shabazz, Abdulalim A. Corporate Members and Institutional Associates The Society also acknowledges with gratitude the support rendered by the following corporations, as Corporate Members or Institutional Associates of the Society during the past year. Corporate Members Institutional Associates AT&T Bell Laboratories Center for Communications Research General Motors Corporation Daniel H. Wagner Associates IMSL Kluwer Academic Publishers International Business Machines Corporation Springer-Verlag New York Incorporated N atimial Security Agency Supercomputer Research Center, Institute for Defense Analyses Princeton University Press SEPTEMBER 1992, VOLUME 39, NUMBER 7 725 ...... _____ .., ...... _. ___ ...... _...... ______._._ ...... _..,. __ ...... ______General Contributions GENERAL CONTRIBUTIONS Adams, William W. Donaldson, James A. Karle, Jerome Mosier, Ronald G. Sharp, Henry, Jr. Aeppli, Alfred Doran, Robert S. Kempachiro, Ohashi Mostow, George Daniel Shelly, Eugene P. Aissen, Michael I. Duren, William L., Jr. Kennedy, Edward S. Muto, Yosio Shenitz, Charles Allen,J. Thonms, III Durfee, William H. Kennison, John F. Nagase, Michihiro Shih, Weishu van Alstyne, John P. Durst, Lincoln K. Kent, George A. Nelligan, John D. Shiraiwa, Kenichi Anantharam, Venkatachalam Dutton, Charles Everett Khan, Amtul Matin Neville, Charles W. Silberger, Allan J. Antnmn, StuartS. Eachus, J. J. Kido, Kazuo Newman, Morris Smith, James L. Arens, Richard F. Ealy, Clifton E., Jr. Killeen, John Nichols, Edward Soret, Mark Arkowitz, Martin A. Edelstein, Michael King, Donald R. Nishiura, Togo Starr, Norton Aroian, Leo A. Edris, Gerrit M. Kishi, Masanori O'Callaghan, Liam J. Stegeman, Jan D. Avedissian, Vahe Yeghishe Eggers, John D. Kitchen, Edward Oguchi, Kunio Steinberg, Robert Babcock, William W. Eisman, Sylvan H. Kiyek,K. Ohta, Haruto Sterba-Boatwright, Blair D. Bachnmn, George Engle, Jessie Ann Kolodner, Ignace I. Olivares, Rene Stock, John R. Baker, Edward D. Everitt, W. Norrie Konhauser, Joseph D. E. Onishi, Hironori Sugrue, Kevin P. Ballard, William R. Pass, Arnold L. · Kossack, C. R. Orlik, Peter P. Sullivan, Richard W. Barner, Klaus Faulkner, Frank D. Kraus, Guenther Orloff, Leo N. Takenaka, Shigeo Bartick, Philip R. Ferrari, Carlo Krause, Ralph M. Orr, Martin Takeuchi, Kisao Baruch, Herbert M., Jr. Ferrer, Jesus Krieger, Henry A. Osner, H. J. Tanimoto, Taffee T. Baruch, Herbert Mark, III Freeman, James H. Krumpholz, Gary R. Oternmt, Scott C. Tatevossian, Leon H. Bass, Barry C. Freundlich, Marianne Kulp, Dauiel Teibi Overholt, Marins Thomas, P. Emery Bellissard, Jean V. Friedberg, Solomon Kunimura, Dennis E. Paciorek, Joseph W. Thron, Wolfgang J. Bencsath, Katalin A. Fujii, Nobuhiko Kunoff, Sharon Palmer, Theodore W. Tin, Saw Bender, John Fukuda, Komei Kurtzke, John F., Jr. Parker, Francis D. Tits, Jacques L. Bengtson, Thonms E. Fuller, William R. Labesse, J. P. Peabody, Mary K. Tolsted, Elmer Beman, Simon J. Furutani, Kenro Lambert, Alan L. Peck, N. Tenney Traina, Charles R. Bjorklund, Peter B. Gantos, Richard L. Landesman, Edward M. Petunin, Yu I. Tsau, Chichen Michael Blattner, Robert J. Gilsdorf, Thomas E. Langenhop, Carl E. Pierce, Richard S. Tsukui, Yasuyuki Blum, Dorothee Jane Gingrich, Ross B. Lauing, J. H. Pless, Vera S. Tugue, Tosiyuki Bochev, Pavel Blagovestov Glass, Michael S. Laush, George Pratt, Vaughan R. Tung, On-Ki A. Boos, William Goldman, William Mark Le Cam, L. M. Protter, Philip E. Uchiyama, Akihito Booss, Bernheim Goss, Robert N. Lee, Bun Hwi Pucci, Patrizia Umeda, Tomio Booth, George W. Grabiel, Federico Lehrer, Gustav I. Pursell, Lyle E. Unai, Yasushi Unai Bradley, John S. Graves, Robert L. Lenmy, William H. Quinn, Frank S. Ungar, Peter Bragg, Arthur E. Greene, Curtis Levit, Robert J. Rassias, John Michael Vasconcelos, Wolmer V. Brauer, Fred Greville, Thonms N. E. Lichnerowicz, Andre Reber, Douglas C: Veech, William A. Brodkey, Jerald S. Griess, Robert Louis, Jr. Lindstrom, Wendell D. Recaman, Bernardo Walborn, Stephanie Arnold Brown, Arthur B. Griffin, E. L., Jr. Long, John M. Regan, Francis Wang, Derming Brown, Ron Haber, Seymour Longbotham, Harold G. Reissner, Eric Ware, Buck Brown, Terrell N. Hassinger, Bill, Jr. Madow, William G. Reitwiesner, George W. Weibel, John L. Bryn, Milo F. Hausnmnn, Jean-Claude Maeda, Hironobu Renno, James G., Jr. Wendel, James G. Buianouckas, Francis R. Heller, Dorothy M. Maehara, Kazuhisa Reznick, Bruce A. Wetzel, Marion D. Bumby, Richard T. Henkin, Leon A. Maim, Dennis R. Richards, John F. White, Edward C., Jr. Busemann, Herbert Higgins, James Logan Mamelak, JosephS. Rickart, Charles E. Whitney, D. Ransom Butler, James William Hijab, Omar Marchand, Margaret 0. Robinson, Paul Lee Willcox, Alfred B. Canjar, Mike Hochwald, Scott H. Margerum, Eugene A. Robinson, Raphael M. Wolff, Manfred P. H. Carlson, Bengt G. Hodgson, Jonathan P. E. Margulies, William Rodriguez-Exposito, Jose Wong, Fu-Hsiang Carmichael, Richard D. Hoft, Hartrnut Marshall, David Imler Rose, N.J. Wong, Yim-Ming Carson, Robert C. Honda, Kin-Ya Martin, George W. Ross, J. Andrew Wright, David J. Chafee, Nathauiel Horn, Jean MacGregor Massey, David B. Ruymgaart, Peter A. Yanmguchi, Hiroshi Chinn, William G. Hughes, Ruth L. Mayor, John R. Sakmann, Pascal Yanmsaki, Masayuki Christensen, Chris lgari, Satoru McAdam, Stephen J. Samelson, Hans Yasuhara, Ann Cleveland, Richard A. Ilmanen, Tom McArthur, C. W. Sarafyan, Diran Yasuhara, Mitsuru Cohen, Dauiell. A. loakimidis, N. I. McBrien, Vincent 0. Sarason, Donald E. Yoshino, Takashi Cole, Paul Dana Ito, Ryuichi McConnell, Thomas Sastri, Chelluri C. A. Zaharopol, Radu Comenetz, Dauiel Itokawa, Yoe McGibbon, Charles A. Schaps, Maika Elisheva Zanolin, Fabio Copeland, Arthur H., Jr. Jockusch, Carl G., Jr. McGill, Richard E. Schauer, Richard L. Zegarlinski, Boguslaw Cordes, Heinz 0. Johnson, Donald G. Meisner, Morris J. Scheier, Wallace M. Zeilberger, Doron Cornelis, Eric Johnson, William B. Mellender, James W. Schirmeier, Horst Zeller, Karl Craft, George A. Jones, Carl Hilton Mielke, Paul T. Schlesinger, Ernest C. Ziebur, Allen D. Davies, Morton J. Jonsson, Bjarni Milman, Mark H. Scott-Thomas, John F. Zilmer, Delbert E. Dean, Arnold A. Kakihara, Ytlichir6 Moller, Raymond W. See, Richard Zizi, Khelifa DeMarr, Ralph E. Kamejinm, Kohji Mooney, John J. Sekigawa, Hisao Zorn, M.A. Devaney, Robert L. Karnishima, Yoshinobu Moore, Richard A. Selby, Alan M. Anonymous (70 ) Dietsche, H. J. Kaplan, Wilfred Morris, Robert A. ·····-······-··-····-···-········· ········-····--·---·-··--····---·-----····--···-····················--· ···············-············-·---· 726 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS Centennial Fellowship Fund AMS CENTENNIAL FELLOWSHIP FUND IMU SPECIAL DEVELOPMENT FUND Abatangelo, L. Maria *Al-Droubi, Akram Anderson, Michael T. Ascenzi, Maria-Grazia Baldwin, John T. Abate, Marco Alegria, Carlos A. Andersson, Lars Aschbacher, Michael Balibrea, Francisco Abbott, H. L. Alexander, John R., Jr. Andima, Susan Asensio Mayor, Jose Balkema, A. A. Abbott, James C. • Alexander, Kathleen M. Ando, Shiro *Ashbaugh, Mark S. *Ball, John M. Abbott, James H. Alexander, Roger K. Ando, Tsuyoshi Askey, Richard A. Ball. Joseph A. Abbott, Rita A. Alexander, Stephanie B. Andre, Peter P. •Asprey, Winifred A. •Ball, Keith Abdel-Megied, Mohamed Alexanderson, Gerald L. *Andreadakis, Stylianos Assmus, Edward F., Jr. Ball, Richard Neal Abe, Terutake Alfonso, Fermin Jorge Andreoli, Dorothy W. Atiyah, Michael F. Ball, Richard W. Abellanas, Pedro Ali, Hydar eAndriamanalimanana, Bruno Atkinson, Frederick V. Ballard, William R. Aberbach, Ian M. Ali, M. Kursheed *Andruskiewitsch, Nicolas Atkinson, H. R. *Ballieu, Michel Andre *Abi-Khuzam, Faruk Fuad Alif, Metod Angad-Gaur, Hendrik W. K. Atkinson, Stuart L. •Ballou, Donald H. *Abikoff, William *Aliprantis, C. D. *Angelos, James Roy *Auchmuty, Giles Baloglou, George Ablow, Clarence M. Allan, Graham R. *Angenent, Sigurd B. Auer, Jan W. *Banchoff, Thomas F. Abolt, James A. Allan, James A. Anger, Frank D. Ault, J. C. Bandle, Catherine Abramovici, Havian Allard, William K. *Angotti, Rodney Auslander, Bernice L. Handler, Wyllis *Abrams, Gene D. Allday, Christopher J. Anichini, Giuseppe *Auslander, Joseph Bandt, Lawrence E. Abramson, Lawrence Allegretto, Walter *Annavedder, Edwin Auslander, Louis Baneljee, Utpal *Abu-Sbeih, Moh'd Z. Allen, David L. Anselone, Philip M. Auslander, Maurice Bang, Chang Mo A'Campo, Norbert Allen, Harry P. Anshel, Michilel Aust, Catherine C. •Bang, Hyunsoo *Acar, Robert Allen, Howard *Ansorge, Rainer Au-Yeung, Yik-Hoi Bankston, Paul J. Accola, Robert D. M. Allen, J. Thomas, lli Anthony, Alan C. Avedissian, Vahe Yeghishe Bannai, Eiichi *Achlival, Elena Claudia Allen, William C., III Anton, Jose Manuel Aversa, Vincenzo L. Bansal, J. K. Adachi, Masahisa Alltop, William 0. Antoniadis, Anestis A. *Avrin, Joel D. Baouendi, M. Salah Adams, Barry G. Almgren, Frederick J., Jr. Antoniadis, Jannis Axelsson, Reyuir Baras, John S. Adams, Colin C. Almgren, Robert Frederick Appel, Kenneth I. Axler, Sheldon Barbeau, Edward J., Jr. Adams, Dennis R. Alonso, Agustin Arai. Hitoshi Ayoub, Christine W. •Barber, S. F. Adams, Jeffrey Alonso, James *Araki, Huzihiro Ayoub, Raymond G. Barber, William E. •Adams, Malcolm R. *Alonso, Javier Arapostathis, Aristotle *Azenhas, Olga Barbieri, Francesco Adams, Scot Robert Alonso, Juan M. Arason, J 6n Kr Azoff, Edward A. Barbosa, J. Lucas M. Adams, William W. Alpay, Daniel A. *Arazy, Jonathan eBa, Boubakar Bardaro, Carlo Adamson, lain T. A. C. Alperin, Jonathan L. Arbarello, Enrico Baartmans, Alphonse H. *Bardell, Paul H. *Addington, Susan L. Alpern, Steven *Archbold, Robert J. Baas. Nils Andreas Bardos, Claude W. •Adelani, Lateef A. Alsholm, Preben Archer, Myla M. Babcock, William W. Barendregt, Henk P. Adelberg, Arnold M. Alsina, Claudi Arena, Orazio Bacciotti, Andrea Barety, Julio Edgardo *Adeyeye, John 0. *Alspach, Brian R. Arenberg, C. Arne Bachman, George Barge, Marcy Adler, Irving Alspach, Dale E. Arens, Richard F. Bachmuth, Seymour *Baribeau, Line *Adluri, lndrasena van Alstyne, John P. • Arenstorf, Richard F. *Back, Allen H. Balja, Jose M. Adolphson, Alan C. Althoen, Steven C. Arias, Fernandez Arturo Bacon, Harold M. Barkauskas, Anthony E. Aeppli, Alfred *Al-Thnkair, Fawzi Ahmed Aribaud, F. Bade, William G. Barmettler, Urs W. Agarwal, Ashok K. *Altomare, Francesco Arirna, Satoshi Badiozzaman, Abdul Jabbar *Barnard, Roger W. Agoston, Max K. Aluffi, Paolo Arisaka, Nakaaki *Bae, Jong Sook Barner, Klaus Aharoni, Israel *Alvarez, Josefina •Arkin, Joseph •Bae, Soon-Sook *Barnes, Bruce A. Aharonov, D. Ambrose, Richard D. • Arkowitz, Martin A. Baer, Robert M. Barnes, David C. Ahmad, Hamid K. •Ames, Karen A. Arlinghaus, Sandra L. Bagby, Richard J. Barnes, Ward C. Aldoo,Emmanue!B. Arnirkhanian J olfai, Vrege Arlinghaus, William C. *Baginski, Frank E. Barnet, Frank Alssen, Michael I. Arnir-Moez, Ali R. Armbrust, Manfred K. *Baildon, John D. Baron, John J. *Altsahlia, Farid • Arnitsur, Shimshon A. Armentrout, Steve Bailey, Donald F. Baron, Simson Aizawa, Sachiko Amsbury, Wayne P. Armon, Mary Vlastnik Bailey, Evelyn C. Barozzi, Elisabetta Aizenrnan, Michael Ananthararnan, Rajan *Arms, Judith M. Bailey, G. H. Barre, Raymond C. Ajan, K. S. Anastasio, Salvatore Armstrong, Ernest Stokes Bailey, Robert E. Barreca, J. R. Akcoglu, Mustafa A. Ancel, Fredric Davis Armstrong, Mark Anthony Bailyn, Paul M. Barrera-Rosillo, Domingo Akin, Ethan J. *Andersen, E. Sparre Armstrong, Thomas E. *Bajusair, Mohamed S. *Barrett, David E. Aksoy, Asuman G. *Andersen, Henning Haahr Amberg, Robert L. Baker, Alan Barros-Neto, Jose *Akyildiz, Yilmaz *Andersen, Kurt Munk •Arnold, David M. *Baker, Andrew James Barry, William Patrick, Jr. AI Assaad, AI Ayham A. Andersen, Lars Dovling Arnold, Douglas N. Baker, Blanche J. Barsky, Daniel Albano, Alberto Anderson, Allan G. Arnold, Leslie K. Baker, Charles R. *Barsotti, Leo Al-Bassam, Mohammed Ali A. Anderson, Berti! *Aron, Richard M. Baker. Edward D. Bart, H. Albert, John P. Anderson, Beverly Jacques Aronson, Donald G. Baker, George A., Sr. Barth, Karl F. Albertson, .Michael 0. *Anderson, Charlie Arrington, Thomas R. Baker, Irvine Noel Bartick, Philip R. *Albeverio, Sergio A. Anderson, Christopher R. *Artemiadis, Nicolas Baker, Kirby A. *Bartnik, Robert A. Albrecht, Ernst Anderson, Donald W. Arthur, James G. *Baker, Peter Fritz de Bartolomeis, Paolo Albrecht, Felix R. Anderson, Douglas R. eAttin, Michael Baksa, Dennis John Barton, Thomas J. Albugues, Alain Vincent *Anderson, Glen D. Artola, Michel *Bakshi, Jagjit •Baruch, Herbert M., Jr. *Alcorn, David P. Anderson, Greg W. Arveson, William B. Bal, Kenan Y. • Baruch, Herbert Mark, III Alder, H. L. Anderson, Joel H. *Arzberger, Peter W. Baladi, Viviane Barwise, Kenneth J. Alderton, Ian W. Anderson, John D. Asano, Kouhei Baldi, Paolo *Basak, Gopal Krishna Aldous, David J. Anderson, John T. Asano, Shigemoto *Baldin, Yuriko Y. Basile, Achille SEPTEMBER 1992, VOLUME 39, NUMBER 7 727 AMS Centennial Fellowship Fund ...... _, ...... ·····································-"'"'''"'''''''' ...... -...... Basor, Estelle Benitez, Carlos Bindschadler, David E. *Borgers, Christoph * Brieskom, Egbert Bass, Barry C. Benkart, Georgia M. Binegar, Bime T. *Borjeson, Lennart Brislawn, Christopher M. •Bass, Hyman Benke, George Binkley, Timothy Bormand, Georges Brisse, Edward M. *Bastero, Jesus Bennett, Fredricka T. Bircher, John J. Borucki, Leonard John Britton, John L. Bastian, Gregory A. Bennett, Graharoe Birman, Joan S. Borwein, Jonathan M. Brlek, Srecko Basu, Somita Bennett, John Makepeace Biroli, Marco Bosch, Carlos Bro, Per Bateman, Felice D. Bennett, Karin R. Birrell, Robert J. Bosch, William W. Broadwin, Judith E. Bateman, Paul T. Bennett, Paul M. *Bischi, ·Gian-Italo Bose, Christopher J. Brobeck, Barbara Caldwell Batt, Jurgen 0. •Bennish, Joseph Bishop, Alan A. *Bosma, Wieb Brodkey, Jerald S. Battaglia, Victor John *Benson, Dave *Bishop, Christopher J. Bossavit, A. *Brokate, Martin Batterson, Steven L. Benson, David Bernard • Bishop, Richard L. Boswell, Rupert D., Jr. Broline, Duane M. Batty, Charles J. K. Benson, Donald C. *Bisson, Terrence Paul *Botelho, Fernanda *Bromberg, Eleazer Bauer, Frances B. Benson, F. Chal Bisztriczky, Tibor Bottema, Murk J. *Brommundt, Eberhard W. Baum, Paul F. Benyamini, Yoav Bivens, Irl C. Bottoms, Charles L. Brons, Kenneth A. *Baumann, Volker H. Bercovici, Hari Bjorklund, Peter B. *Bouchard, Pierre Brooks, Robert *Baumeister, Johann Berenstein, Carlos A. Blackadar, Bruce E. Bouche!, Andre Brosowski, Bruno H. Baumgartner, James E. *Berg, Christian Blackall, Clair J. eBoultbee, Nan Brothers, John E. Baumslag, Gilbert Berg, Gene A. Blackmore, Denis L. Bousfield, Aldridge K. Brotz, Douglas K. Baur, Lynne A. Berger, Alan E. • Blair, Charles E. *Boutot. Jean Francois Broue, Michel Baxendale, Peter H. Berger, Marcel Blair, William D. Bouwsma, Ward D. Broughton, S. Allen Baxter, Kathleen Berger, Marsha J. Blakemore, Carroll F. *Bouzar, Nadjib Browder, William Bayer, David Bergeron, Fran~ols Blanc, Charles Bower, Julia W. Brown, Arthur A. *Bayer, Margaret M. van den Bergh, Michel •Blanc, M. L. Bowie, Harold E. Brown, Arthur B. Bayer, Valmecir Berglund, John F. Blanch, Gertrude Bowman, Leslie W. Brown, Douglas K. Bayer-Fluckiger, Eva M. Bergman, George M. Blanche, Ernest E. Boyce, Donald J. Brown, Edgar H., Jr. Bayo, Enrique Bergstrand, Deborah J. *Blankenbaker, John R. Boyd, John P. Brown, George B. Bazinet, Jacques *Bergvelt, Maarten J. Blanton, George R., Jr. Boyd, Stephen Homer Brown, Gerald D. Beadle, Allen Jay Bergweiler, Walter Blasius, Don M. •Boyer, Delmar L. Brown, Gerald L. Beale, J. Thomas Berin, Alec Blatter, Jorg Boyle, Mike •Brown, Howard H. Beals, R. Michael Beringer, Alfred Blattner, Robert J. *Bozeman, Sylvia T. Brown, Jack B. Beals, Richard W. Berkey, Dennis D. Bledsoe, Woodrow W. Bozonis, Petros Brown, Lawrence G. Bean, Phillip W. Berkovich, Vladimir G. Bleick, Willard E. *Braaksma, B. L. J. •Brown, Patrick J. Bean, Ralph J. Berkovitz, Leonard D. Bleiler, Steven A. *Braam, Peter J. Brown, Richard G. •Beard, Jacob T. B., Jr. Berlekamp, Elwyn R. *Blij, Frederik Van Der Brachman, Malcolm K. *Brown, Richard K. Beatty, Thomas A. Berman, David R. Blitch, Patricia M. Brackx, Freddy F. Brown. Richard L. W. •Beaumont, Ross A. Berman, Robert David Bloch, Ethan D. Bradford, David Bertram Brown, Robert Freeman Beauzarny, Bernard M. Berman, Stephen Blohm, David A. Bradie, Brian D. Brown, Ronald Bechtell, Homer F. Bermudez, Alfredo Bloom, David S. Bradley, John S. Brown, Sharan Inez Beck, William A. Bernardi, Salvatore D. *Bloom, Laura A. Bradley, Richard C. Brown, Terrell N. Beckenstein. Edward Bemau, Simon J. Bluher, Antonia Wilson *Bradley, Robert E. Brown, Wtlliam G. Becker, Eberhard Berner!, Jan •Blum, Dorothee Jane Bradlow, Steven B. Brownawell, W. Dale Becker, James C. Bemis, Francisco Blum, Joseph Bragg, Arthur E. Browne, H. Nelson, Jr. Becker, Thomas Bernstein, Allen R. Blum, Lenore Brakke, Kenneth A. Browne, Patrick J. Beckman, Frank S . Berresford, Geoffrey C. Blllntlinger. Martin Bramble, James H. Brualdi, Richard A. . Beckmann, William H. *Berrick, A. J. Blundell, Solon Frederick Bramsen, John D. *Bruaset, Are Magnus Bedard, Robert Berriozabal, Manuel P. Boardman, John M. Brandt, Dennis E. Bruck, Ronald E., Jr. *Beder, Jay H. Bers, Lipman Bobisud, Larry E. Branner, Bodil Bruckner, Andrew M. Bedford, Eric D. Berti, Patrizia *Bochev, Pavel Blagovestov Brannick, Monika Brucks, Karen M. *Bedford, Tim Bertin, Emile M. Bodlien, Douglas F. *Branson, Thomas Patrick Bruckstein, Alfred M. Beekman, John A. Beschler, Edwin F. Bodnar, Istvan Brant, Larry J. Brueggemann, Wolfgang Beesley, E. Maurice Bessenrodt, Christine Bodnarescu, M. V. Bratholdt, J. Stuart Bruggeman, Roelof W. Beghi, Luigi Betancourt, Carlos M. *Bogar, Gary A. *Brattstrom, Gudrun B. *Brummer, G. C. L. *Behnke, K. Bethelmy, David G. *Bogart, Kenneth P. Brauer, Fred Brunat. Josep M. Behrens, Ernst-August Betsch, Gerhard Bohn, S. Elwood Bravo. Raul Bruner, Robert R. Beig, Robert Betz, Ebon E. Bohnke, G. C. Bray, Nancy J. Brunet, Richard M. *Beissinger, Janet Simpson *Benkers, F. Boivin, Andre *Brechner, Beverly L. Bruni, Anthony J. *Bekkali, Mohamed Bezak, Nicholas J. Bojanic, Ranko Breckenridge, John C. *Brunk, Hugh D. *Belair, Luc Bhattacharya, Rabi N. Bolger, Robert Edwin *Breen, Lawrence S. •Brunner, Hermann Bell, Harold *Bhattacharya, Urmi Bolis, Theodore S. Breitung, Karl W. Bruno, Vincent J. Bell, Mark Robert •Bialostocki, Arie Bolker, Ethan D. Brender, Melvin Bruns, Winfried Bell, Steven R. Bianco, Steven Anthony Bollinger, Robert A. Brendle, James J. Brunschwig, Mildred C. Bell, Wolfgang Bibisi, Keith *Boman, Jan Brennan, Joseph P. *Brunson, Barry W. Bellamy, David P. * Bickart, Theodore A. Bonadio, Allan R. *Brenneis, James M. Brunswick, Natascha A. Belley, J. M. Biech, Ted H. Bonet, Jose Brenner, Alfred E. Bryant, Billy F. Bellissard, Jean V. Biedeuharn, Lawrence C. Bonin, Joseph E. Brenner, Philip Bryant, John G. Benac, Theodore J. Bieri, Robert Bonnington, C. P. *Brenner, Sheila Bryant, Robert L. Ben-Artzi, Asher Bierstedt, Klaus D. Booker, T. Hoy Brent, Richard P. Bryce, Gerald M. Bencslith. Katalin A. Bierstone, Edward Boos, William *Brenti, Francesco Brydges, David C. Bendat, Julius S. Bilaniuk, Stefan Booth, George W. Bressler, David W. eBrylinski, Jean-Luc Bender, John Biles, Charles M. Booth, Raymond S. Bresson, Maurice J. Brylinski, Ranee Kathryn Benedetto, John J. Billigheimer, Claude E. Boothby, William M. Bressoud, David M. Bryn, Milo F. Benedicks, Michael Billik, Martin Borchers, Hans-Jurgen Breves Filho, J. A. Brzenk, Ronald M. Benham, James W. Bilodeau, Gerald G. Borden, RobertS. Brewster, Stephen Thomas Brzezinski, Juliusz Ben-Israel, Adi *Binding, Paul A. Borel, Armand *Bridges, DouglasS. Bshouty, Daoud 728 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS Centennial Fellowship Fund ...... Buccino, Alphonse Calderbank, Robert Cavicchioli, Alberto Cho, Choong Yun *Coen, Salvatore Buchanan, Thomas Calderer, M. Carme Caviness, B. F. Cho, Jung R. *Coffee, Terence Buchsbaum, David A. Calhoun, William C. *Cawley, Robert Choate, Jonathan Coffey, John Buckley, Joseph T. Calica, Arnold B. Cayford, Afton H. Choe, Geon Ho Coffman, Robert L. Bucy, Richard S. Callahan, James J. Cecil, Thomas E. Choe, Young Han *Cogburn, Robert F. Buddrus, Lee Edward Callahan, Kevin Eric *Cegrell, Urban Choi, Hyeong In Cogdell, James Wesley Budney, Paul Edward *Callan, C. David Cerda, Joan Choi, Sung Kyu Cohen, Amy Budnik, Paul, Jr. *Calvi, Jean-Paul Cervone, Davide P. Choi, Yun Sung Cohen, Daniel I. A. Buechler, Steven Allen Camacho, James, Jr. deCesare, Kenneth M. Choksi, J a! R. Cohen, Frederick R. Buehler, Royce E. Camarena Badia, Vicente Chabert, J. L. Chong, Chi Tat Cohen, Henry B. Buekenhout, F. *Camera, Gerardo A. Chafee, Nathaniel Choo, Koo-Guan Cohen, Herbert E. Bugajska, Krystyna M. Cameron, Douglas E. Chakerian, Gulbank D. Choquet, Gustave *Cohen, Leon M. Bugajski, Joseph M. Cantina, A. R. eChaligne, Philippe Chosid, Leo Cohen, Leon W. Buhler, Joe P. Campbell, Duff G. Chalmers, Graham D. *Chouikha, Raouf Cohen, Marshall M. Buianouckas, Francis R. Campbell, Harold E. A. Chamberlin, Richard E. Chouteau, Charles C. Cohen, Martin J. Bullen, P. S. Campbell, L. Andrew Chan, Jack-Kang Chover, Joshua Cohn, Donald L. *Bulman-Fieming, Sydney D. Campbell, L. Lome Chan, Jor-Ting Chow, Tseng Yeh Cohn, Richard M. Bumby, RichardT. *Campbell, Paul J. Chan, Yun K. Chow, Yuan S. ecohn, William S. Bump, Daniel Willis Campillo, Antonio •Chandler, Bruce Christ, F. Michael *Colbourn, Charles J. Bunge, Marta C. Campiti, Michele Chandra, Jagdish Christensen, Chris Cole, Charles A. Burbulla, Dietrich *Candiotti, Alan *Chandrasekar, Srinivasan Christilles, William E. Cole, Floyd B., III Burchard, Hermann G. Canjar, Mike Chang, Chao P. Christy, Joe Cole, Herman D. Burckel, Robert B. Cannon, James W. Chang, Derek Kong Chu, Chinku Cole, Paul Dana Burdon, Marcia Lynne Cantor, David G. Chang, Gerard J. Chu, Tienchen Coleman, A. John Burger, Marc R. Cantrell, James C. Chang, 1-Lok Chuang, Pi-Chun Coleman, Courtney S. Burgess, C. Edmund Cantwell, John C. Chang, Jen-Tseh Chuaqui, Martin S. Coleman, Robert Burgess, Richard Dennis Cap, Clemens Heinrich Chang, Kun Soo *Chuaqui, Rolando B. Colley, Susan Jane *Burgess, Walter D. *Capasso, Vincenzo Chang, Ping-Tung Chung, Dong Myung Collier, Jarrell D. Burghduff, John Brian Caplan, Harry Chang, Shao-Chien Chung, Lung Ock *Collins, Benjamin V. *Burkard, Rainer E. *Capozzoli-Diaz, Anthony B. Chang, Shun-Cheng •Church, Philip T. Collins, Dennis G. *Burke, Maxim R. Cappell, Sylvain E. Chang, Yu Churchill, Richard C. Collins, Heron S. Burke, Tracy Lynn Capuzzo Dolcetta, ltalo *Chanillo, Sagun Ciarlet, Philippe G. Colon, Ivan E. *Burkhart, Jerry C. Caranti, A. E. Chao, J. A. Cieslik, Thomas P. *Colonius, Fritz Burkhart, Richard H. *Carbery, Anthony Chao, Li *Cifarelli, Victor V. Colquitt, Landon A. Burkholder, Donald L. Carette, Jacques Chaperon, Marc *Cifuentes, Patricio Colson, Henry D. Burnham, Donald *Carey, A. L. Chapin, Steven Arthur Cima, Joseph A. Comar, Timothy D. Burns, Daniel M., Jr. Carleson, Lennart A. E. Charney, Ruth M. Cinlar, Erhan Comenetz, Daniel Burns, Keith H. Carlson, Bengt G. *Chatterji, Srishti D. *Cipriani, Fabio Comfort, Steven H. Burridge, Robert Carlson, Bille C. Chauvin, Andre ecivin, Paul Conlon, Joseph G. Burstall, Francis E. Carlson, Jon F. *Chavey, Darrah P. *Claasen, H. L. Conlon, Lawrence W. Burtner, Dale K. Carlson, Philip R. Chawla, La! M. Clapp, Michael H. Conn, Jack Frederick Burton, Leonard P. *Carlson, Robert C. *Chee, Pak Soong *Clapp, Robert E. Connolly, Frank X. Busemann, Herbert Carlson, Timothy J. Cheeger, Jeff Clare. Loren Paul Connor, JefferyS. Busenberg, Stavros N. *Carlsson, Renate Chein, Orin N. Clark, Jeffrey W. Conrad, Bruce P. Buser, Peter J. do Carmo, Manfredo P. Chen, Concordia C. Clark, Robert A. *Conrad, Eric van Fossen Bushnell, Colin J. Carpenter, Sarah A. *Chen, Goong *Clark, W. Edwin •Conrey, J. Brian Bushnell, Michael L. •Carrell, James B. Chen, Gui-Qiang Clarke, Charles L. A. Constantin, Peter S. Busque, Claudi Carrie, Dennis Chen, Louis H. Y. *Clarke, Francis Constantinescu, Corneliu *Buss, Samuel R. Carrington, Walter A. Chen, W. W. L. Clarke, Graham Thomas Contreras, Gonzalo Butcher, John C. Carroll, Timothy B. Chen, Wenxiong Clarke, Wilton E. L. *Cook, Joseph M. Butcher, Ralph Stevens Carruth, James H. Chen, Y. W. Clarkson, Eric W. Cook, Larry T. *Butler, George M. Carson, Robert C. Chen, Yongzhuo *Clarkson, Peter A. Cook, Thurlow A. Butler, James William Cartan, Henri Cheng, Horace Burk Clary, Stuart *Cooke, David B. Butler, John B., Jr. Carter, David W. Cheng, Jih-Hsin Claus, Elly •cooke. Kenneth L. Butts, Thomas R. Carter, Thomas J. Cheng, Kuo-Shung Clee, William A. Cooke, Roger Lee Byerly, Robert E. Cartier, Pierre Cheng, Raymond S. *Clemens, Charles Herbert Cooley, Clifford R. Byrd, Kenneth A. Casazza, Peter G. Chern, Shiing S. Clement, Philippe P. Coolsaet, Arnold A. Byrne, Charles L. Case, Bettye Anne Chern, T. Y. Peter *Clements, George F. *Cooper, Daryl Byrnes, James S. *Casey, Stephen D. Cherniavsky, John C. Cleveland, Richard A. Cooper, J. B. Byrom, Robert Lawrence Casimir, John F. R. Chernoff, Herman Cliborn, James H. Cooper, Jeffery M. Cable, Charles A. Casler, Burtis G. Chernoff, Paul R. Clifford, Alfred H. Cooper, Mark A. *Caboz, Regis Cassidy, Phyllis J. Cheslack-Postava, Kevin A. Clifford, Jane E. Cootz, Thomas A. Caccianotti, Luciano Castagnoli, Brio A. •Cheung, B. K. S. Cline, Edward T. Cope, Davis K. *Cadogan, Charles C. Castillo, Jose E. *Cheung, Chi-Keung Clivio, Andrea Giovanni Copeland, Arthur H., Jr. Caenepeel, Stefaan Castle, Richard Jay Chiang, Peter H. S. Closs, Joseph N. *Copper, Mark L. Caflisch, Russel Castore, Glen M. Chiarenza, Filippo Clover, William J., Jr. Coram, Donald S. *Cagnac, Francis *Castro, Alfonso *Chicone, Carmen C. •Cobb, Shannon S. Corbett, John V. Cahen, Paul-Jean *Catanese, Fabrizio M. E. •Chihara, Theodore S. Cobham, Ian P. Cordero, Luis A. Cahill, Rotraut G. Cateforis, Vasily C. *Chikuse, Yasuko Cochran, James A. •Cordes, Craig M. Cai, Mingliang Cater, FrankS. *Childs, Lindsay N. *Cochran, W. George Cordes, Heinz 0. Cain, Bryan E. Cato, Benjamin R., Jr. Chillag, David Cockburn, Julio Bernardo ecordovil, Raul Caines, Peter E. *Cavallini, Fabio Chillak, Edward W. Cockburn, Sally P. Corduneanu, Constantin Cairns, Grant Cavaretts, Alfred S. Ching, Wai-Sin Cockcroft, Wilfred H. Cornelis, Eric Cairoli, R. Cavender, James A. Chiswell, Ian M. Coddington, Earl A. Cornell, Gary SEPTEMBER 1992, VOLUME 39, NUMBER 7 729 ·············-·······-········ ... ······--·-·--···--··-·-··-································-···--····------··-·-··--·····-······-···-··-····--··-·············--···-·············----·······-····.-······-·········-··················--········--··-··············· AMS Centennial Fellowship Fund ...... ~ ...... ····································· ...... ,...... ~··············· ...... Correia, Frank B. Cutler, Colleen Diane Dekleine, Herbert A. *Di Prisco, Carlos A. *Duncan, T. E. Corrigan, Thomas Carney Cutler, Mark C. Dekster, B. V. Divis-Poracka, Zita M. Dunham, Douglas J. Corsi Tani, Gabriella *Cuttle, Yvonne H. Delange, Hubert Dixon, Albert T. *Dunkers, Dee Ann Corti, Alessio Cwikel, Michael *De La Penha, Guilhenne M. *Dixon, John D. *Diintsch, lvo *Corwin, Stephen P. Dadok, Jiri *Delaware, Richard R. *Dixon, Peter Grant Dunwoody, Martin John Cosgrove, Christopher M. Dahl, Erlend Delbaen, Freddy Dlab, Vlastimil Dupont, Johan L. Cosner, George C. Dahlin, Rolf B. Deleanu, Aristide Dodds, Peter G. Durand, Loyal Cossio, Jorge Dai, Taen-Yu DeLeon, Morris Jack Dodds, Theresa K. Duren, Peter L. Costabel, Martin *Dajczer, Marcos *Dell' Antonio, Gianfausto Dodson, Christopher T. J. *Durfee, Alan H. *Costantini, Cristina Daly, John T. •Delphenich, David H. Dodziuk, Jozef Durkin, Marilyn B. Costenoble, Steven R. D'Ambrosio, Ubiratan *Delporte, Jean Doerfler, Willibald Duszynski, Martin, Jr. Cote, Louis J. Damiano, David B. Del Val, Pablo • Doering, Boro Dutta, Sankar Prasad Cotsaftis, Michel Dana, Martin P. Demana, Franklin D. Dolan, James M. Dutton, Charles Everett Cotter, Christopher S. Danaee, Ali DeMarr, Ralph E. Dolbeault, Pierre E. Duzhin, S. V. Cotton, Robert M. Daney, Charles G. Demetrius, Lloyd A. Dold, Albrecht E. *Dwork, Bernard M. Couch, W. Eugene D'Angelo, John P. Deming, Robert W. Dolgachev, Igor *Dwyer, David J. Coulter, Malcohn A. Daniels, Peg M. •Demko, Stephen Dollard, John D. *Dwyer, William G. Countryman, William Mark Daouda, Sangare Demmel, James W. Dombrowski, Joanne M. Eachus, J. J. Courteau, Bernard D' Aprile, Margherita De Moor, Bart L. R. *Dominici, Paolo eEaiy, Clifton E., Jr. Coutant, Basil W. Daras, Nicholas Dencker, Nils Dornioijanni, Roberto *Eames, William P. Covington, Jacinta Ann D' Aristotile, Anthony J. Dennin, Joseph B. Domino, Laurence E. Easley, David H. *Cowen, Carl C., Jr. Dark, R. S. Dent, Elliod Domokos, Gabor •Eaton, Timothy R. Cowen, Lenore J. Darling, Donald A. Deodhar, Vinay Vithal Donaldson, Simon K. Eaves, Burchet Curtis *Cowling, Michael G. Darnel, Michael R. *DePagter, Bernardus Donaly, James P. Eberlein, Patrick Barry *Cox, David A. Darwish, Qais H. *De Pascale, Espedito Donnay, Victor J. •Ebrahirni Vishki, Hamid Reza Cox, Raymond H. D' Atri, Joseph E. Derdzinski, Andrzej J. Donoho, David Leigh Echeverria, Javier Cox, Samuel H. Datskovsky, Boris A. *Dennenjian, Yves Doob, Joseph L. Ecklund, Earl F., Jr. ecoxeter, H. S. MacDonald D' Attore, Terrance R. Deruaz, Marcel A. F. *van Doorn, Erik A. eEckmann, Beno •crabtree, J. B. D' Attorre, Leonardo *DeShalit, Ehud *Doplicher, Sergio Eddy, Robert P. Craft, George A. Daubechies, Ingrid De Snoo, Hendrik S. V. Doppel, Karl Edelstein, Michael Craggs, Robert F. *Dauben, Joseph W. Desoer, Charles A. Doran, Robert S. Edelstein-Keshet, Leah Craig, Jessica Marguerite Dautray, Robert I. Desquith, Etienne Dordal, Peter L. Edet, Silas B. Craig, Walter L. *Davennan, Robert J. *Detrez, Eric Louis *Dorfmeister, Josef F. Edjvet, Martin *Crandall, Gordon L. *Davey, Brian A. eDeTorck, Dennis Dorroh, James R. Edmonds, Allan L. Crandall, Michael G. Davidow, Amy L. *Deuber, Walter Alfred Dorsett, Charles I. Edmonds, Jack Cranston, Michael Craig *Davidson, Kenneth R. Deumens, Erik Dorwart, Harold L. Edmondson, Don E. Crapo, Henry H. Davidson, Mark G. *Deutsch, Daniel H. *Dos Santos, Antonio F. •Edmundson, H. P. Crauder, Bruce C. Davies, Ian M. Devaney, Robert L. Dou, Alberto M. Edris, Gerrit M. Crawford, James P. Davies, Morton J. Deveney, James K. Dougherty, Michael M. *Edwards, C. M. •Creede, Geoffrey D. Davis, Chandler *Devinatz, Ethan S. Douglas, Jim, Jr. Edwards, Charles H., Jr. Creese, Franklyn G. •Davis, James F. *Devlin, Keith J. Douglas, Ronald G. Edwards, David Albert Creese, Thomas M. •Davis, Lynda Ann Dewallens, Jean H. Douglass, John, Jr. *Edwards, Harold M. *Crippa, D~vid Davis, Marsha J. Dhooghe, Paul F. J. Douglis, Avron Edwards, Robert D. Criscenti, Jacqueline P. Davis, Martin D. Diamond, Fred I. *Doust, Ian R. *Eells, James Crittenden, Richard J. Davis, Paul L. Diamond, Jack Dovennann, Karl Heinz Eeoigenburg, Paul J. Crone, Lawrence J. Davis, Paul W. Dias Da Silva, J. A. Dovidio, Catherine Slanta -•Efrat, Isaac Y. Cronheim, Arno Davis, Robert B. Diaz, Steven P. Dow, Alan Eggers, John D. Cross, James J. Davis, Robert L. Diaz-Miranda, Antonio •Dowds, Richard E. Eggers, William I. Cross, Ronald W. *Davison, J. Leslie Di Biase, Fausto Dowling, Diane M. Ehlers, F. Edward Crothers, Derrick S. F. Dawes, A.M. Dibner, Steve Dowling, Thomas A. Ehrlich, Louis W. Crow, Edwin L. Dawson, Donald A. *Dickenstein, Alicia M. Downey, Rodney G. Ehrlich, Paul Ewing *Cruz, Eliseo G. Day, Jane M. Dickerson, Charles E. Doyen, Jean Eigel, Edwin G., Jr. *Cryer, Colin W. Daybell, Dorothy A. Dickie, Garth A. Doyle, Brian J. Eigen, Stanley J. *Csiszarik, Michael V. Dayton, Barry H. Di Concilio, Anna *Doyle, Peter G. Ellenberg, Samuel Cude, Joe E. Dean, Andrew P. Diderrich, George Drager, Lance D. Einthoven, Isabella H. Cuer, Michel Dean, Carolyn A. Diener, Karl-Heinz Dragt, Alex J. Einwohner, Theodore H. Cummings, James Dean, Nathaniel Dieter, Ulrich Drake, Frank R. Eirola, Timo J. Cunningham, Daniel W. Dean, Richard A. •Dietsche, H. J. Drazin, Michael P. Eisele, Carolyn Cunningham, Frederic, Jr. *Debnath, Lokenath Dieudonne, Jean A. •Dressel, Francis G. Eiseman, Peter R. Cunningham, Richard J. Debrunner, Hans E. Dijksma, Aalt Drew, Gerald C. *Eisenberg, Michael Allen *Cuntz, Joachim De Canniere, Jean Dikshit, G. D. Drouilhet, Sidney James, II Eisenbud, David Cuoco, Albert A. Deckert, Kenneth L. Dilcher, Karl H. •Drucker, Thomas L. Eisenlohr, John Merrick Curjel, Cl!-spar R. De Clerck, Frank Dillon, Meighan Irene Druet, Robert L. Eisenstadt, B. J. Currier, Albert W. Dedrickson, Duane A. •Dilworth, R. P. Dubisch, Roy Eisman, Sylvan H. Currier, Robert J. DeFacio, Brian *Dilworth, Steve Dochamp, Thomas E. Eisner, Ebner Curtis, Charles W. DeFelica, Patricia Ann Di Maio, Giuseppe *Du Cloux, Fokko •Ekambaram, S. Curtis, Cynthia L. •De Figueiredo, Djairo G. *DiMilo, Anthony J. *Dudley, Richard M. *Ekeland, Ivar Curtis, Herbert J. Defrancesco, Henry F. Diminoie, Charles R. Dudziak, James J. Eklund, Anthony D. Curtis, Philip C., Jr. DeGray, Ronald W. Dirnitracopoulos, Constantinos Duer, John L. L. Eldridge, Klaus E. Curto, Raul E. *Dehesa, Jesus Sanchez Dimsdale, Bernard Dugas, Manfred H. Elbadad, Jimmy Cushing, Jim M. Deift, Percy Alec Ding, Wei Yue Dokelow, James S., Jr. EI-Hodiri, Mohamed Cusick, David A. De Iongh, Johan J. *Dioitz, Jeffrey Howard *Dumrnigan, Neil P. Ella, Michele •Cusick, Thomas W. Dejter, ltalo J. *Dionne, Benoit *Dunbar, William Dart, Jr. *Eliahou, Shalom Cuthill, Elizabeth H. Dekker, Jacob C. E. *Di Paola, Jane W. Duncan, Richard D. •Elias, Walter, Jr. 730 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS Centennial Fellowship Fund Eliason, Stanley B. Evens, Leonard *Ferreira, Fernando J. Foulis, David J. Fulton, William *Eliasson, Lars HAkan *Evens, Samuel R. Ferreira Rosa, Jose Humberto Fournelle, Thomas A. Funabashi, Shoichi Elich, Joe Everitt, W. Norrie Ferrer, Jesus Fowler, Frederick C. Fung, Francis Y. C. *Elizondo, Enrique Javier Evers, Joseph J. M. *Ferreyra, Guillermo Segundo Fox, Jeffrey Stephen Fuqua, Jeffry B. El Kacimi Alaoui, Aziz Ewacha, Kevin Ferri, Massimo Fox, John Michael Furutani, Kenro Ellm, Constance B. Ewer, J. Patrick Ferris, Ian M. Fox, Martin *Fusco, Giorgio Ellett, Scott A. *Ewing, John H. Ferro, Ruggero Fox, Ralph Futaki, Akito Elliger, Sigurd Ewy, Daniel J. Ferry, Steven C. Foxby, Hans-Bjorn Fwu, Chihchy Ellingham, Mark N. *Ezeilo, James 0. C. Feser, Victor G. *Franchi, Bruno eFyfe, Andrew Ellingsrud, Geir *Ezin, Jean-Pierre 0. Feuerbacher, Gary A. Franke, Daniel G. Gabardo, Jean-Pierre Elliott, Brady A. *Faber, Carel F. *Field, Michael J. Frankel, Theodore T. Gabay, Jacques *Elliott, David L. Fabes, Eugene B. Fieldsteel, Adam *Franks, David A. Gabber, Ofer Elliott, George A. Fabrykowski, Jacek W. *Figa-Talamanca, Alessandro •Franks, John M. Gabriel, Richard F. Elliott, Joanne Faierman, Melvin Figueres, Maurice C. Fransen, Arne Gabriel, Steven Allen Elliott, Sheldon E. •Faith, Carl Fill, James Allen Frantz, Deborah A. Gacs, Peter Ellis, James W. Falbo, Clement E. *Fillmore, Peter A. *Frappier, Clement Gadella, Manuel Ellis, Robert *Falcone, Maurizio Finch, David V. Frawley, Timothy J. Gage, Michael E. Elman, Richard S. *Falk, Michael J. Finch, Steven Richard Frawley, William J. *Gaier, Dieter *Elmendorf, Anthony D. Falkner, Neil F. Fink, James P. Frazier, Michael W. Gaillard, Pierre Yves *Elmroth, Tony G. Famoye, Kiya Felix Finkelstein, Leib *Frech, Bruce Galbiati, Margherita Eloe, Paul W. Fan, Ky Finkelstein, Louis D. Frederickson, Paul 0. Gale, Carolyn Spencer Elrod, McLowery Farahmandi, Mohammad Fischer, Addison M. Free, Norman S. *Gale, Jose E. El-Zahar, Mohamed Hamed Faran, James J. Fischer, H. Freed, DanielS. Gallego, Eduardo *Elzanowski, Marek •Farenick, Douglas R. Fishback, William T. •Freedman, Marvin I. Gallian, Joseph A. Emch, Gerard G. *Farmer, William Michael Fisher, Stephen D. Freeland, MarkS. Gallier, Jean H. Emert, John Wesley Farrand, Scott M. Fishman, Louis Freeman, James H. Galliher, Herbert P. Emmanuele, Giovanni Farrell, Roger H. Fisk, Steve Freeman, Robert S. *Gallo, Daniel M. Emmer, Michele Farris, Frauk A. *Fitzgerald, Eugenia E. Freese, RalphS. Galvin, James W. *Enayat, Ali Fass, Arnold L. Fitz-Gerald, Gary F. Freidlin, Mark *Garnst, Jens •Endsley, Neil H. Faulkner, Frank D. FitzGerald, Gilbert C. Freire Nistal, J. L. Ganelius, Tord H. *Engber, Michael Fauntleroy, Amassa C. Fitzsimmons, Patrick J. Freitag, Herta T. Gangolli, Ramesh A. Engle, Jessie Ann Faurre, Pierre L. • Fixrnan, Uri Freundlich, Marianne Gani, Joseph M. Engler, Hans P. *Favro, Ruth G. Fjelstad, Paul T. Fricker, Francois Ganser, Carl C. *Engquist, Bjorn Fearn, Dean H. Flahive, Mary Elizabeth Fridman, Burna L. *Ganster, Maximilian Engstrom, Philip G. Feeman, George F. *Flajolet, Philippe Fried, David Gantner, Thomas E. *Ennis, Pemle K. *Feeman, Timothy G. Flanders, Harley Friedberg, Stephen H. Gantos, Richard L. Enomoto, Kazuyuki Feferrnan, Solomon Flanigan, Francis J. Friedland, Shmuel Gao, Ji Enomoto, Masatoshi Fegan, H. D. Flannery, David A. *Friedlander, John B. Gapaillard, Jacques Enqvist, Arne Fegreus, John F. Flaschka, Hermann Friedlander, Leonid Garaban, James C. Ensey, Ronald J. *Feichtinger, Hans Georg Fleishman, Bernard A. Friedman, Merwyn M. Garb, Regina H. Epstein, Benjamin Feigenbaum, Joan Fleissner, William G. Friedman, Nathaniel A. Garcia, Jose Luis Epstein, Bernard Feighn, Mark E. Fleming, Daniel J. Friedman, Robert David Garcia de Morgado, Maria A. Epstein, Charles L. Fein, Burton I. Fleming, Richard J. Friedman, Sy D. Garcia-Loygorri, Cristobal Epstein, David B. A. *Feinberg, Eugene A. Flensted-Jensen, Mogens Friese, John L. Gardiner, Cyril F. Erban, Daniel •Feingold, Alex J. Flesner, Harold E: *Fritsch, Rudolf Garding, Lars *Erbland, John P. Feit, Paul *Fletcher, Peter •Fritsche, Richard T. Gardner, Merritt P. Erdahl, Robert M. Feit, Walter *Fleury, Patrick J. Frizzoni, Piero F. G. Gardner, Robert A. *Erdelyi, Tamas *Fejer, Peter Andrew Florence, John B. Frohardt, Daniel E. Garfuokel, Solomon A. Erdman, John M. Feldman, Arnold D. Floret, Klaus Frohliger, John A. Garimella, Ramesh V. *Erdos, John Feldman, Chester Flosser, H. 0. From, Steve G. •Garland, Howard Erdos, Paul Feldman, Jacob *Floyd, William J. *Frosali, Giovanni Garrett, John W. *Erez, Boas Feldman, Norman *Flynn, Lawrence E. Fry, Cleota G. Garrison, Betty B. Ericksen, Wilhelm S. Feldman, William Alan Flytzanis, E. Frye, Roger E. Garsia, Adriano M. Erickson, Roger P. Felho, Sandor F. Fogel, Micah E. Fu, Yen-Tzu Gasper, George, Jr. *Erkama, Timo Feliciano-Dodonoff, Manuel de Foglio, Susana F. L. Fuchs, Peter Rudolf eGass, Frederick Stoart *Erie, Dieter H. Fell, James M. G. Foias, Ciprian Ilie *Fuchssteiner, Benno Gatterdam, Ronald W. Em, Alexandre Felland, Michael E. Folland, Gerald B. Fuglede, Bent Gauchman, Hillel *Ernst, Claus Fellers, Norman V., Jr. Flillmer, Hans *Fuhrken, E. Gebhard Gauthier, Paul M. Errico, Thomas G. *Felhnan, Johan Fong, Che-Kan Fuji-Hara, Ryoh Gautschi, Walter Escassut, Alain Fellows, Michael Ralph Fong, Kirby W. Fujii, Nobuhiko Gaviano, Marco *Escobales, Richard H., Jr. Fender, T'tmothy N. Fong, Paul *Fujimagari, Tetsuo Gechter, Jerry • Eskin, Gregory eFendrich, John W. Fonseca, Irene Fujiwara, Daisuke Geddes, Keith 0. Eslinger, Robert C. Fenley, John C. *Fontana, Joseph M. Fujiwara, Hidenori Gehring, Frederick W. Esquivel, Manuel Leote •Fenley, Sergio Roberto Fontenot, Robert A. Fujiwara, Masahiko *Gehrke, Mai *van den Essen, Amo R. Fenske, Christian Foote, S. Ashby Fukuda, Komei Geissinger, Ladnor D. Essen, Ma~ R. Fenstad, Jens E. Forbes, Stephen H. Fukushima, Masatoshi Gelbart, Abe Esser, An11e-Marie Simon Ferguson, David R. Ford, David James Fukushima, Mitsuo *Gelbart, StephenS. *Esteban, Maria J. *Ferguson, Harold E. Forman, Robin FulJer, F. Brock Geller, Daryl Neil Estivill-Castro, Vladimir Ferguson, Helaman Fornaess, John Erik *Fuller, Kent R. Geman, Stoart Alan *Estrada, Luis Ferguson, Pamela A. *F6rster, Klaus-Jurgen FulJer, Leonard E. •Genensky, Samuel M. eEtgen, Garret J. Ferlini, Vmcent J. •Forsythe, Keith W. Fuller, William R. Genet, Jean Raymond Etter, Daniel 0., Jr. Fernandez-Rodriguez, Maria L. Forte, Bruno Fuller, William R. Gentili, Graziano *Eudave-Munoz, Mario Fernando, Thotage Sarath Fossum, Robert M. *Fulton, Charles T. Geoghegan, Ross Evans, Steven Neil Ferrari, Carlo *Foster, Lorraine L. T. Fulton, Curtis M. Georgakis, Peter SEPTEMBER 1992, VOLUME 39, NUMBER 7 731 AMS Centennial Fellowship Fund *Georghiou, Constantinos Goldberg, Seymour •Graves, William H. Guilarte, Juan Mateos Hansen, Fred W. Geramita, Anthony V. Golden, Kenneth M. Gravesen, Jens Guilbault, Craig R. Hansen, ldar Geramita, Joan M. Goldhaber, J. K. *Gray, Jack D. Guillemin, Victor W. Hansen, R. 0. *Gerards, Albertus M. H. *Goldin, Gerald A. Gray, Jeremy John Guillermo, Fernandez Anaya Hansen, Vagn Lundsgaard Gerhardt, C. Goldman, Jerry Gray, John W. Gulden, S. L. Hansen, Verner T. Gerig, Stephen R. •Goldman, Lawrence Gray, Robert E. Gulliver, Robert D., IT *Happel, Dieter Gerlach, Eberhard G. P. Goldman, William Mark Greaves, G. Gundelfinger, Benjamin F. Hara, Takashi Geronazzo, Lucio Goldstein, Gerald Green, Charles A. Gundersen, Gary G. Harada, Shigeharu Geronimo, James H. Goldstein, Richard Z. Green, James A. Guner, Mahmut Haralampidou, M. Marina Gershenson, Hillel H. Goldstine, Herman H. Green, Mark L. Guner, Necdet Harbater, David Gerstenhaber, Murray *Goldston, Daniel A. Green, William L. Gunnarsson, Thomas E. W. Harborth, Heiko *Gervais, Jean Jacques Goldstone, Richard J. Greenbaum, Anne Gunning, Robert C. Harboume, Brian Gerver, Joseph L. Golightly, William L., Jr. Greenbaun, Nicholas N. *Gupta, Laxmi N. Hardarson, Askell Gessaman, Margaret P. Golomb, Michael *Greenberg, Peter A. Gupta, Ram Prakash Harden, Milton W. Gessel, Ira M. Gomez Pardo, Jose Luis Greenblatt, George E. Gupta, S. N. Hardy, Darel W. *Gesztesy, Friedrich Gomez-Ruiz, Francisco Greene, Curtis Guralnick, Robert M. Hargraves, Beverly Bailey Getu, Seyoum *G omez Tato, Antonio Greene, John Robert *Gurney, David Robert Harmelin, Reuven *Getzler, Ezra Gomi, Kunio Greengard, Leslie F. •Gustafson, Philip E. Hamad, John P. Ghanaat, Patrick H. Gompf, Robert E. Greenleaf, Frederick P. Gustafson, Sven-Ake *Harnett, Gerald P. Ghent, K. S. *Gondard-Cozette, Danielle J. Greenleaf, Newcomb *Gustavsson, Jan Harrington, Walter J. Ghisa, D. *Gonzaga, Clovis C. *Greenlees, John P. C .. Guterman, Martin M. Harris, Gary A. Ghoudi, Kilani Gonzalez, Jimenez Santos •Greenwood, Robert E. *Gutierrez, Cristian E. Harris, Joe *Giambalvo, Vincent W. Gonzalez, Leon A. Gregory, David A. Guy, Wynne Alexander Harris, John C. Giaquinta, Mariano *Gonzalez, Raul Emesto Gregory, Thomas Bradford *Guzman, Miguel de Harris, Melanie J. Gibi, Debra J. *Gonzalez-Diez, Gabino Greicar, Richard K. *Gyllenberg, Mats *Harris, Michael H. *Gibson, Richard G. Gonzalez-Sprinberg, Gerard Greif, Anthony David Ha, Ki Sik •Harris, Mortun E. *Gieseker, David *Gonzalo, Jesus Greif, Stanley J. Haack, W. Harris, Theodore E. Giga, Yoshikazu Good, Donald I. Oreville, Thomas N. E. Haber, Seymour *Harris, Timothy S. *Gilat, David Goodearl, Kenneth R. Grey, Louis D. *Hackborn, William W. Harrop, Fred F. Gilbarg, David Goodloe, Alwyn Earle Griess, Robert Louis, Jr. •Haddad, Labib S. Hart, Bradd T. Gilbert, Michael D. Goothnan, A. W. Griffin, E. L., Jr. Haddix, George F. •Hart, Garry D. Gilchrist, Martin P. Goothnan, Frederick M. Griffin, William Gerald *Hadjidimos, Apostolos Hart, Neal *Gildenhuys, Dion Goothnan, Roe W. Griffiths, Phillip A. *Haebich, William Hart, Susan 0. Giles, John C. Goodwillie, Thomas G. Griffor, Edward R. Haemmerlin, Guenther Hartl, Johann *Giles, John R. Gopal, Marigalam R. Grigni, Michelangelo Hag, Per Hartman, James L. Gilewicz, Jacek Gopalsamy, Kondalsamy Grillakis, Manoussos Hagis, Peter, Jr. Hartmanis, Juris *Gilfeather, Frank L. Gopinath, Bhaskarpillai Grilliot, Thomas J. Hagler, James N. Hartvigsen, David B. *Gillis, Joseph Gordon, B. Brent Grinuner, Ronald C. Hahn, Gena Haruki, Hiroshi Gillman, David S. Gordon, C. M. Grinstead, Dana L. Hahn, Kyong T. Haruki, Shigeru Gilman, Jane P. *Gordon, Daniel M. Grivel, Pierre P. Hahn, Sang-Geun Harvey, F. Reese *Gilmore, Maurice E. Gordon, Robert •Grochenig, Karlheinz U. Hahn, Susan G. *Harvey, William J. Gilmour, Grant James *Gorelishvili, Albert Groenenboom, Albert Hahne, Gerhard E. *Hasegawa, Keizo Gilsdorf, Thomas E. Gorenstein, Daniel Groer, Peter G. Haiman, Mark •Hasegawa, Minoru Gimigliano, Alessandro Goss, David M. van Groesen, E. Hain, Richard Martin *Haskell, Deirdre Gingrich, Ross B. Goss, Robert N. Grognard, Rene J. M. Haken, Wolfgang *Haslach, Henry W., Jr. •Ginzburg, Viktor L. Gosselin, John A. *Groisser, David Halberstam, Heiui *Haslinger, Friedrich Gioia, Anthony A. Goth, John A. Gromoll, Detlef Hales, Alfred W. Hassinger, Bill, Jr. Giordmaine, Joseph A. Goto, Hideo Gromov, Mikhael •Hales, R. Stanton, Jr. *Hastad, Johan *Giraldo, Luis Edo Goto, Midori S. *Gronbaek, Niels Hall, Mark Edwin Hastings, Harold M. Girela, Daniel Goto, Shiro •Gross, Benedict H. Hall, Peter Hasumi, Morisuke Giroux, Gaston 0. Gottlieb, Daniel H. Gross, Daniel Joseph Haller, Thomas Hatori, Asako Giuli, Eraldo Gottlieb, David Gross, Fletcher I. *Hallett, Michael Hatori, Osamu Gladue, Earl C. *Gotusso, Laura *Gross, Kenneth I. Hamalainen, Timo T. Hattori, Akio Glass, Michael S. Goutier, Claude Gross, Leonard Hamana, Masamichi *Haughton, Dominique M.A. Glass, Milton A. Gouvea, Fernando Quadros *Grosse-Erdmann, Kari-Goswin Hamenstadt, Ursula *Haunsperger, Deanna B. Glauberman, George *Gove, David B. Grossman, Edward H. Hammack, William D. Hausknecht, Adam O'Neill Glaz, Sarah Gover, Eugene H. •Grossman, Marvin W. Hammer, Carl Hausmann, Jean-Claude Glazebrook, James F. *Goyo, J. 0. *Grotowski, Joseph Francis Hammer, Frederick David Hautau, Ralph H. Glenn, Paul G. Goze, Michel Grove, Edward A. Hammer, Peter L. *Hawkes, Trevor 0. Glover, Henry H. •Grabiner, Sandy •Grove, John W. Hammond, William F. Hay, George E. Glover, Robert A. Graham, Aly Grove, K. Han, Chong-Kyu Hayashi, Eric Gluck, Herman R. Graham, C. Robin *Groves, J. R. J. *Han, Zheng-Chao Hayashi, Mikihiro Goblirsch, Richard P. *Graham, Colin C. Grow, David E. Handel, David *Hayashi, Nakao Goddard, J. D. Graham, Ian Grubb, Gerd Handel, Michael Hayashi, Takao *Goddard, Wayne Dean Graham, Sidney W. Gruber, Peter M. •Handwerker, A. M. Hayashida, Tsuyoshi Goddyn, Luis A. *Grainger, Gary R. Grodin, Arnold Hanes, Kit Haydn, Nicolai T. A. Goebel, K. Gramsch, Bernhard von Grudzinski, Olaf Hanges, Nicholas Haydon, Richard G. Goerss, Paul G. *Grannell, Michael John *Gruenberg, Karl W. •Hanisch, Herman Hayek, Nacere Gllettfert, Rainer Grantham, Stephen B. Gruenhage, Gary F. Hank, John L. Hayes, David F. Goetz, Abraham Granville, Andrew J. Guaraldo, Rosalind J. Hanlon, Philip J. Hayes, David R. •Goetz, James R. •Grasse, Kevin A. Guenard, Francois Hann, Kathleen Marie Hayne, Roger M. *Golan, Ana Maria Gravel, Pierre Guerin, Esther E. Hanna, J. Ray Haynes, Nola A. Goldberg, Samuel Graver, Jack E. Guerrieri, Bruno Hannan, Edward J. Hays, H. John Goldberg, Seth I. Graves, Larry K. *Guest, Martin A. Hano, Jun-ichi *Hays, M. M. R. 732 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY m•••••••mTU ill -- ...... AMS Centennial Fellowship Fund ...... - ...... ,,,_ ...... -...... -.. *Hazewinkel, Michie! Herrera, R. B. Hoefer, Edwin T. Huang, Tayuan Ihara, Yasutaka *He, Zheng-Xu Herreshoff, James B. Hoesman, Cynthia M. *Huard, James G. Iino, Riichi Headley, Velmer B. Herriot, John G. Hofer, Helmut H. W. *Hubeny, Frank L. lio, Tutomu Heard, Elizabeth A. Herrmann, Joseph M. Hofer, Robert D. Huber, Alfred 0. Ikebe, Teruo Heard, Melvin L. *Herron, David A. Hoffman, Jerome William Huber, Birkett T. Ikeda, Kazumasa Hearst, Will Herwitz, Paul S. Hoffman, Michael E. Hubler, Shane L. Ikeda, Kazuoki Heath, Robert W. *Herz, Carl S. Hoffman, Michael J. Hudgins, Archibald Perrin Ilmanen, Tom Heath-Brown, Roger *Herzberg, Agnes Margaret Hoffman, William C. Hudson, Anne Lester *Im, Bokhee P. *Hebert, Michel *Herzberger, Juergen P. Hoffmann, Detlev W. *Hudson, Robin L. Imam, Ali Hechler, Stephen H. Herzog, Emil R. Hofmann, Karl H. Huebschmann, Johannes Imayoshi, Yoichi Hecht, Henryk Herzog, Ivo Hoft, Hartmut Huerta, Carlos Cuevas Im Hof, Hans Christoph Hecker, David A. Hess, Jacob J. Hoft, Margret H. Huet, Denise Imrich, Wilfried *Hedberg, Lars I. *Hesterberg, Timothy C. *Hogbe-Nlend, Henri •Huff, Charles W. Infante, Ettore •Hedlund, Gustav A. Hethcote, Herbert W. Hogesteeger, F. W. •Huff, W. N. Ingram, Nancy Jane Hegland, Markus Hettling, Karl F. *Hognas. Goran Hufford, George A. *Innami, Nobuhiro Heifetz, Daniel B. Hetzer, Georg *Hogreve, H. J. Hughes, Anne Inoue, Hiroshi *Heijmans, Johannes G. Heuer, Gerald A. Hohs, Stephen M. Hughes, Anthony Insall, Eugene M., Jr. •Hell, Christopher E. Heumos, Michael J. Holberton, John V. Hughes, C. Bruce Ioakimidis, N. I. *Heine, George W., III •Heuver, John G. *Holland, David Hughes, Cephas D. *Joffe, Alexander Heineken, Hermann Heyer, Herbert K. Holland, Finbarr Hughes, Gary B. Ipina, Lynne Kamstra *Heinicke, Allan G. *Hiai, Fumio *Holland, Martin P. Hughes, John Forbes Ipsen, lise *Heinig, Hans P. *Hickling, Fred Holland, Samuel S., Jr. Hughes, Joseph A. Irving, Ronald S. Heinrich, Katherine Hicks, Robert L. Holland, W. Charles Hughes, Kim Isaac, Richard E. Heins, Albert E. Hida, Haruzo Holman, Wayne James, III Hughes, Rhonda J. Isaacs, Godfrey L. Heins, Maurice H. Hida, Takeyuki Holmes, Charles S. Hughes, Ruth L. Isaacs, I. Martin Heinze, Joachim Higgins, James Logan •Holmes, John P. Huh, Won Isaacson, Eli *Hejna, Matthew J. Higgins, John C. Holmes, Philip John Huibregtse, Mark E. Isaacson, Eugene *Helbig, Siegfried Higgins, Stanley B. •Holmes, Randall Reed *Huige, Gustavus E. *Isaak, Garth T. eHelgason, Sigurdur Higman, Donald G. Holmes, Richard B. Huilgol, Raja R. *Isbell, John R. Hellberg, H. Stefan Higuchi, Yasunari Holton, Derek A. Hulkower, Neal D. Iseki, Kiyoshi Heller, Alex Hijab, Omar Holvoet, Roger Hull, Thomas E. *Isenberg, J. Heller, Daniel J. *Hijazi, Oussama Honda, Kin-Ya Hulsbergen, Wilfred W. J. Ishihara, Hajime Heller, Dorothy M. Hilbert, Stephen R. Hong, Geck Chan Hummel, James A. Ishihara, Toru *Heller, Fred L. •Hildebrandt, Theodore W. *Hong, Man-Soo Humphreys, James E. Ishii, Hitoshi Hellerman, Leo •Hilgers, John W. Hong, Seung Hee Huneke, Craig L. Ishii, Jyun Hellerstein, Simon Hill, C. Denson Honold, Thomas Hung, Henry Hin-Lai Ishii, Shihoko • Helminck, Gerard Franciscos Hill, David G. B. Hoobler, Raymond T. Hunt, Bruce Ishimoto, Hiroyasu Helson, Henry Hill, E. Stamford, II Hoover, D. N. Hunt, FernY. Ismail, Mourad E. H. Helton, J. William Hill, James Hoover, Thomas B. Hunt, Richard A. Istrail, Sorin Helwig, Karl-Heinz Hill, Shirley A. Hopkins, Mark R. Hunt, Walker E. Itai. Masanori Hemasinha, Rohan Hillman, Jonathan Arthur Hopkins, Neil E. Hunter, Maxwell Norman Ito, Kiyosi *van Hemmen, J. Leo Hilt, Sandra N. Hoppensteadt, Frank C. Hunter, Roger H. Ito, Noboru Hemmingsen, Erik Hilton, Peter J. Horn, Alfred • Hunzeker, Hubert L. Ito, Ryuichi Hempel, J. A. Himonas, Alexandrou A. Hom, Jean MacGregor Hupperich, Marcel Ito, Yoshifumi Hempel, John P. Hind, Hugh Robert Horner. Mary Lynn *Hurlbert, Glenn H. Ito, Yuji Hemstead, Robert J. Hinder, Rainer Horner, T. S. Hurley, James F. Itokawa, Yoe Henderson, David W. Hindman, Neil B. Horrigan, Timothy J. Hurley, Michael G. Iwamiya, Toshiyuki Henderson, Francis MeVey Hingston, Nancy Horrocks, Geoffrey *Hurrelbrink, Jurgen Iwanaga, Yasuo Henderson, Gregory P. Hinman, Peter G. Horsfield, Christopher H. Hurtado, Fernando Iwaniec, Henryk Henderson, James P. Hinohara, Yukitoshi *Horst, Ernst S. Hurtubise, Jacques C. Iwasaki, F. Shigeo Hendirman, Dadang *Hinrichsen, D. Horvath, John M. Hurwitz, Solomon I washita, Hirokazu *Hendy, Michael D. Hintzman, William R. Horvath, Jozsef Husain, Taqdir Iwata, Koichi Henkin, Leon A. Hirano, Norimichi Hosack, John M. *Hosler, Jurg R. Ize, Jorge A. Henniart, Guy M. Hironaka, Heisuke eHoste, Jim E. Rustin, Deborah L. Izuchi, Keiji *Henniger, J.P. *Hirsch, Michael D. *Hostettler, Maria Hutches, David J. Izumino, Saichi Henriques, AnnaS. Hirsch, Morris W. *Hotta, Ryoshi Hutchinson, George A. Izumiya, Shyuichi *Henris, John B. Hirschfeld, James W. P. Hotze!, Eckehart *Hutchinson, Joan P. Izzo, Alexander J. Hensley, Douglas A. Hirschfelder, John J. Householder, James E. Hutton, Edward L. Jackson, Lloyd K. Henstock, Ralph Hirschfelder, Rosemary Houston, Evan G. Hveberg, Steinar Magne *Jackson, Raymond W. Hepp, Klaus Hirshfeld, Joram Howard, Edgar J. Hwang, Jang C. Jackson, Stanley B. Herb, Rebecca A. Hirzebruch, F. E. P. Howard, Fredric T. Hwang, John Jew-Chen Jaco. William H. *Herbst, Ira W. Hislop, Peter David Howard, Paul E. Hyers, Donald H. Jacob, Henry G. Hering, Roger H. *Hitchin, Nigel J. *Howard, William A. Hyllengren, Anders R. Jacob, Niels Herman, Franklin B. Hitotsuyanagi, Nobuo Howe, Roger E. Hyvonen, Jaakko P. Jacob, William Burkley *Herman, Michael *Hoare, A. Howard M. *Howell, Joseph·O. Iannelli, Mimmo *Jacobs, David Pokrass Herman, Richard H. *Hobart, Sylvia A. Howes, Frederick A. Iarrobino, Anthony A., Jr. Jacobs, Felix J. Hermann, Margaret A. *Hobbs, Ann Kahlow *Howie, John M. *Ibbotson, Jeffrey J. Jacobs, Harold Hermann, Robert Hochschild, Gerhard P. Hoye, Laurence G. *lbort-Latre, Luis A. Jacobs, Jonathan M. Hernandez, Fernandez Teresa • Hochstadt, Harry Hoyt, W. L. Ibrahim, A. Shawky Jacobsen, Martin Hernandez, Jesus Hochster, Melvin Hratz, Joseph A. Igarashi, Akira Jacobson, David W. Hernandez, Rafael Hochwald, Scott H. Hsia, J. S. Igarashi, Masao Jacquet, Herve M. *Hernandez, .Rene A. Hodges, Lucille M. Hsiang, Wu-Chung Igari, Satoru *Jaffard, Stephane P. Hernandez Ruiperez, Daniel Hodges, Wilfrid A. Hsieh, Wan-Chen Igodt, Paul G. Jaffe, Martha A. Herod, James V. Hodgson, Jonathan P. E. Hu, Bei Iha, Franklin T. Jaffe, William J. SEPTEMBER 1992, VOLUME 39, NUMBER 7 733 ____ , ______,,..... ,. ______,...... ______, ______,,_., ______.. _...... _...... - ...... _...... _...... _...... AMS Centennial Fellowship Fund '''''''''''''''''"''''''''''w''"'''''W''•·•••••• ...... ,, __ Jager, H. Johnson, Robert Shepard *Kamal, Abdullah A. Kelley, Robert L. Kirby, Robion C. Jagy, William C. Johnson, Rodney W. *Kambayashi, T. Kellogg, Charles N. Kirch, Allan M. *Jahren, Bjorn Johnson, S. L. Kameda, Masumi Kelly, David Kirchgassner, Klaus W. Jain, Naresh C. Johnson, Theodore D. Kamejima, Kohji Kelly, G. Maxwell Kirchgraber, Urs *Jakobsen, Arne •Johnson, William B. Kamin, Shoshana *Kelly, Theresa D. Kirchherr, Walter W. Jambois, Thomas F. *Johnston, Katherine G. Kaminker, Jerry Kemp, Daniel Campbell *Kirk, Paul A. James, David M. Johnstone, P. T. Kaminsky, Jay Kemp, Yvonne A. Kirk, William A. James, Gordon D. *Jolson, Sheldon B. Kamishima, Yoshinobu Kempachiro, Ohashi •Kirkman, Ellen E. Jameyson, Stephen Jones, Carl Hilton Kamiya, Shigeyasu Kendall, Wilfrid Stephen Kirley, Paul 0. Jamjoom, Fatmah B. *Jones, Christopher K. R. T. Kammler, David W. Kenison, Jeanne H. Kirmser, P. G. •Jankins, Mark Jones, Daniel Fuller Kamowitz, Herbert M. Kennedy, Edward S. Kirwan, Frances C. *Jannsen, U. *Jones, F. Burton Kanai, Masahiko Kennedy, Gary P. Kirwan, William E., II Janowsky, Steven A. Jones, G. A. Kanamori, Akihiro Kennedy, Judy Anita Kiselrnan, Christer 0. Jans, James P. Jones, Harold T. *Kanemitsu, Shigeru *Kennedy, Stephen F. Kishi, Masanori Janson, Richard W. *Jones, James P. Kanenobu, Taizo Kennison, John F. •Kister, Jane *Janson, Svante Jones, John D. S. Kang, Hyeonbae *Kenschaft, Patricia Clark Kita, Hiroo Jantosciak, James S. Jones, Kathryn A. *Kang, Pyung-Lyun Kent, George A . Kitada, Yasuhiko . *Jantzen, Chris S. *Jones, Marsha Finkel Kangas, George W. Kenyon, Hewitt Kitano, Koh-!chi Jantzen, Jens Carsten •Jones, Vaughan F. R. *Kaniuth, Eberhard *Kerby, Rodney B. Kitazaki, Knniaki Janusz, Gerald J. Jongen, Hubertus Th Kanjin, llichi Kernast, John C. Kitchen, Edward Jara Martinez, Pascual Jonker, Leo B. Kann, Edgar D. *Kerr, Jeanne Wald Kittel, Phyllis M. *Jarchow, Hans Jonsdottir, Kristin Halla Kanner, Richard A. • Kerr, Sandria N. Kiyek, K. *Jarvi, Pentti K. Jonsson, Bjami Kanold, Hans-Joachim Kerzman, Norberto L. Kiyohara, Mineo *Jarvis, Peter M. *Jonsson, Thordur Kaplan, Samuel R. *Keselman, Dmitry • Klabosh, Charles Jarvis, Trevor M. Jorba, Angel Kaplan, Stanley Keshishyan, Joseph Klass, Michael J. Jea, Hae-Pyng *Jordan, G. Samuel Kaplan, Wilfred Kesten, Harry Klassen, Eric P. Jean, Michel Jordan, Kirk E. Karamatsu, Yoshikazu *Key, Eric Stephen Klassen, John E. *Jefferies, Nigel Jordan, Steven L. *Karasu, Sinan I. Khajah, H. G. Klatman, DavidS. Jeffrey, Alan Jorgensen, Troels Karel, Martin Lewis Khalifah, M. F. Klauder, John R. Jenkins, Emerson D. Jorgenson, Jay A. Karle, Jerome • Khalirnsky, Efim Davidovich Klay, John W. Jenkins, Joe Wiley Joris, Henri E. Karlsson, Johan Khan, Mizan Rahman Klay, Matthias P. Jennings, Leslie Stephen Jose Manuel, Gonztllez Karp, Richard M. Khapalov, Alexandre *Kleban, Peter H. Jensen, Arne Rodriguez Karpishpan, Yakov Khuri, Soumaya Makdissi Klein, Edwin M. *Jensen, Bruce P. Josephson, William Allen Karrass, Abraham Kichenassamy, Satyanad Kleiner, Bruce A. Jensen, Christian Ulrik *Josephy, R. Michael Karreman, Herman F. Kido, Kazuo *Kleiner, Mark Jensen, Robert R. *Joshi, Nalini Karrer, Gnido *Kidwaii, Hariss *Kleisli, H. Jeon, Youngmok Jouanolou, Jean-Pierre Kaschube, Paul August Kiefer, James E. Kleitman, Daniel J. Jeong, Dal Young Juberg, Richard K. Kashihara, Kenji Kierlanczyk, Marek Kleppner, Adam Jerison, David *Julian, Alfredo J., Jr. *Kashiwagi, Yoshimi Kiesel, Harry A. •Kietzing, Dennis R. Jerome, Carlos *Jun, Kil Woung Kasper, Brian J. Kiessling, Michael K. H. K!iemann, Wolfgang H. Jerome, Joseph W. del Junco, Andres • Kasriel, Robert H. Killeen, John ·*Klitigsbei:g, Paul R; *Jessup, B. J. *Junker, Brian W. *Katavolos, Aristides Killgrove, Raymond B. *Knapp, Wolfgang D. Jessup, Peter G. Jurca, Dan *Kato, Junji Kiltinen, John 0. *Knaust, Helmut Jha, Vlkram Jure, John D. *Kato, Takao Kim, Byung Young Knight, Frank B. Jian, Alan S. Just, Wmfried Kato, Tosio *Kim, Dohan Knight, Julia Jimenez, Jose Alfredo Justice, James H. Katok, Anatole Kim, Dongsu Knill, Ronald J. *Jin, Gyo Taek Juvenal, Richard S. Katok, Svetlana R. Kim, Hong Jong *Knio, Omar M. *Job, Vanessa R. Jyoo, Yeong-Heum Katsura, Toshiyuki •Kim. Hong Oh Knopf, Peter M. Jockusch, Carl G., Jr. Kaashoek, Marinus A. Katz, Victor J. *Kim, Hyuk Knopfmacher, Arnold Johannson, Klaus Kadlecek, David Katzen, Dahn Kim,lhn Sue Knopfmacher, John *Johansson, Bo lngvar Kageorgis, Irena H. Katznelson, Y. Kim, Ohoe Knopp, Marvin I. Johansson, Hans Kagstrom, Bo T. Kauffman, Louis H. Kim, Sangman Knorr, K. R. K. John, David J. Kahan, William M. Kauffman, Robert M. •Kim, Soon-Kyu Knowles, J. David Johnsen, Ronald L. Kahane, Charles S. Kaufman, William E. Kim, Young-Kook Knudsen, John R. *Johnson, Aimee S. A. Kahaner, David Kenneth Kaushanski, Anatole Kimber, John E., Jr. Knuth, Donald E. Johnson, Barry E. Kahn, Daniel S. Kavanagh, John P. Kimberling, Clark Knutson, Donald I. Johnson, Ben Kahn, Donald W. *Kawahigashi, Yasuyuki *Kime, Katherine A. Ko, Bongsoo Johnson, Bradford W. Kahn, Jeff N. *Kawamoto, Naoki Kimmel, Marek Ko, Hai-Ping Johnson, C. H. J. Kahn, Peter J. Kawamoto, Shunji Kimura, Tatsuo Ko, Ki Hyoung Johnson, Charles N. Kaijser, Sten Kawasaki, Tetsuro Kincaid, Wilfred M. Kobayashi, Shoshichi Johnson, D. Randolph, Jr. Kajiwara, Joji *Kay, Joseph A. *King, Alastair D. Kobayashi, Tsuyoshi Johnson, David Copeland *Kakas, Andonakis Constantinos Kazamaki, Norihiko King, Brian S. Kobayashi, Yuji Johnson, David L. Kakihara, YQichirO Kearton, Cherry *King, Christopher K. Kobayashi, Yukio Johnson, David Lewis Kakiichi, Yoshiaki *Keating, Kevin P. King, Donald R. Kober, Wolfgang Johnson, Donald G. Kalfa, Komilia S. *Keen, Linda • King, Hala Khuri *Koblitz, Neal I. Johnson, Guy, Jr. *Kalhoff, Franz B. Keenan, Edward L. King, Henry C. Kocan, Daniel Johnson, James E. Kalinde, Albert Kasangu Keeping, Anthony J. *King, James R. Koch, Charles F. Johnson, Jean T. Kalisch, Gerhard K. Keet, Arnold Peter King, Joseph F. Koch, Jeffrey W. Johnson, Jennifer M. Kalish, Diana Keever, Robert Dudley King, L. Richardson Koch, Richard M. *Johnson, Jon L. *Kalivas, Nickolas Keiding, Hans King, Stephen C. •Kodama, Tetsuo Johnson, Kenneth Walter Kall, Peter *Kelemen, James Allison Kinghorn, Donald B. Koditschek, Daniel Eliezar *Johnson, Kimberly A. Kallstrom, Anders Kelesoglou, Constantine Kinkel, John F. Koditz, Helmut *Johnson, Peter M. *Kalmbach, Gudrun Keller, Clayton W. Kinukawa, Masakiti Koehler, Anne B. Johnson, Robert L. Kalton, N. J. Keller, Wilfrid Kipps, Thomas C. Koh, Jee Heub 734 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY . ·-···· ..... ······-----·-· ··---HWII'!I'il! l'iWilllll1r·--· ···------~--·-···-·------·-····-···-···-·------··-- AMS Centennial Fellowship Fund Koh, Kwangil Kropholler, Peter Hendrikus Lagnese, John E. Lazarsfeld, Robert K. Levaro, Richard A. Koh, Sung Eun Krueger, Charles G. Laine, Ilpo Lazzari, Claudio •Levatin, JoAnne Lee Kohler, Peter Krurnpholz, Gary R. *Laksov, Dan *Le, Chu Quang LeVeque, Randall J. Kohn, Joseph J. Kruskal, Joseph B. Lam, Tsit-Yuen · Le, Dung Trang LeVeque, William J. Kohn, Robert V. Kruszynski, Pawel *Lam, Tsz Kin Le, Phat Thanh Levin, Jacob J. *Koivisto, Pertti T. Ku, Hsu-Tung Lambert, Alan L. Leahey, William J. Levin, Richard G. Kojima, Sadayoshi Kubo, Fujio Lambert, John Patrick Lear, Dale A. Levine, Harold I. Koksal, Semen Kubo, Fumio Lambert, Richard W. *Leary, Christopher C. Levine, Jack • Kolaitis, Phokion G. *Kubota, Yoto *Lami Dozo, Enrique Jose Leavitt, William G. Levine, Jerome P. •Kolasa, Lawrence A. Kudla, Stephen S. Lampe, William A. Lebel, Jean E . Levitt, Norman J. .Kolbig, Kurt Siegfried Kudo, Tatsuji Lampert, David S. Lebow, Arnold *Levy, Azriel Kolesar, R. J. Kuenzi, Norbert J. Lampone, Leo W. Lebowitz, Joel L. Levy, Gene Kolibal, Joseph G. Kugler, Lawrence D. Lancaster, Kirk E. Le Cam, L. M. Levy. Joel •Kolitsch, Louis Worthy Kuhlmann, Norbert Lancaster, Peter Lee, Chun-Nip Levy, Lawrence S. *Kolk, Johan A. C. *Kuhn, Gabriella Maria *Landau. Susan Lee, Do-Won Lewan, Douglas *Koller, Herbert Kuhn, Nicholas J. Lander, Felix I. Lee, Eun Hwi Lewin, Jacques Kolm, John Michael Kuhne!, Wolfgang Landesman, Edward M. *Lee, Jeh Gwon Lewis, David W. Kolodner, Ignace I. Kuiken, Kathryn Landin, Joseph Lee, John M. Lewis, George M. Kolsrud, Torbjorn Sigurd Kuiper, Nicolaas H. Landrock, Peter Lee, Jong-Hyeon *Lewis, John B. Komanska, Henryka Krystyna Kulisch, Ulrich *Landstad, Magnus B. Lee, Jyh-Hao Lewis, Kathleen Edwards Komatsu, Hikosaburo *Kulp, Daniel Teibi Landweber, Peter S. Lee, Ke-Seung Lewis, L. Gaunce, Jr. Komatu, Yusaku Kumagai, Donna J. Lanford. Oscar E .. III Lee, Peng-Yee Lewis, R. P. Komiya, Yurin Kumaham, Keisaku Lang, Serge Lee, Ronnie Lewis, Roger T. Komura, Takako Kumasawa, Nin •Lang, William E. Lee, Sin-Min • Lewis, William James Kon, Mark Andrew Kumazawa, Toshihisa *Lange, Charles G. Lee, WillY. L'heureux, James E. Konhauser, Joseph D. E. Kumjian, Alexander Langebartel. Ray G. Lee, Young Whan Li, Bingxi Konig, Heinz J. Kumlin, Peter Langenhop, Carl E. Leemans, H. W. Li, Chi-Kwong Konno, Yasuko Kunimura, Dennis E. Langsam, Joseph A. Leep, David B. Li, Kezheng Koo, Ja-Kyung *Kunisch, Karl K. Laning, J. H. Lefkovitch, Leonard P. *Li, Luen-Chau • Koosis, Paul J. Kuule, Heinz Lanteri, Antonio Leggett, Robert N., Jr. *Li. Yi Kopperman, Ralph D. * Kunzle, Hans Peter Lanza de Cristoforis. M. eLegner, Mary M. Lial, Margaret L. Koranyi, Adam Kupferwasser, Marcelo *Lapeyre, Bernard Lehman, R. Sherman Liardet, Pierre Korevaar, Nicholas Jacob Kuranishi, Masatake Lapidus, Arnold Lehner, Joseph Libby, Richard Allan Koriyama, Akif'd Kurata, Yoshiki Lapidus, Michel L. Lehrer, Gustav I. Liberman, Zvie •Korman, Philip L. Kuroda, S. T. Lappan, Peter A., Jr. Lehto, Markku S. J. Lichnerowicz, Andre Kose, Tairoku Kurpita, Bohdan Ihor Lardy, Lawrence J. Lehtonen, Ari Taavi Einari Lichtenbaum, Stephen Kosinski, Antoni A. Kurshan, Robert P. Larmore, Lawrence L. Leibnitz, Edward A. *Lichtin, Benjamin L. *Kosmann-Schwarzbach, Yvette Kurss, Herbert Larrazabal, J. M. *Leichtweiss, Kurt Lick, Dale W. Kossack, C. R. Kurtz, Stuart A. Larson, Dean S. Leinbach, L. Carl Liddell, Ger=d F. Kostelich, Eric J. Kurtz, Thomas G. Larson, Loren C. Leipnik, Roy B. Lieb, Elliott H. Kostenbauder, Adnah G. Kurtzke, John F., Jr. Larson, Richard G. Leith, Cecil E., Jr. Lieberman, David I. Kotiuga, P. Robert Kushner, Harvey Larson, Suzanne Lynne Leitzel, James R. C. Lieberman, Gary M. Kottas, Evagelia S. *Kustak, Jamie E. LaSalle, Margaret M. Leizarowitz, Arie Light, F. W., Jr. *Kourouniotis, Christos Kusunoki, Yukio Lashof, Richard K. Leland, Kenneth 0. Lightbourne, James H., III •Kovacevic, Nata~a Kutzko, Philip C. Laska, Michael Lelong, P. J. Ligozat, Gef'dfd Yvon Kovarik, Zdislav V. Kuwabam, Ruishi Lassettre, Edwin R. *Lemaire, Jean-Michel Lima, Asvald Kovesi-Domokos, S. Kwak, Do Y. eLassey, Karen C. *Lemaire, Luc Lima-Filho, Paulo Kozlowski, George Kwak, Nosup Latch, Dana May Lemei, Han *Lin, Bor-Luh • Kf'd, Irwin Kwembe, Tor A. *Latif, Steve James *LeMesurier, Brenton John Lin, Cantian Krabbe, Gregers L. Kwon, Kil H. Latzenhofer, Ulrich Lemire, Denis Lin, Jindro Kraft, Hanspeter Kwon, Yonghoon Laubenbacher, Reinhard Lempert, L:iszl6 Lin, Shen Kraines, David P. Kwun, Kyung W. Lauchli, Hans Lenstra, H. W., Jr. *Lin, Wen-Hsiung Krakowski, Fred Kye, Seung-Hyeok Laudenbach, Francois Lenstra, Jan Karel Linden, Alexander N. Kramer, Earl S. Kyrouz, Thomas J. Lauer, Mark D. Lentin, Andre Lindenstrauss, Joram Kramer, Jurg Kyuno, Shoji Laufer, Henry B. Lenz Peckham, Kathryn E. Linder, David W. Kf'dmer, Linus K. H. *Laasonen, Pentti Laumon, Gef'dfd Leon, Jeffrey S. Lindgren, Georg Kramer, Raymond F., Jr. Labahn, George Lauria, Francesco E. Leonard, Philip A. Lindgren, John E. Kramer, Thomas R. Labbe, Marcel Adrien Laurie, Cecelia. Leong, Yu Kiang *Lindsay, J. Martin •Kranzer, Herbert C. LaBerge, Timothy J. *Laurinolli, Teuvo Lepowsky, James I. Lindsay, John W. Krasny, Robert *Labouriau, Isabel Salgado Lauro, Giuliana Leray, Jean Lindstrom, Mikael Krause, Ralph M. Labrousse, Jean-Philippe LaValle, Irving H. Lerche, Kenneth D. Lindstrom, Tom L. Kraut, Gertrud L. LaBudde, Christian D. Lavine, Richard B. Lerner, David E. Lindstrom, Wendell D. Krliuter, Arnold R. Labute, John P. Law, Peter R. Leroy, Andre G. *Ling, Joseph M. Kreider, Donald L. Lacey, Michael T. *Lawlor, Gary R. Leschen, John G. *Ling, Tianwen *Kreinovich, V. Ya Lachance, Michael Anthony Lawniczak, Anna T. Lesieur, Leonce Ling, William Halstead Krener, Arthur J. *Lachaud, Gilles Lawrence, John W. Leslie, Joshua A. Linnell, P. A. *Kreuzman, Mary Joan Lachlan, Alistair H. Laws, Zane John Lesmes, Jaime Lipkin, Leonard J. Krieg, Aloysius August Lachtrnan, Mark E. *Lawson, David F. *Letac, Gerard G. Lipman, Joseph Krieger, Henry A. Lackey, Thomas A. Lawson, H. Blaine, Jr. Leth, Steven C. Litchfield, Kay P. Kriegsman, Helen F. *LaCombe, Carl Andrew Lawson, Walter R. Letzter, Edward S. Little, Charles H. C. KrishnaprdSad, P. S. Laduke, Jeanne Lawvere, F. William *Leu, Ming-Guang Little, John B. Kristensen, Soren Lafferty, John D. Lax, Anneli Leung, Issie K. C. Little, Robert D. Krompart, Lucia Beth Lafontaine, Jacques Lax, Peter D. Leung, Ka Hin Littman, Walter eKronstein, Karl M. Lagarias, Jeffrey C. Lax, Robert F. Leung. Tat-Wing Liu, Tsai-Sheng SEPTEMBER 1992, VOLUME 39, NUMBER 7 735 AMS Centennial Fellowship Fund Livingston, Albert E. •Lyons, Jeremiah J. Maniatopoulou, Angeliki *Matsumoto, Yukihiro McCulloh, Leon R. *Lizarraga, Carlos C. Lyons, Richard N. Manjarrez, Victor M. Matsumoto, Yukio *McCullough, Darryl Llave, Rafael de Ia Lyons, Russell D. Mann, Benjamin M. Matsumura, Hideyuki McDonald, James Wade Lloyd, Stuart P. Lysko, Janusz M. *Manning, Anthony K. Matsuoka, Yasushi McDonald, John N. Lo, Tzee-Nan Kuo Lyubeznik, Gennady M. *Mann-Nachbar, Pauline Matsushita, Yasuo McDonald, Judith M. Lo, William *Ma, Daowei Manogue, Joseph F. Matsuzawa, Tadato McDoniel, Douglas Lobo-Pereira, Fernando M. F. Mac an Airchinnigh, Micheal Mantel, Heinrich Mattei, Jean-Francois McDonough, Joseph Michael Lockhart, Deborah Frank Macbeath, A. M. Mapa, Felina G. *Mattes, Josef McDougal, James A. Lockhart, Jody Meyer MacCamy, Richard C. Marathe, Kishore B. *Matthews, Jane McDuff, Dusa *Loday, Jean-Louis MacCluer, Barbara D. Marble, Robert P. Matti, Joseph T. *McFarland, Robert L. Loeb, Peter A. Macdonald, I. G. Marcellan, Francisco *Mattila, Pertti *McGarry, Dorothy *Loewe, Stefan MacDonnell, John J. Marchand, Margaret 0. Mattinger, George W. McGavran, Dennis R. Loewner, Paul G. Macfarlane, Andrew Ian Marchetti, Federico Mattson, Leroy T. McGehee, 0. Carruth Loftin, John C. MacGregor, Thomas H. Marchiafava, Stefano Mattuck, Arthur P. McGibbon, Charles A. Ulh, GUnter Machover, Maurice Marcus, Brian Harry *Matumoto, Hisayosi McGoveran, David 0. Lok, Walter L. *Maciocia, Antony Marcus, David J. Matumoto, Takao McGraw, Michael J. Lolli, Gabriele Mack, John Michael Marcus, Steven I. Mauceri, G. C. *Mcilwain, Mary Hope Lombay-Quinones, Jose A. •Mackenzie, Dana Nance Margerum, Eugene A. Maugin, Gerard A. *Mcintosh, Alan G. R. Loncaric, Josip Mackenzie, Kirill C. H. Margolis, Stuart W. *Mauldin, R. Daniel Mcintosh, William D. *Londen, Stig Olof *Mackey, D. Steven Margosian, Zaven Maule, Robert G. McKay, James H. London, David Mackey, Michael C. Margulies, William Maurer, Donald E. McKay, Thomas G. Long, David Darren *Mac Lane, Saunders Maria, May H. *Maurer, Stephen B. McKee, Thomas Glenn, Jr. Long, John M. MacLaren, M. Donald *Marin, Irwin C. *Mavinga, Honore Panzu McKelvey, Robert W. Longbotham, Harold G. MacNaughton, John S. Markel, Scott A. Mawata, Christopher P. McKenzie, Gary W. Longley, James Wildon Macphail, Moray S. Markvorsen, Steen Mawyer, Farley McKinney, Richard L. Longobardi, Patrizia Maddux, Roger D. Marie, Charles Michel *Max, Nelson L. *McLachlan, Robert I. •Loo, Joseph C. Mader, Adolf *Marley, Thomas J. Maxson, Carlton J. McLaman, Timothy J. Looijenga, Eduard J. N. Madison, Bernard L. Marlowe, Thomas J., Jr. Maxwell, James W. McLaughlin, Harry W. Lopez. Amparo Madow, William G. Marotto, Frederick R. May, J. Peter McLaughlin, Jack E. Lopez, Antonio Fernandez Madrid Nuilez, Bertha Alicia Marques, Francisco May, Michael K., SJ McLaughlin, Joyce R. Lopez-Carmona, Antonio *Madsen, lb Marsden, Edwin L., Jr. May, William McMillan, Brockway *Lorch, Lee *Maeda, Fumi-Yuki Marsden, Jerrold E. Mayer, John Clyde McMillan, Daniel R., Jr. Lord, James M. Maeda, Hironobu Marsh, Marcus M. Mayer, Karl Heinz McMillan, Evelyn R. Lord. Nicholas J. Maeda, Michie Marshall, David Imler Mayer, Raymond A., Jr. McMillin, Ronald A. Lorentz, George G. Maeda, Yohiaki Marshall, Murray Angus *Mayer-Wolf, Eddy McMinn, Trevor J. *Lorentz, Rudolph A. Maeder, Roman E. Marsiliano, Judy Mayfield, J. D. *McMullen, John R. Lorenz, Martin Maehara, Kazuhisa *Martelli, Mario Umberto *Maynadier-Averous, Genevieve *McMullen, Peter Loss, Michael P. Magenes, Enrico Martens, Henrik H. Maynard, James W. McMurtrie, Kenneth A. •Lou, You-Shi Magill, Kenneth D., Jr. Marti, Jurg T. Mayor, John R. McNerney, Gerald M. Loud, Warren S. Magnus, Arne Martin, Donald A. *Mayorga, Jose B. McNulty, George F. Low, Emmet F., Jr. Magnuson, Alan William Martin, Gary A. Mayost, Daniel McNulty, Nieves Austria *Lowe, Peter G. Magnusson, Kjartan G. *Martin, Geoffrey K. Maziarz, E. A. McOwen, Robert C. *Lubarsky, Robert S. •Magruder, Richard B. Martin, George E. Mazur, Barry *McPhail, Joseph G. *Lubiw, Anna •Maher, Mary Anne Martin, George W. Mazzeo, Rafe R. Meacham, Robert C. Lucas, Billy Joe Mahoney, Anne Martin, John R. Mazzocca, Francesco Meakin, John C. Lucas, Thomas G. Mahowald, Mark Martin, Nathaniel F. G. Mbuyi-Kalala, Alafuele *Meaney, Christopher *Lucas, William F. Maier, Franz W. *Martin, Nigel McAdam, Stephen J. Mears, Florence M. Luce, R. Duncan *Maier, Robert S. Martin, Norman M. McArthur, C. W. *Meda, Stefano Luchins, Edith H. Mairhuber, John C. Martindale, Wallace S., Til McAsey, Michael J. Meeker, Loren David Lucier, Bradley J. Maj, Mercede Martino, James R. *McCabe, John H. Megginson, Robert Eugene Ludden, Gerald D. Majda, Andrew J. Martinon, Antonio *McCabe, Terence W. Meier, David Lue, Derrick A. Majeed, Abdul Martin-Reyes, Francisco Javier McCann, Annamary Meisner, Morris J. Lue, Huei-Shyong Makar-Limanov, L. G. Martins, Joyce A. McCarthy, John David Mejia, Radhames Luecking, Daniel H. Makepeace, Coline M. Marumoto, Yoshihiko *McCarty, GeorgeS. Mejlbo, Lars C. Luehr, Charles P. Makkai, Michael Maruyama, Toru McCaughan, Dennis J. Melas, Antonios D. •Liieneburg, E. Makovoz, Yuly Marvin, John W. McClanahan, Ray A. Melendez, Enrique Asensio Lucthy, Adrian Malafronte, Thomas A. Mascioni, Vania D. McCleary, John H. *Melendez-Sierra, Ramon Luke, Jonathan H. C. Malcohnson, Peter Maskit, Bernard *McCleary, Stephen H. Melin, Anders Lumpkin, Morris C. Malina, Lubor Mason, Dorothy Alice McClenahan, Manrice D. Mellender, James W. Luna, Eduardo A. •Malkevitch, Joseph Mason, Robert M. •McClure, Don W. •Melrose, Richard B. *Lundberg, Bruce N. Mallet-Pare!, John J. Massey, David B. *McClure, Donald E. Menninga, Nadine L. Lundelius, Rolf E. • Mallette, Richard Masson, David R. McClure, James E. *Meredith, David B. Lundell, Albert T. Malliavin, Marie-Paule Masuda, Kyuya McColm, Gregory Loren Merikoski, J orrna K. *Luo, Feng Mallo, Ted J. Masumoto, Makoto McConnell, John C. Merkel, Rudolph B. Luther, C. F. Maim, Dennis R. Masunaga, David K. *McConnell, Mark W. Merriell, David M. Luther, Norman Y. Malon, David M. Matchett, Andrew J. McConnell, Terry R. Merrien, Jean •Lutzer, David J. Maloof, Giles W. Mate,Attila McConnell, Thomas Merrill, Kathy Donovan Luxemburg, Wilhelmus A. J. Maltese, George J. Mather, John Norman McConnick, Ferris E. Merritt, John E. Lyberopoulos, Athanasios N. Mamelak, JosephS. Matheson, John D. McCoy, N.H. Mess, Geoffrey *Lyche, Tom J. *Manca, Vincenzo Mathis, Frank H. McCoy, Thomas L. Metas, Nick Lynch, Robert E. *Manders, Kenneth L. Mathsen, Ronald M. McCracken, Marjorie Frost •Metzen, Gerhard Lynch, William C. Manderscheid, David C. Matijevic, Jacob R. McCray, Patrick D. *Metzler, David Scott *Lyon, Herbert C. Mane, Ricardo Matovsky, John-Anton Charles McCrea, Michael M. Metzler, Richard C. Lyons, Carter G. Manfredi, Juan J. • Matsuda, Shigeo eMcCroan, Keith D. Meurman, Arne 736 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ---~-- 115~: . ... -- AMS Centennial Fellowship Fund ······················································· Meuser, Diane Miner, Robert R. Morawetz, Cathleen S. Myers, Earle F. Neville, Charles W. Meush, Anatol A. Miniere, Michael A. Morduchow, Morris Myers, Russell W. Newberger, Stuart M. Meyer, Donald V. Minsker, Steven Morewood, Robert Paul Myerson, Gerald Newlander, August, Jr. Meyer, Helmut Minsky, Yair N. Morey, Philip S .. Jr. Myrvold, Wendy J. Newman, Charles M. Meyer, Herman Miraglia, Anthony C. Morgan, Frank Myung, Hyo Chul Newman, Morris Meyer, Jean-Pierre G. Miranda, Rick Morgan, Jacqueline Nachman, Louis J. *Newsam, G. N. Meyer, Kenneth R. *Mirkovic, Ivan *Mori, Andrea N acinovich, Mauro *Newstead, Peter E. Meyer, Paul R. Mirsky, Norman D. Moriah, Yoav Nadel, Mark E. Ng, Ho Kuen Meyer, W. Weston Mislin, Guido *Morillon, Marianne N aevdal, Geir *Ng, Tsz Yin Neville Meyer, Wolfgang T. Mitchell, A. Richard Morimoto, Akihiko N agahara, Takasi Nguiffo, B. Michel *Mez. Hans-Christian •Mitchell, Alan R. Morley, Larry J. Nagai, Osamu *Nguyen, Bao Gia Miao, Lung-Chi Mitchell, Stephen Ames Morrel, Bernard B. Nagano, Tadashi Nguyen, Dung X. Michael, Ernest A. *Mitchell, Stephen G. *Morris, Howard C. Nagao, Hirosi *Niblo, Graham A. Michael, T. S. Mitchell, William J. • Morris, L. E. *Nagarajan, K. R. Nichols, Edward Michaelis, Walter J. Mitchem, John A. Morris, Peter C. Nagasaka, Kenji Nichols, Eugene D. Michaux, Christian Mityagin, Boris Morris, Robert A. N agase, Michihiro *N(Chu(v, N6ra Michel, Rene Miura, Takashi Morrison, David R. Nagel, Alexander J. Nickel, James A. de-Michele, Leonede Miyadera, !sao Morrison, Ian L. Nagel, Bengt C. H. Nicol, Charles A. *Michels, John Joseph Miyahara, Yoshio Morrison, John A. Nakagawa, Kiyokazu eNicolaenko, Basil Michiaki, Watanabe Miyakawa, Tetsuro Morrison, Kent E. Nakagawa, Yoko Nicolau, Monica *Michler, G. Miyamoto, Hiroo Morrison. Sally D. Nakajima, Shoichi Nicols, Angela C. *Michor, Peter Miyazaki, Ken-Ichi Morrow, James R. Nakamura, Masahiro •Niederhausen, Heinrich Mickens, Ronald E. Mizel, Victor J. Morse, Burt J. Nakamura, Masataka *Niedzwecki, G. P. Middleton, David Mizumoto, Hisao Mortland, Richard L. Nakamura, Yoshimasa Niefield, Susan B. Mielke, Marvin V. Mizuno, Hirobumi Morton, Keith W. Nakanishi, Yasutaka Nielsen, Lance W. Mielke, Paul T. Mizutani, Tadayoshi Moschovakis, Joan Rand Nakano, Kazumi *Niessner, Herbert *Migliore, Juan C. Mochizuki, Masaya Moser, Jurgen K. Nakata, Masaomi Nievergelt, Yves Mihalik, Michael L. Mochizuki, Shin Moser, Lucy I. *Nakauchi, Hiroshi Niino, K.iyoshi Mihnea, Tatiana *Mockenhaupt, Gerd Moser, William 0. J. Namba, Kanji Nijhoff, Frank W. Mikarni, Kentaro Modica, Luciano Mosier, Ronald G. Nambooripad, K. S. S. *Nillsen, Rodney V. Mikarni, Toshio Modugno, Marco Moss, Carl J. N amioka, Isaac Nirenberg, Louis Mikolic-Torreira, Igor Moen, Courtney H. Moss. Kenneth N. Narnkoong, Kyu-Oh Nishida, Takaaki *Mikulska, Margaret Moerdyk, !eke Moss, Lawrence Stuart *Nandakumar, N. R. Nishimura, Yasuichiro *Milcetich, John G. Moghaddam, Mohammad Reza Moss, William F., III *Narang, Kamal Nishiura, Togo Miles, Thomas J. R. Mostuw, George Daniel Narayan. Sivaram K. Nishiyama, Kyo Milgram, R. James Mohamed, I. J. Motoyarna, Tetsuro Narayanaswarni, P. P. Nissirn, Leonard J. *Milic, Natasa Mohamed, Saad Moll, Orville B. Nariboli, Gundo A. Nita, Valerian M. Milicic, Dragan Mohapeloa, Khomo T. S. Mould, Rowan P. N arushima, Hiroshi Nitecki, Zbigniew H. Millar, Robert F. Moite, Sally M. Mount, Kenneth R. Nashed, M. Zuhair •Nitsche, Johannes C. C. Millar, T. S. Molino, Pierre Moussa, Nabil *Nassiri-Toussi, Karim Niven, Ivan Miller, Arnold W. *Moller, Jesper M. Moy, Allen *Nation, James B. *Nixon, John Harold Miller, Charles F., III *Moller, Manfred H. Moyls, Benjamin N. N atsume, Toshikazu *Niziol, Wieslawa K. Miller, Dale A. Moller, Raymond W. Mrowka, Stanislaw G. Naumann, David A. Njastad, Olav Miller, DonaldS. Molzon, Robert E. Mueller, Bruno J. W. Navarro, Francisco J. Nkashama, Mubenga Ngandu •Miller, Donald W. Monaghan, Joseph John Mueller, James R. Nayar, Brij M. *Noble, Christopher Miller, Edward *Monk, J. Donald Mugele, Raymond A. Nduka, A. Nobusawa, Nobuo Miller, Ellen Rammelkamp •Monna, Antonie F. Muhly, Paul S. •Nechvatal, James R. Nocilla, S. Miller, Gary R. Monsky, Paul H. Muir, Pamela H. *Neeb, Karl-Hermann Noel, Guy G. J. Miller, Hugh D. B. Montes De Oca, Francisco Rafael Muldoon, Martin E. Neggers, Joseph Noguchi, Hiroshi Miller, Jack M. Montgomery, Deane Muller, George M. *Nebs, Robert M. Noguchi, Mitsunori Miller, John Boris Montgomery, Hugh L. Muller, Gert H. Neidhardt, Arnold L. N ogura, Tsugunori Miller, John G. •Montgomery, M. Susan Mullin, Albert A. *Neidinger, Richard Dean Nobel, John A. •Miller, Kenneth S. Montgomery, Peter L. Mulvey, Irene Nelan, Cornelius P. *Nolan, John P. *Miller, Matthew *Montgomery, Philip R. *Munday, S. Nelligan, John D. •Noonburg, Virginia A. *Miller, Michael J. Montgomery, Richard W. eMundt, Marvin G. Nelson, Edward Noor, Khalida Inayat Miller, Nicholas S. Monticone, Leone C. Munkholm, Hans J. Nelson, Edward 0. *Noot, Rutger *Miller, Richard Alan Moody, Philip J. Munkres, James R. Nelson, Gail S. Norden, JeffreyS. Miller, Stephen S. *Moody, Robert V. Munoz-Porras, Jose M. Nelson, Gary S. Nordgren, Eric A. Miller, Thomas Len Mooney, John J. Munro, John K. •Nelson, Robert R. Nordhaus, Edward A. Miller, Willard, Jr. Mooningham, John W. Munroe, M. Evans *Nelson, Roger B. Norman, Francis Alexander Miller, William David Moons, Theodoor M. Murase, Nobuyuki Nemethi, Csaba Norman, R. Daniel Miller, Zevi Moore, James Andrew Murata, Hiroshi Neri, Umberto Norman, Robert Z. •Millett, Kenneth C. Moore, John C. Murayarna, John T. Nerode, Ani! Norris, John W. Mills, Janet E. Moore, Lawrence C., Jr. Murphy, Donald P. Nesbitt, Cecil J. Northcutt, Robert A. Mills, William H. Moore, Marvin G. Murphy, Grattan P. Nesin, Ali H. Northrup, James I. Milman, Mario Moore, Omar K. Murphy, Paul F. Neubauer, Gerhard J. *Northshield, Sam Milman, Mark H. Moore, Polly Murphy, R. B. *Neuberger, John W. Norton, Alec Milnor, John W. Moore, Richard A. Murphy, Thomas N. *Neubrander, Frank Notamicola, Filippo •Milojevic, P. S. Moore, Robert H. Murray, G. Graham Neugebauer, Christoph J. Notestine, Ronald D. *Mimura, Yoshio Moore, Robert Laurens Murray, Margaret A. M. Neumann, Bernhard H. *Nottrot, Roe! Minac, Jan Moore, William E. Murre, Jacob P. Neumann, Walter David Novella, Joseph D. Minagawa, Takizo *Morales, Jorge F. Musson, Ian M. Nevai, Paul *Novikoff, Albert B. Minda, C. David Moran, Charles W. Muto, Hideo Neves, Vitor M. C. *Nowak, Werner Georg Minemura, Katsuhiro Moran, William eMycielski, Jan Neveu, Jacques Nulton, James D. SEPTEMBER 1992, VOLUME 39, NUMBER 7 737 AMS Centennial Fellowship Fund Nussbaum, Roger D. O'Neill, Anne F. Palmer, Theodore W. Peixoto, Mauricio M. Piccinni, Paolo Nusse, Helena E. Onishi, Hironori Palmieri, Jobn H. Peleg, Bezalel Pickel, Paul Frederick Nutt, Michael D. Ono, Takashi *Panangaden, Prakash Peletier, Lambertus A. Pickering, Douglas Arthur *Nyikos, Peter J. Ono, Yoshie Pandit, Onkar Nath *Peltier, Charles F. *Piene, Ragni Nymann, James E. *Onose, Hiroshi Papageorgiou, Nikolaos S. *Peltola, Veli-Pirkka Pierce, Jobn Festos Oakland, David 0. Onstott, Edward D. Papangelou, Fredos Pemantle, Robin A. Pierce, Richard S. Oates-Williams, Sheila Oodaira, Hiroshi Papantonopoulou, Aigli Helen Pence, Dennis D. •Pierce, Robert Allen Oba, Roger M. Oohashi, Tsunemichi Papas, Theodore Thomas *Pengelley, David Jobn Pietrowski, Alfred *Obaid, Samih A. *Ooms, Alfons I. Pappas, Peter C. Pennell, Stephen A. Pigeon, Joseph G. Obata, Morio Opfer, Gerhard H. Pardee, Otway O'M *Pennings, Timothy James Pigozzi, Don L. *Oberguggenberger, Michael B. Ordman, Edward T. *Pardis, Cyrus Jason Pennisten, Jobn W. Pihko, Jukka A. de las Obras, Carmen Orellana, Chacin Mauricio Pareja-Heredia, Diego Penrose, Kim R. Piirila, Olli-Pekka O'Cairbre, Fiacre Ailbhe Orihuela, Jose Paris, Alan Terry Pepper, Paul M. Pila, Jonathan S. O'Callaghan, Liam J. Orlik, Peter P. Paris, Luis Perdew, Paul M. Pilz, Gunter Ochanine, Serge Orloff, Leo N. •Park, Chull Pereira-Leite, Margarida M. A. Pimbley, George H., Jr. Ochiai, Mitsuyuki Ornelas, Ant6nio Park, Hyungbin *Perelli, Alberto Pinch, Richard G. E. Ochs, Jon *Orponen, Pekka Park, Jae Keol Perera, Mahapatabedige Ryle Pinkham, Henry C. Ocone, Daniel L. Orr, Jobn L. Park, Jea-Nam Perez Gonzalez, Fernando Pinney, Edmund O'Connell, James R., Jr. Orr, Martin Park, Kwang S. Perez-Munuzuri, V. *Pinney, Karen R. O'Connor, M. Lesley Orsted, Bent Park, Samuel Pericas, Jordi Pinsky, Mark A. Octavio, Alfredo Ortiz-Quil\ones, Carmen A. Park, Sang Ro Perk, Jacques H. H. Pinsky, Ross George Oda, Tadao Osborn, J. Marshall Park, Young Soo *Perkel, Manley *Pinter, Joseph Kalman Odani, Kenzi *Osborn, T. A. Park, Young-June *Perkins, Peter Piranian, George Odlyzko, Andrew M. Osborne, Mason S. Parker, Bob Perko, Lawrence M. *Pirinen, Aulis A. A. *Odom, Earl T., Jr. Osborne, Michael Robert Parker, Elwood G. Pedis, Robert V. Pirtle, Robert W. Oehmke, Robert H. *Osborne, William Jobn D. Parker, Francis D. Perlman, Sanford Pischettola, Cos D. *Oeljeklaus, E. Osgood, Brad G. Parker, Thomas H. Permpoon, Pirnpa Pisier, Gilles *Offner, Carl D. Osgood, Charles F. Parks, Teresa A. Pernice, Michael Pistone, Giovanni Ogawa, Hajimu O'Shea, Donal B. *Parlett, Beresford N. Perrine, Serge Pitcher, Everett Ogg, Andrew P. Oslon, Steve G. Parr, James T. Perry, Peter Anton Pitt, Loren D. Oguchi, Kunio Osofsky, Barbara L. *Parrott, David Persek, Stephen C. *Pittie, Harsh V. •oh, Hi-Jun Osondu, Kevin E. e Parry, Walter R. *Persson, illf • Pittnauer, Franz *Oh, Yong-Geun Osserman, Robert Parry, William Pertica, Horacio N. *Pitts, Andrew M. Oh, Yoon Yong Ostedt, Gary W. Parsons, Charles D. Pervine, Robert H. Pixley, Carl P. *O'Halloran, Joyce *Osterwalder, Konrad Paschke, William L. •Peskin, Charles Samuel Pizer, Arnold K. Ohta, Haruto Ostrom, T. G. Pascual-Gainza, Pere Pesotan, Hoshang Piziak, Robert Okada, lkutaro Ota, Clem Z. Pascucci, RichardS. Petermann, G. E. Plachky, Detlef Okada, Masami Ota, Kaori Imai Pasini, Antonio Peters, John E. Plank, Donald L. Okamoto, Kiyosato Otal, Javier Passell, Nicholas *Peters, Justin R., III Plano, Richard A. Okayasu, Takateru Otal, Jean-Pierre J.P. Passerini, Henry J. Peters, Klaus Plassmann, Paul E. Okoh, Frank Otermat, Scott C. Passman, DonaldS. Petersen, Bent E. Plesken, Wilhelm *Oksendal, Bernt K. Otero, Maria Carmen Passty, Gregory B. Petersen, Johannes A. Pless, Vera S. Okubo, Tanjiro *Otsu, Yukio • Paterson, Alan L. T. Petersen, Michael P. Plexousakis, Michael Okumura, Haruhiko Otsuki, Nobukazu *Pathak, Vijay Damodar *Peterson, Annalisa Marie Plohr, Bradley J. Okuyama, Akihiro Otway, Thomas H. Patterson, Reba Peterson, Gary L. Pogu, Marc Oldham, Frank Ernest Overholt,. Marins •Patton, Charles M. *Peterson, John C. *Poguntke, Detlev *Oldbam, Janis Marie Overtun, Steve Randall *Paul, Pedro J. Peterson, William P. Pokorny, Martin Peter *O'Leary, Robbin Lerch Owa, Shigeyoshi Paulley, Glenn N. • Peters son, H. P. Polachek, Harry Oler, Norman Owings, James C., Jr. *Panlowich, David G. Petro, Jobn W. •Polimeni, Albert D. Olesen, Dorte Marianne Owre, Sam *Paur, Sandra 0. Petty, Clinton M. *Poliquin, Rene A. Olesen, Mogens Norgaard Oyabu, Takashi *Pavani, Raffaella Petty, James Alan Pollack, Richard *Oliger, Joseph E. Ozaki, Isao Paveri-Fontana, Stefano L. Peyerimhoff, Alexander Pollatsek, Harriet S. Olin, Robert F. Ozeki, Michio Pawelke, Siegfried H. R. Peyriere, Jacques Pollingher, Adolf Olivares, Rene •Ozimkoski, Raymond E. Pawlaczyk, Thomas J. Pfeiffer, Paul E. Pollington, Andrew D. Oliver, Henry W. Ozsvath, Istvan Payne, Lawrence E. •Pfiefer, Richard E. Polonsky, Ivan P. Oliver, Kenneth S. Pacella. Filomena epazy, Amnon J. Pflug, Peter Pomeranz, Shirley B. Oliver, Robert A. Pacheco-Castelao, Jose M. Peabody, Mary K. *Pflugfelder, Hala 0. Pommerening, Klaus *Olivier, Reinhard M. Paciorek, Joseph W. Pears, Alan R. *Phadke, Bhalchandra Balvant *Ponnley, James Olmsted, Jobn M. H. Pade, Offer Pearson, Robert W. *Pham, Giao V. Pons, Montserrat *Olsen, Martin Padma, Narasimhachari Pearson, Ronald K. Pheidas, Athanasios C. Poole, George D. Olshen, A. C. Pagano, Miriam E. Pearson, Stephen C. Phelps, Robert R. Poorman, Alan G. Olson, Dwight M. •Page, Stanley S. *Peart, Paul B. Phili, Christine Melle van der Poorten, Alfred J. Olson, Loren D. Paisner, Helen L. Peccati, Lorenzo *Philippeaux, Hugues J. *Poritz, Alan B. Olson, Mark N. Pak, Jingyal Peck, Emily Mann *Phillips, Anthony V. *Porst, Hans E. Olum, Paul Palais, RichardS. Peck, PaulS. *Phillips, Daniel Port, Sidney C. *Oluyede, Broderick 0. Palais, Robert A. Peckham, Bruce B. Phillips, G. Edric Porte, Jean Olver, Peter J. Palanques-Mestre, August Pedersen, Edward A. Phillips, Ralph S. *Porter, Gerald J. Oman, Jobn Arthur Palka, Bruce P. Pedersen, Erik Kjaer Phillips, Richard E. Porter, Jobn F. O'Meara, Kevin C. Pallara, Diego Massimo •Pedersen, Franklin D. Piacentini, Giulia Maria Porter, Kathryn Frost Omori, Hideki Pallares, Antonio Jose • Pedersen, Katherine L. Piacenza, Robert John *Pllschel, Jlirgen O'Nan, Michael E. Pallaschke, Diethard *Pedersen, Stig Andur Piatetski-Shapiro, I. *Posner, Edward C. Onat, Emin T. Palled, Shivappa V. *Pedregal, Pablo Picard, Rainer H. Post, Karel A. *Onder, Torgut M. Palmer, Edgar M. Peglar, George W. Picavet, Gabriel Poston, Tim O'Neil, Kevin A. Palmer, Susan M. Pego, Robert L. Piccinini, Renzo A. Potthoff, Jurgen K. 738 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS Centennial Fellowship Fund Potts, Donald H. Randell, Richard C. Renno, James G., Jr. Robinson, Susan D. Roth, Rodney J. Pour-El, Marian B. Raney, George N. Renshaw, James H. Robkin, Eugene E. Rothaus, Oscar S. Powell, C. Spencer Range, R. Michael *Repka, Joe Roby, Donald A. Rothberger, Fritz Powell, Charles H. *Rankin, R. A. •Retzloff, David G. Rockhold, Todd D. Rothman, Neal J. *Power, Stephen Charles Rankin, Samuel Murray, III Reyes, Francisco G. Rod, David L. *Rothschild, Bruce L. Powers, Morris Walton Rankin, Stuart A. Reyes, Miguel *Roddy, Michael S. Rothschild, Linda Preiss Powers, Robert T. Ransom, Adelbert W. Reynolds, Donald F. Rodin, Yury L. Rothstein, Mitchell J. *Powers, Victoria Ann Rao, Ranga R. Reynolds, Robert J. Rodriguez, Gerardo Rotthaus, Christel Powls, Keith W. Rao, Salvatore •Rhai, Tong-Shieng Rodriguez, Sanjurjo Jose *Rouche, Nicolas Prakash, Nirmala *Rao, Vidhyanath Kajana Rhee, Choon Jai Rodriguez-Exposito, Jose Roush, Fred Prather, Carl Lindell eRapp, P. E. Ribenboim, Paulo Roe, John Rousseau, Cecil C. *Pratt, Randall N. Ras, Antoni *Ribes, Luis Roezin, Sofyadi * Rouviere, Francois Pratt, Vaughan R. Raskind, Wayne Mark *Ricci, Fulvio Rofman, Edmundo Rouys, Robert L. Preiss, Mitchell Paul •Ratcliff, Gail D. L. Ricci, Stephen J. Rogawski, Jonathan David Roxin, Emilio 0. *Preissendorfer, Manfred W. Ratiu, Tudor Stefan *Rich, Andrew Rogers, Cleon L. Royden, Halsey L. Prenowitz, Walter Ratliff, Louis J., Jr. *Richard, Philip Henry, Jr. Rogers, Deborah G. Royer, James Samuel *Prest, Michael Y. Ratz, Jurg J. Richards, Franklin B. Rogers, Jack W., Jr. Royle, John C. *Prestel, Alexander Rauch, Lawrence L. Richards, Pamela C. Roggenkamp, Klaus W. •Royster, Wimberly C. Preston, Gordon B. Rauhauser, Ronald J. Richardson, Kenneth S. *Rohl, Frank D. Rozovskii, Boris L. *Price, G. Baley Rausen, John Richert, Hans-Egon Rohlfs, Jurgen *Ruben, Flores Espinoza *Price, Jack Raussen, Martin Richert, Norman J. Rohm, Dale M. Ruberman, Daniel Price, Justin J. Rave, Werner J. Richman, Fred Rohrlich, David E. Rubin, Herman Price, Roderick A. Rawnsley, John H. Richmond, Glayvera Roitman, Judith Rubin, Jean E. Priddy, Stewart B. *Rawsthorne, Daniel A. Richmond, Lawrence B. Roitman, Moshe Rubin. Jonathan Eric Prieto, Carlos Ray-Chaudhuri, Dwijendra K. Richter, Guenther E. Rolf, Howard L. • Rubin, Robert J. *Prince, Geoffrey Eamonn *Raymond, Frank A. Richter, Michael M. Rolfsen, Dale P. 0. Rubinstein, Joachim H. Propp, James Gary *Rayner, Francis J. Richter, Stefan Romaguera, Salvador *Rubinstein, Zalman Protas, David S. *Read, Thomas T. Richter, Wayne H. *Romanelli, S. Rudnick, Ze'ev •Protter, Murray H. Reardon, Philip C. Richtmyer, Robert D. Romero Chesa, Carles *Rudolph, Daniel Jay Protter, Philip E. Reba, Marilyn A. Rickart, Charles E. Ronga, Felice L. L. Ruelle, David P. Proulx, Viera Krnanova Reber, Douglas C. Rickert, John H. *Rousse, Gregory S. Ruess, W. Pruitt, William E. Recaman, Bernardo Rickert, Neil W. Rooney, Paul G. Ruh, Ernst A. Pruss, Jan Rechard, Ottis W. Rickey, V. Frederick Roos, Bernard W. Ruijsenaars, Simon Norbert Prussner, Laird Drew *Redfield, Robert H. Rickman, B. *Roos, Guy *Ruiz, Alberto *Przytycki, Jozef H. Redheffer, Raymond M. Riddle, Malcohn Lee Rope, Crispin M. Ruiz, Ceferino Pucci, Patrizia Redmond, Don Riddlebaugh, Mary Jane F. Rosay, Jean-Pierre * Rumbos, Beatriz Irma Pujol Ferran, Magda *Redner, Richard A. Rider, Heather L. Rose, N.J. Rumely, Robert S. Pnkanszky, Lajos Reed, Coke Stevenson Rieffel, Marc A. *Rosebrugh, Robert D. Rupert, Carl P. Purnaras, Joannis C. *Reed, Michael C. Rieger, Georg J. Roselle, David P. *Ruskai, M. Beth Pursell, Lyle E. Reed, Robert E. Rigdon, Robert D. Roseman, Joseph J. Rusodimos, Iason Putnam, Alfred L. Reedy, Christopher L. Rigo, Pietro Rosen, Kenneth H. Russo, Bernard ePutnam, Calvin R. Reese, Richard H. Riley, Geoffrey William Rosen, Lon M. Russo, Paula A. *Pym, John S. Regan, Francis Rinne, Dan C. *Rosen, Michael I. Rutland, Leon W., Jr. Qi, Anmin Regan, Kenneth W. Rio, Jose Rosen, Ned Ira Rutledge, Dorothy S. Qian, Maijian Regazzini, Eugenio Rishel, Thomas W. Rosen, William G. Rutman, Elizabeth W. Quach-Hongler, Cam Van Regev, Arnitai * Risnes, Martin Rosenbaum, Robert A. Ruttimann, Gottfried T. Quarles, D. A., Jr. * Rego, Eduardo F. Ritter, David L. *Rosenberg, David • Ruymgaart •. Peter A. Quigley, Frank D. *Rehm, Allan S. *Rizvi, Syed Mohantmad Tariq Rosenberg, Jonathan M. Ruzsa, Imre Z. *Quine, J. R. Reichaw, Meir Rno, Jung-Sik Rosenberg, Steven Ryan, Patrick J. Quinn, Declan P. F. *Reichel, Lothar Roach, Michael D. Rosenblatt, Joseph Max Ryan, Robert D. Quinn, Frank S. •Reid, Alan W. Robatino, Andre E. Rosenbloom, J. H. Ryan, Robert M. Quinn, John M. Reid, James D. *Robbiano, Lorenzo Rosenfeld, Gerald Rydeen, Clarence F. Quint, Richard A *Reid, K. Brooks Robbin, Joel W. Rosenstein, George M., Jr. Ryeburn, David *Quintero, Antonio Reid, Les Robbins, David A. •Rosenthal, Arthur J. Rykken, Charles John Quinto, Eric Todd Reid, William H. *Roberts, Anne Drinkwater Rosenthal, Eric S. Sablatash, Mike Quiring, Donald K. Reilly, Norman Raymond Roberts, David Peter Rosenthal, Erik J. Saccoman, John J. Rabinowitz, Paul H. Reineck, James F. Roberts, Joel L. Rosenthal, Haskell P. Sacks, Paul E. Racquet, John C. Reiner, Irma M. Roberts, Joseph B. *Rosenthal, Kimmo I. *Sadofsky, Hal Radcliffe, Andrew J. *Reiner, Victor S. *Roberts, Leslie G. Rosenthal, Steven M. *Sadosky, Cora S. Radick, Jeffrey P. Reinhardt, William N. *Roberts, Mark *Rosentrater, C. Ray *Sadun, Lorenzo A. *Radjavi, Heydar Reinoehl, John H. Roberts, Richard C. • Ross, Bertram Saff, Edward B. Radkowski, Alfred F. Reinschke, K. J. Roberts, Roger A. Ross, J. Andrew Sagan, Bruce E. Radulescu, Nicholas Andrew Reise!, Robert B. Roberts, Stephen G. Ross, Kenneth A. •Sagarman, Elma Rebecca Rafels i Pallarola, Carles Reissner, Eric Robertson, Charles William, II *Ross, Martin Sah, Chih-Han Rajnak, Stanley L. Reitberger, Heinrich Robertson, James B. Ross, Robert G. *Sahab, Salem A. Rakesh Reitwiesner, George W. Robertson, Neil *Ross, Shepley L., II Saigo, Megumi Rail, Louis B. Rejto, Peter A. Robinson, Daniel A. Rossi, Guido A. Saito, Akira *Ralph, William J. Rembis, Frederick C. Robinson, David Hill *Rossler, Otto E. Saito, Atsushi Ralston, James V. Rempel, Richard S. Robinson, Derek J. S. Rosson, John Sait6, Kazuyuki * Ramalho, Margarita Remseth, Biorn Robinson, E. Arthur, Jr. van Rossum-Wijsmuller, Marijke Saito, Kichi-Suke Ramanujan, Melapalayam S. Renardy, Michael *Robinson, Helen Drummond Rostand, John S. •Saito, Shiroshi Ramirez, Arturo Flores *Renault, Jean N. Robinson, Mark Preuss Rota, Gian-Carlo Saitoh, Saburou Ranck, James B. Renegar, James M. Robinson, Paul Lee Roth, James W. Sakai, Furnio Randall, John D. Renner, Lex E. Robinson, Raphael M. Roth, Richard L. *Sakai, Katsuro SEPTEMBER 1992, VOLUME 39, NUMBER 7 739 RIJl!IDill 0 Rfi!!00P 1 ifmt ___ AMS Centennial Fellowship Fund *Sakamoto, Kunimochi Schauer, Richard L. *Schulze-Pillot, R. *Sertoz, A. Sinan Shorter, William Ivan Sakamoto, Kunio Schaumberger, Norman Schumacher, Carol S. *Servedio, Frank J. Shoucri, R. M. Sakmann, Pascal *Schechtman, Gideon Schumacher, Scott Sesay, Mohamed W. I. Shreve, David C. Sakuma, Motoyoshi Schechtman, Vadim V. Schumaker, John A. esethuraman, J. Shrier, S. *Salamanca-Riba, Susana Alicia Scheffer, Vladimir *Schumann, Shannon L. Sevenster, Aljen Shub, Michael Salamin, Eugene Scheinerman, Edward R. Schupp, Paul E. Sever, Michael Shubsda, Stanley R., Jr. Salas, Hector N. Schell, Emil D. Schuster, Seymour Sevilla, Alicia N. Shuchat, Alan H. Saldanha, Nicolau C. *Schellhorn, Jean-Pierre Schlitt, Carsten Sexauer, Norman E. Shull, Ernest E. Salehi, Habib Schellwat, Holger Schutt, Ingo Shabazz, Abdulalim A. Shure, Patricia D. Salisbury, Thomas S. Schembari, Nunzio Paul *Schwaller, Thomas Emmanuel Shader, Bryan L. Shutt, Elsie G. Salkind, William Schempp, Walter *Schwartz, Alan L. Shaftman, David H. *Siapas, Athanassios G. Sallee, G. Thomas Scherkoske, Kenneth D. Schwartz, Charles Freund Shahidi, Freydoon Sibner, Lesley M. Salles, Maurice *Scheurle, Jurgen K. Schwartz, Jacob T. *Shahriari, Shahriar Sibner, Robert J. Sally, Paul J., Jr. *Schichl, Hermann Roland Schwartz, Karen L. •Shaio, Jack Sichler, J. Saltiel, Leon Schiffer, Max M. Schwartz, Lionel Shallit, Jeffrey Outlaw Sidney, Stuart J. Samelson, Christopher L. Schiffmann, Gerard M. Schwarz, Binyamin *Shank, Robert James *Siebeneicher, Christian Samelson, Hans Schiller, John J. Schwarz, Gerald W. Shapiro, Daniel B. *Siegel, Eli A. *Sampson, Gary Schilling, Randolph James Schweiger, Fritz Shapiro, Dawn M. Siegel, Martha J. Samuel, Pierre Schillo, Paul J. Schweitzer, Eric *Shapiro, George S. Siegel, Paul H. •Sanchez, David A. Schindler, Christian *Schweitzer, Larry Britt •Shapiro, Jay A. Siegrist, Kyle T. Sanchez, Juan Miguel *Schirmeier, Horst *Schweitzer, Paul A. *Shapley, Lloyd S. Siemons, Johannes Sanchez, Rafael J. Schlesinger, Ernest C. •Schweizer, Berthold Sharp, James Dimitri *Siersma, Dirk Sanchez-Vazquez, Gonzalo Schlessinger, Michael Schwietzer, Michael J. Sharpe. Michael J. Sigman, Karl Sanders, Robert W. *Schlichenmaier, Martin Scott, Damon Sharpe, Richard W. Sigrist, Francois Sanderson, Brian J. *Schlick, Tamar Scott, Dana S. •Sharpton, John T. Sikorav, Jean-Claude Sandri, Guido V. H. •schlipf, John S. *Scott, David R. Shatz. Stephen S. Silberger, Allan J. Sands, Jonathan Winslow Schmeelk, John F. Scott, Leonard L., Jr. Shaw, Douglas J. Silberger, Donald Morison Sangren, Ward C. Schmerl, James H. Scott, Peter Shaw, Guy B. Silva, Jorge-Nuno Oliveira San Miguel, Angel Schmets, J. *Scott, Richard A. *Shaw, Karl E. Silver, Daniel S. *Sansigre, Gabriela *Schmetterer, Leopold K. Scott, Ridgway *Shaw, Mei-Chi Silverman, Herb Santalo, L. A. Schmid, Josef Scott, Warner Henry Harvey, III *Shaw, Sen-Yen Silverman, Joseph H. Santiago, Freddie Schmid, Jurg Scott-Thomas, John F. Shearer, James W. Silvia, Evelyn Marie *Santos Filho, Jose Ruidival S. D. Schmid, Wilfried Scourfield, Eira J. Sheffer, Isador M. Sim, Raymond Sanz, Miguel Angel Schmidlin, Dean J. * Scriba, Christoph J. Sheil-Small, Terence Brian *Simanca, Santiago R. Sanz-Serna, J. M. Schmidt, Dieter S. Seal, Charles Edwin *Shell. Niel eSime, Patrick J. Saphar, Pierre David Schmidt, Harvey J ., Jr. •Searcy, Charles J. Shelly, Eugene P. Simeoli, Giorgio Sarafyan, Diran Schmidt, Henry J., Jr. Sears, Michael Shelly, Maynard W. Simo, Carles *Sarantopoulos, Joannis C. Schmidt, Kenneth C. eSeddighi, Karim *Shelton, Richard M. Simon, Imre Sarason, Donald E. *Schmidt, Klaus D. Sedory, Stephen A. *Shemanske, Thomas R. Simonis, Juriaan Sario,Leo *Schmidt, Roland Sedwick, Jackson L. Shen, Zhong-Wei Simons, Lloyd D. *Sarkar, Asis K. *Schmidt, Thomas A. Seebach, J. Arthur Shene, Ching-Kuang Sims, Benjamin T. *Samak, Peter Clive Schmidt, Volker Seebeck, Charles L., III Shenitz, Charles Sims, Charles C. Sarrat, Charles F. Schmidt, Wolfgang M. Seeley, Robert T. Shenitzer, Abe Singer, Michael F. Sasaki, Takeshi *Schmitt, Peter esegawa, Shigeo Shepherd, J. C. *Singer, Seymour Sasano, Kazuhiro Schmuland, Byron A. Segert, Jan *Shepherdson, John C. Singer, William M. eSatake, lchiro *Schmutz, Eric J. Sehnert, James Ellis Sherk, F. A. Singerman, David Sato, Hiroki Schneebeli, H. R. Seid, Howard A. Sherlock, Philip Thomas *Singh, Bhagat Sato, Hiroshi Schneider, Hans •Seidman, Thomas I. •Sherman, Bernard *Singh, Premjit *Sato, Ken-iti *Schneider, Manfred F. Seifert, George Sherman, Clayton C. Singman, David H. Sato, Masako *Schneider, Todd J. • Seifter, Norbert Shiba, Masakazu Singrnaster, David B. ------Saut, Jean Claude Schneiders, Jean-Pierre *Seikkala, Seppo A. Shibata, Masanori K. Sinkala, Zachariah Sauvigny, Friedrich Schnitzer, Franz J. *Seiler, Wolfgang K. Shibuya, Yuji *Sinnott, Warren Mann Sawada, Hideki Schochet, Claude L. Sein, Hla Hla Shieh, Jung-Sheng *Sipe, Patricia Lilaine Sawyer, Eric T. *Schochet, Steven H. *Seip, Kristian Shiffman, Bernard Siu, Man-Keung Sawyer, Patrice Schoen, Richard M. Seitoh, Akira Shiffman, Max *Sivakumar, N. Scalzo, Richard C. *Schoenwaelder. Ulrich F. •Seitz, Gary M. Shiflett, Ray C. Sivera, Rafael Scaramuzzi, Roberto Scholl, Anthony J. Sekigawa, Hisao Shiga, Koji *Sizer, WalterS. Scarpellini, Bruno J. Scholz, E. Selby, Alan M. Shimada, Nobuo *Sjogren, Jon A. Scarpi, Giambattista Schonbek, Maria Elena Seligman, George B. Shimamoto, Don H. eskafl, Michael S. escarsini, Marco *Schram, Erin J. Seligman, Mark L. Shimizuike, Yuzi Skau. Christian F. Schaal, Werner G. H. Schreiber, Bert M. *Seligson, Stuart A. Shimura, Goro Skiffington, John Joseph, III Schacher, Murray M. Schreiner, Walter J. Semmes, Stephen William Shin, Dong Sun Skillings, John H. Schafer, Alice T. Schremmer, Francoise Sempi, Carlo E. Shin, Kee-Young Sklar, David Schafer, Richard D. Schreyer, Lynn L. *Senechal, Lester J. *Shin, Yong-Tae Skof, Fulvia Schaffer, Juan Jorge Schrijver, Alexander Senechal, Marjorie Shinohara, Yaichi Skora, Richard Kevin Schafke, R. Schroder, M. Senge, George Shiohara, Hiroshi Skoug, David L. Schanberger, Joseph Anthony Schroeder, Carolyn L. Sengupta, Ambar Niel Shipp, R. Dale Slack, Michael D. Schapira, Pierre B. Schryer, Norman L. Sengupta, Dipendra C. Shiraiwa, Kenichi Slack, Stephen Schapiro, Philip J. *Schubert, Cedric F. Seppala-Holtzman, David Shiratani, Katsumi Slade, Gordon D. *Scharlau, Rudolf M. E. Schubert, David C., Jr. *Sepulveda, Eric *Shirley, Kevin L. Slater, John B. Scharlemann, Martin G. Schuett, Werner Serapioni, Raul Shizuta, Yasushi Sleeman, Brian D. *Schattschneider, Doris W. Schultz, Jason P. Serre, Denis A. Sholander, Marlow C. Slocum, Stacy S. *Schatzman, James Carl Schultz, Martin Harvey *Serre, Jean-Pierre •shor, S. W. Williston Slook, Thomas H. Schatzman, Michelle *Schultz, Phillip eserrell, Robert Shores, Thomas S. *Slowikowski, Wojciech • 740 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS Centennial Fellowship Fund Slucbin, Benny Sorvali, Thomas Steinby, Magnus Strohmer, Gerhard 0. Szczarba, Robert H. Slud, Eric V. Souganidis, Panagiotis E. *Steiner, Anne K. Strom, Arne *Szczechla, Witold W. Slye, John M. *Sourour, Ahmed Ramzi Steinert, Leon A. Stromberg, J. 0. Szekeres, George *Smale, Nat *Sousa Ramos, Jose .Steinborn, Charles I. Stromquist, Walter R. Szepessy, Anders Small, Lance W. Southgate, Theodore J. *Steketee, Jakob A. *Stroth, Gemot H. W. Szeto, Mabel Small, Lynne Barnes Spaltenstein, Nicolas Stell, John Greenwood Stroud, Eric G. Szucs, Joseph M. Smart, John R. Sparr, Gunnar Stella, Sergio Strobe, Richard F. E. *Szulkin, Andrzej Smarzewski, R. Spatz, Ian N. Stembridge, John R. Struwe, M. *Szymanski, Andrzej *Smid, Harm J. Spatzier, Ralf J. Stenger, Frank Stuckwisch, Stephen E. *Szymaiiski, Wojciech Smiley, Leonard Spears, Otis S. Stengle, Gilbert A. *Stueben, Michael A. Tadic, Marko Smillie, John Specht, Edward J. Stenson, David L. Stueckle, Samuel K. Taft, Margaret W. Smith, Bruce T. *Speiser, Robert •Stenzel, Matthew B. *Stufken, John Tagawa, Masa-Yoshi Smith, David A. Spencer, Philip H. Stephens, James H. Stuhler, Ulrich Taiaui, Geraldine •Smith, F. R. Spencer, Thomas Crawford Stephens, Stanley L. Sturm, Teo Taibleson, Mitchell H. Smith, Frank D., Jr. Spiegel, W. *Stephenson, Kenneth *Sturmfels, Bernd Taira, Kazuaki Smith, George Rowan Spielberg, Jack Stepp, James Wilson *Styer, Robert A. Takacs, Lajos F. *Smith, Hal L. Spielberg, Stephen E. Sterba-Boatwright, Blair D. *Su, Yuh-Ling Takahashi, Joji Smith, James L. Spolter, Pari D. Sterk, Henri J. Suarez, Jorge F. Takahashi, Masako *Smith, John Howard Sprague, Alan P. Sterling, Theodor D. Suarez, Pedro A. *Takahashi, Reiji Smith, John M. Sprecher, David A. Stem, Alan Spector Suarez, Rodolfo Takahashi, Shuichi *Smith, Kay E. *Spring, David H. Stem, Robert B. esucheston, Louis Takahashi, Yuji Smith, Kennan T. Springer, Tonny A. Stem, Ronald J. Sueyoshi, Yutaka Takenaka, Shigeo •Smith, Kirby C. Spurr, Michael J. Sternberg, David Sugarman, Paul J. Takesaki, Masarnichi *Smith, Mark A. Srinivasan, Bhama *Sternberg, Peter J. Sugita, Kimio Takeuchi, Kisao *Smith, Martha K. Sritharan, Sivaguru Stevens, Glenn H. Sugiura, Mitsuo Takeuchi, Masaru Smith, Michael F. Staab, Peter E. Stevens, T. Christine Sugrue, Kevin P. Takizawa, Kiyoshi Smith, Michael G. Stacey, Peter John *Stewart, Cameron L. Suita, Nobuyuki Taleghaui, Kaveh Smith, Penny D. Stackelberg, Olaf P. Stewart, James D. Su!anke, Robert A. *Talenti, Giorgio G. Smith, Perry B. Stafford, J. T. Stewart, James W. Sulis, William H. Talmadge, Richard B. Smith, Ralph C. Stafney, James D. Stewart, Robert C. Sullivan, Richard W. *Tamari, Dov Smith, Richard Allan *Stahel, Andreas Stiadle, Thomas A., Jr. Su!sky, D. L. Tan, Henry K. Smith, Robert Colman Stahl, Saul *Slifer, Sabine Summers, Arthur R. Tanabe, Hiroki Smith, Roland F. Stahmer, Karl Pangburn Stiles, Joseph L. Summerville, Richard M. Tanaka, Hisao Smith, S. Paul Staicu, Vasile Stock, John R. Sun, Tien-Yu Tanaka, Jun-Ichi •Smith, Spurgeon E. Stakgold, lvar Stocker, Harold Edward Sundar, P. Tanaka, Katsumi •Smith, Stephen B. Staknis, Victor R. Stockmeyer, Paul K. Sundararaman, D. Tanaka, Minoru Smith, Wayne Stewart Staley, Russell L. Stoker, James R. Sunderland, Benjamin B., Jr. *Tanaka, Toshie Smith, Wilbur L. Stallmann, Friedemann W. *Stolberg, Harold J. •sung, Li-yeng Tanasi, Corrado *Smith, Wtlliam K. Stamey, William L. Stoll, Wilhelm F. Sunley, Judith S. Tancreto, Daniel Louis Smithies, Frank Stammbach, Urs Stoltenberg-Hansen, Viggo Sunouchi, Gen-ichiro Tang, Alfred S. *Smolarski, Denuis C. •Stampfli, Joseph G. Stoltzfus, Neal W. Sunouchi, Haruo Tang, Hwa Tsang Smolinsky, Lawrence J. Stanley, Lee James Stolz, Stephan A. Sunseri, Mary V. •Tang, Qi Smoller, Joel A. Stanley, Richard P. *Stone, Arthur H. Suri, Mauil Tanimoto, Taffee T. Smyth, William F. Stanley, Walter C. *Stone, Arthur L. Suryanarayan, E. R. *Tanis, Elliot A. Snaith, Victor P. Stanton, Charles S. *Stone, David A. Susanka, Lawrence A. *Tankou, Victoire Tyntynou Snavely, Mark R. Stanton, Dennis W. Stone, David R. Sussman, Myron M. Tanno, Shukichi Sneddon, Ian N. *Stanton, Nancy K. *Stone, Dorothy Sutton, Charles S. Tao, Yoko Snodgrass, James T., III Stanton, Robert J. Stone, Eugene A. Sutton, Michael D. Tapia, Joseph A. Snover, James E. Staples, Edmund Beauclerc, III Stone, Lawrence D. Sutton, P. P. *Targonski, Jolan M. Soedirman, Massy Staples, John C. Stone, Michael G. Sutton, Ronald F. Tariq, Nessirn *Soedjak, Heroe Starbird, Thomas W. Stong, Richard A. Suzuki, Haruo Tarres, Joan Soemadi, Andreas H. Stark, Christopher W. *Stonier, Rus.sel J. Suzuki, Humio Tartakoff, DavidS. Sokolowski, Carole P. Stark, Richard K. *Stormer, Erling Suzuki, Michio Tasche, Manfred Sola-Morales Rubi6, Joan *Starr, Norton Storrer, Hans H. Suzuki, Naoyoshi Tashiro, Yoshihiro del Solar-Petit, Emilio Staton, William A., III Stortz, Clarence B. Suzuki, Shinichi Tashjian, Gloria J. Soldate, Albert M., Jr. Stavroudis, Orestes N .. Story, Leon A., Jr. *Svensson, Erik J. Tatevossian, Leon H. *Solian, Alexandru Steams, Joseph E., Jr. Stout, Edgar Lee Sverdlove, Ronald •Taub, Abraham H. *Sologuren, Santiago Steele, Alfred T. *Stout, Lawrence Neff Swamy, Srikanta M. N. Taussky, Olga Solomon, Bruce Steele, William F. *Straffin, Philip D., Jr. Swan, Richard G. Tavantzis, I ohn Solomon, David R. Steen, F. H. Straight, H. I. Swanek, I ames J. Taylor, Angus E. Solomon, Louis Steenbrink, J. Stralka, Albert R. Swank, L. I ames Taylor, B. A. Solomon, Ronald M. Stefani, Stefano T. Strang, Gilbert *Swann, Howard S. G. Taylor, Donald E. *Solovej, Jan Philip Stegeman, Jan D. Strassberg, Helen A. Sward, Marcia P. Taylor, Jean E. *Somer, Lawrence E. Steger, Arthur *Straube, Emil J. Swardson, Mary Anne Taylor, John Russell Soni, Raj Pal Steger, Trm J. Straubing, Howard Sweeney, Edward T. Taylor, Kenneth Douglas Sonneborn, Lee M. •steggles, Irving Strauss, Frederick B. Sweeney, William J. Taylor, Laurence R. Sonner, Johann Stegun, Irene A. Strauss, Leon Sweet, Melvin M. Taylor, M. A. Sons, Linda R. Steif, Jeffrey Edward Strauss, Walter A. *Swiatek, Grzegorz Taylor, Michael D. esopka, John J. Stein, Howard Street, Ross H. Swick, Kenneth E. Taylor, Michael E. Sorbi, Andrea Stein, Sherman K. Strehl, Volker Swickard, Joe S. Taylor, Monty B. Sorenson, John R. Steinberg, Leon Stretch, Christopher T. Swokowski, Earl W. Taylor, Thomas J. Sore!, Mark Steinberg, Paraskevi Strikwerda, John C. Sylvester, Donna L. G. Tazawa, Yoshihiko Soria, Fernando Steinberg, Robert Stroeker, R. J. Symes, William W. Tee, Garry J. Sormani, Michael J. Steinberg, Stanly Lee Strohl, G. Ralph, Jr. Szabo, Zoltan I. Teirlinck, Luc M. SEPTEMBER 1992, VOLUME 39, NUMBER 7 741 ·······-··-·-·-·-······-····-·-········--··-····-·-··-··-····-···--······--···· ···-·-·-·-·------AMS Centennial Fellowship Fund *Teissier, Bernard Tjiok, Mouw-Ching Tubaro, Luciano *Van Emde Boas, Peter Voreadou, Rodiani *Teixidor i Bigas, Montserrat Toda, Nobushige Tucci, Ralph P. Van Geemen, Bert * Vrabec, Franz *Teleman, Constantin Todd, John Tucker, Albert W. *Van Lint, Jacobus H. Vrbik, Jan Teleman, Silvio Todor, Fabian Tuckerman, Bryant Vanniasegaram, Gnanalakshmi Wada, Hidekazu Temam, Roger Todorov, Gordana *Tudor, David W. evan Osdol, Donovan H. Wada, Junzo Tena, Juan Tolosa, Juan Tugue, Tosiyuki Van Rootselaar, Bob Wada, Toshimasa Tenenbaum, Gerald Tolsted, Elmer Tuler, Randy *Van Rossum, Herman Wadhwa, Bhushan La! *Tenenblat, Keti Tomari, Masataka Tulipani, Sauro Van Slyke, Richard M. Waelbroeck, Lucien Tennant, Raymond Frederick Tomer, Eugene R. Tuller, Annita Van Strien, Sebastian J. Wagener, Raymond Tepedino A., Gaetano Tominaga, Hisao Tuncali, H. Murat Van Trung, Tran •Wagner, Daniel H. Terao, Hiroaki Tomita, Yoshihito Tung, On-Ki A. Van Tuyl, A. H. Wagner, David H. Terman, David H. Tomiyama, Jun Turesson, Bengt Ove Van Veldhuizen, M. Wagner, Diane M. Temg, Chuu-Lian Tong, Mary Powderly *Turett, J. Barry Van Vleck, Fred S. Wagner, Gretchen B. *Terrell, William J. Tonne, Philip C. Turgeon, Jean M. Vaquie, Michel Wagner, Joyce K. Terry, Raymond D. *Top, Jaap Turiel, F. J. Varadhan, Srinivasa S. R. Wagner, William M. Terwilliger, Paul M. *Topsoe, Flemming Turisco, Joann Stephanie Varadi, Ferenc Wagoner, John B. · Terzakis, Dimitris Torre, Nicolo Goodrich Turner, T. Rolf Varberg, Dale E. Wagreich, Philip D. Terzuoli, Andrew J. *Torres, Luz G. Turquette, Atwell R. Varela, Januario eWahba, Grace *Textorius, Bjorn 0. B. Torres; M. *Turyn, Lawrence Varouchas, Jean Wahlbin, Lars B. Thibon, Jean-Yves *Torres de Squire, Maria L. Tutte, W. T. Vasak, Janet Trzcinski Wainger, Stephen •Thickstun, Thomas L. Toth, Gabor Twersky, .Victor Vasconcelos, Walmer V. Wainwright, John Thickstun, W. R., Jr. Tourville, Suzanne E. *Tymchatyn, Edward D. *Vatsala, A. S. *Wajda, Louis W. Thiele, Emst-Jochen Town, George G. Tysk, Johan Vaughan, Herbert E. Wakae, Masarni Thieme, Horst R. *Townsend, Douglas Wayne Uchiyama, Akihito Vaught, Robert L. Wakana, Kaoru Thoele, Edward C. *Towsley, Gary W. Uchiyama, Saburo Vaz Pinto, Maria Rasquilha Walborn, Stephanie Arnold *Tholen, Walter P. Traina, Charles R. Ueno, Kazushige *Vazquez, Juan L. Walcher, Sebastian Thorn, Rene *Traldi, Lorenzo Ueno, Kenji Vega, Jose Manuel Waldinger, Hermann V. Thoma, Elmar H. Transue, William R. Ueno, Yoshiaki Vega, Luis Walker, Homer F. Thomas, Alan T. Trauber, Philip Uhl, J. Jerry, Jr. Velazquez, Robert Walker, James D. Thomas, Clayton J. Trautman, David A. Ukegawa, Takasaburo Vella, David C. Walker, James S. Thomas, Erik G. F. *Trebels, Walter Ullery, William D. *Velleman, Daniel *Walker, James W. Thomas, George B., Jr. Treibergs, Andrejs E. Ullman, Joseph L. * Vemuri, Murali Krishna Walker, Marshall Thomas, Janet D. *Treiman, Jay S. * Uhner, Douglas L. Veukataraman, Rangachari *Walker, Michael F. *Thomas, Jean-Claude Treisman, Philip Uri Ulrich, Bernd Ventoso, Ramon *Wall, Charles T. C. Thomas, Ken E. *Trejos, Javier Umeda, Takata *Ventura, Belisario Augusto Wall, Curtiss E. Thomas, Lawrence E. Tremmel, John J. Umeda, Tomio Vera, Gabriel Wall, G. E. Thomas, Marc Phillip Trench, William F. Umegaki, Hisaharu *Verde Star, Luis *Wallace, David A. R. Thomas, P. Emery Trenholme, Alice Ruth Unai, Yasushi Unai Verduyn Lunel, Sjoerd M. Wallace, William *Thomas, Pascal J. Treves, Francois . Underwood, Douglas H. Verma, Ghasi R. Wallen, C. J. *Thomas, Robert S. D. Treybig, L. Bruce Ungar, Peter Vermeer, Johannes Wallen, Lawrence J. Thomee, Vidar Trias Capella, Rosa M. Unger, Ernst R. Vermes, Robert *Walling, Lynne H. *Thompson, Ha!'old B. Trias Pairo, Joan *Unger, Luise *VerNooy, Stan Walls, Gary L. Thompson, Jon H. Tricerri, Franco Uno, Katsnhiro Verona, Andrei Walnut, David F. Thompson, Layton 0. *Trillas, Enric Upatisringa, Visutdhi Vershik, A. M. Walrand, Jean Thompson, Mary E. Trimble, Cynthia E. Upmeier, Harald Vershum, Eugene A. •Walsh, John J. *Thompson, Thomas M. Trimble, Selden Y. Upton; John A. W. * Vervaat, Wirn Walsh, John Thomas Thomson, Brian S. Trivieri, Lawrence A. Urbas, John Vesentini, Edoardo Walter, Charles H. Thome, John Farley, ill Trager, Hans *Urbina, WJ.!fredo 0. Vetter, Udo Walter, Gilbert G. *Thorpe, John A. *Tromba, A. J. *Uribe, Alejandro Vietsch, W. Karel Walter, John H. Thrall, .Robert M. Trone!, Gerard Ursini, Aldo Vilcius, AI R. Walter, Martin E. Thrash, Joe B. Trunzo, Mark D. •van der Vaart, H. 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Viviente, Jose L. Wang, Stuart Sui-Sheng Tillmann, Heinz G. Tschantz, Steven T. Vance, Garrett H., Jr. Vogan, David A., Jr. *Wang, Wenyang Timm, Mathew T. Tsirnis, Emmanuel M. Van Daalen, Diederik T. Vogel, Thomas I. Wantland, Evelyn K. *Timoney, Richard M. Tsuchikura, Tamotsu *Van Den Ban, Erik P. Vogelius, Michael Steenstrup Ward, Doug E. Timourian, James G. Tsuchiya, Morimasa Vanden-Brueck, Jean-Marc Vogt, Dietmar Ward, Harold N. Timper, James M., Jr. Tsuchiya, Talmya *Vanderbauwhede, A. L. Vogt, E. *Ward, Josephine A. Tin, Saw Tsuji, Kazo Van der Geer, Gerard Vogtmann, Karen Wardle, Robin W. Tintera, George D. *Tsujishita, Tom Van Der Kallen, Wilberd Voichick, Michael Ware, Buck Tirta, I. Made Tsukada, Makoto *VanDer Mee, Camelis V. Voiculescu, Dan Warne, Ronson J. Tischler, David C. Tsukiyama, Kouzou Vandevelde, J. Richard Vojta, Paul A. Warner, Frank W., III Titani, Satoko Tsukni, Yasuyuki Van de Wetering, R. Lee •Volkmann, Bodo * Warrinnier, Alfred E. 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Westwood, Derek J. •Wilson, Jody T. Wylie, Clarence R., Jr. Zaballa, Ion Watkins, Mark E. Wetton, Brian T. R. Wilson, Leslie Charles Wyman, Bostwick F. *Zacher, Giovanni G. Watnick, Richard M. Wetzel, John E. Wilson, Raj Wyn-Jones, Alun Zafrullah, Muhammad Watson, David K. Wheeler, Charles H., III Wilson, Richard Xenophontos, Christos Zaharopol, Radu Watson, Martha F. Wheeler, John A. Wilson, Robert Lee Xenos, Philippos John Zalik, R. A. Watson, Rodwell B. Wheeler, Robert F. Wingate, John W. Xu, Jia Gu Zama, Nobuo Watson, Stephen *White, Alexander Wingler, Eric J. *Yale, I. Keith Zambrini, Jean-Claude Watt, Jeffrey Xavier White, Alvin M. * Wingren, Peter Yamada, Hirofumi Zame, Alan Wavrik, John J. White, Arthur T. Winkler, Jorg H. Yamada, Hiromichi Zamfirescu, Christina M. Wayne, Alan White, Benjamin S. Winograd, Shmuel Yamada, Miyuki Zanolin, Fabio Weaver, John C. White, Brian Cabell Winston, Kenneth Yamada, Naoki Zapf, Hermann Webb, David L. White, Denis A. Winther, Ragnar Yamada, Osanobu *Zarach, Andrzej Michal Webb, Glenn F. White, George N., Jr. Wintrobe, F. Yamada, Shiniclii *Zaremba, Leszek S. *Webb, Peter J. White, Lee Wayne Wirszup, Izaak Yamada, Toshihiko Zaslavsky, Thomas Webster, Sidney M. White, Myron E. Wise, Gary Lamar Yamaguchi, Itaru Zedek, Mishael •Wechsler, Martin T. •White, Neil L. Wiskott, Bettina Yamaguchi, Jinsei *Zeeman, Mary Lou Week, Norbert Whitehart, F. E. Witsch, K. J. *Yamaguchi, Keizo Zegarlinski, Boguslaw Wefelmeyer, Wolfgang Whitehead, George W. Witsenhausen, Hans S. Yamaguchi, Kohhei Zehnder, Eduard J. Wehausen, John V. Whitehead, Kathleen B. Witten, Edward Yamaguchi, Seiichi Zelle, Joseph Wehlen, Joseph A., Jr. Whitfield, John H. M. Witten, Louis Yamakawa, Mineo Zeller, Karl *Weibel, Charles A. Whitley, W. Thurmon Wittner, Ben Scott Yamaki, Hiroyoshi Zemmer, Joseph L., Jr. Weibel, John L. Whitman, Andrew P. Woerdeman, Hugo J. Yarnanoshita, Tsuneyo Zerzan, John M. Weidmann, Joachim Whitman, Philip M. Woerner, Edwin L. Yamasaki, Masayuki Zhang, Zhao Zhi Weidner, Jens Whitney, Stephen ewoldar, Andrew J. Yamashita, Michinori *Zhao, Hua Wei!, Clifford E. Whitt, Lee B. Wolf, Edwin M. Yamawaki, Noriaki Zheng, Weian Weill, Lawrence R. Whittaker, James V. Wolfe, Dorothy W. Yanagawa, Minoru *Zhou, Y'lshao *Weinberger, Peter J. Whyburn, Kenneth G. Wolfram, Stephen Yanagi, Kenjiro *Zhu, Qiji Weiner, Jerome H. Wickerhauser, Mladen Victor Wolfskill, John Yang, Chung-Chun Zhu, Xiao-Wei Weiner, Joel L. •Wicklin, Frederick J. *Wolfson, Paul R. Yang, Deane Zia, Lee L. Weingarten, Ellen Keer Widman, Kjell-Ove H. Wolk, Elliot S. Yang, George Keith *Ziegler, John Alan Weinitschke, Hubertus J. eWidom, Harold Wolkowicz, Gail S. K. *Yang, Jae-Hyun Ziegler, Zvi Weinkam, James J. Wiegand, Roger A. Wollman, Stephen Yang, Jeong Sheng Ziemer, William P. Weinstein, Alan D. Wiegand, Sylvia Margaret Wolpert, Scott A. Yang, Kung-Wei Zierau, Roger Craig Weinstein, Gideon L. Wiegmann, Klaus Werner Womble, David E. 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Yoneda, Kaoru Zuckerman, Gregg J. Wendel, James G. Williams, Georganna Wright, David G. Yoo, Ki-Jo *Zumoff, Nancy E. Wene, Gregory P. Williams, Hugh M. Wright, David J. Yood, Bertram Zweibel, John A. Wente, Henry C. *Williams, John K. Wright, Jeffrey Allen Yoshihara, Ken-lchi Zweifel, Paul F. Wermer, John Williams, Joyce W. Wright, Jill D. Yoshino, Ken-ichi *Zwick, D. Werner, Dirk *Williams, Lawrence R. Wright, Mary H. Yoshino, Masafumi Anonymous (145 ) Werner, Elisabeth •Williams, Mark *Wright, Ron Yoshino, Takashi Werner, Peter *Williams, Neil H. Wright, Thomas Perrin, Jr. Yoshizawa, Taro Wernick, Robert J. *Williams, Peter David *Wschebor, Mario Young, Barry H. Werschulz, Arthur G. Williams, Susan Gayle Wu, Chia-Lin Young, Lael M. SEPTEMBER 1992, VOLUME 39, NUMBER 7 743 ...... ·············--···································------······················-·················-···············-·-········ ········--·-·-····················--···-································ Memorial Gift List Memorial and Commemorative Gift Listing Memorial and commemorative gifts are a distinctive and thoughtful way to memorialize or honor a colleague, friend, or family member and to support the Society's work to promote mathematical scholarship and research. The Society acknowledges these gifts upon receipt of the gift and through the listing below. The list designates gifts made through March 1992. In addition, notification of the gift is sent to persons designated by the donor. MEMORIAL GIFT In Memory of Regina Ruth Love In Memory of Emil Stamm In Honor of the AMS Roderick R. Love Akira Tsutsumi Diethard Pallaschke In Memory of My Father, Giovanni Marchiafava In Memory of Professor Leonard Sulski Dieter Pumplun Stefano Marchiafava Dr. & Mrs. Vincent McBrien In Honor of Edward M. Arnold, Sr. In Memory of (Hans Heinrich) Wilhelm Magnus In Honor of Professor Haruo Suzuki Stephanie Arnold Walborn Bernhard H. Neumann Shyuichi Izumiya In Honor of Adrian Ayala In Honor of Professor Carl Maxson In Memory of Kazimirz Twardowski, Rafael Ayala-Gomez GunterPilz on the !25th anniversary of his birth In Honor of Monsieur Nicolas Bourbaki In Memory of Marilyn Miller Mosier Giuseppe Scollo Alexander Stuebinger Ronald G. Mosier In Memory of Cuiyi Zhang In Memory of Professor Leon W. Cohen In Honor of Professor Minyou Qi JieChen Beatrice Kleppner Juncheng Wei In Honor of Professor Craig Comstock In Honor of Roy F. Reeves OTHER MEMORIAL GIFT DONORS Frank D. Faulkner William M. Wagner Gregory A. Bastian In Honor of Carl Cowen In Memory of Irving Reiner Peter B. Bjorklund Shamim Ismail Ansari Irma M. Reiner Horace B urk Cheng In Memory of Frances S. Edris In Honor of Judith B. Reuning Michael Edelstein Gerrit M. Edris William M. Wagner Masao Igarashi In Honor of the Founders of AMS In Honor of Malcolm S. Robertson Kenji Kashihara Leonardo D'Attorre John Bender Amtul Matin Khan In Memory of Izrail Markovich Glazman In Memory of Julia Robinson WilliamLo W. Norrie Everitt Jean Porte Katarzyna Saxton Edward Silverman In Honor of Professor Emeritus Gustav A. Hedlund In Memory of Glenn Schober James L. Smith Leo Hellerman GinaM. Hieb Sing Keung Wong In Memory of Grant Wallace Heil In Honor of Jean-Pierre Serre Ken-Ichi Yoshihara Ruth L. Hughes Kazuyuki Hatada In Memory of Domingo Herrero In Honor of Dr. Donald J. Smeltzer Edward A. Azoff William M. Wagner CENTENNIAL FELLOWSHIP FUND In Memory of Einar Hille In Memory of Clifford Spector In Honor of Arnold Ross John Boris Miller Alan S. Stern G. Baley Price 744 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY 1992 AMS Elections In an effort to increase the number of ballots returned in the election There has been a small but recurring and distressing problem process, the Society has decided to include in the Notices all the concerning members who state that they have not received ballots in pertinent election material, including biographies and statements of the annual election. It occurs for several reasons, including failure of the candidates in the upcoming election. The information is provided local delivery systems on university or corporate properties, failure of in order to assist the members in filling out the ballots that will soon members to give timely notice of changes of address to the Providence be mailed. The officers of the Society encourage the members to office, failures of postal services, and other human errors. return ballots. To help alleviate this problem, the following replacement proce I urge you to study the material printed below. More importantly, dure has been devised: A member who has not received a ballot by I urge you to look for the ballot that will arrive shortly in the mail October 10, 1992, or who has received a ballot but has accidentally and to return a completed ballot. In recent elections, only 15% of the spoiled it, may write after that date to the Secretary of the AMS, Post members participated. I hope this figure can be greatly increased. Office Box 6248, Providence, RI 02940, asking for a second ballot. The request should include the individual's member code and the Robert Fossum address to which the replacement ballot should be sent. Immediately Secretary upon receipt of the request in the Providence office, a second ballot, which will be indistinguishable from the original, will be sent by first Candidates class or air mail. It must be returned in an inner envelope, which will OFFICERS be supplied, on the outside of which is the following statement to be Vice-President (one to be elected) signed by the member: Melvin Hochster Anil Nerode The ballot in this envelope is the only ballot that I am submitting in this election. I understand that if this statement is not correct then Member-at-Large of the Council (five to be elected) no ballot of mine will be counted. James H. Curry Peter Li Gloria C. Hewitt Kenneth A. Ribet Svetlana R. Katok Philip D. Wagreich Steven George Krantz Jonathan M. Wahl signature James I. Lepowsky Susan Gayle Williams Although a second ballot will be supplied on request and will be sent by first class or air mail, the deadline for receipt of ballots will not be Board of Trustees (one to be elected) extended to accommodate these special cases. Roy L. Adler Richard W. Beals NOMINATING COMMITTEE FOR 1993 SUGGESTIONS FOR 1993 NOMINATIONS (Approval voting, three to be elected) Each year the members of the Society are given the opportunity to Jerome A. Goldstein Louise A. Raphael propose for nomination the names of those individuals they deem Vaughan F. R. Jones Yum Tong Siu both qualified and responsive to their views and needs as part of Brian J. Parshall Nancy K. Stanton the mathematical community. Candidates will be nominated by the Council to fill positions on the Council and Board of Trustees to replace those whose terms expire January 31, 1994. See the AMS EDITORIAL BOARDS COMMITTEE FOR 1993 Reports and Communications section of this issue for the list of (Approval voting, two to be elected) current members of the Council and Board of Trustees. Members Bryan J. Birch Paul H. Rabinowitz are requested to write their suggestions for such candidates in the Fan R. K. Chung Masamichi Takesaki appropriate spaces below. Election Information The ballots for election of members of the Council and Board of SUGGESTIONS FOR 1993 NOMINATIONS Trustees of the Society for 1993 will be mailed on or shortly after President-Elect (1) September 10, in order for members to receive their ballots well in advance of the November 10 deadline. Prior to casting their ballots members are urged to consult the following articles and sections of Vice-President (1) the Bylaws of the Society: article I, section 1; article II, sections 1, 2; article ill, sections 1, 2, 3; article IV, sections 1, 2, 4; article VII, Members-at-large of the Council (5) sections 1, 2, 5. The complete text of the Bylaws appears on pages 1177-1182 of the November 1991 issue of the Notices. A list of the members of the Council and Board of Trustees serving terms during 1992 appears in the AMS Reports and Communications section of this issue. Member of the Board of Trustees (1) REPLACEMENT BALLOTS This year ballots for the AMS election will be mailed September 10, The completed form should be addressed to AMS Nominating Com 1992, or within a day or two thereafter. The deadline for receipt of mittee, Post Office Box 6248, Providence, RI 02940, to arrive no later ballots is November 10, 1992. than November 10, 1992. SEPTEMBER 1992, VOLUME 39, NUMBER 7 745 Biographies of Candidates 1992 AMS Committees: Committee to Se Math., No. 24, Amer. Math. Soc., 1975. lect Hour Speakers for Western Sectional MR 51 #8096; 3. with Craig Huneke, Biographical information about the candi dates has been verified by the candidates, Meetings, 1977-1979 (Chair, 1979); Tight closure, invariant theory, and although in a few instances, prior travel ar Bulletin Editorial Committee (Associate the Briancon-Skoda theorem, J. Amer. rangements of the candidate at the time of Editor, Research Announcements), 1981- Math. Soc. 3 (1990), 31-116. MR 91g assembly of the information made commu 1983; Program Committee for National #13010; 4. with Craig Huneke, Infi nication difficult or impossible. A candidate Meetings, 1982-1984 (Chair, 1983- nite integral extensions and big Cohen had the opportunity to make a statement of 1984); Executive Committee of the Macaulay algebras, Ann. of Math. 135 not more than 200 words on any subject matter without restriction and to list up to Council, 1983-1986; Mathematical Re (1992), 53-89. five of her or his research papers. views Editorial Committee, 1984-1989 Statement: I am concerned with a cur Abbreviations: American Association (Chair, 1984-1989); Committee on Long rent paradox. Federal funds are be for the Advancement of Science (AAAS); Range Planning, Board ofTrustees, 1985 ing poured into graduate support at a American Mathematical Society (AMS); (Chair); Committee to Select the 1985 time when the job market is dreadful, American Statistical Association (ASA); while traditional funding for researchers, Association for Computing Machinery Cole Prize in Algebra; Mathematical (ACM); Association for Symbolic Logic Reviews-Zentralblatt Negotiating Team, akeady inadequate, is being steadily (ASL); Association for Women in Mathe 1985; Committee to Select the 1990 Cole eroded. matics (AWM); Canadian Mathematical So Prize in Algebra (Chair). ciety, Societe Mathematique du Canada Selected Addresses: Invited Address, Anil Nerode* (CMS); Conference Board of the Mathemat San Antonio, January 1976; Interna Goldwin Smith Professor of Mathemat ical Sciences (CBMS); Institute of Mathe matical Statistics (IMS); International Math tional Congress of Mathematicians, ics and Director of the Mathematical ematical Union (IMU); London Mathemat Helsinki, August 1978. Sciences Institute, Cornell University ical Society (LMS); Mathematical Associa Additional Information: Principal Lec Born: June 4, 1932, Los Angeles, Cal tion of America (MAA); National turer, CBMS Regional Conference, Uni ifornia Academy of Sciences (NAS); National versity of Nebraska, 1974; Principal Ph.D.: University of Chicago, 1956 Academy of Sciences/National Research Lecturer, CBMS Regional Conference, AMS Committees: Committee on Sci Council (NASINRC); National Aeronautics and Space Administration (NASA); Nation George Mason University, 1979; Frank ence Policy, 1976-1978. al Council of Teachers of Mathematics Nelson Cole Prize in Algebra, 1980; Selected Addresses: Summer Research (NCTM); National Science Foundation Guggenheim Fellow, 1982; Board of Institute on Recursion Theory, Ithaca, (NSF); Operations Research Society of Trustees, MSRI, 1985-1987; Board of June-July 1982; Logic in Computer Sci America (ORSA); Society for Industrial Governors, IMA, 1985-1987; Scientific ence, IEEE Conference, Boston, 1986; and Applied Mathematics (SIAM); The Advisory Council, MSRI, 1989-1993 Asian Logic Colloquium, Beijing, China, Institute of Management Sciences (TIMS). An(*) indicates the individual was nom (Chair, 1992-1993); Human Resources 1988; Logic Week, Oberwohlfach, 1989; inated in response to a petition. Committee, MSRI, 1992- (Chair); Mem Logical Foundations of Computer Sci ber: AMS, MAA, AWM. ence, TVER92, Tver, Russia, 1992. Selected Publications: 1. with J. L. Additional Information: The Commit Vice President Roberts, Rings of invariants of reduc tee on Applied Mathematics of the NRC, Melvin Hochster tive groups acting on regular rings 1967-1970; Council, Association for Professor, University of Michigan are Cohen-Macaulay, Adv. in Math. Symbolic Logic, 1968-1983; The NSF Born: August 2, 1943, Brooklyn, New 13 (1974), 115-175. MR 50 #311; 2. Advisory Panel for Mathematical Sci York Topics in the homological theory of ences, 1970-1973; Chair, Department of Ph.D.: Princeton University, 1967 modules over commutative rings, Proc. Mathematics, Cornell University, 1982- Offices: Member-at-large of the Coun Nebraska Regional CBMS Conference, 1987; NRC Computational Mathemat cil, 1982-1986. CBMS Regional Conference Series in ics Ad Hoc Panel, 1984; Distinguished 746 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY m 0000000 m00000 mooomOOOOO mmm000 000000000 OOOOOmm•• OOOOOOOOOOOOOOOOOOOOOOOOKAfi! Visiting Scientist, U.S Environmental mathematics (EXXON); initiated a pro ing in 1973; AMS-MAA-NCTM-SIAM Protection Agency, 1985-1987; Science gram to bring college teachers into the Committee on Women in the Mathemat Advisory Board of the U.S. Environ University for updating (PEW, DANA); ical Sciences, 1984; AMS-ASA-IMS mental Protection Agency, 1986-; Ad initiated many dozens of conferences in MAA-NCTM-SIAM Committee on visory Board, The Center for Intelli new areas (MSI); been a consultant for Women in the Mathematical Sciences, gent Control of MIT-Brown-Harvard, EPSCOR Kentucky and Puerto Rico; 1985-1986. 1987-; Advisory Panel, The Army High initiated cooperative research programs Selected Addresses: Limits of Univer~ Performance Computing Institute, Uni with minority institutions; advised many sal Algebras, Missoula, 1976; Noethe versity of Minnesota 1989-; Advisory government and industrial laboratories rian Conditions, Cleveland, 1978; Cat Board, The Center for AI, University and institutes. I have also worked with egory Theory and Automata (Series of of Pennsylvania, 1991. Editor: Proceed EPA for fourteen years, have been on the Lectures), Cleveland, 1981; Generalized ings of the American Mathematical So U.S. Environmental Protection Agency Noetherian Rings, China, 1990; Polyno ciety, 1962-1965; Journal of Symbolic Science Advisory Board, and am cur mial Rings Which are Principal Ideal Logic, 1967-1983; Annals of Pure and rently Chair, USEPA Global Change Rings, China, 1990. Applied Logic, 1984-; Future Genera Program Technical Advisory Panel. Additional Information: NSF Fellow, tion Computing, 1984-; Annals ofMath 1966; MAA Visiting Lecturer, 1964-- ematics and AI, 1990-; Member: AMS, Member-at-Large of the Council 1972; Executive Council of Pi Mu Ep MAA, ASL, AWM, ACM, IEEE, SIAM. James H. Curry silon, 1972-1975; GRE Examination Selected Publications: 1. Diophantine Professor ofApplied Mathematics, Uni Committee, 1976-1986 (Chair, 1984-- correct non-standard models in the isols, versity of Colorado, Boulder 1986); College Board AP Calculus De Ann. Math. 84 (1966), 421-432. MR 34 Born: July 24, 1948, Oakland, Califor velopment Committee, 1987-1991; GRE #2465; 2. with J. N. Crossley, Com nia Technical Advisory Committee, 1992-; binatorial functors, Ergebnisse series, Ph.D.: University of California, Berke MAA (PNW) Distinguished Teaching Springer-Verlag, New York-Heidelberg, ley, 1976 Award Committee, 1992; CUPM Sub 1974. MR 52 #10397; 3. with G. Meta AMS Committees: Committee on Com committee on Assessment~ 1990-1994; kides, Effective content of field theory, munications, 1992-. Member: AWM, MAA, NAM. Ann. Math. Logic 17 (1979), 289-320. Selected Addresses: AMS Summer Selected Publications: 1. The existence MR 82b:03082; 4. with J. B. Remmel Seminar on Factorization Algorithms, offree unions in classes ofabstract alge and W. Marek, Non-monotone rule sys Fort Collins, July 1988; Conference on bras, Proc. Amer. Math. Soc.l4 (1963), tems. I., Ann. Mathematics and Artificial Chaos and Strange Attractors, Univer 417-422. MR 26 #6098; 2. Limits in cer Intelligence, 1991; 5. with A. Yakhnis sity of Colorado, Denver, 1988; Con tain classes of abstract algebras, Pacific andY. Yakhnis, Concurrent programs as ference on the Numerical Solution of J. Math. 22 (1967), 109-115 .. MR 35 strategies in games, Logic From Com Simple Equations, Clarkson University, #1529; 3. Characterizations of general puter Science (Y. N. Moschovakis, ed.), 1988; Conference on Bairstow's Algo ized Noetherian rings, Acta. Math. Hun Springer-Verlag, New York-Heidelberg, rithm, University of Minnesota, 1989; gar. 53 (1989), 61-73. MR 90g:16039. 1992, pp. 405-480. Conference on Polynomial Factoriza Statement: If elected, I would help tion Algorithms, University of Califor Svetlana R. Katok AMS take a lead in: (1) Promoting the nia, Davis, May 1989. Associate Professor, Pennsylvania State unity of the mathematical sciences; (2) Additional Information: NSF Post University Integrating mathematics with the rest of doctoral Fellowship Evaluation Panel, Born: May 1, 1947, Moscow, Russia scientific life; (3) Making contributions 1990-. Ph.D.: University of Maryland, 1983 of mathematics to government, business Selected Publications: 1. with Sharon Selected Addresses: Summer Research and industry known to the Public and L. Blish, On the geometry of factoriza Conference on Kleinian Groups, Boul Congress; (4) Integrating the teaching tion algorithms, Computational Solution der, August 1983; Conference on Ge community with the research commu of Nonlinear Systems of Equations, Lec ometry, Lie Groups and Ergodic The nity; (5) Identifying the mathematically tures in Appl. Math., vol. 26, pp. 47-60, ory, Mathematical Sciences Research talented among minority groups and Amer. Math. Soc., Providence, Rl, 1990; Institute, Berkeley, May 1984; Collo women, drawing them into our commu 2. Eye ofNewton: The Movie, September quium Lecture, University of Califor nity. Besides a long research career un 1989. nia, San Diego, February 1986; Inter der NSF, ARO, ONR, AFOR, and many national Centre for Theoretical Physics, other sources of research support, I have: Gloria C. Hewitt Trieste, Italy, July 1990; Workshop on had thirty-four Ph.D. students, including Professor, University of Montana Discrete Groups, Number Theory and Louise Hay and Charlotte Lin (I joined Born: October 26, 1935, Sumter, South Ergodic Theory, Mathematical Sciences AWM at its inception); run MAT pro Carolina Research Institute, Berkeley, November grams (NSF); been consultant for MAA Ph.D.: University of Washington, 1962 1991. for about eighty colleges; initiated a AMS Committees: Committee on Lo Additional Information: NSF Post freshman program to hold students in cal Arrangements for the Summer Meet- doctoral Research Fellow, 1986-1988; SEPTEMBER 1992, VOLUME 39, NUMBER 7 747 ...... ______...... -...... •...... •. _.. _...... - .. -.... ---·-····-··-···· Biographies of Candidates Seminar Leader, Summer Mathematics mains, Math. Ann. 261 (1982), 425-446. State University, University Park, July Institute, Intensive Mathematics Pro MR 84c:32032; 4. Invariant metrics and 1991. gram for Women Undergraduates, NSF the boundary behavior of holomorphic Additional Information: Member, In Special Project, Mills-Berkeley, June functions on domains in C. n, J. Geom. stitute for Advanced Study, 1975-1976, July 1991; Member: AMS, AWM. Anal. 1 (1991), 71-98; 5. Convexity in 1980, 1985, 1987-1988; Sloan Fellow, Selected Publications: 1. Closed geo complex analysis, Proc. Sympos. Pure 1976-1978; Visiting Associate Profes desics, periods and arithmetic of mod Math., vol. 52, part 1 (E. Bedford, J. sor, Universite Paris VI, 1978; Member, ular forms, Invent. Math. 80 (1985), D'Angelo, R. Greene, and S. Krantz, Mathematical Sciences Research Insti no. 3, 469-480. MR 86j:11048; 2. Ap eds.), American Mathematical Society, tute, 1983-1984; Guggenheim Fellow, proximate solutions of cohomological Providence, RI, 1991, pp. 119-137. 1987-1988; Organizer, Special Session equations associated with some Anosov Statement: The two most severe crises on Infinite-Dimensional Symmetries in flows, Ergodic Theory Dynamical Sys facing our professions today are the Mathematics and Physics, Worcester, tems 10 (1990), no. 2, 367-379. MR shortage of jobs and the difficulty of April 1989; Organizing Committee, 91g:58120; 3. Elliptic operators and so obtaining research funding. Although Workshop on Mathematical Ideas Aris lutions of cohomological equations for the first crisis stems in part from transient ing from Conformal Field Theory, As geodesic flows with hyperbolic behav social phenomena, the end is not in sight. pen Center for Physics, 1989; Organiz ior, Intemat. J. Math. 2 (1991), 701-709; The second crisis is also complicated, ing Committee, AMS-IMS-SIAM Joint 4. Fuchsian groups, The University of is linked in part with rising salaries and Summer Research Conference on Con Chicago Press, to appear; 5. with P. Sar shortage of money, but also has complex formal Field Theory, Topological Field nak, Heegner points, cycles and Maass social aspects. In any event, the two Theory and Quantum Groups, South forms, to appear. problems are proving disheartening both Hadley, June 1992; Associate Editor of Statement: I believe that AMS should to those who are considering entering the new Journal of Knot Theory and its exercise leadership in the commitment the profession and to those who are Ramifications; Member: AMS, MAA, of the research mathematics commu already established as mathematicians. I AAAS, American Physical Society. nity to excellence in undergraduate ed would like to see the AMS council seek Selected Publications: 1. with R. L. ucation. Together with improvement of methods to deal with the job crisis and Wilson, Construction of the affine Lie graduate support, this will make math the funding situation. algebra A~1 >, Comm. Math. Physics 62 ematics more attractive as a career and I would also like the AMS coun (1978), 43-53. MR 58 #28089; 2. with will bring the best talent to the profes cil to function more openly and to be R. L. Wilson, The structure of stan sion. more accountable to the AMS member dard modules, I. Universal algebras ship at large. My personal experience and the Rogers-Ramanujan identities, Steven George Krantz with the council in the last few years Invent. Math. 77 (1984), 199-290. MR Professor, Washington University has suggested that there is room for 85m:17008; 3. Calculus of twisted ver Born: February 3, 1951, San Francisco, improvement in both these categories. tex operators, Proc. Nat. A cad. Sci. USA California 82 (1985), 8295-8299. MR 88f:17030; Ph.D.: Princeton University, 1974 James I. Lepowsky 4. with I. B. Frenkel and A. Meur Selected Addresses: Invited Lectures: Professor, Rutgers University man, Vertex operator algebras and the Stanford University, 1987; Mittag-Leffler Born: July 5, 1944, New York, New Monster, Pure and Applied Math., vol. Institute, 1988; International Complex York 134, Academic Press, Boston, 1988. MR Analysis Conference, Cetraro, Italy, 1989; Ph.D.: Massachusetts Institute of Tech 90h:17026; 5. with Y.-Z. Huang, Toward National Academy of Sciences Frontiers nology, 1970 a theory of tensor products for repre of Science Forum, 1990; Yale Univer AMS Committees: Contemporary sentations of a vertex operator algebra, sity, 1991. Mathematics Editorial Committee Proc. 20th International Conference on Additional Information: NSF Fellow, (Associate Editor), 1980-1985; AMS Differential Geometric Methods in The 1975- ; Chauvenet Prize, MAA, 1992; IMS-SIAM Committee on Joint Summer oretical Physics, New York, 1991, S. Member: AMS. Research Conferences in the Mathemat Catto and A. Rocha, eds., World Scien Selected Publications: 1. H olomorphic ical Sciences, 1987-1988. tific Publishing, Singapore, 1992, vol. 1, functions of bounded mean oscillation Selected Addresses: International Con 344-354. and mapping properties of the Szego gress of Mathematicians, Helsinki, Au Statement: In conjunction with its pri projection, Duke Math. J. 47 (1980), gust 1978; Invited Address, Duluth, mary goal of fostering innovative re 743-761. MR 82i:32010; 2. with R. E. August 1979; Special Session on Fi search, the AMS should continue, and Greene, Deformations of complex struc nite Group Theory, Anaheim, January seek new ways, to: (1) take an active ture, estimates for the a-equation, and 1985; Symposium on the Mathemati role in the improvement of mathemat stability of the Bergman kernel, Adv. in cal Heritage of Hermann Weyl, Duke ics teaching at all levels; (2) emphasize Math. 43 (1982), 1-86. MR 84b:32026; University, May 1987; Summer Re to funding sources and to the general 3. with R. E. Greene, The automorphism search Institute on Algebraic Groups public the importance of mathematics groups of strongly pseudoconvex do- and their Generalizations, Pennsylvania especially the kind of undirected basic 748 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ·····--·············---·· --·········-·xswra:illliB~·-········· Biographies of Candidates research carried out by individual inves structure of complete manifolds, J. Diff. Statement: I would be honored to serve tigators; (3) facilitate interdisciplinary Geom., to appear. as Member-at-Large of the Council. I interaction both within mathematics and Statement: In the last 2 years, the job come to the AMS with no platform or between mathematics and other fields; market in mathematics seems to have political agenda. I am acutely aware of (4) strongly encourage talented students, caved in overnight. This sudden change the numerous challenges faced by our including women and members of mi caught the mathematics community by profession, and hope that I can make nority groups, to consider mathematics surprise. It is crucial at this stage, to be a contribution to sensible and equitable as a career; and (5) provide a forum for able to project and accurately assess the solutions. mathematicians to discuss the relations future market. In this sense, it should be between mathematics and society. the responsibility of the American Math Philip D. Wagreich ematical Society to set up a task force to University of Illinois at Chicago Peter Li effectively deal with this problem. Born: July 25, 1941, New York, New Professor, University of California, York Irvine Kenneth A. Ribet Ph.D.: Columbia University, 1967 Born: Aprill8, 1952, Hong Kong Professor ofMathematics, University of AMS Committees: Organizing Com Ph.D.: University of California, Berke California, Berkeley mittee, 1981 Summer Institute on Sin ley, 1979 Born: June 28, 1948, New York, New gularities; Committee on NCTM Stan AMS Committees: AMS-IMS-SIAM York dards, 1989. Committee on Joint Summer Research Ph.D.: Harvard University, 1973 Selected Addresses: Special Session Conferences in the Mathematical Sci AMS Committees: Committee on Far on Transformation Groups, Milwau ences, 1990-; Proceedings Editorial Com Western Sectional Meetings (Select Hour kee, November, 1971; Special Session mittee, 1991-; Progress in Mathematics Speakers for), 1980-1981 (Chair). on Singularities, San Antonio, January, Editorial Committee, 1991-. Selected Addresses: Invited Address, 1980; Summer Institute on Singulari Selected Addresses: Invited Address, Seattle, August 1977; Special Session on ties, Arcata, July 1981; Special Ses Logan, October 1986; The 9th Congress Arithmetical Algebraic Geometry, San sion on Asymptotic Properties of Hyper of the International Association of Math Francisco, January 1991 (Organizer); In bolic Groups, Anaheim, January 1985; ematical Physics: Session on Analysis of vited Address, San Francisco, January Special Session on Mathematicians and Manifold, Swansea, July 1988; Summer 1991; Special Session on Number The Education Reform, Baltimore, January Research Institute on Differential Geom ory, Joint Meeting of the American and 1992. etry: Plenary Address, Los Angeles, July London Mathematical Societies, Cam Additional Information: ONR Post 1990; MSRI Summer Program on Geo bridge, England, June 1992. doctoral Fellow, 1968-1969; Member, metric Analysis, Berkeley, July-August Additional Information: Organizing Institute for Advanced Study, 1968- 1990; Osaka Conference on Complex Committee, 1985 Summer Research 1970; Co-organizer, U.S.-France Joint Geometry and Related Topics: Plenary Conference on Current Trends in Arith Seminar on Singularities, Paris, 1982; Address, Osaka, December 1990. metical Algebraic Geometry (Chair); Co-organizer, U.S.-Japan Joint Semi Additional Information: Sloan Fellow, NSF Postdoctoral Fellowship Evalua nar on Complex Analytic Singularities, 1982; Guggenheim Fellow, 1989; Pro tion Panel, 1988-1992 (Chair, 1992); Tsukuba, 1983; Director, University of ceedings of the American Mathemati Prix Fermat, 1989; Member, NSF Re Illinois at Chicago Office of Mathe cal Society, (Coordinating Editor, Lie view Panel on Undergraduate Curricu matics and Computer Education, 1985- groups, geometry, and topology), 1992- lum Development, 1990-1992. 1990; Co-director, Mathematicians Ed 1994. Selected Publications: 1. A modular ucation Reform Network, 1988-; Mem Selected Publications: 1. with S. T. construction of unramified p-extensions ber, MAA Committee on Mathematics Yau, On the parabolic kernel of the of Q(JLp), Invent. Math. 34 (1976), Education of Teachers, 1990-; Member, SchrOdinger operator, Acta Math. 156 151-162. MR 54 #47424; 2. with P. Illinois Governor's Science Advisory (1986), 153-201. MR87f:58156; 2. with Deligne, Values of abelian L1unctions Committee; Co-director, VIC Institute L. F. Tam, Positive harmonic functions at negative integers over totally real for Mathematics and Science Education; on complete manifolds with nonnegative fields, Invent. Math. 59 (1980), 227- Member: MAA, NCTM. curvature outside a compact set, Ann. 286. MR 81m:l2019; 3. Congruence Selected Publications: 1. with Peter of Math. 125 (1987), 171-207. MR relations between modular forms, Proc. Orlik, Isolated singularties of algebraic 88m:58039; 3. On the structure of com 1982 ICM (1985), 503-514; 4. On mod surfaces with C* -action, Ann. of Math. plete Kiihler manifolds with nonnegative ular representations of Gal(QjQ aris 93 (1971), 205-228. MR 44 #1662; 2. curvature near infinity, Invent. Math. ing from modular forms, Invent. Math. Algebras ofautomorphic forms with few 99 (1990), 579-600. MR 91c:53063; 4. 100 (1990), 431-476. MR91g:11066; 5. generators, Trans. Amer. Math. Soc. with L. F. Tam, The heat equation and From the Taniyama-Shimura conjecture 262 (1980), 367-389. MR 82e:l0044; harmonic maps of complete manifolds, to Fermat's last theorem, Annales de la 3. with Howard Goldberg, A model in Invent. Math. 105 (1991), 1-46; 5. with Faculre des Sciences de l'Universite de tegrated mathematics science program L. F. Tam, Harmonic functions and the Toulouse 11 (1990), 116-139. for the elementary school, Perspectives SEPTEMBER 1992, VOLUME 39, NUMBER 7 749 ·------·-···············"""""""""""""'""""'""""""'""""""""""'"""""""""""""""""""""""""""""""""""""""""""""""""'"""""" Biographies of Candidates on Research in Mathematics Education, Selected Publications: 1. Equations cal Systems 8 (1988), 483-490. MR International Journal of Educational Re defining rational singularities, Ann. Sci. 90i:28027; 3. Covers of non-almost fi search 14 (2) (1990), 193-214; 4. with Ecole Norm. Sup. 10 (1977), 231-263. nite type sofic systems, Proc. Amer. Howard Goldberg, Teaching Integrated MR 56 #3005; 2. A cohomological Math. Soc. 104 (1988), 245-252. MR Math and Science: A Curriculum and characterization of lP n, Invent. Math. 90c:28028; 4. Lattice invariants for sofic Staff Development Project for the El 72 (1983), 315-322. MR 84h:14024; shifts, Ergodic Theory Dynamical Sys ementary School, Mathematicians and 3. with E. Looijenga, Quadratic func tems 11 (1991), 787-802. Education Reform, Proceedings of the tions and smoothing surface singulari Statement: A substantial proportion of July 6-8, 1988 Workshop, CBMS, Is ties, Topology 25 (1986), 261-291. MR AMS members are faculty at small col sues in Mathematics Education, vol. 87j:32032; 4. Gaussian maps on alge leges and universities which have few 1, Amer. Math. Soc., Providence, Rl, braic curves, J. Differential Geom. 32 resources to support research. This pro 1990, pp. 63-130; 5. with Peter Shalen, (1990), 77-98. MR 91h:l4028; 5. A portion is growing as the bleak job mar Growth rates, Zp-homology, and vol characteristic number for links of sur ket causes more talented young math umes of hyperbolic 3-manifolds, Trans. face singularities, J. Amer. Math. Soc. 3 ematicians with a strong dedication to Amer. Math. Soc., to appear, 1992. (1990), 625-637. MR 91c:14043 .. research to take jobs at less prestigious Statement: A vigorous research com Statement: While the main purpose of schools. This segment of the member munity depends upon a source of new the Society is to promote mathematical ship has little representation on the AMS students, the continuation of research research, several survival issues must be Council, and it is sometimes overlooked. funding, and understanding and accep addressed. Most importantly, the Coun For example, the Academic Hiring Sur tance by the general public. Therefore, cil needs to have frank discussions about vey in the April Notices sampled only in addition to the direct support of math practical ways to stem the flow of Amer doctorate-granting institutions, and half ematics research, the AMS should in ican college and graduate students away of the 40 schools surveyed were chosen volve itself in reform of mathematics from mathematics and the sciences. Be from the 39 "Group I" institutions. education and in communication with cause of the need to increase research If we want broad public support for government agencies and the general support for individual investigators, a mathematical research, we must con public. The AMS should find appro close look ought to be taken at the effect vince the public that mathematics is not priate ways to facilitate the process of on NSF grants of the removal of the a product which can be manufactured institutional and cultural change. salary cap. by a few to be consumed by many; that knowledge and discovery go hand in Susan Gayle Williams hand at all levels of mathematics. The Jonathan M. Wahl Professor, University of South Alabama AMS will be in a better position to do Professor, University ofNorth Carolina, Born: May 26, 1953, Orange, New this if its Council reflects the diversity Chapel Hill Jersey of its membership. Born: January 29, 1945, Washington, Ph.D.: Yale University, 1981 DC Selected Addresses: Special Session Ph.D.: Harvard University, 1971 on Texas Topology and Geometry, Den Trustee AMS Committees: Committtee on Hu ton, November 1990; Conference on Roy L. Adler man Rights, 1992. Symbolic Dynamics and its Applica Research StaffMember and Senior Man Selected Addresses: Special Session tions, New Haven, August 1991; Col ager, Mathematical Sciences Depart on Stratification of Algebraic and An loque Arithmetique et Dynamique Sym ment, Research Division, IBM Corpora alytic Varieties, Ann Arbor, Novem bolique, Marseille, September 1991; tion ber 1976; Organizer, Special Session on Special Session on Ergodic Theory and Born: February22, 1931,Newark,New Classification and Deformation of Sin Dynamical Systems, Tuscaloosa, March Jersey gularities, Charleston, November 1978; 1992. Ph.D.: Yale University, 1961 Special Session on Singularities of Alge Additional Information: Organizer, AMS Committees: Eastern Section Pro braic and Analytic Varieties, New York, Southeast Dynamical Systems Confer gram Committee, 1992-. April 1983; Invited Address, Canadian ence, Mobile, February 1990; Program Selected Addresses: Colloquium Lec Mathematical Society Summer Semi Committee, Mathematical Sciences Re ture, Cornell University, 1964; Invited nar in Algebraic Geometry, Vancouver, search Institute Special Half-Year Pro Address, Kalamazoo, August 1975; Sum July 1984; Invited Address, Fayetteville, gram in Symbolic Dynamics, Fall1992; mer Research Conference on Ergodic March 1990. Member: AMS, AWM. Theory and Applications, Durham, June Additional Information: Member, In Selected Publications: 1. Toeplitz min 1982 (organizer); Keynote Speaker, Aus stitute for Advanced Study, 1972-1973, imal flows which are not uniquely er tralian Mathematical Society, Monash 1979; Director of Undergraduate Stud godic, Z. Wahrsch. Verw. Gebiete 67 University, Melbourne, May 1984; Prin ies, UNC, 1981-1983; Organizer, Alfred (1984), 95-107. MR 86k:54062; 2. A cipal Speaker, Special Year in Dynam Brauer Lectures at UNC, 1985-1992; sofic system which is not spectrally of ical Systems, University of Maryland, Member: AMS. finite type, Ergodic Theory Dynami- December 1986; Colloquium Lecture, 750 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ...... ··········~~-~~:.::t:~.£.~:-~::~~-UJIIIHIIJB11···-··· ... ··-····· ...... _...... _...... Biographies of Candidates Pennsylvania State University, October dress, Pittsburgh, August 1981; Special ety; Institute of Mathematical Statis 1991. Session on Inverse Problems, Newark, tics, Sigma Xi, Sociedade Matematica Additional Information: Chair, Math April 1987; Summer Research Confer Brasileira, London Mathematical Soci ematical Sciences Research Institute ence on Inverse Scattering and Applica ety; served on various committees of the Workshop, Berkeley, December 8-13, tions, Amherst, June 1990. MAA and SIAM and on three editorial 1983; Panelist: National Science Re Additional Information: Co-editor, boards of research journals. search Council, Panel for Associateship Communications in Partial Differential Selected Publications: 1. with H. Bre Programs, 1986-; Trustee, Mathemati Equations, 1976--1986; Member: AMS, zis, Liouville theorems for some improp cal Sciences Research Institute, Febru MAA. erly posed problems, Improperly Posed ary 1986--1991; Chair: Coding Theory, Selected Publications: 1. with C. L. Boundary Value Problems (A. Carasso Fourth SIAM Conference on Discrete Fefferman, On local solvability of lin and A. P. Stone, eds.), Res. Notes in Mathematics, San Francisco, June 1988; ear partial differential equations, Ann. Math., vol. 1, Pitman, London (1975), Member: Editorial Board, Ergodic The of Math. 97 (1973), 482-498. MR 50 65-75. MR 57 #16883; 2. with James ory and Dynamical Systems, March #5233; 2. A general calculus of pseu T. Sandefur, Jr., Equipartition of energy 1989; Chair, Symbolic Dynamics Pro dodifferential operators, Duke Math. J. for higher order abstract hyperbolic gram, Mathematical Sciences Research 42 (1975), 1-42. MR 51 #3972; 3. equations, Comm. Partial Differential Institute, Fall 1992; Fellow, New York with R. R. Coifman, Scattering and in Equations 7 (1982), 1217-1251. MR Academy of Sciences, June 1985; IEEE, verse scattering for first order systems, 83k:34060; 3. with Pierre Baras, The Information Theory Group 1985 Best Comm. Pure Appl. Math. 37 (1984), heat equation with a singular potential, Paper Prize. 39-90. MR 85f:34020; 4. with P. C. Trans. Amer. Math. Soc. 284 (1984), Selected Publications: 1. with A. G. Greiner and N. K. Stanton, The heat 121-139. MR 85f:35099; 4. Semigroups Konheim and M. H. McAndrew, Topo equation on a CR manifold, J. Differ of linear operators and applications, logical entropy, Trans. Amer. Math. Soc. ential Geom. 20 (1984), 343-387; 5. Oxford Univ. Press, New York and Ox 114 (1965), 309-319. MR 30 #5291; Indefinite Sturm-Liouville problems and ford, 1985; 5. with Philippe Benilan and 2. with B. Weiss, Similarity of auto half-range completeness, J. Differential Gisele Ruiz Rieder, A nonlinear elliptic morphisms of the torus, Mem. Amer. Equations 56 (1985), 391-407. system arising in electron density theory, Math. Soc. 98 (1970). MR 41 #1966; Comm. Partial Differential Equations, to 3. with B. Marcus, Topological entropy Nominating Committee appear. and equivalence of dynamical systems, Jerome A. Goldstein Statement: The business of the AMS Mem. Amer. Math. Soc. 219 (1979). Professor, Louisiana State University is to promote mathematical activity and MR 83h:28027; 4. with D. Coppersmith Born: AugustS, 1941, Pittsburgh, Penn scholarship at the highest levels. High and M. Hassner, Algorithms for sliding sylvania standards should be maintained while block codes, IEEE Trans. Inform. The Ph.D.: Carnegie Mellon University, avoiding elitism. All qualified and inter ory 29 (1983), 5-22. MR 85b:94009; 1967 ested individuals should be encouraged 5. with L. Flatto, Geodesic flows, inter AMS Committees: Committee on Aca to pursue careers in mathematics and to val maps, and symbolic dynamics, Bull. demic Freedom, Tenure, and Employ advance their careers as far as possible. Amer. Math. Soc. 25 (1991), 229-334. ment Security, 1986--1990 These positions imply advocacy of af Statement: It is incumbent upon a Selected Addresses: NATO Conference firmative action, concern for the welfare Trustee to see that issues of our pro on the Mathematical Theory of Scatter of individual mathematicians, concern fession are seriously attended to such as: ing, Denver, 1973; Opening Lecture, over educational issues, and advocacy scarcity of jobs, educational reform, in Conference Honoring Einar Hille, La for research support for larger numbers equities due to race and sex, government guna Beach, 1980; Conference on As of mathematicians. support of research, and careful use of pects of Positivity in Functional Anal Society funds. I shall try my best. ysis, Tiibingen, Germany, 1988; Fourth Vaughan F. R. Jones Annual Korea Institute of Technology Professor, University of California, Richard W. Beals Workshop (3 lectures), Taejon, Korea, Berkeley Professor, Yale University 1989; 23rd Voronezh Winter School Born: December 31, 1952, Gisbome, Born: May 28, 1938, Erie, Pennsylva in Mathematics (3 lectures), Veronezh, New Zealand nia Russia, 1990. Ph.D.: Universite de Geneve, Switzer Ph.D.: Yale University, 1964 Additional Information: Member, In land, 1979 AMS Committees: Committee on stitute for Advanced Study, 1967-1968; AMS Committees: Committee on Steele Prizes, 1984-1987 (Chair, 1987); Sigma Xi Faculty Research Award, Tu Steele Prizes, 1992. Editorial Board, Contemporary Math lane University, 1970-1971; First An Selected Addresses: Special Session ematics, 1989- (Chair, 1990-). nual Excellence in Research Award, Fac on C*-Algebras, Reno, April 1981; In Selected Addresses: Special Session ulty of Arts and Sciences, Tulane Uni vited Address, Amherst, October 1985; on Partial Differential Equations, Min versity, 1985; Member: AMS, AWM, Special Session on Braids, Links, and neapolis, November 1973; Invited Ad- MAA, Edinburgh Mathematical Soci- Operator Algebras, Amherst, October SEPTEMBER 1992, VOLUME 39, NUMBER 7 751 ...... ··············-·············-·-······························------·--·······-····-···········--·····················-···-··························--····-·--····-·················-·-···-·········-······- Biographies of Candidates 1985; International Congress of Mathe tute on Algebraic Groups, July 1991; (4) Orleans, January 1986; Special Session maticians, 1986; Invited Address, AMS Yale Conference on Lie Algebras, April on Hopf Algebras, San Francisco, Jan Centennial, Providence, 1988; Plenary 1992. uary 1991. Address, International Congress of Math Selected Publications: 1. withE. Fried Additional Information: NSF Sum ematicians, 1990. lander, Support varieties for restricted mer Fellow, 1963-1964; NASA Fellow, Additional Information: Sloan Fellow, Lie algebras, Invent. Math. 86 (1986), 1965-1966; Visiting Positions: MIT, Vis 1983; Guggenheim Fellow, 1986; Fields 553-562. MR 88f:17018; 2. with E. iting Associate Professor, 1977-1978 Medal, 1990; Executive Committee, In Cline and L. Scott, Finite dimensional and Visiting Professor, 1989-1990; Uni ternational Association of Mathematical algebras and highest weight categories, versity of California at Berkeley, Henkin/ Physics. J. Reine Angew. Math. 391 (1988), 85- Treisman's Summer Institute Mathe Selected Publications: 1. Actions of 99. MR 90d:18005; 3. Finite dimen matics Faculty, 1990. Member: AMS, finite groups on the hyperfinite type sional algebras and algebraic groups, AWM, MAA, NAM, NCTM, SIAM, II, factor, Mem. Amer. Math. Soc. 28 Contemp. Math. 82, Amer. Math. Soc., EX. (1980), no. 237. MR 81m:46094; 2. Providence, Rl, 1989, pp. 97-114. MR Selected Publications: 1. with Mark Index for subfactors, Invent. Math. 72 90j:20091; 4. withE. Friedlander,lnduc Kon and James Young, Kernels and eq (1983), 1-25. MR84d:46097; 3.Apoly tion, deformation, and specialization of uisummation properties of uniformly el nomial invariant for knots via von Neu Lie algebra representations, Math. Ann. liptic operators, J. of Differential Equa mann algebras, Bull. Amer. Math. Soc. 290 (1991), 473-489; 5. with Jian-pan tions 67 (1987), 256-268. MR 88b: 12 (1985), 103-111. MR 86e:57006; Wang, Quantum linear groups, Mem. 35143; 2. with Charles Chui and Harvey 4. On knot invariants related to some Amer. Math. Soc. 439 (1991). MR Diamond, Interpolation by multivariate statistical mechanical models, Pacific 91g:16028. splines, Math. Comp. 51 (1988), no. J. Math. 137 (1989), 311-334. MR Statement: The American Mathemati 183, 203-218. MR 89j:41002; 3. with 89m:57005. cal Society should aim to promote math Robert Carroll, Some inverse problems Statement: With a background in func ematics in general and mathematical with spectral limitations on data, SIAM tional analysis, I am interested in the research in particular. Besides through J. Appl. Math. 48 (1988), no. 5, 1194- rich interplay between various branches its publications and meetings, it can 1205. MR 89k:35248; 4. with Philip of mathematics, physics and biology. I realize these goals in a number of im S. Hirschhorn, Coalgebraic foundations see such work as vital for the health portant ways: by providing meaningful of the method of divided differences, of mathematics, . while not failing to aid to young mathematicians in hard Adv. Math. 91(1992), no. 1, 75-135; 5. appreciate the value of singled-minded times, by strengthening contacts with with Harvey Diamond and Daniel Wil dedication to a difficult problem in a other sciences, by aggressively influenc iams, Box-spline-based approach to the specific area. ing funding agencies (and by coming up formulation of numerical methods for with new sources of money), and by ed partial differential equations, Numer. Brian ]. Parshall ucating the public on the importance of Methods Partial Differential Equations Professor of Mathematics, University of mathematics in society. If elected to the 8 (1992), 291-301. Virginia Nominating Committee, I will support Statement: I will recommend the best Born: October 28, 1945 in Penn Yan, people with these objectives in mind. qualified mathematicians, with special New York care to promote the candidacies of Ph.D.: Yale University, 1971 Louise A. Raphael women and minorities for AMS of AMS Committees: Committee on Sum Professor, Howard University fices, council, committees, and boards mer Institutes and Special Symposia, Born: October 24, 1937, New York, in order to ensure that the AMS has the 1989- ; Chair, Committee on Summer NY benefit of the best mathematical talent Institutes and Special Symposia, 1991- Ph.D.: Catholic University, 1967 and wisdom of all its members. 1993. AMS Committees: AMS-MAA-SIAM Selected Addresses: Invited Address, Congressional Science Fellowship Se Yum-Tong Siu Michigan State University, March 1988; lection Panel, 1985-1986; Liaison Com Professor, Harvard University Special Session on Quantum Groups and mittee on Education in Mathematics, Born: May 6, 1943, Canton, China Finite Dimensional Algebras, Penn State 1989- ; Liaison Committee with AAAS, Ph.D.: Princeton University, 1966 University, April1990. 1992-. AMS Committees: Committee to Se Additional Information: Organizing Selected Addresses: Special Session lect Hours Speakers for Eastern Section Committees: (1) AMS Summer Re on Summability and Related Topics, Meetings, 1983-1984. search Conference on Finite and Alge Biloxi, January 1979 and Cincinnati, Selected Addresses: International Con braic Groups: Modular Representations January 1982; Special Session on Par gress of Mathematicians, Helsinki, 1978 and Cohomology, Arcata, July 1989; tial Differential Equations, Theory and and Warsaw, 1983. Invited Address, At (2) MSRI Workshop on Representation Application, San Luis Obispo, Novem lanta, January 1978; CBMS Regional Theory of Reductive Groups, November ber 1983; Special Session on Analytic Conference, Charleston, lllinois, August 1990; (3) AMS Summer Research Insti- Methods in Differential Equations, New 1988. 752 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ········-·································--~·-····-························-·········-························. ·------····-·Biographies of Candidates Additional Information: Sloan Fellow, Selected Addresses: Invited Address, This must be done without enlarging the 1971-1973; Gauss Professor, Gottingen Bryn Mawr, March 1982; Special Ses Society's bureaucracy and without mak Academy of Sciences, 1980; Chair, Or sion on Geometry and Analysis on CR ing the Society increasingly impersonal. ganizing Committees: Symposium on Manifolds, Salt Lake City, August 1987; I would try to find candidates who reflect Several Complex Variables, Madison, Summer Research Institute on Several the diversity of the Society's member April 1982; Summer Research Confer Complex Variables, Santa Cruz, July ship, who have a broad view of mathe ence on Complex Differential Geom 1989; MAA Invited Address, Boulder, matics, and who have the creativity to etry and Nonlinear Differential Equa August 1989; Summer Research Insti help the Society meet its goals. In par tions, Brunswick, August 1984; Mem tute on Differential Geometry, Los An ticular, candidates should be sensitive ber, Committee on Mathematics, Na geles, July 1990. to critical issues involving mathemat tional Academy of Sciences, 1985; Gug Additional Information: Member, In ics research and support for research, genheim Fellow, 1985-1986; Chair, Panel stitute for Advanced Study, 1979-1980; mathematics education, employment for to Select Speakers for the Complex Sloan Fellow, 1981-1985; Visitor, In mathematicians, increased participation Analysis Section of the International stitut des Hautes Etudes Scientifiques, of underrepresented groups, and public Congress of Mathematicians, 1986; Ed 1982-1983; Gastprofessor, Max Planck awareness of mathematics. itor: Journal of Differential Geometry, Institut fur Mathematik, 1983; Organiz 1986-1989. ing Committee, Symposium on Pseu Selected Publications: 1. A Hartogs dodifferential Operators and Fourier In Editorial Boards Committee type extension theorem for coherent an tegral Operators with Applications to Bryan ]. Birch alytic sheaves, Ann. of Math. (2) 93 Partial Differential Equations, Notre Professor, University of Oxford (1971), 166-188. MR 43 #5064; 2. Dame, April 1984; AMS Representa Born: September 25, 1931, Burton-on Analyticity of sets associated to Le tive, Evaluation Panel for NSF Postdoc Trent, England long numbers and the extension of toral Research Fellowships, 1984-1990 Ph.D.: Cambridge University, 1957 closed positive currents, Invent. Math. (AMS Representative, Executive Com Selected Addresses: Symposium on 27 (1974), 53-156; 3. The complex mittee, 1990); NSF Ad Hoc Panel on Number Theory, Pasadena, November analyticity of harmonic maps and the Quick Response Research Grants, 1989; 1963; International Congress of Mathe strong rigidity of compact Kaehler man MAA Representative, Selection Panel maticians, Moscow 1963. ifolds, Ann. of Math. (2) 112 (1980), for Presidential Awards for Excellence Additional Information: Delegate of 73-111. MR 81j:53061; 4. Every K3 in Science and Mathematics Teaching, Oxford University Press; EditorofTopol surface is Kaehler, Invent. Math. 73 1990; Member: AMS, AWM, MAA, ogy; Formerly on editorial boards of ln (1983), 139-150. MR 84j:32036; 5. NCTM. ventiones Mathematicae, of the Journal Global nondeformability of the com Selected Publications: 1. with David of Number Theory, and of the journals plex projective space, (Proc. the 25th S. Tartakoff, The heat equation for the of the London Mathematical Society; Taniguchi Colloquium in Katata, Japan, Db-Laplacian, Comm. Partial Differen Fellow of the Royal Society; Member: 1989), J. Noguchi and T. Ohsawa (Edi tial Equations 9 (1984), 597-686. MR AMS, the Fachbeirat of the Max-Planck tors), Lecture Notes in Math., vol. 1468, 85f:58114; 2. with Richard Beals and Institut in Bonn, and the Beirat of the Springer, Berlin-New York, 1991, pp. Peter C. Greiner, The heat equation on Institut fiir Experimentelle Mathematik 254-280. a CR manifold, J. Differential Geom. in Essen. 20 (1984), 343-387. MR 86g:58135; Selected Publications: 1. Forms in Nancy K. Stanton 3. with Richard Beals, The heat equa many variables, Proc. Royal Soc. Ser. A Professor, University of Notre Dame tion for the 8-Neumann problem. I. 265 (1962), 245-263. MR 27 #132; 2. Born: March 23, 1948, San Francisco, Comm. Partial Differential Equations with H.P.F. Swinnerton-Dyer, Notes on California 12 (1987), 351-413. MR 89b:58199; II. elliptic curves, I. J. Reine Angew. Math. Ph.D.: Massachusetts Institute of Tech Canadian J. Math. 40 (1988), 502-512. 212 (1963), 7-25. MR 26 #3669; 3. with nology, 1973 MR 89e:58112; 4. A normal form for H.P.F. Swinnerton-Dyer, Notes on ellip AMS Committees: Committee to Se rigid hypersurfaces in C 2 , American J. tic curves. II. J. Reine Angew. Math. 218 lect Hour Speakers for Central Sec Math. 113 (1991), 877-910; 5. Infinites (1965), 79-108. MR31 #3419; 4. edited tionMeetings, 1986-1987 (Chair, 1987); imal CR automorphisms of rigid hyper with W. Kuyk, Modular Functions of Committee on Research Fellowships, suifaces in C2, J. Geometric Analysis 1 One Variable. IV. Lecture Notes in 1987-1988; Notices Editorial Commit (1991), 231-267. Math., vol. 476, Springer-Verlag, Berlin tee, 1987-1990; Program Committee Statement: The mission of the AMS is New York, 1975. MR51 #12708; 5. with for National Meetings, 1991- (Chair, "to further the interests of mathematical N. M. Stephens, Computation of Heeg 1992); AMS-MAA Joint Program Com research and scholarship," broadly con ner Points, Modular Forms (Durham mittee for the 1992 Baltimore Meeting, strued. The recent report of the Strategic Symposium, 1983), pp. 13-41, Ellis 1991 (Chair); AMS-CMS Joint Program Planning Task Force articulates a broad Horwood Ser. Math. Appl.: Statist. Oper. Committee, 1991- ; Ad Hoc Meetings vision of the goals of the AMS in fulfill Res., Horwood, Chichester, 1984. MR Committee, 1992. ing its mission over the next few years. 87f: 11036a. SEPTEMBER 1992, VOLUME 39, NUMBER 7 753 Biographies of Candidates Statement: As mathematicians, we are making crucial contributions throughout linear Partial Differential Equations, San fortunate that our community is an in the whole spectrum of this development. Antonio, January 1976; Special Sessions ternational one, in which cooperation The AMS, as the major organization for on Partial Differential Equations, Albu has always been possible; and we must fostering mathematics research, has a querque, November 1976 and Madison, be glad that collaboration has become special resposibility to maximize the April 1982; International Congress of easier. impact of mathematicians and to attract Mathematicians, 1978; Invited Address, the best talent, including, in particular, Kent, November 1979; Colloquium Lec Fan R. K. Chung women and minorities. The publication tures, Eugene, August 1984. Bellcore Fellow, Visiting Professor at program of the AMS is a primary vehicle Additional Information: Guggenheim Harvard University by which it serves its members as well Fellow, 1978; Member: AMS. Born: October 9, 1949, Taiwan as the world mathematical community. Ph.D.: University of Pennsylvania, It is therefore important that editorial 1974 boards of the AMS journals reflect the Masamichi Takesaki Offices: Member-at-Large of the Coun broad spectrum of AMS members and Professor ofMathematics, University of cil, 1989-1992. their interests. California, Los Angeles AMS Committees: AMS-IMS-SIAM Born: July 18, 1933, Sendai, Japan Committee on Joint Summer Research Ph.D.: Tohoku University, 1965 Conferences in the Mathematical Sci Paul H. Rabinowitz Selected Addresses: International Con ences, 1990-. Professor, University of Wisconsin, gress of Mathematicians, Nice, 1970; Selected Addresses: Invited Address, Madison Invited Address, San Francisco, January First China-USA Graph Theory Confer Born: November 15, 1939, Newark, 1982; Principal Lecturer, CBMS Re ence, Jinan, China 1986; Invited Ad New Jersey gional Conference, University of Iowa, dress, Second Japan Conference on Ph.D.: New York University, 1966 April 1982; Summer Research Institute Graph Theory, Combinatorics and Com AMS Committees: Transactions and on Operator Theory/Operator Algebras puting, Hakone, Japan 1986; AMS Memoirs Editorial Committee, 1980- and Applications, Durham, July 1988. MAA Invited Address, Orono, August 1983; Committee on Postdoctoral Fel Additional Information: Sakkokai Fel 1991; Invited Address, Washington, DC, lowships, 1981-1983; Committee on low, 1964-1967; Guggenheim Fellow, April1993. the .1983 AMS-SIAM Summer Insti 1973-1974; Fujiwara Prize, June, 1990; Additional Information: Allendoerfer tute on Nonlinear Functional Analy Member: AMS, International Associa Award, 1990. sis and its Applications; AMS-MAA tion of Mathematical Physics; Mathe Selected Publications: 1. Diameters Joint Committee for the New Orleans matical Society of Japan. and eigenvalues, J. Amer. Math. Soc. Meeting, 1986; Committee on Com Selected Publications: 1. Tomita's the 2 (1989), 187-196. MR 89k:05070; 2. mittees, 1986-1988; Program Commit ory of modular Hilbert algebras and its Sphere-and-point incidence relations in tee for National Meetings, 1986-1988 applications, Lecture Notes in Math., high dimensions with applications to (Chair, 1987-1988); AMS-MAA Joint vol. 128, Springer-Verlag, Berlin-New unit distances and furthest neighbor Program Committee for the Atlanta York, 1970. MR 42 #5061; 2. Duality pairs, Discrete Comput. Geom. 4 (1989), Meeting, 1987; AMS-MAA Joint Pro for crossed products and the structure 183-190. MR 90g:52011; 3. Universal gram Committee for the Salt Lake City of von Neumann algebras of type Ill, graphs and induced-universal graphs, J. Meeting, 1987 (Chair); Journal of the Acta Math. 131 (1973), 249-310. MR Graph Theory 14 (1990), 443-454; 4. AMS Editorial Committee (Associate 55 #11068; 3. with A. Cannes, The with Ronald Graham, Quasi-random set Editor), 1987-1991; Committee on the flow of weights on factors of Type Ill, systems, J. Amer. Math. Soc. 4 (1991), Internal Organization of the American Tohoku Math. J. 29 (1977), 473-575. 151-196. MR91m:05138; 5. Construct Mathematical Society, 1988; Commit MR 82a:46069a; 4. Theory of opera ing random-like graphs, Proc. Sympos. tee on Summer Institutes and Special tor algebras. I. Springer-Verlag, New Appl. Math., vol. 44, Amer. Math. Soc., Symposia, 1988-1989; Committee on York-Heidelberg, 1979. MR 81e:46038; Providence, RI, pp. 21-56. Progress in Mathematics, 1989-1990. 5. Structure of factors and automor Statement: We are today in the midst of Selected Addresses: Special Session phism groups, CBMS Regional Con a technological revolution. Mathematics on Nonlinear Functional Analysis, St. ference Series in Mathematics, vol. 51, will play a vital role both in laying Louis, April 1975; Special Session on Amer. Math. Soc., Providence, Rl, 1983. the foundation for this process and in Functional Analytical Methods for Non- MR 84k:46043. 754 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Dayton, Ohio Wright State University October 30-November 1, 1992 Second Announcement The eight-hundred-and-seventy-sixth meeting of the Ameri Differential and integral equations, Muhammad N. Is can Mathematical Society (AMS) will be held at Wright State lam, University of Dayton, and Lawrence Turyn, Wright University, Dayton, Ohio, on Friday, October 30, Saturday State University. October 31, and Sunday, November 1, 1992. Invited addresses Knots and topological quantum field theory, Louis H. will be in the auditorium of the Medical Sciences Building; Kauftinan. sessions will be held in the Russ Engineering Center and in Riccatti equations and transport theory, Hendrik J. Rik:e Hall. Kuiper, Arizona State University, and Tapas Mazumdar, Wright State University. Invited Addresses Topology of affine hypersutfaces and related number theory, Anatoly S. Libgober, University of Illinois at By invitation of the Central Section Program Committee, Chicago, and Steven Sperber, University of Minnesota, there will be four invited one-hour addresses. The speakers, Minneapolis. their affiliations, and the titles of their talks are: Set-theoretic topology, Joe D. Mashburn, University of Martin Golubitsky, University of Houston, Symmetry Dayton. and chaos. Function theory, C. David Minda, University of Cincin Jonathan I. Hall, Michigan State University, Finite nati. methods in infinite groups and discrete geometries. Abstracts for consideration for these sessions should have Louis H. Kauftinan, University of illinois at Chicago, been submitted by the July 13, 1992 deadline. This deadline From knots to quantum field theory and back. was previously published in the Calendar of AMS Meetings J. Toby Stafford, University of Michigan, Ann Arbor, and Conferences and in the Invited Speakers and Special Noncommutative graded algebras and projective geometry. Sessions section of the Notices. Special Sessions Contributed Papers By invitation of the same committee, there will be twelve There will also be sessions for contributed ten-minute papers. special sessions of selected twenty-minute papers. The topics Abstracts for consideration of these sessions should have of these sessions, and the names and affiliations of the been submitted by the August 3, 1992 deadline previously organizers, are as follows: published in the Calendar of AMS Meetings and Conferences. Hyperbolic manifolds, Colin C. Adams, Williams Col Late papers will not be accommodated. lege, and Ara S. Basmajian, University of Oklahoma. Quantum groups and regular algebras, Carolyn A. Dean, Registration University of Michigan, Ann Arbor, Timothy J. Hodges, University of Cincinnati, and J. Toby Stafford. The meeting registration desk will be located in the first Operator theory and operator algebras, Joanne M. Dom floor lobby of the Russ Engineering Center. The registration browski and Richard Mercer, Wright State University. desk will be open from 12:30 p.m. to 5:00 p.m. on Friday, Combinatorics and graph theory, Anthony B. Evans and October 30; and 8:00 a.m to 3:00 p.m. on Saturday, October Terry A. McKee, Wright State University. 31. The registration fees are $30 for members of the AMS, Groups and geometries, Daniel E. Frohardt, Wayne State $45 for nonmembers, and $10 for students or unemployed University. mathematicians. Control theory and partial differential equations, Lop Accommodations Fat Ho, Wright State University, Srdjan D. Stojanovic, University of Cincinnati, and Thomas Svobody, Wright State Rooms have been blocked for participants at the Holiday Inn University. (Fairborn I-165 location), Homewood Suites, and the Red SEPTEMBER 1992, VOLUME 39, NUMBER 7 755 ...... _. ______...... - ...... ,_. ., ..•.....•...... •....•.. _...... _...... __ ...... ______Meetings Roof Inn (Fairborn location), located just south of the street for breakfast, lunch, and dinner on Friday. October 30, and (Colonel Glenn Highway) that borders the south edge of the for brunch and dinner on Saturday, October 31 and Sunday, Wright State Campus. Rooms have also been blocked at the November 1. Several restaurants and fast food establishments Ramada Inn (Fairborn location), and the Comfort Inn Wright are located adjacent to the Wright S~te campus. Some of Patterson in central Fairborn. Participants should make their these are convenient to the buildings in which the meeting own arrangements with the hotel of their choice and ask for will be held; others are close to the Holiday Inn Fairborn, the the AMS conference rate. Homewood Suites, or the Red Roof Inn-Fairborn. Likewise, Fairborn is a suburb of Dayton and most lodgings are other restaurants and fast food establishments are located in chains with other locations in the metropolitan Dayton area. downtown Fairborn, near the Comfort Inn Wright-Patterson Thus, participants are advised to verify the street address of or the Ramada Inn. the lodging when making reservations. All rates are subject to a twelve percent tax. The AMS is not responsible for rate Parking changes or the quality of the accommodations offered by these hotels/motels. Free parking will be available to participants throughout the meeting. On the afternoon of Friday, October 30, participants Comfort Inn Wright-Patterson (5 miles from Russ Engi neering Center) should park in the PE Lot located southwest of the Russ Engi neering Center. From Friday night through Sunday afternoon, 616 North Broad Street, Fairborn, OH 45324 participants may park in essentially all campus lots (excepting Telephone: 513-879-7666 or 800-245-3127 those spaces marked as reserved). The most convenient will The deadline for reservations is October 16, 1992. be FW Lot, Health Sciences Lot, Biological Sciences Lot,. Single $39 Double $43 Rike Lot, Visitor Lot, Allyn Lot, and PE Lot. These lots are shown on the campus map, as are the buildings in which the Holiday Inn Fairborn 1-675 (0.4 miles from Russ Engi neering Center) sessions will be held: Russ Engineering Center (RC on the map), Rike Hall (R), and Medical Sciences Building (MS). 2800 Presidential Drive, Fairborn, OH 45324 Telephone: 513-426-7800 or 800-465-4329 The deadline for reservations is October 9, 1992. Travel and Local Information Flat rate $63 up to four occupants Please note: The previously published rate was incorrect. Arriving by air: Dayton International Airport is served by We regret any inconvenience this may have caused. several major airlines. Car rental agencies are located in the airport terminal. Ground transportation is available by Homewood Suites (0.5 miles from Russ Engineering Cen Dayton Yellow Cab (513-228-1155) and Charter Vans, Inc. ter) (513-898-4043 or 898-7171). The airport is approximately a 2750 Presidential Drive, Fairborn, OH 45324 thirty-minute drive from the campus. Rental car companies Telephone: 513-429-0600 or 800-225-5466 are located in the airport terminal. The deadline for reservations is October 9, 1992. Arriving by car: The principal highways through the Flat rate $69 Dayton metropolitan area are 1-70, 1-75, and US Route 35. Suite with king bed, sleeper sofa (four occupants) Participants arriving from the north of Dayton on 1-75 should take 1-75 South to 1-70 East, then Ohio Route 4 South to Ohio Ramada Inn (5 miles from Russ Engineering Center) Route 444 North to Kauffman Avenue. 800 North Broad Street, Fairborn, OH 45324 Participants arriving from south of Dayton on 1-75 should Telephone: 513-879-3920 or 800-272-6232 take 1-75 North to 1-675 North and exit at the North Fairfield The deadline for reservations is October 16, 1992. Road exit (exit 17). Tum left on North Fairfield and left on Single or double occupancy $42 Colonel Glenn Highway. (Alternatively, at exit 17 one may take 444A and follow it to the Wright State exit). Red Roof Inn - Fairborn, #205 (.7 miles from Russ Participants arriving from east of Dayton on 1-70 should Engineering Center) take 1-70 West to 1-675 South and exit at North Fairfield Road 2580 Colonel Glenn Highway, Fairborn, OH 45324 (exit 17); Tum right on North Fairfield and left on Colonel Telephone: 513-426-6116 or 800-874-9000 Glenn Highway. The deadline for reservations is October 20, 1992 Participants arriving from east of Dayton on US 35 should When making reservations partcipants should mention the take US 35 West and exit onto 1-675 North. On 1-675 North, following confirmation number: 205AA92304. exit at the North Fairfield Road exit (exit 17) and tum Single $35.99 Double $42.99 Triple $45.99 left on North Fairfield and left on Colonel Glenn Highway. (Alternatively, at exit 17 one may take 444A and follow it to the Wright State exit). Food Service Participants arriving from west of Dayton on 1-70 should The cafeteria in the University Center (a convenient walk from take 1-70 East to Ohio Route 4 South to Ohio Route 444 North the buildings in which the meeting will held) will be open to Kauffman Avenue. 756 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings Participants arriving from west of Dayton on US 35 should is the United States Air Force Museum, approximately a ten take US 35 East to 1-675 North to the North Fairfield Road minute drive from campus. This is the largest military aviation ~YXit (exit 17). Tum left on North Fairfield and left on Colonel museum in the world. Admission is free. The museum is open Glenn Highway. (Alternatively, at exit 17 one may take 444A from 9:00a.m. to 5:00p.m. every day. Exhibits include about and follow it to the Wright State exit). two hundred aircraft and missiles, many other displays of Ohio Route 4 may be under construction when this meeting related historical artifacts, and free documentary films. For occurs. Therefore, participants arriving by car from north of a $4 admission, one can also view films in the huge-screen Dayton on 1-75 or from west of Dayton on 1-70 should be IMAX Theater. Rounding out the facility are a book shop, gift prepared to alter the directions above as follows: follow 1-70 store, and cafe. East; skip the exit at Ohio Route 4 and continue on 1-70 East to 1-675 South and exit at North Fairfield Road (exit 17). Turn Andy R. Magid right on North Fairfield and left on Colonel Glenn Highway. Associate Secretary Norman, Oklahoma Weather and Local Attractions The average temperatures in Dayton for early November are 57-58°F (high) and 38-39°F (low). The closest local attraction 0 [!]p MS Medical Sciences R Rike Hall RC Russ Engineering Center PE SEPTEMBER 1992, VOLUME 39, NUMBER 7 757 Los Angeles, California University of Southern California November 7-8, 1992 Second Announcement The eight-hundred-and-seventy-seventh meeting of the Amer Topics in geometry and physics, Robert C. Penner, ican Mathematical Society (AMS) will be held at the Uni University of Southern California, and Edward Witten, versity of Southern California (USC) on Saturday, November School of Natural Science, lAS. 7, and Sunday, November 8, 1992. This meeting will take Nonlinear hyperbolic PDE and fluid mechanics, Gustavo place concurrently with a meeting of the Southern California Ponce, University of California, Santa Barabara, and Thomas section .of the Mathematical Association of America (MAA). C. Sideris. The invited addresses will be held in the Seeley G. Mudd Abstracts for consideration for these sessions should have Building, one block east of the Denny Building, and most been submitted by the July 13, 1992 deadline. This deadline other sessions will be held in Kaprielian Hall, north across was previously published in the Calendar of AMS Meetings 36th Place from the Denny Building. and Conferences and in the Invited Speakers and Special Sessions section of the Notices. Invited Addresses Contributed Papers By invitation of the Western Section Program Committee, There will also be sessions for contributed ten-minute papers. there will be three invited addresses. The speakers, their affiliations, and the titles of their talks are: Abstracts for consideration of these sessions should have been submitted by the August 3, 1992 deadline previously Robert L. Lazarsfeld, University of California, Los published in the Calendar of AMS Meetings and Conferences. Angeles, Syzygies of algebraic varieties. Late papers will not be accommodated. Tomasz S. Mrowka, California Institute of Technology, Gauge theory and embedded surfaces. Thomas C. Sideris, University of California, Santa Bar Registration bara, The life span of 3D compressible and incompressible flow. The meeting registration desk will be located in the lobby of the Denny Research Center, on the southeast corner of Vermont Avenue and 36th Place, and will be open on Special Sessions Saturday, November 7, from 7:30 a.m. to 5:00p.m. and on By invitation of the same committee, there will be eight special Sunday, November 8, from 7:30a.m. to noon. The registration sessions of selected twenty-minute papers. The topics of these fees are $30 for members of the AMS, $45 for nonmembers, sessions, and the names and affiliations of the organizers, are and $10 for students or unemployed mathematicians. as follows: Finite and algebraic groups, Michael Aschbacher, Cali Accommodations fornia Institute of Technology, Robert M. Guralnick, Univer sity of Southern California, and David B. Wales, California Rooms have been blocked for participants at the University Institute of Technology. Hilton hotel located across from the university on Figueroa Spectral Geometry, Robert Brooks, University of South Street at Exposition Boulevard. Participants should make their ern California, and Peter A. Perry, University of Kentucky. own reservations directly with the hotel, and participation in Hyperbolic geometry, Francis Bonahon and Robert the AMS-MAA meeting should be mentioned to receive the Meyerhoff, University of Southern California. special rates quoted below. The AMS is not responsible for Algebraic and complex geometry, Lawrence Ein, Univer rate changes or the quality of the accommodations offered sity of lllinois at Chicago. by these hotels/motels. Dynamical systems, Eugene Gutkin and Nicolai T. A. University Hilton Haydan, University of Southern California. 3540 South Fugueroa Street Gauge theory and four manifolds, Tomasz S. Mrowka. Los Angeles, CA 90007 758 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings Telephone: 213-748-4141 (10) and the Harbor Freeway (110). Shuttle service is readily 800-244-7331 (within California) available from the Los Angeles International Airport to the 800-872-1104 (outside California) campus. The fare for the "Super Shuttle" (limo service) from the airport to the University Hilton is $12 per person, each Single $70 Double $75 way. To reach the campus by car, exit the Harbor Freeway (110) at Exposition Boulevard. The Hilton is on the right at Figueroa Street, and Main Entrance I to the university Food Service is approximately one-quarter mile farther down Exposition On campus facilities include the Commons Cafeteria, located Boulevard, at Hoover Street. in the Commons Building, open on Saturday from 9:00 a.m. to 5:00 p.m.; Carl's Junior, located south of the Commons Weather and Local Information Building, open on Saturday from 9:00a.m. to 5:00p.m. and on Sunday from 11:00 a.m. to 5:00 p.m.; and Cafe 84, located The average high temperature in Los Angeles in the month of in the Frank L. King Hall, open on Saturday from 11:00 a.m November is 73°F, and the average low temperature is 52°F. to 8:00p.m., and on Sunday froin 11:00 a.m. to 11:00 p.m. Rain is possible, but not very likely. Hot weather of approxi Cafe 84 has a soup, sandwich, and salad bar, as well as a mately 90°F is also possible at this time of year. The city of grill, pizza, pasta, pastries, and ice cream. In addition to the Los Angeles and the surrounding area have many worthwhile restaurant in the University Hilton, several chains have outlets museums and other interesting attractions. Those closest to on Figueroa Street. campus are the Los Angeles County Museum of Science and Industry, and the Museum of Natural History located Parking directly opposite the campus, across Exposition Boulevard. The Natural History Museum has recently opened the third Parking permits are required and cost $5 per day. Participants largest live insect zoo in the nation, and also has a Discovery should park in Parking Structure A and note that the west end Center of hands-on exhibits for children. The Science and of Structure A is closest to the registration area. There are Industry Museum runs IMAX theater presentations. Use of stairwells at each comer of the building, although the only the pool and gym at the Lyon University Center is possible by elevator in Structure A is at the northeast comer. presenting a meeting badge and a $5 entry fee. Lance W. Small Travel Associate Secretary The campus is located about four miles south of downtown Los La Jolla, California Angeles near the intersection of the Santa Monica Freeway Journal of the American Mathematical Society When the Journal of the American Mathematical Society first appeared in 1988, it gained instant respect for its careful selection of relevant, important, and timely research. The editors are devoted to publishing research articles of the highest quality in all areas of pure and applied mathematics. Editors of this journal include: H. Blaine Lawson, Jr., Robert D. MacPherson, Richard Melrose, Andrew Odlyzko, and Wilfried Schmid. 1993 Subscription Prices List $144*, Institutional member $115*, Individual member $86* (ISSN 0894-0347) Back volumes are also available. Call AMS Customer Services for prices. *Add for postage: Surface delivery to destinations outside the U.S. and India- $8; to India- $18. Expedited delivery to destinations in North America- $13; elsewhere- $36. A 10% late charge applies. All prices subject to change. Prepayment required. Order from: American Mathematical Society, P.O. Box 1571, Annex Station, Providence, RI 02901-1571, or call toll free 800-321-4AMS in the continental U.S. and Canada to charge with VISA or MasterCard. Canada residents, please include 7% GST. SEPTEMBER 1992, VOLUME 39, NUMBER 7 759 Invited Addresses and Special Sessions Invited Addresses Dekalb, IL, May 1993 at AMS Meetings Susan J. Friedlander Clark Robinson The individuals listed below have accepted invitations to Russell D. Lyons address the Society at the times and places indicated. For some meetings, the list of speakers is incomplete. Invited addresses Vancouver, British Columbia, Canada at Sectional Meetings are selected by the Section Program August 1993 Committee, usually twelve to eighteen months in advance Louis Nirenberg (AMS-CMS) Jill Pipher (AMS-CMS) of a meeting. Members wishing to nominate candidates for invited addresses should send the relevant information to the Associate Secretary for the Section who will forward it to the College Station, TX, October 1993 Section Program Committee. Steven P. Lalley Stephan A. Stolz Gilles Pisier Dayton, OH, October 1992 Organizers and Topics Please see the second announcement of this meeting elsewhere in this issue. of Special Sessions The list below contains all the information about Special Sessions at meetings of the Society available at the time this Los Angeles, CA, November 1992 issue of the Notices went to the printer. The section below Please see the second announcement of this meeting elsewhere entitled Information for Organizers describes the timetable in this issue. for announcing the existence of Special Sessions. October 1992 Meeting in Dayton, Ohio San Antonio, TX, January 1993 Central Section Associate Secretary: Andy R. Magid George E. Andrews Robert Osserman Deadline for organizers: Expired (AMS-MAA) (AMS-MAA) Deadline for consideration: R-rpired Richard A. Brualdi Charles S. Peskin Please see the second announcement of this meeting elsewhere (AMS-MAA) (Gibbs Lecture) in this issue. Luis A. Caffarelli Bernd Sturmfels (Colloquium Lectures) Leon Takhtajan Jim Douglas, Jr. Alexander Varchenko November 1992 Meeting in Los Angeles, California Carolyn S. Gordon Mary E Wheeler Western Section Associate Secretary: Lance W. Small Wu-Yi Hsiang (AMS-MAA) Deadline for organizers: Expired Deadline for consideration: fupired Please see the second announcement of this meeting elsewhere Knoxville, TN, March 1993 in this issue. Paul R. Blanchard Richard A. Tapia Olav Kallenberg Michelle L. Wachs January 1993 Meeting in San Antonio, Texas Associate Secretary: W. Wistar Comfort Deadline for organizers: Rwired Washington, DC, Apri/1993 Deadline for consideration: September 17, 1992 Fan R. K. Chung Joel Sprock Kathleen T. Alligood and Judy A. Kennedy, Continuum theory Leopold Flatto A. Zamolodchikov and dynamical systems 760 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Thomas Archibald and Victor Katz, History of mathematics Tim Kelley, Numerical methods in optimization Alvaro Arias, Banach space theory John C. Mayer, Continua theory and dynamical systems Charles E. Aull, History of general topology Balram S. Rajput and Jan Rosinski, Stochastic processes Melvyn S. Berger and Daniel Goroff, Small divisor problems Michelle L. Wachs, Algebraic combinatorics in nonlinear analysis Scott T. Chapman, Commutative algebra April1993 Meeting in Salt Lake City, Utah William J. Coles and B. A. Fusaro, Environmental modeling Western Section David Cox and Bernd Sturmfels, Combinatorial methods in Associate Secretary: Lance W. Small computational algebraic geometry Deadline for organi::ers: Expired Deadline for consideration: January 6. 1993 Raul E. Curto and David R. Larson, Operator theory and triangular operator algebras Michael R. Darnel, Ordered algebraic structures April1993 Meeting in Washington, DC Eastern Section RobertS. Doran, C*-algebras: 1943-1993 (a 50-year cele Associate Secretary: bration) W. Wistar Comfort (until1131193) Ed Dubinsky, The state of research in undergraduate mathe Lesley M. Sibner (after 1131193) matics education: problems and prospects (AMS-MAA) Deadline for organi::ers: Expired Krishan L. Duggal, Differential geometry Deadline for consideration: January 6, 1993 Saber N. E1aydi, John R. Graef, and William F. Trench, Roy L. Adler and Leopold Flatto, Geodesic flows, hyperbolic Stability and asymptotic behavior of difference equations geometry, and symbolic dynamics Dennis R. Estes and Donald James, Quadratic forms Joseph A. Ball and Cora S. Sadosky, Dilation and intelpola Naomi Fisher, Harvey B. Keynes, and Philip D. Wagreich, tion: operator theoretic methods Mathematics and education reform (AMS-MAA) John J. Benedetto and Rodney B. Kerby, Wavelets in sampling Robin Forman and John E. Luecke, Topology and geometry theory and signal processing Dennis DeTurck and Carolyn S. Gordon, Eigenvalues in Joseph E. Bonin, Geometric methods in combinatorics Riemannian geometry Nathaniel Dean, Graph theory Morris W. Hirsch and Halbert White, Dynamics and compu Edward Frenkel, Mathematical physics tation in neural networks Anant P. Godbole and Gary J. Sherman, Undergraduate Hans A. Koch, Rafael de la Llave, and Charles Radin, research in applied mathematics Dynamics of systems with infinitely many degrees of Anant P. Godbole and Gary J. Sherman, Undergraduate freedom research in pure mathematics Xinzhi Liu and Seenith Sivasundaram, Integro-differential Valentina S. Harizanov and James C. Owings, Pure and equations: stability and control applied recursion theory David E. Marker and Philip H. Scowcroft, Model theory and Kevin G. Hockett and E. Arthur Robinson, Ergodic theory, algebra dynamical systems, and applications John E. McCarthy, Holomorphic spaces Yongwu Rong, Low dimensional topology Alec Norton and Mary Lou Zeeman, Low dimensional geo Joel Spruck, Nonlinear elliptic problems in geometry and metric dynamical systems physics L. Alayne Parson and Mark Sheingorn, Modular forms and related topics May 1993 Meeting in DeKalb, Illinois Nikolay Reshetikhin, Leon Takhtajan, and Alexander Var Central Section chenko, Quantum groups Associate Secretary: Andy R. Magid Deadline for organizers: Expired Deadline for consideration: February 3, 1993 March 1993 Meeting in Knoxville, Tennessee Michael A. Filaseta, Number theory Southeastern Section Susan J. Friedlander, Mathematical topics in fluid dynamics Associate Secretary: Joseph A. Cima (until1/31/93) Zoltan Furedi, Combinatorics Robert J. Daverman (after 1/31193) Andrew J. Granville, Analytic number theory Deadline for organizers: Expired Frank Harary, Beautiful graph theory Deadline for consideration: December 15, 1992 Mohsen Pourahmadi, Stochastic processes David F. Anderson and David E. Dobbs, Commutative ring Linda R. Sons, Function theory theory Joel H. Spencer, Probabilistic methods Bettye Anne Case, Interventions to assure success: calculus Peter Weaterman, Discrete groups through junior faculty Ben G. Fitzpatrick and Suzanne M. Lenhart, Optimal control August 1993 Meeting in Vancouver, and applications British Columbia, Canada Alexandre S. Freire, Variational problems in geometry Associate Secretary: Lance W. Small Don B. Hinton and Kenneth Shaw, Sturm-Liouville operators, Deadline for organi::ers: November 11, 1992 applications, and extensions Deadline for consideration: April 27, 1993 SEPTEMBER 1992, VOLUME 39, NUMBER 7 761 --··-·----··-···--·-·-······-····-·-·······-····-·-····--·-····-··-···---·········-···-·············------·················-············-······················-···················-···-·········-··-·····-·······-········-·····--··· Invited Addresses and Special Sessions September 1993 Meeting in Syracuse, New York January 1995 Meeting in Denver, Colorado Eastern Section Associate Secretary: Andy R. Magid Associate Secretary: Lesley M. Sibner Deadline for organizers: April 20, 1994 Deadline for organizers: December 17, 1992 Deadline for consideration: To be announced Deadline for consideration: April 27, 1993 October 1993 Meeting in Heidelberg, Germany March 1995 Meeting in Chicago, Illinois (Joint Meeting with the Deutsche Central Section Mathematiker-Vereinigung e. V.) Associate Secretary: Andy R. Magid Deadline for organizers: June 24, 1994 Associate Secretary: Robert M. Fossum Deadline for consideration: To be announced Deadline for organizers: December 23, 1992 Deadline for consideration: April 27, 1993 October 1993 Meeting in College Station~ Texas January 1996 Meeting in Orlando, Florida Central Section Associate Secretary: Lance W. Small Associate Secretary: Andy R. Magid Deadline for organizers: April 12, 1995 Deadline for organizers: January 22, 1993 Deadline for consideration: To be announced Deadline for consideration: July 14, 1993 Randall K. Campbell-Wright, Carl C. Cowen, and Barbara D. MacCluer, Composition operators on spaces of analytic March 1996 Meeting in Iowa City, Iowa functions Central. Section David R. Larson, Non self adjoint operator algebras Associate Secretary: Andy R. Magid Deadline for organizers: June 22, 1995 Efton L. Park, Noncommutative differential geometry Deadline for consideration: To be announced Sung Yell Song and Paul M. Terwilliger, Algebraic combina torics Information for Organizers January 1994 Meeting in Cincinnati, Ohio Special Sessions at Annual and Summer Meetings are held Associate Secretary: under the supervision of the Program Committee for National Joseph A. Cima (until 1131193) Meetings (PCNM). They are administered by the Associate Robert J. Daverman (after 1131193) Secretary in charge of that meeting with staff assistance from Deadline for organizers: April 5, 1993 the Meetings Department in the Society office in Providence. Deadline for consideration: September 23, 1993 According to the "Rules for Special Sessions" of the Society, Special Sessions are selected by the PCNM from a list of proposed Special Sessions in essentially the same March 1994 Meeting in Lexington, Kentucky manner as individuals are selected to give Invited Addresses. Southeastern Section Associate Secretary: The number of Special Sessions at a Summer or Annual Joseph A. Cima (until1131193) Meeting is limited. The algorithm that determines the number Robert J. Daverman (after 1131193) of Special Sessions allowed at a given meeting, while simple, Deadline for organizers: June 18, 1993 is not repeated here, but can be found in "Rules for Deadline for consideration: To be announced Special Sessions" on page 614 in the April 1988 issue of the Notices. Each person selected to give an Invited Address is invited March 1994 Meeting in Manhattan, Kansas to generate a Special Session, either by personally organizing Central Section one or by having a Special Session organized by others. Pro Associate Secretary: Andy R. Magid Deadline for organizers: June 25, 1993 posals to organize a Special Session are sometimes requested Deadline for consideration: To be announced either by the PCNM or by the Associate Secretary. Other proposals to organize a Special Session may be submitted to the Associate Secretary in charge of that meeting (who is an June 1994 Meeting in Eugene, Oregon ex-officio member of the committee and whose address may Western Section be found below). These proposals must be in the hands of the Associate Secretary: Lance W. Small PCNM at least nine months prior to the meeting at which the Deadline for organizers: September 7, 1993 Special Session is to be held in order that the committee may Deadline for consideration: To be announced consider all the proposals for Special Sessions simultaneously. Proposals that are sent to the Providence office of the Society, to the Notices, or directed to anyone other than the Associate October 1994 Meeting in Stillwater, OK Secretary will have to be forwarded and may not be received Central Section Associate Secretary: Andy R. Magid in time to be considered for acceptance. Deadline for organizers: January 28, 1994 It should be noted that Special Sessions must be announced Deadline for consideration: To be announced in the Notices in such a timely fashion that any member of 762 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY -·-· - ······ -· -· -· ---· ···· ··- -···- .!1 M lliil II II Jltilii-BIIfl"- lnvited Addresses and Special Sessions the Society who so wishes may submit an abstract for Robert J. Daverman, Associate Secretary (beginning February 1, 1993) consideration for presentation in the Special Session before Department of Mathematics University of Tennessee the deadline for such consideration. This deadline is usually Knoxville, TN 37996-1300 three weeks before the deadline for abstracts for the meeting (Telephone 615-974-6577) in question. As a general rule, members who anticipate organizing Special Sessions at Special Sessions are very effective at Sectional Meetings AMS meetings are advised to seek approval at least nine months prior to the and can usually be accommodated. The processing of pro scheduled date of the meeting. No Special Sessions can be approved too late to provide adequate advance notice to members who wish to participate. posals for Special Sessions for Sectional Meetings is handled Proposals for Special Sessions at the October 1-3, 1993 meeting in in essentially the same manner as for Annual and Summer Heidelberg, Germany, only, should be sent to Professor Fossum at the Department Meetings by the Section Program Committee. Again, no Spe of Mathematics, University of lllinois, Urbana, 11 61801, Telephone: 217-244- cial Session at a Sectional Meeting may be approved so late 1741, email:[email protected]. that its announcement appears past the deadline after which members can no longer send abstracts for consideration for Information for Speakers presentation in that Special Session. A great many of the papers presented in Special Sessions at The Society reserves the right of first refusal for the meetings of the Society are invited papers, but any member publication of proceedings of any Special Session. These of the Society who wishes to do so may submit an abstract for proceedings appear in the book series Contemporary Mathe consideration for presentation in a Special Session, provided matics. it is received in Providence prior to the special early deadline More precise details concerning proposals for and orga announced above and in the announcements of the meeting at nizing of Special Sessions may be found in the "Rules for which the Special Session has been scheduled. Contributors Special Sessions" or may be obtained from any Associate should know that there is a limitation in size of a single Secretary. Special Session, so that it is sometimes true that all places are filled by invitation. Papers not accepted for a Special Session are considered as ten-minute contributed papers. Abstracts of papers submitted for consideration for presen Proposals for Special Sessions to the tation at a Special Session must be received by the Providence Associate Secretaries office (Meetings Department, American Mathematical Soci The programs of Sectional Meetings are arranged by the ety, P. 0. Box 6887, Providence, RI 02940) by the special Associate Secretary for the section in question: deadline for Special Sessions, which is usually three weeks Western Section earlier than the deadline for contributed papers for the same Lance W. Small, Associate Secretary meeting. The Council has decreed that no paper, whether Department of Mathematics invited or contributed, may be listed in the program of a University of California, San Diego La Jolla, CA 92093 meeting of the Society unless an abstract of the paper has Electronic mail: [email protected] been received in Providence prior to the deadline. (Telephone 619-534-3590) Electronic submission of abstracts is available to those who Central Section use the 1FX typesetting system. Requests to obtain the pack Andy R. Magid, Associate Secretary age of files may be sent electronically via the Internet to Department of Mathematics University of Oklahoma [email protected]. Requesting the files electron 601 Elm PHSC 423 ically likely will be the fastest and most convenient way, Norman, OK 73019 but users may also obtain the package on IBM or Macintosh Electronic mail: [email protected] diskettes, available free of charge by writing to: Electronic (Telephone 405-325-6711) Abstracts, American Mathematical Society, Meetings Depart Eastern Section ment, P.O. Box 6887, Providence, RI 02940, USA. When W. Wistar Comfort, Associate Secretary (until January 31, 1993) Department of Mathematics requesting the abstracts package, users should be sure to Wesleyan University specify whether they want the plain '!FX, --4MS'-'IFX, or the Middletown, CT 06457 li\1EX package. Electronic mail: [email protected] (Telephone 203-347-9411) Lesley M. Sibrier, Associate Secretary (beginning February 1, 1993) Number of Papers Presented Department of Mathematics Joint Authorship Polytech University of New York Brooklyn, NY 11201-2990 Although an individual may present only one ten-minute (Telephone 718-260-3505) contributed paper at a meeting, any combination of joint Southeastern Section authorship may be accepted, provided no individual speaks Joseph A. Cima, Associate Secretary (until January 31, 1993) more than once. An author can speak by invitation in more Department of Mathematics than one Special Session at the same meeting. University of North Carolina, Chapel Hill An individual may cont,ribute only one abstract by title Chapel Hill, NC 27599-3902 Electronic mail: [email protected] in any one issue of Abstracts, but joint authors are treated as (Telephone 919-962-1050) a separate category. Thus, in addition to abstracts from two SEPTEMBER 1992, VOLUME 39, NUMBER 7 763 ------·--·--·-·--·····-----·--··-·---···-······------·-·-··--·-··--···-····-----·· Invited Addresses and Special Sessions individual authors, one joint abstract by them may also be Host departments supply local information, ten to twelve accepted for an issue. rooms with overhead projectors for contributed paper sessions and Special Sessions, an auditorium with twin overhead Site Selection for Sectional Meetings projectors for invited addresses, and registration clerks. The Sectional Meeting sites are recommended by the Associate Society partially reimburses for the rental of facilities and Secretary for the Section and approved by the Committee of equipment, and for staffing the registration desk. Most host Associate Secretaries and Secretary. Recommendations are departments volunteer; to do so, or for more information, usually made eighteen to twenty-four months in advance. contact the Associate Secretary for the Section. 1992 Symposium on Some Mathematical Questions in Biology Cell Biology Denver, Colorado, November 1992 The twenty-sixth annual Symposium on Some Mathematical Elson (Washington University School of Medicine, St. Louis), Questions in Biology, focusing on Cell Biology, will be Interpretation of measurements of cellular deformability; held during the annual meeting of the American Society Byron Goldstein (Los Alamos National Laboratory), Cell for Cell Biology, November 15-19, 1992, at the Colorado activation through the aggregation of cell surface receptors; Convention Center in Denver, Colorado. The symposium is Jennifer Linderman (University of Michigan, Ann Arbor), sponsored by the American Mathematical Society, the Society Cell-cell interactions and the activation of T cells in an for Industrial and Applied Mathematics (SIAM), and the immune response; George Oster (University of California, Society for Mathematical Biology (SMB). Berkeley), The dynamics of single-motor molecules; and Michael Reed (Duke University), The transport oforganelles Committee on Mathematics in the The AMS-SIAM-SMB in axons. Life Sciences serves as the Organizing Committee for the Proceedings of the symposium will be published by the symposium. The committee members are Jack D. Cowan, AMS in the series Lectures on Mathematics in the Life James W. Curren, Marcus W. Feldman, Eric S. Lander, Marc Sciences. Mangel (Chair), and James D. Murray. Byron Goldstein and Discount airfares are available from United Airlines for Carla Wofsy serve as organizers. travel November 12-22, 1992. Call 1-800-521-4041 and There will be sessions on Monday and Tuesday afternoons, refer to file number 524YM. November 16 and 17, each including three invited lectures on For further information on the symposium, contact the mathematical and biophysical approaches to problems in cell Symposium Conference Coordinator, AMS, P.O. Box 6887, biology. The speakers and their topics are: Micah Dembo (Los Providence, RI 02940, or DLS®MATH.AMS.COM by elec Alamos National Laboratory), Modeling cell adhesion; Elliot tronic mail. 764 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Joint Mathematics Meetings in San Antonio AMS Special Sessions and Contributed Papers MAA Contributed Papers The Joint Mathematics Meetings in San Antonio will be or Macintosh diskettes, available free of charge by writing held Janmuy 13-16 (Wednesday-Saturday), 1993. (Please to: Director of Meetings, American Mathematical Society, note that incorrect dates were published in this article in P.O. Box 6887, Providence, RI 02940. When requesting the the May/June issue.) The first full announcement of the abstracts package, users should be sure to specify whether meetings will appear in the October 1992 issues of the Notices they want the plain lEX. -4NP' -lEX, or the ID}3X package. and FOCUS. This preliminary announcement is made to Only abstracts should be sent to [email protected]. encourage member participation and to provide lead time for Questions regarding an abstract should be addressed to submission of abstracts for consideration for presentation in [email protected]. Questions regarding meetings AMS Special Sessions and for submission of abstracts for should be addressed to [email protected]. AMS and MAA Contributed Paper Sessions. AMS Special Sessions MAA Contributed Papers A list of Special Sessions for this meeting can be found in the Contributed papers are being accepted on several topics in Invited Addresses and Special Sessions section of this issue. collegiate mathematics for presentation in contributed paper Most of the papers to be presented at these Special sessions at the meeting. The organizers listed below solicit Sessions will be by invitation; however, anyone contributing contributed papers pertinent to their sessions' interests and an abstract for the meeting who feels that his or her paper concerns; material should be sent to the organizer whose would be particularly appropriate for one of these sessions name is followed by an asterisk (*). A full description of each should indicate this clearly on the abstract, and should submit session appeared in the May/June and July/August Notices. it by September 18, 1992, three weeks earlier than the Please note that any days scheduled for any session are normal deadline for contributed papers, in order that it be tentative. The topics, organizers, and their affiliations are:· considered for inclusion. Abstracts should be prepared on the standard AMS form • Assessment programs for the undergraduate major, Friday available from the AMS office in Providence or in departments morning and Saturday afternoon of mathematic~ and should be sent to Abstracts, Meetings Charles F. Peltier* Department, American Mathematical Society, Post Office Box Department of Mathematics 6887, Providence, RI 02940. A charge of $16 is imposed for Saint Mary's College retyping abstracts that are not in camera-ready form. Notre Dame, IN 46556 email: [email protected] AMS Contributed Paper Sessions fax: 219-284-4492 Abstracts should be prepared on the standard AMS form James W. Stepp, University of Houston available from the AMS office in Providence or in departments • "Capstone" courses for senior mathematics majors, of mathematics and should be sent to Abstracts, Meetings Wednesday and Thursday mornings Department, American Mathematical Society, Post Office Box 6887, Providence, RI 02940, so as to arrive by the abstract Christopher E. Barat and Pamela Crawford* deadline of October 8, 1992. A charge of $16 is imposed Department of Mathematics for retyping abstracts that are not in camera-ready form. Late Randolph-Macon College papers will not be accepted. Ashland, VA 23005 • Empowering the mathematical community, Wednesday morning and Thursday afternoon Electronic Submission of AMS Abstracts This service is available to those who use the 1FX typeset Gloria F. Gilmer* ting system and can be used for abstracts of papers to be Math-Tech, Inc. presented at this meeting in AMS sessions only. Requests to 9155 N. 70 St. obtain the package of files may be sent by electronic mail on Milwaukee, WI 53223 the Internet to [email protected]. Requesting the Marilyn Frankenstein, University of Massachusetts, Boston files electronically will likely be the fastest and most conve Patricia C. Kenschaft, Montclair State College nient way, but users may also obtain the package on IBM Alvin M. White, Harvey Mudd College SEPTEMBER 1992, VOLUME 39, NUMBER 7 765 ····································-················-············-····················-·············... ····-······················-··················------Joint Mathematics Meetings in San Antonio • Impact ofnon-traditional instructional methods on testing • Use ofvisualization in the teaching ofmathematics, Friday and evaluation, Wednesday and Thursday afternoons morning and Saturday afternoon Linda H. Boyd* Howard Lewis Penn* Mathematics Department Mathematics Department DeKalb College 572 Holloway Rd. 555 North Indian Creek Dr. United States Naval Academy Clarkston, GA 30021 Annapolis, MD 21402-5002 Elizabeth Teles, Montgomery College, Maryland email: [email protected]. usna.navy.mil • Interactive learning environments, Wednesday and Thurs James R. King, University of Washington day mornings • Using data and computers in teaching statistics, Wednes Katherine Pedersen* day morning and Thursday afternoon NSF Statewide Systemic Initiative Mary Parker* 435 S. Chapelle Department of Mathematics Pierre, SD 57501 Austin Community College Sandra Z. Keith, St. Cloud State University 11928 Stonehollow Drive Austin, TX 78758-3101 • Linear algebra, Wednesday and Friday afternoons, and Thursday evening George Cobb, Mount Holyoke College Donald R. LaTorre* Presentations are normally limited to ten minutes, although Department of Mathematical Sciences selected contributors may be given up to twenty minutes. Clemson University Individuals wishing to submit a paper for any of these Clemson, SC 29634-1907 sessions should note the following NEW PROCEDURES: Steven J, Leon, University of Massachusetts, Dartmouth The name(s) and address(es) of the author(s) and a one A. Duane Porter (for the LACSG), University of Wyoming page summary of the paper should be sent directly to • Mathematics and the arts, Thursday afternoon and Satur the organizer whose address is given. The purpose of daymoming this summary is to enable the organizer(s) to evaluate the JoAnne S. Growney* appropriateness Of the paper for the session, so this summary Department of Mathematics and Computer Science should be as detailed and informative as possible within the Bloomsburg University one-page limitation. This summary must reach the organizer Bloomsburg, PA 17815 by September 10, 1992. Summaries should NOT be sent to the MAA Washington office. Friday morning • Recreational inathemagical computing, The organizer will acknowledge receipt of the summary. and Saturday afternoon If the paper is accepted for presentation, the organizer will Dr. Michael W. Ecker* send the author(s) a standardized abstract form to be used to Editor/Publisher prepare a brief abstract, which will be published in the journal Recreational & Educational Computing Abstracts (copies will be available in the registration area). 909 Violet Terrace Completed abstract forms must be returned to the organizer Clarks Summit, PA 18411 promptly and no later than September 24. Do not send • Recruitment and retention of women in mathematics the abstracts to the AMS, and do not submit them revisited, Saturday morning and afternoon electronically. Abstracts not received by that date cannot be Marcelle Bessman* published. If desired, an abstract form may be obtained in 328 Braddock, #212 advance from either the AMS office in Providence or the Frostberg, MD 21532 MAA Washington office and the abstract may be submitted email: [email protected] along with the summary. fax: 813-872-9342 Rooms where MAA contributed paper sessions will be (May 10-Aug. 20, mailing address will be 644 Geneva Place, held are equipped with an overhead projector and screen. Tampa, FL 33606) Blackboards are not available. Persons having other equip • Teaching mathematics to multicultural and multilingual ment needs should contact the MAA Associate Secretary students, Friday morning and afternoon (Kenneth A. Ross, Department of Mathematics, Univer sity of Oregon, Eugene, OR 97403-1222; electronic mail: Richard O'Lander* [email protected]) as soon as possible, but in any case Division of Computer Science, Mathematics & Science prior to November 9. Upon request, the following will St. John's University be made available: one additional overhead projector/screen, St. Vincent's College 35mm carousel slide projector, or 1/z" or 3/4'' VHS video Grand Central & Utopia Parkways cassette recorder with one color monitor. Jamaica, NY 11439 766 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Mathematical Sciences 1992 Meetings and Conferences 1992. IMACS Symposium on Symbolic Computation in Engineering Design, IDN, Lille, France. (Jul./Aug. 1990, p. 746) 1992. IMACS International Conference on Computational Physics, University of Col orado, Boulder, CO. (Oct. 1990, p. 1141) September 1992 16-18. Second SIAM Conference on Control in the 90s, Minneapolis, MN. (Feb. 1991, THIS SECTION contains announcements of meetings and conferences of interest to some p. 148) segment of the mathematical public, including ad hoc, local, or regional meetings, and 16-20. IMACS/SICE International Sympo meetings or symposia devoted to specialized topics, as well as announcements of regularly sium on Robotics, Mechatronics and Man scheduled meetings of national or international mathematical organizations. (Information on ufacturing Systems, Kobe, Japan. (Jan. 1992, meetings of the Society, and on meetings sponsored by the Society, will be found inside the p. 53) front cover.) AN ANNOUNCEMENT will be published in the Notices if it contains a call for papers, 17-19. International Conference on Group and specifies the place, date, subject (when applicable), and the speakers; a second Theory, University of Timisoara, Romania. announcement will be published only if there are changes or necessary additional information. (Jul./Aug. 1991, p. 646) Once an announcement has appeared, the event will be briefly noted in each issue until it has 17-19. SIAM Conference on Control and its been held and a reference will be given in parentheses to the month, year, and page of the Applications, Minneapolis, MN. (Mar. 1992, issue in which the complete information appeared. Asterisks (*) mark those announcements containing new or revised information. p. 248) IN GENERAL, announcements of meetings and conferences held in North America carry 20-26. Funktionalgeichungen, Oberwolfach, only date, title of meeting, place of meeting, names of speakers (or sometimes a general Federal Republic of Germany. (Feb. 1991, statement on the program), deadlines for abstracts or contributed papers, and source of p. 148) further information. Meetings held outside the North American area may carry more detailed 21-23. Seventh International Conference on information. In any case, if there is any application deadline with respect to participation in the meeting, this fact should be noted. All communications on meetings and conferences in Multivariate Analysis in Memory of Ronald the mathematical sciences should be sent to the Editor of the Notices, care of the American A. Fisher, Barcelona, Spain. (Jan. 1992, p. 53) Mathematical Society in Providence. 21-23. Workshop on Algebraic Cycles, DEADLINES for entries in this section are listed on the inside front cover of each issue. In Mathematical Sciences Research Institute, order to allow participants to arrange their travel plans, organizers of meetings are urged Berkeley, CA. (Jan. 1992, p. 53) to submit information for these listings early enough to allow them to appear in more than one issue of the Notices prior to the meeting in question. To achieve this, listings should be 21-23. SIAM Workshop on Evolution of received in Providence SIX MONTHS prior to the scheduled date of the meeting. Phase Boundaries and Microstructure, Lees EFFECTIVE with the 1990 volume of the Notices, the complete list of Mathematical Sciences burg, VA. (Jul./Aug. 1992, p. 627) Meetings and Conferences will be published only in the September issue. In all other issues, 21-24. Colloque de Probabilites, Marseille, only meetings and conferences for the twelve-month period following the month of that issue France. (Jul./Aug. 1992, p. 627) will appear. As new information is received for meetings and conferences that will occur later than the twelve-month period, it will be announced at the end of the listing in the next possible Con 21-25. IMA Workshop on Robust issue. That information will not be repeated until the date of the meeting or conference falls trol Theory, Institute for Mathematics and its within the twelve-month period. Applications, University of Minnesota. (Sep. 1991, p. 839) 21-25. Sixth Seminar "NUMDIFF'' on Nu and En CONFERENCE TOPICS: Approximation meth merical Solution of Differential Equations and Stochastic Methods in Science Moscow, Russia. integral and pseudodifferential and Applications, Halle, Federal Republic of gineering (INTERVAL '92), ods for Numerical analysis for boundary Germany. (Jul./Aug. 1992, p. 627) (Jul./Aug. 1992, p. 627) equations; 26-27. Thirty-second Midwest Partial Dif integral equations on nonsmooth surfaces; ~ 21-25. Introduction to Industrial Engineer- Purdue Univ., Banach algebra techniques in operator the ing, Dallas, TX. ferential Equations Seminar, West Lafayette, IN. (May/Jun. 1992, p. 493) ory; Applications of integral and pseudo PRoGRAM: This seminar is designed to 27 -October 3. Darstellungstheorie Endlicher differential equations. strengthen job performance and to give a Gruppen, Oberwolfach, Federal Republic of INFORMATION: S. ProBdorf/M. Teuchert thorough indoctrination in industrial engi Germany. (Feb. 1991, p. 148) (Conference Manager), Institute for Ap neering basics. It focuses on the basics of * 28-0ctober 2. Sixth Workshop on Computer plied Analysis and Stochastics (IAAS), methods engineering, work measurement, Science Logic, San Miniato, Italy. (Jul./Aug. Hausvogteiplatz 5-7, D-0-1086 Berlin, capital investment analysis, quality con 1992,p.627) Germany, Tel: + 030 20377 555/+ 030 trol, production/inventory control, material 28-0ctober 2. International Symposium on 20377 594; FAX: +030 2004975. handling, and plant layout. * Operator Equations and Numerical Analy INFORMATION: Call liE Customer Service sis, Gosen near Berli~, Germany. Center at 404-449-0460. 29-0ctober 2. Theorie Analytique des ORGANIZING COMMITTEE: S. ProBdorf Nombres, Marseille, France. (Jul./Aug. 1992, 22-26. International Conference on Interval (Berlin), B. Silbermann (Chemnitz). p. 627) SEPTEMBER 1992, VOLUME 39, NUMBER 7 767 ...... _.lllllllllllll ______r Meetings and Conferences 30-0ctober 2. Thirtieth Annual Allerton 15-17. Jumelage 92, Mathematical Sciences day of Joe Lehner, Swarthmore College, Conference on Communication, Control, Institute, Ithaca, NY. (Apr. 1992, p. 348) Swarthmore,PA. and Computing, University of Illinois, IL. 15-17. Interface and Layer Dynamics, Re INVITED SPEAKERS: G. Andrews, A.O.L. (Feb. 1992, p. 147) search Institute for Mathematical Sciences, Atkins, B. Berndt, D. Bressoud, L. Ehren 31-0ctober 4. Third International Confer Kyoto University. (Jul./Aug. 1992, p. 627) preis, H. Iwaniec, M. Knopp, M. Newman, ence on Function Spaces, Institute of Mathe 15-19. SIAM Conference on Applications L.A.' Parson, D. Rosen, M. Sheingorn, Sis matics, Adam Mickiewicz University, Poznan, of Dynamical Systems, Salt Lake City, UT. ter A. Heath. Poland. (Feb. 1992, p. 147) (Mar. 1992,p.249) INFORMATION: D. Rosen (215-543-2752, * 16-17. Fourteenth Midwest Probability Col drosenl @cc.swarthmore.edu.) and M. loquium, Northwestern University, Evanston, Knopp (215-664-3534 or 215-787-7589), IL. 410 Lancaster Ave., Apt. 221, Haverford, PA 19041. October 1992 INVITED SPEAKERS: H. Kesten (two lectures October 1992. Workshop on Superpro on first- and last-passage percolation); T. 22-24. General and Geometric Topology cesses and Interacting Systems, Centre de McConnell and S. Evans (one lecture). and Related Problems, Research Institute Recherches Mathematiques, Universite de INFORMATION: M. Pinsky, Dept. of Math., for Mathematical Sciences, Kyoto University. Montreal, Montreal, Quebec, Canada. (Apr. Northwestern U., Evanston, IL 60208; (Jul./Aug. 1992, p. 628) 1992, p. 348) email: [email protected]. 22-24. Mathematical Analysis of Phenom 2-3. Fourth Midwest Conference on the * 16-17. 1992 Mathematical Sciences Depart ena in Fluid and Plasma Dynamics, Research History of Mathematics, Miami University, ment Chairs Colloquium, Arlington, VA. (See Institute for Mathematical Sciences, Kyoto Oxford, OH. (Mar. 1992, p. 249) the News and Announcements section of the University. (Jul./Aug. 1992, p. 628) 4-10. Funktionalanalysis, Oberwolfach, Fed 1992 July/August Notices, p. 601, for further 22-25. Semi-Annual Regional Workshop eral Republic of Germany. (Feb. 1991, p. 148) details.) in Dynamical Systems and Related Top 5-9. Option: Journees Thematiques Medi ics, Penn State University, State College, PA. CONFERENCE THEME: Chairing the chang (May/Jun. 1992, p. 493) cis, Marseille, France. (Jul./Aug. 1992, p. 627) ing mathematical sciences department of 22-30. Forty-sixth Conference and Con 9-10. Developments from the Stone Age, the 1990s. gress of the International Federation for University of Chicago, Chicago, IL. (May/Jun. KEYNOTE SPEAKER: D. Allan Bromley, Information and Documentation, Madrid, 1992,p.493) Assistant to the President for Science and Spain. (May/Jun. 1991, p. 477) ~9-12. Workshop on Vector Bundles on Technology. Algebraic Varieties, University of California, INFORMATION: Board on Mathematical Sci 25-31. Stochastische Analysis, Oberwolfach, Los Angeles. ences, National Research Council, NAS Federal Republic of Germany. (Feb. 1991, 312, 2101 Constitution Ave., NW, Wash p. 148) INVITED SPEAKERS: A. Beauville, F. Bogo ington, DC 20418; 202-334-2421; FAX: 26-30. Holomorphic Mappings and Dio molov, R. Friedman, D. Gieseker, S. Mukai, 202-334-1597; email: [email protected] or phantine Geometry, Research Institute for S. Ramanan, A. Szenes. [email protected]. Mathematical Sciences, Kyoto University. INFORMATION: R. Lazarsfeld, Dept. of (Jul./Aug. 1992, p. 628) Math., UCLA, Los Angeles, CA 90024; 17. Three Decades of Numerical Linear email: [email protected]. * 27-29. NSF/DoD's National SBIR Confer- Algebra at Berkeley: A Conference in Honor ences, Washington, DC. of the Sixtieth Birthdays of Beresford Parlett 11-17. Arbeitsgemeinschaft mit Aktuellem and William Kahan, University of California, PROGRAM: The NSF/DoD-sponsored Na Thema, Oberwolfach, Federal Republic of Berkeley. (Mar. 1992, p. 249) tional Small Innovation Research (SBIR) Germany. (Feb. 1991, p. 148) 18-24. Geometrie, Oberwo1fach, Federal Re Conferences provide a unique marketing 12-14. Mathematical Topics in Biology, public of Germany. (Feb. 1991, p. 148) opportunity by bringing together scores of Research Institute for Mathematical Sciences, personnel from Federal agency and major 19-21. The Fourth Symposium on the Fron Kyoto University. (Jul./Aug. 1992, p. 627) corporations in one place at one time. Rep tiers of Massively Parallel Computation, 12-16. IMA Workshop on Control Systems resentatives from the Depts. of Defense, McLean, VA. (Dec. 1991, p. 1340) Design for Advanced Engineering Systems: Health & Human Services (including NIH), Complexity, Uncertainty, Information, and 19-23. Modeles Arch et Applications a Ia Energy, Education, Transportation, Com Organization, Institute for Mathematics and Finance, Marseille, France. (Jan. 1992, p. 54) merce, and NASA, National Science Foun its Applications, University of Minnesota. (Sep. 19-23. Fourth International Symposium on dation, Environmental Protection Agency, 1991, p. 840) Orthogonal Polynomials and their Applica and Nuclear Regulatory Commission will 12-16. Workshop on Visualization of Ge tions, Evian, France. (Feb. 1992, p. 148) discuss R&D opportunities at their agen ometric Structures, Mathematical Sciences 20-23. Second Beijing International Con cies in seminars and one-on-one meetings. Research Institute, Berkeley, CA. (Jan. 1992, ference on System Simulation and Scientific Also participating are companies such as p. 54) Computing-BICSC '92, Beijing, China. (Jan. Boeing, General· Dynamics, Martin Ma 12-16. International Conference on Poly 1992,p.54) rietta, Motorola, TRW, Honeywell, ffiM, nomial Automorphisms and Related Topics, 21-23. Documents, Computation, and Pref Hughes, Texas Instruments, United Tech CIRM, Luminy, France. (Jan. 1992, p. 54) erence, Washington, DC. (Apr. 1992, p. 349) nologies, and Teledyne. INFORMATION: Contact the Conference Co 14-20. First African Conference on Re 21-25. Workshop on Conservative Systems ordinator at 407-274-4005. search in Computer Science, Yaounde, and Quantum Chaos, Fields Institute for Cameroon. (Feb. 1992,p. 147) Research in Mathematical Sciences, Waterloo, 27-31. International Workshop on Mod 15-16. Fuzzy Logic: Entwicklungsmetho Ontario. (Jul./Aug. 1992, p. 627) ern Group Analysis: Advanced Analytic den und Werkzeuge, Bonn, Federal Republic * 22-23. Conference on Modular Forms and and Computational Methods in Mathe of Germany. (Jul./Aug. 1992, p. 627) Number Theory to Celebrate the 80th Birth- matical Physics, Acireale (Catania), Italy. 768 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY -··--·-····-·-·-····--····-~······-···--··-··-· ·······--~·~····-······-····-·······-·······- ························-··· ······································-························ Meetings and Conferences (May/Jun. 1992, p. 493) 4-6. Mathematical Methods for Wave Phe Boston. MA. (Feb. 1992, p. 148) ~ 28-November 1. Symposium on Trends in nomena in Fluids and Their Application, 15-21. Komplexitatstheorie, Oberwolfach, Discrete Mathematics, Bielefeld, Germany. Research Institute for Mathematical Sciences, Federal Republic of Germany. (Feb. 1991, Kyoto University. (Jul./Aug. 1992, p. 628) p. 148) PuRPOsE: The purpose of this symposium 4-6. Fundamental Technologies in Numeri is to give an overview on current and future 16-18. Workshop on Higher Dimensional cal Computation, Research Institute for Math trends in discrete mathematics. Geometry, Mathematical Sciences Research ematical Sciences, Kyoto University. (Jul./Aug. ORGANIZING COMMITTEE: W. Deuber (Bi Institute, Berkeley, CA. (Jan. 1992, p. 54) l992,p.628) elefeld), H.-J. Promel (Bonn), B. Voigt 16-18. Hardy Spaces and Uniform Al (Frankfurt). 4-6. Structure of Solutions of Partial Differ gebras, Research Institute for Mathematical INVITED SPEAKERS: M. Aigner, Berlin; B. ential Equations, Research Institute for Math Sciences, Kyoto University. (Jul./Aug. 1992, Bollobas, Cambridge; P. Erdos, Budapest, ematical Sciences. Kyoto University. (Jul./Aug. p. 629) 1992,p.628) R.L Graham, Murray Hill; P. Gritzmann, 16-20. International Congress on Numeri Trier; M. Grotschel, Berlin; J.H. Spencer, 5-8. Eighteenth Annual Conference of the cal Methods in Engineering and Applied Sci NY; C. Thomassen, Kopenhagen; W.T. American Mathematical Association of Two ences, University of Concepcion, Concepcion, Trotter, Morristown; I. Wegener, Dort Year Colleges, Indianapolis, IN. (Jul./Aug. Chile. (Jul./Aug. 1991, p. 646) mund. 1992, p. 628) 16-20. IMA Period of Concentration: Flow INFORMATION: W. Thumser, Fakultiit fiir 7-11. Mathematics and Molecular Biology Control, Institute for Mathematics and its Mathematik, Universitiitsstr. D-4800 Biele lll: Computational Approaches to Nucleic Applications, University of Minnesota. (Sep. feld; thumser@math l O.mathematik.uni Acid Structure and Function. Santa Fe, NM. 1991, p. 840) bielefeld.de; or T. Valentin, ZiF, Wellenberg (May/Jun. 1992, p. 494) * 16-20. The Fifth Annual High Performance l, D-4800 Bielefeld; FAX: (0) 5211106- 8-14. Numerische Integration, Ober 2782. Computing and Communication Conference wolfach, Federal Republic of Germany. Supercomputing 92, Minneapolis, MN. (Please 30--31. Seventh Annual Pi Mu Epsilon (February 1991, p. 148) note updated program information from May/ Regional Undergraduate Mathematics Con 8-14. Third Austrian Symposium on the Jun. 1992, p. 494) ference, St. Norbert College, DePere, WI. History of Mathematics, Neuhofen an der Program The program will include 18 tu (Jul./Aug. 1992, p. 628) Ybbs (Lower Austria). (Mar. 1992, p. 249) torials, 8 invited lecturers, and 80 technical 3D--November 1. Central Section, Wright 9-11. Fundamental Problems in Quantum paper presentations. There will be exhibitions State University, Dayton, OH. Field Theory, Research Institute for Mathe sponsored by over 50 companies plus Research matical Sciences, Kyoto University. (Jul./Aug. Exhibits, a Visualization Theater, and Poster INFORMATION: W. Drady, American Mathe 1992, p. 628) Exhibits. The education program at Supercom matical Society, P.O. Box 6887, Po vidence, puting '92 will introduce secondary school RI02940. 9-13. IMA Workshop on Control and Op timal Design of Distributed Parameter Sys teachers to high-performance computing and 31. Differential Geometry Day, Eastern tems, Institute for Mathematics and its Appli will host over 100 high school students visiting lllinois University, Charleston, IL. (May/Jun. cations, University of Minnesota. (Nov. 1991, Supercomputing '92. Also, current develop 1992,p.493) p. 1171) ments in supercomputing technology utilizing * 9-13. Introduction to Industrial Engineer- the scientific network, SCinet '92, a high ing, Seattle, WA. speed communications network linking ex hibitors and remote locations will be featured. November 1992 PROGRAM: This seminar is designed to SCinet offers an opportunity to see and experi November 1992. The International Lie strengthen job performance and to give a ence hands-on demonstrations of the technical Lobachevsky Colloquium Dedicated to the thorough indoctrination in industrial engi feasibility for building a networked super Anniversaries of Sophus Lie's 150 birthday neering basics. It focuses on the basics of computing environment using HIPPI, FDDI, and Nikolai Lobachevski's 200 birthday, methods engineering, work measurement, Ethernet, local fiber, T3, and other technolo Tartu (Estonia). (Feb. 1992, p. 148) capital investment analysis, quality con gies. In addition, a heterogeneous computing November 1992. Workshop on Stochastic trol, production/inventory control, material challenge will be hosted. Control, Centre de Recherches Mathematiques, handling, and plant layout. 16-20. Automorphic Forms and L-functions, Universite de Montreal, Montreal Quebec, INFORMATION: Call liE Customer Service Research Institute for Mathematical Sciences, Canada. (Apr. 1992, p. 349) Center at 404-449-0460. Kyoto University. (Jul./Aug. 1992, p. 629) 1-6. The First Pan American Conference 10--13. Interdisciplinary Studies on Number 16-22. Workshop on Normal Forms, Homo on Pre-Columbia Mathematics, Astronomy, Theory, Research Institute for Mathematical clinic Bifurcations and Chaos, Fields Institute and Modes of Thought, Univ. Francisco Mar Sciences, Kyoto University. (Jul./Aug. 1992, for Research in Mathematical Sciences, Water roquin, Guatamala City and Tikal. (Dec. 1991, p. 628) loo, Ontario. (Apr. 1992, p. 350) p. 1340) 13-15. Second Joint Meeting of the Mid * 17-19. NSF/DoD's National SBIR Confer- 1-7. Kombinatorik, Oberwolfach, Federal west Conference on Ordinary Differential ences, Phoenix, AZ. Republic of Germany. (Feb. 1991, p. 148) Equations and the Southeastern-Atlantic PRoGRAM: The NSF/DoD-sponsored Na 2-4. Colloque Mathematique-Informatique, Regional Conference on Differential Equa tional Small Innovation Research (SBIR) Marseille, France. (Jul./Aug. 1992, p. 628) tions, University of Kentucky, Lexington, KY. Conferences provide a unique marketing 2-6. Workshop on Symbolic Dynamics, (Apr. 1992, p. 349) opportunity by bringing together scores of Mathematical Sciences Research Institute, Berke 14-16. The Third Biennial Conference of the personnel from Federal agency and ma ley, CA. (Jan. 1992, p. 54) Allahabad Mathematical Society, Allahabad, jor corporations in one place at one time. 2-20. Fourth Autumn Course on Math India. (May/Jun. 1991, p. 477) Reprsentatives from the Depts. of Defense, ematical Ecology, Trieste, Italy. (Jul./Aug. 15-20. An Applications Symposium on Op Health & Human Services (including NIH), 1992, p. 628) tics, Electro-Optics, and Lasers in Industry, Energy, Education, Transportation, Com- SEPTEMBER 1992, VOLUME 39, NUMBER 7 769 ···-··········-··· .. ··-····"-""""""""""""""""""""""""""""""-····-······...... ______...... Meetings and Conferences merce, and NASA, National Science Foun eties, and their Moduli, Mathematical Sci 3-9.. Grundlagen der Geometrie, Oberwol dation, Environmental Protection Agency, ences Research Institute, Berkeley, CA. (Jan. fach, Federal Republic of Germany. (Jan. 1992, and Nuclear Regulatory Commission will 1992, p. 54) p. 55) discuss R&D opportunities at their agenices 4-5. International Workshop on Matrix 3-9. Extensions of Buildings and Geome in seminars and one-on-one meetings. Also Methods for Statistics, University of Auck tries, Oberwolfach, Federal Republic of Ger participating are companies such as Boeing, land, Auckland, New Zealand. (Feb. 1992, many. (Jan. 1992, p. 55) General Dynamics, Martin Marietta, Mo p. 148) 4-9. Advances in Computational Mathe torola, TRW, Honeywell, IBM, Hughes, 6-12. Theory and Numerical Methods for matics, India International Center, New Delhi, Texas Instruments, United Technologies, Initial-Boundary Value Problems, Oberwol India. (Feb. 1992, p. 149) and Teledyne. fach, Federal Republic of Germany. (Feb. 1991, * 5. Short Course on Nonlinear Dynamics INFORMATION: Contact the Conference Co p. 148) ordinator at 407-274-4005. and Chaos, Arizona State University, Tempe, 7-11. IMACS Symposium on Scientific AZ. Computing and Mathematical Modelling, 18-20. Mathematical Optimization and its SHORT CoURSE TOPICS: Introduction and Bangalore, India. (May/Jun. 1991, p. 477) Applications, Research Institute for Mathe basic concepts; strange attractors; bifurca matical Sciences, Kyoto University. (Jul./Aug. 7-11. Algebraic Number Theory-Recent tions to chaos; fractal basin boundaries; 1992, p. 629) Developments and Their Backgrounds, Re attractor reconstruction (time series analy 20-22. Academic Knowledge and Power, search Institute for Mathematical Sciences, sis); controlling chaos. University of Maryland, College Park, MD. Kyoto University. (Jul./Aug. 1992, p. 629) INVITED SPEAKERS: J.A. Yorke and C. (May/Jun. 1992, p. 494) 8-11. International Conference on Com Grebogi of the University of Maryland. ~ 22-26. Geometry of Hamiltonian Sys- puter Science and Control, Paris, France. INFORMATION: E. Kostelich, Dept. ofMath., tems, Conference Center "Woudschoten", The (Apr. 1992, p. 350) Arizona State Univ., Tempe, AZ 85287- Netherlands. 11-16. Workshop on Generalized Inverses 1804; 602-965-5006; FAX: 602-965-8119; PROGRAM: This school is meant for Ph.D. Computational Techniques and Applica email: eric@ saddle.la.asu.edu. students who are willing to prepare them tions, Indian Statistical Institute, Delhi, India. (Mar. 1992, p. 249) *6-9. Dynamics Days Arizona, Twelfth An selves thoroughly in order to reach research nual International Workshop, Arizona State 13-19. Asymptotische Statistik, Oberwol level in this subject. The school consists University, Tempe, AZ. of three courses of eight lectures each, fach, Federal Republic of Germany. (Feb. 1991, exercising hours and discussions. p. 148) ORGANIZERS: E. Kostelich, Arizona State SPEAKERS AND TOPICS: V. Guillemin 15-17. Third IMA Conference on Mathe U.; R. Behringer, Duke U. symplectic aspects of multiplicity theory; matics Signal Processing, University of War CONFERENCE TOPICS: Mathematical, nu A. Kirillov - geometric quantization and the wick, England. (Feb. 1992, p. 149) merical, and experimental aspects of non orbit method; P. Van Moerbeke - integrable 17-19. Algebraic Combinatorics, Research linear dynamics and chaos; pattern forma Hamiltonian systems. Institute for Mathematical Sciences, Kyoto tion; turbulence; applications to the physi INFORMATION: Autumn School "Geome University. (Jul./Aug. 1992, p. 629) cal, chemical and biological sciences; and related topics. try of Hamiltonian Systems", Attn: Jean 27-31. Holiday Symposium on Lie Group Arthur, Math. Instituut RUU, P.O. Box INFORMATION: E. Kostelich, Dept. of Math., Representations and Combinatorics, New Ariwna State Univ., Tempe, AZ 85287- 80010, 3508TA Utrecht, The Netherlands; Mexico State University, Las Cruces, NM. email: [email protected]. 1804; 602-965-5006; FAX: 602-965-8119; (Sep. 1991, p. 840) email: eric@ saddle.la.asu.edu. 23-25. European Symposium on Research in Computer Security, Toulouse, France. * 7-11. Conference on Evolution Equations, (Feb. 1992,p. 148) 1993 Louisiana State University, Baton Rouge, LA. 23-27. Seminaire Sud-Rhodanien de Ge CONFERENCE TOPICS: Linear and nonlinear 1992-1993. Mittag-Lemer Institute's Aca ometrie, Marseille, France. (Jan. 1992, p. 54) partial differential equations, semigroups of demic Program for 1992-1993: Special Prob operators, equations of evolution, control 24-26. Spectral and Scattering Theory lems in Mathematical Physics, Djursholm, theory, calculus of variations, and related for Differential Equations, Research Institute Sweden. (Nov. 1991, p. 1171) for Mathematical Sciences, Kyoto University. topics. (Jul./Aug. 1992, p. 629) Spring 1993. IMACS Symposium on Math INFORMATION: J. Robert Dorroh, G. Fer ematical Modelling, Wiener Neustadt, Ger- reyra, G. Goldstein, J. Goldstein, F. Neubran 24-26. Theory and Applications in Com many. (Jan. 1992, p. 54) · puter Algebra, Research Institute for Mathe der, or P. Wolenski at the Dept. of Math., matical Sciences, Kyoto University. (Jul./Aug. 1993. Second IMACS International Con Louisiana State Univ., Baton Rouge, LA 1992, p. 629) ference on Computational Physics, Univ. of 70803. Colorado, Boulder, CO. (Jan. 1992, p. 55) 29-December 5. Theory of Large Deviations, 10-15. First Panamerican Workshop in Oberwolfach, Federal Republic of Germany. Applied and Computational Mathematics, (Feb. 1991, p. 148) Simon Bolivar University, Caracas, Venezuela. ~ 30-December 2. Algorithm, Fractal, and Dy January 1993 (May/Jun. 1992, p. 494) namical Systems, Research Institute for Math 1-3. International Symposium on Statisti 10-16. Computational Methods for Non ematical Sciences, Kyoto University. (Jul./Aug. cal Physics, Salt Lake City, Calcutta, India. linear Phenomena, Oberwolfach, Federal Re 1992, p. 629) (Jul./Aug. 1992, p. 629) public of Germany. (Jan. 1992, p. 55) 3-7. International Conference on Scientific 12-14. ·Topology and Field Theory of 3- December 1992 Computation and Differential Equations, 4 Dimensional Algebras, Research Institute Auckland, New Zealand. (May/Jun. 1991, for Mathematical Sciences, Kyoto University. 2-4. Workshop on Curves, Abelian Vari- p. 477) (Jul./Aug. 1992, p. 629) 770 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Meetings and Conferences 13-16. Joint Mathematics Meetings, San Lawrence Corwin, Rutgers University, New * 15-19. 1993Mathematics-in-IndustryStudy Antonio, TX. (including the annual meetings Brunswick, NJ. Group, Melbourne, Australia. of the AMS, AWM, MAA, and NAM) PROGRAM: The main objective of the con PROGRAM: The goals of the study group INFORMATION: H. Daly, AMS, P.O. Box ference is to present recent developments are: To stimulate greater awareness in 6887, Providence, RI 02940. in representation theory and analysis on Australian industry of the need for arid homogeneous spaces, with an emphasis on role of mathematics; to establish better 15-16. 1992-1993 ASL Winter Meeting, San nilpotent Lie groups and reductive p-adic links between industry and academic math Antonio, TX. (May/Jun. 1992, p. 495) groups, two fields to which L. Corwin ematicians; to provide improved univer * 15-17. International Conference on Com made important contributions. The pro sity education of mathematicians through plex Analysis and its Applications, Hong gram of invited one-hour talks will include 1). expanded employment prospects for Kong University of Science and Technology, both surveys and more specialized lectures, mathematics graduates, 2). fresh research Hong Kong. (Please note the updated Informa directed toward mathematicians working in problems for mathematicians, and 3). in tion section from Jul./Aug. 1992, p. 630) a broad range of areas related to Lie group novative material for teaching courses; and INFORMATION: Chung-Chun Yang or Yue representations. to provide Australian industry with high Kuen Kwok, Mathematics Dept., Hong ORGANIZING COMMITTEE: S. Gindikin (Rut level mathematical advice on challenging Kong Univ. of Science and Technology, gers), R. Goodman (Rutgers), F. Greenleaf problems, and to provide an opportunity Clear Water Bay Rd., Hong Kong; email: (Courant), R. Howe (Yale), J. Lepowsky for industrial scientists to receive expert [email protected]; FAX: 852-358- (Rutgers), L. Rothschild (UC San Diego), training in mathematical modelling. 1643. P. Sally (Chicago), N. Wallach (UC San INFORMATION: N.G. Barton, CSIRO Di Diego), J. Wolf (UC Berkeley). vision of Math. and Stats., P.O. Box 17-22. 1993 IEEE International Symposium 218, Lindfield, NSW 2070; tel: (02) 413 INFORMATION: R. Goodman, S. Gindikin, or on Information Theory, San Antonio, TX. 7702; FAX: (02) 416 9317; email: noel@ J. Lepowsky, Dept. of Math., Rutgers Univ., (Feb. 1992, p. 149) syd.dms.csiro.au. New Brunswick, NJ 08903; Fax: 908-932- 17-23. Combinatorial Optimization, Ober 5530; goodman @math.rutgers.edu. 21-27. Curves, Images, Massive Computa wolfach, Federal Republic of Germany. (Jan. tion, Oberwolfach, Federal Republic of Ger 1992,p.55) *7-11. The 29th Australian Applied Math many. (Jan. 1992, p. 55) 18-21. Numerical Analysis of Partial Differ ematics Conference (AMC '93), Hochstens, 22-28. Workshop on Pattern Formation ential Equations in Engineering and Related Hahndorf, South Australia. and Symmetry Breaking, Fields Institute for Topics, Research Institute for Mathematical PRoGRAM: The conference provides an in Research in Mathematical Sciences, Waterloo, Sciences, Kyoto University. (Jul./Aug. 1992, Ontario. (Apr. 1992, p. 351) p. 630) teractive forum for presentation of results and discussions on applied problems de 25-March 1. A Conference on Numerical 20-22. Hyperfuoctions and Differential rived in many scientific fields and amenable Analysis with Automatic Result Verification, Equations, Research Institute for Mathemat to quantitative description and solution. Lafayette, LA. (May/Jun. 1992, p. 495) ical Sciences, Kyoto University. (Jul./Aug. 1992,p.630) SPEAKERS AND TOPICS: J. Filar (U. of 28-March 6. Medical Statistics: Statistical South Australia) - greenhouse modelling, Methods for Risk Assessment, Oberwolfach, 24-30. Optimale Steuerung Partieller Dif control/system theoretic approach to green Federal Republic of Germany. (Jan. 1992, ferentialgleichungen, Oberwolfach, Federal house effect; R. May (Oxford U.)- mathe p.55) Republic of Germany. (Jan. 1992, p. 55) matical biology, spatial chaos and its role in 25-27. Fourth ACM-SIAM Symposium on ecology and evolution; B. Moran (Flinders Discrete Algorithms (SODA), Austin, Texas. U.) -neural networks and image processing; March 1993 25-29. IMA Workshop on Robotics, Institute C.J. van Duijn (Delft U.) - nonlinear dif for Mathematics and its Applications, Univer fusion, convection/diffusion, groundwater 7-13. Mathematische Stochastik, Oberwol sity of Minnesota, Minneapolis, MN. (Nov. hydraulics; B. Haverkort (U. of Twente) fach, Federal Republic of Germany. (Jan. 1992, 1991, p. 1171) - performance analysis of communica p. 55) 26-28. The Development of Algebraic tion networks and computer systems; K.R. 14-20. Gewtihnliche Differentialgleichun Toplogy, Research Institute for Mathematical Sreenivasan (Yale U.)- self-similarity, self gen, Oberwolfach, Federal Republic of Ger Sciences, Kyoto University. (Jul./Aug. 1992, affinity and turbulence dynamics. many. (Jan. 1992, p. 55) p. 630) INFORMATION: Conference Secretary, * 15-18. Arithmetic Geometry with an Em 31-February 6. Asymptotics and Adaptivity 29AMC, Dept. of Applied Math., The phasis on Iwasawa Theory, Arizona State in Computational Mechanics, Oberwolfach, Univ. of Adelaide, GPO Box 498, Ade University, Tempe, AZ. Federal Republic of Germany. (Jan. 1992, laide, South Australia 5001. p. 55) ORGANIZERS: N. Childress, J. Jones. 7-13. Partielle Differentialgleichuogen, Ober INVITED SPEAKERS: Tentative: N. Elkies wolfach, Federal Republic of Germany. (Jan. (Harvard), B. Gross (Harvard), T. Met 1992,p.55) sankyla (Finland), B. Perrin-Riou (France), February 1993 K. Ribet (California), K. Rubin (Ohio 8-17. IMA WorkshoponNonsmoothAoaly State), G. Stevens (Boston U.). 1-3. IMA Minisymposium on Biological sis and Geometric Methods in Deterministic TALKS: Participants wishing to give a talk Control of Movement, Institute for Math Optimal Control, Institute for Mathematics should send an abstract to the address ematics and its Applications, University of and its Applications, University of Minnesota, below. Please indicate the desired length Minnesota, Minneapolis, MN. (Nov. 1991, Minneapolis, MN. (Mar. 1992, p. 250) for the talk (30 or 50 minutes). The deadline p. 1172) 14-20. Applicable Algebra, Oberwo1fach, for submission of abstracts is January 15, *5-7. Representation Theory and Analy Federal Republic of Germany. (Jan. 1992, 1993. Submissions by email (in 'JEX) are sis on Homogeneous Spaces in Memory of p. 55) welcome. SEPTEMBER 1992, VOLUME 39, NUMBER 7 ...... __ .______...... _...... _..... -...... _.... _...... _.. _ ...... _...... Meetings and Conferences FUNDING: Graduate students and recent Dept. of Math. Sci., SCEN 301, Univ. merce, and NASA, National Science Foun Ph.D.s are encouraged to apply for funding of Arkansas, Fayetteville, AR 72701. dation, Environmental Protection Agency, by sending a C. V. to the address below. The and Nuclear Regulatory Commission will deadline is December 15, 1992. 9-10. Western Section, University of Utah, discuss R&D opportunities at their agenices INFORMATION: Arithmetic Geometry Meet Salt Lake City, Utah. in seminars and one-on-one meetings. Also ing, Dept. of Math., Arizona State Univ., INFORMATION: W. Drady, AMS, P.O. Box participating are companies such as Boeing, Tempe, AZ 85287; email: meeting@ 6887, Providence, RI 02940. General Dynamics, Martin Marietta, Mo artin.la.asu.edu. torola, TRW, Honeywell, IBM, Hughes, 11-17. Arbeitsgemeinschaft mit Aktuellem Texas Instruments, United Technologies, 15-19. IMA WorkshoponSystemsandCon Thema, Oberwolfach, Federal Republic of and Teledyne. trol Theory for Power Systems, Institute for Germany. (Jan. 1992, p. 56) INFORMATION: Contact the Conference Co Mathematics and its Applications, University 12-16. IMA Workshop on Adaptive Control, ordinator at 407-274-4005. of Minnesota, Minneapolis, MN. (Nov. 1991, Filtering, and Signal Processing, Institute for p. 1172) Mathematics and its Applications, University 17-20. Pure and Applied Linear Algebra: of Minnesota, Minneapolis, MN. (Nov. 1991, May 1993 The New Generation, University of West p. 1172) Florida, Pensacola, FL. (May/Jun. 1992, p. 495) * 12-16. GAMM-Jahrestagung1993,Dresden, 3-7. IMA Tutorial: Verification Issues in 21-24. Sixth SIAM Conference on Par Germany. Discrete Event Systems, as well as Perfor allel Processing for Scientific Computing, mance and Control, Institute for Mathematics Norfolk, VA. (Mar. 1992, p. 250) INFORMATION: M. Ludwig, Abteilung Math and its Applications, University of Minnesota, 21-27. Analysis auf Lokalsymmetrischen ematik, Technische Universitiit Dresden, Minneapolis, MN. (Nov. 1991, p. 1172) Raumen, Oberwolfach, Federal Republic of Mommsenstrabe 13, D-0-8027 Dresden, 3-9. Workshop on Ecological Systems, Germany. (Jan. 1992, p. 55) Germany. Fields Institute for Research in Mathemati cal Sciences, Waterloo, Ontario. (Apr. 1992, 22-28. Workshop on Pattern Formation in 14-16. Seventh SEFI European Seminar p. 352) Earth Sciences and Biology, Fields on Mathematics in Engineering Educa Institute for Research in Mathematical tion, Eindhoven University of Technology, 9-15. Reelle Algebraische Geometrie, Ober Sciences, Waterloo, Ontario. (Apr. 1992, p. 351) The Netherlands. (Feb. 1992, p. 149) wolfach, Federal Republic of Germany. (Jan. 1992,p.56) 28-April 3. Combinatorial Convexity and * 14-16. The Mathematics of Food Produc Algebraic Geometry, Oberwolfach, Federal tion, Processing, and Presentation, Belfast, 9-17. Jerusalem Combinatorics '93, He Republic of Germany. (Jan. 1992, p. 56) Great Britain. brew University of Jerusalem, Israel. (Jul./Aug. 29-April 2. Workshop on Diophantine Ge 1992,p.631) INFORMATION: The Conference Officer, ometry, Mathematical Sciences Research In 10-12. IMACS Symposium on Signal Pro The Institute of Math and its Applications, stitute, Berkeley, CA. (May/Jun. 1992, p. 495) cessing and Neural Networks-SPANN '93, 16 Nelson St., Southend-on-Sea, Esex, SS1 Universite du Quebec at Montreal, Canada. 1EF, UK. (Jan. 1992, p. 56) April1993 15-22. Symposium on Analytic and Ge 10-14. IMA Workshop on Discrete Event ometric Aspects of Hyperbolic Geometry: Systems, Manufacturing Systems, and Com ~ 4-7. First International Conference on Research Level Workshop, University of munication Networks, Institute for Mathe Mathematical Linguistics, Barcelona, Spain. Warwick, Coventry, UK. (Mar. 1992, p. 250) matics and its Applications, University of Min CHAIRMAN: C. Martin-Vide. 18-24. The Arithmetik of Fields, Oberwol nesota, Minneapolis, MN. (Nov. 1991, p. 1172) INFORMATION: C. Martin-Vide, Univ. de fach, Federal Republic of Germany. (Jan. 1992, 16-22. Mathematical Problems in VIScoelas Barcelona, Facultat de Filologia, Seccio p. 56) tic Flows, Oberwolfach, Federal Republic of de Linguistica, Gran Via de les Corts, 18-24. Mathematische Grundlagen und Germany. (Jan. 1992, p. 56) Catalanes, 585, E-08007 Barcelona. Numerische Verfahren bei Transsonischen 20-23. International Conference on Ap 4-10. Topics in Pseudo-Differential Op Stromungen, Oberwolfach, Federal Republic proximation Probability and Related Fields, University of California, Santa Barbara, CA. erators, Oberwolfach, Federal Republic of of Germany. (Jan. 1992, p. 56) Germany. (Jan. 1992, p. 56) 19-21. SIAM Conference on Mathemati (May/Jun. 1991, p. 477) 5-9. IMA Tutorial: Design and Analysis of cal and Computational Issues in the Geo 21-22. Central Section, Northern illinois Adaptive Systems, Institute for Mathematics sciences, Houston, TX. (Jul./Aug. 1992, p. 631) University, DeKalb, IL. and its Applications, University of Minnesota, 25-May 1. Low Dimensional Dynamics, INFORMATION: W.S. Drady, AMS, P.O. Box Minneapolis; MN. (Nov. 1991, p. 1172) Oberwolfach, Federal Republic of Germany. 6887, Providence, RI 02940. ~ 8-10. Clifford Algebras in Analysis, Univer- (Jan. 1992, p. 56) sity of Arkansas, Fayetteville, AR. * 27-29. NSF/DoD's National SBIR Confer- 23-29. Differentialgeometrie im Grossen, ences, Minneapolis, MN. Oberwolfach, Federal Republic of Germany. PRINCIPAL SPEAKER: A. Mcintosh, Mac (Jan. 1992, p. 56) quarie University, Australia. PRoGRAM: The NSF/DoD-sponsored Na 24-27. COMPEURO '93, Paris-Evry, France. INVITED SPEAKERS: H.B. Lawson, R. Coif tional Small Innovation Research (SBIR) (Jul./Aug. 1992, p. 631) man, J. Gilbert, B. Jawerth, C. Kenig, Conferences provide a unique marketing 30-June 1. Canadian Society for the History M. Michelsohn, M. Mitrea, M. Murray, J. opportunity by bringing together scores of * and Philosophy of Mathematics, Carleton Pipher, S. Semmes, G. Verchota, Z.J. Wu. personnel from Federal agency and ma University, Ottawa, Ontario, Canada. (Please CALL FOR PAPERS: Contributed papers jor corporations in one place at one time. note additions to Jul./Aug. 1992, p. 631) should be submitted before February 15, Reprsentatives from the Depts. of Defense, 1993. Health & Human Services (including NIH), SPECIAL SESSION: There will be a special INFORMATION: J. Ryan or I. Monroe, Energy, Education, Transportation, Com- session on the philosophy of mathemat- NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ·····-·-·······················-·- ·lllllii.-:W,a'lii!I-IIWJ:' 1-'IIBF??TTa!!'i' Meetings and Conferences ics organized by R.S.D. Thomas, Applied ulation, Oberwolfach, Federal Republic of algebraic methods in complexity theory; Math. Dept., University of Manitoba, Win Germany. (Jan. 1992, p. 56) algebraic coding theory; and cryptography. nipeg, Manitoba, R3T 2N2, Canada. 14-17. The Fifth Asian Logic Conference, CALL FOR TOPICS: A three page summary National University of Singapore, Singapore. of proposed talk should be submitted by 30-June 5. Funktionalanalysis und Nicht (May/Jun. 1992, p. 496) November 15, 1992. lineare Partielle Differentialgleichungen, INFORMATION: I. Shparlinski, Dept. no. 14-18. IMA Workshop on Mathematical Oberwolfach, Federal Republic of Germany. 4 ICSTI Kuusinena str., 21 B, Moscow, Finance, Institute for Mathematics and its (Jan. 1992, p. 56) 12552, Russia; FAX: (095) 943 00 89; Applications, University of Minnesota, Min email: [email protected] or G.L. Mullen, neapolis, MN. (Nov. 1991, p. 1172) Math. Dept., Pennsylvania State Univ., Uni June 1993 14-18. Linear Logic Workshop, Mathe versity Park, PA 16802; email: mullen@ matical Sciences Institute, Cornell University, June 1993. Fourth IMACS International math.psu.edu. Ithaca, NY. (May/Jun. 1992, p. 496) Symposium on Computational Acoustics, Cambridge, England. (Jan. 1992, p. 56) 15-18. Third IMACS International Work shop ·on Qualitative Reasoning and Deci *June 1993. GAMMIIFIP - Workshop on July 1993 sion Technologies-QR&DT-3, Polytechnique Stochastic Optimization: Numerical Meth of Barcelona, Spain. (Jan. 1992, p. 56) 4-9. Fifth International Fuzzy Systems ods and Technical Applications, Neubiberg/ Association World Congress, Seoul, Korea. Miinchen, Germany. 20-26. Konvexgeometrie, Oberwolfach, Fed eral Republic of Germany. (Jan. 1992, p. 56) (Mar. 1992, p. 250) PROGRAM COMMITTEE: H.A. Eschenauer *21-25. Twenty-second Conference on Sto 4-10. Freie Randwertprobleme, Oberwol (Siegen), P. Kall (ZUrich), K. Marti (Neu chastic Processes and their Applications, fach, Federal Republic of Gerinany. (Jan. 1992, biberg), F. Pfeiffer (Mtinchen), G.l. Schuel Amsterdam, The Netherlands. p. 57) ler (lnnsbruck). * 4-10. Fifth International Congress on Al INFORMATION: K. Marti, lnstitut fur Math INFORMATION: SPA '93, c/o CWI, P.O. Box gebraic Hyperstructures and Applications, ematik und Rechneranwendung, Fakultiit 4079, NL-1009 AB Amsterdam. lasi, Romania. ftir Luft - und Raumfahrttechnik, Univer sitiit der Bundeswehr Mtinchen, Werner *21-25. Graphs on Surfaces, Johns Hopkins SciENTIFIC CoMMITTEE: P. Corsini (Italy), Heisenberg-Weg 39, D-8014 Neubiberg/ University, Baltimore, MD. J. Jantosciak ((U.S.A.), J. Mittas (Greece), Mtinchen, Tel: (089) 6004-2541/21 09; FAX: PRoGRAM: The 16th Mathematical Sciences Y. Sureau (France), T. Vougiouklis (Greece). (089) 6004-3560. Lecture Series will feature ten lectures by CONFERENCE TOPICS: Semihypergroups, hy C. Thomassen on the subject "Graphs on pergroups, hyperrings, hyperspaces; Or * 2-5. Ninth Biennial Conference of the As surfaces". A few additional invited talks dered hyperstructures; Related topics as sociation of Christians in the Mathematical will supplement Thomassen's lectures. join spaces, cogroups, polygroups, and Sciences, Westmont College, Santa Barbara, INFORMATION: Organizer, E.R. Scheiner other multivalued structures. CA. man, Dept. of Math. Sciences, The Johns INVITED SPEAKERS: P. Corsini (Italy), J. INVITED SPEAKERS: J. Dauben, CUNY; D. Hopkins Univ., Baltimore, MD 21218- Mittas (Greece). Knuth, Stanford U. 2689; voice: 410-516-7210; FAX: 410-516- CALL FOR PAPERS: Abstracts should be CALL FOR PAPERS: Abstract deadline: De 7459; Internet: [email protected] or Bitnet: typewritten, ready for reproduction, and cember 1, 1992. ers@jhunix. should not exceed one page. The deadline INFORMATION: R. Howell, Westmont Col is May 1, 1993. lege, Santa Barbara, CA 93108; 805-565- 23-26. Convergence in Ergodic Theory and INFORMATION: M. Stefanescu, I. Tofan, and 6178; email: [email protected]. Probability, Ohio State University, Columbus, M. Gutsan, Faculty of Math., Al.I.Cuza OH. (May/Jun. 1992, p. 496) University, 6600 - lasi - Romania. 6-9. Annual Meeting of the Statistical 27-July 3. Algebraische K-Theorie, Ober 6-9. European Multigrid Conference '93, Society of Canada, Wolfville, Nova Scotia, wolfach, Federal Republic of Germany. (Jan. Canada. (Feb. 1992,p. 149) Amsterdam, The Netherlands. (May/Jun. 1992, 1992, p. 57) p. 496) 6-12. Analysis auf Kompakten Varietliten, * 29-July 2. Number Theoretic and Algebraic * 7-10. The Second International Confer Oberwolfach, Federal Republic of Germany. Methods in Computer Science, International (Jan. 1992, p. 56) ence on Fluid Mechanics (ICFM-11), Beijing, Center of Scientific and Technical Information China. 7-10. SIAM Conference on Mathematical (ICSTI), Moscow. and Numerical Aspects of Wave Propagation CONFERENCE TOPICS: Flow instability and PRoGRAM: There will be invited and con Phenomena, University of Delaware, Newark, turbulence; aerodynamics and gas dynam DE. (Jul./Aug. 1992, p. 631) tributed talks, a poster session, and a prob ics; geophysical' and astrophysical fluid me lem session. chanics; hydrodynamics; plasma dynamics 7-11. IMA Tutorial: Mathematical The CONFERENCE COMMITTEE: H. Zimmer ory which Has become an Integral Part of and magneto-hydrodynamics; biofluid me (Chair), G. Cohen, S. Cohen, J. von zur Ga chanics; physico-chemical fluid dynamics; Modern Financial Economics, Institute for then, D. Grigorev, M. Kaminski, G. Mullen, Mathematics and its Applications, University nonNewtonian fluid and multiphase flows; H. Niederreiter, A. Odlyzko, M. Pobst, C. industrial and environmental fluid mechan of Minnesota, Minneapolis, MN. (Nov. 1991, Pomerance, A. Poorten, C. Schnorr, I. Sh p. 1172) ics; and others. parlinski, S. Vladuts. INFORMATION: Z. Zhaoshun, Dept. of En 7-13. Workshop on Pattern Formation CONFERENCE TOPICS: Factoring and pri gineering Mechanics, Tsinghua University, and Cellular Automata, Fields Institute for mality testing; computational algebraic num 100084, Beijing, China. Research in Mathematical Sciences, Waterloo, ber theory; number-theoretical methods in Ontario. (Apr. 1992, p. 352) computing; irreducible, primitive, permu 11-17. Nonlinear Evolution Equations, So 13-19. ·Differential-Algebraic Equations: tation and other special polynomials; re lutions and the Inverse Scattering Trans Theory and Applications in Technical Sim- curring sequences and finite automata; form, Oberwolfach, Federal Republic of Ger- SEPTEMBER 1992, VOLUME 39, NUMBER 7 773 Meetings and Conferences many. (Jan. 1992, p. 57) * 7-21. Semigroups and their Applications, 3120; FAX: (040) 7718-2684. 12-16. SIAM Annual Meeting, Philadelphia, York, England. PA. (Mar. 1992, p. 251) 17-20. The Mathematical Heritage of Sir INFORMATION: J. Fountain, Dept. of Math., William Rowan Hamilton, Dublin, Ireland. 12-23. Conference on Universal Algebra Univ.ofYork,Heslington, YorkY015DD, (May/Jun. 1992, p. 497) and Category Theory, Mathematical Sciences UK. Research Institute, Berkeley, CA. (May/Jun. * 17-20. International Symposium on Statis 1992, p. 496) 8-14. Konstruktive Approximationstheorie, tics with Non-precise Data, Innsbruck, Aus tria. 18-24. Dynamische Systeme, Oberwolfach, Oberwolfach, Federal Republic of Germany. (Jan. 1992, p. 57) Federal Republic of Germany. (Jan. 1992, INFORMATION: R. Viertl, Institut fiir Statis p. 57) 9-12. Joint Statistical Meetings, San Fran tik und Wahrscheinlichkeitstheorie, Tech 21-25. Twenty-Second Conference on cisco, CA. (Nov. 1991, p. 1172) nische Univ. Wien, A-1040 Wien. Stochastic Processes and Their Applica * 9-13. Sixth International Conference on tions, Amsterdam, The Netherlands. (Jan. Structural Safety and Reliability (ICOSSAR * 17-21. Second International Conference 1992, p. 57) '93), Innsbruck, Austria. on Finite Fields: Theory, Applications, and Algorithms, University of Nevada, Las Vegas. 25-31. Geometric Methods in Theoreti CHAIRMEN: G.l. Schueller, Innsbruck; M. cal and Computational Mechanics, Ober Shinozuka, Princeton. PRoGRAM: The conference will feature sev wolfach, Federal Republic of Germany. (Jan. INFORMATION: ICOSSAR '93 Secretariat, eral invited one-hour lectures and several 1992,p.57) c/o Institute of Engineering Mechanics, invited half-hour lectures. There will also Univ. of Innsbruck, TechnikerstraBe 13, be sessions for 15 minute contributed pa A-6020 Innsbruck. pers. A refereed conference proceedings is planned. August1993 13-17. Second International Colloquium on INVITED SPEAKERS: Tentative: S. Cohen, J. Numerical Analysis, Plovdiv, Bulgaria. (Dec. 1-7. Abelsche Gruppen, Oberwolfach, Fed Dillon, R. Evans, M. Fried, M. Fushimi, 1991, p. 1341) eral Republic of Germany. (Jan. 1992, p. 57) J. von zur Gathen, D. Hayes, N. Koblitz, 15-21. Noncommutative Algebra and Rep H. Lenstra, R. Lidl, G. Mullen, H. Nieder 1-14. Groups 93 Galway/St. Andrews, Gal reiter, A. Odlyzko, V. Pless, V. Shoup, I. way, Ireland. (May/Jun. 1992, p. 496) resentation Theory, Oberwolfach, Federal Re public of Germany. (Jan. 1992, p. 57) Shparlinski, S. Vanstone, J. Yu. 2--6. Second Gauss Symposium, Munich, INFORMATION: P. Shiue or D. Wan, Dept. Germany. (May/Jun. 1992, p. 497) 16-19. Third SIAM Conference on Lin ear Algebra in Signals, Systems, and Con of Math. Sci., Univ. of Nevada, Las * 2--6. International Symposium on the Math trol, University of Washington, Seattle, WA. Vegas, NV 89154; 702-739-3748; FAX: ematical Theory of Networks and Systems, (Jul./Aug. 1992, p. 632) 702-597-4343; email: [email protected], Regensburg, Germany. [email protected], or G. Mullen, Math. * 16-20. First European Nonlinear Oscilla- Dept., Pennsylvania State Univ., University PURPOsE: The symposium offers theoret tions Conference, Hamburg, Germany. ically oriented engineers and mathemati Park, PA 16802; 814-865-9413; mullen@ cians in systems, control, and circuit theory INVITED SPEAKERS: P.S. Landa (Moscow math.psu.edu. State U.), J.E. Marsden (U. of California, a platform to discuss recent developments, 18-22. Fourth International Colloquium to exchange new ideas, and to analyze Berkeley), P.D. Panagiotopoulos (Aristo tle U.), W.O. Schiehlen (U. of Stuttgart), on Differential Equations, Plovdiv, Bulgaria. trends for future research. (Dec. 1991, p. 1341) CONFERENCE TOPICS: Mathematics for con J.M. T. Thompson (University College Lon trol, multivariable and robust control, sys don), H. True (Technical University of 22-28. Special Complex Varieties, Oberwol tems modeling, systems identification, Denmark), Y. Ueda (Kyoto U.), F. Verhulst fach, Federal Republic of Germany. (Jan. 1992, stochastic and adaptive control, optimal (U. of Utrecht). p. 57) control, filtering, robotics, signal process CONFERENCE TOPICS: Qualitative analysis 22-29. Twenty-ninth International Con ing and circuit theory, VLSI, neural net of nonlinear dynamic systems; quantitative gress of History of Science, Zaragoza, Spain. works and control theoretic aspects of methods for nonlinear systems; bifurcation (Apr. 1992, p. 352) theory; numerical methods in nonlinear artificial intelligence. 23-28. International Conference on Al dynamics; nonlinear random vibrations; CALL FOR PAPERS: Deadline for submission gebra Dedicated to the Memory of M.I. phenomena and criteria of chaotic oscilla of papers and proposals of special sessions: Kargapolov, Krasnoyarsk, Russia. (Jul./Aug. tions; computer aided symbolic methods in November 1, 1992. Please submit three 1992, p. 632) copies of an unpublished paper in English. dynamics; vibration control; experimental The length of the paper should not exceed methods in vibration theory; and applica 25-September 3. Forty-ninth Biennial Ses 10 pages. tions in mechanical engineering, electrical sion of the International Statistical Institute, INFORMATION: MTNS 93, U. Helmke, De engineering, physics, biology, chemistry, Firenze, Italy. (Nov. 1991, p. 1172) partment of Math., University of Regens and other sciences. 29-September 4. Random Graphs and Com burg, D-8400 Regensburg, Germany; FAX: CALL FOR PAPERS: Prospective authors are binatorial Structures, Oberwolfach, Federal +49-941-943-4005/2305; email: helmke@ invited to submit three copies of a 300- Republic of Germany. (Jan. 1992, p. 57) 400 word summary (one single page only) vaxl.rz.uni-regensburg.dbp.de. * 30-September 3. Inverse Problems: Princi indicating one of the topics from above to 2-13. Georgia International Topology Con ples and Applications in Geophysics, Tech which it should be assigned. Summaries nology, and Medicine, Potsdam (near Berlin), ference, University of Georgia, Athens, GA. must be received by February 1, 1993. Germany. (May/Jun. 1992, p. 497) INFORMATION: lng. E. Kreuzer, Arbeits 4--6. SIAM Conference on Simulation and bereich Meerestechnik II, Technische Uni INFORMATION: G. Anger, Rathausstr. 13, Computational Probability, San Francisco, versitat Hamburg-Harburg, Eillendorfer Str. W g. 11/09, D-0-1020 Berlin; email: anger@ CA. (Jul./Aug. 1992, p. 632) 42, D-2100 Hamburg 90, Tel: (040) 7718- de.dbp.uni-hal1e.mathematik. 774 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ··························------Meetings and Conferences 31-November 6. Algorithmische Methoden matical work, the "lineale Ausdehnungs der Diskreten Mathematik, Oberwolfach, lehre" (1844), will be the occasion to September 1993 Federal Republic of Germany. (Mar. 1992, present a comprehensive picture of this 5-11. Novikov Conjectures, Index Theorems p.251) great scholar's life and work. Particular and Rigidity, Oberwolfach, Federal Republic emphasis will be given to his influence, of Germany. (Jan. 1992, p. 57) which has scarcely been studied in detail as 5-12. First World Conference on Branching November 1993 yet-in mathematics as well as in physics and in linguistics. Processes, Varna, Bulgaria. (May/Jun. 1992, 21-27. Mathematische Modelle in der Bi INFORMATION: G. Schubring, lnstitut fiir p. 497) ologie, Oberwolfach, Federal Republic of Ger Didaktik der Mathematik, Universitiit Biele many. (Mar. 1992, p. 251) 12-18. Topologie, Oberwolfach, Federal Re feld, Postfach 100131, D-W 4800 Bielefeld public of Germany. (Jan. 1992, p. 57) 28-December 4. Nonlinear Equations in 1. 13-17. Fourth European Software En Many-Particle Systems, Oberwolfach, Fed gineering Conference, Garmisch, Germany. eral Republic of Germany. (Mar. 1992, p. 251) (Jul./Aug. 1992, p. 632) June 1994 13-18. Different Aspects of Differentiability, Warsaw, Poland. (May/Jun. 1992, p. 497) January 1994 13-17. Fifth International Conference on 19-25. Mathematical Game Theory, Ober 5-8. Joint Mathematics Meetings, Cincin Hyperbolic Problems Theory, Numerical wolfach, Federal Republic of Germany. (Jan. nati, OH. (including the annual meetings of the Methods, and Applications, Stony Brook, 1992, p. 57) AMS, AWM, MAA, and NAM) NY. (May/Jun. 1992, p. 497) 22-23. Central Section, Texas A&M Univer INFORMATION: H. Daly, AMS, P.O. Box sity, College Station, TX. 6248, Providence, RI 02940. August 1994 INFORMATION: W.S. Drady, AMS, P.O. Box 6887, Providence, RI 02940. 1-5. Third World Congress on Computa February 1994 tional Mechanics (WCCM ill), Chiba, Japan. 26--0ctober 2. Diophantische Approxima 2-4. IMACS Symposium on Mathematical (May/Jun. 1992, p. 497) tionen, Oberwolfach, Federal Republic of Ger * Modelling, Vienna, Austria. 3-11. The International Congress of Math many. (Jan. 1992, p. 57) ematicans 1994, ZUrich, Switzerland. (Mat. INFORMATION: I. Troch, Inst. fiir Analysis, 1992,p.249) Technische Mathematik und Versichrungs mathematik, TU Wien, Wiedner Hauptstr. 8- 10, A-1040 Wien, Tel: 0222/588 01.. The following new announcements will not be repeated until the criteria in the last 1995 paragraph in the box at the beginning of this March 1994 Second International Conference on Nu section are met. merical Methods for Volterra and Delay 25-26. Central Section, Kansas State Univer Equations (A conference to celebrate the sity, Manhattan, KS. tOOth anniversary of Volterra's birth.), Italy. (Mar. 1992, p. 251) October 1993 INFORMATION: W.S. Drady, AMS, P.O. Box 6887, Providence, RI 02940. 3-9. Arbeitsgemeinschaft mit Aktuellem Tbema, Oberwolfach, Federal Republic of March 1995 Germany. (Jan. 1992, p. 57) May 1994 17-23. Geometrie, Oberwolfach, Federal Re 24-25. Central Section, DePaul University, public of Germany. (Jan. 1992, p. 57) * 24-27. Conference on Hermann G. GraB Chicago, IL. (Please note date was previously mann (1809-1877), Isle of Rugen, Germany. incorrectly listed as 1993.) 25-29. Third SIAM Conference on Geo metric Design, Seattle, WA. (Jul./Aug. 1992, PROGRAM: The 150th anniversary of the INFORMATION: W.S. Drady, AMS, P.O. Box p. 632) publication of GraBmann's major mathe- 6887, Providence, RI 02940. SEPTEMBER 1992, VOLUME 39, NUMBER 7 775 New Publications Offered by the AMS ADVANCES IN SOVIET MATHEMATICS AMERICAN MATHEMATICAL SOCIETY TRANSLATIONS, SERIES 2 Entire and Subharmonic Functions Second Siberian Winter B. Ya Levin, Editor School "Algebra and Volume 11 Analysis" The papers in this collection, written I. A. Aleksandrov, by participants of the Research Seminar on the Theory of Functions at Kharkov L. A. Bokut', and Yu. G. University, primarily address the theory Reshetnyak, Editors of entire and subharmonic functions. Volume 151 Founded in 1953 by B. Ya. Levin and still functioning today, this seminar ranges This book, the second in the series over different problems in the theory of functions, functional analysis, of proceedings of Soviet Regional and related problems in calculus and mathematical physics. Entire Conferences, contains papers presented at the Second Siberian Winter School: Algebra and Analysis, held at and Subharmonic Functions contains works presented recently in the seminar. Tomsk State University in 1989. The papers touch on a variety oftopics, including Lie algebras and Lie groups, sheaves, superalgebras, graded Contents Lie algebras, Teichmiiller theory, nonstandard functional analysis, A. M. Ulanovskll, On the completely regular growth of analytic functions hyperbolic geometry, p-adic £-functions, automorphic forms, and having maximum on a Ray; M. Sodin, Value distribution ofsequences of rational resolution of singularities. functions; M. Simbirskii, Inverse problem for the Sturm-Liouville operator with Contents almost-periodic potential having only positive Fourier exponents; L. I. Ronkin, A. V. Alekseevskii, On gradings of simple Lie algebras connected with groups Subharmonic functions of completely regular growth in a closed cone; L. R. .generated by transvections; A. B. Verevkin, On a noncommutative analogue of Podoshev, Complete description of the pair indicator-lower indicator of an the category of coherent sheaves on a projective scheme; I. L. Kantor, Jordan entire function; I. V. Ostrovskll, Solvability conditions for the homogeneous and Lie superalgebras determined by a Poisson algebra; S. L. Krushkal', New Riemann boundary problem with an infinite index; Yu. I. Lyubarski'i and V. A. methods and trends in geometric fimction theory; A. G. Kusraev and S. S. Tkachenko, Completeness of a system offunctions on sets in the complex plane; Kutateladze, Nonstandard methods in geometric functional analysis; A. D. Yu. I. Lyubarskll, Frames in the Bargmann space of entire functions; B. Ya. Mednykh, Automorphism groups of three-dimensional hyperbolic manifolds; Levin, V. N. Logvinenko, and M •. L. Sodin, Subharmonic functions offinite A. A. Panchishkin, Automorphic forms, L-functions, and p-adic analysis; S. I. degree bounded on subsets of the "Real Hyperplane"; A. A. Goldberg and Trifonov, Resolution of singularities in one-parameter analytic families of V. A. Pyana, Uniqueness theorems for algebraic functions; A. E. Fryntov, differential equations. Subharmonic functions and cos(1r >.)-theorems for entire functions represented by gap series; V. N. Logvinenko and S. Yu. Favorov, Lacunarv series and Fourier 1991 Mathematics Subject Classification: llSXX, 14F05, 17-XX, 32-XX, integrals offunctions of several variables; A. E. Eremenko. and M. L. Sodin, 46S20; llFXX, 30-XX, 58-XX Parametrization of entire functions of sine-type by their critical values; L. B. ISBN 0-8218-3142-9, LC 92-15960, ISSN 0065-9290 Golinskll and G. P. Chistyakov, On stability estimates in the Marcinkiewicz 145 pages (hardcover), September 1992 theorem and its generalization; V. S. Azarin and V. B. Giner, Limit sets and Individual member $78, List price $130, Institutional member $104 To order, please specify 1RANS2/151N multiplicators of entire functions. 1991 Mathematics Subject Classification: 14H05, 30B05, 30C80, 30015, 30020,30035, 30E05, 30E25, 31A02, 31A05, 34A55, 34B24, 42Bl0, 60E10; 31A05, 34Ll0, 34L15, 42A75 ISBN 0-8218-4110-6, LC 91-640741, ISSN 1051-8037 275 pages (hardcover), September 1992 Individual member $88, List price $147, Institutional member $118 To order, please specify AOVSOV/llN Use the order form in the back of this issue or call800-321-4AMS (800-321-4267) in the U.S. and Canada to use VISA or MasterCard. 776 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ...... ~ .. --.lllll!l!llllllll!ll!i!llllllll!ll!l!llllllll!ll!l!llllllll!ll!l!llllllll!ll!l!llllllll!ll!l!llllllll!ll!l!llllllll!ljiii!I!IIIIIIII!IJI.'J!lliiliillillllll!l!llllllll!l~·-·""""'"-~'"""""" New Publications Offered by the AMS subjects covered here range from topology and geometry to logic and theoretical computer science, from homotopy to braids and conformal field theory. Although generally aimed at experts in the various fields represented, the book will also provide an excellent opportunity for APPLIED DISCRETE MATHEMATICS AND nonexperts to get a feel for the diversity of current applications of category theory. THEORETICAL COMPUTER SCIENCE Contents A. Bagchi, DeMorgan' s law and related idellfities in classifying topoi; B. Banaschewski and A. Pultr, A Stone duality for metric spaces; R. Betti, Sheaves in cocomplete categories; D. Bourn, Low dimensional geometry of --... Convergence Theory the notion of choice; M. Bunge, Classifying toposes and fundamentallocalic --- of Feasible Direction groupoids; A. Carboni, M. C. Pedicchio, and N. Pirovano, Internal graphs Convergence Theory of and internal groupoids in Mal' cev categories; G. Castellini, J. Koslowski, and Feasible Direc!lon Methods Methods G. E. Strecker, Hereditary and modal closure operators; H. A. Chen and P. H. Du Dingzhu Chu, What is a Gabriel topology over a graded ring?; J. R. B. Cockett and Volume 1 D. Spencer, Strong categorical datatypes I; Y. Diers, The Zariski category of ""- graded commutative rings; R. C. Flagg, Completeness in continuity spaces; This monograph, the first in a new series published by Science Press New K. A. Hardie and K. H. Kamps, Variations on a theme of Dold; H. Hu, York and Science Press Beijing and Dualities for accessible categories; J. Isbell, Some problems in descriptive distributed by the AMS, covers various locale theory; J. F. Jardine, Modelling homotopy coherence; G. Jarzembski, aspects of convergence theory for feasible Elementary reflections of concrete categories of mixed structures; M. Johnson direction methods in nonlinear programming. In particular, slope and S.-H. Sun, Remarks on representations of universal algebras by sheaves lemmas play an important role here, providing a means for simplifying of quotient algebras; V. Lyubashenko, Categorical aspects of conformal field the theory. Following the historical development, Dingzhu uses gradient theory; S. Mac Lane, Coherence theorems and conformal field theory; S. Majid, projection methods as threads throughout the book. Many basic Braided groups and duals of monoidal categories; C. J. Mulvey and J. W. results included here have not appeared in other books on this subject. Pelletier, A quantisation of the calculus of relations; D. Pavlovic, A logical view Providing a state-of-the-art review of activity in convergence theory, on the adjoint functor theorem; G. Richter, Axiomati::ing algebraically behaved this small book will prove useful as an introduction to the field as well categories of Hausdorff spaces; R. Rosebrugh and R. J. Wood, Relational as a reference for specialists. databases and indexed categories; K. I. Rosenthal, Linear indexed quantales and quantalic hyperdoctrines; M. Sobral and W. Tholen, Effective descent Contents morphisms and effective equivalence relations; V. Trnkova, Functorial selection Introduction and preliminaries; Slope lemmas; Rosen's method and its ofmorphisms. convergence; Combining with variable metric methods; E:-Active set strategy; Reduced gradient methods; Point-to-set mapping; On other topics. 1991 Mathematics Subject Classification: 18-06; OOBIO, 18-02 ISBN 0-8218-6018-6, LC 92-24186, ISSN 0731-1036 1991 Mathematics Subject Classification: 90, 49 447 pages (softcover), September 1992 ISBN 1-880132-00-1; 7-03-002633-0/0.495 Science Press, Beijing Individual member $46, List price $76, Institutional member $61 118 pages (hardcover), 1991 To order, please specify CMSAMS/13N List price $31 To order, please specify ADM/IN CONTEMPORARY MATHEMATICS CONFERENCE PROCEEDINGS, CANADIAN MATHEMATICAL SOCIETY Deformation Theory and Quantum Groups with Applications to Category Theory 1991 : Mathematical Physics Proceedings of the Murray Gerstenhaber and 1991 Summer Category James D. Stasheff, Editors Theory Meeting, Montreal, Volume 134 catagory Thaory 1991: P/0Ct8dlngsotthe 1991 SUmmer Canada Quantum groups are not groups at ' Montreaf.canada. R.A.G. Seely, Editor all, but special kinds of Hopf algebras --- of which the most important are closely Volume 13 related to Lie groups and play a central role in the statistical and wave As category theory approaches its mechanics of Baxter and Yang. Those occurring physically can be first half-century, it continues to grow, studied as essentially algebraic and closely related to the deformation finding new applications in areas that theory of algebras (commutative, Lie, Hopf, and so on). One of would have seemed inconceivable a generation ago, as well as in more the oldest forms of algebraic quantization amounts to the study of traditional areas. The language, ideas, and techniques of category theory deformations of a commutative algebra A (of classical observables) are well suited to discovering unifying structures in apparently different to a noncommutative algebra Ah (of operators) with the infinitesimal contexts. Representing this diversity of the field, this book contains deformation given by a Poisson bracket on the original algebra A. the proceedings of an international conference on category theory. The SEPTEMBER 1992, VOLUME 39, NUMBER 7 777 ...... -·--·····-·······"··-···-····-·······-·······-·········-··········-········-··········-·-·········------··········-···-············... ·································-·-················································-···········"····--················-······ New Publications Offered by the AMS This volume grew out of an AMS-IMS-SIAM Joint Summer conjugacies of shifts offinite type are uniquely so; C. Bernhardt and E. M. Research Conference, held in June 1990 at the University of Coven, A polynomial time algorithm for deciding the forcing relation on cyclic Massachusetts at Amherst. The conference brought together leading permutations; F. Blanchard, Fully positive topological entropy and topological researchers in the several areas mentioned and in areas such as "q mixing; M. Boyle, The stochastic shift equivalence conjecture is false; special functions", which have their origins in the last century but A. Broglio and P. Liardet, Predictions with automata; D. Fiebig, Common whose relevance to modern physics has only recently been understood. closing extensions and finitary regular isomorphism for synchronized systems; Among the advances taking place during the conference was Majid's D. Fiebig and U.-R. Fiebig, Covers for coded syste~ns; L. Flatto, Z-numbers reconstruction theorem for Drinfel' d's quasi-Hopf algebras. Readers and {3-transformations; M. V. Jakobson, Quasisymmetric conjugacies for some will appreciate this snapshot of some of the latest developments in the one dimensional maps inducing expansion; J.-M. Gambaudo and C. Tresser, A mathematics of quantum groups and deformation theory. monicity property of one dimensional dynamics; D. Handelman, Finiteness of conjugacy classes of restricted block upper triangular matrices; D. Handelman, Contents Polynomials with some power being positive; D. Handelman, Spectral radii of M. Cohen, Hopf algebra actions---revisited; P. Cotta-Ramusino and primitive integral companion matrices and log concave polynomials; R. Kenyon, M. Rinaldi, Link-diagrams, Yang Baxter equations, and quantum holonomy; Self-replicating tilings; B. P. Kitchens and K. Schmidt, Markov subgroups L. Crane, Duality and topology of 3-manifolds; M. Gerstenhaber and S. D. of (Z/2)z 2 ; F. Ledrappier, On the dimension of some graphs; D. Perrin and Schack, Algebras, bialgebras, quantum groups, and algebraic deformations; M.P. Schutzenberger, Synchronizing prefix codes and automata and the road J, M. Gracia-Bonctia, Generalized Moyal quantization on homogeneous coloring problem; S. Mozes, A zero entropy mixing of all orders tiling system; symplectic spaces; R. Grossman and D. Radford, A simple construction W. Parry, A cocycle equation for shifts; W. Parry, In genral a degree 2 map is of bialgebra deformations; G. F. Helminck, Integrable deformations of an automorphism; C. Radin, zn versus Z for syste/ns offinite type; F. Rhodes, meromorphic equations on IP' 1(1C); N.H. Jing, Quantum groups with two Principal vectors of commuting block maps; I. A. Salama, On the recurrence parameters; H. T. Koelink, Quantum group theoretic proof of the addition of countable topological Markov chains; B. Solomyak, Substitutions, adic formula for continuous q-Legendre polynomials; H. T. Koelink and T. H. transformations and beta-expansions; M. Smorodinsky, Finitary isomorphism Koomwinder, q-specialfunctions, a tutorial; T. H. Koornwinder, q-special ofm-dependent processes; P. Trow, Constant to one factor maps and dimension functions and their occurrence in quantum groups; V. Lakshmibai and groups; S. Tuncel, Faces of Markov chains and matrices ofpolynomials; J, B. N. Reshetikhin, Quantum flag and Schubert schemes; L. A. Lambe, Wagoner, Classification of subshifts offinite type; R. F. Williams, Strong shift Homological perturbation theory, Hochschild homology, and formal groups; equivalence of matrices in GL(2, Z). S. Ml\iid, Tannaka-Krein theorem for quasi-Hopf algebras and other results; S. Montgomery, Simple smash products; J, H. Przytycki, Quantum group 1991 Mathematics Subject Classification: 28D99, 54H20; 58F99, 60J10 of links in a handlebody; A. Jeu-Liang Sheu, Quantum Poisson SU(2) and ISBN 0-8218-5146-2, LC 92-20203, ISSN 0271-4132 quantum Poisson spheres; S. Shnider, Deformation cohomology for bialgebras 452 pages (softcover), September 1992 and quasi-bialgebras; J, Stasheft', Dririfel' d's quasi-Hop! algebras and beyond; Individual member $33, List price $55, Institutional member $44 To order, please specify CONM/135N M. Takeuchi, Hopf algebra techniques applied to the quantum group Uq(sl(2)); D. N. Yetter, Framed tangles and a theorem ofDeligne on braided deformations of Tannakian categories; C. Zachos, Elementary paradigms of quantum ~ Curves, Jacobians, algebras. CONTEMPOI<'ARV and Abelian Varieties: 1991 Mathematics Subject Classification: 16W30, 17B37, 18010, 81R05 ;MAiTI:ItMII.IrlCS ISBN 0-8218-S141-l, LC 92-13890, ISSN 0271-4132 ------~------Proceedings of a Summer 377 pages (softcover), September 1992 Research Conference Individual member $33, List price $55, Institutional member $44 To order, please specify CONM/134N on the Schottky Problem Ron Donagi, Editor Volume 136 ~ Symbolic Dynamics CoNTEM'"OfM:'RY This volume contains the proceedings MATHEMATICS and its Applications of an AMS-IMS-SIAM Joint Summer ------Peter Walters, Editor Research Conference on the Schottky Volume 135 Problem, held in June 1990 at the University of Massachusetts at Amherst. The conference explored various aspects of the Schottky This volume contains the proceedings problem of characterizing Jacobians of curves among all abelian of the conference, Symbolic Dynamics varieties. Some of the articles study related themes, including the moduli and its Applications, held at Yale of stable vector bundles on a curve, Prym varieties and intermediate University in the summer of 1991 in Jacobians, and special Jacobians with exotic polarizations or product honor of Roy L. Adler on his sixtieth structures. • birthday. The conference focused on symbolic dynamics and its applications Contents to other fields, including ergodic theory, smooth dynamical systems, R. D. M. Accola, Theta vanishings for some smooth Abelian coverings of information theory, automata theory, and statistical mechanics. One Riemann surfaces; K. Berry and M. Tretkoff, The period matrix of Macbeath' s hundred thirty-nine participants attended from thirteen countries, curve of genus seven; R. Brooks, The continued fractions parameter in the representing mathematics, applied mathematics, electrical engineering, deformation theory of classical Schottky groups; R. Donagi, The fibers of and physics departments in universities and in industry. Featuring a the Prym map; C. J, Earle, Some Riemann surfaces whose Jacobians have range of contributions from some of the leaders in the field, this volume strange product structures; L. Ehrenpreis, The Schottky relation in Genus 4; presents an excellent overview of the subject. H. M. Farkas, The trisecantformula and hyperelliptic surfaces; J, Fay, The Contents non-abelian Szego kernel and theta-divisor; G. Gonzalez Diez, Theta functions on the boundary of moduli space; A. I. Iliev, Geometry ofthefano threefold of R. L. Adler, The torus and the disk; B. Weiss, On the work of Roy Adler in degree 10 of the first type; J. Jorgenson, Some uses of analytic torsion in the ergodic theory and dynamical systems; B. Marcus, The impact ofRoy Adler's study of Weierstrass points; G. R. Kempf, A problem of Narasimhan; H. H. work on symbolic dynamics and applications to data storage; J, Ashley, L. R. 778 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ••••• ••••mmmm mmm ~m. ~~® ~--~m~mm New Publications Offered by the AMS Martens, On the reduction of Abelian integrals and a problem of H. Hopf; R. Rochberg, A correspondence principle for Toeplitz and Calderon-Toeplitz M. Mulase, Normalization of the Krichever data; J, F. X. Ries, Splittable Jacobi operators; P. A. Shvartsman, K-functionals of weighted Lipschitz spaces and varieties; M. Teixidor-1-Bigas and L. W. Th, Theta divisors for vector bundles. Lipschitz selections ofmultivalued mappings; L. V. Veselova and N. M. Zobin, On a tensor approach to interpolation theory. 1991 Mathematics Subject Classification: 14H42; 14H40, 14K25, 32G20 ISBN 0-8218-5143-8, LC 92-20586, ISSN 0271-4132 1991 Mathematics Subject Classification: 46B70; 41A30, 42C05, 42CIO, 342 pages (softcover), September 1992 46Al6, 46A62, 46B42, 46110, 46M35 Individual member $37, List price $62, Institutional member $50 ISSN 0792-4119 To order, please specify CONM/136N 294 pages (softcover), August 1992 Individual member $24, List price $40, Institutional member .$32 To order, please specify IMCP/SN ISRAEL MATHEMATICAL CONFERENCE PROCEEDINGS MEMOIRS OF THE AMS Interpolation Spaces ~ iVJ! \l( llf'"' lmbeddings of and Related Topics Three-manifold Groups Michael Cwikel, - Wilbur C. Whitten and Mario Milman, and F. Gonzalez-Acuiia Richard Rochberg, Editors Volume 99, Number 474 \Wbvr¢, Wbttten VolumeS F.- This work deals with the two broad This book contains the proceedings questions of how three-manifold groups of the International Workshop on imbed in one another and how such Interpolation Spaces and Related Topics, imbeddings relate to any corresponding held at Technion in Haifa, Israel, in the 1r1-injective maps. The focus is on when summer of 1990. Interpolation spaces have their roots in the classical a given three-manifold covers another given manifold. In particular, interpolation theorems of Marcik:iewicz and Riesz-Thorin. In the the authors are concerned with 1) determining which three-manifold last three decades, the study of these spaces has developed into an groups are not cohopfian-that is, which three-manifold groups imbed extensive theory with applications in several fields, including harmonic properly in themselves; 2) finding the knot subgroups of a knot analysis, partial differential equations, and geometry of Banach spaces. group; and 3) investigating when surgery on a knot K yields lens (or Substantial contributions have come from both sides of the former "lens-like") spaces and how this relates to the knot subgroup structure of "Iron Curtain", and the Haifa Workshop was the first time that sizable 1r1 (83 - K). The authors use the formulation of a deformation theorem contingents of experts from East and West could meet and interact. for 1r1-injective maps between certain kinds of Haken manifolds and The twenty-one research papers in this volume reflect recent develop some algebraic tools. developments at the frontier of research in several directions in interpolation theory. In addition, the volume provides a concise and Contents convenient summary of interesting but hitherto less well-known work Deformation theorems; Cohopficity; Coverings between knot exteriors; in interpolation from the Russian schools of Yaroslavl and Kazan. One Subgroups offinite index; Knot subgroups of torus-knot groups; Depth, and highlight is an extensive list of unsolved problems in interpolation loose and tight subgroups; Knot subgroups of knot groups. theory, including contributions from a number of experts who were 1991 Mathematics Subject Classification: 55N99, 57M05, 57M10, 57M25, unable to attend the workshop. This volume was published by Bar-llan 57N10, 57N35 University and is distributed by the AMS. ISBN 0-8218-2534-8, LC 92-18062, ISSN 0065-9266 71 pages (softcover), September 1992 Contents Individual member $14, List price $23, Institutional member $18 A. Bernal, Some results on complex interpolation of r: spaces; Y. A. To order, please specify MEM0/99/474N Brudnyi, Some recent general results in interpolation theory; M. J, Carro and J, Cerda, On the interpolation of analytic families of operators; F. Cobos and I. Resina, An interpolation formula for approximation spaces; W. C. Connett - M U;]{ >]!\', On the Existence of and A. L. Schwartz, Interpolation of Banach algebras; M. Cwikel and Feller Semigroups with A. Sharif, Complex interpolation spaces generated by the Gagliardo completion - Boundary Conditions of an arbitrary Banach couple; E. Hermindez and J, Soria, Interpolation theorems of some weighted quasi-Banach spaces; B. Jawerth and M. Milman, Kazuaki Taira New results and applications of extrapolation theory; B. Jawerth and Volume 99, Number 475 M. Milman, Wavelets and best approximation in Besov spaces; N. J, Kalton, On a question of Pisier; N. J, Kalton, Remarks on lattice structure in fp and This monograph provides a careful Lp when 0 < p < 1; R. A. Kerman, Convergence of approximate identities and accessible exposition of functional in weighted Lebesgue spaces; M. MastyJ:o, Interpolation functors commuting analytic methods in stochastic analysis. with direct products; M. Milman, Local operators vs Lorentz-Marcinkiewicz The author focuses on the relationship spaces; I. Ya. Novikov, Inner estimates; B. P. Osilenker, The generalized among three subjects in analysis: Markov A-translation in a multiple orthogonal polynomial system; V.I. Ovchinnikov, processes, Feller sernigroups, and elliptic boundary value problems. On the description of interpolation orbits in couples of Lp spaces when they The approach here is distinguished by the author's extensive use of are not described by the K -method; Y. Raynaud, On Lorentz-Sharpley spaces; the theory of partial differential equations. Filling a mathematical gap between textbooks on Markov processes and recent developments in SEPTEMBER 1992, VOLUME 39, NUMBER 7 779 ...... ········-·············-················lllllllllllllll------················-···············-········-······-·······-···········-··-····························-·-··-····-·······-·······-····-·····--· New Publications Offered by the AMS analysis, this work describes a powerful method capable of extensive Contents further development. The book would be suitable as a textbook in a Basic constructions; Coordinates and coordinate relations; Groups of rank one-year, advanced graduate course on functional analysis and partial two; Th:: subregular spurious divisor; The subregu/ar fundamental divisor; differential equations, with emphasis on their strong interrelations with Rationality and characters; Applications to endoscopic groups. probability theory. 1991 Mathematics Subject Classification: 20025; 12B27, 22E35 Contents ISBN 0-8218-2539-9, LC 92-18060, ISSN 0065-9266 Introduction and results; Theory of Feller semigroups; Theory of pseudo 142 pages (softcover), September 1992 Individual member $17, List price $28, Institutional member $22 differential operators; Proof of Theorem I; Proof of Theorem 2; Appendix the To order, please specify MEM0/99/476N maximum principle. 1991 Mathematics Subject Classification: 35125, 47007; 47005, 60135, 60160 - ISBN 0-8218-2535-6, LC 92-18061, ISSN 0065-9266 lV1 L \]\ lll~~ The Continued Fractions 65 pages (softcover), September 1992 Found in the Uno~ganized Individual member $14, List price $23, Institutional member $18 ~ To order, please specify MEM0/99/475N Portions of Ramanujan's Notebooks George E. Andrews, Bruce ~ The Subregular Germ 1\:1! \ji )ll\c;_ C. Berndt, Lisa Jacobsen, Orbital Integrals of and Robert L. Lamphere Thomas C. Hales - Volume 99, Number 477 Volume 99, Number 476 • The SUbregular Genn Among his thirty-three published of Orbital Integrals Langlands theory predicts deep papers, Ramanujan had only one continued fraction, the Rogers relationships between representations of Ramanujan continued fraction. However, his notebooks contain over different reductive groups over a local or 100 results on continued fractions. At the end of his second notebook are global field. The trace formula attempts 100 pages of unorganized material, and the third notebook comprises to reduce many such relationships to thirty-three pages of disorganized results. In these 133 pages of material problems concerning conjugacy classes are approximately sixty theorems on continued fractions, most of them and integrals over conjugacy classes new results. In this monograph, the authors discuss and prove each (orbital integrals) on p-adic groups. It is possible to reformnlate these of these theorems. Aimed at those interested in Ramanujan and his problems as ones in algebraic geometry by associating a variety Y work, this monograph will be of special interest to those who work to each reductive group. Using methods of Igusa, the geometrical in continued fractions, q-series, special functions, theta-functions, and properties of the variety give detailed information about the asymptotic combinatorics: The work is likely to be of interest to those in number behavior of integrals over conjugacy classes. This monograph constructs theory as well. The only required background is some knowledge of the variety Y and describes its geometry. As an application, the author continued fractions and a course in complex analysis. uses the variety to give formulas for the leading terms (regular and subregular germ~) in the asymptotic expansion of orbital integrals over 1991 Mathematics Subject Classification: 30B70, 40A15 p-adic fields. The final chapter shows how the properties of the variety ISBN 0-8218-2538-0, LC 92-18059, ISSN 0065-9266 may be used to confirm some predictions of Langlands theory on orbital 71 pages (softcover), September 1992 Individual member $14, List price $23, Institutional member $18 integrals, Shalika germs, and endoscopy. To order, please specify MEM0/99/477N History of Mathematics, Volume 5 • George W. Mackey, Editor This volume presents a sweeping view of the importance, utility, and beauty of harmonic analysis and its connections to other areas of mathematics and science. Aimed at mathematicians in all areas as well as mathematically-oriented theoretical physicists and advanced graduate students, Mackey's book is not directed to specialists but is intended to help specialists learn about fields other than their own and about the relationships among fields. Readers will appreciate this book for its lucid expository presentations and for its wide-ranging treatment of the subject. This volume is published jointly with the London Mathematical Society. 1991 Mathematics Subject Classification: 00; 01, 11, 22, 81 ISBN 0-8218-9000-X, 370 pages (hardcover), July 1992 Individual member $31, List price $52, Institutional member $42 Your ordering code is HMATH/5NA All prices subject to change. Free shipment by surface: for air delivery, please add $6.50 per title. Prepayment required. Order from: American Mathematical Society, P.O. Box 1571, Annex Station, Providence, RI 02901-1571, or call toll free 800-321-4AMS (321-4267) in the U.S. and Canada to charge with VISA or MasterCard. Residents of Canada, please include 7% GST. 780 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY AMS Reports and Communications Statistics on Women women would also be collected using the Mathematicians Compiled AMS-MAA Annual Survey. Since name Members of the AMS by the AMS identification was used, the information Residing in the U.S. At its August 1985 meeting, the Council for some categories necessitated the use Male: 14,423 72% of the AMS approved a motion to regu of four classifications: Female: 3,398 17% larly assemble and report in the Notices Unknown: 1,776 9% Male: names that were obviously information on the relative numbers of Foreign: 468 2% male; men versus women in at least the fol Total checked: 20,065 Female: names that were obviously lowing categories: membership in the female; Invited Hour Address Speakers AMS; invited hour addresses at AMS Unknown: names that could not be at AMS Meetings (1982-1991) meetings; speakers at special sessions at identified as clearly male or female (e.g., Male: 353 92% AMS meetings; and members of edito only initials given); and Female: 32 8% rial boards of AMS journals. Foreign: foreign names that could Unknown: I 0% It was subsequently decided that this Foreign: 0 0% not be identified as clearly male or information would be gathered by deter Total checked: 386 female. mining the sex of the individuals in the above categories based on name identi The following is the seventh report Speakers at Special Sessions at AMS Meetings (1987-1991) fication and that additional information ing of this information. Updated reports Male: 4,051 on the number of Ph.D.'s will appear annually in 85% granted to the Notices. Female: 361 8% Unknown: 167 3% Foreign: 204 4% Total checked: 4,783 Trustees and Council Members ...l.22L ____!22Q_ ~ ~ Total: 50 52 53 56 Male: 45 90% 45 87% 46 87% 46 82% Female: 5 10% 7 13% 7 13% 10 18% Members of Editorial Boards of AMS Journals 1991 1990 1989 1988 1987 1986 1985 1984 1983 1982 Total: 169 183 194 161 133 109 102 93 90 83 Male: 156 92% 171 93% 182 94% 148 92% 125 94% 104 95% 94 92% 85 91% 84 93% 77 93% Female: 13 8% 12 7% 11 6% 13 8% 8 6% 5 5% 8 8% 8 9% 6 7% 6 7% Ph.D.s Granted to U.S. Citizens 1991 1990 1989 1988 1987 1986 1985 1984 1983 1982 Total: 461 401 411 363 362 386 396 433 455 519 Male: 349 76% 312 78% 313 76% 287 79% 289 80% 304 79% 315 80% 346 80% 366 80% 431 83% Female: 112 24% 89 22% 98 24% 76 21% 73 20% 82 21% 81 20% 87 20% 89 20% 88 17% SEPTEMBER 1992, VOLUME 39, NUMBER 7 781 Officers and Committee Members Numbers to the left of headings are used as points of reference in a index to W. Wistar Comfort 1992 AMS committees which follows this listing. Primary and secondary headings Andy Roy Magid 1993 are: Lance W. Small 1993 Treasurer Franklin P. Peterson 1992 Officers Associate 1.1 Uaison Committee Treasurer Steve Armentrout 1992 2 Council 2.1 Executive Committee of the Council 3 Board of Trustees 2.0.2. Representatives of Committees 4 Committees American Journal of 4.1 Committees of the Council Mathematics M. Salah Baouendi 1992 4.2 Editorial and Communications Committees Bulletin FrankS. Quinn 1993 4.3 Committees of the Board of Trustees Colloquium G. D. Mostow 1993 4.4 Internal Organization of the AMS Executive Committee Arthur M. Jaffe 1994 4.5 Program and Meetings Executive Committee Hugo Rossi 1992 4.6 Status of the Profession Journal of the AMS Wilfried Schmid 1993 4. 7 Prizes and Awards Committee to Monitor 4.8 Institutes and Symposia Problems in 4.9 Joint Committees Communication Judy Green 1992 5 Representatives Mathematical Reviews B. A. Taylor 1992 6 Index Mathematical Surveys and Terms of members expire on January 31 following the year given unless Monographs Marc A. Rieffel 1994 otherwise specified. Mathematics of Computation Walter Gautschi 1992 Proceedings Irwin Kra 1994 Science Policy Committee 1. Officers------Frank W. Warner ill 1993 President Michael Artin 1992 Transactions and Memoirs President-Elect Ronald L. Graham 1992 James E. Baumgartner 1995 Vice-Presidents Lenore Blum 1992 Chandler Davis 1993 2.0.3. Members-at-Large Linda Keen 1994 Secretary Robert M. Fossum 1992 Sheldon Axler 1992 Rebecca A. Herb 1994 Associate Joan S. Birman 1992 Elliott H. Ueb 1994 Secretaries Joseph A. Cirna 1992 Ruth M. Charney 1994 Carl Pomerance 1992 W. Wistar Comfort 1992 Charles Herbert Clemens 1992 Gunther A. Uhlmann 1994 Andy Roy Magid 1993 Carl C. Cowen, Jr. 1994 Steven H. Weintraub 1993 Lance W. Small 1993 DavidA. Cox 1993 Ruth J. Williams 1993 Treasurer Franklin P. Peterson 1992 John M. Franks 1993 Shing-Tung Yau 1992 Associate Frank Gilfeather 1993 Treasurer Steve Armentrout 1992 1.1. Liaison Committee All members of this committee serve ex officio. 2.1. Executive Committee of the Council Chair Michael Artin ex officio Chair Michael Artin M. Salah Baouendi 1993 Robert M. Fossum Joan S. Birman 1995 Franklin P. Peterson Robert M. Fossum ex officio Ronald L. Graham ex officio Arthur M. Jaffe 1994 2. Council------Hugo Rossi 1992 2.0.1. Officers of the AMS President Michael Artin 1992 President-Elect Ronald L. Graham 1992 3. Board of Trustees------Vice-Presidents Lenore Blum 1992 Steve Armentrout ex officio Chandler Davis 1993 Michael Artin ex officio Unda Keen 1994 Frederick W. Gehring 1992 Secretary Robert M. Fossum 1992 Associate * Only one Associate Secretary at a time is a voting member of the Council, Secretaries* Joseph A. Cima 1992 namely the cognizant Associate Secretary for the scientific sessions. 782 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Om mmm$ ,, lr?PWTfmiii!M- Officers and Committee Members ...... Maria M. Klawe 1996 Associate Editors for Research Announcements Secretary M. Susan Montgomery 1995 Franklin P. Peterson ex officio Gergory L. Cherlin 1992 Zoltan Furedi 1993 John C. Polking 1994 William G. Dwyer 1993 Harry Kesten 1993 Chair Paul J. Sally, Jr. 1993 Charles L. Epstein 1993 Robert Lazarsfeld 1992 DanielS. Freed 1993 Paul S. Muhly 1993 Michael D. Fried 1993 Associate Editors for Research - Expository Papers 4. Committees Persi W. Diaconis 1992 David A. Vogan, Jr. 1992 Jerry L. Kazdan 1992 Alan D. Weinstein 1992 4.1. Committees of the Council Barry Mazur 1992 Guido L. Weiss 1992 4.2.4. Collected Works Standing Committees Richard A. Askey 1992 Joan S. Birman 1992 Chair R. Keith Dennis 1992 4.1.1. Editorial Boards Steve Gersten 1992 Linda Keen 1992 Dennis P. Sullivan 1992 Richard James Milgram 1993 4.2.5. Colloquium Barry Simon 1992 A. 1994 Bhama Srinivasan 1994 Luis Caffarelli 1992 Chair Nolan R. Wallach 1993 H. Jerome Keisler 1993 Robert J. Zimmer 1994 Chair G. D. Mostow 4.2.6. Committee to Monitor Problems 4.1.2. Nominating Committee in Communication Chair Michael Aschbacher 1993 William Abikoff 1993 Daniel M. Bums, Jr. 1994 Jon Barwise 1992 Jerry L. Kazdan 1993 James H. Curry 1994 Barbara Lee Keyfitz 1992 Chair Judy Green 1992 Ray A. Kunze 1992 William H. Jaco ex officio Joseph Lipman 1994 Brian Markus 1994 Walter David Neumann 1993 Diane Meuser 1993 Robert F. Williams 1992 CarolS. Wood 1994 4.2.7. Contemporary Mathematics Chair Richard W. Beals 1994 Ad Hoc Committee Craig Huneke 1992 Clark Robinson 1994 4.1.3. Nominating Procedures Linda Preiss Rothschild 1992 Peter M. Winkler 1994 Chair Chandler Davis Robert M. Fossum ex officio 4.2.8. Graduate Studies in Mathematics Frank L. Gilfeather Ronald R. Coifman 1992 Jerry L. Kazdan William Fulton 1992 Ray A. Kunze Lance W. Small 1992 James W. Maxwell ex officio 1992 Ruth J. Williams 4.2.9. Journal of the AMS H. Blaine Lawson, Jr. 1994 4.2. Editorial and Communications Robert D. MacPherson 1993 Committees Richard B. Melrose 1993 Andrew M. Odlyzko 1994 4.2.1. Abstracts Editorial Committee Chair Wilfried Schmid 1993 All members of this committee serve ex officio. Associate Editors Joseph A. Cima James G. Arthur 1992 Andrew J. Majda 1992 W. Wistar Comfort Persi W. Diaconis 1994 DusaMcDuff 1994 Chair Robert M. Fossum Gerd Faltings 1991 Hugh L. Montgomery 1993 Andy Roy Magid Charles L. Fefferman 1992 Paul H. Rabinowitz 1991 Lance W. Small Michael H. Freedman 1993 Marina Ratner 1994 Daniel Friedan 1991 Richard Schoen 1994 4.2.2. American Journal of Mathematics, Ronald L. Graham 1992 Richard P. Stanley 1994 Society's Representatives Joe Harris 1993 W. Hugh Woodin 1993 Chair M. Salah Baouendi 1992 Hendrik W. Lenstra, Jr. 1991 1994 4.2.10. Mathematical Reviews 4.2.3. Bulletin (New Series) Wendell H. Fleming 1994 Richard S. Palais 1992 John L. Selfridge 1994 Murray H. Protter 1994 Chair B. A. Taylor 1992 Chair FrankS. Quinn 1993 Hans F. Weinberger 1993 SEPTEMBER 1992, VOLUME 39, NUMBER 7 783 Officers and Committee Members OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOONOH ...... ·········································································· 4.2.11. Mathematical Surveys and Monographs Franklin Tall 1993 Robert E. Greene 1992 John Trangenstein 1995 David W. McLaughlin 1994 James E. West 1995 Chair Marc A. Rieffel 1994 4.2.15. Proceedings of Symposia in Applied Bhama Srinivasan 1993 Mathematics 4.2.12. Mathematics of Computation Chair Alexandre J. Chorin 1991 Chair Walter Gautschi 1992 Bjorn E. J. Dahlberg 1991 Andrew M. Odlyzko 1994 Ronald L. Graham 1992 Frank W. J. Olver 1993 4.2.16. Transactions and Memoirs Lars B. Wahlbin 1992 Avner D. Ash 1994 Associate Editors Chair James E. Baumgartner 1995 Robert L. Bryant 1995 James Bramble 1994 Carl Pomerance 1994 Sun-Yung Alice Chang 1994 E. W.Cheney 1994 Rene Schoof 1992 Ralph L. Cohen 1992 James W. Demmel 1994 Ridgway Scott 1992 Richard Durrett 1994 Eugene Isaacson 1992 Daniel Shanks 1993 Philip J. Hanlon 1995 Heinz-Otto Kreiss 1993 Frank Stenger 1992 David Jerison 1994 James N. Lyness 1993 Hans J. Stetter 1994 Wen-Ching Winnie Li 1995 Harald Niederreiter 1993 G. W. Stewart 1992 John J. Mallet-Paret 1995 Jorge J. Nocedal 1993 Nico M. Temme 1992 Judith D. Sally 1993 Syvert P. N(llrsett 1993 Vidar C. Thomee 1994 Peter B. Shalen 1995 John Osborn 1992 Hugh C. Williams 1994 Masarnichi Takesaki 1993 Stanley J. Osher 1992 John W. Wrench, Jr. 1993 4.2.17. Translation from Chinese 4.2.13. Notices Sun-Yung Alice Chang John S. Bradley ex officio S.-Y. Cheng Michael G. Crandall 1992 Chair Tsit-Yuen Lam Amassa C. Fauntleroy 1994 Tai-Ping Liu Chair Robert M. Fossum ex officio Chung-Chun Yang Carolyn S. Gordon 1994 D. J. Lewis 1992 4.2.18. Translation from Japanese Ridgway Scott 1994 Shoshichi Kobayashi Robert E. L. Turner 1992 Chair Katsumi Nomizu Associate Editors Standing Committees Special Articles Ronald L. Graham Jeffrey C. Lagarias 4.2.19. Electronic Publications 4.2.14. Proceedings Nancy Anderson 1993 Vice-Chair William W. Adams 1992 Keith J. Devlin 1992 Dale Alspach · 1995 Chair John M. Franks 1994 J. Marshall Ash 1992 Maria M. Klawe 1994 Maurice Auslander 1992 FrankS. Quinn 1993 Albert Baemstein 1995 Consultant David Rodgers Eric Bedford 1995 4.2.20. History of Mathematics Andreas Blass 1992 Andrew M. Bruckner 1993 Charles W. Curtis 1993 Chris Croke 1995 Chair Harold M. Edwards 1994 Clifford J. Earle, Jr. 1992 Guido Weiss 1994 Eric M. Friedlander 1995 4.2.21. Reprinted Books Theodore W. Gamelin 1994 Eugenio Calabi James G. Glimm 1995 Charles W. Curtis Roe Goodman 1995 Chair Oscar S. Rothaus Thomas Goodwillie 1995 Lawrence F. Gray 1993 4.2.22. University Lecture Series Dennis A. Hejhal 1995 Theodore W. Gamelin Palle E. T. Jorgensen 1992 DonaldS. Ornstein Jeff Kahn 1993 Leonard L. Scott Barbara Lee Keyfitz 1995 Chair Irwin Kra 1994 Peter W. K. Li 1994 Ad Hoc Committee Wei Y. Loh 1995 JosephS. B. Mitchell 1995 M. Susan Montgomery 1995 4.2.23. Member Publications Charles Pugh 1994 Michael Artin ex officio David Sharp 1995 Sheldon Axler HalL. Smith 1995 John H. Ewing Ronald M. Solomon 1994 John M. Franks Ronald J. Stern 1995 Judy Green 784 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY • omO-- J L£2 ~ .·••••• Officers and Committee Members William H. Jaco ex officio 4.3.10. Membership Haynes R. Miller M. Salah Baouendi 1993 Richard S. Palais Consultant Carol-Ann Blackwood John C. Polking Susan Friedlander 1992 Hugo Rossi Chair Frederick W. Gehring 1992 Carol S. Wood Wen-Ching Winnie Li 1993 Hugo Rossi 1994 4.3. Committees of the Board of Trustees 4.3.11. The Publication Program 4.3.1. Agenda and Budget Steve Armentrout 1993 Chair Robert L. Devaney 1992 All members of this committee serve ex officio. Robert M. Fossum ex officio Steve Armentrout Eric Friedlander 1992 Michael Artin Ramesh A. Gangolli 1992 Robert M. Fossum William H. Jaco ex officio Franklin P. Peterson Elliott H. Lieb 1994 Hugo Rossi Andrew M. Odlyzko 1992 Paul J. Sally, Jr. John C. Polking ex officio Paul J. Sally, Jr. ex officio 4.3.2. Appeals Committee on Discounted B. A. Taylor 1992 Subscriptions 4.3.12. Salaries Consultant Carol-Ann Blackwood William H. Jaco ex officio All members of this committee serve ex officio. Chair Morton Lowengrub Steve Armentrout Franklin P. Peterson Franklin P. Peterson Paul J. Sally, Jr. John C. Polking Consultant B. A. Taylor Chair Paul J. Sally, Jr. 4.3.3. Audit 4.3.13. Staff and Services All members of this committee serve ex officio. Chair Steve Armentrout ex officio Franklin P. Peterson Franklin P. Peterson ex officio Paul J. Sally, Jr. Paul J. Sally, Jr. 4.3.4. Computer Operations and Facilities, Ad Hoc Committee Visiting Committee on Maria M. Klawe ex officio 4.3.14. Institutional Membership Richard Mandelbaum 1992 Consultant Carol-Ann Blackwood Jill P. Mesirov 1994 Ramesh A. Gangolli Chair Peter J. Weinberger 1993 Chair Frederick W. Gehring 4.3.5. Corporate Relations Jeremy J. Soldevilla ex officio Chair Ramesh A. Gangolli William A. Veech Maria M. Klawe Oscar S. Rothaus 4.4. Internal Organization of the 4.3.6. Endowment American Mathematical Society Andrew M. Gleason Chair W. Ted Martin Cathleen S. Morawetz Standing Committees 4.3. 7. Investment 4.4.1. Archives Steve Armentrout ex officio Andrew M. Gleason Frederick W. Gehring ex officio Franklin P. Peterson Chair Franklin P. Peterson ex officio Chair Everett Pitcher T. Benny Rushing 1994 4.3.8. Legal Aid 4.4.2. Committee on Committees James G. Arthur 1992 Steve Armentrout Michael Artin ex officio Todd Dupont M. Salah Baouendi 1992 Chair Murray Gerstenhaber Chair Lenore Blum 1992 4.3.9. Long Range Planning Robert M. Fossum ex officio All members of this committee serve ex officio. John M. Franks 1992 Ronald L. Graham ex officio Chair M. Salah Baouendi Tsit-Yuen Lam 1992 Robert M. Fossum Joshua A. Leslie 1992 William H. Jaco George R. Sell 1992 Arthur M. Jaffe James D. Stasheff 1992 Franklin P. Peterson William Yalas Velez 1992 Paul J. Sally, Jr. Sylvia M. Wiegand 1992 SEPTEMBER 1992, VOLUME 39, NUMBER 7 785 ·-····------···-··· .. --·············"-"'''''''"'--······························································... ·-"""'''""""'"" ______, ...... Officers and Committee Members 4.4.3. Subcommittee to Study the Committee Structure 4.5.4. Eastern Section Program Committee Steve Armentrout Roy Adler 1993 Michael Artin ex officio W. Wistar Comfort ex officio Robert M. Fossum ex officio John C. Moore 1992 William H. Jaco ex officio Chair Lesley M. Sibner 1992 Maria M. Klawe Gregg J. Zuckerman 1993 Tsit-Yuen Lam 4.5.5. Southeastern Section Program Committee Joshua A. Leslie Ann Renauer Joseph A. Cima ex officio William Y slas Velez Sue E. Goodman 1992 Steven H. Weintraub Jean Larson 1993 Chair Sylvia M. Wiegand Chair Carl Pomerance 1992 Donald St.P. Richards 1993 4.4.4. Library Committee 4.5.6. Western Section Program Committee Co-chair Nancy Anderson 1994 F. Michael Christ 1993 Richard A. Askey 1993 Janos Kollar 1992 R. Keith Dennis 1994 Robert R. Phelps 1993 RobertS. Doran 1993 Lance W. Small ex officio Dorothy McGarry 1994 Chair Ronald J. Stem 1992 Co-chair James Rovnyak 1994 Mary Ann Southern 1994 4.5.7. Agenda for Business Meetings Jack Weigel 1993 M. Salah Baouendi 1992 Chair Robert M. Fossum Ad Hoc Committees Carol L. Walker 1992 4.5.8. Gibbs Lecturer for 1993 and 1994, 4.4.5. Applications of Mathematics Committee to Select Frederick J. Almgren, Jr. Michael Atiyah Chair Jerry L. Bona Cathleen S. Morawetz Hermann Flaschka Michael 0. Rabin Barbara Lee Keyfitz Chair Thomas Spencer David Mumford Ivar Stakgold 4.5.9. Progress in Mathematics F. Hans Weinberger Chair Hyman Bass 1992 4.4.6. 1991 Election Tellers John B. Friedlander 1994 Peter W. K. Li 1993 Leo P. Comerford, Jr. Haynes R. Miller 1993 Robert E. Megginson James B. Serrin 1994 4.5. Program and Meetings Ad Hoc Committees Standing Committees 4.5.10. Arnold Ross Lecture Series Committee Harvey B. Keynes Chair Paul J. Sally, Jr. 4.5.1. Program Committee for National Meetings Jean E. Taylor Spencer Bloch 1992 Hermann Flaschka 1994 Robert M. Fossum ex officio 4.5.11. Meetings Committee H. W. Lenstra 1994 Lenore Blum Dusa McDuff 1993 Consultant H. Hope Daly Chair Nancy K. Stanton 1993 Chair Andy Roy Magid Mary F. Wheeler 1994 Nancy K. Stanton Ruth J. Williams 4.5.2. Short Course Subcommittee Chair Stefan Burr 1992 4.6. Status of the Profession Lis! Novak Gaal 1992 Jeffery C. Lagarias 1994 Patrick D. McCray 1994 Standing Committees James J. Tattersall 1993 1994 4.6.1. Academic Freedom, Tenure, and 1994 Employment Security 4.5.3. Central Section Program Committee Josefina Alvarez 1993 Rodrigo Banuelos 1993 Leon Brown 1994 Chair John M. Franks 1992 Ellis Kolchin 1992 Julia Knight 1993 Lawrence E. Morris 1993 Andy Roy Magid ex officio Chair Mary Ellen Rudin 1992 Jang-Mei Wu 1992 Gail S. Young 1992 786 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY •••••• m •• m mmmm•••mmm••••••••••••••••••••••••••m••••••m•••••••••mm••m• •••••mm••mmmm••• - lliiiiili I f Officers and Committee Members 4.6.2. Academic Review 4.6.9. Service to Mathematicians Frederick W. Gehring in Developing Countries Frank L. Giifeather Chair Raymond G. A¥oub Andrew M. Gleason James A. Donaldson Chair J. K. Goldhaber James Eells 4.6.3. Education Donald M. Hill Michael Artin ex officio Chair Rarnesh A. Gangolli 1992 Ad Hoc Committees Andrew M. Gleason 1992 FernY. Hunt 1992 4.6.10. Advisory Committee on Fonner Soviet Union William H. Jaco ex officio Mathematics Harvey B. Keynes 1992 Don J. Lewis 1992 Chair Michael Arlin Richard A. Tapia 1992 William H. Jaco ex officio Alan C. Tucker 1993 Robert D. MacPherson Frank W. Warner ill ex officio Cathleen S. Morawetz John C. Polling 4.6.4. Human Rights of Mathematicians Linda Preiss Rothschild Raymundo Bautista 1994 Daniel Stroock Sufian Y. Husseini 1994 Wen-Ching Winnie Li 1993 4.6.11. Advisory Committee on Professional Ethics Cora S. Sadosky 1992 Murray Gerstenhaber Chair Alice T. Schafer 1993 Frank L. Gilfeather Jonathan M. Wahl 1994 Judy Green Steven H. Weintraub 1992 Chair Linda Keen Hung-Hsi Wu 1993 Elliott H. Lieb 4.6.5. Liaison Committee on Education in Mathematics John A. Dossey 4.6.12. CAFTES (Academic Freedom, Tenure and Melvin Hochster Employment Security) and COPE (Committee Rogers J. Newman on Profesional Ethics) Louise A. Raphael Chair Joan S. Birman Chair Paul J. Sally, Jr. Frank L. Gilfeather James D. Stasheff Elliott H. Lieb Lynn Arthur Steen 4.6.6. Pi Mu Epsilon Liaison Committee 4.6.13. Cooperation with Latin American Mathematicians David W. Ballew 1993 Lynne M. Butler 1993 Chair Charles Herbert Clemens Mary B. Martin 1994 Samuel Gitler Chair Eileen Poiani 1992 Carlos E. Kenig Bruce Reznick 1993 Joseph J. Kohn De Witt Sumners 1994 Horacia A. Porta Cora S. Sadosky 4.6. 7. Professional Ethics Leonard D. Berkovitz 1993 4.6.14. Coordinating Committee for the Doctoral Donald J. Lewis 1994 Program in Mathematics Albert Marden 1994 Chair R. Creighton Buck Chair Everett Pitcher 1992 Franklin P. Peterson Judith Roitman 1993 Murray H. Protter 4.6.8. Science Policy 4.6.15. Employment Task Force Michael Artin ex officio James A. Donaldson 1993 S.-Y. Cheng Eric M. Friedlander 1994 Ronald M. Davis Ramesh A. Gangolli ex officio Helen G. Grundman Ronald L. Graham ex officio Chair D. J. Lewis Rhonda J. Hughes 1993 Bernard L. Madison William H. Jaco ex officio James W. Maxwell ex officio Linda Keen 1993 Donald E. McClure Joseph J. Kohn 1992 Calvin C. Moore Joel L. Lebowitz 1992 CarolS. Wood William James Lewis 1994 Michael C. Reed 1992 4.6.16. Soviet Mathematicians, Committee to Study Linda Preiss Rothschild 1994 Relations with Paul J. Sally, Jr. 1992 Chandler Davis Chair Frank W. Warner ill 1993 Chair Robert D. MacPherson Mary F. Wheeler 1992 Hugo Rossi 1994 Lance W. Small SEPTEMBER 1992, VOLUME 39, NUMBER 7 787 Officers and Committee Members 4. 7. Prizes and Awards 4.7.9. Cole Prize, Committee to Select the Winner of Gerd Faltings Standing Committees Wolfgang Schmidt Chair Harold M. Stark 4.7.1. Award for Public Service, Committee to Select the Winner of 4.8. Institutes and Symposia Chair William Browder 1995 Kenneth M. Hoffman 1996 Robert M. Fossum 1992 Standing Committee John C. Polking 1994 David P. Roselle 1993 4.8.1. Liaison Committee with AAAS 4.7.2. Centennial Fellowships Efraim P. Armendariz ex officio Terms expire on June 30 Alfred W. Hales 1993 Johnson Richard M. Hain 1993 Raymond ex officio C. Kutzko 1993 Douglas A. Lind 1993 Philip A. Raphael 1993 Chair Henry Pinkham 1993 Louise V. Frederick Rickey ex officio Peter Sarnak 1994 Beth Ruskai Birgit Speh 1994 M. 1993 Sah Lai-Sang Young 1994 Chih-Han ex officio 1994 Melvin Thornton ex officio 4.7.3. National Awards and Public Representation 4.8.2. Summer Institutes and Special Symposia Chair Michael Artin ex officio Terms expire on February 28 Joan S. Birman 1993 Donald L. Burkholder 1995 Robert M. Fossum ex officio Lawrence Craig Evans 1994 Ronald L. Graham ex officio Melvin Hochster 1995 Richard S. Palais 1993 Nicholas Katz 1993 4. 7 .4. Subcommittee on Appointments of the Committee Chair Brian Parshall 1993 on National Awards and Public Representation Francois Treves 1993 Edward Witten 1994 Robert M. Fossum ex officio Chair Irwin Kra John C. Polking 4.9. Joint Committees 4. 7.5. Satter Prize for 1993, Committee to Select the Winner of the 4.9.1. AMS-AAAS-MAA Committee Joan S. Birman 1992 on Opportunities in Mathematics Chair DusaMcDuff 1993 for Underrepresented Minorities Alan D. Weinstein 1993 Sylvia T. Bozeman 1992 4.7 .6. Steele Prizes Claudette Bradley 1992 Johnny E. Brown 1992 Terms expire on June 30 Chair Gloria F. Gilmer 1992 Eugenio Calabi 1995 Shirley Malcom ex officio Chair Sylvain E. Cappell 1993 Consultant Argelia Velez-Rodriguez Vaughan F. R. Jones 1994 Harry Kesten 1993 4.9.2. AMS-ASA-AWM-IMS-MAA-NCTM-SIAM Joseph J. Kohn 1993 Committee on Women in the Robert P. Langlands 1995 Mathematical Sciences Paul Rabinowitz 1995 NCTM members' terms expire April! of the year given. 1994 Jane Cronin Scanlon Margaret B. Cozzens (SIAM) 1992 Jean Taylor 1994 Marjorie M. Enneking (NCTM) 1992 Nancy Flournoy (lMS) 1992 Ad Hoc Committees Sue E. Goodman (AMS) 1992 Joan Hutchinson (AWM) 1993 4. 7.7. AMS Prizes and Awards Patricia C. Kenschaft (MAA) 1994 Joan S. Birman Jeanne W. Kerr (AMS) 1992 Frederick W. Gehring Don J. Lewis (MAA) 1994 Ronald L. Graham J. Peter May (AMS) 1994 Joseph J. Kohn Anita McDonald (MAA) 1994 Gian Carlo Rota Joyce R. McLaughlin (SIAM) 1993 Chair Joseph L. Taylor Anne Parkhurst (ASA) Magda Peligrad (IMS) 1991 4. 7.8. Automatic Theorem Proving, Committee to Linda R. Petzold (SIAM) 1992 Recommend Winners of Prizes for Frances Rosamond (MAA) 1992 Chair David Mumford Chair M. Beth Ruskai (AMS) 1992 Jacob T. Schwartz Evelyn Silvia (AWM) 1993 John L. Selfridge Patricia S. Wilson (NCTM) 1993 788 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY milllllllll!! 7rr"=71-1Rlll.• 7iM~m Officers and Committee Members 4.9.3. AMS-ASL-IMS-SIAM Committee on 4.9.8. AMS-MAA Data Committee Translations from Russian and Other Slavic Edward A. Connors (AMS) 1993 Languages Consultant Lincoln K. Durst Chair Peter S. Landweber (AMS) 1992 John D. Fulton (MAA) 1994 James F. Hurley (AMS) 1994 AMS Subcommittee Members Charlotte Lin (AMS) 1992 Don 0. Loftsgaarden (MAA) 1993 Consultant V. I. Arnol'd David J. Lutzer (MAA) 1993 Luchezar Avramov 1994 James W. Maxwell (AMS) ex officio Igor Dolgachev 1994 Chair Donald E. McClure (AMS) 1993 Consultant S. G. Gindikin Donald C. Rung (AMS) 1992 Consultant Askol'd Georgievic Khovanskii Chair Peter S. Landweber (AMS) 1992 Arunas Liulevicius 1993 4.9.9. AMS-MAA Committee on Teaching Assistants Consultant N. K. Niko11skili and Part Time Instructors (TAIPTI) Washek Pfeffer 1993 Thomas F. Banchoff (AMS) 1992 Reuben C. Drake (MAA) 1994 ASL Subcommittee Members Deborah Hughes Hallett (AMS) 1993 Vladimir Lifschitz 1993 Chair John P. Huneke (MAA) 1992 Chair Elliott Mendelson 1992 Timothy L. Lance (AMS) 1994 Grigori Mints 1993 Daniel J. Madden (AMS) 1994 Benjamin F. Wells 1992 Shelba J. Morman (MAA) 1992 Boris I. Zil'ber 1994 Stephen B. Rodi (MAA) 1994 IMS Subcommittee Members 4.9.10. AMS-MAA Joint Archives Committee Chair M. I. Freidlin Leonard Gillman B. Pittel Uta C. Merzbach A. Rukhin Everett Pitcher W. J. Studden Chair Sanford L. Segal 4.9.4. AMS-CMS Joint Program Committee 4.9.11. AMS-MAA Joint Meetings Committee Spencer Bloch (AMS) All members of this committee serve ex officio. David W. Boyd (CMS) Chair Carl Herz (CMS) Consultant H. Hope Daly Robert M. Fossum Dusa McDuff (AMS) Chair William H. Jaco Victor P. Snaith (CMS) Kenneth A. Ross Nancy K. Stanton (AMS) Marcia P. Sward 4.9.5. AMS-DMV Liaison Committee 4.9.12. AMS-MAA Arrangements Committee for the San Heinz Bauer Antonio Meeting Klaus D. Bierstedt Albrecht E. Dold January 13-16, 1993 Robert M. Fossum Chair Shair Ahmad Dale Husemoller Don Bailey Bernd Ulrich W. Wistar Comfort ex officio William H. Jaco ex officio 4.9.6. AMS-IMS-SIAM Committee on Joint Carol Redfield Summer Research Conferences in the Kenneth A. Ross ex officio Mathematical Sciences David A. Sanchez Terms expire on June 30 Gene Sims Marcia P. Sward ex officio John A. Bums (SIAM) 1992 Betty Travis Fan R. K. Chung (AMS) 1993 Leonard Evens (AMS) 1993 Chair Martin Golubitsky (SIAM) 1992 4.9.13. AMS-MAA Joint Program Committee for the San Alan F. Karr (AMS) 1996 Antonio Meeting W. K. Li Peter (AMS) 1993 Richard A. Askey (MAA) Stewart B. Priddy (AMS) 1994 Hermann Flaschka (AMS) Robert J. Serfling (IMS) 1993 Chair Roger Horn (MAA) Michael Shub (AMS) 1994 Richard A. Tapia (AMS) Sue Whitesides (AMS) 1996 4.9.7. AMS-LMS Joint Program Committee 4.9.14. AMS-MAA Committee on Summer Meetings William Abikoff (AMS) Consultant H. Hope Daly (AMS) Sir Michael Atiyah (LMS) Robert M. Fossum (AMS) J. M. Ball (LMS) Co-chair William H. Jaco (AMS) Hyman Bass (AMS) Gerald J. Porter (MAA) Chair Robert M. Fossum (AMS) Co-chair Kenneth A. Ross (MAA) Sir John Kingman (LMS) John M. Smith (MAA) SEPTEMBER 1992, VOLUME 39, NUMBER 7 789 ______...... -...... Officers and Committee Members 4.9.15. AMS-MAA-SIAM Joint Administrative Mary Ellen Rudin (AMS) Committee David A. Sanchez (AMS) All members of this committee serve ex officio. Andrew Sterrett (MAA) Staff Marcia P. Sward (MAA) Gerald L. Alexanderson (MAA) Alan C. Tucker (MAA) I. Edward Block (SIAM) Chair Robert M. Fossum (AMS) 4.9.23. AMS-MAA-SIAM Committee on Preparation Samuel Gubins (SIAM) for College Teaching William H. Jaco (AMS) Donald W. Bushaw Donald L. Kreider (MAA) Chair Bettye Anne Case Robert E. O'Malley, Jr. (SIAM) Robert H. McDowell Franklin P. Peterson (AMS) Richard S. Millman Marcia P. Sward (MAA) Robert R. Phelps 4.9.16. AMS-MAA-SIAM Joint Committee on Richard D. Ringeisen Employment Opportunities Stephen B. Rodi James G. Simmonds Stanley Benkoski (AMS) 1993 Guido L. Weiss Peter E. Castro (SIAM) 1992 Ronald M. Davis (MAA) 1993 Frank R. Demeyer (AMS) 1994 5. Representatives------James W. Maxwell ex officio Chair S. Brent Morris (MAA) 1994 Leon H. Seitelman (SIAM) 1994 5.0.1. Advisory Board of the National Translations Center of the John Crerar Library 4.9.17. AMS-MAA-SIAM Joint Policy Board Ralph P. Boas for Mathematics (see 1992 Mathematical Sciences Professional Directory, page 28) 5.0.2. American Association for the Advancement of Science 4.9.18. AMS-SIAM Committee Terms expire on February 21 on Applied Mathematics Section A Raymond Johnson 1995 Marsha J. Berger 1994 Section B Chih-Han Sah 1995 Paul C. Fife 1994 Section L V. Frederick Rickey 1995 Chair James M. Hyman 1993 Section Q Efraim P. Armendariz 1995 Andrew J. Majda 1992 Section T Melvin Thornton 1995 Michael Shub 1993 Joel Spencer 1992 5.0.3. Commission on Professionals in Science and 4.9.19. AMS-SIAM Committee to Select the Winner of Technology the Birkhoff Prize for 1993 Edward A. Corrnors Constantine M. Daferrnos 5.0.4. Committee on the American Mathematics Andrew Chi-Chih Yao Competition Term expires on June 30 4.9.20. AMS-SIAM Committee to Screen Applicants RichardP. Stariley 1994 for Graduate Study from the People's Republic of China 5.0.5. Conference Board of the Mathematical Sciences David Benney Robert Bryant Michael Artin 1992 4.9.21. AMS-SIAM-SMB Committee on 5.0.6. Fulkerson Prize Committee Mathematics in the Life Sciences Alan J. Hoffman James W. Curran 1993 5.0.7. MAA Committee on Guidelines Leah Edelstein-Keshet 1994 Donovan H. Van Osdol 1992 Eric S. Lander 1993 Chair Marc Mangel 1992 5.0.8. MAA Committee on Undergraduate Program James Murray 1992 in Mathematics 1994 Harvey B. Keynes 1992 Ad Hoc Committees Kathy O'Hara 1993 5.0.9. U.S. National Committee on Theoretical and 4.9.22. AMS-MAA Committee on Cooperation Applied Mechanics Gerald L. Alexanderson (MAA) Term expires on October 31 Michael Artin (AMS) ex officio Constantine M. Dafermos 1996 Susan Forman (MAA) Robert M. Fossum (AMS) Ramesh A. Gangolli (AMS) 6. Index------Deborah Tepper Raimo (MAA) ex officio Staff William H. Jaco (AMS) 1991 Election Tellers ...... 4.4.6 Chair Donald L. Kreider (MAA) ABC Committee ...... 4.3.1 M. Susan Montgomery (AMS) AMS Prizes and Awards ...... 4.7.7 790 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ·-·-~ni ratllf'llil T"'iiflfii&lflllflfllf~ Officers and Committee Members AMS-AAAS-MAA Committee on Opportunities in Mathematics for Commission on Professionals in Science and Technology . 5.0.3 Underrepresented Minorities ...... 4.9.1 Committee Structure, Subcommittee to Study the . . . . 4.4.3 AMS-ASA-AWM-IMS-MAA-NCTM-SlAM Committee on Women in Committee on Committees ...... 4.4.2 the Mathematical Sciences ...... 4.9.2 Committee on the American Mathematics Competition . 5.0.4 AMS-ASL-IMS-SIAM Committee on Translations from Russian and Committee to Monitor Problems in Communication . 4.2.6 Other Slavic Languages . . . . . 4.9.3 Committees ...... 4 AMS-CMS Joint Program Committee ...... 4.9.4 Committees of the Board of Trustees ...... 4.3 AMS-DMV Liaison Committee ...... 4.9.5 Committees of the Council ...... 4.1 AMS-IMS-SIAM Committee on Joint Summer Research Conferences Communication, Committee to Monitor Problems in . 4.2.6 in the Mathematical Sciences ...... 4.9.6 Computer Operations and Facilities, Visiting Committee on . . 4.3.4 AMS-LMS Joint Program Committee ...... 4.9.7 Conference Board of the Mathematical Sciences . . . 5.0.5 AMS-MAA Arrangements Committee for the San Antonio Meeting Contemporary Mathematics ...... 4.2.7 January 13-16, 1993 ...... 4.9.12 Cooperation with Latin American Mathematicians ...... 4.6.13 AMS-MAA Committee on Cooperation ...... 4.9.22 Coordinating Committee for the Doctoral Program in Mathematics . 4.6.14 AMS-MAA Committee on Summer Meetings ...... 4.9.14 Corporate Relations . . 4.3.5 AMS-MAA Committee on Teaching Assistants and Part Time Council ...... 2 Instructors (TAIPTI) ...... 4.9.9 Data Committee ...... 4.9.8 AMS-MAA Data Committee ...... 4.9.8 Developing Countries, Service to Mathematicians in . . 4.6.9 AMS-MAA Joint Archives Committee . 4.9.10 Discounted Subscriptions, Appeals Committee on . . . 4.3.2 AMS-MAA Joint Meetings Committee . 4.9.11 Doctoral Program in Mathematics, Coordinating Committee for . 4.6.14 AMS-MAA Joint Program Committee for the San Antonio Meeting 4.9.13 EC ...... 2.1 AMS-MAA-SIAM Committee on Preparation for College Teaching 4.9.23 Eastern Section Program Committee . . . . . 4.5.4 AMS-MAA-SIAM Joint Administrative Committee ...... 4.9.15 Editorial Boards ...... 4.1.1 AMS-MAA-SIAM Joint Committee on Employment Opportunities . 4.9.16 Editorial and Commnnications Committees . 4.2 AMS-MAA-SIAM Joint Policy Board for Mathematics (see 1992 Education ...... 4.6.3 Mathematical Sciences Professional Directory, page 28) .... 4.9.17 Education in Mathematics, Liaison Committee on . 4.6.5 AMS-SIAM Committee on Applied Mathematics .. ·...... 4.9.18 Election Tellers ...... 4.4.6 AMS-SIAM Committee to Screen Applicants for Graduate Study from Electronic Publications . . . 4.2.19 the People's Republic of China ...... 4.9.20 Employment Opportunities . 4.9.16 AMS-SIAM Committee to Select the Winner of the Birkhoff Prize for Employment Task Force . 4.6.15 1993 ...... 4.9.19 Endowment ...... 4.3.6 AMS-SIAM-SMB Committee on Mathematics in the Life Sciences .. 4.9.21 Ethics ...... 4.6.7 Abstracts Editorial Committee ...... 4.2.1 Executive Committee of the Council . 2.1 Academic Freedom, Tenure, and Employment Security . 4.6.1 Fulkerson Prize Committee ...... 5.0.6 Academic Review ...... 4.6.2 Gibbs Lecturer for 1993 and 1994, Committee to Select . . 4.5.8 Administrative Committee ...... 4.9.15 Graduate Studies in Mathematics ...... 4.2.8 Advisory Board of the National Translations Center of the John Crerar Graduate Study from the People's Republic of China . 4.9.20 Library...... 5.0.1 Guidelines, MAA Committee on . . 5.0.7 Advisory Committee on Former Soviet Union Mathematics . 4.6.10 History of Mathematics ...... 4.2.20 Advisory Committee on Professional Ethics 4.6.11 Human Rights of Mathematicians . 4.6.4 Agenda and Budget ...... 4.3.1 Index ...... 6 Agenda for Business Meetings ...... 4.5.7 Institutes and Symposia ...... 4.8 American Association for the Advancement of Science 5.0.2 Institutional Membership ...... 4.3.14 American Journal of Mathematics, Society's Representatives 4.2.2 Internal Organization of the American Mathematical Society . 4.4 American Mathematics Competition, Committee on . 5.0.4 Investment . . 4.3.7 Appeals Committee on Discounted Subscriptions . . 4.3.2 JCEO ...... 4.9.16 Applications of Mathematics ...... 4.4.5 JPBM ...... 4.9.17 Applied Mathematics, AMS-SIAM Committee on . . 4.9.18 Japanese, Translation from . 4.2.18 Archives ...... 4.4.1 Joint Administrative Committee . 4.9.15 Arnold Ross Lecture Series Committee...... 4.5.10 Joint Archives Committee . . 4.9.10 Arrangements Committee for the San Antonio Meeting . 4.9.12 Joint Committees ...... 4.9 Audit ...... 4.3.3 Joint Meetings Committee . 4.9.11 Automatic Theorem Proving, Committee to Recommend Winners of Joint Policy Board ...... 4.9.17 Prizes for ...... 4.7.8 Joint Summer Research Conferences . 4.9.6 Award for Public Service, Committee to Select the Winner of . 4.7.1 Journal of the AMS ...... 4.2.9 Birkhoff Prize . . . . 4.9.19 LRP ...... 4.3.9 Board of Trustees . . 3 Latin American Mathematicians, Cooperation with . 4.6.13 Bulletin (New Series) 4.2.3 LegalAid ...... 4.3.8 CAFTES ...... 4.6.1 Liaison Committee ...... 1.1 CAFTES (Academic Freedom, Tenure and Employment Security) and Liaison Committee on Education in Mathematics . 4.6.5 COPE (Committee on Profesional Ethics) 4.6.12 Liaison Committee with AAAS . . 4.8.1 CBMS ...... 5.0.5 LibraryCommittee . . .4.4.4 CSP ...... 4.6.8 Life Sciences ...... 4.9.21 Centennial Fellowships ...... 4.7.2 Long Range Planning ...... 4.3.9 Central Section Program Committee 4.5.3 MAA Committee on Guidelines . 5.0.7 Chinese, Translation from ...... 4.2.17 MAA Committee on Undergraduate Program in Mathematics . . 5.0.8 Cole Prize, Committee to Select the Winner of . 4.7.9 Mathematical Reviews ...... 4.2.10 Collected Works . . 4.2.4 Mathematical Surveys and Monographs ...... 4.2.11 Colloquium . . . 4.2.5 Mathematicians in Developing Countries, Service to . . 4.6.9 Comm-Comm .. . 4.2.6 Mathematics in the Life Sciences ...... 4.9.21 SEPTEMBER 1992, VOLUME 39, NUMBER 7 791 ··!IIIIa& 1 1a· Officers and Committee Members Mathematics of Computation ...... 4.2.12 Reprinted Books ...... 4.2.21 Meetings Committee ...... 4.5.11 Russian and Other Slavic Languages, Translations from ...... 4.9.3 Member Publications ...... 4.2.23 Salaries ...... 4.3.12 Members-at-Large ...... 2.0.3 Satter Prize for 1993, Committee to Select the Winner of the ..... 4.7.5 Membership ...... 4.3.10 Science Policy ...... 4.6.8 Memoirs ...... 4.2.16 Service to Mathematicians in Developing Countries ...... 4.6.9 Monitor ·Problems in Communication, Committee to ...... 4.2.6 Short Course Subcommittee ...... ·4.5.2 Monographs ...... 4.2.11 Southeastern Section Program Committee ...... 4.5.5 National Awards and Public Representation ...... 4.7.3 Soviet Mathematicians, Committee to Study Relations with ...... 4.6.16 National Meetings ...... 4.5.1 Special Symposia ...... 4.8.2 National Translations Center of the John Crerar Library, Advisory Staff Salaries ...... 4.3.12 Board of the ...... 5.0.1 Staff and Services ...... 4.3.13 Nominating Committee ...... 4.1.2 Status of the Profession ...... 4.6 Nominating Procedures ...... 4.1.3 Steele Prizes ...... 4.7.6 Notices ...... 4.2.13 Subcommittee on Appointments of the Committee on National Awards Officers ...... 1 and Public Representation ...... 4.7.4 Structure . . . . · ...... 4.4.3 Opportunities in Mathematics for Underrepresented Minorities . . . . 4.9.1 Subcommittee to Study the Committee Subscriptions ...... 4.3.2 PSAM ...... 4.2.15 Summer Institutes and Special Symposia ...... 4.8.2 Pi Mu Epsilon Liaison Committee ...... 4.6.6 Summer Research Conferences ...... 4.9.6 Prizes and Awards ...... 4. 7 Tellers, 1991 Election ...... 4.4.6 Proceedings ...... - ...... 4.2.14 The Publication Program ...... 4.3.11 Proceedings of Symposia in Applied Mathematics ...... 4.2.15 Theoretical and Applied Mechanics ...... 5.0.9 Professional Ethics ...... 4.6.7 Transactions and Memoirs ...... 4.2.16 in Science and Technology, Commission on ...... 5.0.3 Professionals Translations: Program Committees: Chinese ...... 4.2.17 4.5.3 Central ...... Japanese ...... 4.2.18 Eastern ...... 4.5.4 Russian and Other Slavic Languages ...... 4.9.3 National Meetings ...... 4.5.1 Trustees ...... ·...... 3 Southeastern ...... 4.5.5 U.S. National Committee on Theoretical and Applied Mechanics ... 5.0.9 Western ...... 4.5.6 Undergraduate Program in Mathematics, MAA Committee on . . . . 5.0.8 Program and Meetings ...... 4.5 Underrepresented Minorities ...... 4.9.1 Progress in Mathematics ...... 4.5.9 University Lecture Series ...... 4.2.22 Publication Program ...... 4.3.11 Western Section Program Committee ...... 4.5.6 Representatives ...... 5 Women in the Mathematical Sciences ...... , ...... 4.9.2 Representatives of Committees ...... 2.0.2 Matching of Asymptotic Expansions of Solutions of Boundary Value Problems Translations of Mathematical Monographs, Volume 1 02 • A.M. ll'in This book deals with the solution of singularly perturbed boundary value problems for differential equations. It presents, for the first time, a detailed and systematic treatment of the version of the matching method developed by ll'in and his colleagues. The book covers formal constructions of asymptotic expansions and provides rigorous justifications of these asymptotics. One highlight is a complete asymptotic analysis of Burger's equation with small diffusion in the neighborhood of the gradient catastrophe point. The book is suitable as a text for graduate study in asymptotic methods in calculus and singularly perturbed equations. 1991 Mathematics Subject Classification: 34; 41 ISBN 0-8218-4561-6, 281 pages (hardcover), July 1992 Individual member $101, List price $169, Institutional member $135 Your ordering code is MMON0/1 02NA All prices subject to change. Free shipment by surface: for air delivery, please add $6.50 per title. Prepayment required. Order from: American Mathematical Society, P.O. Box 1571, Annex Station, Providence, Rl 02901- 1571, or call toll free 800-321-4AMS (321-4267} in the U.S. and Canada to charge with VISA or MasterCard. Residents of Canada, please include 7% GST. 792 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Miscellaneous Personals Donald J, Brown, of Saint Albans G. de B. Robinson, Professor Emer Rose Ann Dios, of the New Jersey In School, died on January 13, 1992, at itus of the University of Toronto, died on stitute of Technology, was presented the the age of 39. He was a member of the April 8, 1992, at the age of 85. He was Outstanding Women Scientist award of Society for 1 year. a member of the Society for 59 years. the Metro New York Chapter of the As Henry L. Garabedian, of Laguna Bernard W. Roos, of Rancho Santa sociation for Women in Science Inc. She Hills, California, died on May 24, 1992, Fe, California, died on February 29, was honored for her accomplishments at the age of 90. He was a member of 1992, at the age of 64. He was a member and contributions in the areas of teach the Society for 65 years. of the Society for 32 years. ing and research in mathematics and for Albert E. Heins, of the University Sergei A. Schelkunoft', Professor serving as an exceptional role model for of Michigan, died on June 24, 1992, at Emeritus of Columbia University, died other women. the age of 79. He was a member of the on May 2, 1992. He was a member of John H. Morrison, of the Univer Society for 52 years. the Society for 65 years. sity of Delaware, Newark, has taken a M. F. Khalifah, of the Teacher Roland F. Smith, Professor Emer position as an options research asso Training College, Ruwi, Oman, died itus of Russell Sage College, died on ciate at Meredith Overbrook Partners, on April 2, 1992, at the age of 50. He April 21, 1992, at the age of 75. He was L.P., Inc., a member of the Cooper-Neff was a member of the Society for 11 a member of the Society for 44 years. Group. years. FrankL. Spitzer, of Cornell Uni Paul Rabinowitz, of the University James A. King, of Brooklyn, New versity, died on February 1, 1992, at of Wisconsin, Madison, was awarded York, died on October 27, 1991, at the the age of 65. He was a member of the an honorary degree (Doctorat Honoris age of 62. He was a member of the Society for 39 years. Causa) by the University Pierre et Marie Society for 8 years. Elmer Tolsted, Professor Emeritus Curie (Paris VI) for his exceptional Morris Monsky, of Westborough, of Pomona College, died on June 23, contributions to the analysis of nonlinear Massachusetts, died on June 28, 1990, 1992, at the age of 72. He was a member problems. at the age of 85. He was a member of of the Society for 49 years. the Society for 61 years. HerbertE. Vaughn, Professor Emer Deaths J, Ian Richards, of the University itus of the University of lllinois at Ralph P. Boas, Professor Emeritus of of Minnesota, died on June 21, 1992, at Urbana-Champaign, died on April 21, Northwestern University, died on July the age of 56. He was a member of the 1992, at the age of 81. He was a member 25, 1992, at the age of 79. He was a Society for 34 years. of the Society for 58 years. member of the Society for 56 years. SEPTEMBER 1992, VOLUME 39, NUMBER 7 793 ·------····-·······-················-·········... ··············-·········································································································· Classified Advertisements SUGGESTED USES for classified advertising are positions available, books or lecture notes for ILLINOIS sale, books being sought, exchange or rental of houses, and typing services. THE 1992 RATE IS $60 per inch on a single column (one-inch minimum), calculated from the NORTHWESTERN UNIVERSITY top of the type; $30 for each additional if.;. inch or fraction thereof. No discounts for multiple ads or Department of Mathematics the same ad in consecutive issues. For an additional $10 charge, announcements can be placed 2033 Sheridan Road anonymously. Correspondence will be forwarded. Evanston, Illinois 60208-2730 Advertisements in the "Positions Available" classified section will be set with a minimum one-line headline, consisting of the institution name above body copy, unless additional headline Applications are invited for one or more antici copy is specified by the advertiser. Advertisements in other sections of the classified pages will pated tenure-track positions starting September be set according to the advertisement insertion. Headlines will be centered in boldface at no extra 1993. Priority will be given to young, excep charge. Classified rates are calculated from top of type in headline to bottom of type in body copy, tional research mathematicians; however, more including lines and spaces within. Any fractional text will be charged at the next if.;. inch rate. Ads senior candidates with very exceptional creden will appear in the language in which they are submitted. tials may be considered for a tenured position. Prepayment is required of individuals but not of institutions. There are no member discounts Fields of interest within the department in for classified ads. Dictation over the telephone will not be accepted for classified advertising. clude Algebra, Analysis, Dynamical Systems, DEADLINES are listed on the inside front cover or may be obtained from the AMS Advertising Probability, Partial Differential Equations, and Department. Topology. Northwestern is an affirmative action, U. S. LAWS PROHIBIT discrimination in employment on the basis of color, age, sex, race, equal opportunity employer committed to fos religion or national origin. "Positions Available" advertisements from institutions outside the U. S. tering a diverse faculty; women and minority cannot be published unless they are accompanied by a statement that the institution does not candidates are especially encouraged to apply. discriminate on these grounds whether or not it is subject to U. S. laws. Details and specific Candidates should arrange that at least three wording may be found near the Classified Advertisements in the January and July/August issues letters of recommendation be sent to Prof. C. of the Notices. Robinson, Chair, Personnel Committee, Depart SITUATIONS WANTED ADVERTISEMENTS from involuntarily unemployed mathematicians ment of Mathematics, Northwestern University, are accepted under certain conditions for free publication. Call toll-free 800-321-4AMS (321-4267) Evanston, Illinois 60208-2730. Alternatively, ap in the U.S. and Canada for further information. plications and supporting documentation can SEND AD AND CHECK TO: Advertising Department, AMS, P. 0. Box 6248, Providence, be sent via email to "[email protected]". In Rho~e Island 02940. AMS location for express delivery packages is 201 Charles Street, order to receive full consideration, applications Providence, Rhode Island 02904. Individuals are requested to pay in advance, institutions are not should be received by January 1 , 1993. Hiring is required to do so. AMS FAX 401-455-4004. contingent upon eligibility to work in the United States. The University of Arizona is an Affirmative Action/Equal Opportunity Employer. NORTHWESTERN UNIVERSITY Mathematics Department ARIZONA 2033 Sheridan Road Evanston, Illinois 60208-2730 UNIVERSITY OF ARIZONA The Mathematics Department will sponsor an Department of Mathematics FLORIDA Emphasis Year in probability and stochastic Tucson, AZ 85721 UNIVERSITY OF FLORIDA analysis. This program will include two-year as The Mathematics Department at the University Department of Mathematics sistant professorship positions starting Septem of Arizona will have tenure-track and postdoc ber 1993 and possible visiting positions for toral positions available beginning Fall 1993. We invite applications for one or more antici more senior mathematicians for part or all of Tenure-track positions. Excellent research pated tenured or tenure-track appointments in the academic year. Applications should be sent record or potential, strong commitment to mathematics, effective August 1993. In the case to Professor Mark A. Pinsky at the department teaching required. Fields should complement of junior candidates, preference will be given address and include a curriculum vitae and but not duplicate existing department research to applicants with postdoctoral experience who three letters of recommendation. In order to strengths in arithmetic geometry, computational have made substantial research contributions ensure full consideration, an application must science, dynamical systems, differential geom beyond the doctoral dissertation. Senior can be received by January 1 , 1993. Northwest etry, nonlinear science, and number theory. didates are expected to have demonstrated ern University is an affirmative action, equal Postdoctoral Fellowships (Research As leadership in research. Applicants should for opportunity employer committed to fostering a sociates). Applicants with strengths in all areas ward a curriculum vitae, a list of publications, diverse faculty; women and minority candidates compatible with department interests are en and a small number of reprints and/or preprints are especially encouraged to apply. Hiring is couraged to respond. In addition, special Center to contingent upon eligibility to work in the United of Excellence Awards in nonlinear optics and Chair of Search Committee States. fluid mechanics are available. Department of Mathematics The Mathematics Department may also have University of Florida MARYLAND several visiting positions for next year. Gainesville, FL 32611-2082 We encourage early application. Deadline Candidates should supply evidence of commit THE JOHNS HOPKINS UNIVERSITY mart to teaching and arrange for at least three date.will be December 15, 1992, or whenever· Department of Mathematical Sciences positions are filled. Women and minority appli letters of recommendation to be forwarded. cants are especially welcome. Send application, UF is an Affirmative Action Employer, and the Applications are invited for 3 anticipated faculty which should include a letter of interest, cur Department especially welcomes applications positions within the areas of riculum vitae with a list of publications, and a from women and minority candidates. Full 1) numerical linear algebra (Senior appli minimum of three (3) letters of recommendation consideration will be given to candidates whose cants preferred), 2) statistics, 3) operations (enclose or arrange to be sent) to: materials arrive by December 31, 1992. research, 4) applied discrete mathematics. Personnel Committee Selection is based on demonstration and Department of Mathematics promise of excellence in research, teaching, University of Arizona and innovative applications. Tucson, Arizona 85721, U.S.A. Minority and women candidates are encour aged to apply. The Johns Hopkins University 794 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY ··························~·~------Classified Advertisements is an Affirmative Action/Equal Opportunity Em ysis. This is a one-year (twelve-month) joint ployer. appointment by the Center and Department of Applicants are asked to furnish a curriculum Mathematics. Recipients will teach at most one vitae, transcripts Gunior applicants only), reprints BRYN MAWR COLLEGE course per semester. Applicants should send a (if available), a letter describing professional Department of Mathematics vita, list of publications, a statement describing interests and aspirations, and to arrange for current and planned research, and arrange to three letters of recommendation to: Applications are invited for positions in Mathe have at least three letters of recommendation Prof. John C. Wierman, Chair matics and Computer Science, starting Septem sent to the committee. The deadline for applica Department of Mathematical Sciences ber 1993. They should be sent to the appropriate tion is January 20, 1993; late applications may 220 Maryland Hall committee, Department of Mathematics, Bryn be considered on a space-available basis. All The Johns Hopkins University Mawr College, Bryn Mawr, PA 19010. communications should be addressed to: Post Baltimore, Maryland 21218-2689 MATHEMATICS POSITIONS: One tenure doctoral Appointments Committee, Department Applications are requested by January 15, 1993. track assistant professorship and one three of Mathematics, Carnegie Mellon University, Applicants whose primary research is in al year renewable lectureship. Candidates must Pittsburgh, PA 15213. Carnegie Mellon Univer gebra, analysis, geometry, logic, number theory, have completed a doctorate in a mathematical sity is an Affirmative Action/Equal Opportunity or topology will not be considered. science by the starting date, and must show Employer. promise in research and a serious commitment to undergraduate and graduate teaching. All fields are acceptable, with a preference for applied mathematics or geometry. Please send CARNEGIE MELLON UNIVERSITY a vita, research plan and three letters of Department of Mathematics recommendation to the Mathematics Search WILLIAMS COLLEGE Committee. The Department invites applications for a senior Department of Mathematics COMPUTER SCIENCE POSITION: Three level appointment in Computational Mathemat Williamstown, Massachusetts 01267 year renewable lectureship ..Candidates should ics/Numerical Analysis. We are particularly inter have completed a doctorate in computer science ested in candidates who will enhance existing One or possibly two anticipated positions, one or a related field by the starting date, and computational and analytical programs which of them preferably in statistics, probably at the must display a commitment to both teaching involve continuum models in fluid dynamics, rank of assistant professor, for Fall 1993. Strong and scholarship, and an interest in curriculum mechanics of solids including microstructure, commitment to both teaching and scholarship is development in a joint program with Haverford phase transitions as well as other aspects essential. College. Please send a vita and three letters of materials science. Applicants should send Please have a vita and three letters of. of recommendation to the Computer Science a vita, list of publications, and a statement recommendation on teaching and research Search Committee. describing current and planned research, and sent to Hiring Committee. Formal evaluation of Bryn Mawr College is an equal oppor arrange to have at least three letters of recom applications will begin November 15, 1992, and tunity affirmative action employer. The col mendation sent to: Computational Mathematics continue until the positions are filled. AAIEOE. lege wishes particularly to encourage applica Search Committee, Department of Mathemat tions from individuals interested in joining a ics, Carnegie Mellon University, Pittsburgh, PA multicultural/international academic community. 15213. Carnegie Mellon University is an Affir Minority candidates and women are espe mative Action/Equal Opportunity Employer. cially encouraged to apply. CLOSING DATE: NEW YORK 1 January 1993 (late applications may be considered). Telephone: (215)526-5348. Email: STATE UNIVERSITY OF NEW YORK CARNEGIE MELLON UNIVERSITY msearch@ cc.brynmawr. AT BUFFALO Zeev Nehari Assistant Professorship in Mathematics The Department of Mathematics anticipates the appointment of several tenured or tenure-track CARNEGIE MELLON UNIVERSITY The Zeev Nehari Assistant Professorships have faculty members beginning September 1 , 1993. Department of Mathematics been instituted in the Department of Mathemat Salary will be competitive. We seek applicants ics of Carnegie Mellon University to honor the in all areas with excellent research accomplish The Department expects to make two or more memory of Professor Zeev Nehari, a member ments/potential and a strong commitment to tenure-track appointments, to begin in the Fall of the Department from 1954 to his death in teaching. of 1993, at the Assistant Professor level. We 1978. The position available is for an initial Applicants should send supporting informa seek candidates in areas of research which period of one or two academic years, begin tion, including a c.v. with a list of research strongly intersect those of the current faculty of ning in September 1993, and extendable for interests, and have four letters of recommenda the Department. Applicants should send a vita, one additional year when mutually agreeable. tion sent to: list of publications, and a statement describing It carries a reduced academic year teaching Search Committee Chairman current and planned research, and arrange to load of six hours per week during one semester Department of Mathematics have at least three letters of recommenda and three hours per week during the other. SUNY/Buffalo tion sent to the committee. All communications Applicants are expected to show exceptional 106 Diefendorf Hall should be addressed to: Tenure-track Appoint research promise, as well as clear evidence of Buffalo, New York 14214 ments Committee, Department of Mathemat achievement and should have research inter The deadline for applications is November 1, ics, Carnegie Mellon University, Pittsburgh, PA ests which intersect those of current faculty of 1992. Late applications will be considered until 15213. Carnegie Mellon University is an Affir the Department. Applicants should send a vita, positions are filled. mative Action/Equal Opportunity Employer. list of publications, and a statement describ SUNY/Buffalo is an Equal Opportunity/Affirm ing current and planned research, and arrange ative Action Employer. We are interested in to have three letters of recommendation sent identifying prospective minority and women to the committee. All communications should candidates. No person, in whatever relationship CARNEGIE MELLON UNIVERSITY be addressed to: Appointments Committee, with the State University of New York at Buffalo CENTER FOR NONLINEAR ANALYSIS Department of Mathematics, Carnegie Mellon shall be subject to discrimination on the basis Department of Mathematics University, Pittsburgh, PA 15213. Carnegie Mel of age, creed, color, handicap, national origin, lon University is an Affirmative Action/Equal race, religion, sex, marital or veteran status. The Center for Nonlinear Analysis expects to Opportunity Employer. make four to five Post-Doctoral appointments for 1992-1993 in the area of applied anal- SEPTEMBER 1992, VOLUME 39, NUMBER 7 795 Classified Advertisements CARNEGIE MELLON UNIVERSITY THE UNIVERSITY OF THE SOUTH TEXAS A&M UNIVERSITY Richard J. Duffin Department of Mathematics Head, Department of Mathematics Assistant Professorship in Mathematics and Computer Science · Texas A&M University is a: major coeducational The Richard J. Duffin Assistant Professorship Tenure-track position in mathematics, to begin institution, serving over 40,000 students, and was established in '1990 to honor Professor Fall 1993, at a highly selective church-related ranks in the top ten nationally iri research Emeritus Duffin. The position available is for an (Episcopal) liberal arts college of 11 00 students funding, number of National Merit Scholars, initial period of one or two academic years, be located on a 10,000-acre forested domain in and value of its permanent endowment. The ginning in September 1993, and extendable for the Tennessee uplands. Applicants should have College of Science has a research and teach one additional year when mutually agreeable. an appreciation for the liberal arts and some ing budget of approximately $40,000,000 and It carries a reduced academic year teaching interest in computing. Applications from women comprises the Departments of Biology, Chem load of six hours per week during one semester and minorities are especially encouraged. The istry, Mathematics, Physics, and Statistics and and three hours per week during the other. position is at the level of assistant professor, with the Cyclotron· Institute. The Mathematics De Applicants are expected to show exceptional excellence in teaching and continued interest in partment is large, energetic, and committed research promise, as well as clear evidence of research expected. A complete application will to excellence. Its dynamic faculty, represent achievement and should have research inter include a letter stating one's professional aims, ing pure and applied mathematics, is actively ests which intersect those of current faculty of a resume, graduate and undergraduate tran involved in research and both graduate and the Department. Applicants should send a vita, scripts, and three recommendations. All should undergraduate education. list of publications, and a statement describ be sent to Sherwood F. Ebey, The University of The position of Head will be filled by a person ing current and planned research, and arrange the South, 735 University Avenue, Sewanee, TN with an outstanding record of achievement in to have three letters of recommendation sent 37375-1 000. Applications received by Novem research and teaching and with demonstrable to the committee. All communications should ber 27 will have first consideration. AAIEOE. administrative skills. Effective communication, a be addressed to: Appointments Committee, talent for management, and ability to provide Department of Mathematics, Carnegie Mellon visionary leadership are especially important. University, Pittsburgh, PA 15213. Carnegie Mel Applications, consisting of a resume and lon University is an Affirmative Action/Equal the names of five persons from whom we may Opportunity Employer. TEXAS request letters of reference, will be accepted until November 1, 1992, or until the position SOUTHERN METHODIST UNIVERSITY is filled. Women and minorities are especially Department of Mathematics encouraged to apply. Texas A&M University is an equal opportu The Department of Mathematics at Southern nity, affirmative action employer: TENNESSEE Methodist University invites applications for a Respond to: Dr. Jon Pitts, Chair senior level tenure track position, with em Mathematics Department Head Search EAST TENNESSEE STATE UNIVERSITY ployment beginning in Fall 1993. Applicants Committee Mathematics Department must have demonstrated leadership in research College of Science Johnson City, Tennessee in applied mathematics, must have a strong Texas A&M University Faculty Vacancy commitment to high quality undergraduate and College Station, TX 77843-3257 graduate teaching, and must be ready and Phone: 409-845-7361 Mathematics Department of East Tennessee qualified to offer supervision in some area FAX: 409-845-6077 State University invites applications for a tenure of the doctoral program in physical applied Email: [email protected] track position with rank of Assistant Professor mathematics, numerical analysis and scientific available 8/93. Applicants must hold an earned computation. A strong grant record would be doctorate and be able to demonstrate excel advantageous. The standard teaching load is lence in teaching and have an active, ongoing two courses (six hours) per semester. program of research. Although candidates from Departmental research interests include all areas of mathematics will be considered, asymptotic and perturbation methods, bifur preference will be given to a person with training cation theory, combustion theory, dynamical and research in applied statistics. Proficiency systems, fluid mechanics, mathematical biol VIRGINIA in spoken English is required. ETSU employs ogy, mathematical software, nonlinear waves, only U.S. citizens, permanent residents, and and numerical analysis of differential equa WASHINGTON AND LEE UNIVERSITY aliens authorized to work in the U. S. Rank and tions. Thirteen of the sixteen faculty are applied Department of Mathematics salary commensurate with qualifications and mathematicians. Senior faculty include W.E. Lexington, VA 24450 experience. Ferguson (numerical partial differential equa East Tennessee State University is a com tions), I. Gladwell (mathematical software), R. RADFORD PROFESSOR I DEPARTMENT prehensive university of 12,000 students nestled Haberman (perturbation methods and nonlinear HEAD. The Radford Chair of Mathematics will in the hills and mountains of scenic East Ten waves), M.V. Melander (computational fluid dy be filled in September 1993. An applicant should nessee. Residents enjoy a wholesome climate namics), G.W. Reddien (numerical bifurcation have a background that. warrants tenure and marked by four distinct, but moderate seasons. theory), D.A. Reinelt (fluid mechanics), and the rank of full professor, a record of effective Review of applicants will begin October L.F. Shampine (numerical ordinary differential teaching and scholarship, and a commitment to 1992 and continue until the position is filled. equations). mathematics education in a liberal-arts setting. Send letter of application, resume, and have The application deadline is October 15, The Radford Professor will assume the position four letters of professional reference sent to: T. 1992. Send a letter of application and a vita to: of department head for a five-year term. Henry Jablonski, Jr., Chair, Search Committee, Professor I. Gladwell, Chairman, Department The mathematics faculty numbers seven, Department of Mathematics, ETSU, Box 70663, of Mathematics, Southern Methodist University, all with Ph.D.s. The University is primarily a Johnson City, TN 37614-0663. Phone 615-929- Dallas, TX 75275; tel: 214-692-2506. liberal-arts college with 1600 undergraduates. 6973. I. Gladwell's email addresses: gladwell@ It is 240 years old and is located in the lower Applicants who do not hold a current, full csvax.seas.smu.edu; h5nr1001 @smuvm1.bitnet; Shenandoah Valley. Address inquiries to Prof. time faculty appointment as indicated on the or h5nr1001 @vm.cis.smu.edu. T. 0. Vinson, Search Committee, Mathematics resume must also submit transcripts. Women SMU is an equal opportunity/affirmative ac Department. The selection process will begin in and minorities are encouraged to apply. AA/EOE tion/Title IX employer. November 1992. AA/EOE. 796 NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY Classified Advertisements UNIVERSITY OF TORONTO be given to Canadian citizens and permanent CANADA Department of Mathematics residents. The Department solicits applications for a UNIVERSITY OF TORONTO tenure-stream appointment in Geometric Anal Department of Mathematics ysis. The position is subject to budgetary The Department solicits applications for a approval. The appointment is at the downtown (St. ENGLAND tenure-stream appointment in Analysis. Pref George) campus at the level of Assistant erence will be given to researchers in the areas Professor, to begin July 1, 1993. Candidates are of non-linear analysis and geometric analysis. The appointment is at the Erindale campus at expected to have at least three years experience THE UNIVERSITY OF SUSSEX in teaching and research after the Ph.D., and to the level of Assistant Professor, to begin July Lectureship in Mathematics 1 , 1993. Candidates are expected to have at be able to demonstrate excellence in each. In particular, a candidate's research should show least three years experience in teaching and Applications are invited for a permanent Lecture research after the Ph.D., and to be able to· clearly the ability to make significant original ship in Mathematics from January or October and independent contributions to Mathematics. demonstrate excellence in each. In particular, 1993 or such date as can be agreed. The ap a candidate's research should show clearly the Salary commensurate with qualifications. pointee is expected to have research interests in Applicants should send their complete C.V. ability to make significant original and indepen the general area of Algebra/Topology/Geometry, dent contributions to Mathematics. Applicants including a list of publications and any ap and interact with existing faculty in these fields, propriate material about their teaching, and should send their complete C. V. including a but outstanding candidates, with research in arrange to have at least four letters of reference list of publications and any appropriate material terests in the areas of Analysis, Statistics or about their teaching, and arrange to have at sent directly to Professor K. Murty, Associate Applied Mathematics already represented at least four letters of reference sent directly to Chair, Department of Mathematics, University Sussex should also apply. Professor J. Repka, Associate Chair, Depart of Toronto, Toronto, Canada M5S 1A 1. At least It is intended to make the appointment on one letter should be primarily concerned with ment of Mathematics, University of Toronto, the Lecturer A scale (£12860-£17827, under re Toronto, Canada M5S 1A 1. At least one letter the candidate's teaching. To insure full consid view). Further particulars and application forms eration, this information should be received by should deal with the candidate's teaching. To may be obtained from Paula Boyle, Personnel insure full consideration, this information should December 31 , 1992. Office, Sussex House, University of Sussex, be received by October 31, 1992. The University The University of Toronto encourages both Falmer, Brighton BN1 9RH, Tel (0273) 678202. of Toronto encourages both women and men to women and men to apply. In accordance with Completed forms should be returned by 23 apply. In accordance with Canadian immigration Canadian immigration requirements, priority will October 1992. be given to Canadian citizens and permanent requirements, priority will be given to Canadian An equal opportunity employer. citizens and permanent residents. residents. FOR SALE UNIVERSITY OF TORONTO UNIVERSITY OF TORONTO PASCAL-XSC Department of Mathematics Department of Mathematics The programming language for mathematicians. The Department solicits applications for a The Department solicits applications for a Compilers and documentation. FBSoftware, P. tenure-stream appointment in Analysis. Pref tenure-stream appointment in Applied Math 0. Box 44666, Madison, WI 53744-4666. (608) erence will be given to researchers in the areas ematics. Preference will be given to researchers 273-3702. of harmonic analysis, geometric analysis, and in the areas of probability and nonlinear partial differential equations. differential equations. The position is subject to The . appointment is at the downtown (St. budgetary approval. George) campus at the level of Assistant The appointment is at the downtown (St. Professor, to begin July 1, 1993. Candidates are George) Campus at the level of Assistant expected to have at least three years experience Professor, to begin July 1 , 1993. Candidates are PUBLICATIONS FOR SAL in teaching and research after the Ph.D., and to expected to have at least three years experience be able to demonstrate excellence in each. In in teaching and research after the Ph.D., and to particular, a candidate's research should show be able to demonstrate excellence in each. In MATH SCI PRESS, 53 Jordan Rd., Brookline, clearly the ability to make significant original particular, a candidate's research should show MA 02146, 617-738-0307. Geometric Struc and independent contributions to Mathematics. clearly the ability to make significant original tures and Nonlinear Physics, $95. Geometric Applicants should send their complete and independent contributions to Mathematics. Computing Science, $85, both by R. Her C. V. including a list of publications and any Salary commensurate with qualifications. mann. To appear: Lie Theory and Generalized appropriate material about their teaching, and Applicants should send their complete C.V. Function Algebras. arrange to have a least four letters of reference including a list of publications and any ap sent directly to Professor K. Murty, Associate propriate material about their teaching, and Chair, Department of Mathematics, University arrange to have at least four letters of reference of Toronto, Toronto, Canada M5S 1A 1. At least send directly to Professor K. Murty, Associate one letter should be primarily concerned with Chair, Department of Mathematics, University PUBLICATIONS WANTED the candidate's teaching. To insure full consid of Toronto, Toronto, Canada M5S 1A1. At least one letter should be primarily concerned with eration, this information should be received by Wanted: Mathematical books, journals, reprints, December 31, 1992. the candidate's teaching. To insure full consid eration, this information should be received by ephemera. Contact R. K. Dennis, Math. Dept., The University of Toronto encourages both White Hall, Cornell U., Ithaca, NY 14853-7901. women and men to apply. December 31, 1992. The University of Toronto encourages both Tel: 607-255-4027, FAX: 607-255-7149. email: women and men to apply. In accordance with [email protected] Canadian immigration requirements, priority will SEPTEMBER 1992, VOLUME 39, NUMBER 7 797 MATHEMATICAL REVIEWS ASSOCIATE EDITOR - HALF-TIME Applications and recommendations are invited for a one- or two-year half-time appointment as an Associate Editor of Mathematical Reviews (MR), to commence in January 1993. Applications will be welcome from persons taking leave from other positions and in particular from tenured faculty members who can take leave to come to MR for one or two years. The MR office of the American Mathematical Society is located in Ann Arbor, Michigan, not far from the campus of the University of Michigan. The editors, although employees of the AMS, enjoy many privileges at the University. At present, MR employs fourteen mathematical editors, about six consult ants, and over sixty nonmathematicians. It produces Mathematical Reviews, Current Mathematical Publications, various indexes, the on-line service MathSci and MathSci Disc. The responsibilities of an Associate Editor fall primarily in the day-to-day operations of selecting articles and books suitable for review, classifying these items, assigning them to reviewers, editing the reviews when they are returned, and correcting the galley proof. An individual with considerable breadth in pure or applied mathematics is sought and preference will be given those applicants with expertise in numerical analysis. The ability to write good English is essential and the ability to read mathematics in major foreign languages is important. (The ability to read mathematical articles in Russian or Chinese is especially desirable.) Persons interested in combining a sabbatical or other leave with this half-time appointment as an Associate Editor are encouraged to write (by letter or email) for further information. The twelve-month salary is negotiable and will be commensurate with the experience the applicant brings to the position. Applications (including curriculum vitae, bibliography, and names and addresses of at least three references) should be sent to Dr. D. G. Babbitt, Executive Editor Mathematical Reviews P. 0. Box 8604 Ann Arbor, MI 48107-8604 Telephone: 313-996-5255 FAX: 313-996-2916 INTERNET: [email protected] Interested applicants are urged to inquire without delay. The American Mathematical Society is an equal opportunity employer. Then consider joining a highly talented group of Statistics, Combinatorics and more. And they function as a mathematicians whose job it is to deduce structure where true community, exchanging ideas and working with some of structure is not apparent, to fmd patterns in seemingly the finest minds-and most powerful computers-in the country. random sets, to create order out of chaos. lf you love problem-solving and like the idea that those These are the mathematicians of the National Security solutions will be applied to real world look into a Agency. They contribute to the solution of cryptologic career with NSA. Send your resume to National problems using Number Theory, Group Theory, Finite Field the address below or contact your Security Theory, Linear Algebra, Probability Theory, Mathematical campus placement office. Agency Attn: M322 (AFL). Ft. Meade, Maryland 20755-6000 The Opportunities of a Lifetime An equal opportunity employer. U.S. dtlzenship required for appllcant aDd lmmediate family members. THE UNIVERSITY OF AUCKLAND- NEW ZEALAND Department of Mathematics and Statistics A CHAIR IN PURE MATHEMATICS Vacancy UAC.l97 Applications are invited for a Chair of Pure Mathematics. The successful applicant will have an outstanding academic and research background in some branch of Pure Mathematics with personal qualities and experience which will enable her/him to contribute significantly to the continuing development of Pure Mathematics at Auckland both in research and teaching. This position, is one of four established Chairs in the Department of Mathematics and Statistics, two being in Pure Mathematics and one in each of Applied & Computational Mathematics and statistics. Three other staff hold Personal Chairs. The Department has research strength in a number of areas of Pure Mathematics, including logic, group theory, discrete mathematics, finite geometry, functional analysis, summability theory, complex analysis, quasiconformal analysis, topology and differential equations. The Department of Mathematics and Statistics at the University of Auckland is the largest Department of the largest University in New Zealand. It is in the process of boosting its graduate student enrolments. The Department has an undergraduate computing laboratory currently being enlarged and has a collection of Macintosh microcomputers and Sun workstations. The Pure Mathematics collection of periodicals in the University Library is the best in the country and includes a number ofjournals obtained by exchange with the New Zealand Journal of Mathematics (formerly known as the Mathematical Chronicle), produced locally in collaboration with the New Zealand Mathematical Society. Commencing salary will be established within the range NZ$80,080 - NZ$94,840 per annum. Further information, Conditions of Appointment and Method of Application, should be obtained from the Assistant Registrar, Academic Appointments, The University of Auckland, Private Bag 92019, Auckland, New Zealand, telephone (64) 9 373-7999, fax (64) 9 373-7454. Three copies of applications should be forwarded to reach the Registrar by 20 November 1992. Please quote Vacancy Number UAC.197 in all correspondence. W B NICOLL, REGISTRAR. An Equal Employment Opportunity Employer OKLAHOMA STATE UNIVERSITY Grayce B. Kerr Chair in Mathematics The Department of Mathematics invites applications and nominations for the Kerr Chair in Mathematics. Candidates should have an outstanding record of scholarly accomplishments and a strong commitment to research. The person selected to fill this position will be expected to maintain a strong research program and be actively involved in the development of the department, including the graduate and undergraduate programs. Salary, discretionary fund, and teac::hing load are negotiable. Send inquires, nominations, and applications to: Alan Adolphson Chairman, Chair Search Committee Department of Mathematics, Oklahoma State University Stillwater, Oklahoma 74078 Email: [email protected] For full consideration, applications should be received by November 1 , 1992. Applications should include a vita and names and addresses of references. Oklahoma State University is an affirmative Action/Equal Opportunity Employer. Women and minorities are encouraged to apply. -~~MASSEY National University of Singapore \ \\~(1/ UNIVERSITY ~ PROFESSOR OF PURE ~/ MATHEMATICS Department of Mathematics Faculty of Science Scllool of Mathematical and Information Sciences Applications are invited for faculty positions/appointments in one of the following Applications are invited for a disciplines from candidates who must possess a relevant PhD degree. Prefer- newly-established Chair in Pure . ence will be given to those who are able to teach in more than one of the areas Mathematics within the Department listed under the discipline they are applying to and with proven ability in research. of Mathematics. The Department is one of four in the School of Mathe matical and Information Sciences MATHEMATICS which comprises the Departments of Mathematics, Computer Science, Pure Mathematics • Applied Mathematics • Operations Research • Statistics Information Systems and Statistics. This Chair is designed to provide leadership in research and teaching in COMPUTATIONAL SCIENCE PROGRAMME the more theoretical branches of Computational Mathematics-Applicants should specialize in either geometric mathematics. The other established modelling or statistical computing. Experience with UNIX graphics workstations Chair in Mathematics is held by Professor Graeme C Wake who is also is essential. currently Head of Department. Besides appointments on normal 3-year contracts, visiting appointments for one The appointee will be expected to provide direction within the or two years will also be considered. Department, University, and in the Gross annual emoluments range as follows: wider community. Applicants should be distinguished in research in one or Lecturer S$50,39Q-64,200 more fields of Pure Mathematics and Senior Lecturer S$58,68Q-1 00,310 have proven ability in teaching. The Associate Professor S$88,650-122,870 appointee will be expected to take a full part in teaching, research and (US$1.00 = S$1.62 approximately) administration and may be expected The commencing salary will depend on the candidate's qualifications, experience to serve a term as Head of Department. It is envisaged that the appointee and the level of appointment offered. would take up the Chair in 1993. Leave and medical benefits will be provided. Depending on the type of contract The Department of Mathematics offers a full undergraduate programme offered, other benefits may include: provident fund benefits or an end-of-contract in mathematics including service gratuity, a settling-in allowance of S$1 ,000 or S$2,000, subsidised housing at teaching. Most undergraduate courses nominal rentals ranging from S$100 to S$216 p.m., education allowance for up to are taught both to internal students three children subject to a maximum of S$16,425 per annum per child, passage and by correspondence to extramural assistance and baggage allowance for the transportation of personal effects to students throughout New Zealand and overseas. The graduate study Singapore. Staff members may undertake consultation work, subject to the programmes include masterate and approval of the University, and retain consultation fees up to a maximum of 60% PhD thesis supervision - currently for of their gross annual emoluments in a calendar year. fifteen students. The University reserves the right There are eight faculties in the National University of Singapore with a current to make no appointment or to fill the student enrolment of some 18,000. All departments are well-equipped with a Chair by invitation. wide range of facilities for teaching and research. Reference number NAMS 54/92 must be quoted. All academic staff have access to the following computer and telecommunication Closing date: 31 October 1992. resources: an individual microcomputer, an IBM 3090 mainframe, an NEC SX Further details of the above supercomputer, on-line library catalog~e, all networked through optical fibre position together with Conditions of based FDDI technology. International contact is maintained through BITNET and Appointment are obtainable from Mrs V B Bretherton, Personnel Section, to INTERNET. In addition, the Computational Science Laboratory is equipped with whom applications, including a full a SUN parallel processing and scientific visualization platform and two clusters of curriculum vitae, and the names, DECstation 5000 workstations. addresses and fax numbers of three referees should be sent before the Application forms and further information on terms and conditions of service may closing date specified. be obtained from: B.R.H. Monks Registrar The Director Department We are an Equal Opportunity Employer. Personnel National University of Singapore 10 Kent Ridge Crescent Palmerston North Singapore 0511 New Zealand Telephone (64) 6 356-9099 Enquiries may also be sent through BITNET to: PERPL @ NUS3090, or through Fax (64) 6 350-5615 Telefax: (65)7783948 FORUM MATHEMATICUM An international journal devoted to pure and applied mathematics as well as mathematical physics Editors: M. Brio (College Park, MD) F. R. Cohen (Rochester, NY) V. Enss (Aachen, Germany) R. Fintushel (East Lansing, Ml) M. Fliess (Gif-sur-Yvette, France) M. Fukushima (Osaka, Japan) G. Gallavotti (Rome, Italy) R. Gobel (Essen, Germany) K. H. Hofmann (Darmstadt, Germany) J. Lindenstrauss (Jerusalem, Israel) D. H. Phong (New York, NY) D. Ramakrishnan (Pasadena, CA) A. Ranicki (Edinburgh, UK) P. ~A. Raviart (Palaiseau, France) P. Sarnak (Stanford, CA) D. S. Scott (Pittsburgh, PA) D. Segal (Oxford, uK) B. Shiffman (Baltimore, MD) F. Skof (Turin, Italy) K. Strambach (Erlangen, Germany) H. J. Sussmann (New Brunswick, NJ) G. Talenti (Florence, Italy) Subscription Information: FORUM MATHEMATICUM ISSN 0933-7741 1992, Volume 4 (6 issues) Annual subscription rate: $255.00, plus postage and handling Single issue price: $55.00 Back volumes available. Sample issues upon request. Prices subject to change. Walter de Gruyter le'l Berlin • New York For North America: Walter de Gruyter, Inc. 200 Saw Mill River Road, Hawthorne, New York 10532 Tel: (914) 747-0110 Fax: (914) 747-1326 TEICHMULLER THEORY IN ALGORITHMS FOR MATH INTO TEX RIEMANNIAN GEOMETRY RANDOM GENERATION by George Gratzer, University of Manitoba based on lecture notes by Jochen Denzler AND COUNTING This book is for the mathematician, engineer, or by Anthony J. Tromba, Ludwig-Maximilians A Markov Chain Approach scientist, who wants to write and typeset articles with Universitiit Miinchen, Miinchen, Germany mathematical formulas but who does not want to by Alistair J. Sinclair, University of Edinburgh spend a great deal of time learning how to do it. It These lectures develop Teichmiiller theory within assumes little familiarity with TEX or LaTEX. the context of Riemannian geometry and elliptic This monograph studies two classical computational partial differential equations. This new approach, problems: counting the elements of a finite set of CONTENTS: Part 1: The One-Day Course • Typing Your First Article • Part II: A Leisurely Introduction • Typing Text • Typing which is more in the spirit of modem general relativ combinatorial structures, and generating them at ran dom from some probability distribution. The author Math • The Preamble and the Topmatter • The Document • The ity, will provide a substantially more accessible Bibliography • Multiline Math Displays • Displayed Text • Part III: framework within which to study the properties of aims to classify the computational difficulty of these Customizing • Customizing AMSTEX • Macros in TEX Teichmiiller space. problems for various naturally occurring structures; the emphasis is on positive results that demonstrate 1993 187 pp. (approx.) ISBN: 0-8176-3637-4 CONTENTS: Mathematical Preliminaries • The Manifolds of the existence of efficient algorithms. This book will Softcover $34.50 (tent.) Teichmiiller Theory • The Construction ofTeichmUller Space • T(M) is a Cell • The Complex Structure on Teichmtiller Space • Properties serve as an introduction to an expanding research of Weil-Petersson Metric • The Pluri-Subhannonicity of Dirichlet's topic within the area of design and analysis of algo Energy on T(M)3; T(M) is a Stein-Manifold rithms, and should be of interest to researchers and MATHEMATICAL 1992 220 pp. ISBN: 0-8176-2735-9 graduate students in theoretical computer science and CONTROL THEORY Softcover $29.00 probability and statistics, as well as theoretical physi cists with an interest in Monte Carlo methods. An Outline by Jerzy Zabczyk, Institute of Mathematics, Polish 1992 ISBN: 0-8176-3658-7 Hardcover Academy of Sciences, and Warsaw University, Po Price to be announced ADVENTURES IN land STOCHASTIC PROCESSES by Sidney Resnick, Cornell University This book presents basic concepts and results of the STOCHASTIC mathematical control theory, and its aim is to give a This textbook provides easy access to Stochastic APPROXIMATION direct access to the theory in a self-contained and Processes for many students of applied science at concise way. The book tries to give a complete many levels. With its carefully modularized discus AND OPTIMIZATION picture of the subject, and to teach the basic methods, sion and crystal clear differentiation between rigor OF RANDOM SYSTEMS while covering all deterministic theory in one volume. ous proof and plausibility argument, it is very ac by Lennart Ljung, Linkoping University, CONTENTS: Part 1: Elements of classical control theory • Part II: cessible to beginners but flexible enough to serve Sweden, Georg Pflug, Universitiit Wein, Austria Nonlinear control systems • Part III: Optimal control • Part IV: those who come to the course with strong back & Harro Walk, Universitiit Stuttgart, Germany Infinite dimensional linear systems • Appendix grounds. The book contains many examples, exer 1993 260 pp. (approx.) ISBN: 0-8176-3645-5 cises, and applications of a practical and serious This text provides an approach to theory and applica Hardcover $65.00 (tent.) nature, with underlying principles of complex tion of stochastic approximation in view of optimiza problems and computations cleanly and quickly de tion problems, especially in engineering. This work lineated through lively and rich vignettes of a person is based on the seminar lectures of the Stochastische alized group of characters inhabitating our random Approximation and Optimierung zuflilliger Systeme, COMPACT RIEMANN world. Each chapter is fully supplemented with held at Blaubeuren in 1989. SURFACES exercises. CONTENTS: Foundations of Stochastic Approximation • Applicational by Raghavan Narasimhan, University of CONTENTS: Preliminaries: Discrete Index Sets and/or Discrete State Aspects of Stochastic Approximation • Applications to Adaption Chicago, IL Spaces • Markov Chains • Renewal Theory • Point Processes • Algorithms These are the lecture notes forming a course given at Continuous Time Markov Chains • Brownian Motion • The General 1992 113 pp. ISBN: 0-8176-2733-2 Random Walk • References the ETH. The course was meant to provide an Softcover $24.50 introduction to the function theory and the geometry 1992 640 pp. (approx.) ISBN: 0-8176-3591-2 of compact Riemann surfaces. Hardcover $64.50 CONTENTS: Algebraic functions • Riemann surfaces • The sheaf of genns ofholomorphic functions • The Riemann surface of an algebraic function • Sheaves • Vector bundles, line bundles and divisors • THE SELF-AVOIDING WALK Finiteness theorems • The Dolbeault isomorphism • Weyl's lemma by Neal N. Madras, York University, Ontario, and and the Serre duality theorem • The Riemann-Roch theorem and some Gordon D. Slade, McMaster University, Ontario applications • Further properties of compact Riemann surfaces • Hyperelliptic curves and canonical map • Some geometry of curves in This book provides the first unified account of the projective space • Bilinear relations • The Jacobian and Abel's theorem • The Riemann theta function • The theta divisor• Torelli·s theorem • rigorous results for the self-avoiding walk, with Riemann's theorem on the singularities off) particular emphasis on its critical behavior. It is self-contained, accessible to beginning graduate stu 1992 120 pp. ISBN: 0-8176-2742-1 dents, and will be of interest to researchers in prob Softcover $24.50 ability theory, statistical mechanics, and mathemati cal physics. CONTENTS: Introduction • Scaling, polymers and spins • Some com binatorial bounds • Decay of the two-point function • The lace expansion •Above four dimensions • Pattern theorems • Polygons, slabs, bridges, and knots • Analysis of Monte Carlo methods • Related topics Birkhiiuser 1992 436 pp. (approx.) ISBN: 0-8176-3589-0 Hardcover $64.50 (tent.) Boston • Basel • Berlin E. Marsden, Elementary Classical Analysis, W.••. ==r- proof of Theorem 2. Defme the function G: A c R• x R•--> R• x R• by is of class C'' and the identity mapping is of class c.·'' ;:;;~r-.c: C'. The matrix of partial derivatives of G (JacObian -· 0 1 0 ... 1 0 ... 0· BF1 BF1 OFt ax, .. ax. ;y, ... niCally ./.\' -, It's a breeze. Scientific Word is a front end to TEX. It includes a Windows version of l..f\TEX and a Windows previewer. It stores files It will have you typing mathematics in in ASCII l..f\TEX format and imports most minutes. 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FJ/-n- HEWLETT ~~PACKARD ESSENTIAL MATHEMATICS FROM CAMBRIDGE Lectures on Mechanics Groups and Combinatorics Jerold E. Marsden Edited by Martin W. Liebeck and Jan Sax/ London Mathem«tical Society Lecture Note Series 174 London Mathematical Society Lecture Note Series 165 1992 254 pp. 42844-0 Paper $34.95 1992 350 pp. 40685-4 Paper about $34.95 Supermanifolds Arakelov Geometry Second Edition C. Soule, D. Abramovich, J. F. Sumo/, and J. K. Kramer Bryce DeWitt Cambridge Studies in Advanced Mathematics 33 Cambridge Monographs on Mathematical Physics 1992 183 pp. 41669-8 Hardcover $44.95 1992 425 pp . .41320·6 Hardcover $95.00/42377-5 Paper $37.95 Now in paperback ... Functional Programming Winner of The Most Outstanding Book in the Chemistry, Antony J. T. 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Completions of Admissable (g,K) modules. The Theory ofthe Leading Term. The Harish-Chandra Plancherel Theorem. Abstract Representation Theory. The Whit taker Plancherel Theorem. Appendix to Insight Chapter 15. Bibliography. Index. June 1992,480, $105.00/ISBN: 0-12-732961-7 A First Course in Differential Manifolds The Linear Rational Continuum Antoni A. Kosinski Complementarity Problem Mechanics CONTENTS: Differentiable Structures. Richard W. Cottle, Jong-Shi Pang, and Immersions, Imbeddings, Submanifolds. Richard E. Stone Volume1 Normal Bundle, Tubular Neighborhoods. SECOND EDITION Transversality. Foliations. Operations CONTENTS: Introduction. Background. C. Truesdell on Manifolds. The Handle Presentation Existence and Multiplicity. Pivoting Meth Theorem. TheH-Cobordism Theorem.· ods. Iterative Methods. Geometry and De CONTENTS: Bodies, Forces, and gree Theory. Sensitivity and Stability Anal Motions. Kinematics. The Stress Framed Manifolds. Surger. Appendix. Bibliography. ysis. Chapter Notes and References. Bibli Tensor. Constitutive Relations. Ap ography. Index pendixes: General Scheme ofN ota October1992, c. 224 pp., $49.95 (tentative) tion. Some Definitions & Theorems ISBN: 0-12-421850-4 1992,762 pp .. $59.95/ISBN: 0-12-192350-9 of Algebra, Geometry, and Calculus. Solutions of the Exercises. Index. Order from your local bookseller or directly from 1991,391 pp., $99.50/ISBN: 0-12-701300-8 • ACADEMIC PRESS CALL TOLL FREE HBJ Order Fulfillment Dept. #17915 1·800·321·5068 6277 Sea Harbor Drive, Orlando, FL 32887 FAX 1·800-336·7377 Prices subject to change without notice. © 1992 by Academic Press, Inc. All Rights Reserved. SUCEP/WR- 32092 •I ••· The Fourth Annual .ICBMS Ulam Mathematics Conference CONFERENCE BOARD OF THE MATHEMATICAL SCIENCES March 10- 13, 1993 Subfactors and Knots Palm Beach Atlantic College West Palm Beach, Florida Vaughan F. R. Jones Subfactors and Knots provides an extensive introduction to Deadline the theory of von Neumann algebras and to knot theory and for abstracts: braid groups. The presentation follows the historical develop ment of the theory of subfactors and the ensuing applications to ~ovember2, 1992 knot theory, including full proofs of some of the major results. Jones treats in detail the Homfly and Kauffman polynomials, introduces statistical mechanical methods on knot diagrams, and attempts an analogy with conformal field theory. 1991 Mathematics Subject Classification: 46, 57; 16, 22, 81. 82 For more ISBN 0-8218-0729-3, 113 pages (softcover), November 1991 All individuals $26, List price $43 information, To order, please specify CBMS/80NA contact: Lilian Hill (407) 835-4306 or Piotr Blass (407) 650-7700 All prices subject to change. Free shipment by surface; for air delivery. please add $6.50 per title. Prepayment required. Order from: American Mathematical Society, P.O. 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CONTEMPORARY MATHEMATICS p-Adic Methods in Number Theory and Algebraic Geometry Mark Gotay, Vincent E. Moncrief, Alan C. Adolphson, Steven Sperber, and Jerrold E. Marsden, Editors and Marvin D. Tretkoff, Editors This book contains the proceedings of the Two meetings of the AMS in the fall of 1989- AMS-IM&-SIAM Joint Summer Research Con one at the Stevens Institute of Technology and · ference on Mathematical Aspects of Classical the other at Ball State University-included Spe Field Theory, held in July 1991 at the University cial Sessions on the role of p-adic methods in of Washington at Seattle. This volume contains number theory and algebraic geometry. This vol thirty refereed papers, both survey and research ume grew out of these Special Sessions. Drawn articles, and is designed to reflect the state of the from a wide area of mathematics, the articles art as well as chart the future course of the sub presented here provide an excellent sampling of ject. 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Box 6248 Providence, RI 02940-9943 · lllaaaaalallalaaalaalllaaalalaalalaaalaalaallallaaal Fold here 40 o/o Discounts to AMS Individual Members on these Exciting Journals from Oxford University Press! THE QUARTERLY JOURNAL OF MATHEMATICS Editors: S.M. Salamon, B. F. Steer, and W. B. Stewart, all at the Mathematical Institute, University of Oxford, UK. For all main branches of algebra, analysis, combinatorics, and topology, refer to The Quarterly Journal of Mathematics. Publishing original contributions to pure mathematics, the journal avoids specialization. Areas such as algebra, differential geometry, and global analysis receive particular emphasis reflecting the interest of the Oxford faculty of math ematics, although the great majority of the contributions come from institutions throughout the world. Recent papers have included: On Zero Sum Ramsey Numbers-Complete Graphs, Y. Caro Imprimitive Automorphism Groups, C. Chute Miller Prime Links in Differential Operator Rings, K. R. Goodearl Notes on Interpolation of Mixed Norm Spaces and Applications, M. Milman A Note on the Relative Index Theorem, J. Roe Volume 43, 1992 (4 issues), ISSN 0033-5606, List $145, AMS Member $87 Volume 44, 1993 (4 issues), ISSN 0033-5606, List $155, AMS Member $93 THE QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS Executive Editors: L. M. Hocking, Department of Mathematics, University College, London; P. A. Martin, Department of Mathematics, University of Manchester; and A. D. Rawlins, Department of Mathematics and Statistics, Brunei University, UK. For original papers on all aspects of mechanics, especially theoretical mechanics, The Quarterly Journal of Mechanics and Applied Mathematics leads the way. Acting as the international forum for mathematicians and engineers to present their latest discoveries, the journal specializes in such areas as: solid mechanics-including composite materials, elastic waves and cracks; fluid mechanics-including boundary layers, waves, acoustics and stability; classical electromagnetism; diffusion; nonlinear dynamics; and relevant math ematical and numerical methods. Recent papers have included: Bubble Contraction in Hele-Shaw Cells, V. M. Entov and P. Etingof Low Frequency Acoustic Scanering by a Hard Inverse Prolate Spheroid, D. Gintides and K. Kiriaki Image Singularities of Green's Functions for Anisotropic Half-Spaces and Bimaterials, T. C. T. Ting On Finite Amplitude Patterns of Convection Near a Lateral Boundary, P. G. Daniels and M. Weinstein Slow Oscillations of a Circular Cylinder or Sphere in a Viscous Fluid, E. J. Watson Volume 45, 1992 (4 issues), ISSN 0033-5614, List $190, AMS Member $114 Volume 46, 1993 (4 issues), ISSN 0033-5614, List $210, AMS Member $126 To subscribe to these journals or request a free sample issue, please write to: Journals Marketing Department, Oxford University Press, 2001 Evans Road, Cary, NC 27513. I VOLUME 104 Wulff Construction: A Global Shape from Local Interaction Roland Dobrushin, R. Koteckyand Senya Shlosman A theory of. the equilibrium $hape of crystal assuming minimal surface free energy was formulated at the,beginning of the century by Wulff. Assuming that the anisotropic interfacial free energy is known, the Wulff constru<::tion yields the shape of crystal• in equilibrium and allows one to understand its main features. This research monograph considers the Wulff construction in the case of a two-dimensional Ising ferromagnet with periodic boundary conditions and at sufficiently low temperatures. Heuristically, themain result can be stated this way: a droplet of one phase immersed in the opposite one will be formed with the separation line following with high accuracy the shape yielded by the Wulff construction. The book brings the.reader through the entire· devefopment of· the proof of this result. 1991 Mathematics Subject Classification: 82, 85; 60 ISBN O!l82'11'~2J204,.,_ (~~er~; August 1992 ••~Ml,.,.,_ $78; 4$ ~ Jt®•. tnstitutbNil mernl'ler $104 Your ordering code is MMONOI104NA · Mathematical Scattering. Theory: General Theory D. R. Yafaev Yafaev presents a comprehensive and systematic exposition of the theory, covering different methOds (of trace class and smooth perturbations) and approaches (time dependent and stationary) and discussing the relationships among them. Yafaev also fills some gaps in the monographic literature, such as the properties of the scattering matrix and the theOry of the spectral shift function. Addressed to graduate students as well as· researchers, this book will prove an invaluable reference and research l All prices subject to Change. Free shipment by surface: for air delivery, please add $6.50 per title. Prepayment required. Order from: AmeriCan MathematiCal Society, P.O. Box 1571, Annex Station, Providence, Rl 02901·1571, or call toll free 8()()..321·4AMS (321·4267) in the U.S. and Canada to charge with VISA or MasterCard. Residents of ~nada, please include 7% GST. Large Discounts for Members of the AMS LIBRARIES AND INDIVIDUAL MEMBERS One-Parameter Semigroups by Ph. Clement, H.J.A.M. Heijmans, S. Angenent, C.J. van Duijn and B. de Pagter · 987 x + 238 pages CWI Monographs, 5 Price: US $ 114.50 I Dfl. 200.00 1987 x + 312 pages 0-444-70184-2 List Price: US $ 69.00 I Dfl. 121.00 of Theorie des Operations Lineaires (PWN, ISBN 0-444-70284-9 '1979). The theory of semigroups of operators was initiated by classic work by the late Stefan Banach contains the E. Hille in 1948. The possible range of applications is of the algebra of operators. It presents results enormous and includes problems in mathematical linear operators defined in general spaces of physics, probability theory and control theory. The kind, principally in Banach spaces. A new purpose of this book is to illustrate the richness of the section ("Some Aspects of the Present Theory theory of one-parameter semigroups by examining Spaces") completes this important some of its various aspects. Recursive Functionals Introduction to Harmonic by L.E. Sanchis Representations and ADII)Iicatic Studies in Logic and the Foundations of Mathematics, py D. Gurarie 131 North-Holland Mathematics 1992 xii + 278 pages List Price: US 1 1992 viii + 454 pages $ 00.00 I Dfl. 175.00 ISBN 0-444-89447-0 List Price: US $ 128.50 I Dfl. enough to warrant a coherent This exposition of the theory of recursive functionals ISBN 0-444-88612-5 body of differential topology in the includes advanced results. Although aiming at a theory This book introduces concepts, i I I seethisbookasareliable of higher order computability, attention is restricted to techniques that evolve around wAII-rlAfilr,,.rJ subject; the possibility to second order functionals, where the arguments are representations and Laplacians. the feeling of security when numerical functions and the values, when defined, are concerns geometrical objects uHrr!ltoruu:;realms of infinite natural numbers. This theory is special, for to some discrete or continuous, that · geometry."· extent it can be reduced to first symmetry group G, such as order theory, but when properly extended and relativized symmetric Riemannian manifolds. it requires the full machinery of higher order computations. List price Discount SPECIAL DISCOUNT as shown price ORDER FORM Send this form (or a photocopy) to: ELSEVIER SCIENCE PUBLISHERS Attn: Marijcke Haccou, P.O. 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PEITGEN, H. JURGENS and NUMERICAL ALGEBRA D. SAUPE, all of the University of Bremen, Germany MATHEMATlCS An Approach via Module Theory CHAOS AND Translated by L. SCHUMAKER, Vanderbilt Algebra is designed as a text for a University, Nashville, TN first-year graduate-level course in FRACTALS Covers the classical topics of numeri algebra. Instead of an encyclopedic New Frontiers of Science cal analysis and includes an up-to approach, the authors used a the date treatment of both splines and matic, consistent point of view. The For almost ten years chaos linear optimization methods. The unifying theme is the concept of a and fractals have been riding text is designed to be used in a first module (a generalization to rings of a wave that has enveloped cou·rse in numerical analysis at the the concept of a vector space, which many areas of mathematics upper undergraduate and beginning is defined on a field). To promote and the natural sciences in its graduate levels. A careful balance understanding, the book provides power, creativity and ex proofs with a maximum of insight between mathematical rigor and panse. Traveling far beyond numerical insight is featured. Each and with a minimum of computation section concludes with an extensive as well as chapters stressing compu the traditional bounds of set of exercises which instructors tational techniques. Beginning with mathematics and science to should find useful in helping students an introduction to group theory and the distant shores of popular to master the material. Moreover, the ring theory, the book then develops culture, this wave captures authors have also provided carefully the basics of module theory. A re the attention and enthusiasm researched historical notes which view of the basics of linear algebra of a world wide audience. will be of particular interest to ex demonstrates the power of module The fourteen chapters of perts as well as to students. theory in the derivation of canonical the book cover the central forms and the spectral theorem. The 1991/422 PP., 76 ILLUS. /SOFTCOVER ideas and concepts of chaos book then uses module theory to $39.95/ISBN 0.387-97494-6 and fractals as well as many UNDERGRADUATE TEXTS IN MATHEMATICS investigate bilinear, sesquilinear and READINGS IN MATHEMATICS quadratic forms. Finally, a discus related topics including, the sion of ring theory and multilinear Mandelbrot Set, Julia Sets, forms leads to a chapter on group Cellular Automata, L-Sys S. AXLER, Michigan State University, East representations, which again uses tems, Percolation and Lansing, Ml; P. BOURDON , Washington & module theory to powerful effect. Strange Attractors. Each Lee University, Lexington, VA and W. RAMEY, Michigan State University, East 1992/APP. 536 PP., 2 ILLUS., 16 TABS. chapter is closed by a "Pro Lansing, Ml HARDCOVER/$44.50/ISBN 0-387-97839-9 gram of the Chapter" which HARMONIC FUNCTION GRADUATE TEXTS IN MATHEMATICS, VOL.136 provides computer code for THEORY a central experiment. Two appendices complement the S. V. BECHTOLSHEIM, W. Lafayette, IN The authors approach the field of book, the first, by Yi val harmonic functions from a more TEX IN PRACTICE Fisher, discusses the details function-theoretic perspective, and ideas of fractal image VOLUME 1: BASICS: 1992/APP. 384 PP., emphasizing techniques and results. 9 ILLUS./HARDCOVER/$49.00 compression; the second, by Topics covered include: basic prop ISBN 0.387-97595-Q Carl J. G. Evertsz and Benoit erties of harmonic functions defined VOLUME 2: PARAGRAPHS, MATH AND FONTS: Mandelbrot, introduces the 1992/APP. 368 PP., 22 ILLUS., 12 TABS. on subsets of R", including Poisson foundations and implications integrals; properties of bounded HARDCOVER/$49.00/ISBN 0-387-97596-9 functions and positive functions, VOLUME 3: TOKENS, MACROS: 1992/APP. of multifractals. 544 PP., 22 ILLUS./HARDCOVER/$49.00 including Liouville's and Cauchy's ISBN 0.387-97597-7 1992/APP. 992 PP., 24 COLOR theorems; the Kelvin transform; VOLUME 4: OUTPUT ROUTINES, TABLES: PLATES/HARDCOVER/$49.00 spherical harmonics; and hp theory 1992/APP. 576 PP., 10 ILLUS., 92 TABS. ISBN 0-387-97903-4 on the unit ball and on half-spaces. HARDCOVER/$49.00/ISBN 0-387-97598-5 An appendix describes routines for 4 VOLUME SET PRICE/$169.00 ISBN 0-387-97296-X use with Mathematica to manipulate some of the expressions that arise in the study of harmonic functions. J.JD; ,-----,,,,.• , •••1111 -----, 1992/APP. 248 PP., 16 ILLUS./HARDCOVER $39.50/ISBN ().387-97875-5 ~~\ Three Easy Ways to Order: GRADUATE TEXTS IN MATHEMATICS, VOL.127 \tJ; Call Toll Free 1-800.SPRINGER (NJ call 201-348-4033) or FAX 201-348-4505. Springer -Verlag Please mention 5223 when ordering. NEW YORK by phone. 7/92 REFERENCE #: 5223