Notices of the American Mathematical Society

November 1985, Issue 244 Volume 32, Number 6, Pages 737- 872 Providence, Rhode Island USA ISSN 0002-9920 Calendar of AMS Meetings

THIS CALENDAR lists all meetings which have been approved by the Council prior to the date this issue of the Notices was sent to the press. The summer and annual meetings are joint meetings of the Mathematical Association of America and the American Mathematical Society. The meeting dates which fall rather far in the future are subject to change: this is particularly true of meetings to which no numbers have yet been assigned. Programs of the meetings will appear in the issues indicated below. First and supplementary announcements of the meetings will have appeared in earlier issues. ABSTRACTS OF PAPERS presented at a meeting of the Society are published in the journal Abstracts of papers presented to the American Mathematical Society in the issue corresponding to that of the Notices which contains the program of the meeting. Abstracts should be submitted on special forms which are available in many departments of mathematics and from the headquarters office of the Society. Abstracts of papers to be presented at the meeting must be received at the headquarters of the Society in Providence. Rhode Island, on or before the deadline given below for the meeting. Note that the deadline for abstracts for consideration for presentation at special sessions is usually three weeks earlier than that specified below. For additional information consult the meeting announcements and the list of organizers of special sessions. ABSTRACT MEETING# DATE PLACE DEADLINE ISSUE 825 January 7-11. 1986 New Orleans. Louisiana EXPIRED January (92nd Annual Meeting) 826 April 11-12. 1986 Indianapolis. Indiana February 5 March 827 May 3-4. 1986 Baltimore. Maryland February 10 March August 3-11. 1986 Berkeley. California AprilS (International Congress of Mathematicians) October 1o-11. 1986 Logan, Utah October 31-November 1. Denton. Texas 1986 January 21-25. 1987 San Antonio. Texas (93rd Annual Meeting) January 6-11. 1988 Atlanta. Georgia (94th Annual Meeting) August 8-12. 1988 Providence. Rhode Island (AMS Centennial Celebration) January 11-15. 1989 Phoenix, Arizona (95th Annual Meeting)

DEADLINES: Advertising (January 1986 Issue) Nov. 14, 1985 (March 1986 Issue) Feb. 19, 1986 News/Special Meetings (January 1986 Issue) Oct. 28, 1985 (March 1986 Issue) Feb. 7, 1986

Other Events Sponsored by the Society

January 5-6. 1986. AMS Short Course: Approximation Theory, New Orleans. Louisiana. Details: January issue. June 22-August 2. 1986. Joint Summer Research Conferences in the Mathematical Sciences. University of California. Santa Cruz. California. Details: October issue and this issue. July 7-25. 1986. AMS Summer Research Institute on Representations of Finite Groups and Related Topics. California location to be announced. Details: January issue.

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Volume 32, Number 6, November 1985 EDITORIAL COMMITTEE Paul F. Baum, Ralph P. Boas Raymond L. Johnson. Mary Ellen Rudin 739 Julia Bowman Robinson Steven H. Weintraub. Daniel Zelinsky Everett Pitcher (Chairman) 7 43 Future Directions in Computational MANAGING EDITOR Mathematics, Algorithms, and Scientific James A. Voytuk Software ASSOCIATE EDITORS 758 29th Annual AMS Survey Stuart Antman. Queries Faculty Salaries. Tenure. Women. 758: Salaries Hans Samelson. Queries Ronald L. Graham. Special Articles of New Doctorates. 763: 1985 Survey of New SUBSCRIPTION INFORMATION Doctorates. 768; Fifteen Year Retrospective Subscription prices for Volume 32 on Academic Salaries. 772; Doctoral Degrees (1985) are $65 list; $52 institutional Conferred in 1984-1985. 774; (1983-1984 member; $39 individual member. (The subscription price for members is Supplement. 787) included in the annual dues.) A late 788 News and Announcements charge of 10% of the subscription price 791 Washington Outlook will be imposed upon orders received from nonmembers after January 1 of the 793 News from Washington subscription year. Subscribers outside 795 Letters to the Editor the United States and India must pay a postage surtharge of $5; subscribers in 798 Queries India must pay a postage surcharge of 800 Future Meetings of the Society for AMS $15. Subscriptions and orders New Orleans. January 7-11. 800; Amendments publications should be addressed to the American Mathematical Society, P.O. to the Bylaws. 803: Indianapolis. April11-12. Box 1571, Annex Station, Providence. Rl 804: Baltimore. May 3-4. 805; Invited prepaid. 02901. All orders must be Speaker and Special Sessions. 807 ADVERTISING & INQUIRIES Summer Research Conference Series The Notices publishes situations 809 Joint wanted and classified advertising, and 810 Special Meetings display adv.ertising for publishers and 814 New AMS Publications academic or scientific organizatons. Requests for information: 818 Miscellaneous Advertising: Wahlene Siconio Personal Items. 818: Deaths. 818: Visiting Change of address or subscriptions: Mathematicians (Supplementary List). Eileen Linnane Book order number 800-556-7774. 818; Application Deadlines. 820 CORRESPONDENCE. including 822 AMS Reports and Communications changes of address should be sent to Bylaws of the AMS. 822: Funds. 827: Officers American Mathematical Society, P.O. and Lecturers of the Society. 834 Box 6248, Providence. Rl 02940. Second class postage paid at Providence. 836 Advertisements Rl. and additional mailing offices. 864 Preregistration Forms Copyright © 1985 by the American Employment Register. 864, 865, 866 Mathematical Society. All rights reserved. Printed in the United States of America. New Orleans MAA Minicourses. 867 The paper used in this journal is acid-free New Orleans Preregistration and Housing. and falls within the guidelines established 869, 870 to ensure permanence and durability. Julia Bowman Robinson Julia Bowman Robinson 1919-1985

Julia Robinson was a remarkable person. Within The seventies brought recognition, honorary hours of her death on July 90, Everett Pitcher degrees, an invitation to give the colloquium called to ask if we could prepare "a personal lectures, election to the National Academy; but appreciation" of her to appear in the Notices. This none of these went to her head. She remained is the result. always the same thoughtful, levelheaded, and Pitcher explained that Robinson was only the considerate person who knew what she wanted third person to die while an active member and usually got her way. of the AMS Council; the death of a retiring Things were moving fast in the eighties. She president was unprecedented. I undertook to became president of the AMS and got a MacArthur solicit short contributions from various people who prize fellowship. She took both of these honors in knew her well, and to consult with her husband her stride. She was looking forward to returning Raphael Robinson and her sister Constance Reid to research as soon as her term as president to determine whether these contributions could expired, and it is a great pity that she was not be effectively combined to convey some personal given that chance. It was during the AMS meeting sense of Julia, leaving an account of her work for a in Eugene, over which she was presiding, that later occasion. Twelve short pieces came in. Reid she learned that she had leukemia. She will be arranged them in roughly chronological order of long remembered for her devotion to mathematics content, and made minor editorial suggestions and for her sterling character as well as for her primarily to shorten some and to eliminate achievements. repetitions. We hope readers can get some feeling for the human side of the mathematician who Elizabeth Scott served as AMS President during 1989 and 1984. Julia Robinson and I were graduate students Leon Henkin together at Berkeley. During World War II we University of California, also did a lot of heavy computing in a large group Berkeley organized by Jerzy Neyman. After the war we were glad to return to our studies and research, I D. H. and Emma Lehmer to astronomy and Julie to mathematics, but there We knew Julia Robinson first in the early forties was still overlapping in statistics. when she worked at the Statistical Laboratory Julie was by then married to Raphael Robinson, in Berkeley during the Second World War. We who had an appointment in mathematics; a admired her, not only for her mathematical University rule made it quite difficult for the ability, but also for the steadfast way in which mathematics department to employ both of them. she resisted the efforts of Jerzy Neyman to make Professor Neyman felt that Julie should be a statistician out of her. She was sure that employed and encouraged to do research. He mathematical logic was her field. argued that statistics, although technically in Then came the disruptive fifties with the oath mathematics, had a lot of autonomy in budget controversy, student unrest, the McCarthy era, and appointments, including a "line item" for and school integration. She put her energies into a research assistant. Although I already held politics, voter registration, and other good causes. this position, he arranged that I would be moved The sixties brought her back where she really to another research position to accommodate belonged, and by the end of the decade she Julie's appointment. Fine, except that Personnel had become famous for her contribution to the suddenly interfered, contending that the position, solution of Hilbert's tenth problem. We will long now that it had changed, should be under remember how excited she was the evening that Personnel-in essence, out of research. Julie Julia and Raphael came to our house to put was asked to submit a "job description" of what on the board Matijasevich's proof of the missing she did each day, so she did: Monday-tried to link to the solution of the problem. A lesser prove theorem, Tuesday-tried to prove theorem, person could have felt regret or even resentment Wednesday-tried to prove theorem, Thursday­ at not having done the work herself, but for her tried to prove theorem, Friday-theorem false. the problem was uppermost. She soft-pedaled Personnel withdrew. The position remained in the her own accomplishments and lavished praise on graduate division, and Julie got the appointment. Matijasevich and others who had contributed to Throughout her life Julie stood up for offering the solution. opportunities to all students. She also encouraged

739 graduate students and young faculty to have more August AMS meeting in Laramie, Wyoming, we confidence in their real abilities. She felt that considered the possibility of a side trip to see the women and minority mathematicians especially Tower. Unfortunately she did not live to attend needed this support, which she provided with that meeting. She would have loved, not only spirit yet in a quiet way. As an example, once the strangely shaped mountain itself, but also the at a monthly luncheon of women faculty she wildlife around it, especially the enormous prairie­ gave a wonderful seminar about her own research, dog colony. She loved animals in the wild-the but at the same time we could not help but migrating whales, the sea otters, the Monarch hear of the obstacles that should never have been butterflies wintering in Pacific Grove, the birds there. She was not complaining, just stating facts, at Point Reyes. She was interested in everything and pointing out that the situation is improving, around her. even in the sciences, even in mathematics. She She also loved to ride her bicycle and feel the encouraged us to work together so that all wind against her cheek and in her hair. On my women who have the ability and the desire to do visits to Berkeley, no matter how brief, we always mathematical research can have the opportunity tried to fit in a bicycle ride, sometimes in Tiburon, to do so. sometimes on the Sacramento River delta, or­ John Kelley when time was very short-on the Nimitz Trail in Tilden Park. I met Julia not long after I came to Berkeley To me Julia's love of travel and of nature­ in 1947. We were a small department then­ combined, if at all possible, with bicycling-was less than a third of our present size-and we got as much a part of her as her mathematics. to know each other rather easily. Julia was in the last year of graduate school, very much a David Gale part of the excitement about set theory and the I first heard of Julia Robinson in 1950. A foundations of mathematics that Alfred Tarski group of us at Princeton had become interested in had brought to Berkeley. I remember her as game theory. Simultaneously there was a flurry a tall slender young woman of gentle demeanor activity in the subject at the newly with a nice sense of humor and a gift for lucid of creative coast. In mathematical discourse. formed Rand Corporation on the west fact, the main result of my thesis was discovered The year of Julia's Ph.D. was also the first at the same time by people at Rand. There was, of the years of ferment marking the arrival of however, one problem which neither group had McCarthyism at the University. But the time been able to solve, a conjecture that if two people was also distinguished by a special cameraderie in played a game repeatedly and each kept track the mathematics department, a closing of ranks. the opponent was doing and responded We levied special assessments upon ourselves to of what to the make up a "math fund" which would support any optimally, then the pay-off would converge game. What we learned in 1950 one of us who got into trouble in connection with value of the the infamous loyalty oath. Julia was very much was that the problem had finally been cracked­ a part of our department's unified opposition to by Julia Robinson. Her solution remains to this the oath. I remember well seeing her in the day among the deeper results of elementary game Sacramento courtroom at the penultimate legal theory. vindication of those who had been dismissed for Although she was no longer at Rand when I refusing to sign the oath. visited as a consultant in the summer of 1955, I Julia was offered a professorship at the Univer­ recall reading some of her reports: in particular, sity of California about a year after she was one in which a certain military type game was elected to the National Academy of Sciences. Her solved by making surprising use of Archimedes's gracious acceptance of the University appoint­ discovery that the area of a zone on a sphere ment honored the University; her mathematical depends only on its height. discoveries honor us all. From the start Julia was associated in my mind with California and the way of life there. Lisl Gaal When I ended up in Berkeley ten years later Julia and I first met in Professor Tarski's course and got to know her, I sensed this geographical and seminar in the fall of 1950. I had just returned connection even more strongly. It's a bit ironical. from a summer in Europe so it was only natural Berkeley in 1965, as we all remember, was the that we should talk of travelling-a subject and birthplace of the radical student movement which an activity of which she never tired. was soon to spread all over the world; but She always tried to combine her trips to my geographical association verged on-heaven AMS meetings with explorations of the places forbid-patriotism, one of the cardinal crimes of where they were held. After seeing the movie the "establishment." Having spent much of my life "Close Encounters of the Third Kind," in which in a very Europeanized culture on the east coast, the extra-terrestrials land on the Devil's Tower I couldn't help feeling that there was something National Monument, she wanted to go there wonderfully American about Julia Robinson. I herself. So last May, as we talked about the won't even try to describe what that quality

740 was. In any case, because of my association with with one of her sisters, and together they enjoyed her, I have succumbed periodically to spells of the festivities which the Academy puts on for patriotism, by which I mean feelings of pleasure its members and their guests-the reception in and, okay, pride in belonging to a country which a huge tent on the Academy lawn, the evening once in a while produces its own special kind of concert, the formal introduction of new members person. Of course, Julia was exceptional in many (when the President of the Academy describes ways; but one thing that really sets her apart, in the major accomplishments of each one), the my mind-and I hope that historians will take scientific talks, and the final dinner. Later, note of this-is that she was so completely "home her election as the first woman President of grown." the American Mathematical Society apparently seemed somewhat more daunting to her, for she Martin Davis promptly came to ask advice of me and other Julia Robinson's writings bear ample testimony former presidents. When her term began, she to the power and elegance of her work. I would like took on the responsibilities of the office with a to tell something of how I personally experienced will and her usual quiet competence. this power and elegance. In the summer of 1959, Hilary Putnam and Ivan Niven I worked out a flawed proof of an important Julia Robinson's term of office as the President theorem. The theorem, which was a key lemma in of the American Mathematical Society coincided Matijasevich's solution of Hilbert's tenth problem, with my term of office as President of the may be stated as follows: Mathematical Association of America. One of If S is a computable set of natural numbers her first actions as president was to call me to (i.e., if there is an algorithm for deciding of a express her concern over whether our respective given number whether it belongs to 8), then organizations were doing all that they could to there is an exponential Diophantine equation help mathematically talented young people from E(a,xt,···,xn) = 0 which is solvable in natural minority groups to achieve their potential. She numbers for given a if and only if a E S. felt certain that there were many young people of Our proof was flawed mainly because it used promise in these groups who could enjoy successful the unproved (though likely true) assertion that careers in mathematics if they could be located there are arbitrarily long arithmetic progressions and encouraged. consisting of primes. In addition, it used a Knowing that others with the same idea had good deal of messy elementary analysis (including worked on this problem, we started by surveying approximations to the logarithmic derivative of what was being achieved; for example, by getting the r-function). Hilary and I sent our work to in touch with knowledgeable leaders like Gloria Julia at once because she had already worked Gilmer. We concluded that it was best not to on this problem and, in fact, we had used some dilute these efforts by launching any new program, of her methods. Her first move, almost by but rather to strengthen them in every way we return mail, was to show how to avoid the messy could by our support. analysis. A few weeks later she showed how No one working with Julia could fail to be to replace the unproved hypothesis about primes impressed by the depth of her compassion, and in arithmetic progression by the prime number by the extent of her dedication to the goal of theorem for arithmetic progressions. At this point removing barriers that limit the full development we agreed that Hilary and I would withdraw the of the mathematical talents of young members of paper we had submitted for publication and the minority groups. result would be published under all three of our names (with a footnote indicating the history). Everett Pitcher Julia then greatly simplified the proof, which had I had met Julia Robinson only once prior to become quite intricate. In the published version, her selection by the Nominating Committee of the proof was elementary and elegant. the American Mathematical Society as President Elect. As Secretary of the Society it is frequently Saunders MaeLane my lot to make the initial approach to candidates. Julia was a valued member of the National Thus I can report that Julia Robinson was Academy of Sciences. Among the members (1442 astonished to be asked to be President. She of them in spring 1985) there are now a number studied the matter for several days, and I thought of women, but Julia was at the time of her that she might be waivering over accepting. I death still the only woman in the mathematics learned later that one strong consideration in her section of the Academy. In such matters there deliberations was the fact that a woman had is inevitably a first; Julia's accomplishments in never been President and that if she did not logic put her in that position. She was elected accept the position it might be a long time before in 1976. Subsequently she came regularly to a woman who was a natural candidate appeared the spring meetings of the Academy and took again. To decline would be a disservice to the a modest but effective part in the activities of cause of equality for women, a cause which she the section of mathematics. Usually she came strongly supported. Having decided to accept,

741 she took the duties of the office very seriously. I was hesitant to call her after I learned that she Her approach and action were always carefully was in the hospital but found that she welcomed considered but forthright, direct, and based on my call. We talked of logic and logicians and high ethical principle. As a result, the affairs open problems and things worth reading. She was of the Society were effectively managed and the particularly interested in news of progress on the Society well represented during her term of office. editorial project of publishing Godel's works, with I always found it easy and pleasant to work for which I have been involved in the last few years. her. I would like to insert a footnote in this respect. A few years ago when the Gooel project was Lenore Blum struggling for funding, Julia made a substantial During the early 1970s, when the Association personal donation that helped get us started, but for Women in Mathematics was actively working the condition of her gift was that it be anonymous. to change the position of women in mathematics We learned of her death just as the first volume departments across the country, we always of Gooel's Collected Works was going to press and wanted then to publicly acknowledge her felt encouraged by Julia Robinson's support. generosity. We are grateful to her family for It was difficult, however, for us to maintain agreeing to let us do so. A statement about her the delicate balance between acknowledging her gift will now appear in the volume-a volume obvious symbolic importance to us while at the which she helped to bring into existence and same time respecting her desire to remain out of which she would have liked, very much, to see. the limelight. Julia's optimism and courage during the period With her election to the National Academy of of her final illness were very impressive to me. But Sciences and her acceptance of the presidency of then Julia always impressed me. There are few I the American Mathematical Society, she herself know who were so universally liked and admired. recognized and accepted the role of public person. Also, on a more personal level, I believe that Leon Henkin the public recognition helped her to acknowledge From my long acquaintance with Julia Robin­ the significance of her own contributions to son, over more than three decades, I derived many mathematics. things of great value. Here I want to mention two In this regard, I feel privileged to have from the realm of the spirit. witnessed a side of Julia that I think many other A picture of Julia remains in my mind. She mathematicians may never have seen. We had and I and some friends are involved in the 1956 presidential campagin of Adlai Stevenson, and she arranged to meet for lunch with Nancy Kreinberg is wearing a funny hat and carrying a homemade of the Lawrence Hall of Science to discuss ways sign aloft on a mop-handle. Her usual speech, of encouraging girls and women in mathematics. dress, and manner were the very opposite of When I arrived at the Women's Faculty Club, flamboyant; but on a few occasions her strong, Julia was sitting in one of those high backed continuing concern for improving the conditions of Victorian chairs in a bright floral dress, looking mankind would break through. The style of quiet quite majestic. As I came up, she broke into decorum she generally adopted was in contrast to one of her broad impish grins: "Guess what? I the flashes of lively spirit that could be discerned have just received some great news-I have been in a wide range of bright or strong feelings when awarded a MacArthur Prize Fellowship for my she spoke. Especially strong was her stubborn part in solving Hilbert's tenth problem!" insistence that opportunity ought to be freely I insisted that we order a bottle of champagne to accessible to all-whether economic opportunity celebrate. I can't remember now the details of our or opportunity for access to a mathematical career. luncheon, but I do remember clearly the warmth She also did not hesitate to take a leadership role of three women thoroughly enjoying each other's in a Berkeley protest against Soviet restrictions company and sharing excitement, triumph, and aimed at Jewish mathematicians. plans for the future. There were several rounds of When her leukemia was diagnosed during the toasts, and by the end of the meal we had very 1984 Summer Mathematics Meeting and she nearly finished off the bottle of champagne. returned to Berkeley for treatment, many of her friends were hesitant about telephoning her. Later, when I mentioned this lunch to a friend What could they honestly say that would not in the Berkeley math department, he protested, add their own worries to hers? I was able to "But don't you know? Julia Robinson never reassure them-she would lighten their worries! drinks!" She faced her illness with a rare combination of I appreciate that Julia included me in her joy. detennination to understand and conquer it, a It's a way in which I will always remember her. realistic appreciation of the odds against her, and an insistence on continuing to maintain all her Solomon Fefennan other interests in life. I gained strength to tackle Modest and straightforward about her own my own problems each time I talked to her. outstanding contributions to mathematics, Julia Over the years I learned much from Julia Robinson always took a genuine interest in the about how to strengthen my spirit and clarity its work of others and helped foster work of the expression. It was one of my great fortunes to highest quality. have known her.

742 Future Directions in Computational Mathematics, Algorithms, and Scientific Software

1. Overview subject that has become known as computational Scientific computation has become a vital mathematics. component and even a basic mode for research Today's computer technology is dominated, and development in science and engineering. The on the one hand, by the introduction of micro­ impact of computers upon science and technology computers and their widespread acceptance, and, has already been extremely profound. A principal on the other hand, by the development of su­ reason for this certainly is attributable to the fact percomputers with architectures that represent a that the computer has increased and will increase major departure from traditional sequential ma­ enormously the range of solvable problems. The chines. These supercomputers and other machines rapid progress which we see today is a strong sign advancing the state of the art (e.g. in graphics that this impact of computers may be expected or symbol manipulation), rather than the micros, to continue for some time to come. are essential in areas of frontier science. In A decade ago this nation was pre-eminent in fact, it has been frequently observed that the all aspects of electronics, computers, and com­ most challenging problems always require more putational technology. This leadership position resources than can be provided by the fastest is being challenged from various sides. Some available computer. The reasons that these prob­ expressions of serious concern have already been lems are under-computed is that each advance in presented in several reports. In particular, the computing-power or algorithm design opens up report of the Lax panel [1] observed that "U.S. new possibilities for further research. Just as the leadership in super-computing is crucial for the increased resolution of the optical and electron advancement of science and technology, and there­ microscope resulted in the discovery of whole new fore, for economic and national security" , but that realms of science, so successive generations of "under current conditions there is little likelihood computing hardware and software have led and that the U.S. will lead in the development and will lead to fundamental advances in science and application of this new generation of machines." technology. Computational mathematics plays a central Here, more than ever, computational math­ and perhaps critical role in this connection. The ematics is of crucial importance. The effective computational solution of today's highly complex utilization of supercomputers and, in particular, problems of engineering and science involves ques­ of the planned highly parallel architectures, is tions ranging from the design of suitable computer far from being understood. There is a critical architectures and the study of algorithms to the need for developing new-and re-examining old­ modeling of physical, chemical, biological, and algorithms which will take full advantage of all engineering processes by means of mathematical the power of these computers. New advances equations. These issues are tied together by in numerical mathematics, algorithm design, and mathematical theory, which seeks a full under­ computer languages, will be essential for learn­ standing of the nonlinear phenomena contained ing to exploit the new facilities. It is expected in the models, and by numerical mathematics that new research contributions of the community which conceives, analyses, and tests the required of computational mathematicians and computer computational methods. In a complementary and scientists to these fundamental issues will be at equally essential role, mathematics is the science least as important in the development of new of algebraic and logical manipulation which, in generations of machines as the new hardware turn, represents the basis of such widely differing developments themselves. operations as the control of complex decisions These observations certainly support the con­ through artificial intelligence, the design and en­ clusion that computational mathematics is a high­ coding of large data sets, or the exact solution of leverage element of our nation's scientific and scientific problems of an algebraic nature. The technological effort. The field has developed vig­ span of this wide range of activities forms the orously during the past few decades. But the

743 Panel on Future Directions in Computational Mathematics, Algorithms, and Scientific Software

The complete text of this panel's report is published in this issue of the Notices, except for an Executive Summary and two appendices; Appendix B: Laboratory Facilities for Scientific Computing, Appendix C: Letters and Position Papers. Appendix A is included as the References section. The work of this panel was supported by grant DMS-8503483 from the National Science Foundation. Any opinions, findings, conclusions, or recommendations expressed in this report are those of the panel and do not necessarily reflect the views of the National Science Foundation. The full report is distributed by the Society for Industrial and Applied Mathematics (SIAM) and is reprinted here with their permission. Copies of this report can be obtained from SIAM, 1400 Architects Building, 117 South 17th Street, Philadelphia, Pennsylvania 19103. Members of the Panel Werner C. Rheinboldt, Chairman Mitchell Luskin University of Pittsburgh University of Minnesota Stanley Eisenstat Andrew Majda Yale University Princeton University Dennis Gannon Thomas Manteuffel Purdue University Los Alamos National Laboratory James G. Glimm Anil Nerode New York University Cornell University Gene H. Golub Marcel F. Neuts Stanford University University of Delaware Peter J. Huber Andrew Odlyzko Harvard University AT & T Bell Laboratories

744 current vitality and level of achievement notwith­ In order to meet the immediate need for standing, there are reasons to be concerned about making supercomputers available to academic sci­ the future. There exists at present a considerable entists and engineers, the National Science Foun­ shortage of personnel on all levels in the area dation in April 1984 announced the formation of of computational mathematics. Moreover, the the Office of Advanced Scientific Computing. The educational opportunities in the field are limited office was formed to: (1) increase the access to ad­ and do not produce the required people, espe­ vanced computing resources for the scientific and cially the much needed young researchers. At engineering research community, (2) promote co­ the same time, the computational mathematics operation and sharing of computational resources research effort in academic institutions is seriously among all members of the community, and (3) hindered by low funding levels, lack of stability in develop an integrated research community with the support for facilities and support personnel, respect to computing resources. This is certainly and limited access to up-to-date computer equip­ a most important step toward overcoming some ment. These problems have already been noted of the critical problems in scientific computing in by several previous reports. For instance, the NRC the country. report [3] recommended the following: But, in line with our earlier observations, any 1. Increased research support for computa­ such program of expanded access to supercom­ tional modeling and applied mathematics. puters can only be a first step. Its benefits to the 2. Increased support for computing facilities country will remain severely limited unless there dedicated to computational modeling and applied is the vigorous, accompanying program of aca­ mathematics. demic research and education on computational mathematics, software, and algorithms necessary 3. Increased support for education and man­ for the effective and efficient use of such large power development in computational and applied computer systems. mathematics. The panel does not find it sufficient to con­ In part, some of these problems reflect those sider simply an increase in the funding level for of the mathematics community as a whole. In support of the work of individual researchers fact, as the David report [4] documents, "(s)ince in computational mathematics. The solution of the late 1960s, support for mathematical sciences today's computing research problems in science research in the United States has declined sub­ and technology requires an interdisciplinary ap­ stantially in constant dollars, and has come to be proach involving contributions from various areas markedly out of balance with support for related of science, engineering, applied and numerical scientific and technological efforts". Moreover, mathematics, statistics, and computer science. "( o)ver the historical period 1968-82 . . . the Moreover, such work cannot proceed without ap­ annual number of U.S. citizens obtaining doc­ propriate computer hardware and software facili­ torates in the mathematical sciences from U.S. ties and the associated support personnel. Indeed institutions has been cut in half, from over 1,000 it will not be very effective unless there is a cer­ to fewer than 500". "Overall demand for Ph.D.'s tain continuity and stability in this infra-structure exceeds supply" . which supports the research. Computational mathematics has fared some­ This calls for an increased emphasis on the what better with respect to federal research sup­ support of teams which have a common intellec­ port than mathematics as a whole. But never­ tual focus but are sufficiently interdisciplinary to theless this support lagged far behind the growth span a significant portion of the broad range from of the field. Moreover, with respect to manpower an application area through applied and numerical resources, the field clearly is in worse shape than mathematics to scientific software and computer most other parts of mathematics. The David science. In order to assure the required stability report observes in this connection: "Particularly and continuity of the research effort, such support worrisome are the scarcity of senior personnel has to have reasonably long duration. It also in this area and the extremely small number of should include funds for the initial acquisition of young researchers and graduate students". "A the necessary hardware and software and for the major effort in this area is needed to attract, subsequent operation and maintenance of these educate, and support graduate students, postdoc­ facilities. In this connection it is also important to torals, and young researchers, and to provide the foster more cooperation and coordination between computational equipment essential for the proper researchers who often work on the same or similar conduct of this research". "Significant additional problems. There is a great need for an extensive resources for the mathematics of computation electronic network linking groups in mathematics, may be needed in the years ahead". computer science, and related areas. Such a

745 network would lead to greater standardization of in Appendix A present such examples and there software and less duplication of effort. is certainly no need for duplication. Instead we The proposed emphasis on group efforts does endeavored to stress topics that were not covered have the added benefit of optimal utilization of very extensively in the cited reports. the limited number of active researchers in com­ In the last two decades many developments putational mathematics. Moreover, such groups in numerical analysis have had a large impact on provide an excellent training ground for graduate scientific computations. As examples we mention students and post-doctoral fellows. This would here only the fast Fourier transform, the evolution help in alleviating some of the manpower prob­ of the finite element methods, variable step/order lems, although it would not remove the need for a ordinary differential equation solvers, adaptive more concerted program of strengthening the ed­ mesh-refinements, spline approximations, spectral ucational programs in the mathematical sciences methods, fast matrix algorithms including, for in general and in computational mathematics in instance, multigrid techniques, and effective op­ particular. A broad plan for educational sup­ timization methods. But there are a host of port in mathematics has been presented in the problems waiting to be understood. Perhaps David report. In computational mathematics the greatest opportunity provided by the modern there appears to be some added urgency for in­ computational approach is that it has opened creasing the level of support of graduate students the wide realm of strongly nonlinear phenomena and post-doctorals, and to study effective modes to systematic, relatively accurate, and efficient of undergraduate education which capture the modeling, improving the chance that important experimental and laboratory components of the phenomena can be isolated and analyzed. This field. represents one of the great challenges to numerical On the basis of its findings the panel strongly analysis today. recommends the following actions: 2.2 Nonlinear Elliptic Equations: The solu­ 1. The appropriate federal agencies should tion of coupled systems of nonlinear elliptic par­ strengthen their. support for research in compu­ tial differential equations is important in many tational methods, algorithms, and software for applications. These systems arise in steady state scientific computing. problems and as steady state subsystems or im­ 2. The agencies should support the develop­ plicit solution steps within a dynamical problem. ment of interdisciplinary research teams in com­ Many efficient discretization and solution methods putational mathematics and scientific computing. have been developed over the past thirty years by 3. Such support should permit the estab­ computational mathematicians. lislnnent and continued operation of a suitable The solution of coupled nonlinear partial dif­ research infrastructure for the teams, including ferential equations plays an especially important computer hardware and software and the associ­ role in semiconductor simulation. It is now pos­ ated support personnel. Moreover, the support sible to analyze many different designs without should be of sufficient duration to ensure conti­ building a prototype. The numerical problems nuity and stability of the research effort in the encountered here, however, require computing academic environment. equipment of the most modern type. Undoubt­ 4. The agencies should increase the support edly, more powerful computers will stimulate the for graduate students and postdoctorals directly use of more complex models, especially for three­ involved in the research of some interdisciplinary dimensional problems. team in computational mathematics and scientific The selection of suitable discretization pro­ computing. cedures is influenced by various considerations. 5. The agencies should increase the support These include the goals of the analysis of the for young researchers and cross-disciplinary visi­ physical problem, known mathematical properties tors who can contribute to the research work of of that problem and of the solution algorithm, one of the interdisciplinary teams. hardware considerations, such as parallelity, data management requirements and other computer 2. Research Opportunities science considerations, and, last but not least, re­ 2.1 Introduction: In this section we discuss strictions on computation time and expense. For several research areas and directions in computa­ any choice of discretization there are questions tional mathematics and examine how results in about the accuracy and stability of the method, this field have a high leverage effect on broad the efficient solvability of the resulting equations, areas of science and technology. The examples the robustness of the method with respect to the chosen are illustrative only and are not intended input data, and, for nonlinear problems, the sep­ to be complete. Moreover, all the reports listed aration of legitimate approximate solutions from

746 spurious approximate solutions, which do not cor­ improved optimization methods. Broadly speak­ respond to any exact solution. Much important ing, the goal is to optimize the distribution of work on the various discretization methods re­ electrical power over a network; the constraints mains to be done, especially when it comes to are nonlinear, and the number of variables in any adaptive forms of these methods. realistic case is very large. The OPF problem occurs in many areas of power engineering and 2.3 Linear and Non-Linear Equations: The power engineers have been working on it for at mentioned discretizations typically give rise to least 20 years. The methods used in the 1960s­ systems of linear equations. In particular, large when the computer solution of the OPF problem sparse systems with tens or hundreds of thou­ was first attempted-were slow and unreliable. sands equations are relatively common, and the Because of inadequacies in the methods, it was iterative solution of nonlinear problems usually widely considered that large OPF problems were involves such a linear system at each step. Much essentially impossible to solve. For example, research has gone into the development of efficient the objective function was believed to be almost methods for the solution of systems of linear equa­ "flat", with many local optima, simply because tions. This includes direct solution techniques, older methods usually failed to make any signifi­ such as the various forms of matrix decomposi­ cant progress after the first few iterations. Within tions, banded and frontal elimination techniques, the last two years, however, sequential quadratic nested dissection, and different approaches to programming methods have been applied with sparse elimination, such as the minimal degree al­ great success to general OPF problems of a size gorithm, etc. We also refer to iterative processes, previously considered intractable. In fact, very such as the successive overrelaxation method, the large OPF problems can now be solved routinely. alternating direction method, the conjugate gra­ This breakthrough received considerable attention dient method, as well as the hybrid methods such in the power industry after the results were re­ as block and multi-grid methods. The study of ported at a national power engineering conference efficient algorithms for solving large systems of in February 1984. linear equations remains a very active field of research. In particular, interest centers on fast Despite such success stories, improved com­ methods for non-symmetric systems, the devel­ putational power is still necessary if certain prob­ opment of methods for computers with different lems are to be solved effectively. For example, architectures, especially parallel machines, and stochastic linear programs have been the sub­ the development of methods which are effective ject of intense study since World War II. The for problems involving singularities. Moreover, "natural" approach to such problems would be to partitioning of large problems has just begun to explore the largest possible number of alternatives be studied and represents an area of considerable at each step of the solution process. However, the challenge. inherent complexity of this approach has meant There are various classes of solution algo­ that less satisfactory methods based on averaging rithms which are of similar importance. These had to be used instead. With the advent of include, for example, methods for solving linear new computer architectures involving substantial eigenvalue problems, and optimization methods parallelism, it appears to be likely that, for the for linear and nonlinear problems. For instance, first time, stochastic problems can be treated in large scale linear least squares problems come their "natural" most desirable way. from a variety of sources. A particularly chal­ In the case of nonlinear equilibrium problems lenging set of such problems arises in geodetic we usually encounter a number of parameters. computations. Here the data often are obtained Then the solution set forms a manifold in the from remote sensing devices and very large data combined state and parameter space, and for a sets are acquired. Fortunately, the nature of these deeper understanding of the system it is necessary problems leads to matrices which are highly struc­ to analyze the shape of this manifold. Here tured and for which some of the modern iterative continuation methods are to be used. Moreover, techniques are applicable. Other classes of such questions about the stability of the solutions problems cannot be handled even with the most typically involve the determination of the location modern computing devices and in these cases new and character of the singular points of this solution algorithms are required which take account of the set. Another important but as yet incompletely fine structure of the matrices. explored question concerns the comparison of the The optimal power flow (OPF) problem is solution manifold of the original equations with an example of an important application whose the manifold defined by a discretized form of these solution has become practical only because of equations.

747 The study of singular points on the men­ connection with modern computer architectures. tioned solution manifolds constitutes an aspect For situations in which the localized behavior is of bifurcation theory-the static case. The dy­ known to be approximated well by very sharp namic case is of equal importance in modern fronts (e.g. shocks or flames), front tracking computational mathematics. In fact, it has been methods often have significant advantages. Such remarked that one of the most engaging problems methods, as well as related vortex methods, in nonlinear dynamics is that of understand­ insert analytic information concerning solution ing how simple deterministic equations can yield singularities in to the numerical algorithm. apparently random solutions. Both static and 2.6 Ill-Posed Problems: The notion of a well­ dynamic bifurcation problems involve challenging posed problem is due to Hadamard: a solution mathematical and computational questions and must exist, be unique, and depend continuously represent active areas of research. on the data. The term "data" can have a 2.4 Nonlinear Hyperbolic Equations: Nonlin­ variety of meanings; in a differential equation it ear hyperbolic equations are equally important for may include, for instance, the boundary or initial a number of applications including, for instance, values, the forcing terms, or even the coefficients high speed gas dynamics. These problems are of the equation. Since data cannot be known or often characterized by the simultaneous presence measured with arbitrary precision, it was thought in their solution of significantly different time and for a long time that real physical phenomena length scales. The solutions to these models will had to be modeled by mathematically well-posed have regions of strongly localized behavior, such problems. This attitude has changed considerably as shocks, steep fronts, or other near disconti­ in recent years, and it is now recognized that many nuities. In recent years, a series of improved important applied problems require the solution methods for these problems have been introduced of less well-posed problems. by computational mathematicians, culminating in One important class of such applications currently very refined agreement between compu­ falls, loosely speaking, under the heading of tation and experiment for complex shock wave tomography. In a narrow sense, tomography diffraction patterns. We refer here to upwind is the problem of reconstructing the interior of methods, flux limiters, higher order Godunov an object by passing radiation through it and methods and methods based on solutions of Rie­ recording the resulting intensity over a range mann problems. Areas of research important of directions. Tomography has also come to in coming years include the extension of such include applications where the source of radiation highly accurate solution techniques to more diffi­ is inside the object or when radiation is reflected cult problems, including those arising in reactive by features inside the object. chemistry and combustion, and especially also to Probably the most widely known applications problems in three space dimensions. of tomography are in medicine. Computer assisted 2.5 Adaptive Mesh Methods: In these prob­ tomography (CAT scan) uses x-rays directed from lems, as well as in the earlier mentioned elliptic a range of directions to reconstruct the density boundary value problems, adaptive mesh con­ function in a thin slice of the body. Recent struction has come to be of critical importance. advances in medical tomography include nuclear Such techniques allow extra computational effort magnetic resonance (NMR), where strong magnetic to be concentrated in regions where the solutions fields are used to make the hydrogen atoms are singular or nearly so. The design of efficient resonate. By varying the fields and their direction adaptive mesh refinement methods is an active the plane integrals of the density of hydrogen research area. An important related research can be measured and an "approximate" two topic is the development and application of a or three dimensional hydrogen density can be posteriori error estimates. Such estimates can be reconstructed. One advantage over the CAT scan used to assess the errors of the computed results is that the use of potentially harmful x-rays can and to form the basis of adaptive procedures. be avoided. The requirement of designing error estimators Another important source of applications of with appropriate properties for realistic classes tomography is nondestructive evaluation (NDE). of problems, different solution methods, and suit­ There is considerable need in industry to evalu­ able error norms certainly represents a demanding ate the integrity and remaining reliable lifetime research task in computational mathematics. of components and structures, as, for example, Often local mesh refinement leads to nested nuclear reactor vessels, bridge girders, or turbine levels of meshes which can be solved effectively disks. Once again the component is subjected to on parallel computers as independent tasks. This penetrating radiation with the aim of deducing makes this topic also very important for use in information about its internal state. Types of

748 radiation used include ultrasounds, x-rays, and An increase in computing power makes it neutrons. In other applications, electrical cur­ feasible to approach problems that are intractable rents are induced in the material which produce in closed form. This includes, for example, the es­ fields that may allow the determination of existing tablishment of properties of statistical procedures cracks. through Monte Carlo simulations (as, for instance, The search for oil depends heavily upon in Efron's bootstrap methods), and the solution of the analysis of seismic data. This is another problems in Bayesian statistics through the direct example of the reconstruction of internal features computation of multi-dimensional integrals. On of a body from monitored reflections of radiation a more basic level, it now becomes possible to or energy flows. Another example occurs in attack concrete statistical tasks through direct the study of confined plasmas in reverse-pinch numerical optimization. We note here that a machines that are being studied as a possible majority of statistical problems are naturally for­ source of fusion energy. Radiation is reflected mulated in terms of optimality principles (such as off the plasma in an attempt to determine the the classical maximum likelihood estimates, opti­ cross-sectional density function. In this example mal designs, robust alternatives to least squares, only a handful of data are available. In an even projection pursuit methods, etc.), but that they more compelling example, a suggested method of rarely have closed form, or even easily calculable on-site monitoring of a limited test ban treaty solutions. Often, the function to be optimized is depends upon the ability to resolve a problem of not available in closed form and must be found this type. by integration and Monte Carlo simulation, or The idealized mathematical problem under­ the optimization itself occurs inside a simulation lying all these problems is the reconstruction of a loop. Frequently, not only the location of the op­ function f(x, y) of two variables from its integral timum is needed, but also contour surfaces around along lines. This is an interesting example of a the optimum (for confidence regions); this cer­ mathematical problem that was considered and tainly compounds the computational problems. solved long before its applicability was seen. In The research challenge here is to develop the fact, this problem, as well as its three-dimensional methodology in a safe and efficient manner. version, was solved by J. Radon in 1917 and later Large data sets represent a central problem rediscovered in various settings such as probabil­ for computational statistics. Here the compu­ ity theory (recovering a probability distribution tational work is typically storage bound rather from its marginal distributions) and astronomy than processor bound. The long range research (determining the velocity distribution of stars challenge is to identify basic building blocks (both from the distribution of radial velocities in vari­ in hardware and software) that are suitable for ous directions). Of course, much work was needed massively parallel data base operations, and to to adapt the Radon inversion formula to the in­ build tools for analyzing large, highly structured, complete information available in practice. The inhomogeneous data sets. Research opportunities computational solution of ill-posed problems of in this area are wide open; in fact, none of the cur­ the form arising in the general area of tomography rently available data base management systems is is a very active research topic in computational designed to deal with the specific requirements of mathematics. Recent years have brought much scientific/statistical data. progress in this field, but much work remains to Statistical data analysis requires software and be done. Because of the overwhelming importance hardware suitable for interactive, often graphi­ of the applications that lead to these problems, cal, improvisation. The computing requirements this area of research may be expected to yield here are similar to those in artificial intelligence many important dividends. work and include an integrated programming en­ 2. 7 Computational Statistics: As in mathe­ vironment with instant, high resolution, easily matical physics and engineering, methodological improvisable, real-time graphics, and a mixture of breakthroughs in statistics tend to be a com­ symbolic and numerical manipulation capabilities. bination of many factors. For example, the These requirements are beginning to be met by major breakthrough in numerical spectrum anal­ the single-user super-workstations now reaching ysis in the 1960s involved the theory of stationary the market (with a raw power exceeding that stochastic processes, the fast Fourier transform, of a VAX-11/780). There are major challenges statistical sampling theory, and, behind all that, for the computational statistician; we need to driving examples from geophysics. Statistical develop better interactive languages for statistical research is now poised for some major method­ data analysis, and we must design and imple­ ological advances through access to improved ment effective methods that provide the required computing resources of various types. intelligent machine assistance to the analyst.

749 2.8 Stochastics and Computational Probabil­ such widely differing applications as text read­ ity: Stochastic processes and the need for proba­ ing or submarine detection. In the case of bilistic reasoning arise in the solution of numerous image reconstructions, random disturbances may problems. These range from queuing and inven­ blur or obliterate a transmitted image. One tory studies to the fault tree analysis of safety recently proposed method for the mathematical design factors, and from economic and finan­ reconstruction of such images involves the use of cial studies to the analysis of voting behavior. stochastic dynamics based on Ising models. A Modern applications of probability theory involve dynamical evolution to an image with a lower problems of very high dimension which present Ising model energy ffiters out much of the noise massive computational problems. The analysis while leaving the original image unchanged. of the related probabilistic models has called for Numerical and nonnumerical computing are new methodological approaches. Among recent often regarded as two different areas which use advances are the product-form solution used in their own software, interfaces, and algorithms even the analysis of networks of interacting queues, and when sharing the same hardware environments. the matrix-analytic methods of structured Markov An important form of nonnumerical computa­ chains. The product-form solution has stimulated tion involves the use of symbolic manipulation extensive research on stochastic networks and is systems for carrying out algebraic operations on widely used in the design of interconnected com­ a computer. These systems perform indefinite puter systems. Structured Markov chains arise integration, factor polynomials, simplify complex commonly in telecommunication engineering in expressions, and operate on matrices. They have the design of buffers and in the study of operating been applied very successfully in several situa­ protocols. The computation of various measures tions, for instance in the computation of orbits of performance leads to the numerical solution of space objects, and in the calculation of Feyn­ of various types of nonlinear matrix-integrals and man integrals in physics. In each of these cases matrix-equations. the required algebraic computations were so ex­ As noted earlier, most probability models tensive that only computers could perform them lead to very high dimensional computational sufficiently rapidly and accurately. The develop­ problems. Often already very simple descriptions ment of computer algebra systems required the require the study of a higher-dimensional stochas­ invention of numerous new algorithms and the tic process. For example, a typical econometric adaptation of various old ones. Some of the most model of a country or group of countries may be notable ones are those for indefinite integration characterized as a stochastic nonlinear system of and polynomial factorization. Further work is hundreds or thousands of equations. They often needed on algorithms that are more efficient than involve some nonconcavity in the system, and presently known ones and on algorithms that can hence, already the computational problems in an­ deal with new classes of problems. There is also alyzing the dynamic properties of the system are need for new computer-algebra systems that are formidable. Moreover, the process of search for more portable than present ones, run on smaller approximate optimal control strategies for policy machines, and can be interfaced more easily with authorities, especially when more than one active other programs. Moreover, there is a strong authority is involved, introduces game theoretical need for studying more closely the coupling of aspects. The resulting system will tax most of the automatic reasoning algorithms with mathemati­ available computing resources. As this example cal modeling and data base techniques to produce already indicates, progress in this area requires effective control processes for complex systems not only statistical methods of a nonclassical type, and for effective modeling of complex systems but also new approaches in nonlinear numerical involving human and mechanical components. analysis, and new techniques for data handling 2.10 Computational Methods in Pure Mathe­ and computer graphics. matics: Some of the most interesting applications of symbolic mathematics are in mathematics it­ 2.9 Pattern Recognition and Symbolic Com­ self. Areas of both pure and applied mathematics, putations: The area of pattern recognition, in­ including coding theory, cryptography, probabil­ cluding image processing, acoustical processing ity theory, analysis, combinatorics, and number and speech recognition, requires integrated math­ theory, have all gained from the availability of ematical techniques from several areas including symbolic manipulation tools. These tools have signal processing, mathematical logic and linguis­ been used to prove a number of results directly. tics, numerical mathematics, Fourier transforms, Their main application, however, has been to ob­ and algebra. The objective is a classification tain insight into behavior of various mathematical of sequences of images as they might arise in objects, which then led to conventional proofs.

750 This rather new, direct impact of computation mathematical models and more efficient numeri­ upon pure mathematics is not limited to symbolic cal methods. Because computer architectures will manipulation and will no doubt expand consider­ certainly change, there is a need to re-examine ably in coming years. In doing so it may lead to traditional methods and to develop new meth­ the development of computational tools, methods, ods that use the inherent structure of the new and concepts of broad applicability. For instance, machines. But, at the same time, it will be impor­ the four color problem was reduced to a check of a tant to avoid locking the software into a particu­ very large but finite number of specific cases. This lar architecture. Software flexibility, modularity, final step, too tedious for humans, was performed reliability, efficiency, restricted data flow and doc­ on a computer. Computers have been used in umentation are here fundamental requirements. exploratory studies of the iterates of mappings There is certainly a need for the development which in turn led to new insight into the nature of of high quality mathematical libraries to support chaos and turbulence. They also played a role in large-scale scientific computing. This will require the classification of all finite simple groups. Finite close cooperative work between applications pro­ groups certainly play a very important role in grammers, numerical analysts, and the scientific the study of many topics in applied mathematics computing research community. and science, such as discrete computational struc­ 2.12 Parallel Computing: Despite the fact tures, enumeration of combinatorial designs, the that electronic components are becoming faster, definition of stereo-isomers in organic chemistry, the limits of raw machine speed are now clearly the cataloguing of crystallographic structures, etc. visible. Further gains will eventually have to The recent invention by Lovasz of a fast be made by the use of novel architectures and algorithm for finding good bases for lattices has algorithms, and, in particular, by some form of had a striking impact on several fields. The parallelism. Many of the new designs now under problem of finding the shortest nonzero vector consideration represent a sharp break from previ­ in a high-dimensional lattice is considered to ous computer architectures and introduce issues be very hard, but has been of great interest of scheduling, coordination, and communication because many other problems in diverse areas which previously did not arise. Thus it will be nec­ can be reduced to it. The Lovasz algorithm essary to rethink and reconstruct the vast number does not in general find the shortest nonzero of familiar numerical methods from the point of vector, but it does rapidly find a relatively short view of these new issues. It appears that in many one, and in many situations that is sufficient. cases software, not hardware, will pose the most The algorithm has been applied, for example, to difficult problems and will account for the most the determination of integer solutions of linear impressive advances. programs and to the factorization of polynomials. As an illustration we discuss here some issues But perhaps its most important application is relating to parallel computing. Recent progress to cryptography. Among public key secrecy toward solving large problems, such as full body systems (that is, those that do not require the air flow simulations, has concentrated on the use two communicating users to exchange secret keys of local mesh refinements and adaptive methods. beforehand) there was a large class for which Data structure design is evolving toward the pro­ the presumed security relied on the difficulty of duction use of networks of overlapping grids some solving the knapsack problem. Essentially all of of which are coarse and stationary while others these knapsack-based secrecy systems have been are fine grids which may be moving to track a shown to be breakable by application of the front. For the solution of elliptic problems the lattice-basis reduction algorithm. As a result the algorithms that show the greatest promise are only public key cryptosystems that still appear multilevel methods such as hybrids of multigrid credible are those for which security depends methods and methods that are well suited to on the difficulty of factoring large integers or substructured grids, such as the conjugate gradi­ computing logarithms in finite fields. ent method. From the point of view of software 2.11 Quality Software: Quality software is an design there are two important features of these indispensible tool in many modern science and techniques. First, the algorithm and data struc­ engineering projects. The continuing develop­ ture are dynamic. Second, while the global grid ments in micro-electronics will decrease the cost structure is very nonuniform, the local structure of computing and increase the speed and mem­ is based on deformations of uniform grids. These ory available. But these hardware improvements two facts have a large impact on the problems of will allow present codes to be pushed only a programming the next generation of computers. limited amount beyond their current capabilities. In particular, we face three fundamental research Additional capabilities must come from better problems:

751 (1) Numerical algorithms: We must under­ formulation of a scientific or engineering problem stand the dynamic structure and formulate the to the construction of appropriate mathematical mathematical model in terms of high level parallel models, the design of suitable numerical methods, operations. For example, the computation may their computational implementation, and, last but be viewed and expressed as a system of higher not least, the validation and interpretation of the order tasks which encapsulate the large scale dy­ computed results. For most of today's complex namic/adaptive structure of the algorithm. Each scientific or technological computing problems a higher order operator can be composed of lower team approach is required involving scientists, order parallel operations on uniform fine struc­ engineers, applied and numerical mathematicians, tures such as subgrids of a large network. The statisticians, and computer scientists. point is that no matter how the algorithm is Unlike theoretical mathematics, computa­ formulated, we will need to employ much more tional mathematics, by its very own nature, has parallelism than we currently do in order to utilize a strong experimental component. As a result, the power of a massively parallel machine. research work proceeds in part in a laboratory (2) Algorithm analysis: A more accurate mode similar to that in the experimental sciences. model of parallel algorithms is needed to describe The laboratory equipment required for modern the expected performance of the new software. scientific computing ranges from local worksta­ In particular, parallel algorithm analysis must tions, micro- and mini-computers, to mainframe capture the cost of communication, process syn­ machines of various sizes and supercomputers. chronization, and initiation. An ideal model This hardware is complemented by appropriate would be machine independent but have parame­ software systems and libraries. Moreover, the ters that are easily set to a specific architecture. multidisciplinary nature of the work requires a Such a model also could be of great value in the new level of interchange between researchers in design of new architectures. widely different fields. For this the communica­ (3) The mapping problem: Given a parallel tions capabilities of modern computer networks architecture and a parallel specification of an form an ideal mechanism to link scientists from algorithm, find an optimal mapping from one widely differing fields and to allow them to share to the other. This problem takes on special ideas and information. As in the traditional lab­ significance in the case of massively parallel non­ oratory sciences, support personnel is required to shared memory systems. In this case, the machine ensure efficient usage of all facilities and to avoid can be viewed as a graph where processors are any unnecessary waste of research time. Un­ nodes and the communication network describes der current funding practices projects involving the edges between the nodes. The algorithm is a support staff are certainly not very common in graph of communicating processes (or data flow mathematics. graph) which, in the case of adaptive methods, Clearly, the investment costs, as well as has a dynamic structure. the longer duration of typical computational Clearly, as this brief sketch already shows, projects--especially when extensive software de­ research in this important area of computational velopment is involved-necessitate a certain con­ mathematics will require well integrated team tinuity and stability of the entire research infra­ efforts between algorithm designers, numerical structure and hence calls for a sharing of the analysts, and researchers in the applications areas. facilities among several researchers. Once again research teams are best suited to sustain such an 3. New Modes of Research operation. Traditionally, individual researchers working As has been noted before, computational alone or in pairs have characterized the style of mathematics currently faces a critical manpower much of the work in the mathematical sciences. problem. Any national effort to strengthen the This situation is different in computational math­ field has to take special account of this fact ematics where increasingly a multidisciplinary and has to include steps toward making optimal team approach is required. There are several use of existing manpower resources. In the compelling reasons for this. opinion of the panel, the most advantageous First and foremost, as noted already several approach will be to ensure the establishment of times in the previous section, problems in modern a sufficient number of viable research teams in scientific computing transcend the boundaries of computational mathematics. Such groups are not a single discipline. In general, the computational only most appropriate for research in the field, but approach has made science more interdisciplinary they ensure that the most effective use is made than ever before. There is a unity among the vari­ of the scarce talents of established researchers, ous steps of the overall modeling process from the and they provide a means of bringing additional

752 young researchers as quickly as possible into the subsequent annual maintenance of the hardware mainstream of the work. and software. The overall funding for such a group Generally, the emphasis should be on a need not be in the form of one large institutional concentration of effort. In other words, teams grant, but may well be in the form of several grants should have a common intellectual focus yet be and contracts from different funding sources. In interdisciplinary, spanning a significant portion­ some cases, it may also be appropriate to establish and ideally all-of the broad range from an cooperation with industrial research groups and application area through applied mathematics and to secure some support from non-governmental numerical analysis to mathematical software and sources. computer science. This concentration of effort on This multidisciplinary team work in a labo­ a common research interest will allow the group to ratory setting represents a significant departure take a problem all the way from the application to from the traditional style of research in mathe­ working software. This commonality and range of matics. It is also a departure from the standard research interest is considerably more important funding mode of the federal agencies supporting than a particular administrative structure, such computational mathematics. It will take special as a center or institute. Of course, for vitality of efforts on the part of these agencies and the such an organizational unit it may be desirable to mathematical community to accept the changing ensure a certain stability in a particular academic situation and to help in the development of this setting, but it should not be the sole driving force. new mode of research in computational mathe­ In order to be viable, it appears that a group matics. In line with this, it is of considerable should consist of at least three faculty level re­ importance that the proposed new funding effort searchers, one post-doctoral fellow, five to eight for the establishment of such research teams is Ph.D. level graduate students and one full-time meant to complement rather than replace the tra­ support person. In most cases it will be highly ditional project support for individual researchers desirable to include additional junior faculty level in the field. The proposed team approach is researchers in such teams. The support person intended to focus on different categories of sci­ would do both systems and applications program­ entific computing than are feasible for individual ming for the group, and generally ensure smooth researchers and to strengthen the productivity operation of the local computing facilities. While and effectiveness of the researchers involved in some groups might survive without such a person, such interdisciplinary projects. they would do so only at the expense of re­ searchers performing these tasks which is a waste of valuable and scarce talent. As noted before, each group will require some 4. Educational Needs local computing facilities, but access to super­ computers can be provided by suitable high-speed The Lax report [1] recommended a long­ networks. The quality of the computing facilities term National Program on Large-Scale Com­ has a decisive effect on the overall research ef­ puting which included as one of its goals the fort. It is highly desirable that the group has at "( t )raining of personnel in scientific and engineer­ least high-performance personal workstations, to ing computing", and in [3] this was reiterated support the research work of the individual mem­ in the form of a recommendation for "(i)ncreased bers, to provide for efficient access to appropriate support for education and manpower development large computing facilities, and to allow for very­ in computational and applied mathematics". high bandwidth communication, such as needed Basically, the educational needs addressed in graphical post-processing. If the group has here are part of a much broader problem concern­ to operate more substantial computing facilities, ing all of mathematical education in the country. then there should be at least two support people. Throughout the past two years several pieces of But in all this, it is important to note that the legislation were introduced in the Congress in re­ requirements described here are minimal rather sponse to the report of the National Commission than average. Some further discussion of possible on Excellence in Education entitled "A Nation laboratory facilities is presented in Appendix B at Risk." Then, in August 1984 the President below. signed into law the "Emergency Mathematics and In order to assure the required stability and Science Education and Jobs Act." continuity of the research effort, funding should The David report [4] addressed some of the be provided on a multi-year basis, say, on the educational problems in mathematics on the post­ order of five years. Moreover, it is necessary secondary level. Its fundamental observation was to support both the initial purchase and the that "( t )he field is not renewing itself".

753 There is little question that there are formi­ lured away to industry not only by the attraction dable problems with our undergraduate and grad­ of higher salaries but also by the much better uate educational programs in all areas of math­ computing environments. ematics; that is, in pure mathematics, com­ Significant additional manpower resources for putational and applied mathematics, statistics, computational mathematics will be needed in the operations research, etc. The quickly broadening years ahead. In fact, the David report presents the need for computational modeling in all areas of following estimate: "Expectations are that a few science, engineering, and business has produced hundred supercomputers for academic, industrial, an increasing demand for more college-level math­ or· governmental use will be put in place over the ematical education. This is evident by the 33% next decade. Each machine will require approxi­ increase of enrollments in the mathematical sci­ mately 10 scientists with sophisticated knowledge ences at four year institutions during the period of applied mathematics related to computation. 1975-80. But during the same period the number Demand for such new scientists may run 50Q-800 of faculty members increased only by 8%. At the per year. Even though numbers of these scientists same time, mathematics is failing to secure its will come from computer science, the physical share of qualified young people. When compared sciences, or engineering, the demand for new with 1970, the number of undergraduate degrees Ph.D. mathematical scientists in computing could in the mathematical sciences has decreased by easily reach 100 per year in the future. Federal 40%, and the number of Ph.D. degrees has been support of a subfield of this size could not be dropping monotonically since 1970. Moreover, absorbed within the resources we have recom­ the percentage of foreign recipients of the Ph.D. mended". The projections of the report appear in mathematics has now increased to about 40% to be rather conservative. In fact, recent studies of the total. As the David report observes a "gap by the Institute for Constructive Capitalism of has been created between demand for faculty and the University of Texas at Austin indicate that supply of new Ph.D.s. It may well widen as by 1990 the projected number of supercomputer retirements increase in the 1990s". installations will be most likely around 200 per The reasons for the difficulties in the math­ year and that worldwide supercomputer sales may ematical sciences are complex. A strongly con­ exceed 1,500 per year by 1993. tributing factor is certainly to be found in the These brief remarks already indicate that drastic decreases in federal funding for mathemat­ there is no easy response to the recommenda­ ics during the past fifteen years as documented in tions in [1] and [3] that there be an increase [4]. Another factor is the earlier noted and widely in the education and manpower development in discussed range of problems with mathematics computational and applied mathematics. The education at the elementary and high school David report recommended a broad "National level. At the same time, the typical undergrad­ Graduate and Postdoctoral Education Plan in the uate mathematics curricula are largely inflexible Mathematical Sciences". There is no need to and have not responded well to the challenges repeat here the details. But we note particu­ introduced by the fact that today much of the larly the strong emphasis on additional support student-interest centers in areas of applied math­ for graduate students, post-doctorals, and young ematics, computational modeling and scientific investigators. computing. As a result, talented young people The special situation of computational math­ often turn away disappointedly from the field. ematics requires added attention to these recom­ The problems are even worse in computa­ mendations. In the field there exists a very urgent tional mathematics. The rapid growth of the field need for increased support of graduate students has largely outstripped the available educational to help in inducing more of them to continue opportunities. There is a profound lack of senior their studies up to the Ph.D. degree. However, faculty members in the field and a paucity of care needs to be taken that such students are not graduate students and young researchers. At the assigned to standard teaching duties but should same time, there has been a growing demand for participate as much as possible in the work of computational mathematicians in industry. In multidisciplinary research teams in computational fact, during the last few years nearly one-third mathematics. of the new Ph.D.s in the mathematical sciences In contrast to chemistry, physics, and biology, have taken positions in industry. At the same there exists very little funding for post-doctoral time students often terminate their studies early positions in mathematics. In part this corresponds to accept high paying positions in the computing to the sociological fact that post-doctoral studies industry. Similarly, the best young faculty mem­ are not a traditional requirement in the core areas bers in computational mathematics are frequently of mathematics. In computational mathematics,

754 however, there are growing indications that this • support of basic and applied research in prob­ situation is changing. Typically a new Ph.D. lems that require computing across all areas of has had time to become somewhat familiar only science and engineering; with one particular application area. As in the • training of mathematicians, scientists, and en­ other experimental sciences, there is a need for gineers in the concepts, design, and use of a subsequent deeper involvement in some other computing systems; application and problem area. Without such addi­ tional post-doctoral experience the young Ph.D.'s • assured access for researchers and graduate research is likely to remain severely restricted. students to computing facilities. At the same time, the proposed research teams During the past year several funding agencies represent an ideal training mechanism for such responded to some of the recommendations of the post-doctoral fellows. We recommend strongly Lax report [1] and the Bardon-Curtis report [2]. that the National Science Foundation increase its We mention here only the Fast Algorithm initia­ support for post-doctoral positions in computa­ tive at the Air Force Office of Scientific Research, tional mathematics. the establishment of the Scientific Computing In view of the severe shortage of compu­ Program in the Office of the Director of Energy tational mathematics faculty, it appears to be Research at the Department of Energy, and the desirable to consider retraining qualified persons formation of the Office of Advanced Scientific from other areas of mathematics or other fields. Computing at the National Science Foundation. In part, this process can be aided by means The Air Force initiative is based on the earlier of longer visits of such people at places where noted observation that new advances in numerical there are established computational mathematics analysis, and algorithm design are required to teams. Some consideration should be given to exploit the new computer architectures that are providing appropriate support for such visits, for now being introduced. In line with this, a example, in the form of competitive grants to the moderate number of team-research efforts for potential visitors. the development of "fast algorithms" for large There appears to be a need for a closer study scientific problems are being funded. of suitable modes of undergraduate education in computational mathematics. In analogy with the The aims of the Scientific Computing Pro­ experimental sciences, courses certainly require a gram at DOE agree closely with many of the ideas meaningful laboratory component. This raises and recommendations described in Section 3. The questions about suitable hardware and software, program consists of the Applied Mathematical Sci­ and even more critically about well-designed tex­ ences Research Program and the Energy Research tual material. The funding agencies, and, in Advanced Computation Project. The Applied particular, the National Science Foundation may Mathematical Sciences Program has initiated sev­ be able to stimulate some developments in this eral major interdisciplinary projects at universi­ area by means of some well-targeted support. ties and laboratories through its initiative in the For instance, this may be in the form of some development of Advanced Computing Concepts support for interdisciplinary study groups to pre­ and the Energy Research Advanced Computation pare material for novel courses in computational Project in providing access to supercomputers at mathematics, or of challenge grants to design new the NMFECC and the Supercomputer Computa­ and innovative programs. But this also raises the tion Research Institute at Florida State University question of funding of appropriate computational via the nationwide MFE network. facilities for educational purposes. The formation of the Office of Advanced Scientific Computing (OASC) by the National Sci­ 5. Funding Considerations ence Foundation represents an important step toward providing much needed supercomputer In paraphrasing the Bardon-Curtis report [2] service for a broader community involved in aca­ the Committee believes strongly that the general demic research and science education. The OASC role of the Federal funding agencies supporting Supercomputing Centers Program is supporting scientific computing should be to maintain strong access to advanced scientific computing resources programs that are designed to provide: and advanced prototype computers, as well as • support of basic and applied research in uni­ projects in the area of software productivity and versities in computational mathematics and ad­ computational mathematics for supercomputers. vanced computer concepts including software, In addition the OASC Networking Program will algorithms, architecture, subsystems, and com­ facilitate the establishment of a national network ponents; and support of local access to that network.

755 In connection with the OASC support for Associated Research Costs software productivity and computational math­ secretarial costs, printing and ematics it should be noted that the emphasis reproduction, travel, etc. (5 is here not on basic research but on projects times $7) 35 that enhance the effectiveness of scientists and engineers in their use of supercomputers. But $362 as pointed out in Section 1 above, there is a fundamental need for establishing a companion Indirect Costs (50% of direct costs) 181 program of support for research and education in computational mathematics itself. Evidently Total Per Year $543 this is not part of the current program of OASC, There are currently about 15-20 small more although there may well be reasons to consider or less informal research groups in computational modifications of that program. mathematics and scientific computing around the As summarized in Section 1 our fundamen­ country. Clearly they would constitute natural tal recommendation is to expand and strengthen nuclei for the proposed research teams. This the programs of the various funding agencies in would suggest that funds are needed for the support of research and education in the com­ establishment and continued support of about 3-4 putational mathematical sciences and scientific such teams each year for a period of five years. computing. In line with the discussions in the As noted in the earlier sections, this sup­ previous sections, such expanded programs should port need not be in the form of one grant. In have at least the following components: particular, funding for the work of the senior 1. New funding programs specifically focused investigators might already exist in the form of on the establishment of a number of viable re­ project grants. However, the currently available search teams in computational mathematics and support for post-doctoral fellows, support person­ scientific computing and on ensuring the continu­ nel, and additional graduate students is certainly ity of their work for several years. inadequate and needs to be expanded. More­ 2. Support programs for establishing and over, most importantly, some mechanism has to maintaining an appropriate research infra-struc­ be found to ensure some stability and continuity ture for such research teams consisting of suitable in the support of such a team over a period of computer hardware and software and the associ­ several years. For this the current, relatively ated support personnel. short term project grants, are not well suited. 3. A concentrated effort for overcoming some A long-range approach can substantially increase of the manpower shortages in computational the productivity and efficiency of computational mathematics. This should include, in particu­ mathematics research in this country. lar, support for graduate students, post-doctoral The above figures do not include computer fellows, and young researchers. costs. Here funds are needed for the acquisition of In order to give some indication of the re­ computer hardware and software, the continued quired funds, the following table presents an operation and maintenance of these facilities, and estimate of the yearly cost of a team of five re­ access to national networks and supercomputers. searchers: (All figures are in thousands of dollars) The existing support program for computer equipment appears to be in need of consider­ Salaries able expansion if it is to meet the requirements 5 investigators at an average of of the proposed strengthening of computational $45, two months summer mathematics research and the formation of the support each $50 indicated research teams. Some cost-data for two months released time per these laboratory facilities are given in Appendix academic year each 50 B. [This is contained in the complete report which is available from SIAM.] As summarized there the 2 full time support persons 60 minimal equipment cost for the above research 1 post-doctoral fellow 25 team is of the order of $250,000 to $300,000. The cost of operating and maintaining com­ 185 puting equipment is an increasingly difficult prob­ Fringe Benefits (at 25%) 46 lem for most colleges and universities. In fact, fre­ quently, institutions find it easier to acquire some Graduate Students computing equipment through one-time funds, 8 students at $12 each for stipend gifts, or bequests, than to operate and maintain and tuition benefits 96 it. Such costs have been estimated at about

756 15-20% of equipment costs per year. Since these References are an essential part of the computing facilities [1] Report of the Panel on Large-Scale Computing research, there is a computational mathematics in Science and Engineering, Sponsored by support for these ongoing need to establish some DOD and NSF in cooperation with DOE and normal funding of this work. costs as part of the NASA, P.D. Lax, Chairman, National Science The mentioned third component of support Foundation, Dec. 26, 1982. for computational facilities, namely, the access to [2] A National Computing Environment for Aca­ a national network and suitable supercomputers demic Research, NSF Working Group on Com­ is a part of the already established program of puters for Research, K.K. Curtis, Chairman, the NSF Office of Advanced Scientific Computing. Report prepared under the direction of M. But as noted earlier there is an equal need Bardon, National Science Foundation, July for a broadly based network which links groups 1983. in mathematics, computer science, and related [3] Computational Modeling and Mathematics Ap­ areas, and which provides the much needed closer plied to the Physical Sciences, National Acad­ cooperation and coordination between researchers emy of the Sciences/National Research Coun­ who often work on the same or similar problems. cil, Committee on the Applications of Mathe­ matics, W.C. Rheinboldt, Chairman, National As discussed in Section 4 above, there is no Academy Press, 1984. easy solution to the required strengthening of the [4] Renewing U.S. Mathematics, Critical Resource educational situation in mathematics, in general, for the Future, National Academy of Sci­ and in computational and applied mathematics, ences/National Research Council, Ad Hoc in particular. The proposed establishment of a Committee on Resources for the Mathemati­ number of research teams in computational math­ cal Sciences, E.E. David, Chairman, National ematics will certainly have a positive effect in Academy Press, 1984. this regard, at least on the graduate and post­ doctoral level. As noted earlier, these teams can also provide the opportunity for faculty level visitors interested in switching to computational EDITOR'S NOTE: This report has generated mathematics. All funding agencies should give considerable interest in the funding agencies. As strong consideration to an expansion of their a result of the report the chairman of the panel, support for graduate research assistants, post­ Weiner C. Rheinboldt, was invited last spring to doctoral fellows, young investigators, and faculty the National Science Foundation to speak on its level visitors in the general area of the com­ subject matter. Moreover, the Advisory Commit­ putational mathematical sciences. In addition, tee for the Mathematical Sciences Division of NSF through support of studies by professional soci­ at its May 1985 meeting recommended that the eties and special groups, there exist possibilities division undertake an initiative in computational for mobilizing the mathematical sciences research mathematics, patterned after this report. The community to address the critical problems of Notices will report on future developments as mathematical education in this computer age. they occur.

757 29th Annual AMS Survey 1985 First Report The following pages contain a first report on the 1985 AMS Survey. Included in this report are salary and other data on faculty members in four-year colleges and universities, a report on the 1985 survey of new doctorates, a report on salaries of new doctorates, and a list of names and thesis titles for members of the 1984-1985 Ph.D. class. The Annual AMS Survey is conducted in two parts. Questionnaires were distributed in May to departments in the mathematical sciences in colleges and universities in the United States and Canada, and later to the recipients of doctoral degrees granted by these departments between July 1984 and June 1985, inclusive. This report is based on the information collected from these questionnaires. A second round of questionnaires was distributed in September; these are concerned with data on fall enrollments, class size, teaching loads and faculty mobility. These data will be reported in the March 1986 issue of the Notices. This Survey is the twenty-ninth in an annual series begun in 1957 by the Society's Committee on the Economic Status of Teachers. The present Survey is under the direction of the Committee on Employment and Educational Policy (CEEP), whose members are Lida K. Barrett, Stefan A. Burr, Philip C. Curtis, Jr., Lis! Novak Gaal, Gerald J. Janusz, and Donald C. Rung (chairman). The questionnaires were devised by CEEP's Data Subcommittee consisting of Lida K. Barrett, Edward A. Connors, Lincoln K. Durst, Arthur P. Mattuck, James W. Maxwell, Donald E. McClure, and Donald C. Rung (chairman).

Faculty Salaries, Tenure, Women

The questionnaires sent to departments in the Groups I and ll include the leading departments mathematical sciences asked for information on of mathematics in the U.S. according to the 1982 salaries and tenure. Departments submitted a assessment of Research-Doctorate Programs conducted minimum, median, and maximum salary figure by the Conference Board of Associated Research for each of four academic ranks, for staff members Councils in which departments were rated according to the quality of their graduate faculty.1 both with and without doctorates. Annual salaries of full-time faculty members for the academic Group I is composed of 39 departments with scores in the 3.0-5.0 range. year of 9 or 10 months were sought. The 1985 questionnaire requested information for both the Group ll is composed of 43 departments with scores in the 2.0-2.9 range. years 1984-1985 and 1985-1986. The sample in this survey is thus the same for both years and Group m contains the remaining U.S. departments reporting a doctoral program. is different from the sample used in the Twenty­ Group IV contains U.S. departments (or programs) AMS In Eighth Survey in 1984. the salary tables of statistics, biostatistics and biometrics reporting a on the following pages the numbers in parentheses doctoral program. give the range of the middle fifty percent of salaries Group V contains U.S. departments (or programs) reported. The figures outside the parentheses in applied mathematics/applied science, operations represent the minimum and maximum salary research and management science which report a listed by any reporting institution. In some doctoral program. categories relatively few departments reported Group VI contains doctorate-granting departments and, because significant figures were not available, (or programs) in the mathematical sciences in Canadian salaries are not listed. universities. The information reported this year on the Group M contains U.S. departments granting a number of faculty members is based on returns master's degree as the highest graduate degree. from 639 departments in the mathematical Group B contains U.S. departments granting a sciences, 127 of which did not contain usable baccalaureate degree only. salary information. 1 These findings were published in An Assessment of Research-Doctorate Programs in the United States: For these reports, the departments are divided Mathematical and Physical Sciences, edited by Lyle V. into groups according to the highest degree Jones, Gardner Lindzey, and Porter E. Coggeshall, offered in the mathematical sciences. The National Academy Press, Washington, D.C., 1982. The doctorate-granting departments are in six groups information on mathematics, statistics and computer as described in the box. science was presented in digest form in the April 1983 issue of the Notices, pages 257-267, and an analysis of the above classifications was given in the June 1983 Notices, pages 392-393.

758 'l2IBIE 1: 'lUrAL E2\CUL'IY J.dSllORI'EO FOR FOOR-YFAR

FACULTY WJMEN FACULTY WJMEN With With With With Total Tenure Total Tenure Total Tenure Total Tenure

WITHCXJT IXJCI'ORATE Instructor/Lecturer 820 44 470 21 781 38 438 19 Assistant Professor 501 257 151 59 501 241 157 58 Associate Professor 375 351 62 53 365 338 57 47 Professor 107 100 15 12 104 97 14 12 1803 752 698 145 1751 714 666 136

WITH IXJCI'ORATE Instructor/Lecturer 203 22 36 5 222 21 45 5 Assistant Professor 1865 177 286 34 1913 177 298 32 Associate Professor 2336 2034 214 181 2361 2052 215 181 Professor 3803 3742 173 166 3902 3828 183 171 8207 5975 709 386 8398 6078 741 389

TABLE 2: Percent of TABLE 3: Response Rates Doctorate Faculty with Tenure U.S. Departments Fall1984 Fall1985 Group I II ill N V M B Groups I, II, ill 76.2% 75.7% %Response 77 79 65 68 54 44 35 GroupsN, v 73.7% 73.0% Canadian Departments Group VI 89.4% 89.6% Masters and Bachelors 67.1% 66.7% Group VI % Response 46

Response Rates. Response rates among the relative changes from one year to the next with various classes of departments vary widely, thus somewhat more confidence. This year's response making it difficult to draw firm conclusions about rates are given in Table 3. As in past years, the the sizes of the faculty groups studied. Because greatest rates of response are in Groups I, II, and the questionnaires request data for two years m, which have a combined response rate of 71%. in a row, however, it is possible to estimate

759

281 281

820 820

528 528

503 503

397 397

339 339

797 797

Maximum Maximum

(232-265)270 (232-265)270

(638-800) (638-800)

(352-434) (352-434)

(280-330)366 (280-330)366 (280-335) (280-335)

(245-276)286 (245-276)286 (200-260) (200-260)

(160-217)322 (160-217)322

(200-252) (200-252)

(555-687) (555-687)

(360-410) (360-410)

(330-395)406 (330-395)406

(229-269) (229-269)

(230-258) (230-258)

(160-210) (160-210)

(448-528) (448-528)

(301-362) (301-362)

(318-375) (318-375)

(314-395) (314-395)

(260-294) (260-294) (253-291) (253-291)

(196-250) (196-250)

(180-231) (180-231)

(409-478) (409-478)

Median Median

1985-1986 1985-1986

312) 312)

268-345) 268-345)

220-259) 220-259)

272- 334-407) 334-407)

230-258) 230-258)

170-225) 170-225)

(250-273) (250-273)

( (

( (

( (

( (

(280-395) (280-395)

( (

( (

(176-221) (176-221)

(323-386) (323-386)

Minimum Minimum

222 222

217(230-255) 217(230-255)

262 262

262 262

223 223

249 249 254 254

115(160-210) 115(160-210)

186 186

192 192 160 160

170 170

274 274

330 330

310 310

770 770

450 450

388 388

396 396

776 776

(220-263)305 (220-263)305

(160-240) (160-240)

(601-'726) (601-'726)

(336-380) (336-380)

(275-377) (275-377)

(272-293) (272-293)

(225-260) (225-260) (200-225)320 (200-225)320

(179-242)268 (179-242)268

(550-675) (550-675)

(340-380)528 (340-380)528

(260-307) (260-307)

Maximum Maximum

(217-254) (217-254)

(210-250) (210-250)

(152-224) (152-224)

(166-212) (166-212)

(396-460) (396-460)

(434-487) (434-487)

(295-343) (295-343)

(308-345) (308-345)

(275-377) (275-377)

(240-285) (240-285)

(245-275) (245-275)

(180-225) (180-225)

Median Median

1984-1985 1984-1985

215-242) 215-242)

144-214) 144-214)

(212-248) (212-248)

(210-250) (210-250)

( (

(310-360) (310-360) (318-385) (318-385)

(254-377) (254-377) ( (

(150-225) (150-225)

95 95

240 240

237(259-322) 237(259-322)

254 254

216(220-259) 216(220-259)

ill ill 262 262

223(256-300) 223(256-300)

172 172

113 113

143(165-197) 143(165-197)

186 186

Minimum Minimum

6 6

3 3

2 2

0 0

0 0

2 2

1 1

0 0

0 0

1 1 3 3

0 0

1 1

3 3

11 11

20 20

43 43

21 21

34 34

20 20

13 13

Tenure Tenure

1 1 1

1 1 1

7 7

0 0

0 0

5 5 1

0 0

1 1 1

7 7

63 63

50 50

80 80

11 11

31 31

21 21

21 21

48 48

46 46

20 20 63 63

17 17

12 12

14 14

WOMEN WOMEN

Total Total

reporting) reporting)

reporting) reporting)

reporting) reporting)

3 3

71 71

2 2

6 6

43 43

2 2 3 3

2 2

39 39

6 6

51 51

26 26

15 15

20 20

13 13

981 981

339 339

With With With

829 829

195 195

1985-1986 1985-1986

TV TV

Tenure Tenure

of of

1029 1029

of of

of of

7 7 7

9 9 8 2

4 4 4

2 2 2

2 2

81 81

30 30

15 15

37 37

86 86

71 71

97 97

13 13

(46 (46

(34 (34

133 133

632 632 627

FACULTY FACULTY

367 367 256 256

(29 (29

201 201

208 208

829 829

Total Total

1292 1292

1335 1335

FACUL FACUL

Ill Ill

II II

OF OF

9 9

I I

3 3

1 1

1 1

3 3

0 0

0 0

0 0

2 2

0 0 0 0

2 2 8 1

4 4

1 1

1 1 1 1

1 1 2 2 1

4 4

14 14

20 20

42 42

19 19

37 37

22 22

14 14

With With

Tenure Tenure

1 1

6 6

0 0

0 0

Group Group

3 3 2

8 8

0 0

6 6

Group Group

Group Group

WOMEN WOMEN

SIZE SIZE

63 63

78 78

13 13

79 79

21 21

33 33

57 57

19 19

54 54 22 22 62 62

15 15

17 17

Total Total

6 6 1

3 3

2 2

6 6

4 4

3 3

8 8

54 54

27 27

18 18

22 22

14 14

10 10

With With

1984-1985 1984-1985

972 972

337 337

619 619

Tenure Tenure

826 826

197 197

1030 1030

7 7

2 2 2

4 4 4

2 2 2 1

3 3 3

7 7 2 4

1 1 1 1

32 32

93 93

18 18

38 38

90 90

11 11

78 78

FACULTY FACULTY

13 13

625 625

358 358 251 251

150 150

Total Total

216 216

827 827 204 204

107 107

1272 1272

1325 1325

DEPARTMENTS. DEPARTMENTS.

DEPARTMENTS. DEPARTMENTS.

DEPARTMENTS. DEPARTMENTS.

I I

GRANTING GRANTING

GRANTING GRANTING

GRANTING GRANTING

Professor Professor

Professor Professor

Professor Professor

Professor Professor

Professor Professor

Professor Professor

Professor Professor

Professor Professor

Professor Professor

Professor Professor

OOCI'ORATE OOCI'ORATE

OOCI'ORATE OOCI'ORATE

OOCI'ORATE OOCI'ORATE

OOCI'ORATE OOCI'ORATE

OOCI'ORATE OOCI'ORATE

Faculty Faculty

Salaries Salaries

DOCTORATE DOCTORATE

Instructor/Lecturer Instructor/Lecturer

Professor Professor

Instructor/Lecturer Instructor/Lecturer

Professor Professor

Associate Associate

Assistant Assistant

Instructor/Lecturer Instructor/Lecturer

Associate Associate

Assistant Assistant Professor Professor

Instructor/Lecturer Instructor/Lecturer

WITHOtJI' WITHOtJI' DOCTORATE DOCTORATE

Associate Associate

Assistant Assistant

DOCTORATE DOCTORATE

Instructor/Lecturer Instructor/Lecturer

Professor Professor

Professor Professor

WITH WITH

Associate Associate

Assistant Assistant

WITHour WITHour

Associate Associate

Assistant Assistant

WITH WITH

WITHour WITHour

"-.J "-.J

0 0 0'1 0'1 WITH DJCI'ORATE Instructor/Lecturer 17 1 3 0 14 1 3 0 168 ( 173-220) (173-225) (180-230) 275 180 ( 183-229) (185-229) (190-232) 285 Assistant Professor 291 32 36 7 292 30 39 5 184 (216-245) (237-265) (250-293)354 200 ( 232-264) (251-280) (269-320) 371 Associate Professor 360 337 20 19 358 333 18 18 182(248-285) (286-320) (320-379) 481 185(254-290) (301-336) (331-401)521 Professor 513 505 11 9 519 512 12 9 243 (304-343) (360-428) (431-563) 757 249(320-382) (393-454) (462-616)850 1181 875 70 35 1183 876 72 32

DOCTORATE GRANTING DEPARTMENTS. Group IV (45 of 66 reporting)

WITHOUI'DJCI'ORATE Instructor }LeCturer 10 1 4 0 9 1 5 0 Assistant Professor 7 2 2 0 3 2 0 0 Associate Professor 0 0 0 0 0 0 0 0 Professor 3 3 0 0 3 3 0 0 20 6 6 0 15 6 5 0

WITH DJCI'ORATE Instructor/Lecturer 7 1 3 2 8 1 5 2 ------Assistant Professor 126 3 18 0 136 5 19 0 205 ( 232-278) (242-285) (254-310)424 205(246-280) (270-303) (279-340) 458 Associate Professor 110 95 13 12 121 107 15 13 233 (276-334) (293-349) (299-377) 513 237(283-346) (312-380) (323-397) 540 Professor 285 283 13 11 296 290 9 9 290 ( 316-435) (397-515) (511-640) 830 301 ( 355-444) (419-580) (506-700) 892 528 382 47 25 561 403 48 24

DOCTORATE GRANTING DEPARTMENTS. Group V (15 of 28 reporting)

-..I WITIKXJI'DJCI'ORATE ~ Assoc1ate Professor 2 2 0 0 2 2 0 0 2 2 0 0 2 2 0 0

WITH DJCI'ORATE Instructor/Lecturer 2 0 1 0 2 0 1 0 Assistant Professor 36 0 2 0 37 0 3 0 230 ( 248-298) (262-324) (281-340) 383 260 (263-350) (290-350) (305-361) 422 Associate Professor 42 38 3 2 40 34 3 2 290 (331-357) (350-402) (350-428) 435 296 (342-380) (372-425) (372-450) 478 Professor 107 107 3 3 112 112 3 3 217(393-480) (447-525) (553-664) 690 230 ( 440-500) (500-555) (600-690) 740 187 145 9 5 191 146 10 5

DOCTORATE GRANTING DEPARTMENTS. Group VI (13 of 28 reporting) (Canadian Departments)

WITHOUI'DJCI'ORATE Instructor/Lecturer 2 1 1 1 2 1 1 1 Assistant Professor 7 2 0 0 7 2 0 0 Associate Professor 3 3 0 0 3 3 0 0 Professor 7 7 0 0 7 7 0 0 19 13 I I 19 13 I I

WITH DJCI'ORATE Instructor/Lecturer 0 0 0 0 0 0 0 0 Assistant Professor 47 12 4 1 45 12 4 2 230(236-300) (261-329) (290-370) 408 220(230-300) (265-324) (290-380) 408 Associate Professor 125 123 5 4 131 127 7 5 288 (303-383) (359-437) (392-481) 486 290 (303-390) (367-437) (399-487) 494 Professor 179 179 3 3 182 182 4 4 350 (353-463) (428-544) (480-686)700 337(350-470) (446-562) (480-686)700 N 314 12 8 358 m 15 TI SIZE OF FACUL TV SALARIES 1984-1985 1985-1986 (in hundreds of dollars) FACULTY WOMEN FACULTY WOMEN 1984-1985 1985-1986 With With With With Total !!!!!!!! Total Tenure Total Tenure Total Tenure Minimum Median Maximum Minimum Median Maximum

MASTER DEGREE GRANTING DEPARTMENTS (125 of 282 reporting)

WITHOUI' IXlCI'ORATE Instructor/Lecturer 298 18 179 9 300 15 185 9 120 (150-189) (169-198) (178-220) 304 123 (161-202) (172-209) (190-240)350 Assistant Professor 172 116 48 29 167 108 51 29 164 (218-273) (227-290) {242-302) 361 170 (230-284) (243-290) {256-314) 391 Associate Professor 144 142 25 24 143 138 23 20 193 (253-311) {257-323) (263-330) 480 205 {267-333) (271-334) (280-353) 480 Professor 41 40 5 5 44 41 5 5 193 (320-404) {323-404) (323-421)570 219 ( 316-405) (316-405) (340-464)608 655 316 257 67 654 302 264 63

WITH JXlCI'ORATE Instructor/Lecturer 43 10 9 3 42 10 11 3 172{180-283) {180-283) {180-302) 304 172{180-314) (181-314) (181-314)335 Assistant Professor 459 64 79 12 487 66 82 13 183 (215-249) (230-264) (244-290)419 195 (231-259) (243-279) (251-310)380 Associate Professor 624 526 76 69 644 542 73 66 197{253-291) (278-330) (305-361) 441 203 (264-304) (291-340) (312-393) 469 Professor 768 751 51 51 801 779 56 55 253 (300-360) (334-404) (377-453) 601 280 {313-380) {358-426) {401-487) 652 1894 1351 215 135 1974 1397 222 137

..... ~ BACHELOR DEGREE GRANTING DEPARTMENTS (332 of 943 reporting) N WITIJOOl' JXlCI'ORATE Instructor/Lecturer 320 13 165 4 310 11 146 3 102(163-193) (170-200) (171-213) 313 130 ( 173-209) (179-214) (180-222)336 Assistant Professor 280 107 87 20 291 100 94 22 80 ( 195-240) (203-253) (210-260) 360 121(208-254) (214-265) (222-273)374 Associate Professor 194 173 33 26 191 170 31 25 126 {231-301) (234-309) (241-314) 466 132(240-314) (242-320) (248-322)513 Professor 43 38 8 5 37 33 7 5 150 (263-347) {263-355) (263-360)648 226(293-371) (293-388) (293-388) 685 837 ill 293 55 829 314 278 55

WITH JXlCI'ORATE Instructor/Lecturer 18 5 6 0 22 5 6 0 195 (200-240) (200-249) (200-258)313 206 ( 210-260) (210-260) (210-269)336 Assistant Professor 451 48 97 10 459 48 103 9 160 ( 203-230) (210-250) (212-265)400 177 ( 220-250) (230-265) (231-280)430 Associate Professor 501 381 61 41 492 375 64 44 180 (239-286) (250-308) {260-325)429 160 {254-309) {263-325) (270-341) 451 Professor 499 472 51 48 531 497 58 50 188 (269-354) (281-373) {291-398) 600 195 {283-369) (299-394) (309-427) 601 1469 906 215 99 1504 925 231 103 Salary Survey for New Recipients of Doctorates

The figures for 1985 in this article were receiving a doctorate had been employed in their compiled from questionnaires sent to individuals present position for several years. (X+ Y) means who received a doctorate in the mathematical there are X men and Y women in the 1985 sample. sciences during the 1984-1985 academic year from Quartile figures are given only in cases where the universities in the United States and Canada. number of responses is large enough to make them Questionnaires requesting information on meaningful. salaries and professional experience were dis­ Graphs. For each category and year, the tributed to 622 recipients of degrees using median starting salary is denoted by a horizontal addresses provided by the departments which bar; a vertical bar extends to the extremes. The granted the degrees. Of these, 3 were returned salary information in the graphs is in hundreds of by the postal service as undeliverable and could dollars. not be forwarded. There were 269 individuals who returned forms between late June and early The connected line segments equate value of September. The tables below are based on the the dollar from one year to the next, using responses from 243 of these individuals (200 men 1965 median starting salary as a benchmark and 43 women). Data from 26 responses were not and adjusting that to current dollars by the used in the compilation of the tables below; forms implicit price deflators prepared annually by the with insufficient data, or from individuals who had Bureau of Economic Analysis, U.S. Department indicated they had part-time employment, were of Commerce. Because the deflator is not yet not yet employed, or were not seeking employment available for this year, the 1985 figures do not were considered unusable. appear on the graphs. If the rate of change in the actual starting salaries is less than the slope of Readers should be warned that the data in this the corresponding line segment, median starting report are obtained from a self-selected sample and salaries did not keep up with inflation. inferences from them may not be representative of the population. More comprehensive information Note that starting salaries for all categories on the number, the sex-minority group status­ fall behind the cost of living change in 1975 citizenship, and the employment status of the as compared to 1970. Some of this loss was recipients of new doctorates granted last year in made up between 1980 and 1982. Between 1982 the mathematical sciences in the U.S. and Canada and 1983, academic salaries just kept up with may be found in the previous article of this report inflation, research and industry salaries showed on the 1985 Survey. real increases, and government salaries showed no increase and thus a drop when adjusted for Key to Tables. Salaries are listed in hundreds inflation. Between 1983 and 1984, nine-month of dollars. Years listed refer to the academic year academic salaries showed a slight gain on inflation, ending in the listed year. M and F are Male twelve-month academic, twelve-month research, and Female respectively. One year experience and industry salaries generally held constant means that the persons had experience limited and, thus, effectively dropped when adjusted to one year or less in the same position or a for inflation, but government salaries actually position similar to the one reported; some persons decreased. Generally, the range of salaries is increasing with time.

763 Nine-Month Salaries Nine-Month Salaries

1965 Salary 1965 Salary Year Min Ql Median Q3 Max Median in Year Min Median Max Median in Current $ Current $ RESEARCH TEACHING OR TEACHING AND RESEARCH (5 + 0) (118 + 28) 1960 52 65 80 75 1960 49 65 80 74 1965 71 81 90 81 1965 70 80 105 80 1970 78 105 160 100 1970 85 110 195 98 1975 100 110 137 1975 90 120 128 135 173 135 1980 125 137 180 195 1980 105 155 171 185 250 192 1981 143 145 213 1981 130 175 190 210 320 210 1982 180 190 235 226 1982 160 190 206 229 370 223 1983 100 200 230 235 1983 80 200 217 240 350 232 1984 205 205 205 244 1984 140 215 230 255 380 241 1985 205 235 250 1985 170 230 250 270 380 l982M 180 190 190 1982M 160 192 210 229 370 1982F 235 1982F 160 175 198 225 285 l983M 100 200 230 1983M 95 204 220 240 350 1983F 205 205 205 1983F 80 198 210 227 330 l984M 205 205 205 1984M 140 215 232 255 380 1984F 1984F 161 215 228 251 325 1985M 205 226 250 1985M 186 232 250 270 380 l985F 1985F 170 215 242 270 366 One Year Experience (4 + 0) One Year Experience (102 + 24) l985M 205 226 250 1985M 186 230 250 265 380 1985F 1985F 170 270 239 263 366

Nine-Month Teaching

Graph omitted because 400 sample size too small

300

200

100

1960 1965 1970 1975 1980 19831984

764 Twelve-Month Salaries Twelve-Month Salaries

1965 Salary 1965 Salary Year Min Median Max Median in Year Min Median Max Median in Current $ Current $ RESEARCH TEACHING OR TEACHING AND RESEARCH (19 + 3) (11 + 7) 1960 97 lOS 140 86 1960 ••••••••• NO mTA •••••••••• 1965 81 93 107 93 1965 78 104 121 104 1970 90 120 205 114 1970 95 128 200 128 1975 90 119 180 157 1975 87 145 204 176 1980 120 180 321 224 1980 143 195 350 250 1981 140 200 280 245 1981 156 203 400 274 1982 130 245 364 259 1982 100 250 500 290 1983 155 262 450 269 1983 160 260 320 301 1984 145 261 415 280 1984 134 260 450 313 1985 190 342 520 1985 220 273 470 1982M 144 230 336 1982M 180 250 500 1982F 130 265 364 1982F 100 266 367 1983M 195 262 450 l983M 160 255 320 1983F 155 260 364 1983F 240 265 270 1984M 170 283 415 1984M 134 260 450 l984F 145 200 253 l984F 240 275 330 1985M 190 360 520 1985M 230 240 470 1985F 279 300 323 1985F 220 280 420 One Year Experience (13 + 2) One Year Experience (8 + 6) l985M 190 315 432 l985M 230 260 470 1985F 279 290 300 1985F 220 273 420

Twelve-Month Teaching Twelve-Month Research

500

400 400

~Q ...... ,0 "0 300 300 ~ "0 =§

200 200

100 100

0

1960 1965 1970 1975 1980 19831984 1960 1965 1970 1975 19801983 1984

765 Twelve-Month Salaries Twelve-Month Salaries

1965 Salary 1965 Salary Year Min Median Max Median in Year Min Median Max Median in Current $ Current $ mvERNMENI' BUSINESS AND INDUSTRY (11 + 0) (36 + 5)

1960 72 93 130 117 1960 78 110 150 126 1965 70 126 160 126 1965 100 136 180 136 1970 100 150 223 155 1970 96 170 235 167 1975 78 182 247 213 1975 114 187 240 230 1980 156 244 501 303 1980 190 284 400 327 1981 220 290 460 332 1981 195 308 500 358 1982 228 325 470 351 1982 196 354 550 379 1983 160 322 422 365 1983 276 375 580 394 1984 140 315 490 379 1984 180 378 660 409 1985 263 325 440 1985 260 400 493 1982M 228 331 470 1982M 196 366 550 1982F 282 326 369 1982F 230 350 430 1983M 160 313 422 1983M 300 370 580 1983F 293 320 350 1983F 276 375 413 1984M 288 326 490 1984M 180 383 660 1984F 140 202 263 1984F 200 342 416 1985M 263 325 440 l985M 260 400 493 1985F 1985F 295 370 430 One Year Experience (8 + 0) One Year Experience (27 + 2) 1985M 263 323 411 1985M 260 396 493 1985F 1985F 370 400 430

Twelve-Month Government Twelve-Month Business and Industry

600

500 500

400 400

~0 ._Q 0 ~ 300 300 ~ """§ :.:

200 200

100 100

1960 1965 1970 1975 1980 19831984 1960 1965 1970 1975 1980 1983 1984

766 New Publications in the Contemporary Mathematics Series

Integral Bases for Affine Lie Algebras and their ISBN 0-8218-5045-8, LC 85-9241 ISSN 0271-4132 Universal Enveloping Algebras ix + 216 pages (softcover), August 1985 David Mitzman List price $22, Institutional member $18, (Contemporary Mathematics, Volume 40) Individual member $13 To order, please specify CONM/42 N Contents 1. Introduction; 2. Chevalley bases for semisimple and type Group Actions on Rings 1 affine Lie algebras of types A. D. E; 3. Chevalley bases for Susan Montgomery, Editor the remaining semisimple and affine Lie algebras; 4. Integral Volume 43) forms of enveloping algebras of affine Lie algebras {Contemporary Mathematics. ISBN 0-8218-5043-1, LC 85-1374 This volume consists of the proceedings of a 1984 meeting ISSN 0271-4132 that brought together ring theorists and researchers in viii + 160 pages (softcover), July 1985 invariant theory and operator algebras. A high percentage List price $19, Institutional member $151 Individual member $11 of the papers here are expository; they reveal many topics To order, please specify CONM/40N common to the three fields, such as K-theory, dual actions, semi-invariants and crossed products. Particle Systems, Random Media and Large Partial Contents Deviations Hyman Bass, Algebraic group actions on affine spaces; Richard Durrett, Editor Edward Formanek, Noncommutative invariant theory; Melvin Hochster, Invariant theory of commutative rings; {Contemporary Mathematics. Volume 41) D. S. Passman, Algebraic crossed products; Marc A. Reiffel, This volume provides a handy summary of results and K-theory of crossed products of C* -algebras by discrete groups unsolved problems from some of the most exciting areas in probability theory today: interacting particle systems, ISBN 0-8218-5046-6, LC 85-11242 percolation, random media, the Ising model and large ISSN 0271-4132 xii + 277 pages (softcover), September 1985 deviations. An undergraduate course in probability is sufficient List price $27, Institutional member $22, to understand many of the articles. The book will be Individual member $16 especially valuable to probabilists interested in mathematical To order, please specify CONM/43N physics and to physicists interested in statistical mechanics or disordered systems. Combinatorial Methods in Topology and Contributors Algebraic Geometry M. Campanino, J. (hayes, L. (hayes, J. T. Cox, D. A. John R. Harper and Richard Mandelbaum, Editors Dawson, A. DeMasi. R. Durrett. R. Ellis, P. Ferrari. P. Gacs, {Contemporary Mathematics, Volume 44) H. 0. Georgii. S. Goldstein, L. Gray, A. Greven, D. Griffeath, G. Grimmett, M. Z. Guo, Y. Higuchi, K. J. Hochberg, This collection surveys several areas in topology and R. Holley, H. Kesten, E. Key, C. Kipnis, S. Kotani, G. Lawler, geometry where combinatorial methods are proving especially N. Madras, C. Newman, S. Orey, G. Papanicolaou, G. Rost, fruitful: topology and combinatorial group theory, knot C. Schroeder, L. Schulman, S. Schumacher, J. van den Berg, theory, 3-manifo\ds, homotopy theory and infinite-dimensional M. E. Vares, D. Wick, J. Wierman topology, four manifolds and algebraic surfaces. The material ISBN 0-8218-5042-3, LC 85-6181 is accessible to advanced graduate students with a general ISSN 0271-4132 course in algebraic topology along with some work in x + 381 pages (softcover), August 1985 List price $32, Institutional member $26, combinatorial group theory and geometric topology. Individual member $19 Section Headings To order, please specify CONM/41N Topology and Combinatorial Group Theory Knot Theory Classical Real Analysis 3-Manifo\ds Daniel Waterman, Editor Homotopy Theory and Infinite Dimensional Topology {Contemporary Mathematics, Volume 42) Four Manifolds and Algebraic Surfaces These papers, presented to honor Casper Goffman, ISBN 0-8218-5039-3, LC 85-11244 focus on the many areas where his influence has been felt: ISSN 0271-4132 xviii + 358 pages (softcover), October 1985 differentiation and integration theory, structure theory of real List price $32, Institutional member $26, functions, ordered systems, surface area, Sobolev spaces, Individual member $19 Fourier analysis, measure theory, bases and approximation To order, please specify CONM/44 N theory. Though aimed primarily at specialists in real function theory of one or several variables, the papers will also interest mathematicians working in the areas of Fourier analysis, surface area, mapping theory and control theory.

Shipping/Handling: 1st book $2, each additional $1, maximum $25; by air, 1st book $5, each additional $3, maximum $100 Prepayment required. Order from American Mathematical Society, P.O. Box 1571, Annex Station Providence, Rl 02901-1571, or call toll free 800-556-7774 to charge with Visa or MasterCard Report on the 1985 Survey of New Doctorates

by Edward A. Connors

This report presents a statistical profile of new departments). These numbers are obtained from doctorates in mathematical sciences awarded by the Annual Survey Reports in the November universities in the United States and Canada dur­ Notices and are tabulated in Table lA. Table lA ing the period July 1, 1984, through June 30, 1985. does not include degrees from computer science It includes the employment status of recipients of departments. 1984-1985 doctorates in mathematical sciences (as As is customary, a second, updated report is of August 20, 1985) and an analysis of the data by planned for the March 1986 issue of the Notices. sex, minority group, and citizenship. In addition, Table lB contrasts the number of new doctorates trends in the number of doctoral degrees are reported in the November Reports with the more reported for each of the Groups I through V (see complete totals reported in the following spring the first page of this Report of the 1985 Annual Reports for the years 1979-1980 to 1983-1984. The AMS Survey for a description of the classification last column is the number reported in this Survey. system and the Notices, June 1983, for a listing Note that the table entries prior to 1982-1983 of the departments in Groups I and IT. Table 0 include the computer science departments and, provides information on the response rates for this thus, this table is an extension of the comparable part of the Survey. one from last year's Report (Notices, November TABLE 0: Response Rates 1984, page 754). The data for 1984-1985 indicate a decline of Group I 38 of 39 including 1 with 0 degrees 3% in doctorates awarded from the corresponding Group II 39 of 43 including 8 with 0 degrees Group ill 59 of 71 including 20 with 0 degrees figures for 1983-1984, and a decline of 5% from the Group N 54 of 66 including 5 with 0 degrees 1980-1981 figures. Of the 732 doctorates reported Group V 28 of 54 including 7 with 0 degrees from US universities (there were 37 doctorates from Canadian universities) the citizenship is We continue the practice adopted in the 1983 reported as known for 726 recipients, with US Report and do not report doctorates granted by citizens accounting for 55% (396) of this total. computer science departments (formerly included The 1983-1984 figures were 59% (433) and the with the totals for Group V departments). The 1982-1983 figures were 61% (455). The percentage reporting rate of computer science doctorates of doctorates who are us citizens has declined was considered too small to merit inclusion. In consistently and dramatically from 73% in 1979- the 1982 Survey, for example, 105 doctorates 1980 to 55% in 1984-1985. Thus, in 1984-1985, in computer science were reported whereas the us institutions produced only approximately 400 actual number of degrees granted was, in all doctorates in the mathematical sciences who are likelihood, more than twice that number. In US citizens. contrast, virtually all of the mathematical sciences Females comprise 20% of the us citizens doctorates are reported. Thus, any year to receiving doctorates from us institutions in 1984- year comparisons that bridge the 1982 and 1983 1985. This percentage is the same as for the last Surveys should accommodate this modification. two years. Table 6 gives these figures for the TABLE lA: New Doctorates, Fall Counts period 1972-1973 to 1984-1985. Since 1972-1973, 80-81 81-82 82-83 83-84 84-85 the percentage of female US citizens rece1vmg doctorates in mathematical sciences from us 812 755 792 789 769 universities has doubled. TABLE 1B: New Doctorates, Fall and Spring Counts The employment matrix, Table 2, is similar 79-80 80-81 81-82 82-83 83-84 84-85 to last year's, with three exceptions: 51 new doc­ torates were employed by Group Ill departments Fall 858* 904* 860* 792 789 769 Spring 898* 927* 914* 840 827 ** compared to 35 last year, 66 new doctorates were hired by Group M departments compared to 88 *Includes computer science. last year, 140 new doctorates were reported to **To appear in the Notices, March 1986. have taken employment outside of the US and The number of new doctorates reported for Canada, compared with 113 last year. The num­ 1984-1985 was 769 (fall 1985 count) compared ber of those reported as still seeking employment to 789 for 1983-1984 (fall 1984 count). The is 27 (compared with 39 last year) and 45 were comparable figure for 1982-1983 was 792, and the classified as having unknown employment status figures for 1981-1982 and 1980-1981 are 755 and (compared with 48last year). 812, respectively (the latter two figures do not Employment Status of New Doctorates, 1984- include doctorates awarded by computer science 1985. Table 2 shows the employment status, by

768 TABlE 2: Ebployment Status of 1984-1985 New Doctorates in the Mathematical Sciences

I PURE MATHEMATICS

Type of Employer

Group I 22 16 19 4 3 8 8 80 Group II 3 8 8 1 3 4 7 2 36 Group III 7 8 7 1 6 6 1 12 3 51 Group IV 3 13 2 18 Group V 2 1 4 7

Masters 11 17 4 2 3 19 1 5 1 3 66 Bachelors 17 9 5 7 1 9 1 3 6 4 4 66 Two-year College 2 2 1 1 6 Other Academic Departments 4 1 4 1 22 3 12 7 3 57

Research Institutes 2 3 1 2 2 5 2 5 2 24 Government 3 1 4 5 1 14 Business and Industry 4 5 3 5 6 30 6 12 14 19 104

Canada, Academic 3 5 2 8 2 1 21 Canada, Nonacademic 1 1 4 1 7 Foreign, Academic 6 9 10 4 2 28 3 3 20 1 9 95 Foreign, Nonacademic 2 4 1 24 3 7 4 45

Not seeking employ. Not yet employed 5 4 1 1 3 2 2 5 1 3 27 Unknown 7 11 5 4 8 1 8 1 45

Total 94 105 70 27 39 189 15 41 115 7 67 769

1N!LE 3: Sex, Mirnrity Group, and Citi:oenshi.p of New Doctorates

July 1, 1984--June 30, 1985

U.S. DEGREES MEN WJMEN 'IUI'AL CITIZENSHIP CITIZENSHIP Not Total Not Total RACIAL/E'HlNIC GROUP u.s. Canada Other Known Men u.s. Canada Other Known l'bnen

Asian, Pacific Islander 18 l 117 4 140 6 l3 19 159 Black 4 11 15 l l 16 American Indian, EskillK), Aleut 3 3 3 Mexican American, Chicano, Puerto Rican 7 7 l 3 4 ll

None of those above 275 10 137 2 424 72 l 23 96 520 Unknown 15 2 4 21 1 l 2 23

Total Nunber 315 l3 276 6 610 81 l 40 122 732

CANADIAN !EGREES MEN WJMEN 'IUI'AL

CITIZENSHIP CITIZENSHIP Not Total Not Total RACIAL/E'HlNIC GROUP u.s. Canada Other Known Men u.s. Canada Other Known l'bnen

Asian, Pacific Islander l l l Black 2 2 2 American Indian, Eskiioo, Aleut Mexican American, Chicano, Puerto Rican l l l

None of those above 2 l3 6 21 ll l 12 33 Unknown

Total Nunber 2 13 10 25 11 1 12 37

769 type of employer and field of degree, of the 769 last year in these two latter groups were 24% and recipients of doctoral degrees conferred by the 13%, respectively. mathematical sciences departments in the US and Trends in the Number of New Doctorates. Canada between July 1, 1984 and June 30, 1985. Table 4 gives the number of doctorates granted The names of these 769 individuals are listed with during 1982-1983, 1983-1984, and 1984-1985 by their thesis titles in a later section of this Report. those departments in Groups I-VI which reported In rows 1 through 5, the numbers represent in all three years (as of August 20, 1985). This those who have accepted appointments in us is the same criterion used in last year's Report. doctorate-granting mathematical sciences depart­ The number of such departments out of the ments (Groups I-V). In the next two rows, the total is given in parentheses. (Computer science figures represent those accepting appointments in departments are not included.) The entries for the 1982-1983 and 1983-1984 columns should not be US mathematical sciences departments granting expected to agree with the corresponding columns masters and bachelors as the highest degree. The in last year's Report, due to the criterion for information was obtained from the departments inclusion. For example, a department that did granting the degrees and from the recipients not respond to this year's Survey is not included themselves. this year although it may have been included in Among the 1984-1985 new doctorates employed the tally for last year. [Moreover, last year there in the us (529), 61% (324) took positions was a numerical error in the entry for Group I: the in university or four-year college mathematical 283 in the column labeled 82-83 should have been sciences departments; 22% (118) took positions 252 (see the Notices for November 1984, page 756, in government, business or industry; while the Table 4).] remaining 17% (87) are employed by research institutes, other academic departments or two­ TABLE 4: Number of New Mathematics and Statistics Doctorates Reported year colleges. These percentages are the same as by Selected Departments the corresponding ones reported last November. Table 2 shows as "not yet employed" about 82-83 83-84 84-85 4% of the 1984-1985 new doctorates, excluding Group I 276 245 302 those whose employment status is unknown. The (38 out of 39 depts.) data in Table 2 were obtained in many instances Group n 107 110 69 (36 out of 43 depts.) early in the summer of 1985 and do not reflect Group Ill _11. _1Q _lffi subsequent hiring; an update of Table 2 is planned (47 out of71 depts.) for the March 1986 Notices. A similar update Subtotal 460 431 430 last year revealed that all but 16 new 1983-1984 Group N 151 136 150 doctorates found positions by fall 1984 (see the (44 out of 66 depts.) Notices, November 1984, page 755, and March Group V 92 97 83 1985, page 179). Eleven persons included in Table (21 out of 54 depts.) 2 reported taking part-time employment. Group VI __Qll __36 _1Q (20 out of 28 programs) Table 2 shows that recipients in the two Subtotal 281 269 276 employment categories foreign academic and TOTAL 741 700 706 foreign nonacademic comprise a total of 140 or 18% of the 769 new doctorates-corresponding Citizenship and Sex of U.S. Doctorates, 1972- numbers for last year were 113 and 14%, 1985. Again this year, information is presented on respectively. the annual number of doctorates granted by US Sex, Minority Group and Citizenship of New universities to US citizens (Table 5). This number Doctorates, 1984-1985. Table 3 presents a is divided into male and female doctorates (Table breakdown according to sex, minority group and 6). These data are presented for the period 1972- citizenship of these 769 new doctorates. The 1985 using the Annual AMS Survey Reports on information reported in this table was obtained new doctorates published each year in the October from departments granting the degrees and in or November Notices. Thus Tables 4 and 5 are some cases from the recipients themselves. extensions of tables in last year's Report. In Table 5 the first column (headed Adjusted Total Analyses of the 1984-1985 employment forms of Doctorates given by US Universities) gives the of the new doctorates indicate that of the 167 number of doctorates granted between July 1 and new doctorates employed by Group I, II, or ill June 30 of the indicated years whose citizenship departments, 13% are women, an increase of is known. Column 2 gives the number who 3% over the 10% reported in each of the three were US citizens and Column 3 the percentage previous years. that this represents. In Table 6 the number Of the 132 new doctorates employed by in Column 2 of Table 5 is further divided into bachelors and masters granting departments, 26% men and women. Note that in both tables all are women, and of the 118 new doctorates years but 1982-1983, 1983-1984, and 1984-1985 employed by government, business or industry, include doctorates granted by computer science 15% are women. The corresponding figures for departments.

770 TABLE 5: U.S. Citizen Doctorates It is quite clear that there has been a consistent Adjusted Total Total of and dramatic decline in the number of new doc- of Doctorates Doctorates' torates in the mathematical sciences awarded to given by U.S. who are U.S. US citizens by US institutions. If this pattern universities citizens % continues, the impact on us educational institu- tions will be significant. Particularly vulnerable 1972-1973 986 774 78% 1973-1974 938 677 72% are the masters and bachelors degree-granting 1974-1975 999 741 74% institutions which, in addition to their other es- 1975-.1976 965 722 75% sential and valuable contributions to the American 1976-1977 901 689 76% educational system and society, are a great source 1977-1978 868 634 73% of potential scientific scholars and technical ex- 1978-1979 806 596 74% perts. A shortage of well-trained personnel for 1979-1980 791 578 73% masters and bachelors degree-granting institutions 1980-1981 839 567 68% will further serve to exacerbate current difficulties 1981-1982 798 519 65% caused by inadequate funding and support ser- 1982-1983 744 455 61% Bernard Madison's article 1983-1984 738 433 59% vices (see, for example 1984-1985 726 396 55% Institutional Support for Mathematical Science Departments in the Notices, October 1985, pages TABLE 6: U.S. Citizen Doctorates, 584 to 588). Male and Female Doctorates who are % U.S. Citizens Male Female Female 1972-1973 774 696 78 10% 1973-1974 677 618 59 9% 1974-1975 741 658 83 11% 1975-1976 722 636 86 12% 1976-1977 689 602 87 13% 1977-1978 634 545 89 14% 1978-1979 596 503 93 16% 1979-1980 578 491 87 15% 1980-1981 567 465 102 18% 1981-1982 519 431 88 17% 1982-1983 455 366 89 20% 1983-1984 433 346 87 20% 1984-1985 396 315 81 20%

771 A Fifteen Year Retrospective on Academic Salaries of U.S. Doctorate Holding Faculty by Donald C. Rung

Since 1957 the Society has published a survey of index along with the multipliers is given in Table annual salaries of mathematical sciences faculty so III. The index has been revised recently by the the mathematical community may assess general government and the most recent index is given in salary levels. It is apparent to even the casual this article. It differs slightly from the index used reader of these surveys that since 1970 salaries in the previous articles. (after adjusting for inflation) have declined. In an A further word of explanation on the tables. attempt to assess how dramatic this decline is, the The figures used to compute salaries in Table I author published two previous articles appearing for new recipients of the doctorate were obtained in the October 1979 Notices and November 1981 from the Society's Annual Survey reported in Notices comparing salary levels after adjusting the October Notices of 1970 and 1975 and the for inflation. The present article updates these November Notices of 1980 and 1985 respectively. articles and extends the analysis to all of the A slightly different technique was used to arrive groups (Group I, II, III, N, M, and B) used in at the professorial salaries given in Table II. The reporting salaries. salaries for each of the years given in Table II The figures show that over the last several years were computed using the salary for that year as salaries have kept pace with inflation but have reported in the succeeding year's Survey except not recovered from the dismal decline experienced for the current year. Thus, the 1970 numbers in the period 1970-1980. Thus salary levels are from the Survey as reported in the October today are still significantly lower than in 1970. 1971 Notices, the 1975 figures are from the This is especially true for salaries in Group B, October 1976 Notices, the 1980 figures are from the bachelor granting departments. If a person the November 1981 Notices, and the 1985 figures began as an assistant professor in 1970, earning are from this issue of the Notices. To arrive at the 1970 average salary reported for this rank a representative salary for each rank, the median (in 1985 dollars) of $28,100 and is now a full salaries for the 25th and 75th percentiles were professor earning the 1985 reported average salary averaged. The classification of departments of of $34,700, the real increase in salary has been universities and colleges for Groups I, II and III 24%! The corresponding number for Group I changed in 1983. However, as was noted at the faculty is 66%. In 1985 for Group I, the average time of the change, the salaries in each of the new assistant professor salary is 57% of a full professor groupings changed little. (See the first page of salary, while in Group B the corresponding this report of the 1985 Survey for definitions of number is 71%. Thus Group B salaries give the groups.) a vivid example of the so called "compression" To attract the talented young student to an phenomenon. These various figures are reported academic career in mathematics is essential. Ade­ in Table II. quate salaries are an important incentive, espe­ We also include an analysis of salary for new cially with competing disciplines (and industry) recipients of the doctorate taking nine-month offering competitive salaries. We have begun to positions combining teaching and research (Table reverse the inflationary decline but are a long way I). It is interesting to note that these numbers from the salary levels attained in 1970. The Group parallel closely the average salary of assistant B salary scale especially needs to be monitored in professors in Group B departments. hopes that some improvement in salary levels will For the years surveyed, salaries are given both occur. The vitality of our profession is essential in actual dollars and 1985 dollars. The actual for the vitality of science. It is hoped that the dollar figures were converted to 1985 dollars using general improvement in salaries over the last few the implicit price deflator index prepared by years will continue. the Bureau of Economic Analysis of the U.S. Professor Edward Connors of the University Department of Commerce and often used by of Massachusetts, Amherst, is now the principal educational planners. It is a somewhat more author of these surveys. I wish to thank the conservative index than, say, the Consumer Price secretariat of the Society, especially Lincoln K. Index. The 2nd quarter index for the years Durst, James W. Maxwell, Virginia M. Biber and 1970, 1975, 1980, and 1985 was used. Using this Marcia C. Almeida for their kind and efficient index, the 1970 dollar is multiplied by 2.535, the help in preparing these articles. I hope that these 1975 dollar multiplied by 1.856, and the 1980 articles have been, and will continue to be, of dollar by 1.308 (to equal the 1985 dollar). The benefit to our profession.

772 TABLE 1: Salary for New Recipients of the Doctorate {Nine month teaching and research) In 1985 dollars (current dollars in parentheses) 1970 1975 1980 1985 27,900 23,800 24,400 25,000 {11,000) {12,800) {17,100)

TABLE ll: Faculty Salaries In 1985 dollars (current dollars in parentheses)

1970 1975 1980 1985 1970 1975 1980 1985 Group I Group IV (Statistics) Inst. 26,300 22,400 NA 24,400 Inst. NA NA NA NA {10,400) {12,600) Asst. Prof. 30,400 27,000 26,400 28,700 Asst. Prof. 29,400 25,600 25,900 27,700 {12,000) {14,600) {20,200) (11,600) {13,800) {19,800) Assoc. Prof. 36,800 35,100 34,700 34,600 Assoc. Prof. 36,800 33,200 32,800 34,700 {14,500) {18,900) {26,500) {14,500) {17,900) {25,100) Full Prof. 49,400 50,700 48,100 50,000 Full Prof. 57,000 52,300 49,500 48,800 {19,500) {27,300) {36,800) {22,500) {28,300) {37,800) Group M Group n Inst. NA 23,900 21,500 24,800 Inst. NA 21,900 21,800 22,300 {12,900) {16,400) {11,800) {16,700) Asst. Prof. 29,900 26,500 25,100 26,100 Asst. Prof. 30,900 27,100 25,400 27,200 {11,800) {14,300) {19,200) {12,200) {14,600) {19,400) Assoc. Prof. 35,500 32,700 30,600 31,600 Assoc. Prof. 38,300 33,600 32,100 33,200 {14,000) {17,600) {23,400) {15,100) {18,100) {24,500) Full Prof. 44,600 39,700 38,200 39,200 Full Prof. 54,700 48,400 44,200 44,400 {17,600) {21,400) {29,200) {21,600) {26,100) {33,800) Group B Group ill Inst. NA NA NA 23,500 Inst. NA 18,900 19,600 20,700 Asst. Prof. 28,100 23,600 22,400 24,800 {10,200) {15,000) {11,100) {12,700) {17,100) Asst. Prof. 30,900 26,600 24,500 26,600 Assoc. Prof. 35,000 28,600 27,600 29,400 {12,200) {14,300) {18,700) {13,800) {15,400) {21,100) Assoc. Prof. 38,500 33,400 31,400 31,900 Full Prof. 40,800 35,800 33,600 34,700 {15,200) {18,000) {24,000) {16,100) {14,300) {25,700) Full Prof. 51,500 44,000 41,900 42,400 {20,300) {23,700) {32,000) *NA = not available.

TABLE ill: Implicit Price Deflator {2nd Quarter Index) Proposed by Bureau of Economic Analysis U.S. Department of Commerce Index Year Value Multiplier* 1970 91.1 2.535 1975 124.4 1.856 1980 176.5 1.308 1985 230.9** 1 *To obtain 1985 dollars. **Flash estimate.

773 Doctoral Degrees Conferred 1984-1985 THE ANNUAL AMS Jist of doctoral degrees in the mathematical sciences and related subjects reports 769 degrees conferred between July 1, 1984, and June 30, 1985 by 193 departments in 135 universities in the United States and Canada. Each entry contains the name of the recipient and the thesis title. The numbers in parentheses following the names of universities have the following meanings: the first number is the number of degrees listed for that university; the next seven numbers are the number of degrees in the categories of 1. Pure mathematics (i.e., algebra, number theory, analysis, functional analysis, geometry, topology, logic, or probability); 2. Statistics; 3. Computer science; 4. Operations research; 5. Applied mathematics; 6. Mathematics education; 7. Other. ALABAMA Stanley, Elizabeth Ann, Diffusion in Svoronos, Alexander Nikolaos, Duality glassy polymers. theory and finite horizon approximations for discrete time z'nfinite horizon economic Auburn University MATHEMATICS (2;2,0,0,0,0,0,0) models. Blaum, Mario, Error correcting codes for STATISTICS MATHEMATICS computer memories. Glover, James Ervin, On the construction Klemes, Ivo, I. Idempotent multipliers of Burr-Doss, Deborah, On errors-in­ variables in binary regression-Berkson of almost resolvable Mendelsohn triple H 1 on the circlej II. A mean oscillation case. systems having prescribed intersections. inequality for rearrangements. Dehnad, Khosrow, Boundary detection Smith, Cheryl Mays, Complex stable laws Lewy, Michael Robert, The indecompos­ smoothers for classification of spatial and their domains of attraction. ables of rank 3 permutation modules. data. ARIZONA Stanford University Emoto, Sherrie Emiko, The preferred (25;4, 7,1,6,2,0,5) choice between the maximum likelihood es­ Arizona State University timator and the Kaplan-Meier estimator. ENGINEERING-ECONOMIC SYSTEMS (2;1,0,0,0,1,0,0) Hastie, Trevor John, Principal curves and Brandeau, Margaret L., Exploiting con­ surfaces. MATHEMATICS vexity and separability properties of loca­ Marhoul, Joseph Charles, A model for Charris, Jairo, Sieved Pollaczek and tion problems. large sparse contingency tables. random walk polynomials. Freeman, Darrell, Incentives in electric Stein, Michael Leonard, Estimation of Clarkson, Eric Wayne, Clifford algebras utility rate regulation. spatial variability. in relativistic quantum mechanics and in Holtzman, Samuel, Intelligent decision Tibshirani, Robert John, Local likelihood the gauge theory. systems. estimation. University of Arizona Ikhwan, Muhammad-Ali, Comparison University of California, (2;0,0,0,0,1,0,1) of alternative development paths, the Berkeley example of oil economies. (54;31, 7,1,3, 7,0,5) APPLIED MATHEMATICS Logan, Douglas, The value of probability West, Karen Frances, An extension to assessment. BIOSTATISTICS the analysis of the shift-and-add method: Lounamaa, Pertti, Models of multi­ Fang, Ji-Qian, Multistate survival analysis Theory and simulation. agent behavior: A simulation and expert with time-dependent covariates and cen­ soring. MATHEMATICS environment approach. Salinas-Ortiz, Jose A., Technology, ac­ Kampert, James B., The modified score Gossett, Eric James, Partitioning strongly cumulation and distribution in the north­ estz'mator of logistic regression coefficients regular graphs. south relationsj a unified theoretical in epidemiologic case-control studies. analysis. ARKANSAS INDUSTRIAL ENGINEERING AND .MATHEMATICS OPERATIONS RESEARCH University of Arkansas Flaminio, Livia, Ridgidity properties of Agah, Mahmoud, A seasonal forecasting (1;1,0,0,0,0,0,0) horospherical foliations. model. Dincerler, Abdurrezak, Project scheduling Hitt, John Daniel, Hardy spaces on an MATHEMATICAL SCIENCES in· project-oriented production systems. annulus. Li, Lide, Order-theoretic and ring-theoretic Lin, Cher-Sern Brian, Design of a Johnson, Stewart, Continuous measures approaches to inverse semigroups. decision support system for a multi-single and strange attractors in one dimension. machine production system. Liao, Ming, Riesz representation and CALIFORNIA Park, Jin Woo, Design of a demand duality. forecasting system for planning production California Institute of Technology Tam, Luen-Fai, The behavior of capillary of consumer products. (8;2,0,0,0,5,0,1) surfaces as gravity tends to zero. Subramanian, G. S., Bayesian approaches Yelling, John Arthur, Spherical geometry to evaluate system reliability. APPLIED MATHEMATICS and the Schwartzian differential equation. Tsao, Hsiao-Shen Logy, An extension to Fier, Jeffrey Michael, Part 1: Fold OPERATIONS RESEARCH the dynamic linear model. continuation and the flow between rotating coaxial disksj Part II: Equilibrium chaosj Chadee, Floyd Fitz-Hubert, Sparse MATHEMATICS Part ill: A mesh selection algorithm for quasi-Newton methods and the continua­ Allen, David Lawrence, Strong rates two-point boundary value problems. tion problem. of convergence for differences between Henderson, Michael Edward, Complex Perkins, Mark Mathiesen, On maximiz­ the sample distribution function and the bifurcation. ing the expected lifetime of replaceable quantile process. Henshaw, William Douglas, Part 1: The systems. Andrews, Darry, Sample path continuity numerical solution of hyperbolic systems Scott, Dan Martin, A dynamic program­ of Wick polynomials in the free Markov of conservation laws. Part II: Composite ming approach to time-staged convex field. overlapping grid techniques. programs. Blicher, Albert Peter, Edge detection and Molloy, Charles Thomas, Contributions So, Kut-cheung Rick, Optimal main­ geometric methods in computer vision. to the kinetic theory of traffic flow with tenance policies for single-server queueing Buffo, Alberto, Inverse problem of poten­ queuing. systems subject to breakdowns. tial scattering in three dimensions.

774 Chen, Ten-Ging, On Henkin's solution of Strouse, Elizabeth Jane, Embedding the Clark, Charles R., Asymptotic properties the a-problem on strictly convex domains algebra of formal power series in several of some multidimensional diffusions. inC". variables into a Banach algebra. Dutt, Pravir Kumar, Stable boundary Coonen, Jerome Tolzy, Contributions to Wongkew, Richard Alexander, The conditions and difference schemes for a proposed standard for binary floating­ complexity of finding zeroes. Navier-Stokes type equations. point arithmetic. Woodin, W. Hugh, Discontinuous Gartenberg, Philip Alan, Fast rectangular Csizmazia, Anthony Paul, Invariants homomorphisms of C(rl) and set theory. matrix multiplication. under congruence for infinite dimensional Zierau, Roger Craig, Geometric con­ Harabetian, Eduard, A Cauchy- operators. struction of unitary highest weight repre­ Kovalevsky theorem for strictly hyper­ Dougherty, Randall Lee, Narrow cover­ sentation. bolic systems of conservation laws with ings of w-product spaces. Zizza, Frank, K 2 and automorphisms of piecewise inital data. Doyle, John Comstock, Matrix interpola­ hyperbolic dynamical systems. Hoang, Bao Ngoc, Classical and general­ tion theory and optimal control. STATISTICS ized Lefschetz numbers. Embid-Droz, Pedro Fermin, Well­ Hong, Chia Jon, On characterizations of posedness of the nonlinear equations for Chen, Hung, Optimal rates of convergence . some distributions. zero Mach number combustion. for locating the global maximum of a Exel, Ruy Filbo, Rotation numbers for regression function. Khabazian, Hossain Esfaliani, Mojahed rings. automorphism of c* -algebras. Chiu, Shean-Tsang, Statistical estimation Fortune, Barry Alan, A symplectic fi:z;ed of the parameters of a moving source Kim, Young-wook, On the group of point theorem for complex projective from array data. isometries of Riemannian metrics on spaces. Jeliliovschi, Enio Galinkin, Estimation compact differentiable manifolds. Greengard, Claude A., Three dimensional of Poisson parameters, subject to con­ Kranjc, Marko, Imbedding complexes vortex methods. straints. of dimension two in the 4-dimensional Heumos, Michael Justin, Produced repre­ Jhun, Myoungshic, Bootstrap methods for Eculidean space. sentations of Lie Algebras. density estimates and k-means clustering. Melolidakis, Constantine, On stochastic Howard, Mark Gilbeau, Vaught's conjec­ Morita, June Gloria, Nonparametric games with lack of information on one ture and the closed unbounded filter. methods for matched observations from side. Hymowech, Marvin, Complete regular life distributions. Nguyen, Bao Gia, Certain critical local rings of mixed characteristic. Permutt, Thomas Joshua, Preliminary exponent inequalities for percolation Kostlan, Eric James, Statistical com­ testing for serial correlation in time-series processes. plexity of numerical linear algebra. regression. Pipher, Jill Catherine, Double index Li, Ke-Zheng, Classification of supersin­ Weintraub, Marisa Yadlin, Development square functions and bounded mean gular abelian varieties. of a model for probabilistic discrete oscillation on the bidisc. Lipshutz, Robert Jay, Stable rank 2 decisions. Poon, Yiu-Tung, A K-theoretic invariant vector bundles on P4 . University of California, for dynamical systems. Megory-Cohen, Igal, Properties of hyper­ Davis Schubert, David Crawford, Jr., bolic crossed-product algebras. (3;0,1,1,0,1,0,0) Compactifications of moduli spaces for Ng, Kan Ching, Relation algebras with curves. transitive closure. MATHEMATICS Schumacher, Scott, Diffusions with ran- O'Hara, Kathleen Marie, Structure and DeSanti, Albert James, Boundary and dom coefficients. complexity of the involution principle for interior layer behavior of solutions of partitions. the singularly perturbed semilinear elliptic University of California, Onsiper, Hursit Mustafa, Rational maps boundary value problem. Riverside and Albanese schemes. Wang, Richard Li-Chih, Least squares (3;0,3,0,0,0,0,0) Paul, Deirdre Wynne, Topics in bounded piecewise polynomial approximation for cohomology of groups. volterra integral equations of the first STATISTICS Perline, Ronald Keith, Some aspects kind. Gallavan, Rosemary, An experiment in of the theory of time and band limited STATISTICS collective strategic assessment. operators associated with Lame's equa­ Gomez-Aguilar, Roberto, Study on in­ Whitaker, Lyn, Contributions to non­ tions. terpenetrating subsampling ratio and parametric estimation in reliability. Phillips, Norman Christopher, K­ regression estimation with or without theoretic freeness of actions of finite University of California, jackknifing. groups on c* -algebras. Irvine Soofi, Ehsanolali, Information theoretic Putnam, Ian Fraser, The c* -algebras (1;1,0,0,0,0,0,0) approach to regression. associated with Denjoy homemorphisms. MATHEMATICS University of California, Rimlinger, Francis Stewart, The struc­ White, Donald Brian, Limit theorems for ture of pregroups. San Diego sums arising from sampling without re­ (5;3,1,0,0,0,0,1) Shaio, Jack, Approximate equivalence for placement from finite multivariate popula­ representations of C • -algebras and C *­ tions. MATHEMATICS dynamical systems. Behr, Erazm J erzy, Aspects of affine Shapiro, Jacob, Finite algebras with University of California, algebras. abelian properties. Los Angeles Sheu, Albert Jeu-Liang, The cancellation (18;11,2,1,0,4,0,0) Berg, Michael Christian, Modular forms and Dirichlet series for congruence sub­ property for modules over the group c* - BIOSTATISTICS groups and aspects of group representation algebras of certain nilpotent Lie groups. Perdue, Sondra, Timing and interaction theory. Spielberg, John Samuel, Extensions of of major risk factors in renal regrajts in subalgebras of AF algebras. Mummy, Mark Stephen, Representable humans. matroids and matroid algorithms. Sterling, Ivan Charles, New examples of imbedded spherical soap bubbles in MATHEMATICS Schwartz, David Frederick, Optimization over families of bounded analytic func­ sn(l) and a generalization of Delaunay's Banuelos, Rodrigo, Martingale transforms tions. theorem. related singular integrals and A 11 -weights. Stern, Alan Spector, The lattice of local Brio, Moysey, Upwind schemes for the Staniswalis, Joan Georgette, Local bandwidth selection for kernel estimates. interpretability of theories. MHD equations.

775 University of California, CONNECTICUT Cowan, Charles Douglas, Effects of Santa Barbara misclassification on estimates from (6;4,1,1,0,0,0,0) University of Connecticut capture-recapture studies. (1;0,1,0,0,0,0,0) Johnson, Ayah Evelyne, Two-stage pro­ MATHEMATICS STATISTICS cedures for selecting the best of k systems Mustafa, Ibrahim, On Darbouz semi­ when the total number of tests is fixed continuous functions. Davis, Marsha Jane, An estimation of Stein-type estimation: Estimators that and small. Russo, David Allen, Structural properties shrink toward multiple subspaces. Johnson, Wayne Ellett, Combining de­ of complexity classes. pendent tests with incomplete repeated Schulte, Thomas Robert, Minimal sur­ Yale University measurements. faces, Gauss map, second variation and (10;8,2,0,0,0,0,0) Mohadjer, Leyla, The efficiency of the applications to topology. MATHEMATICS normal discriminant analysis compared Taylor, Kevin B., Darbouz-like properties to the logistic regression for the prediction Bar Yaacov, Daniel, Analytic properties and monotonicity for generalized deriva­ criterion. tives. of scattering and inverse scattering for first order systems. Womack, James Michael, Stationary Howard University pairwise independent stochastic processes. Belair, Luc, Topics in the model theory of (1;0,0,0,0, 1,0,0) p-adic fields and spectra. Wu, Hsiu-fen, Sequential likelihood pro­ MATHEMATICS cedure for selecting a subset of size s Mayer, Laura L., Vaught's conjecture for containing the t best population ( s ;::: t). 0-minimal theories. Zekeria, Abdulkeni, Singularly perturbed Nesin, Hiiseyin Ali, Groups of finite second order differential equations with University of California, Morley rank. a discontinuous coefficient 'n a Hilbert Santa Cruz Sahi, Siddhartha, Spherical unitary rep­ space. (1;1,0,0,0,0,0,0) resentations of general linear groups over MATHEMATICS local fields. FLORIDA Scaramuzzi, Roberto G., Unitary repre­ Metzen, Gerhard, Semilinear boundary sentations of small rank of general linear Florida State University value problems in unbounded domains. groups. (4;0,3,0,0, 1,0,0) University of Southern California Torop, Robert, The homology of lattices generated by complex reflections. MATHEMATICS AND (2;2,0,0,0,0,0,0) COMPUTER SCIENCE Wickerhauser, Mladen Victor, Nonlinear MATHEMATif'q evolutions of the heat operator. Lee, Sang Myung (David), A numberical Chi, Ta-min, Automor;.'lisms of PI­ STATISTICS and analytical study of drag on a sphere algebras. in Oseen 's approximation. Au, Siu-tong, Estimation of a change­ Poffald, Esteban Ivan, Second order point. STATISTICS differential equations associated ·with ac­ cretive operators in Banach space. Carlstein, Edward G., Asymptotic nor­ Chan, Wai Tat, Partial orderings, with mality and variance estimation for a applications to reliability. COLORADO general statistic from a stationary process. Guess, Frank Mitchell, Testing whether mean residual life changes trend. DELAWARE Colorado State University Schell, Michael Joseph, An increasing (2;0,2,0,0,0,0,0) University of Delaware failure rate approach to conservative low dose extrapolation. STATISTICS (2;0,1,0,1,0,0,0) Abdulal, Khaled I., On density estima- MATHEMATICAL SCIENCES University of Florida tion. Meier, Kathleen Susan, A statistical (9;1,7,0,0,1,0,0) Wang, Antonia Chien-Chun, Distribution procedure for fitting Markov-modulated MATHEMATICS of quadratic forms in Gaussian processes. Poisson processes. Chang, Sung Kag, Riccati equations Saccucci, Michael Stephen, The effect of University of Colorado for nonsymmetric and nondissipative variance-inflated outliers on least squares 2 (1;1,0,0,0,0,0,0) and ridge regression. hyperbolic systems with L -boundary MATHEMATICS controls. DISTRlCT OF COLUMBIA Kurihara, Eiji, Essential families, map­ Eberly, David, Two problems of the pings in dimension theory and hereditarily type ~u + Af(u) = 0 where f(u) grows American University infinite-dimensional spaces. exponentially. (2;0,0,0,0,1,1,0) STATISTICS University of Denver MATHEMATICS, STATISTICS (1;0,0,1,0,0,0,0) AND COMPUTER SCIENCE Bumrungsup, Chinnaphong, Parameter­ free design and confidence regions for MATHEMATICS AND Bath, Barbara Blake, The effect of nonlinear models. COMPUTER SCIENCE the computational ability of children Daley, Richard, Nonparametric com­ Blumer, Janet Andrea, Algorithms for with acute lymphocytic leukemia due parison of slopes of regression lines. the DAWG and related structures. to prophylactic treatment of the central nervous system. Lai, Pan-Yu, Some new results on two simple time series model-prediction University of Northern Colorado Booker, T. Hoy, Singular value decom­ coverage for AR( 1) and model building (2;0,2,0,0,0,0,0) position using a Jacobi algorithm with an for jittery cosine waves. unbound angle of rotation. MATHEMATICS AND APPLIED Mullenix, Paul, Testing uniformity on the STATISTICS George Washington University hypersphere. Hodges, DeWayne Lee, The relation­ (5;0,5,0,0,0,0,0) Perkins, Laura Lynn, Bivariate symmetry ship between sample size and statistical STATISTICS/COMPUTER AND INFOR­ tests with censored data. significance in published studies. MATION SYSTEMS Piepel, Gregory Frank, Models and designs for mixture experiments when Moore, Alan D., A comparison of multiple Belcher, Gary Paul, Development ofMSE the response depends on the total amount. linear regression and structural equation estimates and confidence intervals when models in the analysis of selected school large proportions of the population are Wijesinha, Mane!, Design of experiments achievement-related variables. sampled. for multiresponse models.

776 University of Miami IDAHO Barer, Steven Mitchell, Bifurcation (2;2,0,0,0,0,0,0) analysis of neuron models. Idaho State University Chan, Joseph Oh-Piu, Second derivatives MATHEMATICS AND (3;1,0,0,0,0,0,2) COMPUTER SCIENCE of secondary characteristic classes. MATHEMATICS Meehan, James Michael, The instruc­ Cuervo, Maria Teresa, Properties of tional use of computer simulation of atriodic hereditarily unicoherent continua. Lauder, Donnald Hall, Estimation of random variables. Peyrovian, M. Reza, Maximal compact parameters of a linear model with auto Winker, Steven Karl, Quandles, knot subgroups in locally compact groups. correlation. invariants, and the N-fold branched cover. Mesri, Bahman, Orthogonality in normed University of South Florida linear spaces. University of lliinois, (4;4,0,0,0,0,0,0) Odegard, Barbara Jean, The evaluation Urbana-Champaign MATHEMATICS of the b'variate normal distribution in­ (18;10,1,0,0, 7,0,0) Abbas, Yousef Hasan, On fundamental tegral. MATHEMATICS sets over a finite field. Challener, David Carroll, Convergence Chattopadhyay, Rita, On some problems ll..LINOIS properties of the eigen function expansion in the theo,..J on non-homogeneous Markov of the biharmonic equation on rectangular chains. Illinois State U Diversity and semi-infinite strips. Craig, Jessica, Functional evolution equa­ (1;0,0,0,0,0,1,0) Chang, Li Fung, An information-theoretic tions involving T -accretive and T­ MATHEMATICS study of ratio-threshold antijam tech­ Lipschitz operators in banach lattices. niques. Bogacz, Margaret M., An intuitive ap­ Dannon, Victor C., The generation of an proach to understanding calculus concepts Crabtree, James Claude, First exit evolution operator in a Banach lattice. in business applications using probability time through curvilinear boundaries for theory. stochastic sequences. GEORGIA Currier, Robert John, Isometric immer­ Northwestern University sions and embeddings of nonnegatively Georgia Institute of Technology (8;6,0,0,0,2,0,0) curved hypersurfaces in hyperbolic space. (2;0,0,0,0,2,0,0) Filaseta, Michael Anthony, Topics in MATHEMATICS MATHEMATICS combinatorial number theory. Cohen, Sara, A free boundary problem in Gary, James Daniel, On the supremum Ervin, Vincent J., Group analysis of the lubrication theory. pellet fusion process. of the counting function for the A values de Rezende, Ketty, Smale flows on the of meromorphic functions. Herndon, John A., Limit periodicity of three-sphere. sequences defined by certain recurrence Hashimi, Jamil Rasool, On certain Frank, George Nelson, Templates, maximal operators on classes, 0 relations and Julia sets. HP branched one-manifolds, and laminations. p 1. University of Georgia Hinson, Edward Kuell, On unimodular Juhlin, Kenton Duane, Sequential and (3;1,2,0,0,0,0,0) vectors over commutative rings. non-sequential confidence intervals with Kulich, James, Homotopy models for guaranteed coverage probability and beta­ MATHEMATICS desuspensions. protection. Abubucker, C. P., Stopping times in Von Laubenbacher, Reinhard, Generalized Kan, Ittai, Strange attractors of uniform Neumann algebra with applications to Mayer- Vietoris sequences and the al­ flows. Martingales and Amarts. gebraic K -theory of Dedekind-like rings. Lindsay, Peter Alexander, Alternative STATISTICS Shick, Paul L., Periodic phenomena in and omega-type tutoring acceptors. Mithongtae, Jirawan Sirichote, Selection the classical Adams spectral sequence. O'Neil, Kevin Anthony, Stationary of the best exponential population. Trembinska, Antoinette, Variations on configurations of point vortices. Mithongtae, Uechai, Interval estimation Carlson's theorem. Somer, Lawrence Eric, The divisibility of requirements in input-output analysis. and modular properties of kth-order linear University of Chicago recurrences over the ring of integers of (6;4,1,0,0,1,0,0) HAWAll an algebraic number field with respect to MATHEMATICS prime ideals. University of Hawaii Albert, John Paul, On the stability of Uno, Katsuhiro, Generalized Clifford (6;2,1,0,0,0,0,3) solitary waves and the decay of small­ theory. Wu, Jinn-Wen, Exponential decay for the MATHEMATICS amplitude waves in non-linear dispersive systems. Saints-Venant principle. Arakaki, Gary K., Complexity of sorting and related problems. Costenoble, Steven R., Equivariant THEORETICAL AND APPLIED cobordism and K-theory. MECHANICS Harrison, Thomas A., If P is a nontrivial modular variety of lattices and V is a Parish, James Lindsey, Maximal isotropy Chien, Chi-Hui, Further research on wire nonmodular variety of lattices such that divisors on abelian varieties. rope. V o P is a variety, then V is the variety Rusin, David John, The cohomology of Chim, Edwin Siu-Man, Tensile .fatigue of all lattices. groups generated by involutions. damage and degradation of random short­ fiber SMC composites. Pickering, Douglas A., Minimal non­ Witte, David Slocumb, Measurable Arguesian lattices. isomorphisms of unipotent translations Hoger, Anne G., On residual stress in an elastic body. Sheung, Kwok Hay Julian, On the on homogeneous spaces. Stango, Robert James, Process-induced preduals of certain operator algebras. STATISTICS viscoelastic stress and deformation in PUBLIC HEALTH SCIENCES Karrison, Theodore, Restricted mean life composite laminates. Islam, M. Ataharul, A new method of with adjustment for covariates. INDIANA constructing increment-decrement life table University of Dlinois, Chicago with application to analysis of nuptiality (5;3,0,0,0,1,1,0) Indiana University and fertility. (6;4,0,0,0,2,0,0) Suleman, Mahammad, Epidemiological MATHEMATICS, STATISTICS AND and parasitological studies to evaluate the COMPUTER SCIENCE MATHEMATICS effectiveness of malarial control in small Ahlbrandt, Gisela E., Totally categorical Frohman, Charles D., One-sided incom­ villages of Punjab, Pakistan. structures of modular type. pressible surfaces in Seifert fiber spaces.

777 Herrmann, Joseph Michael, An Treanor, Mary T., Isomorphisms of KANSAS asymptotic analysis of an interface crack orthogonal groups in characteristic 2. within finite elasticity. Kansas State University (2;0,1,0,0,0,1,0) McGuire, Paul Joseph, Essentially nor­ IOWA mal subnormal operators and related MATHEMATICS topics. Namazi, Javad, On a singular integral. Iowa State University Ewing, David Eugene, A study of student 15 ,0,0,2,0,0) cognitive processes with respect to selected Rammaha, Mohammad Ahmad, On (19;2, albegra I word problems. non-linear Cauchy problems. MATHEMATICS Russo, Paula A., Boundary behavior of STATISTICS DeAlba, L uz Maria, A characteriza­ holomorphic functions in the unit ball of tion of semi-crossed products of finite­ Johnston, Denise Farha, Likelihood en. ratio and optimal rank test procedures dimensional c* -algebras. Purdue University for populations with linearly related Hoefiin, David Arthur, Oscillations of parameters. (17;3,4,0,3,0,1,6) nonlinear feedback systems which contain INDUSTRIAL ENGINEERING tightly coupled subsystems in cascade. KENTUCKY Chu, Chi-Chung, An adaptive decision Johnson, Jean Thomas, Ergodic making methodology for material handling properties of nonhomogenous, continuous­ University of Kentucky equipment in a computer integrated time Markov chains. (2;1,1,0,0,0,0,0) Krenz, Gary Steven, On the stability manufacturing system. MATHEMATICS Fisher, Edward Lynn, Knowledge-based in oscillations in a class of nonlinear facilities design. feedback systems containing numerator Pervine, Robert Howard, Ic(R) and other analytic extensions of Hwang, Sheue-Ling, Human supervisory dynamics. ideals related to the a commutative ring. performance in flexible manufacturing STATISTICS systems. STATISTICS stochas­ Kincaid, Rex Kevin, The location of Arnold, Robert James, Optimal tic paths. Tong, Lee-Ing, Inference in the simple central structures in graphs. linear regression model with one-fold Chang, Stephen Fu-Chung, Error-free Leemis, Lawrence Mark, Stochastic nested-error structure. lifetimes: A general model. computations in solution of linear systems and linear programming problems. Thuruthickara, John Chandy, Studies in LOUISIANA Multicriteria scheduling problems. de Pareja, Gilda Piaggio, Fitting a Venugopal, Raghunath, Thermal effects logistic curve to population size data. Louisiana State University, on the accuracy of numerically controlled Guerrero, Margarita F., Optimal Baton Rouge machine tools. confidence bounds. (3;3,0,0,0,0,0,0) Jobe, John Marcus, Error rates for Wu, Herng-Liang, Computer-aided MATHEMATICS configuration of flexible manufacturing Poisson process discrimination. systems. Kim, Byung Chun, A conjugate gradient Foreman, David Litton, Some results algorithm for analysis of variance com­ about value sets of quadratic forms over MATHEMATICS putations. fields. Hettling, Karl, On K2 of rings of integers Bagga, Kunwarjit Singh, Some structural Lee, Moun-Shen (Carl), Constrained of totally real number fields. properties of bipartite tournaments. optimal designs. Bautista, Maurino, A nonlinear approach Sullivan, Fred, Ordered models for the Martin, Cindy Lynn, Applications of the to inverse scattering by an acoustically lambda calculus. distance measures between the prior and soft obstacle. posterior distributions. Tulane University Carlson, James Wayne, Weighted com­ Mazloum, Reda Ibrahim, Admissibility (1;0,0,0,0,1,0,0) position operators on 1P in choosing between experiments with MATHEMATICS Hu, Shaing, Representations and embed­ applications. dings on weakly inverse semi-groups. McGovern, Paul Gerard, Two statistical Verosky, John, Applications of the formal Ozaydin, Murad, An integer invariant of analysis procedures applied to multivariate variational calculus to the equations of a group action. smoking cessation data. fluid dynamics. STATISTICS Miazaki, Edina Shisue, Estimation for University of Southwestern Louisiana Liang, TaChen, Some contributions to time series subject to the error of rotation ( 4;0,4,0,0,0,0,0) sampling. empirical Bayes, sequential and locally MATHEMATICS AND STATISTICS optimal subset selection rules. Ostrouchov, George, Large sparse least Ayeni, Babatunde J., The empirical Shyr, Jing-Yun, Comparative precisions squares computations. characteristic function estimation ap­ in linear structural relationships. Park, Byung Sul, N-person simple games and n-component reliability structures. proach in a mixture of two normal Whittinghill, Dexter C., III, Block distributions. designs: General optimality results with van Schaik, Jan William, Bradley­ Cascio, Grace C., Comparisons of es­ applications to situations where balanced Terry models for paired comparisons timators of the fraction defective in the designs do not exist. incorporating judge variability. normal distribution. Woods, Anthony Keith, Two locus Wilson, Jeffrey Rupert, Statistical Neube, Matoteng, Some new quality haploid populations with unequal recom­ methods for frequency data from complex control procedures. bination rates. sampling schemes. Tuprah, K wami, Dispersion quality con­ University of Notre Dame University of Iowa trol procedures. (3;3,0,0,0,0,0,0) (2;2,0,0,0,0,0,0) MARYLAND MATHEMATICS MATHEMATICS Kreuzman, Mary Joan, Local properties Boyle, Jeffrey Allan, Knotted surfaces in Johns Hopkins University and covering spaces of parabolic the four-sphere. (11;5,2,0,3,0,0,1) manifolds. of high Mazur, Mark Steven, The 2-adic Schur Lien, Magnhild, Construction BIOSTATISTICS index using modular and integral repre­ dimensional knot groups from classical Huster, William J., A model of multi­ groups. sentation theory. knot variate survival data.

778 MATHEMATICAL SCIENCES Pearn, Wen Lea, Capacitated Chinese Arsenis, Spyros Panagis, Towards a Bennett, Bart Emil, Modeling and postman problem. statistical analysis of genetic sequences analysis of a two-level production schedul­ Toll, Charles Hansen, A multiplica­ data with particular reference to protein ing problem. tive asymptotic for the prime geodesic sequences. Cheung, Albert K. T., Network optimiza­ theorem. Berman, Piotr, The expressive power of tion in ecosystem development analysis. Xu, Weixuan, Quadratic minimal span­ deterministic conte~-free dynamic logic. Choudhury, Japobrata, Sequential fixed­ ning tree problem and related topics. Boyack, Stephen Wayne, The robustness width confidence intervals based on of combinatorial measures of Boolean MASSACHUSETTS generalized order statistics, and a study matrix complexity. of generalized Hodges-Lehmann location Bretherton, Christopher Stephen, An Boston University analytic theory of moist convection. estimators. (2;0,2,0,0,0,0,0) Hong, Yoo Pyo, Consimilarity: Theory MATHEMATICS Clemens, Laura Elizabeth, An applica­ and applications. tion of the Malliavin calculus to infinite Won, Eun Sang, Algorithms for ordinal Beiser, Alexa, Moment tests of nor- dimensional diffusions. two-person games. mality applied to first order autoregressive Coley, Raymond Alan, Proiective dimen­ processes. sion of BP .BG for finite groups. MATHEMATICS Kezim, Boualen, On changes in the mean Devinatz, Ethan Sander, A nilpotence Menn, Stephen Philip, Total foliations on of a sequence of auto correlated random theorem in stable homotopy theory. 3-manifolds and the geometry of spaces variables. Franzblau, Deborah Sharon, Geometric of coframefields. covering and partitioning. Nakos, George, On the Brown-Peterson Brandeis University (7;7,0,0,0,0,0,0) Fu, Joseph Howland Guthrie, 'I'u.bular homology of certain classifying spaces. neighborhoods of planar sets. Nelan, Cornelius Patrick, Jr., Unstable MATHEMATICS Grant, David Ross, Theta functions and BP-operations and immersions of real Ascenzi, Maria-Grazia, The restricted division points on abelian varieties of proiective spaces. tangent bundle. dimension two. Svirsky, Janet Burstein, On the class Cutkosky, Steven, Numerically effective Haiman, Mark David, The theory of numbers of imaginary quadratic fields. divisors on algebraic varieties. linear lattices. Svirsky, Roman, Potentials producing Lejarraga, Pablo, The moduli of rational Hammond, Janice H., Solving asymmetric mazimally sharp resonances. elliptic surfaces. variational inequality problems and sys­ University of Maryland, Baltimore Luo, Zhaohua, Kodaira dimension of tems of equations with generalized non­ (1;0,0,0,0,1,0,0) algebraic function fields. linear programming algorithms. McDaniel, Andrew, Lie algebras repre­ Hefez, Abramo, Duality for proiective MATHEMATICS AND COMPUTER sentation and Toda lattices. varieties. SCIENCE Serrano-Garcia, Fernando, Surfaces hav­ Intissar, Allmed, On the distribution of Becker, Arthur H., Jr., Optimal adaptive ing a hyperplane section with a special the scattering poles for the Schrodinger control for Markov chains and auto pencil. equation in even dimensional spaces Rn. regressive moving average processes. Smolinsky, Lawrence, Double disk knots Kim, Don Yoon, A robust estimator of University of Maryland, and link invariants. location using an adaptive spline model. College Park Harvard University Lander, Julian Charles, Area-minimizing (14;4,0,0,0,9,0,1) (10;10,0,0,0,0,0,0) integral currents with boundaries in­ variant under polar actions. MATHEMATICS MATHEMATICS Nemchenok, Jacob Mark, Fourier Banerjee, Uday, Approximation of eigen­ Cheung, Wing-Sum, On higher order of coefficients of modular forms and Gaus­ values of differential equations with rough conservation laws. sian sums. coefficients. Cho, Koji, Postitivity of the curvature of O'Connor, Mary Geraldine, Randomness Chen, Ming-san, Hopf bifurcation of the Weil-Petersson metric on the moduli within a computationally restricted en­ Beck's problem. space of stable vector bundles. vironment. Colonna, Flavia, Block and normal Forman, Robin, Jilunctional determinants Orloff, Jeremy Michael, Limit formulas functions. and applications to geometry. and Riesz potentials for orbital integrals Gui, Wenzhuang, The h-p version of Kuhn, Robert, On the canonical closure on symmetric spaces. finite element method for one-dimensional of the universal elliptic curve over Xt(n). Scrimshaw, Nevin Baker, Fine structures problems. Laks, Mitchell, On the characters of the and the power set axiom. Guo, Benqi, The h-p version of the finite representations of division algebras over Simanca Perez, Santiago Ramon, Mixed element in two-dimensions-mathematical a weak field . elliptic boundary value problems. McMullen, Curt, Families of rational theory and computational experience. Stembridge, John Reese, Com- maps and iterative root-finding algo­ Kinsey, Laura Christine, Pseudoisotopics binatorial decomvositions of characters rithms. and submersions of a compact manifold ofSL(n,C). to the circle. Mirollo, Renato, Rank conditions on sub­ Vatan, Pirooz, Max-infinitely divisible and varieties of Grassmannians. Lee, Sungyun Lee, Product formulas for max-stable laws on infinite dimensional volumes of tubes and Chern's kinematic Pantazis, Stefanos, Prym varieties and spaces. formulas. the geodesic flow on SO(n). Vayl, Vladimir, Systems of postulates of Reider, Igor, Bounds on irregularity of Li, Chun Wah, Almost sure stability, op­ Gentzen style for set theory. timal control and scheduling of stochastic surfaces of general type. Worley, Dale Raymond, A theory of systems with point process coefficients. Spivakovsky, Mark, Sandwiched sin­ shifted Young tableaux. Moorish, Kathleen, A model of flow in gularities and the Nash resolution for the renal proximal tubule. surfaces. Wu, Eleanor, The a-degrees of unso~ vability: Global results. Nestor, John Jay, ill, Uniform asymptotic Massachusetts Institute of approximations of solutions of second Technology Northeastern University order linear differential equations with a (27;15,2,4,1,1,0,4) (3;2,0,0,1,0,0,0) simple turning point and a simple pole. O'Connor, Regina Kesler, An iterative MATHEMATICS MATHEMATICS method for determining periodic solutions Arnold, Friedemann, Automorphisms of Miri, Abderrahim, Artin modules having to dynamical systems possessing a first fields of algebraic functions in one ememal Hilbert series: Compressed integral. variable. modules.

779 Pavlicek, Glenn H., The deviations of Khajeh-Khalili, Parviz, Non-linear dis­ Shelton, Chrispian Ellis, Regular modules local n:ngs. sipative wave equation. for subgroups of solvable groups. Wang, Ding-!, The channel assignment Meerschaert, Mark Marvin, Multivari­ Shemesh, Meir, Clustering and weak problem and closed neighborhood contain­ able domains of attraction and regular convergence of a sequence of stochastic ment graphs. variation. processes. Ortland, David Arthur, Moduli of finite STATISTICS MICIDGAN point sets in projective space. Bedrick, Edward John, Analysis of Slaminka, Edward Eugene, A Brouwer categorical data from clustered samples. Miehigan State University translation theorem for free homeomor­ Ho, Siu Chuen, Small sample inference (3;0,3,0,0,0,0,0) phisms. for the Bingham distribution. Westwood, Derek John, On the structure STATISTICS AND PROBABILITY of the predual of various operator algebras. Chari, Ravi T., Weak covergence of MISSOURI distribution-valued semimartingales and STATISTICS associated SDE 's. Bednarz, David, Open ended tests of St. Louis University Godbole, Anant P., Strong laws of large invariant hypothesis. (1;1,0,0,0,0,0,0) numbers and laws of the iterated logarithm Coffey, Mary Patricia, A categorical MATHEMATICS AND COMPUTER in Banach spaces. model with random effects and its estima- SciENCE Merkle, Milan J., Infinitely divisible tion by integrated maximum likelihood. Azarian, Mohammad Khan, Near Frat­ measures on multi-Hilbertien spaces and Kim, Jai Young, Simultaneous estimation tini subgroups of ammalgamated free a Levy-Ito decomposition. of multiple Poisson parameters under products of groups. weighted squared error loss. University of Michigan, Ann Arbor Lenk, Peter, Bayesian nonparametric University of Missouri, Columbia (25;8,10,0,5,0,0,2) predictive distributions. (3;1,2,0,0,0,0,0) BIOSTATISTICS MATHEMATICS Wayne State University Belle, Steven H., Analysis of dependent (2;0,2,0,0,0,0,0) Allison, Dean Edwin, Lorentzian warped right-censored data. MATHEMATICS products and static space-times. Gimotty, Phyllis Ann, Goodness-of-fit STATISTICS chi-square tests using imputed data. Alyass, Kussiy K., Asymptotic distribu­ Beji, Mohammad Ali, Evidental approach Perry, Barbara Holland, Case-control tion of the quadratic nonns of the devia­ to hypothesis testing. sampling for the Coz regression model. tion of orthogonal series type density Boyle, James P ., Constrained optimisation Schooley, Gordon Leroy, Evaluation estimates. in Hilbert space with applications to of statistical procedures for analyzing Ho, Hwai-Chung, Limit theorems for non­ restricted cubic splines. ordered response categorical data with linear functions of a stationary Gaussian small sample sizes. process. Washington University Steiner, Richard Paul, A counting process Western Michigan University (5;1,0,0,0,0,0,4) approach to the Coz proportional hazards (1;0,0,0,0,0,0,1) MATHEMATICS regression model with covariate errors. MATHEMATICS Han, Yongsheng, Certain Hardy-type INDUSTRIAL AND OPERATIONS spaces that can be characterised by ENGINEERING Ralm, Joan Marie, On the genus of a block design. maximal functions and variations of the Al-Yahya, Yahya, Matching and covering square functions. algorithms. MINNESOTA SYSTEMS SCIENCE AND MATHEMATICS Brown, Donald, A justification for cross­ Chen, Yi-Long, Nonlinear feedback and entropy minimisation with applications to University of Minnesota, reliability and risk assessment. computer control of robot anns. Minneapolis Huang, Peiqing, Emergency control in Chung, Min K., Development of a statis­ (12;3,2,0,0,1,0,6) tical methodology for improved analysis blanket viability crisis. of workplace injuries. BIOMETRY Lu, Keh-Wen, A textured model and its Goldberg, Jeffrey Bruce, The modular Church, Timothy Robert, Biometric uses in reactive power management and design problem with linear separable side design and analysis in trials of mass control. constraints: Heuristics and applications. screening for chronic disease. Zhou, Zheng, Feedback synthesis of Higle, Julia Lynne, Detenninistic equiv­ Glaser, John, An investigation of the s'ngular systems-A geometric approach. ·alence in stochastic infinite horizon prob­ relationship between the introduction of lems. a computer system and coordination in NEW HAMPSHrn.E Partovi, Mohammad, A study of health care organisations. Dartmouth College degeneracy in the simplez algorithm for Neaton, James Dennis, The use of the (2;2,0,0,0,0,0,0) linear programming and network flow logistic model in the design of intervention problems. studies. MATHEMATICS AND COMPUTER SCIENCE MATHEMATICS Smith, Judy, Sample size detennination in studies of etiologic fraction. Beaudoin, Robert Emile, On uncountable Aksoy, Asuman Giiven, Appraxim.ation trees and linear orders. schemes, related s-numbers and applica­ MATHEMATICS Henrion, Claudia Andrea, Subtle ideas tions. Baeten, Josephus Cornelius Maria, Fil­ on subtle ideals. Clark, Curtis, An approach to graph ters and ultrajilters over definable subsets achievement games: Ultimately economi­ of admissible ordinals. NEW JERSEY cal graphs. Chihara, Laura Mariko, Applications Cochrane, Todd Eugene, Small solutions of the Askey-Wilson polynomials to Prineeton University of congruences. association schemes. (10;6,2,0,0,0,0,2) Dunn, Gerald Joseph, Uniqueness of n­ McLeod, Kevin Bryce, Uniqueness of fold delooping machines. positive radial solutions of semi-linear MATHEMATICS Herron, David Alan, Confonnally in­ elliptic equations in n-space. Buss, Samuel, Bounded arithmetic. variant metrics and the geometry of Ricou, Manuel Paul DeOliveira, Energy, Feit, Paul, On the poles and the analyticity uniform domains. entropy and the laws of thennodynamics. of Eisenstein series.

780 Goroff, Daniel, A variational study of Jorge del Carmen, Maria, Perturbation Shi, An-Jen, Optimum penetration levels twist maps. solution of a non-linear boundary value of wind farms. Levy, Silvio Vieira, Critically finite problem arising in connection with the Zhang, Zhen, Optimum diversity source rational maps. earth's gravitational field. coding. Pichardo-Maya, Agustin, Brownian mo­ Pati, Vishwambhar, L 2-cohomology of BIOMETRICS algebraic varieties. tion in random environments. Kremers, Walter Karl, The statistical Saper, Leslie, L2 -cohomology and inter­ NEW YORK analysis of sum-quota samphng. section homology of certain algebraic Skalski, John Raymond, Use of capture varieties with isolated singularities. Adelphi University data to quantify change and test for effects Sogge, Christopher, Oscillatory integrals (2;1,0,0,0,1,0,0) on the abundance of wild populations. and spherical harmonics. MATHEMATICS Stenonses, Berit, Envelopes of holomor­ MATHEMATICS AND COMPUTER phy. SCIENCE Brady, Sheryl Silibovsky, Recursive topology in Euclidean space. STATISTICS Eswarathasan, Arulappah, Densities of some sequences in algebraic number fields. Yang, Wei-Shih, The Simon-Lieb in­ Amaratunga, Dhammika Jayanath, equality for the ¢4 -theory in two dimen­ Pushing back regression coeificient:J and Zand, Manoucher, Some notes on conser­ vation laws. sions. evaluating performance via orthogonal samples. CUNY, Graduate Center New York University, Mendozo, Carlos E., Smoothing direc- (3;3,0,0,0,0,0,0) Courant Institute tional data. (12;8,0,0,0,4,0,0) MATHEMATICS MATHEMATICS Rutgers University, New Brunswick Rywkin, Richard J. F., Applications of (9;6,2,0,0,0,0,1) the stationary phase to solution of the Anjilvel, Satish, Isometric Volterra operators. MATHEMATICS Helmholtz equation in exterior domains. Chou, Mo-Hong, A numerical method for Cheng, Yungchen, Hopf algebras with Sarkisian, Richard G., Wei! numbers and forms for varieties over finite fields. 2-D inviscid incompressible flow past an antipodes of finite orders. inclined plate. Greenbaum, Nicholas Neil, Three­ Weld, Kathryn, Computability of homotopy groups of nilpotent complexes. Datti, Pampanna, Long-time existence dimensional models of the Belousov­ of classical solutions to non-linear wave Zhabotinskii chemical reaction. Clarkson University equations in exterior domains. Hutson, Holmes Leroy, On zero­ (2;0,0,1,0,1,0,0) David, Florin, Reflections of singularities dimensional rings of quotients and the at a boundary for nonlinear equations. geometry of minimal primes. MATHEMATICS AND COMPUTER SCIENCE Davidoff, Giuliana, Statistical properties Martin, Gary Alan, Two classification of certain exponential sums. problems: Rank one structures which Al-Jaber, Ahmad, Combinatorial Golden, Kenneth, Bounds for effective coordinatize aleph-zero categorical aleph­ properties of heapsort. parameters of multicomponent media by zero stable structures; reducts of algebrai­ Osman, El-sayed M., The motion of analytic continuation. cally closed fields. damped Sine-Gordon kinks in the presence Guo, Maozheng, Limit theorems for Nash, John C. M., Result:J on bases in of thermal fluctuations. interacting particle systems. additive number theory. Kress, Michael Edward, Optimal iterative Pfister, Richard J., Spin representations Columbia University (8;7,1,0,0,0,0,0) techniques for simulation of plasma of A~l). reconnection. Raychaudhuri, Arundhati, Intersection STATISTICS Mio, Washington, Non-linearly equivalent assignments, T coloring, and powers of Baldursson, Fridrik Mar, Topics in representations of quatemionic 2-groups. graphs. singular stochastic control and optimal Moll, Victor H., Stability in the large STATISTICS stoppzng. for solitary wave solutions to McKean's Cox, Ross Mitchell, Stationary and nerve conduction caricature. Miceli, Robert John, Minimax estimation discounted control of diffusion processes. Riedel, Kurt, The spectrum of resistive of location parameters for distribution viscous magnetohydrodynamics. of random vectors with independent Zhang, Cunhui, Random walk and renewal theory. component:J. Schochet, Steven H., Initial-boundary­ Zheng, Zukang, Regression analysis with value problems for quasilinear symmetric Proskin, Howard, An admissibility hyperbolic systems, existence of solutions theorem with applications to the estima­ censored data. to the compressible Euler equations, and tion of the variance of the normal dis­ MATHEMATICS their incompressible limit. tribution. Arapura, Donn Verghese Biswajit, Threefolds with semipositive tangent Rensselaer Polytechnic Institute NEW MEXICO bundles. (5;0,0,0,1,4,0,0) Katz, Mikhail, Jung's theorem in complex New Mexico State University MATHEMATICAL SCIENCES projective geometry. (1;1,0,0,0,0,0,0) Bilazarian, Peter, Sensitivity of under­ Scattone, Francesco, Compactifications of water sound transmissions to sound-speed MATHEMATICAL SCIENCES moduli spaces for K3 surfaces. profile selection. Parsons, John Daniel, Rearranged maxi­ Zweibel, John, Transformations of some Bosworth, Kenneth W., A general method mal operators. first order linear systems of PDE 's. for the computation of best uniform norm University of New Mexico Cornell University approximations. (4;0,2,0,0,2,0,0) (8;2,2,0,0,4,0,0) Ech-Cherif, Ahmed, Rank-two and vari­ able bounds ellipsoid algorithms for convex MATHEMATICS AND STATISTICS APPLIED MATHEMATICS programming. Fountain, Robert Lewis, Systematic Castro, Jose Mildred, Equilibrium and Rogers, Edwin, Feedback stabilization of sampling in the presence of polynomial stability of bioeconomic models of renew­ Volterra integral equations. trends. able resources under diverse harvesting Rousseau, Thomas Harrison, Mathemati­ Jones, Rondall Eugene, Solving linear regimes. cal analysis of oceanic fronts and sloping systems arising in the solution of integral Chang, Chih, Solution concepts for n- bottoms on underwater sound transmis­ equations of the first kind. person cooperative games. sions.

781 SUNY at Albany MATHEMATICS University of North Carolina, {5;2,3,0,0,0,0,0) Carr, Rodney, Manifolds of positive scalar Chapel Hill MATHEMATICS AND STATISTICS curvature, Yang-Mills fields, the Kalusa­ {18;5,0,0,1,0,0,12) Klein model. BIOSTATISTICS Ali, Mirza, Test of equality of expected Dar, Aparna, Intersection R-torsion and values of positive definite quadratic forms. analytic torsion for pseduomanifolds. Brittain, Erica H., Determination of?­ Hurley, Susan, Tame and Galois Hopf Gao, Zhiyong, Applications of minimal values for a K -sample extension of the objects with normal bases. surfaces theory to topology and Rieman­ Kolmogorov-Smirnov procedure. Jiang, Jyh-Ming, Distributional properties nian geometry contructions of negatively Brooks, Gary, Incorporating historical of linear forms in a Dirichlet vector and Ricci curved manifolds. control information in bioassay testing applications. Heltai, Blaise, Involutions and torsion accounting for survival differences. Kabbaj, Saad, Identification of a sine subgoups of F'uchsian groups. Buck, RaYTUond Douglas, Product hazard wave perturbed by weakly stationary noise. Sengupta, Dipendra, On the cohomology models in carcinogenic risk assessment. Tesser, Steven Barry, On certain rep­ of Kleinian groups. Clemmer, Anne Fakler, Estimating in­ resentations of a generalized Clifford tracluster homogeneity in multistage algebra. Syracuse University samples. {1;0,0,0,0,0,1,0) SUNY at Binghamton Fairclough, Diane L., Mixed effects {4;2,1,1,0,0,0,0) MATHEMATICS model analyses of incomplete longitudinal Vatanavigkit, Surapon, A personalized pulmonary function measurements in MATHEMATICAL SCIENCES system of instruction in a mathematics children. Johnson, Robert A., Uniform inverse set course for Thai college students. Folsom, Ralph, Probability sample U­ convergence and inverse limits. statistics: Theory and applications for University of Rochester Kelly, Michael R., Minimizing the number complex sample designs. {3;3,0,0,0,0,0,0) of fixed points for self-maps of compact Kammerman, Lisa, Selected optimal surfaces. MATHEMATICS values for ITy in the unrelated question Miller, Russ, Pyramid computer algo­ Coffey, John Joseph, Uniformly dis­ randomized response model, ITy known. rithms. tributed D-sequences in ergodic theory. Kasica, Violette Anne, An analysis of Wender, Abraham, 'I'ypes of equilibria for Dorninijanni, Roberto, A resolvent es­ cancer mortality in North Carolina using non-deterministic economies. timate approach to a problem of scattering generalized Poisson modeling methods for theory in £2{Z). the classification of rare events. SUNY at Buft'alo Rochon, James, Inference from the {5;3,1,0,0,1,0,0) Miller, Michael J., On Rieff's conjecture and the geometry of polynomials. incomplete longitudinal design under a MATHEMATICS arma covariance structure. Nassar, Mostafa A., Ergodic measures NORTH CAROLINA Wilson, Steve, The estimation of recent levels of adult sibling mortality. and recurrent points in the Stone-Cech Duke University compactification of amenable semigroups. Yoshizawa, Carl Nobuo, Some tests of {2;1,0,0,0,1,0,0) Talebi, Nourollah, Aspects of the model symmetry. theory of logics with an infinitary MATHEMATICS Yuan, Yang Chyuan, Some aspects of quantifier. Hartz, David G., The fine structure of estimation and hypothesis testing for Tang, Yun, Nonlinear stability of vortex hyperarithmetic inductive definitions. generalized multivariate linear models. patches. Pitman, Eric Bruce, The flow of granular MATHEMATICS material in converging hoppers. STATISTICS Bourdon, Paul Stephen, Invariant sub­ Chakraborti, Subhabrata, A generaliza­ North Carolina State University, spaces for the shift operator on some tion of the control median test. Raleigh Hilbert spaces of analytic functions. Chao, Chern-Ching, On the number of {8;1,3,0,3,0,0,1) Masri, Mahmud llayyan, Compact com­ position operators on the Nevanlinna and excesses and last e:z:it over a boundary. OPERATIONS RESEARCH Smirnov classes. Gaytan-Iniestra, Juan, Two-phase algo- SUNY at Stony Brook Monn, David Robert, Regularity of {13;5,2,0,1,5,0,0) rithm for minimizing ma:z:imum functions. the complex Monge-Ampere equation for Pulat, Pakize Simin, Ma:z:imum flow radially symmetric functions of the unit APPLIED MATHEMATICS AND problem for generalized networks. STATISTICS ball. Sichona, Francis Joseph, A multi-stage Al-Towaiq, Mohammed, On a two-term Wilson, John Herman, Coding for a birth and death process in a random T -user binary adder channel. based on incomplete factorization of large enivronment. sparse systems. OPERATIONS RESEARCH AND STATISTICS Chen, Bee-Lian, Nonparametric regres­ SYSTEMS ANALYSIS Alwi, Nong, Peanut groups and their sion. Nickel, Ronald Harlan, A sequential Chen, Y"Ih-Ren, Stochastic scheduling. symbiotic relationship with rhizobium strains. quadratic programming algorithm for Driscoll, Michael A., Numerical methods solving large, sparse, nonlinear programs. Lee, Kay-O, Comparison of some succes­ for the solution of integral equations of sive occasions sampling schemes from mathematical physics. STATISTICS spatially correlated processes. Garcia, Maria, On the numerical solution Hsing, Tailen, Point processes associated McCutchan-Hise, Barbara, Design of nonlinear equations by homotopy with extreme value theory. efficiencies with planned and unplanned methods. unbalance for the estimation of heritability Kim, Chul, Continuum structure func­ in forestry. omo tions: modules, bounds, a:z:iomatization Richardson, Gary, Consistent estimators and reliability importance. in non-linear regression for a non­ Bowling Green State University Tang, Yong-Nian, Application of GPST compact parameter space. {1;1,0,0,0,0,0,0) algorithm to history matching. Smith, Luther Aubrey, The effects of MATHEMATICS AND STATISTICS Wang, Shyue-Liang, Numerical deter­ acid deposition on fresh water algae mination of the shape and size of e:z:terior and cyanobacteria: A simulation analysis Diny, Debra Ann, Bound graphs result­ and interior boundaries for the Helmholtz for Falls Lake, NC using CE-QUAL-R1 ing from certain digraphs and partially equation. model. ordered sets.

782 Case Western Reserve University QUANTITATIVE ANALYSIS PENNSYLVANIA (3;0,0,0,3,0,0,0) AND INFORMATION SYSTEMS Carnegie-Mellon University OPERATIONS RESEARCH Feinauer, Richard A., A mechanism for natural language access to data base. (5;1,4,0,0,0,0,0) Ho, Chin-Chih, Optimal inventory and replacement policy with production de­ Hall, Richard A., The clustered traveling STATISTICS pendent equipment deterioration. salesman problem. Dalzell, Catherine Jane, A statistical Lee, Chin-Kyooh, Improving and expand­ analysis of atom probe data. ing the role of D-optimality in experimen­ OKLAHOMA Gavasakar, Umesh K., A study of tal designs with emphasis on response education procedures by modelling the surfaces. Oklahoma State University errors in responses. Liang, Lung-Kuang, Some generaliza­ (7;0,7,0,0,0,0,0) Lee, Tzao-Lin, Modelling random convex tions and applications of thinning of point sets. processes-covariance analysis. STATISTICS Lim, Youngho, Performance analysis of integrated voice data networks. Kent State University Abdullatif, Dalal Abdulrazzak, An Sahlroot, Jon Todd, Performance evalua- (2;2,0,0,0,0,0,0) analysis for grouped survival data with split plot variance component models. tions of multiaccess network protocols. MATHEMATICAL SCIENCES Al-Mousawi, Jaffar Selman, Fixed-size Drexel University Barton, Thomas J., Bounded Reinhardt confidence regions for the mean vector of (1;1,0,0,0,0,0,0) domains in complex Banach spaces. a multinormal distribution. Chu, Larry Kah Bai, Summability Ekwo, Maurice Ene, Sequential estima­ MATHEMATICS AND methods based on the Riemann zeta tion for parameters of Pareto distribu­ COMPUTER SCIENCE function. tions. Fratini, Stephen Sylvester, Algorithms Hilton, George F., ill, Sequential and for a dynamic priority queue with two Ohio State University two-stage point estimation problems for types of customers. (13;9,3,0,0,0,0,1) negative exponential distributions. Lehigh University MATHEMATICS Shaarawy, Samir Moustafa, A Bayesian (2;1,0,0,1,0,0,0) Bauldry, William Charles, Orthogonal analysis of moving average processes. polynomials associated with exponential Vik, Gaute, Asymptotic results for stop­ MATHEMATICS weights. ping times based on U-statistics. Hakawati, Abdallah A., Interpolation Brackebusch, Ruth Elaine, James space Woldie, Mammo, Inverse Gaussian regres­ problems and Hilbert spaces of sequences. on general trees. sion models. Muganda, Godfrey Chamba, Optimality Brink, James Robert, The class field conditions for mixed constraint problems. University of Oklahoma tower for imaginary quadratic number Pennsylvania State University fields of type (3, 3). (1;0,1,0,0,0,0,0) (15;10,3,1,0,1,0,0) Frangos, Nicholas E., On convergence BIOSTATISTICS AND EPIDEMIOLOGY and regularity of vector-valued processes MATHEMATICS Cucchiara, Andrew Joseph, Linear indexed by directed sets. Aladro, Gerardo Jose, Some conse­ regression of the multiple additive ex­ Hong, Yiming, On the existence of perfect quences of the boundary behavior of ponential model. e-codes and tight 2e-designs in Hamming the Caratheodory and Kobayashi metrics schemes. and applications to normal holomorphic Ku, Jong-Min, Irreducible subquotients OREGON functions. of Verma modules over Kac-Moody Lie Bou Nader, Elham, Best approximation algebras. Oregon State University in spaces of continuously differentiable Narang, Kamal, The group of automor­ (4;2,1,0,0,1,0,0) functions. phisms of non-associative commutative Brackin, Stephen H., On Ramsey-type algebras associated with PSL(m, q)m 2:: MATHEMATICS theorems and their provability in weak 3. Keinert, Fritz, The divergent k-plane formal systems. Singer, Phyllis E., Kac-Moody algebras transform. Chen, Jiin-Chu, On a conjecture of with nonsymmetrical Carlan matrices. Kharab, Abdelwahab, A nonlinear free Lovasz and some results of chromatic Woldar, Andrew J., On the maximal boundary value problem. graph theory. subgroups of Lyon's group and existence O'Regan, Daniel J., Initial and boundary Dutko, Michael, Limit theorems for of a 3-dimensional faithful LyS-module value problems via topological methods. infinite um models in probability theory. over a field of characteristic 5. Gass, Michael David, Wreath product STATISTICS STATISTICS coverings involving syntactic transforma­ tion monoids. Chan, Wen Yaw, Optimal policies directed Limam, Mohammed, Simultaneous Golshan, Bahram, Higher order cohomol­ at reducing pest damage for a pest tolerance intervals in the linear regression ogy operations and desuspension of in­ predator. model. volutions. Harry, Diane Sue, A Markov model University of Oregon Kolitsch, Louis Worthy, Some analytic for Drugy response in patients with (5;5,0,0,0,0,0,0) and arithmetic properties of generalized osteoarthritis. Frobenius partitions. Qadri, Syed S., Classification of objects, MATHEMATICS Legrand, Mark Stephen, Coanalytic sets given their classification by a number of in the absence of analytic determinacy. classifiers. Ettlich, Sheryl Anne, Successor groups. Takche, Jean Halim, On the complexity Sen, Pali, A stochastic model for coupled Harper, James Dale, Analysis on hyper- of bilinear computations. enzyme system and parameter estimation groups. for the compartmental model. Judson, Thomas, Complete filtered Lie Udomkavanich, Patanee, Codes and algebras and the Spencer cohomology. inverse semigroups. University of Cincinnati Valente, Kenneth, The p-primes of a Weerakoon, Sunethra, An initial value (3;1,0,1,1,0,0,0) commutative ring. control problem for the burgers equation. MATHEMATICAL SCIENCES Willis, Linden, Invariance theory STATISTICS Kim, Yoobong, Some contributions to the of Riemannian geometry and the Gabbara, Sami, Nested and crossed theory of fuzzy measures and integrals. asymptotics of the heat equation. repeated measures models.

783 Hlynka, Myron, Optimality for a class Mcintire, Roland Scott, A new technique University of Tennessee of perishable inventory policies under for discussing the development of sin­ (1;0,0,0,1,0,0,0) stochastic demand. gularities in quasilinear hyperbolic PDE 's Tableman, Mara, Two-sample procedures with applications to a model problem in MANAGEMENT SCIENCE based on one-sample linear signed rank nonlinear thermoelasticity. Hooker, John N., Jr., Nonlinear network statistics. Nadler, Edmond Josef, Piecewise linear location models. approzimation on triangulations of a Temple University planar region. Vanderbilt University (3;0,3,0,0,0,0,0) Rocha, Carlos V., Generic properties and (1;0,0,0,0,1,0,0) STATISTICS bifurcation diagrams of scalar parabolic MATHEMATICS equations. Frederick, Partial lag Spline approxima­ Heyse, Joseph Shannon, Kathleen Marie, Convex sets, Barr, Thomas Harold, and partial process age-dependent autocorrelation support functions, Lemoine points, and tion for a problem in with autocorrelation for vector time series Steiner points with generalizations. population dynamics. applications. Sternberg, Natalja, Bound states of a Pigeon, Joseph George, Residual effect nonltnear hyperbolic wave equation. TEXAS designs for comparing treatments with a Tzavaras, Athanassios E., Shear band control. formation for materials exhibiting thermal North Texas State University Weideman, Carol A., Non-adaptive hy­ softening, strain hardentng and strain rate (2;2,0,0,0,0,0,0) pergeometric group testzng designs for at sensitivity. defectives. MATHEMATICS most two Zia, Lee Lynn, Parameter estimation of Pennsylvania techniques for two-dimensional transport Leavelle, Tommy L., The recipro­ University cal Dunford-Pettis and Radon-Nikodflm (1;1,0,0,0,0,0,0) equations with application to models of insect dispersal. properties in Banach spaces. MATHEMATICS Richardson, Walter Brown, Jr., Non­ MATHEMATICS Yetter, David Nelson, Aspects of synthetic linear boundary conditions in Sobolev Shepard, Allen D., A cellular description spaces. differential geometry. of the derived category of a stratified University of Pittsburgh space. Riee University (6;3,0,0,0,1,0,2) Zimmermann, Karl F., Subgroups of (6;0,1,0,0,5,0,0) generic formal groups. BIOSTATISTICS MATHEMATICAL SCIENCES Abdel-Aty, Fatma A., A multivariate SOUTH CAROLINA Bunch, David Samuel, Parameter estima­ statistical analysis of the risk of infection tion of probablistic choice models. in surgical wounds. Clemson University Celis, Maria Rosa, A trust region (5;1,3,0,0,1,0,0) Caplan, Richard J., A sequential Cusum strategy for nonlinear equality constrained monitoring procedure to detect sudden MATHEMATICAL SCIENCES optimization. departures from expected morbidity. Abernathy, Roger Ward, Multivariate Dean, Edward Jerome, A model trust region modification of inexact Newton's MATHEMATICS AND STATISTICS tests for goodness-of-fit. Domangue, Rickie James, On some method for nonlinear two point boundary Chou, So-Hsiang, A network-model for balanctng algorithms for the implementa­ value problems. two-fluid flow and its numerical solution. tion of robust sampling designs. Jee, James Rodney, A study of projection Kwak, Do Young, Norm estimates of Forney, Glenn Peter, Computing the pursuit methods. holomorphic functions ln the ball of en, Fourier transform of functions with Parks, Teresa Anne, Nonlinear pro­ in terms of their Taylor coefficients. compact support. gramming problems with variables that Shakhs, Adnan Abdulredha, Conditions Patch, Steven Curtis, Tests of goodness­ separate. under which a E #-space is a u -space. of-fit based on the empirical characteristic Woods, Daniel John, An interactive ap­ Wagner, Kathleen A., 0-refinability and function. proach for solving multi-objective op­ strict p-spaces. Schnibben, George Ernest, Jr., Polyno­ timization problems. mials and polynomial functions on infinite RHODE ISLAND algebraic extensions of finite fields and Southern Methodist University their related matrix algebras. (11;0,4,0,5,2,0,0) Brown University University of South Carolina MATHEMATICS (16;5,0,0,0,11,0,0) (1;1,0,0,0,0,0,0) Attili, Basem, Computation of high order APPLIED MATHEMATICS singular points and multiple shooting. MATHEMATICS AND STATISTICS Sun, Ren-ji, Caustics for dispersive waves: Anderson, Joyce Ellen, Estimating Optimal nonparametric Inoue, Hiroshi, Asymptotics of nonlinear Schrodinger projected images from a m=mum and stochastic con­ function estimation equation and its Riemann-Hilbert prob­ likelihood and a Bayesian point of view. sums of random vergence for weighted lems. Blazquez, Camilo Miguel, Homoclinic variables and random sets. orbits in parabolic differential equations. OPERATIONS RESEARCH TENNESSEE Boldrini, Jose Luiz, Is elasticity the Allen, Ellen Parker, Using two sequences proper asymptotic theory for materials of pure network problems to solve the with viscosity and capillarity? Memphis State University (2;0,2,0,0,0,0,0) multicommodity network flow problem. Dupuis, Paul Gilbert, Large deviations Chen, Berhord David, Forward network theorems for non-Markovian systems with MATHEMATICAL SCIENCES programming. applications to stochastic systems theory. Gastardo, Maria Teresa, A stochastic Farhangian, Keyvan, Networks with side of Fiagbedzi, Yawvi Aklasu, Stabilization model for carcinogenesis with special ap­ constraints: An LU factorization update a class of autonomous differential-delay plications to the initiation and promotion for the working basis inverse. systems. phenomena. Patty, Bruce Willard, The basis suppres­ Fusco, Giorgio, On mechanical systems Tabatabai, Mohammad A., Robust pro­ sion method for linear programs with with non-holonomic constraints. cedures for comparing several means and special structure excluded by an objective Lin, Xiao-Biao, Symbolic dynamics and testing for parallelism for several straight side column. transversal homoclinic orbits in functional lines under heteroscedasticity and non­ Bala, The equal flow problem. differential equations. normality. Shetty,

784 STATISTICS Melrose, Gordon, Triple trigonometric Forstneril\, Franc, Proper holomorphic Alassaf, Mohammad, A comparison of series and their application to mixed mappings in several complex variables. four variance component estimators sn boundary problems. Nievergelt, Yves, Radon transforms of rerrular group divisible partially balanced Mittal, Mukul, Estimating the parameters closed positive currents. 'ncomplete Bloch designs. of truncated distributions. Ostaszewski, Krzysztof Maciej James, Bonnego, Salvador, The economic University of VIrginia Henstock integration on the plane. geometric moving average X-bar charts. {3;0,0,0,0,2,0,1) Ray, Gary Alan, Relations between Lakshminarayanan, Mani Y., Estimation Mahler's measure and values of L-series. APPLIED MATHEMATICS in simple linear regression models when STATISTICS both variables are sv.bject to error. AND COMPUTER SCIENCE Shyu, Jyh-Cherng, Tolerance intervals for Flinn, Kelton Francis, Preconditioned Ossiander, Mina Egbert, Weak conver­ the double exponential distribution. conjugate gradient for the nonlinear shell gence and a law of the iterated logarithm equations. for processes indexed by points in a metric Texas A & M University Weidman, Scott Thomas, Mathematical space. (4;0,4,0,0,0,0,0) analysis of correlation in homogeneous Washington State University nucleation theory. STATISTICS {3;1,1,0,1,0,0,0) Baker, Joshua S., Conditional least MATHEMATICS MATHEMATICS squares estimation and design for Yin, Zhong, Qv.antum lattice systems continuo'IJ.B-time stochastic processes. and Markov semigroups on spin lattice Al-Saket, Amal Hikmat, An algorithm Green, John William, Variance com­ systems. with degeneracy resolution for solving ponents estimates and diagnostics. certain quadratic programming problems. Olson, David Ray, Residence time Virginia Commonwealth University Lee, Cheng-Shyong, Generalizations of moments of stochastic compartmental (4;0,4,0,0,0,0,0) the Lebedev-Milin inequalities. models with age-dependent and time­ BIOSTATISTICS Lee, Kwang Young, On theE and MY­ dependent rates. Dornseif, Bruce Edwin, Modelling asym­ optimality of block designs having unequal Saito, Tokuji, An application of stochastic metric quantal dose-response curves. block sizes. compartmental theory to modeling plant Elswick, Ronald K., The missing data growth and plant yield. problem as applied to the extended version WISCONSIN University of Texas, Arlington of the GMANOVA model. {2;0,0,1,0,0,0,1) Finman, Jeftrey S., Interval estimation University of Wisconsin, Madison for an odds ratio. {27;18,7,0,0,1,1,0) MATHEMATICS Gregg, Mary Hall, The use of multiple MATHEMATICS Cleveland, Frederick Hart, Finite correlation coefficients in the partially difference solutions of Maxwell's equations weighted GMANOVA. Burke, Maurice, The use of cov.n­ in three dimensions. terexample logic by adolescents. Virginia Polytechnic Institute Pandian, Maharaja C., Numerical studies Castillo-Chavez, Carlos, Linear and non­ of nonlinear systems and quasilinear and State University linear deterministic character-dependent boundary value problems with application {10;1,8,0,0,1,0,0) models with time delay in popu.lation to gas lubricating films. MATHEMATICS dynamcis. Chavey, Darrah Perry, Periodic tilings Ntantu, Ibula, The compact-open topology University of Texas, Austin and tilings by regu.lar polygons. on C{X). (4;3,1,0,0,0,0,0) Chin, William, Prime ideals in differential Tarnawski, Maciej, Asymptotic phase operator rings and crossed products. MATHEMATICS diagrams for lattice spin systems. Czitrom, Anne Veronica, D-optimal ex­ Farmer, William Michael, Length of STATISTICS perimental designs and alternative models proofs and unification theory. for quadratic blending with process vari­ Kim, Kang-Kyun, Nonparametric mu.lti­ Feldman, Alexander, Recursion theory in ables. variate two-sample tests based on empiri­ a partial order with greatest lower bound. Neidinger, Richard Dean, Properties of cal probability measures. Gunter, Carl A., Profinite solutions for Tauberian operators on Banach spaces. O'Gorman, Mary Ann, Outliers and recursive domain equations. Shirley, Frank Theodore, Regular and robust response surface designs. Hatziafratis, Telemachos E., Integral rep­ strongly 1r rerrular rings. Park, Changsoon, Nonparametric proce­ resentation formu.las on analytic varieties. Skora, Richard Kevin, Maps between dures for process control when the control Jacobs, Jonathan M., Unfoldings of surfaces. value is not specified. fixed points of one-dimensional dynamical Rashed, Dhafir, Designs for mu.ltiple com­ systems. UTAH parisons of control verBUS test treatments. Klingler, Lee, Modules over ZG, G a Shing, Chen-Chi, Structures and non-abelian group of order pq. University of Utah properties of repeated measv.rement Kwong, Ying-Chuen, Asymptotic be­ {2;0,0,0,0,1,0,1) designs. haviour of the plasma equation. Thattil, Raphel 0., Design and analysis MATHEMATICS Lee, Tien-you {Daniel), Some problems of intercropping experiments. in cardinal spline interpolation and Faltenbacher, Wolfgang, A numerical Walker, Esteban, Influence, colinearity, approximation. integral solution of a scattering problem and robust estimation in regression. in a hal/space. Neidhardt, Wayne L., The BGG resolu­ Wardrop, Daniel M., Optimality criteria tion, character and denominator for­ Rescorla, Kim L., Mu.ltivariate interpola­ applied to certain response surface mu.las, and related results for Kac-Moody tions. designs. algebras. Pritikin, Daniel, Extremal problems VffiGINIA WASHINGTON in graph homomorphisms and vertex Old Dominion University University of Washington identifications. {3;0,2,0,0,1,0,0) {6;5,0,0,0,0,0,1) Quinn, Declan P., Group-graded rings, differential operator rings and duality. MATHEMATICS MATHEMATICS Rebarber, Richard Lewis, Control of McKeon, James, Statistial calibration Bone, Terrence M., Qualitative stability holomorphic semigroups generated by a theory. properties of matrices. class of spectral operators.

785 Slavin, Charles Paul, Properties of power­ Seager, Suzanne Marie, A bound on the Universite Laval series coefficients of H 2( 1r +) functions rank of solvable primitive permutation (3;2,0,0,0,1,0,0) and related Poisson integrals with weights. groups. MATHEMATIQUES, STATISTIQUES ET Solomon, Wiremu, Limit theorems for Dalhousie University random measures with applications. ACTUARIAT (1;1,0,0,0,0,0,0) Tomaszewski, Boguslaw, Interpolation by Boudreau, Jean-Rene, Stationnarite pour Lipschitz holomorphic functions and inner MATHEMATICS, STATISTICS une classe de systimes aleatoires a maps that preserve measure. AND COMPUTING SCIENCE liaisons completes. Weiner, Daniel Charles, Limit theorems, Ward, Douglas Eric, Tangent cones, Fortin, Andre, Methodes d'elements finis regularity and moments for affine nor­ generalized subdifferential calculus and pour les equations de Navier-Stokes. malized sums of independent, identically optimization. Hebert, Michel, Sur la nature et !'existence distributed random vectors. des algebres libres. McMaster University STATISTICS (3;3,0,0,0,0,0,0) University of Alberta Chen, Chung, On a random level shift time series model. MATHEMATICAL SCIENCES (2;0,0,0,0,2,0,0) Cho, Sinsup, Robust model-free prediction Poole, David Gordon, Prime ideals and MATHEMATICS and control. localization in Noetherian-Ore extensions. Deng, Lih-Yuan, Statistical inference in Roddy, Michael Stewart, Varieties of So, Joseph Wai Hung, A study on some finite population sampling when auxiliary modular ortholattices. one-and two loci predator-prey interaction models. information is available. Torres de Squire, Maria Luisa, Amalgams Ferreiro, Osvaldo, Strategies for estimat­ of Il' and .f!l. Wolkowicz, Gail Susan Kohl, An analysis ing missing observations in time series. of mathematical models related to the Koschat, Martin Anselm, Simultaneous Queen's University chemostat. inference in linear regression models. (2;0,2,0,0,0,0,0) University of Calgary Tse, Siu-Keung, Estimation and ex­ MATHEMATICS AND STATISTICS perimental design for quantal response (1;0,0,0,0,0,0,1) Bayes and empirical models. Nebebe, Fassil, Bayes shrinkage estimates for regression MATHEMATICS AND STATISTICS Wincek, Michael, Estimation of coefficients, with application to WISC parameters of regression-time series El-Zahar, Mohamed Hamid, Three prob­ data. models with possibly nonconsecutive data. lems in graph theory and partially ordered Ross, William H., Measuring influence in sets. University of Wisconsin, Milwaukee nonlinear regression. (3;2,0,0,0,1,0,0) University of Waterloo Fraser University Simon (9;4,4,0,0,1,0,0) MATHEMATICAL SCIENCES (2;1,0,0,0,1,0,0) APPLIED MATHEMATICS Benzaid, Zoubir, Global null control­ MATHEMATICS lability of perturbed linear control systems. Kamran, Niky, Contributions to the Danielson, John Ernest, The r- Croitoro, Elena, Perturbations about a finite elastic inflation. study of the separation of variables and semicritical socle series of a module. wave Russ, Mary Elizabeth, Varieties of lattice symmetry operators for relativistic Marafino, John, Concerning boundary equations on curved space-time. behavior under conformal mappings. ordered groups. Universite de Montreal COMBINATORICS AND OPTIMIZATION WYOMING (6;2,3,0,0,1,0,0) Celmins, Uldis Alfred, On cubic graphs that have no edge 3-colouring. University of Wyoming MATHEMATIQUES ET STATISTIQUE Mahadev, Nadimpalli V. R., Stability (2;1,0,0,0,1,0,0) Colin, Dominique, L 'etude de tests numbers in structured graphs. asymptotiquement non parametriques en MATHEMATICS regression lineaire multiple. PURE MATHEMATICS Fausett, Laurene Van Camp, An analysis Dahel, Sahnoun, Estimation et injerence Blanton, George R., Jr., Disjoint groups of mathematical models of underground pour la moyenne d 'une loi multinormale of homeomorphisms on an open interval. coal gasification. avec information additionnelle. Riedel, Herbert Heinz Joachim, Existen­ STATISTICS Fournier, Richard, Quelques nouveaux resultats a propos de certaines classes de tially closed algebras and the Boolean Shorland, Michael D., The detection and product construction. correction of multi-variate outliers with fonctions univalentes. application in factor analysis. Froda, Sorana, Etude non parametrique STATISTICS AND ACTUARIAL SCIENCE de questions d'estimation et de tests Dewanji, Anup, Analysis of incomplete d'hypotheses relatives au probleme d'un CANADA life time data. echantillon. Ouansafi, Abdellatif, Methodes Ramsay, Colin Mark, Compound birth­ Carleton University death processes and the ruin problem of (5;4,1,0,0,0,0,0) d'approximation discontinue des problemes de commande optimale. risk theory. MATHEMATICS AND STATISTICS Tanguay, Monique, Variante continue Struthers, Cyntha Anne, Asymptotic Bleuer, Susana G., Confidence intervals d'un probl

786 Doctoral Degrees Conferred 1983-1984 Fluids and Plasmas: Geometry and Dynamics Supplementary List Jerrold E. Marsden. Editor The following entries supplement the list of thesis titles published in the The AMS-IMS-5/AM Joint Summer Research November 1984 Notices, pages 757-770, Conference on Fluids and Plasmas: Geometry and and in the March 1985 Notices, page Dynamics, held July 17 - 23. 1983, in Boulder. 184. Colorado, was a highly successful effort to foster interaction among people working on mathematical. FLORIDA numerical and physical aspects of fluid and plasma dynamics. The organizing committee. consisting of J. University of Florida Marsden (Chairman), P. Holmes and A. Majda, with (1;0,1,0,0,0,0,0) A. Chorin and A. Weinstein as advisors, selected 27 speakers whom they felt would help achieve this STATISTICS interaction; the result was a fine sense of Popovich, Edward, Nonparametric camaraderie, with the speakers making every effort to analysis of bivariate censored data. bridge communication gaps. Researchers using this book will be brought up to OREGON date on work being done in these areas. The three groups of contributors are listed below. University of Oregon (1;0,0,0,0,0,0,1) Part I. Geometric-Analytic Methods (Hamiltonian structures, perturbation theory MATHEMATICS and nonlinear stability by variational Alzamel, Ali, Best multipoint local *LP­ methods) approzimation. B. Boghosian R. Dewar Gerald Goldin Miroslav Grmela Darryl Holm Allan Kaufman Robert Littlejohn Jerrold Marsden Meinhard Mayer Richard Montgomery Philip Morrison Tudor Ratiu Alan Weinstein Part II. Analytic and Numerical Methods (contour dynamics, spectral methods, and functional analytic techniques) Tom Beale Robert Glassey Andrew Majda Robert Miller Peter Olver Harvey Segur Philippe Spalart Walter Strauss Multiple Trigonometric Sums Yieh-Hei Wan Stephen Wollman Norman Zabusky G. I. Arhipov, A. A. Karacuba and V. N. Cubarikov Part Ill. Bifurcation and Dynamical Systems (experimental and numerical methods, CONTENTS bifurcation theory, and chaos) Basic Notation John Crawford James Curry Introduction John Guckenheimer P. Holmes I. Theorem on the mean value D. McLaughlin J. Moloney II. Estimates for multiple trigonometric sums Alan Newell Jiirgen Scheurle Ill. Applications of the theory of multiple trigono­ Eric Siggia James Swift metric sums Harry Swinney E. Wayne 1980 Mathematics Subject Classifications: 10G10; 10815, 12C25 1980 Mathematics Subject Classifications: 58Fxx, 76Exx Proceedings of the Steklov Institute Contemporary Mathematics Volume 151, viii + 126 pages (soft cover) Volume 28, xvi + 448 pages (soft cover) List price$48, institutional member $38, List price $35, institutional member $28, individual member $29 individual member $21 ISBN 0-8218-3067-8; LC 82-18403 ISBN 0-8218-5028-8; LC 84-3011 Publication date: October 1982 Publication date: April 1984 To order, please specify STEKL0/151 N To order, please specify CONM/28N

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787 News and Announcements

Marcel Berger, IHES Director Institute for Retraining in Computer Science (IFRICS) Professor Marcel Berger of the University of Paris and the CNRS has assumed the position The IFRICS program was established in an effort of director of the Institut des Hautes Etudes to help meet the critical shortage of qualified Scientifiques (lliES) in Bures-sur-Yvette, France. college teachers of computer science by providing The retired director, Professor Nicolaas Kuiper, retraining for faculty from other fields such as who has been director since 1971, will remain mathematics. Each IFRICS class participates in associated with lliES as a long term visitor two summers of intensive course work. During after his sabbatical this year. Professor Jacques the intervening academic year each participant is Tits will continue as editor of the Publications expected to teach a computer science course at Mathematiques. Jean Bourgain, professor at the their home university and to complete a major Free University of Brussels, will occupy the chair programming project. The curriculum consists of Permanent Professor in mathematics left vacant of eight four-week courses designed to prepare by Pierre Deligne. Marcel Boiteux has assumed participants to teach a major portion of the the presidency of the Council of Administration ACM '78 core curriculum in computer science. of lliES, succeeding Renaud de la Geniere. Since the first class entered the Institute at The lliES, now in its twenty-seventh year of Clarkson University at Potsdam, New York, in operation, is a foundation supported by grants the summer of 1983, the Institute has enrolled from the French government and by smaller grants 214 participants representing 180 schools from from many other countries including the United 42 states and 6 foreign countries. The institute States. In addition to the permanent professors expanded to include a second campus at Kent and long term visitors, there are usually about State University in Kent, Ohio, in the summer of forty visitors each year with one third coming 1985. IFRICS has been guided since its creation from the United States. by the joint ACM/MAA Committee on Retraining Research at lliES is characterized by the for Computer Science. Faculty for both branches interests of the permanent professors: Rene Thorn of the Institute are selected from among the top (catastrophe theory and morphology), Dennis computer science departments in North America Sullivan (manifolds), Mikhael Gromov (differential based upon outstanding records in both research geometry), Jean Bourgain (functional analysis), and teaching. Louis Michel (physical structure of solids), David The dates for the classes scheduled to begin Ruelle (statistical mechanics), Oscar Lanford III in the summer of 1986 are as follows: Clarkson (statistical mechanics); and the long term visitors: University, June 2, 1986-August 1, 1986 and Alain Cannes (operator algebras), Ofer Gabber Kent State University, June 16, 1986-August 15, (algebra), Henri Epstein (quantum field theory), 1986. Interested candidates should write for Krzysztof Gawedzki (quantum field theory). more information and application forms to either: Ed Dubinsky, IFRICS Director, Department of Robert E. Kahn Receives Mathematics and Computer Science, Clarkson First ACM President's Award University, Potsdam, New York 13676 or Darrell Turnidge, IFRICS Director, Department of Math­ The first ACM President's Award for exemplary ematical Sciences, Kent State University, Kent, leadership and contributions to computer science Ohio 44242. was presented to Dr. Robert E. Kahn by ACM President, Dr. Adele Goldberg, at the ACM 1985 Request for Photos Annual Conference, held in Denver, Colorado on October 14-16, 1985. In the period 1966 to In conjunction with the Centennial of the 1972, Dr. Kahn was a Senior Scientist at Bolt American Mathematical Society which is to be Beranek and Newman, Inc., where he worked celebrated in Providence in 1988, the AMS would like to set up an exhibit of group photos from on computer communications network design and meetings and similar items of interest. techniques for distributed computation, and was one of the principal designers of ARPANET. If anyone has memorabilia of this kind which they · would like to give or loan to tee AMS, Since 1972, he has been with the Defense please write to William J. LeVeque, Executive Advanced Research Projects Agency, (DARPA), Director, American Mathematical Society, P.O. Department of Defense, most recently as Director Box 6248, Providence, Rhode Island 02940. for Information Processing Techniques.

788 AMS Research Fellowships Citizens of the United States who are members Invitation for Applications, 1986-1987 of one of the designated minority groups, who are preparing for or already engaged in college These fellowships are open to individuals five or university teaching, and who hold doctoral or to ten years past the Ph.D. degree (or equivalent), other terminal degrees may apply for a fellowship regardless of age, but below the academic rank award of one year's duration. The deadline for of professor. Applicants should have received submission of applications is January 17, 1986. the Ph.D. degree between January 1, 1976, and All inquiries concerning application materials December 31, 1981. Moreover, the vita must and program administration should be addressed include the equivalent of at least three full years to the Fellowship Office, National Research postdoctoral teaching or industrial experience, Council, 2101 Constitution Avenue, Washington, i.e., non-fellowship years. DC 20418. The stipend has been set by the Trustees of the Society at $30,000 for nine months of full-time Senior and Postdoctoral research or its equivalent. In addition, there will Research Associateships be an expense allowance of $1,000. Applicants must be citizens or permanent residents of a The National Research Council (NRC) has country in North America. Fellowships may be announced the 1986 Resident, Cooperative, and held at any institution the Fellow selects or at Postdoctoral Research Associateship Programs more than one in succession. There is flexibility for research in the sciences and engineering to be in the choice of time interval( s) and manner in conducted on behalf of twenty-five federal agencies which the Fellow may draw funds. For instance, or research institutions, whose laboratories are given the opportunity, a Fellow may elect to hold located throughout the United States. The a half-time academic appointment with a teaching programs provide Ph.D. scientists and engineers responsibility not exceeding one course per term of unusual promise and ability with opportunities while holding the fellowship at one-half stipend to perform research on problems largely of over a two-year period. The Fellow should consult their own choosing yet compatible with the with the Secretary of the Society to learn whether research interests of the supporting laboratory. the arrangement proposed is acceptable to the Initiated in 1954, the Associateship Programs Society. have contributed to the career development of The number of fellowships depends on the over 4000 scientists ranging from recent Ph.D. amount of money contributed to the program. recipients to distinguished senior scientists. The Trustees have arranged the matching program Approximately 350 new full-time Associateships from general funds in such fashion that funds for will be awarded on a competitive basis in 1986 at least one fellowship are guaranteed. for research in: chemistry, earth and atmospheric The deadline for receipt of applications is sciences; engineering and applied sciences; biologi­ December 2, 1985. Awards will be announced late cal, health and behavioral sciences; mathematics; in January 1986. space and planetary sciences; and physics. Most of the programs are For application forms, write to William J. open to both U.S. and non­ U.S. nationals, LeVeque, Executive Director, American Mathe­ and to both recent Ph.D. degree recipients and senior investigators. matical Society, P.O. Box 6248, Providence, RI Awards are made for one or two 02940. (It should be noted that completed ap­ years; senior applicants who plication and reference forms should NOT be sent to this address, but to the address given on the Notice to Authors forms.) There has been a recent change in the AMS policy regarding Copyright Transfer Agreements Ford Foundation for papers published by the Society. In the Postdoctoral Fellowships for Minorities past a signed transfer agreement was required from only one author for each paper being published. It The National Research Council (NRC) plans is the policy now that these transfer agreements to award approximately thirty-five Ford Foun­ must be received from each author before a paper can dation Postdoctoral Fellowships for Minorities be published by the Society. These forms in a program designed to provide opportunities are sent to all authors upon receipt of the accepted manuscript for continued education and experience in re­ in the Providence office. It is necessary for an search for American Indians and Alaskan Natives author to sign this form and return it to the (Eskimo or Aleut), Black Americans, Mexican Providence office as quickly as possible so as Americans/Chicanos, and Puerto Ricans. Fellows to avoid delay in publication. The Society will will be selected from among scientists, engineers, not publish a paper unless a Copyright Transfer and scholars in the humanities who show greatest Agreement has been received from each author promise of future achievement in academic re­ that collaborated on the manuscript. search and scholarship in higher education.

789 Applicants must be U.S. citizens and have Unpublished Lecture Notes a doctoral degree or its equivalent by the time of the intended visit in mathematics; the a column containing The Notices will institute physical, biological, or engineering sciences; social lecture notes available lists of unpublished or behavioral sciences; or biomedical sciences. from departments in the mathematical sciences, Necessary expenses will be met by the NAS and other organizations in research institutes, and the foreign academy, including reimbursement the nonprofit sector. for long-term visitors for salary lost up to Readers are invited to submit material for this a predetermined maximum and expenses for column; items submitted for inclusion in this accompanying family members for long-term section of the Notices should be accompanied visits. by the following information: Requests for applications should reach the Name of author(s), title, year, number of National Academy of Sciences not later than pages, price; February 14, 1986. Deadline for receiving Address for orders and information about completed applications is March 3, 1986; ap­ payment (postal surcharge, if any, or whether plications must be postmarked by February 28, postpaid, to whom checks should be made). 1986. Further information and applications Items should be sent to the Providence office can be obtained from the National Academy of (Notices Lecture Notes, American Mathematical Sciences, Office of International Affairs, Soviet and Society, Post Office Box 6248, Providence, East European Affairs, 2101 Constitution Avenue, ·Rhode Island 02940). N.W., Washington, DC 20418; 202-334-2644. have held the doctorate at least five years may request shorter tenure. Stipends for the 1986 Research Program at ONR program year will begin at $26,350 a year for New recent Ph.D.'s and be appropriately higher for The Office of Naval Research has announced senior Associates. a new research program entitled Discrete and Re­ Applications to the National Research Council lated Mathematical Methods for Communication must be postmarked no later than January 15, Networks. The overall objective of the program 1986 (April 15 and August 15, 1986). Initial is to develop the mathematical foundations for a awards will be announced in March and April (July rigorous theory of communication over networks. and November for the two later competitions). Information on specific research opportunities Issues of particular importance include: and federal laboratories, as well as application ( 1) Discrete mathematical techniques for the materials, may be obtained from the Associateship design and analysis of network configurations Programs, Office of Scientific and Engineering for high connectivity and efficiency in the static Personnel, JH 608-D3, National Research Council, network case. 2101 Constitution Avenue, N.W., Washington, (2) The development of a dynamic theory DC 20418; 202-334-2760. of graphs for high reliability and survivability relative to probabilistic connectivity and to vertex Exchanges with USSR and and edge deletion. East European Academies of Sciences (3) The application of combinatorial mathe­ matics and statistical communications theory to The National Academy of Sciences (NAS) invites the development of effective channel access proto­ applications from American scientists who wish to cols, flow controls, and routing algorithms for a make visits beginning during the period January variety of message traffic processes. 1, 1987, through December 31, 1987, in the Unsolicited proposals should be sent to Math­ USSR, Bulgaria, Czechoslovakia, the German ematical Sciences Division, Office of Naval Re­ Democratic Republic, Hungary, Poland, Romania, search, Attn.: Code 411, Arlington, Virginia and Yugoslavia. Long-term research visits of five to twelve months' duration are encouraged, 22217-5000. For further information, call Richard particularly those where contact with colleagues D. Ringeisen, Scientific Officer for Discrete Math­ in the other country has already been established. ematics, 202-696-4320; Neil L. Gerr, Scientific The minimum length of visits is one month. Officer for Signal Processing, 202-696-4321.

790 Washington Outlook Kenneth M. Hoffman

This is the first article in a new feature • Formation of the David Committee at the column which will appear regularly in the Notices. National Research Council (NRC), to produce Articles in this column will be written by Kenneth an in-depth review of research funding for the M. Hoffman, of the Massachusetts Institute of mathematical sciences and pursue the imple­ Technology, who is currently the Executive Secre­ mentation of its own basic recommendations. tary for National Affairs of the Joint Policy Board • Establishment last year of the NRC Board for Mathematics {JPBM). The JPBM is a consult­ on Mathematical Sciences, to strengthen our ing committee among the American Mathematical ongoing ability to set long-range goals and Society, the Mathematical Association of Amer­ priorities. ica, and the Society for Industrial q,nd Applied • The September start of a new JPBM pub­ Mathematics. It bonds together the common in­ lic information program, utilizing Kathleen terests of the organizations in education, research, Holmay & Associates, specialists in media and applications. The Executive Secretary for consulting and public affairs. National Affairs provides the liaison for the three • The launching in late October of NRC's bold organizations with various government agencies education initiative, the Mathematical Sci­ and Congress. These articles are intended to pro­ ences Education Board. The process of vide information and insight into the Washington formation of this Board, which grew out of scene as it affects the mathematical community. CBMS recommendations, has begun to bind our research and teaching communities to­ Mathematics Leaves Isolationism Behind gether more strongly. Its work will give the Recent appearances by several of our col­ country a capability to continuously renew leagues at the extensive House Committee on mathematics education which it has never Science and Technology hearings on science policy had. (See the News from Washington section are another reminder that the era of isolationism of this issue.) in American Mathematics is coming to an end. It does not seem too harsh to describe these The testimony of Dick Anderson (LSU) on in­ structural changes collectively as a movement ternational science and John Hubbard (Cornell) away from isolationism. For too many years, on the impact of information technology, when we as a community remained aloof from the af­ combined with staff briefings by Jim Glimm and fairs of government and science policy, save for the more frequent oral and written contacts main­ the herculean efforts of two or three individual tained by Ed David (Exxon), Lynn Steen (MAA mathematicians and those of our colleagues in President), and the author, signal the beginnings government funding agencies. We took it for of major change. A concerted effort is now under granted that policy makers and the public un­ way to make both the importance and the basic derstood the importance of our work and would needs of mathematics known to Congress. In automatically provide for our needs. contrast, there was virtually no sustained contact It is worth noting that behind the recent between our community and the House or Senate changes in structure and action lies something during the previous decade. more fundamental, the movement away from By the standards of the scientific community scientific isolationism. As the David Report at large, congressional contact by mathematicians stressed, mathematics is looking outward now, constitutes a trickle, not a flood. Yet, its toward its intellectual involvement with science recent increase is significant, when seen in the and engineering. This is a healthy trend, which light of other outreach activities initiated by our will continue. community in the last few years: Some members of our community will ask, • Reconstitution of the Joint Policy Board for of course, whether it is equally healthy for us to Mathematics (JPBM) as a joint action arm of expand and regularize our contact with Congress. AMS-MAA-SIAM. It won't be healthy if we do it badly, that is, • Restructuring of the Conference Board of the if we engage in generalized special pleading or Mathematical Sciences (CBMS) as a commun­ try to bypass scientific decision-making processes. ication/project-initiation body comprised of To do it well, we must begin (as we have) by the presidents of 13 professional mathemati­ informing ourselves about Congress and informing cal sciences organizations. Congress about the mathematical sciences. Then,

791 since our field generally lacks massive projects future is to create among key legislators and staff which provide foci for congressional attention and the awareness which we have made pervasive in contact, we must have some central organization federal funding agencies: that research support and be systematic about what we do. for mathematics is out of balance with support As for what we hope to accomplish, the most for related fields of science. This will create a basic goal is simple: to keep our discipline on supportive climate for the current efforts of the the minds of Congress when matters of research executive branch to remedy the situation. Other and education are discussed. We cannot rely such goals can be set as we develop the reasoned on people in other disciplines to tell our story. analyses to support them. They won't. A more specific goal for the near

Combinatorics and Algebra Curtis Greene, Editor (Contemporary Mathematics. Volume 34)

This volume contains the Proceedings of the classical subject of hyperplane arrangements and AMS-NSF Joint Summer Research Conference on its recently discovered connections with lattice Combinatorics and Algebra held at the University theory and differential forms. and on the surprising of Colorado during June 1983. connections between algebra. topology. and the Although combinatorial techniques have counting of faces of convex polytopes and related pervaded the study of algebra throughout its complexes. There also appears an instructive history. it is only in recent years that any kind of example of the interplay between combinatorial and systematic attempt has been made to understand algebraic properties of finite lattices. and an the connections between algebra and interesting illustration of combinatorial reasoning combinatorics. This Conference drew together to prove a fundamental algebraic identity. specialists in both algebra and combinatorics. and In addition. a highly successful problem session provided an invaluable opportunity for them to was held during the conference; a list of the collaborate. problems presented appears at the end of the The topic most discussed was representation volume. theory of the symmetric group and complex Papers are included by the following: general linear group. The close connections with Eiichi Bannai N. Metropolis combinatorics. especially the theory of Young Margaret M. Bayer Peter Orlik tableaux. was evident from the pioneering work of Louis J. Billera Amitai Regev G. Frobenius. I. Schur. A. Young. H. Weyl. and Anders Bjorner J. Remmel D. E. Littlewood. Phil Hanlon gave an introductory Gian Carlo Rota Jeffrey B. Remmel survey of this subject. whose inclusion in this Y. M. Chen Louis Solomon volume should make many of the remaining papers Paul Edelman Richard P. Stanley more accessible to a reader with little background A.M. Garsia Dennis Stanton in representation theory. Ira M. Gessel Hiroaki Terao Ten of the papers impinge on representation Curtis Greene Michelle Wachs theory in various ways. Some are directly Phil Hanlon Dennis E. White concerned with the groups. Lie algebras. etc .. themselves. while others deal with purely 1980 Mathematics Subject Classifications: 05A15, 05A17, 05A19, 20C30, 22E46 combinatorial topics which arose from ISBN 0-8218-5029-6, LC 84-18608 representation theory and suggest the possibility of ISSN 0271-4132 a deeper connection between the combinatorics x + 318 pages (softcover), December 1984 List price $30, Institutional member $24, and the algebra. Individual member $18 The remaining papers are concerned with a wide Shipping and handling charges must be added To order, please specify CONM/34N variety of topics. There are valuable surveys on the

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792 News from Washington

National Research Council past quarter-century surely has taught us that sig­ Launches Mathematics Education Board nificant and long-term reform in education in the October 28, 1985 was an historic day for mathematical sciences requires the cooperation mathematics education in the United States as and coordination of many groups' efforts: teach­ the first meeting of the Mathematical Scie~ces ers and school officials, policy makers, parents, Education Board of the National Research Coun­ the public's representatives, business and industry cil (NRC) began in Washington, DC. Dr. Frank and other employers, mathematicians and those Press, NRC President, speaking on behalf of the who use mathematics. This NRC Board, as it National Academies of Sciences and Engineering brings together these diverse groups who have an applauded the unity of the mathematics research interest and a stake in mathematical sciences ed­ and education communities and outlined the am­ ucation, has perhaps the greatest opportunity for bitious hopes he has for the Board to provide: national leadership toward reform that we have national leadership in mathematics education, co­ seen in a long, long time." She also stressed the ordination among ongoing projects, advice and importance of systematic, sustained effort and the recommendations to local, state, and federal gov­ need for staff support of the highest quality. ernment, and service to localities and states as The staff of the Board is to be led by Dr. they struggle toward educational excellence. Con­ Marcia Peterson Sward, who comes to the role gressional leaders echoed the need for such a of Executive Director from her positions as Asso­ national effort at a premeeting dinner. ciate Director of the Mathematical Association of The outcome of the two and a half day America and Administrative Officer of CBMS. meeting matched expectations, as the Board laid out an Action Agenda for its first year's activities. Mathematical Sciences Education Board Detailed were major projects and the associated Membership List leadership roles the Board would attempt to play Shirley A. Hill, Chairman in several critical areas of precollege education: Professor of Mathematics and Education the constraints imposed by testing; the impact University of Missouri at Kansas City of technology on the classroom; articulation of Gordon M. Ambach core competencies in mathematics; standards for Commissioner of Education teacher preparation and development; improved State of New York information exchange and coordination among reform efforts. J. Myron Atkin The Conference Board of the Mathematical Dean, School of Education Stanford University Sciences ( CBMS) recommended to the NRC late in 1984 that it establish a national board of David H. Blackwell mathematical sciences education. The proposal Professor of Statistics and Mathematics to the NRC was developed by a committee chaired University of California, Berkeley by Professor Paul J. Sally, Jr. of the University of Gail Burrill Chicago. Mathematics Chairman The new Board is chaired by Professor Shirley Whitnall School District A. Hill, University of Missouri at Kansas City, Greenfield, Wisconsin whose distinguished career spans the spectrum Iris M. Carl from classroom teacher to university professor, Mathematics Teacher /Supervisor and includes terms as President of the National Houston (Texas) Public Schools Council of Teachers of Mathematics, Chairman Herbert Clemens of the U. S. Commission on Mathematical In­ Professor of Mathematics struction and Chairman of the CBMS National University of Utah Advisory Committee on Mathematics Education. She is presently on the Steering Committees of Clyde L. Corcoran ICM~86 and ICME-6. California High School In her opening remarks, Professor Hill de­ Whittier, California scribed the diverse makeup of the 31-member F. Joe Crosswhite Board (listed below) as one of the unique features Professor of Mathematics Education of the effort. She stated that, "Experience of the Ohio State University

793 Richard DeAguero Joan Leitzel Principal Assistant Provost Miami (Florida) Public Schools Ohio State University

John Dossey Peggy C. Neal Professor of Mathematics Jimior High School Teacher Illinois State University Bishop (Georgia) Public Schools

James Fey Henry 0. Pollak Professor of Mathematics Assistant Vice President University of Maryland Bell Communications Research

Robert Glaser Jack Price Director, Learning Resources Superintendent, Palos Verdes (California) and Development Center Peninsula United School District University of Pittsburgh Anthony Ralston Professor of Mathematics and Computer Science M. Gleason Andrew SUNY, College at Buffalo Professor of Mathematics Harvard University Stephen Rodi Professor of Mathematics Brother Neil Golden Austin (Texas) Community College Brother Martin High School New Orleans, Louisiana Paul Sally Professor of Mathematics Gene Hoffman University of Chicago Illinois State Legislature Lynn Steen Kenneth M. Hoffman Professor of Mathematics Professor of Mathematics St. Olaf College M.I.T. Dorothy Strong Joseph R. Hoffmann Mathematics Supervisor Mathematics Supervisor Chicago Public Schools State of California Calvin Wolfberg David R. Johnson President Nicolet High School Pennsylvania School Board Association Milwaukee, Wisconsin NRC Liaison Members Ann Kahn Hirsh G. Cohen President, National Congress of Parents Vice President, Divisional Operations and Teachers T. J. Watson Research Center, ffiM Corp.

Jeremy Kilpatrick Morris H. DeGroot Professor of Mathematics Education Professor of Statistics University of Georgia Carnegie-Mellon University

794 Letters to the Editor

Refereeing Process brought to bear by the AMS and others. Many I have read with interest the letters which in our country are silent today, as once people have appeared in recent times which question the were silent in Nazi Germany. The power of the refereeing process. These have in turn inspired American voice and that of its many organizations me to submit one of my own pet gripes. must shake some people in our country to the I do a fair amount of refereeing, and with realization that apartheid and the suffering it one exception have always submitted my referee's causes must end. report within a week of receipt of the manuscript. I hope these few general remarks are helpful in While I have often received letters of appreciation deciding on what needs to be done. from editors for my promptness, I have virtually On behalf of my family and my fellow accused, never received a letter from an editor which said I thank the members of the AMS for the support "Thank you for your report; I have acted on given. it as follows ...". Isn't it common courtesy, Ismail Mohamed not to mention good old- fashioned positive University of the reinforcement, to let people know what effect Witwatersrand, their opinion has had? Isn't the referee liable to Johannesburg learn something from the refereeing process, and (Received September 5, 1985) perhaps become a better referee, if he gets some feedback? Romanian Visa I imagine that my question has some obvious Following my joint papers with I. M. Gel'fand, answer, but I have yet to hear it. Perhaps my in integral geometry, the Institute for Advanced letter will generate some useful discussion. Study has invited us to a membership in its School Steven G. Krantz of Mathematics for the academic year 1985-1986. Pennsylvania State University That is an exceptional opportunity for us and, University Park taking into account that in the last 20 years, (Received August 16, 1985) because of the lAS' prestige, all other Roumanian members succeeded to obtain Roumanian visas, South Mriean Mathematicians I have formally accepted the membership. But My family and I very much appreciate the my first two attempts to obtain exit visas were telephone calls by yourself [Joshua A. Leslie] and unsuccessful and following a letter from director· other mathematicians in the USA. It is a source Harvey Woolf, the Communist Party Organization of strength to us to know that mathematicians at Bucharest University Center will not give their in the AMS, in the London Mathematical Society OK (necessary under Roumanian circumstances and in Canada cared about what happened to us. today) to my new application for a visa. Because of the support of so many people abroad The huge sufferings of the peoples in Europe we live in the fond hope that we too shall join the in this century have proved that it is a human ranks of the free nations of the world as a free duty not to accept repression, so, as long as it lies people one day. within my power, I will contest this act of political Now it is difficult to pursue the mathematics persecution. and the things we love but we live in hope and I appeal to the mathematical community, determination to see that day. especially to former members of the lAS to express In the final analysis our pain in South Mrica concern for such cases by support letters to can only be resolved by creating a free, democratic Nicolae Ceausescu, Honorary president of the and non-racial South Mrica. Perhaps that pain Roumanian Academy, Victoriei 125, Bucharest 1 is necessary and we will have to bear it. But I and Elena Ceausescu, Head of the Roumanian believe that the growing concern in the USA can Council for Sciences and Technology, Victoriei Sg. help bring about the changes we yearn for. We 1, Bucharest 1, Roumania. watch with great interest developments in the USA Radu R()fju to support us in this struggle, and appreciate all Institute for Advanced Study statements of concern and pressures which can be (Received August 13, 1985)

795 The Mathematical Descendants Descendants of Irving Kaplansky Irving Kaplansky 15. Eben Matlis Thomas Kabele 1. Cheater Feldman Stephen Bronn Examples of mathematical genealogy may 2. Flora Dinkines George Grossman 3. Alex Roaenberg Willy Branda! help to illustrate the remarkable growth and Vera Stephen PleBS Daniel Opitz Richard Jenson James Hein dissemination of mathematics on this continent Deborah Bergstrand William D. Weakley Thom Grace 16. Hyman Baas since 1945. For example, in June 1984 the Astrid J. Berkson Tait-Yuen Lam Alan McConnell Richard S. Elman University of Chicago, with the welcome support Bodo Pareigh Robert Fihgerald Hans Ehrbar Daniel B. Shapiro of the National Science Foundation, held a Thomas S. Ligon Jonathan L. Merael Rudolf Haggenmuller Jonathan Harman conference "Algebra in its Variety'' to honor the Muhamed Seaud Lawrence Berman Cornelius Greither Peter Curran contributions of Irving Kaplansky. The attached Lindsay Nathan Childs Charles Small Susan Hurley Anthony Bak list of his mathematical descendants was prepared Steven Teaser Frank Servedio Gerald J. Garfinkel Michael Stein at that ·time. Chin-Shui Hsu Bruce Magurn David Earl Dobbs Dennis Harmon There is some ambiguity at the start, Ira J. P a pick Seth Alpert Robert Alan Morris Man-Keung Siu Kaplansky's introduction to mathematics was Kenneth H. Mandel berg David Lee Wright Vansanti Arun Jategaonkar Robert Martin much influenced by Richard Brauer, but there John David Emerson David Carter Thomas Curtis Craven Deborah Tryantaphyllou is no doubt that he was Mac Lane's first Ph.D. Stuart Sui-shing Wang Robert Valensa Jerrold Lewis Kleinstein Marilena Pittaluga at Harvard. In his turn, Mac Lane had fol­ Mark Steven Freeland Xiaolong Wu 4. Isidor Fleischer 17, Joseph Rotman lowed the usual American custom of studying at 5. William F. Daraow David Arnold 8. Oscar Litoff' Ulrich Albrecht GOttingen. His thesis was written there in 1933 7. Fred B. Wright, Jr. J oerg Steber David J. Foulis Randall K. Walters under the direction of Paul Bernays. However, M. F. Janowih Mary Turgi Billie Joe Thorne Richard Levaro Hitler had dismissed Bernays, so Mac Lane's Gary D. Crown 18. Gunter Lumer Christopher Hardy Kwok-Wai Tam doctoral examination was conducted by Hermann Carlos S. Johnson, Jr. Charles Widger Forrest Baulieu David F. Neu Weyl (who found that Mac Lane could not E. A. Schreiner Luc Paquet Alan A. Bishop Roger M. Dubois recall the Hausdorff separation axiom!) Weyl Linda Brown 19. Stephen U. Chaae J, C, Derderian Morris Or11ech (who had discovered the Hausdorff axioms for Jean H. Bevis Margaret Ann Beattie Kenneth B. Garren Hei-sook Lee Riemann surfaces) was one of Hilbert's many John W. Hogan Frank Anger D. E. Catlin Harold Stolberg students. Hilbert's thesis was officially directed R. J. Greechie Manju Bewtra Richard Schelp Kenneth Newman by the transcendental Lindemann, but, according Glenn Powers John Yeagley Meenakohi Rajagopalan George Angwin to the biography by Constance Reid, he was Gerald Schrag Susan Geller Larry Cammack Maryse Desrochers most influenced by a young Privat-Dozent, Adolf Frank Bernhart 20. Robert E. MacRae Eric Gerell Victor Albia Hurwitz. Cheryll Gerell Rai Markanda Mary K. Bennett 21. Edward D. Davia We have not pursued the ancestry further. J. C. Dacey 22. John A. Eagon E. L. Marsden, Jr. Marshall M. Fraser The attached list is intended to be complete R. J. Weaver Floyd Barger Robert Piziak Selmer Moen up through degrees granted in the summer of L. M. Herman Koonyui Poon W. R. Collins Karen Whitehead 1984. The undersigned would be glad to learn of D. P. Sumner Steven Johnson Lynn Pearce 23. Kolumum R. Nagarajan additions and corrections. Dennis P. Geoffrey 24. Fred Richman Manton Matthews Louis Duncan Patricia Blitch Laurel Rogers Saunders Mac Lane N. K. Roth David Tabor Barbara Jeffcott E. Lee Lady The University of Chicago Ron Wright Judy Moore Karen Zak 25. Ronald Hamelink (Received September 17, 1984) Patricia Framer Lock 26. Jacob Towber Arthur B. Simon 27. Hwa Tsang Stephen H. Friedberg 28. Yung-yung Lu Kuo David M. Topping 29. Samuel M. Gedwiser Warren Wogen 30. Gerson Levin Mahmoud Masri 31. Diana Taylor In the list of descendants, each of Kaplansky's John W. Brunce 32. Wolmer Vasconcelos Catherine L. Olsen Brian Greenberg Ph.D. students are numbered from 1 through 53 Mary Catherine Flanders Hu Sheng John M. McVoy Ana M. Viola Prioli (in chronological order). The second generation 8. Malcolm Goldman Jeffrey Dawson 9. Harold Widom James Carrig of students are indented under their advisors, the Lidia Luquet Sarah Glas third generation indented further, etc., through five Estelle Baaor 33. Dean Heller Raymond Roccaforte 34. Alphonse Buccino generations. The list is intended to include all such 10. Sterling K. Berberian 35. Michael Day Roy A. Johnson 36. Howard Gorman doctorates up through June, 1984. R. Bruce Merick 37. Richard J. Shaker John C. Bradshaw 38. Susanna Epp Ernest S. Pyle 39. Richard Wagner 11. Haaleton Mirkil 40. Robert E. Kibler 12. Donald Ornstein 41. Richard B. Taray LeeK. Jones 42. Edward Graham Evans Predecessors Douglas Lind Catherine A. Meadows Albert M. Fisher 43. Stephen J. McAdam Michael Boyle Evan Houston Daniel J. Rudolph Keith Whittington Ferdinand Lindemann (Adolf Hurwitz*) Maurice Rahe Daniel Katz Jack E. Clark 44. Bruce Prekowitz David Hilbert Robert Burton 45. Judith Sally Hermann Weyl {Paul Bernays*) Marty Ellis Young Hyun Hong David H. Bailey 46. Peter Kohn Saunders Mac Lane Stephen Polit 47. Adrian Wadsworth Arthur Rothstein 48. Jacob Matijevic Irving Kaplansky Kewon Park 49. Daniel Anderson Jonathan King 50. Charles Hanna 13. Edward C. Posner 51. Michael Modica *See the second paragraph of Saunders 14. George Kolettis, Jr. 52. Warren Nichols John A. Oppelt 53. Harry Hutchins Mac Lane's letter. James B. Wood John D. Waller Francia T. Rush Rene R. Gaudreau Randolph J. Oatlie Paul J. Bernard William J. Keane

796 Royalties In August 1978 Dr. Martin Kerner and I signed a Policy on Letters to the Editor contract with Holden Day to have our precalculus Letters submitted for publication in the Notices are manuscript published. The book was brought reviewed by the Editorial Committee, whose task is into print October 1981 and advertised nationally. to determine which ones are suitable for publication. The publication schedule requires from two to four We have made repeated requests through personal months between receipt of the letter in Providence and letters, phone calls and a lawyer, but as of this publication of the earliest issue of the Notices in which date we have been unable to obtain a detailed it could appear. summary of sales and have been unsuccessful in Publication decisions are ultimately made by majority the collection of royalties due. On December vote of the Editorial Committee, with ample provision 20, 1984 I appealed directly to Mr. Frederick for prior discussion by committee members, by mail or at meetings. Because of this discussion period, some Murphy, the president of Holden Day, to forward letters may require as much as seven months before a royalties due and a full statement of account. In final decision is made. a letter dated December 31, Fred Murphy stated The committee reserves the right to edit letters. that. . . ''We are presently attempting to acquire The Notices does not ordinarily publish complaints additional capital which will allow us to become about reviews of books or articles, although rebuttals current with authors royalties." He further stated and correspondence concerning reviews in the Bulletin that a detailed summary of sales and royalties of the American Mathematical Society will be considered would be ready within a week. We have received for publication. neither royalties nor summary of sales to date, Letters should be mailed to the Editor of the and Mr. Murphy has not bothered to answer my Notices, American Mathematical Society, Post Office Box 6248, Providence, Rhode Island 02940, and will be follow up letter of May 20, 1985. acknowledged on receipt. For the past four years I believed this to be an isolated problem, but informal discussions with other authors lead me to believe this problem is more prevalent than I first assumed. Therefore I am writing this letter to alert the academic community to the existence of my problem and to urge my colleagues carefully to investigate any publisher they consider for future texts. Peter Evanovich Fairfax, Virginia (Received July 12, 1985)

Applied Cryptology, Cryptographic Protocols, and Computer Security Models Richard A. DeMilio, George I. Davida, David P. Dobkin, Michael A. Harrison, and Richard J. Lipton

"Applied Cryptology, Cryptographic Protocols, and Computer Security Models is an excellent treat­ ment of a subject that has attracted substantial attention in both the technical and popular literature. It is a pleasure to read a book that combines an intuitive feel for its subject with mathematical rigor. The book should have broad appeal. New-comers to the field will appreciate its clear motivation of the material and exposition of the mechanics of the various schemes. Researchers and serious students will be aided by its wide scope that pulls together many topics that are generally dealt with separately, condensed proofs, and rationales for the validity and usefulness of the various approaches taken. It is quite comprehensive, with the exception of the exclusion of work in statistical data bases that have been innoculated with errors to prevent compromise." - David L. Wells Southern Methodist University Proceedings of Symposium in Applied Mathematics, 1983, 204 pages, softcover; List price $23, Institutional member $18, Individual member $14. Order code PSAPM/29N Shipping/Handling: 1st book $2, each add'l $1, max. $25; by air, 1st book $5, each add'l $3, max. $100 Prepayment is required. Order from American Mathematical Society, P.O. Box 1571, Annex Station, Providence, Rl 02901-1571, or call toll free 800-556-7774 to charge with Visa or MasterCard.

797 Queries Edited by Hans Samelson and Stuart Antman QUESTIONS ARE WELCOMED from AMS members regarding mathematical matters such as details of, or references to, vaguely remembered theorems, sources of exposition of folk theorems, or the state of current knowledge concerning published or unpublished conjectures. This is not intended as a problem corner, except for occasional lists of problems collected at mathematical meetings. REPLIES from readers will, when appropriate, be edited into a composite answer and published in a subsequent column. All answers received will be forwarded to the questioner. QUERIES and RESPONSES should be typewritten if at all possible and sent to Queries Column, American Mathematical Society, P. 0. Box 6248, Providence, Rhode Island 02940. Queries eventually satisfy a linear recurrence relation rational functions? Seeond reply (a first reply 342. Vladik Ya. Krel'novieh (P. 0. Box 21, appeared in Noticesvol. 32, p. 609, October 1985): Leningrad 22, 197022, U.S.S.R.). ''Psai-logy" Professor Charles Pisot, in his lectures at the is the study of partially subjective a priori University of Pennsylvania (1961-1962) and at information; we are concerned with the fact that the Universite de Montreal (1963) attributed the in real problems initial data, equations and aim theorem to P. Fatou, "Series trigonometriques et functions are often not known precisely. Fuzzy series de Taylor" in the Acta Mathematica 30 sets and interval mathematics are examples. Are (1906), pp. 335-400. (The contributor has not any others known? Is there a survey article in the verified the quoted paper.) literature? Professor Pisot's lectures at the Universite de Montreal are (or were) available at the Department Responses of Mathematics of the Universire de Montreal under the title "Quelques aspects de la thoorie 333. (vol. 32, p. 472, August 1985, Charles des entiers algebriques". (Contributed by E. Small) Are formal power series whose coefficients Grosswald)

The anisotropic Kepler problem is a one-parameter family (of parameter Jl) of Hamiltonian systems with two degrees of freedom. When p = 1 it becomes the Kepler problem (an integrable system). and the authors show the global orbit structure by taking into account the blow-up of the singularities at the origin and at Qualitative Analysis of the infinity. When J1 E (9,18. oc). symbolic dynamics allow the authors to classify its solutions. In fact. Anisotropic Kepler Problem they prove that the dynamic behavior contains a Josefina Casasayas subshift with an infinite alphabet. The symbols of and Jaume Llibre this alphabet take into account the symmetries of (Memoirs of the AMS. Number 312) the problem. For each periodic sequence of this subshift. Casasayas and Llibre show the existence This Memoir is devoted to the qualitative of a symmetric periodic orbit which realizes it. The analysis of the anisotropic Kepler problem. It alsd transition from J1 = 1 (integrable) to J1 > 9/8 surveys the recent results obtained. and the (chaotic) is such that the chaos does not appear techniques that have been developed for attacking until J1 = 9/8. this new problem. which was introduced by Gutzwiller in order to study bound states of an electron near a donor impurity of a semiconductor. 1980 Mathematics Subject Classifications: 34C35, 58F15 The book exhibits many qualitative phenomena of ISBN 0-8218-2309-4, LC 84-18521 interest in the theory of differential equations ISSN 0065-9266 viii+ 115 pages (softcover), November 1984 (non-integrability. chaotic behavior .... ) as was List price $13, Institutional member $10, already seen in the works of Gutzwiller and Individual member $8 Devaney. Shipping and handling charges must be added To order, please specify MEM0/312N

Prepayment is required for all AMS publications. Order from AMS, P. 0. Box 1571, Annex Station, Providence, Rl 02901, or call toll free 800-556-7774 to charge with Visa or MasterCard.

798 Abstract Processing Fee to Be Discontinued

The $15 abstract processing fee will be discontinued beginning with "by title" abstracts to appear in the January 1986 issue of Abstracts of papers presented to the American Mathematical Society and papers to be presented at the January 1986 Annual Meeting of the Society. This decision has been made by the Board of Trustees of the Society on the recommendation of the Council.

New abstract forms have been prepared for use by mathematicians who present papers at AMS meetings or who submit abstracts for presentation "by title" in Abstracts. The new forms are being distributed to departments of mathematics in universities and colleges in the United States and Canada and are available on request from the Editorial Department at the Society's office in Providence. Since there are no changes to the layout or typing instructions for abstracts, the current abstract forms may be used if the new form is not available. If the old form is used, the instructions for payment of the processing fee should be disregarded. Anyone who mistakenly includes the $15 payment with an abstract will be reimbursed.

The AMS will continue the service of preparing abstracts for authors not able to have them typed locally and will retype papers not reproducible as submitted by the author. The fee for having an abstract typed by the AMS will be $16.

799 New Orleans Meetings, January 5-11, 1986 Supplement to Announcement in October Notices

Please refer to the Preliminary Announcement for AMS Special Sessions this meeting which appears on pages 641-663 of the October 1985 issue of the Notices. The Table Updated lists of speakers are now available for of Contents for the preliminary announcement is some of the special sessions. reproduced below for convenience. Graph labelings, GARY S. BLooM, CUNY, City College and D. F. Hsu, Fordham University, 1:00 Josiah Willard Gibbs Lecture p.m. Friday and 8:00 a.m. Saturday. Stefan Burr, The title of the Gibbs lecture to be given by L. E. Fan R. K. Chung, Thomas Grace, Solomon Golomb, ScRIVEN is The third leg: Mathematics and computation Anton Kotzig, Zevi Miller, Christos Papadimitriou, in applicable science and high technology. Fred Roberts, Alexander Rosa, Peter J. Slater, and Invited Address Herbert S. Wilf. The title of the invited address to be given by Mathematical modeling and computer simula­ SERGIU KLAINERMAN is Lorentzian geometry and tion to problems in other disciplines, RICHARD nonlinear hyperbolic equations. BRONSON, Fairleigh Dickinson University, Teaneck, 8:00 a.m. and 2:15 p.m. Tuesday. Allan M. Berlinsky, AT & T Bell Labs; Richard Bronson; Stanley I. Cohen, WHERE TO FIND IT PAGE Pulse Analytics, Inc.; Frank R. Giordano, United PREREGISTRATION AND HOUSING 642, 643 States Military Academy; Chanoch Jacobsen, Israeli ANNUAL MEETING OF THE AMS 641 Institute of Technology; Thomas G. Johnson, Virginia Gibbs Lecture, Colloquium Lectures, Prizes, Polytechnic Institute and State University; Robert Invited Addresses, Special Sessions, Contributed Kinnison, Desert Research Institute; John Oddson, Papers, Other Sessions, Council, and Business Meeting University of California, Riverside; George Palfalvy, AMS SHORT COURSE 645 Norden Systems, Inc.; L. L. Ratcliffe, CONRAIL; EMPLOYMENT REGISTER 664 Joel D. Reiss, Singer-Kearfott Division; and Stephen ANNUAL MEETING OF THE MAA 647 Roberts, Regenstrief Institute Health Care. Retiring Presidential Address, Invited Complex analysis, PETER L. DuREN, University Addresses, Minicourses, Contributed of Michigan, 1:00 p.m. Friday and 8:00a.m. Saturday. Papers, Other Sessions, Business Meeting, Board of Governors, Section Officers, Films J. Milne Anderson, Albert Baernstein, Johnny Brown, JOINT AMS-MAA SESSIONS 650 Peter L. Duren, F. W. Gehring, Julian Gevirtz, OTHER ORGANIZATIONS 651 D. H. Hamilton, Walter Hengartner, D. Khavinson, AAAS, AWM, COMAP, ICEMAP, ISGRHPM, Y. J. Leung, David Minda, Glenn Schober, Terry JPBM, NAM, NSF, RMMC, TUG Sheil-Small, and Carl Sundberg. TIMETABLE 653 Equivalence problems and applications, RoBERT OTHER EVENTS OF INTEREST 652 Book Sales, Exhibits, Information Table, B. GARDNER, University of North Carolina and Petition Table WILLIAM F. SHADWICK, University of Waterloo, ACCOMMODATIONS 652 8:00 a.m. Wednesday and 1:00 p.m. Thursday. R. Hotels Bryant, S. S. Chern, James Faran, P. A. Griffiths, REGISTRATION DESK 656 R. Hermann, N. Kamran, M. Kuranishi, and William Fees, Dates, Locations, Times, Services Shadwick. MISCELLANEOUS INFORMATION 660 Child Care, Local Information, Parking, Radon transforms and tomography, ERic L. Social Event, Travel, Weather GRINBERG, University of Michigan and ERic ToDD MAP 654 QuiNTO, Tufts University, 1:00 p.m. Friday and 8:00 a.m. Saturday. Jan Boman, Carlos Berenstein, Allan IMPORTANT DEADLINES AMS Abatraeta, Cormack, Leon Ehrenpreis, Eric L. Grinberg, Alberto For conaideration for apeeial aessions Expired Griinbaum, Victor Guillemin, Sigurdur Helgason, Of contributed papers Expired Alfred Louis, Frank Natterer, Eric Todd Quinto, L. MAA Abatraeta, A. Shepp, K. T. Smith, Donald C. Solmon, and Of contributed papen Expired Employment Regiater Robert S. Strichartz. (Applicants & Employers) November 15 Harmonic analysis on reductive groups, EARLY Preregiatration and Housing Expired REBECCA A. HERB, University of Maryland and Preregistration and Housing November 15 PAUL J. SALLY, JR., University of Chicago, 8:00 MAA Minicoune Preregiatration November 15 a.m. Wednesday and 1:00 p.m. Thursday. Jeff Adams, Motions for AMS Business Meeting December 9 Preregiatration eaneellationa (50% refund) January 2 James Arthur, Laurent Clozel, Larry Corwin, Tom Enright, Rebecca A. Herb, Phil Kutzko, Allen Moy, Scott Osborne, and David Vogan. Determinacy and large cardinals, ALEXANDER S. KECHRIS, California Institute of Technology

800 and W. HuGH WooDIN, University of California, Lawrence Conlon, Thierry Fack, James L. Heitsch, S. Berkeley, 8:00 a.m. Wednesday and 1:00 p.m. Hurder, F. Camber, J. Kaminker, A. Katok, Connor Thursday. Stewart Baldwin, James E. Baumgartner, Lazarov, M. Ratner, Marc A. Rieffel, J. Rosenberg, Howard Becker, Tim Carlson, Matthew Foreman, Xiaolu Wang, and R. Zimmer. Harvey Friedman, Steve Jackson, Thomas Jech, Recent advances in nonlinear hyperbolic equa­ Richard J. Laver, Alain Louveau, D. A. Martin, tions, JALAL SHATAH, Brown University and SER­ William Mitchell, Robert M. Solovay, and J. R. Steel. GIU KLAINERMAN, Courant Institute of Mathemati­ Operator method of optimal control problems, cal Sciences, New York University, 8:00 a.m. Wednes­ SuNG J. LEE, University of South Florida, 8:00 a.m. day, 1:00 p.m. Thursday and Friday. Michael Beals, Tuesday and Wednesday. N. U. Ahmed, Stephen L. Demetrious Christodoulou, Constantine Dafermos, Campbell, Goong Chen, Ethelbert N. Chukwu, R. Ron DiPerna, Robert Glassey, Jonathan Goodman, Datko, H. 0. Fattorini, J. Lagnese, Irena Lasiecka, Edward Harabedian, John K. Hunter, Fritz John, E. B. Lee, Jack W. Macki, A. Manitius, Clyde F. Peter Lax, Tai Ping Liu, Richard B. Melrose, N. Martin, M. Z. Nashed, A. N. V. Rao, Stephen H. Ritter, I. Segal, Jalal Shatah, Thomas Sideris, Mar­ Saperstone, and Roberto Triggiani. shall Slemrod, Panagiotis Souganidis, Walter Strauss, Convexity, ERWIN LUTWAK, Polytechnic In­ Enrique Thomann, and Dean Yang. stitute of New York, 8:00a.m. and 2:15p.m. Tuesday. Positive operators and their applications, LUTZ J. R. Alexander, Gerald Beer, L. Billera, Marilyn WEIS, Louisiana State University, 1:00 p.m. Thursday Breen, Michael E. Gage, Evarist Gine, Paul Goodey, and Friday. C. D. Aliprantis, Simon J. Bernau, Owen H. Groemer, Victor Klee, Clinton M. Petty, J. R. Burkinshaw, Nassif Ghoussoub, Jerome Goldstein, Sangwine-Yager, Gilbert Strang, Richard A. Vitale, William B. Johnson, Michel L. Lapidus, H. Lotz, and T. Zamfirescu. W. J. Luxemburg, Haskell Rosenthal, Paulette Saab, Ordered algebras, JoRGE MARTINEZ, University Anton R. Schep, Robert Sharpley, Jerry Uhl, and of Florida, Gainesville, 1:00 p.m. Thursday and Manfred Wolff. Friday. Marlow Anderson, Paul Conrad, Michael Special Invited Address Darnel, A. M. W. Glass, A. W. Hager, Melvin Henriksen, Charles W. Holland, James Madden, The title of the special invited address by GEORGE Steven H. McCleary, Wayne Powell, R. H. Redfield, F. CARRIER is Nuclear winter, current knowledge and Constantine Tsinakis. and understanding. Analytic methods in differential equations, MathSei PETER A. McCoY, United States Naval Academy, Online demonstrations of MATHSCI, the electronic Annapolis, 8:00 a.m. and 2:15 p.m. Tuesday. Robert form of Current Mathematical Publications (CMP) Carroll, James A. Donaldson, Robert P. Gilbert, and Mathematical Reviews (MR), will be held during Jerome T. Goldstein, Deborah Tepper Haimo, Robert exhibit hours at the French Market Exhibit Hall. M. Kauffman, Ralph E. Kleinman, Mark A. Kon, For the first time, it is possible to display the Peter A. McCoy, J. W. Neuberger, Thomas H. Pate, mathematical symbols in MATHSCI references on a Louise A. Raphael, and Gilbert G. Walter. PC or to print them from a PC. The demonstration Homotopy theory, STEPHEN A. MITCHELL, will show how a PC with a modem is used University of Washington, Seattle, 8:00 a.m. and 2:15 to search for information in CMP and MR. The p.m. Tuesday. Gunnar Carlsson, Fred Cohen, Ralph resulting references and MR review text are processed Cohen, Ethan Devinatz, Mike Hopkins, Nicholas J. with commercially available software (MICRO'JEX or Kuhn, Mark Mahowald, Stephen A. Mitchell, Joe PC'IEX) and appropriate 'lEX definitions provided by Neisendorfer, David Pengelley, Stewart Priddy, Doug the AMS. The file is then printed on the PC printer Ravenel, Jeff Smith, and Clarence Wilkerson. or displayed on the screen, and the mathematical Operator theory and several complex variables, expressions appear in the same form as in the printed PAUL S. MUHLY, University of Iowa, 2:15 p.m. MR. The display will demonstrate these capabilities Tuesday and 8:00 a.m. Wednesday. Richard Carey, of MATHSCI on both IBM PC and Apple Macintosh Douglas N. Clark, Lewis A. Coburn, Michael Cowen, machines. Raul Curto, Ron Douglas, Palle E. T. Jorgensen, In addition to MR, MATHSCI now contains all the Barbara MacCluer, Joel Pincus, Richard Rochberg, entries from CMP that have not yet been published Norberta Salinas, Harald Upmeier, and Jingbo Xia. in MR (about 60,000 references) as well as from Mathematical biology, JANE CRONIN ScANLON, the Current Index to Statistics and the Index to Rutgers University, 1:00 p.m. Thursday and Friday. Statistics Probability by John Tukey and Ian Ross. Steve Baer, Gail A. Carpenter, Jerome Eisenfeld, Stephen Grossberg, Warren Hirsch, Zsuzanna Kadas, MAA Invited Addresses Michael Lacker, Daniel S. Levine, Stephen J. Merrill, Updated information on invited addresses is as Ennio Mingolla, Victor Moll, P. E. Rapp, and follows: Matthew Witten. RoNALD L. GRAHAM, AT&T Bell Labs, Some Operator algebras and foliations, CLAUDE L. remarks on the finite radon transform, 1:10 p.m. SCHOCHET, MSRI and Wayne State University and Friday. KENNETH C. MILLETT, University of California, PETER J. HILTON, SUNY at Binghamton, A new Santa Barbara, 8:00 a.m. and 2:45 p.m. Tuesday. algorithm in number theory, 8:00a.m. Friday.

801 VICTOR L. KLEE, University of Washington, JOHN PHILIP HUNEKE, Ohio State University, and Complexity of linear programming: The d-step DAVID P. KRAINES, Duke University. conJ·ecture and its relatives, 2:15 p.m. Friday. CHARLES F. KELEMEN, Swarthmore College, HENRY 0. PoLLAK, Bell Communications Re­ is organizing a panel titled Model curriculum for search, School buses, baseball, and public key a liberal arts degree in computer science, a cryptography, 10:00 a.m. Saturday. curriculum created at a workshop funded by the Sloane Foundation, from 2:10 p.m. to 3:30 p.m., The invited address by CATHLEEN MORAWETZ Saturday, January 11. The panel, including the will not be presented as previously scheduled. organizer, will consist of STUART HIRSHFIELD, MAA Minicourses Hamilton College, JEFFREY PARKER, Amherst College, ALLEN TucKER, Cologate University, and The description and enrollment limitation for Min­ HENRY M. WALKER, Grinnell College. icourse #11 has been changed as follows: Minicourse A presentation by B. A. FusARO, Salisbury #11: The teaching of applied mathematics is being State College, on The mathematical competition in organized by W. GILBERT STRANG, Massachusetts modeling will be held from 1:00 p.m. to 2:00 p.m. Institute of Technology. Part A is scheduled from on Saturday, January 11. The first Mathematical 7:00 p.m. to 9:00 p.m. on Thursday, January 9 and Competition in Modeling (MCM) was held in February Part B from 10:30 a.m. to 12:30 p.m. on Friday, 1985. The MCM has the goal of increasing January 10. Total enrollment for this Minicourse is the presence of applied mathematics on campuses. limited to 50 persons. Ninety teams of undergraduates representing 70 The organizer will describe a unifying framework colleges, participated in the contest. Faculty advisors for the basic courses in modern applied mathematics. helped organize and prepare the three-student teams. The syllabus emphasizes ideas that are shared by Each team chose one of two problems and had a wide range of applications (discrete as well as a weekend to work on it. The problems were continuous). It combines linear algebra with calculus, realistic, and computers or reference works were so that matrix equations are seen in parallel with allowed. Six outstanding papers appeared in a special differential equations. It includes numerical as well November issue of Mathematical Modelling, and two were featured in the January issue of the College as combinatorial algorithms, such as the Fast Fourier Mathematics JournaL The MCM is administered by Transform, which fit into the framework and make the Consortium for Mathematics and Its Applications it more specific and useful. The response from (COMAP) and has been funded for three years by engineers and computer scientists is encouraging; a the Fund for the Improvement of Post-secondary fresh approach is welcomed there also. Participants Education (FIPSE). The presentation will describe may contribute to the discussion of this fundamental the general nature of the contest, summarize two of course, which deserves to be more timely and the papers, and suggest how faculty members can coherent, and more interesting to teach. become involved. Other MAA Sessions Joint AMS-MAA Sessions The Committee on Computers in Mathematical Further information on the Joint AMS-MAA sessions Education (CCIME) is sponsoring a panel discussion follows: on Evaluating instructional software from 8:20 a.m. VICTOR W. GuiLLEMIN, Massachusetts Institute to 9:50a.m. on Saturday, January 11. The organizer of Technology, title to be announced, 11:10 a.m., will be R. STEPHEN CuNNINGHAM, California State Friday. College at Stanislaus. The other participants will be PAUL R. HALMOS, University of Santa Clara, JuDITH R. BROWN, University of Iowa, SHELDON Matrices I have met, 11:10 a.m., Thursday. P. GORDON, Suffolk County Community College and THOMAS HAWKINS, Boston University, title to be announced, 2:15 p.m., Thursday. STUART THOMAS, Wadsworth Publishing Company. CCIME will also sponsor a panel discussion titled Activities of Other Organizations Computing in calculus: Its past history, present The time of the symposium sponsored by the status, and prospects for the future. The panel is American Association for the Advancement of scheduled for 3:30 p.m. to 5:00 p.m. on Thursday, Science (AAAS) will now take place at 7:30 p.m. to January 9. GERALD J. PORTER, University of 9:30 p.m. on Wednesday, January 8. Pennsylvania will chair the panel. Panelists will The Association for Women in Mathematics be GERALD J. PoRTER, L. CARL LEINBACH, (AWM) will sponsor jointly with AMS and MAA a Gettysburg College, and DAVID A. SMITH, Duke session titled In honor Julia Bowman Robinson, 1919-1985, at 9:00 a.m. on Thursday, January University and Benedict College. 9. The speakers will be CoNSTANCE REID and A panel discussion on Teaching assistants and MARTIN DAVIS. LENORE BLUM will moderate the part-time or temporary instructors is being spon­ session. sored by the CTUM Subcommittee on Teaching The Preregistration/Housing Form, Employment Assistants and Part-time Instructors. The panel is Register Forms, with instructions, and the Minicourse scheduled from 9:00 a.m. to 11:00 a.m., Friday, Form can be found at the back of this issue. January 10. The moderator will be BETTYE ANNE CASE, Florida State University. The other panelists Frank T. Birtel will be WENDELL H. FLEMING, Brown University, New Orleans, Louisiana Associate Secretary

802 Proposed Amendments to the Bylaws for Presentation at the Business Meeting of 8 January 1986 in New Orleans

At the Council's meeting in Laramie, August 11, 1985, the following amendments to the bylaws were approved for action at the Business Meeting in New Orleans, January 8, 1986. Material to be deleted is e.ers~rliek and material to be inserted is set in boldface type. Article IX Dues and Privileges of Members

Section 11. -Aity- Htemeer wfie .eee- it flfe Htelfttier .Befere Oe~eeer ~ ~ ~ ~ f!II:YHteiK ei it 8tilft Ele~erHtilleEl ill ~~>eeerElMee ~ 8e~ltMi&l J!Pilleif!lee, 8ft8ll ft!we fer flfe ~ ~ illlEl f!Pi • ileges ef illl erElinM~ tll8lltSer ~ ~ f!~ lftetK ei e- f\+6 8Elai~iell&l 8f!f!lieMielle fer flfe Htelfttiereltif!s will -Se 8ee8f!~eEl. Any person who has attained the age of 62 and has been a member for at least twenty years may become a life member by making a single payment equal to five times the dues of an ordinary member for the coming year. Insofar as there is more than one level of dues for ordinary membership, it is the highest such dues that shall be used in the calculation. A life member is subsequently relieved of the obligation of paying dues. The status and privileges are those of ordinary members. (This section does not affect those persons who became life members before October 25, 1941. They remain life members with the status and privileges of ordinary members. When the class of them is empty, this parenthetical remark is to be removed.)

Article Xill Amendments

These bylaws may be amended or suspended M ~ ~ ef ~ ~ ell reeeJBHtellElMiell ei ~ ~ il:llEl ~it ~ .. e ~ltirEle ~ ei ~ Htelfttiere ~ f!Pe.iEleEl ~ ei 8lleB f!PBJ!eeeEl ~ il:llEl ef ~ ~ ft8MHoe 8ft8ll lttwe -8eelt gi¥ell ill ~ e8ll fer 8lleB Hte~illg. on recommendation of the Council and with the approval of the membership of the Society, the approval consisting of an affirmative vote by two-thirds of the members present at a business meeting or of two-thirds of the members voting in a mail ballot in which at least ten percent of the members vote, whichever alternative shall have been designated by the Council, and provided notice of the proposed action and of its general nature shall have been given in the call for the meeting or accompanies the ballot in full.

803 Indianapolis, April 11-12, Indiana University-Purdue University First Announcement of the 826th Meeting

The eight hundred and twenty-sixth meeting Special Sessions of the American Mathematical Society will be Several special sessions of selected twenty-minute held at Indiana University-Purdue University in papers are being organized and these will be Indianapolis, Indiana, on Friday and Saturday, April announced in the January issue of the Notices. 11-12, 1986. This meeting will be held in conjunction with a meeting of the Association for Symbolic Logic. Contributed Papers All scientific sessions will take place on the downtown There will also be sessions for contributed ten­ campus. minute papers. Abstracts should be prepared on the Invited Addresses standard AMS form available from the AMS office in Providence or in Departments of Mathematics. By invitation of the Committee to Select Hour Abstracts should be sent to the Editorial Department, Speakers for Central Sectional Meetings, there will American Mathematical Society, Providence, Rhode be four invited one-hour addresses'. The speakers are Island 02940, so as to arrive before the February 5, as follows: 1986, abstract deadline. Participants are reminded STEVEN BELL, Purdue University, Riemann that a charge of $16 is imposed for retyping abstracts mapping theorems in several complex variables. that are not in camera-ready form. JEAN BouRGAIN, lliES and the University of Information concerning registration, accommoda­ Illinois, at Urbana-Champaign, title to be announced. tions, food service, etc. will be available in the RICHARD McGEHEE, University of Minnesota, January issue of the Notices. Minneapolis, Singularities in classical celestial mechanics. Robert M. Fossum NIELS NYGAARD, University of Chicago, title to Urbana, Illinois Associate Secretary be announced.

Conference on Algebraic Topology in Honor of Peter Hilton Renzo Piccinini and Denis Sjerve, Editors

This book. which is the proceedings of Beno Eckmann. Surface groups and Poincare duality a conference held at Memorial University of Leonard Evens and Stewart Priddy, The cohomology of the semi-dihedral group Newfoundland. August 1983. contains 18 papers Richard Kane. Finite H-spaces and the U(M) property in algebraic topology and homological algebra by Kee Yuen Lam. On stable Hopf invariant one elements collaborators and associates of Peter Hilton. It is in RP00 dedicated to Hilton on the occasion of his 60th C. A. McGibbon and J. A. Nelsendorfer. Various applications of Haynes Miller's theorem birthday. The various topics covered are homotopy lb Madsen and Jan-Aive Svensson. Induction in theory. H-spaces. group cohomology. localization. unstable equivariant homotopy theory and non-in variance classifying spaces. and Eckmann-Hilton duality. of Whitehead torsion Students and researchers in algebraic topology Mark Mahowald, Lin's theorem and the EHP sequence will gain an appreciation for Hilton's impact upon J. P. May, Stable maps between classifying spaces Joseph Roltberg, Residually finite, Hopfian and mathematics from reading this book. co-Hopfian spaces J. F. Adams. The fundamental representations of Es Victor Snalth. On the classifying spaces of Galois groups Israel Bersteln. On covering spaces and Lie group James Stasheff. Hilton-Eckmann duality revisited actions K. Varadarajan. Projective and free approximations On the homotopy classification of A. K. Bousfield. xii + 164 pages (softcover), March 1985 K-theoretic spectra and infinite loop spaces List price US$20, Institutional AMS member US$16, William Browder. 5 1-actions on open manifolds Individual AMS member US$12 F. R. Cohen. An analogue of ""Hopf invariant one"" To order, please specify CONM/37 N W. G. Dwyer and D. M. Kan. Reducing equivariant homotopy theory to the theory of fibrations

Shipping/Handling: 1st book 12, each add'l 11, max. 125; by air, 1st book 15, each add'l 13, max. 1100 Prepayment required. Order from American Mathematical Society, P.O. Box 1571, Annex Station Providence, Rl 02901-1571, or call toll free 800-556-7774 to charge with VISA or MasterCard

804 Baltimore, May 3-4, Johns Hopkins University First Announcement of the 827th Meeting

The eight hundred and twenty-seventh meeting of Contributed Papers the American Mathematical Society will be held at There will also be sessions for contributed ten­ Johns Hopkins University in Baltimore, Maryland, on minute papers. Abstracts should be prepared on the Saturday and Sunday, May 3-4, 1986. standard AMS form available from the AMS office Invited Addresses in Providence or in Departments of Mathematics. Abstracts should be sent to the Editorial Department, By invitation of the Committee Select Hour to American Mathematical Society, Post Office Box Speakers for Eastern Sectional Meetings, there will 6248, Providence, Rhode Island 02940, so as to arrive be four invited one-hour addresses. The speakers, the before the February 10, 1986, abstract deadline. titles of their talks, and the times of presentation are Participants are reminded that a charge of $16 is as follows: imposed for retyping abstracts that are not in camera­ DEMITRIOS CHRISTODOULOU, Syracuse Univer­ ready form. It appears unlikely that late papers can sity, The global initial value problem for the be accommodated. Einstein equations, 1:30 p.m. Saturday. DAVID A. Cox, Amherst College, title to be Registration announced, 11:00 a.m. Sunday. The meeting registration desk will be located in ANTHONY W. KNAPP, Cornell University, the lobby of Shaffer Hall, on the southern part of Recent progress in classifying irreducible unitary the campus near the Wyman Park Drive entrance. representations, 1:30 p.m. Sunday. The desk will be open from 8:15 a.m. to 3:00 STEVEN M. ZUCKER, Johns Hopkins University, p.m. on Saturday, and from 8:00 a.m. to 11:00 L 2 -cohomology, 11:00 a.m. Saturday. a.m. on Sunday. The registration fees are $10 for members, $16 for nonmembers, and $5 for students Special Sessions or unemployed mathematicians. By invitation of the same committee, there will be several special sessions of selected twenty-minute Petition Table papers. The topics of some of these sessions, and A petition table will be set up in the registration the names and affiliations of the mathematicians area. Additional information can be found in a box organizing them, are as follows: in the New Orleans meeting announcement on page Complex analysis and its applications, CARLOS 652 in the October issue of the Notices. BERENSTEIN, University of Maryland, and BER­ NARD SHIFFMAN, Johns Hopkins University. Accommodations Nonlinear evolution equations, DEMITRIOS A block of rooms is being held at the Holiday Inn­ CHRISTODOULOU. Inner Harbor, where individuals should make their Number theory, T AKASHI 0No, Johns Hopkins own reservations directly and identify themselves as University, and LAWRENCE WASHINGTON, Univer­ participants in the AMS meeting at Johns Hopkins sity of Maryland. University. The rates do not include applicable tax Probability and mathematical statistics, and are subject to change after the April 2 deadline, ROBERT J. SERFLING and JoHN C. WIERMAN, at which time reservations will be accepted on a space Johns Hopkins University. available basis. Representations of Lie groups, DAVID VoGAN, Holiday Inn-Inner Harbor Massachusetts Institute of Technology. 301 West Lombard Street, Baltimore, MD 21201 Homotopy theory and algebraic topology, W. Telephone: 301-685-3500 STEPHI<;N WILSON, Johns Hopkins University. Single $59 Double $69 Hodge theory, STEVEN M. ZuCKER. The Holiday Inn is within easy walking distance of Most of the papers to be presented at these special Harborplace and the Inner Harbor downtown. The sessions will be by invitation. However, anyone JHU Shuttle bus will be provided on Saturday and submitting an abstract for the meeting who feels that Sunday mornings only to transport participants to his or her paper would be particularly appropriate the campus, which is approximately three miles to for one of these special sessions should indicate the north. Public transit buses also provide frequent this clearly on the abstract form and submit it by service, and schedules will be available at the Holiday January 20, 1986, three weeks before the deadline Inn. for contributed papers, in order that it may be Although rooms have not been blocked at the considered for inclusion. Participants are reminded following location, it is included here for information that a charge of $16 is imposed for retyping abstracts purposes. that are not in camera-ready form.

805 Comfort Inn Persons driving from the north on I-95 should 24 West Franklin Street, Baltimore, MD 21201 proceed south until reaching the Baltimore Beltway Telephone: 301-576-8400 (I-695) and take I-695 west toward Towson to Charles Street (exit #25). Follow Charles Street south for Single $43 Double $51 approximately eight miles to University Parkway, and do not The above rates are subject to change continue on Charles and enter the curb lane to the Inn is also include applicable tax. The Comfort right of the divider past University Parkway. Proceed the distance from downtown approximately a third of one block and bear right onto Wyman Park Drive; campus, and the Inner Harbor to the Johns Hopkins turn right onto the University campus. is located close to convenient bus lines. Those driving from the north on I-83 should stay Food Services on the left when approaching the Baltimore Beltway There are several inexpensive restaurants within (I-695). Follow the signs to I-695 east and exit a block or two of the campus. In addition, there immediately at Charles Street, then proceed as above are many restaurants with varying price ranges and to the University. cuisines in the Inner Harbor and downtown area. A Persons arriving from the south on I-95 should list of restaurants will be available at the meeting proceed north past I-695 and follow signs to I- registration desk. 95 Downtown, then take the exit to I-395. Stay Travel to the right and follow signs to Martin Luther King Jr. Boulevard; go approximately two miles on Major airlines and several regional carriers provide that Boulevard and turn left onto Howard Street. Inter­ regular service to the Baltimore-Washington Continue on Howard Street past 29th Street, then Airport. Taxi fare from the airport to national bear left onto Wyman Park Drive. Turn right onto $17. An airport the University costs approximately the University campus. limousine stops at the Holiday Inn-Inner Harbor Drivers heading to the Holiday Inn-Inner Harbor upon request, the fare for which is currently $5 per should look for signs indicating the Convention person. Center, since the Holiday Inn is situated one block AMTRAK Sta­ serves Baltimore at Pennsylvania north and two blocks west of that facility. tion. It is located between the University and the Holiday Inn-Inner Harbor, and may be reached either Parking by taxi or transit buses. (Buses #3, #9, and #11 on Ample free parking will be available at several lots Charles Street go to the University, and bus #3 on on the campus, except in restricted spaces. Parking St. Paul Street stops near the Holiday Inn). permits are not required on the weekend.

W. Wistar Comfort Middletown, Connecticut Associate Secretary

Population Biology Simon A. Levin, Editor

'The reviewer knows of no book which provides access to so many different major topics in population biology. It is not a text for any topic. but it is a road map for the reader. pointing out background. basic structure and important questions. either directly or by references. The stated purpose of acquainting readers with the important mathematical ideas and applications in population biology is achieved. by each author in his own way." -Fred Brauer University of Wisconsin-Madison SIAM Review Simon Levin. Mathematical population biology James Frauenthal. Population dynamics and demography Thomas Nagylaki. Some mathematical problems in population genetics Ethan Akin. Evolution: Game theory and economics Wayne Getz. Optimal control and principles in population management George Sugihara. Graph theory, homology and food webs Proceedings of Symposia in Applied Mathematics, Volume 30, 1984, 112 pages (softcover) List price $21, Institutional member $17, Individual member $13. To order, please specify PSAPMS/30N

Shipping/Handling: 1st book $2, each add'l $1, max. $25; by air, 1st book $5, each add'l $3, max. $100 Prepayment required. Order from American Mathematical Society, P.O. Box 1571, Annex Station Providence, Rl 02901-1571, or call toll free 800-556-7774 to charge with VISA or MasterCard

806 Invited Speakers Jalal Shatah and Sergiu Klainerman, Recent ad­ vances in nonlinear hyperbolic equations and Special Sessions Lutz Weis, Positive operators and their applications Invited Speakers at AMS Meetings April1986 Meeting in Indianapolis The individuals listed below have accepted invita­ Central Section tions to address the Society at the times and places Deadline for organizers: Expired indicated. For some meetings, the list of speakers is Deadline for consideration: January 15, 1986 incomplete. May 1986 Meeting in Baltimore New Orleans, January 1986 Eastern Section Joseph N. Bernstein Haynes R. Miller Deadline for organizers: Expired Lennart A. E. Carleson Jane Cronin Scanlon Deadline for consideration: January 20, 1986 Alexander S. Kechris S. T. Yau Carlos Berenstein and Bernard Shiffman, Complex Sergiu Klainerman (Colloquium Lecturer) analysis and its applications Indianapolis, April1986 Demitrios Christodoulou, Nonlinear evolution equa­ tions Steven Bell Richard McGehee Takashi Ono and Lawrence Washington, Number Jean Bourgain Niels Nygaard theory Baltimore, May 1986 Robert J. Serfling and John C. Wierman, Probability Demitrios Christopoulou Anthony W. Knapp and mathematical statistics David A. Cox Steven M. Zucker David Vogan, Representations of Lie groups W. Stephen Wilson, Homotopy theory and algebraic Organizers and Topics topology of Special Sessions Steven M. Zucker, Hodge theory The list below contains all the information about Spring 1986 Meeting Special Sessions at meetings of the Society available Far Western Section at the time this issue of the Notices went to the No meeting will be held printer. The section below entitled Information for Organizers describes the timetable for announcing Spring 1986 Meeting the existence of Special Sessions. Southeastern Section January 1986 Meeting in New Orleans No meeting will be held Associate Secretary: Frank T. Birtel October 1986 Meeting in Logan Deadline for organizers: Expired Far Western Section Deadline for consideration: Expired Gary S. Bloom and D. F. Hsu, Graph labelings Deadline for organizers: April15, 1986 Deadline for consideration: To be announced Richard Bronson, Mathematical modeling and computer simulation to problems in other October 1986 Meeting in Denton disciplines Central Section Peter L. Duren, Complex analysis Deadline for organizers: April15, 1986 Robert B. Gardner and William F. Shadwick, Deadline for consideration: To be announced Equivalence problems and applications Eric L. Grinberg and Eric Todd Quinto, Radon Fall1986 Meeting transforms and tomography Eastern Section Rebecca A. Herb and Paul J. Sally, Jr., Harmonic Deadline for organizers: April15, 1986 analysis on reductive groups Deadline for consideration: To be announced Alexander S. Kechris and W. Hugh Woodin, Deter­ Fall 1986 Meeting minacy and large cardinals Sung J. Lee, Operator method of optimal control Southeastern Section problems Deadline for organizers: April15, 1986 Erwin Lutwak, Convexity Deadline for consideration: To be announced Jorge Martinez, Ordered algebras Peter A. McCoy, Analytic methods in differential Information for Organizers equations Special Sessions at Annual and Summer meetings Stephen A. Mitchell, Homotopy theory are held under the general supervision of the PaulS. Muhly, Operator theory and several complex Program Committee. They are administered by variables the Associate Secretary in charge of the meeting with Jane Cronin Scanlon, Mathematical biology staff assistance from the Society office in Providence. Claude L. Schochet and Kenneth C. Millett, Operator Some Special Sessions arise from an invitation to algebras and foliations a proposed organizer issued through the Associate

807 Secretary. Others are spontaneously proposed by 6248, Providence, RI 02940) by the special deadline interested organizers or participants. Such proposals for Special Sessions, which is usually three weeks are welcomed by the Associate Secretaries. earlier than the deadline for contributed papers for The number of Special Sessions at a Summer or the same meeting. The Council has decreed that no Annual Meeting is limited to twelve. Proposals, paper, whether invited or contributed, may be listed invited or offered, which are received at least in the program of a meeting of the Society unless an nine months prior to the meeting are screened for abstract of the paper has been received in Providence suitability of the topic and of the proposed list prior to the deadline. of speakers, and for possible overlap or conflict with other proposals (specific deadlines for requesting approval for Special Sessions at national meetings are Send Proposals for Special Sessions to the given above). If necessary, the numerical limitation Associate Secretaries is enforced. The programs of sectional meetings are arranged by Proposals for Special Sessions should be submitted the Associate Secretary for the section in question: directly to the Associate Secretary in charge of the Far Western Section (Pacific and Mountain) meeting (at the address given in the accompanying Hugo Rossi, Associate Secretary box). If such proposals are sent to the Providence Department of Mathematics University of Utah office, addressed to the Notices, or directed to anyone Salt Lake City, UT 84112 other than the Associate Secretary, they will have (Telephone 801-581-8159) to be forwarded and may not be received before the Central Section quota is filled. Robert M. Fossum, Associate Secretary In accordance with an action of the Executive Department of Mathematics Committee of the Council, no Special Session may University of lllinois be arranged so late that it may not be announced in 1409 West Green Street Urbana, IL 61801 the Notices early enough to allow any member of the (Telephone 217-333-3975) Society, who wishes to do so, to submit an abstract Eastern Section for presentation in the Special for consideration W. Wistar Comfort, Associate Secretary Session before the deadline for such consideration. Department of Mathematics Special Sessions are effective at Sectional Meetings Wesleyan University and can usually be accommodated. They are arranged Middletown, CT 06457 by the Associate Secretary under the supervision of (Telephone 203-34 7-9411) the Committee to Select Hour Speakers for the Southeastern Section section. The limitation on the number of sessions Frank T. Birtel, Associate Secretary Department of Mathematics depends on the space and time available. The same Tulane University restriction as for national meetings applies to the New Orleans, LA 70118 deadline for announcing Special Sessions at sectional (Telephone 504-865-5646) meetings: no Special Session may be approved too As a general rule, members who anticipate organizing late for its announcement to appear in time to Special Sessions at AMS meetings are advised to seek approval at least nine months prior to the scheduled date allow a reasonable interval for members to prepare of the meeting. No Special Sessions can be approved and submit their abstracts prior to the special early too late to provide adequate advance notice to members deadline set for consideration of papers for Special who wish to participate. Sessions. The Society reserves the 'right of first refusal for the publication of proceedings of any special session. These proceedings appear in the book series Contemporary Mathematics. Information for Speakers A great many of the papers presented in Special Sessions at meetings of the Society are invited papers, but any member of the Society who wishes to do so may submit an abstract for consideration for presentation in a Special Session, provided it is received in Providence prior to the special early deadline announced above and in the announcements of the meeting at which the Special Session has been scheduled. Abstracts of papers submitted for consideration for presentation at a Special Session must be received by the Providence office (Editorial Department, American Mathematical Society, Post Office Box

808 Joint Summer Research Conferences in the Mathematical Sciences University of California, Santa Cruz, June 22 to August 2, 1986

The 1986 Joint Summer Research Conferences participate in these conferences. The deadline for in the Mathematical Sciences will be held at the receipt of applications is February 3, 1986. Those who University of California, Santa Cruz, from June 22 wish to apply for a grant-in-aid should so indicate to August 2, 1986. It is anticipated that the series on the application form; however, funds available for of conferences may be supported by a grant from the these conferences are limited and so individuals who National Science Foundation. can obtain support from other sources should do so. There will be six conferences in six different Speakers will be selected by the chairman· and the areas of mathematics. Each week participants will Organizing Committee. arrive on Sunday and leave the following Saturday. For information on the scientific program, inter­ Lectures will begin on Monday morning and end ested participants should contact the chairman of the Friday afternoon. The topics and organizers for the conference they plan to attend. six conferences were selected by the AMS-IMS-SIAM The Joint Summer Research Conferences in the Commmittee on Joint Summer Research Conferences Mathematical Sciences are under the direction of in the Mathematical Sciences. The selections were the AMS-IMS-SIAM Committee on Joint Summer based on suggestions made by the members of Research Conferences in the Mathematical Sciences. the committee and individuals submitting proposals. The following committee members chose the topics for The committee considered it important that the the 1986 conferences: Ronald L. Graham, Benedict H. conferences represent diverse areas of mathematical Gross, Malcolm R. Leadbetter, Angus J. Macintyre, activity, with emphasis on areas currently especially Jerrold E. Marsden, John R. Martin, James McKenna, active, and paid careful attention to subjects in Tilla Klotz Milnor, Evelyn Nelson, Katsumi Nomizu, which there is important interdisciplinary activity at and R. 0. Wells, Jr. (chairman). present. Descriptions of the subject matter of each of the The conferences will be similiar in structure to 1986 Conferences appeared in the October Notices, those held throughout the year at Oberwolfach. These pages 672 and 673; they were accompanied by lists of conferences are intended to complement the Society's members of the respective organizing committees. program of annual Summer Institutes and Summer Seminars, which have a larger attendance and are June 22 to June 28 substantially broader in scope. The conferences are Mathematics in general relativity research conferences, and are not intended to provide JAMES IsENBERG (University of Oregon), Chairman an entree to a field in which a participant has not already worked. June 29 to July 5 It is expected that funding will be available for Large scale data analysis via computer graphics a limited number of participants in each conference. ANDREAS BuJA (University of Washington), Co­ Others, in addition to those funded, will be welcome, Chairman within the limitations of the facilities of the campus. WERNER STUETZLE (University of Washington), Housing accommodations will be available on campus Co-Chairman for those attending the conferences. A brochure describing the facilities available at the University of July 6 to July 12 California, Santa Cruz, will be available from the Time reversal of Markov processes and potential theory AMS office in March 1986. The brochure will include JOSEPH GLOVER (University of Florida), Chairman information on firm room rates, the residence and dining hall facilities, as well as local information July 13 to July 26 and a reservation form to be used for requesting Artin 's braid group accommodations on campus. Each participant is JOAN S. BIRMAN (Columbia University), Chairman expected to pay a registration fee and a social fee to cover the cost of refreshments served at breaks and July 20 to July 26 for social events. Discrete and computational geometry Those interested in attending one of the conferences JACOB E. GoODMAN (City College, CUNY), Co­ should request an application form from Carole Chairman Kohanski, Summer Research Conference Coordinator, American Mathematical Society, Post Office Box RICHARD POLLACK (Courant Institute of Mathe­ 6248, Providence, RI 02940 (401-272-9500, extension matical Sciences, New York University), Co-Chairman 286), specifying which conference they wish to attend. July 27 to August 2 Selection of the participants and the allocation of Representation theory of Lie groups support will be made by the Organizing Committee for each individual conference. Women and members WILFRIED ScHMID (Harvard University), Chairman of minority groups are encouraged to apply and to

809 Special Meetings

THIS SECTION contains announcements of meetings of interest to some segment of the mathematical public, including cul lwc, local, or regional meetings, and meetings or symposia devoted to specialized topics, as well as announcements of regularly scheduled meetings of national or intemational mathematical organizations. (Information on meetings of the Society, and on meetings sponsored by the Society, will be found inside the front cover.) AN ANNOUNCEMENT will be published in the Notices if it contains a call for papers, and specifies the place, date, subject (when applicable), and the speakers; a second full announcement will be published only if there are changes or necessary additional information. Once an announcement has appeared, the event will be briefly noted in each issue until it-has been held and a reference will be given in parentheses to the month, year and page of the issue in which the complete information appeared. IN GENERAL, announcements of meetings held in North America carry only date, title of meeting, place of meeting, names of speakers (or sometimes a general statement on the program), deadlines for abstracts or contributed papers, and source of further information. Meetings held outside the North American area may carry more detailed 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 special meetings should be sent to the Editor of the Notices, care of the American Mathematical Society in Providence. DEADLINES for entries in this section are listed on the inside front cover of each issue. In order to allow participants to arrange their travel plans, organizers of meetings are urged to submit information for these listings early enough to allow them to appear in more than one issue of the Notias prior to the meeting in question. To achieve this, listings should be received in Providence SIX MONTHS prior to the scheduled date of the meeting.

1984-1985. Academic Year Devoted to Nonlinear Differ­ NOVEMBER 1985 ential Equations, The Mittag-Leffler Institute, Djursholm, Sweden. (February 1984, p. 194) 4-15. Workshop on Large Deviation Theory, University of Minnesota, Minneapolis, Minnesota. (June 1985, p. 402) 1984-1985. Special Year Devoted to Minimal Surfaces and their Applications to Low-Dimensional Topology, De­ 13--19. International Conference, Algebraic Geometry, partment of Mathematics, University of Califomia, Santa Humboldt-Universitat, Berlin, German Democratic Re­ Barbara, California. (October 1984, p. 690) public. (August 1985, p. 524) 1984-1985. Special Year Devoted to Reacting Flows: 14-15. Conference on Applied Analysis in Aerospace Combustion and Chemical Reactors, Center for Applied and Industrial Research, University of Houston, Houston, Mathematics, Comell University, Ithaca, New York. (April Texas. (August 1985, p. 524) 1984, p. 333) 16--18. Seminaires Bourbaki, Paris, France. 1984-1985. Special Year in Mathematical Logie and Irifarmation: Association des Collaborateurs de Nicolas Theoretical Computer Science, University of Maryland, Bourbaki, Rue d'Ulm 45, F-75230 Paris Cedex 05, College Park, Maryland. (March 1985, p. 267) France. 1984-1985. Special Year in Singularities and Algebraic 11!-20. Second SIAM Conference on Parallel Process­ Geometry, University of North Carolina, Chapel Hill, ing and Scientific Computing, Norfolk, Virginia. {January North Carolina. (June 1985, p. 397) 1985, p. 93) October 7, 1984-December 14, 1985. Mathematisches 18-21. Second SIAM Conference on Parallel Processing Forsehungainatitut Oberwolfach {Weekly Conferences), for Scientific Computing, Omni Hotel, Norfolk, Virginia. Federal Republic of Germany. (October 1984, p. 689) (October 1985, p. 675) 1985. European Mechanics Colloquia, Various locations. 18--22. Conference on Function-Theoretic Operator The­ (October 1984, p. 690) ory, Indiana University, Bloomington, Indiana. (August 1985, p. 524) 1985-1986. Academic Year Devoted to Nonlinear Dif­ ferential Equations, Mittag-Leffler Institute, Djursholm, 18-24. Mathematical Methods in Technology, Jamol­ Sweden. (January 1985, p. 89) towek, Poland. Infarmation: S. Gladysz, Technical University of Opole, 1985-1986. Special Year in Complex Analysis, Univer­ ulica Zrzeszenia Studentow Polskich 5, P-45-233 Opole, sity of Maryland, College Park, Maryland. (August 1985, Poland. p. 522) 21-22. Twentieth Actuarial Research Conference, Univer­ 1985--1986. Special Year in Differential Geometry, Uni­ sity of Texas, Austin, Texas. (June 1985, p. 402) versity of illinois, Urbana-Champaign, illinois. (October 26--30. Geometrie diffi!rentielle, CIRM-Luminy, France. 1985, p. 674) {August 1985, p. 524) 1985-1986. Special Year in Operator Theory, Indiana University, Bloomington, Indiana. {August 1985, p. 522) DECEMBER 1985 1985-1986. Year in Mathematical Logie, University of Notre Dame, Notre Dame, Indiana. {October 1985, p. 674) 7-9. Canadian Mathematical Society Annual Winter August 19, 1985--July 31, 1986. Program on Stochastic Meeting, University of Calgary, Calgary, Ontario, Canada. Differential Equations and Their Applications, University (August 1985, p. 524) of Minnesota, Minneapolis, Minnesota. {Note date change 16--19. International Symposium on Foundations of Statis­ from June 1985, p. 397) tical Reference, Mandarin Hotel, Tel-Aviv, Israel. {October October 1985-0ctober 1986. Material Instabilities in 1985, p. 675) Continuum Mechanics, Heriot-Watt University, Edinburgh, 16--20. Second Chilean Mathematics Symposium, Univer­ Scotland. {June 1985, p. 397) sidad de Talca, Chile. (October 1985, p. 675)

810 16--21. Methods of Functional Analysis in Approximation APRIL 1986 Theory, Indian Institute of Technology, Bombay, India. (March 1985, p. 272) 1-4. Symposium on Algebraic Groups in Honour ofT. A. Springer, Utrecht, The Netherlands. Organizers: A. M. Cohen, W. H. Hesselink, W. van der ****** Kallen, J. R. Strooker. No registration fee is required. No financial support is available from the organizers. JANUARY 1986 Infarm.atinn: W. van der Kallen, Mathematical Institute, Postbus 80.010, NL-3508 TA Utrecht, The Netherlands. Workshop on Regularity of P.D.E., Harmonic Analysis, 2·-8. Barcelona Conference on Algebraic Topology, Insti­ Malliavin Calculus, Institute for Mathematics and its tut d'Estudis Catalans, Barcelona, Spain. (October 1985, Applications, University of Minnesota, Minneapolis, Min­ p. 676) nesota. (October 1985, p. 675) 6--10. Saint-Etienne: Congres international sur lea prob­ 4-5. Illinois Number Theory Conference, University of lemes byperboliques: theorie, methodes numeriques, Illinois, Urbana, Illinois. grandes applications, Universite Saint-Etienne, 23 rue lnfarm.atinn: H. Diamond, Mathematics Department, Uni­ Doct. P. Michelon, 42023 Saint-Etienne Cedex, France. versity of Illinois, 1409 West Green Street, Urbana, (October 1985, p. 675) Illinois 61801. 11. TJ!jX Seminar, To be held at a location (to be 7-11. XI Jornadas Hispano-Lusas de Mateuuiticas, Bada­ announced) in the immediate vicinity of the Joint Meeting joz, Spain. in New Orleans. (October 1985, p. 675) Priru:ipal Speaker: L. Nachbin, University of Rochester and 13-17. Fifth International Symposium on Approximation University of Rio de Janeiro. Theory, Texas A & M University, College Station, Texas. Call for Papers: Contributed papers in the following gen­ (June 1985, p. 402) eral fields are welcomed: Analysis, Algebra, Geometry, Topology, Statistics, Didactic and Applied Mathematics. FEBRUARY 1986 Infarm.atinn: J. M. Garcia-Lafuente, Departamento de Mate­ maticas, Universidad de Extremadura, 06071-Badajoz, 3-July 26. Special Semester and International Confer­ Spain. ence on Holomorphic Dynamical Systems, lnstituto de Matematicas, Universidad Nacional Aut6noma de Mexico. 14-18. Joint IMA/SIAM Conference on the State of the (August 1985, p. 525) Art in Numerical Analysis, University of Birmingham, Birmingham, England. (October 1985, p. 677) 4--6. Fourteenth Annual Computer Science Conference, Cincinnati Convention Center, Cincinnati, Ohio. (October 21-24. Sixth International Conference on Decision Sup­ 1985, p. 676) port Systems, Washington, District of Columbia. 6--7. ACM SIGCSE Symposium: Technical Symposium Program: The objective of this conference is to provide on Computer Science Education, Cincinnati Convention a forum for learning about and exchanging experiences Center, Cincinnati, Ohio. (October 1985, p. 676) and ideas on Decision Support Systems (DSS). A tutorial on understanding DSS and getting started is planned for 17-21. Workshop on Disordered Systems, Percolation, and the first day of the conference. This track is designed for Self-Avoiding Random Walks, University of Minnesota, people new to DSS. Minneapolis, Minnesota. (June 1985, p. 402) lnfarm.atinn: J. Eldridge, DSS-86, 290 Westminster Street, Providence, Rhode Island 02903. MARCH1986 24-25. Seventeenth Annual Pittsburgh Conference on 3-8. International Conference on Differential Equations Modeling and Simulation, School of Engineering, Univer­ and Mathematical Physics, University of Alabama at Birm­ sity of Pittsburgh. ingham, Birmingham, Alabama. (October 1985, p. 676) Program: Special emphasis for the 1986 Conference will be 13-15. The 250th Anniversary Conference on Graph The­ on microprocessors, personal computer applications and ory, Indiana University-Purdue University at Fort Wayne, software, artificial intelligence, expert systems, robotics, Fort Wayne, Indiana. (October 1985, p. 676) and social, economic, regional science, and global mod­ eling and simulation and papers on all traditional areas 13-18. Workshop on Holomorphic Functions and Mod­ of modeling and simulation. uli, Mathematical Sciences Research Institute, Berkeley, California. (October 1985, p. 676) Call for Papers: Two copies of titles, authors, all author's addresses, abstracts and summaries should be submitted 14-15. Several Complex Variables and Partial Differential by January 31, 1986. The abstract should be approxi­ Equations, Montreal, Canada. mately 50 words in length and the summary should be of PartioJ List of Speakers: B. Aupetit, R. Dwilewicz, P. C. sufficient length and detail to permit careful evaluation. Grenier, J. Kohn, F. Triwes. Identify one author as the correspondent for the paper. Infarm.atinn: P. Gauthier, Centre de Recherches Mathll­ lnfarm.atinn: W. G. Vogt or M. H. Mickle, Modeling matiques, Universite de Montreal, C. P. 6128, Succursale and Simulation Conference, 348 Benedum Engineering A, Montreal, Quebec, Canada H3C 3J7, 514-343-6691. Hall, University of Pittsburgh, Pittsburgh, Pennsylvania 17-21. Workshop on Hydrodynamic Behavior of Interact­ 15261. ing Particle Systems, University of Minnesota, Minneapo­ lis, Minnesota. (June 1985, p. 402) 24-26. Viscosity Solutions of Hamilton-Jacobi Equations, The University of Arkansas, Fayetteville, Arkansas. 19-22. Matrix Theory Conference, Auburn University, Speakers: M. G. Crandall, N. Barron, L. C. Evans, R. Auburn, Alabama. (October 1985, p. 676) Gariepy, R. Jensen, S. Lenhardt, R. Sanders, M. Soner, 24-26. Fifth ACM SIGACT-SIGMOD Symposium on P. Souganides. Principles of Database Systems, Cambridge, Massachu­ Abstract Deadline: February 15, 1986. Contributed talks are setts. (October 1985, p. 676) welcome. 24-28. Fourth International Symposium on Numerical lnfarm.atinn: D. Brewer or W. Summers, Department of Methods in Engineering, Atlanta, Georgia. (June 1985, Mathematical Sciences, University of Arkansas, Fayet­ p. 402) teville, Arkansas 72701, 501-575-6317 or 6333.

811 MAY1986 7-11. The Fourth International Conference on Bound­ ary and Interior Layers-Computational and Asymptotic 12-16. Thirtieth Annual Conference of the Australian Methods, Institute of Mathematics, Siberian Branch of Mathematics Society, Perth, Western Australia. (October the U.S.S.R. Academy of Sciences, Novosibirsk, U.S.S.R. 1985, p. 677) (October 1985, p. 678) 18-21. International Symposium on Flood Frequency and 14-25. Partial Differential Equations, Eighth Latin Amer­ Risk Analyses, Louisiana State University, Baton Rouge, ican School of Mathematics, Institute de Matematica Pura Louisiana. (October 1984, p. 694) e Aplicada, Rio de Janeiro, Brazil. (October 1985, p. 678) 18-23. Third International Spring School on Nonlinear 14·-26. Oscillation, Bifurcation and Chaos: An Interna­ Mathemati­ Analysis, Function Spaces and Applications, tional Conference in Differential Equations, The University cal Institute, Czechoslovak Academy of Sciences, Prague, of Toronto, Toronto, Canada. Czechoslovakia. (October 1985, p. 677) Organizi-ng Committee: F. V. Atkinson, V. Jurdjevic, W. F. 19-23. Workshop on Complexity Aspects of Parallel and Langford, A. B. Mingarelli. Distributed Computing, Mathematical Sciences Research Program: The conference is being organized on two ma­ Institute, Berkeley, California. (October 1985, p. 677) jor themes. One of the themes is oscillation and its 19-24. NATO Advanced Research Workshop: Infinite ramifications, as inspired by the 150th anniversary of Dimensional Systems, Lisbon, Portugal. (October 1985, Sturm's pioneering work with Memoire: Sur les equations p. 677) diffbentielles lineaires du second ardre. This theme will be the focus for the first week of the conference which will International Conference on the Physics of Phase 2G-23. concentrate on second order operators and their general­ of Maryland, College Park, Maryland. Space, University izations. The theme of the second week of the conference 1985, p. 525) (August is bifurcation phenomena and the chaotic behaviour of solutions of differential equations. JUNE1986 Call far Papers: Contributed papers related to the themes of the conference are invited. Abstracts must be received 1-5. First Japan Conference on Graph Theory and its by April 30, 1986. Applications, Tokai University, Hiratsuka, Japan. (October InforrnatUm: W. F. Langford, Department of Mathematics 1985, p. 677) and Statistics, University of Guelph, Guelph, Ontario, 2-4. The Second Symposium on Computational Geometry, Canada N1G 2W1. Heights, IBM T. J. Watson Research Center, Yorktown 21-26. International Congress on Computational and Ap­ (October 1985, p. 677) New York. plied Mathematics, University of Leuven, Belgium. (Octo­ 4-{1. 1986 National Educational Computing Conference, ber 1985, p. 678) Town and Country Hotel, San Diego, California. (October 1985, p. 677) 22-·26. Conference on Constructive Function Theory, Uni­ versity of Alberta, Edmonton, Alberta, Canada. (August 9-19. Stochastic Differential Systems with Applications 1985, p. 525) to Control Theory, Electrical/Computer Engineering, and Operations Research, University of Minnesota, Minneapo­ 23· 31. 1986 Corvallis Conference: Quadratic Forms and lis, Minnesota. (June 1985, p. 402) Real Algebraic Geometry, LeSell Stuart Center, Oregon State University, Corvallis, Oregon. 16-20. Fifteenth International Symposium on Rarefied Program: full schedule of eight to ten Gas Dynamics, Grado, Gorizia, Italy. (October 1985, There will be a thirty-minute talks (some longer) on each of the five p. 677) weekdays. These will be grouped into special topics and 17-21. Analysis Conference, National University of Singa­ scheduled by the organizers. Evenings are reserved for pore, Republic of Singapore. (October 1985, p. 677) problem seesions and extra talks if needed. Saturday 19-23. Combinatoric& and Graph Theory, National Uni­ is fully reserved for workshops. Special topics include: versity of Singapore, Republic of Singapore. (October 1985, Abstract Witt Rings, Arithmetic Theory of Quadratic p. 677) Forms, Spaces of Orderings, Model Theory, Galois The­ ory and Quadratic Forms, Sums of Squares, Structure Society of Women Engineers 1986 National Con­ 22-29. of Semialgebraic Sets, Real Commutative Algebra, Real Sheraton Hartford and Parkview Hilton, Hartford, vention, Spectrum, Witt Rings of Varieties, Analytic and Sub­ (October 1985, p. 678) Connecticut. analytic Geometry. 24-27. Seventh International Conference on Analysis and InforrnatUm: W. B. Jacob orR. 0. Robson, Department of Optimization of Systems, Antibes, France. (October 1985, Mathematics, Oregon State University, Corvallis, Oregon p. 678) 94331. 3G-July 4. Tenth Prague Conference on Information The­ 27-30. Tenth Summer Symposium on Real Analysis, Uni­ ory, Statistical Decision Functions and Random Processes, versity of British Columbia, Vancouver, British Columbia, Institute of Information Theory and Automation of the Canada. Czechoslovak Academy of Sciences, Prague, Czechoslo­ Program: Developments in integration and differentiation. vakia. (October 1985, p. 678) Recent work on a general integral that integrates the exterior derivative of any differentiable exterior form JULY 1986 will be featured. Extensions of derivatives, continuity and variation. 2-12. LMS Symposium on Non-classical Continuum Me­ Call far Papers: Those interested in contributing a paper chanics: Abstract Techniques and Applications, University should send an abstract to the address below. of Durham, Durham, England. Information: P. S. Bullen, Department of Mathematics, Pr£ncipal Speakers: I. Muller, 0. A. Oleinik, P. J. Olver, G. University of British Columbia, 121-1984 Mathematics Papanicolaou, L. E. Payne, L. Tartar. Road, Vancouver, British Columbia, Canada V()T 1Y4. Informati,on: A. A. Lacey, Department of Mathematics, Heriot-Watt University, Riccarton, Edinburgh, EH14 27--August 1. Thirteenth International Biometric Confer­ 4AS, Scotland. ence, Seattle, Washington. (June 1985, p. 402) 7-9. The Fourth IMA Conference on the Mathematical 28-August 1. The Seventh International Conference on Theory of the Dynamics of Biological Systems, University Nonlinear Analysis and Applications, The University of of Oxford, Oxford, England. (October 1985, p. 678) Texas, Arlington, Texas. (October 1985, p. 678)

812 29--August 1. Conference on Continuous Time, Fractional SEPTEMBER 1986 and Multiobjeetive Programming, St. Lawrence University, Canton, New York. 4-7. Polish Symposium on Interval and Fuzzy Mathe­ Span3ars: GTE Company and St. Lawrence University. matics, Technical University of Poznan, Poznan, Poland. Principal Spealrers: M. Avriel, J. Borwein, M. A. Hanson, (October 1985, p. 679) R.N. Kaul, F. A. Lootsma, S. Schaible. 8-13. Algebra-Tagung Halle 1986, Martin Luther Uni­ Topics: Duality Theory, Optimality Conditions, Algo­ versitat, German Democratic Republic. (October 1985, rithms, Computer Softwares, Foundational topics like p. 679) Convexity, Differentiability, Theorem of Alternatives, 8-14. First World Congress of the Bernoulli Society etcetera. for Mathematical Statistics and Probability, Tashkent, lrifarmatian: C. Singh, Department of Mathematics, St. U.S.S.R. (October 1985, p. 679) Lawrence University, Canton, New York 13617, 315-379- 5293. 22-27. Orthogonal Polynomials and Their Applications, Segovia, Spain. 3D-August 1. Conference on Universal Algebra and Lattice Theory, National Institutes of Health, Bethesda, Maryland. Organizin{} Committee: M. Alfaro, J. S. Dehesa, F. Marcellan. Program: The program includes lectures and sessions for (October 1985, p. 678) contributed papers. 3D-August 2. Computers in Mathematics, Stanford Uni­ Principal Speakers: T. Koornwinder, A. M. Krall, P. Nevai, versity, Palo Alto, California. J. L. Geronimo. Program: This conference will be devoted to the exposition Gonl:ributed Papers: Deadline is May 1, 1986. Acceptance of the fruits and potentials of computers to research or rejection notification by June 1, 1986. Camera-ready in mathematics and related areas. The conference will copies by the date of the Conference. consist of invited addresses, poster sessions, tutorial lrifarmatian: F. Marcellan, Departamento de Matematicas, mini-courses, and demonstrations of mathematical soft­ Universidad Politecnica de Madrid, Calle Gutierrez ware systems. Abascal 2, E-28006 Madrid, Spain. Gall far Papers: Authors for poster session contributions should submit four copies of a paper (maximum ten OCTOBER 1986 pages) by April 15, 1986 to J. H. Davenport, School of Mathematics, University of Bath, Claverton Down, Bath 5-9. International Symposium on Operator Theory, Uni­ BA2 7AY, England. versity of Michigan, Ann Arbor, Michigan. (October 1985, lnfarmatian: R. D. Jenks, IBM Research Center, Post Office p. 679) Box 218, Yorktown Heights, New York 10598 or D. V. Chudnovsky, Department of Mathematics, Columbia University, New York, New York 10027. JUNE1987 15-July 3. Microprogram on Commutative Algebra, Math­ AUGUST1986 ematical Sciences Research Institute, Berkeley, California. (October 1985, p. 679) 3-11. International Congress of Mathematicians, Berkeley, California. (February 1984, p. 159) 11-16. Second International Conference on Teaching Statistics, University of Victoria, Victoria, British Colum­ bia, Canada. (January 1985, p. 93) 18-22. Bifurcation, Analysis Algorithms Applications, Universitat Dortmund, Dortmund, Federal Republic of Germany. (October 1985, p. 679) Restricted Orbit Equivalence 25-29. Sixth Prague Topological Symposium, Prague, Daniel J. Rudolph Czechoslovakia. (June 1985, p. 402) (Memoirs of the AMS. Number 323) 25-September 13. Microprogram on Nonlinear Diffusion Equations and their Equilibrium States, Mathematical Sciences Research Institute, Berkeley, California. (October These notes develop a theory of restricted orbit 1985, p. 679) equivalence which has as particular examples Ornstein's isomorphism theorem for Bernoulli processes. Dye· s orbit equivalence theorem for ergodic processes and the theory of Kakutani equivalence developed by Feldman. Ornstein. Weiss and Katok. Other examples are also given. A number of results from the Bernoulli theory are shown to be true for any restricted orbit equivalence.

1980 Mathematics Subject Classifications: 28005, 28020 ISBN 0-8218-2324-3, LC 84-28119 ISSN 0065-9266 vi + 150 pages (softcover), March 1985 List price $18, Institutional l}lember S14, Individual member Sll Shipping and handling charges must be added To order, please specify MEM0/323N

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813 New AMS Publications

Fair Allocation 1980 Mathematics Subject Classification: 90-XX H. Peyton Young, Editor ISBN 0094, LC 85-18542 (Proceedings of Symposia in Applied Mathematics. ISSN 0160-7634 xiv + 170 pages, December 1985 AMS Short Course Lecture Notes. Volume 33) Hardcover: List price S26, Institutional member $21, Individual member $16 This collection of six papers provides a valuable Softcover: List price S21, Institutional member source of material on the real-world problem of $17, Individual member $13 Shipping and handling charges must be added allocating objects among competing claimants. To order, please specify PSAPM/33N The examples given show how mathematics. (hardcover), PSAPMS/33N (softcover) particularly the axiomatic method. can be applied to give insight into complex social problems. Structure of the Standard Originally presented as an AMS Short Course. these papers could serve as a suitable text for Modules for the Affine courses touching on game theory. decision sciences. Lie Algebra A( 1) economics. or quantitative political science. Most James Lepowsky Mirko Prime of the material is accessible to the mathematically ~nd (Contemporary Mathematics. Volume 46) mature undergraduate with a background in advanced calculus and algebra. Each article surveys The affine Kac-Moody algebra A~1 ) has the recent literature and includes statements and recently served as a source of new ideas in the sketches of proofs. as well as unsolved problems representation theory of infinite-dimensional affine which should excite student curiosity. Lie algebras. In particular. several years ago it The articles analyze the question of fair was discovered that Ai1l and then a general class allocation via six examples: the apportionment of affine Lie algebras could be constructed using of political representation. the measurement of operators related to the vertex operators of the income inequality, the allocation of joint costs. physicist's string model. This paper develops the the levying of taxes. the design of voting laws. calculus of vertex operators to solve the problem of and the framing of auction procedures. In each of constructing all the standard A~1 >-modules in the these examples fairness has a somewhat different homogeneous realization. significance. but common axiomatic threads reveal Aimed primarily at researchers in and students broad underlying principles. Each of the topics of Lie theory. the book's detailed and concrete is concerned with norms of comparative equity exposition makes it accessible and illuminating for evaluating allocations or with standards of even to relative newcomers to the field. procedures for effecting them: it is this focus on normative properties which suggests that a Contents mathematical analysis is appropriate. Though The Lie algebra Ai1l game theory provides a useful tool in many of The category Pk these allocation problems. the emphasis here is on standards rather than strategy and equity rather The generalized commutation relations than rationality. an approach which aims to more Relations for standard modules accurately mirror real-world social problems. Basis of OL for a standard module L Contents M. L. Balinski and H. P. Young. The Schur functions apportionment of representation Proof of linear independence James E. Foster. Inequality measurement Combinatorial formulas H. Peyton Young. Cost allocation H. Peyton Young. The allocation of debts and 1980 Mathematics Subject Classifications: 17B65,05A17, 05A19 taxes ISBN 0-8218-5047-4, LC 85-15639 Herve Moulin. Fairness and strategy in voting ISSN 0271-4132 Robert J. Weber. Auctions and competitive x + 84 pages (softcover), November 1985 List price $13, Institutional member SlO, bidding Individual member $8 Shipping and handling charges must be added To order, please specify CONM/46N

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814 Linear Algebra and its Role m T. Kailath and H. Lev-Ari. On mappings between Systems Theory covariance matrices and physical systems J. Kautsky and N. K. Nichols. Robust multiple Biswa Nath Datta, Editor eigenvalue assignment by state feedback in linear (Contemporary Mathematics. Volume 47) systems This collection of 35 papers resulting from L. H. Keel, J. A. Fleming and S. P. Bhat­ the 1984 AMS-IMS-SIAM Summer Research tacharyya. Minimum norm pole assignment via Conference displays the cross-developments Sylvester's equation between linear algebra (including numerical linear M. F. Silva Leite. The uniform finite generation algebra) and systems and control theory. Linear problem of Lie groups and its application to algebraists will see how some beautiful and strong control systems results of control and systems theory can be L. Lerer and M. Tismenetsky, On the location of derived using the concepts of linear algebra: control spectrum of matrix polynomials and systems theorists will find numerically viable Raphael Loewy. Two matrices which have equal algorithms which can be developed for some corresponding principal minors important control problems. A full appreciation of Michael Neumann and Ronald J. Stern. Cone the material requires an advanced course in linear reachability for differential systems algebra. a basic course in matrix computation. and Christopher C. Paige. Covariance matrix a first course in control theory. representation in linear filtering R. V. Patel. A condensed form for linear systems Contents over principal ideal domains Abraham Berman and Daniel Hershkowitz. T. E. S. Raghavan. On pairs of multidimensional Graph theoretical methods in studying stability matrices and their applications M. W. Berry and Robert J. Plemmons. Mark A. Shayman. Parametrization of the flags Computing a banded basis of the null space on fixed by a unipotent matrix the Denelcor HEP multiprocessor Eduardo D. Sontag. An introduction to the N. K. Bose. A system-theoretic approach to stabilization problem for parametrized families of stability of sets of polynomials linear systems Ralph Byers. Numerical condition of the algebraic Robert C. Thompson. Smith invariants of a Riccati equation product of integral matrices Stephen L. Campbell. Rank deficient least George Trapp. The Ricatti equation and the squares and the numerical solution of linear geometric mean singular implicit systems of differential equations Paul M. Van Doren and Michael Verhaegen. On J. Casti. Linear methods for nonlinear problems the use of unitary space-state transformations G. Conte and A. M. Perdon. Zero modules and Charles Van Loan. How near is a stable matrix to factorization problems an unstable matrix? Biswa Nath Datta and Karabi Datta. Sequential Jan C. Willems. An approach to exact and and parallel computations and complexities for approximate modeling of time series determining relative primeness. stability and Harald K. Wimmer. Straight bases of finite inertia Abelian groups and a Jordan factorization Vera W. de Spinadel. On optimal control theorem for integer matrices David A. Field. The focal point method and Bostwick F. Wyman and Michael K. Sain. almost linear systems of equations Poles. zeros. and lattices Shmuel Friedland. Classification of linear systems Paul A. Fuhrmann. 1980 Mathematics Subject Classifications: On the partial realization 15-XX, 65-XX, 93-XX problem and the recursive inversion of Hankel ISBN 0-8218-5041-5, LC 85-18620 and Toeplitz matrices ISSN 0271-4132 xiv + 506 pages (softcover), November 1985 Bijoy K. Ghosh. Some recent results in List price $36, Institutional member $29, simultaneous system design Individual member $22 R. E. Hartwig, Shipping and handling charges must be added F. J. Hall and I. J. Katz. Block To order, please specify CONM/47N striped and block nested matrices Daniel Hershkowitz and Hans Scheider. Semistability factors and semifactors D. Hinrichsen and D. Pratzei-Wolters. State and input transformations for reachable systems-a polynomial approach

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815 Harish-Chandra The Spectral Theory of Homomorphisms for ~-adic Geometrically Periodic Groups Hyperbolic 3-Manifolds Roger Howe Charles L. Epstein (CBMS Regional Conference Series. Number 59) (Memoirs of the AMS. Number 335) This book introduces a systematic new approach This paper develops the spectral theory of to the construction and analysis of semisimple the Laplace-Beltrami operator for geometrically p-adic groups. The basic construction presented periodic hyperbolic 3-manifolds. Using the Selberg here provides an analogue in certain cases of trace formula and estimates for the eigenfunctions the Harish-Chandra homomorphism. which has of elliptic operators. the author demonstrates played an essential role in the theory of semisimple the power of spectral methods for studying the Lie groups. The book begins with an overview asymptotic geometric properties of manifolds. of the representation theory of Gln over finite Finally the Lax-Phillips wave equation method is groups. The author then explicitly establishes used to estimate the asymptotic density of lattice isomorphisms between certain convolution algebras points in H 3 . of functions on two different groups. Because of The treatment requires a background in analysis the form of the isomorphisms. basic properties of linear operators. hyperbolic geometry. trace of representations are preserved. thus giving a formulae. and the theory of the wave equation on concrete example to the correspondences predicted hyperbolic space. by the general philosphy of Langlands. 1980 Mathematics Subject Classifications: The first chapter. suitable as an introduction for 58G35, 35P10, 35P15, 35P20, 53C22, and others graduate students. requires only a basic knowledge ISBN 0-8218-2336-1, LC 85-21443 of representation theory of finite groups and some ISSN 0065-9266 familiarity with the general linear group and the x + 161 pages (softcover), December 1985 List price $16, Institutional member $13, symmetric group. The later chapters introduce Individual member $10 researchers in the field to a new method for the Shipping and handling charges must be added explicit construction and analysis of representations To order, please specify MEM0/335N of p-adic groups. a powerful method clearly capable of extensive further development. Varieties of Representations Contents of Finitely Generated A Heeke algebra approach to the representations Groups of GLn(Fq) Alexander Lubotsky Heeke algebras for GLn over local fields: and Andy R. Magid introduction (Memoirs of the AMS. Number 336) Harish-Chandra homomorphism in the unramified This Memoir studies the geometric structure anisotropic case of the affine varieties parametrizing the finite­ 1980 Mathematics Subject Classifications: dimensional representations of finitely generated 22E50, 16A27, 16A95 ISBN 0-8218-0709-9, LC 85-18649 groups. It systematically assembles several ISSN 0160-7642 techniques for studying these varieties and applies x + 76 pages (softcover), January 1986 them to obtain some genuinely new results and List price $13, All individuals $8 Shipping and handling charges must be added examples. especially for nilpotent and solvable To order, please specify CBMS/59N groups. The book presents for the first time the basic definitions and properties of representation varieties in a complete and precise manner. These representation varieties are of interest in several active mathematical contexts. in particular low-dimensional topology, differential geometry. system theory and discrete subgroups of lie groups. Its exposition of the foundations of the topic is self-contained. so that it can serve as a basic reference and introduction to the field for

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816 mathematicians with graduate-level training in the Finitary Measures for theory of finitely generated groups and in algebraic Subshifts of Finite Type geometry. and Sofie Systems Contents Bruce Kitchens and Selim T uncel of representations Schemes and varieties (Memoirs of the AMS. Number 338) Tangent spaces and first cohomology This Memoir identifies and studies a class Cohomology and Fox derviatives of finitary measures on sofic systems. These measures are defined in terms of finite semigroups. Cohomology and the proalgebraic hull using stochastic transition matrices. thus the term The character twisting operation semigroup measures. The authors investigate the Representation varieties of nilpotent groups analogy that these semigroup measures are related to Markov measures as sofic systems are related to Historical remarks subshifts of finite type. They show these measures 1980 Mathematics Subject Classifications: are realizable as images of Markov measures under 20C15, 14M99, 14L30, 20F18 1-1 a.e. resolving maps and that they form the ISBN 0-8218-2337-X, LC 85-21444 ISSN 0065-9266 closure of Markov measures under factor maps that xii + 117 pages (softcover), December 1985 identify periodic orbits only when the orbits have List price S12, Institutional member $10, Individual member S7 the same weight. Shipping and handling charges must be added Contents To order, please specify MEM0/336N Sofie systems and factor maps Computing the Homology of Semi-group measures the Lambda Algebra The structure of defining matrices Martin C. Tangora Examples (Memoirs of the AMS. Number 337) Homomorphisms of semi-groups Memoir is one of the rare publications This Equilibrium states of locally constant functions in which a mainframe computer is utilized to obtain a result on a significant problem in pure Thermodynamic properties mathematics. The author first gives a brief The weight condition historical background and summary of properties measures for the lambda algebra associated with each prime Characterization by conditional p, which also serves as an E1 term for the (stable Minimal covers and minimal semi-groups or unstable) Adams spectral sequences. He then 1980 Mathematics Subject Classifications: describes the algorithms and the programs used to 28D99, 60J10, 20M35, 68D25, 68E10, 68F05 compute the homology of these algebras. Tables of ISBN 0-8218-2340-X, LC 85-19986 ISSN 0065-9266 results are given for p = 2 and p = 3. iv + 68 pages (softcover), December 1985 The book's primary audience is algebraic List price S11, Institutional member $9, the Individual member $7 topologists interested in the lambda algebra. Shipping and handling charges must be added Steenrod algebra. or Adams spectral sequences. To order, please specify MEM0/338N However. its expository and self-contained chapters were designed also to be accessible to the mathematician or computer scientist with some knowledge of homology and spectral sequences and an interest in computer applications to pure mathematics. 1980 Mathematics Subject Classifications: 55T15, 55-04, 55040, 18-04 ISBN 0-8218-2338-8, LC 85-22818 ISSN 0065-9266 vi + 163 pages (softcover), December 1985 List price $16, Institutional member $13, Individual member S10 Shipping and handling charges must be added To order, please specify MEM0/337N

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817 Miscellaneous

Personal Items Unpublished Lecture Notes James M. Greenberg of Ohio State University and the United States Department of Energy has been appointed Chairman of the Department The following lecture notes are available from the of Mathematics at the University of Maryland, sources listed. Baltimore County, effective January, 1986. University of Washington Charles W. Groetseh of the University of 1. Frederic Y. M. Wan, "Some Mathematical Models Cincinnati has been appointed Department Head and Their Analysis," 1980 first printing; 1985 of the Department of Mathematical Sciences at that second printing (161 pages), $15, postpaid. institution. Checks should be made payable to Frederic Wan. David Herron of the University of California, Los Send orders to Applied Mathematics Department FS- Angeles, has been appointed an Assistant Professor 20, University of Washington, Seattle, Washington at the University of Cincinnati. 98195. Vietor G. Kaftal of the University of Cincinnati University of Delaware has been promoted to Associate Professor at that institution. 1. M. Schneider, "Introduction to Partial Differential Equations of Mixed Type," Technische Joanna B. Mitro of the University of Cincinnati Universitiit-Berlin (55 pages), $3. has been promoted to Associate Professor at that institution. Professor Mitro has also been awarded a 2. R. P. Gilbert, "Elliptic Systems in the Plane," Lady Davis Fellowship for research at the Technion, University of Delaware (99 pages), $5. Haifa, Israel. 3. Z. Schuss, "Theory and Application of Stochas­ tic Differential Equations," Tel-Aviv University, Deaths Israel (199 pages), $5. 4. H. Begehr, "Topics in Complex Analysis," Freie George Polya, Professor Emeritus at Stanford Universitiit-Berlin (49 pages), $3. University, died on September 7, 1985, at the age of 5. D. L. Colton, "Integral Operator Methods in 97. He was a member of the Society for 44 years. (See the Theory of Wave Propagation and Heat the News & Announcements section of the October Conduction," University of Strathclyde-Glasgow, issue of the Notices.) Scotland (54 pages), $3. Allen J. Pope of Potomac, Maryland, died on 6. R. Kress, "Integral Equation Methods for August 29, 1985, at the age of 45. He was a member Boundary Value Problems in Electromagnetism," of the Society for 5 years. University of Gottingen, Germany (56 pages), $3. Peter Seherk of the University of Toronto died on June 6, 1985. He was a member of the Society for 45 7. R. Timman, "Water Waves," Delft Technical years. University (95 pages), $3.50. Stephen James Wolfe, Associate Professor of 8. R. Reemtsen, "Local Best Chebyshev Approxima- Mathematical Sciences at the University of Delaware, tions," University of Delaware (68 pages), $3.50. died on September 5, 1985, at the age of 42. He was Checks made payable to Department of Mathematical a member of the Society for 15 years. Sciences, University of Delaware, Newark, Delaware 19716.

Visiting Mathematicians (Supplementary List)

The list of visiting mathematicians includes both foreign mathematicians visiting in the United States and Canada, and Americans visiting abroad. Note that there are two separate lists. American Mathematicians Visiting Abroad Name and Home Country Host Institution Field of Special Interest Period of Visit Arkowitz, M. (U.S.A.) Max-Planck lnstitut, Algebraic Topology 9/85 - 1/86 West Germany Assadi, A. (U.S.A.) Max-Planck lnstitut, Algebraic Topology 9/85 - 7/86 West Germany

Buchdahl, N. (U.S.A.) Max-Planck I nstitut, Special· Functions 9/85 ° 8/86 West Germany

818 Fania, M. (U.S.A.) Max-Planck lnstitut, 9/84. 2/86 West Germany Husemoller, D. (U.S.A.) Max-Planck lnstitut, Algebraic Topology 1/86 - 6/86 West Germany lgusa, Jun-ichi (U.S.A.) I.H.E.S., France Automorphic Forms 9/85 - 12/85 Kulkarni, R. (U.S.A.) Max-Planck lnstitut, Differential Geometry 9/85 - 8/86 West Germany Mackey, G. (U.S.A.) Max-Planck lnstitut, Lie Groups 9/85 - 8/86 West Germany Morava, Jack (U.S.A.) University of Leiden, Global Analysis 1/86- 2/86 Netherlands Nisnevich, Yevsey (U.S.A.) I.H.E.S., France Algebraic Groups 2/86 - 6/86 Sekiguchi, Tetsundo (U.S.A.) Mexican National University Fourier Transforms 9/85 - 5/86 Sterling, I. (U.S.A.) Max-Planck lnstitut, 9/85- 8/86 West Germany van den Dries, L. (U.S.A.) Max-Planck lnstitut, Algebraic Geometry 9/85- 8/86 West Germany Wolfson, J. (U.S.A.) Max-Planck lnstitut, Differential Geometry 7/85- 7/86 West Germany Zagier, D. (U.S.A.) Max-Planck lnstitut, Number Theory 1/86 - 3/86 West Germany

Visiting Foreign Mathematicians Berrut, Jean-Paul (Switzerland) University of North Carolina, Numerical Analysis 8/85 - 6/86 Chapel Hill Bhatnagar, Rakesh (Brazil) University of Toledo Fluid Mechanics 9/85 - 6/86 Favaro, Luiz A. (Brazil) University of North Carolina, Singularities and Algebraic Geometry 8/85 - 12/85 Chapel Hill Gieraltowska-Kedzierska, Maria University of Kansas Convex Analysis 8/85 - 5/86 (Poland) Has linger, F. (Austria) University of California, Berkeley Functional Analysis, Complex Analysis 8/85 . 8/86 Hohle, Ulrich (West Germany) University of Cincinnati Fuzzy Sets 9/85 - 6/86 Kimura, Tatsuo (Japan) Johns Hopkins University Prehomogeneous Vector Spaces 1/86 - 6/86 Krishnaiah, Venkata (India) University of Toledo Number Theory 9/85 - 6/86 Labuda, lwo (Poland) University of Kansas Measure Theory and Descriptive 8/85 - 5/86 Set Theory Malik, S. K. (India) Simon Fraser University Applied Mathematics 5/86 - 8/86 McAvaney, K. L. (Australia) Simon Fraser University Discrete Mathematics 8/85 - 1/86 Nesetril, J. (Czechoslovakia) Simon Fraser University Discrete Mathematics 9/85 - 12/85 Orbanz, Ulrich (Germany) University of Kansas Algebra 8/85 - 5/86 Papageorgiou, Haralambos University of Kansas Probability and Statistics 8/85 . 5/86 (Greece) Petrich, M. (Yugoslavia) Simon Fraser University Discrete Mathematics 1/86 - 4/86 Ramanathan, Annamalai (India) Johns Hopkins University Algebraic Geometry 7/85 - 6/86 Ruiz, Sergio (Chile) Western Michigan University Graph Theory 12/85 - 3/86 Singh, Raj Kishor (India) University of Arkansas Functional Analysis 7/85 - 12/85 Sitaramachandrarao, R. (India) University of Toledo Number Theory 9/85- 6/86 Swart, Henda (South Africa) Western Michigan University Graph Theory 8/85 - 12/85 Swart, John (South Africa) Western Michigan University Differential Equations 8/85 - 12/85 Zhou, Z. (China) University of Cincinnati Partial Differential Equations 1/86 - 6/86

819 Application Deadlines for Grants and Assistantships

Many fellowship programs have deadlines for November 30 receipt of applications. These deadlines are noted North Atlantic Treaty Organization [TSA] in news items and in the Stipends Section of the December Notices. They are listed below for your December 1 convenience, and as a reminder since many of American Philosophical Society [PS] these deadlines occur before the publication date * Lady Davis Fellowship Trust [TSA] of the special December issue on Assistantships Lady Davis Visiting Professorships [TSA] and Fellowships. Dates taken from the 1984 * Royal Norwegian Council for Scientific and special issue have been updated with information Industrial Research (Postdoctorate Fellow­ received in preparation for the December 1985 ships) [TSAJ issue. For information about the various pro­ Sigma Delta Epsilon, Graduate Women in Sci­ grams, the reader is referred to the appropriate ence (Eloise Gerry Fellowship) [GS] part of the Stipends Section of the December 1984 * University of California, San Diego (S. E. Notices as follows: [GS] =Graduate Support Sec­ Warschawski Assistant Professorship) [PS] tion; [PS] = Postdoctoral Support Section; [TSA] = Travel and Study Abroad Section; [SFN] = December 2 Study in the U.S. for Foreign Nationals. • AMS Research Fellowships [PS] * Information from the December 1984 issue not December 15 yet confirmed for this year. Los Alamos National Laboratory (J. Robert • Refers to a news item in this issue of the Oppenheimer Research Fellowship) [PS] Notices. October 1 December 31 American Philosophical Society [PS] Institute for Advanced Study Memberships [PS] John Simon Guggenheim Memorial Foundation Massachussetts Institute of Technology (C. L. E. Fellowships [PS] Moore Instructorships in Mathematics) [PS] * Rotary Foundation (Graduate and Undergrad­ University of Wisconsin, Madison (Van Vleck uate Scholarships) [TSA] Assistant Professorship in Mathematics) [PS] October 15 January 1 Bunting Institute of Radcliffe College (Science Courant Institute (Instructorships in Mathe­ Scholar Fellowships) [PS] matics) [PS] Fulbright Teacher Exchange Program [TSA] Courant Institute (Postdoctoral Visiting Mem­ berships) [PS] October 25 Harvard University (Benjamin Peirce Lecture­ Kennedy Scholarships [SFN] ships) [PS] Indiana University, Bloomington (Vaclav November 1 Hlavaty Research Assistant Professorships) American-Scandinavian Foundation [TSA] [PS] Fannie and John Hertz Foundation Fellowships Mathematical Sciences Research Institute [PS] [GS] University of California, Los Angeles (Earle North Atlantic Treaty Organization (Postdoc­ Raymond Hedrick Assistant Professorships toral Fellowships) [TSA] in Mathematics) [PS] November 15 January 6 Kosciuszko Foundation [GS] [SFN] University of Michigan, Ann Arbor (T. H. Kosciuszko Foundation (Graduate and Post­ Hildebrandt Research Assistant Professor­ graduate Exchange with Poland) [TSA] ships) [PS] NSF Graduate Fellowships [GS] NSF Mathematical Sciences Postdoctoral Re­ January 15 search Fellowships [PS] Dartmouth College (John Wesley Young Re­ NSF Minority Graduate Fellowships [GS] search Instructorships) [PS] Weizmann Institute of Sciences (Feinberg Grad­ Minna-J ames-Heinemann-Stiftung (Research uate School Postdoctoral Fellowships) [TSA] Abroad) [TSA]

820 IBM Thomas J. Watson Research Center (Math­ February 1 ematical Sciences Department Postdoctoral * AAAS Science, Engineering and Diplomacy and Junior Faculty Research Fellowships) Fellowships [PS] [PS] AAAS Summer Fellowship [GS] Institute for Mathematics and its Applications American Philosophical Society [PS] [PS] American Society for Engineering Education National Research Council (Research Associ­ (NASA-ASEE Summer Faculty Fellowships) ateship Programs) [PS] [PS] • Natural Sciences and Engineering Research American Society for Engineering Education Council of Canada (Visiting Fellowships) (Navy- and DOE-ASEE Summer Faculty Re­ [TSA] search Programs) [PS] Rice University (Griffith Conrad Evans Instruc­ Sigma Delta Epsilon, Graduate Women in Sci­ torships) [PS] ence (Grants-in-Aid) [GS] Rutgers University (Hill Assistant Professor­ University of Cincinnati (Charles Phelps Taft ships) [PS] Postdoctoral Fellowships) [PS] Smithsonian Institution (Predoctoral Fellow­ ships) [GS] February 11 Smithsonian Institution (Postdoctoral Fellow­ California State Graduate Fellowships [GS] ships) [PS] February 15 University of Chicago (Leonard Eugene Dickson University of California, Irvine (Visiting Irvine Instructorships in Mathematics) [PS] Lectureship) [PS] University of Pittsburgh (Andrew Mellon Post­ doctoral Fellowships) [PS] February 28 Australian Institute of Nuclear Science and January 16 Engineering (Research Fellowships) [PS] California Institute of Technology (Harry Bate­ man Research Instructorships) [PS] March 1 Fulbright Program (Collaborative Research American Philosophical Society [PS] Grants) [TSA] March 15 January 17 Hubert H. Humphrey Doctoral Fellowships [GS] Committee on Institutional Cooperation (Mi­ Weizmann Institute of Sciences (Feinberg Grad­ norities Fellowships in the Sciences, Mathe­ uate School Postdoctoral Fellowships) [TSA] matics and Engineering) [GS] March 31 • National Research Council (Postdoctoral Fel­ lowships for Minorities) [PS] North Atlantic Treaty Organization [TSA] April! January 28 National Center for Atmospheric Research (Ad­ American Philosophical Society [PS] vanced Study Program) [PS] June 15 January 30 Indo-American Fellowship Program [TSA] Centro de Investigacion del lPN (Solomon Lef­ August 1 schetz Research Instructorships) [TSA] American Philosophical Society [PS] January 31 August 15 American Society for Engineering Education North Atlantic Treaty Organization [TSA] (ONR Graduate Fellowship Program) [GS] Yale University (Josiah Willard Gibbs Instruc­ August 31 torships) [PS] Australian Institute of Nuclear Science and Engineering (Research Fellowships) [PS]

821 Bylaws of the American Mathematical Society

Article I Article III Officers Committees Section 1. There shall be a president, a Section 1. There shall be eight editorial com­ president-elect (during the even-numbered years mittees as follows: committees for the Bulletin, only), an ex-president (during the odd-numbered for the Proceedings, for the Colloquium Publica­ years only), three vice-presidents, a secretary, four tions, for Mathematical Surveys and Monographs, associate secretaries, a treasurer, and an associate for Mathematical Reviews; a joint committee for treasurer. the Transactions and the Memoirs; a committee consisting of the representatives Section 2. It shall be a duty of the president of the Society on the Board of Editors to deliver an address before the Society at the of the American Journal of Mathematics; and close of his term of office or within one year a committee for Mathematics thereafter. of Computation. Section 2. There shall be a Science Policy Committee. Section 3. There shall be a communications Article II committee called the Committee to Monitor Prob­ Board of Trustees lems in Communication. Section 4. The size of each committee shall Section 1. There shall be a Board of Trustees be determined by the Council. consisting of eight trustees, five trustees elected by the Society in accordance with Article VII, together with the president, the treasurer, and Article IV the associate treasurer of the Society ex officio. Council The Board of Trustees shall designate its own presiding officer and secretary. Section 1. The Council shall consist of fifteen members-at-large and the following ex officio Section 2. The function of the Board of members: the officers of the Society specified in Trustees shall be to receive and administer the Article I, except that it shall include only one funds of the Society, to have full legal control of associate secretary, the chairman of each of the its investments and properties, to make contracts, editorial committees and of the communications and, in general, to conduct all business affairs of committee and of the Science Policy Committee, the Society. any former secretary for a period of two years Section 3. The Board of Trustees shall have following his terms of office, and members of the power to appoint such assistants and agents the Executive Committee (Article V) who remain as may be necessary or convenient to facilitate on the Council by the operation of Article VII, the conduct of the affairs of the Society, and to Section 4. fix the terms and conditions of their employment. The chairman of any committee designated The Board may delegate to the officers of the as a Council member may name a deputy from Society duties and powers normally inhering in the committee as substitute. The associate secre­ their respective corporative offices, subject to su­ tary shall be the one charged with the scientific pervision by the Board. The Board of Trustees program of the meeting at which the Council may appoint committees to facilitate the conduct meets except that at a meeting associated with of the financial business of the Society and dele­ no scientific meeting of the Society the secretary gate to such committees such powers as may be may designate the associate secretary. necessary or convenient for the proper exercise of There is one exception. Council members by those powers. Agents appointed, or members of virtue of membership on an editorial committee committees designated, by the Board of Trustees or as associate secretary on January 1, 1986 need not be members of the Board. shall remain members of the Council through Nothing herein contained shall be construed their elected terms. This paragraph is no longer to empower the Board of Trustees to divest effective after December 31, 1989 and shall then itself of responsibility for, or legal control of, be deleted. the investments, properties, and contracts of the Section 2. The Council shall formulate and Society. administer the scientific policies of the Society

822 and shall act in an advisory capacity to the Board and other items which tend to affect the dignity of Trustees. and effective position of mathematics. Section 3. In the absence of the secretary With the exception noted in the next para­ from any meeting of the Council, a member may graph, a favorable vote of two-thirds of the entire be designated as acting secretary for the meeting, membership of the Council shall be necessary either by written authorization of the secretary, to authorize any statement in the name of the or, failing that, by the presiding officer. Society with respect to such matters. With the Section 4. All members of the Council shall exception noted in the next paragraph, such a be voting members. Each member, including vote may be taken only if written notice shall deputies and the designated associate secretary, have been given to the secretary by the proposer shall have one vote. The method for settling of any such resolution not later than one month matters before the Council at any meeting shall prior to the Council meeting at which the matter be by majority vote of the members present. If is to be presented; and the vote shall be taken not the result of a vote is challenged, it shall be the earlier than one month after the resolution has duty of the presiding officer to determine the true been discussed by the Council. vote by a roll call. In a roll call vote, each Council If, at a meeting of the Council, there are member shall vote only once (although he may be present twelve members, then the prior notifica­ a member of the Council in several capacities). tion to the secretary may be waived by unanimous Section 5. Any five members of the Council consent. In such a case, a unanimous favorable shall constitute a quorum for the transaction of vote by those present shall empower the Council business at any meeting of the Council. to speak in the name of the Society. Section 6. Between meetings of the Council, The Council may also refer the matter to a business may be transacted by a mail vote. Votes referendum by mail of the entire membership of shall be counted as specified in Section 4 of this the Society, and shall make such reference if a Article, "members present" being replaced by referendum is requested, prior to final action by "members voting." An affirmative vote by mail the Council, by two hundred or more members. on any proposal shall be declared if, and only if, The taking of a referendum shall act as a stay (a) more than half of the total number of possible upon Council action until the votes have been votes is received by the time announced for the canvassed, and thereafter no action may be taken closing of the polls, and (b) at least three-quarters by the Council except in accordance with a of the votes received by then are affirmative. If plurality of the votes cast in the referendum. five or more members request postponement at Article V the time of voting, action on the matter at issue Executive Committee shall be postponed until the next meeting of the Council, unless either (1) at the discretion of the Section 1. There shall be an Executive Com­ secretary, the question is made the subject of a mittee of the Council, consisting of four elected second vote by mail, in connection with which members and the following ex officio mem­ brief statements of reason, for and against, are bers: the president, the secretary, the president­ circulated; or (2) the Council places the matter at elect (during even-numbered years), and the ex­ issue before the Executive Committee for action. president (during odd-numbered years). Section 7. The Council may delegate to the Section 2. The Executive Committee of the Executive Committee certain of its duties and Council shall be empowered to act for the Council powers. Between meetings of the Council, the on matters which have been delegated to the Executive Committee shall act for the Council Executive Committee by the Council. If three on such matters and in such ways as the Coun­ members of the Executive Committee request that cil may specify. Nothing herein contained shall any matter be referred to the Council, the matter be construed as empowering the Council to di­ shall be so referred. The Executive Committee vest itself of responsibility for formulating and shall be responsible to the Council and shall administering the scientific policies of the Society. report its actions to the Council. It may consider Section 8. The Council shall also have power the agenda for meetings of the Council and may to speak in the name of the Society with respect make recommendations to the Council. to matters affecting the status of mathematics or Section 3. Each member of the Executive mathematicians, such as proposed or enacted fed­ Committee shall have one vote. An affirmative eral or state legislation; conditions of employment vote on any proposal before the Executive Com­ in universities, colleges, or business, research or mittee shall be declared if, and only if, at least industrial organizations; regulations, policies, or four affirmative votes are cast for the proposal. acts of governmental agencies or instrumentalities; A vote on any proposal may be determined at a

823 meeting of the Executive Committee, but it shall shall continue to serve until their successors have not be necessary to hold a meeting to determine been duly elected and qualified. The members of a vote. a communications committee with terms ending on December 31 are designated as past members Article VI through February 10 of the following year. Executive Director Section 2. The president-elect, the vice-pres­ idents, the secretary, the associate secretaries, the Section 1. There shall be an Executive Di­ treasurer, the associate treasurer, the trustees, rector who shall be a paid employee of the Society. the members of the editorial and communications He shall have charge of the central office of the committees, and the members-at-large of the Society, and he shall be responsible for the gen­ Council shall be elected by written ballot. An eral administration of the affairs of the Society in official ballot shall be sent to each member of accordance with the policies that are set by the the Society by the secretary on or before October Board of Trustees and by the Council. 10, and such ballots, if returned to the secretary Section 2. The Executive Director shall be in envelopes bearing the name of the voter and appointed by the Board of Trustees with the received within thirty days, shall be counted. consent of the Council. The terms and conditions Each ballot shall contain one or more names of his employment shall be fixed by the Board of proposed by the Council for each office to be Trustees. filled, with blank spaces in which the voter may Section 3. The Executive Director shall work substitute other names. A plurality of all votes under the immediate direction of a committee cast shall be necessary for election. In case of consisting of the president, the secretary, and failure to secure a plurality for any office, the the treasurer, of which the president shall be Council shall choose by written ballot among the chairman ex officio. The Executive Director shall members having the highest number of votes. attend meetings of the Board of Trustees, the Each communications committee elects one of its Council, and the Executive Committee, but he members as chairman in a manner and for a term shall not be a member of any of these bodies. designated by the Council. Past members, as He shall be a voting member of the Committee designated in Section 1, may be authorized to to Monitor Problems in Communication but shall vote in this election. not be its chairman. Section 3. At the end of his term of office, the president-elect shall become the president. At Article VII the end of his term of office, the president shall Election of Officers and Terms of Office become the ex-president. the sec­ Section 1. The term of office shall be one Section 4. On or before January 15, year in the case of the president-elect and the retary shall send to all members of the Council for ex-president; five years in the case of the trustees; a mail vote a ballot containing two names for each two years in the case of the president, the vice­ place to be filled on the Executive Committee. presidents, the secretary, the associate secretaries, The nominees shall be chosen by a committee of the the treasurer, and the associate treasurer. The appointed by the president. Members term of office in the case of members of the Council may vote for persons not nominated. editorial committees and elected members of the Any member of the Council who is not an ex communications committees shall be four years officio member of the Executive Committee (see for the Proceedings and the Transactions and Article V, Section 1) shall be eligible for election Memoirs committees and three years for the to the Executive Committee. In case a member remaining committees, except that when the size is elected to the Executive Committee for a term of an editorial or communications committee is extending beyond his regular term on the Council, of changed, the Council may authorize the election he shall automatically continue as a member of a member for a shorter term. The term of the Council during his term on the Executive office for members-at-large of the Council shall be Committee. three years, five of the members-at-large retiring Section 5. The president and vice-presidents annually. The term of office for elected members shall not be eligible for immediate re-election to of the Executive Committee shall be four years, their respective offices. A member-at-large or an one of the elected members retiring annually. ex officio member of the Council shall not be All terms of office shall begin on January 1 and eligible for immediate election (or re-election) as terminate on December 31 with the exception that a member-at-large of the Council. the officials specified in Articles I, II, III, IV, and Section 6. If the president of the Society V (excepting the president-elect and ex-president) should die or resign while a president-elect is in

824 office, the president-elect shall serve as president on a blank provided by the secretary. Such ap­ for the remainder of the year and thereafter shall plications shall not be acted upon until at least serve his regular two-year term. If the presi­ thirty days after their presentation to the Council dent of the Society should die or resign when no (at a meeting or by mail), except in the case of president-elect is in office, the Council, with the members of other societies entering under special approval of the Board of Trustees, shall designate action of the Council approved by the Board of one of the vice-presidents to serve as president Trustees. for the balance of the regular presidential term. Section 4. An ordinary member may become If the president-elect of the Society should die or a contributing member by paying the dues for resign before becoming president, his office shall such membership. (See Article IX, Section 3.) remain vacant until the next regular election of a Section 5. A university or college, or a firm, president-elect, and the Society shall, at the next corporation, or association interested in the sup­ annual meeting, elect a president for a two-year port of mathematics may be elected a corporate term. If the ex-president should die or resign or an institutional member. before expiration of his term of office, the Coun­ Article IX cil, with the approval of the Board of Trustees, shall designate a former president of the Society Dues and Privileges of Members to serve as ex-president during the remainder Section 1. Any applicant shall be admitted to of the regular term of the ex-presidency. Such ordinary membership immediately upon election vacancies as may occur at any time in the group by the Council (Article VITI) and the discharge consisting of the vice-presidents, the secretary, within sixty days of election of his first annual the associate secretaries, the treasurer, the asso­ dues. Dues may be discharged by payment or by ciate treasurer, and the members of the editorial remission when the provision of Section 7 of this and communications committees shall be filled by Article is applicable. The first annual dues shall the Council with the approval of the Board of apply to the year of election, except that if any Trustees. If a member of an editorial or commu­ applicant is elected after August 15 of any year, nications committee should take temporary leave he may elect to have his first annual dues apply from his duties, that committee shall nominate to the following year. a substitute for consideration by the Council. Section 2. The annual dues of an ordinary The Council shall then elect a substitute. The member of the Society shall be established by the Council shall fill from its own membership any va­ Council with the approval of the Trustees. The cancy in the elected membership of the Executive Council, with the approval of the Trustees, may Committee. establish special rates in exceptional cases and Section 7. If any elected trustee should die for members of an organization with which the or resign during his tenure of office, the vacancy Society has a reciprocity agreement. thus created shall be filled for his unexpired term Section 3. The minimum dues for a con­ by the Board of Trustees. tributing member shall be three-halves of the Section 8. If any member-at-large of the dues of an ordinary member per year. Members Council should die or resign more than one year may, upon their own initiative, pay larger dues. before the expiration of his term, the vacancy for Section 4. The minimum dues of an insti­ the unexpired term shall be filled by the Society tutional member shall depend on the amount of at the next annual meeting. published material credited to that member in Section 9. In case any officer should die or certain journals during a specific period. The decline to serve between the time of election and formula for computing these dues shall be estab­ the time at which he was to assume office, the lished from time to time by the Council, subject vacancy shall be filled in the same manner as if to approval by the Board of Trustees. Institutions he had served one day of his term. may pay larger dues than the computed minimum. Section 5. The privileges of an institutional Article VIII member shall depend on its dues in a manner to Members and Their Election be determined by the Council, subject to approval Section 1. Election of members shall be by by the Board of Trustees. These privileges shall vote of the Council or of its Executive Committee. be in terms of Society publications to be received Section 2. There shall be four classes of by the institution and of the number of persons members, namely ordinary, contributing, corpo­ it may nominate for ordinary membership in the rate, and institutional. Society. Section 3. Application for admission to ordi­ Section 6. Dues and privileges of corporate nary membership shall be made by the applicant members of the Society shall be established by

825 the Council subject to approval by the Board of action on business which has been recommended Trustees. for consideration by the Council and has been Section 7. The dues of an ordinary member accepted by the vote of four-fifths of the Society of the Society shall be remitted for any years present and voting at such a meeting. Such during which he is the nominee of an institutional notification shall be made only when so directed member. by a previous business meeting of the Society or Section 8. After retirement from active ser­ by the Council. vice on account of age or on account of long term Section 2. Meetings of the Executive Com­ disability, any ordinary or contributing member mittee may be called by the president; he shall call who is not in arrears of dues and with member­ a meeting at any time upon the written request ship extending over at least twenty years may, by of two of its members. giving proper notification to the secretary, have Section 3. The Council shall meet at the his dues remitted, on the understanding that he annual meeting of the Society. Special meetings will thereafter receive the Notices but not the of the Council may be called by the president; Bulletin. he shall call a special meeting at any time upon Section 9. An ordinary or contributing mem­ the written request of five of its members. No ber shall receive the Notices and Bulletin as priv­ special meeting of the Council shall be held unless ileges of membership during each year for which written notice of it shall have been sent to all his dues have been discharged. members of the Council at least ten days before Section 10. The annual dues of ordinary, the day set for the meeting. contributing, and corporate members shall be due Section 4. The Board of Trustees shall hold by January 1 of the year to which they apply. at least one meeting in each calendar year. Meet­ The Society shall submit bills for dues. If the ings of the Board of Trustees may be called by the annual dues of any member remain undischarged president, the treasurer, or the secretary of the beyond what the Board of Trustees deems to be a Society upon three-days' notice of such meetings reasonable time, his name shall be removed from mailed to the last known post office address of the list of members after due notice. If a member each trustee. The secretary of the Society shall wishes to discontinue his membership at any time, call a meeting upon the receipt of a written re­ he shall submit his resignation in writing to the quest of two of the trustees. Meetings may also Society. be held by common consent of all the trustees. Section 11. Any member who became a life Section 5. Papers intended for presentation member before October 25, 1941, by the payment at any meeting of the Society shall be passed upon of a sum determined in accordance with actuarial in advance by a program committee appointed by principles, shall have for life the status and or under the authority of the Council; and only privileges of an ordinary member without further such papers shall be presented as shall have payment of dues. No additional applications for been approved by such committee. Papers in life memberships will be accepted. form unsuitable for publication, if accepted for presentation, shall. be referred to on the program Article X as preliminary communications or reports. Meetings Article XI Section 1. The annual meeting of the Society shall be held between the fifteenth of December Publications and the tenth of February next following. Notice Section 1. The Society shall publish an of­ of the time and place of this meeting shall be ficial organ called the Bulletin of the American mailed by the secretary or an associate secretary Mathematical Society. It shall publish three to the last known post office address of each journals, known as the Transactions of the Amer­ member of the Society. The times and places ican Mathematical Society, the Proceedings of the of the annual and other meetings of the Society American Mathematical Society, and Mathemat­ shall be designated by the Council. There shall ics of Computation. It shall publish a series be a business meeting of the Society at the annual of mathematical papers known as the Memoirs meeting and at the summer meeting. A business of the American Mathematical Society. The ob­ meeting of the Society shall take final action only ject of the Transactions, Proceedings, Memoirs, on business accepted by unanimous consent, or and Mathematics of Computation is to make business notified to the full membership of the known important mathematical researches. It Society in the call for the meeting, except that shall publish a periodical called Mathematical the business meetings held at either the annual Reviews, containing abstracts or reviews of cur­ meeting or the summer meeting may take final rent mathematical literature. It shall publish a

826 series of volumes called Colloquium Publications Section 1. The editorial management of the No­ which shall embody in book form new mathe­ tices shall be in the hands of a committee chosen matical developments. It shall publish a series in a manner established by the Council. of monographs called Mathematical Surveys and Monographs which shall furnish expositions of the Article XII principal methods and results of particular fields Communications of mathematical research. It shall also cooperate in the conduct of the American Journal of Math­ The Committee to Monitor Problems in Com­ ematics. It shall publish a news periodical known munication shall perform such tasks in the field as the Notices of the American Mathematical So­ of communication of mathematics as are assigned ciety, containing programs of meetings, items of to it by the Council. news of particular interest to mathematicians, and such other materials as the Council may direct. Article XIII Amendments These bylaws may be amended or suspended at any meeting of the Society on recommendation Section 2. The editorial management of the of the Council and by a two-thirds vote of publications of the Society listed in Section 1 of the members present, provided notice of such this article, with the exception of the Notices, and proposed action and of its general nature shall the participation of the Society in the editorial have been given in the call for such meeting. management of the American Journal of Math­ ematics shall be in the charge of the respective editorial committees as provided in Article III, As amended August 1985

AMS Funds, Prizes, Officers and Lecturers

Endowment Fund First (preliminary) award, 1923: To G. D. Birkhoff for his memoir, Dynamical systems with In 1923 an Endowment Fund was collected two degrees of freedom. Transactions of the Amer­ to meet the greater demands on the publication ican Mathematical Society, volume 18 (1917), pp. program of the Society, these demands caused by 199-300. the ever-increasing number of important mathe­ matical memoirs. Of this fund, which amounted Second award, 1924: To E. T. Bell for his mem­ to approximately $94,000 in 1960, a considerable oir, Arithmetical paraphrases. I, II, Transactions proportion was contributed by members of the So­ of the American Mathematical Society, volume ciety. In 1961, upon the death of the last legatees 22 {1921), pp. 1-30, 198-219; and to Solomon under the will of the late Robert Henderson-for Lefschetz for his memoir, On certain numerical many years a Trustee of the Society-the entire invariants with applications to Abelian varieties, principal of the estate was received by the Soci­ Transactions of the American Mathematical So­ ety, thereby bringing the total of the Endowment ciety, volume 22 (1921), pp. 407-482. Fund to approximately $648,000. Third award, 1928: To J. W. Alexander for his memoir, Combinatorial analysis situs, Transac­ tions of the American Mathematical Society, vol­ Prize Funds ume 28 (1926), pp. 301-329. The BOc:her Memorial Prize Fourth award, 1933: To Marston Morse for his This prize was founded in memory of Profes­ memoir, The foundations of a theory of the sor Maxime Bocher with an original endowment calculus of variations in the large in m-space, of $1,450. It is awarded every five years for a Transactions of the American Mathematical So­ notable research memoir in analysis which has ciety, volume 31 (1929), pp. 379-404; and to appeared during the past five years. Either the Norbert Wiener for his memoir, Tauberian theo­ recipient is a member of the Society or the Mem­ rems, Annals of Mathematics, Series 2, volume 33 oir is published in a recognized North American (1932), pp. 1-100. journal; this provision, introduced in 1971, is a Fifth award, 1938: To John von Neumann for his liberalization of the terms of the award. memoir, Almost periodic functions and groups. I,

827 II, Transactions of the American Mathematical Fifteenth award, 1984: To Richard B. Melrose for Society, volume 36 (1934), pp. 445-492, and his solution of several outstanding problems in volume 37 (1935), pp. 21-50. diffraction theory and scattering theory and for developing the analytical tools needed for their Sixth award, 1943: To Jesse Douglas for his mem­ resolution. oirs, Green's function and the problem of Plateau, American Journal of Mathematics, volume 61 (1939), pp. 545-589; The most general form of the The Frank Nelson Cole Prize in Algebra problem of Plateau, American Journal of Math­ The Frank Nelson Cole Prize in Number Theory ematics, volume 61 (1939), pp. 590-608; and These prizes were founded in honor of Pro­ Solution of the inverse problem of the calculus of fessor Frank Nelson Cole on the occasion of his variations, Proceedings of the National Academy retirement as secretary of the American Mathe­ of Sciences, volume 25 (1939), pp. 631-637. matical Society after twenty-five years of service as editor-in-chief of the Bulletin. The original Seventh award, 1948: To A. C. Schaeffer and fund was donated by Professor Cole from moneys D. C. Spencer for their memoir, Coefficients of presented to him on his retirement, was aug­ schlicht functions. I, II, III, IV, Duke Mathe­ mented by contributions from members of the matical Journal, volume 10 (1943), pp. 611-635, Society, and was later doubled by his son, Charles volume 12 (1945), pp. 107-125, and the Proceed­ A. Cole. The present endowment is $2,250. The ings of the National Academy of Sciences, volume prizes are awarded at five-year intervals for con­ 32 (1946), pp. 111-116, volume 35 (1949), pp. tributions to algebra and the theory of numbers, 143-150. respectively, under restrictions similar to those for Eighth award, 1953: To Norman Levinson for his the Bacher Prize. contributions to the theory of linear, nonlinear, First award, 1928: To L. E. Dickson for his book ordinary, and partial differential equations con­ Algebren und ihre Zahlentheorie, Orell Fiissli, tained in his papers of recent years. Zurich and Leipzig, 1927. Ninth award, 1959: To Louis Nirenberg for his Second award, 1931: To H. S. Vandiver for his work in partial differential equations. several papers on Fermat's last theorem published Tenth award, 1964: To Paul J. Cohen for his in the Transactions of the American Mathematical paper, On a conjecture of Littlewood and idempo­ Society and in the Annals of Mathematics during tent measures, American Journal of Mathematics, the preceding five years, with special reference to volume 82 (1960), pp. 191-212. a paper entitled On Fermat's last theorem, Trans­ actions of the American Mathematical Society, Eleventh award, 1969: To I. M. Singer in recogni­ volume 31 (1929), pp. 613-642. tion of his work on the index problem, especially his share in two joint papers with Michael F. Third award, 1939: To A. Adrian Albert for his Atiyah, The index of elliptic operators. I, III, An­ papers on the construction of Riemann matrices published in the Annals of Mathematics, Series 2, nals of Mathematics, Series 2, volume 87 (1968), volume 35 (1934) and volume 36 (1935). pp. 484-530, 546-604. Fourth award, 1941: To Claude Chevalley for his Twelfth award, 1974: To Donald S. Ornstein in paper, La tMorie du corps de classes, Annals recognition of his paper, Bernoulli shifts with of Mathematics, Series 2, volume 41 (1940), pp. the same entropy are isomorphic, Advances in 394-418. Mathematics, volume 4 (1970), pp. 337-352. Fifth award, 1944: To Oscar Zariski for four pa­ Thirteenth award, 1979: To Alberto P. Calderon pers on algebraic varieties published in the Amer­ in recognition of his fundamental work on the ican Journal of Mathematics, volumes 61 (1939) theory of singular integrals and partial differential and 62 (1940), and in the Annals of Mathematics, equations, and in particular for his paper Cauchy Series 2, volumes 40 (1939) and 41 (1940). integrals on Lipschitz curves and related operators, Proceedings of the National Academy of Sciences, Sixth award, 1946: To H. B. Mann for his paper, USA, volume 74 (1977), pp. 1324-1327. A proof of the fundamental theorem on the density of sums of sets of positive integers, Annals of Fourteenth award, 1984: To Luis A. Caffarelli Mathematics, Series 2, volume 43 (1942), pp. for his deep and fundamental work in nonlinear 523-527. partial differential equations, in particular his work on free boundary problems, vortex theory Seventh award, 1949: To Richard Brauer for his and regularity theory. paper, On Artin's L-series with general group

828 characters, Annals of Mathematics, Series 2, dimension one, Journal of Algebra, volume 12 volume 48 (1947), pp. 502-514. (1969), pp. 585-610. Eighth award, 1951: To Paul Erdos for his many Sixteenth award, 1972: To Wolfgang M. Schmidt papers in the theory of numbers, and in particular for the following papers: On simultaneous ap­ for his paper, On a new method in elementary proximation of two algebraic numbers by ratio­ number theory which leads to an elementary proof nals, Acta Mathematica (Uppsala), volume 119 of the prime number theorem, Proceedings of the (1967), pp. 27-50; T-numbers do exist, Sym­ National Academy of Sciences, volume 35 (1949), posia Mathematica, volume IV, Academic Press, pp. 374-385. 1970, pp. 1-26; Simultaneous approximation to algebraic numbers by rationals, Acta Mathemat­ Ninth award, 1954: To Harish-Chandra for his ica (Uppsala), volume 125 (1970), pp. 189-201; papers on representations of semisimple Lie alge­ On Mahler's T-numbers, Proceedings of Sympos­ bras and groups, and particularly for his paper, ia in Pure Mathematics, volume 20, American On some applications of the universal enveloping Mathematical Society, 1971, pp. 275-286. algebra of a semisimple Lie algebra, Transactions of the American Mathematical Society, volume 70 Seventeenth award, 1975: To Hyman Bass for (1951), pp. 28-96. his paper, Unitary algebraic K-theory, Springer Lecture Notes in Mathematics, volume 343, 1973; Tenth award, 1958: To John T. Tate for his and to Daniel G. Quillen for his paper, Higher paper, The higher dimensional cohomology groups algebraic K-theories, Springer Lecture Notes in of class field theory, Annals of Mathematics, Mathematics, volume 341, 1973. Series 2, volume 56 (1952), pp. 294-297. Eighteenth award, 1977: To Goro Shimura for his Eleventh award, 1980: To Serge Lang for his two papers, Class fields over real quadratic fields paper, Unramified class field theory over function and Heche operators, Annals of Mathematics, fields in several variables, Annals of Mathematics, Series 2, volume 95 (1972), pp. 130-190; and On Series 2, volume 64 (1956), pp. 285-325; and to modular forms of half integral weight, Annals of Maxwell A. Rosenlicht for his papers, Generalized Mathematics, Series 2, volume 97 (1973), pp. Jacobian varieties, Annals of Mathematics, Series 440-481. 2, volume 59 (1954), pp. 505-530, and A universal mapping property of generalized Jacobians, Annals Nineteenth award, 1980: To Michael Aschbacher of Mathematics, Series 2, volume 66 (1957), pp. for his paper, A characterization of Chevalley 80-88. groups over fields of odd order, Annals of Mathe­ matics, Series 2, volume 106 (1977), pp. 353-398; Twelfth award, 1962: To Kenkichi Iwasawa for and to Melvin Hochster for his paper Topics his paper, Gamma extensions of number fields, in the homological theory of commutative rings, Bulletin of the American Mathematical Society, CBMS Regional Conference Series in Mathemat­ volume 65 (1959), pp. 183-226; and to Bernard ics, Number 24, American Mathematical Society, M. Dwork for his paper, On the rationality of the 1975. zeta function of an algebraic variety, American Journal of Mathematics, volume 82 (1960), pp. Twentieth award, 1982: To Robert P. Langlands 631-648. for pioneering work on automorphic forms, Eisen­ stein series and product formulas, particularly Thirteenth award, 1965: To Walter Feit and John for his paper Base change for GL(2), Annals G. Thompson for their joint paper, Solvability of of Mathematics Studies, volume 96, Princeton groups of odd order, Pacific Journal of Mathemat­ University Press, 1980; and to Barry Mazur for ics, volume 13 (1963), pp. 775-1029. outstanding work on elliptic curves and Abelian Fourteenth award, 1967: To James B. Ax and varieties, especially on rational points of finite Simon B. Kochen for a series of three joint order, and his paper Modular curves and the papers, Diophantine problems over local fields. I, Eisenstein ideal, Publications Mathematiques de II, III, American Journal of Mathematics, volume l'Institut des Hautes Etudes Scientifiques, volume 87 (1965), pp. 605-630, 631-648, and Annals of 47 (1977), pp. 33-186. Mathematics, Series 2, volume 83 (1966), pp. Twenty-First award, 1985: To George Lusztig for 437-456. his fundamental work on the representation the­ Fifteenth award, 1970: To John R. Stallings for ory of finite groups of Lie type. In particular his paper, On torsion-free groups with infinitely for his contributions to the classification of the many ends, Annals of Mathematics, Series 2, irreducible representations in characteristic zero volume 88 (1968), pp. 312-334; and to Richard of the groups of rational points of reductive G. Swan for his paper, Groups of cohomological groups over finite fields, appearing in Characters

829 of Reductive Groups Over Finite Fields, Annals manifolds, and for his work on the complex of Mathematics Studies, volume 107, Princeton Monge-Ampere equation on compact complex University Press, "1984. manifolds.

The Oswald Veblen Prize in Geometry The George David Birkhoff Prize in Applied Mathematics This prize was established in 1961 in memory of Professor Oswald Veblen through a fund con­ This prize was established in 1967 in honor tributed by former students and colleagues. The of Professor George David Birkhoff. The ini­ fund was later doubled by the widow of Professor tial endowment of $2,066 was contributed by the Veblen, bringing the fund to $2,000. The first two Birkhoff family and there have been subsequent awards of the prize were made in 1964 and the additions by others. It is normally awarded every next in 1966; thereafter, an award will ordinarily five years, beginning in 1968, for an outstand­ be made every five years for research in geometry ing contribution to "applied mathematics in the or topology under conditions similar to those for highest and broadest sense." The award is made the BOcher Prize. jointly by the American Mathematical Society and the Society for Industrial and Applied Math­ First award, 1964: To C. D. Papakyriakopoulos ematics. The recipient must be a member of one for his papers, On solid tori, Annals of Mathe­ of these societies and a resident of the United matics, Series 2, volume 66 (1957), pp. 1-26, and States, Canada, or Mexico. On Dehn's lemma and the asphericity of knots, Proceedings of the National Academy of Sciences, First award, 1968: To Jiirgen K. Moser for his volume 43 (1957), pp. 169-172. contributions to the theory of Hamiltonian dy­ namical systems, especially his proof of the stabil­ Second award, 1964: To Raoul Bott for his pa­ ity of periodic solutions of Hamiltonian systems pers, The space of loops on a Lie group, Michigan having two degrees of freedom and his specific Mathematical Journal, volume 5 (1958), pp. 35- applications of the ideas in connection with this 61, and The stable homotopy of the classical work. groups, Annals of Mathematics, Series 2, volume 70 (1959), pp. 313-337. Second award, 1973: To Fritz John for his out­ standing work in partial differential equations, in Third award, 1966: To Stephen Smale for his numerical analysis, and, particularly, in nonlin­ contributions to various aspects of differential ear elasticity theory; the latter work has led to topology. his study of quasi-isometric mappings as well as Fourth award, 1966: To Morton Brown and Barry functions of bounded mean oscillation, which have Mazur for their work on the generalized Schoen­ had impact in other areas of analysis. fl.ies theorem. Third award, 1973: To James B. Serrin for his Fifth award, 1971: To Robion C. Kirby for his fundamental contributions to the theory of non­ paper, Stable homeomorphisms and the annu­ linear partial differential equations, especially his lus conjecture, Annals of Mathematics, Series 2, work on existence and regularity theory for non­ volume 89 (1969), pp. 575-582. linear elliptic equations, and applications of his work to the theory of minimal surfaces in higher Sixth award, 1971: To Dennis P. Sullivan for his dimensions. work on the Hauptvermutung summarized in the paper, On the Hauptvermutung for manifolds, Fourth award, 1978: To Garrett Birkhoff for Bulletin of the American Mathematical Society, bringing the methods of algebra and the highest volume 73 (1967), pp. 598-600. standards of mathematics to scientific applica­ tions. Seventh award, 1976: To William P. Thurston for his work on foliations. Fifth award, 1978: To Mark Kac for his impor­ tant contributions to statistical mechanics and to Eighth award, 1976: To James Simons for his probability theory and its applications. work on minimal varieties and characteristic forms. Sixth award, 1978: To Clifford A. Truesdell for his outstanding contributions to our understanding of Ninth award, 1981: To Mikhael Gromov for his the subjects of rational mechanics and nonlinear work relating topological and geometric properties materials, for his efforts to give precise mathe­ of Riemannian manifolds. matical formulation to these classical subjects, for Tenth award, 1981: To Shing-Tung Yau for his his many contributions to applied mathematics in work in nonlinear partial differential equations, the fields of acoustic theory, kinetic theory, and his contributions to the topology of differentiable nonlinear elastic theory, and the thermodynamics

830 of mixtures, and for his major work in the history to $145,000 from Leroy P. Steele. From 1970 to of mechanics. 1976 one or more prizes were awarded each year for outstanding published mathematical research; Seventh award, 1983: To Paul R. Garabedian for his important contributions to partial differential most favorable consideration was given to papers equations, to the mathematical analysis of prob­ distinguished for their exposition and covering lems of transonic flow and airfoil design by the broad areas of mathematics. In 1977 the Council method of complexification, and to the develop­ of the AMS modified the terms under which the ment and application of scientific computing to prizes are awarded. Since then, up to three prizes problems of fluid dynamics and plasma physics. have been awarded each year in the following categories: (1) for the cumulative influence of the The Norbert Wiener Prize total mathematical work of the recipient, high in Applied Mathematics level of research over a period of time, particular This prize was established in 1967 in honor influence on the development of a field, and of Professor Norbert Wiener and was endowed by influence on mathematics through Ph.D. students; a fund amounting to $2,000 from the Department (2) for a book or substantial survey or expository­ of Mathematics of the Massachusetts Institute research paper; (3) for a paper, whether recent of Technology. The prize is normally awarded or not, which has proved to be of fundamental every five years, beginning in 1970, for an out­ or lasting importance in its field, or a model of standing contribution to "applied mathematics in important research. the highest and broadest sense." The award is August 1970: To Solomon Lefschetz for his paper, made jointly by the American Mathematical So­ A page of mathematical autobiography, Bulletin ciety and the Society for Industrial and Applied of the American Mathematical Society, volume 74 Mathematics. The recipient must be a member of (1968), pp. 854-879. one of these societies and a resident of the United August 1971: To James B. Carrell for his paper, States, Canada, or Mexico. written jointly with Jean A. Dieudonne, Invariant First award, 1970: To Richard E. Bellman for theory, old and new, Advances in Mathematics, his pioneering work in the area of dynamic pro­ volume 4 (1970), pp. 1-80. gramming, and for his related work on control, August 1971: To Jean A. Dieudonne for his paper, stability, and differential-delay equations. Algebraic geometry, Advances in Mathematics, Second award, 1975: To Peter D. Lax for his volume 3 (1969), pp. 223-321, and for his paper, broad contributions to applied mathematics, in written jointly with James B. Carrell, Invariant particular, for his work on numerical and theoret­ theory, old and new, Advances in Mathematics, ical aspects of partial differential equations and volume 4 (1970), pp. 1-80. on scattering theory. August 1971: To Phillip A. Griffiths for his pa­ Third award, 1980: To Tosio Kato for his dis­ per, Periods of integrals on algebraic manifolds, tinguished work in the perturbation theory of Bulletin of the American Mathematical Society, quantum mechanics. volume 76 (1970), pp. 228-296. Fourth award, 1980: To Gerald B. Whitham for August 1972: To Edward B. Curtis for his pa­ his broad contributions to the understanding of per, Simplicial homotopy theory, Advances in fluid dynamical phenomena and his innovative Mathematics, volume 6 (1971), pp. 107-209. contributions to the methodology through which August 1972: To William J. Ellison for his pa­ that understanding can be constructed. per, Waring's problem, American Mathematical Fifth award, 1985: To Clifford S. Gardner for Monthly, volume 78 (1971), pp. 10-36. his contributions to applied mathematics in the August 1972: To Lawrence F. Payne for his paper, areas of supersonic aerodynamics, plasma physics Isoperimetric inequalities and their applications, and hydromagnetics, and especially for his con­ SIAM Review, volume 9 (1967), pp. 453-488. tributions to the truly remarkable development of inverse scattering theory for the solution of August 1972: To Dana S. Scott for his paper, A nonlinear partial differential equations. proof of the independence of the continuum hy­ pothesis, Mathematical Systems Theory, volume The Leroy P. Steele Prizes 1 (1967), pp. 89-111. These prizes were established in 1970 in January 1975: To Lipman Bers for his paper, honor of George David Birkhoff, William Fogg Uniformization, moduli, and Klein ian groups, Osgood, and William Caspar Graustein, and are Bulletin of the London Mathematical Society, endowed under the terms of a bequest amounting volume 4 (1972), pp. 257-300.

831 January 1975: To Martin D. Davis for his paper, function, Pure and Applied Mathematics, number Hilbert's tenth problem is unsolvable, American 58, Academic Press, New York and London, 1974; Mathematical Monthly, volume 80 (1973), pp. and Fermat's last theorem, Graduate Texts in 233-269. Mathematics, number 50, Springer-Verlag, New January 1975: To Joseph L. Taylor for his paper, York and Berlin, 1977. Measure algebras, CBMS Regional Conference August 1980: To Gerhard P. Hochschild for his Series in Mathematics, Number 16, American significant work in homological algebra and its Mathematical Society, 1972. applications. August 1975: To George W. Mackey for his paper, August 1981: To Oscar Zariski for his work in Ergodic theory and its significance for statistical algebraic geometry, especially his fundamental mechanics and probability theory, Advances in contributions to the algebraic foundations of this Mathematics, volume 12 (1974), pp. 178-286. subject. August 1975: To H. Blaine Lawson for his paper, August 1981: To Eberhard Hopf for three pa­ Foliations, Bulletin of the American Mathemati­ pers of fundamental and lasting importance: cal Society, volume 80 (1974), pp. 369-418. Abzweigung einer periodischen Losung von einer 1976, 1977, 1978: No awards were made. stationiiren Losung eines Differential systems, January 1979: To Salomon Bochner for his cumu­ Berichte iiber die Verhandlungen der Siichsischen lative influence on the fields of probability theory, Akademie der Wissenschaften zu Leipzig. Math­ Fourier analysis, several complex variables, and ematisch-Naturwissenschaftliche Klasse, volume differential geometry. 95 (1943), pp. 3-22; A mathematical example displaying features of turbulence, Communica­ January 1979: To Hans Levy for three funda­ tions on Applied Mathematics, volume 1 (1948), mental papers: On the local character of the pp 303-322; and The partial differential equa­ solutions of an atypical linear differential equation tion ut + uu, = f..tUxx, Communications on Pure in three variables and a related theorem for reg­ and Applied Mathematics, volume 3 (1950), pp. ular functions of two complex variables, Annals 201-230. of Mathematics, Series 2, volume 64 (1956), pp. 514-522; An example of a smooth linear partial August 1981: To Nelson Dunford and Jacob T. differential equation without solution, Annals of Schwartz for their expository book, Linear opera­ Mathematics, Series 2, volume 66 (1957), pp. 155- tors, Part I, General theory, 1958; Part II, Spectral 158; On hulls of holomorphy, Communications theory, 1963; Part III, Spectral operators, 1971, in Pure and Applied Mathematics, volume 13 Interscience Publishers, New York. (1960), pp. 587-591. August 1982: To Lars V. Ahlfors for his exposi­ August 1979: To Antoni Zygmund for his cumu­ tory work in Complex analysis (McGraw-Hill Book lative influence on the theory of Fourier series, Company, New York, 1953), and in Lectures on real variables, and related areas of analysis. quasiconformal mappings (D. Van Nostrand Co., Inc., New York, 1966) and Conformal invariants August 1979: To Robin Hartshorne for his exposi­ (McGraw-Hill Book Company, New York, 1973). tory research article Equivalence relations on alge­ braic cycles and subvarieties of small codimension, August 1982: To Tsit-Yuen Lam for his exposi­ Proceedings of Symposia in Pure Mathematics, tory work in his book Algebraic theory of quadratic volume 29, American Mathematical Society, 1975, forms ( 1973), and four of his papers: K o and K 1 -­ pp. 129-164; and his book Algebraic geometry, an introduction to algebraic K-theory (1975), Ten Springer-Verlag, Berlin and New York, 1977. lectures on quadratic forms over fields (1977), August 1979: To Joseph J. Kohn for his fun­ Serre's conjecture (1978), and The theory of or­ damental paper: Harmonic integrals on strongly dered fields (1980). convex domains. I, II, Annals of Mathematics, Se­ August 1982: To John W. Milnor for a paper of ries 2, volume 78 (1963), pp. 112-248 and volume fundamental and lasting importance, On mani­ 79 (1964), pp. 450-472. folds homeomorphic to the 7 -sphere, Annals of August 1980: To Andre Weil for the total effect Mathematics (2) 64 (1956), pp. 399-405. of his work on the general course of twentieth August 1982: To Fritz John for the cumulative century mathematics, especially in the many areas influence of his total mathematical work, high in which he has made fundamental contributions. level of research over a period of time, particular August 1980: To Harold M. Edwards for math­ influence on the development of a field, and ematical exposition in his books Riemann's zeta influence on mathematics through Ph.D. students.

832 August 1983: To Paul R. Halmos for his many differentiable functions on closed sets, in geomet­ graduate texts in mathematics and for his articles ric integration theory, and in the geometry of the on how to write, talk and publish mathematics. tangents to a singular analytic space. August 1983: To Steven C. Kleene for three Special Funds important papers which formed the basis for later developments in generalized recursion theory and AMS Research Fellowship Fund descriptive set theory: Arithmetical predicates and This fund was established by the Society in function quantifiers, Transactions of the American 1973 and provides one-year Research Fellowships Mathematical Society 79 (1955), pp. 312-340; On awarded each year in March. The number of the forms of the predicates in the theory of fellowships granted each year depends on the constructive ordinals {second paper}, American contributions the Society receives, matched by a Journal of Mathematics 77 (1955), pp. 405-428; contribution from the Society of between $9,000 and Hierarchies of number-theoretic predicates, and $20,000. Bulletin of the American Mathematical Society First Award, 1974-1975: Fred G. Abramson and 61 (1955), pp. 193-213. James Li-Ming Wang. August 1983: To Shiing-Shen Chern for the cu­ Second award, 1975-1976: Terence J. Gaffney, mulative influence of his total mathematical work, Paul Nevai, and George M. Reed. high level of research over a period of time, par­ ticular influence on the development of the field Third award, 1976-1977: Fredric D. Ancel and of differential geometry, and influence on mathe­ Joseph A. Sgro. matics through Ph.D. students. Fourth award, 1977-1978: Steven Kalikow, August 1984: To Elias M. Stein for his book, Sin­ Charles Patton, Duong-Hong Phong, and David gular integrals and the differentiability properties Vogan. of functions, Princeton University Press (1970). Fifth award, 1978-1979: Alan Dankner, David August 1984: To Lennart Carleson for his papers: Harbater, Howard Hiller, Steven P. Kerckhoff, An interpolation problem for bounded analytic and Robert C. McOwen. functions, American Journal of Mathematics, vol­ Sixth award, 1979-1980: Scott W. Brown, Jeffrey ume 80 (1958), pp. 921-930; Interpolation by E. Hoffstein, Jeffry N. Kahn, James E. McClure, bounded analytic functions and the Corona prob­ Rick L. Smith, and Mark Steinberger. lem, Annals of Mathematics (2), volume 76 (1962), pp. 547-559; and On convergence and growth of Seventh award, 1980-1981: Robert K. Lazarsfeld, partial sums of Fourier series, Acta Mathematica Thomas H. Parker, and Robert Sachs. volume 116 (1966), pp. 135-157. Eighth award, 1981-1982: Lawrence Man-Hou Ein August 1984: To Joseph L. Doob for his fun­ and Mark Williams. damental work in establishing probability as a Ninth award, 1982-1983: Nicholas J. Kuhn. branch of mathematics and for his continuing Tenth award, 1983-1984: Russell David Lyons. profound influence on its development. Eleventh award, 1984-1985: Richard Timothy August 1985: To Michael Spivak for his five­ Durrett. volume set, A Comprehensive Introduction to Differential Geometry (second edition, Publish or Twelfth award, 1985-1986: R. Michael Beals. Perish, 1979). The Ernest William Brown Fund August 1985: To Robert Steinberg for three pa­ From the estate of Professor Ernest William pers on various aspects of the theory of alge­ Brown, a fund of $1,000 is available. The Board braic groups: Representations of algebraic groups, of Trustees stipulated that the interest from this Nagoya Mathematical Journal, volume 22 (1963), fund should be used for the furtherance of such pp. 33-56; Regular elements of semisimple alge­ mathematical interests as (a) the publication of braic groups, lnstitut des Hautes Etudes Scien­ important mathematical books, memoirs, and tifiques, Publications Mathematiques, volume 25 periodicals, and (b) for lectures to be delivered on (1965), pp. 49-80; and Endomorphisms of lin­ special occasions by invited guests of the Society. ear algebraic groups, Memoirs of the American Mathematical Society, volume 80 (1968). The Levi L. Conant Fund August 1985: To Hassler Whitney for his funda­ Levi L. Conant bequeathed a sum of $9,500 mental work on geometric problems, particularly which the Trustees incorporated with the perma­ in the general theory of manifolds, in the study of nent endowments for prize funds.

833 Officers and Lecturers of the Society Presidents Colloquium Lecturers William Browder, 1977 Herbert Federer, 1977 J. H. Van Amringe, 1889, 1890 James Pierpont, 1896 Maxime BOcher, 1896 Hyman Bass, 1978 J. E. McClintock, 1891-1894 Philip A. Griffiths, 1979 G. W. Hill, 1895, 1896 W. F. Osgood, 1898 A. G. Webster, 1898 George D. Mostow, 1979 Simon Newcomb, 1897, 1898 Julia B. Robinson, 1980 R. S. Woodward, 1899, 1900 Oskar Bolza, 1901 E. W. Brown, 1901 Wolfgang M. Schmidt, 1980 E. H. Moore, 1901, 1902 Mark Kac, 1981 T. S. Fiske, 1903, 1904 H. S. White, 1903 F. S. Woods, 1903 Serge Lang, 1981 W. F. Osgood, 1905, 1906 E. B. Van Vleck, 1903 Dennis Sullivan, 1982 H. S. White, 1907, 1908 E. H. Moore, 1906 Morris W. Hirsch, 1982 Ma.xime BOcher, 1909, 1910 E. J. Wilczynski, 1906 Charles L. Fefferman, 1983 H. B. Fine, 1911, 1912 Max Mason, 1906 Bertram Kostant, 1983 E. B. Van Vleck, 1913, 1914 G. A. Bliss, 1909 Barry Mazur, 1984 E. W. Brown, 1915, 1916 Edward Kasner, 1909 Paul H. Rabinowitz, 1984 L. E. Dickson, 1917, 1918 L. E. Dickson, 1913 Daniel Gorenstein, 1985 Frank Morley, 1919, 1920 W. F. Osgood, 1913 Karen K. Uhlenbeck, 1985 G. A. Bliss, 1921, 1922 G. C. Evans, 1916 Oswald Veblen, 1923, 1924 Oswald Veblen, 1916 Gibbs Lecturers G. D. Birkhoff, 1925, 1926 G. D. Birkboff, 1920 Virgil Snyder, 1927, 1928 F. R. Moulton, 1920 M. I. Pupin, 1923 E. R. Hedrick, 1929, 1930 L. P. Eisenhart, 1925 Robert Henderson, 1924 James Pierpont, 1925 L. P. Eisenhart, 1931, 1932 Dunham Jackson, 1925 E. T. Bell, 1927 H. B. Williams, 1926 A. B. Coble, 1933, 1934 E. W. Brown, 1927 Solomon Lefschetz, 1935, 1936 Anna Pell-Wheeler, 1927 A. B. Coble, 1928 G. H. Hardy, 1928 R. L. Moore, 1937, 1938 R. L. Moore, 1929 Irving Fisher, 1929 G. C. Evans, 1939, 1940 Solomon Lefschetz, 1930 E. B. Wilson, 1930 Marston Morse, 1941, 1942 Marston Morse, 1931 P. W. Bridgman, 1931 M. H. Stone, 1943, 1944 J. F. Ritt, 1932 R. C. Tolman, 1932 T. H. Hildebrandt, 1945, 1946 R. E. A. C. Paley, 1934 Albert Einstein, 1934 Einar Hille, 1947, 1948 Norbert Wiener, 1934 Vannevar Bush, 1935 J. L. Walsh, 1949, 1950 H. S. Vandiver, 1935 H. N. Russell, 1936 John von Neumann, 1951, 1952 E. W. Chittenden, 1936 C. A. Kraus, 1937 G. T. Whyburn, 1953, 1954 John von Neumann, 1937 Theodore von Ka.nmin, 1939 R. L. Wilder, 1955, 1956 A. A. Albert, 1939 Sewall Wright, 1941 Etichard Brauer, 1957, 1958 M. H. Stone, 1939 Harry Bateman, 1943 E. J. McShane, 1959, 1960 G. T. Whyburn, 1940 John von Neumann, 1944 Deane Montgomery, 1961, 1962 Oystein Ore, 1941 J. C. Slater, 1945 J. L. Doob, 1963, 1964 R. L. Wilder, 1942 S. Chandrasekbar, 1946 A. A. Albert, 1965, 1966 E. J. McShane, 1943 P. M. Morse, 1947 C. B. Morrey, Jr., 1967, 1968 Einar Hille, 1944 Hermann Weyl, 1948 Oscar Zariski, 1969, 1970 Tibor Rad6, 1945 Norbert Wiener, 1949 Hassler Whitney, 1946 G. E. Uhlenbeck, 1950 Nathan Jacobson, 1971, 1972 Oscar Zariski, 1947 Saunders Mac Lane, 1973, 1974 Kurt GOdel, 1951 EtichardBrauer, 1948 Marston Morse, 1952 Lipman Bers, 1975, 1976 G. A. Hedlund, 1949 R. H. Bing, 1977, 1978 Wassily Leontief, 1953 Deane Montgomery, 1951 K. 0. Friedrichs, 1954 Peter D. Lax, 1979, 1980 Alfred Tarski, 1952 Andrew M. Gleason, 1981, 1982 J. E. Mayer, 1955 Antoni Zygmund, 1953 M. H. Stone, 1956 Julia B. Robinson, 1983, 1984 Nathan Jacobson, 1955 H. J. Muller, 1958 Irving Kaplansky, 1985, 1986 Salomon Bochner, 1956 J. M. Burgers, 1959 N. E. Steenrod, 1957 Julian Schwinger, 1960 Secretaries J. L. Doob, 1959 J. J. Stoker, 1961 S. S. Chern, 1960 C. N. Yang, 1962 T. S. Fiske, 1888--1895 G. W. Mackey, 1961 C. E. Shannon, 1963 F. N. Cole, 1896-1920 Saunders Mac Lane, 1963 Lars Onsager, 1964 R. G. D. Etichardson, 1921-1940 C. B. Morrey, Jr., 1964 A. P. Calderon, 1965 D. H. Lehmer, 1965 J. R. Kline, 1941-1950 Martin Schwarzschild, 1966 E. G. Begle, 1951-1956 Samuel Eilenberg, 1967 D. C. Spencer, 1968 Mark Kac, 1967 J. W. Green, 1957-1966 E. P. Wigner, 1968 Everett Pitcher, 1967- J. W. Milnor, 1968 Raoul H. Bott, 1969 R. L. Wilder, 1969 Harish-Chandra, 1969 W. H. Munk, 1970 Treasurers R. H. Bing, 1970 E. F. F. Hopf, 1971 Lipman Bers, 1971 F. J. Dyson, 1972 T. S. Fiske, 1890, 1891 J. K. Moser, 1973 Harold Jacoby, 1892-1894 Armand Borel, 1971 Stephen Smale, 1972 Paul A. Samuelson, 1974 R. S. Woodward, 1895, 1896 Fritz John, 1975 Harold Jacoby, 1897-1899 John T. Tate, 1972 M. F. Atiyah, 1973 Arthur S. Wightman, 1976 W. S. Dennett, 1~1907 E. A. Bishop, 1973 Joseph B. Keller, 1977 J. H. Tanner, 1908-1920 F. E. Browder, 1973 Donald E. Knuth, 1978 W. B. Fite, 1921-1929 Louis Nirenberg, 1974 Martin D. Kruskal, 1979 G. W. Mullins, 193(}-1936 John G. Thompson, 1974 Kenneth G. Wilson, 1980 P. A. Smith, 1937 H. Jerome Keisler, 1975 Cathleen S. Morawetz, 1981 B. P. Gill, 1938--1948 Ellis R. Kolchin, 1975 Elliott W. Montroll, 1982 A. E. Meder, Jr., 1949--1964 Elias M. Stein, 1975 Samuel Karlin, 1983 W. T. Martin, 1965-1973 I. M. Singer, 1976 Herbert A. Simon, 1984 F. P. Peterson, 1973-. Jiirgen K. Moser, 1976 Michael 0. Rabin, 1985 The Delbert Ray Fulkerson Fund The Helen A. Merrill Fund Gifts of friends of the late Professor Fulkerson From the estate of Professor Helen A. Merrill, have provided a fund in excess of $7,000. Part a fund of $650 is available for use of the Society or all of the proceeds is to be used jointly by at the discretion of the governing bodies. the Mathematical Programming Society and the American Mathematical Society for the award of The Eliakim Hastings Moore Fund one or more prizes in discrete mathematics at This fund was donated in 1922 in honor of regular intervals. Professor Eliakim Hastings Moore on the occasion First award, 1979: To Richard M. Karp, for On of the twenty-fifth anniversary of the Chicago the computational complexity of combinatorial (Western) section of the Society. The income problems, Networks, volume 5 ( 1975), pp. 45- from this fund, which is $2,575, is to be used at 68; to Kenneth Appel and Wolfgang Haken, the discretion of the Council for the publication of for Every planar map is four colorable, Part important mathematical books and memoirs and I: Discharging, Illinois Journal of Mathematics, for the award of prizes. volume 21 (1977), pp. 429-490; and to Paul The Marion Reilly Fund D. Seymour, for The matroids with the max­ flow min-cut property, Journal of Combinatorial Dean Marion Reilly willed to the American Theory, Series B, volume 23 (1977), pp. 189-222. Mathematical Society a portion of her estate to be used for the advancement of research in Second award, 1982: To D. B. Judin and A. S. pure mathematics. The principal of this fund is Nemirovskil, for Informational complexity and $23,600. effective methods of solution for convex extremal problems, Ekonomika i Matematicheskie Metody The Joseph Fels Ritt Memorial Fund 12 (1976), 357-369, and to L. G. Khachiyan for From the estate of Estelle F. Ritt, the in­ A polynomial algorithm in linear programming, come from a fund of $22,500 is available for the Akademiia Nauk SSSR. Doklady 244 (1979), 1093- publication of works in the field of mathematics 1096; to G. P. Egorychev, for The solution of van as shall be determined by the governing bodies of der Waerden's problem for permanents, Akademiia the Society. Nauk SSSR. Doklady 258 (1981), 1041-1044, and D. I. Falikman, for A proof of the van der The James K. Whittemore Fund W aerden conjecture on the permanent of a doubly From the estate of James K. Whittemore, a stochastic matrix, Matematicheskie Zametki 29 fund of $1,000 is available for use by the Society. (1981), 931-938; and to M. Grotschel, L. Lovasz and A. Schrijver, for The ellipsoid method and Library Proceeds Fund its consequences in combinatorial optimization, A fund of $66,000 was established by the Combinatorica 1 (1981), 169-197. Board of Trustees in 1951 from the proceeds of The Genevra B. Hutchinson Fund the sale of the library of the Society. From the estate of Genevra B. Hutchinson, Friends of Mathematics Fund a fund of $1,000 is available to be used at An anonymous gift of $2,700 was received by the discretion of the Council and the Board of the Society in 1970. A special fund called the Trustees. Friends of Mathematics Fund was created; further donations The Solomon A. Joffe Fund have been included in this fund, the proceeds of which are a part of the invested assets A gift of $3,000 was presented to the Society of the Society. The principal of this fund is now by Solomon A. Joffe, and the Board of Trustees $29,584. set this aside in a fund bearing his name.

835 Classified Advertisements

SUGGESTED USES for classified advertising are books or lecture notes for sale, books being sought, positions available, exchange or rental of houses, and typing services. THE RATE IS $.55 per word with a minimum of $5.00. The same ad in 6 consecutive issues is $3.00 per word. Type will b"e set solid unless centering and spacing are requested. A centered line of any length or the equivalent in white space is $5.00. A word is defined as a group of characters with space at each end. Prepayment is required of individuals but not of institutions. For an additional $10.00 charge, announcements can be placed anonymously. Correspondence will be forwarded. DEADLINES are listed on the inside front cover. U. S. LAWS PROHIBIT discrimination in employment on the basis of color, age, sex, race, religion or national origin. "Positions Available" advertisements from institutions outside the U. S. cannot be published unless they are accompanied by a statement that the institution does not discriminate on these grounds whether or not it is subject to U. S. laws. Details and specific wording may be found following the Classified Advertisements in the January and August issues of the Notices. SITUATIONS WANTED ADVERTISEMENTS from involuntarily unemployed mathematicians are accepted under certain conditions for free publication. Call toll-free 800-556-7774 and speak to Wahlene Siconio for further information. SEND AD AND CHECK TO: Advertising Department. AMS. P. 0. Box 6248, Providence, Rhode Island 02940. Individuals are requested to pay in advance, institutions are not required to do so.

POSITIONS AVAILABLE Applications are invited for a tenure-track position at the Assistant Professor level starting July, 1986. Requirements DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE are a Ph.D. and proven ability or demonstrated potential RUTGERS UNIVERSITY AT NEWARK for research and teaching. Starting salary approximately PROFESSOR OF MATHEMATICS $30,316 (Canadian) per annum. Send vitae and arrange for three letters of reference to be sent to: J. W. Macki, Chair­ The Department of Mathematics and Computer Science man, Department of Mathematics, University of Alberta, anticipates an opening at the Rank of Professor beginning Edmonton, Alberta, T6G 2G1. The University of Alberta Fall 1986. Candidates should exhibit strong research accom· is an equal opportunity employer, but in accordance with plishments. Salary and teaching load are negotiable. Canadian Immigration requirements, this advertisement is Applicants from all fields are invited. Areas of research directed to Canadian citizens and permanent residents. interest in the department include number theory, represen· Closing date for applications is January 31, 1986. tation theory and automorphic forms, combinatorics and logic, and low dimensional topology and Teichmuller theory. FACULTY APPOINTMENT Candidates should send a resume and the names of three references to: The Department of Mathematical Sciences invites applica· Jane· Gilman, Chair tions for a tenured professorship in the area of operations Department of Mathematics & Computer Science research, effective Fall 1986. Specializations of particu- Rutgers - The State University lar interest include decision science, production and distribu­ Newark, New Jersey 07102 tion systems, mathematical programming, stochastic models, The closing date for applications is January 15, 1986. Rut­ network flow, algorithms, combinatorial optimization, gers University is an equal opportunity, affirmative action simulation methods, and reliability. Candidates should be employer. active researchers with outstanding accomplishments in re­ search, teaching and/or innovative applications. Interested persons are asked to send their vitas to Robert J. Serfling, INSTITUTE FOR DEFENSE ANALYSES Search Committee, Department of Mathematical Sciences, COMMUNICATIONS RESEARCH DIVISION The Johns Hopkins University, Baltimore, Maryland 21218. Applications are invited from Ph.D. level mathematicians The Johns Hopkins University is an Equal O.pportunity/ for research positions on our technical staff. Initial appoint· Affirmative Action Employer. Employment is offered with­ ment would be for one or two years, possibly leading to a out discrimination on the basis of race, color, religion, sex or permanent position. national origin. Additionally, we also organize each year a summer pro· gram (SCAMP) for which places are available. Wide mathe­ LAWRENCE UNIVERSITY matical interests, and the ability to motivate one's own work DEPARTMENT OF MATHEMATICS are more important than knowledge of specific areas of Tenure-track position at the assistant professor level mathematics. Facility in computer programming and some starting fall 1986. The Department seeks candidates special­ knowledge of statistics would be definite assets. izing in differential geometry or probability, but will con· Salaries will be competitive and commensurate with ex· sider especially strong candidates in any area. Lawrence is a perience and qualifications. liberal arts college with a national reputation, small classes, IDA/CRD is an equal opportunity /affirmative action and excellent students. Teaching load two courses each ten employer, and encourages applications from women and week term. Salary competitive. Send resume, transcripts, and members of minority groups. Send resume and publication three or four supporting letters to Bruce Pourciau, Chair, list to: Department of Mathematics, Lawrence University, Appleton, Dr. N.J. Patterson WI 54912. These letters should provide specific evidence on Deputy Director the candidate's potential for outstanding undergraduate IDA/CRD teaching and continued research. Deadline January 15 but Thanet Road application by December 20 makes possible an interview at Princeton, NJ 08540 the January AMS meeting in New Orleans. Equal Oppor­ U.S. citizenship required. tunity Employer.

836 POSITIONS AVAILABLE Chairperson Department of Mathematics Southwest Texas State University POSITION OPEN Southwest Texas State University has reopened the search CHAIRPERSON for chairperson of the Department of Mathematics. Candi­ DEPARTMENT OF MATHEMATICAL SCIENCES dates should have an outstanding record of scholarly research Loyola University of Chicago invites nominations and ap­ and high quality instruction as well as related professional plications for the position of Chairperson of the Department activities. They must be able to provide strong academic of Mathematical Sciences. The position will be open on or leadership for a diverse department which is involved in both about july 1, 1986. pure and applied mathematics, mathematical education, and Loyola is the oldest university in Chicago and one of the diagnostic testing and placement of students. The Depart· largest and most complex of 236 Catholic Church-related ment currently has almost forty FTE faculty with over 200 colleges and universities in the United States. majors at the bachelors and masters levels. Some 6500 stu­ dents per semester enroll in the Department's courses; a More than 15,000 students attend classes on four campuses: large number of these are in service courses for the School the Lake Shore Campus, the Water Tower Campus in down­ of Business and the School of Education. town Chicago, the Medical Center in Maywood, Illinois, Texas is a regional university of over 19,000 and the Rome Center in Rome, Italy. Southwest undergraduate and graduate students in eight schools. It is Sciences offers Bachelor's The Department of Mathematical located in San Marcos, a friendly residential community of areas: mathematics; computer degrees in the following 35,000 located midway between Austin and San Antonio and computer science; mathematics science; mathematics in the hill and lake country of Texas. Master's degrees are offered in mathematics and statistics. The position of chairperson at Southwest Texas State is and in computer science. a twelve-month appointment with a rank of associate or full The Department has 22 full·time faculty, and about 530 professor depending upon qualifications. The current salary undergraduate majors and 100 graduate students. In addi­ range for chairpersons is $55,400 to $57,300. Applicants tion, it provides service courses for approximately 2,100 should send a letter of intent and a complete vita, and should students per semester. arrange to have at least three current letters of reference sent to: Candidates must have an earned Doctorate, teaching ex­ Dr. B. j. Yager, Chairman perience, a record of scholarly activity and commitment Mathematics Search Committee to the goals and traditions of jesuit education. Southwest Texas State University Closing date for applications is December 1, 1985. Letters San Marcos, Texas 78666 of application and a curriculum vitae should be sent to the The closing date for applications is November 30, 1985. following address: The position will become available no later than September Ralph L. Pearson 1' 1986. Dean, University College Southwest Texas State University is an Affirmative Loyola University of Chicago Action, Equal Opportunity Educational Institution. 820 North Michigan Avenue Chicago, Illinois 60611 UCLA DEPARTMENT OF MATHEMATICS AN EQUAL OPPORTUNITY, AFFIRMATIVE ACTION TEMPORARY POSITIONS EMPLOYER One or two E. R. Hedrick Assistant Professors. Applicants show strong promise in research and must have received UCLA DEPARTMENT OF MATHEMATICS must the past three or four years (but may be of REGULAR POSITIONS the Ph.D. during age): no restrictions as to field; anticipated salary IN APPLIED/COMPUTATIONAL MATHEMATICS any $33,400. Three year appointment: research supplement of positions in applied and computa­ Three or four regular $3,700 first summer. Teaching load: Four quarter courses Preference will be given to candidates in tional mathematics. per year, which may include one advanced course in candi­ mathematical modeling, and scientific/ numerical analysis, dates field. Deadline for applications is january 1, 1986. Very strong research and teaching engineering computing. Also, subject to administrative approval, a few adjunct Positions initially budgeted at the background required. assistant professorships; two year appointment; strong re· professor level. Sufficiently outstanding candidates assistant search and teaching background; no restriction as to field. at higher levels and/or in other fields will also be considered. Anticipated salary $28,700 for academic year. Teaching load: quarter courses per year. Teaching load: Five Five quarter courses per year. write to Yiannis N. Moschovakis, Chair, Los To apply, Also several positions for visitors and lecturers. CA 90024. Attention: Faculty Search Committee. Angeles, To apply, write to Yiannis N. Moschovakis, Chair, Los opportunity/affirmative action employer. UCLA is an equal Angeles, CA 90024. UCLA is an equal opportunity/affirmative action UNIVERSITY OF CALIFORNIA, SANTA BARBARA employer. DEPARTMENT OF MATHEMATICS Applications are invited for an assistant professor position UCLA DEPARTMENT OF MATHEMATICS in the area of either differential geometry or geometric REGULAR POSITIONS IN PURE MATHEMATICS topology. Effective july 1, 1986. Successful candidates Three or four regular positions in pure mathematics. must have demonstrated outstanding research potential and Preference will be given to candidates in number theory have superior teaching ability. Candidates must possess a (including modular forms) and probability (including statis­ Ph.D. degree by September, 1986. Senior applicants of tical mechanics). Other fields of particular interest include exceptional stature will be considered, with salary and rank analysis, geometry /topology, differential equations, and alge­ dependent upon qualifications. Applicants must send bra (especially representation theory). Very strong research vitae and publication lists, and arrange for three letters and teaching background required. Positions initially bud­ of recommendation to be sent to: The Geometry /Topology geted at the assistant professor level. Sufficiently outstand­ Committee, Department of Mathematics, University of ing candidates at higher levels and/or in other fields will also California, Santa Barbara, California, 93106. Applications be considered. Teaching load: Five quarter courses per year. must be received by january 15, 1986. To apply, write to Yiannis N. Moschovakis, Chair, Los UCSB is an equal opportunity /affirmative action Angeles, CA 90024. Attention: Faculty Search Committee. Employer. UCLA is an equal opportunity/affirmative action employer.

837 POSITIONS AVAILABLE DEPARTMENT OF MATHEMATICS University of Kansas UCLA DEPARTMENT OF MATHEMATICS Applications are invited for tenure-track and temporary REGULAR POSITIONS positions at all levels, commencing 8/16/86 or as negotiated. IN MATHEMATICAL COMPUTER SCIENCE First preference will be given to numerical analysts, and One or two positions in mathematical computer science. then to candidates in other applied areas related to those Preference will be given to candidates in analysis of algo· represented in the department. Require Ph.D. or Ph.D. rithms, coding theory, computational complexity, and the dissertation accepted with only formalities to be com­ theory of programming languages. Very strong research and pleted. teaching background required. Positions initially budgeted at Application, detailed resume with description of research, the assistant professor level. Sufficiently outstanding candi­ and three recommendation letters should be sent to C. j. dates at higher levels and/or in other fields will also be con· Himmelberg, Chairman, Department of Mathematics, sidered. Teaching load: Five quarter courses per year. University of Kansas, Lawrence, KS 66045-2142. To apply, write to Yiannis N. Moschovakis, Chair, Los Deadlines: 11 /01/85 for first consideration, then monthly Angeles, CA 90024. until August 1, 1986. UCLA is an equal opportunity/affirmative action employer. The University of Kansas is an AA/EOE. NAVAL POSTGRADUATE SCHOOL THE UNIVERSITY FACULTY POSITION IN OPERATIONS RESEARCH OF ALABAMA AT BIRMINGHAM DEPARTMENT OF MATHEMATICS The Operations Research Department invites applicants Applications for a tenure track position are invited. Mathe­ for either visiting or tenure track faculty positions. Duties maticians with major research in one of the areas of nonlinear in either case include teaching (graduate level), thesis direc­ analysis, mathematical physics, or dynamical systems are tion (mainly Master of Science), and research. In the case particularly encouraged to apply. Applicants should be strong of tenure track our preference is for junior applicants, but or promising researchers, good teachers and able to interact consideration will be given to a senior applicant with a with other researchers in the department. Rank and salary strong research record. A Ph.D. is required, not necessarily are open. The teaching load for researchers is competitive. Appli· in Operations Research. Areas of emphasis within the OR cants should send C. V. and have at least three letters of Department include statistics, stochastic modelling, math reference sent to Roger T. Lewis, Mathematics Department, programming, human factors, simulation, combat modelling, University of Alabama at Birmingham, Birmingham, AL 35294, systems analysis, logistics, and war gaming. by january 1, 1986. UAB is an Affirmative Action/Equal Located in Monterey, the Naval Postgraduate School is Opportunity Employer. a graduate institution offering degrees in science, engineer­ ing, and administration. Excellent research and teaching facilities include an IBM 3033/AP (16MB), a secure war The Department of Mathematics, University of California at gaming laboratory with a DEC·VAX 11/780 and extensive Davis, is seeking to fill one or more tenure track positions graphics, and other computational facilities. The OR Depart· beginning july 1, 1986. ment has 28 civilian and 7 military faculty. Faculty appoint­ We are particularly interested in applicants with broad ments follow AAUP guidelines. Please send detailed resume backgrounds in one of the following areas: with names, addresses, and telephone numbers of three or more references to: 1. Functional Analysis and Partial Differential Equations Chairman, Department of Operations Research 2. Dynamical Systems and the Geometric Theory of Naval Postgraduate School Differential Equations Monterey, CA 93943-5100 These positions are at the Assistant Professor level. Re· (408) 646-2381/2594 quirements are a doctorate in mathematics or in a closely The Naval Postgraduate School is an Equal Opportunity related field and evidence of achievement or potential in Affirmative Action Employer. research and teaching. Candi<;lates should send a letter of application, a vitae, and THE GEORGIA INSTITUTE OF TECHNOLOGY the NAMES ONLY of three referees to: The School of Mathematics expects to have available Chair, Search Committee some visiting and tenure-track positions beginning in the Department of Mathematics Fall of 1986. Priority will be given to applicants in statistics, University of California scientific computing (parallel and vector computing, graphics, Davis, California 95616 robotics) and ordinary differential equations. Excellent Applications must be postmarked no later than january 13, accomplishments or potential in research is required. Send 1986. resume and four letters of reference to W. F. Ames, Director, The University of California is an equal opportunity/affirm· School of Mathematics, Georgia Institute of Technology, alive action employer. Atlanta, Georgia 30332. Georgia Tech, a unit of the Univer· sity System of Georgia, is an Equal Opportunity/Affirmative Applications are encouraged for anticipated tenure-track, Action Employer. tenured positions, and visiting positions at all levels for the academic years 1986·87 and 1987·88. Application, vita, and The Ohio State University three letters of recommendation should be sent to William A. Kirk, Chair, Department of Mathematics, University of Department of Mathematics Iowa, Iowa City, Iowa 52242. Selections will be based on Research Instructorships in Mathematics evidence of the applicants' effective teaching and research Applications are invited for the position of research in· achievements and potential; instructional needs of the structor in mathematics for the academic year 1986-87. Department; and the potential for interaction with the faculty Candidates should hold a Ph.D. (or equivalent) in mathemat· at the research level. Special attention will be given to ics and show strong research promise. applicants in partial differential equations, differential geom· Please send credentials and have letters of recommenda· etry, and numerical analysis. The selection process will begin tion sent to Professor Alan Woods, Department of Mathe· as applications are received. The University of Iowa is an matics, The Ohio State University, 231 W. 18th Avenue, Affirmative Action and Equal Opportunity Employer and Columbus, Ohio 43210. The Ohio State University is an specifically encourages applications from women and minori· Equal Opportunity/Affirmative Action Employer. ties.

838 POSITIONS AVAILABLE UNIVERSITY OF CALIFORNIA, IRVINE DEPARTMENT OF MATHEMATICS UNIVERSITY OF ILLINOIS AT CHICAGO IRVINE, CALIFORNIA 92717 Department of Mathematics Two faculty positions at the level of Assistant Professor in Statistics and Computer Science Applied Mathematics, available beginning academic year Box 4348, Chicago, IL 60680 1986-87. A Ph.D. degree, publications, and evidence of Applications are invited for tenure-track or tenured positions active interest in quality teaching are required. Examples of in pure mathematics, applied mathematics and numerical preferred research areas: partial differential equations, non­ analysis, probability and statistics, and theoretical computer linear phenomena, applied functional analysis, and numerical science. Outstanding research record required: junior candi­ analysis. Send applications, a curriculum vitae, and the names dates with post-doctoral experience preferred. Applications of three or more references to Professor Martin Schechter are also invited for visiting positions of 1 or more quarters, Department of Mathematics, University of California, Irvine, especially in connection with a planned 1986-87 emphasis CA 92717. An Affirmative Action/Equal Opportunity year in Combinatorics and Complexity. Send vita and direct Employer. 3 letters of reference to john Wood, Chairman, Search Com­ mittee (address above). Availability of positions contingent THE OHIO STATE UNIVERSITY on budgetary allocations. AA/EOE. CHAIR IN SCIENTIFIC COMPUTATION The Department of Mathematics has been awarded a UNIVERSITY OF SOUTH FLORIDA Chair in Scientific Computation. Applications are invited Department of Mathematics from individuals with outstanding credentials in any area of Tenure-track teaching and research positions are available applied mathematics whose research activities make significant beginning August, 1986. Applicants must possess a Ph.D. use of high speed computers. The appointee will hold the degree. Applicants specializing in Approximation Theory, academic rank of Professor of Mathematics and will be ex­ Computer Science, Differential Equations, Logic, Numerical pected to provide the academic leadership in the developing Analysis, Probability, or Statistics are preferred. Rank and field of scientific computation at Ohio State. salary will depend on credentials. To apply send curriculum Individuals interested in this position should contact vitae and have three letters of recommendation sent to Alan Woods, Chairman Kenneth L. Pothoven, Chairman, Tampa, FL 33620. The Department of Mathematics University of South Florida is an equal opportunity The Ohio State University employer. 231 W. 18th Avenue Columbus, Ohio 4321 0 Applied Mathematics Telephone: 614/422-7173 University of Virginia Tenure-track assistant professorships and possible senior DEPARTMENT OF MATHEMATICS positions for january, 1986 and later. Preferred areas are THE OHIO STATE UNIVERSITY partial differential equations, numerical analysis and The Department of Mathematics of The Ohio State Uni­ applied probability. Ph.D. required with strong research and versity hopes to fill several positions at all ranks, both visit­ teaching ability. Applicants for senior positions must have ing and permanent, effective Autumn Quarter 1986. Candi­ established record of research and grant support. Send dates in areas of applied and pure mathematics are invited resume and names of three references to j. M. Ortega, to apply. Significant research accomplishments or excep­ Chairman, Department of Applied Mathematics, Thornton tional research promise and evidence of good teaching ability Hall, University of Virginia, Charlottesville, VA 22901. An will be expected of successful applicants. EO/AA Employer. Please send credentials and have letters of recommendation sent to Professor Alan Woods, Department of Mathematics, THE UNIVERSITY OF WYOMING The Ohio State University, 231 W. 18th Avenue, Columbus, HEAD-DEPARTMENT OF MATHEMATICS Ohio 43210. Review of resumes will begin immediately. The Ohio State University is an Equal Opportunity/ The Department of Mathematics at the University of Affirmative Action Employer. Wyoming invites applications for the position of Department Head. The University is the sole four-year institution of CASE WESTERN RESERVE UNIVERSITY higher education in the state of Wyoming with an enroll­ Tenure-track and/or visiting positions anticipated to begin ment of 10,000 students. The mathematics program offers August 15, 1986. Outstanding research record and/or proven degrees in mathematics, applied mathematics, and several research potential and teaching excellence required. Ranks joint-degree options at the bachelor, master and doctoral open. Preferred areas: statistics, partial differential equations levels. The department has a growing major research (including numerical methods for p.d.e's), global analysis, component in applied mathematics including a petroleum dynamical systems, control theory, probability and functional research institute with funding from major industrial sup­ analysis. Visiting positions most likely in the area of applica­ porters. Other active research areas in the department in­ tions of probability and graph theory to chemistry. Send clude numerical analysis, partial differential equations, vita plus three letters of recommendation to Professor functional analysis, optimization theory, dynamical systems, W. A. Woyczynski, Chairman, CWRU, Department of Mathe­ rigidity theory, and combinatorics. matics & Statistics, Case Western Reserve University, Cleve­ Candidates should have a strong research record com­ land, Ohio 44106. patible with department interests and a commitment to An affirmative action, equal opportunity employer. excellence in instruction. Applicants should submit a current curriculum vitae and the names of at least three UNIVERSITY OF NORTHERN IOWA suitable references to: Tenure track position at Assistant Professor level. Salary W. G. Bridges, Chair and benefits competitive. Preferred specialty of algebra. Search Committee Doctorate in mathematical specialty, demonstrated teaching Mathematics Department ability, and scholarly productivity/promise required. Closing University of Wyoming date of February 20. For complete announcement, contact Laramie, WY 82070 Dr. David Duncan, Head, Department of Mathematics and Applications will be considered through january 31, 1986. Computer Science, University of Northern Iowa, Cedar Falls, The University of Wyoming is an equal opportunity Iowa 50614. An Equal Opportunity Affirmative Action employer. Employer.

839 POSITIONS AVAILABLE DEPARTMENT OF MATHEMATICS UNIVERSITY OF WISCONSIN-MADISON UNIVERSITY OF ILLINOIS AT CHICAGO POSITIONS AVAILABLE FOR 1986-87 MATHEMATICS AND COMPUTER EDUCATION The Mathematics Department solicits applications from The Department of Mathematics, Statistics, and Computer candidates of established excellence for tenure-track or Science invites applications for tenure-track, tenured or possible tenure appointments starting fall 1986. Appoint­ visiting positions in Mathematics and Computer Science ments will be made at the Assistant Professor level unless Education. qualifications and experience require appointment at higher The Department offers the stimulating environment of a rank. Consideration will begin November 25, 1985 ·and highly rated Mathematics Department along with a strong continue until the positions are filled. Application forms commitment to the improvement of pre-college education. are available from Professor Thomas G. Kurtz, Chairman, It currently has a number of successful programs in the area Department of Mathematics, 223 Van Vleck Hall, 480 of pre-college mathematics and computer education. These Lincoln Drive, Madison, WI 53 706. AA/EOE. include undergraduate programs for the certification of elementary and secondary teachers; an M.S.T. degree program; LOUISE NOUN CHAIR IN WOMEN'S STUDIES a Doctor of Arts program; courses for gifted pre-college stu­ Grinnell College announces the endowment of the Louise dents; and extensive teacher in-service and continuing educa­ Noun Chair in Women's Studies. The College invites nomi­ tion programs. nations and applications to fill this distinguished position, The department has received funding to expand and improve beginning in the 1986-87 academic year. these programs and to set up a center for further develop­ The Louise Noun Professor will be expected to teach ment of the following activities: research in the teaching several courses each year, selected from appropriate disci­ and learning of mathematics; study of the impact and applica­ plinary, interdisciplinary, and women's studies areas. The tions of new technology such as microcomputers; curriculum Louise Noun Professor will also have administrative respon­ improvement in pre-college mathematics and computer in­ sibility for the integration of women's studies into the cur­ struction; in-service programs for the enhancement of primary riculum of Grinnell College. A program budget and some and secondary teachers. clerical support are available. Applicants must have a Ph.D. in Mathematics, Mathematics Grinnell College se.eks a distinguished individual who Education, Computer Science, or related field, an outstand· would serve as a catalyst to introduce both faculty and ing research and publication record, experience in undergrad­ students to women's studies. Experience in undergraduate uate and graduate teaching and previous involvement with teaching and the ability to work effectively with all con­ teacher education programs. Applications are also invited stituencies in the College are necessary. The Ph.D. degree for visiting positions of 1 or more quarters. Send vita and and a publication record suitable for appointment as Pro­ direct 3 letters of reference to John Wood, Chairman, Search fessor in an appropriate department will be expected, and Committee, Dept. of Mathematics, Statistics, and Computer the specific discipline or department is open. Preference Science, Univ. of Illinois at Chicago, Box 4348, Chicago, IL may but will not necessarily be given to a scholar with 60680. AA/EOE. cross-cultural interests. Please send letters of nomination or application to CARNEGIE-MELLON UNIVERSITY Catherine S. Frazer, Dean of the Faculty, Grinnell College, Department of Mathematics Box 805, Grinnell, Iowa 50112-0810. Nominations will Assistant Professorships close on November 30, 1985. Grinnell College is an equal opportunity/affirmative action employer and especially seeks The Mathematics Department expects to have three women and minority candidates. tenure-track positions at the assistant professor level in the fall of 1986 in the areas of convex analysis, combinatorics/ combinatorial optimization, and numerical analysis. An CLEVELAND STATE UNIVERSITY Department of Mathe­ interested candidate with a strong background and research matics. Tenure track assistant professor for fall 1986 (sub- interest in one of these fields should send a resume and ject to budget approval). Preference will be given to candidates three letters of reference to Professor Steven E. Shreve, in fields compatible with current research interests of the Chairman of Search Committee, Department of Mathemat· department. Ph.D. with established record and/or strong ics, Carnegie-Mellon University, Schenley Park, Pittsburgh, potential in research required. Commitment to excellent PA 15213. Carnegie-Mellon is an Affirmative Action/Equal teaching necessary. Department offers courses through the Opportunity Employer. Master's level. Normal teaching load is 2 courses per quarter. Competitive salary and excellent fringe benefits. Applications received after January 15, cannot be guaranteed full consid­ OKLAHOMA STATE UNIVERSITY eration. Send curriculum vitae and at least three letters of DEPARTMENT OF MATHEMATICS recommendation, to: T. W. Hungerford, Chairman, Depart­ Several tenured, tenure-track, and visiting positions at all ment of Mathematics, CLEVELAND STATE UNIVERSITY, professorial ranks for Fall, 1986. Preference will be given to 1983 E. 24th Street, Cleveland, Ohio 44115. Equal oppor­ hiring groups of mathematicians (e.g., a senior person and tunity employer, m/f/h. two junior people) in areas in which the Department plans to develop a strong research group. There will be additional financial support available to groups as "Seed money" to­ Miami University, Middletown, Ohio ward establishing active research programs in their areas. All has a tenure track assistant professorship, beginning in areas are currently under consideration. August, 1986. Miami University Middletown is a two-year Minimum qualifications are a Ph.D. in Mathematics, evidence regional campus of Miami University. Duties include teaching of research achievement or potential, and a commitment to an average of 12 hours per semester, university and com­ teaching. Post-doctoral experience is desirable. Normal duties munity professional service, and scholarship. Applicants include research and at most six hours teaching per semes­ should have a Ph.D. in mathematics, statistics or mathematics ter. For full consideration, send a resume and arrange to education by 8/86 and a strong interest in teaching. Please have three letters of reference sent by January 15, 1986 to send vita, transcripts and three reference letters to D. J. William Jaco, Head, Department of Mathematics, Oklahoma Lutzer, Mathematics and Statistics Department, Miami Uni­ State University, Stillwater, OK 74078. OSU is an equal versity, Oxford, Ohio 45056 by February 1, 1986. Late opportunity/affirmative action employer. Women and applications may be considered. Women and minorities are minorities are especially encouraged to apply. urged to apply. AA/EOE.

840 POSITIONS AVAILABLE HEAD, DEPARTMENT OF MATHEMATICAL SCIENCES COLLEGE OF LIBERAL ARTS AND SCIENCES SOUTHWEST TEXAS STATE UNIVERSITY, SAN MARCOS, BUTLER UNIVERSITY TX 78666-4616. Applications are invited for a tenure track Applications are invited for the position of Head of the position in Mathematics Education at the Assistant Professor Department of Mathematical Sciences. The department of level. Applicants must possess a Ph.D. or equivalent in Math. twelve full-time faculty offers undergraduate programs in Ed., and must have at least three years of teaching experi­ mathematics, computer science, and actuarial science. Aca­ ence at the secondary level. The potential for excellence in demic computing facilities include a VAX-11 /780 and micro­ teaching and research is required. Applicants should send computers. The department also offers courses in astronomy, vita, official transcripts, and three letters of recommenda­ and operates an observatory with a 38" telescope. tion to Dr. Ernest Ratliff, Acting Chair, Dept. of Math/CS, Butler University is an independent, non-sectarian, coeduca­ Southwest Texas State University, San Marcos, Texas tional institution located on a scenic three-hundred-acre 78666-4616. Deadline for receipt of applications is 1/31/86. campus in a lovely residential section of Indianapolis. There SWTSU is an EO/AA employer. are approximately 3,000 full-time-equivalent undergraduate and graduate students in the colleges of liberal arts and sci­ SOUTHWEST TEXAS STATE UNIVERSITY, SAN MARCOS ences, business administration, education, fine arts, and TX 78666-4616. Applications are invited for a tenure track pharmacy. Nearly two-thirds of the undergraduate students position in Non-linear Analysis or Number Theory at the live on campus. Assistant Professor level. Applicants must possess a Ph.D. or equivalent in Mathematics and must possess the poten­ Qualifications for the position of department head include tial for excellence in teaching and research. Applicants an earned doctorate in mathematical sciences, successful should send vita, official transcripts, and three letters of college teaching experience, documented evidence of con­ recommendation to Dr. Ernest Ratliff, Acting Chair, Dept. tinuing research and scholarly activity consistent with of Math/CS, Southwest Texas State University, San Marcos, appointment to senior faculty rank, evidence of leadership Texas 78666-4616. Deadline for receipt of applications is ability and effective communication skills, and interest in 1/31/86. SWTSU is an EO/AA employer. program development. Salary is competitive; benefits include TIAA/CREF. The position is available for the summer of ARIZONA STATE UNIVERSITY 1986. Department of Mathematics Applications received by january 15, 1986, will receive first The Department of Mathematics at Arizona State Uni­ consideration. Send a comprehensive curriculum vitae along versity will make one or more appointments, to begin with with the names, addresses, and telephc,,e numbers of at least the 1986-1987 academic year. The Department seeks an three references to: Assistant Professor (tenure-track), preferably in Applied Dr. Prem Sharma, Chairman Mathematics (broadly construed). It is possible that addi­ Mathematical Sciences Search Committee tional positions will be available. Minimum qualifications Butler University are a Ph.D. in Mathematics or Statistics and evidence of 4600 Sunset Avenue strong research potential. Some post-doctoral experience Indianapolis, IN 46208 and a record of publication are desirable. Butler University is an Affirmative Action/Equal Opportunity Applicants should send a Curriculum Vitae and direct Employer. at least three letters of recommendation to: P. Leonard, Acting Chair UNIVERSITY OF PUERTO RICO AT MAYAGUEZ Department of Mathematics Department of Mathematics Arizona State University Faculty position at the Assistant Professor level in the Tempe, AZ 85287 area of Mathematics- Algebraic Number Theory and/or Deadline for receipt of application materials is Febru­ Algebraic Geometry. Responsibilities include research and ary 1, 1986. teaching courses in Mathematics/Computer Science both at Arizona State University is an Equal Opportunity/Affirma­ the undergraduate and graduate level. Applicants must tive Action Employer. possess a Doctorate (Ph.D.) in Mathematics with specializa­ tion in Algebraic Number Theory and/or Algebraic Geometry. Computer background and fluency in spoken and written Miami University, Oxford, Ohio English or Spanish is required. Applicants should have at anticipates at least one tenure track assistant professorship least one (1) year of academic or industrial/research experience. beginning August, 1986. Duties include teaching an average Salary: $1,680 per month. Applicants should send a com- of 8-9 hours per semester, continuing scholarship, and plete resume and three letters of recommendation to Prof. committee service. Applicants should have a Ph.D. in pure Laura R. Cuebas, Acting Chairman, Department of Mathe­ or applied mathematics by 8/86. Please send vita, transcripts matics, UPR - Mayaguez Campus, MayagUez, P. R. 00708. and three reference letters to David Lutzer, Mathematics An affirmative action/equal opportunity employer. and Statistics Department, Miami University, Oxford, Ohio 45056 by February 1, 1986. Late applications may be con­ DEPARTMENT OF MATHEMATICS, UNIVERSITY OF sidered. Women and minorities are urged to apply. AA/EOE. CALIFORNIA, IRVINE, CA 92717 IRVINE VISITING ASSISTANT PROFESSORSHIP 1986-87 Mary Washington College The position enables mathematicians (of any age) beginning Mathematics Department their career who show definite promise in research to partic­ Tenure track position in mathematics beginning Fall, 86. ipate in an environment of vigorous mathematical research Assist. Prof. or higher. Rank commensurate with qualifica­ and instruction. Appointment is for 1 year; can be renewed tions and experience. Ph.D. preferred. Candidates should for second year. Annual salary: $28,300. Teaching duties have a strong interest in teaching and developing profession­ comparable to those of regular faculty. Appointees are ally at a small, u-grad, state supported, liberal arts college. expected to direct seminars in their specialty. Applications Teaching load is 12 hr/sem. Applicants should send resume, and three letters of recommendation must be received by graduate transcript, and 3 letters of reference to arrive no February 15, 1986 and should be accompanied by a cur­ later than Feb. 15, 1986. Send to: ). Zeleznock, Search riculum vitae and an account of work in print or preparation Committee Chairman, Dept. of Math Science, Mary Wash­ and brief description of research plans. An Affirmative ington College, Fredericksburg, VA 22401. AA/EOE. Action/Equal Opportunity Employer.

841 POSITIONS AVAILABLE EMORY UNIVERSITY Department of Mathematics and Computer Science NORTH CAROLINA STATE UNIVERSITY The Department of Mathematics and Computer Science DEPARTMENT OF MATHEMATICS at Emory University seeks to fill three permanent positions Beginning july 1, 1986, junior level tenure track posi­ this academic year. Applications are invited in the following tions are available in applied analysis (PDE, dynamical sys­ areas: 1) ordinary differential equations, preferably with tems, optimal control). an interest in population biology or mathematical physics Applicants must have a Ph.D. degree in mathematics and 2) nonlinear partial differential equations or differential have a strong record or potential in both research and in­ geometry, 3) computer science. The last position also can struction. Send a resume, relevant reprints, thesis abstract, be filled by a mathematician able to teach computer sci­ and three letters of reference to Professor J. C. Dunn, ence at the advanced undergraduate level but with a research Search Committee Chairman, Department of Mathematics, program in a different area. The rank for each position is Box 8205, North Carolina State University, Raleigh, North open. Basic requirements are a strong research record (or Carolina 27695-8205. promise of such in the case of a new Ph.D.), a commitment to excellence in teaching, and a desire to help build a North Carolina State University is an Affirmative Action strong graduate program. A senior applicant should demon­ and Equal Opportunity Employer. strate the ability to attract and direct graduate students. Emory University is a private institution, located NORTH CAROLINA STATE UNIVERSITY in suburban DEPARTMENT OF MATHEMATICS Atlanta. It has a well established Ph.D. Program in mathematics and a Masters Program in mathematics/ Beginning july 1, 1986, junior level tenure track posi­ computer science. The graduate programs are expanding as tions are available in algebra, Lie groups and related areas. part of a general effort by Emory to enlarge its overall Applicants must have a Ph.D. in mathematics and have contribution to graduate education. a strong record or potential in both research and instruction. An application for the above positions will consist of an Send resume, relevant reprints, thesis abstract and three expression of interest, a vita, and the names of at least letters of reference to Professor J. Luh, Search Committee three references. Junior applicants are encouraged to have Chairman, Department of Mathematics, Box 8205, North their letters sent directly. Applications close on February 1, Carolina State University, Raleigh, North Carolina 27695- 1986. All material should be sent to Professor Paul Waltman, 8205. Department of Mathematics and Computer Science, Emory North Carolina State University is an Affirmative Action University, Atlanta, Georgia 30322. and Equal Opportunity Employer. Emory University is an affirmative action/equal oppor­ tunity employer. Michigan Technological University Head of the Mathematical Sciences Department UNIVERSITY OF CALIFORNIA, LOS ANGELES, We invite applications and nominations for the position of PROGRAM IN COMPUTING, LOS ANGELES, CA 90024 department head. Candidates should have an established R. ). Miech, Director research record and a special interest in applied mathematics The Program in Computing has an opening at the adjunct or statistics, with a commitment to active research and assistant professor level. Responsibilities consist of teaching teaching. The department has 35 faculty members and offers lower division courses in elementary and intermediate pro­ B.S. and M.S. degrees in mathematics and statistics. Michigan gramming, with Pascal being the language of instruction. Technological University is a state university in Michigan's Minimum qualifications are a Ph.D. in one of the sciences, Upper Peninsula; it has an enrollment of 6500, with a special 30 or more semester units at the upper division and/or emphasis on science and engineering. graduate level in computer science, a through knowledge Applicants should send a resume and arrange for at least of Pascal, and one year's experience in teaching large (100+) three letters of recommendation to be sent to: Headship lower division courses. The workload is five quarter courses Search Committee, Mathematical Sciences, Michigan Tech­ per year. Salary is at the $30,000 level. nological University, Houghton, Ml 49931. Michigan Tech Send resume and names of three references by january is an equal opportunity institution and an equal opportunity 15, 1986 to: employer. Ronald J. Miech Department of Mathematics THE CITADEL University of California Applications are invited for two tenure track positions at Los Angeles, CA 90024 the assistant or associate level. Teaching responsibilities at all undergraduate levels of'Computer Science and Mathemat­ ics. Qualifications include a Ph.D. in Mathematics, Statistics, DEPARTMENT OF MATHEMATICS AND COMPUTER or Computer Science with a capacity for research and a SCIENCE dedication to undergraduate teaching. At least one position THE UNIVERSITY OF TEXAS OF THE PERMIAN BASIN will be filled with someone who has a strong background in ODESSA, TEXAS 79762 computing. Salary negotiable. Liberal benefits include possible Two positions at the rank of Assistant or Associate resources for assistance to pursue advanced computer Professor. One position is open from january 1, 1986, until science degrees. filled. The second position is planned for the Fall 1986 The Citadel is state-supported, liberal arts, military college semester. Successful candidates for the first position will offering undergraduate degrees in the Arts, Sciences, Engin­ have the Ph.D. in Computer Science, or a closely related dis­ eering, Education and Business Administration. The Depart­ cipline. The second position will require the teaching of ment of Mathematics and Computer Science offers the B.S. some mathematics and/or statistics. Successful candidates and B.A. Degree in Mathematics and also the B.S. Degree will have the Ph.D. in Mathematics, Computer Science, or in Computer Science. a closely related discipline. Preference will be given to can­ Please send resume and three letters of reference to didates who can teach Computer Science courses. UT Charles E. Cleaver, Head, Department of Mathematics and Permian Basin is an upper level institution enrolling about Computer Science, The Citadel, Charleston, South Carolina 2000 students, approximately 130 of which are majoring 29409. Applications should be received by February 15, in Computer Science or Mathematics. A master's degree 1986, to insure consideration. program in Computer Science is anticipated, pending final Minorities and women are encouraged to apply. The Coordinating Board approval. Citadel is an equal opportunity/affirmative action employer. Contact: Dr. james A. Nickel, Chairman

842 POSITIONS AVAILABLE INDIANA UNIVERSITY-PURDUE UNIVERSITY DEPARTMENT OF MATHEMATICAL SCIENCES Southern Illinois University-Carbondale: Applications are INDIANAPOLIS, INDIANA invited from qualified candidates for a tenure track position The Department of Mathematical Sciences at IUPUI is in Numerical Analysis at the rank of Assistant or Associate seeking applicants for a tenure-track position to begin in Professor at Southern Illinois University (Carbondale) begin­ August, 1986. The applicant must have an earned doctorate ning August 16, 1986. Minimum qualifications are a Ph.D. and excellent research potential in an applied area related with a strong background in numerical analysis. Candidates to present interests of our faculty (Theoretical and Compu­ must have demonstrated evidence of excellence in research. tational Fluid Dynamics, Hydrodynamic Stability, Com­ Evidence of teaching excellence is preferred. Rank and bustion Theory, Non-linear Waves, Scientific Computation, with qualifications. A substan­ salary will be commensurate and Dynamical Systems). tial research record is required for appointment at the IUPU I offers B.S., M.S., M.A.T., and Ph.D. degrees from Associate level. Closing date is December 15, 1985, or until Purdue University. The normal teaching load in the depart­ position is filled. Applications plus three letters of recom­ ment is two courses per semester. Excellent fringe benefits mendation should be sent to: Numerical Analysis Position; and competitive salary. Apply to Professor Neal Roth man, c/o Ronald Kirk, Chairman; Department of Mathematics; Chairman, Department of Mathematical Sciences, I UPUI, Southern Illinois University; Carbondale, Illinois 62901. 1125 East 38th Street, Box 647, Indianapolis, IN 46223. SIU-C is an Equal Opportunity/Affirmative Action Employer. Closing date, january 1, 1986. Applications are Southern Illinois University-Carbondale: UNIVERSITY OF CALIFORNIA, IRVINE invited for a tenure track position in Statistics at the Assis­ DEPARTMENT OF MATHEMATICS tant Professor Level, at Southern Illinois University (Carbon­ Professor dale), beginning August 16, 1986. Minimum qualifications Applications for an opening in 1986 for an Assistant An ideal can­ are a Ph.D., with a background in mathematical statistics specializing in probability/statistics are invited. and in and interests in applied statistics. Evidence of teaching didate will have background in mathematical statistics excellence is preferred. Closing date is December 15, 1985, probability, in particular, the modern theory of stochastic He or she will not only be active in research in or until position is filled. Applications plus three letters of processes. statistics recommendation should be sent to: Statistics Position; those areas but will also be active in the graduate program within the Department of Mathematics: participating cfo Ronald Kirk, Chairman; Department of Mathematics; ad­ Southern Illinois University; Carbondale, Illinois 62901. in the seminars, supervising students working toward teaching mathematically advanced statistic SIU-C is an Equal Opportunity/Affirmative Action Employer. vanced degrees, courses, and consulting for research personnel in medicine and biology. Candidates for this position must have a Ph.D. UNIVERSITY OF ARIZONA, DEPARTMENT OF MATHE­ Send applications, curriculum vitae, work in print or in MATICS preparation, and three letters of recommendation to Professor TUCSON, ARIZONA 85721 Howard Tucker, Department of Mathematics, University of Tenure-track and visiting positions at level depending on California, Irvine, CA 92717. Appointment begins on july qualifications of applicants. Ph.D., excellent research 1, 1986. U. C. Irvine is an Affirmative Action/Equal Oppor· record or potential, and strong commitment to teaching re­ tunity Employer. quired. Tenure track positions are in the areas of algebraic on applications to geometry, global analysis with emphasis LOYOLA COLLEGE IN MARYLAND nonlinear problems, probability, dynamical systems, and computational science. Outstanding senior candidates in any Department of Mathematical Sciences, Baltimore, Maryland area are encouraged to apply. Postdocs also available. Send 21210 application to Department Head, Department of Mathemat­ Several positions anticipated: 1) Assistant Professorship, ics. An Equal Opportunity/ Affirmative Action Employer. Ph.D. (or near), interest in one or more: combinatorics, applied or abstract algebra, graph theory, algorithms. CALIFORNIA STATE UNIVERSITY, LONG BEACH 2) Assistant Professorship, Ph.D. (or near), interest in one Department of Mathematics & Computer Science or more: general statistical methodology, statistical model­ analysis, operations research. 3) Instructorship, Tenure-track position, Assistant or Associate Professor, Fall ling, survival Master's Degree, to teach basic courses. The Department 1986. Specialties related to faculty interests in Algebra, offers a strong undergraduate program in Mathematical Functional Analysis or Differential Equations preferred. Sciences with concentrations in pure math, operations re· PhD in Mathematics, evidence of effective teaching and search, statistics, and computer science. Normal teaching strong research potential required. Must be U.S. citizen or load is three courses. Applicants should send vita, three permanent resident. Also 4 to 6 two-year Lecturer positions, letters, and transcripts to john Hennessey, Chairman. Appli­ PhD in Mathematics or Computer Science, any specialty, cations accepted until positions are filled. AAE. citizenship/permanent residence not required. Selection be­ gins Feb. 1, 1986; late applicants considered until positions UNIVERSITY OF SOUTHERN are filled. Send resume, transcript and three reference letters CALIFORNIA to C. W. Austin, Chairman, Math. & Camp. Sci., CSU, Long DEPARTMENT OF MATHEMATICS Beach, CA 90840. Affirmative Action/Equal Opportunity LOS ANGELES, CA 90089-1113 employer. Applications are invited for several tenure track Assistant Professorships, available for September 1986, and for some Burroughs Corporation, Austin Research Center has a posi­ senior level positions at the ranks of Professor and Associate tion available for a strong research mathematician to work Professor. Assistant Professors are expected to teach two in the area of parallel processing of functional programming courses per semester, and must show strong research promise. languages. Knowledge of mathematical logic, semantics, Applicants for senior level positions should have an out­ lambda calculus, functional programming LISP or PROLOG standing record of research and scholastic achievements. is desirable. Demonstrated research ability in mathematics Persons specializing in Statistics, Partial Differential Equa­ is required. Candidates must desire to work on specific tions, Combinatorial Analysis and areas of Applied Mathe­ problems related to the concurrent implementation of matics such as Numerical Analysis are especially encouraged functional programming languages. Reply to Dr. Carl Pixley, to apply. Applications should be addressed to Chairman, Austin Research Center, 12201 Technology Blvd., Austin, Search Committee, University of Southern California, De­ Texas 78727. Burroughs Corporation is an Equal Oppor­ partment of Mathematics, DRS 306, Los Angeles, California tunity /Affirmative Action employer. 90089-1113.

843 POSITIONS AVAILABLE CHAIRPERSON, DEPARTMENT OF MATHEMATICS AND STATISTICS UNIVERSITY OF SOUTH ALABAMA UNIVERSITY OF TORONTO ERINDALE CAMPUS Applications are invited for the position of Chairperson Department of Mathematics of the Department of Mathematics and Statistics. Starting date for the position is September 1, 1986. Applicants must Applications arc invited for a contractually limited have an earned doctorate, a successful record in teaching and appointment at the assistant professor level beginning research, and must qualify for appointment as Professor or July 1, 1986. The initial appointment will be for three Associate Professor of Mathematics. Considerable adminis­ years with a possible two year renewal. Base Salary for trative and leadership skills are required. Responsibilities in· assistant professors is currently $27,000. Duties consist of elude teaching, advising, curriculum development, fostering research and teaching and candidates must demonstrate research, budgeting, recruiting, and evaluating performance clear strength in both. of faculty members. Applications should be sent to: Professor D. K. Sen, The University of South Alabama, located in the greater Associate Chairman, Department of Mathematics, University Mobile area and established in 1963, serves as the only of Toronto, Toronto, Ontario, Canada, M5S 1 A1, and should major public institution of higher learning on the upper Gulf include a complete curriculum vitae and the names of at Coast. Enrollment currently exceeds 9,500. The 24 full-time least three referees. The deadline is February 15, 1986. faculty of the department participate in undergraduate and In accordance with the Canadian Immigration require· graduate degree programs in mathematics, as well as a minor ments, this advertisement is directed to Canadian citizens in applied statistics. A major in statistics is planned for 1986. and permanent residents. A wide variety of service courses for other colleges on cam­ pus is provided. DEPARTMENT OF MATHEMATICS Applicants must submit a letter of intent, a detailed UNIVERSITY OF WISCONSIN-MADISON resume, and must arrange to have at least three current letters of reference sent by January 15, 1986 to: POSITIONS AVAILABLE FOR 1986-87 Dr. L. Richard Hitt, Chair The Department of Mathematics at the University of Screening Committee for Mathematics/ Wisconsin-Madison invites applications for one or more posi· Statistics Chairperson tions as Van Vleck Assistant Professor commencing August, c/o Office of the Dean 1986. Appointments are for specified terms of two or three College of Arts and Sciences academic years at a salary of at least $25,000. Candidates University of South Alabama must receive their doctorate prior to September 1986. Mobile, AI. 36688 Candidates should have a strong commitment to good The University of South Alabama is an Affirmative Action, teaching and exhibit outstanding potential for mathematical Equal Opportunity Educational Institution. research. Preference will be given to candidates who are likely to interact well with other members of the Depart· WORCESTER POLYTECHNIC INSTITUTE ment. The Department of Mathematical Sciences anticipates The usual teaching load is two courses per semester, with filling for fall, 1986, several tenure track assistant profes­ some in your specialty. There is a high probability of ad­ sorships in these areas of applied mathematics (current ditional income through research or teaching during summers research interests in parentheses): between consecutive years of appointment. Classical Applied Mathematics (mathematical modeling, Application forms are available from Professor Thomas G. mathematical physics, dynamical systems, nonlinear PDE) Kurtz, Chair, Department of Mathematics, 480 Lincoln Statistics/Applied Probability (times series, estimation) Drive, Madison, WI 53706. Supporting materials should in· Discrete Mathematics (coding theory, combinatorics and elude a vita, a one to three page abstract of the candidate's graph theory, game theory) dissertation, and three or four letters of recommendation, Applicants should have a Ph.D., evidence of quality teaching, at least one of which discusses the candidate's capabilities and a commitment to ongoing scholarship. Duties include as a teacher. undergraduate/graduate teaching four hours per week and In order to ensure full consideration, the application and all advising student projects. Further, one will be expected to supporting materials must be received by December 31, 1985. carry out a program of professional development in teach· AA/EOE ing skills and in research. WPI, the nation's third oldest college of science and WESLEYAN UNIVERSITY engineering, offers a unique project based undergraduate DEPARTMENT OF MATHEMATICS education. A wide variety of master's and Ph.D. programs Tenure-track assistant professorship in combinatorial or are available in science, engineering and management. Appli· discrete mathematics. Four-year contract beginning academic cations must include curriculum vitae, transcripts, thesis year 1986-87; six hours teaching weekly. Candidates should abstract and names of at least three references. Application have a serious interest in teaching and an ongoing research materials to: Dr. Bruce McQuarrie, Department of Mathe­ program. Send vita, three letters of recommendation to: matical Sciences, Worcester Polytechnic Institute, 100 Search Committee, Department of Mathematics, Wesleyan Institute Road, Worcester, MA 01609. An Equal Opportunity University, Middletown, CT 06457 by January 31, 1986. Employer. Wesleyan University is an Equal Opportunity/Affirmative University of Texas Action Employer. Department of Mathematics University of Nebraska-Lincoln. Tenure-track positions at Austin, TX 78712 the Assistant Professor and Senior level beginning Fall, 1986. A number of appointments are expected for Fall 1986 Ph.D. required along with potential for excellence in research at the Instructor level (customarily new Ph.D.'s) and the and teaching. Areas of consideration are classical and modern Assistant Professor level (customarily at least two years ex­ analysis, differential equations, applied mathematics, and perience beyond the Ph.D.). Candidates should have strong optimization and control. The deadline for applications is research credentials. Salaries will be competitive. Applicants January 15 (or until suitable candidates are found). Appli­ should send vita, detailed summary of research interests and cants should send vita and arrange for three letters of recom­ at least three letters of recommendation to the Recruiting mendation to: David Logan, Chair, Department of Mathe­ Committee Chairman at the above address as soon as pos­ matics and Statistics, University of Nebraska-Lincoln, Lincoln, sible and in any event no later than January 15, 1986. The Nebraska 68588-0323. AA/EOE. University of Texas is an equal opportunity employer.

844 POSITIONS AVAILABLE UNIVERSITY OF UTAH DEPARTMENT OF MATHEMATICS COMPUTATIONAL MATHEMATICS invites applications for the following positions NORTHWESTERN UNIVERSITY 1. Three or four non-renewable 3-year Instructorships. The Department of Mathematics will sponsor an emphasis Persons of any age receiving a Ph.D. degree in 1985 or year during 1986-87 on the theme "Computation in the 1986 are eligible. Applicants will be selected on the basis Mathematical Sciences." It is being organized by George of ability and potential in teaching and research. Starting Gasper, Shelby Haverman, and Joseph Jerome. Two entry salary this year is $24,000 and cost of living increases are level, nonrenewable positions will be available, starting in contingent on action by the State Legislature. Duties September, 1986, and terminating in June, 1988. These consist of teaching two courses through the academic year. positions will be awarded to candidates with computing 2. One visiting position of one year or less. Selection criteria expertise in symbolic manipulation applications statistics, are teaching ability and potential contribution to our or numerical analysis/applied mathematics. Appointees must research environment. assume the normal teaching load of the department and possess the Ph.D. as of September, 1986. Applications must include curriculum vita, bibliography Applications should include curriculum vitae, dissertation and three references. (Instructorship applications must also include an abstract of thesis and a list of graduate courses and software development summaries, and three letters of completed or transcripts.) Experts in your specialized field reference. Please send to: may be contacted to evaluate your work. Applications will Professor Joseph W. Jerome be accepted until all available positions are filled. Department of Mathematics Northwestern University Please send your application to: Evanston, IL 60201 COMMITTEE ON STAFFING Northwestern University is an Affirmative Action/Equal DEPARTMENT OF MATHEMATICS Opportunity employer. UNIVERSITY OF UTAH SALT LAKE CITY, UTAH 84112

THE UNIVERSITY OF ALABAMA Department of Mathematics DEPARTMENT OF MATHEMATICS I ohn I ay College of Criminal I ustice The Mathematics Department has at least five vacancies for The City University of New York positions beginning August 16, 1986. Rank and salary will Assistant Professor, tenure-track position. Requirements: depend upon qualifications. A Ph.D. (or the equivalent) and Ph.D; demonstrated potential for research; strong commit­ the promise of excellence in teaching and research is required. ment to teaching. Computer science, numerical analysis or We are looking in particular for people who will complement operations research background preferred. John Jay College the research interests of our current faculty, but applications of Criminal Justice, located in Manhattan, is a senior college in all areas will be considered. We currently have active in CUNY. Send resume, graduate transcript, relevant reprints, groups in algebra, analysis, applied mathematics, differential dissertation abstract and three letters of reference to Samuel equations and topology. We invite applications both from Graff, Chairperson, Department of Mathematics, John Jay mathematicians seeking a tenure track position and from College of Criminal Justice, 445 West 59th Street, N.Y., N.Y. mathematicians interested in a one year visiting position. 10019 by January 17,1986. AA/EO Employer. (Each position may be filled either way.) At least three letters of recommendation which address teaching and research should be sent to the department. Send a curriculum vita STATE UNIVERSITY OF NEW YORK and reprints/preprints to: James Wang, Chairman, Mathematics AT BINGHAMTON Search Committee, Box 1416, University, AL 35486. Department of Mathematical Sciences THE UNIVERSITY IS AN EQUAL OPPORTUNITY/ Pending approval from the administration, the Department AFFIRMATIVE ACTION EMPLOYER. of Mathematical Sciences at the State University of New York at Binghamton invites applications for a senior level Applications invited for tenure-track position at Assistant appointment. Applicants should have an outstanding research Professor level beginning August 1986. Responsibilities: record. All areas of pure and applied mathematics (especially Teach courses in mathematics, particularly combinatorics and statistics and computer science) will be considered. Vita and discrete structures for largely engineering or computer science letters to: David L. Hanson, Chairman, Dept. of Math. majors and pursue research in combinatorial analysis, graph Sciences, SUNY-Binghamton, Binghamton, NY 13901. An AA/EO employer. theory, etc. Candidates must have Ph.D. in Mathematics with emphasis on some area of discrete mathematics. Teach­ ing experience desirable. Send resume and at least three WESLEYAN UNIVERSITY letters of recommendation to David A. Sanchez, Chairman, COMPUTER SCIENCE Mathematics and Statistics, University of New Mexico, Wesleyan University is seeking candidates for positions at all Albuquerque, NM 87131. Selection procedure will begin on levels in an expanding computer science program. Demon­ February 1, 1986. AA/EOE. strated research potential is important; area of specialization is open. Applicants should have the ability to develop and TEXAS A&M UNIVERSITY teach courses at both undergraduate and graduate levels. A Applications are invited for tenure-track positions in Ph.D. in computer science or equivalent experience is Mathematics starting September 1, 1986. Candidates must expected. have a Ph.D. in Mathematics and salaries are competitive. Wesleyan is a leading liberal arts college with 2600 students, We are especially interested in applicants in algebra, applied located midway between Hartford and New Haven. Ph.D. mathematics, and non-linear analysis. There is a possibility programs are offered in the sciences (as well as in ethnomusi­ of appointments at Professor, Associate Professor, and cology). The current teaching load in computer science is Assistant Professor ranks. Visiting positions are also expected. three courses per year. Send vita and arrange for three reference letters to be sent to To apply send resume and three letters of reference to: Dr. H. E. Lacey, Head Alan Cobham, Department of Mathematics, Wesleyan Univer­ Department of Mathematics sity, Middletown, CT 06457. All applications received by Texas A&M University February 15, 1986 will be considered, however, early appli­ College Station, Texas 77843-3368 cation is encouraged. Wesleyan University is an Equal Texas A&M is an equal opportunity employer. Opportunity/Affirmative Action employer.

845 POSITIONS AVAILABLE THE AUSTRALIAN NATIONAL UNIVERSITY invites applications from suitably qualified men and women for UNIVERSITY OF QUEENSLAND appointment to the position of LECTURER in the DEPART­ CHAIR OF COMPUTATIONAL MATHEMATICS MENT OF MATHEMATICS, FACULTY OF SCIENCE. The University is seeking a mathematician with an out­ Applicants should have a Ph.D or equivalent qualifications standing research record and with considerable experience and some postdoctoral research experience. The Department in the practical applications of mathematics. Specialisation would prefer to make an appointment in some area of is expected in at least one major area of applied computa­ modern applied mathematics such as optimization, compu­ tional mathematics such as numerical analysis, operations tational mathematics or dynamical systems. However, per­ research and mathematical programming. sons with active research interests in other areas of modern The Professor will lead the computational mathematics applied or pure mathematics are encouraged to apply. The group with in the department and will be required to engage appointee will be expected to contribute to the Depart· in teaching of undergraduates and the promotion of research ment's undergraduate teaching program and to carry out and postgraduate studies. Consultation with industry is research and supervise graduate students in his or her own strongly encouraged. area of research. The Department has close links with The Centre for Mathematical Analysis and other mathemat­ Salary: $A54,948 per annum ical science departments at the University. The position is Closing date: 31st December, 1985 Ref. 36785 available from the start of the 1986 academic year. For The University provides prescribed travelling and removal further information contact: Professor M. N. Barber, Head expenses, superannuation, housing assistance and special of the Department of Mathematics, Phone (062) 494179. studies programs. Closing date: 1 December 1985. Ref: FS 29.8.1. Salary Additional information and applications forms are available will be in accordance with qualifications and experience from the Staff Officer, University of Queensland, St. Lucia, within the range: Lecturer $26,236- $34,467 p.a.; current 4067, Queensland, Australia. (21530) exchange rate: $A 1 = US 69c. Appointment as Lecturer The University of Queensland is an Equal Opportunity will be for four years in the first instance with the possibil­ Employer. ity, after review, of appointment to retiring age. Grants towards travel, assistance with housing, superannuation. MACALESTER COLLEGE Maternity leave is available. The University reserves the The Department of Mathematics and Computer Science right not to make an appointment or to make an appoint· is inviting applications for a tenure track position beginning ment by invitation at any time. Applicants should quote in Fall, 1986. Applicants should have or be very near com­ the reference number when submitting applications to pletion of· a Ph.D. in either Mathematics or Computer Patricia M. White, Acting Registrar, GPO Box 4, Canberra, Science and will be expected to participate in the develop­ ACT, 2601 Australia. THE UNIVERSITY IS AN EQUAL ment and teaching of upper level courses in computer sci­ OPPORTUNITY EMPLOYER. ence. Macalester is a four-year, residential liberal arts college York University of approximately 1700 students. The department offers Toronto, Canada majors in both mathematics and computer science. Appli­ Department of Mathematics cants should be committed to excellence in undergraduate teaching and scholarship. Salaries and benefits are com­ Applications are invited for a tenure-track position in Statis· petitive. Macalester is an equal opportunity employer. tics, rank open, and for one or more tenure-track or limited­ Applications should be directed to john Schue, Chairman; term positions, areas unspecified, to begin july 1, 1986. Department of Mathematics and Computer Science, Applicants should have proven .ability or demonstrated Macalester College, St. Paul, MN 55105; providing a resume potential for research and teaching. Positions are subject to and three references. Applications will be accepted until the university approval. Send resumes and three letters of position is filled. recommendation by February 1, 1986 to: j. Wick Pelletier, Chair, Department of Mathematics, 4700 Keele Street, North UNIVERSITY OF ARIZONA, DEPARTMENT OF York, Ontario, M3j 1 P3 Canada. In accordance with MATHEMATICS Canadian Immigration requirements this advertisement is TUCSON, ARIZONA 85721 directed to Canadian citizens and permanent residents of Canada. Tenure track positions at all levels. Ph.D., excellent research record or potential, strong commitment to teaching re­ THE UNIVERSITY OF ALABAMA quired. Field is less important than ability but should com­ DEPARTMENT OF MATHEMATICS plement existing strengths in algebra, computational science, As part of ongoing development in applied mathematics, differential equations, dynamical systems, geometry, mathe­ we have received funding for a new position in applied mathe­ matical physics, nonlinear analysis, number theory, proba­ matics. Salary will be negotiable, up to a maximum of bility and statistics. Closing date for applications is $35,000 and rank will depend upon qualifications. We invite February 1, 1986 or whenever position is filled. Send applications from experienced mathematicians in applied application to Department Head, Department of Mathematics. mathematics with excellent records in research and teaching. The University of Arizona is an Equal Opportunity/Affirma­ We are looking for someone who will help us develop our tive Action Employer. research group and our graduate programs in applied mathe­ matics. Applications or inquiries should be sent to: Alan The University of Vermont Hopenwasser, Chairman, Department of Mathematics, P.O. Department of Mathematics and Statistics Box 1416, University, AL 35486. THE UNIVERSITY IS 16 Colchester Avenue AN EQUAL OPPORTUNITY/AFFIRMATIVE ACTION Burlington, VT 05405 EMPLOYER. Applications are invited for two tenure track positions, one at the associate/assistant professor level and one at the DUKE UNIVERSITY, DEPARTMENT OF MATHEMATICS, assistant professor level. Excellence in research and teaching DURHAM, NC 27706: Positions open at all levels. Salary is required. All mathematics research areas will be con­ negotiable. Fields of primary interest: geometry, analysis, sidered although some preference will be given to areas 'applied mathematics, numerical analysis. Send application compatible with those of the department. Send resume and including curriculum vitae and list of references to Professor have three letters of recommendation sent to james C. William K. Allard, Chairman, by February 1, 1986. Nomina­ Becker, Chairman, by january 20, 1986. tions and inquiries are welcome. Duke University is an equal UVM is an Equal Opportunity/Affirmative Action Employer. opportunity/affirmative action employer.

846 POSITIONS AVAILABLE Dartmouth College BELOIT COLLEGE The John Wesley Young Instructorship is a 2-year post· doctoral appointment for promising new or recent Ph.D.'s Visiting instructor or Assistant or Associate Professor.* whose research interests overlap with those of some other Could be for three semesters starting January 1986, or for department member. Current fields of interest include algebra, two semesters starting August 1986. Qualifications: Ph.D. analysis, combinatorics, computer science, logic and set or A.B.D. in a mathematical science, interest in liberal theory, number theory, probability and topology. Teaching arts education, excellence in teaching. responsibilities average less than 6 hours per week and include Apply by letter and vita to Philip Straffin, Chair, Mathemat­ introductory, advanced undergraduate, and graduate courses, ics and Computer Science, Beloit College, Beloit WI 53511. usually including one in the Instructor's specialty. The Arrange for transcripts and three recommendation letters. 9-month salary of $21,500 is supplemented by a $3,000 Deadline: December 7, 1985 for January; February 1, 1986 research stipend for Instructors in residence during 2 addi­ for August. tional months. Applicants should send a letter of application, Beloit College is an Affirmative Action/Equal Opportunity resume, graduate school transcript, thesis abstract, and employer. should arrange for three letters of recommendation to be *This position is subject to final administrative approval. sent to: Recruiting Secretary, Dept. of Mathematics and Computer Science, Bradley Hall, DARTMOUTH COLLEGE, Department of Mathematics Hanover, NH 03755. The department will give first consider­ University of Houston ation to applications completed by January 31, 1986. University Park Dartmouth is committed to affirmative action and strongly The Department of Mathematics will have one or two encourages applications from women and minorities. visiting faculty positions, and these will be available for The Department of Mathematics and Statistics at Mississippi visits of either one or two semesters. The visiting faculty members will be named State University anticipates two or more tenure track posi­ tions at the Assistant Professor level for the 1986-87 aca­ D. G. Bourgin Visiting Scholars demic year. A Ph.D. is preferred. Responsibilities include Some teaching duties will be required, but the main purpose teaching and research. Candidates should submit a vita and of the visit is to collaborate with the permanent faculty three letters of recommendation to Roger C. McCann, Chair­ on research centered in the areas of algebra, analysis or man Screening Committee, Department of Mathematics and topology. Interested persons should apply by February 15, Statistics, Mississippi State, MS 39762. Screening will begin 1986, to Professor G. Etgen, Chairman, Department of December 15, 1985, and continue until positions are filled. Mathematics, University of Houston - University Park, Mississippi State University is an equal opportunity/affirma­ Houston, Texas 77004. Telephone: (713) 749·4827. tive action employer. Inquiries should include a vitae and the names of at least three references. Department of Mathematics The University of Houston is an equal opportunity/ University of Kansas . affirmative action employer. Anticipate some instructorships beginning fall semester 1986, which are normally renewable for second and third year. Carnegie-Mellon University Salary to be determined. Research interests should be in Zeev Nehari Assistant Professorship in Mathematics areas closely related to those of current staff. Ph.D. or dis· This position has been instituted in the Department of Mathe­ sertation accepted with only formalities to be completed. matics of Carnegie-Mellon University to honor the memory Send detailed resume and dissertation abstract; arrange for of Professor Zeev Nehari, a member of the Department from three letters of reference to be sent directly to C. J. Himmel­ 1954 to his death in 1978. Applicants are expected to show berg, Chairman, Department of Mathematics, University of exceptional research promise as well as clear evidence of Kansas, Lawrence, KS 66045-2142. Deadline date: December achievement. Each appointment is for two academic years, 1, 1985, then monthly until August 2, 1986. extendable for one further year when mutually agreeable. It The University of Kansas is an Affirmative Action/Equal carries a reduced academic year teaching load of six hours Opportunity Employer. per week during one semester and three hours per week during the other. The applicant should have research interests THE UNIVERSITY OF PITTSBURGH which intersect those of current faculty of the Department. Applications invited for tenure-track or visiting faculty The stipend for the academic year 1986·87 will be $28,000- positions anticipated in 1986. Preferred area: POE's, analysis, $30,000. Application forms and further information on the applied mathematics, statistics. Present teaching load: two position and the Department can be obtained by writing to classes per term, 2-term 8-month academic year. Ph.D., pub­ Professor David R. Owen, Chairman, Zeev Nehari Assistant lications and active research program, effective teaching Professorship Committee, Department of Mathematics, ability required. C. V., four letters of recommendation, Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213. reprints, preprints should be sent to W. E. Deskins, Chairman, To ensure consideration applications should be filed by Department of Mathematics and Statistics, University of February 1, 1986. Carnegie-Mellon University is an Equal Pittsburgh, Pittsburgh, Pennsylvania 15260. U. P. is an Opportunity Employer. Equal Opportunity /Affirmative Action Employer. SAINT LOUIS UNIVERSITY DEPARTMENT OF MATHEMATICS WESTERN MICHIGAN UNIVERSITY AND COMPUTER SCIENCE DEPARTMENT OF MATHEMATICS St. Louis, MO 63103 The department has a tenure-track position in Graph Theory/ Two tenure track positions are available at the Assistant Combinatorics open at the assistant professor level beginning Professor level to begin fall 1986. The department offers Fall, 1986. A second tenure-track position in Mathematics undergraduate majors in Mathematics and Computer Science Education, at the Assistant Professor level is possible for and a doctorate in mathematics. Persons holding a Ph.D. in Fall, 1986. These positions require a Ph.D. as well as strong Mathematics or Computer Science who are committed to commitment and potential for teaching and research. Send teaching and research and are willing to participate in the undergraduate Computer Science program are invited to inquiries to Dr. Joseph Buckley, Chair, Department of Mathe­ apply. Have a vita and three letters of recommendation sent matics, Western Michigan University, Kalamazoo, Ml 49008. to Professor Charles Ford at the above address. An AA/EO Western Michigan University is an Affirmative Action/Equal employer. Opportunity Employer.

847 POSITIONS AVAILABLE HOBART AND WILLIAM SMITH COLLEGES DEPARTMENT OF MATHEMATICS Department of Mathematics AND COMPUTER SCIENCE University of Kansas Applications are invited for a tenure-track position, begin­ Applications are invited for tenure-track and temporary posi­ ning September 1986. The Ph.D. in Mathematics is required, tions at all levels, commencing August 16, 1986 or as nego­ as well as a strong background (preferably a Master's) in tiated. Field is unrestricted but preference will be given to Computer Science. Duties include teaching all levels of under­ probability/statistics and algebra, and to areas meshing well graduate mathematics and computer science, and participation with the department's needs. Require Ph.D. or Ph.D. disser­ in the General Curriculum. Candidates should have strong tation accepted with only formalities to be completed. commitment to excellence in teaching and promise of con­ Application, detailed resume with description of research, tinued scholarly activity. The teaching load is two courses and three recommendation letters should be sent to C. J. per trimester. Salary is negotiable and competitive. Himmelberg, Chairman, Department of Mathematics, Univer­ Hobart and William Smith Colleges are coordinate, four sity of Kansas, Lawrence, KS 66045-2142. year, liberal arts colleges with a combined enrollment of Deadlines: December 1, 1985 for first consideration, then approximately 1800. They are located in Geneva, New York, monthly until August 1, 1986. a city of 15,000 on the northern shore of Seneca Lake. The University of Kansas is an AA/EOE. Within an hour's drive are three major universities: Cornell, Rochester, and Syracuse. OREGON STATE UNIVERSITY Applicants should send detailed resume, three letters of recommendation (at least one including comments on teach­ Assistant Professor of Mathematics in Pure or Applied ing ability), and undergraduate and graduate transcripts Mathematics may become available. Candidates in geometry, (unofficial photocopies are acceptable) to: probability, and topology are encouraged to apply. Salary Professor Lawrence Smolowitz, Chair negotiable, depending on qualifications. Start September Department of Mathematics and Computer Science 1986. Closing date January 15, 1986. Write to: Hobart and William Smith Colleges Professor P. M. Anselone, Chairman Geneva, New York 1445 6 Department of Mathematics The Colleges are an Oregon State University Equal Opportunity Employer. Corvallis, OR 97331 INDIANA STATE Attn: Staff Selection Committee UNIVERSITY DEPARTMENT OF MATHEMATICS Oregon State University is an Affirmative Action/Equal AND COMPUTER SCIENCE Opportunity Employe· and complies with Section 504 of The· Mathematics and Computer Science Department is the Rehabilitation Act of 1973. extending its search to fill two tenure-track Assistant Pro­ fessor positions beginning either in January or September of Chair, Depa··tment of Mathematics 1986. The Department has 22 full-time faculty members Illinois Wesleyan University seeks a Department Head in and offers BA and BS degrees in Mathematics and in Com­ Mathematics. The department is composed of four full-time puter Science, and the MA and MS in Mathematics. Appli­ faculty and offers BA's in both Mathematics and Mathematics­ cants should possess an earned Ph.D. and potential for Computer Science. The department seeks to offer a strong teaching and research excellence. program for its majors as well as to serve the broader inter­ Indiana State University has extensive computing facili­ ests of the University. We are looking for a dynamic person ties, including a CYBER 830, an IBM 4361, two PRIME who will provide effective leadership in a liberal arts setting. 750's and several microcomputer laboratories. The Depart­ The successful applicant must be able to work well with ment operates its own microcomputer laboratory and a faculty leaders in various areas of the University that depend VAX-11 /750 with both Bell and Berkeley UN IX available. on an effective program in Mathematics. Candidates must Send vita and three letters of recommendation to: have the Ph.D. in Mathematics, and a proven record of high Dr. Donald F. Reynolds, Chairman quality teaching and research. Rank and salary are negotiable. Interested candidates should send a current CV and have Department of Mathematics and Computer Science three letters of reference sent to: Dr. Roger Schnaitter, Indiana State University Terre Haute, IN 4 7809 Director, Division of Natural Science, Illinois Wesleyan Uni­ versity, Bloomington, IL 61702. Equal Opportunity Employer. Applicants should be U.S. citizens or hold a resident visa. Applications received after December 2, 1985, cannot be guaranteed consideration for a January appointment. UNIVERSITY OF SOUTH CAROLINA Applications received after March 31, 1986, cannot be Department of Mathematics guaranteed consideration for a September appointment. Applications are invited for anticipated tenure-track faculty Indiana State University is an EO/AA employer. positions at all levels. The Department intends to build on existing strengths and also to supplement these with a num­ Mathematics: The State University of New York, ber of appointments in other areas, particularly in applied College at Potsdam invites applications for a full time tenure track mathematics. However, applications in all areas of pure and position, commencing August 1 986, to teach undergraduate applied mathematics will be considered. The Ph.D. degree or and beginning graduate courses. Potsdam College features its equivalent is required, and all appointments will be con­ a robust undergraduate sistent with the Department's commitment to excellence in mathematics major, a four-year B.A./ M.A. program, and a Masters' program in a research and in teaching at both graduate and undergraduate liberal arts atmosphere. Nearly 20 percent of the student body elects levels. A detailed resume, containing a summary of research Mathematics as either a first or second major. accomplishments and goals, and four letters of recommen­ Qualifications: Ph.D. in any area of Mathematics, evidence of excellent dation should be sent to: teaching skills required. Rank and salary: open. Deliberations Dr. Colin Bennett will begin on February 15, 1986 and continue until a suitable Chairman candidate is identified. Send letter of application, vita and Department of Mathematics supporting documents to: W. Mitchell, Chairman of Search University of South Carolina Committee, Department of Mathematics, State University Columbia, South Carolina 29208 College of Arts and Science, Potsdam, New York 13676. The University of South Carolina is an Affirmative Action/ Women and Minorities are encouraged to apply. An Equal Equal Opportunity employer. Opportunity/Affirmative Action Employer.

848 POSITIONS AVAILABLE NORTHEASTERN UNIVERSITY Department of Mathematics University of Missouri-Columbia Applications are invited for position of Assistant or Associate Department of Mathematics Professor and possibly one Post-Doctoral Lectureship. A Applications at the Assistant or Associate Professor level Ph.D. is required, and priority will be given to candidates are invited for one or more anticipated tenure track posi­ with strong records of scholarship and excellence in teaching. tions beginning with the 1986-87 Academic year. The De­ Particular needs of the department are in Statistics and partment seeks Ph.D. degree holders with strong interests in Applied Mathematics. All positions start Fall 1986. Please research who are able to teach effectively at both the under­ send resume and three letters of reference to: Hiring Com­ graduate and graduate levels. Preference will be given to mittee Chairman, Department of Mathematics, Northeastern candidates in harmonic and probabilistic analysis, algebraic University, Boston, MA 02115. Northeastern is an Equal geometry, differential equations, and computational mathe­ Opportunity/Affirmative Action Employer. matics. A letter of application, vita, publication list, and three letters of recommendation should be sent to Keith Schrader, Chair, Department of Mathematics, University of MATHEMATICS POSITION Missouri, Columbia, MO 65211. The deadline date for ap­ The Mathematics and Statistics Department of Radford plications is Feb. 1, 1986 or until positions are filled. The University is seeking applicants for a tenure track position University of Missouri is an equal opportunity /affirmative beginning Fall 1986. A doctorate in mathematics by June action employer. 31, 1986 is required. Preference will be given to applicants with specialization in algebra. This position entails a four BELOIT COLLEGE course, twelve semester hour teaching load, in a department Tenure track Assistant or Associate Professorship, beginning which offers Bachelor's and Master's degrees. Rank and August 1986. Qualifications: Ph.D. in a mathematical sci­ salary are dependent on experience and qualifications. Send ence, interest in liberal arts education, dedication to excel­ letter of application, vita, three recent letters of reference lence in teaching and continued professional growth. and copies of all graduate and undergraduate transcripts by Candidates must be able to teach some upper level compu­ December 2 to: ter science courses, and have computer science as one area Dr. David L. Albig of professional interest. Chairman, Dept. of Mathematics and Statistics Apply by letter and full vita to Philip Straffin, Chair, Radford University Mathematics and Computer Science, Beloit College, Beloit, Radford, VA 24142 WI 53511. Arrange to have three letters of recommendation and graduate and undergraduate transcripts sent. Deadline: February 1, 1986 for assured consideration. POSITIONS WANTED Beloit College is an Affirmative Action/Equal Opportunity Teaching/Research, Ph.D. 1969. Analysis/D. E. over twenty employer. years' teaching. Several publications. c/o November classi­ fied, AMS, P. 0. Box 6248, Providence, Rl 02940. UNIVERSITY OF OKLAHOMA Department of Mathematics Applications are invited for one or more tenured or tenure­ track positions in Mathematics, beginning Fall 1986. The department also expects to offer some visiting positions. FOR SALE Candidates must have demonstrated excellence in research and teaching. Preference will be given to those whose re­ search interests are compatible with those of our current faculty. Applicants should send their vita and have at least MATH SCI PRESS, 53 Jordan Rd, Brookline MA, 02146, three letters of reference sent to Paul R. Goodey, Search 617-738-0307. just published: Proceedings of the Berkeley­ Committee Chair, Department of Mathematics, University Ames Conference on Nonlinear Problems in Control and of Oklahoma, Norman, Oklahoma 73019. Closing dates are Fluid Dynamics, L. R. Hunt and C. F. Martin, (eds), 450 Dec. 15, 1985 and every two weeks thereafter. The Univer­ pages, $50. (Lie Groups Series B: Systems Information and sity of Oklahoma is an Affirmative Action/Equal Oppor­ Control, vol. II). Topics in the Geometric Theory of Linear tunity Employer. Systems, by Robert Hermann, $50. (Interdisciplinary Mathe­ matics, v. 22). The Geometric theory of Ordinary Differen­ DEPARTMENT OF MATHEMATICS tial Equations and Algebraic Functions, by G. Valiron, $75. University of Connecticut (Lie Groups, v. 14). Topics in the Geometry Theory of In­ tegrable Systems, $65, by Robert Hermann (Interdisciplinary The department is seeking to significantly strengthen its Mathematics, v. 23.). Write or call for special prices on back program in applied and computational mathematics and list. invites candidates with demonstrable research potential and a strong commitment to teaching to apply for several tenure track and visiting positions. Rank and salary will be com­ petitive and commensurate with qualifications. For a senior level appointment proven excellence in research and teaching is expected. Foundations of Semiological Theory of Numbers The preferred areas of hiring will be Numerical analysis, H. A. Pogorzelski and W. J. Ryan especially numerical linear algebra, approximation techniques, numerical solutions to ODE's and POE's; Differential equa­ Volume 7 (1982), General Semiology, 597 pp., $29.95 tions, especially nonlinear PDE, control theory and dynamical Volume 2 (1985), Semio. Functions, 695 pp., $34.95 systems, integral equations, inverse problems, and stochastic UMO Press, Univ. of Maine, Orono, ME 04469 differential equations; Optimization. (Post free within US if check included) Screening will begin january 15, 1986 and continue until all positions are filled. Please send vita and direct at least three letters of reference to Professor J. Tollefson, Head, Department of Mathematics, U--9, University of Connecticut, Mathematics library. Request list. Bert Ross, University of Storrs, CT 06268. EO/AA employer. New Haven, West Haven, Ct. 06516.

849 FOR SALE ANNOUNCEMENT

ISTITUTO NAZIONALE Dl ALTA MATEMATICS MATHEMATICAL SCIENCES INSTITUTE FRANCESCO SEVERI CORNELL UNIVERSITY ROME- ITALY Postdoctoral and Senior Visitors Recent publications: The newly established Mathematical Sciences Institute Free boundary problems will support research in the areas: Applied Analysis Proceedings of a seminar held in Pavia- September-October 1979, by: (P. j. Holmes, 607-256-4335/4276/5062) S. Albertoni, H. W. Alt, A. Ambrosetti, L. Amerio, I. Ath· Physical Mathematics hanasopoulos, C. Baiocchi, ). Bear, M. Biroli, P. Boieri, (J. T. jenkins, 607-256-7185/5062) C. M. Brauner, H. Brezis, M. Bulgarelli, L.A. Caffarelli, Numerical Analysis & Computing ). R. Cannon, A Capelo, G. Capriz, V. Casulli, j. Cea, M. (L. B. Wahl bin, 607-256-2397 /4013) Statistics & Applied Probability Chipot, G. Cimatti, L. Citrini, L. Collatz, V. Comincioli, B. Coppi, P. Cortey·Dumont, C. W. Cryer, B. D'Acunto, (N. U. Prabhu, 607-256-4856) A. Damlamian, E. De Giorgi, A. S. Demidov, E. Di Bene· Details about the program in an area can be obtained from detto, ). Douglas, G. Duvaut, A. Fasano, A. Franchi, J. the corresponding Coordinator, whose name and telephone Frehse, A. Friedman, F. Gastaldi, G. Geymonat, G. Gilardi, number(s) are shown in parentheses. Each year there will B. Glowinski, L. Guerri, C. Guillope, W. Hager, G. D. lancu· be at least 8 Workshops; for '86-'87 these are: lescu, R. Jensen, S. Kamin, j. L. Lions, P. L. Lions, G. Maier, Numerical and Symbolic Computational Methods for Non­ U. Maione, G. Meyer,). C. Miellou, M. Miranda, U. Mosco, linear Dynamics (Guckenheimer) B. Nicolaenko, j. A. Nitsche, j. R. Ockendon, G. A. Pozzi, Infinite Dimensional Dynamical Systems and Their Finite M. Primicerio, G. Prouse,). W. Rogers, L. I. Rubinstein, Dimensional Analogues (Holmes) G. Sacchi, A. Taroni, R. Temam, F. Tomarelli, A. Torelli, Micromechanical Aspects of Creep Fracture in Metals and B. Turkington, P. Villaggio, A. Visintin. Polymers (Hui and Phoenix) Two volumes for 523 + 606 pages, $70.00. High Mach Number Combustion (Buckmaster and Ludford) Monge·Ampere equations and related topics Fast Preconditioned Methods for POE's (Bramble and Proceedings of a seminar held in Firenze- September-Octo­ Schatz) ber 1980, by: T. Aubin, I. Bakel man, B. Bojarski, R. Dwilewicz, A. Kum· Algorithms for Aerodynamic Problems (Caughey) pera, V. I. Oliker, C. Pucci, G. Talenti. Supercomputers and Numerical Linear Algebra (Van Loan) One volume, 248 pages, $25.00. Sequential Experimentation ( Bechhofer, Santner and Topics in modern harmonic analysis Turnbull) Proceedings of a seminar held in Torino and Milano·- May­ Deterministic and Stochastic Control (Heath, Prabhu and june 1982, by: Thorp) M. W. Baldoni Silva,). j. Benedetto, A. Berenstein, II, The organizer of each Workshop is shown in parentheses. C. Berenstein, B. E. Blank, R. Blei, G. Brown, R. Brum­ Starting 1 June '86 the following visiting positions will melhuis, R. Burger, j. L. Clerc, R. R. Coifman, M. Cowling, be available. A. H. Dooley, P. Eymard, ). Faraut, H. G. Feichtinger, Postdoctoral Visitors M. Gatesoupe, G. I. Gaudry, S. Helgason, A. lozzi, R. john­ son, P. Jones, J. P. Kahane, A. W. Knapp, T. H. Koorn· Scientists who are (preferably) no more than 5 years winder, A. Koranyi, R. A. Kunze,).). Manfredi, 0. C. beyond the doctoral degree are eligible for 12 or 24 McGehee, Y. Meyer, M.A. Picardello, G. Pisier, E. Prestini, month appointments. The salary is $24,000/yr. plus H. M. Reimann, R. Rochberg, J. L. Rubio de Francia, fringes, and may be augmented from other sources. C. Sadosky, P. Sjolin, S. Wainger, G. Weiss. Deadline for '86-'87 applications is 31 january '86; Two volumes for 541 + 536 pages, $80.00. awards will be made by 1 5 March '86. In addition to Orders must be prepaid and should be addressed to: a curriculum vitae, three (3) letters of recommenda­ lstituto Nazionale di Alta Matematica Francesco Severi tion are required, one of which should come from P. le Aldo Moro 5 the thesis advisor. The candidate should specify a Citta U niversitaria mathematical scientist at Cornell with whom (s)he 00185 ROMA, ltalia. expects to be associated. Senior Visitors Partial support for visits extending from a few weeks up to a few months is available. Applications should normally be made through a mathematical scientist at Cornell who, in sponsoring the visit, will be ex­ pected to find supplemental support if necessary. Some preference in the selection of Visitors will be given to those who will participate in Workshops during their stay. A list of Cornell mathematical scientists is available from the Institute Office (607-256-4335). Inquiries should, in genera!, be addressed to the appro­ priate Program Coordinator, who can also be reached by mail at: Mathematical Sciences Institute, Cornell University Caldwell Hall, Ithaca, NY 14853-2602 The Director (G. S. S. Ludford, 607-256-4079/4335/5062) will be glad to answer any remaining questions. The Institute is funded by the U. S. Army Research Office. Cornell University is an Equal Opportunity/Affirmative Ac­ tion Employer.

850 Position Open Associate Director

Mathematical Association of America

The Mathematical Association of doctoral level. However, a strong master's America will have an opening in its head­ degree, especially when combined with ad­ quarters office for the position of Associate ministrative experieince, may qualify. Director, beginning on January 1, or as This position offers the possibility of soon as possible thereafter. For an excep­ an exciting leadership career in publishing tional candidate, a starting date as late as and association management. July may be negotiated. Applications will be accepted at any The responsibilities of the Associate time. However, a telephone inquiry in Director will be largely in the area of advance is recommended after December publications, as editor of FOCUS and ad­ 1. Applicants should send a curriculum ministrative supervisor of a publications vitae and arrange to have three letters of program which includes three journals and recommendation sent to A. B. Willcox, 5-10 books per year. The AD will also Executive Director, Mathematical Associ­ work on special projects and assist the ation of America, 1529 Eighteenth Street, Executive Director in the administration N.W., Washington, DC 20036. Telephone: of the headquarters office. (202) 387-5200. Mathematical training is a require­ The MAA is an equal opportunity ment for the position, preferably to the employer.

Wiley Mathematics ... from Theory to Practice APPLIED AND COMPUTATIONAL Also available: COMPLEX ANALYSIS Vol. 3 APPLIED AND COMPUTATIONAL Discrete Fourier Analysis, Cauchy Integrals, COMPLEX ANALYSIS, Vol. 1 Construction of Conformal Maps, Univalent Power Series-Integration-Conformal Functions Mapping-Location of Zeros PETER HENRICI, Eidgenossische Technische (0-471-37244-7) 682 pp. 1974 $59.95 Hochschu/e, Zurich APPLIED AND COMPUTATIONAL At a mathematical level accessible to the non-spe­ COMPLEX ANALYSIS, Vol. 2 cialist, the third of a three volume work shows how to Special Functions-Integral Transorms­ use methods of complex analysis in applied mathe­ Asymptotics-Continued Fractions matics and computation. Examines two-dimensional (0-471-01525-3) 662 pp. 1977 $69.95 potential theory and the construction of conformal maps for simply and multiply connected regions. To order, write L. Sullivan, Dept. #6-0643 Provides an introduction to the theory of Cauchy Or, call Toll-Free: integrals and their applications. Presents an elemen­ 1·800·526·5368 tary account of de Branges' recently discovered In NJ, call collect: (201) 342-6707 proof of the Bieberbach conjecture in the theory of Order Code #6-0643. VISA, MC, AMEX accepted. univalent functions. The proof offers some interest­ ing applications of material that appear in Volumes 1 and2. to~~H~~~~~!. !~!~~~J~~a In Canada: 22 Worcester Rd (0-471-08703-3) 688 pp. Nov. 1985 $59.95 Rexdale, Ontario M9W 1L 1 3 VOLUME SET: (0-471-84241-9) Prices subject to change and higher in Canada. 1974/Nov. 1985 $169.00 092-6-0643 MATHEMATICS EDUCATION, COGNITIVE SCIENCE AND EDUCATIONAL TECHNOLOGY

UNIVERSITY OF CALIFORNIA, BERKELEY Two tenure-track assistant professorships are to be filled, pending final budgetary approval, starting August 1986, by the Graduate School of Education as part of a multi-year effort to build outstanding programs of research, doctoral education, and professional train­ ing concerned with education in mathematics, science, and technology. The highest priorities for our recruitment this year are for (1) a specialist in mathematics education at the elemen­ tary or middle school level, and (2) a cognitive scientist specializing in the analysis of acquir­ ing intellectual skills from technology-based instruction in the physical sciences and mathe­ matics. Candidates should have a doctoral degree, preferably in a field such as mathematics, cognitive science, a physical science, or computer science. They should have both expertise and interest in the applications of cognitive science and computational technology for the improvement of knowledge in cognition, learning and instruction. Preference will be given to candidates having demonstrable ability for collaborating with colleagues in mathematics, physical sciences, cognitive science, anthropology, linguistics, psychology, and sociology. Applicants should send a resume, a statement describing qualifications and interests, and the names of at least three references to MST Search Committee, Graduate School of Education, University of California, Berkeley, CA 94720, so as to be received by December 2, 1985. They should also have their references send letters of recommendation directly to the Committee by this deadline. The University of California is an Equal Opportunity, Affirmative Action Employer.

.C••.C•·tC••4C••.C••.C•·.C••.C••4( ·•>·•)J·•)It·•)o·••·•)lo••>••)o Recursion Theory Anil Nerode and Richard A. Shore, Editors THE UNIVERSITY OF FLORIDA (Proceedings of Symposia in Pure Mathematics. DEPARTMENT OF MATHEMATICS Volume 42} invites applications for at least two tenure The proceedings of the 1982 AMS Summer track positions. All areas of mathematics Research Institute in Recursion Theory. this volume will be considered. Candidates should have represents the largest and most comprehensive meeting ever devoted to recursion theory. The book strong research potential, an interest in contains major surveys with expository papers as teaching and at least two years of postdoc­ well as important new research. toral experience. Rank and salary will be Graduate students and active researchers alike commensurate with experience and achieve­ with interests in any aspect of recursion theory. ments. Candidates should forward a resume including its interactions with set theory, model (including a list of publications) and should theory. constructive mathematics, foundations of mathematics and computer science. will be arrange for at least three letters of reference interested in this book. Some papers require only a to be sent to: basic course in logic or recursion theory; others are Joseph Glover aimed at active researchers in the field. Chair of Search and Screen Committee 1980 Mathematics Subject Classifications: Department of Mathematics 03025, 03030, 03045, 03055, and others ISBN 0-8218-1447-8, LC 84-18525 University of Florida ISSN 0082-0717 Gainesville, Florida 32611 viii + 528 pages (hardcover), March 1985 List price $60, Institutional member $48, Application deadline is January 15, 1986. Individual member S36 The University of Florida is an equal To order, please specify PSPUM/42 opportunity employer,. Shipping/Handling: 1st book $2, each add'! $1, $25 max. By air, 1st book $5, each add'! $3, $100 max. Prepayment required. Order from AMS, P.O. Box 1571, Annex Station, Providence, RI 02901-1571, or call 800-556-7774 to use VISA or MasterCard.

852 INSTITUTE FOR MATHEMATICS AND ITS APPLICATIONS UNIVERSITY OF MINNESOTA SCIENTIFIC COMPUTATION AUGUST 16, 1986 TO JULY 31, 1987 Organizing Committee: B. Engquist (chairman). R. Glowinski, M. Luskin, A. Majda See the article in the October Notices for details of the program. VISITING MEMBERSHIPS AVAILABLE POSTDOCTORAL MEMBERSHIPS will normally be for the 12-month period beginning August 16, 1986. All requirements for a doctorate should be completed by this date. Applicants must show evidence of mathematical excellence, but they do not need to be specialists in scientific computation or even "applied mathematicians", The following materials must be submitted: (1) Personal statement of scientific interests, research plans, and reasons for wishing to participate in this program. (This is an essential part of the application.) (2) Curriculum vitae and a list of publications. (3) Three letters of recommendation, to be sent directly to the IMA. All material should arrive by January 15, 1986. SENIOR MEMBERSHIPS are also available. Preference will be given to supplementary support for persons with sabbatical leaves, fellowships, or other stipends. All correspondence should be sent to HANS WEINBERGER, DIRECTOR, INSTITUTE FOR MATHEMATICS AND ITS APPLICATIONS, UNIVERSITY OF MINNESOTA, 514 VINCENT HALL, 206 CHURCH STREET, MINNEAPOLIS, MN 55455-0436- PHONE: (612) 373-0355. The University of Minnesota is an equal opportunity educator and employer, and specifically invites and encourages applications from women and minorities .

.;orMath"' The Department of Mathematics expects to a text-formatter for mathematical appoint at least one Assistant Professor for a term papers, books and theses beginning September 1, 1986. Salary will be com­ n petitive. Outstanding applicants in all fields of r~~ _~_ 1 rj ., log(l-x) ~-~ mathematics are encouraged to apply; priority will . : i(i+l) 2i .1 ·~ dx -1 be given to applicants in algebraic/geometric topol­ ;~~ I I '==_!_ .O L _t!_L_l_l 2 1/J I ogy, numerical analysis/applied mathematics, dif­ I 2' 7f2} L _! ferential geometry/Lie groups/harmonic analysis, i=l and ring/module theory. We seek applicants with high research potential and a strong commitment • matrices, big symbols sized and to teaching. placed automatically Applicants should send any supporting infor­ • concise command syntax; macros mation and have four letters of recommendation further reduce typing sent to: • automatic numbering; bibliographic Dr. Jonathan Bell references, chapters, equations, Search Committee Chairman cross-references Department of Mathematics • table of contents, indexes SUNY /Buffalo • automatic justification, word­ 106 Diefendorf Hall splitting Buffalo, New York 14214 • automatic numbering and place­ The deadline for applications is December 1, 1985. ment of footnotes Late applications will be considered until positions are filled. • multiple fonts, sizes, special symbols SUNY/Buffalo is an Equal Opportunity/ • output on CRT, dot-matrix printers, Affirmative Action Employer. We are interested in daisywheels, laser printers, identifying prospective minority and women can­ photo-typesetters didates. No person, in whatever relationship with • use on micros !CP/M:" PC"'-DOS, the State University of New York at Buffalo, MS"'-DOSl or mainframes cany IBM:" shall be subject to discrimination on the basis of VAX/VMS"'l age, creed, color, handicap, national origin, race, religion, sex, marital or veteran status. • Write or call SHANTHA SOFTWARE, INC. so west 97 st., Room 11-N New York, NY 10025 212-222-SNIP Try toll-free: 950-1088- pause-FORMATH

853 A Paid Advertisement MATHEMATICIANS CALL FOR A HALT TO THE ARMS RACE

Mathematicians significantly contribute to military planning and the design of weapons systems both indirectly, by providing the theoretical basis for science and technology and directly, by working on arms research projects or by producing mathematical results which later are found to have military significance. We, mathematicians from all over the world, therefore feel obliged to publicly express our deep concern about the present acceleration of the arms race. By consuming vast amounts of human and natural resources which otherwise could be used to help solve many of the urgent problems mankind now faces, the arms race is a major cause of much suf­ fering, hunger and death in the world, especially in the developing nations. Also, the arms race does not prevent local wars. We share the opinion of many colleagues in other scientific fields and of several military experts that in fact, if left unchecked, the arms race will most probably lead to nuclear war between the two ma­ jor military blocs. The increased danger of nuclear war, initiated either intentionally or unintentionally, stems mainly from the following facts which have been clearly brought out in the current public debate: Many of the nuclear weapons systems and space weapons presently being developed and, in some cases, already being deployed are designed to be war-fighting rather than deterrent wea­ pons. The associated control and warning systems are becoming more and more complex and they are fallible. The success of negotiations depends greatly on the ability to verify compliance to arms control agreements. We still have a chance to solve the verification problem. As the arms race proceeds, this problem will become more and more difficult, if not impossible, to solve. Nuclear war must be averted and initial steps toward this end must be made now. A necessary first step is a freeze on all nuclear weapons systems and space weapons. The freeze should not be postponed until the conclusion of time-consuming negotiations. Each nation can immediately enforce a comprehensive freeze on a unilateral basis without endangering its own security or that of its allies.

We call for an agreement to freeze all nuclear weapons systems and space weapons, that is, to stop their development, testing, production and deployment. Meanwhile, each nation should unila­ terally enforce this freeze. We urge that measures then be taken to significantly reduce the present number of nuclear weapons and that serious efforts be made to reach further, more comprehen­ sive agreements on other types of weapons, in particular chemical and biological weapons.

Signatories as of September 25th, 1985 include: Australia: Roger Grimshaw, William Moran, Alan Roberts, D.E. Taylor. Austria: Maria Hoffmann-Ostenhof. Brazil: Antonio Conde, Daciberg Lima Goncalves. Canada: H.S.M. Coxeter, Israel Halperin, Eric C. Milner, Anatol Rapo­ port. P.R. China: Wu Wen-tsiin. Colombia: Guillermo Restrepo. Denmark: Ib Madsen. Egypt: Fouad Mohamed Ra­ gab. France: Vazgain Avanissian, Claude Berge, Jean-Michel Bony, Jacques Faraut, Claude Godbillon, Jean-Pierre Ka­ hane, Klaus Krickeberg, Bernard Malgrange, Yves Meyer,Gabriel Mokobodzki. German Democratic Republic: Giinter Asser. Federal Republic of Germany: Hendrik Bramhoff, E. Brieskorn, Andreas Dress, Gunter Harder, William Kerby, Detlef Laugwitz, lngo Lieb. Hungary: Akos Csaszar, Pal Erdos, Gabor Halasz, Bela Szokefalvi-Nagy. India: R.P. Bambah, C.G. Khatri, S. Raghavan, K.G. Ramanathan, N. Sankaran, K. Venkatachaliengar. Israel: S.A. Amitsur. Ita­ ly: Bruno de Finetti. Japan: Yasumasa Akagawa, Yasunori Fujikoshi, Yasutaka Ihara, Kiyosi Ito, Shokichi lyanaga, J .-iti Nagata. Mexico: Samuel Gitler. Netherlands: Michie! Hazewinkel. Nigeria: Samuel A. Ilori, Aderemi Kuku, Ade­ goke Olubumma. Poland: Z. Ciesielski, Cz. Olcch. Spain: Baltasar Rodrigues-Salinas. Switzerland: Alexander Ostrows­ ki. United Kingdom: J.F. Adams, Sheila Brenner, M.C.R. Butler, Daniel Cohen. USA: Lars Ahlfors, Herbert Buse­ mann, Martin Davis, J.L. Doob, Bradley Efron, Peter Hilton, Stephen C. Kleene, Neal Koblitz, John Lamperti, Serge Lang, Robert D. Langlands, Louis Nirenberg, Richard Pollack, George Polya t, Steven Smale, Arthur H. Stone, Dorot­ hy M. Stone, Robert E. Tarjan, William Thurston, Hassler Whitney. USSR: Alexander Alexandrov, N.N. Bogolubov, Anatoli A. Dorodnicyn, Mark A. Krasnosclskii, E. Mishchenko, A.A. Samarski, V. Vladimirov. Vietnam: Hoang Tuy. A Paid Advertisement A Paid Advertisement This appeal is published in several mathematical journals in the USA, the USSR and other coun­ tries. We are asking all mathematicians for support in the form of additional signatures and of financial contributions. We plan to publish the appeal in at least one important newspaper and to send it together with the list of all signatories to governments and international organizations.

Please send signed copies of this appeal to one of the contact persons given below. Financial contributions should be sent directly to one of the special bank accounts also given below (in the form: name of account; account number; name and address of bank).

I am in agreement that my name appear with the publication of this appeal. (Please PRINT CLEARLY)

NAME TITLE INSTITUTION ADDRESS SIGNATURE

Contact persons in the U.S. as of September 25th, 1985: Martin Davis and Richard Pollack, Courant Institute of Math. Sci., 251 Mercer Street, New York, NY 10012

Contact persons outside the U.S. as of September 25th, 1985: Giinter Asser, Ernst-Moritz-Arndt-UniversiUit, Sektion Mathematik, 2200 Greifswald, Ludwig-Jahn-Str. 15a, German Democratic Republic. Hendrik Bramhoff and William Kerby, Dept. of Computer Sci., Univ. of Hamburg, Rothen­ baumchaussee 67/69, 2000 Hamburg 13, Federal Republic of Germany. Daniel Cohen, Dept. of Math., Queen Mary College, Univ. of London, Mile End Road, London El4NS, England, U.K. H.S.M. Coxeter, Dept. of Math., Univ. of Toronto, Toronto, Ontario M5SIA1, Canada. Akos Csaszar, L.Eotvos University Budapest, Budapest, parizsi utca 61 A, H-1052, Hungary. Anatoli A. Dorodnicyn, Computing Centre of the Academy of Sciences of the USSR, Moscow 117333, Vavilova 40, USSR. Michie! Hazewinkel, Mathematical Centre, P.O.Box 4079, 1009 AB Amsterdam, Nether­ lands. Bernard Malgrange, Institut Fourier, Univ. de Grenoble I, Laboratoire de Mathematiques Pures, Boite Postale 116, 38402 Saint-Martin-d'Heres Cedex, France. J.-iti Nagata, Department of Mathematics, Osaka Kyoiku University, Tennoji, Osaka, 543 Japan. Cz. Olech, ul. Nowy Swiat, 23/25 m1, 00-029 Warszawa, Poland. S. Raghavan, Tata Insti­ tute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India. Alan Roberts, Dept. of Physics, Monash Univ., Clayton, Vic. 3168, Australia. Wu Wen-tsiin, Academia Sinica, Institute of Systems Science, Zhong Guan Cun, Beijing 100080, P.R. China

Bank accounts as of September 25th, 1985: Mathematicans' Freeze Appeal; 0908163; Canadian Imperial Bank of Commerce, St. Clair and Vanghan branch 535, St. Clair West Toronto Canada Mathematicans' Freeze Appeal; 84075N; Credit Lyonnais, Agence U 421 Paris, 22 Boule­ vard St. Michel, 75006 Paris France · Hendrik Bramhoff, Kennwort: Mathematicans' Freeze Appeal; 3602208; Deut­ sche Bank BLZ 200 700 00, Grindelallee 188, 2000 Hamburg 13, Fed. Rep. of Germany · Mathematicans' Freeze Appeal; 7112447; Midlands Bank branch 400427, 91 Mile End Road London E1 United Kingdom Mathematicans' Freeze Appeal; 110-26-6859; NYU Credit Union, 240 Greene Street, New York NY 10003 USA A Paid Advertisement TENURED POSITION TENURE TRACK POSITIONS University of California, Berkeley University of California, Berkeley Department of Mathematics Department of Mathematics Berkeley, CA 94720 Berkeley, CA 94720 Subject to budgetary approval, applications are invit­ Applications are invited for two positions (subject to ed for a position effective July 1st, 1986, at tenure budgetary approval) effective July 1st, 1986, at tenure level (Associate or full Professor) in the areas of alge­ track Assistant Professor level, in the areas of algebra, bra, analysis, applied mathematics, foundations, or analysis, applied mathematics, foundations, or geometry. Applicants should have demonstrated sub­ geometry and topology. Applicants should have stantial achievements in research and teaching. Send demonstrated substantial achievements in research by January 15, 1986 a curriculum vitae, list of publi­ and teaching. Send by January 15, 1986 a curriculum cations, a few selected reprints or preprints, and the vitae, list of publications, a few selected reprints or names of three references to Marc A. Rieffel, Vice preprints, and the names of three references to Marc Chair for Faculty Affairs, at the above address. The A. Rieffel, Vice Chair for Faculty Affairs, at the above University of California is an Equal Opportunity, address. The University of California is an Equal Affirmative Action Employer. Opportunity, Affirmative Action Employer.

----·++++++++~~·--- SPECIAL DEVELOPMENT FUND TEMPORARY POSTDOCTORAL POSITIONS OF THE INTERNATIONAL MATHEMATICAL UNION University of California, Berkeley The Special Development Fund is used pri­ Department of Mathematics Berkeley, CA 94720 marily for travel grants to young mathemati­ cians from developing countries or from Several temporary positions beginning in Fall 1986 are anticipated for new and recent Ph.D.'s of any age countries where severe money regulations in the areas of algebra, analysis, applied mathematics, exist, to help their attendance to the Inter­ foundations, or geometry and topology. The term of national Congresses of Mathematicians. The these appointments may range from one to three next goal is to collect money for travel grants years, depending partly on pending administrative de­ for the 1986 Congress in Berkeley. cisions. Applicants for NSF or other postdoctoral fel­ Donations to the Special Development fund lowships are encouraged to apply for these positions; can be sent at any time and in any convertible combined teaching/research appointments may be made for up to three years. Mathematicians whose currency to the following accounts: research interests are close to those of regular depart­ No. 0862-656208-21 ment members will be given some preference. Send, Schweizerische Kreditanstalt by January 15, 1986 a resume, and reprints, pre­ Stadtfiliale Ziirich-Rigiplatz Universitiitstrasse 105 prints, and/or a disseration abstract. Ask three peo­ CH-8033 Ziirich ple to send letters of recommendation to Marc A. Switzerland Rieffel, Vice Chair for Faculty Affairs at the above No.100020-411-USD-5705 FR address. The University of California is an Equal Kansallis-Osake-Pankki Opportunity, Affirmative Action Employer. Aleksanterinkatu 42 SF-00100 Helsinki Finland

856 NEW EDITIONS NEW TITLES FOR 1986! FOR 1986!

Algebra for College Elementary Linear Students, 2nd Edition Algebra Hardcover 688 pages Hardcover 416 pages College Algebra Richard 0. Hill, Jr. and Trigonometry Michigan State University 2nd Edition Hardcover 576 pages Arnold Shapiro Elementary Partial Temple University Bernard Kolman Differential Equations Drexel University with Boundary Value Problems Hardcover 448 pages Calculus of One Variable Larry C. Andrews 2nd Edition University of Central Florida Hardcover 912 pages Multivariable Calculus, Linear Algebra, and A Second Course in Differential Equations, 2nd Elementary Differential Edition Equations Hardcover 1024 pages Hardcover 288 pages Stanley I. Grossman Paul Waltman University of Montana Emory University

To receive a review copy of any of these quality textbooks, please write to Academic Press, College Division, Dept. 240 @ Orlando, FL 32887

857 PC'JEXTM A Complete Implementation of 'lEX For the IBM PC /XT and AT

Now available for your microcomputer: a real typesetting system, capable of producing journal quality output! Your IBM PC/XT or AT can now run '!EX, the state-of-the-art typesetting program developed by PROF. DONALD E. KNUTH at Stanford University. 'lEX reads standard ASCII files and produces files that can be used to obtain printed output on a wide variety of devices-from dot matrix printers to laser printers to photo­ typesetters. 'lEX is being supported as a standard language for mathematical typesetting by the American Mathematical Society, which has produced the AMS-'IE;X macro package. AMS-'lEX greatly simplifies the setting of complex mathematical formulas and also al­ lows the same computer file to be printed in the style of different journals. You can produce preprints of a paper on your own printer, while a journal can use the same file to print the version that will be published.

PC 'lEX is a complete '!EX-with input and output files compatible with all implemen­ tations of '!EX. PC 'lEX was developed by Lance Carnes, the first to implement 'lEX on a small computer (Hewlett-Packard 3000) and the editor for the "•man" 'lEX department of the 'lEX Users Group Newsletter. Minimum system requirements: IBM PC/XT or AT or work-alike with a 10M hard disk and 360K floppy. 512K memory to run '!EX, 640K to run IA'!EX.

• Price $279.00. PC-DOT, the program to produce printed ouput on the IBM graphics printer, or on the Epson RX, MX, FX series, is priced separately at $100.00. Prof. Knuth's 'lEX manual, The T'JY(book, is also available, for $15.00. • California residents, please add sales tax.

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'lEX is a trademark of the American Mathematical Society, PC '!EX is a trademark of Personal '!EX, Inc., IBM is a registered trademark of International Business Machines, Inc., Epson is a registered trademark of Epson, Inc., Imagen is a trademark of Imagen, Inc., and QMS is a trademark of QMS, Inc.

858 Pseudodifferential Operators and Applications Franc;ois Treves, Editor

This volume gathers together nineteen papers devoted to microlocal analysis, that is to say, the precise application of Fourier transforms to analysis on manifolds, a vital and far-reaching method which has emerged as the most powerful tool of linear analysis since distribution theory. These papers are written versions of lectures first presented at the 1984 AMS Symposium held at Notre Dame, the first national conference on partial differential equations in over 10 years, and they reflect the splendid successes of the field. The field of partial differential equations flourished in the 1970s as new classes of pseudodifferential operators and Fourier integral operators were introduced and used to tackle many classical and outstanding problems in partial differential equations. In fact, research has been so vigorous that it has produced several important ramifications in other fields, namely group representations, harmonic analysis, several complex variables, differential geometry and symplectic geometry. Recently, in a very promising area of research, pseudodifferential operators have been used to tackle nonlinear differential problems.

Contents S. Allnhac and G. Metivier. Propagation of local analyticity for the Euler equation J. L. Antonlano and G. A. Uhlmann, A functional calculus for a class of pseudodifferential operators with singular symbols M. S. Baouendl. Uniqueness in a class of nonlinear Cauchy problems Michael Beals. Propagation of smoothness for nonlinear second-order strictly hyperbolic differential equations R. Beals and R. R. Colfman, Multidimensional inverse scatterings and nonlinear partial differential equations R. R. Colfman and Yves Meyer. Nonlinear harmonic analysis and analytic dependence H. 0. Cordes. On some C*-algebras and Fnkhet-algebras of pseudodifferential operators G. Eskin, Boundary-value problems for second-order elliptic equations in domains with corners P. C. Greiner. Imbedding C" in Hn VIctor Gulllemln. On some results of Gelfand in integral geometry Lars HOrmander. The propagation of singularities for solutions of the Dirichlet problem M. Kashlwara and P. Schaplra. Applications of the microlocal theory of sheaves to the study of Ox C. E. Kenlg, Recent progress on boundary-value problems on Lipschitz domains J. J. Kahn, Estimates for ab on compact pseudoconvex CR manifolds Yves Meyer. Recent analysis and operator theory L. P. Rothschild. Integrability and holomorphic extendibility for rigid CR structures Johannes SJOstrand. Multiple wells and tunneling N. K. Stanton and D. S. Tartakoff, The real analytic and Gevrey regularity of the heat kernel foro b M. E. Taylor, Fefferman-Phong inequalities in diffraction theory Proceedings of Symposia in Pure Mathematics, Volume 43, August 1985, 309 pages (hardcover) List price $44, Institutional member S35, Individual member $27. To order, please specify PSPUM/43N

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COMPUTER ACTIVITIES FOR CALCULUS WITH ANALYTIC CALCULUS GEOMETRY Technology Training Associates Alternate Third Edition 1986 IBM-PC Roland E. Larson and Robert P. Hostetler, Items included: 3 disks, demonstration disk, both of The Pennsylvania State University, User's Manual The Behrend College 1986 Applell 1986 Paper 1000 pages est. Items included: 6 disks, demonstration disk, Study and Solutions Guide!Three-Volume User's Manual Complete Solutions Guide!Transparencies This software offers activity-based programs Based on the enormously successful Calculus, that enhance the teaching and learning of cal­ Second Edition, this intuitive and highly read­ culus. Each unit contains both exploratory and able text introduces transcendental functions in directed activities. Chapters 7 and 8. Maintaining the proven orga­ nization of its predecessor, the text has been CALCULUS WITH ANALYTIC revised for greater mathematical accuracy. GEOMETRY Third Edition CONTEMPORARY Roland E. Larson and Robert P. Hostetler, ABSTRACT ALGEBRA both of the Pennsylvania State University, Joseph Gallian, University of Minnesota, Duluth The Behrend College 1986 Paper 480 pages est. 1986 Paper 1013 pages Answer Key Study and Solutions Guide!Three-Volume Along with traditional topics of abstract algebra, Solutions Guide!Transparencies this text examines such subjects as finite simple This clearly written text has been reorganized to groups-and Cayley digraphs. A range of applica­ reflect the latest needs of engineering and sci­ tions, including some unique to this text, as well ence students, with each chapter reworked for as historical and biographical information, stimu­ greater mathematical rigor and accuracy. Tran­ late and add interest. scendental functions appear in the first six chap­ ters ofthe Third Edition.

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862 Applications of Group Theory in Physics and Mathematical Physics Moshe Flato, Paul Sally and Gregg Zuckerman, Editors

(Lectures in Applied Mathematics. Volume 21) Contents Y. Nambu. Topological excitations in physics The past decade has seen a renewal in the close I. Bars. Supergroups and their representations ~ies between mathematics and physics. Completely Peter G. 0. Freund. Topics in dimensional mtegrable systems. classical and quantum field reduction theories. in particular. gauge theories. Mary K. Gaillard. Bound state spectra in supersymmetry and supergravity. and grand unified extended supergravity theories theories were developed with the aid of. and. in John H. Schwarz. Mathematical issues in turn. brought new developments into. several superstring theory diverse areas of mathematics. The Chicago P. van Nieuwenhuizen. Gauging of groups and Summer Seminar on Applications of Group Theory supergroups in Physics and Mathematical Physics. held in July. C. Fronsdal. Semisimple gauge theories and 1982. was organized to bring together a broad conformal gravity spectrum of scientists from theoretical physics. Roger Howe. Dual pairs in physics: harmonic mathematical physics. and various branches of oscillators. photons. electrons. and singletons pure and applied mathematics in order to promote A. W. Knapp. Langlands' classification and interaction and an exchange of ideas and results in unitary dual of SU(2.2) areas of common interest. George W. Mackey. Quantum mechanics from This volume contains the papers submitted by the point of view of the theory of group speakers at the Seminar. The reader will find several groups of articles varying from the most representations Daniel Siernheimer. Phase-space representations abstract aspects of mathematics to a concrete David A. Vogan, Jr .. Classifying representations phenomenological description of some models applicable to particle physics. The papers have by lowest K-type Joseph A. Wolf. Indefinite harmonic theory and been divided into four categories corresponding to the principal topics covered at the Seminar. This is unitary representations Gregg J. Zuckerman. Induced representations only a rough division. and some papers overlap two or more of these categories. and quantum fields L. Dolan. Why Kac-Moody subalgebras are interesting in physics I. B. Frenkel. Representations of Kac-Moody algebras and dual resonance models Bernard Julia. Kac-Moody symmetry of gravitation and supergravity theories J. Lepowsky. Some constructions of the affine Lie algebra A1l Jacques C. H. Simon. Nonlinear representations and the affine group of the complex plane

1980 Mathematics Subject Classifications: 16A58, 17665, 20G45, 22-06, 22EXX, and others ISBN 0-8218-1121-5, LC 84-24191 ISSN 0075-8485 Approx. 430 pages (hardcover). February 1985 List price $70, Institutional member $56, Individual member $42 Shipping and handling charges must be added To order, please specify LAM/21N

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863 MATHEMATICAL SCIENCES EMPLOYMENT REGISTER Instructions for Applicant's Form on facing page The form. Applicants' forms submitted for the Employment Register will be photographically repro­ duced in the December 1985 issue of Employment Information in the Mathematical Sciences. Resumes of those attending will be posted at the meeting. The forms must be carefully typed using a fresh The Theory of Gauge Fields black ribbon. The best results are obtained with a carbon-coated polyethylene film ribbon, but satisfac­ in Four Dimensions tory results may be obtained using a ribbon made of H. Blaine Lawson nylon or other woven fabric if suitable care is exer­ (CBMS Regional Conference Series. Number 58 cised. It is important that the keys be clean and make Supported by the National Science Foundation) a sharp, clear impression. Do not erase--it causes smudges which reproduce when photographed. Use Lawson's expository lectures. presented at a a correcting typewriter or correction tape or fluid if necessary. Submit the original typed version only. CBMS Regional Conference held in Santa Barbara Copies will not reproduce properly and are not accept­ in August 1983. provide an in-depth examination able. Hand lettered forms will be returned. of the recent work of Simon Donaldson. of Applicants' forms must be received by the Society especial interest to both geometric topologists by November 15, 1985 in order to appear in the and differential geometers. This work has excited special issue of ElMS, and must be accompanied particular interest in light of Mike Freedman's recent by the Preregistration/Housing Form printed in this profound results: the complete classification. in issue, if attending the meeting. See the Meeting the simply connected case. of compact topological Announcement in the October issue of NOTICES for information. Forms received past the deadline or not 4-manifolds. Arguing from deep results in gauge completed will be returned. field theory. Donaldson has proved the nonexistence The summary strip. Information provided here will of differentiable structures on certain compact be used to prepare a printed list of applicants for dis­ 4-manifolds. Together with Freedman's results. tribution to employers. Please supply all information Donaldson's work implies the existence of exotic requested, and confine your characters to the boxes differentiable structures in R4-a wonderful example provided. Use the codes below. Circled letters identify of the results of one mathematical discipline corresponding items on the form and the strip. yielding startling consequences in another. @ Specialties The lectures are aimed at mature mathematicians AL = Algebra AN = Analysis with some training in both geometry and topology. BI = Biomathematics BS = Biostatistics CB = Combinatorics CM = Communication but they do not assume any expert knowledge; in CN = Control CS = Computer Science addition to a close examination of Donaldson's CT = Circuits DE = Differential Equations arguments. Lawson also presents as background EC = Economics ED = Mathematical Education material the foundation work in gauge theory FA = Functional Analysis FI = Financial Mathematics FL = Fluid Mechanics GE = Geometry (Uhlenbeck. Taubes. Atiyah. Hitchin. Singer. et al.) HM = History of Math LO = Logic which underlies Donaldson's work. MB = Mathematical Biology ME = Mechanics MO = Modelling MP = Mathematical Physics Contents MS = Management Science NA = Numerical Analysis NT = Number Theory OR = Operations Research 1. Introduction PR = Probability SA = Systems Analysis 2. The Geometry of Connections ST = Statistics TO = Topology 3. The Self-dual Yang-Mills Equations ® Career Objectives 4. The Moduli Space AR = Academic Research AT = Academic Teaching 5. Fundamental Results of K. Uhlenbeck NR = Nonacademic R&D NC = Nonacad. Consulting 6. The Taubes Existence Theorem NS = Nonacademic Supervision 7. Final Arguments @(!)Duties 1980 Mathematics Subject Classifications: T =Teaching U = Undergraduate 47H15, 53C05, 53C80, 97R10, 57N99, others. G =Graduate R =Research ISBN 0-8218-0708-0, LC 85-441 C = Consulting A = Administration ISSN 0160-7642 S = Supervision IND = Industry viii + 101 pages (softcover), August 1985 GOV = Government DP = Data Processing List price $16, all individuals $10 Shipping and handling charges must be added Location To order, please specify CBMS/58N E =East S =South C =Central M =Mountain Shipping/Handling: 1st book $2, each add'l $1, $25 W =West 0 =Outside U.S. I= Indifferent max. By air. 1st book $5, each add'l $3, $100 max. Prepayment required. Order from AMS, P.O. Box 1571. © U.S. Citizenship Status Annex Station, Providence, Rl 02901-1571. C = U.S. Citi~en P = Permanent Resident Call 800-556-7774 to use VISA or MasterCard. T = Temporarily in U.S. N = Non-U.S. Citi~en

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867 Topics m Complex Analysis

Dorothy B. Shaffer, Editor

(Contemporary Mathematics. Volume 38) In the paper by B. Bshouty and W. Hengartner a conjecture of Bombieri is proved for some cases. Most of the mathematical ideas presented in Other interesting problems for special subclasses this volume are based on papers given at an AMS are solved by B. A. Case and J. R. Quine: M. meeting held at Fairfield University in October 0. Reade. H. Silverman and P. G. Todorov: H. 1983. The unifying theme of the talks was Silverman and E. M. Silvia. Geometric Function Theory. New univalence criteria for integral transforms Papers in this volume generally represent are given by Edward Merkes. Potential theoretic extended versions of the talks presented by the results are represented in the paper by Jack Quine authors. In addition. the proceedings contain with new results on the Star Function and by David several papers that could not be given in person. Tepper with free boundary problems in the flow A few of the papers have been expanded to around an obstacle. Approximation by functions include further research results obtained in the which are the solutions of more general elliptic time between the conference and submission of equations are treated by A. Dufresnoy, P. M. manuscripts. In most cases. an expository section Gauthier and W. H. Ow. or history of recent research has been added. The At the time of preparation of these manuscripts. authors' new research results are incorporated nothing was known about the proof of the into this more general framework. The collection Bieberbach conjecture. Many of the authors of this represents a survey of research carried out in recent volume and other experts in the field were recently years in a variety of topics. interviewed by the editor regarding the effect of The paper by Y. J. Leung deals with the Loewner the proof of the conjecture. Their ideas regarding equation. classical results on coefficient bodies future trends in research in complex analysis are and modern optimal control theory. Glenn Schober presented in the epilogue by Dorothy Shaffer. writes about the class L. its support points and A graduate level course in complex analysis extremal configurations. Peter Duren deals with provides adequate background for the enjoyment of support points for the class 5. Loewner chains and this book. the process of truncation. A very complete survey about the role of 1980 Mathematics Subject Classifications: 30C50, 30C70, 30C55, 30C80, 30C10 and polynomials and their limits in class 5 is others contributed by T. J. Suffridge. ISBN 0-8218-5037-7, LC 84-24550 ISSN 0271-4132 A generalization of the univalence criterion due x + 142 pages (softcover), March 1985 to Nehari and its relation to the hyperbolic metric List price $18, Institutional member $14 is contained in the paper by David Minda. The Individual member $11 ' Shipping and handling charges must be added omitted area problem for functions in class 5 is To order, please specify CONM/38N solved in the paper by Roger Barnard. New results ?n angular derivatives and domains are represented m the paper by Burton Rodin and Stefan E. Warschawski. while estimates on the radial growth of the derivative of univalent functions are given by Thorn McGregor.

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Fasten PAYMENT securely Graphs Geometry of Geodesics and Third Revised Edition Related Topics by C. BERGE Proceedings of a Symposium held at the University of Tokyo, Japan, 29 November - 3 December 1982 NORTH-HOLLAND MATHEMATICAL LIBRARY, Volume 6 edited by K. SHIOHAMA

This is the revised and updated version of the first part ADVANCED STUDIES IN PURE MATHEMATICS, of the widely referenced text Graphs and Hypergraphs, Volume3 published by North-Holland in 1973. This third volume in the Japanese symposia series This new edition includes new theorems (e.g. the surveys recent advances in five areas of Geometry, Perfect Graph Theorem, due to Lovasz) as well as new namely Closed geodesics, Geodesic flows, Finiteness proofs of classical results. In particular, sections 9.3, and uniqueness theorems for compact Riemannian 10.3, 12.2 and 13.3 have been significantly revised. manifolds, Hadamard manifolds, and Topology of complete noncompact manifolds. Topics concerning topological subjects (such as graph planarity, genus and thickness) have been removed 1984 x + 486 pages. Price: US $95.00/011. 275.00 from this edition to allow for a more comprehensive ISBN 0-444-87545-X treatment in a separate text. This second half, Hypergraphs, will be published in the near future, also brought up to date with substantial revisions.

1985 about 400 pages. Price: US $50.00/011. 150.00 ISBN 0-444-87603-0 Holomorphic Automorphism Groups in Banach Spaces Singularities and Dynamical An Elementary Introduction Systems by JOSE M. ISIDRO and LASZLO L. STACH6 Proceedings of the International Conference, NORTH-HOLLAND MATHEMATICS STUDIES, 105 Heraklion, Greece, 30 August- 6 September 1983 Notas de Matematica (97), Editor: Leopolda Nachbin Edited by SPYROS N. PNEVMATIKOS This volume is an elementary and self-contained NORTH-HOLLAND MATHEMATICS STUDIES, 103 introduction to the group of holomorphic automorphisms of bounded domains from the The main purpose of the Conference was to create fundamental principles of Banach spaces and conditions of scientific contact between mathematicians elementary Complex Function Theory in this abstract and physicists who have singularities and dynamical setting. systems as common interests. The volume contains 31 articles, devoted to recent progress in the following topics: For arbitrary bounded domains, the Banach-Lie algebra of complete holomorphic vector fields and the Banach­ - the global study of dynamics generated by diffeo­ Lie group of holomorphic automorphisms are studied. morphisms of foliations - the local study of the The basic theory of bounded circular domains is singularities of differential equations of real and discussed and the group of automorphisms of the unit complex fields - the singularities of symplectic ball of several classical Banach spaces is explicitly geometry, contact geometry, and Riemannian computed. geometry - the singularities of functions and complex hypersurfaces - the bifurcations in dynamical systems The book concludes with an introduction to the Jordan and the appearance of chaos - the study of some theoretic approach and the convexity of the Harish­ specific dynamical systems, non linear differential Chandra realization of bounded symmetric Banach equations, and solitons space domains.

1985 viii + 460 pages. Price: US $57.75/011. 150.00 1985 xii + 292 pages. Price: US $44.50/011. 120.00 ISBN 0-444-87641-3 ISBN 0-444-87657-X

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Geometric Theory of Dynamical Systems "This remarkable book is based upon examples An Introduction that richly illustrate the phenomena of bifurca­ Jacob Palls, Jr. and Welington de Melo tion and chaos in both continuous and discrete Translated by A.K. Manning dynamical systems. The work is remarkable for "This graduate-level text is a beautiful its excellence in style and pedagogy . .. treatment of the foundations of dynamical " ... Pure and applied mathematicians and their systems, a large and thriving area if modern graduate students should find this book a rich mathematics . .. source of examples, phenomena, and conjec­ "As a preparatory text for students interested in tures on which to base new theorems." doing research in dynamical systems this text is -SIAM Review to be highly recommended." Applied Mathematical Sciences, Volume 42 -Math Reviews 1983/453 pp/206 illus/cloth $34.00 "The book contains ample detail, plenty of ISBN 0-387-90819-6 examples, and 62 figures illustrating the text. The Lorenz Equations Both authors have themselves made important Bifurcations, Chaos, and Strange Attractors contributions to the subject, and it is to be Colin Sparrow hoped that their effort will attract new "The book is an attempt to gather together graduate students to a beautiful subject." known results about the system. The organiza­ -American Math Monthly tion is quite effective, with each chapter 19821198 pp/114 illus/cloth $31.50 treating one or two themes . .. Moreover, vir­ ISBN 0-387-90668-1 tually no background is assumed on the part of Variational Inequalities and Flow in the reader in the area of dynamical systems, Porous Media and as a consequence the book could serve as a M. Chipot nice introduction to the subject . .. " The first part of this book presents the main -Math Reviews results on regularity for the solution of obstacle Applied Mathematical Sciences, Volume 41 problems and contains a unique treatment of the 1982/269 pp/91 illus/paper $23.50 one- and two-obstacle problem. The second ISBN: 0-387-90775-0 part gives a self-contained treatment of the Forthcoming ... theory of fluid flow through porous media. Global Stability of Dynamical Systems Applied Mathematical Sciences, Volume 52 Michael Shub ~ 1984/118 pp/13 illus/paper $16.00 0 LIJ 0 ISBN 0-387-96002-3 For your copies of these and other mathematics N u '<:!' 0\ 0\ titles, check your local bookstore, or write to: 0 N Nonlinear Oscillations, Dynamical Systems, ~ Ill 0 Springer-Verlag New York, Inc., Dept Sl66, N and Bifurcations of Vector Fields 175 Fifth Avenue, New York, NY 10010 0 ...J John Guckenheimer and Philip Holmes < 02 "The hook is rewarding reading . .. The 8 u u~ z u elementary chapters are suitable ji1r an i= 1: Ill < u introductory graduate course for mathemati· Ill :::l! "C ".. ciam and physicists . . . Its excellent survev of LIJ ·;;;:: ~ Ill 0 c the mathematicallitaalllre makes it a mhwhle :::t: ... ~ :::l! I- Q, ref•• renee." Springer-Verlag .& < < 00~ "' \.!)" -Journal of Statistical Physics ~ New York Berlin Heidelberg Tokyo u :::l! '<:!' ..c z N ...... 10 ~ 0 < )( "'0 u 0 c.. ...u 02 u LIJ = E ... 0 E 0 :::l! .. z < a.: ~