Notices of the American Mathematical Society
August 1986, Issue 249 Volume 33, Number 4, Pages 593- 704 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 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 August 3-11, 1986 Berkeley, California EXPIRED (International Congress of Mathematicians) 828 October 1Q-11, 1986 Logan. Utah tAugust 18 October 829 October 17-18. 1986 Charlotte, North Carolina tAugust 20 October 830 October 31-November 1. Denton, Texas tAugust 25 October 1986 831 January 21-24, 1987 San Antonio, Texas October 15 January (93rd Annual Meeting) 832 March 27-28, 1987 Honolulu, Hawaii 833 April 3-4, 1987 Kent. Ohio 834 April 25-26. 1987 Newark, New Jersey January 6-9, 1988 Atlanta, Georgia (94th Annual Meeting) August 8-12, 1988 Providence, Rhode Island (AMS Centennial Celebration) January 11-14, 1989 Phoenix, Arizona (95th Annual Meeting) t Please note change from March 1986 calendar.
DEADLINES Advertising (Oct. 1986 Issue) Sept. 3. 1986 (Nov. 1986 Issue) Oct. 1. 1986 (Jan. 1987 Issue) Nov. 12. 1986 News/SMIC (Oct. 1986 Issue) Aug. 18. 1986 (Nov. 1986 Issue) Sept. 15. 1986 (Jan. 1987 Issue) Oct. 27. 1986
Other Events Sponsored by the Society June 22-August 2, 1986, Joint Summer Research Conferences in the Mathematical Sciences, University of California, Santa Cruz. California. Details: January issue. July 7-25, 1986. AMS Summer Research Institute on Representations of Finite Groups and Related Topics, Humboldt State University, Arcata, California. Details: March issue.
Subscribers' changes of address should be reported well in advance to avoid disruption of service: address labels are prepared four to six weeks in advance of the date of mailing. Requests for a change of address should a/ways include the member or subscriber code and preferably a copy of the entire mailing label. Members are reminded that U. S. Postal Service change-of-address forms are not adequate for this purpose. since they make no provision for several important items of information which are essential for the AMS records. Suitable forms are published from time to time in the Notices of the American Mathematical Society (e.g. October 1985. page 725). Send change of address notices to the Society at Post Office Box 6248. Providence. Rl 02940. [Notices of the American Mathematical Society is published seven times a year (January, March, June, August. October, November. December) by the American Mathematical Society at 201 Charles Street, Providence. Rl 02904. Second class postage paid at Providence, Rl and additional mailing offices. POSTMASTER: Send address change notices to Notices of the American Mathematical Society, Membership and Sales Department. American Mathematical Society, P. 0. Box 6248. Providence, Rl 02940.) Publication here of the Society's street address, and the other information in brackets above. is a technical requirement of the U. S. Postal Service. All correspondence should be mailed to the Post Office Box. NOT the street address. Members are strongly urged to notify the Society themselves of address changes. since reliance on the postal service change-of-address forms is liable to cause delays in processing such requests in the AMS office. Notices of the American Mathematical Society Volume 33, Number 4, August 1986 EDITORIAL COMMITTEE Paul F. Baum. Ralph P. Boas Raymond L. Johnson. Mary Ellen Rudin Steven H. Weintraub, Daniel Zelinsky Everett Pitcher (Chairman) MANAGING EDITOR James A. Voytuk 595 R H Bing ASSOCIATE EDITORS Stuart Antman, Queries 597 Mathematical Text Processing Hans Samelson. Queries 608 Reports to the Members of the Society Ronald L. Graham. Special Articles 612 ICM letter SUBSCRIPTION INFORMATION 617 Subscription prices for Volume 33 (1986) WashinRton Outlook are $85 list: $68 institutional member: 618 News a••d Announcements $51 individual member. (The subscription 622 NSF News &. Reports price for members is included in the annual dues.) A late charge of 10% of 625 News from Washington the subscription price will be imposed 629 Queries upon orders received from nonmembers after January 1 of the subscription 633 letters to the Editor year. Add for postage: Surface delivery 634 1986 AMS Elections outside the United States and lndia-$8: to lndia-$18: expedited delivery to 635 Election Information destinations in North America-$12: 636 Future Meetings of the Society elsewhere--$15. Subscriptions and Logan, October 1D-11, 636; Charlotte, orders for AMS publications should be addressed to the American Mathematical October 17-18, 639; Denton, October Society, P.O. Box 1571. Annex Station, 31-November 1, 642; Invited Speakers and Providence. Rl 02901. All orders must be Special Sessions, prepaid. 645 ADVERTISING &. INQUIRIES 648 Call for Topics for 1988 Conferences Notices publishes situations wanted 650 Special Meetings and classified advertising, and display 656 New AMS Publications advertising for publishers and academic or scientific organizations. Requests for 671 Miscellaneous information: Personal Items, 671; Deaths, 671; Visiting Advertising: Wahlene Siconio Mathematicians, 672; Backlog, 674 Change of address or subscriptions: Cheryl Rotella 676 AMS Reports and Communications Book order number 800-556-7774. Report of the Treasurer, 676; Recent Appointments, 678; Reports of Past Meetings: CORRESPONDENCE, including Baltimore, 678; Baltimore Council Meeting, changes of address should be sent to 679; Officers of the Society, American Mathematical Society, P.O. 680 Box 6248, Providence. Rl 02940. 684 AMS Policy on Recruitment Advertising Second class postage paid at Providence. 685 Reciprocity Agreements Rl. and additional mailing offices. Copyright © 1986 by the American 692 Advertisements Mathematical Society. All rights reserved. 703 New AMS Publications Order Form and Printed in the United States of America. Mailer Notices: highlights
R H Bing, who died on April 28, is remembered as a family man and a distin guished mathematician by two of his close friends, Richard Anderson and Edwin Burgess. Page 595.
Larry Siebenmann's article, in Palais' column, examines the pros and cons of using TEX as a mathematical word processing language and addresses the input problem by describing a preprocessor called Sweet-TE)<. Page 597.
Officers and Principal Administrators of the AMS report on some recent activities of the Society, including the publication of a new journal, the relationship between the AMS and ICM-86, the appointment of a new Executive Editor at MR, and the current status of merger negotiations with Zbl. Page 608.
Andrew Gleason and Irving Kaplansky send an open letter to the mathe matical community about the upcoming International Congress of Mathematicians at Berkeley. Page 612.
Kenneth Hoffman, in his Washington Outlook column, reports on recent tes timony given before House and Senate committees and emphasizes the need for continuing dialogue with the legislative branch. Page 617.
AMS Fellowship applications are invited for 1987-1988. Page 618.
JPBM presents a public service award to Kenneth Hoffman for his "farsighted and effective initiation of the planning and the implementation of a national math ematical sciences policy." Page 618.
NSF Postdoctoral Research Fellowships guidelines and deadlines are an nounced for 1987-1988. Page 622.
William R. Graham has been chosen to be President Reagan's new Science Adviser. Page 625.
National Science Week was highlighted by a conference on "Mathematics: The Unifying Thread in Science." Page 626.
Nominations for AMS Officers and Council, which usually appear in the June issue, are reported for the information of the membership. Page 634. R H Bing October 20, 1914- April 28, 1986
R H Bing, President of the AMS in 1977 and 1978, died at age 71 at his home in his study in Austin, Texas. A major contributor to geometric topology, especially with his work on 3-manifolds, he saw many of his basic ideas and techniques used by others in recent major breakthroughs in higher dimensional manifolds. He was the retired "Mildred Caldwell and Baine Perkins Kerr Centennial Professor Emeritus in Mathematics" at The University of Texas at Austin. From 1947 to 1973 he was on the faculty at the University of Wisconsin, where he was "Rudolph E. Langer Research Professor of Mathematics" during the last nine of these years. R H Bing was a long time member of the National Academy of Sciences and a former member of the National Science Board. He was also President of the Mathematical Association of America (MAA) in 1963 and 1964, and is one of only four people who have, since the forties, served both the Society and the Association as President. He was former Chairman of the Conference Board of the Mathematical Sciences, former Chairman of the Mathematics Section of the National Academy of Sciences and of the Division of Mathematical Sciences of the National Research Council, and former Chairman of Section A and Vice-President of the American Association for the Advancement of Science. He served on count less committees for many organizations. In 197 4 he received the MAA award for Distinguished Service to Mathematics. Few mathematicians in our lifetime have served our community so well and with such distinction. He was justly proud of his collection of thirty-five doctoral students at Wisconsin and Texas. Many are in important academic positions throughout the country, and many are active in current research. Participation with him in a seminar or class was a lively, rewarding, and stimulating experience. He had great influence on many young mathematicians who came into contact with him at Wisconsin or at Texas, at the Institute for Advanced Study or at the University of Virginia where he held visiting positions, or in his many travels in this country and abroad. He presented invited lectures at over two hundred colleges and universities with locations in nearly every state of the Union and in seventeen foreign countries. He was the Hedrick Lecturer for the MAA in 1961 and the Colloquium Lecturer for the AMS in 1970. His book on the geometric topology of 3-manifolds was recently published by the AMS. R H, as he was known to many of us, had, in an old southern tradition, no given names to go with his initials. On occasion, he was required to list his name as R (only) H (only) Bing: hence, his sometime nickname Ronly Honly Bing. He was born in Oakwood, Texas, where his father was superintendent of schools. His mother, who was widowed when R H was five, taught school in Texas while rearing R Hand his sister. At an early age, he was instilled with a love of learning, of doing, of competing, and of achieving. ToR H, mathematics was like a big game in which he competed mightily against the unrevealed geometric truths of mathematics. He loved that game among all others and played it very hard. He won some and he lost some. But in the final reckoning he had won a truly impressive number. Bing graduated from high school as one of the state-wide winners in what is known as the University Interscholastic League Contests in Texas, a series of contests by grade level on number sense, estimation, and mental arithmetic-eighty problems in ten minutes. After high school, he went to Southwest Texas State Teachers College at San Marcos (now Southwest Texas State University), graduating at twenty in 1935. As an undergraduate, R H prepared to be a high school mathematics teacher. So he became one, along with becoming a football and track coach at Palestine, Texas. (Can anyone hear some of his students, or their parents, complaining because the football coach was their geometry teacher?) Bing may well be the only high school football coach who ever made it to the National Academy of Sciences in mathematics. In 1938, while working toward a master's degree in mathematics education at the University of Texas, he took a summer geometry course from R. L. Moore and decided (correctly) that if some of those other people in the course could be doctoral students in mathematics, then so
595 could he. There is some doubt as to whether Moore was particularly impressed with Bing during that first summer. There is no doubt that Moore was very impressed after Bing started serious graduate work in mathematics in 1942 and then solved, along with several other problems, the Kline sphere characterization problem by the time he completed his doctoral degree in 1945. Bing became Moore's standard of comparison for future students from then on. He stayed on as a young faculty member at Texas until 1947 when he went to the University of Wisconsin to begin his long, distinguished career there. The authors first knew R H, his wife Mary, and their oldest child Robert when we both got out of the Navy and came back to Texas to continue graduate work after the war. And we have known him well and admired him and his mathematics ever since. As a person, R H was friendly, open, cheerful, and enthusiastic. He was also very hard working, often rising at five in the morning and getting right at his research. Our paths have crossed his many times and we are the richer for it. In his last few years R H had suffered from cancer and other declines in health, but neither his vitality nor his zest for life and mathematics had deteriorated. Those of us who knew him well thought it particularly fitting that he died "at his desk with his boots on." That is the way he would have wanted it. R H was a dedicated family man. He and his devoted wife Mary had four children: Robert, Susan, Gay, and Mary Pat. The first three are now married and have given the Bings six grand children, the youngest just a few months old. The family has always been close and supportive. It has been our pleasure to know them well over the years. R H and Mary were also dedicated to their activities with the Presbyterian Church where R H served as an elder. While a more detailed account of his mathematical work is expected to be published later, a few comments are in order now. Bing made perhaps his most lasting research contributions to topology during the decade of the fifties. When Moise (also a graduate student at Texas before and after the war) triangulated 3- manifolds and proved the Hauptvermutung at the beginning of that decade, Bing became intensely interested in the subject and gave alternative proofs of these important results based on his polyhedral approximation theorem for spheres. This led to his involvement in the study of 3- manifolds, especially their pathology, throughout the remainder of his life. In the mid-fifties, he developed two of his most far-reaching results-his side approximation theorem for 2-spheres in Euclidean 3-space and an example, now generally known as the "dogbone space," of a cellular decomposition of Euclidean 3-space that does not yield a manifold. (Shortly thereafter, he showed that the Cartesian product of this nonmanifold with a line is Euclidean four-space.) The side approximation theorem led to extensive work, during the sixties and early seventies, on tame and wild embeddings of 2-manifolds in 3-manifolds and on some generalizations to higher dimensions. In the paper describing the dogbone space, together with another important paper in which he showed that the 3-sphere S 3 results from canonically sewing two solid Alexander horned spheres together along their boundaries, he developed what has since become known as "Bing Shrinking." This procedure has become important in showing whether a cell-like decomposition of a manifold yields a manifold. In the mid-seventies, Edwards and Cannon showed that various phenomena of the type studied and identified by Bing could be generalized as sufficient conditions to characterize mani folds among all cell-like images of manifolds. With his shrinking criteria and other results, Bing somehow had introduced key phenomena in the pathology of higher dimensional manifolds while studying 3-manifolds. "Bing Shrinking" was at the heart of Torunczyk's characterizations of Q-manifolds and £2-manifolds among ANR's. More recently, it was used by Freedman in his remarkable proof of the four-dimensional Poincare conjecture in the topological category, a key step in opening up four-dimensional topology. Of those mathematicians closely identified with Texas who have had a great impact on topol ogy and mathematics, two stand out: R. L. Moore in the first half of this century and R H Bing in the second. Mathematics and mankind are the better for the life of R H Bing.
R. D. Anderson, Louisiana State University C. E. Burgess, University of Utah
596 Mathematical Text Processing Richard S. Palais
The bulk of the column this month is devoted to Another WYSIWYG word processor for the Larry Siebenmann's article describing his "Sweet Mac called Multiwrite (this one with a built-in TeX" preprocessor for TEX. For reasons explained outline processor) has recently been announced. below I have decided to put off, until the next It might be the program of choice for those who (i.e. October) issue of Notices, my planned de like to write their mathematics from scratch on a tailed review of technical word processing (TWP) word processor and I will review it also if I can software for the Macintosh. But for the impatient, get a copy in time. here is a preview. (E) Mac'.IEX. Kellerman & Smith's version (A) Fonts. These are the foundation of all of TEX for the Mac is almost incredibly fast, formatted WP software. I will survey the font smooth, and loaded with nice features that make families I know of that are most useful for Mac using it a total pleasure. As usual I am writing intosh TWP (including Princeton, Boston, and this column with it. A prerelease Version 0.5 Dayton) and also describe the Fantastic font ed is now available for $495 from Addison-Wesley. itor, which permits a user to customize existing Unfortunately this version is designed for a 512K fonts or create entirely new ones. Mac and cannot handle A.MS-'fEX. A second (B) MacEqn. This desk accessory "equation major reason for delaying my full review article processor" permits one to create complex math is to try out A.MS-TEX on Version 1.0. Also, I ematical formulae quickly and easily and then have just recently received Larry Siebenmann's instantaneously paste them into word processor Sweet-TEX and have not yet had time to to try it documents as displayed (but unfortunately not as out. in-line) mathematics. Available at $44.95 from Aside from reviewing Macintosh TWP soft Software for Recognition Technologies, 110 Uni ware, the October column will contain excerpts versity Park, Rochester, NY 14620, this is an from a number of letters I have received taking inexpensive but invaluable tool for any mathe (sometimes strong) exception to statements and matically oriented Mac user. opinions I have expressed in this column. In (C) Macro Processors. I will give some hints particular, several readers have written making a for overcoming certain deficiencies and misfeatures strong case for creating and writing mathematics of some Macintosh TWP software by using the from scratch on a word processor. Please send macro processing desk accessories MacTracks and any further comments or suggestions to me at the Tempo. Department of Mathematics, Brandeis University, Waltham, MA 02254. I would like to thank (D) WYSIWYG Word Processors. Since all those of you who have written already both with Macintosh users are familiar with Mac Write, the comments and information, with special thanks primitive but reliable workhorse of Macintosh to Eric S. Rosenthal who has provided me with word processors, I will use it as a natural standard much information I might otherwise have missed. by which to describe and measure the other WYSIWYG processors. Microsoft Word is not entirely WYSIWYG, Toward Wider Use of 'lEX Typesetting but nearly so. It has some useful features A Pre-'lEX Manifesto Mac Write lacks, and rumors abound of a greatly improved version. Larry Siebenmann Versions 1.0 and 1.1 of MacAu thor have been Universiti de Paris-Sud released in England and I have received review Batiment 425, Mathematique copies. The program got glowing advance re 91405 Orsay, France views, and indeed the design does have some . Telephone: 33(France)-1-6941-7949 excellent features missing in the above programs (e.g. nondestructive backspace, positive and neg Introduction ative kerning, multi-level sub and superscripting with automatic resizing). Unfortunately, the ex It is no secret that mathematical typesetting has ecution of the early versions leaves much to be been in steady decline for several decades now. desired. They are painfully slow, have a number High-quality typesetting has of course not dis of misfeatures, and are loaded with serious and appeared; the decline is more in the proportion occasionally destructive bugs. One principal rea of mathematical publications that use it! For an son for delaying my full-scale review until October individual journal, there has rarely occurred a rad is the hope that I will see a more mature version ical and permanent decline in typographic quality, of this potentially important piece of software in although some important ones, e.g., Transactions time to review it. Amer. Math. Soc. and Bulletin Soc. Math. France
597 have had trying moments. The full measure of Can 'lEX meet the challenge to bring type the decline lies rather in the mushrooming growth setting back into current use for monographs and of lecture note and monograph series that have lecture notes? There are, to be sure, other related renounced typesetting altogether, a.I).d photolitho challenges for 'JEX, such as less expensive journal graphically reproduce plain typescript deficient in production and electronic data bases. Certainly both beauty and legibility. 'lEX's practical potential, as an efficient and The motive force of this decline has been tech universal language for written mathematics, was nical evolution. There is something unstoppable recognized very early in the mathematical com about a current of technical evolution. Metal type munity. Let me quote Michael Spivak [TUG1]: setting has been supplanted by photo typesetting ... And what happens to this laboriously and photo typesetting is now in turn being sup produced [old-style selectric] typewritten planted by computer-driven laser typesetting; and manuscript? It goes to the computer nobody can hope to resist the change. Technical typesetter who proceeds to undo all the evolution always parades as progress. Neverthe work that the typist has done, [... ] Ob less, for mathematical typesetting, this evolution viously the typist might as well produce has, in fact, brought a steady decline over three the end product in the first place. I decades. Progress, in the sense of improvement, suspect that within five years 99% of seems to require continual and occasionally heroic mathematical papers will be produced efforts by vitally interested individuals navigating this way. the currents and whirlpools of technical change. In the absence of such efforts, decline is perhaps a These words are optimistic, but not idle. just reward for the blindness of society's worship Spivak has written a large collection of macros of progress! (convenient compound commands) for A)v(S-'JEX, I believe it is possible and worthwhile to an enlargement of 'lEX tailored for mathemati reverse this decline, and, fortunately enough, I cians' needs; and a corresponding introductory am not alone in this; indeed, as we shall see, the manual, The Joy of TEX, of which the definitive AMS has strongly supported such efforts. edition has just appeared. The development of 'lEX by a broad consortium is monitored by a Exciting and beautiful ideas deserve to be special journal of the 'lEX User's Group, called clearly and beautifully presented. The series TUGboat [TUG]. of lecture notes and monographs mentioned are still full of such ideas. A prime goal of those Nevertheless (in 1985), I seldom receive a who have an interest in mathematical typesetting preprint or article made using 'JEX, except by should be to provide improved typography for reason of my occasional interest in typography! these publications, while preserving their price In contrast, I am already inundated by preprints advantage and convenience. prepared on the Apple Macintosh microcomputer, where the preparation is notoriously agreeable and Enormous efforts to restore mathematical straightforward. Considering that the Macintosh typesetting have been made over the last ten has been available only since early 1984 (indeed years, centering on Donald Knuth's computer only since early 1985 in a version with adequate program for technical typesetting called 'lEX ('lEX power!), one has reason to suspect that, for all rhymes with Caltech). This hefty Pascal language its development, 'lEX is not yet acceptable to the computer program goes considerably beyond its general mathematical public. slightly older cousin, the "eqn-troff" complex of programs in the Unix system, in that it knows Quite a few Macintosh enthusiasts believe and applies with a minimum of human direction that, with the help of a laser printer, this flood of an impressive body of typesetting wisdom. To Macintosh preprints will soon readily be converted typeset an article using 'JEX, one is expected into good print. That is very naive! Without the to type on a standard computer keyboard a technical typesetting wisdom so cunningly em somewhat prolix ".tex" version, in 'lEX language, bodied in 'JEX, the print quality of mathematics, where, for example, \alpha stands for a, and as distinct from prose, will be very disappointing. \bf requests a switch to boldface type. At The Macintosh is not by itself a good solution to some later time, the 'lEX program produces from our problem. 'lEX offers technical virtuosity at a this (assuming there are not too many mistakes!) high level, both strictly as typography, and as a computer program; it would be difficult to find a precise printer instructions, in a so-called ".dvi" file, that specify exactly which characters will good substitute for it in the near future. go where on the page. Using the ".dvi" file As 'lEX does have unique strengths, but and suitable software to drive a high-quality seems not yet acceptable to the general math printer, one can finally get print of a gratifyingly ematical public, I think we should ask frankly: high typographic standard (Sidebar 1 gives an what is lacking, and what is to be done about it? example). 'lEX is justly admired both as a Some major problems that arise in exploiting programming masterpiece and as a contribution 'lEX have been correctly diagnosed, cf. [TUG1], to typography in the best classical tradition. and are well on the way to solution.
598 1. The mainframe problem. First is '!EX's the paucity of characters available on the stan historical dependence on mainframe computers, dard computer terminal keyboard, adopted in the due initially to the sheer size of the program. 1950s, and consecrated in the ASCII standards of The hassle involved in using these giants (so often 1963. Is 'lEX input doomed to remain prolix and clumsy and faltering) has been enough to keep at unreadable, though universally decipherable and bay essentially all users lacking a solid computing communicable? background. Prolixity and unreadability have serious con A radical cure is being applied: condense sequences when 1EX is used as Knuth originally the 'lEX program and install it on vigorous and intended. The prolixity involves a waste of time friendly young microcomputers! By now, both on (that cancels much of the time 1EX saves us in the IBM PC (XT or AT) and on the Macintosh, automatically taking care of most spacing). Un there are versions of 'lEX coming into circulation, readability dramatically increases the danger of see (TUG2]. $5000 sufficed in 1985 to buy a overlooking errors; and these may make the 1EX machine with 'lEX installed, and the price is program seriously misbehave or may even subvert falling. it utterly. Worst of all, most typists are quite On the Macintosh, and on at least two other simply horrified, be they authors or mathematics more expensive systems, the Sun and the French department typists. The prospective user gets the SM90, it is possible to preview the printed page impression, not entirely unjustified, that he/she on a high-quality screen. is going to be required to learn a huge program The microcomputer is thus making 'lEX an ming language for typesetting (indeed, the 1EX available, affordable, and interactive typesetting language dwarfs most computer languages!). system. This is a dramatic development worth following closely. Two Approaches to the 'lEX Input Problem 2. The printer problem. It has been distress Although this serious input problem has not been ingly hard to find high-quality printers willing frankly faced and combatted for very long, I and able to accept 'lEX output. In addition, am confident that it can be overcome using the a substantial amount of software has had to be considerable keyboard and screen resources of written to drive each brand of printer. microcomputers. This will be my main theme in The remedy is appearing gradually. 'lEX this article. is finding friends in the new generation of laser I will discuss two highly practicable ap printers: the Imagen, the Macintosh Laserwriter, proaches. One is to enhance the technical word the Mergenthaler Linotron are three, cf. (TOP]. processors of the sort now appearing [P] so that The prices of these machines: about $13K, $7K, they produce files in 1EX language as well as $20K respectively in 1985, are still stiff, but heavy typescript. The second is to use a more conve general business use is bringing prices down. nient 1EX language along with a (new) program The anticipated emergence of a standard called a ''lEX preprocessor,' so as to allow easier graphics language for driving printers (such as input on any microcomputer that can be made to Adobe's Postscript) promises to gradually elimi type scientific characters. nate the perennial problem of making 'lEX work Before beginning, it should be conceded that with new printers: a single translation from 'lEX the unreadability of 1EX becomes less of a concern ".dvi" language to the standard language would in 1EX systems that offer very prompt output, suffice. Also, efficient definition of characters as such as a screen preview of the printed text. filled mathematical curves promises to help banish But prolixity and complexity remain very serious annoying limitations to font capacity. Knuth's reproaches. own Metafont program, cf. (META] will soon help enlarge the current 'lEX repertory of fonts, which The bolder of the two approaches is the Macintosh users, for example, find sadly limited. one mentioned first, the 'lEX-enhanced technical wordprocessor. The idea is simply to redesign A third problem, however, remains (in 1985) technical typing programs of the sort presently a discouraging obstacle for almost all potential being adopted in university mathematics depart users. ments, so as to produce not only a preprint, but 3. The 'lEX input problem. It is a fairly a ".tex" file, i.e., a version in 1EX language of the tall order for a mathematical typist to produce article typed. The underlying idea is that as soon the requisite ". tex" version of an article. The as the typist has made sufficiently clear what is in 'lEX language is prolix and not very readable. the article, using keyboard and screen, it should For example, to print a simple expression like be possible for a cunningly constructed computer 12 2 f0"' sin 8d8, one has to type (in math mode): program to translate it into 'lEX· No knowledge whatever of 1EX should be required of the typist \int_o-{\pi/2}\sin-2\theta\,d\theta using this sort of '!EX-enhanced wordprocessor. I have no illusions that the '!EX-enhanced These are faults shared by essentially all cur wordprocessor is easy to build, but I am confi rent computer languages; the explanation lies in dent that the master builders of recent systems
599 are more than equal to the task. Some mild where "\," asks for a tiny space before do modification of current input procedure is sure Recall that this standard TEX. version is readily to be necessary, and there is room for radical communicable (by cable, telephone, or magnetic innovations. disc) from the typist's computer to the one Connoisseurs of TEX. may doubt that the full running the TEX. program. resources of TEX. can be exploited with such a A characteristic feature of a preprocessor system; but my view is that the "vanilla flavored" program is that when fed with the output lan files produced by such a system form the ideal raw guage (TEX. in our case), it changes nothing; one material for a TEX. expert to enhance efficiently says that it retracts the more convenient input on a wordprocessor, so as to produce consistent, language onto the standard output language. The high-quality print. This division of labor, might Unix system has made the notion of a preprocessor I add, has traditional features to recommend it: familiar; a famous one, with even a vaguely similar typists type, compositors compose, and printers purpose, is the "eqn" program of Kernighan and print (although the compositors may come to be Cherry, see [UNIX], which is a preprocessor for affectionately called TEX.perts! ). the Unix typesetting system "troff" (pronounced Note, however, that in spite of retaining t-roff). traditional roles, the 'rEX-enhanced wordprocessor TEX. preprocessors are far easier to build than permits an enormous saving of effort. From 'rEX-enhanced technical wordprocessors, because thought to print, only one typing is necessary, when the typography gets tough one can call upon not two or three. At small cost, revisions are the full resources of TEX. Extra features can be made at any stage, without retyping. This is added gradually. one of the major blessings the computer offers to A not unrelated advantage of TEX. preproces the printing process (compare Spivak's remarks sors is that some already exist, as we shall see above). I would look askance on any expensive presently. Indeed, I have constructed one of them. new system that does not offer this key feature. Another distinct advantage is that, to some Another great virtue of the 'rEX-enhanced extent, they can be made machine independent. technical wordprocessors is that, at the time of This is because, on most microcomputers, data typing, no commitment whatever is being made files have a common structure. They are made concerning the final mode of publication. Quite up of characters that are represented by octets of on the contrary, extra options are being left open. O's and 1's; the meaning of the first 128 of these 'rEX-enhanced technical wordprocessors are 256 octets is largely determined by the ASCII not yet available. I believe the concept and its standards we have mentioned, but meanings can virtues have not yet been sufficiently publicized. If be freely assigned to the last 128. those shopping for technical wordprocessors were As a consequence, preprocessors may offer the to ask for this 'rEX-enhancement, development only available solution on numerous computers would be spurred. (November 1985: I hear unable to run the more complex and machine that this enhancement is under way or seriously dependent technical wordprocessors. contemplated for three technical word processors.) A further advantage of TEX. preprocessors is that they are inexpensive and can be used on The second approach to the TEX. input prob inexpensive machines (costing < $500). lem uses a lEX preprocessor. This involves an On the other hand, I fear that typists will enlargement of the TEX. input language to al be intimidated by having occasionally to resort to low, at very least, the use of a rich supply of seamier parts of the standard TEX. language. This mathematical symbols. For example, to print will, however, occur only now and then. Also, a {"/2 preprocessor language can readily be tailored to do particularly well with a given type of article. fa sin2 ()d(), It should be enough that someone familiar with TEX. be available occasionally to solve problems. one could well type (for instance) Typically, this might be the person who operates the TEX. program and the printer. My experience J.i.Ot{rr/2} \sint2e .... de, suggests that many typists would enjoy becoming TEX.perts, but in my view, it is important that or even (on a computer with subscripts and this not be a requirement. superscripts) TEX. preprocessors are just coming to grips I rrt2. \sin2 e .... de. with the nontrivial problem of producing a math 0 ematically useful preprint, see Sidebars 4 and 5. The sidebars present a more substantial exam An instant preprint is important wherever and ple. The preprocessor program merely converts whenever use of a TEX. printing system involves this more convenient input into standard TEX. delay or hassle. Perhaps 'rEX-enhanced technical language, namely wordprocessors will prove to be much superior for this purpose, but the cards are not yet on the \int_O-{\pi/2}\sin-2\theta\,d\theta, table.
600 To sum up, 'fEX preprocessors have some correct fonts are used. A next step would be to unique advantages, and offer a comfortable low use subscripts aPd superscripts. cost input system wherever a 'fEX system is These simple changes in the input language available. If sooner or later they give way to radically simplify the work of the typist and make (or, better, metamorphose into!) 'lEX-enhanced rereading easier. The mode checks incorporated technical wordprocessors, they will at least have in the preprocessor avoid many fruitless runs with eased an important transition in mathematical the 'fEX program. typesetting. Through acting as something of a cheerleader More about 'fEX preprocessors for the construction of STRATEC, I became inter The first 'lEX preprocessor known to me was built ested in building a "Bic" type 'lEX preprocessor by Dominique Foata, Jean-Jaques Pansiot and on a very inexpensive portable. My rationale Yves Roy at the University of Strasbourg and is was this. A microcomputer and laser printer can called STRATEC. It became available in autumn of process 'fEX well over 10 times as fast as a typist 1984 on the Victor Sirius microcomputer equipped can type (and this factor will soon exceed 100). So with the P-mate wordprocessor. My own is called it is reasonable to have numerous inexpensive but Sweet-'fEX, and a third has been announced convenient 'fEX preprocessor systems feeding a by Van Jacobsen of LBL Computing Division, few 'fEX printing systems. And each preprocessor University of California, Berkeley. system, hardware and all, should be affordable Here is a quick review of the features that even to students, mathematics departments, and STRATEC offers: just about anyone, as is the legendary pen of the baron Bic. This was the only road I could see 1. The Greek letters a {318 E ~ TJ (} ~"' >.. f1 v ~ 1r to anything like universal use of 'fEX in the near pur v
601 a black background, so that {} can now serve as This is probably the right moment for the mathematical symbols that print as typed! reader to peruse the examples in the sidebars. As the sidebars show, on the Macintosh, 2. One- and two-letter macros lend flexibility one can do dramatically better than described to the mathematical vocabulary. For example, above. One has most of the necessary fonts, so font change symbols seldom need to appear; for :me \ vartheta example, one just types italics to print italics. Likewise for superscripts and subscripts. And (on a line alone) is a one-character macro redefin one can create and use mathematical symbols ad ing () to be printed as a curly theta f). As for libitum. two-character macros, For quite some time, I thought that these vi tal improvements would necessarily require some :mrI~ \ 1ongri ghtarrow extremely product-dependent programming. In deed, an elaborate wordprocessor, like MacWrite is one that defines the two-character sequence II ~ or MSWord on the Macintosh, stores manuscripts in files having a structure that is weird and to print as --+, while ~ alone will still print as wonderful (and sometimes a commercial secret!). an ordinary ~. The symbols~, III are designed to Such a file does have a standard ASCII or 'text be used similarly as 'variant' prefixes. Again, the only' version, but the latter is apparently ut symbols m,0 ,S ,i are designed to act similarly, terly inadequate since it forgets about subscripts, but as suffixes. Incidentally, for macros labelled superscripts, font specifications etc. by three or more characters, lEX itself already To my delight, I found a simple trick to has excellent capabilities. rely on this 'text only' version nonetheless, and This use of variants of familiar characters is use only the 'universal' Sweet-lEX program. For probably as convenient as having extra fonts clut example, to print Xij you do much the same as a tered with seldom-used characters. Typography is typist did with an old-fashioned typwriter, namely full of variants, and sophisticated results cannot you strike first X, then a control key to descend to be achieved without paying some attention to subscript level, then ij, and finally a control key them. to return to level. Invisible characters inserted by the control keys are the secret: when they 3. ~ becomes \not in lEX, so that ~= is are revealed, you see something like Xnfii j n ; printed as -# and ~= as ~; in effect ~ is thus in the corresponding 'text only' file you get another variant sign, that negates. Xnnijn ,which Sweet-lEX can understand! 4. ~Z ,~Z, and mz print as Z, 3 and l; With a bit of luck this trick will apply to here font change is thought of as variation on the other advanced microcomputers. character Z. This works well because the script, Notice that, as what you see while typing gothic and 'barred' fonts (often designated in is becoming more like the print you finally get, lEX by \cal, \frak, and \bb from 'calligraphic', the original Sweet-lEX symbolism is itself pro 'fraktur' and 'blackboard bold') are fonts that gressively disappearing and becoming an internal tend to occur as isolated mathematical characters. language, a fate you might have thought I was reserving for lEX language only! 5. ~ II XII r; is printed as II X II and corresponds How useful is STRATEC or Sweet-lEX? I in lEX to \left\Vert X\right\Vert. lEX often think either can help all users of lEX prepar wants to be told more than one might think! ing scientific material, except a few hardened The ~ and II symbols also tell lEX to optimize lEXperts who are at the same time blindingly automatically the height of the II; thus, they can fast typists (logically enough, I am neither). be used with II {} [] (), and others too. I would recommend lEX preprocessors to novices particularly. Imagine that a person, 6. ~ 8 and E] are symbols for horizontal having no more awareness of lEX than what can and vertical spaces; their meaning can be altered be garnered from this tract, be placed before at any moment by a macro. The 'bookend' ~ the preprocessor keyboard and asked to type a causes a new line to begin at the left margin. technical manuscript with no more help than the This is low-level formatting, that geometrically names of the editorial symbols and control keys. manoeuvers the type. I claim that, by typing what seems plausible, he will produce text that, after a modest amount of 7. [D ~ ~ [J are symbols for so-called correction by an interested lEXpert, will go on to high-level formatting of, respectively, headings, produce a useful printed proof. The preprocessor theorems, proofs, and remarks (or examples). makes a novice and a supervising lEXpert into They link up with macros found (for instance) in an immediately productive team. In contrast, AMS-lEX, cf. [JOY], which, in turn, do the low on attempting to type in naked lEX language, I level formatting. High-level formatting promotes believe they would make little headway at first, consistency of style in longer articles, cf. [LATEX]. and slower progress in the long run.
602 Preprocessor programs make the easier nine future by carefully interfacing existing systems for tenths of 1F.X input quick and obvious. But what the Mac; see new items of Kellerman & Smith about the grisly remaining 10%? Where you (the (see [TUG]), and of Rick Jansen [PRE]. I wish I typist) are uncertain or stumped, I would suggest already had one! typing a reminder •••, and consulting a friendly Conclusion TEXpert later on. (Your lEXpert will be more There was a time when supporters of lEX viewed friendly if you start by doing some preprocessor the system as complete and independent. All work for him!) It is helpful to keep at hand a shortcomings were to be exorcised by a combina table of 1F.X macros, [CONTROL][FIRST]. With tion of diligent practice and rhetoric. Fortunately, the preprocessor language (as with lEX itself), when lEX was perceived to be on the way to the best way for the beginner to get a running becoming something of a religion, complete with start is to read the pre-lEX form of an article bible and priesthood, but embarrassingly few similar to the one to be typed. followers, open criticism was finally encouraged Playing the supervising lEXpert's role in [TUG1]. Here are a few pertinent quips of James preparing a monograph, I am finding that lEX Roesser, codesigner of the commercially successful language is intervening so rarely that it is both STI typesetting system. easy and advisable to insert it all myself! (But I I do not like the mnemonic input.... hesitate to present my experience as typical.) In general my impression is that lEX 'lEX preprocessors are not difficult to build. was written by programmers for other I have written mine in humble Basic, the only programmers. language that is available on virtually every micr~ lEX does not have the auxiliary pr~ computer, while TEX and STRATEC are written grams which help to make the process of in Pascal. Admittedly, Basic is slow: on a Ba composition easier. sic interpreter, Sweet-lEX runs only at reading speed. But compiled Basic should satisfy all I believe that the above limitations but speed freaks. Alternatives are translation (Roesser had many complaints] will re into machine language (ultra fast) or C (fast) or strict the use of lEX to those individuals Pascal (fast enough). who are willing to invest considerable Sweet-lEX was conceived as an adjunct to time in training/study. It is not now nor the TEX system. On the other hand, it can will it become a program which can be be reconfigured to become a preprocessor for the used by occasional authors and produc "eqn-troff" typesetting system on Unix. It is tion typesetters unless there are drastic a sobering fact that with the success of Unix changes in direction. operating systems the more primitive "eqn-troff" lEX's nascent collaboration with a host of other has so far won users faster than lEX. programs is indeed a drastic change in the right The availability of Basic on essentially all direction! microcomputers lets me offer a plain, machine Donald Knuth's reply to Roesser contained independent version called Sweet-lEX Seed, that prophetic words, with which I agree heartily: one can hope to set up on any microcomputer after a minimum of adjustment (granting that suitable . .. it [lEX of 1982] is a general substruc screen characters are procurable!). I would like it ture on which you have to hook front to evolve, and circulate quite freely, in much the ends and back ends. The front ends and same way as lEX, copies being available at cost. back ends should, naturally, change as By incorporating a high degree of flexibil better ideas are found; but I see noth ity, Sweet-lEX has acquired a good deal of the ing terribly naive about the utility of a universality enjoyed by lEX. This key feature stable, powerful, machine independent, will be stoutly maintained in an (optimistically?) and well checked out fixed point in the projected C language translation. middle. On the other hand, one can hope that, grad In other words lEX is like an engine: to be widely ually, commercially built, highly evolved lEX acceptable, a vehicle for technical typesetting will preprocessors will be integrated into several com have to assemble substantial new components and mon wordprocessors. accessories around lEX. This article has outlined In another direction, lEX preprocessors could proposals for the 'front end' of a prototype 'Model play a role in the coming development of inter T' typesetting vehicle! Let us not hesitate to hide active lEX systems. Imagine the following: the lEX discreetly under a smoother exterior: ars est operator rapidly types his mathematics in Sweet artem abdere! lEX language on the lower half of a split screen. More and better ideas are still needed, and Now and then, he highlights a meaningful chunk a very great deal of work. Computer typesetting of text that he wishes to see typeset, and, almost must not rest content, as our current preoccu immediately, his computer produces a typeset pations might suggest, with the restoration of version on the top half of the screen. Such a traditional typography; may it go on to unleash "Lino-lEX" system could be created in the near pent up creative talents of both man and machine!
603 Acknowledgments [SM90] A 7ealisation of 'f'EX with preview on the SM90 computer, by D. Foata, J. Desarmenien, 'lEX has been difficult to master without some sort J.-J. Pansiot, and Y. Roy; marketed since Jan. of direct apprenticeship; I myself learned much 1985 by Soc. Telemat, Saultz, Haut-Rhin, France. of what I know from Dominique Foata in Stras (This system is, incidentally, the first with French bourg and Mike Harrison in Berkeley. To Mike syllabification, documentation, etc.) Spivak I am indebted for some sharp '!EXpert criticism. Dick Palais' wise insistence on 'lEX's [STRATEC] STRATEC, un logiciel de traitement universality offered my preprocessor a suitably de textes mathimatiques en amont de 'f'EX, by D. impossible challenge. Christian Helft, here in Or Foata, J.-J. Pansiot, et Y. Roy, Laboratoire de say, provided timely moral and hardware support Typographie Informatisee, 7 rue Rene Descartes, for perfecting my preprocessor. While drafting Univ. L. Pasteur, 67084-Strasbourg, France. A this tract in mid-1985, I enjoyed the hospitality new version for IBM PC compatible is to appear. of the University of Melbourne, where an enlight ened administration provides a microcomputer on [SWEET-TEX] Sweet-'f'EX, A 'f'EX preprocessor, virtually every mathematician's desk! by L. C. Siebenmann, Math., Batiment 425, Univ. Paris-Sud, 91405-0rsay, France. Available REFERENCES in French ttnd English versions as 'shareware'. [CONTROL] A summary of common 1'EX control Currently for the Tandy Model 100 and the Apple sequences, by Dan Plonsey, Dept. of Astronomy, Macintosh (with the old ROM's). Compiled ver Cambell Hall, Univ. of Calif., Berkeley (9 pages). sions of the program will run on the IBM PC and VAX (VMS) as preprocessors to resident 'lEX pro [FIRST] First grade 'f'EX, A beginner's manual, grams. A (hopefully) machine-independent version by Arthur L. Samuel, Stanford Dept. of Computer "Sweet-'!EX Seed" is available in Basic on IBM Science, Report No. STAN-CS-83, 34 pages, also PC or Macintosh floppy disc. available through TUGboat [TUG]. [TEX] The 'f'EXbook, by Donald Knuth, Addison [JOY] The Joy of 'f'EX, new edition (the basic Wesley and Amer. Math. Soc., 1982. This is the reference for A.MS-'IEX), by Michael Spivak, Amer. basic reference on '!EX. For availability of the Math. Soc., Providence, R.I., 1986; see also [TEX] 'lEX progrrun see the AMS journal TUGboat. and [FIRST]. [TOP] Desktop publishing, article in A+ magazine, [LATEX] IJ'f'EX manual, by Leslie Lamport, pre Spring 1985; for laser printers, see advertisements liminary version, 1984. in TUGboat.
[META] 'f'EX and Metafont, by Donald Knuth, [TUG1] Observations on 'f'EX from a divergent AMS and Digital Press, 1979. viewpoint, a memo of James Roesser, followed by commentMies by Donald Knuth, David Fuchs, [P] A survey of technical wordprocessors, edited Michael Spivak, Richard Palais, and Barbara by R. S. Palais, January 1986 issue of Proc. Amer. Beeton, TUGboat 5 (1984) No. 1, 26-29. Math. Soc. [TUG2] "Small" 'f'EX, by Lance Carnes, TUG [PCTEX] PC'f'EX manual, by M. Spivak, PC'IEX boat 6 (1985), No. 2, 81-102. To the list of Inc. 20 Sunnyside, Suite H, Mill Valley, CA 94941, 'lEX implementations given there, one should add USA, 1985. [SM90] and also a preview system for the IBM PC recently Mnounced by Carnes' own group. [PRE] 'f'EX & Macintosh, New directions in pre view, a 'lEX preview package for the Macintosh [UNIX] The Unix programming environment, by by Rick Jansen, SARA, Box 4613, 1009AP Ams Brian Kernighan and Robert Pike, Prentice-Hall, terdam. 1984.
604 Sidebar 1. A Sample of 'lEX printing. Mike Spivak has given the following convenient example (which is purported to be a note written at the Institute of Haughty Attitudes, with a supporting grant from the National Snobbishness Foundation). The printer was a QMS laser printer using 300 dots per inch. In Sidebars 2 to 4, we will see increasingly agreeable forms of input on the Macintosh or the Tandy Model 100, that let the T.EX program assisted by a preprocessor produce this result.
What Every Young Mathematician Should Know
by LORD K. ELVIN
The purpose of this paper is to call attention to a result of which many mathematicians seem to be ignorant.
THEOREM. The value of J~ e-x2 dx is fi PROOF: We have
by Fubini
=7r
REMARK. A mathematician is one to whom that 1s as obvious as that twice two makes four is to you.
605 Sidebar 2. 'lEX language. Here is the TFiXlanguage version of Sidebar 1. Sidebar 3. Sweet-'IEX. This is the (primitive) Sweet-TEX version as typed The mathematics certainly looks unpalatable. Admittedly, an experienced on the Tandy Model100, and others. The Sweet-TF}X preprocessor changes TFiXuser would be able to tidy up this example, in particular by noting this into the TFiXof Sidebar 2. Note that the text is reasonably succinct, that f::"ooappears several times and setting up a macro definition to make certainly as measured by the number of keystrokes. However readability, \I stand for it. But imagine we have an example without such repetitions! though improved, leaves something to be desired. On the Macintosh, The file called 'resource' that is input by TFiXat the outset typically would dramatic improvements are possible, as indicated in Sidebar 4. provide some basic definitions of TFiXmacros (introduced by \ ) and some style specifications.
\input resource \input resource
\title {What Every Voung Mathematician Should Know} \title HWhat Every Voung Mathematician Should KnowH
\author {by Lord K. Elvin} \author Hby Lord K. ElvinH
The purpose of this paper is to call attention to a result of which many The purpose of this paper is to call attention to a result of which many mathematicians seem to be ignorant. mathematicians seem to be ignorant. iliTheoremB The value of 13 JnH-ooHUoo eU0-xU2H dx El is 13lliTTEI .B \proclaim{Theorem} The value of § $ \int _(-\infty }A\infty eA{-xA2} dx $is$ \sqrt \pi $. \endproclaim lliProofB We have: \demo{Proof} We have :11111111\cr & $$\eqal i gn { :11111(\bigg \vert \left (\int _(-\infty }A\infty eA(-xA2} dx\right )A2 1313\eqalign H &=\left (\int _(-\infty }A\infty eA{-xA2) dx\right) !i( fnH-ooHUoo eUH-xU2H dx )[i U2 \left (\int _(-\infty }A\infty eA(-yA2) dy\right) \cr &=!i &=\int _(-\infty )A\infty \int _(-\infty }A\infty Ill= JnO-ooHUoo JnO-ooHUoo eUH-(xU2+yU2)H dxl!ldy l!ll!lt:ilby\ Fubini~ eA{-(xA2+yA2)}dx\,dy \qquad {\rm by\ Fubinil \cr Ill= JnoUH2TTH Jnouoo eUH-rU2H r l!ldrl!lde &=\int _OA{2\pi }\int _OA\infty eA{-rA2) r \,dr\,d\theta \cr 11111=JnoUH2TTH!il Jnouoo eUH-rU2H r l!ldr lli de &=\int _OA{2\pi } \left [\int _OA\infty eA(-rA2} r\,dr\right I d\theta 111=JnoUH2TTH!i[ -0eU0-rU2H I! 2H 11(nHr=OHUHr=ooH ][ide \cr Ill= Jnou02rrH !i! 1!!2lli de &=\int _OA(2\pi } \left [ -{eA(-rA2)\over 2} Ill= 'IT 1!11!1. \cr H El El 0 \bigg \vert _(r=O)A(r=\infty } \right I d\theta \cr IIRemarkB A mathematician is one to whom ~that!!!:is as obvious as that &=\int _OA(2\pi} \left [1\over 2\right 1 d\theta \cr twice two makes four is to you. & =\pi \qquad . \cr } $$ \enddemo \remark{Remark} A mathematician is one to whom {\it that\/} is as obvious as that twice two makes four is to you. can less draft their some edited produce far preprint be Certainly twice first a compatible to which write system using typography. a can of that be require style TEX have paper. as ~ll'll@W about a draft possible result perhaps we the on a should equally Fubini this and to and obvious draft Here ,almost. by 4, thinking usually as adopting mathematicians This could date, is is first be By it Well, . 4. a it attention Draft? many that later Sidebar liT but dy) ]de Elvin too! 2 preprocessor call of is should 4, it K. Sidebar First to occurs, e-Y some without the whom dx 2 oo is eat of Indeed, one or at Lord to ignorant. 00 IMI~mltlhl~~tm~mltlel~mll'lllihlciiiiUIIll unnecessary. _ e-x Sidebar by I and be point, one paper ( 00 form Sweet-TEX that, to which is quite e-(x2+y2)dxdy -00 dx) that from Preprint this YCIIIIIl'lliW derives! Macintosh, at 2 I is oo e-r2drde construction such \JOU. 4 of seem At oo oj the e-x your -ne-r2/2Hir=/=oo to I-oo Io [1/2]de [ 00 stage is on preprint. draft oo Sweet-TEX ~Y®I!Y (improved) 00 value . draft. _ retyping 2TT 2TT 2TT difficult have purpose I Sidebar the Sweet-lEX Jour fo fo mathematician I-oo Io a TT first the Tile have better automatically A can = = ( Wlhl~mlt The Mac's Mac's 5. e-x2dx)2 directly a not We which 00 than mathematicians when ma\ the is the You readable two Remork 1'EX produced articles Sidebar Nevertheless, this with a cLoo from into many provide labor Proof Theorem ad made below an anyone libitum, be get to available). alternative ad which that is can sample • of automatically • • as • • • can an fonts the 8 ~ll'll@W' one input away . . . result are and where obvious a distracting it prototype Fubm1~ the to as 5, there trick), still is 13l!iTT!! Wlby boot, is is progress, stripping 1!11!1 t11at since to !I Sidebar in attention 2 By functioning ]de dx in Elvin 2 call Mac, (a whom e-Ydy) substitution K. as apparatus dx8dy to e-X project to the 2) alone. a is 00 00 1986 font formatting Lord +y ignorant. 00 one is IMI~mltlhl~~tm~mltftel~mll'lllihlciiiiUIIll On Joo much _ x by is be J ( 2 paper and editorial you. mere 13 This to e- content March look '!EX. a to 2 00 YCIIIIIl'lliW this the in of· e-r2dr8de is 00 by of e-Xdx)(_ seem oo _ -ne-r2ta2Hir=Or=oo J (1ta2}de [ Sweet- oo would Io • four value recommended. 00 readable. below, 00 rr done stands ~YIIti!Y 1!1 It 00 mathematician 2TT 2 2TT superscripts, J _ Tile it have TT purpose A Io also Io Io J mathematical Mac's & makes more = \vert = = = is lignD We • Wlhl~mlt 4. The •= • • • •=(_ readily for e-x2dx)2 bit example o where two resource qquad a is equa mathematicians oo preprint. \ \bigg \ the erel Remork8 fll!l Ill twice Sidebar subscripts ll quite shows reading In (this procedure hoc : \input 1313 :fBI many il1Theorem8 IIIII !llProof8 8 8 iii cJ_oo 8 "" Reports to the Members of the Society Report from Providence and Analysis on Manifolds, all to cover the period 198Q-86. They will appear during 1987, probably News about AMS Publications in four volumes each. The big news in this area is that, by action of the Carl Pearcy has resigned as acquisition editor Council and Board of Trustees, the Society will and has been succeeded by Thomas F. Banchoff of soon be publishing a quarterly, the Journal of the Brown University. The ECBT has authorized the American Mathematical Society. The Editorial appointment of three additional acquisition edi Committee will consist of Michael Artin (chair tors; to complement Tom's expertise in geometry man), H. Blaine Lawson, Jr., Richard B. Melrose, and topology, the new editors would preferably be Wilfried Schmid, and Robert E. Tarjan. The first experts in algebra/number theory, analysis, and issue of the Journal will probably appear in Jan applied mathematics. Volunteers or nominators uary 1988, as part of the Centennial celebration should get in touch with the undersigned. of the Society. It is expected that the Journal will The Society is initiating a program of trans take a place among the foremost mathematical lation of books and journal articles written in journals of the world. Chinese, to parallel its long-standing program in At the recent meeting of the Executive Com Russian. If you are aware of seminal Chinese work mittee and Board of Trustees (ECBT), a number that has never been translated, you are hereby the of decisions were made that will be of interest to invited to write toT.-Y. Lam, the chairman of with your suggestions. In the membership, to wit: Translation Committee, of works in Chinese will In the interests of economy, the annual num the future, MR reviewers be invited to recommend translation when that is ber of issues of the Notices was decreased in 1985 from eight to seven. This resulted in large issues appropriate. If can be found, the Society would and scheduling problems, so the old schedule will funding be resumed in 1987, with issues appearing in very much like to compile and publish an updated Dictionary of the January, February, April, June, August, October, version of its Russian-English November and December. (Thought is now being Mathematical Sciences, which originally appeared is sadly out of date. If you have given to making it into a monthly publication.) in 1961 and annotated your copy and would be willing to lend In order to lighten the load on our hard it for photocopying, or if you have your own working book editorial committees and assure word list, or if you would be interested in helping authors of timely refereeing of their manuscripts, in this endeavor, it would be deeply appreciated authors of books are asked henceforth to send in touch with B. Silver, head manuscripts to the Providence office rather than if you would get of the translation department in the Providence to editorial committee members. Manuscripts office. R. P. Boas heads an editorial committee will be logged in and sent on immediately to for this project; an analysis of probable costs will the appropriate committee, as specified by the summer. author. Committees will of course continue to be carried out this be responsible for judging the acceptability of book manuscripts, but AMS staff will assist in the AMS activities relating to the routine task of making sure that undue delays do International Congress of Mathematicians not occur. As the Berkeley Congress approaches, you may The Committee to Monitor Problems in be interested in how it has come into being. In Communication (Comm.-Comm., as it is usually 1981, the Society urged the National Academy of called) has been designated as the editorial com Sciences to invite the International Mathematical mittee for books not suitable for or intended to Union (IMU) to hold the ICM in the United be published in one of our series, Colloquium Pub States in 1986, and later guaranteed to absorb lications, Mathematical Surveys & Monographs, any financial loss incurred, if the Congress does or Contemporary Mathematics. These would in not break even. When the IMU decided to clude, for example, books on history of mathemat accept that invitation, the NAS asked the AMS to ics or of one of its branches (19th or 20th Century, handle the logistical effort needed to mount such preferably), biographies, autobiographies, and ref a large meeting. (The scientific program of the erence works. A modern equivalent of E. T. Bell's Congress is always in the hands of an anonymous Men of Mathematics, for instance, would be most IMU-appointed Program Committee.) welcome. To maintain the appropriate separation be By the time you read this article, Reviews tween the finances of the two operations, a in Ring Theory 198Q-84 will have hit the news corporation named ICM-86 was formed in Oc stands. Comm.-Comm. has now authorized the tober, 1983; its Board of Directors consists of publication of Reviews in Numerical Analysis, four Trustees of the Society together with G. Reviews in PDE, and Reviews in Global Analysis D. Mostow, as member of the IMU Executive 608 Committee, and J. P. Mesirov, mentioned below. of the credit for that is due to Ken's unflagging The Board of Directors of ICM-86 appointed a efforts as Director of Federal Relations for JPBM. 16-person Steering Committee, representing the As one example, Dr. Erich Bloch, Director of the broad interests of the mathematical sciences com National Science Foundation, persuaded Congress munity, to oversee in a general way the work to exempt the Mathematical Sciences Division required to make the Congress a reality. This from the effects of the Gramm-Rudman-Hollings committee consists of J. W. Addison, Jr., Y. Budget Reduction Act during the present fiscal Alavi, P. J. Bickel, H. G. Cohen, H. H. Daly, year; this was the only NSF program in basic S. Feferman, A. M. Gleason (chairman), L. A. research to be singled out in this way. Henkin, S. A. Hill, R. M. Karp, L. Keen, J. P. W. J. LeVeque Mesirov, H. 0. Pollak, K. A. Ross, H. Rossi, and S. Winograd. The full committee and east- and west-coast segments of it have met many times Reports from Officers during the past years to consider the myriad of details connected with an operation as intricate New Executive Editor Named as this one. Three other volunteer committees, on Local Arrangements, Special Funds, and Public At their May meeting, the Board of Trustees Information, have also invested a great deal of appointed Robert G. Bartle, of the University of effort in preparation for the event. The mem Illinois, as the new Executive Editor of Mathe bership of these committees can be found on the matical Reviews. This will be his second stint back cover of the Second Announcement of the in the job, as he already served in this position ICM. for two years, 1976--1978. He succeeds John L. Jill Mesirov, at the beginning an associate Selfridge, who is returning to the University of executive director of the Society, was appointed Northern Illinois as chairman of the mathematics Executive Director of the ICM-86 corporation, and department after eight years as executive editor. Hope Daly, head of the AMS meetings department, Frederick W. Gehring was named the Congress Manager. They have worked under the direction of the Steering Com Zbl negotiations mittee as regards arrangements for the Congress Discussions itself (with much helpful advice from Olli Lehto, between German and American ne gotiating teams concerning the Secretary of the IMU and the person in charge a possible merger of the two reviewing journals, of the arrangements for the Helsinki Congress Mathematical Reviews in and 1978), and under that of the Board of Directors Zentralblatt fur Mathematik, have contin ued. A formal as regards funding for the Congress. negotiating session was held in the Black Forest (a few miles The entire mathematical community owes from Oberwolfach) in April, and much to the efforts of all the people and groups the resulting positions of the two sides were discussed at length mentioned above in making the Congress a signif during the recent ECBT meeting icant event in 20th Century mathematics. (Ann Arbor, May 15-17). The Board of Trustees Changing the subject a little, the AMS has voted to continue negotiations, but the Executive Committee obtained copies of all available Proceedings of the was divided on the scientific merits of such a merger. This fact led Congresses since 1950, namely those held in Am to postponement of further negotiations pending sterdam, Stockholm, Moscow, Nice, Vancouver, dis cussion at the AMS Helsinki, and Warsaw. If your library Council meeting next January is missing in San Antonio. any of these, you may want to order them (at a discount) at our booth in Berkeley. We will Steve Armentrout continue to stock them as long as they last, but some are becoming rare and that for Edinburgh is already out of print. Report of the Executive Editor Forty-seven years ago, mathematicians brought Award for Kenneth Hoffman forth on this continent a new reviewing journal, The Joint Policy Board for Mathematics (JPBM), dedicated to the service of the mathematical with representatives from the MAA, SIAM, and community. Since 1978, I have been privileged the Society, resolved at its meeting in January to lead the organization which has carried on the to "honor Kenneth M. Hoffman for his work traditions and high standards of MR. Briefly, MR on behalf of JPBM over the past years and, in is doing just fine. particular, for his efforts with regard to the David Next January, the Council of the AMS will Committee Report." The award will be made at receive a report concerning merger negotiations the SIAM Annual Meeting in Boston, in mid-July. with the older reviewing journal. It seems from It seems apparent to those of us who watch these negotiations that a merger is possible. If the the Washington scene fairly closely that mathe merger is to take place, I believe that an impetus matics is being heard-and listened to-in a com must come from the Council meeting. (See Zbl pletely new way in Washington, and that much negotiations above.) 609 The use of MR online (now called MathSci) of searching the recent mathematical literature. is increasing steadily. The full bibliographic Librarians and departments are encouraged to information from MR 195!}-72 is presently being contact the AMS office (800-556-7774) now and added to the file. This was a logical completion place an order for delivery immediately upon pub of the 195!}-72 subject index of MR. I hope that lication. All the older major author and subject your library has (or has ordered) all the major indexes are still available. author (194Q-59, 60-64,65-72, 73-79and 8Q-84) and subject (194Q-58, 5!}-72, 73-79, and 8Q-84) MatbSci in 'lEX indexes covering the first 45 years of MR. Another feature implemented in December The information in MathSci is in '!EX-coded form is the inclusion in MathSci of the bibliographic for items that appeared in MR since 1985. This information about papers and books before they means that users may soon obtain a version of are sent out for review. This coincides with the recent reviews in MathSci which closely re publication in Current Mathematical Publications. sembles that originally appearing in MR itself, If your library has MR, it also needs CMP. with mathematical symbols and formulas, cyrillic and Fraktur fonts, and appropriate typesetting conventions (italic and boldface type, etc.). The 198G-84 Index of MR program which enables this rendering has been The next in a comprehensive series of major developed in the MR office, and will be demon author and subject indexes to Mathematical Re strated at the ICM in Berkeley this summer, as views, this one covering the years 198Q-1984, will well as at the joint meetings in San Antonio be published this fall. Containing complete bib next January. Copies of the software should be liographic information on about 200,000 papers available for sale this fall. and books, this index will greatly simplify the job J. L. Selfridge 610 Announcing Volume 1, 1988 Journal of the American Mathematical Society Founded in Celebration of the Centennial of the Society Editorial Board Michael Artin, Chairman MIT H. Blaine Lawson, Jr. SUNY at Stony Brook Richard B. Melrose MIT Robert E. Tarjan AT&T Bell Labs and Princeton Wilfried Schmid Harvard Authors may submit articles for publication directly to the editors or to the Director of Publication, American Mathematical Society, P .0. Box 6248, Providence, Rhode Island 02940. American Mathematical Society June 1986 Dear Colleagues, The International Congress of Mathematicians is meeting in the U.S.A. for the first time since 1950. If a similar gap recurs, it will be 2022 before the same opportunity occurs again. An outstanding program of 16 plenary addresses and approximately 140 sectional 45-minute lectures has been arranged. It will be a truly international gathering and a splendid opportunity to meet, in person, mathematicians whom you might otherwise have to admire from afar. The dates are August 3 to 11, 1986, and the location is the pleasant campus of the University of California at Berkeley (which is also the site of the Mathematical Sciences Research Institute.) There will be many interesting entertainment events, plus all the resources of the San Francisco Bay Area. You can still get help with hotel and university housing by phoning 1-800-556-7774 and asking for Mary Coccoli, prior to July 23. We hope to see you there. a.. . .to, .. , 'l'vl ....zu~ ...... ,_ Andrew M. Gleason Chairman of the Steering Committtee, ICM-86 ~~~~1 ·Y~//0kif'/. Irving Ka~lansky President, American Mathematical Society Director, Mathematical Sciences Research Institute 612 an expansion of mathfile Your KEY to the RESEARCH LITERATURE in the MATHEMATICAL SCIENCES. MathSci is an expanded version of Mathfile. It contains, in addition to MATHEMATICAL REVIEWS, a current awareness subtile and two statistics subfiles with coverage back to 1902. MathSci brings you comprehensive coverage in MATHEMATICS AND STATISTICS and applications in: • COMPUTER SCIENCE • BIOLOGY • MECHANICS • ECONOMICS • PHYSICS • AGRICULTURE • ENGINEERING • PSYCHOLOGY • DIALOG: File 239 • BRS: MATH • ESA: File 80 Also available on evening end-user systems BRS/After Dark and Knowledge Index. For more information on MathSci and user aids, write: American Mathematical Society, P.O. Box 6248, Providence, Rl 02940 or call toll-free: Taissa Kusma 800-556-7774 Produced by the Amencan Mathematical Soc1ety 1n cooperat1on w1th the American Stat1St1cal Association and the lnst1tute of Mathematical Stat1st1cs. SAVE THIS PAGE :- ~~'\: te"lh- 1---Jv,£_ ~~;~ J See the Latest I G '\:\\\S Check your s£p selection Visit I NOW I 0 Applications of Algebraic K-Theory to I Algebraic Geometry and Number Theory, 0 The Joy of TE;X, by M. D. 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A.MS-TEX '!EXt. was designed to simplify the input of math This book is designed as a user's guide ematical material in particular, and to for to the A.MS-TEX macro package and details mat the output according to any of various many features of this extremely useful text preset style specifications. processing package. Parts 1 and 2, entitled There are two primary features of the "Starters" and "Main Courses," teach the 'lEX system: it is a computer system for reader how to typeset most normally en typesetting technical text, especially text countered text and mathematics. "Sauces containing a great deal of mathematics; and Pickles," the third section, treats more and it is a system for producing beautiful exotic problems and includes a 60-page dic text, comparable to the work of the finest tionary of special 'fEXniques. printers. Exercises sprinkled generously through Most importantly, 'lEX's capabilities are each chapter encourage the reader to sit not available only to '!EXperts. While down at a terminal and learn through ex mathematicians and experienced technical perimentation. Appendixes list summaries typists will find that 'lEX allows them to of frequently used and more esoteric sym specify mathematical formulas with greater bols as well as answers to the exercises. accuracy and still have great control over ,t,l-~\\EM~I'tc;t ISBN 0-8218-2999-8, LC 85-7506 PREPAYMENT REQUIRED. Order from .;cfi:;::W>~~ -:.\9, 290 pages, Due April 1986 American Mathematical Society ~v,~-\ .~ . ~ \ _ AMS Indiv.. Memb. $24, AMS Inst. PO Box 1571 ~I. • ; ; 2J Memb. $28, List price $32 Annex Station 1 "'-. ·• To order soecify JOYT / NA Providence, RI 02901-1571 "'ouNoED \'¢!' or call 800-556-7774 to use VISA or MasterCard. Shipping/Handling: 1st book $2, each add'! $1, max. $25; by air, 1st book $5, each add'! $3, max. $100 Washington Outlook Kenneth M. Hoffman Speaking to Congress interested in science and mathematics education. The testimony provides a thorough summary of The effort to present our needs to Congress, which the importance of quality mathematics educa began with Ed David's February testimony before tion. The testimony documents the efforts of the the Science, Research, and Technology Subcom mathematics community to strengthen mathemat mittee of the House Committee on Science and ics education through the Mathematical Sciences Technology (February 26, 1986), continued in Education Board. Also included were MAA's rec March and April when the Joint Policy Board for ommendations.to institute: (1) a summer training Mathematics (JPBM) was invited to testify before program for h1gh school students of exceptional five subcommittees: the Senate and House De mathematical ability; and (2) a faculty fellowship fense Appropriations Subcommittees, the Senate program for professional development of under and House BUD-Independent Agencies Appropri graduate mathematics faculty. The testimony also ations Subcommittees, and the Senate Labor and detailed the needs for increased funding in math Human Resources Committee. These subcommit ematics research. Effort was made to present a tees, along with two others whose agendas we federal funding profile by documenting that about were unable to penetrate this year, were chosen 94% of mathematics research funding comes from because t~ey have jurisdiction over funding for the DOD (40%) and the NSF (54%). This funding mathematics research or mathematics education. profile may help the Congress understand where Andrew M. Gleason of Harvard University action must be taken for funding increases as presented oral testimony on behalf of the JPBM recommended by the David Committee. before the four appropriations subcommittees. Gleason spoke from remarks prepared by Jennifer Written Testimony before the Senate LHR Vance, General Counsel for JPBM. Both written Committee. The Senate Labor and Human Re and oral te~timony varied in length, according ~o~rc~ ~LHR) Committee, which has authorizing to the reqmrements set by each subcommittee JUrisdictiOn over the NSF, had only one oral wit and were guided by the general congressional ness on the fiscal year 1987 authorization of the strategy Jennifer outlined in a recent article for NSF, Erich Bloch. The JPBM submitted written our community ("Congressional Strategy for the testimony to the LHR Committee that was similar Mathematical Community," June 1986 Notices, to the extensive documentation submitted to the pages 509-511). appropriation subcommittees, with one exception. Testimony for the House and Senate Defense The JPBM recommended that the Senate Appropriations Subcommittees, which provide Labor and Human Resources Committee hold funding . for the De~artment of Defense (DOD), joint hearings with the authorizing committee summarized the findmgs of the David Committee wit~ jurisdiction over the DOD to review joint ~ep?r~, particularly the funding imbalance among pohcy concerns for mathematics research funding. diSCiplmes and the likely impact of low levels of The oral testimony, as presented by Andrew support for mathematics research. G~eason, was visibly effective, usually ending Two recommendations were included in that with a relaxed, substantive interchange with the ~estimony: (1) that funding levels for mathemat subcommittee chairman. In just five words: he Ics research at the DOD be augmented; and (2) did a superb job. that the Congress request the DOD to report Through National Mathematics Awareness ~nnually on the nature of support for mathemat Week and this round of testimony, we have Ics res~ar:ch within each of the service agencies be~n to make friends on Capitol Hill, to develop and w1thm DARPA. The latter recommendation basic understanding of the varied important roles was J?ade to strengthen the ability of the math of mathematics, and to suggest how Congress ematics community to enhance the dialogue on can help us. Follow up work will now be mathematics research between the Congress and ?one to t~anslate understanding and suggestions the Executive Branch. mto tangible benefits, and planning is already Testimony before the House and Senate underway for next year's hearings. Part of BUD-Independent Agencies Appropriations Sub next year's strategy will be to make widespread c?mmittees, which provide funding for the Na use of contacts in home districts by the many tional Science Foundation {NSF), focused on both mathematicians who responded to our Combined ~athematics research and mathematics educa Membership List mailing and offered to help. tion. Both subcommittees have been extremely 617 News and Announcemen..,., Newly Elected Members country in North America. Fellowships may bf of the National Academy of Sciences held at any institution the Fellow selects or at more than one in succession. There is flexibility The following mathematical scientists have been in the choice of time interval(s) and manner in elected to membership in the U. S. National which the Fellow may draw funds. For instance, Academy of Sciences: Peter J. Bickel, University given the opportunity, a Fellow may elect to hold of California at Berkeley; Bradley Efron, Stanford a half-time academic appointment with a teaching University; Robert M. Solovay, University of responsibility not exceeding one course per term California at Berkeley; Shlomo Z. Sternberg, while holding the fellowship at one-half stipend Harvard University; and Karen K. Uhlenbeck, over a two-year period. The Fellow should consult University of Chicago. with the Secretary of the Society to learn whether the arrangement proposed is acceptable to the Mina Rees and Jacob T. Schwartz Society. Received New York City Award The number of fellowships to be awarded is small and depends on the amount of money Two mathematical scientists, Mina Rees and contributed to the program. The Trustees have Jacob T. Schwartz, were among the five recipients arranged a matching program from general funds of the second annual New York City Mayor's in such fashion that funds for at least one fellow Awards of Honor for Science and Technology. ship are guaranteed. In recent years, it has not The awards were presented by New York City been financially possible to award more than one Mayor Edward I. Koch on Wednesday, May 7, at fellowship. Gracie Mansion, the Mayor's official residence. A The deadline for receipt of applications is Commission for Science and Technology, estab December 1, 1986. Awards will be announced in lished by Mayor Koch in 1984 to encourage the February 1987, or earlier if possible. growth of scientific and technological activities in For application forms, write to William J. New York City, identifies and nominates individu LeVeque, Executive Director, American Mathe als for specific achievement or for a lifetime body matical Society, P.O. Box 6248, Providence, RI of work that benefits not only New Yorkers, but 02940. (It should be noted that completed appli the rest of the country and the world, in the bi cation and reference forms should NOT be sent ological, engineering, physical, mathematical and to this address, but to the address given on the medical sciences. forms.) Mina Rees is currently Emeritus Professor of Mathematics and President Emeritus of the Newly Elected Members of the AAAS Graduate School and University Center at the City University of New York. The following mathematical scientists were elected Jacob T. Schwartz is the Director of the to the American Academy of Arts and Sciences: Division of Computer Science at the Courant Raghu R. Bahadur, University of Chicago; Peter Institute of Mathematical Sciences, New York J. Bickel, University of California at Berkeley; University. Patrick P. Billingsley, University of Chicago; Luis A. Caffarelli, University of Chicago; John Cocke, T.J. Watson Research Center, International Busi AMS Research Fellowships ness Machines Corporation; Stephen A. Cook, Invitation for Applications, 1987-1988 University of Toronto; Daniel Z. Freedman, Mas Deadline December 1, 1986 sachusetts Institute of Technology; Ronald L. Graham, AT&T Bell Laboratories; Alan Manne, These fellowships are open to individuals five to Stanford University; Richard B. Melrose, Mas ten years past the Ph.D. degree (or equivalent), sachusetts Institute of Technology; and Hans F. regardless of age, but below the academic rank Weinberger, University of Minnesota. Jacques L. of professor. Applicants should have received Lions, College de France, was elected a foreign the Ph.D. degree between January 1, 1977, and honorary member. December 31, 1982. Moreover, the vita must include the equivalent of at least three full years Kenneth M. Hoffman to Receive postdoctoral teaching or industrial experience, JPBM Public Service Award i.e., non-fellowship years. The stipend has been set by the Trustees of The Joint Policy Board for Mathematics (JPBM) the Society at $30,000 for nine months of full-time has announced that it will present a Public Service research or its equivalent. In addition, there will Award to Kenneth M. Hoffman on July 24, 1986, be an expense allowance of $1,000. Applicants at the Society for Industrial and Applied Mathe must be citizens or permanent residents of a matics national meeting in Boston, Massachusetts. 618 The JPBM is a consulting committee comprised the formation of two newly established boards of representatives of the American Mathematical at the National Research Council: the Board on Society, the Mathematical Association of Amer Mathematical Sciences, and the Mathematical ica, and the Society for Industrial and Applied Sciences Education Board, and still serves on the Mathematics. executive committee of the latter. The award is being made to Hoffman for his "farsighted and effective initiation of the planning Oscar E. Lanford III and the implementation of a national mathemati Receives National Academy of Sciences cal sciences policy; for his contributions, through these efforts, to both mathematical sciences re Award in Applied Mathematics search and to mathematical sciences educational and Numerical Analysis communities in the United States; and for his Eleven awards honoring outstanding contributions energetic and successful pursuit of wide recogni to science were presented at a ceremony on Mon tion for the best of the mathematical sciences and day, April28, 1986, during the National Academy mathematical scientists." of Sciences' 123rd annual meeting. The National Hoffman, Professor of Mathematics and for Academy of Sciences Award in Applied Mathe mer head of the Department of Mathematics matics and Numerical Analysis was presented to at the Massachusetts Institute of Technology, is Oscar E. Lanford III, professor of physics, Institut well known for his mathematical research, hav des Hautes Etudes Scientifiques, and professor of ing made significant contributions to his field of mathematics, University of California at Berke specialization, function algebras, and has worked ley,· for "his profound and penetrating solution effectively as a university administrator. He has of outstanding problems of statistical mechanics". been a member of the M.I.T. faculty since 1959. This award was established in 1972 through funds Since 1981, he has been active at the interface provided by the International Business Machines of mathematics and public policy. From 1981 Corporation and is awarded every three years to 1984, he served as Executive Director of in recognition of outstanding work in applied the Committee on Resources of the National mathematics and numerical analysis. Research Council whose report, "Renewing U.S. Mathematics: Critical Resource for the Future" , documented a serious imbalance between federal Kovalevskaia Fund support for the mathematical sciences and support Travel Grant Awarded for related sciences. Also from 1981 to 1984, he was Chairman of the Committee on Science Policy Dr. Arlene Ash of the Health Care Research Unit of the AMS and in 1984-1985 was Chairman of the of Boston University Medical School has been Advisory Committee for Science and Engineering awarded the Kovalevskaia Fund Travel Grant to Education at the National Science Foundation. spend the month of January 1987 lecturing in Hoffman is currently the Director of Federal Vietnam. Dr. Ash is an expert in applications of Relations for the JPBM, providing the liaison for statistics to biology and medicine. the three organizations with various government The terms of the grant provide $2,000 for agencies and Congress. He has been active in travel and expenses from the Kovalevskaia Fund. In addition, all hotel accommodations, meals, and transportation within Vietnam will be paid News from the Mathematical for by the Hanoi Mathematical Institute, which originally requested a visiting scholar in applied Sciences Institute mathematics or statistics. The grant is part of Cornell University the ongoing activities of the Kovalevskaia Fund The Mathematical Sciences Institute, sponsored to encourage women in science in developing by the U.S. Army, announces a Workshop on countries. Sequential Experimentation to be held October 22-23, 1986. The objective of the workshop is Peter L. Renz to create a cross-fertilization of problem formu New MAA Associate Director lation and research effort by bringing together medical and industrial statisticians. Partici Peter L. Renz of Bard College has been named pants include D. L. DeMets, T. R. Fleming, A. the new Associate Director of the Mathemati B. Hoadley, C. Jennison, G. Lan, T. A. Louis, J. cal Association of America (MAA). He replaces Schmee, R. L. Smith, J. R. Whitehead, C.F.J. Marcia P. Sward, who is on leave to head the Wu, and S. Zacks. The Organizing Committee newly formed Mathematical Sciences Education consists of R. E. Bechhofer, T. J. Santner, B. Board. In addition, Dr. Renz has been appointed W. Turnbull, and L. I. Weiss, School of Op Administrative Officer for the Conference Board erations Research and Industrial Engineering, of the Mathematical Sciences (CBMS), a position Cornell University, Ithaca, NY 14853. which was also held by Dr. Sward. During the period January-June 1986, Andrew Sterrett filled 619 ICIAM '87 Institute for Mathematics For the first time, the applied mathematics so and its Applications cieties of four countries are co-organizing an Minneapolis international conference. The first International Conference on Industrial and Applied Mathemat Avner Friedman has agreed to become the sec ics will be held from June 29 to July 3, 1987, in ond Director of the Institute for Mathematics Paris, France. The conference is being organized and its Applications (IMA) at the University of by the Gesellschaft fiir Angewandte Mathematik Minnesota. He will assume his duties in the und Mechanik (BRD), the Institute of Mathe early summer of 1987. Professor Friedman is matics and its Applications (UK), the Institut an expert on partial differential equations, dif National de Recherche en Informatique et en ferential games, and distributed control theory. Automatique (France), the Society for Industrial He will replace Hans Weinberger, the present and Applied Mathematics (USA), and the host director. Willard Miller will replace George Sell society, the Societe de Mathematiques Appliquees as Associate Director of the IMA in January of et Industrielles (France). 1987. The program of the conference will include The 1986-1987 IMA program on Scientific invited presentations, contributed paper sessions, Computation will begin on August 18 with an poster presentations, minisymposia, and computer opening workshop on Basic Methods of Numer software and hardware exhibits. The topics will ical Analysis and Introduction to State-of-the include applied mathematical analysis, scientific Art Research. This program is being organized computing, control theory and signal processing, by Bjorn Engquist, Roland Glowinski, Mitchell discrete mathematics, applied probability and Luskin, and Andrew Majda. statistics, mathematics of natural sciences, and The fall part of the program will be de software and hardware aspects. voted to Computational Fluid Dynamics and For further information contact: SIAM Related Topics. Highlights will include a work Society for Industrial and Applied Mathematics, shop on Computational Fluid Dynamics and 14th Floor, 117 South 17th Street, Philadelphia, Reacting Gas Flows from September 15-26, a PA 19103-5052, USA (Telephone: 215-564-2929); November workshop on Numerical Algorithms or INRIA-Service des Relations Exterieures, Bu for Modern Parallel Computer Architectures reau des Colloques, Domaine de Voluceau, BP organized by Martin Schultz, and a Decem 105, 78153 Le Chesnay Cedex, France (Telephone: ber mini-symposium on Numerical Simulation 33.1 39.63.56.00, telex: 697 033 F). in Oil Recovery organized by Mary Wheeler. All proposals (contributed papers, posters, Nineteen postdoctoral and senior members, in minisymposia) should be submitted on a stan cluding Jim Douglas, Jr., and Bjorn Engquist, dard form which may be obtained from INRIA, will be in residence during the fall term. Others or from SIAM for North American participants. will visit for shorter periods of time. Deadline dates are October 31, 1986 for min Plans for the 1987-1988 program on Ap isymposia proposals and November 28, 1986 for plied Combinatorics are well under way. As contributed papers and poster presentations. in other years, there will be some support available for postdoctoral fellows and other long-term visitors. Reciprocity Agreement with Sociedad Colombiana de Matematicas the MAA position on an acting basis and Louise Raphael filled the CBMS position, also on an The American Mathematical Society and the acting basis. Sociedad Colombiana de Matematicas, Colombia, Renz, who received his Ph.D. from the Uni have recently concluded a "reciprocity agreement" versity of Washington, served on the mathematics under which members of either of these societies faculties first at Reed College and then at Welles may join the other at reduced dues. Members of ley College during the period 1968-1973. He was the Sociedad Colombiana de Matematicas receive Mathematics Editor with W. H. Freeman from as privileges of membership a free subscription 1974-1984. From 1984-1986, he was head of to either Revista Colombiana de Matematicas or the department of mathematics at Bard College. Lecturas Matematicas. During this period he continued as a consulting See the section entitled Reciprocity Agree editor for Scientific American Books. ments in this issue of Notices for further details. 620 Microlocal Analysis Ill. Nonlinear problems M. Salah Baouendi. Richard Beals. and S. Alinhac and G. Metivier. Propagation of analyticity Linda Preiss Rothschild. Editors for solutions of nonlinear partial differential equations This volume is the proceedings of the M. Beals. Nonlinear wave equations with data singular AMS-IMS-SIAM Joint Summer Research Conference at one point on Microlocal Analysis and its Applications to Partial P. Godin. Nonlinear oblique derivative problems with Differential Equations. held July 1Q-16. 1983 in nonsmooth solutions Boulder. Colorado. It contains refereed articles which J. Rauch and M. Reed. Ray-like solutions of were delivered at the conference. Two of the papers semilinear wave equations are survey articles. one on uniqueness and non-uniqueness in the Cauchy problem and one on IV. Asymptotlcs hypoanalytic structures; the rest are either detailed V. lvrii. Global and partially global operators. announcements or complete papers covering such Propagation of singularities and spectral areas as spectrum of operators. nonlinear problems. asymptotics asymptotics. pseudodifferential operators of multiple R. Melrose. The trace of the wave group characteristics and operators on groups and M. Taylor. Airy operator calculus homogeneous spaces. V. Pseudodlfferentlal operators of The volume should be useful to active multiple characteristics mathematicians and graduate students working on G. Mendoza. A necessary condition for solvability for linear and nonlinear partial differential equations and a class of operators with involutive double related areas. characteristics 1. Survey articles J. Nourrigat. Approximation of systems of S. Alinhac. Uniqueness and non-uniqueness in the pseudodifferential operators Cauchy problem VI. Operators on groups and F. Treves. Hypo-analytic structures homogeneous spaces II. Spectrum of operators D. Geller. Toward analytic pseudodifferential G. Eskin. J. Ralston and N. Trubowitz. The operators for the Heisenberg group multidimensional inverse spectral problem with a K. Miller. Microhypoellipticity on step two nilpotent periodic potential Lie groups D. Jerison and J. Lee. A subelliptic. nonlinear A. Unterberger. Symbolic calculi and the duality of eigenvalue problem and scalar curvature on CR homogeneous spaces manifolds 1980 Mathematics Subject N. Stanton and D. Tartakoff. The heat equation for Classification: 35-xx Contemporary Mathematics Db Volume 27, viii + 256 pages (soft cover) List price $26, institutional member $21, individual member $16 ISBN 0-8218-5031-8; LC 84-2852 Publication date: April 1984 To order, please specify CONM/27N 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 Combined Membership List Shipping and Handling Charge As a privilege of membership, individual members of the Society are entitled to receive a free copy of the Combined Membership List ( CML) in even-numbered years. While the CML is free, the Society can no longer absorb the cost of shipping it to members. If you wish to receive the 1986-1987 CML when it is published, kindly remit $2 before September 19, 1986. If you want to include this charge with your dues payment, please indicate this clearly when paying your bill. 621 National Science Foundation News 8 Reports Postdoctoral Research Fellowships Florida State University (Florida); University of Alabama at Birmingham (Alabama); Louisiana NSF Postdoctoral Research Fellowships in the State University (Louisiana); University of Ten mathematical sciences will be offered only to nessee (Tennessee); University of Kentucky (Ken persons who 1. are U.S. citizens or nationals as tucky); and West Virginia University (West Vir of January 1, 1987; 2. will have earned by the ginia). doctoral beginning of their fellowship tenure a The network's goal is to provide productive sciences; 3. degree in one of the mathematical and collaborative electronic communications tools no more than will have held the doctorate for to American scientists and engineers. The key five years as of January 1, 1987; and 4. will not impetus for the network is to provide access to postdoctoral previously have held any other NSF the NSF's five new supercomputer centers. fellowship. The Office of Advanced Scientific Computing For copies of the application brochure or ( OASC) is endorsing the regional network concept Special Projects further information, contact the by funding SURAnet and other regional network Division of Mathematical Sciences, Na Program, proposals. Dr. Connolly said the OASC encour Science Foundation, Washington, D.C. tional ages the submission of proposals for the formation Mathe 20550, (202)357-9764; or the American of additional regional networks. matical Society at (401 )272-9500. The University of Maryland will provide tech The deadline for applications is November nical services for SURAnet under subcontract to 15, 1986. SURA. Maryland already has gained considerable experience by operating its own campus-based Supercomputer Access Gained by NSF high speed data network. The state of Maryland intends to capitalize on this expertise by establish Twelve states in the southeastern United States ing a state-wide fiber optics telecommunications and the District of Columbia will gain access network under a new telecommunications master to NSF supercomputers through a new regional plan approved by its state legislature this spring. network. The NSF announced the award of more Other SURA members are expected to pro than $1.4 million to the Southeastern Universities pose or fund connections to SURAnet in the Research Association (SURA) for construction coming year. Because SURAnet provides a con and operation of SURAnet, the first component nection point in each state, additional links will regional network of NSFnet, a national scientific be proportionally less expensive than the initial network being established by the Foundation. The interstate SURA links. network will use medium speed (56,000 bits SURA For more information, contact Southeastern to link one per second) telecommunications lines Universities Research Association at (703)841- leading academic institutions in each state of the 2694, or NSF's Acting Program Manager for SURA has member institutions. where Networking, Dan VanBelleghem at (202)357-9776. John Connolly, Director of the Office of - NSF News Release Advanced Scientific Computing, said that SURA is taking responsibility for implementing NSFnet in the southeastern United States. Likewise, Proposals Sought for 1987 and 1988 each institution in SURAnet will coordinate the Regional Conference Series linking of other institutions in its own state. The in Mathematical Sciences individual institutions are responsible for linking their own scientists and engineers. The National Science Foundation is seeking pro In addition to the SURAnet point-of-presence posals from host institutions in the U.S. for in each state, other schools will be connected five-day regional conferences. Each conference through their own lines to SURAnet and NSFnet. is to feature a distinguished lecturer who will The institutions and states taking initial deliver ten lectures on a subject of current re responsibility for SURAnet are: University of search interest in the mathematical sciences. It is Delaware (Delaware); University of Maryland expected that the lecturer will give two lectures (Maryland); George Washington University (Dis per day during the five days, with the remaining trict of Columbia); Virginia Polytechnic Univer time available for study, informal discussion, and sity (Virginia); Triangle Universities Computing exchange of ideas. Center (North Carolina), including Duke, North All applying institutions having at least some Carolina State, and the University of North Car research competence in the area of its proposal are olina; Clemson University (South Carolina); Uni eligible and encouraged to apply. The conference versity of Georgia and Georgia Tech (Georgia); should be planned for a summer week in 1987 622 (not earlier than May 1) or held during a recess He assumed the Chairmanship of the Commit in the succeeding academic year. The host tee on Science and Technology in 1979 upon the institution is responsible for arranging conference retirement of Congressman Olin E. Teague of details, hotels, and social events during the five Texas. -NSF News Release day conference. Participants in the conference will receive allowances for travel and subsistence under the host institution's grant from the NSF. Visiting Professorships for Women The principal lecturer receives from the The Visiting Professorships for Women program Conference Board of the Mathematical Sciences was instituted to provide opportunities for women (CBMS) a fee for delivering his/her lectures and to advance their careers in the disciplines of a second fee for organizing these lectures into a science and engineering and to provide greater substantial expository monograph which will be visibility and wider opportunities for women sci submitted to the NSF for approval and published entists and engineers employed in industry, gov by one of three organizations: the American ernment and academic institutions. In providing Mathematical Society, the Society for Industrial support for the program, NSF is addressing the and Applied Mathematics, or in conjunction, the need to make full use of the scientific and technical American Statistical Association and the Institute resources of the nation. of Mathematical Statistics. Proposals will compete for awards on the Proposals (twenty copies) by prospective in basis of the scientific merit of the proposed re stitutions should be sent directly to the Data search and a specific plan for lecturing, mentoring Support Service Section, National Science Foun and counseling activities. The deadline for ap dation, 1800 G Street, N.W., Washington, D.C. plications is October 1, 1986, with a scheduled 20550. Proposals must follow the guidelines issued announcement of awards April 15, 1987. For fur by CBMS. Deadlines for 1987 and 1988 confer ther information about guidelines and eligibility ences are September 1, 1986, and April 1, 1987, requirements, write to the Visiting Professorships respectively. for Women Program, National Science Founda Please address all inquiries and requests for tion, Washington, D.C. 20550. information sheet/guidelines to Conference Board of the Mathematical Sciences, 1529 18th Street, N.W., Washington, D.C. 20036. Telephone: Positions Open in NSF (202)293-1170. NSF's Division of Mathematical Sciences is seek ing qualified applicants for positions which pe Fuqua Receives riodically become available. Incumbents will be NSF Distinguished responsible for the planning, coordination, and Service Award management of basic research activities primarily Representative Don Fuqua, Chairman of the through Federal grants and contracts to academic House Committee on Science and Technology, has institutions and nonprofit, nonacademic research received the Distinguished Public Service Award institutions. A broad, general knowledge of of the National Science Foundation. the field and some administrative experience are The award is given periodically to persons required. For technical information about the who have distinguished themselves through their position, contact Dr. John C. Polking, Direc leadership, public service, and dedication in sup tor, Division of Mathematical Sciences, National port of American science and engineering and Science Foundation. Telephone: (202)357-9669. science and engineering education. The award, the highest honor conferred by the NSF on persons NSF FY 1987 Proposals for not employed by the Foundation, includes a gold medal and a citation. Scientific Research Project Support Presentation of the award was made at a Each year the Divison of Mathematical Sciences dinner sponsored by the National Science Board (DMS) receives about 1,200 proposals for research (NSB) on May 14 at the Department of State. The project support to be reviewed in accordance NSB is the policymaking body of the NSF. The with standard procedures. In the past, most of presentation was made in conjunction with the those proposals have been received in October second annual National Science Week which was or November for decisions in May and June. sponsored May 11-17 by the NSF to emphasize The Foundation is committed to the expeditious the importance of science to our national life. handling of all proposals, and is moving toward a From his earliest days in Congress, Mr. Fuqua processing time of six months for most proposals. was a member of the subcommittee overseeing the With this in mind, DMS is eliminating formal U. S. space program and served continuously as deadlines for submission of proposals for research Chairman of the Subcommittee on Space Science project support. Proposers should consider two and Applications from 1971 until 1981. He has things in timing their submissions: 1. the date served since 1981 as Chairman of the Subcom by which they wish to know whether an award mittee on Energy Development and Applications. is being made (that should be listed as the 623 requested start date); and 2. the likelihood that their research program might be jointly funded by DMS and some other division or agency. In Complex general, proposals should be received by the contour integral representation Foundation no less than six months prior to the requested start date. If there is any likelihood of cardinal spline functions of joint funding, more time should be allowed Walter Schempp as there might be a two-stage decision-making process that would extend the time needed for consideration. This book contains a very comprehensive Finally, on the subject of start dates, it has treatment of most of the author's original been the custom for most proposers to request results in the theory of complex integral as a start date the day on which they want to representation of cardinal spline functions. start receiving summer salary. In fact, any start The basic idea of the book is to use a suitable date which is convenient to the proposer can inverse integral transform instead of the direct be requested. For example, if graduate student transform itself and then to have recourse support is requested on a proposal, it would to the methods of complex analysis applied certainly be convenient to know whether it was to cardinal exponential splines and cardinal awarded sometime in early Spring. Therefore, a logarithmic splines. The method of complex start date of March 1 would be appropriate. If academic year support for a postdoctoral associate contour integral representation yields a unified is being requested, similar reasoning could lead to treatment of both cases. Besides presenting a requested start date of January 1. an outline of inverse integral transform technique. the book investigates several Advisory Panel Meeting related topics. These include: (1) various complex integral representations of the basis The Advisory Comittee for the Mathematical spline functions. (2) a useful complex contour Sciences will meet at the National Science Foun integral representation of the Euler-Frobenius dation on October 1-3, 1986. The Committee's polynomials and its consequences. and advice is very important to the Division in set (3) the classical Meray-Runge phenomenon. ting priorities and developing long-range plans. This approach to cardinal spline functions The mathematical community is welcome to at tend public portions of the meeting or to suggest provides a very instructive illustration of topics for discussion by contacting the Division the application of inverse integral transform administration at (202}357-9764. Chair of this techniques combined with complex variable year's committee is Professor D. J. Lewis of the methods to recent problems arising in University of Michigan. approximation theory. Each section of the book ends with a few references Computing Research Equipment and comments. In the reviewer's for the Mathematical Sciences opinion. this book will be very useful to a broad audience. interested in present The Division of Mathematical Sciences of the Na developments of approximation theory. tional Science Foundation plans a limited number of grants for the purchase of scientific computing In the reviewer's opinion. this book will be equipment for research in the mathematical sci very useful to a broad audience. interested ences. Eligible institutions include U.S. graduate in present developments of approximation degree granting institutions with departments or theory. - Gheorghe Micula (Ciuj-Napoca) research programs in mathematics, applied math MR85c:41020 ematics, or statistics. Character of equipment Contemporary Mathematics, Volume 7, 1983, xiii + 109 requested should be such that it is required by pages ( softcover) List price $11, Institutional member $9, Individual more than one research project and difficult to member $7. To order, please specify CONM/7N justify for a single project. Minimal cost should be $20,000. Significant cost-sharing on the part of Shipping/Handling: tat book 12, each edd'l 11, 125 the institution is expected. Deadline for propos max. By elr, 1at book 15, each edd'l 13, 1100 max. als is Deeember 1, 1986. For further information, Prepayment required. Order from AMS, P.O. Box 1571, Annex Station, Providence, Rl 02901-1571. contact the Special Projects Program, Division Cell 800-556-7774 to uee VISA or MasterCard. of Mathematical Sciences, National Science Foun dation, Washington, D.C. 20550. Telephone: (202}357-9764. 624 News from Washington Graham Chosen as The qualities which are being sought at each President Reagan's Science Adviser stage are a high level of achievement early in one's chosen career or profession, a demonstration of President Reagan has chosen William R. Gra leadership capability, an assemblage of skills that ham, the deputy administrator of the National would make one a good special assistant in the Aeronautics and Space Administration, to be his short term and a national leader in the long term, new science adviser. George A. Keyworth II, and substantial indication of a commitment to the former science adviser, resigned at the end of service to others in the community in which one 1985. The position has been filled on an acting has lived. basis since then. Individuals should apply directly. Appli William Graham chaired President Reagan's cation materials and additional information are General Advisory Committee on Arms Control readily obtainable by contacting the President's and Disarmament for three years. He has also Commission on White House Fellowships, 712 served on other national and international ad Jackson Place, N.W., Washington, D.C. 20503. visory groups on nuclear weapons and was a Telephone: (202)395-4522. Applications are ac member of the President's transition team after cepted during the fall of each year; the submission the 1980 election. He has worked in the Rand Cor deadline is November 15. poration's Physics Department and as a project officer at the U.S. Air Force Weapons Laboratory These fellowships may be an excellent oppor in Albuquerque, New Mexico. He is a graduate of tunity for the mathematical community to become the California Institute of Technology and has a more involved in the administrative branch of the doctorate in electrical engineering from Stanford government. University. White House Fellowships NRC Establishes a Computer Science and Technology Board The White House Fellowship is a highly com petitive opportunity to participate in and learn U.S. leadership in computer research and manu about the Federal Government from a unique facturing has been seriously eroded. The National perspective. For one year, thirteen to twenty per Research Council (NRC) has established a Com sons chosen as White House Fellows are full-time puter Science and Technology Board to advise Schedule A employees of the Federal Government, federal agencies and private firms on ways to working in a Cabinet-level agency, in the Exec strengthen U.S. international competitiveness in utive Office of the President, or with the Vice this field and to ensure that the full promise President. Rather than fit the fellows to their of this area is realized. The eighteen-member prefellowship specialties, the program aims at board includes national leaders from industry and utilizing their abilities and developing their skills universities. The NRC is the principal operating in the broadest sense possible. In most cases, agency of the National Academy of Sciences and a fellow serves as a special assistant, performing the National Academy of Engineering. tasks for a cabinet secretary, the Vice President, "The board's first job is to identify the most an assistant to the President, or for appropriate important national issues relevant to computer sci under or deputy secretaries. In this sense, the ence and technology, and then form strategies for White House Fellow's year is a high-level intern dealing with them," said Board Chairman Joseph ship in government. An education program, which F. Traub of Columbia University. "Computing complements the full-time work assignment, gives drives all other technologies, and its continued fellows the opportunity to meet as a group with good health is essential to the basic sciences as top-level government officials and private sector well as industry, commerce, and the national leaders for off-the-record discussions. defense." Based on the results of regional interviews, As part of its first meeting, held May 7 and thirty-three candidates are selected to meet with 8 in Washington, D.C., the board heard senior members of the President's Commission for three federal officials give their views of the critical days of interviews in Washington, D.C. The Com national issues in the field. These officials in mission then recommends to the President those cluded Congressman Don Fuqua, Chairman, U.S. individuals whom it finds to be most qualified for House of Representatives Committee on Science significant work experiences at a high level in a and Technology; John McTague, then Acting Sci Cabinet agency, the Executive Office of the Pres ence Advisor to President Reagan; Gordon Bell, ident, or with the Vice President. Appointments Director, Computer and Information Science and are for one year, beginning on September 1 and Engineering, National Science Foundation; Robert concluding August 31 of the following year. C. Duncan, Director, Defense Advanced Research 625 Projects Agency; and Alvin Trivelpiece, Director One of the highlights of National Science of Research, U.S. Department of Energy. Week was a public conference on the theme Initial topics identified by the board for "Mathematics: The Unifying Thread in Science" study include: competitiveness, talent, scope and on May 12 at the National Academy of Sciences. support, supercomputers, software, and infras The conference was sponsored by the National tructure. Reseach Council's Board on Mathematical Sci Funding for the board's activities will be ences. Presentations, illustrating the essential sought from federal and private sources. role that mathematics played in their scientific -NRC News Release achievements, were made by three Nobel laure ates: Allan M. Cormack (Nobel Prize in medicine, 1979), Herbert Hauptman (Nobel Prize in chem CBMS Committee istry, 1985), and Steven Weinberg (Nobel Prize in physics, 1979). The program opened with remarks The Conference Board of the Mathematical Sci by Phillip A. Griffiths, Chairman of the Board ences (CBMS), a consortium of mathematics or on Mathematical Sciences, and was moderated by ganizations including the American Mathematical Isadore M. Singer, John D. MacArthur Professor Society, has appointed a "Committee on American of Mathematics at M.I.T. Graduate Mathematics Enrollment" comprised of were followed by a ques Joe Kohn, Betty Lichtenberg, Willard Miller, Paul These presentations Sally, and Barry Simon (Chairman). The charge tion and answer period which focused on the importance of mathematics gain to this Committee includes: reasons for the ing greater exposure in the public eye and the Whereas, there has been a great deal of methods by which this could be accomplished. discussion on the lack of U.S. citizens in The program continued with a reception for the our graduate programs and the impact approximately 250 participants and concluded of this on our future research programs, with a dinner at which Robert McTague, then technology, and education. The charge Acting Science Advisor to the President, reiter to the committee is to: ated the theme that mathematics is a discipline which has made significant contributions to the 1. obtain concrete facts and, if need be, scientific well-being of this country. anecdotal data, on graduate enrollments It is notable that the mathematical commu for the mathematical sciences; and, if nity, over the last few years, has organized itself possible, compare them with enrollments to the point where it can contribute to an event, in other scientific fields; such as National Science Week, by organizing a 2. present the mathematical commu major program which highlights the importance of nity's perception of this problem; mathematics and its relevance to other disciplines. 3. explore the significance of this data for the future of American mathematics and sciences; and consequently on research 1986 National Chairmen's Colloquium technology, defense and education; The 1986 National Chairmen's Colloquium will 4. make recommendations to the math be held in Washington on October 10 and 11. ematical community and the country on This year, the Saturday meeting on federal and how to encourage our talented Amer science policy issues will be preceded by a half ican youth to pursue a career in the day meeting with three parallel programs. The mathematical sciences. Friday afternoon focuses will be on computational mathematics programs, mathematics education The Committee solicits comments from mem programs, and a session for chairmen or represen bers of the mathematical community. They may tatives of statistical science departments. Friday be addressed to: Professor Barry Simon, CBMS evening will feature a dinner speaker and discus Committee on American Graduate Mathematics sion. As last year, there will be opportunities for Enrollment, Mathematics Department, 253-37, informal discussions with all federal mathematical California Institute of Technology, Pasadena, CA agency personnel. In addition, an opportunity for 91125. To be most useful to the Committee, your regional interaction will be attempted. The em comments should arrive before December 1, 1986. phasis of this meeting is on federal mathematical agency programs and federal policies relating to National Science Week mathematical science departments. This annual meeting facilitates the inter National Science Week was initiated by the Na change of information between mathematical sci tional Science Foundation in 1985 to increase pub ences, department chairmen, and federal agency lic awareness and understanding of science and personnel. Past meetings have been highly suc technology and to encourage students to consider cessful not only in strengthening federal university careers in science and mathematics. National relations, but also in promoting greater commu Science Week 1986 was May 11-17. nication between chairmen. 626 For further information, or if you have any develop new studies and respond to re comments or suggestions, please contact Dr. quests for studies from federal agencies; Frank L. Gilfeather, Staff Director, Board on Mathematical Sciences, National Academy of Sci assure prompt and effective response to ences, 2101 Constitution Avenue, N.W., Wash problems relevant to the basic knowledge ington, DC 20418, (202)334-2421. and capabilities of the mathematical sci ences; Board on Mathematical Sciences insure representation and participation of the mathematical sciences in inter The National Research Council (NRC) established national programs and research projects the Board (?P Mathematical Sciences (BOMS) in through maintenance of a strong U.S. December 1983 to oversee activities formerly con National Committee; ducted by the Office of Mathematics and the Committee on Applied and Theoretical Statis maintain awareness of developments in tics (CATS). BOMS, chaired by Phillip Griffiths, the mathematical sciences and their in consists of eleven members. BOMS has three disci terfaces with other disciplines; pline standing committees: The Committee on Ap maintain a liaison with the mathemati plied and Theoretical Statistics (CATS), chaired cal sciences communities and academia, by Ron Pyke; the Committee on Mathematics government agencies and laboratories, (COM), chaired by Joe Kohn; and the Committee on Applications of Mathematics (CAM), chaired industry, and appropriate professional societies; by Jim Infante. Additional panels and committees carry out various projects. Frank Gilfeather is the recommend, upon request, individuals Staff Director and is assisted by Meg Knemeyer knowledgeable in various mathematical and Seymour Selig. sciences areas to participate in NRC In 1985, a group of state-of-the-art reviews studies. was initiated by the NRC at the request of the National Science Foundation (NSF). The purpose Currently, BOMS is preparing a proposal of these reviews is to assess and monitor world for a series of expository reports in the area of trends, relative strengths, and competitiveness cross-disciplinary research opportunities and fo of the United States in rapidly evolving areas cused state-of-the-art reports in mathematics and of science and technology. Three study areas, statistics. The David report based its arguments cell biology, pure and applied mathematics, and for enhanced federal funding in mathematical sci materials science, were chosen for review. The ences on the necessity that mathematics gain study on mathematics was conducted by the Panel parity with other disciplines. To significantly on Mathematical Sciences under the auspices of increase funding, federal agencies must also make BOMS. The Panel has described major trends in arguments primarily on sound scientific grounds. mathematics in a report, Mathematical Sciences: With the healthy and intense research activity A Unifying and Dynamic Resource. (See the in mathematical sciences, this can be done and June 1986 issue of Notices.) Another report, these studies will aid that process by produc Survey of U.S. Mathematics, is in final preparation ing outlines of areas that are ripe for enhanced and should appear in 1986. This document is funding. The reports to be issued will not make directed at the ICEMAP agencies and reports specific recommendations, but will instead de on recent excitement in mathematical sciences scribe the opportunities and potential inherent in research. Already, early versions have been useful the ctoss-disciplinary areas under study. in highlighting areas of increasing interest and hopefully will serve a useful purpose both to the BOMS hopes to establish a panel for the agencies and to the community. evaluation of the federal role in graduate and The program of BOMS is designed primarily postdoctorate education. The panel's purpose to undertake studies involving pure mathemat will b.e to determine the impact of the increased ics, applied mathematics, and statistics, and to federal role in the support of graduate students maintain an active presence at the NRC for the and postdoctoral researchers on U.S. mathemati mathematical sciences. More specifically, the cal sciences. The panel will address issues includ functions of BOMS and its committees are to: ing: the impact of the NSF Mathematical Sciences Postdoctoral Research Fellowship Program on the serve as the focal point in the NRC mathematical community; the effect of an in for issues connected with the mathe crease in federally funded research assistantships matical sciences and provide support for on Ph.D. production in the mathematical sciences; related NRC efforts, especially in com an analysis of the factors involved in the recruit puter science and mathematical sciences ment of graduate students; and the distinction education; between undergraduate background and student identify new and critical issues in the interest in and motivation to pursue education in field; mathematics at all types of institutions. 627 Travel Grants for ICM-86 Awarded University), Atul Jain (Univ:rsi~y of Illinoi~, Urbana-Champaign), Rong-Hm J1 (State Um The U.S. National Committee for Mathematics versity of New York, Stony Brook), John Laffer~y (USNCM) has announced that it has offered travel (Princeton University), Mark. L~e (Vanderbilt awards of approximately $500 each to sixty-one University), William Lang (Umvers1ty of Oregon), new Ph.D.'s to attend ICM-86. The funding Tzong-Yow Lee (New York University, Courant for these awards was provided by the National Institute), Lieh-San Lin (University of Illinois, Science Foundation. The awards will give these Chicago), Juan Manfredi (Washington Univ~r young mathematicians a unique ?pportunity. to sity), Gordano Matio (University of Utah),_ Tim interact with the world mathematics commumty. McLarnan (University of California, San Diego), Dr. Mary Ellen Rudin, chairperson of the USNCM, Dezso Miklos (Ohio State University), Michael J. said that these awards, in addition, demonstrate Monsour (University of Maryland), John Moody the commitment on the part of federal agencies (Columbia University), Monica ~icol~u (Rutgers to encourage young people in mathematics. University), Steven S. Noble (Umvers1ty o~ W~h The awardees are: John Anderson (Brown ington), Thomas Pascal (University of ~ahf?rma, University), Amer Beslagic (University of Wis Los Angeles), Paul F. Ringseth (Umvers1ty. of consin, Madison), Frederic Bien (Massachuset~s Washington), Margaret Robinson (Johns Hopkms Institute of Technology), Ye Yang Bo (Columbia University), James Rulla (University of. Tex~, University), Gregory Call (Harvard University), Austin), Brian H. Sako (University of ~al1f?rma, David T. Calvis (University of Michigan), Sheldo!l Los Angeles), Ji-Ping Sha (State Umvers1t! of Chang (Princeton Universi~y), L.~K. Chen (Un~ New York, Stony Brook), Mike Shelley (Umver versity of Chicago), Young-Ju Chme (Temple Um sity of Arizona), Richard A. Smith (Iowa ~tate versity), Shang-Ching Chou_(Un~versity of.Tex~, University), Folkert Tangerman (Boston. Un~ver Austin) Bennet Chow (Umvers1ty of Cahforma, sity), Jeremy Te_ite~baum (Harva:d l!mvers~ty), San Di~go), Brad Currey (Purdue University), Brian Thelen (Michigan State Umvers1ty), Lmda Bruce Driver (Cornell University), Lisa Fauci C. Thiel (Drexel University), Chris Tiah~t (C?l (New York University, Co~ran~ Institute), Ma:k orado State University), Aysenur Unal (Umvers1ty Feldman (Washington Umvers1ty), Manos Gril of Michigan), Carlos Videla (Rutgers University), lakis (Brown University), Daniel Gr~bb (Kans~ Masaaki Wada (Columbia University), Yar-Yi State University), Douglas P. Hardm (Georgia Wang (University of Massachusetts, Amherst), Institute of Technology), Peter Heller (Princeton Xiaolu Wang (University of Chicago), Howard N. University), Alex Himonas (Purdue University), Weiss (University of Maryland), Chi-Ming Yau Chi Fai Ho (California Institute. of Technology)~ (University of California, Los Angeles), Zhen_g Kevin Hockett (Cornell University), Steven Hm Fang Zhou (New York University, Courant Insti (University of Washington), Pedro Isaza (Syra tute). cuse University), Kenshi Ishiguro (Wayne State Ordered Fields and Real Algebraic Geometry D. W. Dubois and T. Recio, Editors 'The book's most significant contribution is its breadth. It encompasses the e~tire spectr_u~ of present research in ordered fields and real algebraic geometry. The field is very act;ve. and th1s IS the first attempt at such a comprehensive coverage." - W. Vogel (Halle) Periodica Mathematica Hungarica. V. 15(2) 1984 Contemporary Mathematics, Volume 8, 1982, 368 pages (softcover) . List price $22, Institutional member $18, Individual member $13. To order, please spec1fy CONM/8N Shipping/Handling: 1st book 12, each add'l 11, max. 125; by air, 1st book 15, each add'l 13, max. 11~ I Prepayment required. Order from American Mathematical Society, P.O. Box 1571, Annex tat on Providence, Rl 02901-1571, or call toll free 800-556-7774 to charge with VISA or MasterCard 628 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 Responses 356. Albert A. Mullin (506 Seaborn Drive, Hunts The editors would like to thank all those who sent ville, Alabama 35806). Consider a plane rectangle in replies. divided into N unequal squares in which all N 238. (vol. 28, p. 255, April 1981, John Thorne) of the squares have integer length sides (a perfect Applications of mathematics to law. (See earlier squared rectangle of order N in the sense of R. L. reply, vol. 28, p. 512, October 1981.) Reply: There Brooks, C. A. B. Smith, A. H. Stone, and W. T. are of course applications of statistics to law. A Thtte, The dissection of rectangles into squares, list of a number of such items is available from Duke Math. J. 7 (1940), 312-340). (1) What is the AMS office. (Contributed by J. S. Weber) the status of perfect squared rectangles? (2) Does there exist a perfect squared rectangle such that 341. (vol. 32, p. 608, October 1985, A. A. Mullin) the lengths of the sides of all squares involved Distribution of highly composite numbers. Reply: form an arithmetic progression? (3) Prove or A few papers about highly composite numbers disprove that for a squared square the number of have been published by P. Erdos, and myself, squares with prime-number-length sides divided after the first one of Ramanujan. by the order never exceeds ! . [There exists (a) There does not seem to exist a simple a perfect 4 7 x 65 squared rectangle of order 10 rule to determine the gap between two consecutive with 6 prime-side squares.] Did Alan Turing ever highly composite numbers. Actually, with nk the express an interest in squared rectangles? kth such number, we don't know whether 357. Francis D. Lonergan (8 Spring Street, Web ster, Massachusetts 01570). Is it known for which integers m, n with m 2: n 2: 1 the group pre sentations G( m, n) = (x, y: xmynx-my-n = 1) holds for some constant c and k > ko. However, a are those of (necessarily two-component) one good algorithm exists to compute these numbers dimensional link groups? Also, are there specific (G. Robin, R.A.I.R.O./Theoretical Informatics examples of such links in the literature? I know 17, n° 3 (1983), pp. 239-247). of such examples for the cases n = 1, all m; and (b) Define uo = 0, Uk+ 1 = 2"k. The smallest n = 2, all m (possibly). integer such that v( n) = k is uk. In Canad. J. Math. 23 (1971), pp. 116-130, it is proved that 358. David Halprin (P. 0. Box 186, North Carlton the set of exponents in the prime factorization 3054, Victoria, Australia). Does any reader know of a highly composite number n contains all the of any references of an expository nature to the integers up to plane curve known variously as Elastica, Linteira, River Meander? Same question for the property log2 n 1 1 of a plane curve known as sinuosity, which I ( + o( )) (log3 n)(log 2)' have seen only in articles on river meander in geomorphology texts. and its biggest element is O(log2 n). From this result, we can determine v(n) with an error of 359. L. Petkovic (Faculty of Mechanical Engi at most 1. Here log2 n = log log n, log3 n = neering, Beogradska 14, 18000 NI$, Yugoslavia). logloglogn. (Contributed by J. L. Nicolas) With 0 < r < 1 and k E N, let Dr be the image of the disk Iz - 11 ~ r under the map 345. (vol. 33, p. 335, March 1986, R.N. Gupta and V. K. Grover) Intervals of given length, containing z -> z 1I k. How does one establish the fol lowing properties: (a) The diameter of Dr is no square-free number. Reply: There is a slightly better upper bound known than that (1 r) 11k - (1 - r) 11k; (b) Dr is contained in + described in the query. The reference is P. 1 1 the circle of radius !((1 + r) 1k- (1- r ) /k) with Erdos, Some problems and results in elementary center !((1 + r)1/k + (1 _ r)1/k)? number theory, Publ. Math. Debrecen 2 (1951), 629 103-109. Unfortunately the article deals with a infinitely many k, where C = -1/ log(1 - 6j1r 2 ). more general situation, and the discussion of the This is based on a heuristic argument similar special case that we are interested in is marred by to that which was used by Cramer for gaps some inaccuracies. Let Sk be the kth square-free between consecutive primes. This would imply number. For all c; > 0 and infinitely many k it is that m( k) < exp( ( 1 + c; )k /C) for k sufficiently claimed on page 107 of the article that large. This may serve as some explanation for the small values of m(k) when k is small. 1r3 log Sk (Contributed by K. S. McCurley) Sk+l- Sk > (1- c)- l l , 6 og og Sk Comment on the reply to 331 (vol. 33, p. 335, March 1986): The fact that for a given n there but in fact the argument only gives 1r2 /12 in place is only one group (cyclic of course) of order n of 1r3 /6. When stated in the notation of the iff (n, Conference on Algebraic Topology in Honor of Peter Hilton Renzo Piccinini and Denis Sjerve, Editors (Contemporary Mathematics. Volume 37) This book contains 18 papers in algebraic Richard Kane. Finite H-spaces and the U(M) topology and homological algebra by collaborators property and associates of Peter Hilton. It is dedicated Kee Yuen Lam. On stable Hopf invariant one to Peter Hilton on the occasion of his 60th elements in RP 00 birthday. The various topics covered are homotopy Charles A. McGibbon and theory. H-spaces. group cohomology. localization. Joseph A. Neisendorfer. Various applications classifying spaces. and Eckmann-Hilton duality. of Haynes Miller's theorem Students and researchers in algebraic topology lb Madsen and Jan-Aive Svensson. Induction will gain an appreciation for Peter Hilton's impact in unstable equivariant homotopy theory and upon mathematics from reading this book. non-invariance of Whitehead torsion Mark Mahowald. Lin's theorem and the EHP Contents sequence F. Adams. The fundamental representations of J. J. P. May. Stable maps between classifying spaces E8 Joseph Roitberg. Residually finite. Hopfian and Israel Berstein. On covering spaces and Lie group co-Hopfian spaces actions Victor Snaith. On the classifying spaces of Galois A. K. Bousfield. On the homotopy classification groups of K -theoretic spectra and infinite loop spaces James Stasheff. Hilton-Eckmann duality revisited Browder. 5 1 -actions on open manifolds William K. Varadarajan. Projective and free approximations F. R. Cohen. An analogue of "Hop( invariant one" W. G. Dwyer and D. M. Kan. Reducing 1980 Mathematics Subject Classification: 55-06 equivariant homotopy theory to the theory of ISBN 0-8218-5036-9, LC 84-24518 fibrations ISSN 0271-4132 xii + 164 pages (softcover), March 1985 Beno Eckmann. Surface groups and Poincare List price $20, Institutional member $16, duality Individual member $12 Shipping and handling charges must be added Leonard Evens and Stewart Priddy. The To order, please specify CONM/37N cohomology of the semi-dihedral group 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 630 EMPLOYMENT INFORMATION IN THE MATHEMATICAL SCIENCES The American Mathematical Society, the Mathematical Association of America, and the Society for Industrial and Applied Mathematics publish Employment Information in the Mathematical Sciences six times a year. The following resolution was passed on October 25, 1974, by the Council of the American Mathematical Society: •·The Council of the AMS adopts principles that all positions in the mathematical sciences shall insofar as practicable be advertised, and that the standard place for the advertisements to appear is the publication Employment Informa tion." A similar resolution was subsequently approved by the Board of Governors of the Mathematical Association of America. The November, January, March, May, and August issues contain listings of open positions, information for which has been provided by heads of mathematics departments of colleges and universities in the United States, Canada, and overseas. In addition, these issues contain descriptions of open positions within government, industrial, and other nonacademic areas. The December issue contains resumes of job applicants who will be participating in the Employment Register at the January Annual Meeting. Subscription rates include first-class delivery in North America and airmail delivery elsewhere. The 1987 subscription starts with the November 1986 issue and ends with the August 1987 issue. All subscribers receive all six issues regardless of when the order is received. 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The American Mathematical Society Transactions of the Moscow Mathematical publishes books and journals at the Society graduate and research levels in pure and Translations of Mathematical Monographs applied mathematics. About 70 new books REVIEWS VOLUMES are published annually and a backlist of Reviews in Graph Theory about 1,300 titles is maintained. Fifteen Reviews in Group Theory journals are published, including primary Reviews in Number Theory research journals, translation journals, and Reviews in Ring Theory Papers in Algebraic and the prestigious abstracting journal Reviews of Differential Topology, Topological which contains Mathematical Reviews, Groups. and Homological Algebra 40,000 reviews annually of mathematics Reviews in K-theory books and research journals from around INDEXES AND DICTIONARIES the world. 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Providence. Rhode Island 02940 USA Letters to the Editor Militarization of Mathematics I deeply regret the growing trend toward the Policy on Letters to the Editor militarization of mathematics in the U.S. The Letters submitted for publication in Notices are reviewed announcement of DARPA Funding in the March by the Editorial Committee, whose task is to determine which ones are suitable for publication. The publication 1986 Notices (p. 325) is a case in point. This is schedule requires from two to four months between re clearly an unabashed attempt to recruit mathe ceipt of the letter in Providence and publication of the maticians into military work. While I believe in earliest issue of Notices in which it could appear. I the principle of academic freedom, which includes Publication decisions are ultimately made by ma the rights of my colleagues to sell their jority vote of the Editorial Committee, with ample pro soul to vision for prior discussion by committee members, by whichever devil they choose, I certainly do not mail or at meetings. Because of this discussion period, applaud the trend. I must say I am shocked some letters may require as much as seven months before that Professor Kenneth Hoffman characterizes the a final decision is made. DARPA funding as "good news" and "a bright The committee reserves the right to edit letters. Notices does not ordinarily publish complaints spot for us" (p. 319). Is it good news that more of about reviews of books or articles, although rebuttals our students may become unwitting pawns in the and correspondence concerning reviews in Bulletin of the superpower arms race? We must not forget that American Mathematical Society will be considered for pub even such a noble, brilliant and warm-hearted lication. person as Andrei Sakharov allowed Letters should be mailed to the Editor of Notices, his mind to be American Mathematical Society, Post Office Box 6248, exploited in the development of weapons that are Providence, Rhode Island 02940, and will be acknowl now pointed at hundreds of American cities. Is it edged on receipt. nobler that the products of our students' minds will only be pointed at Soviet cities? I am even disturbed by the less blatant insertion of military money into mathematical research. For example, here at Cornell the Army Research Office has funded a Mathematical Sciences Institute (March Notices, p. 315) that CONFERENCE ON appears to be free of direct military work. I ALGEBRAIC GEOMETRY have resigned from the Cornell Center for Applied Mathematics in order to protest this develop J. B. Carrell, A. V. Geramita, ment, and in order to disassociate myself with and P. Russell, Editors the Army Institute. I have two concerns with this apparent no-strings-attached Department of These research and expository papers Defense funding of mathematical research-what cover a cross-section of very recent developments in modern algebraic I call "picking the devil's pocket". The first is geometry. The volume is especially useful that in the event of a national crisis the ground to researchers and to those who want rules might change very quickly. The second is to keep abreast of the latest directions that if and when sanity returns to Washington, in the field. Aimed at those with an and the military budget is cut to only its former expert background in the field, the bloated levels, which military programs do you topics covered include algebraic groups think will be the first to go? It is far better in and representation theory, enumerative my view to trust our research funding to agencies geometry, Schubert varieties, rationality, which, when faced with a choice between bombs compactifications, and surfaces. Of and mathematics, would make the right choice. particular significance are the articles by Bogomolov, Looijenga, Kleiman, Kurke, These are important issues, and the AMS and Springer. leadership should not be allowed to propel us into a posture of support of Department of Defense ISBN 0-8218-6010-0, LC 85-28720 funding without protest. ISSN 0731-1036 503 pages ( softcover), March 1986 Robert S. Strichartz List price $56, Institutional member $45, Professor of Mathematics Individual member $34 Cornell University To order, please specify CMSAMS/6NA (Received March 31, 1986) ~~~~~~~~~~~~~~~~~ 633 1986 AMS Elections COLLOQUIUM Council Nominations PUBLICATIONS for Vice-President and Members-at-Large One vice-president and five members-at-large of The Geometric Topology of 3-Manifolds the Council will be elected by the Society in a R H Bing contested election in the fall of 1986. The book starts with a treatment of some of the The vice-president will serve for a term of geometric and topological properties of the plane. two years effective January 1, 1987. The Council This treatment is expanded to study such funda has nominated two candidates for the position. mental properties of 3-space as the PL Schoenflies They are: theorem, Dehn's lemma, the loop theorem, and the William P. Thurston Karen Uhlenbeck side approximation theorem. Applications of these The five members-at-large will serve for a fundamental results are made to develop further term of three years. The Council nominated ten properties of 3-manifolds. candidates. They are: This book is most meaningful to a mathematician interested in geometry who has had at least a begin C. E. Burgess Yiannis N. Moschovakis ning graduate course in topology. While a student David Drasin Linda A. Ness can start the book with less preparation, the chances H. Blaine Lawson Mark A. Reiffel are that those with weaker backgrounds will bog Howard A. Masur Scott W. Williams down if they work without the benefit of discussion. Eric C. Milner Carol S. Wood The book belongs in both graduate and under The deadline for petitions proposing addi graduate libraries. It can serve as a useful reference tional nominations is July 7. Such proposals will for a graduate student in topology or a researcher not reach the Council for action by mail ballot in topology. A study of the book should provide until after that date. the reader with a better understanding of the phys ical properties of Euclidean 3-space-the space in President's Candidates which we presume we live. The reader should learn of some unsolved problems that continue to baffle for the Nominating Committee researchers. 1987 and 1988 The most profound result in the volume is the Four members of the Nominating Committee are side approximation theorem. However, as a reference to be elected in the fall of 1986. Continuing tool some of the preliminary results and some of the members are: applications may be used more frequently. John T. Baldwin Catherine L. Olsen James W. Cannon Burton Rodin Contents President Irving Kaplansky has named six Preface candidates for the other four places. They are: 1. Planar complexes 2. PL planar maps M. Salah Baouendi Werner C. Rheinboldt 3. The Schoenflies theorem Robert L. Devaney Bruce L. Rothschild 4. Wild 2-spheres Carl Pomerance Frank L. Spitzer 5 .. The generalized Schoenflies theorem If nominations by petition have not appeared 6. The fundamental group bringing the total number of candidates to at 7. Mapping onto spheres least eight, it will be brought up to eight by the 8. Linking president. 9. Separation Everett Pitcher 1980 Mathematics Subject Classification: 57 -XX Bethlehem, Pennsylvania Secretary Colloquium Publications Volume 40, viii + 240 pages (hard cover) List price $54, institutional member $43, individual member $32 ISBN 0-8218-1040-5; LC 83-14962 Publication date: October 1983 To order, please specify COLL/40N Shipping and handling charges: surface delivery - $2 first book. $1 each additional. maximum $25: air delivery - $5 first book. $3 each additional. maximum $100. Prepayment Is required. Order from American Mathematical Society. PO Box 1571. Annex Station. Providence. Rl 02901-1571 USA. 634 Election Information The ballots for election of members of the Council and SUGGESTIONS FOR 1987 NOMINATIONS Board of Trustees of the Society for 1987 will be mailed Council and Board of Trustees on or shortly after September 10, in order for members to receive their ballots well in advance of the November Vice President ( 1) 10 deadline. Prior to casting their ballots members are urged to consult the following articles and sections of the Bylaws of the Society: article I, section 1; article II, sections 1, 2; article III, sections 1, 2, 3; article IV, sections 1, 2, Associate Secretaries ( 2) 4; article VII, sections 1, 2, 5. The complete text of the Bylaws appears on pages 822-827 of the November 1985 issue of Notices. A list of the members of the Council and Board of Trustees serving terms during 1986 appears in the AMS Reports and Communications section of this issue. Member of the Bulletin Editorial Committee ( 1) SUGGESTIONS FOR 1987 NOMINATIONS Each year the members of the Society are given the oppor Member of the Colloquium Editorial Committee (1) tunity to propose for nomination the names of those indi viduals they deem both qualified and responsive to their views and needs as part of the mathematical community. Candidates will be nominated by the Council to fill posi Member of the Mathematical RevieWB Editorial Committee tions on the Council and Board of Trustees to replace those (1) whose terms expire December 31, 1987. See the AMS Re ports and Communications section of this issue for the list of current members of the Council and Board of Trustees. Member of the Mathematical Surveys Editorial Committee Members are requested to write their suggestions for such (1) candidates in the appropriate spaces on the form in the next column. REPLACEMENT BALLOTS Member of the Mathematics of Computation Editorial Com This year ballots for the AMS election will be mailed Sep mittee (1) tember 10, 1986, or within a day or two thereafter. The deadline for receipt of ballots in Providence is November 10, 1986. There has been a small but recurring and distressing Members of the Proceedfngs Editorial Committee (3) problem concerning members who state that they have not received ballots in the annual election. It occurs for several reasons, including failure of local delivery systems on uni versity or corporate properties, failure of members to give timely notice of changes of address to the Providence office, failures of postal services, and other human errors. Members of the 'Jioarl8actions and Memoirs Editorial Com To help alleviate this problem, the following replace mittee (4) ment procedure has been devised: A member who has not received a ballot by October 10, 1986, or who has received a ballot but has accidentally spoiled it, may write after that date to the Secretary of the AMS, Post Office Box 6248, Providence, RI 02940, asking for a second ballot. The re quest should include the individual's member code and the address to which the replacement ballot should be sent. Immediately upon receipt of the request in the Providence Members of the Committee to Monitor Problems in Com office, a second ballot, which will be indistinguishable from munication (2) the original, will be sent by first class or air mail. It must be returned in an inner envelope, which will be supplied, on the outside of which is the following statement to be signed by the member: The ballot in this envelope is the only ballot that I am Members-at-large of the Council (5) submitting in this election. I understand that if this state ment is not correct then no ballot of mine will be counted. signature Although a second ballot will be supplied on request and wilt be sent by first class or air mail, the deadline for re ceipt of ballots will not be extended to accommodate these Member of the Board of Trustees ( 1) special cases. The completed form should be addressed to AMS Nomi nating Committee, Post Office Box 6248, Providence, RI 02940, to arrive no later than November 10, 1986. 635 Logan, October 10-11, Utah State University Second Announcement of the 828th Meeting The eight hundred and twenty-eighth meeting of David Gabai, Dennis Garity, Matt Grayson, Jim the American Mathematical Society will be held Henderson, Jim Haste, Stephen Humphries, Louis at Utah State University in Logan, Utah, on Kaufman, Chris Lacher, Duane Loveland, Jerr Friday and Saturday, October 10-11, 1986. Levine, Vo Thanh Liem, John Luecke, Dale Rolf son, T. Benny Rushing, Martin Scharlemann, Jon Invited Addresses Simon, Mike Starbird, Abigail Thompson, Keith By invitation of the Committee to Select Hour Wolcott, and David Wright. Speakers for Far Western Sectional Meetings, Most of the papers to be presented at these there will be two invited one-hour addresses. The special sessions will be by invitation. However, speakers and the titles of their talks are: anyone submitting an abstract for the meeting PETER LI, University of Utah, Harmonic who feels that his or her paper would be particu functions on complete manifolds. larly appropriate for one of these special sessions KENNETH C. MILLETT, University of Cali should indicate this clearly on the abstract form fornia, Santa Barbara, New combinatorial methods and submit it by July 28, 1986, three weeks before in three dimensional topology. the deadline for contributed papers, in order that it may be considered for inclusion. Participants Special Sessions are reminded that a charge of $16 is imposed for By invitation of the same committee, there will retyping abstracts that are not in camera-ready be five special sessions of selected papers. The form. topics of these sessions, the names and affiliations of the organizers, and partial lists of the speakers, Contributed Papers are as follows: There will also be sessions for contributed ten Applications and computational aspects of minute papers. Abstracts should be prepared numerical continuation methods, EUGENE ALL on the standard AMS form available from the GOWER, Colorado State University. The tentative AMS office in Providence or in Departments of speakers are Eusebius Doedel, Kurt Georg, Her Mathematics. Abstracts should be sent to the bert Keller, Hans Mittelmann, T.-Y. Li, Alexan Editorial Department, American Mathematical der Morgan, Aubrey Poore, Chris Tiahrt, and Society, Post Office Box 6248, Providence, Rhode Layne Watson. Island 02940, so as to arrive before the August Analysis on manifolds, S. Y. CHENG, Uni 18, 1986, abstract deadline. Participants are versity of California, Los Angeles. Some of the reminded that a charge of $16 is imposed for speakers are Michael Anderson, Robert Brooks, retyping abstracts that are not in camera-ready Hui-Dong Cao, Robert Greene, Douglas Moore, form. Late papers will not be accommodated. V. Oliker, Luen-Fai Tam, Andrejs Treibergs, and Johan Tysk. Registration Representations of reductive groups, DAVID The meeting registration desk will be located on H. COLLINGWOOD, University of Oregon. Some the main floor of the Eccles Conference Center. of the speakers are Brian Boe, J. Chang, Tom The desk will be open from 10:00 a.m. to 4:30 Enright, Devra Garfinkle, Henryk Hecht, R. Irv p.m. on Friday, and from 8:00 a.m. until noon ing, J. Johnson, Dragan MiliCic, Ivan Mirkovic, on Saturday. The registration fees are $10 for Hugo Rossi, R. Scaramuzzi, Brad Shelton, Peter members of the AMS, $16 for nonmembers, and Trombi, and Joseph Wolf. $5 for students or unemployed mathematicians. Random fields, random measures and appli cations, ED WAYMIRE, Oregon State University. Petition Table The speakers are Kenneth S. Alexander, Florin A petition table will be set up in the registration Avram, Rabi Bhattacharya, Michael D. Bren area. Additional information can be found in a nan, Peter Brockwell, Robert M. Burton, Colleen box in the New Orleans meeting announcement Cutler, Richard Darling, Stuart Ethier, Peter on page 72 of the January 1986 issue of Notices. Gaenssler, Evarist Gine, J. Horowitz, Thomas G. Kurtz, Charles M. Newman, Mina Ossian Accommodations der, Richard F. Serfozo, Winfried Stute, Murad A block of rooms is being held for conference Taqqu, and Stanley C. Williams. participants at the University Inn. This is a Geometric topology, DAVID WRIGHT and full-service hotel complex located on campus. J. W. CANNON, Brigham Young University. Other motels are located within 1.5 to 3 miles of The speakers are Colin Adams, Ric Ancel, campus in downtown Logan. Participants should Mladen Bestvina, Steven Bleiler, John Bryant, Ed make their own reservations directly with the Burgess, J. W. Cannon, Bill Eaton, Bill Floyd, University Inn or other motel of their choice. 636 UTAH STATE UNIVERSITY CONFERENCE VISITOR PARKING TERRACE VALLEY VIEW CACHE ECCLES CONFERENCE NATIONAL CENTER FOREST FROM SAlT lAKE CITY TO lOGAN BEAR LAK£ TAKE THIS EXIT TO UTAH STATE '"" ~N::~RS~ ~UTAH'S SKI COUNTRY "" SNOW BIRO PARK CITY AlTA BRIGHTON VIA INTERSTATE 15 AND HWY 89/91 - APPRO.X:. 90 ~ILES DRIVING TIME I HR. 45 MIN. 637 Rates are subject to possible change and do not Persons driving from Salt Lake City to Logan include local taxes. should take I-15 north to Brigham City, exit at University Inn 363 and take US highway 89-91 to Logan. In Utah State University, Logan, UT 84322 Logan, turn east off Main Street to 400 North Telephone: 801-750-1153 and then turn left off 400 North to 700 East to Single $28 Double $32 the University Campus. Baugh Motel Parking is available in the visitor parking ter 153 South Main Street, Logan, UT 84321 race on 700 North, adjacent to the University Inn, Telephone: 801-752-5220 and to the east of campus at 1200 East. Terrace parking will be validated for conference partici Single $26 and up Double $30 and up pants and the University Inn guests. Parking is Best Western Weston's Lamplighter permitted virtually anywhere on weekends. 250 North Main Street, Logan, UT 84321 Regularly scheduled limousine service be Telephone: 801-752-5700 tween Salt Lake City and Logan is available Single $28 Double $32 through Key North Limousine. Current one-way Holiday House prices are $36.40 for one person and $25 each for 447 North Main Street, Logan, UT 84321 two or more persons. Up to six departure times Telephone: 801-752-9141 per day are offered weekdays, and four times Single $26 and $28 Double $31 and $33 per day on weekends, with additional limousines added as needed. Reservations must be made no Food Services later than 24 hours in advance by calling Key The cafeteria in the Taggart Student Center North Limousine, 801-394-7743. will be open during both days of the meeting. Logan is at an elevation of 4000 feet. Autumn In addition, there are numerous restaurants along days are cool and frost is likely at night. Rain or Main Street, and a restaurant list will be available snow is possible, but unlikely. at the registration desk. Hugo Rossi Travel and Local Information Salt Lake City, Utah Associate Secretary Logan is located approximately 90 miles north of Salt Lake City. Salt Lake City is served by Amtrak, Greyhound and major airlines. Most car rental agencies have counters at the airport terminal. Pettis Integral and Measure Theory Michel Talagrand This book is concerned with the notion of The book is organized into three parts. Chapters pointwise compact sets of measurable functions 1 through 7 deal with Pettis integration and and related measure-theoretic problems. The topological measure theoretic tools. Abstract author provides an extensive self-contained measure theoretic tools are used in Chapters 2. 6 development of the theory of Pettis integration. the and 7. but since they are more technical. their natural field of application. Other fields of study is delayed until Chapters 8 through 14. application included are Riemann-measurable Chapters 15 and 16 deal with applications and functions on groups. measurability problems and more specialized questions. empirical measures. should be The main results of this work Memoirs of the AMS accessible with only a working knowledge of Number 307, x + 226 pages (softcover) abstract measure theory and an elementary 1980 Mathematics Subject Classifications: 46G10; 28805, 28A20, 44A99, 46822 and knowledge of functional analysis and topological others ~~-~~~~~0 measure theory. No previous knowledge of Pettis ISBN 0-8218-2307-8; LC 84-14614 rfli'"' 0 '""?!f 638 Charlotte, October 17-18, Adam's Mark Hotel Second Announcement of the 829th Meeting The eight hundred and twenty-ninth meeting of retyping abstracts that are not in camera-ready the American Mathematical Society will be held form. at the Adam's Mark Hotel in downtown Charlotte, North Carolina, on Friday and Saturday, October Contributed Papers 17-18, 1986. This meeting will be hosted by the There will also be sessions for contributed ten University of North Carolina at Charlotte. minute papers. Abstracts should be prepared on the standard AMS form available from the Invited Addresses AMS office in Providence or in Departments of By invitation of the Committee to Select Hour Mathematics. Abstracts should be sent to the Speakers for Southeastern Sectional Meetings, Editorial Department, American Mathematical there will be three invited one-hour addresses. Society, Post Office Box 6248, Providence, Rhode The speakers are as follows: Island 02940, so as to arrive before the August PATRICK EBERLEIN, University of North 20, 1986, abstract deadline. Participants are Carolina, Chapel Hill, Structure of manifolds of reminded that a charge of $16 is imposed for non-positive curvature, 1:00 p.m. Saturday. retyping abstracts that are not in camera-ready STEVEN C. FERRY, University of Kentucky, form. Closing open manifolds, 8:30 a.m. Saturday. FRANK RAYMOND, University of Michigan, Charlotte Mathematics Conference Ann Arbor, title to be announced, 12:30 p.m. The University of North Carolina, Charlotte, will Friday. also host the Charlotte Mathematics Conference in Analysis and Probability at the Adam's Mark Spec:ial Sessions Hotel. The name of the major speaker and title By invitation of the same committee, there will of the talk to be presented at 10:00 a.m. on be four special sessions of selected twenty-minute Friday will be announced later. Special sessions papers. The topics of these sessions and the of twenty-minute invited talks will also be sched names and affiliations of the organizers are as uled on Friday and Saturday in the following follows: areas: Semilinear parabolic systems, organized by Singularities and algebraic geometry, GARY Joel Avrin; Operator theory, organized by Alan KENNEDY, Duke University. The tentative speak Lambert; and Probability theory, organized by ers include James Damon, A. Iarrobino, A. Lib Bob Anderson. All of these organizers are at the gober, Lee McEwan, David Morrison, Walter University of North Carolina, Charlotte. Any Neumann, Leslie Saber, and Ted Shifrin. one interested in obtaining additional information Geometric topology, JOHN MAYER, Univer should contact David Royster, Department of sity of Alabama, Birmingham. Mathematics, UNCC; telephone 704-597-2649, or Group actions on manifolds, DAVID ROYS after July 23 call 704-547-2649. TER, University of North Carolina, Charlotte. Tentative speakers are R. Dotzel, C. Giffen, S. Registration Kahn , H. T. Ku, K. B. Lee, R. Lee, D. McCul The meeting registration desk will be in the lough, D. Royster, R. Schultz, H. Singh, C. Stark, Adam's Mark Hotel at a location to be announced. and N. Stoltzfus. The desk will be open from 10:00 a.m. to 5:00 Twistor theory and four-dimensional geome p.m. on Friday, and from 9:00 a.m. to noon try, ALBERT L. VITTER III, Tulane University. on Saturday. The registration fees are $10 for Tentative speakers include Charles Boyer, Robert members of the AMS, $16 for nonmembers, and Bryant, Nicholas Buchdahl, Dan Burns, Andrzej . $5 for students or unemployed mathematicians. Derdzinski, Jacques Hurtubise, Claude R: Le Brun, Yat Sun Poon, Pankaj Topiwala, and Philip Petition Table B. Yasskin. A petition table will be set up in the registra Most of the papers to be presented at these tion area. Additional information can be found special sessions will be by invitation. However, in a box on page 72 of the New Orleans meet anyone submitting an abstract for the meeting ing announcement in the January 1986 issue of who feels that his or her paper would be particu Notices. larly appropriate for one of these special sessions should indicate this clearly on the abstract form Accommodations and submit it by July 30, 1986, three weeks before A block of rooms is being held at the Adam's Mark the deadline for contributed papers, in order that Hotel. These rooms will be held until October it may be considered for inclusion. Participants 3, after which reservations will be accepted on a are reminded that a charge of $16 is imposed for space available basis. Participants should make 639 DOWNTOWN CD Adam's Mark Hotel Q) Quality Inn Downtown C H A R L 0 T T E @ Radisson Plaza Hotel @) Marriott City Center ---+----...... - N GRAHAM ST. ~:::.=::::.=::::.=:d:T~RY=O~N::-:::S1::;' ·=r==~~Q)~ @) 1 COLLFG E ST. f----+-t---1---t---t----1 640 their own arrangements directly with the hotel Travel and be sure to identify themselves as participants Major carriers, including Delta, Eastern, People at the AMS meeting. The rates do not include Express, Piedmont, TWA, United, and USAir, as applicable taxes, and are subject to change after well as several regional carriers, provide regular October 3. service to Charlotte's Douglas Municipal Airport. Adam's Mark Hotel {Headquarters) Most of the downtown hotels provide limousine 555 South McDowell Street, Charlotte 28204 service to and from the airport. Telephone: 704-372-4100 or 800-231-5858 Charlotte is on Interstate Routes I-77 and Single $60 Double $70 I-85 South, and there are several exits from I-77 Rooms have not been blocked at the following to the downtown area. From either I-77 North locations, but they are included here for informa or South, drivers should take the Brookshire Ex tion purposes. Rates do not include applicable pressway exit, and from Brookshire Expressway taxes and are subject to change without notice. take the McDowell Street exit, proceed approx Charlotte Marriott City Center ( 10 blocks) imately nine blocks to the Adam's Mark Hotel 100 West Trade Street, Charlotte 28202 which is on the left. Telephone: 704-333-9000 or 800-228-9290 Parking Single or double $70 up Ample free parking is available to meeting partic Quality Inn Downtown (2 blocks) ipants at the Adam's Mark Hotel. 201 South McDowell Street, Charlotte 28204 Telephone: 704-372-7550 or 800-228-5150 Frank T. Birtel Single $40 Double $52 New Orleans, Louisiana Associate Secretary Radisson Plaza Hotel {9 blocks) Two NCNB Plaza Trade and Tryon Streets, Charlotte 28280 Telephone: 704-377-0400 or 800-228-9822 Single or Double $78 to $110 Food Service Two restaurants are located within the Adam's Mark Hotel, and there is also a large number of restaurants in the downtown area. A list of restaurants will be available at the meeting registration desk. 1-~\IEM.-t]J. .$~~\9, Applied Cryptology, Cryptographic Protocols, ~\~.$ and Computer Security Models "'ouNow'@' 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. 641 Denton, October 31- November 1, North Texas State University Second Announcement of the 830th Meeting The eight hundred and thirtieth meeting of the J.P. Brennan, V. Doedhar, S. Doty, R. Fossum, R. American Mathematical Society will be held at Gustafson, W. Haboush, A. Helminik, C. Huneke, North Texas State University in Denton, Texas, R. Joshua, V. Lakshmibai, A. Magid, A. Neeman, on Friday, October 31 and Saturday, November B. Parshall, R. Proctor, J. Stembridge, B. Ulrich, 1, 1986. All scientific sessions will be held in the and J. Weyman. Union Building on the campus. Most of the papers to be presented at these special sessions will be by invitation. However, Invited Addresses anyone submitting an abstract for the meeting By invitation of the Committee to Select Hour who feels that his or her paper would be particu Speakers for Central Sectional Meetings, there larly appropriate for one of these special sessions will be four invited one-hour addresses. The should indicate this clearly on the abstract form speakers are as follows: and submit it by August 4, 1986, three weeks PAUL FONG, University of Illinois at Chicago, before the deadline for contributed papers, in Modular representations of finite groups. order that it may be considered for inclusion. RAVI S. KULKARNI, Indiana University, Participants are reminded that a charge of $16 Bloomington, Geometric structures on manifolds. is imposed for retyping abstracts that are not in ALEXANDER NAGEL, University of Wiscon camera-ready form. sin, Madison, title to be announced. MARY WHEELER, Rice University, title to Contributed Papers be announced. There will also be sessions for contributed ten minute papers. Abstracts should be prepared Special Sessions on the standard AMS form available from the By invitation of the same committee, there will be AMS office in Providence or in Departments of seven special sessions of selected twenty-minute Mathematics. Abstracts should be sent to the papers. The topics of the sessions, and the names Editorial Department, American Mathematical and affiliations of the organizers are as follows: Society, Post Office Box 6248, Providence, Rhode Banach spaces and related topics, ELIZABETH Island 02940, so as to arrive before the August BATOR, RUSSELL BILYEU and PAUL LEWIS, 25, 1986, abstract deadline. Participants are North Texas State University. The tentative reminded that a charge of $16 is imposed for speakers include Dale Alspach, Kevin Andrews, retyping abstracts that are not in camera-ready Gerald Edgar, Nassif Ghoussoub, Peter Greim, form. It appears unlikely that late papers can be Bob Huff, Nigel Kalton, Tenny Peck, Bob Phelps, accommodated. Haskell Rosenthal, Elias Saab, Paulette Saab, Mark Smith, Bob Wheeler, and John Whitfield. Registration Connections between combinatorics, algebra The meeting registration desk will be located in and geometry, NEAL BRAND and JOSEPH KUNG, the foyer of the Lyceum in the Union Building. North Texas State University. The desk will be open from 7:00 p.m. to 9:00 p.m. Differential equations, ALFONSO CASTRO, on Thursday, from 8:00 a.m. to 2:00 p.m. on Southwest Texas State University, and JOHN Friday, and from 8:00 a.m. to noon on Saturday. NEUBERGER, North Texas State University. The registration fees are $10 for members, $16 for Mathematics for large scale computing, J. nonmembers, and $5 for students or unemployed C. DIAZ, University of Oklahoma. mathematicians. Computational mathematics, WARREN FER GUSON, JR., Southern Methodist University. Petition Table Tentative speakers are John Dennis, Roland A petition table will be set up in the registra Glowinski, T. Y. Li, Theresa Parks, Patrick Ra tion area. Information concerning placement of bier, Larry Shampine, William Symes, Kathryn petitions can be found in a box on page 72 of Turner, and David Young. the New Orleans meeting announcement in the Geometric structures on manifolds and Klein January 1986 issue of the Notices. ian groups, RAVI S. KULKARNI. Tentative speakers include F. Bonahon, R. Brooks, D.B.A. Accommodations Epstein, M. E. Feighn, F. Gardiner, F. W. Special rates have been negotiated at selected Gehring, J. Gilman, W. Goldman, L. Keen, A. local hotels, all of which are located on the I- Koranyi, G. Martin, B. Maskit, B. Osgood, R. 35 corridor. Both the Royal Hotel Suites and Skora, C. Stark, P. Waterman, and N. Wielenberg. the Sheraton are within easy walking distance Invariant theory, V. LAKSHMIBAI, Texas of the campus. Participants should make their A & M University. Tentative speakers are K. Akin, own arrangements directly with the hotel of their 642 ---NORTH TEXAS STATE UNIVERSITY----. DENTON, TEXAS CD Holiday Inn Q) Ramada Inn us 380 G) La Quinta @ Royal Hotel Suites ;.J G) Union Building z z 0 ® Sheraton Hotel CCI SCRIPTURE G) Motel 6 +-OAK ~ NTSU campus HICKORY-+ . ~§ ~~PRAIRIF. ' '///< //// 643 choice and ask for the special AMS meeting rate. Parking The rates listed are subject to change and do A metered parking garage (50 cents per hour; not include applicable taxes·. The deadline for $2.25 per day) is located immediately east of the reservations at all locations is October 10. Union Building. Visitors may also park in the Holiday Inn (2.5 miles from campus} Fouts Field parking lot and take a shuttle (25 1500 Dallas Drive, Denton 76205 cents each way) to the Union Building. Parking in Telephone: 817-387-3511 designated lots is unregulated on Saturday only. $45 Single $40 Double Travel Motor Inn (1.5 miles from campus) LaQuinta is located approximately 35 miles north of Worth Drive, Denton 76205 Denton 700 Ft. Ft. Worth and 25 miles north of DFW Telephone: 1-81)(}.531-5900 Dallas and Airport, which is served by most Double $32 International Single $28 major domestic airlines. Airport shuttle service Motel6 (3 miles from campus} is available from the DFW International Airport 1-35 North of University Drive, Denton 76205 to Denton (telephone 817-383-2007), with regular Telephone: 817-387-0571 stops at the Holiday Inn, Ramada Inn, LaQuinta, Single $20.85 Double $25.25 and Sheraton. However, since one-way fare is $14 Ramada Inn (2 miles from campus} and only the Royal Hotel Suites and Sheraton 820 S I-35E at Teasley Lane, Denton 76205 Hotel are within easy walking distance of campus, Telephone: 1-81)(}.228-2828 or 817-387-0591 those flying to DFW should consider renting a car Single $36 Double $36 and driving to Denton. Participants driving to Royal Hotel Suites (.5 miles from campus) Denton from DFW should take the North Airport 1210 I-35E, Denton 76205 Exit to State Highway 121 to I-35E and proceed Telephone: 817-383-2007 north on I-35E to Denton. To reach the campus, Single $32 Double $36 take the Avenue D exit from I-35E and proceed D one block to Eagle Drive. Sheraton Hotel (.5 miles from campus) north on Avenue and proceed four blocks 2211 I-35E North, Denton 76205 Turn east on Eagle Drive turn north on Welch Street. Telephone: 817-565-8499 to Welch Street, then metered parking garage adjacent to the Union Single $49 Double $54 The Building is on Welch Street, three blocks north of Food Service Eagle Drive. are located within two Many fast food restaurants M. Fossum and more formal dining is Robert blocks of the campus, Associate Secretary available at the Sheraton Hotel and several local Urbana, Illinois restaurants. Food service in the Union will only be available according to the following schedule: Breakfast, lunch, and sandwiches until 5:00 p.m. on Thursday; breakfast and lunch on Friday; and lunch only on Saturday. semisimple Lie algebras by W. Bohro, LIE ALGEBRAS AND a course on Kac-Moody Lie algebras by RELATED TOPICS I. G. Macdonald, and a course on formal groups by M. Hazewinkel. D. J. Britten, F. W. Lemire, and R. V. Moody, Editors 1980 Mathematics Subiect Classifications: 17-xx, 22-xx As the Proceedings of the 1984 Canadian ISBN 0-8218-6009-7, LC 85-26818 Seminar, ISSN 0731-1036 Mathematical Society's Summer 1986 some recent 392 pages (softcover), February these papers focus on List price $44, Institutional member $35, advances in the theory of semisimple Individual member $26 Lie algebras and some direct outgrowths To order, please specify CMSAMS/5NA of that theory. Of particular interest are notes for several courses presented an important survey Shipping/Handling: 1st book $2, each add'l $1, $25 at the meeting: max. By air, 1st book $5, each add'l $3, $100 max. article by R. Block and R. Wilson on Prepayment required. Order from AMS, P.O. Box restricted simple Lie algebras, a survey 1571, Annex Station, Providence, RI 02901-1571, or of universal enveloping algebras of call 800-556-7774 to use VISA or MasterCard. 644 Invited Speakers Ed Waymire, Random fields, random measures and applications and Special Sessions David Wright and J. W. Cannon, Geometric topology Invited Speakers at AMS Meetings The individuals listed below have accepted invi October 1986 Meeting in Charlotte tations to address the Society at the times and places indicated. For some meetings, the list of Southeastern Section speakers is incomplete. Deadline for organizers: JiJJ;piml Deadline for OOI"I8idemtion: July 90, 1986 Logan, Gary Kennedy, Singularities and algebraic geom- October 1986 etry Peter Li Kenneth C. Millett John Mayer, Geometric topology David Royster, Group actions on manifolds Charlotte, October 1986 Albert L. Vitter, III, Twistor theory and four- dimensional geometry Patrick Eberlein Frank Raymond Steven C. Ferry October 1986 Meeting in Denton Denton, October 1986 Central Section Deadline for organizers: E1q1ired Paul Fong Alexander Nagel Deadline for consideration: August 4, 1986 Ravi S. Kulkarni Mary Wheeler Elizabeth Bator, Russell Bilyeu, ~d Paul Lewis, Banach spaces and related toptcs San Antonio, January 1987 Neal Brand and Joseph Kung, Connections be tween combinatorics algebra and geometry Marc Culler Robert J. McEliece Alfonso Castro and Joh~ W. Neuberger, Differ Ronald J. DiPerna David J. Saltman ential equations Robert Hardt Lesley M. Sibner J. C. Diaz, Mathematics for large scale computing Peter D. Lax Thomas Spencer Warren Ferguson, Jr., Computational mathemat {Colloquium Lecturer) (Gibbs Lecturer) ics Ravi S. Kulkarni, Geometric structures on mani Honolulu, March 1987 folds and Kleinian groups Martin Scharlemann V. Lakshmibai, Invariant theory Newark, April 1987 Fall 1986 Meeting Robert V. Kohn Birgit Speh Eastern Section Rodolfo Rosales Lars S. Wahlbin No meeting will be held Organizers and Topics January 1987 Meeting in San Antonio of Special Sessions Associate Secretary: Robert M. Fossum The list below contains all the information about Deadline for organizers: ExfYired Deadline Special Sessions at meetings of the Society avail for consideration: september 2.4, 1986 Ronald J. DiPerna, Nonlinear able at the time this issue of Notices went to partial differential the printer. The section below entitled Infor equations Michael J. mation for Organizers describes the timetable for Evans and Paul D. Humke, Classical announcing the existence of Special Sessions. real analysis Burton Fein, David J. Saltrnan, and Murray Schacher, Brauer groups October 1986 Meeting and Galois the~ry. in Logan Michael Gage and Erwin Lutwak, Geometnc m Far Western Section equalities Deadline for organizers: &,ired Joseph Glover and A. 0. Pittenger, Stochastic Deadline for consideration: July 28, 1986 processes and analysis Eugene L. Allgower, Applications and compu Philip J. Hanlon, Combinatorics and group repre tational aspects of numerical continuation sentations methods Lesley M. Sibner, Gauge theory S. Y. Cheng, Analysis on manifolds Lynn McLinden and Jay S. 'freiman, Theoretical David Collingwood, Representations of reductive optimization groups Gregory P. Wene, Mathematical physics 645 March 1987 Meeting in Honolulu In accordance with an action of the Executive Committee of the Council, no Special Session may Far Western Section be arranged so late that it may not be announced Deadline far organizers: October 15, 1986 Deadline far coruideration: To be anrwunced in Notices early enough to allow any member George Csordas, Complex function theory of the Society, who wishes to do so, to submit Heiner Doverman, Algebraic topology an abstract for consideration for presentation in Kent R. Fuller, Rings and modules the Special Session before the deadline for such Jerry Griggs, Combinatorics consideration. Thomas Jech, Set theory and its applications Special Sessions are effective at Sectional Meetings and can usually be accommodated. They are arranged by the Associate Secretary April 1987 Meeting in Kent under the supervision of the Committee to Select Central Section Hour Speakers for the section. The limitation Deadline far organizers: October 15, 1986 on the number of sessions depends on the space Deadline far consideration: To be announced and time available. The same restriction as for national meetings applies to the deadline for an April1987 Meeting in Newark nouncing Special Sessions at sectional meetings: no Special Session may be approved too late for Eastern Section its announcement to appear in time to allow a Deadline far organizers: October 15, 1986 reasonable interval for members to prepare and Deadline far consideration: To be announced submit their abstracts prior to the special early deadline set for consideration of papers for Special Spring 1987 Meeting Sessions. The Society reserves the right of first refusal Southeastern Section for the publication of proceedings of any special No meeting will be held session. These proceedings appear in the book series Contemporary Mathematics. Information for Organizers Special Sessions at Annual and Summer meetings Information for Speakers are held under the general supervision of the A great many of the papers presented in Special Program Committee. They are administered by Sessions at meetings of the Society are invited the Associate Secretary in charge of the meeting papers, but any member of the Society who with staff assistance from the Society office in wishes to do so may submit an abstract for Providence. consideration for presentation in a Special Session, Some Special Sessions arise from an invita provided it is received in Providence prior to t~e tion to a proposed organizer issued through the special early deadline announced above and m Associate Secretary. Others are spontaneously the announcements of the meeting at which the proposed by interested organizers or participants. Special Session has been scheduled. Contributors Such proposals are welcomed by the Associate should know that there is a limitation in size of a Secretaries. single special session, so that it is sometimes true The number of Special Sessions at a Summer that all places are filled by invitation. Papers not or Annual Meeting is limited to twelve. Proposals, accepted for a Special Session are considered as invited or offered, which are received at least nine ten-minute contributed papers. months prior to the meeting, are screened for Abstracts of papers submitted for considera suitability of the topic and of the proposed list of tion for presentation at a Special Session must be speakers, and for possible overlap or conflict w_ith received by the Providence office (Editorial De other proposals (specific deadlines for requestmg partment, American Mathematical Society, Post approval for Special Sessions at national meeti_ngs Office Box 6248, Providence, RI 02940) by the are given above). If necessary, the numencal special deadline for Special Sessions, which is limitation is enforced. usually three weeks earlier than the deadline for Proposals for Special Sessions should be sub contributed papers for the same meeting. The mitted directly to the Associate Secretary in Council has decreed that no paper, whether in charge of the meeting (at the address given in the vited or contributed, may be listed in the program accompanying box). If such proposals are ~ent of a meeting of the Society unless an abstract of to the Providence office, addressed to Nottces, the paper has been received in Providence prior or directed to anyone other than the Associate to the deadline. Secretary, they will have to be forwarded and may not be received before the quota is filled. 646 Send Proposals for Speeial Sessions to the Pseudodifferential Operators and Associate Seeretaries Applications The programs of sectional meetings are arranged by the Fra~ois Treves, Editor Associate Secretary for the section in question: (Proceedings of Symposia in Pure Mathematics. Far Western Section (Pacific and Mountain) Volume 43) Hugo Rossi, Associate Secretary Department of Mathematics This volume gathers together nineteen papers University of Utah devoted to microlocal analysis. which has emerged Salt Lake City, UT 84112 as one of the most powerful tools of linear (Telephone 801-581-8159) analysis since distribution theory. New classes of Central Section pseudodifferential operators and Fourier integral operators -re introduced in the 1970s and used Robert M. Fossum, Associate Secretary Department of Mathematics to tackle many classical and outstanding problems University of Illinois in partial differential equations. Recently. in a 1409 West Green Street very promising area of research. pseudodifferential Urbana, IL 61801 operators have been used to tackle nonlinear (Telephone 217-333-3975) differential problems. Eastern Section Content. W. Wistar Comfort, Associate Secretary S. Allnhec: and G. Metivier, Propagation of local Department of Mathematics analyticity for the Euler equation; J. L. Antonlano Wesleyan University and G. A. Uhlmann, A functional calculus for a class Middletown, CT 06457 of pseudodifferential operators with singular symbols; (Telephone 203-347-9411) M. S. 8...... ,..1, Uniqueness in a class of nonlinear Cauchy problems; Mlchllel Beale, Propagation of Southeastern Section smoothness for nonlinear second-order strictly hyperbolic Frank T. Birtel, Associate Secretary differential equations; R. a ..Ja and R. R. Colfmen, Department of Mathematics Multidimensional inverse scatterings and nonlinear partial Tulane University differential equations; R. R. Colfman and Yves Meyer, New Orleans, LA 70118 Nonlinear hannonic analysis and analytic dependence; (Telephone 504-865-5646) H. 0. Conlee, On some c• -algebras and Fnkhet-algebras of pseudodifferential operators; G. Eakin, Boundary-value As a general rule, members who anticipate orga problems for second-order elliptic equations in domains nizing Special Sessions at AMS meetings are advised to with comers; P. C. Greiner, Imbedding C" in Hn; seek approval at least nine months prior to the sched VIctor Gulllemln, On some results of Gelfand in uled date of the meeting. No Special Sessions can be integral geometry; Lara Horm11ncler, The propagation approved too late to provide adequate advance notice to of singularities for solutions of the Dirichlet problem; M. Kaehl-re and P. Schaplre, Applications of the members who wish to participate. microlocal theory of sheaves to the study of Ox; C. E. Kenla;, Recent progress on boundary-value prob'!!"s on C••..C••C••..C••C••.C••C••..C••..C ••)t••,.,••)t••)t••)t••)t••)t••)t Lipschitz domains; J. J. Kahn, Estimates for 8b on compact pseudoconvex CR manifolds; Yves Meyer, Recursion Theory Recent analysis and operator theory; L. P. Rothschild, Anil Nerode and Richard A. Shore, Editors Integrability and holornorphic extendibility for rigid CR structures; Johannes Sjilatrend, Multiple wells and (Proceedings of Symposia in Pure Mathematics. tunneling; N. K. Stanton and D. S. Tartakoff, The real Volume 42) analytic and Gevrey regularity of the heat lcemel forD b; The proceedings of the 1982 AMS Summer M. E. Taylor, Fefferman-Phong inequalities in diffraction Research Institute in Recursion Theory. this volume theory represents the largest and most comprehensive 1980 Mathematics Subject Classifications: meeting ever devoted to recursion theory. The book 22E30, 32F99, 35-XX, 42B20, 43A80 and contains major surveys with expository papers as others well as important new research. ISBN 0.8218-1469-9, LC 85-1419 ISSN 0082-0711 Graduate students and active researchers alike viii + 301 pages (hardcover), August 1985 with interests in any aspect of recursion theory. List price $44, Institutional member S35, including its interactions with set theory. model Individual member S26 [i)~EIIf~l); theory. constructive mathematics. foundations To order, please specify PSPUM/43N ;~ of mathematics and computer science. will be interested in this book. Some papers require only a ~~ basic course in logic or recursion theory: others are '1'.li)NDED'~· aimed at active researchers in the field. Shipping/Handling: 1st book S2, each add'l $1, $25 1980 Mathematics Subject Classifications: max. By air, 1st book S5, each add'l S3, S100 max. 03025, 03030, 03045, 03055, and others Prepayment required. Order from AMS, P.O. Box ISBN 0.8218-1447-8, LC 84-18525 1571, Annex Station, Providence, RI 02901-1571, or ISSN 0082-0717 call 800-556-7774 to use VISA or MasterCard. viii + 528 pages (hardcover), March 1985 List price S60, Institutional member S48, Individual member S36 To order, please specify PSPUM/42 N Shipping/Handling: 1st book $2, each add'l $1, $25 max. By air, 1st book $5, each add'l $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. 647 Call For Topics For 1988 Conferences Suggestions are invited from mathematicians, ei ther singly or in groups, for topics of the various conferences that will be organized by the Soci Topics of Current and ety in 1988. The deadlines for receipt of these Recent Conferences suggestions, as well as some relevant information AMS-SIAM Symposium in about each of the conferences, are outlined below. Applied Mathematics An application form to be used when submitting suggested topic(s) for any of these conferences 1980- Mathematical psychology and psychophysiology, (except the Short Course Series) may be obtained organized by STEPHEN GROSSBERG of Boston Uni by writing to the Meetings Department, American versity. Mathematical Society, P.O. Box 6248, Providence, 1983- Inverse problems, organized by D. W. Rhode Island 02940, or telephoning 401-272-9500, MCLAUGHLIN of the University of Arizona. extension 296. AMS Summer Institute Individuals willing to serve as organizers 1983- Nonlinear functional analysis and applications, should be aware that the professional meeting organized by FELIX BROWDER of the University staff in the Society's Providence office will provide of Chicago. full support and assistance before, during, and 1984- Geometric measure theory and the calculus of after each of these conferences. Organizers should variations, organized by WILLIAM K. ALLARD of also note that for all conferences, except Summer Duke University and FREDERICK J. ALMGREN, Research Conferences, it is required that the JR. of Princeton University. proceedings be published by the Society, and that 1985- Algebraic geometry, organized by DAVID proceedings of Summer Research Conferences are EISENBUD of Brandeis University. frequently published. A member of the Organizing 1986- Representations of finite groups and related top Committee must be willing to serve as editor of ics, organized by JON ATHAN L. ALPERIN of the the proceedings. University of Chicago. All suggestions must include (1) the names and affiliations of proposed members and chair AMS-SIAM Symposium on Some man of the Organizing Committee; (2) a two- or Mathematical Questions in Biology three-page detailed outline of the subject(s) to be 1983- Muscle physiology, organized by ROBERT M. covered, including the importance, timeliness of MIURA of the University of British Columbia. the topic, and estimated attendance; (3) a list 1984- DNA sequence analysis, organized by of the recent conferences in the same or closely ROBERT M. MIURA of the University of British related areas; ( 4) a tentative list of names and Columbia. affiliations of the proposed principal speakers; (5) 1985- Plant biology, organized by ROBERT M. a list of likely candidates who would be invited MIURA of the University of British Columbia. to participate and their current affiliations; and 1986- Modeling circadian rhythms, organized by (6) any other observations which may affect the GAIL A. CARPENTER of Northeastern Univer size of the conference and the amount of support sity. required. Any suggestions as to sites and dates 1987- Models in population biology, organized by should be made as early as possible in order to ALAN HASTINGS of the University of California, allow adequate time for planning. By action of Davis. the AMS Board of Trustees, the Meetings De partment of the Society is responsible for the final AMS-SIAM Summer Seminar selection of the site for each conference and for 1983- Large scale computations in fluid mechanics, all negotiations with the host institution. Indi organized by RICHARD C. J. SOMERVILLE, viduals submitting suggestions for the conferences Scripps Institution of Oceanography. listed below are requested to recommend sites or 1984- Nonlinear systems of PDE in applied mathe geographic areas which would assist the Meetings matics, organized by BASIL NICOLAENKO of Los Department in their search for an appropriate Alamos National Laboratories. site. In the case of Joint Summer Research 1985- Reacting flows: Combustion and chemical re Conferences in the Mathematical Sciences, a one-, actors, organized by G. S. S. LUDFORD of Cornell two-, or three-week conference may be proposed. University. Refer to the accompanying box titled Topics of Current and Recent Conferences for lists of topics. 648 1988 Symposium In 1988 Joint AMS-IMS-SIAM Summer Pure Mathematics Research Conferences in the This four-day symposium in pure mathemat Mathematical Sciences ics usually takes place in even-numbered years, These conferences are similar in structure to those sometimes in conjunction with a spring sectional held at Oberwolfach, and represent diverse areas meeting. Since none is scheduled in 1986, how of mathematical activity, with emphasis on areas ever, the next such symposium is due to be currently especially active. Careful attention held in the spring of 1987 at a location to be is paid to subjects in which there is important announced. Subject to final approval by the interdisciplinary activity at present. Topics for the AMS Board of Tru~ees, the topic selected by fifth series of one-week conferences, being held in the Committee on Summer Institutes and Special 1986, are Mathematics in general relativity, Large Symposia is The mathematical heritage of Her scale data analysis via computer graphics, Time man W eyl. Other topics in recent years have been reversal of Markov processes and potential theory, Relations between combinatorics and other parts Artin's braid group, Discrete and computational of mathematics (1978); The mathematical heritage geometry, and Representation theory of Lie groups. of Henri Poincare (1980); Several complex vari If proceedings are published by the Society, they ables (1982); and Pseudodifferential operators and will appear as volumes in the series Contemporary Fourier integral operators with applications to par Mathematics. tial differential equations (1984). Proceedings are published by the Society as volumes in the series Deadline For Suggestions: February 1, 1987 Proceedings of Symposia in Pure Mathematics. Deadline For Suggestions: August 15, 1986 Call for Topics for 1988 AMS Short Course Series 1988 AMS Summer Institute The AMS Short Courses consist of a series of intro Summer institutes are intended to provide an ductory survey lectures and discussions ordinarily understandable presentation of the state of the art extending over a period of one and one-half days in an active field of research in pure mathematics, immediately prior to the Joint Mathematics Meet and usually extend over a three-week period. ings held in January and August each year. Each of Dates for a summer institute must not overlap the courses is devoted to a specific area of applied those of the Society's summer meeting, which in mathematics or to areas of mathematics used in 1988 is the AMS Centennial Celebration from the study of a specific subject or collection of prob August 8-12, and there should be a period of at lems in one of the physical, biological, or social sci least one week between them. Proceedings are ences. Topics in recent years have been Approxima published by the Society as volumes in the series tion Theory (January 1986), Actuarial Mathematics Proceedings of Symposia in Pure Mathematics. (August 1985), Fair Allocation (January 1985), En vironmental and Natural Resource Mathematics (Au Deadline For Suggestions: August 15, 1986 gust 1984), Mathematics of Information Processing (January 1984). Proceedings are published by the 1988 AMS-SIAM Summer Seminar Society as volumes in the series Proceedings of Sym posia in Applied Mathematics, with the approval of The goal of the summer seminar is to provide an the Editorial Committee. environment and program in applied mathematics Deadline for Suggestions: Suggestions for the in which experts can exchange the latest ideas and January 1988 course should be submitted im newcomers can learn about the field. Proceedings mediately; suggestions for the August 1988 are published by the Society as volumes in the course should be submitted by December 1, series Lectures in Applied Mathematics. 1986. Deadline For Suggestions: August 15, 1986 Submit suggestions to: Professor Stefan A. Burr, Chairman, AMS Short Course Subcommittee, De partment of Computer Sciences, CUNY, City Col lege, New York, New York 10031. 649 Special Meetings THIS SECTION contains announcements of meetings of interest to some segment of the mathematical public, including ad hoc, local, or regional meetings, and meetings or symposia devoted to specialized. topics, as well as announcements of regularly scheduled meetings of national or international 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 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 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 Notices 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. 1985-1986. Academic Year Devoted to Nonlinear Dif 11-16. Second International Conference on Teaching ferential Equations, Mittag-Leffler Institute, Djursholm, Statistics, University of Victoria, Victoria, British Colum Sweden. (January 1985, p. 89) bia, Canada. (January 1985, p. 93) 1985-1986. Special Year in Complex Analysis, Univer 12-14. SIAM Conference on Linear Algebra in Signals, sity of Maryland, College Park, Maryland. (August 1985, Systems and Control, Park Plaza Hotel, Boston, Mas p. 522) sachusetts. (March 1986, p. 368) 1985-1986. Special Year in Differential Geometry, Uni 12-16. Structure, Coherence and Chaos in Dynamical versity of Illinois, Urbana-Champaign, Illinois. (October Systems, The Technical University of Denmark, Lyngby, 1985, p. 674) Denmark. (March 1986, p. 368) 1985-1986. Special Year in Operator Theory, Indiana 13-16. Second International Conference on Fibonacci University, Bloomington, Indiana. (August 1985, p. 522) Numbers and their Applications, San Jose State University, 1985-1986. Special Year in Singularities and Algebraic San Jose, California. (June 1986, p. 558) Geometry, University of North Carolina, Chapel Hill, 13-29. Workshop on Jordan Structures, University of North Carolina. (June 1985, p. 397, note change in years Ottawa, Ottawa, Ontario, Canada. (June 1986, p. 558) since previous listings.) 15-July 31, 1987. Program on Scientific Computing, 1985-1986. Year in Mathematical Logie, University of Institute for Mathematics and its Applications, University Notre Dame, Notre Dame, Indiana. (October 1985, p. 674) of Minnesota, Minneapolis, Minnesota. October 1985-0ctober 1986. Material Instabilities in Organizers: B. Engquist (chairman), R. Glowinski, M. Continuum Mechanics, Heriot-Watt University, Edinburgh, Luskin, and A. Majda. Scotland. (June 1985, p. 397) InformoJ:ion: Institute for Mathematics and its Applications, 1986-1987. Academic Year Devoted to Algebraic Geome University of Minnesota, 514 Vincent Hall, 206 Church try, Mittag-Leffler Institute, Djursholm, Sweden. (January Street Southeast, Minneapolis, Minnesota 55455, 612- 1986, p. 130) 624-6066. 18-20. Conference on Linear Algebra and Systems Theory, AUGUST 1986 Boston, Massachusetts. of Computer Science, 2. United States Commission on Mathematical Instruction Information: B. Datta, Department of Illinois, Urbana, Pre-Congress Series of Invited Survey Talks, New York 1304 West Springfield, University City Technical College, Brooklyn, New York. (March 1986, Illinois 61801. p. 368) 18-22. Bifurcation, Analysis Algorithms Applications, 3-5. 1986 International Statistical Symposium, Taipei, Universitat Dortmund, Dortmund, Federal Republic of Republic of China. Germany. (October 1985, p. 679) Informoi:ion: D. Wei, Bureau of Statistics, DGBAS, 2 Kwang 18-29. Opening Workshop on Basic Methods of Numerical Chow Street, Taipei, Taiwan 10729, Republic of China. Analysis and Introduction to State of the Art Research, Telephone: (886-2)381-1982; (886-2)381-4910, extension University of Minnesota, Minneapolis, Minnesota. (March 264. 1986, p. 368) 3-11. International Congress of Mathematicians, Berkeley, 19-21. SIAM Conference on Linear Algebra in Signals, California. (February 1984, p. 159) Systems and Control, Boston, Massachusetts. 4-8. Workshop on Micromechanical Aspects of Creep Information: SIAM LASSC Conference, 117 South 17th Fracture in Metals and Polymers, Mathematical Sciences Street, Suite 1400, Philadelphia, Pennsylvania 19103- Institute, Cornell University, Ithaca, New York. (June 5052. 1986, p. 557) 19-24. Thlrd International Conference on Applied Systems 6-9. First IMACS Symposium on Computational Acous Research, Information, and Cybernetics and International tics, Yale University, New Haven, Connecticut. (January Symposium on Mathematics and Logic, Baden-Baden, 1986, p. 134) Federal Republic of Germany. (March 1986, p. 369) 650 2o--September 6. Seizieme Ecole d'Etll de Calcul des 2-3. Mathematical Modelling of Non-Destructive Evalua Probabilitlls, Saint-Flour, France. (June 1986, p. 558) tion, Cambridge, Great Britain. (June 1986, p. 558) 23-25. Optimisation and Simulation of Large Scale Sys 2-4. Computers in the Teaching of the Mathematical teDIB, Reading, United Kingdom. (January 1986, p. 134) Sciences in Higher Education, Canterbury, Great Britain. 23-26. International Symposium on Probability and lnfarmati.an: G. Makinson, School of Math Studies, Uni- Bayesian Statistics, Innsbruck, Austria. (January 1986, versity of Kent at Canterbury, Kent CT2 7NZ, Great p. 134) Britain. 24-29. Eighth Australian Statistical Conference, Univer 2-4. Economics and Artificial Intelligence, Aix-En- sity of Adelaide, Adelaide, South Australia. Providence, France. Information: D. Street, Waite Agricultural Research In Infarmati.an: AFCET, 156 Boulevard Pereire, 75017 Paris, stitute, Private Bag Number 1, Glen Osmond, South France. Telephone: 33 (1)766-24-19. Australia 5064. 2-£. Workshop on Sign-Pattern Analysis of Linear 24-30. Fourth Conference on Numerical Methods, Miskolc, and Nonlinear Systems, University of Montreal, Quebec, Hungary. Canada. Information: K. Balla, Janos Bolyai Mathematical Society, Jnfarmati.an: S. L'Ecuyer, Centre de Recherches Mathema Budapest, Ander kos 1-3, 1.111, H-1061, Hungary. tiques, Universite de Montreal, C.P.6128, Succursale A, Montreal, Quebec, Canada H3C 3J7. 25-29. Congres Franco Chilien de Mathllmatiques Ap pliqulles, Santiago, Chile. (June 1986, p. 558) 3-5. Symposium on Control Theory, Somerville Col lege, University of Oxford, Oxford, England. (March 1986, 25-29. Sixth Prague Topological Symposium, Prague, p. 369) Czechoslovakia. (June 1985, p. 402) 3...£. Workshop on Sign-Pattern Analysis of Linear 25-30. Analyse Harmonlque, Marseille, France. (March and Nonlinear Systems, Universite de Montreal, Quebec, 1986, p. 369) Canada. (March 1986, p. 369) 25-30. Third Workshop on Hadronlc Mechanics, Univer 4-7. Polish Symposium on Interval and Fuzzy Mathe sity of Patras, Patras, Greece. Infarmati.an: University of Patras, Faculty of Science, De matics, Technical University of Poznan, Poznan, Poland. partment of Physics, Patras, 26110, Greece. Telephone: (October 1985, p. 679) (61)933-048. 7-9. The Mathematics of Surfaces, University College, 25-September 2. Combinatorial Optlmlaatlon, Centro di Cardiff, United Kingdom. (January 1986, p. 134) Cultura Scientifica A. Volta "Villa Olmo", Como, Italy. 8-10. NCC-Telecommunications, Philadelphia, Pennsylva Infarmati.an: Fondaziona Centro Internazionale Matematico nia. Estivo, care of Istituto Matematico "U. Dini," Viale Jnfarmati.an: NCC-Telecommunications, AFIPS, 1899 Pre Morgagni, 67/A, 1-50134 Firenze, Italy. ston White Drive, Reston, Virginia 22091, 703-620-8955 25-September 13. Microprogram on Nonlinear Dlffuaion or 800-622-1986. Equations and their Equilibrium States, Mathematical 8-10. 1986 ACM Conference on Research and Develop Sciences Research Institute, Berkeley, California. (October ment In Information Retrieval Systems, Pisa, Italy. 1985, p. 679) Infarmati.an: L. Bernardi, CNR, 7 piazzale A. Moro, I-00185 25-September 20. Ecole d'Automne 1986 du CIMPA: Roma, Italy. "L'Analyse Fonctlonelle et Applications", Nice, France. 8-13. Algebra-Tagung Halle 1986, Martin Luther Uni (June 1986, p. 558) versitat, German Democratic Republic. (October 1985, 26-29. IFAC/IFORS Symposium on Large Scale Systems, p. 679) Zurich, Switzerland. 8-14. Firat World Congreu of the Bernoulli Society Infarmati.an: M. Mansour, IFAC/IFORS Symposium, ETH- for Mathematical Statistics and Probability, Tashkent, Zentrum, CH-8092 Zurich, Switzerland. U.S.S.R. (October 1985, p. 679) 31-September 6. International Meeting on Ring Theory, 11-13. Splnora in Physics and Geometry, International Grenada, Spain. (June 1986, p. 558) Centre for Theoretical Physics, Trieste, Italy. (June 1986, 31-September 7. Algebraische Transformationsgruppen p. 558) und lnvariantentheorie, Diisseldorf-Himmelgeist, Federal 12-17. International Conference on Graphs, Steiner Sys Republic of Germany. tems and their Applications, Santa Tecla, Catania, Italy. Infarmati.an: I. Heydrich, Mathematisch Institut, Univer (June 1986, p. 558) sitatstraBe 1, 4000 Dusseldorf 1, Federal Republic of 13-16. Beobachtung, Experiment und Theorie In Natur Germany. wissenschaft und Medizln, Deutsches Museum, Miinchen, Federal Republic of Germany. SEPTEMBER 1986 lnfarmati.an: Gesellschaft Deutscher N aturforscher und 1-3. Elft Symposium iiber Operations Research, Darm Arzte e.V., Postfache 120190, D-5090 Leverkusen 12, stadt, Federal Republic of Germany. (June 1986, p. 558) West Germany. 1-5. Analyse Harmonlque, Marseille, France. (June 1986, 14-17. The 116th Annual Meeting of AFS, Providence, p. 558) Rhode Island. lnfarmati.an: C. Sullivan, 5410 Grosvenor Lane, Suite 110, 1-5. COMPSTAT 1986 Seventh Symposium on Compu Bethesda, Maryland 20814, 301-897-8616. tational Statistics, Universita "La Sapienza," Rome, Italy. (March 1986, p. 369) 14-19. Einlandung sur Jahrestagung der Deutschen Mathematiker-Vereinigung, Marburg, Federal Republic of 1-5. IFIP World Conference, Dublin, Ireland. Germany. lnfarmati.an: IFIP 86, 44 Northumberland Road, Dublin 4, Infarmati.an: W. Schaal, Fachbereich Mathematik der Uni Ireland. versitat Marburg, Hans-Meerwein-StraBe, 3550 Mar 1-5. Reprllsentations des Groupes et Analyse Complexe burg/Lahn, Federal Republic of Germany. (Journees S.M.F.), Marseille, France. (June 1986, p. 558) 14-20. Nonlinear Random Vibration, Oberwolfach, Fed 1-5. Tenth World Computer Congress, Trinity College, eral Republic of Germany. (June 1986, p. 558) Dublin, Ireland. (March 1986, p. 369) 14-20. Sechst Pannonisches Symposium iiber Mathema 1-5. Theorie des Nombres, Marseille, France. (March tische Statlstik, Bad Tatzmannsdorf, Austria. (June 1986, 1986, p. 369) p. 558) 651 15-19. International Conference on Stochastic Program· 29--30. Computers in Mathematical Research, Institute ming, Charles University, Prague, Czechoslovakia. (June for Mathematics and its Applications, University of Min 1986, p. 559) . nesota, Minneapolis, Minnesota. for Mathematics and its Applications, 15-19. Workshop on Global DifFerential Geometry, In Informatian: Institute Vincent Hall, 206 Church ternational Centre for Theoretical Physics, Trieste, Italy. University of Minnesota, 514 Minnesota 55455. (June 1986, p. 559) Street Southeast, Minneapolis, 15-20. Journees de Probability, Marseille, France. (June 29--30. Computers In Mathematical Research, University 1986, p. 559) College, Cardiff, United Kingdom. (January 1986, p. 134) 15-26. Workshop on Computational Fluid Dynamics 29--0ctober 1. Fifth Meeting on Mathematical Physics, and Reading Gas Flows, Institute for Mathematics and University of Coimbra, Coimbra, Portugal. (June 1986, its Applications, University of Minnesota, Minneapolis, p. 559) Minnesota. (March 1986, p. 369) 29--0ctober 2. Wlrtschaftsmathematlk in Beruf und Aua 16-19. CADMO 86, Washington, D.C. blldung, Klagenfurt, Austria. (June 1986, p. 559) Informatian: Wessex Institute of Technology, 125 High Street, Southampton, SOl OAA England. Telephone: OCTOBER 1986 0703-221397. 17-19. The Impact of Mathematical Analysis on the 1-4. Concurrence Imparfalte et Modele& de Marche, Solution of Engineering Problems, University of Maryland, Luminy, France. (June 1986, p. 559) College Park, Maryland. (March 1986, p. 369) 3-4. The Fourteenth Annual Mathematics and Statistics 18-19. Second Catalan International Symposium on Conference, Miami University, Oxford, Ohio. (June 1986, Statistics, Barcelona, Spain. (June 1986, p. 559) p. 559) 21-28. Neure Multivariate Methoden In der Statistlk, 5-9. International Symposium on Information Theory, Dusseldorf-Himmelgeist, Federal Republic of Germany. University of Michigan, Ann Arbor, Michigan. (March Informatian: I. Heydrich, Mathematisch Institut, Univer- 1986, p. 363) 1, Federal Republic of sitatstra6e 1, 4000 Dusseldorf Behandlung steifer Difl'erentlalgleichun· Germany. 5-12. Numerlaehe gen, Dusseldorf-Himmelgeist, Federal Republic of Ger 21-0ctober 4. Mathematics and Computer Science In many. Medical Imaging, II Ciocco, Italy. (June 1986, p. 559) Informatian: I. Heydrich, Mathematisch Institut, Univer 22-26. Euromeeh 216: Integrable Systems In Nonlinear sitatstra6e 1, 4000 Dusseldorf 1, Federal Republic of Analytical Meehanles, Leeds, England. (June 1986, p. 559) Germany. 22-26. First World Congress on Computational Mechan 9--11. Interdisciplinary Conference on Inference, Ohio ics, University of Texas, Austin, Texas. University, Athens, Ohio. (June 1986, p. 559) Informatian: J. Oden, TICOM, University of Texas at 13-November 29. Topology and Number Theory, Univer Austin, Austin, Texas 78712. site de Montreal, Quebec, Canada. (March 1986, p. 369) 22-26. IFAC-IMACS Symposium on Simulation of Control 15-18. Convegno su lpergruppl, Altre Strutture Multi· Systems, Vienna, Austria. (January 1986, p. 134) voche e Appllculonl, Udine, Italy. (June 1986, p. 559) 22-26. Theorie Analytique des Nombres, Luminy, France. 17-18. Fifteenth Annual Midwest DlftTerential Equations (June 1986, p. 559) Conference, Marquette University, Milwaukee, Wisconsin. 22-27. Deuxleme Ecole d'Automne Franco-Espagnole sur (March 1986, p. 369) Ia Simulation Numerique en Meeanique et en Physique, 2Q--24. Lea Sondages, Marseille, France. (June 1986, p. 559) Malaga, Spain. Informatian: A. Valle, Universidad de Malaga, Facultad de 24-25. Second Eastern Small College Computing Confer Ciencias, Departamento de Teoria de Funciones, Colonia ence, University of Scranton and the Hilton at Lackawanna de Sta. Ines, 29071 Malaga, Spain. Station, Scranton, Pennsylvania. (March 1986, p. 369) 22-27. Orthogonal Polynomials and Their Applications, 24-25. The Sixth Southeastern-Atlantic Regional Con· Segovia, Spain. (November 1985, p. 813) ference on DifFerential Equations, Clemson University, Clemson, South Carolina. (June 1986, p. 559) 23-25. Optimisation and Simulation of Large Seale Sys tems, University of Reading, Reading, Berkshire, United 25-26. Twentieth Midwest Partial DifFerential Equations Kingdom. (January 1986, p. 134) Seminar, Purdue University, West Lafayette, Indiana. Informatian: M. Baouendi or A. Friedman, Department on Probability and 23-26. International Symposium of Mathematics, Purdue University, West Lafayette, Austria. (June 1986, p. 559) Bayesian Statistics, Innsbruck, Indiana 47907, 317-494-1908 or 317-494-1926. Congress on Variational Methods In DifFerential 26-28. 28-31. Eighth International Conference on Pattern Recog· Problema, Trieste, Italy. (June 1986, p. 559) nition, Paris, France. 27-28. Firat Fall Foliage Topology Seminar, Moosilauke Informatian: AFCET ICPR Secretariat, 156 Boulevard Ravine Lodge, North Woodstock, New Hampshire. Pereire, F.75017 Paris, France. Telephone: (1)766-24- Program: The seminar will consist of a limited number of 19. with time in between talks to discuss invited addresses Conference, Ohio mathematics. 29--31. Twenty-first Actuarial Research Ohio. P. Latiolais, Department of Mathematics and State University, Columbus, Informatian: and ses Science, Dartmouth College, Hanover, New Program.: The program will include survey talks Computer are the Hampshire 03755. sions for contributed papers. The major topics theoretical foundations for the work of the valuation 28-2 October. 1986 ACSM-ASPRS Fall Convention, An actuary: the individual C-risks; their interdependence; chorage, Alaska. determination of surplus needs. lnformatian: W. French, 210 Little Falls Street, Falls Call fqr papers: Those interested in presenting a paper Church, Virginia 22046, 703-534-6617. should submit a one page abstract to the address below 28-2 October. The 49th Annual Meeting of the American by September 2, 1986. Society for Information Science, Chicago, Illinois. lnformatian: R. Brown, Department of Mathematics, Ohio Informatian: C. Davis, GSLIS, 410 DKH, 1407 West Gregory State University, 231 West 18th Avenue, Columbus, Drive, University of Illinois, Urbana, Illinois 61801. Ohio 43210, 614-422-5584. 652 31-1 November. Eighth Midwest Probability Colloquium, JANUARY 1987 Northwestern University, Evanston, Illinois. Speakers: E. Nelson, Princeton University; M. Aizenmann, January-May. Nonlinear PDE's, Brigham Young Univer Rutgers University; and R. Williams, University of Cal sity, Provo, Utah. (June 1986, p. 560) ifornia, San Diego. 12-14. Conference on Industry-University Collaborations Information: M. Pinsky or M. Rubin, Northwestern Uni In the Mathematical Sciences, Claremont, California. versity, Department of Mathematics, Evanston, Illinois Information: E. Cumberbatch, Claremont Graduate School, 60201. Claremont, California 91711, 714-621-8080. 12-16. Seminar on Approximation and Optimization, NOVEMBER 1986 Havana, Cuba. Information: H. Banks, Applied Mathematics Division, Brown University, Providence, Rhode Island 02912. 2-6. Fall Joint Computer Conference, Dallas, Texas. (March 1986, p. 370) 19-23. Structures for Documents, Aussois, France. Infamwtian: Institut National de Recherche en Informatique 3-7. Workshop on Numerical Algorithms for Modern Par et en Automatique-Service des Relations Exterieures, allel Computer Architectures, Institute for Mathematics Cours et Seminaires, Domaine de Voluceau, Bolte Postale and its Applications, University of Minnesota, Minneapolis, 105, 78153 Le Chesnay Cedex, France. Telephone: Minnesota. (March 1986, p. 370) 39 63 55 15. 9-15. Austrian Symposium on History of Mathematics, 19-30. Twenty-seventh Summer Research Institute of Neuhofen an der Ybbs, Austria. (June 1986, p. 559) the Australian Mathematical Society, University of New 1D--15. Workshop on Artln £-functions and Related England, Armidale, N.S.W., Australia. Topics, Universite de Montreal, Quebec, Canada. (March Speakers: Speakers will include I. Ekelund, M. Golubitsky, 1986, p. 370) and A. Coppel. Information: E. Dancer or B. Sims, Department of Mathe 1D--28. Workshop on Representation Theory of Lie Groups, matics, Statistics and Computing Science, University of International Centre for Theoretical Physics, Trieste, Italy. New England, Armidale, N.S.W. 2351, Australia. (June 1986, p. 560) 2Q--24. Workshop on lwasawa Theory and Special Values 18-22. Didactique des Mathematiques, Marseille, France. of £-functions, Mathematical Sciences Research Institute, (June 1986, p. 560) Berkeley, California. Program: This is the first 19-21. Cours Modulef: Une Bibliotheque Modulaire of two workshops being held at the Mathematical Sciences Research Institute during the d'Elements Finis, Rocquencourt, France. 1986-1987 program on Number Theory with Connections Information: Institut National de Recherche en Informa to Algebraic Geometry. tique et en Automatique, Bolte Postale 105, Rocquen Information: J. Coates, Mathematical Sciences Research court, 78153 Le Chesnay Cedex, France. Telephone: Institute, 1000 Centennial Drive, Berkeley, California (1) 39 63 55 15. 94720. 24-26. Trois Journees sur le Codage, Cachan, France. 29--31. Utah State University Department of Mathe Information: Secretariat du colloque, 3 journees sur le matics Second Conference on Matrix Theory, Utah State codage, LETT!, 9 avenue de Ia Division Leclerc, 94230 University, Logan, Utah. Cachan, France. Information: L. Beasley, Department of Mathematics, Utah 24-28. Geometrie Symplectique, Marseille, France. (June State University, Logan, Utah 84322-4125. 1986, p. 560) FEBRUARY 1987 DECEMBER 1986 February. Semlnaire International Grands Calculateurs Scientiflques, Paris, France. 1-5. Minisymposium on Numerical Simulation In Oil Information: Institut National de Recherche en Informa Recovery, Institute for Mathematics and its Applications, tique et en Automatique, Bolte Postale 105, Rocquen University of Minnesota, Minneapolis, Minnesota. court, 78153 Le Chesnay Cedex, France. Telephone: Organizer: M. Wheeler. (1) 39 63 56 00. Infamwtian: Institute for Mathematics and its Applications, 13-18. Annual Meeting, American Association for the University of Minnesota, 514 Vincent Hall, 206 Church Advancement of Science, Chicago, Illinois. (March 1986, Street Southeast, Minneapolis, Minnesota 55455,_ 612- p. 370) 624-6066. 16--20. Workshop on Materials with Nonlinear Constitu 2-5. Second International Conference on Artificial Intel tive Laws, Institute for Mathematics and its Applications, ligence, Marseilles, France. University of Minnesota, Minneapolis, Minnesota. Objective: The_ objective of this international conference is Organizers: T. Belytschko and Z. Bazant. to encourage the scientific exchange between academic Information: Institute for Mathematics and its Applications, researchers and industry concerning the development of University of Minnesota, 514 Vincent Hall, 206 Church knowledge based systems. Street Southeast, Minneapolis, Minnesota 55455, 612- Infamwtian: C. Guyomard, Institut International de Robo 624-6066. tique et d'Intelligence Artificielle de Marseille, Domaine de Luminy, Case 920, F 13288 Marseille Cedex 9, France. MARCH1987 Telephone: (33) 91 26 92 70. · 3-5. Forty Second Annual Conference on Applied Statis 16--20. Seminaire de Probabllites XXII, Laboratoire tics, Atlantic City, New Jersey. (March 1986, p. 370) d'Automatique et d'Analyse des Systemes, Toulouse, France. 3-6. Theory of Robots Symposium, Vienna, Austria. Information: G. Letac, Laboratoire de Statistiques et Proba (January 1986, p. 134) bilites, Universite Paul Sabatier, 118, route de Narbonne, 15-17. Cryptography and Coding, Cirencester, Glos., 31062 Toulouse Cedex, France, or G. Salut, Laboratoire England. (June 1986, p. 560) d'Automatique et d'Analyse des Systemes du CNRS, 7, avenue du Colonel Roche, 31077 Toulouse Cedex, ****** France. 653 22-25. Institute of Mathematical Statistics Central Re JUNE1987 gional Meeting, Dallas, Texas. (March 1986, p. 370) 8-19. Singapore Group Conference Theory, National 23-27. Workshop on Scientiftc Software, Institute for University of Singapore, Republic of Singapore. (March Mathematics and its Applications, University of Min 1986, p. 370) nesota, Minneapolis, Minnesota. Infarmatian: Institute for Mathematics and its Applications, 11-13. Congr- on Educational Computing in Mathe University of Minnesota, 514 Vincent Hall, 206 Church matics, Universita di Roma I, Roma, Italia. Street Southeast, Minneapolis, Minnesota 55455, 612- Infarmatian: M. Emmer, Dipartimento di Matematica, Uni 624-6066. versita di Roma I, Piazzale A. Mora, 00185 Roma, Italia. 23-30. NSF-CBMS Conference on Mathematical Statis tics, Ohio State University. (June 1986, p. 560) 15-July 3. Microprogram on Commutative Algebra, Math ematical Sciences Research Institute, Berkeley, California. (October 1985, p. 679) APRIL 1987 23-26. Sixth IMACS International Symposium on Com 21-25. Conference on Nonlinear Numerical Methods puter Methods for PDE'a, Lehigh University, Bethlehem, Baaed on the Use of Rational Functions, University of Pennsylvania. (January 1986, p. 134) Antwerp, Belgium. 23-27. International Conference on Generalbed Func Call far Papers: Submit a title and a short abstract (at most tions, Convergence Structurea and Their Applications, 1 page) not later than December 1, 1986 to the address Dubrovnik, Yugoslavia. (June 1986, p. 560) below. 29-July 3. Preml~re Conference Internationale sur lea Infarmatian: A. Cuyt, Department of Mathematics and Mathematiquea Appliquee& et Industriellea, Paris, France. Computer Science, University of Antwerp (UIA), Uni lnfarmatian: Institut National de Recherche en Informatique versiteitsplein 1, B-2610 Wilrijk (Antwerp), Belgium. et en Automatique, Services des Relations Exterieures, 27-30. Workshop on Mathematical Modeling In Combus Boite Postale 105, Rocquencourt, 78153 Le Chesnay tion and Related Toplca, Ecole Centrale de Lyon, France. Cedex, France. Telephone: (1) 39 63 56 00 or Society lnfarmatian: C. Schmidt-Laine, Ecole Centrale de Lyon, for Industrial and Applied Mathematics, 14th Floor, 117 Bolte Postale 163, 69131-Ecully Cedex, France. South 17th Street, Philadelphia, Pennsylvania, 215-564- Telephone: (33) 78 33 81 27, extension 4749/4742. 2929. 29-July 4. Joint IMA-GAMM-SIAM-SMAI Conference 29-May 8. AMS-SIAM Summer Seminar on Computa on First Joint International Conference on Industrial tional Aspects of VLSI Deaign with an Emphasis on Semi and Applied Mathematics, Paris, France. (January 1986, conductor Device Simulation, Institute for Mathematics p. 134) and its Applications, University of Minnesota, Minneapo lis, Minnesota. Organizers: R. Bank (Chairman), W. Coughran, E. Grosse, JULY1987 M. Luskin, R. Smith. Infarmatian: Institute for Mathematics and its Applications, July-August. Low Dimensional Topology Symposium, University of Minnesota, 514 Vincent Hall, 206 Church University of Sussex, Brighton, Great Britain. Street Southeast, Minneapolis, Minnesota 55455, 612- Topics: Topics will include low dimensional manifolds, 624-6066. knots, links and associated algebraic problems, and other topics of a geometric topological nature. Infarmatian: R. Fenn, Mathematics Division, University of MAY 1987 Sussex, Falmer, Brighton BN1 9QH, United Kingdom. 13-17. Automata, Languages, and Programming, Karl 11-15. Thirty-Brat Annual Meeting of the Australian sruhe, Federal Republic of Germany. Mathematical Society, Deakin University, Geelong, Victo Infarmatian: ICALP 87, Institute fiir Angewandte Infor ria, Australia. matik u. Formale Beschreibungsverfahren, TH, Postfach Call far Papers: March 31, 1987, is the deadline for original 6980, D-7500 Karlsruhe, Federal Republic of Germany. and survey papers on any area of mathematics, applica tion of mathematics, mathematics education, or history 13-17. Fourteenth International Colloquium on Automata, of mathematics. Languagea, and Programming, University of Karlsruhe, lnfarmatian: K. McAvaney, Division of Computing and Federal Republic of Germany. (March 1986, p. 370) Mathematics, Deakin University, Victoria, 3217, Aus 19-24. Conference on Potential Theory, Charles Univer tralia. Telephone: (052) 471376. sity, Prague, Czechoslovakia. (June 1986, p. 560) 25-27. Workshop on Nonlinear Hyperbolic Waves, Math ematical Sciences Research Institute, Berkeley, California. AUGUST 1987 Program: Nonlinear hyperbolic wave interactions and Rie- mann problems will provide the focus for this workshop. 1-6. Fifth Conference on Graph Theory of China, People's Recent progress and new methods have been introduced Republic of China. by the examination of mathematical questions common Call far papers: Papers are solicited on all branches of graph to a number of specific applications, such as reacting theory. Send an abstract of two hundred words or less fluid Rows, elasticity, astrophysics, plasma physics, flow to the address below by April 30, 1987. in porous media, and modulation theory for weakly lnfarmatian: Z. Zhong-fu, Lanzhou Railway Institute, dispersive systems. Lanzhou, Gansu, People's Republic of China. Infarmatian: J. Glimm, Mathematical Sciences Research 9-15. International Conference on Abelian Groups, Perth, Institute, 1000 Centennial Drive, Berkeley, California Western Australia. (June 1986, p. 560) 94720. 16-21. Sixteenth Conference on Stochastic Processes and 25-29. The Ninth International Symposium on Noise their Applications, Stanford University, Stanford, Califor in Physical Systems, Universite de Montreal, Quebec, nia. Canada. (March 1986, p. 370) Infarmatian: D. Iglehart, Department of Operations Re 28-1 June. Fourth Southeast Asian Conference on Math search, Stanford University, Stanford, California 94305- ematical Education, Singapore. 4022. Infarmatian: 0. Tui, Department of Mathematics, Institute 17-20. International Conference on Rings, Modules, and of Education, Bukit Timah Road, Singapore. Radicals, Hobart, Tasmania. (June 1986, p. 560) 654 24-28. Conference on Difl'erential Equations "Equadifl' 13-19. Journ~s Arlthmetlques 1987, Ulm, Federal Re '87", Democritus University of Thrace, Greece. (January public of Germany. (June 1986, p. 560) 1986, p. 134) 2Q--26. DMV-Jahrestagung 1987, Berlin, Federal Republic 24-28. International Conference on Web Geometry and of Germany. (June 1986, p. 560) Related Fields, Szeged University, Szeged, Hungary. (June 1986, p. 560) OCTOBER 1987 24-28. Second International Conference on Combinatorial Mathematics and Computing, Canberra, Australia. (March October. 81 ICAR-Internatlonal Conference on Advanced 1986, p. 370) Robotics, Paris or Nice, France. lnformntion: IRISA/INRIA, Rennes, France. Telephone: 24-28. Sixth National Conference on Artificial Intelli gence, Seattle, Washington. (March 1986, p. 370) 99 36 20 00. October. Journ~s Methodes Numeriques en Mllchanique 24-29. Meeting on Geometry of Banach Spaces, Mons, des Fluldes, Sophia-Antipolis, France. Belgium. lnformntion: J. Desideri, Institut National de Recherche en Injarmotion: C. Finet, Universite de l'Etat Mons, Faculte a Informatique et en Automatique, Sophia-Antipolis, Av des Sciences, 15 avenue Maistriau, 7000 Mons, Belgique. enue Emile-Hughes, 06560 Valbonne, France. Telephone: 93 65 77 77. SEPTEMBER 1987 9--12. Internatlonale Konfere11.1 iiber Anwendungen und Modellbildung 1m Mathematlkunterrlcht, Kassel, Federal Republic of Germany. (June 1986, p. 560) "The articles in these two volumes cover an enormous range of numerical methods and an equally vast range of scientific applications ... The volumes are indispensable to anyone who wishes to become acquainted with modern practices of large-scale computations." - Peter D. Lax, New York University LARGE-SCALE COMPUTATIONS IN FLUID MECHANICS Bjorn E. Engquist, Stanley Osher and Richard C. J. Somerville, Editors The purpose of the AMS-SIAM Summer Seminar on Applied Mathematics held at Scripps in 1983 was to bring together scientists interested in computational fluid mechanics and numerical analysts and mathematicians working in large-scale computations. The numerical modeling included geophysical problems of the atmosphere, ocean, and interior of the earth, and planetary, solar, and stellar atmospheres. Applications ranged from idealized turbulence in laboratory convection models to operational weather prediction. Engineering applications included aerodynamics, combustion, and flow in porous media. Recent advances in numerical analysis which have applications to these problems were stressed: These include shock capturing algorithms, spectral methods, boundary treatments, vortex methods, and parallel computing. ISBN (Set) 0-8218-1122-3; (Part 1) 0-8218- PREPAYMENT REQUIRED. Order from 1129-0; (Part 2) 0-8218-1130-4, LC 84-24534, American Mathematical Society ISSN 0075-8485 PO Box 1571 387 pp. (Part 1), 422 pp. (Part 2) (hardcover), July Annex Station 1985 Providence, RI 02901-1571 Set: Indlv. mem. 166, List $110, Inst. mem. $88 or call 800-556-7774 to use VISA Part 1: Indlv. mem. 14.0, List $66, Inst. mem. $53 or MasterCard. Part 2: Indiv. mem. 14.0, List $66, Inst. mem. $53 To order, please specify LAM/22NA (set), LAM/22.1NA (part 1), LAM/22.2NA (part 2) Shipping/Handling: 1st hook $2, each add'l $1, $25 max. By air, 1st book $5, each add'l $3, $100 max. 655 NEW AMS PUBLICA liONS mathematicians. He describes the difficulty he had in convincing the experts in the field that THE BIEBERBACH a mathematician, whose work was considered CONJECTURE: PROCEEDINGS to lie in an entirely different area, had actually proved a problem of such long standing. When OF THE SYMPOSIUM ON THE a mathematician is sure that he has the solution OCCASION OF THE PROOF of a problem, he must persist until he convinces Albert Baernstein, David Drasin, Peter others or is actually proved wrong." (Prepublication Duren and Albert Morden comments by James A. Hummel, The University of (Mathematical Surveys and Monographs. Maryland, College Park.) Volume 21) Contents Mathematical Papers For 70 years, the Bieberbach conjecture has Lars V. Ahlfors, Classical analysis: present and intrigued the mathematical world. Many students future of mathematics, who have had a first course in Richard Askey and George Gasper, Inequalities function theory, have tried their hand at a proof. for polynomials But many have invested fruitless years of carefully Arne Beurling, On interpolation. Blaschke manipulating inequalities in an attempt to establish products. and balayage of measures the correct bound. Louis de Branges, Powers of Riemann mapping In 1977, Louis de Branges of Purdue University took functions up the challenge of this famous unsolved problem, Jean Dieudonne, 300 years of analyticity but in his case the outcome was different. He will Paul R. Garabedian, Problems in mathematical be recognized as the mathematician who proved physics connected with the Bieberbach conjecture Bieberbach's conjecture. And more importantly, D. H. Hamilton, Extremal methods his method came from totally unexpected sources: James A. Jenkins, The method of the extremal operator theory and special functions. metric Peter W. Jones, Some problems in complex This book, based on the Symposium on the analysis Occasion of the Proof, tells the story behind I. M. Milin, Comments on the proof of the this fascinating proof and offers insight into the conjecture on logarithmic coefficients nature of the conjecture, its history and its proof. N. K. Nikol'skiT and V. I. Vasyunin, Notes on A special and unusual feature of the book is two function models the enlightened personal accounts of the people Christian Pommerenke, The growth of the involved in the exciting events surrounding the derivative of a univalent function proof. Especially attractive are the photographs Donald Sarason, Shift-invariant subspaces from a of the mathematicians who have made significant Brangesian point of view contributions to univalent functions, the area of Stephen W. Semmes, The Cauchy integral. complex analysis which provides the setting for the chord-arc curves. and quasiconformal mappings Bieberbach conjecture. William P. Thurston, Zippers and univalent functions Research mathematicians. especially analysts, are sure to enjoy the articles in this volume. Most Personal Accounts articles require only a basic knowledge of real and Louis de Branges, The story of the verification of complex analysis. The survey articles are accessible the Bieberbach conjecture to non-specialists, and the personal accounts of all Walter Gautschi, Reminiscences of my who have played a part in this important discovery involvement in de Branges 's proof of the will fascinate any reader. Bieberbach conjecture Richard Askey, My reaction to de Branges·s proof "The remarks by de Branges himself about the of the Bieberbach conjecture discovery of his proof should be read by all young Wolfgang Fuchs, Poem (continued) Use the order form in the back of this issue or call 800-556-7774 to use VISA or MasterCard. Shipping and handling charges will be added. 656 1980 Mathematics Subject Classifications: Contents 30Cxx, 30Dxx. 47Axx ISBN 0-8218-1521-0, LC 86-10843 Some basic concepts of Lie group representation ISSN 0076-5376 theory 260 pages (hardcover), July 1986 Individual member 127. List price $45, The Heisenberg group Institutional member $36 To order, please specify SURV /21N The unitary group Compact Lie groups Harmonic analysis on spheres NONCOM MUTATIVE Induced representations, systems of imprimitivity, HARMONIC ANALYSIS and semidirect products Michael E. Taylor Nilpotent Lie groups (Mathematical Surveys and Monographs, Harmonic analysis on cones Volume 22) SL(2, R) This book explores some basic roles of Lie groups SL(2, C), and more general Lorentz groups in linear analysis, with particular emphasis on the Groups of conformal transformations generalizations of the Fourier transform and the study of partial differential equations. It began as The symplectic group and the metaplectic group lecture notes for a one-semester graduate course Spinors given by the author in noncommutative harmonic analysis. As such, it is a valuable resource for both Semisimple Lie groups graduate students and faculty, and requires only 1980 Mathematics Subject Classifications: an acquaintance with Fourier analysis and basic 43-xx, 35-xx, 22-xx functional analysis, plus the first few chapters of a ISBN 0-8218-1523-7, LC 86-10924 standard text on Lie groups. ISSN 0076-5376 344 pages (hardcover). July 1986 Individual member 141, List price $68, The basic method of noncommutative harmonic Institutional member $54 analysis, a generalization of Fourier analysis, is to To order, please specify SURV /22N synthesize operators on a space on which a Lie group has a unitary representation from operators on irreducible representation spaces. Though the general study is far from complete, this book covers INTRODUCTION TO VARIOUS a great deal of the progress that has been made on important classes of Lie groups. ASPECTS OF DEGREE THEORY IN BANACH SPACES Unlike many other books on harmonic analysis, this book focuses on the relationship between harmonic E. H. Rothe analysis and partial differential equations. The (Mathematical Surveys and Monographs, author considers many classical PDEs, particularly Volume 23) boundary value problems for domains with simple shapes, that exhibit noncommutative groups of Since its development by Leray and Schauder symmetries. Also, the book contains detailed work, in the 1930's, degree theory in Banach spaces which has not previously been published, on the has proved to be an important tool in tackling harmonic analysis of the Heisenberg group and many analytic problems, including boundary harmonic analysis on cones. value problems in ordinary and partial differential equations, integral equations, and eigenvalue BIOGRAPHY------ and bifurcation problems. With this volume E. Michael Taylor works in the area of partial differential H. Rothe has provided a largely self-contained equations. He received his Ph.D. from the University of introduction to topological degree theory, with an California at Berkeley in 1970. In 1977-78 he received an Alfred P. Sloan fellowship for study. Currently he is emphasis on its function-analytical aspects. He professor of mathematics at the State University of New develops the definition and properties of the degree York at Stony Brook. Professor Taylor is the author as much as possible directly in Banach space, of Pseudodifferentia/ Operators. published in 1981 by without recourse to finite-dimensional theory. A Princeton University Press. basic tool used is a homotopy theorem for certain linear maps in Banach spaces which allows one Use the order form in the back of this issue or call 800-556-7774 to use VISA or MasterCard. Shipping and handling charges will be added. 657 to generalize the distinction between maps with positive determinant and those with negative determinant in finite-dimensional spaces. A FORMALIZATION OF SET Rothe's book is addressed particularly to graduate THEORY WITHOUT VARIABLES students who may have only a rudimentary Alfred Tarski and Steven Roger Givant knowledge of Banach space theory. The first (Colloquium Publications, Volume 41) chapter on function-analytic preliminaries provides most of the necessary background. Also for the Completed in 1983, this work culminates nearly benefit of less experienced mathematicians, Rothe a half century of the late Dr. Alfred Tarski's introduces the topological tools (subdivision and foundational studies in logic, mathematics, and simplicial approximation, for example) only to the the philosophy of science. Written in collaboration degree of abstraction necessary for the purpose with Dr. Steven Givant, the book appeals to a at hand. Such a reader will gain insight into the very broad audience, and requires only a familiarity various aspects of degree theory, experience in with first-order logic. It will, of course, be of function-analytic thinking, and a theoretic base for great interest to logicians and mathematicians applying degree theory to analysis. interested in the foundations of mathematics, but also to philosophers interested in logic, semantics, Rothe also describes the various approaches algebraic logic, or the methodology of the deductive that have historically been taken towards degree sciences, and to computer scientists interested in theory, making the relationships between these developing very simple computer languages rich approaches clear. He treats the differential method, enough for mathematical and scientific applications. the simplicial approach introduced by Brouwer in 1911, the Leray-Schauder method (which assumes The authors develop set theory within the Brouwer's degree theory for the finite-dimensional framework of an especially simple and natural space and then uses a limit process in the equational formalism, closely related to the dimension), and more recent attempts to establish formalism of the theory of relation algebras. degree theory in Banach spaces intrinsically, by an There are no variables, quantifiers, or sentential application of the differential method in the Banach connectives. Predicates are constructed from two space case. atomic binary predicates-denoting the relations of Contents identity and set-theoretic membership-by means of repeated applications of four operators that are Function-analytic preliminaries analogues of the well-known operations of relative The Leray-Schauder degree for differentiable maps product, conversion, union, and complementation. All mathematical statements are expressed as The Leray-Schauder degree for not necessarily equations between predicates. There are ten logical differentiable maps axiom schemata and just one rule of inference: the The Poincare-Bohl theorem and some of its one of replacing equals by equals, familiar from applications high school algebra. The product theorem and some of its consequences This formalism appears to be quite weak in its The finite-dimensional case powers of expression and proof. Indeed, it is shown to be equipollent to a system of first-order On spheres logic with just three variables. However, it proves Some extension and homotopy theorems adequate for the formalization of practically all known systems of set theory, and hence for the The Borsuk theorem and some of its consequences development of all classical mathematics. The linear homotopy theorem The book also contains numerous applications of Proof of the Sard-Smale theorem the main results to diverse areas of foundational research: propositional logic; semantics; first-order 1980 Mathematics Subject Classifications: 55M25, 4602 logics with finitely many variables; definability and ISBN 0-8218-1522-9. LC 86-8038 axiomatizability questions in set theory, Peano ISSN 0076-5376 arithmetic, and real number theory; representation 254 pages (hardcover). July 1986 Individual member 136, List price $60, and decision problems in the theory of relation Institutional member S48 algebras; and decision problems in equational logic. To order, please specify SURV /23N (continued) Use the order form in the back of this issue or call 800-556-7774 to use VISA or MasterCard. Shipping and handling charges will be added. 658 BIOGRAPHY------ alphabet from scratch, and creates logos or special Alfred Tarskl studied philosophy and mathematics at symbols. the University of Warsaw. receiving his Ph.D. in 1924 under the direction of the philosopher Lesniewski. For the Concepts are introduced early in the manual, with next fifteen years he taught at the Zeromski Lye~ and more detailed explanations found in later chapters. continued his affiliation with the University of Warsaw Program exercises are found throughout the text, as assistant. and later as adjunct. to Lukasiewcz's philosophical seminar. with answers supplied in an appendix. Special margin "road signs" alert readers to exercises and Following an American lecture tour in 1939, Tarski concepts of greater difficulty. took temporary positions at Harvard. the Institute for Advanced Studies. and the City College of New York. In 1980 Mathematics Subject Classifications: 1942 he obtained a permanent position at the University 00, 68 of California. Berkeley. where he went on to found his ISBN 0-201-13444-6, LC 85-28675 famous school of logic. He became a Professor Emeritus 373 pages (softcover). 1986 in 1968. but continued to teach for about five more years. Individual member 120, List price S20, The last part of his life, until his death in 1985. was Institutional member S20 To order, please specify spent collaborating with Steven Givant on the book. A METAFONT /N formalization of set theory without variables. • Published jointly by the AMS and Addison-Wesley Publishing Company. Tarski's prolific and fundamental contributions to foundational research in mathematics cover an astounding range of subjects. He published more than one hundred research papers. and authored or coauthored over ten research monographs. MINIMAX METHODS IN Steven Glvant attended Dartmouth College. and later CRITICAL POINT THEORY the University of California at Berkeley, where he studied logic with Henkin. Tarski, and Vaught. He received his WITH APPLICATIONS TO Ph.D. in 1975 under the direction of Vaught. He is DIFFERENTIAL currently an Associate Professor of Mathematics at Mills EQUATIONS College. Paul H. Rabinowitz (CBMS Regional Conference Series, Number 65 1980 Mathematics Subject Classifications: Supported by the National Science Foundation) 03B, 03B30, 03C05, 03E30, 03G15, 03B20, 03B25 ISBN 0-8218-1041-3 The book provides an introduction to minimax ISSN 0065-9258 methods in critical point theory and shows their 280 pages (hardcover), September 1986 Individual member 136. List price S60, use in existence questions for nonlinear differential Institutional member S48 equations. An expanded version of the author's To order, please specify COLL/41N 1984 CBMS lectures, this volume is the first monograph devoted solely to these topics. Among the abstract questions considered are the following: the mountain pass and saddle point theorems, THE METAFONTbook• multiple critical points for functionals invariant Donald E. Knuth under a group of symmetries, perturbations from symmetry, and variational methods in bifurcation The METAFONTbook is a user's guide and theory. reference manual to the computer system called The book requires some background in functional METAFONT. METAFONT is a system for the analysis and differential equations, especially elliptic design of symbols and alphabetic characters suited partial differential equations. It is addressed to to raster-based devices that print or display text. mathematicians interested in differential equations The construction of a typeface is an art form and and/or nonlinear functional analysis, particularly this manual is written for people who wish to critical point theory. advance the quality of mathematical typesetting. Contents The METAFONTbook enables readers, with only An overview minimal computer science or word processing The mountain pass theorem and some applications experience, to master the basic as well as the more advanced features of METAFONT programming. Some variants of the mountain pass theorem With this manual, readers will learn how to write The saddle point theorem a program using METAFONT that customize a Some generalizations of the mountain pass theorem type design that already exists, creates an entire (continued) Use the order form in the back of this issue or call 800-556-7774 to use VISA or MasterCard. Shipping and handling charges will be added. 659 Applications to Hamiltonian systems of Partitions. Partitions: Yesterday and Today. and The Collected Papers of P. A. MacMahon. Currently he is a Functionals with symmetries and index theorems Evan Pugh Professor of Mathematics at Pennsylvania State University and holds an Adjunct Professorship at Multiple critical points of symmetric functionals: the University of Waterloo. problems with constraints Contents Multiple critical points of symmetric functionals: the unconstrained case Found opportunities Pertubations from symmetry Classical special functions and L. J. Rogers Variational methods in bifurcation theory W. N. Bailey's extension of Roger's work 1980 Mathematics Subject Classifications: Constant terms 34C25, 35J60, 47H15, 58E05. 58E07, 58F05, 70H05, 70H30 Integrals ISBN 0-8218-0715-3, LC 86-7847 ISSN 0160-7642 Partitions and q-series 112 pages (softcover), July 1986 All Individuals 110, List price S16 Partitions and constant terms To order, please specify CBMS/65N The hard hexagon model Ramanujan Computer algebra q-SERIES: THEIR DEVELOP 1980 Mathematics Subject Classifications: MENT AND APPLICATION IN 33A30, 10A45, 82A67,05A19, 33A25 ISBN 0-8218-0716-1, LC 86-14061 ANALYSIS, NUMBER THEORY, ISSN 0160-7642 110 pages (softcover), 1986 COMBINATORICS, PHYSICS All Individuals 110, List price S16 AND COMPUTER ALGEBRA To order, please specify CBMS/66N George E. Andrews (CBMS Regional Conference Series, Number 66 Supported by the National Science Foundation) APPLICATIONS OF ALGEBRAIC This book integrates recent developments and K-THEORY TO ALGEBRAIC related applications in q-series with a historical GEOMETRY AND NUMBER development of the field, focusing on major breakthroughs and the author's own research THEORY interests. The author develops both the important Spencer J. Block, R. Keith Dennis, Eric M. analytic topics (Bailey chains, integrals, and Friedlander and Michael R. Stein, Editors constant terms) and applications to additive (Contemporary Mathematics, Volume 55) number theory. He concludes with applications to physics and computer algebra and a section These two volumes of forty papers present a on results closely related to Ramanujan's "Lost state-of-the-art description of some of the exciting Notebook." applications of algebraic K-theory to other branches With its wide range of applications, the book will of mathematics, especially algebraic geometry and interest researchers and students in combinatorics, algebraic number theory. As the proceedings of additive number theory, special functions, a 1983 AMS-IMS-SIAM Joint Summer Research statistical mechanics, and computer algebra. It Conference, they include current and important is understandable to even a beginning graduate work by some of the best researchers in the field. student in mathematics who has a background The diverse scope includes the following topics: in advanced calculus and some mathematical the matrix/vector bundle tradition of concrete maturity. computations for specific rings, the interaction with algebraic cycles, and the generalization of the BIOGRAPHY------ regulator map for units in an algebraic number field George E. Andrews received his Ph.D. from the to higher K-groups of varieties over number fields. University of Pennsylvania in 1964 as the last student of Hans Rademacher. He presented the Hedrick Lectures for Of particularly high research value are the ideas of the MAA in 1980. and in 1982-83 he was a Guggenheim Beilinsonon, which are presented here for the first fellow. His books include Number Theory. The Theory Use the order form in the back of this issue or call 800-556-7774 to use VISA or MasterCard. Shipping and handling charges will be added. 660 time, the work of Merkurjev and Suslin relating found in fluid dynamics, particularly in studying K-theory to the Brauer group (as reported by the routes to chaos in two laboratory systems, Merkurjev and Wadsworth), and the papers by Taylor-Couette flow between rotating cylinders and Kato on algebraic cycles. Rayleigh-Benard convection in a fluid layer. Directed towards mathematicians working in 1980 Mathematics Subject Classifications: 58F14, 34C35, 76E30 algebraic K-theory, algebraic geometry, and ISBN 0-8218-5060-1. LC 86-8106 algebraic number theory, this volume is also of ISSN 0271-4132 interest to the algebraic topologist. The reader 408 pages (softcover). August 1986 Individual member 120, List price $34, should be familiar with basic K-theory and Institutional member $27 interested in its applications to other areas of To order, please specify CONM/56N mathematics. 1980 Mathematics Subject Classifications: 18F25, 16A54. 19E, 19F ISBN (Set) 0-8218-5054-7; (Part 1) 0-8218-5055-5; (Part 2) 0-8218-5056-3, COMBINATORICS AND LC 86-7904, ISSN 0271-4132 424 pages (part 1); 432 pages (part 2) ORDERED SETS (softcover). July 1986 Ivan Rival, Editors Set: Individual member 137. List price $62. (Contemporary Mathematics, Volume 57) Institutional member S50 Part 1: Individual member 121. List price $35. Institutional member $28 For the mathematician interested in discrete Part 2: Individual member 122. List price $36, mathematics, from the senior undergraduate to the Institutional member $29 To order. please specify CONM/55N (set), professional level, this volume provides first-rate CONM/55.1N (part 1). CONM/55.2N surveys of the important combinatorics themes in (part 2) ordered sets. These expository lectures, given at a 1985 Joint Summer Research Conference, covers a wide MULTIPARAMETER range of topics, which includes: the three-machine problem to illustrate the order-theoretic aspects of BIFURCATION THEORY scheduling theory; the techniques used in settling Martin Golubitsky and John M. the "matching conjecture"; the decomposition Guckenheimer, Editors of ordered sets into few chains; the reorientation (Contemporary Mathematics, Volume 56) of graphs; the varied occurrences of the meet distribution property; surveys techniques used in This 1985 AMS Summer Research Conference settling binary sorting problems; the formulation brought together mathematicians interested of a general view point for retraction; the survey in multiparameter bifurcation with scientists of cutsets; and the role played by subdiagrams in working on fluid instabilities and chemical reactor ordered sets. dynamics. This proceedings volume demonstrates Contents the mutually beneficial interactions between the Werner Poguntke, Order-theoretic aspects of mathematical analysis, based on genericity, and scheduling experimental studies in these fields. Various papers Joseph P. S. Kung, Radon transforms in study steady state bifurcation, Hopf bifurcation to combinatorics and lattice theory periodic solutions, interactions between modes, Henry A. Kierstead, Recursive ordered sets dynamic bifurcations, and the role of symmetries Oliver Pretzel, Orientations and reorientations of in such systems. A section of abstracts at the end graphs of the volume provides guides and pointers to the Paul Edelman, Abstract convexity and literature. meet-distributive lattices Peter M. Winkler, Correlation and order The mathematical study of multiparamater EI-Mostapha Jawhari, Driss Misane, and bifurcation leads to a number of theoretical and Maurice Pouzet, Retracts: graphs and ordered practical difficulties, many of which are discussed in sets from the metric point of view these papers. The articles also describe theoretical Mohamed EI-Zahar and Nejib Zaguia, and experimental studies of chemical reactors, Antichains and cutsets which provide many situations in which to test Ivan Rival, Stories about order and the letter N the mathematical ideas. Other test areas are (continued) Use the order form in the back of this issue or call 800-556-7774 to use VISA or MasterCard. Shipping and handling charges will be added. 661 1980 Mathematics Subject Classifications: Madhav V. Nori, The Schottky groups in higher 06, 05 dimensions ISBN 0-8218-5051-2 C. Patton and H. Rossi, Cohomology on complex ISSN 0271-4132 304 pages ( softcover), August 1986 homogeneous manifolds with compact subvarieties Individual member 117, List price $29, C. A. M. Peters, Some applications of the Institutional member S23 Lefschetz fixed point theorems in (complex) To order, please specify CONM/57N algebraic geometry Jayant Shah, Stability of two-dimensional local rings. II Roy Smith and Horacia Tapia-Recillas, The THE LEFSCHETZ CENTENNIAL connection between linear series on curves and CONFERENCE, PART 1: Gauss maps on subvarieties of their Jacobians Peter F. Stiller, Some applications of algebraic PROCEEDINGS ON ALGEBRAIC geometry to systems of partial differential equations GEOMETRY and to approximation theory D. Sundararaman, Editor Lucien Szpiro, Small points and torsion points (Contemporary Mathematics, Volume 58 (Part 1)) Domingo Toledo and Vue Lin L. Tnog, Green's theory of Chern classes and the Riemann-Roch This volume contains many of the papers in the formula area of algebraic geometry presented at the 1984 1980 Mathematics Subject Classification: 14 Solomon Lefschetz Centennial Conference held ISBN (Part 1) 0-8218-5061-x, LC 86-14040 this ISSN 0271-4132 in Mexico City. The conference focused on 288 pages (softcover), August 1986 topic along with the areas of Algebraic Topology Individual member 117, List price S29, and Differential Equations where Lefschetz Institutional member S23 made significant contributions. The proceedings To order, please specify CONM/58.1N begins with two interesting articles: A Page of Mathematical Autobiography that has been reprinted from an early edition of the Bulletin of the AMS and Solomon Lefschetz, a biography by FUNCTION ESTIMATES William Hodge that is reprinted from the Bulletin J. S. Marron, Editor of the London Mathematical Society. (Contemporary Mathematics, Volume 59) Contents Solomon Lefschetz, A page of mathematical This volume collects together papers presented at autobiography the 1985 Conference in Function Estimation held Sir William Hodge, Solomon Lefschetz at Humboldt State University. The papers focus C. Banica and 0. Forster, Multiplicity structures especially on various types of spline estimations on space curves and convolution problems. Spencer Bloch, Algebraic cycles and the Beilinson conjectures The use of estimation and approximation methods analysis and Herbert Clemens, The infinitesimal Abel-Jacobi as applied to geophysics, numerical mapping for hypersurfaces nonparametric statistics was a special feature of I. Dolgachev, Infinite Coxeter groups and this conference. automorphisms of algebraic surfaces Contents Shalom Eliahou, A problem about polynomial Charles J. Stone, Logspline density estimation ideals Wolfgang Dahmen and Charles A. Micchelli, Carlos Gomez-Mont Avalos, Local Torelli Statistical encounters with B-splines theorem for certain extremal varieties K. S. Lii and M. Rosenblatt, Estimation of a Xavier Gomez-Mont, Transverse deformations of transfer function in a nongaussian context holomorphic foliations Finbarr O'Sullivan, Evaluating the performance of F. Hirzebruch, Singularities of algebraic surfaces an inversion algorithm and characteristic numbers Robert L. Parker, Harmonic splines in N. J. Hitchin, Metrics on moduli spaces geomagnetism George F. Kempf, Varieties with rational K. P. Schwarz, Problems in estimating the singularities anomalous gravity potential of the earth from A. S. Libgober and J. W. Wood, Remarks on discrete data moduli spaces of complete intersections (continued) Use the order form in the back of this issue or call 800-556-7774 to use VISA or MasterCard. Shipping and handling charges will be added. 662 Wolfgang Hardie, What regression model should Charles A. Micchelli, Algebraic aspects of be chosen when the statistician misspecifies the interpolation error distribution Klaus Holling, Multivariate splines Dennis D. Cox, Approximation theory of method 1980 Mathematics Subject Classifications: of regularization estimators: applications 41-01, 41-02. 30E10, 65Dxx Grace Wahba, Partial spline modelling of the ISBN 0.8218-0098-1. LC 86-10846 tropopause and other discontinuities ISSN 0160.7634 144 pages, August 1986 John A. Rice, Choice of a smoothing parameter in Hardcover: Individual member 116, List price deconvolution problems $26. Institutional member $21 David L. Donoho and lain M. Johnstone, Softcover: Individual member 113, List price $22, Institutional member $18 Regression approximation using projections and To order. please specify PSAPM/36N isotropic kernels (hardcover). PSAPMS/36N (softcover) J. S. Marron, Will the art of smoothing ever become a science? 1980 Mathematics Subject Classifications: 62G05, 62G99 REVIEWS IN RING THEORY ISBN 0.8218-5062-8, LC 86-14203 ISSN 0271-4132 198Q-84 188 pages (softcover), August 1986 Individual member 113, List price $22. Lance W. Small, Editor Institutional member $18 To order, please specify CONM/59N This volume is a sequel to the original Reviews in Ring Theory and collects the reviews that appeared in Mathematical Reviews from 1980 through 1984 with primary or secondary classification 16 APPROXIMATION THEORY (Associative rings and algebras). The reviews are classified according to the 1980 MR scheme and Carl de Boor, Editor appear in each subsection according to their MR (Proceedings of Symposia in Applied Mathematics, number. After each review, a list of reviews citing Volume 36) that review will be given. An author index appears at the end of the volume. These six papers, first presented as the 1986 1980 Mathematics Subject Classifications: AMS Short Course, give a brief introduction to 13, 16. 17, 18, 20 approximation theory and some of its current areas ISBN 0.8218-0097-3, LC 86-10907 of active research, both theoretical and applied. 704 pages (softcover), August 1986 The first lecture describes and illustrates the basic Individual member 151, List price $85, Institutional member $68 concerns of the field. Topics highlighted in the To order, please specify REVRNG/84N other lectures include the following: approximation in the complex domain, N-width, optimal recovery, interpolation, algorithms for approximation, and splines, with a strong emphasis on a multivariate SELECTED TABLES IN setting in the last three topics. MATHEMATICAL STATISTICS, These lectures are aimed at mathematicians VOLUME 10 interested in an introduction to areas of current research and to engineers and scientists interested Institute of Mathematical Statistics in exploring the field for possible applications to R. E. Odeh and J. M. Davenport, Co-Editors their own fields. They are best understood by those (Selected Tables in Mathematical Statistics, with a standard first graduate course in real and Volume 10)' complex analysis, but some of the presentations are accessible with the minimal requirements of This is the tenth in a series of statistical tables advanced calculus and linear algebra. prepared under the aegis of the Institute of Contents Mathematical Statistics and published jointly with the American Mathematical Society. It consists of Ronald A. DeVore, Approximation of functions 2 series of tables and related textual material: The ~- B. SafT, Polynomial and rational approximation distribution of positive m the complex domain definite quadratic forms, by B. K. Shah and Confidence limits on the correlation A. Pinkus, N-widths and optimal recovery coefficient, by Robert E. Odeh. E. W. Cheney, Algorithms for approximation (continued) Use the order form in the back of this issue or call 800-556-7774 to use VISA or MasterCard. Shipping and handling charges will be added. 663 For the first tables Shah has developed a recurrence Chapters include: lists of the serial titles covered, relation to calculate the coefficients in a Laguerre the mathematics subject classification systems series representation. He uses this Laguerre used, an index of terms occurring in the subject series representation, which is orthogonal to classification, and mnemonic codes representing the chi-square density function, to tabulate the the mathematical symbols. Chapters 3, 4, and percentile points of the distribution of positive 5 are also sold as separate publications. They definite quadratic forms for n = 2 to 10. are entitled Serials List, Subject Classification Schemes, and Index of Subject Classification In the second section of the book Odeh gives tables Words, respectively. for finding upper, lower, and 2-sided limits and confidence intervals on the population correlation 450 pages (softcover), August 1986 Individual member 156, List price $70. coefficient for a bivariate normal distribution. He Institutional member S56 gives an extensive section on the distribution To order, please specify USERGUIDE/N theory and numerical methods used to compute the tables. 1980 Mathematics Subject Classifications: 62005, 62E15, 62E99, 62G15, 62J99 POLES AND RESIDUES OF ISBN 0.8218-1910.0, LC 74-6283 ISSN 0094-8837 EISENSTEIN SERIES FOR 360 pages (hardcover), 1986 Individual member 123, List price $39, SYMPLECTIC AND UNITARY Institutional member $31 To order. please specify TABLES/iON GROUPS Paul Feit (Memoirs of the AMS, Number 346) WORLD DIRECTORY OF This memoir evaluates Dirchlet series which arise in studying Fourier coefficients of certain Eisenstein MATHEMATICIANS 1986 series for a wide variety of groups. The author uses this technical calculation to prove many theorems Published by the International Mathematical Union, about automorphic forms, finding generalizations of is based on this eighth edition of the directory the classical theorems for series of small weights. Committees for material supplied by the National He also locates all of the poles of an Eisenstein It Mathematics or corresponding organizations. series of arbitrary weight. contains names and addresses of participating organizations and of the members of these Directed at specialists in the theory of automorphic organizations. Members of Societies listed in the forms in several variables, the book demonstrates seventh edition who have not responded have been that for certain algebraic groups, there is a family included with the addresses from that edition. of Eisenstein series whose Fourier expansions can 976 pages (softcover), August 1986 be thoroughly described. Thus it suggests that Individual member 130, List price $30, such a "good" family of Eisenstein series must Institutional member $30 exist for other groups as well. To order, please specify WRLDIR/8N Contents Formal Dirichlet series The finiteness problem MathSci USER GUIDE Analyticity Algebraic properties This is a search manual to assist users of 1980 Mathematics Subject Classification: the database MathSci. Formerly called the 11F55 MATHFILE User's Guide, this manual describes ISBN 0.8218-2347-7, LC 86-3386 ISSN 0065-9266 the bibliographic content of MathSci. The 93 pages (softcover), May 1986 published equivalents for the database include: Individual member 17. List price $12, Mathematical Reviews and Current Mathematical Institutional member $10 Publications (both published by the AMS), Current To order, please specify MEM0/346N Index to Statistics (published jointly by the American Statistical Association and the Institute of Mathematical Statistics), and Index to Statistics and Probability by John Tukey and lan Ross. Use the order form in the back of this issue or call 800-556-7774 to use VISA or MasterCard. Shipping and handling charges will be added. 664 KK~(A, B). For A commutative and B trivial, this reduces to a spectral sequence relating K~ (X) to PARABOLIC SUBGROUPS OF KG(X), with X a compact G-space. ALGEBRAIC GROUPS AND The memoir is aimed at research mathematicians INDUCTION interested in algebraic topology, K-theory, and/or David Vella operator algebras. It assumes familiarity with (Memoirs of the AMS, Number 347) topological K-theory and homological algebra, and preferably also some exposure to the K-theory of The author uses a Mackey decomposition theorem c· -algebras. for two parabolics to study the rational G-modules 1980 Mathematics Subject Classifications: induced from a parabolic subgroup P of G. He 46L80. 46M20. 55U20, 55U25, 55N15, 55S25. 46L55 extends the decomposition theorem to the derived ISBN 0.8218-2349-3. LC 86-10959 functor modules and studies the induction from a ISSN 0065-9266 certain nonparabolic subgroup H appearing in the 104 pages (softcover). July 1986 decomposition theorem. Individual member 17. List price $12. Institutional member $10 The results lead to good filtrations on modules To order, please specify MEM0/348N induced from a one-dimensional H-module for G = Sln(k) and SP4 (k) and also to the structure of the cohomology of rank-2 bundles on G/P when G is in SL3(k). H8-EMBEDDINGS IN HILBERT This book is aimed at anyone interested in induced SPACE AND OPTIMIZATION ON modules in general and modular representations G8-SETS of algebraic groups in particular. It requires N. Ghoussoub and B. Maurey graduate-level algebra and some familiarity with (Memoirs of the AMS, Number 349) semisimple groups and their root systems. 1980 Mathematics Subject Classifications: This memoir studies the structure of H0-subsets 20G05, 20J05, 14F05 of locally convex topological vector spaces. These ISBN 0.8218-2348-5. LC 86-10942 ISSN 0065-9266 sets represent the linear analogue of G6-sets and 128 pages (softcover), July 1986 share many of the properties enjoyed by convex Individual member 111. List price S18. compact spaces. The authors examine questions Institutional member $14 about extremal structures, integral representations, To order. please specify MEM0/347N and optimization on such sets. Some applications to the geometry of Banach spaces and to nonlinear minimization problems are given. 1980 Mathematics Subject Classifications: THE KUNNETH THEOREM AND 46A55.46B20. 49A27 ISBN ().8218-2350.7, LC 86-17501 THE UNIVERSAL COEFFICIENT ISSN 0065-9266 108 pages (softcover). July 1986 THEOREM FOR EQUIVARIANT Individual member t7. List price $12. K-THEORY AND KK-THEORY Institutional member $10 Jonathan Rosenberg and Claude Schochet To order, please specify MEM0/349N (Memoirs of the AMS, Number 348) This memoir provides explicit tools for the computation of equivariant K-theory and HANDLEBODY equivariant Kasparov KK-theory. The authors DECOMPOSITIONS OF generalize the Kuiineth Theorem of Hodgkin COMPLEX SURFACES Snaith-Mcleod to give a spectral sequence for John Harer, Arnold Kas, and Robion Kirby computing K~ (A 181 B), for G a compact connected (Memoirs of the AMS, Number 350) Lie group with 1r1 (G) torsion-free, and A and B C* -algebras with continuous G actions. They also develop a Universal Coefficient Theorem This memoir gives handlebody descriptions 1 for computing the equivariant Kasparov groups of the elliptic surfaces over P , including the Kummer surface. The authors derive handlebody Use the order form in the back of this issue or call 800-556-7774 to use VISA or MasterCard. Shipping and handling charges will be added. 665 decompositions of the surfaces obtained by Stability Results performing logarithmic transforms to these elliptic Generalized Feynman Diagrams surfaces. They pay special attention to the The Banach Algebra of Functionals. Connections Dolgachev surfaces D(p, q). with Feynman's Operational Calculus Contents 1980 Mathematics Subject Classifications: Framed Links and Resolutions of Singularities 05A99. 28C20, 47A55, 58030, 81(12, 81C20 Algebraic Descriptions of Elliptic Surfaces ISBN 0-8218-2413-9, LC 86-14154 ISSN 0065-9266 Handlebody Decompositions of Elliptic Surfaces 88 pages (softcover), July 1986 Handlebody Decompositions of Surfaces Defined Individual member 17, List price S11, Using Log Transforms Institutional member S9 To order, please specify MEM0/351N Drawing the 3-handles for the Dolgachev Surface 1980 Mathematics Subject Classifications: 57R65, 57M99, 14J27, 14J26 ISBN 0-8218-2351-5, LC 86-17451 ISSN 0065-9266 ONE-DIMENSIONAL STABLE 108 pages (softcover), July 1986 Individual member 17, List price S12, DISTRIBUTIONS Institutional member S10 V. M. Zolotarev To order, please specify MEM0/350N (Translations of Mathematical Monographs, Volume 65) This is the first book specifically devoted to GENERALIZED DYSON SERIES, a systematic exposition of the essential facts GENERALIZED FEYNMAN known about the properties of stable distributions. DIAGRAMS, In addition to its main focus on the analytic THE FEYNMAN properties of stable laws, the book also includes INTEGRAL AND FEYNMAN'S examples of the occurrence of stable distributions OPERATIONAL CALCULUS in applied problems and a chapter on the problem of Gerald W. Johnson and Michell. Lapidus statistical estimation of the parameters determining (Memoirs of the AMS, Number 351) stable laws. A valuable feature of the book is the author's use of several formally different ways of expressing characteristic functions corresponding The authors study generalized Dyson series to these laws. and their representation by generalized Feynman diagrams as well as the closely related topic This book is written for researchers in the area of Feynman's time-ordered operational calculus of probability theory and its applications, for for noncommuting operators. They obtain engineers, and for graduate students in these areas. these perturbation series by replacing ordinary Contents Lebesgue measure in the time integration involved Examples of stable laws in applications in the Feynman-Kac functional by an arbitrary Analytic properties of the distributions in the Lebesgue-Stieltjes measure. They then calculate family 6 the Weiner and Feynman path integrals of the corresponding functional. Special properties of laws in the class 2U Estimators of the parameters of stable distributions These Dyson series provide a means of carrying 1980 Mathematics Subject Classification: out the "disentangling" that is a crucial element 60E07 of Feynman's operational calculus. The authors ISBN 0-8218-4519-5, LC 86-10943 are also able to treat far more general functionals ISSN 0065-9282 296 pages (hardcover), July 1986 than the traditional exponential function; in fact, Individual member 155, List price $92. the class of functionals dealt with forms a rather Institutional member S7 4 large commutative Banach algebra. The theory To order, please specify MMON0/65N is of interest in its relation to several areas of mathematical physics. Contents A Simple Generalized Dyson Series ( 'Y/ = !-£ + w87 ) The Generalized Dyson Series Examples of Perturbation Expansions Use the order form in the back of this issue or call 800-556-777 4 to use VISA or MasterCard. Shipping and handling charges will be added. 666 V. I. Blagodat-skikh, The maximum principle for differential inclusions THEORY OF LIMIT CYCLES V. S. Vladimirov, A Blaschke product in the Ye Yan-Qian "generalized unit disk" and a complete orthonormal (Translations of Mathematical Monographs, system in the future tube Volume 66) A. A. Gonchar, On the degree of rational approximation of analytic functions Over the past two decades the theory of limit N. l. Grigorenko, The problem of pursuit by cycles, especially for quadratic differential systems, several objects has progressed dramatically in China as well as A. K. Gushchin and V. P. Mikhailov, On uniform in other countries. This monograph, updating stabilization of the solution of the Cauchy problem the 1964 first edition, includes these recent for a second-order hyperbolic equation developments, as revised by eight of the author's V. A. Kondratev, I. Kopachek, D. M. colleagues in their own areas of expertise. Lekveishvili, and 0. A. Oleinik, Sharp estimates in Holder spaces and a precise Saint-Venant The first part of the book deals with limit cycles principle for solutions of the biharmonic equation of general plane stationary systems, including their A. I. Kostrikin, I. A. Kostrikin, and V. A. existence, nonexistence, stability, and uniqueness. Ufnarovskii, On decompositions of classical Lie The second section discusses the global topological algebras structure of limit cycles and phase-portraits of G. I. Marchuk, The environment and optimization quadratic systems. Finally, the last section collects problem important results that could not be included under V. P. Maslo and V. G. Danilov, The Pontryagin the subject matter of the previous two sections or duality principle for computing a Cherenkov type that have appeared in the literature very recently. effect in crystals and difference schemes. I The book as a whole serves as a reference for A. S. Mishchenko, Representations of compact college seniors, graduate students, and researchers groups in Hilbert modules over C* -algebras in mathematics and physics. M. S. Nikolskii, On the we/1-posedness of an 1980 Mathematics Subject Classification: optimal control problem for a linear control system 34C05 with integral quadratic performance index ISBN 0-8218-4518-7, LC 86-14070 S. M. Nikolskii and P. I. Lizorkin, Approximation ISSN 0065-9282 440 pages (hardcover), August 1986 by spherical polynomials Individual member 184, List price $140, S. P. Novikov, Critical points and level surfaces of Institutional member $112 multivalued functions To order, please specify MMON0/66N A. V. Pogorelov, Special infinitesimal bendings of convex surfaces Yu. A. Rozanov, General boundary value problems for linear differential operators and the method of CURRENT PROBLEMS OF adjoint operators MATHEMATICS, DIFFERENTIAL A. N. Rudakov and I. R. Shafarevich, On degeneration of K3 surfaces EQUATIONS, MATHEMATICAL V. R. Telesnin, On a problem of optimizing ANALYSIS AND THEIR transition processes APPLICATIONS 1980 Mathematics Subject Classifications: (Proceedings of the Steklov Institute, Volume 166) 01A70, 14J17, 17B05. 22-03, 30050. 31A30, 32A07, 35B40, 41A10, 49A10, 65M10. 90A30, and others This collection consists of original papers on ISBN 0-8218-3093-7, LC 86-10929 various sections of mathematics: differential ISSN 0081-5438 266 pages (softcover), June 1986 equations, mathematical theory of optimal control, Individual member 161, List price $101, approximation theory, geometry, mathematical Institutional member $81 analysis, and applications. To order, please specify STEKLO /166N Contents D. V. Anasov, R. V. Gamkrelidze, E. F. Mishchenko, and M. M. Postnikov, On the mathematical work of L. S. Pontryagin N. S. Bakhvalov, Numerical solution of problems with nonsmooth data and interpolation problems Use the order form in the back of this issue or call 800-556-7774 to use VISA or MasterCard. Shipping and handling charges will be added. 667 1980 Mathematics Subject Classifications: 35, 46, 60 and others SOCIETE MATHEMATIQUE DE FRANCE, 412 pages (Vol. 1), 294 pages (Vol. II) (softcover). ASTERISQUE 1986 Individual member 120 {1)/114 (11), List price 128 {1)/120 {II) The AMS distributes Asterisque only in the To order, please specify AST /131N (Vol. I) or U.S., Canada, and Mexico. Orders from other AST /132N (Vol. II) countries should be sent to the SMF, B.P. 126-05, 75226 Paris Cedex 05, France, or to OFFILIB, 48 rue Gay-Lussac, 75240 Paris Cedex 05, France. Individual members of either AMS or SMF are SEMINAIRE BOURBAKI, VOL. member price. (ISSN 0303-1179) entitled to the 1984/85, EXPOSES 633-650 (Asterisque, Volume 133-134) Comme les precedents volumes de ce 5eminaire, SYSTEMES DIFFERENTIELS celui-ci contient 18 exposes de synthese sur des ET SINGULARITES sujets d'actualite; six exposes de theorie des A. Galligo, M. Granger, and nombres ou de geometrie algebrique, trois de geometrie, trois de topologie, deux d'algebre, Ph. Maisonobe, Editors un d'equations aux derivees partielles, et un de (Asterisque, Number 130) probabilites. La theorie des /)-modules holonomes etablit un On y trouve entre autres Ia demonstration de Ia lien entre Ia geometrie algebrique, les systemes conjecture de Bieberbach, l'expose des liens entre d'equations aux derivees partielles et l'etude theorie des groupes et singularites de caustiques, des singularites. Ce livre constitue les actes du de fronts d'ondes et de developpantes, ainsi que dernier colloque de Luminy qui a rassemble les des applications de Ia geometrie algebrique a Ia principaux specialistes de ce sujet. On y trouvera theorie des codes et de Ia theorie des algebres de des articles d'exposition de Ia theorie ainsi que les Von Neumann a Ia theorie des noeuds. comptes-rendus des tous derniers developpements. 1980 Mathematics Subject Classifications: 11. 14, 51, 53. 54, 55, 57, 35, 60 1980 Mathematics Subject Classifications: 374 pages (softcover), 1986 14. 35 Individual member 121, List price 130 420 pages ( softcover). 1986 To order, please specify AST /133/134N Individual member 120, List price 129 To order, please specify AST /130N ANALYSE HARMONIQUE DES COLLOQUE EN L'HONNEUR DE MEASURES LAURENT SCHWARTZ, VOLS. 1 B. Host, J.-F. Mela, F. Parreau AND 2 (Asterisque, Volume 135-136) (Asterisque, Volume 131-132) 1980 Mathematics Subject Classification: 43 261 pages (softcover), 1986 Individual member 115, List price 122 Ces deux volumes contiennent les actes du colloque To order, please specify AST /135/136N en l'honneur de Laurent Schwartz, consistant en trois conferences d'ouverture (par H. Cartan, B. Malgrange et B. Maurey), neuf conferences d'interet general (M. F. Atiyah, J. M. Bismut, L. PROJECTIVE GEOMETRY OF Hormander, P. A. Meyer, Y. Meyer, S. Mizohata, A. Pekzynski, G. Pisier, A. Wightman) et les actes ELLIPTIC CURVES de seminaires orientes selon divers themes chers K. Hulek a L. Schwartz: Equations aux Derivees Partielles, (Asterisque, Volume 137) Geometrie des Espaces de Banach, Probabilites et Martingales sur les Varietes, Analyse non This volume is concerned with the projective lineaire et Mathematiques Appliquees, Physique geometry of elliptic curves. It centers around the Mathematique et Analyse sur les Varietes. following aspects: Use the order form in the back of this issue or call 800-556-7774 to use VISA or MasterCard. Shipping and handling charges will be added. 668 1. Using special theta-functions, the symmetries compactness; degree theory for mappings; of elliptic normal curves and the action of the inverse function theorems of the Nash-Moser Heisenberg group can be made very explicit. type; nonlinear semigroup theory; nonlinear control problems; nonlinear partial differential 2. The Horrocks-Mumford bundle is in many ways equations in gauge theory; nonlinear hyperbolic and related to elliptic curves. Among other things, one parabolic problems; the Navier-Stokes equations; can reconstruct the bundle from the tangent scroll nonlinear elliptic equations in differential geometry; of normal quintics. nonlinear elliptic boundary value and eigenvalue 3. The geometry of the Horrocks-Mumford bundle problems; bifurcation theory; periodic solutions of is also closely related to the normal bundle of Hamiltonian systems; a variety of nonlinear partial elliptic space curves of degree five. differential equations; and numerous applications to physical problems. The main purpose of the text is to discuss the interrelation between these different problems. The past two decades have seen a strong upsurge in the field of nonlinear functional 1980 Mathematics Subject Classification: 14 analysis, characterized by a forceful emphasis 146 pages (softcover). 1986 Individual member IG. List price $13 on applications. The 1983 AMS Summer To order. please specify AST /137N Research Institute held at Berkeley, of which these volumes are the proceedings, brought together an international group of researchers to foster a unified view of what has been achieved and to indicate the The following listing is being repeated with possible directions of future developments. The corrections from the March 1986 issue. volumes which have resulted should be of interest to a wide variety of mathematicians, including specialists in partial differential equations, nonlinear NONLINEAR FUNCTIONAL and global analysis, and differential geometry, as ANALYSIS AND ITS well as mathematical physicists and other applied APPLICATIONS mathematicians. Browder, Editor 1980 Mathematics Subject Classifications: Felix E. 34. 35. 46. 47. 49. 58. 30. 31. 45. 54. 65. 76. (Proceedings of Symposia in Pure Mathematics, 81. and others Volume 45) ISBN (Set) 0-8218-1467-2; (Part 1) 0-8218-1471-0; (Part 2) 0-8218-1472-9. LC 85-28725. ISSN 0082-0717 This comprehensive two volume set surveys 570 pages (part 1); 600 pages (part 2) the present state of international research in (hardcover). May 1986 nonlinear functional analysis. It focuses especially Set: Individual member 177. List price $128. Institutional member $102 on the study of boundary value problems for Part 1: Individual member 139. List price $65. nonlinear partial differential equations and related Institutional member $52 problems in geometry and mathematical physics. Part 2: Individual member 142. List price $70. Institutional member $56 Major topics covered in these articles include: To order, please specify PSPUM/45N (set), minimax methods in the calculus of variations; PSPUM/45.1N (part 1), PSPUM/45.2N existence theory for variational problems without (part 2) Use the order form in the back of this issue or call 800-556-7774 to use VISA or MasterCard. Shipping and handling charges will be added. 669 Add shipping and handling: $2 first book. $1 each add'l. max. $25; by air $5 first book. $3 each add'l. max. $100. Order from: American Mathematical Society. P.O. Box 1571. Annex Station. Providence. R.I. 02901-1571 or call 800-556-7774 to charge on VISA or MasterCard. Miscellaneous Personal Items Robert Girse of Idaho State University died on March 29, 1986, at the age of 37. He was a Lowell W. Beineke of Indiana University member of the Society for 12 years. Purdue University at Fort Wayne was named the Jack W. Schrey Professor at that institution. Preston C. Hammer of Milesburg, Pennsyl vania, died on April 14, 1986, at the age of 72. Jun-ichi lgusa, Professor of Mathematics, the He was a member of the Society for 47 years. Johns Hopkins University, has been appointed to the newly created J. J. Sylvester Chair in Gordon R. Magee, Professor Emeritus of the Mathematics at that institution. University of Western Ontario, died on April 2, 1986, at the age of 83. He was a member of the Anthony W. Knapp, Professor at Cornell Society for 40 years. University, has been appointed Professor at the State University of New York at Stony Brook. Clifford Mendel of Cedar Mountain, North For three years he will spend fall semesters at Carolina, died on April14, 1986, at the age of 78. Stony Brook and spring semesters at Cornell. He was a member of the Society for 55 years. John Morrison has been appointed Assis Elisha Netanyahu of Israel Institute of Tech tant Professor of Mathematical Sciences at the nology died on April 3, 1986, at the age of 73. He University of Delaware. was a member of the Society for 36 years. David A. Sanchez, Professor of Mathematics Thomas G. Room of St. Ives, Australia, died at the University of New Mexico, has been named on April 2, 1986, at the age of 83. He was a as Provost and Vice President of Academic Affairs member of the Society for 38 years. at Lehigh University. Franklin G. Rothwell of La Jolla, California, William F. Trench of Drexel University has died on April 5, 1986, at the age of 74. He was a been appointed Andrew G. Cowles Distinguished member of the Society for 20 years. Professor of Mathematics at Trinity University, S. R. Sinha of the University of Allahabad, San Antonio. India, died on April 15, 1985, at the age of 53. He Wolfgang Walter of the University of Karl was a member of the Society for 6 years. sruhe has been elected President of Gesellschaft Eberhard L. Stark of Rheinisch-Westfiilischen fiir Angewandte Mathematik und Mechanik Technischen Hochschule Aachen, Federal Republic (GAMM) for the three-year period 1986-1989. of Germany, died on April 23, 1986, at the age of 46. He was a member of the Society for 6 years. Deaths Serge Vasilaeh of Le Vaudreuil, France, died on February 10, 1986, at the age of 81. He was a R H Bing of the University of Texas at Austin member of the Society for 17 years. died on April 28, 1986, at the age of 71. He was a member of the Society for 43 years. (See the Clement Winston of Washington, D.C., died article at the beginning of this issue of Notices.) on March 16, 1986, at the age of 84. He was a member of the Society for 58 years. Paul Boschan of New City, New York, died on October 4, 1985, at the age of 82. He was a Harold E. Wolfe, Professor Emeritus at Indi member of the Society for 39 years. ana University, died on May 8, 1986, at the age of 95. He was a member of the Society for 56 years. Bel Braun of the University of Hamburg died on May 15, 1986, at the age of 71. She was a Samuel Wolfenatein of Arcueil, France, died member of the Society for 38 years. on September 29, 1985, at the age of 64. He was a member of the Society for 39 years. Donald H. Clanton of Furman University died' on August 1, 1985, at the age of 58. He was a Frances M. Wright of State University of New member of the Society for 24 years. York at Binghamton died on April 4, 1986, at the age of 83. She was a member of the Society for 60 years. 671 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 N arne and Home Country Host Institution Field of Special Interest Period of Visit Aron, Richard (U.S.A.) Trinity College, Ireland Analysis 9/86- 6/87 Hochberg, Kenneth (U.S.A.) Bar-Ilan University, Israel Probability 8/86- 6/87 Jensen, Arne (U.S.A.) University of Aarhus, Denmark Mathematical Physics 7/86- 6/87 Lesley, F. David (U.S.A.) University College, London, Complex Variables 7/86- 12/86 England Salamon, Peter (U.S.A.) Copenhagen University, Thermodynamics 8/86- 6/87 Denmark Sathaye, Avinash (U.S.A.) Tata Institute, India Algebraic Geometry 7/86- 6/87 Weintraub, Steven H. University of Gottingen, West Differential Topology 8/86- 8/87 (U.S.A.) Germany Wright, David J. (U.S.A.) Mathematisches Institut of Automorphic Forms 8/86- 8/87 Gottingen, West Germany Visiting Foreign Mathematicians Alefeld, Gotz E. (West Georgia Institute of Technology Numerical Analysis 9/86- 12/86 Germany) Araki, H. (Japan) Clarkson University Operator Algebra 3/87- 4/87 Bessis, Daniel (France) Georgia Institute of Technology Mathematical Physics 7/86- 6/87 Carverhill, Andrew P. University of North Carolina, Dynamical Systems 8/86- 6/87 (England) Chapel Hill Chung, J. K. (People's University of Waterloo Functional Equations 11/86- 5/87 Republic of China) Costa, David Goldstein University of Utah Partial Differential Equations 9/86- 6/87 (Brazil) Dominquez, Jesus M. University of Oklahoma Topology 8/86- 5/87 (Spain) Drazin, Philip (England) University of Washington Fluid Mechanics 3/87- 6/87 Ellingham, Mark N. Vanderbilt University Combinatorial Optimization 9/86- 5/87 (Australia) Franc;oise, J. P. (France) University of Arizona Differential Equations and 9/86- 12/86 Integrable Systems Fiiredi, Zoltan (Hungary) Massachusetts Institute of Combinatorics 9/86- 5/87 Technology Goodson, Geoffrey (South University of North Carolina, Ergodic Theory 8/86- 12/86 Africa) Chapel Hill Granovsky, Boris (Israel) Case Western Reserve Monte Carlo Methods 8/86- 6/87 University Griffiths, Robert C. University of Utah Mathematical Population 1/87- 6/87 (Australia) Genetics Haruki, H. (Japan) University of Waterloo Functional Equations 9/86 Jahangiri, Massoud University of Kentucky Complex Analysis 8/86- 5/87 (Englan~) Jeyakumar, Vaithilingam University of Kentucky Optimization 8/86- 5/87 (Australia) Kadalbajoo, Mohan (India) University of Kentucky Numerical Analysis; Partial 8/86- 5/87 Differential Equations Kotelenez, Peter (West Case Western Reserve Probability 8/86- 6/87 Germany) University Kurepa, S. (Yugoslavia) University of Waterloo Functional Equations 9/86 Nahlus, Kazih (Lebanon) University of Oklahoma Algebra 8/86- 5/87 Nucci, Maria C. (Italy) Georgia Institute of Technology Applied Mathematics 9/86- 6/87 Orated, Bent (Denmark) Massachusetts Institute of Differential Geometry, Analysis, 9/86- 1/87 Technology Physics Peim, Martin (England) University of Kentucky Algebraic Topology 8/86- 5/87 Pomeau, Yves (France) Massachusetts Institute of Cellular Automata, Dynamical 2/87- 5/87 Technology Systems 672 Narne and Home Countn: Host Institution Field of S:11ecial Interest Period of Visit Richthofer, Wolfgang (West University of Utah Algebraic and Differential 9/86- 6/87 Germany) Geometry, Lie Theory, Several Complex Variables Rubinstein, J. Hyam Oklahoma State University Topology and Geometry 8/86- 1/87 (Australia) Szulga, Jerzy (Poland) Case Western Reserve Probability 7/86- 6/87 University Takat, Peter Vanderbilt University Analysis 9/86- 5/87 (Czechoslovakia) Tsutsumi, A. (Japan) University of Waterloo Functional Equations 9/86 Unsworth, Keith (England) University of Utah Numerical Analysis 9/86- 6/87 Yau, Chi-Ming (Hong University of Oklahoma Geometry 8/86- 5/87 Kong) Ycart, Bernard (France) Case Western Reserve Applied Probability 7/86- 9/86 University Zuily, Claude (France) Purdue University Partial Differential Equations 9/86 "This book is a must for anyone deeply interested in Geometric Function Theory ... -A. W. Goodman Univ. of South Florida "'An interesting and valuable collection of articles . . . The first book to mention the amazing proof of the Bieberbach conjecture by Louis de Branges. Every function-theorist should ... buy this ... - David A. Brannan The Open University, U. K. Topics in Complex Analysis Dorothy Brown Shaffer, Editor The unifying theme of the lectures, presented at the AMS meeting in October, 1983, at Fairfield University was Geometric Function Theory. Some of the papers concern: the class I:, its support points and extremal configuration; support points for the class S, Loewner chains and the process of truncation; estimates on the radial growth of the derivative of univalent functions; and a conjecture of Bombieri proved for some cases. Because the proof of the Bieberbach conjecture was not known at the time of preparation of the papers, many of the authors, as well as experts in the field, were interviewed regarding the effect of the· proof of the conjecture. Their ideas regarding future trends in research in complex analysis are presented in the epilogue. A graduate level course in complex analysis provides a sufficient background for understanding this material. ISBN 0-8218-5037-7. LC 84-24550. ISSN 0271-4132 March 1985. 142 pages (softcover) Individual member $11. Institutional member $14. List price $18 To order. please specify CONM/38NA Shipping/Handling: 1st book $2. each add"l $1. $25 max. By air. 1st book $5. each add"l $3. $100 max. PREPAYMENT REQUIRED. Order from American Mathematical Society. PO Box 1571. Annex Station. Providence. Rl 02901-1571. or call 800-556-7774 to use VISA or MasterCard. 673 Backlog of Mathematics Research Journals Backlog. Information on the backlog of papers and its publication may be much shorter than is for research journals, primarily those published the case otherwise, so these figures are low to that in North America, is reported to the Providence extent. Office by those editorial boards which elect to The observations are made from the latest participate. The figures are an estimate of issue published before the deadline for this issue the number of printed pages which have been of Notices from journals that have actually been accepted, but are in excess of the number required received by a subscriber in the Providence, Rhode to maintain copy editing and printing schedules. Island area; in some cases this may be two months Observed Waiting Time. The quartiles give later than publication abroad. If the waiting time a measure of normal dispersion. They do not as defined above is not given in the journal, if no include extremes which may be misleading. Wait new issue has been received since the last survey, ing times are measured in months from receipt or if the latest issue is for some reason obviously of manuscript in final form to publication of the not typical, no times are given in this report and issue. When a paper is revised, the waiting time such cases are marked NA (not available or not between an editor's receipt of the final revision applicable). Editor's Estimated Observed Waiting Approximate Time for Paper Time in Latest Number Number Backlog of Submitted Currently Published Issue Issues Pages Printed Pages to be Published (In Months) Journal per Year per Year 5/31/86 12/15/85 (In Months) 01 M 03 Acta. Inform. 6 720 0 0 6 5 7 8 Aequationes Math. 6 NR NR 0 NR 17 23 26 Alg. Groups Geom. 4 620 0 0 7 NA Amer. J. Math. 6 NR NR 1578 NR 26 29 31 Ann. of Math. 6 1200 100 100 10 14 15 17 Ann. Probab. 4 1450 700 725 18 13 13 17 Ann. Sci. Ecole Norm. Sup. 4 NR NR 350 NR 13 13 15 Ann. Statist. 4 NR NR NR NR 9 10 10 Appl. Math. Optim. 3 NR NR 0 NR 6 10* 14 Arch. Hist. Exact Scis. 12 1200 0 0 11-12 NA 13 NA Arch. Rational Mech. Anal. 16 1600 0 0 10 11 18 30 Bull. Austral. Math. Soc. 6 960 0 0 8 12 12 13 Bull. Soc. Math. France 4 NR NR 12 NR 12 13 14 Canad. J. Math. 6 1536 256 1000 24 14 17 20 Canad. Math. Bull. 4 512 230 320 18 15 18 20 Comm. Algebra 10 2200 927 1483 12 11 13 14 Comm. Math. Phys. 24 4224 0 0 5 8 8 10 Comm. Partial Diff. Equations 12 1300 200 1000 9 9 11 11 Computing 8 380 0 NR 12 9 11 12 Duke Math. J. 4 NR NR NR NR 9 12 14 Houston J. Math. 4 600 600 NR 20 18 24 28 Illinois J. Math. 4 704 645 809 20 33 33 35 IMA J. Appl. Math. 6 720 100 NA 9 9 9 10 IMA J. Math. Appl. Med. Bioi. 4 350 0 NA 6 NA IMA J. Math. Control Inform. 4 440 120 NA 4.5 NA IMA J. Numer. Anal. 4 500 0 NA 9 10 11 14 Indiana Univ. Math. J. 4 930 100 100 15 12 15 16 lnternat. J. Math. Math. Sci. 4 832 100 0 4-6 13 19 23 Invent. Math. 12 2592 0 NR 6 6 10 12 Israel J. Math. 12 1500 600 NR 10-14 13 18 23 J. Algorithms 4 NR NR 1000 NR 20 25 32 J. Amer. Statist. Assoc. 4 NR NR 150 NR 7 8 9 J. Assoc. Comput. Mach. 4 NR NR 250 NR 8 10 12 674 Editor's Estimated Observed Waiting Approximate Time for Paper Time in Latest Number Number Backlog of Submitted Currently Published Issue Issues Pages Printed Pages to be Published (In Months) Journal per Year per Year 5/31/86 12/15/85 (In Months) o, M o, J. Austral. Math. Soc. Ser. A 6 NR NR 800 NR 18 21 26 J. Austral. Math. Soc. Ser. B 4 512 0 48 16 9 10 12 J. Comput. System Sci. 6 1200 0 NR 12 11 11 13 J. Differential Geom. 6 800-900 800 NR 6-10 7 8 13 J. Math. Bioi. 6 NR 0 0 11 6 7 9 J. Math. Phys. 12 NR NR 0 NR 6 9 10 J. Nigerian Math. Soc. 1 NR NR 0 NR NA J. Operator Theory 4 800 300 600 12 10 13 17 J. Symbolic Logic 4 1148 12 0 15 11 11 13 Linear Algebra Appl. 12 NR NR 600 NR 11 11 12 Manuscripta Math. 12 1500 0 0 5 6 7 8 Math. Ann. 12 2112 0 0 7 5 7 9 Math. Biosci. 10 1500 150 50 8 5 5 6 Math. Comp. 4 1500 100 60 12-15 10 11 14 Math. Oper. Res. 4 704 380 440 14 14 15 15 Math. Programming 9 1100 50 100 12 9 11 16 Math. Social Sci. 6 600 600 0 15 11 12 13 Math. Systems Theory 4 NR NR 0 NR 6 7 7 Math. Z. 12 1968 0 0 10 8 9 14 Mem. Amer. Math. Soc. 7 2800 0 0 2 5 9 34 Michigan Math. J. 3 480 0 300 9 10 14 17 Monatsh. Math. 8 704 0 NR 6 8 10 12 Numer. Funct. Anal. Optim. 6 NR NR 200 NR NA Numer. Math. 12 1416 0 0 8 10 13 19 Oper. Res. 6 1050 1725 NR 12 NA Pacific J. Math. 10 2500 0 NR 11 11 15 19 Probab. Theor. Relat. Fields 12 1920 0 0 9-10 7 8 9 Proc. Amer. Math. Soc. 12 2200 300 500 12 12 13 14 Proc. London Math. Soc. 6 1152 300 NA 15 14 15 16 Quart. Appl. Math. 4 800 700 75 18 10 15 19 Quart. J. Math. Oxford Ser. (2) 4 512 60 NA 9-10 10 14 18 Resultate Math. 4 448 NR NR 14 16 17 17 Rocky Mountain J. Math. 4 768 900 960 26 21 23 24 Semigroup Forum 6 768 0 NR 5 4 5 5 SIAM J. Algebraic Discrete Methods 4 NR NR 26 NR 11 14 16 SIAM J. Appl. Math. 6 NR NR 184 NR 10 10 12 SIAM J. Comput. 4 NR NR 160 NR 15 16 18 SIAM J. Control Optim. 6 NR NR 516 NR 14 15 16 SIAM J. Math. Anal. 6 NR NR 591 NR 18 21 24 SIAM J. Numer. Anal. 6 NR NR 233 NR 13 14 15 SIAM J. Sci. Statist. Comput. 4 NR NR 445 NR 14 15 17 SIAM Rev. 4 NR NR 32 NR 10 10 11 Topology Appl. 9 990 770 1045 10 10 13 16 Trans. Amer. Math. Soc. 12 5000 200 800 12 11 13 13 NR means no response received. NA means not available or not applicable. * From date of acceptance (the only date given in this journal). 675 AMS Reports and Communications Report of the Treasurer The Treasurer this year again presents to the membership an abridged statement of the financial position of the Society, in semi-informal narrative style. A copy of the Treasurer's Report, as submitted to the Trustees and the Council, will be sent from the Providence Office to any member who requests it from the Treasurer. The Treasurer will be happy to answer any questions members may wish to put to him concerning the financial affairs of the Society. I. A DESCRIPTION OF THE FINANCIAL POSITION OF THE SOCIETY AS OF DECEMBER 31, 1985 The Society had cash and temporary investments ...... $ 3,711,668 There was owing to it by subscribers, and others (less allowance for doubtful accounts) ...... 460,632 It had prepaid expenses and deposits ...... 377,781 It had deferred prepublication costs ...... 593,443 It had inventory of completed books and back volumes of journals ...... 916,063 It had invested in the headquarters building, Mathematical Reviews editorial offices, computers, and other equipment ...... 4,908,078 Making a total of operating assets of...... 10,967,665 The Society also held investment securities and uninvested principal cash valued at ...... 3,883,263 (Approximate market value December 31, 1985: $4,168,073) ...... Total assets, therefore, were ...... $14,850,928 Offsetting these assets, the Society had Accounts payable ...... $ 794,535 Reserved unearned dues and subscriptions ...... 6,980,289 Other miscellaneous liabilities ...... 726,787 It had mortgages on the headquarters building ...... 1,420,804 A surplus in its operating funds ...... 1.045,250 Thus, accounting for all the operating funds ...... 10,967,665 The invested funds represent the following: The Endowment Fund, largely the gifts of members ...... $ 100,000 Robert Henderson Endowment Fund .. 00 •••••••••••••• 00 00 •• 00 ••• 548,223 Joseph Fels Ritt Memorial Fund ..... 00 •••••••••• 00 00 •• 00 ••••• 00. 22,521 Future operations fund ...... 1,794,470 The various prize funds ...... 168,704 Undistributed net gains on investment transactions ...... 1,099,988 Friends of Mathematics Fund 00 •••••••• 00 ••••••• 00 •• : •• 00 00 •• 00 •• 77,330 Other funds ...... 72,027 3.883,263 Total liabilities and fund reserves, therefore, were ...... $14,850,928 676 II. AN ACCOUNT OF THE FINANCIAL TRANSACTIONS OF THE SOCIETY DURING THE FISCAL YEAR ENDED DECEMBER 31, 1985 The Society maintains its accounts in three funds. The General Fund includes transactions and balances relating to the general operations of the Society, membership dues and activities, support of special projects, meetings, information services, and sale of services. The Publication Fund includes all transactions and balances relating primarily to the books, journals and back volumes of journals published by the Society. The Special Fund includes transactions and balances relating to prize funds and various special projects, such as government supported institutes and symposia. To meet its obligations, the Society received from Sale of Society journals and back volumes ...... $ 6,241,645 Sale of other publications ...... 2,165,212 Dues of individual members ...... 707,176 Dues of institutional, corporate and associate members ...... 337,825 Government grants ...... 496,174 Sale of services ...... 567,141 Meetings ...... 242,446 Investment and trusts ...... 343,464 All other sources ...... 177.897 Total revenues ...... $11,278,980 These funds were expended for Publication of Society journals and back volumes ...... 5,368,041 Other publications ...... 1,467,729 Meetings, including expenses covered by government grants ...... 827,609 Sale of services ...... 609,203 Membership activities ...... 454,773 Marketing ...... 186,631 All other ...... 633,318 Total expenses ...... 9,547,304 Excess of revenues over expenses before non-recurring items ...... 1,731,676 Non-recurring items Cumulative effect on prior years of change in method of accounting for vacation and sick pay ...... (124,464) Excess of revenues over expenses ...... 1,607,212 Transfers to future operations fund ...... 1,143,758 Balance remaining for current operating needs ...... $ 463,454 Respectfully submitted, Franklin P. Peterson Treasurer 677 Recent Appointments The Joint Committee on Graduate Programs at Traditionally Black Institutions has been dis charged. Committee members' terms of office on standing committees expire on December 31 of the year given in parentheses following their names, Reports of Past Meetings unless otherwise specified. The May Meeting in Baltimore Jane Cronin Scanlon (1988) has been appointed The eight hundred twenty-seventh meeting of the chairman of the Proceedings of Symposia in Ap American Mathematical Society was held at Johns plied Mathematics Editorial Committee by Presi Hopkins University in Baltimore, Maryland on dent Irving Kaplansky. The other member of the Saturday and Sunday, May 3 and 4, 1986. There committee is StuartS. Antman (1988). were 200 registrants, including 165 members of The Council has constituted the Committee the Society. on Translation from Chinese to be a selection Invited Addresses. By invitation of the committee on material to be translated from Committee to Select Hour Speakers for Eastern Chinese. Members of the committee are Sun Sectional Meetings, there were four invited one Yung Alice Chang, Tsit-Yuen Lam, chairman, hour addresses. The speakers, their affiliations, and Tai-Ping Liu. and the titles of their talks are as follows: DEMITRIOS CHRISTODOULOU, Syracuse Uni As chairman of the Data Subcommitte of versity, The global initial value problem for the the Committee on Employment and Educational Einstein equations. Policy, Edward A. Connors has been appointed DAVID A. Cox, Amherst College, Primes by President Irving Kaplansky to serve as the of the form x2 + ny2 : from Fermat to class field Commissioner representing the Society on the theory. Commission on Professionals in Science and ANTHONY W. KNAPP, Cornell University, Technology. The Society has recently become Recent progress in classifying irreducible unitary a society member of the Commission, formerly representations. known as the Scientific Manpower Commission. STEVEN M. ZUCKER, Johns Hopkins Uni J. William Helton (1987) has been reap versity, L 2-cohomology. pointed and Nancy K. Stanton (1988) has been The presiding officers at these sessions were appointed to the Committee on Research Fellow Thomas Sideris, Steven Zucker, David Vogan, and ships by President Irving Kaplansky. Kenneth Eduardo Cattani, respectively. C. Millett has been appointed chairman of the Special Sessions. By invitation of the same committee by President Irving Kaplansky .The committee, there were seven special sessions of continuing member of the committee is Stephen selected twenty- and thirty-minute papers. The Lichtenbaum (1987). Terms expire on June 30. topics, and the names and affiliations of the Louis Solomon (1989) has been appointed by mathematicians arranging them, are as follows: President Irving Kaplansky to the Committee on Complex analysis and its applications, CAR Steele Prizes. Other members of the committee LOS BERENSTEIN, University of Maryland, and are Richard W. Beals (1987), Jerry L. Bona BERNARD SHIFFMAN, Johns Hopkins University. (1987), Hermann Flaschka (1988), John P. Hempel Number theory, TAKASHI 0NO, Johns Hop (1988), and Lawrence E. Payne (1987). Terms kins University, and LAWRENCE WASHINGTON, expire on June 30. University of Maryland. Albert Baernstein II has been appointed Mathematics in molecular sequence analysis, chairman of the Committee on Summer Institutes ARTHUR PITTENGER, University of Maryland, and Special Symposia. Other members of the Baltimore County, and PETER SELLERS, Rocke committee are Eric M. Friedlander (1988), H. feller University. Blaine Lawson, Jr. (1987), and John Wermer Probability and mathematical statistics, (1988). Terms expire on February 28. ROBERT J. SERFLING and JOHN C. WIER MAN, Johns Hopkins University. President Irving Kaplansky has appointed Representations of Lie groups, DAVID VO S.-Y. Cheng, Ronald L. Graham, and Richard GAN, Massachusetts Institute of Technology. S. Palais to be the Committee on Cooperation Homotopy theory and algebraic topology, with the Chinese. Professor Palais will serve as JEFFREY SMITH and W. STEPHEN WILSON, chairman. Johns Hopkins University. Jacob T. Schwartz has been appointed by Hodge theory, STEVEN M. ZUCKER. President Irving Kaplansky to the Committee There was also a discussion session on N onlin to Recommend Winners of Prizes for Automatic ear evolution equations, organized by DEMITRIOS Theorem Proving. Other members of the commit CHRISTODOULOU. tee are David Mumford, chairman, and John L. Contributed Papers. There were three ses Selfridge. sions for contributed 10-minute papers, at which 678 the following mathematicians served as presiding Transactions Ralph Cohen officers: James K. Deveney, Hans Engler, W. G. Ronald K. Getoor Hawkins, Roger A. Horn, Seymour Schuster, and Jerry L. Kazdan Aaron R. Todd. David J. Salt man Council Meeting. The report of the Council Robert M. Zimmer Meeting held in Baltimore follows. Committee to Monitor Problems in Communication Marian B. Pour-El Committee. The Local Arrangements Com Sheldon Axler mittee consisted of Jean-Pierre Meyer, Bernard Shiffman (Chairman), and Steven Zucker. Members-at-Large C. Edmund Burgess David Drasin W. Wistar Comfort H. Blaine Lawson Middletown, Connecticut Associate Secretary Howard A. Masur Eric C. Milner Yiannis N. Moschovakis The Council Meeting in Baltimore Linda A. Ness Marc A. Rieffel The Council met on 3 May 1986 at 5:05 p.m. Scott Warner Williams in the West Ballroom of the Holiday Inn-Inner Carol Wood Harbor in Baltimore. President Kaplansky was in The Council was informed that the contract the chair. with Brown University stipulating that its library The Council enlarged the Editorial Commit should be the custodian of Society archives is now tee of the Proceedings by fourteen members and in place. elected the fourteen former associate editors to The Council adjourned at 6:45 p.m. be members of the Editorial Committee. The Council further agreed that, in any year that Everett Pitcher the managing editor is not already a member of Bethlehem, Pennsylvania Secretary the Editorial Committee, the Committee shall be enlarged by one to include the managing editor. 1986 Symposium on Some Publication of the translations of papers Mathematical Questions in Biology received in Russian by ICM-86 in the series Selected Translations was approved. Modeling Circadian Rhythms The Committee on Translation from Chinese, The twentieth annual Symposium on Some Mathe which had been a policy committee, was recon matical Questions in Biology was held on Wednes stituted as a selection committee for material to day, May 28, 1986 in the Haverford Room of the be translated. The membership is to be Sun Hershey Philadelphia Hotel. Yung Alice Chang, Tsit-Yuen Lam, Chairman, The symposium was held in conjunction with and Tai-Ping Liu, with other members as needed. the annual meeting of the American Association The Council nominated persons for various for the Advancement of Science (AAAS). The offices in the election of 1986. There is one position symposium is sponsored by the American Mathe as vice-president and there are five positions as matical Society (AMS), the Society for Industrial member-at-large. The remaining positions are and Applied Mathematics (SIAM), and Section A uncontested. (Mathematics) of the AAAS. Vice-President William P. Thurston The AMS-SIAM Committee on Mathematics Karen Uhlenbeck in the Life Sciences served as the Organizing Secretary Everett Pitcher Committee for the symposium. The commit Associate Secretaries .Frank T. Birtel tee consisted of Gail A. Carpenter (Northeastern W. Wistar Comfort University); Kenneth L. Lange (Massachusetts Treasurer .Franklin P. Peterson Institute of Technology); Hans G. Othmer (Uni Associate Treasurer Steve Armentrout versity of Utah); Alan S. Perelson (Los Alamos Trustee Ronald L. Graham National Laboratory); Richard E. Plant, chair man (University of California, Davis); and John Members of Publications Committees: Rinzel (National Institutes of Health). American Journal Richard B. Melrose The theme of the symposium was Modeling Bulletin Morris W. Hirsch Circadian Rhythms. There were two half-day Colloquium H. Jerome Keisler sessions, each including three one-hour lectures. Mathematical Reviews Melvin Hochster Twenty-five people registered for the symposium. Mathematical Surveys Support was provided by a grant from the and Monographs Victor W. Guilleman National Science Foundation. Mathematics of Computation Walter Gautschi John E. Osborn Proceedings Paul S. Muhly 679 Officers and Committee Members of the Society Terms of Officers expire on December 31 of the year given. BOARD OF TRUSTEES Liaiaon Committee Steve Armentrout 1986 Irving Kaplanoky 1986 Irving Kaplansky, Franklin P. Peterson (ex offlcio) (ex olficio) chairman Everett Pitcher Rameoh A. Gangolli, 1989 M. Suoan Montgomery 1990 1ecretary Franklin P. Peterson 1986 Frederick W. Gehring, 1987 (ex olficio) COUNCIL chairman Paul J. Sally, Jr. 1988 Ronald L. Graham 1986 Officer• (Member• of the Council, ex officio) President Irving Kaplansky 1986 Committee• of the Board of Truateea President-Elect George D. Moatow 1986 Vice-Presidents Richard A. Askey 1987 Agenda and Budget Linda Preiss Rothschild 1986 Steve Armentrout Irving Kaplanaky Olga Tausoky-Todd 1987 Frederick W. Gehring Franklin P. Peterson Secretary Everett Pitcher 1986 Melvin Hocheter Everett Pitcher Auociate Secretaries Frank T. Birtel 1986 Appealo Committee on Dheounted Subocriptiono W. Wiotar Comfort 1986 R. M. Girouard, conaultant Morton Lowengrub, Robert M. Fonum 1987 Melvin Hochster, conaultant chairman Hugo Rossi 1987 William J. LeVeque Franklin P. Peterson Treasurer Franklin P. Peterson 1986 (ex offlcio) Paul J. Sally, Jr. Auociate Treasurer Steve Armentrout 1986 Audit Executive Committee of the Council Steve Armentrout M. Su1an Montgomery Hyman Baas 1987 Everett Pitcher Melvin Hochoter 1986 (ex olficio) Computer Operation• and Facilitieo, Irving Kaplansky, Jean E. Taylor 1988 (ex olflcio} chairman William A. Veech 1989 Vioitinc Committee on George D. Mostow Lee P. Neuwirth 1985 Peter J. Weinberger 1987 (ex olficio) S. Tucker Taft, 1986 chairman Membera-at-Large Corporate Relationo James G. Arthur 1988 Cora S. Sadooky 1987 Daniel M. Burns 1987 Jean E. Taylor 1986 Rameah A. Gangolli, Maria M. Klawe Michael G. Crandall 1986 Chuu-Lain Terng 1988 chairman Oscar S. Rothauo David Eisenbud 1986 Audrey A. Terras 1987 Jane P. Gilman 1988 William P. Thurston 1986 Endowment Melvin Hochater 1986 William A. Veech 1988 Andrew M. Gleason Cathleen S. Morawetz Joseph B. Keller 1987 David A. Vogan, Jr. 1987 W. Ted Martin, Carlos E. Kenig 1986 Robert F. Williamo 1988 chairman Editorial and Inveatment Communication• Committee• Steve Armentrout Franklin P. Peterson, Editorial Committees Rameah A. Gangolli chairman (The Chairman of each Editorial Committee and any Legal Aid member whose term began on or before January 1, 1986 is a member of the Council, ex officio.) Steve Armentrout Todd Dupont Morton L. Curtia, chairman Murray Geratenhaber American Joumal of Mathematico, Society'• Repreaentativea Liaiaon Committee Spencer Bloch 1988 Richard B. Melrose 1986 Irving Kaplanaky, Franklin P. Peterson chairman Everett Pitcher Bulletin (New Seriea) Long Range Planning Hyman Bass 1986 Edgar Lee Stout 1988 Wu-chung Hsiang, 1987 Hyman Baas, Franklin P. Peterson chairman chairman Everett Pitcher Frederick W. Gehring Jean E. Taylor Auoc.iate Editor• for Reaeareh Announcement• Spencer Bloch 1987 Richard B. Melrose 1987 Memberohip Ronald L. Graham 1987 Yiannis N. Moachovakia Frederick W. Gehring, 1986 Irwin Kra 1987 Roger Howe 1986 1986 chairman Jill P. Mesirov 1989 H. Blaine Lawoon, Jr. 1987 Harold M. Stark 1987 Melvin Henrikoen 1987 Hugo Roooi 1988 Auoeiate Editor• for Reaeareh - Expoaitory Artielea The Publication Program Felix E. Browder 1986 Victor Kac 1987 Benedict H. Groos 1986 Wilfried Schmid 1986 Steve Armentrout 1986 Andrew Odlyoko 1987 Morris W. Hirsch 1987 Guido L. Weiso 1987 Peter L. Duren 1987 Everett Pitcher (ex olficio) Murray Geratenhaber, 1986 Hugo Ro10i 1987 Colloquium chairman Paul J. Sally, Jr. 1987 Mary C. Lane, consultant Raoul H. Bott 1987 Barry Ma111ur, chairman William J. LeVeque Charleo L. Feft"erman 1988 1986 (ex offlcio) Mathematical Review• Salarieo Robert G. Bartle 1988 Morton Lowengrub 1987 Steve Armentrout Ronald L. Graham, Melvin Hochater, 1986 Frederick W. Gehring chairman chairman (ex olficio) Franklin P. Peterson Mathematical Surveys and Monograph• StafF and Service• Irwin Kra 1988 R. 0. Wello, Jr., 1988 Steve Armentrout, Franklin P. Peterson M. Susan Montgomery 1987 chairman chairman Paul J. Sally, Jr. Gian-Carlo Rota 1986 680 Anociate Editor Ad Hoc Committees Thomas F. Banchoft' Centennial Program Committee Editorial Board for Contemporary Mathematic• Hyman Bass John W. Milnor Thomas F. Banchoff 1987 Irwin Kra, chairman 1988 Felix E. Browder, chairman Cathleen S. Morawetz M. Salah Baouendi 1988 Jan Mycielski 1987 Philip A. Griffiths W. H. Jaco 1988 Johannes C. C. Nitsche Gerald J. Janusz 1986 1986 Search Committee for the Position Alan D. Weinstein 1987 of Secretary Hyman Bass Everett Pitcher Mathematic• of Computation Ramesh A. Gangolli, Vera S. Pless Walter Gautschi, 1986 John E. Osborn 1986 chairman Harold M. Stark chairman Hugh C. Williams 1988 Donald Goldfarb 1987 Other Publieationa Committees Associate Editor• James Bramble 1986 Philip Rabinowitz 1987 Standing Committees Bille C. Carlson 1986 Larry L. Schumaker 1988 Eugene Isaacson 1986 Ridgway Scott 1986 Abotracts Editorial Committee Heinz-Otto Kreiss 1987 Daniel Shanks 1987 Frank T. Birtel (ex officio) Everett Pitcher, chairman James N. Lyness 1986 Frank Stenger 1986 W. Wistar Comfort (ex officio) Morris Newman 1986 Hans J. Stetter 1988 (ex officio) Hugo Rossi (ex officio) Syvert P. N!1lrsett 1988 G. W. Stewart 1986 Robert M. Fossum Andrew M. Odlyzko 1988 Vidar C. Thom~e 1986 (ex officio) Frank W. J. Olver 1986 Lars B. Wahlbin 1986 Stanley J. Osher 1986 John W. Wrench, Jr. 1987 Notices Editorial Committee Beresford N. Parlett 1988 Paul F. Baum 1986 Mary Ellen Rudin 1988 Ralph P. Boas 1988 James A. Voytuk (ex officio) Proceeding• Raymond L. Johnson 1986 Steven H. Weintraub 1988 Thomas H. Brylawski Walter Littman Everett Pitcher, chairman Daniel Zelinsky 1986 Dennis Burke R. Daniel Mauldin (ex officio) John B. Conway Haynes R. Miller Doug Curtis 1989 Paul S. Muhly Anociate Editor• William J. Davis Andrew M. Odlyzko 1989 Stuart S. Antman, Hans Samelson, David G. Ebin Donald S. Passman 1988 Queries Queries Bert E. Fristedt George R. Sell 1986 Ronald L. Graham, Richard R. Goldberg 1987 Bhama Srinivasan Special Articles Larry J. Goldstein Daniel W. Stroock 1987 Thomas J. Jech William C. Waterhouse -- Proceedings of Symposia in Applied Mathematics Irwin Kra 1987 Editorial Committee Tranoactiono and Memoir• Stuart S. Antman 1988 1989 Jane Cronin Scanlon, 1988 Robert D. Edwards 1989 Kenneth Kunen 1987 chairman Ronald Getoor 1986 Tilla Klotz Milnor 1987 Ronald L. Graham 1987 Linda Preiss Rothschild Translation from Chinese William B. Johnson, 1986 1986 chairman Lance W. Small 1986 Sun-Yung Alice Chang Tai-Ping Liu Peter W. Jones 1988 Joel A. Smoller 1987 Tsit-Yuen Lam, chairman Vaughan F. R. Jones 1989 Ad Hoc Committee Anociate Editor Ralph Cohen 1986 Advisory Committee on a Russian-English Dictionary Communications Robert G. Bartle Edwin Hewitt (Only the Chairman of this Committee is a member, ex James R. Bunch Hans F. Weinberger, officio, of the Council.) Paul R. Halmos chairman Monitor Problems in Communication Jozef Dodziuk 1988 Marian B. Pour-El, 1986 Program and Meetings Nancy Gubman, chairman Standing Committees consultant Judith D. Sally 1987 Arthur M. Jaffe 1988 Lynn A. Steen 1986 Program Committee for National Meetingo William J. LeVeque Floyd L. Williams 1987 Joan S. Birman 1988 Richard P. Stanley 1987 (ex officio) F. Reese Harvey 1987 Nolan R. Wallach 1988 Everett Pitcher (ex officio) William P. Ziemer 1986 Internal Organimation of the Paul H. Rabinowitz 1988 Ameriean Mathematieal Soeiety Central Sectional Meeting• (Select Hour Speakers for) Standing Committees Robert M. Fossum Jeffrey B. Rauch 1986 (ex officio) Nancy K. Stanton 1987 Committee on Committee• Peter P. Orlik, 1986 Jeffrey D. Vaaler 1987 Michael G. Crandall 1986 Irving Kaplansky 1986 chairman Charles W. Curtis, 1986 George D. MostoW 1988 chairman Everett Pitcher (eX officio) Eastern Sectional Meetings (Select Hour Speakers for) Ronald A. Fintushel 1986 Lance W. Small 1986 Joel M. Cohen 1987 Clifford J. Earle, Jr. 1986 William H. Jaco 1986 Jean E. Taylor 1986 W. Wistar Comfort Srinivasa S. R. Varadhan, (ex officio) chairman 1986 Nominating Committee Roger Keith Dennis 1987 John T. Baldwin 1987 Burton Rodin 1987 James W. Cannon 1987 Mary Ellen Rudin 1986 Far Weotern Sectional Meetings Catherine L. Olsen 1987 Michael Shub 1986 (Select Hour Speaker• for) Vera S. Pless, chairman R. 0. Wells, Jr. 1986 Adriano M. Garsia 1986 Gary M. Seitz 1987 1986 Hugo Rossi (ex officio) Ronald J. Stern, 1987 Murray M. Schacher 1988 chairman Centennial Committee Felix E. Browder Andrew M. Gleason Southeastern Sectional Meetings Harold M. Edwards Everett Pitcher, chairman (Select Hour Speakers for) J. Thomas Beale 1987 James R. Retherford, 1986 Frank T. Birtel (ex officio) chairman Kevin M. McCrimmon 1986 John J. Walsh 1987 681 Agenda for Buaineaa Meeting• Prises and Awards M. Salah Baouendi 1988 Carol L. Walker 1988 Standing Committees Everett Pitcher, chairman National Awarda and Publie Representation Gibba Leeturera for 1987 and 1988, Irving Kaplanaky, 1987 Everett Pitcher (ex officio) Committee to Seleet chairman Stephen Smale 1987 Arthur M. Jaffe, M&rtin D. Kruakal George D. Mostow (ex officio) chairman Joel L. Lebowito Steele Pri1es (Terma expire on June 30) Richard W. Beale 1987 Louis Solomon 1989 Statue of the Profession Jerry L. Bona 1987 ------1989 Hermann Flaschka 1988 ------1989 Standing Committees John P. Hempel 1988 ------1989 Aeademie Freedom, Tenure, and Lawrence E. Payne 1987 ------1989 Employment Seeurity Ad Hoc Committees Edward George Effroo 1986 VeraS. Pleu 1987 Shoohichi Kobayaohi 1987 Halaey L. Royden, 1988 Automatie Theorem Proving, Committee to Charlotte Lin 1986 chairman Reeommend Robert R. Phelpo 1986 Winnera of Prilea for Employment and Educational Poliey David Mumford, chairman John L. Selfridge Jacob T. Schwarto Stefan A. Burr 1986 Donald C. Rung, 1987 Edward A. Connora 1988 chairman Philip C. Curtio, Jr. 1987 Audrey A. Terrae 1988 Cole Prise, Committee to Seleet the Winner of the Gerald J. Janun 1986 Paul T. Bateman, chairman Bernard M. Dwork Enrico Bombieri Data Subeommittee Lida K. Barrett 1988 Charlotte Lin 1986 Edward A. Connora, 1987 Jameo W. Maxwell Institutes and Symposia chairman (ex officio) Lincoln K. Durat, Donald E. McClure 1987 Standing Committee consultant Donald C. Rung 1986 Summer Inatitutea and Speeial Sympoaia Jamea Hurley 1988 (Terma expire on February 28) Employment Coneerna Subeommittee Albert Baernatein II, 1987 John Wermer 1988 Audrey A. Terrae 1986 Barnet M. Weinatock, 1986 chairman ------1989 Robert J. Thompoon 1988 chairman Eric M. Friedlander 1988 ------ 1989 H. Blaine Lawaon, Jr. 1987 Short Couroe Subcommittee Stefan A. Burr, 1986 Gerald J. Janun 1987 Ad Hoc Committee chairman Robert P. Kurahan 1987 Lial Novak Gaal 1986 Barbara L. Ooofaky 1988 1987 Summer lnatitute on Repreaentations of Finite Groupe and Related Topiea Human Righta of Mathematieiana Jonathan L. Alperin, Waite~ Feit Lenore Blum 1986 Leon A. Henkin 1988 chairman Paul Fong Charleo Herbert Clemeno Neil I. Koblito 1988 Charlea W. Curtis 1987 Joahua A. Lealie 1986 Chandler Davia, 1986 Seymour Schuoter 1987 chairman Joint Committees Profeaaional Ethiea AAAS-AMS-MAA Committee on Opportunitiea in C. Edmund Burgen 1987 Anneli Lax 1988 Mathematiea for Diaadvantaged Groupe Judith V. Grabiner 1987 Murray H. Protter, 1986 Paul R. Halmoo 1988 chairman Manuel P. Berriooabal1988 Shirley Malcom Sylvia T. Booeman 1989 (ex officio) Reeruitment of Young Mathematieiana William G. Chinn 1987 Rogera J. Newman 1989 Jameo A. Donaldaon 1988 Argelia Veles-Rodriquez, Paul J. Sally, Jr. Lynn A. Steen Amaua C. Fauntleroy 1987 consultant Jamea D. Staaheft", chairman Tepper L. Gill 1987 Clarence E. Stephens 1989 Gloria F. Gilmer, 1988 Harold J. Stolberg 1987 Reaeareh Fellowahipa (Term• expire on June 30) chairman J. William Helton 1987 Nancy K. Stanton 1988 Stephen Lichtenbaum 1987 ------1988 AMS-ASA-IMS-MAA-NCTM-SIAM Committee on Kenneth C. Millett, 1987 ------1988 Women in the Mathematical Seieneea chairman (NCTM members terms expire April 1 of the year given.) Nancy Angle (NCTM) 1986 Joyce R. McLaughlin 1981 Selenee Polley Raymond G. Ayoub 1986 (SIAM) (The Chairman of thio Committee io a member of the (AMS) Ingram Olkin (IMS) Council, ex offlcio) Susan J. Devlin (ASA) Katherine L. Pedersen 1986 Hyman Baaa 1987 Jamea W. Maxwell Suaan Geller (AMS) 1987 (NCTM) Felix E. Browder, 1987 (ex officio) Marjorie G. Hahn (IMS) Linda Petoold (SIAM) 1986 chairman George D. Moatow Gloria C. Hewitt 1986 Judith Roitman 1986 Carl-Wilhelm R. de Boor (ex officio) (MAA) (AMS) 1988 Robert Osaerman 1988 Julia Knight (AMS) 1986 Alice T. Schafer 1986 Ronald G. Douglao 1986 Judith D. Sally 1988 Carole B. LaCampagne (MAA) Frederick W. Gehring 1987 Guido L. Weiu 1988 (AMS, MAA), Elizabeth L. Scott (IMS) Louie N. Howard 1986 chairman 1986 Irving Kaplanoky Betty K. Lichtenberg 1988 (ex officio) (NCTM) Serviee to Mathematleiana in Developing Countriea AMS-ASL-IMS Committee on Tranalationa from Raymond G. Ayoub, Jameo Eello Russian and Other Foreign Language• chairman Donald M. Hill Boria M. Schein (AMS), Jamea A. Donaldaon Marahall H. Stone chairman 1987 Cooperation with the Chineae S.-Y. Cheng Richard S. Palaia, chairman Ronald L. Graham 682 AMS Subcommittee Member• AMS-MAA-SIAM Joint Policy Board for Mathematics Michael I. Brin 1987 Vladislav V. Goldberg 1988 I. Edward Block (SIAM} Everettt Pitcher 1986 David V. Chudnovsky 1986 Jack K. Hale 1986 (ex officio} (AMS} Charles V. Coffman 1988 John R. Isbell 1988 Gene H. Golub (SIAM) Ivar Stakgold 1986 Allen Devinatz 1988 Dmitry Khavinson 1987 (ex officio) (SIAM) Igor Dolgachev 1987 Boris M. Schein, 1987 Irving Kaplansky (AMS} Lynn A. Steen (MAA) Richard Ericson 1987 chairman (ex officio} (ex officio) Donald Kreider 1986 Alfred B. Willcox (MAA) ASL Subcommittee Member• (MAA} (ex officio} Vladimir Lifschitz 1987 Gregory Mine 1987 William J. LeVeque (AMS) Elliott Mendelson B. F. Wells (ex officio) IMS Subcommittee Memben Cs6rg6 A. Rukhin Mikl6s Joint Policy Board for Mathematics Eugene Dynkin, chairman W. J. Studden Executive Secretary for National Affairs: Klimko Lajoa F. Takaca Eugene M. Kenneth M. Hoffman of Cambridge Office AMS-IMS-SIAM Ad Hoe Executive Committee Room 2-280, Mauachusetta lnatitute of Technology The Evaluation Panel for NSF Postdoctoral Cambridge, MA 02139 Fellowships in the Mathematical Seienees Telephone: 617-253-3214 Washington Office Ablowito (SIAM) William T. Trotter (AMS), Mark Mathematical Association of America chairman George C. Tiao (IMS) 1529 Eighteenth Street, N.W., Washington, DC 20036 Telephone: 202-387-5200 AMS-IMS-SIAM Committee on Joint Summer Research Conferences in the Mathematical Seienees (Terms expire on June 30) AMS-MAA-SIAM Joint Coordinating Committee William B. Arveson 1987 1988 on Public Understanding of Mathematics Ronald L. Graham 1987 1988 Ronald L. Graham (AMS} Lynn A. Steen (MAA) John R. Martin 1987 1988 Joseph B. Keller (SIAM) Tilla Klotz Milnor 1987 1988 Evelyn Nelson 1987 AMS-SIAM Committee on Applied Mathematic• Conatantine M. Dafermoa Francis Sullivan 1988 AMS-IMS-SIAM Committee on Seientifl.e 1986 Robert F. Warming 1987 Collaboration with Latin American Countries James M. Hyman 1987 Richard J. Griego (AMS}, Richard A. Tapia (SIAM) Donald E. McClure 1988 chairman Cesareo Villegas (IMS) George C. Papanicolaou, Juan Jorge Schaffer (AMS) chairman 1986 AMS-MAA Arrangement• Committee for the AMS-SIAM Committee on San Antonio Meeting, January 22-25, 1987 Mathematics in the Life Seieneea 1988 Donald F. Bailey Kenneth A. Ross Gail A. Carpenter 1986 Richard E. Plant, Robert M. Foasum (ex officio} Kenneth L. Lange 1987 chairman John Rinzel 1986 (ex officio) Gregory Wene, chairman Hans G. Othmer 1988 William J. LeVeque Lawrence R.Williams Alan S. Perelson 1987 (ex officio) Bennir A. Zinn AMS-SIAM Committee to Screen Applicants for AMS-MAA Joint Program Committee for the San Graduate Study from the People's Republic of China Antonio Meeting Chia-Chiao Lin Mei-Chang Shen Uhlenbeck Judith V. Grabiner, F. Reese Harvey Beresford N. Parlett Karen chairman W. Gilbert Strang Franklin P. Peterson Paul R. Halmos AMS-MAA Joint Meeting• Committee Representatives William J. LeVeque, Kenneth A. Ron Adviaory Board of the National Tranalationa Center (ex officio) chairman Alfred B. Willcox Library Everett Pitcher of the John Crerar Ralph P. Boas AMS-MAA-SIAM Congressional Fellow for 1986-87 Commiuion on Profeuionale in Seienee and Kenneth M. Hoffman Louise A. Raphael Thomas R. Kramer, T. Christine Stevena Technology chairman Marcia P. Sward Edward A. Connors AMS-MAA-SIAM Committee on Employment Conference Board of the Mathematical Seieneea Opportunities (Terms expire on October 31} Irving Kaplansky 1986 Wilfred E. Barnes 1987 John W. Petro (AMS) 1988 (MAA) Donald C. Rung 1987 Fulkerson Prise Committee Richard E. Ewing 1986 (AMS) Alan J. Hoffman (SIAM) -----·---- (SIAM) 1988 Calvin T. Long 1986 Section A of the American Aaaoeiation for the (MAA}, chairman Advancement of Seienee (Term expires on May 27} AMS-MAA-SIAM Joint Administrative Committee Louise Hay 1989 I. Edward Block (SIAM) Everett Pitcher (AMS}, Paul W. Davis (SIAM} chairman U.S. National Committee on Theoretical and Applied Leonard Gillman (MAA} Kenneth A. Ross (MAA} Meehaniea (Term expires on October 31} William J. LeVeque (AMS} Alfred B. Willcox (MAA) Stuart S. Antman 1988 Franklin P. Peterson (AMS) ------(SIAM) 683 INSTITUTIONS NOT SUBJECT TO U.S. LAWS may be required to execute and submit a copy of this form with the text of recruitment advertisements for the Notices (see Policy Statement below). Publication of recruitment advertisements not accompanied by the completed form may be delayed or denied. Employment at ______(N arne of Institution) (City) (Country) is offered without discrimination on grounds of age, color, race, religion, sex, or national origin. (Signature) (Date) Name (please print) (Title) Please return this form to: Advertising Department Notices of the American Mathematical Society P.O. Box 6248 Providence, RI 02940, U.S.A. · AMS Policy on Recruitment Advertising No listing for a position will be printed if it expresses or implies any preference, limitation, specification, or discrimination based on age, color, race, religion, sex, or national origin in contravention of any federal or state statute prohibiting discrimination in employment on the basis of these criteria. The publisher reserves the right to edit any listing prior to publication which does not conform with federal or state law on discrimination in employment. All employers in the United States are required to abide by the requirements of Title VII of the Civil Rights Act of 1964, announcing a national policy of equal employment opportunity in private employment, without discrimination because of color, race, religion, sex, or national origin. All U.S. listings are accepted with the understanding that the employer complies with federal requirements. Advertisers not subject to U.S. laws may be required to sign a statement that they do not discriminate in employment on grounds of age, color, race, religion, sex, or national origin. Applicants should be aware that institutions outside the U.S. may not be legally bound to conform to these or similar requirements and the AMS cannot assume responsibility for enforcing compliance. Applicants are advised to inform themselves of conditions that may exist at the institutions to which they apply. In particular, readers should note that the Equal Employment Opportunity Act ( 42 U.S.C., §§2000e et seq.), which prohibits discrimination in employment on the basis of race, religion, sex, or national origin, contains (in §2000e-1) an exception from the provisions of the Act for any religious corporation, association, educational institution, or society with respect to employment of individuals of a particular religion to perform work connected with the carrying on by such corporation, association, educational institution, or society of its activities. The Age Discrimination Act of 1967 (29 U.S.C., §§621 et seq., as amended), makes it unlawful for an employer to discriminate against any individual between the ages of 40 and 70 because of age. Thus it is legal to seek as an employee someone who is "over 30," but not one "over 50;" neither is it legal to express a preference for someone who is ''young," or is a "recent graduate," since the latter tend (on statistical grounds) to be young. 684 Reciprocity Agreements The AMERICAN MATHEMATICAL SOCIETY has "reciprocity agreements" with a number of mathematical organizations around the world. A current list appears below. These RECIPROCITY AGREEMENTS provide for reduced dues for members of these organizations who choose to join the AMS and who reside outside of the U.S. and Canada. Reciprocally, members of the AMS who reside in the U.S. or Canada may join these organizations at a reduced rate. Summaries of the privileges available to AMS members who join under the terms of reciprocity agreements are given on the following pages. Members of these organizations who join the AMS as reciprocity members enjoy all the privileges available to ordinary members of the Society. AMS dues for reciprocity members are $39 for 1986 and $42 for 1987. Each organization was asked to review and update its listing in the Spring. An asterisk ( *) after the name of an organization indicates that no response to this request had been received when the August Notices went to press. A disc ( •) before the name of an organization indicates that application forms for that organization may be obtained by writing the American Mathematical Society, P.O. Box 6248, Providence, Rhode Island 02940. Africa B. R. Bhonsle, F. Harary, L. Debnath, S. P. Bandyopadhyay, (Vice-Presidents), B. K. Datta, Nigerian Mathematical Society* (Treasurer), U. Basu (Secretary). Apply to: Christopher 0. lmoru (Secretary), Nigerian Mathematical Society, Department of •Indian Mathematical Society Mathematics, University of Ife, Ile-Ife, Nigeria. Apply to: M. K. Singal, General Secretary, Dues: $10; payable to the Treasurer, Nigerian Indian Mathematical Society, Department of Mathematical Society, Department of Mathemat Mathematics, Meerut University, Meerut 250 005, ics, University of Benin, Benin City, Nigeria. India. Privileges: Journal of the Nigerian Mathematical Dues: $20; payable to V. M. Shah, Hon. Society at the price normally charged to individual Treasurer, IMS, Department of Mathematics, members. M. S. University, Barada, India. Officers: A. Olubummo (President), J. 0. C. Privileges: Journal of Indian Mathematical Soci Ezeilo (Vice-President), C. 0. Nwachuku (Trea ety or Mathematics Student. surer), C. 0. M. lmoru (Secretary), S. A. Ilori Officers: H. C. Khare (President), M. K. Singal (Assistant Secretary), H. 0. Tejumola (Editor-in (Secretary), V. M. Shah (Treasurer), J. N. Kapur Chief). (Academic Secretary), I. B. Passi (Editor of Journal of Indian Mathematical Society), A. M. Asia Vaidya (Editor of Mathematics Student). Allahabad Mathematical Society* •Korean Mathematical Society Apply to: P. Srivastava, Secretary, Allahabad Apply to: Sung Ki Kim, College of Natural Mathematical Society, 10, C.S.P. Singh Marg, Sciences, Seoul National University, Seoul 151, Allahabad-211001, India. Korea. Dues: US $25 (annual), US $250 (life), US $125 Dues: W15,000 (US $20); payable to Sung Ki (life for members of American Mathematical Kim. Society); payable to Allahabad Mathematical Privileges: Free receipt of Bulletin (two issues per Society. year) and Journal of the Korean Mathematical Privileges: The Journal of the Society is sent to Society (two issues per year). members regularly. Officers: Tae Geun Chao (President), Jongsik Kim Officers: U. N. Singh (President), Vachaspati (Vice-President), Suk-Young Lee (Treasurer), (Vice-President), K. K. Azad (Treasurer), P. Sri Sung Ki Kim (Secretary). vastava (Secretary). •Mathematical Society of Japan Calcutta Mathematical Society* Apply to: Setsuko Izawa, Secretary, Mathematical Society of Japan, 25-9-203, Hongo 4-chome, Apply to: U. Basu, Secretary, Calcutta Mathemat Bunkyo-ku, Tokyo 113, Japan. ical Society, 92, Acharya Prafulla Chandra Road, Calcutta 700 009, India. Dues: US $24; payable to Mathematical Society of Japan. Dues: $2; payable to U. Basu, Secretary. Privileges: Journal of the Mathematical Society Privileges: News Bulletin (free of cost). of Japan; Sugaku (in Japanese) for US $5.00 Officers: M. Dutta (President), P. C. Vaidya, additional dues. 685 Officers: Hikosaburo Komatsu (President), Kiyoshi Privileges: Jniiniibha (an interdisciplinary mathe Hasegawa (Treasurer), Setsuko Izawa (Secretary). matical journal currently published once a year); back volumes available at 25%discount. Mathematical Society Officers: H. M. 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Mathematical Society, c/o Department of Mathe Privileges: Boletin de la Asociaci6n Matematica matics, Punjab University, New Campus, Lahore Espanola; Publicaciones de la Asociaci6n Mate (Pakistan). matica Espanola (at reduced prices). Dues: Rupees 15/- per year or Rs. 150/- for life. Officers: Miguel de Guzman, (President), Ireneo (US $1.50 per year or US $15.00 for life); payable Peral (Treasurer), Maria T. Carrillo (Secretary). to Abdul Majeed, Secretary. Privileges: Society News, Punjab University Jour nal of Mathematics, Proceedings of the Confer Berliner Mathematische Gesellschaft e.V. * ences, Symposia and Seminars arranged by the Society. Apply to: D. Kriiger, FB 3, Sekr. H 65 TU Berlin, Strasse des 17. Juni 135, 1000 Berlin 12, Federal Officers: B. A. Saleemi (President), Masud A. Republic of Germany. Malik, Rashid Hayat (Vice-Presidents), Khal ifa Rashid ud-Din (Treasurer), Abdul Majeed Dues: DM 12; payable to G. Preuss, Institut fiir (Secretary). Mathematik I, FU Berlin Hiittenweg 9, 1 Berlin 33, Federal Republic of Germany. Officers: Rudolf Gorenflo (President), Hansgeorg •Southeast Asian Mathematical Society Jeggle (Vice-President), G. Preuss (Treasurer), Apply to: Boon-Yiang Ng, Southeast Asian Math D. Kriiger (Secretary). ematical Society, cfo Department of Mathematics, University of Malaya, Kuala Lumpur, Malaysia. Dansk Matematisk Forening* Dues: US $5; payable to Boon-Yiang Ng, South east Asian Mathematical Society. Apply to: Mogens Esrom Larsen, Secretary, Privileges: SEAMS Newsletter, Southeast Asian Dansk Matematisk Forening, Universitetsparken Bulletin of Mathematics. 5, 2100 K¢benhavn 0, Denmark. Officers: Lim Chong Kong (President), Chong Chi Dues: D.kr. 25; payable to Christian Berg, Tat, Sawai Nualtaranee (Vice-Presidents), Gek Treasurer. Ling Chia (Treasurer), Boon-Yian Ng (Secretary). Privileges: Mathematica Scandinavica (D.kr. 97,50 per volume), Nord. Mat. Tidss. 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(Secretary), Ebbe Thue Poulsen, Bodil Branner. 686 •Deutsche Mathematiker-Vereinigung e. V. •lslenzka Strerdfrredafelagid Apply to: Deutsche Mathematiker Vereinigung Apply to: President, Raunvisindastofnun e.V., J. Flum, Albertstrasse 24, 7800 Freiburg, Hask6lans, Dunhaga 3, 107 Reykjavik, Iceland. Federal Republic of Germany. Dues: $10; payable to islenzka Strerdfrredafelagid. members); payable Dues: DM 30.- (for reciprocity Officers: Halld6r I. Eliasson (President), Beni 16269 (BLZ 641 to Kreissparkasse Tiibingen dikt Johannesson (Treasurer), Ragnar Sigurdsson Federal Republic of Germany or 500 20), (Secretary). Postscheckamt Stuttgart 18517-706 (BLZ 600 100 70), Federal Republic of Germany. 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Osterreichische Mathematische Gesellschaft * Glasgow Mathematical Association Apply to: Curt C. Christian, President, Osterreich Apply to: R. J. Steiner, Department of Mathemat ische Mathematische Gesellschaft, Technische ics, University of Glasgow, University Gardens, Universitiit Wien, Wiedner Hauptstrasse 6-10, Glasgow G12 8QW, Scotland. A-1040 Wien, Austria. Dues: £12.50 (US $25); payable to Glasgow Dues: AS 130; payable to lnge Troch, Treasurer, Mathematical Association. Osterreichische Mathematische Gesellschaft, Tech Privileges: Glasgow Mathematical Journal. nische Universitiit Wien, Wiedner Hauptstrasse Officers: M.K.N. Nair (President), H. J. A. Scott, 6-10, A-1040 Wien, Austria. K. A. Lindsay (Vice-Presidents), R. J. Steiner Privileges: Internationale Mathematische Nach (Treasurer), J. Muir (Secretary). richten (IMN). 687 Officers: Curt C. 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Officers: Vinicio Villani (President), Giulio Ce Apply to: P. Lasacaux, Secretary, Societe de sare Barozzi (Vice-President), Salvatore Coen Mathematiques Appliquees et Industrielles, Lab (Treasurer), Pier Luigi Papini (Secretary). oratoire de Mathematiques Appliquees, Ecole Polytechnique, 91128 Palaiseau, France. Dues: 120 francs (US $20); payable to J. P. Puel, Wiskundig Genootschap* Treasurer, Societe de Mathematiques Appliquees et Industrielles, Laboratoire de Mathematiques Apply to: Membership Department, Mathema Appliquees. tisch Instituut, Budapestlaan 6, 3584 CD, Utrecht, Netherlands. Privileges: Right to receive the membership list and the newsletter; right to participate at SMAI Dues: Hfi 35.-; payable to Amro Bank, Utrecht, sponsored meetings and workshops with a reduced Netherlands, Account 45.65.88.167, Penning fee. meester Wiskundig Genootschap. Officers: R. Temam (President), J. P. Boujot, Privileges: Nieuw Archie/ Voor Wiskunde (three N. Elkaroui, J. 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Aplicada E Computacional Middle East Apply to: Comissao de Admissao da SBMAC, Rua Lauro Miiller, 455, Rio de Janeiro, RJ, Iranian Mathematical Society Brasil. Dues: $6; payable to Sociedade Brasileira de Apply to: Secretary, Iranian Mathematical Soci Matematica Aplicada E Computacional. ety, P. 0. Box 13145-418, Tehran, Iran. Privileges: Vote in election for officers of the Dues: $10; payable to Iranian Mathematical Society, present papers at meetings of the Society. SBMAC, receive the Boletim and Matematica Privileges: Bulletin of the Iranian Mathematical Aplicada e Computacional. Society and reduced rate for participation in the annual Iranian Mathematics conferences. Officers: P. J. Paes-Leme (President), C. Humes, Jr., (Vice-President), A. C. Gadelha Vieira Officers: M. Toomanian (President-Secretary), (Treasurer), M.C.C. Bezerra (Secretary). S. H. Javadpoor (Treasurer). Israel Mathematical Union* eSociedad Colombiana de Matematicas Address for mail: Israel Mathematical Union, c/o Apply to: Sociedad Colombiana de Matematicas, Shoshana Abramovich, Secretary, Department of Apartado Aereo 2521, Bogota, D.E., Colombia. Mathematics, Haifa University, Haifa, Israel. Dues: $16; payable to Sociedad Colombiana de Apply to: Victor Harnik, Department of Mathe Matematicas. matics, Haifa University, Haifa, Israel. Privileges: Either Revista Colombiana de Matema Dues: IS 40; $5 for overseas members; payable to ticas (four issues a year) or Lecturas Matematicas Israel Mathematical Union. (three issues a year). Privileges: Newsletter; may attend and present papers at meetings. Officers: Jaime Lesmes (President), Ivan Castro (Vice-President), Clara H. Sanchez (Secretary). Officers: Rafael Artzy (Chairman), Victor Harnik (Treasurer), Shoshana Abramovich (Secretary). eSociedade Paranaense de Matematica South Pacific Address for mail: Caixa Postal 1261, 80001- Australian Mathematical Society Curitiba-PR-Brasil. Apply to: Sociedade Paranaense de Matematica, Address for mail: Australian Mathematical Soci Caixa Postal1261, 80001-Curitiba-PR-Brasil. ety, c/o Department of Mathematics, University of Queensland, St. Lucia, Queensland 4067, Dues: US $10; payable to Sociedade Paranaense Australia. de Matematica. Apply to: W. R. Bloom, Secretary, Australian Privileges: Boletim da Sociedade Paranaense de Mathematical Society, c/o School of Mathemat Matematica (two issues per year), Monografias da ical & Physical Sciences, Murdoch University, Sociedade Paranaense de Matematica (one issue Murdoch, W. A. 6150, Australia. per year), and Informes da Sociedade Paranaense Dues: $A38.00; payable to D. G. Tacon, Associate de Matematica (two issues per year). Treasurer, Australian Mathematical Society, c/o Officers: C. Pereira da Silva (President), School of Mathematics, The University of New R. Petronzelli (Vice-President), E. Andretta South Wales, P.O. Box 1, Kensington, N.S.W. (Treasurer),J. A. Novelli (Secretary). 2033, Australia. 690 Privileges: Free copies of The Gazette and copies Dues: $5; payable to Mathematical Society of the of Journal Series A and B and The Bulletin at Philippines. members rates. Privileges: Publications and newsletters of the Officers: G. B. Preston (President), R. S. Ander Mathematical Society of the Philippines. ssen, J. A. Giles, R. Lid! (Vice-Presidents), B. D. Officers: Honesto G. Nuqui (President), Jose Jones (Treasurer), W. R. Bloom (Secretary). Marasigan (Vice-President), Josefina C. Fonacier (Treasurer), FeN. 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Officers: Sin-Leng Tan (President), Abdul Razak Privileges: Newsletter of the NZMS (3 per year); Salleh, Gek-Ling Chia (Vice-Presidents), Nik subscription to Mathematical Chronicle at reduced Ahmad Kamal (Treasurer), Boon-Yian Ng (Sec rate. retary). Officers: I. L. Reilly (President), M. R. Carter (Vice-President), J. A. Shanks (Treasurer), Mathematical Society of the Philippines* M.D.E. Conder (Secretary). Apply to: Membership Committee, Mathematical Society of the Philippines, Department of Math ematics, Ateneo de Manila University, P.O. Box 154, Manila, Philippines. PARTICLE SYSTEMS, RANDOM MEDIA AND LARGE DEVIATIONS Richard Durrett, Editor "The book is an excellent introduction to the exciting recent developments which combine ideas from physics with mathematical techniques from the theory of probability." - Frank l. Spitzer Cornell University This volume of proceedings of the 1984 AMS Summer Research Conference The Mathematics of Phase Transitions provides a handy summary of results from some of the most exciting areas in probability theory today: interacting particle systems, percolation, random media (bulk properties and hydrodynamics). the Ising model and large deviations. Thirty-seven mathematicians, many of them well-known probabilists, collaborated to produce this readable introduction to the main results and unsolved problems in the field. In fact, it is one of the very few collections of articles yet to be published on these topics. To appreciate many of the articles, an undergraduate course in probability is sufficient. The book will be valuable to probabilists, especially those interested in mathematical physics and to physicists interested in statistical mechanics or disordered systems. ISBN 0-8218-5042-3. LC 85-6181. ISSN 0271-4132 391 pages. August 1985 Individual member $19. Institutional member $26. List price $32 To order. please specify CONM/41NA Shipping/Handling: 1st book $2. each add'l $1. $25 max. By air. 1st book $5. each add'l $3. $100 max. PREPAYMENT REQUIRED. Order from American Mathematical Society, PO Box 1571. Annex Station. Providence. Rl 02901-1571. or call 800-556-7774 to use VISA or MasterCard. 691 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 $.65 per word with a minimum of $30.00. The same ad in 6 consecutive issues is $3.50 per word. Type will be set solid unless centering and spacing are requested. A centered line of any length or the equivalent in white space is $6.00. 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 $10.00 charge, announcements can be placed anonymously. 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POSITIONS AVAILABLE POSTDOC OR ASSISTANT IN MATHEMATICAL NEUROSCIENCE Le Departement de mathematiques. statistique et actu Research in posture. sensorimotor control. cerebellum, ariat de I'Universite Laval aimerait soumettre au CRSNG vestibular disorders. and/or development. by means of en novembre prochain une (ou des) candidature(s) val appropriate mathematical description. Exposure to many able(s) au programme de chercheurs-boursiers universi areas: concentration on specific problems. Some degree taires pour un poste de chercheur-boursier debutant le or intensive background in mathematics or mathematical 1er juillet 1987 et d'une dun~e-de 5 ans. II aimerait physics required. Send curriculum vitae. list of refer aussi soumettre une (ou des) candidature(s) valable(s) au ences. and letter describing past and present interests to: programme d'attaches de recherche du CRSNG. le but de Dr. Gin McCollum. Neurological Sciences Institute. Good ce programme etant de permettre a certaines universites Samaritan Hospital and Medical Center. 1120 NW 20th francophones d'intensifier leurs activites de recherche. Ave. Portland. Oregon 97209. La contribution du CRSNG est d'environ 32 OOOS. Le The Good Samaritan Hospital and Medical Center is an candidat selectionne recevrait en sus de I'Universite 6 AA/EOE. 500$ et sa tache annuelle d'enseignement. apr!!s entente. se limiterait a au plus un cours (i.e. au plus 45 heures d ·enseignement). UNIVERSITY OF CALIFORNIA, IRVINE Ce concours s'adresse surtout aux excellents mathema DEPARTMENT OF MATHEMATICS ticiens qui ont acquis cinq annees d'experience ou moins IRVINE, CALIFORNIA 92717 apres !'obtention de leur doctorat. et exclut ceux qui Two faculty positions at the level of Assistant Profes deja un poste conduisant a Ia permanence dans une sor in Applied Mathematics. available beginning academic universite canadienne. A cause des lois canadiennes sur year 1987-88. A Ph. D. degree. publications. and evi !'immigration. les candidats doivent i!tre canadiens ou dence of active interest in quality teaching are required. immigrants r~us. Examples of preferred research areas: partial differen Les candidats interesses sont invites a envoyer au plus tial equations. nonlinear phenomena. applied functional tot leur curriculum vitae. une courte description de leurs analysis. and numerical analysis. Send applications. a activites et projets de recherche. et a faire parvenir trois curriculum vitae, and the names of three or more ref lettres de recommandation a l'adresse suivante: erences to Professor Martin Schechter. Department of Postes de chercheur-boursier et d'attache de recherche. Mathematics. University of California. Irvine. CA 92717. Departement de mathematiques. statistique et actuariat. An Affirmative Action/Equal Opportunity Employer. Universite Laval. Quebec. Canada G1K 7P4 Institute for Computer Applications in Science and THE UNIVERSITY OF ALABAMA Engineering (ICASE). A limited number of visiting ap DEPARTMENT OF MATHEMATICS pointments are available for both junior- and senior-level researchers at the Institute for Computer Applications in As part of ongoing development in applied mathemat Science and Engineering (I CASE) which is operated by the ics. we have received funding for a new position in applied Universities Space Research Association. I CASE serves as mathematics. Salary will be negotiable. up to a maxi a center for interaction between Langley Research Center mum of $35.000 and rank will depend upon qualifications. staff and the academic community in the areas of applied We invite applications from experienced mathematicians and numerical mathematics. applied computer science, in applied mathematics with excellent records in research and development of mathematical models in a variety of and teaching. We are looking for someone who will help application areas. Applications for partial support while on us develop our research group and our graduate pro sabbatical leave are encouraged as are applications from grams in applied mathematics. Applications or inquiries Ph.D.'s for two-year renewable appointments. Inquiries should be sent to: Alan Hopenwasser. Chairman. Depart should be addressed to the Director. ICASE. Mailstop ment of Mathematics. P. 0. Box 1416. University, AL 132C. NASA Langley Research Center. Hampton. Virginia 35486. THE UNIVERSITY IS AN EQUAL OPPORTU 23665. An Equal Opportunity Employer. NITY /AFFIRMATIVE ACTION EMPLOYER. 692 POSITIONS AVAILABLE The Department of Mathematics and Statistics at McGill University wishes to sponsor a strong candidate for the Natural Sciences and Engineering Research Council of LAWRENCE UNIVERSITY Canada (NSERC) 1986-87 University Research Fellowship DEPARTMENT OF MATHEMATICS Competition. These Fellowships are five year research Tenure-track position at the assistant professor level positions (with a review in the third year). in the nature of starting fall 1987. The Department has slight preference Research Assistant Professorships. and carry a teaching for candidates specializing in geometry /topology of proba load of at most one course throughout the academic year. bility, but will consider especially strong candidates in any Applicants should have shown some substantial research area. Lawrence is a liberal arts college with a national rep ability beyond their Doctoral thesis. They should be utation. small classes. and excellent students. Teaching Canadian Citizens or landed immigrants by October 17. load two courses each ten week term. Salary competitive. 1986. Send resume. transcripts. and three or four supporting Interested candidates should send their curricula vitae letters to Bruce Pourciau. Chair. Department of Mathe to: matics. Lawrence University. Appleton. WI 54912. These Professor M. Herschorn. Chairman letters should provide specific evidence on the candidate's Department of Mathematics and Statistics potential for outstanding undergraduate teaching and con McGill University tinued research. Deadline February 1. Equal Opportunity 805 Sherbrooke Street West Employer. Montreal. Quebec. Canada H3A 2K6 UNIVERSITY OF ROCHESTER They should arrange for at least two letters of reference CHAIRPERSON, DEPARTMENT OF from competent referees to be sent directly to the same MATHEMATICS address. All documentation should reach the department Applications. inquiries. and nominations are invited by September 12. 1986. The department will make for the position of chairperson of the Department of its recommendations to NSERC early in October 1986. Mathematics. Candidates should have an outstanding NSERC will announce its decision in March 1987. research record and are expected to be able to provide leadership during a period of planned expansion. TEXAS A&M UNIVERSITY Applicants should send a curriculum vitae and names of appropriate references to: Applications are invited for tenure-track positions in Mathematics starting September 1. 1986. Candidates Chairperson Search Committee must have a Ph.D. in Mathematics and salaries are com Mathematics Department of petitive. We are especially interested in applicants in University of Rochester algebra. applied mathematics, and non-linear analysis. 14627 Rochester. NY There is a possibility of appointments at Professor, Asso The University of Rochester is an equal opportunity, ciate Professor. and Assistant Professor ranks. Visiting affirmative action employer. positions are also expected. Send vita and arrange for three reference letters to be sent to Department of Mathematics Southern Methodist Uni Dr. H. E. Lacey. Head versity Department of Mathematics Applications are invited for a Professor and two tenure Texas A&M University track Assistant Professors beginning September 1987. College Station. TX 77843-3368 position should be distinguished Candidates for the senior Texas A&M is an equal opportunity employer. scholars providing leadership in one or more areas of research in applied mathematics. A successful grant record and the supervision of doctoral dissertations are The University of Wyoming desirable. Candidates for the junior positions should have Head-Department of Mathematics an outstanding research record or superior potential. A The Department of Mathematics at the University of commitment to excellence in teaching is expected of all Wyoming invites applications for the position of Depart candidates. ment Head. The University is the sole four-year institution The department has ten active applied mathematicians of higher education in the state of Wyoming with an en doing research in areas such as mathematical modeling. rollment of 10.000 students. The mathematics program nonlinear wave phenomena. numerical analysis (differential offers degrees in mathematics. applied mathematics, and equations and optimization). and scientific computation. several joint-degree options at the bachelor. master and Recently Lawrence Shampine has been appointed the first doctoral levels. The department has a growing major holder of the Betty Clements Chair in Applied Mathemat research component in applied mathematics including a ics. petroleum research institute with funding from major in Applicants should send a vita and three letters of ref dustrial supporters. Other active research areas in the erence (for the senior position. names only) to Richard department include numerical analysis. partial differen Haberman. Chairman. Department of Mathematics. tial equations. functional analysis. optimization theory, Southern Methodist University. Dallas. Texas 75275. or dynamical systems. rigidity theory, and combinatorics. call (214) 692-2506. Candidates should have a strong research record com The university is an Equal Opportunity I Affirmative patible with department interests and a commitment to Action/Title IX employer. excellence in instruction. Applicants should submit a current curriculum vita and the names of at least three UNIVERSITY OF CRETE, GREECE suitable references to Department of Mathematics W. G. Bridges. Chair Applications are invited from Greek-speaking mathe Search Committee maticians. holding the Ph.D. degree. for visiting positions Mathematics Department at all ranks for both semesters of the whole Academic University of Wyoming Year 1986-7. Send expression of interest. vita and Laramie. WY 82070 representative research work to Professor Susanna Pa Applications will be considered through January 31. padopoulou. Chairperson. Mathematics Department. Uni 1986. The University of Wyoming is an equal opportunity versity of Crete. lraklion. Greece. employer. 693 POSITIONS AVAILABLE THE HEBREW UNIVERSITY OF JERUSALEM UNIVERSITY OF TORONTO The Department of Mathematics has an opening for Department of Mathematics a tenure track position. Excellent research accomplish Toronto, Ontario M5S LA1 ments and strong committment to teaching are required. Canada Candidates should apply to the Chairman. Department of Mathematics. Hebrew University, 91904 Jerusalem. Israel. The Department of Mathematics. University of Toronto as early as possible till October 15. and include a resume is looking for strong applicants in pure or applied math and names of three or more references. ematics to nominate as candidates for NSERC Research Fellowships beginning July 1. 1987. These are five year research positions (subject to a review in the third year) FOR SALE with teaching load of at most one course per year. One of the five years may usually be taken as a sabbatical. BOOK SCIENTIFIC Successful candidates may in special circumstances be 18 E. 16th Street considered directly for a tenure-stream position. New York. NY 10003 Applicants should be mathematicians with a relatively (212) 206-1310 recent doctorate and who have demonstrated their ability Toll-free 1-800-621-1220 with some substantive post-thesis research accomplish Mon - Sat. 10am-6pm EST ment. They must be Canadian citizens or landed im Technical book specialists migrants by November 1. 1986. University of Toronto New - Old - Out of print encourages both men and women to apply for these Want lists welcome fellowships. Top prices paid for your books. Applicants should send an up to date curriculum vitae and a short description of their research program to Professor T. Bloom. Chairman. and arrange to have sent Math librarians: do you want $10.000.00 worth of three letters of reference. This material should arrive books free? If gifts to your library are tax deductible. I before Monday. September 15. 1986. The Department's want to donate about 350 books. mostly on the graduate choice of candidates will be made in late September. and and research level. In return I ask that (1) you send the final decision by NSERC is announced (by NSERC) in a receipt stating your own fair appraisal of their present the spring. price. (2) you pay the cost of packing and mailing, and (3) you take them all or none. If you're interested. University of California, Santa Barbara please send $1.00 for a detailed list to P. R. Haimes. Mathematics Department. Santa Clara University, Santa Department of Mathematics Clara. CA 95053. Applications are invited for the KY FAN ASSISTANT PROFESSORSHIP. The Ky Fan assistant professorship DIFFERENTIAL EQUATIONS SOFTWARE is a special two-year non-renewable position which car ries a research stipend. Appointment is effective July 1. Screen and menu driven ordinary differential equations 1987. Candidates must possess a Ph.D by September software for IBMPC. compatibles. Graphics. Classroom 1987. Selection will be based primarily on demonstrated tested. Shareware concept: not copy protected: copying research achievement. Teaching experience is desirable. and dissemination encouraged. $10 handling charge. E. Teaching load will consist of four quarter courses per year. Spitznagel. Box 1146. Washington University, St. Louis. To apply send vita and publication list. and arrange to MO 63130. have 3 letters of recommendation sent to: Faculty Search Committee. Department of Mathematics. University of Math/Stats Library: List from R. Chesters. Suite 1900. 2 California. Santa Barbara. CA 93106. All applications First Canadian Place. Toronto. Canada M5X 1E3. received by January 9. 1987 will be given thorough con sideration. Theory of Numbers UCSB is an equal opportunity /affirmative action em Foundations of Semiological ployer. H. A. Pogorzelski and W. J. Ryan Volume 1 (1982). General Semiology, 597 pp .. $29.95 Volume 2 (1985). Semio. Functions. 695 pp .. $34.95 Department of Mathematics (Eight Volumes Projected) VANDERBILT UNIVERSITY UMO Press. Univ. of Maine. Orono. ME 04469 (Post free within US if check included) CENTENNIAL PROFESSORSHIP in computer-related mathematics beginning Fall. 1987 Mathematics library. Request list. Bert Ross. Univer sity of New Haven. West Haven. CT 06516. This position will become a named. endowed. chair. It is intended for a person of distinction whose primary research involves actual computing. Proceedings of the Nineteenth Have curriculum vitae and letters of recommendation Nordic Congress of Mathematicians, sent to University of Iceland, August 13-17,1984 Professor R. R. Goldberg, Chairman Detailed advertisement with list of contents in the Mathematics Department January 1986 Notices. p. 181. Send order and pay Vanderbilt University ment ($20) to: Icelandic Mathematical Society, Science Nashville, TN 37235 Institute. 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Manufacturer's product names are trademarks of individual manufacturers. This ad was generated using PCTEX, and printed on a Corona Laser Printer. 696 s/ r " ;Mathematics from Princeton ' '' Foundations of Representation Theory of Algebraic Analysis Semisimple Groups Masaki Kashiwara, Takahiro Kawai, and An Overview Based on Examples Tatsuo Kimura Anthony W. Knapp Translated by Goro Kato This book gives a survey of the theory of group The use of algebraic methods for studying representations for semisimple Lie groups in a analysis is an important theme in modern mathe way that reflects the spirit of the subject and matics. The most significant development in this corresponds to a person's natural learning process. field is microlocal analysis, that is, the local study of It is intended both for professionals in other fields differential equations on cotangent bundles. This of mathematics and for graduate students. The treatise provides a thorough description of micro author's approach is based on examples and has local analysis starting from its foundations. The unusual ground rules. Although theorems are book begins with the definition of a hyperfunc always stated precisely in reasonable generality, tion. It then carefully develops the microfunction the work often gives proofs that handle only an theory and its applications to differential equa illustrative example or class of examples. This is tions and theoretical physics. It also provides a especially so when the example captures the idea description of microdifferential equations, the for the general case. 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THE ENCYCLOPAEDIA OF MATHEMATICS WILL HELP YOU: V find the precise definition of a given concept V look up and verify terminology V find the precise statement of a theorem V reach the information you need via AMS classification numbers and/or keywords phrases V check the precise names of concepts and theorems V find reference literature for a given field V find out about applications of a concept and its links with other concepts Write for your free brochure and sample pages today! D. Reidel Publishing Company a member of the Kluwer Academic Publishers Group P.O. Box 17, 3300 AA, Dordrecht, the Netherlands 190 Old Derby Street, Hingham MA 02043 U.S.A. Falcon House, Queen Square, Lancaster LA 1, 1 RN, U.K. 698 New titles ftom Birkhiuser Boston Your sourceformqjormathematical developments PROGRESS IN MATHEMATICS GEOMETRIC THEORY OF FOLIATIONS A LA RECHERCHE DE Cesar Camacho and A. Lins Neto LA TOPOLOGIE PERDUE One of the first books which provides a well I Du cote de chez Roblin written introduction to the field of foliations II Le cote de Casson emphasizing geometric aspects of the theory Lucien Guillou and Alexis Marin and establishing a natural connection with This book is a collection of papers of differential topology and the qualitative theory fundamental importance in the theory of dynamical systems. of 4-dimensional manifolds. Of interest Hardcover/216 pages/$42.00/ to those in all branches of topology, this ISBN: 0-8176-3139-9 valuable book outlines foundations of the field. MATHEMATICAL HISTORY Hardcover/2 72 pages/$39 .00/ PM, Vol. 62/ISBN: 0-8176-3329-4 LINEAR DIFFERENTIAL EQUATIONS AND GROUP THEORY FROM SEMINAIRE DE THEORIE DES RIEMANN TO POINCARE NOMBRES, PARIS 1984-8$ Jeremy Gray Catherine Goldstein, ed. This important book looks at the historical This fifth volume in a series of proceed origins of the geometric side of complex ings from the Paris Number Theory function theory, culminating in Klein's and Seminars presents a wide variety of topics Poincare's theory of automorphic functions. with papers from an international group Two separate lines converge to create that of mathematicians who report on the theory, both of which have their roots in the most important current research in all theory of elliptic functions. aspects of number theory. Hardcover/450 pages/$70.00 (tent.)/ Hardcover/252 pages/$39.00 (tent.)/ ISBN: 0-8176-3318-9 PM, Vol. 63/ISBN: 0-8176-3347-2 THE ANCIENT TRADITION OF MALCEV-ADMISSIBLE GEOMETRIC PROBLEMS ALGEBRAS Wilbur Knorr Hyo Chul Myung Based on original documents, this extensive This book presents a self-contained and study of the mathematical philosophy and detailed account of the mathematical thinking exhibited during the Greek period theory of Lie-admissible algebras which is challenges the standard notions about the based on the research of mathematicians ancient sources. Includes detailed diagrams and physicists since 1977. Many new which emphasize the visual aspect of simple algebras are presented and open geometry as well as photo plates which give problems are suggested. evidence from ancient art used to resolve Hardcover/353 pages/$39.00 (tent.)/ puzzles about ancient mathematical history. PM, Vol. 64/ISBN: 0-8176-3345-6 Hardcover/424 pages/$69.00 I ISBN: 0-8176-3148-8 Available at your local scientific bookstore or order directly from the publisher: Birkhauser Boston Inc. D c/o Springer-Verlag Distribution Center, P.O. Box 2485, Secaucus, NJ 07094 699 ARIZONA STATE UNIVERSITY CHAIR DEPARTMENT OF MATHEMATICS Arizona State University invites nominations and applications in an external search for the position of Chair of the Department of Mathematics. The University is one of the largest comprehensive public institutions in the United States, with a student enrollment of over 40,000, approximately one-quarter of which is at the graduate level, with undergraduate enrollment concentrated at the upper division. Located in the rapidly growing Phoenix metropolitan area, ASU enjoys the change and development characteristic of the American Southwest. A progressive academic setting and high technology environment provide a wide range of Jiving, educational, recreational and cultural opportunities. The Department of Mathematics offers the Bachelor of Arts and Bachelor of Science degrees, as well as the Master of Arts and the Ph.D. It participates in the Master of Natural Science degree and collaborates with the College of Education in offering the Bachelor of Arts in Education and programs leading to the Ed.D. and Ph.D. in education. A regular faculty of 48 supported by visiting faculty, graduate assistants and staff are responsible for general education instruction for students throughout the University, especially those in the sciences, engineering and business, and programs for approximately 200 undergraduate and 50 graduate majors. The Department has growing research programs in various areas of applied mathematics and analysis. Instructional programs are offered in general, computational, and applied mathematics, mathematics education, and statistics and probability. The chair is expected to provide leadership for growth, renewal and development of the Department during a period of rapid change and expanding resources. The position carries significant responsibilities for administering a department which serves a large undergraduate and graduate population with disproportionate needs in the applied, computational and statistical areas, as well as expanding research activities. A successful candidate must be willing to devote substantial effort to further enhancing the general quality of the Department and its programs. The chair reports to the Dean of the College of Liberal Arts and Sciences, which encompasses the physical and life sciences, the social and behavioral sciences, and the humanities. Qualifieations. The Department Chair should possess demonstrated leadership qualities and a strong commitment to academic values and excellence in teaching, research and service. Additional qualifications include the following: • An earned doctorate and outstanding research credentials commensurate with the rank of professor. • Evidence of ability to lead and to manage a complex organization, including responsibilities for personnel and financial resources. • Experience with program planning, development and enhancement, including outreach to those sectors of society which depend on modern mathematics, and a record of university teaching are preferred. • Continuing record of professional activity and involvement in the national mathematical sciences community and broad knowledge of mathematics as a discipline and its role in contemporary society, including higher education, secondary schools, government, and the private sector. • Commitment to curricular and instructional enhancement to ensure a productive learning experience for undergraduates (majors and non-majors) and a quality research-based graduate program for students pursuing careers in education, industry and government. • Commitment to faculty recruitment and development which emphasizes high research and teaching standards. • Commitment to affirmative action in employment and in the diversification of the student population. • Sensitivity to the needs of students and faculty working in all areas of mathematics and demonstrated interpersonal characteristics and skills necessary to relate to the faculty, students, the administration and external publics. Appointment Information. The position carries a 12-month appointment to be effective as early as January 1, 1987 and preferably no later than August 15, 1987. Salary is competitive and commensurate with qualifications and experience. Application. Nominations should be received by September 30, 1986. Candidates should forward a letter of interest, resume, and the names, addresses, and telephone numbers of at least four references no later than October 15, 1986 to Dr. Brice Corder, Assistant Dean and Secretary to the Search Committee, Office of the Dean, College of Liberal Arts and Sciences, Arizona State University, Tempe, Arizona 85287. Arizona State University is an Equal Opportunity, Action, Title IX Women and minorities are encouraged to 700 PARTICLE SYSTEMS, RANDOM MEDIA AND LARGE DEVIATIONS Richard Durrett, Editor THE UNIVERSITY OF VIRGINIA This volume of proceedings of the 1984 AMS Summer Research Conference Applications are invited for: The Mathematics of Phase Transitions (1) Tenure track or senior positions starting provides a handy summary of results Sept. 1, 1987. Preference will be given to from some of the most exciting applicants in algebraic geometry and POE areas in probability theory today: but all strong applications will be considered. interacting particle systems, percolation, random media (bulk properties and (2) The Whyburn Research Instructorship, a two hydrodynamics), the Ising model year appointment with reduced teaching load and large deviations. Thirty-seven starting Sept. 1, 1987. Deadline for receipt mathematicians, many of them well of applications including three letters of known probabilists, collaborated to reference: Feb. 1, 1987. produce this readable introduction to the main results and unsolved problems in Applications should be mailed to: the field; in fact, it is one of the very few David C. Brydges collections of articles yet to be published Department of Mathematics appreciate many of on these topics. To Mathematics-Astronomy Building, Cabell Drive the articles, an undergraduate course in probability is sufficient. The book will University of Virginia be valuable to probabilists, especially Charlottesville, Virginia 22903 those interested in mathematical physics The University of Virginia is an Equal Oppor and to physicists interested in statistical tunity/Affirmative Action Employer. mechanics or disordered systems. List of Contributors: M. Campanino R. Holley J. Chayes H. Kesten L. Chayes E. Key J. T. Cox C. Kipnis JOrMath,. D. A. Dawson S. 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Hochberg cross-references • table of contents, indexes • automatic Justification, word 1980 Mathematics Subject Classification: splitting 60K35 ISBN 0-8218-5042-3, LC 85-6181 • automatic numbering and place ISSN 0271-4132 ment of footnotes 391 pages (softcover), August 1985 • multiple fonts, sizes, special symbols List price $32, Institutional me1nber $26, • output on CRT, dot-matrix printers, Individual member $19 daisywheels, laser printers, To order, please specify CONM/41 NA photo-typesetters • use on micros ICP/M:" PC,.-oos, MS,.-OOSI or mainframes 1any IBM:" VAX/VMS,.I Shipping/Handling: 1st book $2, each add'l $1, $25 call SHANTHA SOFTWARE, INC. max. By air, 1st book $5, each add'l $3, $100 max. • Write or Prepayment required. Order from AMS, P.O. Box so West 97 st., Room 11-N 1571, Annex Station, Providence, RI 02901-1571, or New York, NY 10025 212-222-SNIP cal1 800-556-7774 to use VISA or MasterCard. TrV toll-free: 950-1088-pause-FORMATH 701 ACTA MATHEMATICA SCIENTIA Editor-in-Chief: Li Guoping, Institute of Mathematical Sciences, Academia Sinica, Wuhan, China. Volume 6 appears in 1986. ISSN 0252-9602. *) ANNALS OF OPERATIONS RESEARCH Editor-in-Chief: Peter L. Hammer, RUTCOR, Hill Center for the Mathematical Sciences, Rutgers University, New Brunswick, N.J., USA. Volumes 5-7 appear in 1986. ISSN 0254-5330. APPLIED MATHEMATICS AND MECHANICS Editor-in-Chief: Chien Wei-zang, Quing Hua University, Beijing, China. Volume 7 appears in 1986. ISSN 0253-4827. *) CHINESE ANNALS OF MATHEMATICS Editor-in-Chief: Su Buqing, Institute of Mathematics, Fudan University, Shanghai, China. Volume 7 appears in 1986. ISSN 0252-9599. *) INDIAN JOURNAL OF PURE AND APPLIED MATHEMATICS Editor: A.N. Mitra, Department of Physics, University of Delhi, Delhi, India. Volumes 17 appears in 1986. ISSN 0019-5588. **) MATHEMATICAL SCIENCES, PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES, BANGALORE Chairman Editorial Board: S. Ramanan, Tata Institute of Fundamental Research, Bombay, India. Volume 96 appears in 1986. ISSN 0370-0089. **) QUEUEING SYSTEMS Editor-in-Chief: N.U. Prabhu, Cornell University, Ithaca, N.Y., USA. Volume 1 appears in 1986. ISSN 0256-0130. *)Sole distributors for all countries except China: J.C. Baltzer AG. **) Sole distributors for all countries except India, Pakistan, Sri Lanka, Nepal, Bangladesh, Burma: J.C. Baltzer AG. 702 American Mathematical Society P. 0. Box 6248 Charge by Providence, Rhode Island 02940 Phone (401) 272-9500 c800-556-7774 Ordered by------Mail to (if different) ------ Use your peel-off Notices label. 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Price: US $55.50/Dfl. 150.00 NORTH-HOLLAND MATHEMATICS STUDIES, ISBN 0-444-70024-2 Volume 124 Notas de Matematica (1 09), Editor: Leopolda Nachbin This volume is addressed to those who wish to apply the methods and results of the theory of topological algebras to a variety of disciplines, even though confronted by particular or Matroid Theory less general forms. It may also be of interest to those who wish, from an entirely theoretical point of view, to see how far Edited by L. Lovasz and A. Recski one can go beyond the classical framework of Banach algebras while still retaining substantial results. COLLOQUIA MATHEMATICA SOCIETATIS JANOS 1986 xx + 536 pages. Price: US $64. 75/Dfl. 175.00 BOLYAI, 40 ISBN 0-444-87966-8 Among the large number of international combinatorial colloquia organized in Hungary by the Janos Bolyai Mathematical Society, this was the first one devoted entirely to matroid theory. Tutorial series on regular matroids and matroid minors, oriented matroids, matroid oracles, engineering applications of matroids, and a large number of invited and Aspects of Positivity in contributed talks gave an up-Io-date picture of this rapidly developing branch of discrete mathematics. Special attention Functional Analysis was paid to the applications of matroids, which are becoming more and more important in many areas. Proceedings of the Conference held on the Occasion of H.H. Schaefer's 60th Birthday, 1985 440 pages. Price: US $74.00/Dfl. 200.00 Tiibingen, FAG, 24-28 June 1985 ISBN 0-444-87580-8 Edited by R. Nagel, U. Schlotterbeck and M.P.H. Wolff NORTH-HOLLAND MATHEMATICS STUDIES, Logic Colloquium '84 Volume 122 Notas de Matematica (108), Editor: Leopolda Nachbin Proceedings of the Colloquium, Manchester, UK, July 1984 The contributions collected in this volume exhibit the increasingly wide spectrum of applications of abstract order Edited by J.B. Paris, A.J. Wilkie and G.M. Wilmers theory in analysis and show the possibilities of order theoretical argumentation. STUDIES IN LOGIC AND THE FOUNDATIONS OF The following areas are discussed: potential theory, partial MATHEMATICS, 120 differential operators of second order, SchrOdinger operators, theory of convexity, one-parameter semigroups, Lie algebras, This proceedings volume contains most of the invited talks Markov processes, operator-algebras, noncommutative presented at the colloquium held in Manchester, UK. integration.and geometry of Banach spaces. The main topics treated are the model theory of arithmetic and algebra, the semantics of natural languages, and applications 1986 xii +274 pages. Price: US $40.75/Dfl. 110.00 of mathematical logic to complexity theory. ISBN 0-444-87959-5 IN ALL OTHER COUNTRIES: :r'J~~~~:tcl~=~.fANADA: ELSEVIER SCIENCE PUBLISHERS PUBLISHING CO., INC. BOOK ORDER DEPT. th h II d P.O.BOX211 1000 AE AMSTERDAM • 0 an NEW~~A~~J~~~ALSTATION YORK, NY 10017 nor THE NETHERLANDS US $prices are valid only in the USA and Canada. In all other countries the Dutch Guilder price is definitive. . NHI~ATH/BK/0942 Customers in the Netherlands, please add 5% B. T. W. In New York State, please add applicable sales tax. All prices are subject to change without pnor not/CB. New in the series Graduate Texts tn Mathen1atics Volume I 10 1/olume 107 Algebraic Number Theory Applications of Lie Groups to S. Lang Differential Equations This is a corrected reprint of Lang's well-known P.j. Olver textbook. It covers all of the basic material of das This hook discusses the usc of symmetry methods in sical algebraic and analytic number theory. giving the study of differential equations. and the applica the student the background necessary for the study tion to various areas of applied mathematics. Fol of modern number theory. Pan I introduces some of lowing the exposition of the applkations, the hook the basic ideas of the theory: number fields, ideal develops the underlying theory. Many of the topics dasscs, idcles and adeles. and zeta functions. Pan are presented in a novel way. with an emphasis on II covers Class l'ield Theory. and Pan Ill is devoted e'plil"it examples and computations. Further exam to analytic methods. including an exposition of ples. as well as new theoretical dc\clopments. ap Tate's thesis. pear in the exercises at the end of each chapter. 1986/approx. 360 pages/7 illus./Cioth $29.80 1986/497 pages/10 illus./Cioth $54.00 ISBN: 0-387-96375-8 ISBN: 0-387-96250-6 Volume /09 New and noteworthy Univalent Functions and Global Stability of Dynamical Teichmiiller Spaces Systems 0. Lehto M. Shub This book treats the theory of Teichmiiller spaces, This is an advanced text on the global theory of dy viewing it as a part of classical complex analysis. namical systems. including the stable and center The main emphasis of the book consists of develop manifold theorems. the stability of uniformly hyper ing ideas of Bers which provide an approach to bolic sets, Smale's Axiom A. spectral decomposi Teichmiiller theory which applies to the case of tion. and !!-stability theorems. For some of these compact and non-compact Riemann surfaces. These topics. this is the first complete treatment in book ideas involve the connection between Teichmiiller form. spaces and the theory of univalent analytic functions 1986/approx. 160 pages/40 illus./Cioth $30.00 via the Beltrami equations and the Schwarzian de (tent.) rivative. This book provides a comprehensive intro ISBN: 0-387-96295-6 duction to this area, and includes many of the newer developments in the theory. Constructive Combinatorics 1986/approx. 272 pages/16 illus./Cioth $46.00 D. Stanton and D. White ISBN: 0-387-96310-3 Consrructi•·e Comhinarorics is a modern introducto ry text in combinatoril·s. The emphasis is on the al Volume 108 gorithmic approach: using combinatorial algorithms as constructive proofs of theorems and as sources of Holomorphic Functions and data for nmjecturcs. This hook will be of great in Integral Representations in Several terest to statisticians using combinatorics as well as Complex Variables to computer science students. R.M. Range 1986/183 pages/73 illus./Cioth $19.80 This is a textbook on the theory of functions of sev (Undergraduate Texts in Mathematics) eral complex variables. It differs from existing ISBN: 0-387-96347-2 hooks on the subject in that it approaches the theory through integral representations rather than through Potential Theory sheaf theory. commutative algebra and partial differ An Analytic and ProhahiliSTic Approach to Balamge 0 N ential equations. This enables the author to present j. Bliedtner and W. Hansen C'l substantial results with much less preparatory mate C'l Contell1s: Classical Potential Theory. General Preli CO:. rial. The hook begins with elementary local results. minaries. Excessive Functions. Hypcrharmonic 0 discusses the basic new concepts of the multidimen Functions. Markov Processes. Examples. Balayage 8 sional theory in detail. and presents complete proofs Theory. Dirichlet Problem. Partial Differential z of fundamental global results on domains of holo Equations. ~ morphy. 1986/435 pages/Paper $35.00 1986/386 pages/7 illus./Cioth $49.50 (Unil·ersirexr) ISBN: 0-387-96259-X ISBN: 0-387-16396-4 To order, please write to: Springer-Verlag New York, Inc., Springer-Verlag Attn: G. Kiely S314. New York Berlin Heidelberg 175 Fifth Avenue. Cl) "'u London Paris Tokyo New York. NY 10010 ·;:: z0