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Tacoma Meeting (June 18-20)-Page 667

Notices of the American Mathematical Society

June 1987, Issue 256 Volume 34, Number 4, Pages 601 - 728 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 headquarter's 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 836 August 5-8. 1987* Salt Lake City, Utah May 29 August 837 October 3Q--November 1, Lincoln, Nebraska August 17 October 1987 838 November 14-15, 1987 Los Angeles, California August 18 October 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) January 17-20, 1990 Louisville, Kentucky (96th Annual Meeting)

• Preregistration/Housing deadline is June 1. •• Preregistration/Housing deadline is November 6.

DEADLINES Advertising (June 1987 Issue) Apr. 29, 1987 (Aug. 1987 Issue) June 10. 1987 (Oct. 1987 Issue) Sept. 2, 1987 News/SMIC (June 1987 Issue) Apr. 13. 1987 (Aug. 1987 Issue) May 25, 1987 (Oct. 1987 Issue) Aug. 17. 1987

Other Events Sponsored by the Society

June 14-July 25, 1987, Joint Summer Research Conference in the Mathematical Sciences, University of Colorado, Boulder, Colorado. Details: February issue, page 351. July 19-August 15, 1987, Joint Summer Research Conference in the Mathematical Sciences, Cornell University, Ithaca, New York. Details: February issue, page 351. July 6-24, 1987, Summer Research Institute on Theta Functions, Bowdoin College, Brunswick, Maine. Details: February issue, page 354.

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 always 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 at the back of every issue of Notices of the American Mathematical Society. Send change of address forms to the Society at Post Office Box 6248, Providence, Rl 02940. (Notices of the American Mathematical Society is published eight times a year (January, February, April, 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. Nottces• of the American Mathematical Society Volume 34, Number 4, June 1987 EDITORIAL COMMITTEE Robert J. Blattner. Ralph P Boas LUCY J. Garnett. Mary Ellen R_~,dln Nancy K. Stanton. Steven H v'vemtraub Everett Pitcher (Cha1rman) MANAGING EDITOR 603 Highlights of the Meeting of the NSF James A. Voytuk Advisory Committee for the Mathematical ASSOCIATE EDITORS Sciences Stuart Antman. Queries Reports to the Members of the Society Hans Samelson. Queries 608 Ronald L. Graham. Special Arl icles 615 Council Plan for a Referendum SUBSCRIPTION INFORMATION 616 Commentary on Defense Funding Subscription prices for Volume 34 (1987} 621 Mathematical Text Processing are $90 list; $72 institutional member; Richard S. Palais $54 individual member. (The subscription 625 Washington Outlook price for members is includerl m the 626 News and Announcements annual dues.) A late charg;o of 10% of the subscription price will bf~ imposed 631 NSF News &. Reports upon orders received from nonmembers 635 For Your Information after January 1 of the subscription 637 Letters to the Editor year. Add for postage: SurfaL:E' delivery 640 Queries outside the United States and india-$8· to lndia-:-$18; expedited delivery to ' 641 Acknowledgment of Contributions dest~nat1ons in North America--$12. 663 1987 AMS Elections elsewhere-$38. Subscriptions and (Nominations by Petition) orders for AMS publication:' should be 667 Future Meetings of the Society =ressed to the American Mathematical Tacoma. June 19-20. 667: Salt Lake City. lety, P.O. Box 1571. Anne:-. Station April 5-B. 672: Lincoln. October 3D-November Prov,dence. Rl 02901-9930 ·~II orders · must be prepaid. 1. 673: Los Angeles. November 14-15. 674: Invited Speakers and Special Sessions. ADVERTISING & INQUIRIES Notices publ. h . . 675 and . . IS es S1tuat1ons wanted ad classified advertising, and display 678 Call for Topics for 1989 Conferences or vertsc· ISmfg for publishers and academic 680 Special Meetings 1ent1 1c or · . information: ganlzat,ons Requests for 687 New AMS Publications 693 New Members ~~vertising: Wahlene Siconio 695 Miscellaneous Me~~e of ~ddress or subscriptions: Book d ership and Sales Department Personal Items. 695: Deaths. 695: Visiting CO"' or er number 800-556-777 4 Mathematicians. 696 "'RESPOND . ·. 699 AMS Reports and Communications changes of add ENCE. mclud1ng American Mathress should be sent to Recent Appointments. 699: Reports of Box 6248 p emat1cal Souety. P.O. Past Meetings: Honolulu. 699: Newark. Seco . , rov,dence. Rl 02940 699: Statistics on Women Mathematicians. R nd class Post . . I. and add"t' age pa1d at Providence. 700 ~right ©~~~al rnailing offices. 703 Advertisements ~~thernatical So~~ by the American 718 Registration Forms 1 nnted in the U . ety. A!l r~ghts reserved. 723 AMS Membership Application The Pape nlte:d States of America. ind f r used in th· . 725 New AMS Publications Order Form to ails within th 15 JOurnal is acid-free ensure Pe e gu1delmes established and Mailer rmanence and durability. § Notices: highlights

The NSF Advisory Committee for the Mathematical Sciences met with the officers of the Division of Mathematical Sciences from April 6-7 to provide input into future directions at the NSF. Erich Bloch also participated in the meeting and forcefully presented his views. Page 603.

The Annual Reports to the Members from the Secretary, the Executive Director, and the Treasurer of the AMS review the activities of the Society during the past year. Page 608.

The Council of the AMS has formulated plans for a referendum on the issues concerning federal funding of mathematics. Page 615.

Commentary on Defense Funding is a new section of the Notices set aside by the Council to provide a forum for people to express their views on the funding issue. Statements by Edward J. Wegman, Seymour Parter, and James Glimm appear in this section. Page 616.

Leslie Lamport, as guest writer for Richard Palais' column on text processing, addresses the question "Document Production: Visual or Logical?" Page 621.

Kenneth Hoffman, in his Washington Outlook column, expresses the gratitude of the mathematical community for the excellent work of Frank Gilfeather, John Polking, and John Thorpe during their tours of duty in Washington. Page 625.

AMS Postdoctoral Research Fellowships are awarded to Richard Hain and Bill Jacob. Page 626.

NSF Graduate Fellowships are announced, with thirty-seven awards in mathematics and thirty-four awards in computer science. Page 631.

AMS Reports and Communications contains a report on the Council Meeting in Newark. Page 699. Highlights of the Meeting of the NSF Advisory Committee for the Mathematical Sciences April 6-7, 1987

'!be National Science Foundation's (NSF) Advi­ The meeting on April 6-7 of the National Science flll1 Committee for the Mathematical Sciences, Foundation Advisory Committee for the Mathe­ matical Sciences was enlivened by the appearance which meets with o!ficers of ~he NSF's Divi~ion GfMathematical Sciences twice a year, provides of NSF director Erich Bloch. At one point, die NSF with input from the mathematical Bloch remarked that the NSF's Division of Math­ CIJIIIIII1Illity on the NSF's policies and strate­ ~matical Sciences (DMS) had received significant p.. The committee's role is strictly advisory, mcreases over the last few years and challenged 11111 it has no decision-making power in the the mathematical community to justify support NSF. The committee consists of fifteen mem­ of mathematical research in terms of its contribu­ bela (listed below), and their terms last three tions to science and to the nation. JIUII· The NSF has advisory committees for Bloch's remarks came after the committee eldl of its disciplinary divisions, as well as for heard the presentation on the planning environ­ G&ber purposes. This committee's most recent ment at the NSF by Sandra Toye, NSF Con­ meeting took place April 6-7, 1987, at NSF troller, who commented that mathematics had beldquarters in Washington, D.C. The follow­ "done well" in the last few years and that other ill article is a summary of the committee's NSF disciplinary divisions would have liked to diacussion. have had the DMS's double-digit increases. Both Committee Members comments drew the response from the commit­ tee that, as the David Report (Renewing U. S. Morris H. DeGroot Mathematics: Critical Resource for the Future) Carnegie-Mellon University documented, mathematics research has been un­ Robert D. Edwards derfunded in the past and is only now beginning UnitJersity of California, Los Angeles to catch up with other disciplines. To this retort llamanathan Gnanadesikan Bell Communications Research Bloch replied that the government has a "selfish Julia Knight interest" in supporting mathematics research, not Uni~~ersity of Notre Dame an "obligation" to it, so low funding levels in Dmlald J. Lewis, Chairman the past do not automatically put mathematics Uni~~ersity of Michigan in line for increases. Mathematicians must prove ~J.Majda the worth of their research, Bloch said, and if )ll'rinceton University they do, "I'm with you, if not, I'm against you." ~~.Montgomery This justification must be made every year, "over and over again," not just once in a while. Bloch ~tJeCrsaty of Southern California ·Newell may have been referring obliquely to the David LouisUni~~e rsaty· of Arizona Report, which he has said he wants updated. Nirenberg Bloch's comments are indicative of a new Linda~nt p Ro Institute 01 M at h ematzcal· Sczences. climate at the NSF in which scientific research I'll . • thschild is viewed as a means of boosting the nation's lllllersity of c 1:r . L,n A 8 a ZJornza, San Diego economic strength. Indeed, it was by arguing St. · teen that science is good for the economy that Bloch a.:~! College obtained presidential support for his efforts to Iii Lian Terng double the NSF budget by 1992. Bloch has dis­ AJ.r,~ea:,.~e~n University tilled his ideas into three initiatives for fiscal year ,,_:_ · ~vemstein 1988: developing human resources and broadening v~~~~~ersaty f C I' ~ L W~ a ifornia, Berkeley participation in science and engineering; estab­ IVfllh. · e1ss lishing interdisciplinary science and technology floyd tgwto.n _University centers; and building and improving the NSF's fl,_; •. ilhams ...ller81ty of M disciplinary programs. These initiatives formed assachusetts, Amherst the focus of the committee's discussion during its

603 1 1/2 hours with Bloch, as well as during the rest and software development in add' . of the two-day meeting. research . Swarztrauber sa1d. ' that th'Itlon '·"" '-t Bloch spent most of his time with the com­ $3 million budget including $0.5 mi~' Year, Yfith 1 mittee talking about the initiatives, listening to ware, he had received forty-six pro Jon for~ comments, and responding to questions. In speak­ $12 million. The proposals rangeJ~ ~ ing about the proposed research centers, Bloch to $1.4 million and in size from tw ~ udget 11p said that the proposals would be subject to joint vestigators. He showed the commit~ 0 twelve in­ review conducted by the relevant NSF direc­ from a review of one of the larger ee an~ torates. He also said that the form the centers which the reviewer deemed the pro~:~Joeal!. in excellent, but was uneasy about the p . ~ will take is flexible and should suit the needs of roJects · the center's research focus. On the subject of and cost. The reviewer expressed c III! I oncern ''"' the human resources initiative, Bloch noted that such a arge structure would continually "101 the NSF does not have an accurate assessment large amounts of money, but noneth 1 ~ of how well its human resources programs are convinced of the proposal's scientific e ess 'ill! operating and that, too often, programs were put recommended full support of the projec~ent ~ together with insufficient planning and disbanded Much of the committee's discussion when new programs came along. He called for on a draft document entitled "Strategic ~~n~ a "consistent, persistent" approach, specifically the DMS.'' The document provides guidelinan t noting the important role that mathematics plays growth in DMS programs and for the esta~ in precollege and college education. ment of new pro?rams. Speaking about th! The committee members described some of document, DMS Director John Polking said that their ideas, such as holding CBMS (Conference the document was based on ideas "coming from Board of the Mathematical Sciences) conferences the top" --specifically, from Bloch's three initia­ at minority institutions, giving small travel grants tives for fiscal year 1988. Polking made the point to minorities and women, and establishing an that mathematics must "maximize its position· initiative to stimulate interactions between math­ with respect to the three initiatives. ematics and biology. Bloch listened carefully to One topic that elicited much discussion Vi&! the ideas and appeared very open-minded. He Bloch's initiative for establishing interdisciplinary called for the mathematical community to come research centers. The discussion proceeded 011 forward with any ideas it has and promised they the assumption that the centers should not be would receive full consideration. established at the expense of the traditional At one point, someone asked Bloch the ques­ mode of supporting individuals. The committle tion that was probably at the back of every discussed ways that the mathematics community committee member's mind: is there some assur­ could formulate its needs in the context of centell ance that the DMS's budget will be doubled along and benefit from the initiative. Because this idea with the NSF's? Bloch said no, he hadn't decided is relatively new to the community, the committee on what increase the DMS should receive. "And felt the need to discuss general frameworks for thf even if I had," he said good-naturedly, "I wouldn't centers, although a few specific ideas for c~nttll tell you." Just before leaving, Bloch was asked were offered such as a center in statistical science. how certain he felt that the NSF budget would While the c~mmittee appeared to be approaching be doubled. On this point Bloch was conservative the subject with a cautiousn~ss that ste~ from unfamiliarity some committee members an but optimistic: he said that it may not happen ' . h' thf in five years, but may take six to seven years. NSF officers noted a greater acceptance w1t m He pointed out one of the unwritten rules in committee of the idea of centers than in preVIOU! discussions. t"· government funding matters: "If you don't ask, · · that "' you don't get anything." Polking listed five charactenst1cs Bloch's appearance was one of the meeting's research centers in mathematics must have: highlights, but during the rest of the meeting • a broad mathematical focus; the committee discussed many important issues • an interdisciplinary nature; facing the mathematics community in the new • strong university ties; · d ts· climate at the NSF. In addition, there were • training for postdocs and stu en ' several presentations by NSF program officers • industrial participation. 3 c& and the presentation by NSF Controller Toye. The committee distinguished betweeln feWfl uld invove · Paul Swarztrauber, the new Director of ter and a group: the latter wo The DM~ the DMS's Computational Mathematics program, researchers and have a narrower focush ee centel'i spoke to the committee about the program. Its foresees the establishment of two to t r ups IDlY scientific goals are to use the computer as a tool to and a larger number of group~. The ~ coordi­ solve problems and gain theoretical insight in all simply consist of the expansiOn of rt ~ areas of mathematics, and to increase the speed nation between cooperative efforts t ;d cente~ and accuracy of computations. To achieve these exist. Education is tied to th~ gro~P~ atioo," lll goals, the program supports hardware acquisition by what Polking terms "vert1cal mt f aod tbf (such as workstations and superminicomputers) which the education of young peoP e

604 . h ol and college teachers are planning document also recommends some less . . of high sc o controversial uses of funds. For example, it rec­ [!liDU'g . to the research. iJlltgrated 1 ~ ;t'us Program Director for Ap- ommends over the next five years increasing the Man, 1 , . b An dr zeJ . spoke to the committee a out number of investigators from the present 1,300 to _,;.,l ~lathem.a~I~s,tive entitled ''Innovative Inter­ 2,000; doubling the average grant size to $60,000; P"'u .w;ed JDJtJa d B' I " It providing sabbatical support; increasing support his proy~- \1athematics an 10 ogy. ariioi!S Between · general initiative· w h.Jc h IS· pro- for graduate students to $12,000 per year; in­ f 3 more . d of students per investigator ~nor! 0 t tegJ·c plannmg document an creasing the number • ..-· · the s ra . by 20%; and increasing funds for computational ~ 10 id rornote intera~twns and knowledge .-bich wou p mathematics and other fields. equipment and access, and for support personnel ~ between trailS er . .d s are based on. but not confined such as secretaries and programmers. It should be ·(us s 1 ea. ·. only recommen­ ~lalll 1 t fruitful applicatiOns of mathemat- emphasized that these figures are to. som~ rlecen such as Charles Peskin's artificial dations of the DMS and have not been adopted · to b10 ogy. · b :cs a1 modeling and connectiOns etween by the NSF. Indeed, until Congress finalizes the ht~ v dvke ot theory. Manitius emphasized that NSF budget, no increases are certain. However, $ the favorable budget outlook for the NSF, D:'iAfunds anfor then imtiat . . . 1ve, .about 5 m1'II' Ion per year, given the DMS felt that a plan of significant increases uld me from outside the DMS core budget. ;boCO that such research Js. probbl. a y smt- was in order. lt was no ted . able for a center or group mode of fundmg, so The committee also discussed at length an­ that the funds could be sought from NSF funds other area of emphasis in the strategic plan, that for centers and groups, rather than. drawn from of increasing human resources. Polking remarked the DMS core budget. The committee reacted that the DMS is now responsible for administer­ with enthusiasm to the initiative, for they felt ing some programs in undergraduate education: that it was scientifically promising and, if devel­ the DMS's fiscal 1988 budget request includes oped as a group or center, could provide excellent $2 million for the Research Experiences for Un­ opportunities for education and faculty renewal. dergraduates program (for information on this In addition, Manitius noted that this kind of ini­ program, see NSF News and Reports, Notices, tiative shows that mathematicians are concerned February 1987, p. 297) and $2 million for a with the progress not only of their own discipline, program to renew the calculus curriculum. but of science as a whole. It is just this sort of John Thorpe, Director of the Science and cooperation that Bloch is trying to foster. Engineering Education (SEE) Directorate, spoke While an evaluation procedure for center to the committee about the various programs in proposals has not yet been established, Polking SEE, and about which programs mathematicians explained that there would be an extensive review, do or do not participate in. He described some of probably consisting of the usual peer review (or the projects that mathematicians have initiated, "me~t re.view," as it is now called), in addition such as a project to reform K-12 mathematics cur­ to site VISits and panel reviews. It was noted ricula, an introductory book on chaos and fractals, that. even though some of the NSF's Engineering and a "Quantitative Literacy" project sponsored Research Centers (ERCs) have a mathematical by the American Statistical Association. component. the DMS was not involved in the There appears to be a great deal of impetus selection of any of the ERCs; the committee at the NSF for reform in education, but some ~that the DMS should be involved. Frederic committee members and NSF officers expressed an. Program Director for Applied Mathematics doubt about the success of such efforts in the P811ICipated i · . ' . h n a rev1ew of the ERC m systems re- mathematics community. One committee mem­ searc at the tr ' · . -- 'illversJty of Maryland· this review ber said that mathematicians had "abandoned" ~as condu t d f ' In th c e a ter the center was established. education, and others noted that the problem lay feat: review. he described some of the center's in the system for tenure evaluation where research, ,_ es. such as the establishment of a master's not teaching, is recognized and rewarded. ""~ee program · nities for fello m systems research and opportu- As Controller of the NSF, Sandra Toye at­ He also wslllps and research assistantships. tends many congressional appropriations hearings received ~o~ed ~hat. the center had solicited and and therefore understands shifting congressional felt that f~r ensive mdustrial participation. Wan priorities, as well as the thinking of the upper ech­ tobtmore :m~ller group research, which seems elons of the NSF. One committee member asked tent ... r... ed ective for mathematicians than large "•• lWJ S f . Toye which of the three initiatives she thought !!cure. But rom mdustry might be difficult to would be the most important. One might expect Participatio~ as Bloch later pointed out, industrial her answer to be research centers, because they !asier to obt ?Jay also take forms that would be have received so much attention lately. But Toye ~nne! excahm. such as equipment donations or and human resources anges. replied that the education Much of thP d. . initiative was the likeliest of Bloch's initiatives to !louPs because" t lscusswn focused on centers and grow and continue to be emphasized. She gave lllode for ill'l.-h hey represent a novel research three reasons: it is "politically important," Bloch "· em ar !Clans. · However, the strategic is "serious" about it. and the National Science

605 Board (the policy-making arm of the NSF) is all along and who would probabl "adamant" about it. anyway. Second, a program that t" Y be ~ Central to the human resources initiative is participant must not have had a! 1~'-ta the need to encourage minorities and women to say, the last five years was seen by the "-'­ pursue careers in science and engineering. At an~ DMS officers as a circumvention ~ the meeting, DMS Deputy Director Judith Sunley review system. However, it was noted the1111r described the various programs available specifi­ DMS can increase the number of ~if" cally for minorities and women. The committee perhaps these people would be m::Uta It &hit. agreed that the problem of encouraging minori­ to apply. Also, some mathematiciansencou...d ties in mathematics begins in elementary school. supported by centers and groups ~ bt Several suggestions were offered, such as hav­ outside the DMS core budget, thereby r...:..~ ing mathematicians speak to PTA groups about grant money for others. --.It the importance of mathematics in early educa­ The committee also discussed the .IlL•. tion, conducting parent awareness courses, and of those mathematicians who have ~ summer and weekend programs in mathematics research altogether. Some members pointed~ for high school students. Sunley reminded the that research centers and groups would ~ committee that investigators can request a sup­ intellectual stimuli that would encourap~ plement to support a high school student on an mathematicians to see new possibilities Crt NSF grant and that a new option in the Minority search. Also, it was suggested that~ Graduate Fellowship Program provides a mone­ currently receiving grants could be e tary "reward" to college departments that have to involve other researchers, especially =: produced a fellowship awardee. are isolated because they are the only 11111 il The committee discussed at length the diffi­ ~hei~ fi~ld ~t their institution, or becauae 1e culties of those mathematicians who, discouraged mst1tutwn IS geared toward teaching and IMb because they did not receive NSF support, con­ search. Small travel grants to attend confeftaca tinue to produce high quality research, but no were deemed beneficial in encouragingsuchm6 longer apply for grants. In this sense, the needs ematicians to resume research, but Sunley Iii of mathematicians are quite different from scien­ that the DMS probably could not administeuli tists who require equipment to do their research grants in a cost-effective manner. and therefore would not be able to work without During the discussion, there were some lilt a grant. Nonetheless, mathematicians continue gestions given for revisions in the draft strate;: to need the recognition and encouragement that plan. Once these revisions are incorponlei. NSF grants provide. As one committee member the document will become part of a I~ pointed out, however, those mathematicians who plan of the Mathematical and Physical Scielm have not received funding in the last five years directorate. probably never will. Near the end of the meeting, the commitlet The committee noted some problems with elected Alan Newell of the University of Arid~ targeting these mathematicians with a special the new chairman. With so many changes tame program. First, a program for those who are place at the NSF, the role of this committee 1111 seven to eight years beyond the Ph.D. would not of its chairman will become especially imporlllt exclude those researchers who have been funded

606 SEARCH JfOR AN EXECUTNE DIRECTOR for the AMERlCAN MATHEMATICAL SOCIETY The post of Executive Director of the American Mathematical Society will become va­ ·eant on a date to be established in 1988 upon the retirement of William J. from that position. The Executive Director is employed by the Trustees the Society, who now seek a replacement. Employment could begin at a date mutual convenience in 1988 and might include overlap with the term of the in­ li·•.CmnbeJJ1t, though this is not a requirement. The central office of the Society is in . Providence, R.I. The duties of the position are summarized in Article VI of the bylaws of the Society · follows: , Section 1. There shall be an Executive Director who shall be a paid employee of the Society. He shall have charge of the central office of the Society, and he shall be ,nsponsible for the general administration of the affairs of the Society in accordance with the policies that are set by the Board of Trustees and by the Council. ' Section 2. The Executive Director shall be appointed by the Board of Trustees with the consent of the Council. The terms and conditions of his employment shall be fixed by the Board of Trustees. Section 3. The Executive Director shall work under the immediate direction of a the ·~,.;·COJnmlitt~ee consisting of the President, the Secretary, and the Treasurer, of which ePresident shall be chairman ex officio. The Executive Director shall attend meetings ,. of the Board of Trustees, the Council, and the Executive Committee, but he shall not be a member of any of these bodies. He shall be a voting member of the Committee Monitor Problems in Communication but shall not be its chairman. . Note: In the above statement, "he" is the sexless third person singular pronoun, used .,to avoid the awkwardness of repeated "he or she" or the barbarism "he/she." The purpose of the Society is described in this quotation from the charter: The particular business and objects of the Society are the further­ ance of the interests of mathematical scholarship and research. · The Society accomplishes its purpose through meetings and conferences and through ·publication. There is a diversity of other activity. The annual budget of the Society exceeds thirteen million dollars, about one fifth being in the general fund and four fifths in the publication fund. There are about · 150 employees in Providence and 75 in Ann Arbor. Mathematical Reviews is a semi­ autonomous operation in Ann Arbor under the direction of the Executive Editor. There are about eight general meetings per year and as many as twelve to fifteen specialized conferences. The Society publishes at least sixteen journals of various kinds. It publishes about ': ~ dozen series of books. All of the operations, except for the printing of a couple of · journals with very large print runs, are done in-house. Both the office operations and the publication program are highly computerized. Candidates should have a Ph.D. in mathematics (or the equivalent), published re- ; ~ beyond the Ph.D., and significant administrative experience. Desirable qual­ ifications include experience in mathematical publication, fiscal management, and .computer utilization . .. Asearch committee, with Frederick W. Gehring as Chairman, has been formed to seek .. ~ review candidates. Persons who wish to be considered or to make a nomination ""ould provide supporting documentation to Professor F. W. Gehring Department of Mathematics University of Michigan Ann Arbor, MI 48109 before 1 September 1987 to receive full consideration. Reports to the Members of the Society

Annual Report of the Secretary of Science in May in Philadelphia. Tb •-=- Modeling Circadian Rhythms. e ""''''t 1111 Meetings The Summer Research Confer The Society had a successful set of meetings in jointly with the Institute for Mathema~ 1986. The Annual meeting of 1986 was held tics and the Society for Industrial and ._.. in New Orleans with Colloquium Lectures by Mathematics, consisted of five one-week~ Shing-Tung Yau, Gibbs Lecture by L. E. Scriven, ences and one two-week conference. The;:""­ 1111 six invited hour addresses, and 669 shorter talks Santa Cruz. The program was curtailed from in seventeen special sessions and sessions for more usual ten conferences to allow for the I: contributed papers. There were special invited There was a Summer Institute of three-a addresses by Erich Bloch, Director of the National duration, in Arcata, on Finite Groups and Rel.ted Topics. Science Foundation, and by George F. Carrier. The meeting was joint with the Mathematical Association of America, which sponsored three Publication addresses with the Society and offered the Retiring A signal event is the decision to inallgUl'ale a Presidential Address oflvan Niven and eight other new journal, namely the Journal of the Amerira addresses of its own as well as shorter talks. Mathematical Society, with Michael ArtiD, H. A feature of the Annual and Summer meet­ Blaine Jr., Lawson, Richard B. Melrose, Wllfried ings is the award of prizes. At the New Orleans Schmid, and Robert E. Tarjan as editors. The meeting, the Veblen Prize in geometry and topol­ first issue is scheduled for 1988. ogy was awarded to Michael H. Freedman for his The Society now has a new acquisition editlr. paper The topology of four-dimensional manifolds. namely Edwin F. Beschler, who joins the staf The Steele prizes of 1986 were not presented after a career in commercial publishing. until January 1987 because of the absence of the An event that did not take place should be usual Summer meeting. There were three of them. remarked. The Society has been studying the pos­ The 1986 Steele Prize for Expository Writing went sibility of a merger of Mathematical Revieuuud to Donald E. Knuth for his books (three volumes) Zentralblatt fiir Mathematik since 1983. Although titled The art of computer programming. The initially the idea looked promising and was sup­ 1986 Steele Prize for a Fundamental Paper was ported in principle by the Council, it was fiDally awarded to Rudolf E. Kalman for three papers decided that it was not a realistic venture. The on systems and control theory. The 1986 Steele Executive Committee and the Board of Trustee Career Prize was presented to Saunders Mac reached the position in November 1986 that they Lane for his many contributions to algebra and could not support the plan, and on their. retOOl" topology. mendation the Council of January 1987 Withdrew There were five regional meetings at which the endorsement. there was a total of seventeen invited hour speak­ ers and 451 shorter talks in seventeen special Membership Services sessions and sessions for contributed papers. The International Congress of Mathemati­ In 1983, the Board of Truste~s instit~~ cians in Berkeley in August displaced the usual handling fee for mailing the Combmed Mem esud Summer meeting. It was a highly satisfactory List ( CML) to those AMS members who. r: this Congress, whose extent and merits will not be it, effective in 1984. The Board re~fagain be detailed here. Mathematicians in North America policy in November, an~ the CML ~distributed found it convenient to have the Congress close distributed at no charge m 1988. (It 1)s at hand and welcomed the opportunity to be by the MAA in odd-numbered years. iecuonk hosts rather than guests. The Congress was in The C ML of 1986 was able to carryAe ri)198'1 the United States at the invitation of the Na­ addresses for the first time.· see the t"onP . £rmal · tional Academy of Sciences. It was operated by Notices, page 497, for relate d m 0 Is to create a a separate corporation that contracted with the The Council approved proposa rfe meJDher· Society for a variety of services. Moreover, the new category of membership, t~e es1 for ~ Society agreed to support the Congress financially and to allow members to pay ~or details,,., by paying the deficit, if any. Although the books years ahead at the current rate. ( are not closed, the deficit is negligible. The exact the June 1986 Notices, page 500.) amount of the deficit will not be known until the sale of the Proceedings of the Congress. Society Business 1'bt The Society offered a Symposium on Some financiallY· t Mathematical Questions in Biology at the meeting The Society had a good year ds at aiJOO of the American Association for the Advancement operating fund balance now stan

608 $2,400,000, even after restoring a portion of the a contract between the Society and the MAA reserves that were depleted in recent years. The in 1979, at a level intended to produce enough Treasurer will have more to say about the financial income to break even, approximately, on the two picture. meetings each year. The base rate is indexed to Life membership was reinstated after a lapse the cost of living, and so goes up slowly. The of nearly fifty years. This time, it exists only for costs of planning and running the two meetings members at least of age 62 with twenty years of are nearly equal, even though attendance and reg­ Society membership. istration income are much smaller in the summer. A substantial fraction of the membership As a result, the annual meeting ordinarily yields expressed a preference for a dues reduction in a small surplus and the summer meeting a deficit. place of receiving the Bulletin. The mechanics The total net income was positive in 1986, for the of the operation, such as the amount of dues first time in memory, because there was no sum­ reduction and the necessary change in the bylaws, mer meeting. (The usual net deficit might best are being developed. be thought of as supported by members' dues; The year 1986 saw the beginning of a re­ each member pays something for the possibility duction in the size of the Council, which will of attending meetings, even if he or she chooses shrink from about 60 to about 35 by 1991 as an not to do so.) amendment to the bylaws takes effect. Some other scientific societies include the The Society continues its Research Fellowship price of the proceedings volume with the registra­ program, based on contributions and matching tion fee for a conference. We tried this out for a funds from the Society. The winner in 1986 was year or two but it proved to be quite unpopular, Dinakar Ramakrishnan. so in November the policy was rescinded. The Council nominated Robert M. Fossum In 1947, the Society initiated a series of as the candidate for Secretary in the uncontested Symposia in Applied Mathematics, and one was election of 1988. Should all go as planned, he will held almost every year until 1980. About 10 become Secretary on 1 January 1989. years after SIAM was formed (in 1952), the latter organization became a cosponsor of the series. Everett Pitcher Last August, SIAM withdrew from this activity, and an AMS committee was appointed in the fall to consider new ways in which the Society can best serve the special interests of applied mathe­ Annual Report maticans. These developments will not affect the of the Executive Director annual Summer Seminar in Applied Mathematics and the Symposium in Mathematical Biology; the The Society once again enjoyed a splendid year, 1987 Seminar on Computational aspects of VLSI financially speaking, in 1986. As a result, steady design with an emphasis on semi-conductor device progress is being made toward the 'frustees' goal simulation and the 1987 Symposium on Models of establishing a reserve of about one year's op­ in population biology have already been held, and erating budget. The challenge is to achieve an planning began last year for the corresponding annual surplus while keeping the prices of our 1988 conferences. books and journals low, meeting production and The Centennial of the Society will be ob­ membership costs, and carrying on all the ac­ served in 1988. The main event will unques­ tivities of the Society that produce no income. tionably be the Centennial Meeting itself, in There are three principal aspects to the strategy Providence, and a program committee chaired by for doing this: invest in equipment and tech­ E. Pitcher began its work in earnest in 1986. nology that will keep costs down over the long pull, expand the publication program modestly MR and Related Products to create a broader income base, and maintain a well-qualified staff committed simultaneously to This part of the report deals with activities at excellence and frugality. I am confident that in Mathematical Reviews during 1986 and the first future years this strategy will have yielded a Soci­ part of 1987, and was prepared principally by ety financially strong enough to weather difficult R. G. Bartle, the Executive Editor. times and at the same time flexible enough to In January 1987, the cumulative author and meet new technological or societal demands. The subject indexes for the i980-1984 issues of MR sections following are intended not only to provide were published. This twelve-volume set of indexes a report on individual activities that supplements collects together full bibliographic information the Secretary's Report, above, but to reveal how about the approximately 200,000 books and pa­ this strategy was being carried out in 1986. pers in the mathematical literature that were Meetings and Conferences reviewed during this five-year period, and greatly facilitates searching this recent literature. This The base rate for registration fees at the Joint set of indexes is an indispensible tool for every Annual and Summer meetings was established in mathematical research library.

609 Early 1987 saw the publication of the first two Despite the fact that MR and compilations of subject indexes of all the items fur Mathematik (Zbl), after long dis.-,~~ in probability theory and in statistics that were not merge (see the report of the s~-=~ lid reviewed in MR from 1940-1984. These subject continue to cooperate while they r~~), 111ty indexes provide a compact and inexpensive tool entities. For example, the edito lllain~ for locating information about the authors and reviewing journals are just startin; t~f the '­ titles of all articles and books in these two areas of the 1980 Mathematics Subject ~~ over this span of forty-five years, and should be of which is the classification system p ~ great use to researchers in probability theory and by both journals. The new revis:m'y '-l statistics. Additional subject indexes for specific completed by the end of 1988 in ord ~II! areas will be published in the future. be used in CMP beginning 1989 an~: It to Zbl beginning 1990. We would wei R llli The first six issues of MR for 1987 are comments and suggestions, which we :: lily running about 20% larger than the corresponding with the Zbl editors. ilbaft issues of 1986. While a part of that increase is due to somewhat more material being published, most of it is due to an attempt by MR to Publications streamline its production processes so that MR will be more timely. One of the reasons for The Society's all-time best seller is the R-. the increase in the literature is the growing English Dictionary of the Mathematical Sciencu number of conferences that are being held in the by A. J. Lohwater. A quarter-century hatinj mathematical areas and for which proceedings passed since its publication, the word Jist lad! are published. It is the policy of MR to review many of ~he term~ current in research in ~ only those articles in conference proceedings that mathematics, and Is even more deficient in 110111! are in final form and that will not be published areas of application such as computer sc:ie!Kt. (possibly in fuller form) elsewhere. Most of the With no other source of funding in sight, the Ex­ items that are not in final form will be listed ecutive Committee and Board of Trustees &gl!ed in Current Mathematical Publications ( CMP) and to spend up to $100,000 to prepare and publish will be fully classified and listed in MR indexes, a new edition. The work will be under the V!!! but will not be reviewed. That makes CMP capable direction of R. P. Boas, but of c~ an important acquisition for every mathematics one person cannot know everything in this kind library, so that scholars will be alerted to the of work, and the quality of the final product existence of these somewhat ephemeral conference will depend in part on the amount of expertise proceedings articles as well as the items that will provided him by volunteers in the mathemat~~ be fully reviewed. In response to several requests, community. If you are aware of words, phrase!. the Tables of Contents of the journals that are or meanings that are lacking in the present dk· published in CMP have been moved to the front of tionary, or if you are reasonably fluent in RU&Iian the issues, so that they will be more conspicuous. and are willing to help in this important en­ deavor, please get in touch with Professor Boal. During the past eighteen months, Math\Sci­ at Northwestern University. . the electronic version of MR-has increased dra­ The writer attended the Beijing Internal!~ matically in scope, timeliness, and usefulness. Book Fair in September in order to conturot All current entries from CMP are now added to discussions initiated in December 1985, withh~ the file, so that Math\Sci users now have ac­ of Chinese publishing houses. _Arranging; cess to complete bibliographic information about translate Chinese books is complicate~ ~ items received by MR shortly after their receipt­ fact that there is no copyright Ia~ m(;biDe!! sometimes even before the publication of the items and no international agreement covermg rinl in the original journal. In addition, the files are publications. In principle, we coul~ ~ it being extended back to 1959, so that complete a Chinese book or publish a tr~latt~tie!. bibliographic information will soon be available in without obtaining permission or paymr ditioll! Math\Sci for all items in MR from 1959 to the but of course we would not do so. 0~ce kd present (even the near future). Also added were were agreed to in September whi~h hav:h~tic~ the records from the Current Index to Statistics to firm contracts with all the maJor~\ noftht (CIS), covering statistics items beyond the scope publishing houses in China, and trans a ~ JJdl of MR from 1980 to the present. In 1986, the first two books under these contracts program Math \Sci'lEX was made available; this commence. . 1 Spif8k'! program makes it possible for a user to download The official first edition of Mich~~ wjng edi­ an item (1985 or later) from Math\Sci to his or Joy of TFfX was published in 1986, fo ~stributed her personal computer and obtain a version that tions -2, -1 and 0 which had. be~nb]y read~ is complete with all mathematical symbols. We earlier for testing purposes. This ~g macrovack· urge all mathematicians to discover how useful book is the instruction manual for t e !J)lllisSioned Math\Sci can be for them in their bibliographic age, AMS-TEX, which the Society c\ easierfd searches. Spivak to prepare in order to make 1

610 'ThY in writing mathemat- Activities and Changes in the AMS Offices . ·ans to use J.v• . . h --•heJIIatlCl . ditorial processmg IS muc ~ SlllCe e A s 'ThY jell papers· f le received as an -"M - J. .V" John L. Selfridge left Mathematical Reviews in ~ ... pier for an ar :c paper form, the Executive July 1986, after eight years of distinguished ser­ ,_ for one Ill d h" h h 1,pe than t d a policy un er w 1c sue vice as it~ Executive Editor, to return to Northern ,.OIJllllittee adoP. e an advantage of as much as ,. ·n recetve Illinois University as chairman of the mathemat­ articles WI s between AMS acceptance ~d p~b­ ics department. During his term, the size of MR t11f111Y week information about this policy, grew from about 32,500 reviews to somewhat over . (For more N . 495 ) ]icaUon. .11987 issue of the otzces, page . 40,000 reviews per year, a very considerable back­ 1ft the Apn Joy of 'J'EX, and Math\Sci '!EX log was eliminated, the collection of author and AMS-~~ of the pro~ucts the Society is subject indexes from 1940 on was completed, the art' onlY . , the convemence of authors who online version of MR (now called Math\Sci) was offenng 10r k £ M h\S · ~ typeset papers and b?o s, or at CI developed, and the use of 'lEX was implemented. •ish ~ho wish to convert onhne output to. type­ Many of these changes were made possible by the users d as a service to the commumty to very substantial computerization that has taken ltl form."de a ansingle source for 'ThY.L_v.-re 1a t ed rnat en-· place in both the Providence and Ann Arbor prov! Other software includes -rpc programs for offices in recent years. We in the Society offices ~~rocomputers, previPwers, dnvers, and macro are grateful to John for his dedicated service and packageS other than A.MS -'lEX, and documenta- wish him well in his future endeavors. . 18• available for all these programs. If you During 1986, two long-time Providence de­ uon h" 'ThY l"b d want to know more about t IS .LJY" 1 rary an partment heads retired. Marjorie Cummings don't have an AMS catalogue, please call and ask came to the AMS in 1966, and had been head for one: 800-556-777 4. of the Membership & Sales department for 11 The AMS produces TUGboat, the newsletter years before becoming Director of the Production of the '!EX Users Group. The print run of this & Distribution division in 1977. Because of a re­ ptriodical is now about 3,000. organization following her retirement in October, Ring theorists will welcome Lance Small's she was not replaced. sequel to his Reviews in Ring Theory, this new volume covering the period 1980-1984. Next in Phoebe Murdock was known to many habit­ the series will be review volumes in several applied ual AMS meeting goers as the person in charge of areas in 1987. the book exhibits; she had also been head of the Marketing group. She had been with the Society Overall, we published 55 books in 1986 (ex­ clusive of Memoirs), as compared with 37 in 1985. since 1967 and retired in November. l:nfortunately, we were not quite able to com­ Because of the decision by Digital Equipment plete the preparation of a number of important to discontinue the DEC-20 line of computers, it bibliographic aids: the MR 1980-84 Author and was necessary to begin moving the entire AMS Subject Indexes, the 50-year index to Mathematics system over to VAXs. A VAX 8600 was purchased ofCom?~tation, and the 1940-84 SubJectlndex in in late 1985 and was brought into operation during Probaba!aty Theory and SubJect Index in Statistics 1986, communicating with the DEC-20s through all ~ppeared in the early months of 1987. The an Ethernet local area network. The principal :~e~ c~ntinu~s ~ith its program of supplying use of the new machine has been the development pnnctpal btbhographical tools for Western of an entirely new database for membership and mathematicians. customer records; when this is complete, along has The Society, in cooperation with the MAA with the associated order-fulfillment system, the embarked on a n!'w kind of publication th~ Society will have a powerful, efficient, and flexible vid eotape T . ' one-h A apes ~r~ now available of three tool for carrying on the business side of its loll °~, MS-MAA JOmt lectures: V. Guillemin, activities. 8ur1aces p R H . mt~ and T ' · . · a1 ~os, Matnces I have Similarly, the composition department in the the represe · H~wkms, Epzsodes in the origins of Providence office, and the systems group in the ~ec: ,..., ntat10n theory of Lie algebras. The 1 - .. are exp · MR office, continued to develop the Society's ,.,.,__ osttory and should be useful in facilities for using 'IE;X. Only one link in the chain .... ""~~ and semin ' llpper-level ars 1or students who have an was weak by the end of 1986~a fast typesetting Th ~~I_Jdergraduate background. machine which could produce output in a . e Soctety on . . 'lEX tnbuted th W ce agam prepared and dts- variety of fonts~and this was secured in early on behalf e f orld Dzrectory of Mathematicians 1987. Many books and journals are produced Union. Th? the International Mathematical in 'lEX already, and the commercial typesetting ~t 40,()()~s nlOOO-page eighth edition contains system formerly used will gradually be replaced by tians around t~es and addresses of mathemati­ 'lEX for all purposes. (Essentially all composition ielected by th e ~orld. the names having been and printing of AMS books and journals is done lttofdance w·~hvar~ou~ mathematical societies in in the Providence office except for the printing by the Execu:· cntena for inclusion established of the Bulletin and Notices, which have large IVe Committee of the IMU. print runs, and Mathematical Reviews and CMP,

611 which are partly composed in Ann Arbor and are Summary Balance Sheet printed by an outside firm.) December 31, 1986 Commercial software had been purchased for (Thousands of dollars) handling preregistration and hotel reservations Assets at meetings, but it had to be largely rewritten Cash and temporary investment~ to cope with the special needs of the AMS. Other short-term investments S3~1! Also, the computer program which does the Receivables-members and others (less 2,010 matching of employers and applicants at the allowance for doubtful accounts) Employment Register needed an almost complete Prepaid expenses and deposits overhaul. after about twenty years of patching Deferred prepublication costs and repatching. The new programs were used for Inventory of completed books and the first time at the Laramie and San Antonio back volumes of journals meetings. Property and equipment (less accumulated W. J. LeVeque depreciation) Total operating assets -..m Investments-at cost S12.559 Report of the Treasurer (market value--$5,235) Total assets I. Introduction

During the first five years of this decade (1980- Liabilities and fund balances 1984), the Society incurred losses totalin_g Accounts payable $2,548,000. At December 31, 1984, the Socl­ $ ~; Subscriptions, dues, and other ety 's fund balances (excluding endowments) had revenues received in advance declined to $1,688,000, or 17.7% of the Society's 7.4J.l Other miscellaneous liabilities total assets (excluding endowments) of $9,555,000. 98; Long-term debt (mortgage on building) At December 31, 1979, fund balances were about 1.26i 44% of total assets (excluding endowments) of Total liabilities 10.1~ $6,891,000. Since 1984, the Society has experi­ Operating fund balance _bill enced two very good years of earnings, and at Total operating funds $12.559 the end of 1986, the Society's fund balances (ex­ cluding endowments) had increased to $5,417,000, Invested fund balances: or 34.8% of total assets (excluding endowments). Endowment funds: Included in these fund balances is the Future The Endowment Fund 100 Operations Fund. The Long Range Planning Robert Henderson 54i Committee and the Board of Trustees have rec­ Joseph Fels Ritt 23 ommended that the Society build this fund to an Prize funds ~ amount equal to one year's operating budget. At Eliakim Hastings Moore l December 3L 1986, the Future Operations Fund Undistributed net gains on was $2,778,000, about 21% of next year's budget. investment transactions 9ll The recent improvement in the Society's fi­ Funds other than endowments: nancial health can be only partially attributed to 2.7i9 Future operations !24 cost cutting and fiscal restraint. The Society's Friends of Mathematics finances are very greatly affected by the general Other J economy, library budgets, and even foreign ex­ mJhl change rates. These and other factors are very Total liabilities and fund balances difficult to predict, and the Society often finds itself in the position of reacting to these factors. The Future Operations Fund is an attempt to Summary Statement of Aetivl~t88 prepare for the inevitable deterioration in these For the Year Ended December 31• environmental factors. (Dollars in thousands) II. Summary Financial Statements Revenue ~ ~J~o~u~rn~a~l~s------~$;;;-;;-7 • 958 11~ The Treasurer this year again presents to the Books 1,390 rf. membership summary financial statements of the Dues 1,184 lq Society. A copy of the Treasurer's Report, as Membership Activities 151 ~ submitted to the Trustees and the Council, will Meetings 241 Jlfi be sent from the Providence Office to any member Grants and Contracts 1,288 4Cf who requests it from the Treasurer. The Treasurer Investment Income 566 ~ will be happy to answer any questions members Other _11§ J¢t may wish to put to him concerning the financial affairs of the Society. Total revenue ~

612 Membership activities include such projects as the Employment Register and the Mathematical ~ 62% $ 6,808 Sciences Professional Directory. In total, the 1,048 9% j;gnals activities operate at a deficit, which is considered 287 3% JloOksing to be supported by dues. Other costs which 300 3% Records can be considered to be covered by dues include ~rship 209 2% the cost of maintaining membership records, the ~=bershiP Activities 181 2% deficits of Abstracts, Bulletin, ElMS, and Notices, 1,385 12% Contracts deficits from meetings, and the AMS support of ~==~d __ill 7% ()tber the Joint Policy Board on Mathematics. $10,963 100% fD&I) expense Meetings. For the first time in many years, meetings did not operate at a deficit. The usual £xall of Revenues summer meeting was not held in 1986 because ,..Expenses the International Congress of Mathematicians was held in the United States. I expect that meetings will again operate at a deficit in 1987. Grants and Contracts. The amount of money available from the federal government has declined substantially over the years. Currently, support is III. Operations mainly for travel and subsistence for participants 1now turn to a discussion of the Society's 1986 in research conferences, institutes, and seminars, plus the Society's cost in preparing and running operations. Journals. Journals provide the largest frac­ these conferences. The money received from tionofthe Society's revenues and expenses. In the government agencies is reimbursement only, with past, journals have operated at a net loss. During no profit to the AMS. The Society also has 1985 and 1986, journals operated in the black and contracts to perform services for other nonprofit provided a very significant portion of the Society's organizations, and this helps to recover some fixed 1986 surplus (the excess of revenues over expenses costs. in the su=ary financial statements above). This Other Revenues and Expenses. The principal improvement is the result of a decrease in the components of other revenues and expenses are rate of attrition in subscribers and a variety of Math\Sci (by far the single largest item), TEX cost-cutting procedures implemented by Society related products, and the AMS support of the management. Joint Policy Board for Mathematics. Boob. Included in this category are not only IV. Assets and Liabilities ~ks (monographs or collections of articles) but !'eVJew volumes and indexes to journals. Books, So far, this report has dealt with sources of exclusive of the latter, continue to be financially revenue and applications of expense. Another IOUDd, and selling prices of AMS books compare aspect of the Society's finances is what it owns very favorably with other mathematical books. and owes, or its assets and liabilities, which are ~r the past few years, the book program has reported above in the Summary Balance Sheet. IDC~ at a rate of about 20% each year. The The Society maintains its accounts in fund groups. ;:'tmg efficiencies have allowed the prices of the The operating funds include membership and ks to be kept reasonably low. publications activities; the invested funds include to Review volumes and indexes are very costly both endowment funds (gifts and bequests whose .... ~~duce, resulting in high prices. Each such I"GGWed p bl' . . principal is required to be invested in perpetuity from b u 1 ~atl?n IS scrutinized very carefully and whose income must be used for the purpose and .oth SCientific and financial perspectives stated by the donor) and quasi-endowment funds and pn~es are set accordingly. In 1986 indexe~ rev1ew volu t h ' (those funds set aside by the Board of Trustees had a Sinal!! ~es oget er broke even. They for designated purposes). Most of the quasi­ oss m 1985. endowment funds have been designated for future ..,._ Membership Activities and Member- -.. ~~·"-Ords Th S . , operations. tiona! m b. e oc1ety has about 480 institu- The Society's fiscal year coincides with the 0! the ,:~ ers :nd 20,000 individual members. period covered by subscriptions and dues. Since they are st:dea out 6;000 pay no dues because dues and subscriptions are generally received in or reviewers ~t nommees, emeritus members, advance, the Society reports a large balance of dividuaJ me ~lthout convertible currency. In­ cash and temporary investments on its fiscal year­ IIOtne relief trn t dues .are two-tiered to provide end, December 31. This amounted to about dues are set 0 . ower pa1d members. Institutional $5,500,000 for 1986. The recorded liability for the Pllblished by' 10 Part, by the number of papers revenues received in advance was about $7,400,000 ' in da;:th~rs ~mployed by the institution. on the same date. The difference can be thought lllnuauy by es or mdividual members are set of as having been invested in the Society's other a cost-of-living index. assets. Effectively, the Society borrows from its

613 subscribers to finance current operations. This is these facilities currently exceeds $3 OOo a common practice in the publishing industry and largest part of the Society's office ' . '~· '1'1. . . equipm .... !Ill allows the Society to maintain a very low amount mvestment m computer facilities. "'' 18 ill of bank debt. The Society's Providence land The Society's property, plant, and equip­ secure a mortgage note amountin andt $ hUiJ din&t ment includes land, buildings, and improvements, at year-end. During the first q~ ~ l,2fl8,())) and office furniture, equipment, and software. approximately $330,000 of the balar er of 1987. The Society also owns a small amount of trans­ back. ance was !laid portation equipment. The land, buildings, and include the Society's headquarters improvements Franklin P. Peter.. building in Providence and the Mathematical Re­ views offices in Ann Arbor. The appraised value of

614 Council Plan for a Referendum

Th are two motions [1] pending before the Society. The Committee on Science Pol~~; made recommendations [2] to the Council concerning them. See the references below. The Council of 25 April 1987 considered the recommendations and adopted the following plan. 1. The Council instructs the Managing Editor of the Notices and the Chairman of the Notices Editorial Committee to open its pages for comment related to two motions considered at the Business Meeting of 22 January 1987. 2. The Council instructs the officers of the AMS to hold a mail ballot of the membership, after the January 1988 annual meeting but before February 1988, on the substance of the two motions concerning issues of federal funding of research in mathematics. 3. The Council, at its meeting of 4 August 1987, will adopt the specific wording of the motions to appear on the mail ballot. The President is requested to distribute drafts of these motions as early as possible to the Council for comment and criticism. 4. The Committee on Science Policy is requested to submit to the May meeting of the Executive Committee and Board of Trustees (ECBT) its suggested wording for these motions. Other interested groups are also encouraged to submit possible wording to that ECBT meeting. 5. The Council of 4 August 1987 should decide whether to recommend that the Business Meeting table the two motions before it in view of the upcoming mail ballot. 6. The Notices of June 1987 should include a prominent announcement of the plans above.

This article constitutes compliance with item 6. Compliance with item 1 has been initiated. The references are:

[l] The_ text of the motions, Notices, January 1987, p. 76. The action of the Busmess Meeting to consider the motions, Notices, February 1987, pp. 398- 399· [2] Th~ recommendations of the Science Policy Committee, Notices, April 1987, p. 448. 300·~e ~ay refer to Notices, January 1987, pp. 39-44, February 1987, pp. 235-244, ' prll 1987, p. 502-506; and June 1987, pp. 616-620, 699 for related material.

Bethleh p . Everett Pitcher em, ennsylvama Secretary Commentary on Defense Funding

As recommended by the Committee on Science ~afls. A secondary effect might be to enJ.-­ Policy (see Notices, April 1987, page 448), this m rastructure to encourage addition 1~~ section of the Notices has been instituted to ~o engage in the scientific enterpr~e~ provide a forum through which the mathematical mcrease the total pool of individuals 8IJc! ~ community may comment on the two motions the .scientifi~ enterprise. There is pro~• presented at the January 1987 AMS Business ment to th1s, although arguably· th 1...... lllllt Meeting (see Notices, January 1987, page 76, and the brightest scientific talents are lik:l """ IIIII February 1987, pages 398-399). chosen these fields anyway with the c y to!­ Items to be considered for this section should conclusion that only marginal individU:coanta. be sent to the Managing Editor of Notices, Com­ suaded by the financial rewards. In any are"!. mentary on Defense Funding, American Mathe­ certain!~ is no more than an uncritically Clle, • matical Society, P.O. Box 6248, Providence, RI suppos1tlon that federal funding produc~ 02940 and should be limited to approximately research. lllllt 1,000 words. . Does federal fu.nding produce better l'e81!a1Ql Th1s, of course, 1s the crux of issue. h : Edward J. Wegman argued that peer review subjects resean:IJen: the intense scrutiny of their peers, and thus lilly George Mason University the. best survive. to be funded. Indeed, the peer I read with particular interest the discussions rev1ew concept 1s reverenced almost 88 a hiJ contained in the Report of the Science Policy grail. It could well be argued by outside!a thlt Committee, February 1987 Notices, pages 235- peer review is nothing more than an old ho,s 244. As a member of the American Mathematical club. It could be argued that those who 1ft in Society, the recent past Head of the Mathematical the establishment obviously have a vested inlnt Sciences Division at the Office of Naval Research, in maintaining their influence with the fundiD& and the person who created the original computer agency. It clearly is tempting, for example, b and mathematical sciences efforts in the Innova­ a topologist to prefer second-rate topology Oft! tive Science and Technology Office of the Strategic first-rate statistics. In any case, it is clear lhll Defense Initiative Organization, I am perhaps in peer review tends to be conservative and th1l. a unique position to comment on these matters. I as a system, has biases against the newest ml would like to direct my discussion in three parts. most innovative work. Let me also add tbat, • I would like to comment first on the peer review a member of the federal funding establisbmllll and the National Science Foundation, second on for eight years, I have seen numerous instancesi the two motions regarding respectively, SDI and these effects apparent in peer review. Thesellf DOD, and finally on the prepared statements of not simply idealistic concerns but the realitiesi Hyman Bass, Ettore Infante, Melvyn Nathanson, day to day human interactions. It is a tribute.IO and Steven Weintraub found in the appendix. the professional program managers at the ageooes 1. Peer Review and the NSF. It seems clear that such effects are minimized. to me that it is a virtual article of faith that If more and better is not unequivocally ~ the health of the mathematical sciences in the result offederal funding, what then is thep~ United States is tied to the peer review system I would argue that the primary ~urpose of. i and its implementation in the National Science funding is to shape the directwn and.kifeltS Foundation. If this be the case, it is perhaps well research that is done. Clearly, econoDll~ 11 to consider carefully the fundamental purpose of have shaped the growth of computer. ~ 1e:lht federal funding of academic research and its impli­ the expense of mathematics. Irophc1t ticS i! cations for the National Science Foundation. On arguments for more funding of mat?e~ tbil the surface of it, the purpose must be to facilitate the recognition that this is so. If ~d aqued more and better research with the expectation, is the case, then it certainly can t ·tiJDIIf as Infante points out, that these investments will that the federal government has ~~if provide a return in terms of increasing the health, interest in shaping the directions of ~ industriousness, and security of the nation. Does the good of all citizens. Simply P:\ood rJ federal funding produce more research? The funding of mathematics is not for i ~ citiJIIIS answer is probably not. A look at data on the mathematicians, but for the g~od 0 This ~ number of papers published pre-World War II and who provide the monies for 1t. h NsF Jllll post-World War II (when federal funding of aca­ weakens the argument in favor of ~ e tends to demic research began) shows a relatively smooth its peer review system. Peer rev1:apin& Jtl transition with only the expected statistical fluc­ preserve the status quo rather than h ~ tuation. There is thus relatively little evidence directions. It is my belief tha~ \n~re Cflfl1l of significant increases in productivity of individ- mission agencies can make a mu

616 ederal funding of research done so therefore we should not try. This seems ress for f . ..- to cong . ly because thev are lil a to me to be profoundly anti-intellectual. I would c•- !\SF stmP " h 1 tbaD the '. . to define concrete researc goa s. rather argue, at least in the abstract, that we ;trooger postt!On t be a far better strategy to should consider all the technical and philosophical . to me o . . . t It seenJS t of mathematics m a vane y issues over a reasonable amount of time, and tllcourage supphor than suggest the migration of then come to a carefully considered judgement. I · • rat er . simply do not believe the issues are as clear-cut of agencte"; 0 one agency, particularly, an agency all montes t 1 premises are vulnerable. It as many portray them to be. ,-bose fundam~~t a of Ettore Infante and John What is true is that the politicizing of Star ~ to the creth1 y have recognized the need to Wars has hardened perspectives. It has caused lk. g that e · h. h NSF Po Ill re focused programs w1 t m t e , many advocates of SDI to say, let's do it to prove crt'ate mo thens the case that can be made for it can be done. The real danger of the whole affair , tbt< streng h . 10r "d :-.'SF funding of mat emattcs. is that some ineffective system will be deployed !llCrt'ase . . Th Motions. I have devoted etght years as an emotional response to criticism rather than 2• ,e ·onallife to the proposition that the a decision to deploy or not deploy based on sound f DIY pr01esst . . 0 • t' 1 sciences have a legtttmate role to technical and philosophical reasons. It seems to matbema tea · th strengthening of the defense of the me that if there are substantial misgivings, then lav m e · d' h P. : ed States As to Motwn 2 regar mg t e there is an obligation to embrace SDI and prove .l~ · . . . h . h unequivocally that it cannot be done. Math­ iDcreasm g militanzatJOn of mat emattcs. . researc , . s to me that there is precwus 1ttt 1e cause ematicians should, above all others, recognize 1t seem · . . d & for alarm. As I reckon tt, DOD supp1 1e 38.7 :o the danger in the logical leaps associated with of the federal funding in FY 1~83 and 39.4% m assuming that the obvious is true. FY 1987. (This from the data m Table 1 of the My own dilemma is this. Now that Star .'iotices article.) Indeed, this includes a major Wars has been so politicized. is it possible to new program from DARPA which implies that the achieve a decision based on sound technical and proportion of funding from ONR, AF(_)SR, and philosophical reasons? I don't know. In any case, ARO has slipped. Rather than there bemg alarm I believe boycotts are ineffective. The surest way about the increasing militarization, there should to affect the direction of SDI is to be in dialogue be alarm about the decreasing militarization. I with the officials at SDI, and the surest way to be am able to comment from first hand experience ignored is to disengage with them totally. that, while the total budget available for math­ 3. The Statements. I find these to be an ematics has remained constant, much of what interesting collection of remarks, most interesting, has been available has been directed towards core perhaps, because of the absence of anyone directly mathematics, e.g., the programs in discrete math­ or indirectly connected with the military. I find ematics and topological methods in chemistry at most sympathy with the statements of Ettore the O~R and the finite mathematics program at Infante, who cogently dissects the arguments and the AFOSR. This means that your colleagues in whose arguments are both sound and pragmatic, apphed mathematics and statistics have in fact, and Melvyn B. Nathanson. I was particularly paid for growth in core mathematics. There has struck by Nathanson's clear view of the funda­ been substantial erosion in the support for applied mental role of federal funding in altering the mathemattcs and statistics. direction of research. As to Motion 1 regardirw SDI, I have a The statement of Hyman Bass starts off with somewh t · o a IDLXed reaction. When the SDI program premises that I wholeheartedly endorse. He goes was originally d ( . . 1 bee . announ~e and mc1dentally when on to describe what he calls the civilian mode ame mvolved), 1t was publicly described and the military mode of defense funding. My as a flve-year h . leas'b'l· researc program to examme the only comment here is that all of what I saw as t ttty of t . . cons ructmg and deploymg such a a system Th Program Director and as a Division Head at portrayed. SD e popular press has, however, ONR was in the civilian mode. It is, in fact, with the ass I mu:h more as a development effort the general policy of DOD that all basic research successful . umptwn that the research would be (6.1 funding) be in the civilian mode. Thus, I concJ~ion ~d. that deployment was a foregone would be hard put to describe a setting in which problems · . hts has never been my view. Serious basic research would be funded in the military se11·0us . extst m the technical arena. The most ID rn · mode. My biggest concern with Professor Bass's the massiv Y VIew are our inability to create statement is his remark, "Neither they (program Code nece e amounts of fault tolerant computer directors) nor other DOD personnel who manage ssary t · 1 very seriou 0 Imp ement the system and the and understand science have much discretion or SJlace envir~ Problem of power conditioning in a influence on science policy ... " This is simply to SWitch 0 nment. By the latter, I mean ability not consistent with my experience. There is :<>

617 in all matters but the classic complaint that one in DOD will not again make such a remark, the program directors need more money. Many simply making such a remark has little influence of the program directors including myself would in the broad DOD research establishment. It is have wished that the planning process were less much akin to asking the American Mathematical cumbersome, but conditioned upon having such Society to guarantee that no member of the AMS a process, the views of the scientific personnel will ever again issue an incorrect proof. were heard. In general, it is true that the I like to compare the DOD to the university science budgets pass through military planners system in America. Both are large complex who balance research need with other military organizations, largely decentralized and made up priorities. Their decision about level of budget of many individuals with a spectrum of beliefs may not meet our desires, but I am not aware and persuasions. It is as incorrect to think that of any situation in which there was an attempt the DOD acts with one mind as it is to think by nonscientists within the DOD to shape the that the universities do. What is true is that direction of research. Professor Bass uses this the individuals within the DOD responsible for remark to suggest that it would be a good idea to mathematical science are mathematical scientists seek gradual realignment of funding from the DOD and are susceptible to persuasion. Not only and place it in the hands of the civilian agency, that, but the DOD and Congress as a whole are i.e., the NSF. I personally feel comfortable with susceptible to political persuasion. Thus, it is 40% of the monies in the hands of the program extremely likely that if mathematicians stay in directors of the DOD. They are bright, well­ dialogue at all levels, there is every chance they motivated people who do an excellent job for the will be heard and exhibit the positive influence mathematical sciences community. What is more for which they might hope. dangerous, in my view, is to concentrate total As a final remark, my comments are made as spending authority in a single agency. This is a private citizen and as a member of the AMS. bad because it is an "all your eggs in one basket" They have not been subject to any DOD review strategy. Currently, mathematical sciences are in nor do they represent any DOD position. favor at NSF, but there is certainly no guarantee that they will always be. It is better to have diversity, not only in sources of funding, but also in perspective and imagination. The agencies are complementary in approach and this is, in my Seymour V. Parter view, fundamentally desirable. University of Wisconsin-Madison Finally, the comments of Steven Weintraub Let me begin by asserting that, along with many are those of a mathematician's mathematician, of my friends and colleagues, I have very strong i.e., tightly coupled logic from basic axioms. I reservations about the scientific (military) valid­ find no fault with his arguments. I do, however, ity of the SDI program. I make this statement find that his axioms do not correspond to real­ not because I must make it to have the right to ity. I have already indicated that I believe the participate in this discussion, but rather because mathematical sciences have a legitimate role to I believe it is essential that we understand our play in the defense of the United States. It seems role in this discussion. My views on SDI are not a to me that the American Mathematical Society scientific conclusion. Rather, they are a political should generally be supportive of the American conclusion reached in the same way millions of Department of Defense (i.e., without being blind c>ther citizens have reached their conclusions on to its weaknesses and excesses). The case may this vital question. I have read and listened to be different if we were the International Math­ those scientists (primarily physicists) and engi­ ematical Society. The other comment I would neers who can and do claim scientific expertise. make is that Professor Weintraub endows the Having done this, I have then decided which set DOD with a monolithic character it simply does of experts I would believe. Thus, I came to my not possess. DOD is a massive decentralized conclusions. I would be a liar if I were to claim organization made up of many individuals. It is that my particular professional expertise made me frustrating to get concurrence within the DOD as qualified to render an intelligent scientific judge­ any DOD executive can testify. To use language menton this very complicated question. Further, like "agency A (the DOD) is interested in area I have no reason to believe that any of the math­ X" is naive. The DOD doesn't make decisions, ematicians who have expressed their opinion (in individuals within the DOD make decisions. This the January 1987 Notices or the February 1987 is particularly true of comments such as the re­ Notices) have any more scientific expertise (than marks attributed to Donald Hicks. While Donald I) in this area. Hicks was in a high position in the DOD, his Once we understand how I have come to my unfortunate remarks had no influence whatever opinions on SDI, we must face two possibly un­ in the actual day-to-day decision making process pleasant facts. First: Most of the experts I trust of who gets research contracts. And while I too also strongly support ongoing, if limited, theoret­ would agree that there is no guarantee that some- ical studies on the scientific problems (as opposed

618 d testing problems) involved which is not classified, morality is a private mat­ the hardw~e ~e potential and feasibility of ter. Each person must consider each case, as : lJII(iellltanT.t.R. "star wars" . program. A~d it concerns them-and then decide. Our organi­ zation, the AMS, should not make them second 1 U.S. or ~· 1 the area in wh1ch mathemat1cs .L.t is preciSe Yt be useful to the nation in a class members. 0 ~...til JIIU""f likelYSDI Second: the law o f.. I arge b numbers Finally, there is a very serious matter of !ludY 0 ·there are mathemat1c1ans, mem ers general scientific policy. Some of the statements ~ thatd·ng in the AMS, who have come in favor of Motion 2 suggest that it would be . :.Nl stan 1 . SDI N Ill 5""": t political conclus10n on . ow, good if the nation had two distinct scientific 10 a differen that I'm nght. d an they are wrong, establishments: one academic, open and "pure," we all ~~~he AMS take the position: AMS will the other military and secret. Such a situation but sh~Uto mediate between agencies for an AMS is impossible. But, never mind its feasibility, alteJIIP h wants to study ... a patently useless let's talk about its desirability. Frankly, such a ~be:u~AMS will not mediate between agencies situation would be a national disaster!! Those of :"~ member? If I were that person, I would us concerned with the current national debate on SDI and the earlier (pre-ABM treaty) debate on be outraged. And rightly so. . . . Before anyone forms an opm10n on Mot10n 2, ABM deployment should realize that the reason this debate is even possible is only because of the theY should read : 1. Notices of the AMS 14 (1967) pages structure of our current single scientific enterprise. How is it that there are people both knowledgeable 778-784; 2. Notices of the AMS 15 (1968) pages 49-52; and concerned who bring the discussion into the 3. Notices of the AMS 15 (1968) pages open? These people, those who have helped me formulate my opinions, are usually not full­ 851-855; 4. Notices of the AMS 15 (1968) pages time employees of a DOD or DOE Laboratory. However, by virtue of their interactions with 985-986; they are knowledgeable and 5. Coding Theory: A counterexample to such a laboratory, G. H. Hardy's conception of applied mathemat­ understanding of the technical matters. Since they have great scientific stature and their access ic~ NoriDan Levinson, American Mathematical national laboratories is well known, they Monthly 77 (1970), pages 249-258. to the cannot be dismissed by a simple "ah, if only we In the first four short notes from the Notices, you of what we are accomplishing in we see a situation very similar to the current one. could tell The President and his Administration have un­ our secret laboratories." dertaken a controversial direction. The academic Suppose the only people who knew what coDliDunity, including some mathematicians, has went on in the DOD and DOE Laboratories were loudly objected. Certain people, in relatively high full-time employees of those laboratories who did places in the bureaucracy, e.g., Undersecretary not publish or participate in the academic, open Donald Hicks, make outrageous statements. So scientific environment. Then those people would wha: is new? But, more important, a more careful 1. be very fearful for their livelihood and be reading .of these four short items quickly dispels unwilling to promote a dialog on controversial the no!I.on that NSF is "good," "enlightened," weapons programs and 2. have no scientific ~c ..' wh1le. the DOD agencies are inherently evil, credence to give weight and respectability to . tJ-SCientific, etc. No, unfortunately. the world their criticisms and comments. No, the fact IS j' · ' son'mor e ~omp 1~ated. Fmally, a reading of Levin- is, our healthy democracy which, despite all the ' s article might remind us of the fundamental pain and anger involved, allows for these kinds 'act·· The qu es t'!On ·IS not which agency you credit of discussions, demands that we not have two segregated scientific establishments. onqu thet' bottom. . 0 f the fi rst page of your paper, the yo: 100 ~~-1s ther~ any intellectual content to As you see, I oppose both motions. Moreover, not wor · If there 1s, then whether you like it or should either pass, I would resign from the AMS ' someone will fi d c . at once. I sincerely hope that won't happen. control th t n a use 10r 1t. And you won't content t a use. If on the other hand, there is no Of 0 your work, why should anyone fund it? course I am 't· f research ~hich'" wn mg o the maligned XSF or DOD , I would do anyway, supported by there is su h · For those of you who don't believe .Tames Glimm won't undec tresearch· · · · · s t op read' mg now-you New York University rs and. There is oth Courant Institute Project-oriented er . DOD research: Specific, of Mathematical Sciences sona!) opinion cl po.sslbly classified. In my (per­ on the cam assJfied research does not belong The motions proposed at the San Antonio meeting ,;. · Pus and my · . "UUISter a c t umvers1ty would not ad- concerning NSF vs. DOD funding have been for the m on ract calling for classification As discussed in a thoughtful fashion in the February ore specific, project-oriented res~arch 1987 Notices.

619 There are four important facts that I hope Mathematicians, to the ext will not be obscured by the debate which may concerned with the problems of e~t that a..... r sc1ence ...., lit ensue. ety, usu all y pre.er to work upon th or~._. Mathematics is a part of science. Most major mental aspects of these problems se ll!c!st ~ branches of modern mathematics (e.g., group the­ as individuals vs. group research ~ch ~ ory, Fourier analysis, and differential equations) portant and should be discussed e 0lta lr! a.. not only had their origins in science, but have been than in the context of the San Ant~~ ~ continually enriched by their renewed contact with The proper balance between fund 1110 ~ science. The track record of the mission-oriented pl~ed r~search is ~so important, b~ental. Y8. ap. agencies in identifying topics from science ripe sk1ll will be reqmred to discuss this ~ for mathematical development is probably better that does not pit one group of m t~ 11 ~ than, and certainly is at least as good as, that of against another and, in fact, fragm a t ~ the NSF. ematics community. The central q~nstt}le ~ Mathematics is a part of society. We ac­ followin~. If.we ~re going to make pr: .100 18 til! knowledge this fact by soliciting and receiving fellow sc1en~1Sts mother disciplines, 0~t.o.~ society's support from the NSF as well as from about the Importance of mathematics .BOciel}. the DOD. Our society's real or perceived needs range benefit to society, etc., how can ~;ts ~ change from time to time. I recall a past emphasis that these promises are honestly and lPAii~ on urban planning, alternate energy sources, and made, effectively worked upon, and ;;jf"""'j the protection of our environment. I recall a war fulfilled? The answer is that it should~ on cancer and the moral equivalent of war for the distinction: fundamental vs. applied ~ energy self-sufficiency. Most of these problems that concerns us, but rather that fundamen~ have not been solved and are still appropriate and applied research effectively working ~ for mathematical modeling and problem solving. on common problems, from different perspectivl! The current discussion concerns the military, and should be our goal. · I suspect that major future concerns will in­ Mathematics has a unique joy and a beauty of clude economic competitiveness and modeling of its own. We know this as a fact and the scientifi< the AIDS epidemic. It is the political process community expects us to be true to ourselves an4 which sets these goals, and as knowledgeable and to insist upon it. This message should not be ~t concerned citizens, it is appropriate for us to in the discussion of other matters. participate as individuals in the political process. It is customary, and I think wise, for a profes­ sional society to maintain a certain distance from partisan politics.

620 ~atbern__a~~t~·!al~1~e~x:t~P~r~o~ce~s~s_I·n~g~------­ 1c S Palais ~dRichar ·

Guest Columnist follows that writers of technical documents should concentrate first and foremost on the logical . Ieasure this month to intro- ecJa 1 P f D' · I structure of their ideas (rather than their visual It is IllY sp Jumnist Leslie Lamport o 1g1ta appearance on a page), and that technical word do« as guest co oration's System R~search Center processing software should be optimized both to EqUipllleDt Co)n the computer SCience :ommu­ help the author in this pursuit and to facilitate the in Palo ~It?· well known for his penetratmg and reader's task in assimilating the author's ideas. pity, Leslie d1s. oncerning concurrency and the _,:.:no! stu JeS c . . . th 0£15..,... 1 that anse m provmg e cor- difficult prob ems s ·nvolving parallel processes. Winding Down of program 1 . rectness e is both longtime fnend and former It became apparent several years ago that we were To me, h h has over the years taught me far entering a period of rapid transition, from manual student, WI 0 ht him But to the world at large than taug · · f d to electronic, in the way many mathematicians !DO~ rha s best known for h1s carefully era ~e prepare their papers for publication. To ease he IS .pe ~ gJv popular document preparatiOn and mcreasm J the transition process, the editors of Notices a column on Technical .,.tem 1\'lEX· f h' 1 d'ff had the idea of starting .,- Leslie's article below is a re res mg y I .er- Word Processing, to serve as a clearinghouse for the ongoing controversy concernmg ent v1ew. f o h advice and information. I agreed to run the the relative merits of the WYSIWYG versus t e column with the understanding that it would M k p Language approaches to document prepa­ be temporary. My original estimate was that ~:on~ This debate will be familiar to readers of I could wind things up in about a year. Now. this column, or for that matter to anyone who nearly two years later, it appears that the recent has looked at even a small sample of the sea of frenetic pace may finally be slowing somewhat words that recently has been devoted to "Desktop and that developments in TWP over the next Publishing" in the popular press. Much of th1s few years have become relatively predictable. In debate has consisted less of reasoned argument the next few issues of Notices, I plan to give than of mindless testimonials and opinions by an update of the state of affairs in Macintosh partisans concerning how easy to use (or "user technical word processing, say a little about the friendly") they find their favorite system, or how new "Scholar Workstations" (just now becoming aesthetically pleasing they believe the final prod­ available and seemingly destined to dominate the uct is. academic personal computing field in the next But Leslie, who has thought long and hard decade), and finally make a proposal for a Micro­ about the problems of technical document prepa­ Computer Users Group, organized and run by ration, has something much more fundamental mathematicians for mathematicians. Along with and interesting to say on these matters. His basic many other important roles that such a MUG thesis is that technical papers are not written to could play, it could take over the functions of this be admired for their visual attractiveness, but column in a more permanent way. rather to communicate complex logical ideas. It

Document Production: Visual or Logical? Leslie Lamport

The Choice specifies the logical structure of his document will be called a logical system. Visual systems may be ~ument production systems convert the user's more convenient for short, simple documents like p~~tdhis keystrokes and mouse clicks-into a love letters or laundry lists. However, I will argue of cle ~o~ument. There are many different ways that logical systems are better for more complex ciass·~SI ~mg these systems. I will discuss a documents like books and technical articles. USer 1 catiOn based on the extent to which the rathe~e;:rds his document as a visual structure In a purely visual system. one would simply USer sp ~n a logical one. A system in which the paint a collection of pixels on the scre~n. The 'Will be ec;~es a VJsual description of the output word cat would be no different from a picture of ca ed a t'!sual system, and one in which he a cat --the user could change the shape of the t

621 as easily as he could change the shape of the tail a superscript and _ indicating a subsc . in a picture of a cat. Finding all instances of cat input would have been a partial! 1n~. '1\i and replacing them by dog would be as hard as partially visual description-logicai bOg!cal ~ finding all cats in a picture and replacing them subscript and superscript are denote~ Ill! with dogs. by co~mands rath~r than visually by 1 1~ In a purely logical system, one would enter but v1sual because 1t describes the r p ac~ only the logical structure of a document, describ­ (super- and subscript) rather tha~p~~nlati

622 .t. from one paragraph to the only the general form of the output -technical d trans! lOll · l dd report, journal article, etc.-while the system 111 awkWar f visual system can s1mp Y a oext. the .user 0 c~ between the paragraphs. But, makes the actual formatting decisions amount ....me verucal spa e accomplish? The awkward of paragraph indentation, amount of space above ,.... thlS spac . 'll . d ,..bat does. till there; the reader 1s st1 Jarre a displayed equation, etc. Visual systems give free transition lS 5 ce simply declares that there rein to the author's artistic tendencies, allowing e extra spa h . . h bV it. Th d t ansition and the aut or 1s e1t er him to format everything as he wishes. This · kwarr · is an aw bad a writer to fix 1t. would be fine if documents were meant to be laz" or too . . t f tOO J k d transitwn 1s a symp om o displayed on walls and admired for their aesthetic An aw watrured document; it can be fixed qualities, but they're not. rly struc A l . l a pOO turing the document. og1ca The purpose of writing is to convey ideas byre~ruc . . f onl Y the writer to thmk m terms o to the reader. The purpose of formatting is sys tern forcest's logical structure; 1t· d oesn 't g1ve· to make the document easier to read, not to the doc~lml e~on that he is accomplishing anything look pretty. Document design is a skill acquired hiJ1l the 1 USl with cosmetic formatting changes. through training and experience. A logical sys­ tem can apply the skill of a trained designer to the formatting of a document. A visual system Phosphors or Ink? forces the author to do his own document design, often with disastrous results. Most authors are Proponents of many visual systems b?ast that and make typographic they let the user work with an exact rephca of the not competent designers printed page. In fact, a serious drawback of many errors-formatting decisions that make the docu­ ment harder to read. visual systems is that they fore~ the user to work with an exact replica of the pnnted page. When A li\TE:;X user once complained because he the author is editing his document, he becomes a wanted to format an equation to look something reader. Like any reader, he wants to be presented like this: with the document in a format that is easy to read. A format that is adapted to the printed Vi : f(x;) > g(y;) (7) page is a poor one for a screen. Phosphors are different from ink, and a screen is not a piece of Formatting the equation in this way would have paper: it is not easy to read a picture of a printed been easy with a visual system; he would just page on a screen. have put everything where he wanted it. However, A computer screen differs from a printed li\TE:;X provides no easy way to do this. The user page in many ways, including resolution, width, just enters the equation and li\TE:;X formats it and the availability of different colors. Each of the way it wants. (It also assigns the equation these differences implies differences in the way number.) If the user declares the Vi to be part of information should be displayed. In addition to the equation, the result looks like this: the differences in the two media, the presence of a computer behind the screen also has striking Vi: f(x;) > g(y;) (8) 1mphcations. Consider the problem of pagination. One of the worst features of books is the splitting If he declares the Vi to come before the equation, of text across pages. It would be easier to read then li\TE:;X makes it part of the text preceding a document straight through from front to back the displayed equation. If lt were printed as a conti~uous scroll. We us~ This particular user found the formatting books rather than scrolls because they are easier of (7) more aesthetically pleasing than that of to pr?duce and because documents are not always (8), and I agreed with him. However, (7) is a ~ad m such a linear fashion. The computer offers typographical mistake. Equations are numbered : e best of both worlds. We can scroll through so they can be referred to in the text. When ext, avo!ding distracting page breaks. and still the reader encounters a reference to (7), it is not move easlly t o·- h . - - ,o auot er part of the document. It IS senseless t immediately clear from the formatting whether it complet . 0 use a computer to simulate a book, refers to the entire equation Vi : f(x;) > g(y;) or e ~lth page breaks. just to the inequality f(x;) > g(y;). It is clear two tA typlcal writer of technical material spends from the formatting that (8) refers to the whole 0 e1ght hou · · much of th . rs pe~ page wntmg. He spends equation and that, if the Vi were part of the the do at hme lookmg at the representation of number would cument on h' A . preceding text, then the equation force• th . lS screen. v1sual system that refer only to the inequality. The formatting of (7) ' ' e wnter to · h' · 'ormatted ~ · v1ew on 1s screen a verswn introduces an ambiguity, making the document or paper makes his task harder. harder to read. The purpose of document design is to display Lo ."Who Should do the Formatting? the logical structure of the document through its gJ,aJ syste formatting, thereby making it easier to read. A concerns f ms attempt to remove formatting user with no training in design is easily seduced by rom the author. The author specifies a visual system into formatting the document to

623 be aesthetically pleasing, often making it harder The second reason for specifyi £ to read. to overcome an inherent problem :~h01'1l!attiat~ A visual system can makes things hard even Embodying design principles int 1 colliPuters for a trained designer. An important principle difficult, and a designer will alway~ b~ro~ ~· of document design is uniformity-the same log­ a better job of formatting an individual able to dr. ical element should be formatted the same way than will a computer program th t doc\Uner;. throughout the document. It is difficult to achieve Achieving the highest possible quali~ he ~e>.'i.~ uniformity if the user must specify the formatting ability to make changes to the sys[ re~uireg th. of each instance of the element. For example, This will be a matter of fine tuning c~lll 8 .output all displayed quotations should be indented the things as page breaks and figure plac ang~ng sut:. . . l d ement Th same amount, but this is not likely to happen if IS a v1sua process, an one would l'k · . ·· the user must specify the amount of indentation system for doing it-one that allows\~ a viSUa. whenever he types a quotation. manipulate screen images of the final 0 te USer trJ If sue h v1sua. l ed" 1tmg 1s. ultimatelyU d PUt . · Must the User Ever Format? why not use a visual system in the firs~tr~bif: The answer is that the flea should not P~aee There are two reasons why the author may have dog. The changes will generally be ofwaghth, . h to specify formatting in a logical system. First, no m.mor. nature t .at. they are ~ot worth botherin•a logical system can provide a complete assortment With m a prehmmary versiOn intended 1 g of predefined logical structures. For example, small audience, nor for any document that ;r a a general-purpose system is unlikely to provide widely distributed. They will be done only w:t facilities for formatting recipes. The writer of producing the final copy for the publisher. en a cookbook must tell the system how to format Even using U.TE;X, which does not make recipes-hopefully, after consulting a professional the final formatting very easy, I usually spend designer. A logical system should permit the less than two minutes per page doing the final user to define his own logical structures and to formatting to produce camera-ready output. This specify how they are to be formatted. Several is insignificant compared with the two to eight different formats might have to be specified-for hours per page I spend writing. There is much example, one for a single-column page, one for more to be gained by making writing easier than a double-column page, and one for the computer by simplifying the final formatting task. screen. In a logical system he does this once; in a visual system he must format each recipe individually.

PARTIALLY ORDERED ABELIAN GROUPS WITH INTERPOLATION K. R. Goodearl (Mathematical Surveys and Monographs. Volume 20)

In the past decade a new branch of ordered Choquet simplices. and an expository discussion of algebraic structures has grown. motivated by various applications of interpolation group theory to K-theoretic applications and mainly concerned with rings and c• -algebras via ordered Ko. A discussion partially ordered abelian groups satisfying the Riesz of some open problems in interpolation groups and interpolation property. This book is the first source dimension groups concludes the book. in which the algebraic and analytic aspects of these Of interest of course to researchers in ordered bl interpolation groups have been integrated into a algebraic structures. the book will also be a valua e coherent framework for general reference. The author source for researchers seeking a background 10 provides a solid foundation in the structure theory of interpolation groups and dimension groups for interpolation groups and dimension groups (directed applications to such subjects as rings. operator unperforated interpolation groups). with applications algebras. topological Markov chains. posltl~~ areas to ordered K-theory particularly in mind. polynomials. compact group act1ons. or oth e useful High points of the development include the following: where ordered Grothendieck groups m1ght b characterization of dimension groups as direct limits of finite products of copies of the integers: the 1980 Mathematics Subject Classifications: 06, 46, 19. 16 double-dual representation of an interpolation group ISBN 0-8218-1520-2. LC 86-7876. ISSN QC76· 5370 with order-unit via affine continuous real-valued 358 pages (hardcover), 1986 lnd"rvidual member $41 List price $68, Institutional member $54. functions on its state space: the structure of dimension Code SURV /20NA groups complete with respect to the order-unit norm. as well as monotone sigma-complete dimension groups and dimension groups with countably infinite Shipping/Handling: 1st book $2. each add'l $1. 525 interpolation: and an introduction to the problem max. By air. 1st book $5. each add"l $3. SlOO;:~· 571. of classifying extensions of one dimension group by Prepayment required. Order from AMS. P.O. 11 another. The book also includes a development of Annex Station. Providence. Rl 02901-9930. orca portions of the theory of compact convex sets and 800-556-7774 to use VISA or MasterCard...... ,...

624 h. gton Outlook was 10 ~ M Hoffman Kenneth · 'ty Says "Thank You" the Office of Naval Research. He has generated A Communi . . each year highly visible events as p~~t of N~tional . h again, and w1th 1t comes Science Week, maintained a close ha1son w1th the \V1!11i ~eather. !S ::re many of us--sati~faction heads of math programs in federal agencies, and faaUhaf feehng_ of another academiC year a mpletwn . k has steadfastly driven home to "his" Board the ..;th the co . . ation of real time to wor ~· 'th ant!Clp b' d importance of collegiate mathematics education bleJ!ded WI . that "the year" is over com me for their concerns. and relax; _rehe~ the thought of all that must be John Polking inherited the mantle of .Jim with disquiet a~ er For those who are people- the summ . . I Infante at NSF, and he has worn it well, carrying done over. , t' e of farewells, of reappra1sa s, 1t Irn 't · · forward the program to increase funding for oriell ted ' . s a 11 d commencements. S o 1 IS m --~ f ndmgs ca e mathematical research with imagination and with auu 0. e as well as in academe. a steady perseverance which has earned him the Wasbin~~n, h t'me of year when the "rotators" TbiSISt e I · d respect of the upper management of NSF. One the people from our commumty, an result has been continued Foundation support of depart, 'k 't ho have spent one or more othersbei,W d years substantial increases for the DMS, which still . Washington to help lead an manage on leave m · accounts for 60% of the total federal support for the scientific research and educatiOn progra~s research in our field. .John has pushed to have hich help sustain us. The rewards for th1s NSF resources for collegiate mathematics located ~rt of public service are few. T~e mone~ary in his division. He has initiated a small mentoring ds are negative and the expenence gam:d program for talented undergraduates and plans, i_n ;::bly has a negative impact on status back m addition to his consistent articulation of the bas1c the home department. But much depen~s on the research needs of mathematics, for a substantial uality of the people whom our commumty sends NSF investment in the reformation of calculus. ~Washington for these stints. Unless we show An important legacy he has left is a five-year plan them that we value what they do, it will be very for more than doubling the Division's budget, difficult to count on having successors of the same building on the David Report and paralleling high quality. NSF Director Erich Bloch's plan for a similar This year a special thank you is due to doubling of the Foundation budget. three mathematicians, each of whom has put John Thorpe left his role as undergraduate in (at least) a two-year tour of duty, and each chairman at Stony Brook two years ago to accept a of whom has exercised strong leadership on our temporary position in the Science and Engineering behalf: Frank Gilfeather, who returns to the Education Directorate at NSF. He did this because University of Nebraska from his position as Staff of his conviction that University mathematicians Director of the Board on Mathematical Sciences must become actively involved with precollege (BMS) of the National Research Council (NRC); education issues. As John has said, he went to John Polking, who heads home to Rice University NSF and began to learn about the really hard from his post as Director of the Division of issues and the pockets of creative work going M~thematical Sciences (DMS) of the National on in the development of materials for school Science Foundation (NSF): and John Thorpe, mathematics. He used the knowledge acquired Deputy Director of the Materials Research and and his status as ranking mathematician in the Informed Science Education Division at NSF, who "Science Ed" directorate to create one of the first returns to the State University of New York at Stony Brook. NSF initiated programs in the reincarnation of the Directorate, his $5 million five-year program in the It The BMS grew out of the David Committee development of materials to incorporate compu~er Gi!feather, with ~~rt. F~ank his two chairmen, technology into the early years of mathematics · e Artm and Phil Griffiths has molded it into an effecti < r : education. ve •Orce tor presentmg analyses 1 of the Those of us carrying on in the small com­ :: of mathematical sciences in the national ~he munity of mathematicians who constitute the effort. He has shaped Ch ~c the National ever-changing Washington presence of the math­ !a!I&rman's Research Colloquium into an annual event th t b · . ematics community will feel very directly the inli . a nngs department chairs usable ormation on II h' . absence of Frank Gilfeather, John Polking, and their · · a t mgs Washmgton, gathers John Thorpe. We can find local and immediate mput o·11 I' d' dialogue po Icy 1rections, and promotes ways of expressing respect and gratitude for the lllany ad ~ong the chairmen. He has gotten the jobs they have done. It is to be hoped that U.S N arms of BMS functioning from the . a t~Isory!Dna! C . ' numbers of you out there in the community whose relates US omm1tte_e on Mathematics, which respect they value most will call or write them !.lathemat~·al rnat~emat1cs to the International to say that you appreciate their efforts on your the Air F Umon, to the panels that advise behalf. orce Office of Scientific Research and

625 News and Announcements

AMS Postdoctoral Research Fellowship Institute at Berkeley (1986- 1987) J research interests include the Alg~b~tb ' s clllr1t· The Society has awarded two Postdoctoral Re­ Quadratic Forms, Brauer Groups an~ T~eory r,: search Fellowships for 1987- 1988. The recipients K-Theory. He plans to use his MJS F A,gebr~ , are Richard Hain of the University of Washington visit the University of California at Bellkowship· .• and Bill Jacob of Oregon State University. er eley. RICHARD HAIN received his Ph.D. from the University of Illinois, Urbana, in 1980 where he studied under Professor Kuo-Tsai Chen. Since then he has taught at the University of Washing­ ton (1980- 1983), the University of Utah (1983- 1984), and State University of New York at Buffalo (1984- 1985) . He has been an assistant professor at the University of Washington since 1985. Professor Hain also received a University of Sydney Postgraduate Travelling Scholarship (1978- 1980). He intends to use his AMS Fellow­ ship over a period of two years, beginning with a visit to the University of Chicago next year.

BIUJ11o0

The AMS Research Fellowship fund Wili e; tablished in 1973 in response to the nero fm funds for postdoctoral research. The fellowsb ip:­ are awarded on the basis of mathematical m~r :· to persons who are five to ten years pilit th, Ph.D .. but below the academic rank of profe;;<•: (regardless of age). Fellows must be citizens t•: permanent residents of a country in North Anw~· ica. The awards are intended to support researr:. fe !lows for a pe riod of one year and, at pre;en: h ith an expen' carry a stipend o f $3 0 , 000 eac .w heid u::· allowance of $1 ,000. The competition was . . · t , ComnutH'i' ''· der the supervision of the Soc1~ Y su Willi"': Postdoctoral Fellowships, consJstmo of ~;enba :;, :. Richard Hain Helton, Philip C. Kutzko, Stephen Licch:.irman Georrre Lusztirr Kenneth C. MJllett ( BILL JACOB received his Ph.D. from Prince­ <> " ' c• t · n M. Beth Ruskai and Nancy K . .,tan"u · . ton University in June 1979, under the direction ' h AMS men: of Simon Kochen. He was an E. R. Hedrick Assis­ Because of the generosity oft e ff~r mofi tant Professor at the University of California, Los bership this past year, it was possible to 0n >fvera. . f first tune I - Angeles (1979-1981) and used an NSF Research than one fe llowsh1p or t'ne d b contritn:· Fellowship to visit the University of California. years. The fe llowship is finance . Y1 re'earct Berkeley (1981- 1982). In 1982 , he joined the t10ns. f rom supporters o f mathematica riated. a,·. faculty of Oregon State University, where he is supplemented with Society funds appro~tinuat:'': . currently an associate professor. cording to a matching formula. The c~1 depen1:' Professor Jacob visited the University of of the AMS Research Fellowship progr es £v•'f' · t receiV · California, San Diego, during 1984 - 1985 and is a on the contributions the Soc1e Y ntribute 1' member of the Mathematical Sciences Research member of the Society is urged to co

626 sor of Computer Science and Engineering, Mas­ sachusetts Institute of Technology (The computa­ Mathematical History tional structure of natural language); ALEXAN­ ial Celebration in 1988 pro­ DRE JOEL CHORIN, Professor of Mathematics, 'l'!le AMS Ce~~:y for the Societ~ to highlight University of California, Berkeley (Computa­ yjde8 an oppo tics has played m the devel­ tional methods in turbulence theory); GENE H. dll role mat~ema and technology. One activity GOLUB, Professor of Computer Science, Stan­ ford University (The solution of large sparse - t of sc1enceh. onnection is the publ" 1s h"mg of "l:::..! in t IS c • . . Th systems of linear equations); JOSEPH D. HAR­ ~- art. les of a h1stoncal nature. e >.---k and IC • • d t - . f uch manuscnpts 1s a epar ure RIS, Professor of Mathematics, Brown University -hli at1on o s · · h (The geometry of moduli spaces); NICHOLAS pu-cthe Soc1e · ty's traditional. mvolvement w1t (roll! . ted matenal and, therefore, as- M. KATZ, Professor of Mathematics, Princeton ~--... h-onen . a! . . University (Studies in arithmetic algebraic geom­ ~-froiD the mathematic commun1ty IS ~_:~ · acquiring historical works. The etry); JAMES LEPOWSKY, Professor of Mathe­ nq~~; ~0 interested in locating existing matics, Rutgers University (Studies in infinite­ SocietY · ts about twentieth-century mathe­ dimensional Lie theory); CHUNG LAUNG LIU, ~np and historical accounts, which could Professor of Computer Science, University of Illi­ ~18I1Srporated into a collection of reprints. A nois at Urbana-Champaign (The computer-aided JJemCO . d~' h" · t design of integrated circuits); MARC MANGEL, CIJIDIIlittee has been al?pomte ~or. t 1s proJe~ : Peter Duren University of Michigan, Chair­ Professor of Mathematics and Adjunct Professor . Richard Askey, University of Wisconsin; of Agricultural Economics, University of Cali­ :uta Merzbach, Smithsonian Institution. fornia, Davis (Dynamic models in behavioral and H you are planning to write or are cur­ evolutionary ecology); ALEXANDER NAGEL, Pro­ natly writing a .manuscript .on the ~is tory of fessor of Mathematics, University of Wisconsin­ mathematics, or 1f you have mformatwn about Madison (Studies in harmonic and complex analy­ aisting manuscripts, you are invited to contact sis); WILLIAM I. NEWMAN, Associate Professor Ms. Mary C. Lane, Director of Publication, of Planetary Physics, Astronomy, and Mathemat­ P. 0. Box 6248, Providence, RI 02940, for ics, University of California, Los Angeles (Studies further details about this activity. Information in astrophysical and planetary fluid dynamics); ll1d manuscripts may also be forwarded directly RICHARD A. OLSHEN, Professor of Mathemat­ to the committee members. ics, University of California, San Diego (Studies in modeling and sample reuse techniques); MARINA RATNER, Professor of Mathematics, University the fund. Since the deductibility of charitable of California, Berkeley (Studies in the ergodic contributions was essentially unchanged with re­ theory of semi-simple Lie groups); MURAD S. apect to the new tax laws, contributions to the TAQQU, Professor of Mathematics, Boston Uni­ Fellowship Fund are, in most instances, still tax versity (The probabilistic and statistical aspects deductible. Checks should be made payable to the of self-similar processes); JON A. WELLNER, American Mathematical Society, clearly marked Professor of Statistics, University of Washington "AM~ Research Fellowship Fund," and sent to the (Efficient estimation for semiparametric models). American Mathematical Society, P.O. Box 1571, A!mex Station, Providence, RI 02901. In recognition of the Centennial Celebration Rollo Davidson Trust ~the Society, the Council has approved changing the name. of the research fellowship program to Rollo Davidson Prizes have been awarded to Yu Amer1can Mathematical Society Centennial Yao-Chi of Zhong Shan University, Gangzhou, ;:Fe~lowship. This change will be effective and Zou Jie-Zhong of the Changsha Institute of g With the 1988-1989 program. Railways (joint award) and to Andrew Carverhill of the University of North Carolina. Yu Yao-Chi and Zou Jie-Zhong received the Guggenheim Fellowships Awarded award for their contributions which together led The Johns· to the proof of D. G. Kendall's modified version of lion h unon Guggenheim Memorial Founda- Davidson's conjecture concerning the oscillation in its ~an~~';llced the award of 273 fellowships of p-functions. Andrew Carverhill was cited for Guggenh ~ t lrd annual competition. The new his work on the flows of stochastic dynamical sis of une!m Fellows were appointed on the ba- systems and their Lyapunov exponents. usually d" 1· · h . . Plat and IS mgms ed ach1evement m the The first Rollo Davidson Prize was awarded Plisiunent exc~h~ional promise for future accom­ in 1976. Since then eighteen prizes have been ~ ~ th IS year's list of awards includes awarded. The work of the Trust is supported by Nam e mathematical sciences. royalties and individual donations. Communica­ ... t . es of these re . . t h . . . . "'' UtionaJ aflir . Ciplen s, t e1r positiOns, m- tions relating to the work of the Trust should be Ill!: ROBERT 1 ~ 1 ons, and their proposed studies addressed to its Secretary, The Bursar, Churchill · BERWICK, Associate Profes- College, Cambridge, CB3 ODS, England.

627 A portion of this year's meet· to "'lEX for the :g ~ Mathematical will be devoted News from the However, the overall program will ~tiea: Sciences Institute include sessions on issues of imp]~:t~ to Cornell University hardware and software support; lEXentatiOn: and METRFONT; a macro wizards' ' WEB. Nerode Appointed Director of MSI presentations on output devices and drr?lllldtabie: . . bl Ivers·,.,_ Ani! Nerode has been appointed as the new mercmlly ava1 1a e macro packages; and '~ director of the Mathematical Sciences Institute of the latest TEX products, software andexhihit! at Cornell University. MSI operates primar­ devices; plus many other topics of cu;rent OUtput cOI!tern ily under a contract from the Army Research to the TEX cornrnumty.. AI so, this year £ ... Office to conduct Mathematical Research in will . ~e available for cop~ing floppies, :u:; four areas: Applied Analysis, Physical Math­ partiCipants may share the1r '.!EX wares with ead! ematics, Numerical Analysis and Computing, other. and Statistics and Applied Probability. Ani! In addition to the programs presented at their Nerode succeeds Geoffrey S.S. Ludford who annual meeting, TEX training courses are offend passed away in December 1986 after a short at universities throughout the U.S., and this year illness. the TEX Users Group is expanding its educational After completing his graduate studies at programs to England, The Netherlands, and Nor. Chicago, Ani! Nerode was a postdoctoral fellow way. Courses being offered include Beginning. at the Institute of Advanced Study at Prince­ Intermediate, and Advanced 'lEX, Macro Writing. ton University and then a visiting assistant and Output Routines. professor at The University of California at Requests for additional information about the and Los Angeles. He carne to Cornell in 1959 meeting program and courses should be dire~:ted became Chairman of the Mathematics Depart­ to TEX Users Group, P.O. Box 9506, Provi­ ment in 1982. Professor Nerode's major areas of dence, RI 02940, U.S.A. Telephone: 401-272-9500. research include Mathematical Logic, Recursive extension 323. Function Theory, and Theoretic Computer Sci­ ence. Much of his work has been accomplished through consulting, project directorships, re­ Applied Mathematicians search grants, and research contracts with the to Hold International Meeting Department of Defense, The National Security Agency, The Institute for Defense Analyses, Applied mathematicians will convene on a world­ The Advanced Research Projects Agency, The wide basis for the first time from June 29 to National Science Foundation, The Environmen­ July 3 at the First International Conference on tal Protection Agency, and numerous industrial Industrial and Applied Mathematics (ICIAM87) and nonprofit research organizations. in Paris, France. ICIAM 87 marks the ~t tm:e MSI supports research through an aggres­ that the commonality of applied mathemat~cs will sive program of Cornell faculty support, grad­ be placed on view for an international aud1ence. uate fellowships, postdoctoral associates, and Over one thousand papers from fifty-s~~oun­ senior visitors. Additionally, MSI conducts tries are scheduled along with sixty-nine minJSYID" on topics of workshops throughout the year Posia , each featuring three or four speakers.. ro WM current interest to the mathematical research Four organizations are s~onsonng lied about any of these community. Information 87: the Soc~ety f~r Indu.stnal ~da A:ieti be obtained by calling MSI at programs can Mathematics m PhJ!adelph1a, PA, 11 ·e11es. 607-255-8005, or writing: MSI, 294 Caldwell de Mathematiques Appliquees et In usn d'• f fii Angewan " Hall, Cornell University, Ithaca, NY 14853. Palaiseau, France; Gesellscha t r Gennany: Mathematik und Mechanik, Ha~bur~ its Appli· and the Institute of MathematiCS an B.... :n E Great n ...... · cations, Southend on Sea, ssex, ~ ll()ll'iDg 'lEX Users Group's Annual Conference Invited presentations will cover the 0 Courses and Regional topics: . 1nurnefl~ dynamics: The interactwn ° d mat'· The TEX Users Group's Annual Conference will • Vortex University of Washington, Seattle, cal analysis, scientific computi~J' ~c­ be held at the J · MaJ a, 17-28, 1987. In addition ematical theory, Andrew Washington, August space PI- to its three-day meeting, August 24-26, several University, U.S.A.; i~ a~r~. courses will be offered: Beginning TEX • Numerical flow simulation TEX ete Avi&w-• August 17-21; Intensive Beginning/Intermediate dustry, P. Perrier, Aerodynan;lc Dassault/Bregu 1'E;X, August 17-21; Macro Writing, August 27- Avions Marcel 28; and Output Routines, August 27-28. (All Saint-Cloud, France;. h matics ar instruction is applicable to using TEX on the • Aeronautical acoust1cs: . Mat ~!em. D. (;. industnal pro · Macintosh, PC's, and mainframes.) plied to a major

628 tment of Applied Mathe­ Cri~hton. dD;h:Oretical Physics, Cambridge Mathematical Sciences Research Institute IIJ8~1CS ~t United Kingdom; umvers• y, . Berkeley . /(variate splme?, Carl de Boor, rvhat IS a mu I . U S A . During 1986-1987, MSRI is featuring a large • "'. . of Wisconsm, · · ·' t:o1vers• 1Y . . program in arithmetic algebraic geometry. d differential equatzons, Michael Among the advances which have attracted at­ , To!X'IogyOxfian rd University, United Kingdom; tention during the year is the work of Kenneth Auyah. o . . . { mobility in bzologzcal systems, A. Ribet of the University of California, one of 0 the organizers of the 1986-1987 program. • Model1lmgU iversitiit Bonn, Federal Republic W.At, n Ribet's advance concerns irreducible mod of Germany; p representations of Gal (Q/Q) which arise h t. processes and image analysis, R. from classical cusp forms of a certain type • Stoc as IC Umvers1te• • , P ans- . S d 0 Azenco tt , u , rsay, (newforms of weight 2 and trivial character in France; the language of Atkin-Lehner). Let f be such a St hastic control theory, K. J. Astriim, De- cusp form, let N be its level (or conductor), and • ~ment of Automatic Control, Lund Insti­ let p be the corresponding representation. One tute of Technology, Lund, Sweden; can attach to p a "level" L, where L divides N. According to conjectures made by J.-P. , Algorithms for. n~nlinear equations and u~­ Serre, there should be a cusp form g of level constrained opt1m1zatzon, M.J.D. Powell, Um­ L which gives the same representation as f. versity of Cambridge, United Kingdom; Ribet proved this conjecture in a large class of , The multigrid method: Algorithm, software situations, including that for which N is square and new developments, W. Hack busch, Chris­ free. tian Albrechts University, Kiel, Federal Re­ Ribet's work completes a program begun public of Germany; by G. Frey of Saarbrucken, concerning Fermat's Last Theorem. The final result is that Fermat's , Model driven simulation, J. Hopcroft, Cornell Last Theorem is a consequence of the generally University, Ithaca, NY, U.S.A.; accepted conjecture that all elliptic curves over • Lattices and algorithms, Laszlo Lovasz, Math­ Q arise from cusp forms. The link between ematical Insitute, Eiitviis Lorand University, solutions of Fermat's Last Theorem and elliptic Budapest, Hungary; curves was found by Frey: beginning with a nontrivial solution of aP + bP + cP = 0, Frey • Mathematical modeling and numerical anal­ writes down an elliptic curve E over Q whose ysis of problems with one or several small p-division points give a representation p which parameters in solid mechanics, Philippe G. has conductor 2. If E comes from modular Ciarlet, Universite Pierre et Marie Curie, forms, then p does; by Ribet's theorem, p Paris, France; then comes from a cusp form of level 2. A • Mathematics and computing, P. D. Lax, contradiction arises because there are no level Courant Institute of Mathematical Sciences 2 newforms of the type in question. New York University, U.S.A.; ' Ribet's main ideas were worked out in a preliminary form at the Max-Planck Institut • Mathe~atics and tomography, F. Natterer, in Bonn, prior to the beginning of MSRI's Westfal1sche Willems University Munster, number theory year; then they were amplified Federal Republic of Germany; ' and clarified in Berkeley. 1 ~ a duality relation in the theory of or­ The plans for 1987-1988 at MSRI are nearly .ogonal polynomials and its application in complete as this is being written. A total of ~:al processing, Y. Genin, Philips Research approximately 150 visitors are expected: about oratory, Brussels, Belgium. 75 for the program in Classical Analysis, 55 for the program in Representations of Lie Groups, !evenConre.rence presentations are divided into and 20 in mathematics at large (nicknamed Analys:a.Jr ca~egories: Applied Mathematical "Area III"). The year will conclude with ami­ and Si~a! CI~nhfic ~omputing, Control Theory croprogram on the Structure of Banach Spaces ApPlied Prob ~~~essmg, Discrete Mathematics, running from June 27 to July 15, 1988. of Natural 8 ~ IIty and Statistics, Mathematics In 1988-1989, the two programs will be Ciences, ~ts. and Software and Hardware Combinatorial Group Theory and Geometry, and Symplectic Geometry For prelimin and Mechanics. !ration inform t' ary programs containing regis- Again there will be a microprogram topping dustrial & A 8 _Ion, contact the Society for In­ off the year: Noncommutative Rings from July South 17th ltPhed Mathematics 14th Floor 117 5 to July 19, 1989. For 1989-1990, one program Telephone· 21 ~e5e6t, Philadelphia,' PA 19103-S052. is set: Logic. •

629 Newly Elected Memb Request for Photos of the National Academy ore:. In conjunction with the Centennial of the Amer­ The following mathematical 8 . . lellr.ta I d ClentJsts ~- ican Mathematical Society, which is to be cele­ e ecte to mei?bership in the U 1111lt llf!t brated in Providence in 1988, the AMS would Academy of Sc1ences: ARMAND B.S. N~ like to set up an exhibit of group photos from tute for Ad':anced Study; DANIEL GOREt, ~ meetings and similar items of interest. Rutgers Umversity; and ROBERT E01\ENS'I'tt\ If anyone has memorabilia of this kind AT&T Bell Laboratories. BENOIT. TAJUA.I which they would like to give or loan to the DELBROT, IBM Thomas J W t B. MA.I. C · a son 11--. AMS, please write to William J. LeVeque, enter, was elected a foreign . '""""C!! Academy. assoc1ate

of humans, for which some investigators SOME MATHEMATICAL postulate pacemaker systems with two QUESTIONS IN coupled oscillators, while others propo!f single oscillator models. Other analyses BIOLOGY-CIRCADIAN focus upon the activity patterns of RHYTHMS small vertebrates or upon anatomical data and physiological recordinga. Gail A. Carpenter, Editor The mathematical formulations and analyses utilize nonlinear dynamical The articles in this collection are based systems, stochastic models, and computer on lectures given at the 20th Annual simulations. The articles in this volume Symposium on Some Mathematical discuss, analyze, and compare these Questions in Biology, held in May various experimental, theoretical, and 1986, and sponsored jointly by the mathematical approaches. AMS, the Society for Industrial and Applied Mathematics and Section A 1980 Mathematics Subject Clas•iJicslioftl' of the American Association for the 92, 65 ISBN 0-8218-1169-X, LC 86-072815 Advancement of Science. For the ISSN 0075-8523 987 past thirty years, due particularly to 288 pages (softcover), January 1 S29 the fundamental work of Pittendrigh, List price $36, Institutional roembtr ' Aschoff, and Wever, theoretical analysis Individual member $22 gNA of circadian rhythms and sleep have To order, please specify LLSCI/l gone hand in hand with experimental and clinical studies. Circadian rhythms have been investigated at levels ranging from cell fragments to humans, Shipping/Handling: 1st book $2, ~ ead> from biochemistry to behavior. This add'! $1, $25 max. By air, 1st book ' experimental diversity is reflected in add'! $3, $100 max. olD AltfS, a diversity of modeling approaches, Prepayment required. Order fr f()VidellCf, several of which are represented in this P.O. Box 1571, Annex Station, p 4 to use collection. One class of models focuses RI 02901-9930, or call 8()()-556-777 on the circadian sleep and activity cycles VISA or MasterCard.

630 ·~~I~S~c:ie~nc~e~F~o_u_n_d_a_ti_on______Natt~a -;;s 8 Reports

F-NATO Postdoctoral Fellowships students to incorporate teaching or research as­ NS Awarded sistantships into their education during periods in which they are not receiving their fellowship h announced the award of fifty­ stipends. fbe NS~ science Foundation-North Atlantic sf The new fellows come from 48 states, the :::ag:;anization (NATO) Postdoctoral Fel- District of Columbia, and Puerto Rico. Of the kJWShips in Science. . 505 award offers, 178 were made to women. By The fellowships are to young sci- awar~ed scientific discipline, the distribution of awards was . and engineers for full-time postgra~ua~e as follows: 109 in engineering; 22 in mathematics; mudytistS b ad at institutions and laboratones m 51 a ro . . . · h 15 in applications of mathematics; 34 in computer 'iATO countries or m ne1ghbormg countnes t at science; 37 in physics and astronomy; 37 in ~rate with NATO. . . The four recipients in the mathematical sci- chemistry; 17 in earth sciences; 136 in biological are listed below (institutions in parentheses sciences, including biochemistry; and 98 in the ~he current institution, those outside the social sciences and psychology. ~theses are those at which the fellowship will The recipients in the mathematical and com­ be htld): BRUCE J. BAYLY (New York Univer­ puter sciences are listed below (institutions listed sity) University of Cambridge, England; DEB­ in parentheses are those awarding bachelor's de­ ORAH M. GORDON (Harvard University) Uni­ grees, those listed outside the parentheses are vmity of Oxford, England; PAUL F. MENDLER those at which graduate study will be pur­ (Cornell University) Manchester University, Eng­ sued): ANNAMARIA BEATRICE AMENTA (Yale laud; and JUAN C. MIGLIORE (Drew University) University), University of California, Berkeley; University degli Studi di Trento, Italy. THOMAS D. ANDREWS (Yale University), Mas­ sachusetts Institute of Technology; JAMES DAVID Graduate Fellowship Awards ASPNES (Massachusetts Institute of Technology), Announced Massachusetts Institute of Technology; ANDREW B. BAKER (Harvard University), Stanford Uni­ Five hundred and five outstanding college students versity; ANDREA LOUISE BERTOZZI (Prince­ ~ being offered fellowships for graduate study ton University), Princeton University; AVRIM m the natural and social sciences mathematics LOUIS BLUM (Massachusetts Institute of Tech­ llldengineering, the National Scie~ce Foundatio~ nology), Massachusetts Institute of Technology; l!ttntly announced. JEFFREY STEWART BONWICK (University of . Nearl! 4,7.30 students submitted applications Delaware), Stanford University; INGRID KARIR mthe nationwide competition for the NSF Grad­ BUSCH (Hillsdale College), Johns Hopkins Uni­ ~te F~llowships, which are awarded on the basis versity; CLARA SOPHIA CHAN (Harvard Univer­ ment. sity), University of California, Berkeley; DAVID t~anels of scientis.ts, assembled by the Na­ ARI CHANEN (Massachusetts Institute of Tech­ of&· Research Council of the National Academy nology), Massachusetts Institute of Technology; f Iences, evaluated the applications· final selec­ DOUGLAS ANDREW CHIN (University of Texas, re:,:re made by the NSF. In addltion to the Austin), University of California, Berkeley; JEF­ arable J a'_Vards offered. the NSF awarded Han­ FREY MICHAEL CONROY (University of Califor­ of their en~Ion .to 1,212 applicants in recognition nia, San Diego), Stanford University; GREGORY tareers. po entia! for scientific and engineering ALAN DECROIX (Miami University) Rutgers University; IAN HEPBURN DINWOODIE (Mon­ The new £ 11 h. 112 300 e ows Ips provide a stipend of tana State University), Northwestern University; ~ ratep~r $year for full-time graduate study. ADAM LAWRENCE EPSTEIN (Harvard Univer­ linuation ~sll 100 .Per month higher than for con- sity), Stanford University; OREN WILLI ET­ 14xability ~f ows m order to cushion the effect of ZIONI (Harvard University), Carnegie-Mellon Uni­ ~-of-ed ~ew· fellow's stipends. An annual versity; MICAH ELTOR FOGEL (University of hi..~ ucat10n all ·""'~~by the NSF . o:vance of $6,000 is also pro- Washington), University of California, Berkeley; tht U.s. instit f m heu of all tuition and fees to BJORN N. FREEMAN-BENSON (University of NSF G adu Ion selected by each fellow. Washington), University of Washington; ERICH ~ r uate Fell lh..i ..ate nonpr fit ows may attend any ap- JAY FRIEDMAN (Rose-Hulman Institute of Tech­ "'511er educati 0 U.S. or foreign institution of nology), Cornell University; PETER STEWART ~ Years ofon. Each fellowship is awarded for GEMMELl (Yale University), University of Cal­ lllay he used graduate study. The fellowships ifornia, Berkeley; SANJAY GHEMAWAT (Cornell overafi . . ve-year penod to permit University), University of California, Berkeley;

631 JOHN ROBERT GILLETT (University of Wis­ nia, Berkeley), Massachusetts Institu consin, Madison), Stanford University; ROBERT nology; KEITH WILLIAM SAINTS ( te "\I. LAWRENCE GIVAN, JR. (Stanford Univer­ College), New York University· RI~~ sity), Carnegie-Mellon University;• THOMAS D. SCHWARTZ (University of C~Iifo :-""~' £t-. GODDARD (University of California, Berkeley), geles), Stanford University; ELIZA~La. At. University of California, Berkeley; AARON JAY SCHWERER (Harvard University) N \1 C'-l GOLDBERG (Harvard University), Stanford Uni­ vers~ty; RO~ERT FRA~KLIN SHERB.e;' ~~ versity; ALBERT JAMES. GOODMAN (Grinnell versity), Prmceton Umversity; SEAN~-~ College), Massachusetts Institute of Technol­ SMITH (Princeton University), University~ ogy; CHRISTOPHER PRINCE GRANT (Brigham burgh; ELIOT KEMP SMYRL (University f4 Young University), Brigham Young University; fornia, Berkeley), _Brown_Dniversity; Jon~~ CAROLYN M. HAIBT (Princeton University), TIN STEINKE (Rice Umversity), Prin ~­ Massachusetts Institute of Technology; N OMI versity; DAVID RICHARD STEINSALTZ~~~ LENORE HARRIS (Princeton University), Stan­ versity), Princeton University; LAUREL L '" ford University; DAMON LANE HART (Rice Uni­ STELL (New Mexico Institute ofMininganct.: versity), University of Texas, Austin; LESLIE nology), Cornell University; SARAH R ANN HENDERSON (Rice University), Carnegie­ THOMAS (Massachusetts Institute ofT~ Mellon University; DAVID CHI-CHIRG HO (Har­ Stanford University; DANIEL ROBERT TllETrri vey Mudd College), New York University; BRIAN (Rose-Hulman Institute of Technology) Drum T. HOWARD (Northwestern University), Stanford University; ERIC PAUL TUIETMEYER (Ma. University; DUNCAN GILCHRIST HUDSON, Ill sachusetts Institute of Technology), Univeraityi (University of Texas, Austin), University of Texas, Illinois, Chicago; RANDALL HOWARD WWM>! Austin; REID CHARLES HUNTSINGER (Univer­ (Harvard University), Stanford University; DA\'ID sity of Illinois, Urbana-Champaign), Harvard ISAAC ZUCKERMAN (Harvard University) b. University; ANDREW JAMES IVERSON (Univer­ ford University. ' sity of Utah), New York University; DOUGLAS STEPHEN JUNGREIS (Harvard University), Uni­ versity of Chicago; PHILIP THOMAS KEENAN Presidential Young Investigators (Massachusetts Institute of Technology), Uni­ Competition 1988 versity of Chicago; TIMOTHY BRIAN KEENCE (North Carolina State University), University of The NSF is now accepting nominations for e1r California, Berkeley; BRUCE ALAN KLEINER of its most prestigious awards, the Presidential (University of California, Berkeley), University of Young Investigator award. The deadline b California, Berkeley; AMY KATHERINE KRAM­ nominations for the 1988 awards is October~ MIN (Michigan State University), Stanford Uni­ 1987. versity; GREGORY JOHN KUPERBERG (Harvard The awards, which fund research by OOity University), Princeton University; GUY CHRIS­ at or near the beginning of their careen. ~ TIAN LARSON (Brigham Young University), Up­ intended to help universities attract and main psala, University of Sweden; JULIA LAETI­ outstanding young scientists and engineen wiMI TIA LAWALL (Oberlin College), Carnegie-Mellon might otherwise pursue nonteaching careers. University; MELANIE LEWIS (Cornell Univer­ From 1984 to 1987, there have been32'1 sity), University of Washington; DAVID Es­ from 182 nominations in mathematics out . 1 LEY LORG (California Institute of Technology), total of 700 awards from almost ~,600 nc;;; Stanford University; MONICA ANN MCARTHUR tions. Among the fiel~s ho~ m ~e e. (University of California, Los Angeles), Univer­ Mathematical and Physical Sciences ~ sity of California, Berkeley; DOUGLAS WAR­ mathematics has received 18% of the ematiJl REN MCBETH (University of California, Berke­ with awards over a broad range of math ley), Cornell University; FRANCESMARY MOD­ disciplines. . "bility bllf UGNO (Cornell University), Carnegie-Mellon Uni­ Some of the rules regarding ehgJ f the­ versity; AMY FAY MOORMANN (North Car­ been revised. Below is a list of some 0 olina State University), Massachusetts Institute important features of the awards.. !JaSefl" of Technology; CATHERINE ELIZABETH MY­ Award size. The awards provide~ ~ ERS (University of Delaware), Carnegie-Mellon of $25,000 per year for 5 years. -dollar IJIIil. University; PATRICK FLYNN 0 'NEILL (Uni­ the NSF will match, on a dollar-for . dustr1 rt versity of Arizona), Stanford University; PA­ donations of up to $37,500 fr~rn m(~ TRICIA LYNNE PERKOWSKI (Rice University), from nonprofit private foundatiOns. eJSititl rt University of Maryland; CHRISTINE PIATKO those associated with particular uniV (New York University), Cornell University; KEN­ university systems). ~ !111 rJ NETH STUART RICHARDSON (Rice University), cJJ. The donations may be in the a:ent Rice University; JON GARY RIECKE (Williams ~ College), Massachusetts Institute of Technology; grants, research contracts, or pern: be of •..!! equipment. The equipment mus t the rfJP"­ JOHN TAYLOR ROMPEL (University of Califor- and quality necessary to carry ou

632 dee and would be valued on of United States doctoral scientists and engi­ f the awar ~ o . fa'r market value. neers by using surveys conducted by the National dJt baSis of ,1ts \ minees must have (or have Academy of Sciences/National Research Council. £UglbllitY· · 0ure-track faculty position at Recently, the NSF published highlights from a f) a ten . d 111 offer 0 . .t tion and must be nommate 1985 survey on employment trends among science •• eligible Jnst.J u n·here they are (or will be) and engineering (S/E) doctorates, and the follow­ ... · titutwn " · by the 108 This rulr is different from previous ing summarizes some of the data and conclusions !lllployed. . · s may no longer be made by the of interest to the mathematics community. onunatwn · d h' h l'fiiS: 0. h thr nominee receive 1s or er The total number of S/E doctorates employed institution w ere in all sectors rose to 400,000 in 1985 at an annual Ph.D. add't' a nominee must have begun his rate of 4.1% during the period 1983-1985. During In firstI JOn.tenure-track facu I ty pos1't' 1on a ft er the same period, the number of mathematical or ~er 1984 and must have held a tenure-track scientists employed grew about 1% per year and AP~. 30· ·ger than 3 1/2 years. If the nominee about 3% per year from 1973-1983. The total """itJOnnO 1on k . . h ,..... t held a tenure-trac pos1tJon, e or number of mathematical scientists employed was baS not ye nominated by an ms· t't1 u t'10n w h'1c h 16,000 in 1985. she mus t be k · · bas offered the nominee a tenure-trac positiOn to The computer specialties continued to grow btgin before October 1, 1988, and he o~ she must at a faster rate than other occupations: between h ld that position when the award begms. 1983 and 1985, the number of computer specialists 0 Nominees must be United States citizens or with doctorates grew at a rate of 10.9% per year, permanent residents. . . more than twice the overall rate of 4.1% noted £Jigible institutions. To make a nommat10n, above. For the period 1973-1983, the growth rate an institution must offer a bachelor's, master's, was even larger, more than 16% per year. or doctoral degree in any field supported by the There were several variations in growth rates ~SF. among the various work activities of S/E Ph.D.'s. For more information, call the Research Ca­ During 1983-1985, S/E Ph.D.'s reporting research reer Development program of the NSF, 202-357- and development (R&D) as their primary activity 9466. and ask for the program director of the PYI increased in number to 133,000 in 1985 at an awards. A pamphlet containing the revised rules annual rate of 0.3%. The number engaged in was released in May of this year. teaching grew at an annual rate of 1.6% during the same period to 112,000 in 1985. New DMS Director Announced The largest growth rate among the various work activities occurred in sales and professional Judith S. Sunley has been named Director of the services. In this area, employment of S/E doc­ ~SF's Division of Mathematical Sciences (DMS). torates rose at an annual rate of 10.7% during Having served as Deputy Director of the DMS 1983-1985 (from 30,000 to 36,500). This area has s~ce 1984, Sunley will replace John Polking, who also increased over the long-term: in 1973, 3. 7% t.lllleave the NSF in July. of S/E doctorates were employed in sales and Sunley received her Ph.D. in mathematics in professional services, compared to 9.1% in 1985. 1971 from the University of Maryland, and for In academia, the number of S/E doctorates t?e. nex~ ten. years was on the facurty of American primarily engaged in R&D activities increased l~Jvers1ty m Washington, DC. She originally during 1983-1985 at an annual rate of 5.4%, JOmded the NSF as Program Director for Algebra reaching 61,000 in 1985. During the same pe­ an Number Theory in 1980. riod, the number primarily engaged in teaching increased in 1985 to 110,000 at an annual rate N~F-CBMS Regional Conferences of increase of 1.8%. The report states that m the Mathematical Sciences the more rapid increases in R&D employment in A finn date h academia reflect "the growth in academic R&D regional f as now been announced for the expenditures, which increased (in constant dol­ of.\fultiv~~n erence on Theory and Applications lars) over 6% per year during 1983-1985." The This con~ late Sp_Lznes, Charles Chiu (Lecturer). report attributes the relatively slow growth in the at Howar~re~c: Wll~ be held August 10-14, 1987, number reporting teaching as a primary activ­ contact Dani~lver~ 1 ~Y· For further information, ity to "a number of factors, including changes in eJnatics H Wilh.arns, Department of Math- demographic conditions and enrollment patterns." . oward c · · 20059. Tel h mvers1ty, Washington, DC During 1973-1985, the age profile of Ph.D. ep one: 202-636-6830. scientists and engineers in academia changed con­ siderably. In 1973, 76% were under 50 years of age Ernployment of Ph.D. Scientists and 27% were under 35. In 1985, 67% were under s· and Engineers 50 and only 13% were under 35. The report says thee 1973 the NSF that "the shift toward older age groups reflects, e derno~aph· has collected information on in part, the relatively low growth in employment lc and employment characteristics in educational institutions."

633 The rate of growth in employment of 8/E period. Also, employment of PhD . doctorates accelerated in academia, but slowed in engineers in industry has been.~ sc 1~tiatallld industry. In academia, employment of this group rapidly since 1973 than overall Ph Dcre881l1C ._ increased during 1983-1985 at a rate of 3.9% per There have also been chang~ .· empl~ year, up from 2.4% per year during 1981-1983. ties in industry. In 1973, 45% oft~ Workacti,j. By contrast, the annual rate of increase in in­ in industry reported R&D as theirOSe -~ dustry during 1983-1985 was 5.3%, down from tivity. By 1985, the proportion hal~ at- 7.0% during 1981-1983. However, the report 39%. The report states that a greater ~lined. to states that "it is too early to determine whether of these people were engaged in "a c p b~~ [there has been] a trend reversal," and notes of activities, _incl~ding production ~~ ~ that "during 1973-1983, there was a pronounced control as their pnmary activities." The Quality shift in relative employment from academia to also notes that "to a large extent the d :n industry." For example, the proportion of 8/E the proportion reporting R&D as their ec . 111 Ph.D.'s in academia declined from 59% in 1973 to activity reflects shifts in employment awp": 53% in 1985, whereas the proportion employed in R&D-intensive fields." ay industry grew from 24% to 31% in the same time

~~~~~~~~~~~~~~~~~~~3§~\ 1. Directed towards mathematicians APPLICATIONS OF working in algebraic K-theory, algebraic ALGEBRAIC K-THEORY geometry, and algebraic number theory, this volume is also of interest to the TO ALGEBRAIC algebraic topologist. The reader should GEOMETRY AND be familiar with basic K-theory and interested in its applications to other NUMBER THEORY areas of mathematics. Spencer J. Bloch, R. Keith 1980 Mathematics Subject Classificationa: 18, 16, 19 Dennis, Eric M. Friedlander and ISBN (Set) 0-8218-G054-7; (Part 1) Michael R. Stein, Editors 0-8218-5055-5; (Part 2) 0-8218-5056-3, LC 86-7904, ISSN 0271-4132 These two volumes of forty papers 424 pages (part 1); 432 pages (part 2) ( softcover), 1986 present a state-of-the-art description Set: List price $62, Institutional member of some of the exciting applications of $50, Individual member $37 algebraic K-theory to other branches Part 1: List price $35, Institutional member of mathematics, especially algebraic $28, Individual member $21 geometry and algebraic number Part 2: List price $36, Institutional member $29, Individual member $22 theory. As the proceedings of a 1983 To order, please specify CONM/55NA (set), AMS-IMS-SIAM Joint Summer Research CONM/55.1NA (part 1), CONM/55.2NA Conference, they include current and (part 2) important work by some of the best ------·- researchers in the field. The diverse Shipping/Handling: 1st book $2, each scope includes the following topics: add'! $1, $25 max. By air, 1st book $5, each the matrix/vector bundle tradition of add'! $3, $100 max. concrete computations for specific rings, Prepayment required. Order from AMS, the interaction with algebraic cycles, and P.O. Box 1571, Annex Station, Providence, the generalization of the regulator map RI 02901-9930, or call 800-556-7774 to use for units in an algebraic number field to higher K-groups of varieties over number VISA or MasterCard. fields. Of particularly high research value are the ideas of Beilinsonon, which are presented here for the first time, the work of Merkurjev and Suslin relating K-theory to the Brauer group (as reported by Merkurj~v and Wadsworth), and the papers by Kato on algebraic cycles.

634 For Your Information

~ Ohio • A lecture for undergraduates entitled "The Combinatorics of Soccer Balls" was presented by Terry McKee at Wright State University. • A special college-wide symposium featuring three outside speakers was held at Denison University in Granville to celebrate the 300th anniversary of Newton's "Principia." Mathematics Awareness Week 1987: Missouri A Nationwide Success • A thirty second television spot was prepared for Kathleen Holmay cable and local stations by Southwest Missouri State University in Springfield, which also ar­ Matbemattcs. Awareness Week 1987 demonstrated. . ranged a thirty minute television panel discussion · thematicians possess an 1mpress1Ve on mathematics featuring spokespersons from lo­ that manYf mablic relations know-how and an in- amount 0 pu f h t' cal public schools and nearby colleges. Pl~s, the tereS! in communicating the value o mat ema 1cs mayor of Springfield signed a proclamatwn for · 'ty audiences as well as to the general 10 uruverst Mathematics Awareness Week. public. . . Massachusetts Prompted by a commitment to 1.ncreas~ng • A fractal exhibit, "Frontiers of Chaos," fea­ blic visibility for mathematics, the Jomt Polley turing the work of Heinz-Otto Peitgen, was :W for Mathematics has spons.ored Ma~hema~­ held at the Boston Museum of Science. icsAwareness Week during the th1rd week m Apnl • A symposium on the "Beauty of Fractals" for the past two years. Th~ 1986 focus ~as largely was cosponsored by the M.I.T. Department a na­ national with a presidential proclamatwn, of Mathematics and the Goethe Institute events tional TV spot, and consciousness-raising featuring presentations by Michael Barns­ on Capitol Hill and elsewhere in Washington. held ley, Robert Devaney, Benoit B. Mandelbrot, According to plan, 1987 took an entirely dif­ Heinz-Otto Peitgen, and Richard Voss. ferent focus and called for the inception of local • A proclamation was signed by Governor events. Two mailings to department chairs, MAA Dukakis, and the signing was cove~ed by pernors and PIO's, legislative volunteers, and mathematician and Harvard core curnculum Commit­ the JPBM Public Information Resource teacher, Michael Guillen, on WCVB-TV. tee, yielded a flood of calls. Arkansas AMathematics Awareness Week information • The governor signed a statewide proclama­ kit (the same one that was sent to reporters) was tion for Mathematics Awareness Week, and also mailed to every mathematician who expressed University of Arkansas students gave the gov­ interest in increasing local visibility and awareness about mathematics. ernor a copy of "The Beauty of Fractals" by H. 0. Peitgen and P. H. Richter. And not The results were astounding! Members of the to be outdone, the state legislature passed a ~ematics community came forward with a sig­ Joint Resolution for Mathematics Awareness ~~ant ~ay ~f activities and accomplishments. Week. followmg hst summarizes a few local efforts. Michigan California • A luncheon/reception, sponsored by Central ' ~Mathematics Festival which was held at Michigan University, featured Congressman noma State University included an exhibit, William Schuette and members of the Math­ aw.ards ceremony, public reception, a collo­ ematics Department who gave certificates of ~lll!n lecture, and an alumni reception. The recognition to talented mathematics students . noma County Board of Supervisors also from all surrounding high schools. 7: l8Sued a proclamation. • A series of events was spearheaded by Wil­ lllnessee fred Kaplan at the University of Michigan. 'David W'il' A state proclamation was secured and signed dist 'b 1 tams of Knoxville printed and in Lansing at an April 9 news conference. bumn uted Mathematics Awareness Week The University sponsored a special Saturday N!IJJ Yorrr stickers to schools in his area. program for high school students with presen­ 'A Pub]' 1 tations computer demonstrations, and films. Math ~d ~~t~re on "How Can We Reach Our Posterd saying "Learn Math, It's Exciting, Vassar b uCience Students" was presented at It's Beautiful" were printed and distributed for Ad YHassler Whitney from the Institute to nearby schools and libraries. Mathemati­ · vanced Study. cians gave a demonstration at the Ann Arbor

635 Hands-On Museum, a speech to the Cham­ The Joint Policy Board for M ber of Commerce, and addresses during local interested in getting even more ath~ l high school math classes. There was also an involved as spokespersons, as or ma_th~ . f . f . l ganlzers exhibit on campus about Isaac Newton. wnters o m ormatwna material f M 'and a; or ath • Two luncheons with programs on the role Awareness Week 1988. We are als · etl!atk,. of mathematics were hosted for community getting suggestions about the themo ~te~ lt officials, media, and other guests by West­ The 1987_ th~me, "T~e Beauty ~d the~ ern Michigan University in Kalamazoo and of Mathematics, was illustrated th' ~ Ann Arbor. Mayors of both cities also using two visuals, a straight line d 18. Year ~ issued Mathematics Awareness Week procla­ by David Middleton in the 1940sra(mg ~ mations. direction of G. D_. Bir~hoff) and a frac:der t!-t Oklahoma by Hans-Otto Pe1tgen m this decade. c~~~: • A special afternoon program featuring Curtis Comments and suggestions on Mathe McKnight, author of ''The Underachieving Awareness Week are welcome. Address lllati!! Curriculum," was held at the University of to, Ja~e Heckler, JPBM, 1529 18th St .. ~~ett Oklahoma where awards were also given to Washmgton, DC 20036. · · graduate students for outstanding teaching and scholarship. Pennsylvania • The opening of a new mathematics lab­ oratory for experimental research was the highlight of Mathematics Awareness Week at Pennsylvania State University.

MINIMAX METHODS IN CRITICAL POINT THEORY WITH APPLICATIONS TO DIFFERENTIAL EQUATIONS Paul H. Rabinowitz (CBMS Regional Conference Series, Number 65 Supported by the National Science Foundation) q-SERIES: Their Development and Application in Analysis, Number Theory, Combinatorics, The book provides an introduction to minimax Physics and Computer Algebra methods in critical point theory and shows titer George E. Andrews use in existence questions for nonlinear differential (CBMS Regional Conference Series. Number 66 equations. An expanded version of the author's 1984 Supported by the National Science Foundation) CBMS lectures. this volume is the first monograph devoted solely to these topics. Among the abstract This book integrates recent developments and related questions considered are the following: the mountaJn applications in q-series with a historical development pass and saddle point theorems. multiple critical of the field. focusing on major breakthroughs and the points for functionals invariant under a group of author's own research interests. The author develops symmetries. perturbations from symmetry. and both the important analytic topics (Bailey chains. variational methods in bifurcation theory and applications integrals. and constant terms) The book requires some background in funct~mal to additive number theory. He concludes with analysis and differential equations. especially elhpt( applications to physics and computer algebra and partial differential equations. It is addressed to a section on results closely related to Ramanujan·s mathematicians interested in differential equatiOnS "Lost Notebook· and/or nonlinear functional analysis. particularly With its wide range of applications. the book will critical point theory interest researchers and students in combinatorics. Contents_ d me additive number theory. special functions. statistical An overv1ew. The mountain pass theorem an 501 ~ mechanics. and computer algebra. It is understandable applications. Some variants of the mountatn pass of ttl! to even a beginning graduate student in mathematics The saddle point theorem: So_me _generalt~aat~i~:onian who has a background in advanced calculus and some mounta1n pass theorem:. AppiKatlo~s to d index t~ syst~ms. _Funct1o~als w1th symmetnes a~onals: prQbleiiS mathematical maturity. Mult1ple cnt1~al po1nts ~f sym~_etnc f~nct of symmetriC Contents w1th constramts: Mult1pl~ cntiCal ~omtsrtubations frrft Found opportunities: Classical special functions and functionals: the _un_constramed case .. t~ation theorY L. J. Rogers; W. N Bailey's extension of Roger's work; symmetry. Vanat1onal methods 1n b1.ur Constant terms; Integrals; Partitions and q-series 34 35 47, 58.70 Partitions and constant terms: The hard hexagon model ~~~~ ~-~t;~;~~~~~-~~~~~c~ 6~~a;;;~~~;~~~~160:·r642 Ramanujan Computer algebra 112 pages (softcover), 1986 List price $16. All individuals $10 1980 Mathematics Subject Classifications 33, 11. 82. OS Code CBMS/65 N A ISBN 0-8218-0716-1, LC 86-14061, ISSN 0!60-7642 $ h add'l St. 110 pages (softcover). 1986 Shipping/Handling: 1st book 2. eac ,1SJ. List price $16, All individuals $10 $25 max. By air. 1st book $5. each add Code CBMS/66 NA $100 max Prepayment required. Order from AMS. P.O. Box 1571. Annex Station. Shipping/Handling: 1st book $2. each add'l $1. Providence. Rl 02901-9930. or call d each add'l $3. $25 max By air, 1st book $5. 800-556-7774 to use VISA or MasterCar $100 max. Prepayment required. Order from AMS. P.O. Box 1571. Annex Station. Providence. Rl 02901-9930. or call 800-556-7774 to use VISA or MasterCard.

636 t.ttters to the Editor ~ at San Antonio Business Meeting with the military, The following is closely related to the issue concerned, ~ haps be clarified, even for the sake of A friend of mine, L. E, Faibusovich (Lenin­ It should p~r ok part in the Business Meeting at grad, U.S.S.R), has been employed for about ten who. 0but especially for those who did not, w- years in a corporation which was involved both SaD Anto~I~ended by the format of the discussion with civil and military projects, He worked in ,b&Mt"'~nms 1 and 2" against military funding. At ri" otiO h . , the nonmilitary department conducting research the ~est ion of s.ome oft e motiOns cosponsors, ~n mathema~ical systems theory and related top­ Itt roe attempt this. . . ICS, He published a number of papers in Russian the motwns If so The meeting could not pass journals and recently began publishing in in­ minded. All it could do was put them. before the ternational journals, see e.g., "Algebraic Riccati Meeting. But If only this proposal next Business equation and symplectic algebra,'' Int. J, Control been moved, it m~ght have .se~med to many bad 43:3(1986), 781~792. that the only discussiOn permissible would be In the end of 1985, L. E. Faibusovich was fired discUSSion of whether the motions merited consid­ for his refusal to participate in military projects. eration. The Secretary suggested the procedure He had a very hard time seeking another job. The of going into Committee of the Whole as a means only one he could find (recently) is not only menial ofiD&king discussion of the merits of the motions but also prevents him from doing any research in clearly in order. We followed the suggestion, and the daytime and restricts his access to scientific it had the desired effect: the substance of the libraries. I wish to urge the members of the motions was seriously addressed pro and con. Fur­ Society to send L. E. Faibusovich (home address: ther substantive discussion followed at the panel Veselnaya 4-78, Leningrad 199106, U.S.S.R) their on the subject the same evening. preprints. Those who are going to Let us hope that this dialogue will continue reprints and visit Leningrad (U.S.S.R.), say, on a scientific in the coming months. exchange program are welcome to contact him Chandler Davis personally. University of Toronto (Received February 13, 1987) R. Gurevic University of Illinois at Urbana-Champaign 23, 1987) Military Research in the Soviet Union (Received January !read wit~ interest Bill Thurston's letter (January Nomination by Petition 1987 Notices, pp. 39~44) advocating "no deal" At its meeting in January, the AMS Council Polley on Letters to the Editor passed a resolution that would prohibit an in­ dividual from being nominated by petition more Lettersby th Ed'submitted . for pu bl'1cat10n · m· N ottces. are reviewed wbkhe Itonal ~ommittee, whose task is to determine than twice in any ten-year period. Regardless of ltbed 01nes a.r~ SUitable for publication. The publication the intent of this motion, it will have the effect u e requires from t t f ceipt of the lett . p w? o our month~ b~tween re­ of denying candidacy to some members of the fer m rov1dence and publicatiOn of the earliest . Soc_i~ty who might otherwise be nominated by ISSbl~e ~ N otlces in which it could appear PU Icatio d · · · petitiOn. On behalf of the Executive Committee I~ty vote of th: e~!Sl~ns are ult.imately. made by ma- ••ion !or p . dEditonal Committee, with ample pro- of the Association for Women in Mathematics, I l ll!all. or at meet'nor ISCUS Sion' b Y committee· members, by urge the Council to rescind this resolution at the IIIO!ne letters mam~. ~ecause of this discussion period, earliest possible opportunity. fore a final dec'~ ~U!re as much as seven months be- ~ ISion IS mad L . Rhonda J. Hughes l ~may be, published e. etters which have been, the Mana.,;ng Ed' elsewhere will be considered but Bryn Mawr College I ,.,_ •· Itor of N · ' """ fact when th 1 . ottces should be informed of President, Association for I The . e etter IS submitted. in Mathematics ' committee r . Women I Notices d eserves the nght to edit letters. (Received March 9, 1987) 'abo oes not o d' ·1 I' ut reviews of b k r mar1 Y publish complaints EDITOR'S NOTE: The above was an item on ,:d correspondenceo~ 8 or ~ticles, although rebuttals 1 e American M th oncernmg reviews in Bulletin of the agenda for the April 25 meeting of the AMS !f

637 the right of his colleagues "to sell their soul admired mathematics occasionaU . to whichever devil they choose." I offer two given over to it by a consuming y, Without....._ • COIIJ.n.»:t;_~ comments on the letter. or as the mcarnate realization of ...... : 'IIIII First, it should be obsel)Ved that the letter is misguided ambitions. SOIIle ~·, similar to many written twenty years ago during Are there still school kids arolllld the Vietnam War era. Since then, the murder of the same way? Are there enough f th 1rbo fl!( tens of millions of people throughout Asia has cast our subject alive and well into ~h etn to~ some doubt on the moral equivalence of commu­ century? I'm frankly afraid that t~ twea&y• ._ nist and democratic governments. Certainly, our many of those kids like most of us a:_re &rea't 10 previous allies in Vietnam never committed the I'm afraid that many of us are 80 tJ:~· Alld crimes seen more recently there and in Cambodia own careers, and salaries, and by the With OQr and China. It may also be noted that the Berlin the approval of our mathematical godsse: b Wall still stands as a monument to academic and don't have the time to find out what' ' . lit other freedom in East Europe. with the next generation. We've got 8 ~Ill Second, the desire of scientists to defend listen and nothing to say to our mat~ their country is far from a novel idea. In this sons and daughters, at least until they're aJm..t regard, Sakharov is in a line stretching back to grown up. Archimedes. Laplace, Fourier, and Monge are There certainly aren't many young people. Enlightenment examples. Our country also has the U.S. today who will choose a career in ma: a history of mathematical service for military and there certainly isn't enough new scho!anbi applications. Veblen, Wiener, Von Neumann, and and talent to keep our profession healthy. If : Ulam are prominent examples. weren't that we continue to be able to buy taleat Fortunately there are enough scientists and and inspiration and scholarship from abroad llf'd other people who continue to defend our country. already be in serious trouble. The minu~ that David M. Weiss the U.S. becomes a less attractive place to lift. Ridgewood, NJ relative to the homelands of many of our better (Received March 4, 1987) mathematicians, we'll be in trouble. Those of us who can listen and talk to kim Encouraging Youth to Study Mathematics need to spend time visiting schools to find out I recently resigned from the Mathematical Sci­ what's going on, and then we need to get in touch ences Education Board and the Committee of with our own basic inspiration so that teachers Mathematics of the Board of Mathematical Sci­ and students can share it with us. ences, both affiliated with the National Research Herbert Clemens Council. I'm discouraged, but not because I think University of Utah either body is lacking in talented, energetic and (Received March 6, 1987) well-meaning professionals trying to do their best for mathematics. I'm worried that we are all making a fundamental mistake for which, in his­ AMS-'lEX Abstract Format torical terms, we will pay dearly. Namely, what's Several weeks ago I was lucky to receive from happened to the sense of wonder and enjoyment Associate Editor Patrick D. F. Ion of MathemGII; that brought us all to mathematics in the first cal Reviews a preliminary version of the A.MS·'l&X place? macro package for the Macintosh Plus. P~ When I was beginning high school, I thought of it is the document style 'amsppt'-a prepnnt it was "really neat" (that was the 50s) that some­ format, which I believe is relatively easy t? .~ • them&tiCI8D body had invented algebra and that you could and does not reqmre the 'average ma . de1fl· really do all those arithmetic problems at the to become a 'lEX wizard. I welcome ~- tht same time, and do them forwards, backwards, or opment and am looking forward to receJVJDg sideways. In weak moments, I even communicated final version. . the AMS this feeling to a few carefully chosen, safe friends. I wish now to go on suggestmg tored to tht Lots of other kids did the same thing, even though that a valuable service could be rendebe of tht we didn't get to know each other until much later. members of the Society. Every mem. ~uifed Probably some of our teachers didn't know much AMS wh.o desires to present a pa~~: the past math, or, perhaps they communicated what they to submit an abstract form. Wit t fo['IIIS ~ did know in "bad" or worn-out ways. But some few years, the size of these abs~r~ not fit in of us were conditioned to accept and forgive that increased. It is now so large that Jt ::atheDJal~ and to accept as gospel that the study of math an ordinary typewriter. A numb.er 0 to cCJIIIJllit.er was eternal and noble and even, perhaps, a source cians have switched from typewriters. nallY filii· of sweet satisfaction. Not everybody did that, composed mathematical text, occasJO ...... ntiY essor-"""-· · not even most of us. But, amidst all the usual ten with a mathematical text pro~·chafd pal~ interference caused by the flow of hormones and so well described by Professor ~rocessin'. PI the desperate need to be liked by one's peers, columns on Mathematical Text 1 ms fonoriin' there was room for those of us who liked and these Notices. One of my probe

638 . h t I have an Apple 10" Im- _•• h 1S t a 'l' ll h l)il apP~'~~""'' t as it seems, u t1 Ize a t e .,writer tha~;if:~1~ '(approximately 8 1/2" by OPERATOR ALGEBRAS (111-f 111ade a ct forms. Furthermore, I should AND MATHEMATICAL 4') on the abstr~se the AMS -'lEX macro package PHYSICS perer to ra~h:;sh Plus. It seems to me that. the • 11lY Maclll t bstract forms was determmed Palle E. T. Jorgensen and Paul !iJtOfthe cu~en easy photo-reproduction but ideratwns :r . , S. Muhly, Editors by cons " ist friendlmss. oot those ?f t:~n in the AMS -'lEX macro pack­ This volume contains papers presented 8 What Ia 1.gght call "amsabstr," an abstract at the University of Iowa 1985 Summer l&flS· what one mmodest opmwn,· · It· s h ould not b e Conference in honor of H.-J. Borchers, fanll*· In m~em for one oft he AMS -'lEX wizards N. M. Hugenholtz, R. V. Kadison, JDUcbof:~r~ore than a small exercise) to write and D. Kastler and gives a systematic, (JD&Ybe macros. Suet a proposed abstract up-to-date treatment of the fruitful the n~:::J also be used by the Editorial Staff interaction that the last two decades have brought between operator algebras and for a ~ AMS who produce on demand and mathematical physics. Special Soc. t typed abstracts. In my dreams, I see fee Ie Y · b · · th · b t t attention is paid to an overview of the members of the SoCI(·ty su rruttmg e1r a s rae , algebraic approach to quantum field ~they 80 desire, in 'fEX code-the code eventu­ theory, and, in particular, to quantum ally typeset by the Society for the Abstracts of the statistical mechanics. More than half the AMS. It's only a suggestio~, _but pl~ase consider papers culminate with a presentation of ·1 seriously. I discussed this Idea with Professor new results which have not appeared ~,and he seemed to be in favor of it. previously in journals, and, with a Gerhard F. Kohlmayr few exceptions, these new results are Mathmodel Consulting presented with complete proofs. Bureau This book is addressed to graduate (Received March 24,1987) students and researchers working in a broad spectrum of areas in mathematics and mathematical physics. Functional analysis, operator algebras, operator theory, differential geometry, cyclic cohomology, K-theory, and index theory are applied to questions in the quantum theory of fields and statistical mechanics. The individual papers are ESTIMATES self-contained, but the reader should have FUNCTION some familiarity with the basic concepts J. S. Marron, Editor of functional analysis and operator theory, although no physics background This volume collects together papers is assumed. presented at the 198.5 Conference in 1980 Mathematics Subject Classifications: Function Estimation held at Humboldt 46, 81, 82 ~ateUniversity .. The papers focus ISBN 0-8218-5066-0, LC 86-32070 ~Ial.ly on vanous types of spline ISSN 0271-4132 estimations and convolution problems. 560 pages (softcover), January 1987 List price $45, Institutional member $36, The use of estimation and approximation methods .. d Individual member $27 . as app1IP to geophysics To order, please specify CONM/62NA nu~encal analysis, and nonparam'etrir sta~shcs was a special feature of this con,erence. Shipping/Handling: 1st book $2, each add'l $1, $25 max. By air, 1st book $5, each add'l $3, 1980 Mathe t ' $100 max. ISBN ma tcs ~UhJf"ct ClaBsification: 62 Prepayment required. Order from AMS, P.O. Box 821 , 0- 8-5062-H, I.e 86-14203 1571, Annex Station, Providence, RI 02901-9930, bSN 0271-4132 800-556-7774 to Uoie VISA or MasterCard. 188 Pages ( f or call List price$~~ t~ove~). '\ugust 1980 lnd· . · nst1tutional member $18, "' !VIdual memhn $13 10 order 1 ~fy CONM/59NA Shtppin 'H . add'! sts and!,ng: 1st hook $2, each add'! s3: $~~0tnax. By air. 1st book $5, each Prepayment re m_ax. P.Q B Qtured. Oni<·r from AMS . ox 1571 A . . ' IU 02901_9930 · nnex St at10n, Providence, VISA or M 'or call 800-.556-7774 to use ~terCard.

639 Queries Edited by Hans Samelson and Stuart Antman

QUESTIONS ARE WELCOMED from AMS members regarding mathematical matters su h details of, or references to, vaguely remembered theorems, sources of exposition of folk thea c 88 or the state of current knowledge concerning published or unpublished conjectures. This r:ma• inten.ded as a problem corner, except for occasional lists of problems collected at mathemat: meetmgs. 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 I am inclined to believe that Lorenzen' sion has a better chance of standing u 8 l"!r· 376. Gerhard F. Kohlmayr (Mathmodel Consult­ ing Bureau, Glastonbury, CT 06033-3608). Mor­ scrutiny-although it's possible in princi~ U: ris Kline writes in his book Mathematics, the both A. Wei! and H. Weyl made these sta~ independently. I certainly would appreciate ' loss of certainty (Oxford University Press, New York, 1980), on page 261: "This result prompted rece~ve a definite answer by a historian of~ matJcs. Hermann Weyl to say that God exists because mathematics is undoubtedly consistent and the 3~7. Vasile Ion lstratescu (Westring 331, mi. devil exists because we cannot prove the con­ K1el, West Germany). What is known &boot sistency." On the other hand, Paul Lorenzen arithmetical properties of the values ~(m) ofthr writes in his monograph Metamathematik (Bibli­ Riemann .;-function at natural numbers m> 1' ographisches Institut AG, Mannheim, 1962), on (E.g., from the nature of .;-(2) one can deducetlw page 132: "Am originellsten ist, was der Math­ the set of primes is infinite [see V. I. Istri!escu. ematiker A. Wei! dazu gesagt haben soli: 'Gott Irrational numbers, selected topics]; or, the density existiert, wei! die Mathematik widerspruchsfrei of the set of squarefree integers exists and equal; ist, und der Teufel existiert, wei! wir es nicht .;-(2)- 1 [Joe. cit.].) beweisen koennen.' "

Essentially self-contained, the book includes considerable discussion on a few of the deeper results, not merely a catalog of results. The author addresses pure mathematicians, especially combinatorialists and graduate stud~ts taking graph theory, as well as theoretical EXTREMAL GRAPH computer scientists. He assumes a. THEORY WITH EMPHASIS mature familiarity with combinatonal . methods and an acquaintance with basiC ON PROBABILISTIC graph theory. METHODS 1980 Mathematics Subject Classification.: 05, 60 Bela Bollobas ISBN 0-8218-0712-9, LC 85-30670 ISSN 0160-7642 In this book, an update of his 1978 72 pages (softcover), May 1986 book Extremal Graph Theory, the author List price $i2, all individuals $7 NA focuses on the trend towards probabilistic To order, please specify CBMS/6::.__ methods. He demonstrates both the h add'l fl, Shipping/Handling: 1st book $2, eac ,1 13 direct use of probability theory and, more $25 max. By air, 1st book $5, each add ' importantly, the fruitful adoption of a $100 max. p o. BOX Prepayment required. Order from AMS, g<)1.gg3(), probabilistic frame of mind when tackling 1571, Annex Station, Providence, Rl 02 terCard· main line extremal problems. or call 800-556-7774 to use VISA or Mas

640 I dgment of Contributions Ackno'!w~e~::::.:.------. , d the staff of the Society acknowledge with gratitude gifts and contributions The officed" an the past year. The inside cover of each issue of Mathematical Reviews carries ·ved unng recei f the sponsoring societies· · w h'IC h hsupport t at pu bl'JcatJOn. · C ontn'b utmg · memb ers 0 the names 1 • paid dues of $126 or more. In addition to contributions to the AMS Research of the Soci~ y d there were a number of unrestricted general contributions. Also listed this Fellowshi~:>.I~ rr:embers who have contributed to ICM-86. Some of the contributors have year are · ~in anonymous. All of these gifts provide important support for the Society's asked to re~he names listed below include those whose contributions were received during the Programs. year en ding ·\larch 31, 1987.

CONTRIBUTING MEMBERS

Eckhardt, William Kamp, William P Naimpally, Shabazz, Abdul Alim .\bbotl- Jamee H E<·klund. Earl F, Jr Kaplan, Wilfred Somashekhar A Shaneson, Julius L .\datn•· Elliott T Epstein, D I Kautzmann, Newman, Morris Shields, Allen L .\krmann. Charles A Frank N, III Nishiura, Togo Singmaster, David B .\rzur-Motl. Ali R Nobel, John A Spencer, Joel H Fadell, Edward R Kelly, John B .\adrt'wa. George E Nummela, Eric C Stakgold, Ivar Farrell, Roger H Kendall, Richard P bltPUI. Edward F · Jr Sternberg, David Kiefer, James E Fas~, Arnold L Olum, Paul Strauss, Frederick B Forbes. Stephen H Killeen, John Babcock. William W Orlik, Peter P Strichartz, Robert S Knuth, Donald E Sullivan, Richard W BtbLkir. M A Osofsky, Barbara L Gal uten, Aaron Kopala, Conrad Swokowski, Earl W Baurr, Frances B Otermat, Scott C Krause, Ralph M Baumtlag, Gilbert Glass, AM W Krueger. Charles G Taylor, Laurence R ~hler, Barbara J Gordon, Hugh Palais. Richard S Could, Kunen, Kenneth Palmer, Theodore W BJorklund. Peter B Henry W Papanicolaou, Uhlenbeck, Karen Bootb. George W Grace, Edward E George C Unal, Aynur BrHIOud. David M Graves, Robert L Laning, J H Leger, Pearson, Robert W BuL&nouckaa. Greicar, Richard K George F Perry, William L Veech, William A Francis R Greif, Stanley J Lemay, William H Polking, John C Voytuk. James A Grimmer, Ronald C Lenard, Andrew Pratt, Vaughan R Canon. Robert C Gromov, Mikhael LeVeque, William J Warren, William E Lewis, Hugh L C'hrrnolf, Paul R Ratliff, Louis J, Jr Weintraub, Steven H Wendroff, Burton Clifford. Alfred H Haddad, George F B Lieb, Elliott H Redheffer, White, George N, Jr Cohen. Henry 8 Halberstam, Heini Lieberman, David I Raymond M Whitmore, William F Cohn, Leslie Hartnett. William E Reed, David L Wilkins, J Ernest, Jr Coot1, Thomas A Hassinger, Bill, Jr Mamelak, Joseph S Reedy, Christopher L Williams, Robert F Comcan, Hedlund, Gustav A Mansfield, Maynard J Reese, Matthias F Wilson, Robert Lee Thomaa Carney Hemstead, Robert J Renz, Peter L Mathsen, Ronald M Woeppel, James J Cullen, Helen F Herwitz, Paul S Riney, John S Mattson, H F, Jr Woolf, William B Rosenblum, Marvin Higgins, John C Maxwell, James W Wright, Robert K Ross, Kenneth A Duerman, Robert J Hi ronaka, Heisuke Meder, Albert E, Jr Rovnyak, James L Dt-Facio. Brian Hochstadt, Harry Miles, E P, Jr Yahya, S M DeLeon. Morris Jack Hochster, Melvin Miller, W F Yohe, James M Sally, Paul J, Jr Demana, Franklin D Howe, Roger E Mislfin, Guido Dt \tarr. Ralph E Samit, Jonathan Hufford, George A Morawetz, Cathleen S Ziebur, Allen D Dtnnttn, Gerald p Sawyer, Stanley A Zink, Robert E Hunt, Richard A Moschovakis, Dono1hue, Schori, Richard M Hutchinson, George A Yiannis N William F, Jr Selfridge, John L Anonymous (2) M uhly, Paul S Seligman, Dowd, Michael F George B Johnson, Roy A Murphy, Donald P Sexauer, Norman E

Corporate Members and Institutional Associates ' !~~ ~~~et~ also acknowledges with gratitude the support rendered by the following corporations, Past ye either Corporate Memberships or Institutional ar. Associateships in the Society during the

Corporate Members Institutional Associates ~~~ace Corporation Princeton University Press Bell Laboratories Ge neral M t D. Reidel Publishing Corporation lnternat' 0 ors Corporation Springer-Verlag New York Incorporated ~ation~o;al ~usiness Machines Corporation ecunty Agency

641 GENERAL CONTRIBUTIONS

Abbott, James H Fass, Arnold L Kahn, Donald W Mooney, John J Saeed·ui~I.J Adler, Irving Faulkner, Frank D Kakihara, Yuichiro Moore, Richard A Al-Medhadi, Nora Seif Kaminker, Jerry Sahab, sa.~::· II Ferrari, Carlo Morawetz, Cathleen S Salas M Kanda, Mamoru 8 Alonso, Agustin Ferry, Steven C Morris, Robert A S ' aturnino l Alvis, Dean L Kaplan, Wilfred amelson, Han. Finch, John V Moschovakis, Ancel, Fredric Davis Katz, Talbot Michael Yiannis N Sarafyan, Dirau Flanders, Harley Anshel, Michael Kennedy, Edward S Mount, Kenneth R Saraaon, Donald Foias, Ciprian Ilie Kent, George A Antman, Stuart S May, Allen Sarhan, !dab ....~ Khan, Sasaki, Sbiceo Aribaud, F Folk, Thomas F Muhly, PaulS Asner, Bernard A, Jr Freeman, James H Mohammad Ahmad ~a.st~i, Cbelluri C A Kianos, Martin S Mulla, Fuad S Azarnia, Nazar Frink, Orrin chem, Borit J,f Kiefer, James E Murakami, Shingo Schraut, K C Frohlich, J urg M Kime, Katherine A Muto, Yosio Bachman, George Schreiner, Erik A Kimmerle, Myers, Earle F Baker, Edward D Schroeder, Joh11111 Cantos, Richard. L Wolfgang Otto Ball, N Hansen Scott, Leonard l. Jr King, James A Nagano, Tadashi Ballard, William R Gerstenhaber, Murray Sedgewick King, Randall R Nanyes, Ollie Balser, Arienne S Gilman, Jane P Chari.; H w Kirk, David B Nebs, Robert M Bari, Ruth A Glass, Michael S Selfridge, John L Kita, Hiroo Nelligan, John D Barnet, Frank Goldberg, Seymour Shafii.Mouaavi. Kittaneh, Fuad A Nevai, Paul G Morteza Bartle, Robert G Goldhaber, J K Klatman, David S Newman, Morris Sharma, Ambiiealn.ar Bass, Robert James Goldman, Jerry Klebanoff, Newsom, Carroll V Sharp, Henry, Jr Baum, John D Victor Franklin Goldman, Nichols, Edward Shelly, EugeDe p Bazer, Jack William Mark Klein, Edwin M Beals, R Michael Niino, Kiyoshi Shenitz, Charlet Goodrich, Koditschek, Bennett, Curtis D Niven, Ivan Shiraiwa, KeDithi Suzanne Dinga Daniel Eliezar Bennett, Fredricka T Kolodner, Ignace I Nordhaus, Edward A Sidney, Stua.-t J Gordon, Jonathan Berger, Alan E Komm, Horace Norman, Silberger, Aliaa J Bergman, George M Graham, George P Kossack, C R Francis Alexander SimOea-Pereira, J 111 s Bernstein, Joseph N Gramsch, Bernhard Kra, Irwin Nummela, Eric C Singh, Kanhaya L Bers, Lipman Gray, Robert E Krause, Ralph M Singmaster, DIYid B Biles, Charles M Green, John W Kumagai, Donna J Oehmke, Robert H Slater, Joha 8 Smith, Marianne Boos, William Greenhall, Charles A K unoff, Sharon Oguchi, Kunia Freundlich Booth, George W Kurata, Yoshiki Okoh, Frank Greville, Thomas N E Smith, Michael G Borgman, Lucille C Kurshan, Robert P Omori, Hideki Griffin, E L, Jr Smith, Roy C T Brauer, Fred Kurtzke, John F, Jr Onishi, Hironori Gross, Louis J Kyuno, Shoji Solomon, Loui1 Bressoud, David M Orellana, Guillot, J C Sonnesso, Geraldiae Brown, Arthur B Chacin Mauricio Gulden, S L Laffey, Thomas J Spanier, Jerome Brown, George B Orloff, Leo N Brown, Robert E Lakshmanan, Neela Speara, Oti1 S Langston, Orr, Martin Spencer, Joel H Brownawell, W Dale Haag, Vincent H Michael Davie! Otermat, Scott C Stackelberg, Olaf P Bruna, Joequim Haber, Seymour Bryn, Milo F Lanzano, Paolo Steele, William F Haiman, Mark Lapidus, Michel L Paciorek, Joseph W Buehler, Royce E Stegeman, Jan D Halberstam, Heini Lasher, Sim Pan, Ting K Buis, PaulE Steinberg, Maria W Laska, Michael Papageorgiou, Busemann, Herbert Hale, David R Steinberg, Robert Law, Peter R Nikolaos S Bustelo, Julia Ana Hamstrom, Stevens, RichardS Mary-Elizabeth Lawson, Walter R Parker, Francis D Stinson, Kevin Leavitt, William G Harrington, Walter J Patterson, Larry A Stock, John R Caldwell, Lebow, Arnold Roderick PC Hartnett, William E Phelps, Robert R Streater, David Neil Leger, George F Phillips, Ralph S Carlson, Bengt G Harvey, George G Strout, John E Legrady, Kurt Piger, Jean Strupp&, Daniele C Carmichael, Richard D Hassinger, Bill, Jr Lehrer-Ilamed, Y Pitt, Loren D Sturm, Teo Carroll, Edward M Lewis, John A Hausmann, Polachek, Harry Sun Hugo Sui·HWioD Chang, Weita Jean-Claude Lichnerowicz, Andre Chihara, Theodore S Pop-Stojanovic, Sun~uchi, Gen·icbiro Helton, Burrell W Lima, Asvald Choksi, Jal R Zoran R Sunseri, Mary V Herbst, Albert F Lind, David W Chow, Tseng Yeh Liu, Shih-Chao Porta, Harry J Swartz, Joseph H Christensen, Chris Herrera, R B Lombardo, Charles J Pratt, Vaughan R Churchill, Richard C Hironaka, Heisuke Lopez, Amparo Priest, Cynthia J Clark, Kenneth D Hodgson, Loring, Putnam, Alfred L Clark, Robert A Jonathan P E Terry Atherton Pyle, H Randolph Cohen, Daniel I A Hofer, Robert D Louhivaara, Ilppo S Cole, Paul Dana Haft, Hartmut Louton, Tom Quade, Edward S Coleman, A John Holmes, Philip John Lubin, Clarence I Quinn, Frank S, III Luchins, Edith H Colson, Henry D Hughes, Ruth L Comenetz, Daniel Raney, George N Huibregtse, Mark E Machover. Maurice Craft, George A Raskind, Wayne Mark Crandall, Michael G Hummel, Tamara J Macphail, Moray S Hunt, Walker E Madow, William G Ratcliff, Gail D L Crane, George E Reber, Douglas C Crossman, Howard L Hyers, Donald H Mamelak, Joseph S Rees, MinaS Curtis, Charles W Mann, Benjamin M Martin, Hayden Garth Regan, Francis Iha, Franklin T Mayor, John R Reissner, Eric Darmorly, Laurie M Ilg, David H McAdam, Stephen J Renno, James G, Jr Day, Mahlon M lm Hof, McConnell, Robert K Resco, Richard D Dedecker, Paul Hans Christoph McDonald, Janet Reynolds, Donald F Defrancesco, Henry F Ishimoto, Hiroyasu McGovern, William M Ribe, Martin G DeLeon, Morris Jack McKenzie, Harvey C Deprima, Charles R Iwata, Koichi Richmond, Meadows, Lawrence F Lawrence B Divis-Poracka, Zita M Mears, Florence M Douglis, Avron Jacob, Niels Robbin, Joel W Meyer, Herman Robbins, Leon C, Jr Duncan, Cecil E Jaffe, William J Meyer, W Weston Robinson, G de B Duren, William L, Jr Janusz, Gerald J Michael, William A Robinson, Raphael M Dydak, Jerzy Mielke, Paul T Jeanquartier, Pierre Rosenthal, Arthur J Jerison, David Miller, William David Eachus, J J Ming, Ronald W Ross, Paul Jeroslow, R G Edrei, Albert Mishra, Sudhakara Roth, Rodney J Eisele, Carolyn Jockusch, Carl G, Jr Mitchell, Ian R Rothe, Erich H Ensey, Ronald J Johnson, Gerald W Mitchem, John A Ruess, W Evens, Leonard Johnston, William W Moller, Raymond W Rutledge, Dorothy S

642 Waterhouse, Williamson, Charles K Zalcman, Lawrence A Wagner, R W William C Wilson, Robert Lee Zilmer, Delbert E Walker, Gordon L Wehausen, John V Wong, Sherman K Zuckerberg, Hyam L Walker, Jan ice B Weibel, John L Wrench, John W, Jr Zuckerman, Gregg J Walter, Gilbert G Western, D W Walters, Eleanor B Wh1tney, D Ransom Yasuhara, Mitsuru Anonymous {69) Warner, Frank W, Ill Whittall, Gerald B Yokoi, Hideo Warren, William E Whittlesey, Emmet F Yoshino, Takashi Warschawski, Stefan E Wiener, Howard W Young, Wigner, E P MacDonald Burritt Wass, Noel Christopher Williams, Robert F Young, Paul M

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Seema Alspach, Dale E Antoniadis, Anestis A Atkinson, Stuart L Balibrea, Francisco A~' Sbair Altergott, Dennis A Apostol, Constantin Atsuji, Masahiko Ball, Joseph A AI ' N U Althoen, Steven C Apostol, Tom M Auchmuty, Giles Ball, Richard Neal A~ John F AI- Thukair, Appel, Kenneth I Auer, Jan W Ball, Richard W A'bech; Ja?'es Dwight Fawzi Ahmed Appell, Jurgen Aulaskari, Ballantine, Charles S 4Jdoo • Aasaa Altomare, Francesco Applebaum, Joseph A Rauno Pertti Ballard, David J ' Emmanuel B Altshuler, Amos Appleson, Robert R Ault, J C Ballard, William R Alvis, Dean L Appling, William D L Auslander, Bernice L Ballou, Donald H Aquino, Trania A Auslander, Maurice Balmaceda, GENt;RA;L~~------, Arad, Zvi Aust, Catherine C Jose Maria P IN CONTRIBUTION Arakaki, Gary K Austin, Charles W Baloglou, George C ALtXANMEMORY OF Balser, Arienne S DtR D. WALLACE Araki, Shoro Au-Yeung, Yik-Hoi Arapostathis, Avelsgaard, Roger A Bandle, Catherine ...... __ Alfred ll. Clifford Aristotle A versa, Vincenzo L Sandler, Wyllis Arason, Jon Kr Avioli, John J Banerjee, Utpal

643 AMS Research Fellowship Fund (Continued)

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I Barbut, Erol Beattie, Margaret Susan Grooms Francine Boyce, Willi .... Barcellos, Anthony Beaty, Marjorie Heckel Berkovitz, Leonard D Bland, John S Boyd, Dayicl W Boyer, D--. • Barckett, Joe A Beaudoin, Robert E Berkowitz, Harry W Blank, Brian Evan Steve. Boyle, Jell..,·­ Bardaro, Carlo Beaumont, Ross A Berlekamp, Elwyn R L Blankenship, Gilmer Boyle, Mike Bareiss, Erwin H Beauzamy, Bernard M Berman, David R Blankinship, Barendregt, Henk P Beaven, Michael W Berman, Gerald William A Bozeman, SJIYia T Bozonia, Petro. Barety, Julio Edgardo Beaver, Olga R Berman, J Michael Blaskie, Marc Braakalll&, 8 L J Barge, Marcy Becerra, Linda Berman. Robert David Blatter, Christian Brace, John W Sari, Ruth A Bechtel, Robert D Berman, Stephen Blatter, Jorg Bracbmao., ...._ Barja, Jose M Bechtell, Homer F 1 BermUdez, Alfredo Blattner, Robert J Brackx, Fredd,. p Barker. 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Luc My Ian Redfern Boenecke, Ernst Branton, Mic:Uel C Barros-Neto, Jose Bell, Harold Betsch, Gerhard Boffi, Giandomenico Brattstrom, GHnl B Barshay, Jacob Bell, Howard E Betz, Ebon E Bogart, Kenneth P Braude, Eric J Barsky, Daniel Bell, James M Beukers. F Boghossian, Artin Brauer, Fred Barsotti, Leo Bell, Murray Gordon Bevis. Jean H Bohannon, Barbara Brauer, Georp U Bart, H Bell, Steven R Beyer, \Villiam A Boisvert, Robert E Bravo, Raul Barth, Karl F Bell, Stoughton Beylkin, Gregory Boivin, Andre Breaux, Gar)'R Bartick, Philip R Bellamy, David P Bhaskaran, M Bojars, Juris A Brecbner, BeYerlJ L Bartle, Robert G Belley, J M Bhattacharya, Prabir Boley, David B Breckeoridp, loU C Bartnik, Robert A Bellissard, Jean V Bhattacharya. Rabi !'; Bollinger, Robert A Breece, Wllliaa J Barton, Eric M Bellomo, Nicola Bia, Ahmed Bond, David B Breen, Stephea Barton, Thomas J Bellow, Alexandra Bialostocki, Arie Bonet, .Jose Bremigan, Ralpll J Baruch, Herbert M Jr Belpaire, Gerald Bickel. Thomas F Bonilla, Luis L Brender, MelYiD Barwise, Kenneth J Benac, Theodore J Bieri, Robert Bonner, Richard F Brennan, p A Brenneman,J- Barzilai, Jonathan Bencsath, Katalin Bierstedt, Klaus D Bonnice, William E Franklin 8 Basor, Estelle Bendat, Julius S Bierstone, Edward Boo, Per-Anders Bass, Hyman Bender. John Biggers, Ronald C Boos, William Brent, Richard P Bass. Robert James Benes. Vaclav E Bijan-Zadeh, Booth, David D Brenti, Fr...-, Bateman, Felice D Benitez, Cados Mohammed H Booth, George W Bressler, Da•idid II Bresaoud, Da• C Bateman, Paul T Bennett. Curtis D Bilaniuk, Stefan Boras, Bresaoud, T~ Bates, Grace E Bennett, David G Biles, Charles M Michael Edward Breuer, SblOIDOW Batie Nicolau, N ada! Bennett, Fredricka T Billera, Louis J Borchers, Hans-Jurgen Bator, Elizabeth Mary Bennett, John Bruce Billik, Martin Borel, Armand Bre-wer, J.-:. p Bricke11, Batt, Ji.irgen 0 Benson. Dave Bilodeau, Gerald G Borelli, Mario Eru.cob Brickman, J . Batten, Benson, Bindschadler, David E BOrgers, Christoph Lynn Margaret David Bernard Bing, Kurt Borges, C Freitas Brickman.~­ Batterson, Steven L Benson, Bingen, Franz Borges, Carlos R Brickmanv!.,... 5 Batty, Charles J K Frederick ChailonE"r Bini, Dario Borgnet, Eric N 0 Bridges, OIIIIJ Brieake, Th bel' Bauer, Douglas Benson, Steven R Binkley, Dean H Borkowski, Mark S Brieakorn, Z. II Bauer. Frances B Benyamini, Yoav Binkley, Timothy Borwein, David Briggs, Bauer, Heinz Berard, Pierre H Birch, Bryan J Bosch, William W J~c Brighalll, G Baum, John D Berbee, Henry C P Bircher, John J Bose, N K Brin, Matt:-L Baum. Paul F Bercovici, Hari Biriuk, George Bost. Jean-Benoit Berenbom. Joshua Botoaca, Vasile Britton~ Jo Judhll Baumann, Volker H Birman, Graciela S BroadWID, Baumgartner, Berenstein, Carlos A Birman, Joan S Bottazzini, Umberto Berent. Paul Alan Bouchard, Pierre Brobeck, c,wooll Gerald B Jr Birnbaum, Eric S Barbar':t..-fi Berestycki. Henri Bouchet, Andre Baumgartt~er, James E Birnir, Bjorn Brockett, Beretta, E F Boudourides, Moses Baumslag, Gilbert Birnstihl. D A Brode, Job~ Ill"' Beretta, Giordano B Boultbee, Nan Bausum, David R Bishop, Alan A Brodie, RodJOIJtl' Bautista, Maurine P Berezina, M Bishop, Richard L Bourgeois, Brian A II Baxendale, Peter H Berg. Gene A Bismut, Jean-Michel Bourion, Georges Broi~e, M~o&Df Brohne, ~ Berg. Gunnar Bousfield, Aldridge K Baxter, Willard E Bisson. Terrence Paul Bromberg, Oat"il p Bayer. Pilar Berg, Michael C Boutin, Pierre Bisztriczky, Tibor Bromley, an• Berg, Murray Boutot, Jean Francois Bayer-Fl ucki ger. Bitschnau~ Nichimi. Brons, f{ Eva M Berge. Douglas Titienne Bouwsma, Ward D

644 Fellowship Fund (Continued) ,u~s Research

Burchard, Paul Caranti, A E Chaney, Robin W Chouteau, Charles C Kenneth A Burckel. Robert B Carbonara, Joaquin 0 Chang, Bomshik Chow, Pak S ,_.. su.rrow p Burges::>. C Edm,und Cardenas, Chang, Chao P Chow, Pao-Liu JrOOk•· James 0 Burgess, Juan Donoso Chang, Derek Kong Chow, Tseng Yeh :;::: peterS Richard Dennis Carey, A L Chang, Gerard J Chow, Yuan S Burgess, Walter D Cargal, James M Chang, 1-Lok Chrestenson. ~·· Ro~~~nar A Hubert E 8,_..Jer. Burke, James E Caricato, Gaetano Chang, Jen-Tseh Christ, F Michael Burkhart. Richard H Carleson, Lennart A E Chang, K un Soo 8f01itl~ki~a~uno H Christensen, Chris Burkholder. Donald L Carlisle, Ronald L Chang, Li-Fung Christilles, William E B~en John E Burkholder. Carlson, Bengt G Chang. Bro& 'William Long F Christy, Joe Douglas G Carlson, Dean A Chang, Ping-Tung s:~rAnne E Chu, Chinku Burney, Carlson, Donald E Chang, Shao-Chien Chu, Tienchen :f(JIII'a: Arthur A Herman Matthew Jr Carlson, James A Chang, Shih-Hung Chuang, Pi-Chun 8,_.,, Arthur B Burns, Anne M Carlson, John W Chang, Weita Chung, Fan R K Bto'JD· Edgar : r ~ Burns, Keith H Carlson, Kermit H Chanillo, Sagun Chung, Lung Ock arown. Edwar B Burr, Stefan A Carlson, Robert C C'hantip, Suchat Church, Alonzo Jf(IIII'D. George Burrill, Claude W Carlson, Timothy J Chao, J A srown. Gerald D Church, Philip T Burris. Stanley !'; Carmichael, Richard D Chao, Michael srown. Gordon E S Churchard, Burstall, Francis E Carnes, Neil P Chaperon, Marc srown. Jack B Peter William Burt, Philip B Carone, Patricia L armrn. Jeffrey L Chapin, Steven Arthur Churchill, Edmund Burton, Leonard P Carpenter, arown. Johnny E Charles. Donna G Churchill, Richard C Busemann, Herbert Gail Brown. Kenneth S ~ Alexandra Charney, Ruth M Chyung, Dong Hak Busenberg, Stavros Brown. Lawrence G N Carr, Ralph \\/ Chastkofsky, Leonard Ciarlet. Philippe G Buser. Brown, Patrick J Peter J Carr, Chatzidakis, Zoe Cima, Joseph A Bush, George Brown, C Stephen Timothy Chauvin, Andre Cincotta, Richard Arthur Bushnell, Colin J Carroll, Edward M Chawla, Lal M Dominick Anthony Buskirk, Brown, Richard C Robert D Carroll, Jeffrey S Chazin, Robert Louis Cirina. Marco Brown. Richard J Bu8s, Samuel R Carroll, Michael P Chee, Pak Soong Claasen, H L Butchart, John H Brown. Robert Dillon Carroll. Robert W Cheeger, Jeff Clapp, Michael H Butcher, Brown, Robert E John C Carroll, Timothy B Chein, Orin N Clare, Loren Paul Butcher, Brown, Ronald Carson, Mark Erwin Chemla, Karine C Clark, Charles R Ralph Stevens Brown. William G Cartan, Henri Chen, Concordia C Clark, John Butler, Allen Brownawell, W Dale Carter, David W Chen, Daniel K C Clark. Kenneth D Browne, H Nelson Butler, James William J r Carter, Karen Chen, Etang Clark, Robert A Browne, Butler, Patrick J John B Jr Carter, Chen, Goong Clarke, Brownttein, Alan B Butnariu, Dan Patricia Hawks Chen. Kwan- \\.'ei Graham Thomas Browoatein, Beth Buttke, Thomas F Carter, Thomas J Chen, Li-Chen Jane Clarkson, Helen E Bruck, Ronald E Jr Butts, Thomas R Cartlidge, James M Chen, Louis H Y Clarkson, Peter A Bruckner, Andrew M Byerly, Robert E Carton-Lebrun, C Chen, Mingsan Clary, Stuart Brueo, Aiden A Bykat, Alexander Casanova, Toussaint Chen, W W L Claus, Elly Bruueman, Roelof W Byleen, KarlE Casazza, Peter G Chen, Wen Brumer, Armand Clausing, James A Byrne, Angelina H J Case, Bettye Anne Chen, Y W Brumfiel, Gregory \\ Cleaver, Charles E Byrne, Catriona M Casey. Robert Francis Chen, Yongzhuo Bruaa, Joequim Clemens, Byrne, Charles L Casler. Burtis G Chenciner, Bruner, Robert R Alain Charles Herbert Byrnes, James S Cason, Patricia Lynn Cheng, Kai-Nah Brune•, Hans H Clements, George F Cassel, D Wayne Cheng, Kuo-Shung Clemons, Curtis Brian BrUning, Jochen Cabaniss. Sharon Bnmner, H Cassels, J W S Cheng, Yu-Ting: Clifford, Alfred H Cable. Charles A Cassidy, Phyllis J Cheng, Yungchen Clifford, Jane E Bruno, Vincent J Cacioppo. Bruna, Winfried Castagnoli. Erio A Cheon, Seok-Hyeon Cline, Edward T Robert Joseph BrunBon, Barry W Castellet, Manuel Cherenack, Paul F Clover, William J Jr Cadogan, Charles C Brun•wick, Castore, Glen M Chern, Shiing S Coats, Carlie J Jr Cafiisch, Robert G Sataacha A Castro, Antonio de Cherniavsky, John C Cobb, J Daniel Cafl.isch, Russel Bryan, Charles A Catanese, Ch(:rnoff, Herman Cobham. Ian P Cahill, Rotraut G Bryant, Billy F Fabrizio M E Chernoff, Paul R Cochran, Douglas Cain, Bryan E Bryant, John G Cateforis, Vasily C Cherny, Julius Cochran, James Caines, Peter E A Bryant, John L Cater, FrankS Cherowitzo, Vv"illiam E Cochran, Cairoli, R Tim D Brydcee. David c Cathey, Frederick W Cherri, Mona Y Cockburn, Calbeck. William S Bryl~weki, Thomas H Cattabriga, L Cheung, B K S Julio Bernardo Calderhank. Robert Bryhneki, Jean-Lur Causey. William M Cheung. Maria L Coddington, Earl A Bryn. Milo Calderon. Alberto P F Cavanaugh, Joseph M Cheung, Vv'ing-Sum Cody, William Caldwell, Gordon F Jr BnP~ineki, Juliusz R Cavaretta, Alfred S Jr Chi, Dong Pyo Caldwell. Coen. Salvatore B•bouty, Daoud Cavender, James A Chi, Henjin Coffee, Roderick P (' Jane P :uccino, Alphonse Caveny, James Chiang, Ching- Yuan Coffey, John 8ucbanan, Thomas Caldwell, Thomas E Cavior, Stephen R Chiang, Peter H S Cogburn, Robert F uck. Marshall Caldwell, William V w Cawley, Robert Chiarenza, Filippo Cogdell, James Wesley :llcki, Andrzej J Calkin, Neil J Cayco, Bern Chicane, Carmen C' Cogswell, Richard L Bllckley, Joseph T Callahan, James .J Cecil. Thomas E Chidambaraswamy, Cohen, Amy Bllckley .. Stephen Calmet. Jacquf's ~ Cernuschi-Frias, .layanthi Cohen. ucy. Richard s · Calvf'rt, Bruce D Arjeh M Bruno Chien, Victor Cohen. ~udnik. Paul J r Camarf'na. Vict:>nte Daniel I A Cerruti, Umberto Chihara, Theodore S Cohen, Frederick R oud•ban Cameron. Douglas E Certain, Melinda W Childress. Nancy Ellen Grec~ry Mark Camina, A R Cohen, Gerard D Cesari, Lamberto Chillag, David Cohen. Haskell Buetbler s Campanino, Massimo Blltbler , teven Allen Cha, Hyung Koo Chillak. Edward W Cohen, Herman Campbell. Daniel D J E Chahert, J L Chillingworth, Cohen, Bllekenho!oy~e Campbell, Dave A Joel M Bllbler, Chaffee, James \\' David R J C.:ohen, Jo~· p Campbell, Harold E A Marshall M Chaiken, Seth Chinburg, Ted Butlnoucka.,, Campbell, D C Cohen, Martin J Chakerian, Gulbank D Ching, Wai-Sin Cohen, Moses 8 Francis R Jean McCroskey E Chakravarty, Su binoy Cho, Chong-Man Campbell, L Andrew Cohen, Ralph a::\,~auJ ~ Chalmers, Graham D Cho. Choong Yun Cohn, Donald Bllt-na Dg-Lteu Campillo, Antonio L Chambers, Cho, Eung Chun Cohn. George I Buhrach Richard Campos. L M B c Daniel \iVarren Cho, Sung .Je Cohn, Canavan. Robert I HarvPy llola~d Champagne, Carol Z Choe, Young Han Cohn, Leslie B,u z Candy. Gregory T E denek Chan, Chiu Yeung Choi, Bong Dae a,ll~n ...-erett L Jr Canfield. E Rodney Cohn, Chan, Jack-Kang Choi. Un Haing Stephen Edward ;eter. Canjar. Mike a,llllt~. Chan, Jean B Choksi. Jal R S lerntng Cannon . .James W Cohn. William S Chan, Kit Chak Choksy, N H Col bourn, B,~~~~:Dey .0 . Cannonito. Frank B Chan, Tony F Chong, Chi Tat B,llltr~t Rtch<>.;·d T ~an tor, Robert M Charles Joseph Chan, Y H Chong, Tjee Hung Cole, a,ll. ' ltobert '-'antrell. James C Charles A "·Marta(' Chandler, J D .Jr C~hoo. Koo-Guan Cole. ~ancy Cap, Clemens Heinrich Chandler, Choquet. Gustave <:apozzi. Alberto Cole, Paul Dana Michael Paul Choudhury. Shenaz Coleman. A John

645 AMS Research Fellowship Fund (Continued)

Coleman, Courtney S Cox, S H Jr Dana, Martin P Deift, Percy Alec Coleman, Robert Cox, Stephen E Daney, Charles G De longh, Johan J Diener, kart. Collier, Jarrell D Coxeter, D'Angelo, John P Deiter, Daphne D D~eudonnf 1 J... Collier, William G Jr H S MacDonald Dangello, Frank Ralph De Jong, Frederik J D1kshit, G D... 4 Collingwood, David H Coxson, Pamela G Daniels, M Peg M Dejter, Italo J DH&o, Rui Collins, Carol E Cozzens, Dannan, Fozi Mustafa Dekker, Jacob C E Diicher, k~rl& Collins, Charles R Margaret Barry Danset, Renaud Dekleine, Herbert A Dilka, Anae ..... Collins, Dennis G Crabtree, J B D' Antona, Otavio DeKoninck, Dillon, !Uebrd T Collins, Michael J Craft, George A D'Aprile, Margherita Jean Marie DtMaio, Gi ...... Colliot-ThtHEme, J-L Craggs, Robert F Dar, Karamat Hussain De Koning, Jan D~minnie, Ckut~. Colonius, Fritz Craig, Cecil Jr D'Archangelo, Delahunty, Michael D Damitracoi»>Wot. l Colonna, Flavia Craigen, Robert W James Michael Delange, Hubert Conatanti~e~e Colquitt, Landon A Crandall, Michael G Dare, Adrienne M Delanoe, Philippe D~msdale, &era...~ Colson, Henry D Crandell, Carolyn G D' Aristotle, De La Rica, D~nneen, Gerald p DIOn, Glori 8 Comenetz, Daniel Crane, George E Anthony J Mariano Hermida 1 Dionne, Beaoit Comer, Stephen D Crane, Jane P Dark, R S de las Obras, Carmen Comerford, Leo P Jr Crane, Louis Darken, Joanne S Del baen, Freddy Dionne, Philippe A ll Comez, Dogan D C Crapo, Henry H Darmody, Laurie M Di Paola, J~~e DiPerna, ltoaaad J Comfort, Steven H Crauder, Bruce C Darnel, Michael R Delchamps, David F Comfort, W W is tar Craven, Bruce D Das, Anadijiban Deleanu, Aristide D~ Stefano, Clt.art. J Daute, Patricit, J Compton, Esther A Crawford, James P D' Atri, Joseph E DeLeon, Morris Jack Zi&a M Compton, Kevin J Crawford, John David Datskovsky, Boris A D~vis-Poracka, Delges, H Wolfgang Dtx, David 0 Conlon, Joseph G D Dautray, Robert I Creede, Geoffrey Dell' Antonio, Dixon, Criat D Conlon, Lawrence W Creekmore, Joseph W Daverrnan, Robert J Gianfausto Dixon, Mart Conn, Jack Frederick D3vid, Daniel 11 a... Criscenti, Delporte, Jean Dixon, Michul J Conner, Luther T Jr P David, Florin R Jacqueline Del Riego de Del Dixon, Willi•O Connolly, Mary V Crittenden, Richard J David, Karl Castillo, L Djaparidae, Lwiq Connely, Frank X Crockett, Diane W David, Nancy A del Solar-Petit, Emilio DjokoviC, Dracou t Connor, Jeffery S Cromarty, Andrew S Davidoff, Giuliana P Delver, Robert Dobbins, Robert a Connors, Edward A Croom, Frederick H Davidson, Kenneth R do Carma, Mufrede p Conrad, Bruce P Cross, James J Davidson, Delzell, Charles N Dodd, Jeffrey J Conrey, J Brian Cross, Ronald W William Robert Demana, Franklin D Constantinescu, Crossman, Howard L Davies, Morton J De Marr, Ralph E Dodds, Peter G Corneliu Crothers, Derrick S F Davis, Burgesd J Demetrius, Lloyd A Dodds, Tbereaa K Conte, Giuseppe Crow, Edwin L Davis, Chandler Demeyer, Frank R Dodson, Contessa, Maria Crow, John Anthony Davis, James F de-Michele, Leonede Christopher T J Conti, Roberto Crowe, John A Davis, James J Deming, Robert W Dodziuk, Josef Conway, John B Crowe, Richard C Davis, Jon H Doerfler, Willibalcl Cook, David Edwin Crowell, Richard H Davis, Lincoln Ross Demko, Stephen Dolbeault, Piem I Cook, Joseph M Crowley, James M Davis, Linda M Demmel, James W Dold, Albrecht E Cook, Larry T Crumb, Cyndi A Davis, Lynda Ann de Mottoni, Piero L Doll, Nelly E Cook, Thurlow A Cruse, Allan B Davis, Pa•Il L Deneen, Linda L Dollard, John D Cooke, Kenneth L Cruthirds, John E Davis, Richard L Do mar, Yncve Cooke, Roger Lee Cryer, Colin W Davis, Robert B Denig, William A Dombroski, Miclllel Cooley, Clifford R Csorp;o, Miklos Davis, Ruth M Denman, Domic, Antun Coolsaet, Arnold A Cude, Joe E Davison, Walter F Richard Thomas Dominguea, J M Coolsaet, Arnold A Cudia, Dennis F Davitt, Harold H Dennin, Joseph B Dominijann.i, RoberW Coombes, Kevin R Cullen, Helen F Dawes, AM Dent, Elliod Domino, Laureace E Coonen, Jerome T Cullinane, Steven Dawson, Donald A D'Entremont, Domokoa, Gabor Cooper, Hilda L Cumro, Dennis L Dawson, Shawn S Edward Joseph Donaly, Jamea P Cooper, J B Cunningham, A B Day, B J Deodhar, Vinay Vithal Donkar, Eli N Cooper, Leroy W Cunningham, Day, George W Deprima, Charles R Donoho, David Lticll Cooper, Mark A Frederic Jr Day, Jane M Depue, Bill Earl Dooley, A H Cootz, Thomas A Cunningham, D~y, K Michael Deretsky, Tatiana Doplicher, SertiO Cope, Davis K Richard J Day, Mahlon M De Rezende, Ketty Doppel, Karl Copeland, Arthur H Jr Cuntz, Joachim Day, Martin V Deriggi, Dennis F Doran, RobertS Coppin, Charles A Cupillari, Antonella Daybell, Dorothy A Derighetti, Antoine D'Orazio, SiiYI!lO Coppotelli, Fred Curjel, Caspar R Daykin, Donald R Derr, Leroy J Dordal, Peter LR Coram, Donald S Curran, Peter M Dayton, Barry H Deruaz, Marcel A F Dorroh, Jamet d L Coray, Daniel Currier, Albert W Dealba-Guerra, Derwent, John E Dorwart, Harol Dostal, MiiOI A Corazza, Paul J Currier, Robert J Luz M~ria oesarm€mien, Jacques Dotzel, Ronald M Cordero, Luis A Curtis, Charles W Dean, Andrew P DeShalit, Ehurl Dou, Alberto M Cordes, Craig M Curtis, Doug W DeAmaral, Daniel J Deshouillers, 1 Dougherty, Cordes, Heinz 0 Curtis, Herhert J DeBlassie, Jean-Marc Jtandll Corduneanu, Curtis, Morton L Richard Dante Desmond, James Eddy Douglas, .Jim~~ G Dough~oP, RoD Constantin Curtis, Philip C Jr Debnath, Lokenath De Snoo, Hendrik S V Dougiis, Avron Corrigan, Curto, Raulil E de Boor, Carl Desoer, Charles A Thomas Carney de Brangt::s, Louis Dover man•: Cushing, Jim M Desolneux-Moulis, Karl HeiDI Cortzen, Barbara Cusick, Thoma!1 W De Bruin, Marcel G Nicole Corwin, Lawrence J Cuthill, Elizabeth H De Souza, Vera H G Dov~~toherine SJaDP Cosner, George C Cutkosky, Steven Dale Debrunner, Hans E Detlefsen, Michael E Costa, David G Cutler, Doyle 0 de Caen, D Detofoli, Rino Dow' Ala~ ard E Dowds, Rich M Costanzo-Alvarez, Cutler, William H De Canniere, Jean Detre, Peter A Sabatino Cutrer, M Wayne DeTurck, Dennis Dowl~n, ~~ael L Coste, Alain Cuttle, Yvonne H De Cecco, Giuseppe Deuber, Walter Alfred Dowhng, tboll" A Costenoble, Steven R deCesare, Kenneth M Deumens, Erik Dowling, Rodnef G Cotlar, Mischa Dabrowski, Rornuald Dechene, Lucy I Deutsch, Daniel H g:::~:~, J SeO&I Cotsaftis, Michel Dacor3o Netto, Cesar Devaney, Robert L Doyen, Je$11 Cotton, Robert M Dade, Everett C Decker, Mike DeVault, John L Couch, W Eugene Dadok, Jiri Decker, Naomi H Deveney, James K Ooy le, ~::er G Couch, Dahl, Erlend Decker, Robert James De Villiers, Raoul A Doyle, Lance 0 Drager, )ex J William Garrant Jr Dahlin, Rolf B Deckert, Kenneth L Dewallens, Jean H Coulter, Malcolm A Dale, Knut T Dedecker, Paul Dhooghe, Paul F J Dragt, ~ank R Countryman, Dale, Richard H Deeb, Waleed M Diamond, Beverly E J Drake, pa•id p William Mark Dales, H Garth Deeter, Charles R Diamond, Jack Dras~n, M:icblll DrazJn, aut10D Courter, Richard C D'Alotto, Louis A DeFacio, Brian Dias Da Silva, J A s Dreben(;erald C Coutu, Gerard Daly, John T De Figueiredo, Diaz-Miranda, OreV.:• paniel r.f Couty, R Darni~no, David B Djairo G Antonio DriblO, Marik J Cowan, Jack D Damkohler, Wilhelm L Defrancesco, Henry F Dibner, Steve Cowens, J Wayne Driscoll. aruce" Damon, DeGroot, Jan Dickerson, Charles E Driver, Cowling, Michael G James Norman Dehesa, Jesus Sanchez Diederich, Klas

646 h Fellowship Fund (Continued) A)(S Researc

Eskew, Fellows, Fonseca, Irene oaniel s EinLawrence Man Hon Thomas Eugene Michael Ralph [)rltCier. Jewgent Fontaine, Marc F Eskin, Gregory Fenchel, \Verner ~al·•· Einhorn, Ken H Fontenot, Robert A Einthoven, Isabella H Eslinger, Robert C Fendrich, John W ()ubil(h. ~:~)" J Foran, Jarnes Eirola, Timo J Espina, Carlos L Fenley, John C Forbes, Stephen H o.btkY· Alberto S Eiseman, Peter R Essen, Matts R Fenley, Sergio Roberto Ford, David A Thomas P.~p. E Eisenberg, David C Esser, Fennell, James G Ford, George P :lfy, Richard M Eisenberg, Murray Anne-Marie Simon Fennig, Joseph N Ford, Lisa B [)udsiak. J~mes ~ Eisenberg, Robert. S Estrada, Luis Fenske, Christian Foreman. Matthew D D•tfu•. Owtght Eisenbud, David Etgen, Garret J Feofiloff, Paulo Forman, John W Eisenstadt, B J Etheridge, William L Ferguson, David J Forman, Robin Ouk~~drew Cameron Eisenstat, Stanley C Etter, Daniel 0 Jr Fergu::;~on. David R Forman, William Duke. Richard A , Eisman, Sylvan H Evans, Martin J Ferrari, Car!o Formanek, Edward W Duke! ow, James S J r Eiss, Joseph J Evans, Michael Jon Ferri, Massimo Forsythe, Keith W Oum&J. H Scott Ekeland. Ivar Evens, Leonard Ferris, Ian M Forsythe, W L Eklund, Hans G Evens, Ferro, Alfredo l)un~~iam Dart J r Samuel R Forte, Bruno Eklund, ~eil A .Sveret t., Jeff Ferro, Ruggero Fossum, Robert M J)uacan. Cecil E Ekman, I

647 AMS Research Fellowship Fund (Continued)

Fuhrken, E Gebhard Geissinger, Lad nor D Goldberg, Charles H Grace, Edward E Fujimagari, Tetsuo Gelbart, Stephen S Goldberg, Moshe Grace, Jacqueline R gross, Loui• J Fujisaki, Rieko Gelfand, Hosna Goldberg, Richard R Grace, Thorn rosser s· 1 Fujiwara, Masahiko Geman, Stuart Alan Goldberg, Samuel Graf, Siegfried Gros 8111 ~n ~ k Fukuda, Komei Gemeda, Demissu Goldberg, Seymour Graffi, Daria Grosarnan' Ed •a Fukushima, Masatoshi Genensky, Samuel M Goldberg, Vladislav V Gragg, Karen E Grossrnan' J .. lrd ~ Fukushima, Mitsuo Genet, Jean Raymond Golden, Kenneth ~1 Graham, Aly Grosarnan, Mil~"· Gro88man, Rolrllo \\ Fuller. Kent R Gentili. Graziano Goldfeld, Dorian Graham, C Robin Fuller. Luther B Geoghegan, Ross Goldhaber, J K Graham, Colin C Groaswald', E ~ Fuller. Mark E George, John Clay Goldman, Jerry Graham, George p grove, Edwar~'A Fuller, Robert Arthur Georgiady, Michael S Goldman, Graham, Ian rove, Larry C Fuller. \iVilliam R Georgiou, D A William Mark Graham, Timothy N Grover' Carole L Fuller, William R Geramita, Anthony V Goldner, Siegfried R Graham, Victor W Groves, J R J Fulton, James Paul Geramita, Joan M Goldstein, Gerald Grainger, Arthur D Grow' David E Fulton. William Gerardin, Paul Goldstein, Jerome A Grarnsch, Bernhard Grubb, Gerd Fung, Terry Y Gerber, Marlies Goldstein. Larry J Grant, Caroline Galt Gruenberg, Karl \\' Fuqua, Jeffry B Geremia, Goldstein, Norman J Grantham, Stephen B Gruenhage, Gary f Furutani, Kenro Raymond S Jr Goldstein, Richard Z Grasman, William B Gruter' Michael Futaki, Akito Gerhard. J Arthur Goldstein, Sheldon Grasser, Grzeg~rczyk, Piotr)( Gualtlerotti, A f Futia, Carl A Gerhardt, C Goldston. Daniel A Horst-Siegfried Guerin, Eether Gerig, Stephen R Goldstone, Richard J Gratzer, George A E Craie R GaaL Lis! Novak Gerlach. Golfin, Andrew S Gravel, Pierre Gu~lbault, Gabay, Jacques Eberhard G P Golightly, Gutllemin, Victor\\­ Graver, Jack E Guillot, J c Gabber, Ofer Germain. Paul William L Jr Graves, Glenn W Gulbenklan, Gu&btd, Gabriel. Richard F Geronimo, Jeffrey S Golitzin, George Graves, Robert L Gulden, S L Gershenson, Gacs, Peter Hillel H Golubitsky, Martin Graves, William H Gulick, Dt'nny Gadia, Shashi Kumar Gerstein, Larry J Gray, Gomez Pardo. Alfred Gulliver, Robert 0 Gaffney, Matthew P Gerstenhaber, Murray 11 Jose Luis Gray. Jeremy John Gundenen, Gary C Gerszonowicz, Gage, Michael E Jorge A Gomez-Ruiz, Francisco Gray, John W Gunn, Charlee G Gaga, Felipe Gervais. Jean Jacques Gomi, Kunia Gray, Mary W Gunnarsson, Gagola. Gloria Potter Gerver, Joseph L Gompf. Robert E Gray, Robert E Tboma.e E W Gaillard, Pierre Yves Gessaman, lv1argaret P Gondard~Cozette. Gray. GUnther, Cbriuiu J Gaines, Robert Earl Gessel, Ira M Daniell J Samuel Hutchison Gupta, Haneraj Gallagher, Patrick X Getu, Seyoum Gonshor, Harry Greek, John W Gupta, Narain D Gallier, Jean H Geue, Andrew S Gonzalez, Manuel Greek, Ronald B Gupta, R K Galperin, Efim A Gewirtz, Stephen J Gonzalez, Green. David Jr Gupta, Rajiv Galuten, Aaron Ghaffari. Abolghassem Raul Ernesto Green, James A Gupta, Ranee Kathrn Galvin, Fred Ghatage, Pratibha Gonzalez-Guzman, Green, John W Guralnick, Robert M Gamelin, Theodore W Ghisa, D Jorge Green, Leon W Gurney, David Robert Ganelius, Tord H Gidas. Basilis C Gonzalo, Jesus Green, Mark L Guftin, Morton E Gangolli. Ramesh A Gierz, Gerhard Good. Irving John Green, Scott Wesley Gurwara, S&nd~p Gani. Joseph M Giga, Yoshikazu Goodearl, Kenneth R Green, Simon Gustafson, Richard r Gannon. Robert G Gilbert, Freeman Goodman, A V\' Green, William L Gustafson. Robttt A Ganser, Carl C Gilbert, Goodman, Greenberg, Peter A Gustafaon, Sven·Akf Gantner. Thomas E George Thomas Frederick M Greenberg, Ralph Gustafson, Wil!i&m H Cantos, Richard L Gilbert, Michael D Goodman, Jacoh Eli Greene, John Robert Gustas, Gaposchkin, Peter J A Gilbert, Richard C Goodman, Greene, Peter H Raymond JAJJin Garb, Regina H Gildenhuys, Dian James Thomas Greenfield, Gary R Gutek, Andnej S Garcia, Mariano Jr Giles, John R Goodman, Philip Greenhall, Charles A Guterman, Martin M Garda-Planas. Isabel Gilewicz, Jacek Goodman, Roe W Greenleaf, Allan T Guthery, Scott B Garcia-Rodeja F, Gilfeather, FrankL Goodman, Sue E Greenleaf, Frederick P Gutknecht, Martin H Eduardo Gill, Tepper L Goodrich, Greenleaf, Newcomb Guy, Richard K Gardiner. Gillespie, James R Suzanne Dinga Greenspan. Bernard Guyker, Jamet Christopher J Gillespie, Robert G Goodson, Greenspan, Bernard D Gwyn, Douglu A Gardiner, Cyril F Gilligan, Bruce C Geoffrey Ross Greenspan, Donald Gardiner, Frederick P Gillman, Daniel W Goorjian, Peter M Gregorac, Robert J Haag, Vincent H Carding, Lars Gillman, David S Gopal, Mangalam R Gregory, David A Haario, Heikki Gardner, Maria F Gilman, Jane P Gopinath, Gregory, John Habeb, Jahre\ Gardner, R J Gilman, Robert Bhaskarpillai Gregory, Habegger, Nathan B Gardner, Robert A Gilmer, Gloria Gordh, George R Jr Thomas Bradford Haber, Seymour Gardner. Sharon Kay Gilmer, Patrick M Gordon, B Brent Greicar, Richard K Habetba, Klaus Gardner, Gilmour, Grant James Gordon. Blaine F Greif, Anthony David Habetler, Georce J William Allen Gilsdorf, Thomas E Gordon, Carolyn S Greif, Stanley J Habibullah, G M \\' Hackborn, William Gariepy, Ronald F Gingrich, Ross B Gordon, Hugh Greim, P Garland. Stephen J Gioia, Ant.hony A Gordon, Jonathan Greiner, Peter C Hackler' Donald : B Haddad. George Garner, Lynn E Giovannitti, Gordon, Robert Greller, Larry David Haddad. Hadi M Garnett, John B Anthony J Gordon, Yehoram Gresser, John T Haddad, Labib S Garrett, John Vv' Girela, Daniel Gorenflo, Rudolf Greville, Thomas N E Haddix, George f Garrison, Betty B Gittings, Raymond F Gorenstein, Daniel Griess, Haddock, A Gle~ Garrison, David B Glass, AM W Goresky. R Mark Robert Louis Jr Haddock, John • Garsia, Adriano M Glass, Michael S GOrlich, Ernest Griesser, James W Garzon, Maximiliano Glauberman, George Gorman, William J III Griffin, E L Jr Haeberly, A Gasca, Mariano Glazebrook, James F Gormley, Michael J Griffin, Philip Stanley Jean- P.ierreGuenthtr Haemmerltn, Gaschiltz, Wolfgang Gleason. Andrew M Goroff. Daniel L Griffin. Hafner, James L Gasper, George .Jr Glenn, Paul G Gorton, Robert Bruce William Gerald Gasqui, Jacques H Glimm. James G Goss, Robert N Griffiths, Phillip A Hag, nPe~obert M Jr Gates, Michael A Glover, David W Gosselin, John A Griggs, T S Hag a ' WiJlialll W Gatterdam, Ronald W Glover. Henry H Goth, John A Grillakis, Manoussos Hager, Jr Hagis, !"/ Gatteschi, Luigi Gluck, Herman R Goto, Hideo Grilliot, Thomas J Pet~es Gauchman, Hillel Glynn, John J Goto, Midori S Grimmer, Ronald C Hagler, J;ohn W Hagood, Gauthier, Paul M Glynn, M F X D Goto, Shiro Crimson, W Eric L Gautschi. Walter Goblirsch, Richard P Gould, Henry W Grivel, Pierre P Hahn, ~;!:, r Gayle, Godbole, Arrant P Gouvea, Grobler, Jacobus J Hahn, . rieG Hahn, Mart Herman M Stanford Goddard, J D Fernando Quadros Grognard, Rene J M Hahn, Nea e G Gechter, Jerry Godfrey, Colin Gover, Eugene H Gromov, Mikhael Hahn, susa:ard f: Geddie. Godin, Paul J Gaze, Michel Grone, Bob Hahne, ~e~al!ll!ltd Q Peggy Emmons Goebel, K Grabiel, Federico Gropp, William D Gee, Henry R Goethals, J M E Grabiner, Judith V Gross, Benedict H Hailat, ,;reil E Haile, Rutb M Ge1Sslin. Roger H Goetz, Abraham Grabiner, Sandy Gross, Herbert ~ Hailper~n, 'fheod 11rt Gehrig, Eugene J Golber, David L Grabner, Elise M Gross, Kenneth I Hail penn, Gehring, Frederick W Gold, Robert Grabner, Gary Clem Gross, Leonard

648 Fellowship Fund (Continued) A)IS Research Harte. Robin E Helton, J \Villiam Hill. Shirley A Homsy, Elham Mark Hartl, Johann Helton, Karen A Hillman, Honda, Kin-Ya ttaaii6D· O~borah T Hartman. James L Helton, Robert Arthur Jonathan Arthur Hoobler, Raymond T ya~IDD·Richard Mart Ill Hartman, Jehuda Helwig, Karl-Heinz Hill-Tout, Barry W Hook, Edward C Hartrnanis, Juris Hemmeter, JosephS Hilpipre, Douglas H Hook, Stephen M 0 =~· a... id c Hempel, John P Hilt, Sandra ~ Hoover, D N )la,p-Ghaa.eom. Hartmann, Hilton, Peter J Hoover, Thomas B KaiPran . Frederick W Hemstead, Robert J Ha.l~_r•tam. H~nl Hartnett, William E Henderson, David W Himmelberg, Hopkins, Kevin W Charles J III Hopkins, Mike tfa}clUD· judy Hartshorne, Robin Henderson, tlalt. David R Haruki, Hiroshi Francis McVey Hindman, Neil B Hopkins, Nora C &it Douglas F Haruki, Shigeru Henkin, Leon A Hingston, Nancy Horadam, Kathryn J tl . Alfred W Harvey, Bernard Niel Hennequin, Paul-Louis Hinman, Peter G Horblit, Brian D Haiti· R Stanton Jr Harvey, Charles A Hennessy, Patricia A Hinojosa-Berrones. Horn, Alfred :~·Glen Richard Harvey, Charles M Henniart, Guy M J A Horn, Daniel P Hall. L M Harvey, F Reese Hen niger, J P Hinson, Edward K Horn, Jean Macgregor Hall. Mark Edwi_n Harvey, George G Henrici. Peter Hintzman, William R Hornback, Joseph H tlalltnbeck. David J Harvey, William J Henriksen, Melvin Hirano, Tetsutaro Horne, J G Jr HaiWr, Thomas Harzheim, Egbert Henry, Jackson N Hironaka, Heisuke Horner, Mary Lynn H.alptrn. Her~ert Hasegawa, Keizo Henry, Myron S Hirsch, Kurt A Horner, T S Halprin. Oa~~d berly J Hasenfus, Harold J Hensel, Hirsch, Michael D Horrocks, Geoffrey Hal,eriOD· Jm .. Hashimoto, Ki-ichiro Robin Ann Morgan Hirsch, Morris W Horsfield, Hunana. Masam•chl Haskell, Peter E Hensley, Douglas A Hirschfelder, Christopher H Haaulton. Barbara K Haslach, Henry VV Jr Hensley, Elmer L Elizabeth S Horvath, Ham•lton. Hasselbach, Eric R Hensley, John Vv' Hirzebruch. F E P Charles Daniel David Howard Hassett, Judy J Hensley, Scott Hirzebruch, Ulrich HorvA.th, John M Hamlin. Dennis D Hassmger, Bill Jr Henstock, Ralph Hitchin, Nigel J Horwitz, Alan L H. am mel. Hentzel. Irvin R Hitotsuyanagi, Nobuo Hosack, John M Stephen Mark Hastad, Johan Harold M Herbst. Albert F Hjorth, Poul G Hosoi, Tsutornu Hammer. F David Hastings, Hasumi, Morisuke Herda, Hlavac, Paul P Hoste. Jim E Hun mer, Peter L Hans-Heinrich W Hlavka, James L Hotta, Ryoshi Hammett. Michael E Hatcher, Rhonda L Hathaway, Dale K Herfort, Ho, Chung-Wu Hou, J i<>.shi Hunmond. Norbert Charles C .Jr Householder, James E Michael Eugene Hattori, Akio Wolfgang Hoag, S Hammond. William F Hauptman, Herman, Michael Hoang, Huu Manh Houston, Raymond Edgar J Hamrick, Gary C Herbert Aaron He I man. Richard H Hobbs, Arthur M Howard, tlaJr.trom, Hausmann, Hermann, Robert Hochschild, Gerhard P Howard, Eric J Mary-Elizabeth Jean-Claude Hernandez Ruiperez. Hochster, Melvin Howard, Fredric T H&ll. Jin Kyu Hausner, Melvin Daniel Hochwald, Scott H Howard. Paul E Han. Jongsook Havens, Jim Hernandez, Diego B Hockett, Kevin G Howard, William A Kaudel, David Haver, William E Hernandez, Eugenio Hodel, Richard E Howe, Roger E Hun. Kit Havermann, Hans Hernandez, Rafael Hodges, Lucille M Howe, Vernon \N Hance•. Hawthorn, Ian James Herod, James V Hodges, Wilfrid A Howell, Jo Ann Sicholas William Hay, George E Herrera, Ismael Hodgson, Howell. Louis H Hanlon, Philip J Hay, Louise Herrera, R B Jonathan P E Howie, John M Hanaa, J Ray Hayashi, Eric Herrero, Domingo A Hoefer. Edwin T Hoyt, Kenneth Huna, Peter Hayashi, Kazumichi Herreshoff, James B Hoeffding, Wassily Hoyt, W L Hannan. James F Hayashi, Mikihiro Herring, Susan Kay Hofer, Robert D Hratz, Joseph A Hano, Jun-lchi Hayashi, Yoshio Herschorn, Michael Hoffman, Hrbacek, Karel H~n. ldar Hayes, Hersh, Reuben Jerome William Hsia, J 8 Hwen, R 0 Catherine Cummins Herve, Michel Hoffman, Kenneth R Hsieh, Simon C llllllen, Hayes, David F Herwitz, Paul S Hoffman, Michael E Hsieh, Wan-Chen \'l(n Lundsgaard Hayne, Roger M Herz, Carl S Hoffman, Michael J Hu, K Y Happle, Wolfgang Haynes, Nola A Herzfeld, Noreen L Hoffman, William C Hu, Shou-Jcn Harada, Shigeharu Hays, M M R Herzog, Emil R Hoffmann, Banesh Hua, Yang Harbater, David Hazewinkel, Michie! Herzog, John 0 Hoffmann-J orgensen, Huang, Abigail S Hvborth, Heiko Head, Richard R Hesla. Todd Jorgen Huang, Tsang-Chi Hubourne, Brian Headley, Vel mer B Hess, Jacob J Hofmann, Karl H Huard, James G Hudell, William J Heard, Melvin L Hesselink, Wim H Hofmann, Steve C Huber, Alfred 0 Hudie, Keith A Heath, Lenwood S Hestenes, Magnus R Hoft, Margret H Hudson, D L Hardt, Robert M Heath, Robert W Marshall D Hogan, Daniel A Hudson, John F P Hardy, Darel W Hestenes, Heath-Brown, Roger Gerald A Hogbe-Nlend, Henri Hudson, Richard H Hardy' John T J r Heuer, James J F W Steven M Hue, Donovan R Hebda, Heumos, Michael J Hogesteeger, Hudson, Hal"lnath, K s Hebert, Michel Heuvers, Konrad John HOgniis, GOran H uet, Denise Hu1ne. Hechler, Stephen H Heyer, Herbert K Hoksbergen, Huff, Charles W Hecht, Henry k Katherine Jane Hiai, Fumio Rob RAM Huff, Gerald B Hanna-Smith Hecht, James E Hickernell, Fred J Holberton, John V Huff, Lawrence R Robert H · Hecker, David A Hicks, Darrell Lee Holder, L I Huff, Melvyn E Harker, Patrick Hedberg, Lars I Hicks, Troy L Holenweg, Werner Huff, W N Harmand, Peter Hefez, Abramo Hida, Takeyuki Holladay, Kenneth W Huffman, Ed W :umelin, Reuven Heifetz, Daniel B Higgins, Holland, Daniel L Huffman, William C HlrDion, Dennis R Heil, David L Aparna William Holland, Finbarr Hufford, George A Hlrnl•b, Stephen Heineken, Hermann Higgins, John A Holland, Samuel S Jr Hugger, Jens K&r~r. Ja.meso lldnicke, Allan G Higgins, John C Holland, W Charles Hughart, Stanley P ~tell, Evans M Heinig, Hans p Higgins, John R Holley, Frieda K Hughes, Anne Har rtiJ, Ronald E Heinrich, Katherine Hight, Orian L Holley, Hughes, Anthony Har~Jngton, Walter J Heins, Maurice H Hightower, James K Richard Andrew Hughes, Carl C Heintze, Ernst Higman, Donald G Hollingsworth, B J Hughes, Cephas D Karr::lto8n, Waiter J H . • erna.rd Heinze, Joachim Higuchi, Yasunari Hollister, Lindsay Hughes, John Forbes &rrll D . Heldermann, Norbert Joseph A Hun,' J ahvld Carter Hijab, Omar Holman, Hughes, H , o n C Helgason, Sigurdur Hijazi, Oussama Wayne James III Hughes, Kimball K:::· Lawrence A Hell, Pavol Hilbert, Stephen R Holmann, Harald R A Hughes, Mark P Ku . Morton E Hellberg, H Stefan Hildebrandt, Holmes, Ernest J Hughes, Rhonda J K rll, Steven G Hellen, Gregory R Theodore W Holmes, Hughes, Richard P Jr lrr11 lh uy Harr ' eodore E Heller, Alex Hilden, Hugh M James Samuel Jr Hughes, Ruth L Hlrr lion, David K Heller, Barbara Ruth Hilditch, A Stephen Holmes, John P Huh, Won K •~en. Jim Heller, Dorothy M Hilgers, John W Holmes, Philip John Huibregtse. Mark E K:~~n. Monica L Heller, Robert Hill, David G B Holmes, Richard B Huilgol, Raja R Hlrrop, FOrviiJe G Jr Hellerman, Leo Hill, James Holton, Derek A Hulkower, Neal D IJ.,. ' "d F Hellerstein, Simon Hill, Ned W Jr Holvoet, Roger Hull, Richard B ""'. Oav;d C W Helmer, Gary A Hill, Richard David Holzman, Robert E Hulthen, Lamek . klaaa Pieter Helton, Burrell W Hill, Robert N Homer, Roger H Hummel, James A Helton, Frances J Hill, Sarah Lynn Homer, William D Hummel, Kenneth E

649 AMS Research Fellowship Fund (Continued)

Hummel, Tamara J Ito, Yuji Johnson, David Lewis Kammeyer, Humphreys, James E Itzkowitz, Gerald L Johnson, Diane Louise Janet Whalen Kelinsas, J-. Humphreys, John F Iwamoto, Johnson, Diane M Kammler, David W Kellaber J ~ Huneke, Craig L Lynn Haremi Johnson, Donald G Kamowitz, Herbert M Keller Art~ollloor Huneke, John Philip lwanaga, Yasuo Johnson, Eugene W Kamp, William p Keller:~~-~~~ Hung, Trung Nguyen Iwasaki, F Shigeo Johnson, Guy Jr Kanamori, Akihiro Keller, Wilfrw Hung, Xiao-Kan3: I wasawa, Kenkichi Johnson, James E Kanda, Mamoru Kelley, Waller Kellner W Hunsberger, L Geralc! Iwata, Koichi Johnson, Jean T Kaneda, Masaharu Cia Kelly, Hunt, Richard A Ize, Jorge A Johnson, Jon L Kaneko, Akira GJ.!-c Hunt, Robert W Izuchi, Keiji Johnson, Joseph L Jr Kanemitsu, Shigeru Kelly, Joba~ Hunt, Walker E Izumi, Shin-Ichi Johnson, Kenneth D Kangel, Jay Kelly, P&o~IJ Hunte, Beryl E Johnson, Kaniuth, Eberhard Kemp, Mar;IJa J Hunter, Colin B Jablow, Eric Robert Kenneth Walter Kann, Edgar D Kempacbiro, o-... Hunter, Jackins, Harvey A Kempermaa. JH Johnson, Robert L Kanner, Richard Kendall R,:. __ . 8 M::~.xwell Norman Jackson, Lloyd K Johnson, Kanno, Tsuneo Kendall' •..._., Hunter, Jackson, William D Robert Shepard Kanold, Hans-Joachim Norma Gerkens Jaco, William H Kantorovitz, Shmuel Wil!;id~ Johnson, Roberta F Kengmona,...... Hunter, Roger H Jacob, Henry G Jr Kaper, Hans G Johnson, Roy A Kennedy, 1Jaclf Atka. Hunzeker, Hubert L Jacob, Niels Johnson, Russell A Kaplan, Alan Huotari, Jacobs, Felix J Kaplan, Stanley Kennedy, Jalia p Johnson, Kenner, Paal M Robert Heikki Jacobs, Harold Kaplan, Wilfred Steven Richard Kenney' Cbvloo 8 Hurd, Spencer Peyton Jacobs, Jonathan M Kaplansky, Irving Johnson, William B Kenniaon, Jo.. a r Hurd, Thomas Robert Jacobs, Marc Q Kapouleas, Nicolaos Johnston, Ernest R Kenaehaft, Patricia C Hurder, Steven E Jacobsen, Martin Kappe, Johnston, William W Kent, Georp A Hurley, Donal J Jacobson, Clas A Johnstone, P T Luise-Charlotte Kent, J T Hurley, Michael G Jacobson, Marc Erik Joichi, James T Karal, Frank C Jr Kent, Joeepb p Hurvich, Clifford M Jacobson, Marcel Jonah, David W Karamatsu, Yoshikazu Kent, Stevea L Hurwitz, R Damel Jacquet, Herve M Jones, Alfredo R Karbaliotis, Peter Keown, Naac,. A Husain, Taqdir Jafarian, Ali A Jones, Carl Hilton Karch, Paul T Kcrckhove, Huss, Mary Jaffa, Robert E Jones, Eleanor Green Karch, Richard R Michael Georp Hustin, Deborah L Jager, H Jones, F Burton Karel, Martin Lewis Kernut, Joba C Hutches, David J Jahren, Bjorn Jones, Gary D Karle, Jerome Kerr, Sudria N Hutchinsc.n, George A J alawi, Fahad Jones, Gordon C Karlovitz, Les A Kf'rsting, GUJ ~ Hutton, Edward L Jambois, Thomas F Jones, Harold T Karlsson, Per W Kerzmu, Norbeno L Huynh, Quyen Q James, Robert C Jones, Jeffrey P Karoubi, Max Keaten, H&ITJ Hwang, James, Willard D Jones, Marsha Finkel Karp, L Keatenband, Bub .. C John Jew-Chen Jamieson, Michael W Jones, Peter R Karpilovsky, G Kevorkian, Anm K Hyers, Donald H Janicki, Ryszard Jones, Peter Wilcox Karrer, Guido Key, Eric StepUD Hyllengren, Anders R Jankins, Mark Jones, Vaughan F R Kartsatos, Kezlan, 'fhomu P Hyvonen, Jaakko P Janowitz, Melvin F Jongen, Hubertus Th Athanassios G Kfoury, A J Jans, James P Jongmans, Francois Karube, Takashi Khadr, Amr S larrobino, Jansen, Willem G Jonker, Leo B Kascic, Michael J Jr Khajoh, H G Anthony A Jr Jantosciak, James S Kassel, Christian Khaleelulla, S M Jonsson, Bjarni Ibele, Charles E Janusz, Gerald J Kates, Louis K Khalimaky, Jordan, David A Ibele, Rebecca W Jara Martinez, Kato, Shin-ichi Efim Davidovida Jordan, G Samuel Ibrahim, A Shawky Pascual Kato, Takao Khalique, C M Jordan, Kirk E lei, Yutaka Jarchow, Hans Katok, Anatole Khan, Jorgensen, Colleen K Igarashi, Akira Jarden, Moshe Katok, Svetlana R Mohammad Ahaad Jorgensen, P E T Igarashi, Masao Jardine, Katz, Andrew Khor, Hoe Peas Joris, Henri E Igari, Satoru John Frederick Katz, Melvin L KhoshneviPD, Duar Joseph, Deborah A Iha, Franklin T Jarratt, Mary K Katz, Talbot Michael Kianoa, Martin S Joseph, George J Ihringer, Thomas Jarvi, Pentti K Katz, Victor J Kibler, Robert E Josephson, Iio, Tutomu Jarvis, Trevor M Katzen, Dahn KichenUI&mJ, William Allen Ijjasz Vasquez, Ede J Jayne, John W Katznelson, Y Satyonad Ikebe, Teruo Jea, Hae-Pyng Jouanolou, Katzoff, Myron J Kiefer, Jamfl E Ikeda, Kazumasa Jea, Kang C Jean-Pierre Kauffman, Louis H KiernaD, Bryce M Ill man, SOren A Jeanquartier, Pierre Joyner, David W Kauffman, Robert M Kieval, Harry S Ilmanen, Tom Jech, Thomas J Juberg, Richard K Kaufman, Arthur Kilgore, Theodore A ImHof, Jeffrey, Alan Judson, Thomas W Kaufman, William E Kilgour, D Marc Hans Christoph Jelen, Jaroslaw Jun, Kil Woung Kaufmann-Buhler, Killeen, Joba Imrich, Wilfried Jenkins, Joe Wiley Junghenn, Hugo D Walter Kim, DoaJIU Inaba, Hiroshi Jenness, Jeffrey W Jungnickel, Dieter Kaul, S K Kim, Hayon lndJekofer, K H Jensen, Arne Jurzysta, Sonja H Kaup, Burchard Kim, Hone JoDI Infante, Ettore Jensen, Ulla Kurstein Justice, James H Kautzmann, Kim, Hooc Ob Infante, Ronald P Jerison, David Justus, Charles H Frank N III Kim, Hyuk Ingraham, Edward C Jerison, Meyer Kavanagh, John P Kim, In Su Kim, Jong·Cbul Ingram, John Michael Jerome, Carlos Kaashoek, Marinus A Kawamoto, Shunji Kim, Jonglik Ingram, Nancy Jane Jerome, Joseph W Kaczynski, Tomasz Kawasaki, Tetsuro Kim, MinbyoDI Ingram, Steven K J eroslow, R G Kadlecek, David Kay, Irvin W Kim, Moon W Innami, Nobuhiro Kahane, Jean-Pierre Jerri, Abdul Jabbar Ka.zamaki, Norihiko Kim, Saon·Kyu loakimidis, N I Jessen, Borge Kahn, Donald W Kazdan, Jerry L Kim, Woo Jo~!ot Iorio, Rafael J Jr Jessup, Peter G Kahn, Jeff N Keane, M S Kim, Younc· Jr Ipina, Lynne Kamstra Jha, V Kahn, Peter J Kearfott, R Baker Kimber, Iribarren, Ignacio L Kailath, Thomas Jo~D ~,..,4 Jiang, Boju Kearn, Vickie H Kimmel, Jo 0 Isaacs, I Martin Jimenez, Jose Alfredo Kajiwara, Joji Kearney, Robert D Kimmerle, Isaacson, Eugene Jimenez, Javier Kakihara, Yuichiro Kearton, Cherry Wolfganl Otto Isard, Stephen D Job, Vanessa R Kakiichi, Yoshiaki Keating, Kevin P Isbell, John R Jockusch, Carl G Jr Kalai, Ehud Keating, ME Kimu~a, ~:~~:. lei Iscoe, Ian John, David J Kalas, Ivan K Keating, Maria C K~ncald, PhiliPpe K1ndler, C Isenberg, J Johnen, Hans Kalia, R N Keaty, John Michael King, /.IllY A Ishibashi, Makoto Johnsen, Eugene C Kall, Peter Keeler, Stephen P Ishiguro, Kenshi Johnsen, Ronald L Kalliongis, John E Keenan, K~ng, ~::: R Ishii, Jyun Johnson, Aimee S A Kallman, Ralph A Daniel Macrae K~ng, RichardiOI Ishikawa, Hirofumi Johnson, Ben Kallstrom, Anders Keeping, Anthony J K~ng, ~andoll R Ishimoto, Hiroyasu Johnson, Bradford W Kalman, Dan KIDI• hell C Kegel, Otto H King, SteP Jose-~ Iskra, Joseph A Jr Johnson, Charles N Kalman, Rudolf E Kegel, Otto H Kinnaaark. Sbia'tcllll Ismail, Mourad Johnson, Kalton, N J Kehayopulu, Niovi Kinoshita. El-Houssieny D Randolph Jr Kamejima, Kohji Keiding, Hans Kinser • aJe•i•• lstrail, Sarin Johnson, Daniel P Kamin, Shoshana Keigher, William F Jlub

650 h Fellowship Fund (Continued) ~sResearc

Koiodner, Krystock, Ignace I Robert L Lakshmibai, V Leader, Solomon Komatsu, Hikosaburo Ku, Hsu-Tung ~.oU''eiidi•. John Lallement, Gerard J Leaf, Gary K Komatu, Kubelka, Richard KtralY · :~ery Yiishaku P Lam, Kee Y Leahy, John V Komiya, Yur;n Kubert, Daniel S Lam, Siu-Por ~,rb1· Robion C Leavitt, William G Komm, Horace Kubo, Fumio Lam, Ktrb1 • Allan M Tsi t-Yuen Lebedin, Neal D KOmura, Takaka Kubo, Tadao Lambek, Joachim Lebel, Jean E ~,reb. raber. l'rs , Kon, Mark Andrew Kucera, Thomas K,rcbb Walter \\ Glen Lambert, John Patrick Lebow, Arnold Konhauser. Kudla, Stephen S Lambert, Joseph M LeBrun, Claude R ~~:~bb~~~ ~ Jr Jo~eph Kudo, Tatsuji D E Lambert, Richard W Le Cam, L M ~~ ,· Wilham A Konig, Kuebler, Heinz J Roy R Jr Lampe, William A Lee, Changwod ~:~&iand. Steve~ Konvi&ser, Marc Kueker, David W W Lamphere, Robert L Lee, Ching-ju C J(,r&man. Ellen Koo, Kuenker, Ja-Kyung Kay E Lampone, Leo W Lee, D6-Won Koo, Reginald Kuenzi, Norbert 1\Jrteb. ~~::~:8 c J Lancaster, Peter Lee, In-Ja B Koornwinder, Tom H Kugler, Lawrence ~~rw:· William E II D Lance, Timothy L Lee, Jang Woo Koosis, Paul J Kuhlmann, Norbert ~~m~n. Christer 0 Landau, Henry J Lee, John M Kopacek, Hal W Kuhn, Robert M Landauer, Kill'· Christopher Lee, .Jyh-Hao Terry Le~ Kopell, Nancy J Kuiken, Kathryn 1\~thL, Masanofl Lander, Felix I Lee, Ke-Seung Kopperman, Ralph D Kuiper, Nicolaas H 1\ttbore, Masao Lander, Julian Charles Lee, Kotik K Korre, Roland R J r Arnold Leichtweiss, Kurt Kozin, Frank Kurtz, Stuart A Kn1ght, Frank 8 Lapidus, Michel L Leighly, Joseph Kozlowski, George Kurtz, Thomas Kntgbt, Julia G Lappan, Peter A Jr Leipholz, Horst Kra, Irwin Kurtzke, John F Kntcht, Kar! Jr Lardy, L3.wrence J Hermann Eduard Krabbe, Gregers L Kushner, Harvey 1\ntll. Ronald J Larkin, Martha A Leipnik, Roy B Kracht, Manfred Kusuda, Masaharu Knotrr, Alan P Larney, Violet H Leite, Maria Luiza Krafft, Olaf W Kusunoki, Yukio Knopp, Marvin I Larsen, Soren Leith, CecilE Jr Kraft, Hanspeter Kuttler, Knorr, K R K Larson, David R Leitzel, James R C Kraft, Jiirgen Kenneth Latimer Knowles, J David Larson, Jean Leitzel, Joan P Kraft, Roger L Kutzko, Philip Knox. Nathaniel C Larson, John L Lelek, Andrzej Kraines, David P Kuusela, Maija 1\nudsen, John R Larson, Lee M Lelong, P J Krakowski, Fred Kwak, Nosup Knuth. Donald E Larson, Loren C Lemaire, Luc Krall, Harry L Kwasik, Knutwn, Donald I Stawomir Larson, Richard G Lemei, Han Kramarz, Luis Kwun, Ko. Ki Hyoung Kyung W Larson, Roland E LeMesurier, Kramer, Earl S Kydoniefs, Ko. Ohseun Park Anastasios Larsson, Stig Brenton John Kramer, Kye, Seung-Hyeok ~obayuhi, Shoshicbi Lasher, Sim Lenard, Andrew Kobayuhi, Yuji Raymond F Jr Kyner, Walter T Lashof, Richard K Lengyel, Bela A "io(h. Richard M Kramer, Thomas R Kythe, Prem K Laskowski, Michael C Suzanne Marie Kochman Kranjc, Marko Kyuno, Shoji Lasser, Lewis L Lenstra, Stanle'y Kranzer, Herbert C H W Jr Oscar Lassettre, Edwin Kodttschek Krasny, Robert R Lentin, Andre LaBudde, Christian D Lciszl6, Gabor Kratzke, Thomas M Leonard, Henry S Jr Daniel Eliezar LaSalle, Margaret M Latch, Dana May ~Odtt&, Helmut Kraus, Jon E Leonard, Philip A Labbe, Marcel Adrien Lau, Anthony T 1\orhlu, Anr:e B Krause, Ralph M Leonardi, Sharon Ann Labelle, Gilbert Lauchli, Hans ~orhlrr. T L Krause, Ulrich Lepisto, Timo Valter La brousse, Laufer, Henry B 1\or.tner, Alfred Kraut, Gertrud L Lepowsky, James I Jean-Philippe Lauria, Francesco E Krauter, Arnold R Lerat, Alain ~~t?e, Gottfried M Lacampagne, Carole B Lauritzen, Steffen L Kravitsky, N aft ali Leray, Jean K:rllnan. Stanley Lachance, Lausch, Hans K · Jee Heub Kravvaritis, D Lerch, Robbin L Michael Anthony Laush, George K:::er, Peter Krebs, Neil E Lerche, Kenneth D Lachlan, Alistair H Lavalle, Irving H 1\ob I, Carl \V Kreiss, Heinz-Otto Leschen, John G Lachtman, Mark E Lavine, David 1\ob:· Joseph J Krener, Arthur J Lesieur, Leonce Lackmann, John Law, Peter R 1\ · fiobert y KreogPr, Tanja L Lesmes, Jaime Lacomba, Ernesto A Lawniczak, Anna Krieger, Henry A T Lesniak, Linda K~:~:rt. Ja~r Lada, Thomas J Lawrence, l(otlu Kriegman, David A Le Sturn, Bernard :• Pertti T Ladas, Gerasimos Anthony Lee KoJlfll~l, Shoji Kriegsman, Helen F Lett, G Scott Laderman, Lawrence, John W Kriete, Thomas L III Leung, Allen Yuklun li.t~ittti~ Sa.dayoshi Julian David Lawson, Krinik, Alan David F Leung, Anthony W KC.'b · Photton G C Ladwig, John A Kristiansen Lawson, H Blaine Jr Leung, Denny Ho-Hon l(~;c~~~ ~rt Siegfrit:>d Laffey, Thomas J Lawson, Walter R Gundor~h K Leung, Dominic S P K'>irsar.' R ~ Lafontane, Jacques Lawvere, F William Krompart, Lucia Beth Leung, Tat-Wing Koi:t$ch, Lagarias, Jeffrey C Lax, Anneli Kronheimer, Erwin H Levatin, JoAnne Lee Lagnese, John E Lax, Peter Ko:~u~a Worthy Kronstein, Karl M D LeVeque, William J Lahr, Charles Dwight Lax, Robert F ~ ~114r, oh_an A C Krueger, Charles G Levi, Howard Laidacker, Michael A Lazarov, ~olfllan Janoe Krug, Don K Connor Levi, Inessa Laine, Ilpo Lea, James D Bernard Krumpholz, Gary R Levin, Jacob J Laitinen, Erkki Leach, Ernest Kruskal, Martin B Levin, Richard G D Lakshmanan, Neela Leader, Jeffery J Levin, Simon A

651 AMS Research Fellowship Fund (Continued)

Levine, Daniel S Liu, Li-Qian Lusztig, George Malik, Davender D S Levine, Eugene Liu, Shih-Chao Luther, C F Malkevitch, Joseph Marvin, John W Levine, Harold I Liu, Tai-Ping Luther, Norman Y Mallet-Paret, John J Marzuq, Maher Levine, Howard A Liu, Tsai-Sheng Lutoborski, Adam Malliaris, Tassos G Mascioni, Vania MIt Levitin, Lev 8 Liu, Wei-Nung Lntterodt, Malm, Dennis R Maserick, Peter D Levitt, Norman J Liu, Yung- Way Clement Henry Malon, David M ~ash~, Ed.,ard ~ Levitt, Tad S Liu, Zhishun Lutwak, Erwin Maloney, James J M::~~kaBernltd Levosky, Thomas D Liu, Zhang-Dong Lutzer, David J Maloof, Giles W Levy, Azriel Liulevicius, Arunas L Luvisetto, Maria Luisa Malvern, Lawrence E David' Joaeph Levy, Gene Livingston, Albert E Luxemburg, Mamelak, Joseph S Massam, Helene Levy, Ronnie Fred Livingston, Wilhelmus A J Man, Chi-Sing Massell, Paul B Lewan, Douglas Marilynn L Lyford, William C Manders, Kenneth L Massey, Willit.rQ S Lewand, Robert Llibre Salo, Jaume Lynch, Robert E Manders, Kenneth L Masten, Jeffrey Pa J Lewin, Jacques Llosa, Joseph Lynch, William C Manderscheid, Masten, Jeffrey p~l Lewin, Mordechai Lloyd, Noel G Lyndon, Roger C David C Matchett, Andrew J Mate, Attila Lewis, Charles J Lloyd, Stuart P Lynes, Christopher R Manfredi, Juan J Lewis, George M Lluis, Emilio R Lyon, Mangiarotti, Luigi Mather, John Nonnaa Matheson, John D Lewis, Houston I La, Chi Yeung Herbert Chancellor Manis, Merle E Mathis, Darrell L Lewis, John A Lo, Tzee-Nan Kuo Lyons, Russell D Manjarrez, Victor M Mathis, Frank H Lewis, L Gaunce Jr Loane, Edward P Lysko, Janusz M Mann, Benjamin M Mathison, Neil T Lewis, Robert H Lochs, Gustav E Lyubeznik, Mann, Henry B Mathsen, Ronald M Lewis, Roger T Lockhart, Gennady M Mano-N achbar, Matijevic, Jacob R Lewis, William James Deborah Frank Lyzzaik, Pauline Matos, Joio p Lewy, Hans Lockhart, Jody Meyer Khalil Abdallah Manogue, Joseph F Matovsky, Lhee, Byung Su Loday, Jean-Louis Manoly, Bruce E John-Anton Cbarltt L'heureux, James E Loeb, Henry L MacCamy, Richard C Manougian, Edward Matsuda, Shi~:eo Li, Lide Loeb, Peter A Wendy A MacCaull, Mansfield, Maynard J Matsumoto, Yu!tio Li, Li-Ge Loeser, Francois A M Macbeath, Mantel, Harold John Matsumura, Hideyul Li, Luen-Chau 1 Logan, Rodney W Macdonald, I G Mapa, Felina G Matsunaga, Teru Li, Tien-Yien Lok, Walter L Macdonald, Ian D Marafino, John T Matsuyama, Yoabio Liang, Jaung Lombardo, Charles J MacDonald, John L Marathe, Kishore B Matthies, Karl H Liardet. Pierre London, David MacDonnell, John J Marble, Robert P Matti, Joseph T Libby. Richard Allan Long, David Darren MacDonnell, Joseph F Marchand, Margaret 0 Mattingly, Libera, Richard J Long, John J Jr Macfarlane. Marchetti, Federico Robert Bruce Liberman, Zvie Long, John M Andrew Ian Marchi, Ezio Mattson, Leroy T Libgober, Anatoly S Longley, Macgibbon, Brenda Marchiafava, Stefano Matulis, John J J Jr Lichnerowicz, Andre James 'A-'ildon MacGillivray, A Dean Marcja, Annalisa Maumary, Ser~:e Lichtenbaum, Stephen Longobardi, Patrizia MacGregor, Thomas H Marcus, Marvin Maurer, Donald E Lichtin, Benjamin L Longstaff, W E Machover, Maurice 1.-farcus, Steven I Maurer, Stephen B Lichtman, Alexander Loomis, Irene H Machtinger, Mardl!siC, Sibe Mawhin, Jean L Lieb, Elliott H Lopez Lagomasino, Lawrence A Margolis, Stuart W Maxfield, John E Lieberman, David I Guillermo Mack, John Michael Margosian, Zaven Maxson, Carlton J Lieberman, Gary M Lopez, Amparo MacKenzie, Margaret Margulies, Caryl A Maxwell, Jamet W Lien, Magnhild Lopez-Carmona, Woodward Margulies, William May, J Peter Liggett, Thomas M Antonio Mac Kenzie, Robert E Marhuenda, Francisco Ylay, Roger William Light, F W Jr L6pez-Escobar, Mackey. Michael C Maria, May H May, Warren L Light bourne, Edgar G K \.1aclachlan, Colin Marin. Francisco L Mayberry, John P James H III Lord, Nicholas MacLaren, M Donald Marin, Irwin C Mayer, Dieter H Lighterman, Mark S Lorenz. Dan H MacMurray, Armand J Marion, Jean Albert Mayer, John Clydt Lightner, Michael R Lorenz, Martin MacNaughton, John S Markanda, Raj K Mayer, Raymond A Jr Lim, Chong-Keang Lorimer. Macphail, Moray S Marker. David E Mayes, Vivienne M. Lima, Asvald Joseph \Vilson MacQueen. David B Markert, Matthew J Maynard, Jamet \\ Lin, Charles S C Loring, Terry A Macwilliams, F Jessie Markis, Louise Leon Mayor, John R Lin, Charlotte Losey, Nora E Madan, Manohar L Markoff, Nicholas G Maziarz, E A Lin, Jer-Yan Jerry Loud, Warren S !\1adan, Ved P Markot, Robert P Mazumdar, Tapas Lin, Jindra Louhivaara, llppo S Madden, James Joseph Markowitz, Mazur, Barry Mazur, Martin Al011 Lin, Qing Loustau, John A Maddux. Roger D Michael Jay Lin, Shine-Min Louton, Tom Mader, Adolf Markus. Lawrence Mazzeo, Rare R Lin, Wen-Hsiung Love, Madison, Bernard L Marie, McAdam, Steph~n 'J McAllister. Byron._ Lin, Yi Sister M Genevieve Marlow, William G Charles Michael Lincoln, Robin A Love, Thomas Robert Madsen, Gregory 'A-' Marlowe, Thomas J Jr McArthur. C W Lind, David W Lovell, John R Madsen. Ib H Marotto, Frederick R McArthur, Kelly Marie Lind, Douglas A Lovern, Susan S Maecher, John H P Marques. Carlos A McAsey, Michael J Lindberg, John A Jr Lovett, JaneT Maeda, Fumi- Yuki Marsden, Jerrold E McAuley, Van A 0 Lindemann, Willi Low, Emmet F Jr Maeda, Michie Marsh, Marcus M McBrien, Vincent Linden, Carl N Lowe, Peter G Maehara, Kazuhisa Marshall, Bernard P Lindenstrauss, Joram Lowengrub, Morton Magenes, Enrico Marshall, David Imler McCall, Ed';;l~i:m (; Lindgren, John E Loxton, John Harold Magid. Martin A Marsiliano, Judy McCallum. Charltt ·' Lindquist, W Brent Lozano, Maria Teresa Magill, Kenneth D Jr Marstrand, John M McCarthy, Donald J Lindsay, John W Lu, Chin-Pi Magnus, Arne \1artelli, McCarthy' John Lindstrom, Mikael Lu, Kau-Un Magnus, Wilhelm Mario Umherto McCarthy. Johr. D!~,,~ Lindstrom, Tom L Lubarsky, Robert S Magnuson, :\1artens, Henrik H McCarthy' paul J penni I 1 Lindstrom, Wendell D Lubin, Clarence I Alan William Marti, Jurg T McCarthY' McCaughan. Ray 4 Linnell, P A Lucas, Billy J Magruder, Richard B Martin. E Dale McClanahanJ,ohn H Lions, Pierre Louis Luce. R Duncan . .:\" V R Martin. J Gregory Jr Mahadev McCleary, Lipkin, Leonard J Luchins, Edith H Mahar, T :\1artin. John R ~cClenahan. Lipp, D W Lucian, Miriam Laura Mahdavi, Kazem Martin, Margaret A E Lipps, Lucier, Bradley J Mahmud. Zafer Martin, Nathaniel F G M~uric~·~yne ~cChsh, Frederick Weissner Ludden, Gerald D Mahoney, Anne Martin, Nigel McColm, Loren Lipschutz, Seymour Luecke, John Edwin Mark Mahowald. Martin, Norman M GregorY John C Lipton, R J Luecking, Daniel H Maiellaro, Michele Martin, Robert H Jr McConnelL Robt'rl ~ Liriano, Sal J Lueneburg, E Mairhuber, John C Martindale, McConnell. 'ferrY R E List, Stephen Luersen. Barbara Maj, Mercede Wallace S III McConnell. 'fhocn&J Litchfield, Kay P Luh, Jiang Majda, George J Martinet, Jean McConn~il, FerritE Litherland, Rick Luk, Hing-Sun Makepe-ace, Coline M Martinez, Jorge C Little, Charles H C Lukacs. Eugene Makkai, Michael Martinez-Maurica, McCorrn'~~itY McCoy, Robert A Little, John B Lumer, Gunter Makovoz, Yuly Javier McCoY' fholfl&t L Littman, Walter Lundell, Albert T Makowsky, Martins, Joyce A McCoY' patrick D. Liu, Hongde Lundgren, .J R H Johann Andreas Marty, Roger McCraY' ~fich•'! !-1 Liu, Hsi-Ching Luo. Zhaohua Malafronte. Thomas A Marumoto, Yoshihiko McCrea. Liu, Jong-Diing Luskin. Mitchell B Maleki. Amir Maruyama, Toru

652 h Fellowship Fund (Continued) AMsResearc Ray !\1oore, Steven M Murphy. Michael G Menezes. Lucia S Mines, W Moore. \Villiam E Murphy. Paul F h:f'Vl!l \1 Mennicken, Reinhard Ming, Ronald Steven Maori, Jamshid Murphy, Thomas N l,lct"nm111o~:l!nt (; Menninga. Nadine L Minsker, Ernest J Mora, Roberto H Murray. G Graham \!cCro~Yh Leon R ~erkel. Rudolph B :\iintel, Maung Mora, Xavier Murray, \lcCul o . h DarrYl Merrie!!. David M Min-oo, \lclulloug Robert J) Roland B Moran, Charles \V Margaret A M Merrit.'n, Jean _ "\.iinton. \lcDJ\'t'tt· :\iirchandaney. Moran, William ~urray, \lcDonald. Jant>t Merryfield, Kt•nt c; Sobhraj Morawetz. Cathleen S Michael Kevin ~ertens . .John R Jr Arjan \lcOona\d. Mirsky, Norman D Mordeson, John N Murre, Jacob P to;atht>Tine J Meserve. Bruce E Moreland, Robert A Muse. Archie Hf'nry \(cOonough. J ~~ Mess. Geoffrey ~ischenko. Peter Andrew Moreno, Muto, Hideo IJcOonough. Metas. ;-.;ick Sudhakara Rodrigo Guillermo Muto. Yosio Jost'ph ~irhael ~etrick. c;:oria Mishra, Marjorie A Mydelski, Jan \lcDo"'·ell. Kenneth p Metropolis, ;-.;icholas C Mislin. Guido Moretz, Morey, PhilipS Jr Myers. Earle F Metzler. Richard C :\1isra, A K \!cOil~· ~us;homa;;; L Ram Christopher L Myers, John R Meuser. Diane !Vlae Misra, Prabudh Morgan, Morgan, John \\' Myers. Russell \\' ~~~~~-::n.· Oenni~ R Meyer. Burnett C Mital. J N R Morgan, Raymond Jr Myerson. Gerald \lcGtt. Robert I Meyer. Donald V Mitchell, Alan C Edmonda Myung, Hyo Chul \lcGthre. o. Carruth Meyn. Gerard G L Mitchell, Emerson \.1organtini, E Morimoto, Akihiko \.lcGtht't'. R1rhard P MPyer. Herman Mitchell. George A Bernard N:'i:'iUinen, Marjatta \lcGibbon. Char]PS Meyer. Jean-Pierre G Mitchell. Ian R Morin. Roberto Nachman. Louis J \lcGough. ~ancy Ann Meyn, Paul R :\1itchcll, James C Moriy6n, J Nadel, Mark E \lcGovrrn. Richard .l Meyf'r. \V \Veston Mitchell, Josephine '\.1 Morley, John \1 J :'-J"<->.dell, Paul T \lcGovf'rn. Wdllarn Mever, \Volfgang T Mitchell, Roger W !\.1orley. Larry Robert ;\ I3 :"Jadler. Sam B Jr \lcGutgan. Me;·t.·rhoff. Robert Mitchell, Morrel. Bernard E Nagahara, Takasi \lcGumM'SS. Mez. Hans-Christian Stephen Ames Morrill, John Francis Oisin E Nagai, Osamu Mherian. Hayrenik !\.1 Mitchell. Stephen G Morris. L Harold \ A Nagami. Keio \ldntosh. Miao, Lung-Chi Mitchell, Theodore Morris, Robert \ldntosh. William D Thomas M :'-J" agano, Tad ash i Michael. Ernest A Mitchell, William J Morrisette, McKay. Thomas G R Nagao, Hirosi Michael. \\'illiarn A Mitchem, John A Morrison, David. \lcKran. Henry P Jr J N agasaka, Kenj i Michalakis, Antony A Mitro, Joanna B !\.tforrison. Evelyn \ld\elvey. Robert W Nagata, K Wayne Michiaki. Watanabe Mittal, D M Morrison, John A \lcKenna. James E F Nagel. Alexander J Michler. C Mittcnthal, Lothrop Morrison. John \lcKrnzie. Ralph ~ E Nagisetty, Rao V Michor, Peter Mityagin, Boris Morrison, Kent McK1bben. William P :"Jaglc. R Kent Mickens, ){onalrl E Miura. Robert M Morrison. Michael A McKmn£>v. Richard L D N agurney. Anna B Middleton, David Miyadera. lsao Morrison, Sally \lcLaugh.lin, Harry \\ Naidoo, Logan Mit:>lke, Marvin V Miyahara, Yoshio Morse, Burt J \ld.. aughlin. Jack E Naimpally, Paul T Miyazaki, Kcn-Ichi Morton. Blaise \lcLwd. Edward B J r Mielke, A Miyoshi, Takeo Morton. Keith \\' Somashekhar ~1 Miesner. \\'alter \kLeod. Robert ~airn, Dean C Mignot, Fu!hert Mizel. Victor J Morton, Lynda S McLmden. Lynn Rudolph M Michael L Mizumoto, Hisao Moschovakis. Najar, \hMahon. Douglas C Mihalik. P Hirobumi Yiannis I'\ J';ajarian, John .\lcMahon. Edith ~ary Mikolic-Torreira, Igor Mizuno. Henri Nakagawa. Kiyokazu \lc\lillan, Audrey \\ Milcetich, John G Mlit.z. Rainer Moscovici. K ~·akagawa, Yoko \!cM1llan. Brockway Miles, E P Jr Moak, Daniel Stuart Moser. Jiirgen I ~akai. Mitsuru \lc\ldlan. Daniel R Jr Miles. Philip E Modica. Luciano Moser. Lucy l\"akai, Yuri \lcMillan, Evelyn R Miles. Thornao; J Moeller, Helmut Karl Moser, \V illiam 0 J I\" akamura, Masahiro MiliCiC. Dragan Moen, Courtney H Mosier, Ronald G I'iakanishi. Yasutaka Millar. T ~ Moena, Ricardo Moss, Carl J Nakano, Kazurni Miller, Clark C Moghaddam, Moss, Kenneth N Martin M Miller. Curtis Paul Mohammad Heza R Moss. Lawrence Stuart ~Takashima. Soonkeon Miller, Dale A :\1ohamed, I J Moss. \Villiam F Ill Nam, J';amba, Kanji Miller, Donald S Mohamed, Saad Motose, Kaoru N aruba, Makoto Miller, Donald \V Mohapatra, R N Motto, Michael H Nambooripad. S K S Miller, Forrest R Mohdali, ~orhashidah Moulden, Trevor H N amioka, Isaac Miller, Haynes R Moise, Edwin E Mount. Kenneth R Namkoong, Kyu-Oh Miller, Hugh D B ~oite, Sally M Mourant.. \iVanda J Dana\\' Miller, Jack M \..1oller, Raymond \\' May. Allen Nance, I\"andakumar. N R Miller, James Curtis Mallin, Richard A Moyls, Benjamin ::"J Nannicini, Antonella Miller. John Boris Mong, Kai Cheong Mrowka, Tomasz S Ollie Miller, John G Mongelli, Dominic Muder, Douglas J I'\anyes. Naoum, Adil G !viiliE'r. Kenneth S ~1onheit, Lilly A Mueller, Bruno J VV Deborah Lynn Miller. Michael J Monk, J Donald Mueller, Carl Douglas Narang, Kamal Miller. :'\icholas S Monleon-Pradas, Mueller. James f{ Narang, Miller. Richard Alan Manuel Mueller. Julia Narasimhan. Carolyn C Miller. Richard R Manna. Antonie F Muhly, Paul S Madhuri N Miller. Timothy L Monrad, Dit.lev Mulase, Motohico Narayan~n, Narayanaswami. P P !\.1iller. ·valerie A ~1onsky, Paul H Mulay. Shashikant B Francis J Miller. W F \..1ontaldi. James A Muldowney, James S Narcowich. Gundo A MiliPr, Willard .Jr Montesinos, Jose M ~1ulla, Fuad S Nariholi. Hiroshi rv1iller, \\'illiam David Montgomery, Hugh L Muller. George M N arushima, Peter Miller, Willi&m y Montgomery, John T Muller, Gert H Nash. M Zuhair Miller. Zevi Montgomery. M Susan Mullikin. Thomas W :\lashed, Millett. Kenneth C Montgomery, Peter L Mullin, Albert A Nash-Williams. St J A Millman, Hicha,rd S !\1ontgomery, Mullins. Sarah E CriHpin Mills, Harl&n D \\-' Duane Mullis. Nastopoulos. Cleo C Mills, Janet E Month. Leslie A Robert Harvey J r N a taro, Dean Mills, Stuart E Monticone, Leone C Mulrow, Edward J N ath. Radha G Melvyn B Mills. \Villiam H Moody, Robert V Mulry. Mary H ~athanson. B Milman Mario !\.loon, Kyung-Ho Munkholm. Hans J :"iation, James Milne, . Ann Moon, Myung-suk \llunkres, .lamPs R ;.Jaugle. \\'aketl.t>ld Milner. Eri< Moonf'y, John J Munoz. Edgar :~onnan !\iavarro, Francisco J Milnor, John \\' Moons. Theodoor M ~unoz. Miguel-C K Milojevic. p S Moore, Danny J Murakami, Shingo Nayak, M M ~ilutinoviC, t'roS Moore, Hal G Murali. V :"iayar, Brij K Mimur&. '\.1amoru \.1oore. Lawrence C Jr Murasugi. Kunw !\'eal. David F Mi.n, K&ng-Joo :\1oore, Marion E Murata, HirmJhi ~Pbres. Bienvenido Alejandro B M~n. Kyung Chan Moorf', Polly Murayama, John T :\'ecochea, Neeb, Donna M Mmagawa. Takizo ~oore, Richard A Murphy. Brian B Minda, C David Moore. Robert H Murphy. Donald P N eggers. Joseph L Minehart Moore, Murphy. Grattan P N" egro, Angelo Debor,&h Fairlcv Robert Laurens Murphy, "Jf'gron. Pablo Victor Minf'mura. Katsuiliro Moore, Robert T Katherine Adele ~ eher, Erhard

653 AMS Research Fellowship Fund (Continued}

Nehs, Robert M Northcutt, Robert A Oodaira, Hiroshi Panchapagesan, T V Neidhardt, Arnold L Norton, Afec Oohashi, Tsunemichi Pandit, Onkar Nath Pederaen Neidhardt, Wayne L Norton, V Alan Ooms, Alfons I Pannatoni, Ronald F Nielov..... Nelligan, John D Nottrot, Roel Opfer, Gerhard H Pannullo, Peercy, D-w Peetre, I Nelson, Edward Novikoff, Albert B Oppenheim, Joseph H Jerome Edward J .... Nelson, Edward 0 Nowell, William 0 Jr Oppenheimer, Seth F Pantoja, Jose Pego, Robt.t L Nelson, Evelyn M Nowlin, Benjamin Peiffer R.­ Ordman, Edward T Panzone, Rafael Peixot~, ,...,. L Nelson, J L Nowosad, Pedro Orellana, Pao, Chia Yen Pekelney, ...... Nelson, Larry D Nugent, Mark Chacin Mauricio Papadopoulos, Michael Nelson, Robert R Nulton, James D Orey, Steven Papageorgiou, ltichard 11oo.o Peligracl, Nelson, Timothy L Nummela, Eric C Orihuela, Jose Nikolaos S C.. Nelson, William Nunez, Pelletier 0....,. Orland, George H Papangelou, Fredos Pelloni,'~l Nemethi, Csaba Pascual Ballesta Orlik, Peter P Papas, Pence, D-..o Neri, Umberto Nunke, Ronald J Orloff, Jeremy M Theodore Thomas Nerode, Anil Nusse, Helena E Orloff, Leo N Pennell, S~A Papistas, Athanassios Penner, Nesbitt, Cecil J Nutt, Michael D Ornstein, Avraham J Rober~ Clo.k Pappakostas, Peter F Penney, Car.~w Neubauer, Gerhard J Ornstein, Donald S Pappas, Peter C Penney, D&rid I Neubauer, Michael G Obata, Morio O'Rourke, Joseph Pappas, Richard C Pennisten, Neufeld, Eric Michael Oberguggenberger, W Orr, Kent Edward Parchment, Osborne C Penot, J PaaiJ. Neuman, Gerald L Michael B Orr, Martin Pardee, Otway O'M Pepper, Pql 11 Neuman, Rosalind J Oberlin, Daniel M Orr, Richard J Paris, Alan Terry Perdew, Paul II Neumann, Bernhard H Obi, Wilson C Orated, Bent Park, Bae Hun Perelli, Alberto Neumann, Peter M O'Brien, Robert E Ortmeyer, Park, Chull Perkel, Moalt, Neustadter, Obrock, Arthur E William Albright Park, Hong-Sub Perkina, p"­ Siegfried F O'Callaghan, Liam J Ortner, Brian R Park, Jae Keol Perlia, Robert,y Neuwirth, Lee P Ochoa-Lions, Osborn, Howard A Park, Jong Geun Perlman, a..,_. Nevai, Paul G Jorge Daniel Osborn, J Marshall Park, Samuel Perrine, Serp Neveu, Jacques Ocneanu, Adrian Osborn, T A Park, Sehie Perry, Peter A.a. Newcomb, Lynn T Ocone, Daniel L Osborne, Mason S Park, Young Ho Perry, Willi• J Newhouse, Sheldon E Oda, Tadao Osborne, Richard P Park, Young Sao Perry, Willi•L Newlander, August Jr O'Dea, Paul J Osgood, Brad G Parker, Ellen Maycock Peroek, StepM. C Newman, Morris Odlyzko, Andrew M Osgood, Charles F Parker, Elwood G Persson, Ulf Newsom, Carroll V Odom, Earl T Jr Oslon, Steve G Parker, Francis D Pesotan, HOIIauc Newton, Abba V Odoom, Frank A Osner, H J Parker, George D Peetana, DiniiO.... Newton, Mervin E Oehmke, Robert H Osofsky, Barbara L Parker, Phillip E Petermann, G I Ney, Peter E Oertly, Frederick Jay Osserman, Robert Parker, Willard A Peten, Ja~~~~~ v-. Ng, Kung-Fu O'Farrell, Anthony G Ostaszewski, Parks, Harold R Peters, Joha I Ng, Peh H Offin, Daniel Clyde Krzysztof M Parlett, Beresford N Peters, Ng, Sze-Kui Offord, Cyril A Osterburg, James Parr, James T Thomu-. Nguiffo, B Michel Ogawa, Hajimu Oster by, Ole Parrish, Daniel M Petersen, Ilea& I Nguyen, Hung Thac Ogden, Nancy C Osterwalder, Konrad Parrish, Herbert C Petersen, K.rll Nguyen, True T Ogg, Andrew P Ostrom, T G Petersen, Lana Parrott, David V Nguyen, Van Hien Ogle, Crichton O'Sullivan, John J Petersen, PeMr Parrott, Mary E Nicholls, Peter J Oguchi, Kunio Oswald, Urs Petersen, Trolll Parry, R Bryce Nichols, Edward Ogus, Arthur Ota, Clem Z Petersen, W...., P Parry, Walter R Nichols, Eugene D Oh, Hi-Jun Peterson, AaDIIIIIMi Ota, SchOichi Parsons, Charles D Nicholson, Victor A 0' Halloran, Joyce Peterson, ClalriJa P Otermat, Scott C Parsons, John D Nicholson, W Keith Oharu, Shinnosuke Otero, Daniel E Peterson, G117 L Parsons, Torrence D Nickel, James A Ohta, Haruto Ottmann, Thomas A Peterson, WUU. C Parter, Seymour V Nickerson, Helen K Ohwaki, Shin-Ichi Pethe, S Oursler, C C Paschke, William L Nico, William R Oikawa, KOtara Oversteegen, Lex G Petri, MODica Pascucci, Richard S Nicol, Charles A Okada, Masami Owa, Shigeyoshi Petricka, R...U J Pasini, Antonio Nicol, Sherrie Jean Okada, Susumu Owen, David R Petro, Jolla W Pass, Ralph P III Nicolas, Jean-Louis Okamoto, Kiyosato Owens, Owen G Petryshyn, W V Passell, Nicholas Niederhausen, Okayasu, Takateru Oxford, Edwin P Petty, CliakNI M Passerini, Henry J Heinrich O'Keefe, David F Oxley, Theron D Jr Petulaote, N.. I Passman, Donald 8 Niedzwecki, G P Okoh, Frank Oyabu, Takashi Peyroviao, Raa Passty, Gregory B Niefield, Susan B Oksendal, Bernt K Ozimkoski, Pfeiffer, Paul I Pastijn, Francis J Nievergelt, Yves Okuyama, Akihiro Raymond E Pflaum, CW Pastro, Pier-Ivan Niino, Kiyoshi Oldham, Frank Ernest Ozsvath, Istvan Pflug, PeW Nind, Thomas E W Oldroyd, L Andrew Patel, Alka Pfluger, Alblrl Patrick, E Vincent Nirenberg, Louis Olesen, Pacella, Filomena Pham, Tu,. J)llll p Nishida, Takaaki Dorte Marianne Pacheco-Castelao, Patrizio, Giorgio Phanord, ~C Nishikawa, Seiki Oliger, Joseph E Jose M Patten, Donald L Pheidaa, A R Nishiura, Togo Oliker, Vladimir I Paciorek, Joseph W Patten, Paul R Phelps, Roblrl JltDo Nisnevich, Yevsey A Olin, Robert F Packer, Judith A Patterson, Larry A Pbili, Chriotbl< V Nissim, Leonard J Olive, Gloria Pade, Offer Patton, Charles M Philipp, w:GJ*It Phillipe, .J S Nitecki, Zbigniew H Oliver, Fatma Padma, Patton, L Raphael Nitsche, Johannes C C Oliver, Robert A N arasimhachari Paulling, John M B Phillipe, ~~~~~ J PhillipS, W Niven, Ivan Olivier, Reinhard M Page, David A Paulowich, David G Piacentini, Njastad, Olav Olmstead, P S Paulsen, Vern I Page, Matthew Keith GiuliaMoril ~ NO bauer, Wilfried H Olmsted, John M H Page, Stanley S Paveri Fontana, S L pjacensa, :::: Noble, William Olsen, Martin Paige, Eugene C Jr Payne, Lawrence E 1 Piatetski-8 L Nobusawa, Nobuo Olshen, A C Paige, Lowell J Payne, Stanley E Noel, Guy G J Olson, Dwight M Paisner, Helen L Payton, Robert G Pias••• :::, 8 Picard, paoiO Noguchi, Hiroshi Olson, Loren D Pak, Jingyal Pazy, Amnon J Noguchi, Junjiro Pearce, Kent Piccinni, I ;;...tel Olson, Paul D Pakes, Anthony G Pickel, pau Nobel, John A Olum, Paul Palais, Eleanor G Pearcy, Carl M PickeriPI• ~ Nolan, John P Olver, Frank W J Palais, Richard S Pears, Alan R J)ouglal 11 Nold, Annett Olver, Peter J Pearson, Robert W Palais, Robert A Pickrell, Noll, Landon Curt Oman, John Arthur Palka, Bruce P Pearson, Stephen C o;rc Noonburg, Virginia A O'Meara, 0 Timothy Peccati, Lorenzo Picoult,~ Pallaschke, Diethard Piene, ,_.. Noor, Khalida Inayat Onat, Emin T Peck, Emily Mann Palled, Shivappa V Pierce, Nordhaus, Edward A O'Neil, Philip J Peck, N Tenney J~s Palm, Andrew C pierce, Ri Noren, .Richard Dennis Peck, PaulS O'Neill, Anne F Palmer, Edgar M Piger, JeaDil Norfleet, Jesse Peter O'Neill, Bernard V Jr Pedersen, Edward A Palmer, John Bergin Pigno, LOll L Norman, O'Neill, Ronald C Pedersen, Flemming P Palmer, John N Pigo11i, ~L Francis Alexander Onieva, Victor M Palmer, Theodore W Pedersen, Franklin D Norman, Peter Onishi, Hironori Pedersen, Henrik PilliPI• &II' Palmieri, John H Pil•. GUll (leG'&" II Jr Norman, R Daniel Ono, Takashi Pan, Ting K Pedersen, Jean J Pirnbley, Norris, Douglas A Onose, Hiroshi Panchal, Champak D Pedersen, Katherine L

654 h Fellowship Fund (Continued) ,O{S Researc

Prince, Deborah E Ratliff, Louis J Jr Richardson, Rodriguez, Roger W Jr Sanjurjo .loBe pjJCb:· Richar~ Prine(', Riitz, Jlirg J Gihnour Enc Geoffrey Eamonn Rauch, Lawrence L Richert, Hans-Egon Roe, Robert P Alfredo Prindle . .John C Rausen, John Richert, Norman J Roebuck, Alan Scott HenrY (' Pi~ro. Pritchard. Frank Leon Raussen, Martin Richmond, Glayvera Roeling, Lloyd G fiJihalJlAnan M Proctor. C \\layne Rave, Werner J Richmond, Jean B Roels, Jacques Albert Paaiul, t{aren R Progovac. Rawnsley, John H Richmond, R oettinger-Kaplan, PaaDfY· Ross George Dusan 'Vukosav Rawsthorne, Daniel A Lawrence B Ida faaJiy. joseph Kalman Prornel. Hans Jurgen Raymond, Frank A Richter, Guenther E Rofman, Edmundo p,nu~r. k. Zbigmew Richter, Horst P Rogawski, p.ouow• a, Nicholas Prottt'L Murray H Rayna, Gerhard 0 Richter, Michael M Jonathan David Pippt~gerRaymond E Protter, Philip E Reade, Maxwell Proulx, Ronald J Reardon, Philip C Richter, Wayne H Rogers, Jack W Jr ~:=ia~. George Proulx, Rebarber, Richard L Richtmyer, Robert D Rogers, Robert C Pitcairn. Joel Viera Kri'ianova Reber, Douglas C Rickart, Charles E Roggenkamp, Klaus \\·' P•tcber. Everett Provencher, Normand Rebnord, David A Rickert, Neil W Rohatgi, Vijay K PiU. Loren D M Pruitt, William E Rector, David L Rickman, B Rohl, Frank D P•ttl, Andrew Prussner, Laird Drew Reddy, ~'illiam L Riddle, Malcolm Lee Rohlfs, Ji.irgen PiUt. David R Przebinda, Tomasz Redfield, Robert H Ridenhour, Jerry R Rohrlich, David E Piaiak. Robert Przybylski, Thomas L Redheffer, Rider, Daniel G Roitman, Judith Placbiy. Detlef Pu, Hwang- Wen Raymond M Riedel, Herbert H J Rolin, Plank. Donald L Pucci, Patrizia Redlin, Lothar H Rieffel. Marc A Jean-Marie Gerard Plano. Richard A Puckette, Stephen E Rieger. Georg J Roller, Tow anna A pJeN, VeraS Redmond, Don Puel, Jean Pierre Romanelli, S Plumeri. Charles John Redner, Richard A Riemen, William P Puerta. Fernando S Reed, Bruce E Riemenschneider, Romero, Cristina Plymen, Roger J Romero-Fuster, Podio-Guidugli, .Paolo Puigbo, Jaume Vila Reed, Coke Stevenson o~wald Maria Carmen Potnaru, Valentm A Pukanszky, Lajos Reed, David L Ries, John F X III Ronga, Felice L L PoetChel, Jurgen Pullman, Norrnan J Reed, Ellen E Riesel, Hans I Ronveaux, Andre Pos:untke, Detlev Pulskamp. Richard J Reed, George Michael Riess, Karlem Rood, John J Pobjolainen, Seppo A Pumplun, Dieter Reed, Irving S Riffelmacher, David A Rooney, Gerald E Jr Polachek, Harry Pun, Ping-Sham Reed, James H Rigby, Fred D Rooney, Paul G Polak, Joel A Purtilo, .James M Reed, John K Rigdon. Robert D Roonguthai, Warut Polemarchakis, H Putnam, Alfred L Reed, Myra Jean Riihentaus, Roos. Guy Polimeni, Albert D Pyle, H Randolph Reed, Robert E Leo Juhani Roosenraad, Cris T Polking, John C Pym, JohnS Reedy, Christopher L Rijnks, H Root, William L Pollataek, Harriet S Rees, Charles S Rike, Thomas A Roozernond, Leen Pollingher, Adolf Quade, Edward S Rees, Mina S Riley Akbar, Rosa, Alexander Polly, Mary R Queen. Clifford S Rees. P K Christine C Rosales, Rodolfo Pnlonaky, Ivan P Quigg, John C Reese, Matthias F Riley, Robert F Rosati, Mario Pomerance, Carl Quine, J R Reese, Richard H Rinaman, William C Rose, Donald J Pootbieux, Quinn, Declan P F Reeves, Alyson A Riney, John S Delores Marie Quinn, Frank S III Rose, Gene F Regan, Francis Ringeisen, Richard D Pool, James C T Quinn, Joseph E Rose. I\' .J Rehm, Allan S Ringel, Emanuel I Poon, Vat Sun Quint, Richard A Roseman, Joseph Rehmann, Ulf Ringel, Gerhard Poor, Walter A Quintana. Rosen, Julie A Rehmer, Karl 0 Rio, Jose Poorman, Alan G Ricardo B Jr Rosen, Kenneth H Reichaw, Meir Rishel, Thomas \\' Pope, Darrell R Quiring, Donald K Rosen. Lon M Reicher, Israel R Ritt, Robert K Pop-Stojanovic, Quiroga, Rafael P Rosen, Michael I Ritter. David L Zoran R Reichmann, Rosen, Ned Ira Peter Ivan Rivet, Roger Porit&, Alan 8 Rabinowitz, Paul H Rosenbaum, Ira Reid, Kenneth B Rizvi, Syed P11rt, Sidney C Rabinowitz, Stanley Rosenbaum, RobNt A Reid. R Clay Mohammad Tariq Porta, Harry J Race, David M Rosenberg, David Reid, William H Rno, Jung-Sik Porte, Jean Radford, David E Rosenberg. Ivo G Reilly, Roach, Michael D Porter, Gerald J Radjavi, Heydar Rosenberg, Norman Raymond Robacker, John T Porter, James F Radzikowski, Pawel Jonathan M D James F Robbin, Joel W Porter, Lawrence Rager, John E Reineck, Rosenberg, Milton Porter, Willis B John H Robbins. David A Raggio, Guido A Reinoehl, Rosenberg, Steven Potey, Eldon E Robbins, David P Rains, M A Reise!, Robert B Rof'!enblatt, Poet, Karel A RobNt, Alain Rajca, John F Reissner, Eric Joseph Max Potboven, Kenneth L Roberts, Dorothy K Rajnak, Stanley L Reiten, Idun Rosenfeld, Gerald Potts, Donald H Ralevic, Nebojsa V Rejto, Peter A Roberts, Rosenfeld, Norman S Poulaen, Ebbe T Ellen Rail, Louis B Rem. Martin Florence Rosenfeld, Ronald L :ourabrnadi, Mohsen Ralston . .James V Remillard, Bruno Roberts, Howard M Rosenlicht, Maxwell A pour-El, Marian 8 Rempel, Richard S Roberts, Jean E OU&et, Maurice Ramachandran, Rosen::.tein, Doraiswamy Remus, Dieter Roberts. Joel L George M Jr ~O..el!, Michael H Roberts, Richard C a.rer, Rarnakrishnan, Renardy, Michael RosenthaL Arthur J Dinakar Renner, Lex E Robertson, A Guyan Rosenthal, David S p Stephen Charles Renshaw, James H Robertson, pO..ere, Elizabeth Ramaley, James F Rosenthal, Eric S Resch, Richard I Alexander P p&were, Kathryn A Rarnalho, Margarita Rosenthal, Erik J Rarnamurthi, V S Restrepo, Guillermo Robertson, James B Rosenthal, Haskell P p::ra, Morris Walton Retzloff, David G Robertson, Malcolm S p ere, Robert T Ramanujan, Rosenthal, Jenny E Reynolds, David W Robertf'!on, :"Jeil Victoria Ann Melapalayam S Rosenthal. Kimmo I p:;ra, Randell, Richard C Reynolds, Donald F Robinson, Clark Rosenthal, Peter p 1 • Keith w Reynolds, Jim D Robinson, Daniel A p~:ea, Jean Randol, Burton S Rosenzweig, Raney, George N Reynolds, Mark C Robinson, Derek J S Samson M Prakaa~' J~gdish Rangaswamy, K M Reynolds, William F Robinson, G de B Rosier, Ronald C Preill '• ~nmala Range, R Michael Rhai, Tong-Shieng Robinson, lvor Ross, Kenneth A Prej~ Md itchell Paul n oerfer Rankin, Rheinboldt, Werner C Robinson, Ross, Paul p Ltanfted w ' Samuel Murray Rhodes, Frank Joanna Ryten Rossello, Francese A p:~r, Anne Ransom, Adelbert W Riaza, Roman Rcbinson, Michael L Rossi, Guido A p ey, AN Rao, Ribe, Martin G Robinson, Raphael M Rossi, Hugo p~~~t Michael y Vidhyanath Kajana Ribeiro, Hugo B Robkin, Eugene E Rossi, John F Pr~ce 'G Claude Rapp, p E Ricci, Fulvio Robson, Robert 0 Rossmann, Wulf Prtce' Baley Rascle, Michel Ricci, Michael G Rocha, Carlos V Rosson, John Prtce' ~ohn F Raskind, Wayne Mark Ricci, Stephen J Rocha, Luiz F C Rota, Gian-Carlo Prie.~, ~ 0 tna~ E J r RasRias, Rice, John R Roche, Claude Roth, Richard L Charles Pr~fltley Y?t~,a J George Michael Rice, John William Rockland, Roth, Rodney J Prull a' Wtlliam M Rassias, John Michael Richards, John F Rockwell, Richard D Rothaus, Oscar S Prj~ o~ert C I I I Ra<~sias, Themistocles Richards, Pamela C Rod, David L Rothberger, Fritz Prillle~ Mtrko Michael Richards, Thomas L Rodman, Leiba Rothblum, ' Jeremy 0 Ratcliff, Gail D L Richardson, Henry R Rodrigue, Garry H Criel George Ratiu, Tudor Stefan Richardson, Kari L Rodriguez, Gilmar Rothe, Erich H

655 AMS Research Fellowship Fund (Continued)

Rothman, Neal J Sagarman, Scarborough, Schremmer, Fran'!;oise Rothman, Sheldon N Elma Rebecca Steve Douglas Schrij ver, Alexander Sen, R.N Rothschild, Bruce L Sagle, Arthur A Scarpi, Giambattista Schroder, M Senechal lla.z_ . 1 Rothstein, Mitchell J Sali, Chih-Han Scarsini, Marco Schroeck, Senft, J R. --~~~a~ Rottenberg, Reuven R Sahab, Salem M Scavo, Thomas R Franklin E Jr Senge, G Rotthaus, Christel Saint Mary, Donald F Stedrov, Andre Schryer, Nor man L Senger I s'::: Seppala Rouche, Nicolas Saito, Akira Schaal, Werner G H Schubert, Cedric F 0 Roush, Fred Saito, Kazuyuki Schacher, Murray M Schuett, Werner Mi~K·. Rousseau, Cecil C Saito, Shiroshi Schaefer, Paul T Schulte, Felix Seppalo-Hor::u-..... Rousseau, Christiane SaitO, Yoshimi Schaeffer, John M Schulz, Friedmar J David Rousseau, Thomas H Saitoh, Saburou Schaeffer, John W Schumacher, Carol S Serapiooi a... Rouxel, Bernard Sakai, Katsuro Schaer, Jonathan Schumacher, Georg B Serbyn, \viW.. Rouys, Robert L Schafer, Alice T Schumacher, Scott Servedio, l'raQ D Sakuma, Motoyoshi Sethur&l!laa J Rowe, Niles W Salamin, Eugene Schafer, James A Schumer, Peter David Sethuramaa: Rowell, William W Salamon, Dietmar A Schafer, Richard D Schumitzky, Alan ~ Sevenatea, Arjea Rowen, Louis Halle Schiffer, Juan Jorge Schurrer, Augusta L Salas, Saturnine L Sever, Mlcbaol Roxin, Emilio 0 Salehi, Ebrahim Schaffer, Steven Schuss, Zeev Sevrain, C~ Royden, Halsey L Schafke, R Schuster, Seymour Salehi, Habib Jeaa-Paul Royer, James Samuel Schaller, Kay- U we Schuur, Susan E Salisbury, Thomas S Sexauer, Nora.. I Royster, Wimberly C Schapiro, Philip J Schwab, Frederick R Salkind, William Seydel, E lr Ruben, Schaps, Schwanz, Cheryl L llobort Sallee, G Thomas Sgro, J-bA Flores Espinoza Maika Elisheva Schwartz, Salles, Maurice Sha, Jipina Rubenfeld, Lester A Sallman, Jeffrey E Scharlemann, Charles Freund Ruberman, Daniel Shaabao, 11"­ Sally, Paul J Jr MartinG Schwartz, Ira B Shaba.,, Abc11IIAI;, Rubin, Herman Schatz, James R Schwartz, Jacob T Saltiel, Leon Shaffer,~~ Rubin. Jean E Saltz, Daniel Schatzman, Schwartz, Laurent Shafii-Mouavi Rubin, Robert J Salvadori, Anna James Carl Schwartz, Lionel Morten ' Rubinstein, Joachim H Samayoa, Rodolfo Schauer, Richard L Schwartz, William Shaftman, Dm.i Rubio de Francia, 1 Samelson, Schaum berger, Schwarz, Binyamin Shah, Chudodll c Jose L Christopher L Norman Schwarz, Friedheim Shahabi, II A Rudin, Bernard D Samelson, Hans Schechtman, Gideon Schwarz, Gerald W Shaharir Rudin. Mary E Samolis, Scheffer, Carel L Schwarz, Thomas Shahin, Rudnick, Karl Ruth Anastasia Scheffer, Vladimir Schweiger, Fritz MazeaMO...S Rudolph, Daniel Jay Sampson, Gary Scheinberg, Stephen Schweitzer, Eric Shahahahaa.i, Ruelle. David P Samuel, Pierre Scheinerman, Schwerdtfeger, Mehrdad II Ruess, W Sam:hez, David A Edward R Hans WE Shale, David Ruh. Ernst A Sanchez-Diaz, Rafael Schell, Emil D Schwietzer, Michael J Shallit, JeffrtJ 0.11. Ruijsenaars, Sanchez-Pedreno, Schellhorn, Scissors, Richard H Shamble, Joha P Simon Norbert Jean-Pierre Salvador Sclove, Stanley L Shand, Sbermu. Ill Ruiz, Alberto H Sanchez-Vazquez, Schelp, Richard Scoppola, Carlo M Shannoa, Suaa Ruiz, Ceferino Gonzalo Scherer, Godela Scott, Dana S Shapiro, DaaieiB R ulla, James L Scherkoske, L Sancho San Roman, Scott, Leonard Jr Shapiro, David Edll Rumely, Robert S Kenneth D Juan Scott, Paul James Shapiro, Georp S Rumsey, Howard C Jr Schiffer, Max M Sanders, Georgia E Scott, Peter Shapiro, JackS Runck, Paul Otto Schiffmann, Gerard M Scott, Ridgway Sanders, Jan A Shapiro, Louil W Rund, Hanna Schiller, Ilya Scott, Warner Henry Sharma, Ambi...... , Sanders, Lee Knisley Rung, Donald C Schilling, R J Harvey III Sharma, P L Sanders, Robert W Ruoff, Dieter Schillo, Paul J Scott-Thomas, John F Sharma, Parub1 I Sanderson, Donald E Rus, Teodor Schlag bauer, Hartmut Scourfield, Eira J Sharp, Heor;r Jr Sandomierski, Frank L Ruscheweyh, Stephan Schlichtkrull, Henrik Scoville, Richard Sharp, Jack Carroll Jr Sands, Rush, David Eugene Schmeelk, John F Scriba, Christoph J Sharpe, Michlll J Jonathan Winslow Rushing, T Benny Schmerl, James H Seager, Suzanne M Sharpe, Richard W Sangren, Ward C Rusinak, William A Schmet terer, Seal, Charles Edwin Shaw, Guy B Sangwine-Yager, Ruskai, M Beth Leopold K Searcy, Charles J Shaw, Mei·Cbi Jane Rosamund Rusodimos, Iason Schmid, Josef Sears, Michael Shayib, Mohalllllld A Santalo, LA Russell, David Martin Schmid, Jurg Sedgewick, Shea, Patrick J Santos Filho, Russell, Gary L Schmid, Rudolf Charles H W Shearer, Michael Jose Ruidival S D Russell, Thomas F Schmid, Wilfried Sedory, Stephen A Sheehan, Geofl' Santos, Rafael Russo, Bernard Schmidt, Dieter S Seebach, J Arthur Sheen, Rooa·CIIJG Santosa, Fadil Russo, Dominick A Schmidt, Harvey J Jr Seebach, Linda. Sheffer, Albert D Russo, John A Sanz-Serna, J M Schmidt, Henry J Jr Seebeck, Charles L III Sheffer, Ioador II Russo, Margaret T Saperstone, Stephen H Schmidt, Kenneth C Seeley, Robert T Shelly, Eup";!' W Russo, Paula A Saphar, Pierre David Schmidt, Klaus D Segal, Sanford L Shelly, M11°. . I Rutland, Leon W Jr Sapozhnikova, Vera D Schmidt, Roland Segers, Richard G Shelton, Ch~ Rutledge, Dorothy S Sarafyan, Diran Schmidt, Wolfgang M Segnari, T James Shelton, Rl . 1 Rutschman, David H Saraaon, Donald E Schneebeli, H R Sehgal, Sudarshan K Shelupaky • Dawld 1 Rutter, J W Sarason, Leonard Schneider, David I Sehgal, Surinder Shemanake, ~ Ruttimann, Sarian, Edward Schneider, Hans Sehgal, Virindra M Shen, Yuan· YGII Gottfried T Sario, Leo Schneider, Manfred F Seid, Howard A Shenitl, Ch~lel Ryan, Donald E Sarrat, Charles F Schneider, Victor P Seidel, Johan J Shepherd, J Job C Ryan, Francis D Sastri, Chelluri C A Schnitzer, Franz J Seidenberg, Abraham Shepberdson, Ryan, John G Satake, Ichiro Schnyder, Walter A Seidman, Thomas I Sherif, NaP• Ryan, Kevin M Sato, Hiraki Schochet, Claude L Seifert, George Sherk, FA Ryan, Michael D Sato, Ken-iti Sherlock, Schoen, Alan H Seifert, Herbert Philip Tho .... C Ryan, Patrick J Sato, Masako Schoen, Carl P Seifert, Ralph L Ryan, Peter M Sauder, Dean L Schoen, Richard M Seifter, Norbert Shermao, Cl:: J Ryeburn, David Saut, Jean Claude Schoenenberger-Deuel, Seikkala, Seppo A Sherman, ~bolll' L Rykken, Charles John Savage, James R Johanna Seitelman, Leon H ~~:~~·~~-pbs Savage, Richard P Jr Schoenfeld, Lowell Seitz, Gary M Saade, John Marshall Savariraj, G A Schoenwaelder, Sekino, Kaoru She~iberl Jeu·~K Sabbagh, Gabriel Savin, Gordan Ulrich F Selby, Alan M Saccoman, John J Sawka, John M Scholz, E Seldin, Jonathan P Shibata,~~ Sachs, David Sawtell, Roy G Jr Schommer, John J Jr Selgrade, James F Sh~bataPau~ L Sacks, Paul E Sawyer, Emerson L Schon, Rolf Seligman, George B Sh•ck, .4-ll.. L Shields, }.{P Sacksteder, Richard C Sawyer, Eric T Schonbek, Maria Elena Seligman, Mark L Shifftn8Do C Sadosky, Cora S Sawyer, Stanley A Schoneborn, Heinz Sell, George R Shiftett, 1111...... Sadun, Lorenzo A Saxton, Ralph Arthur Schrauf, Geza H Sellers, Peter H Shifrin, T~ Saeed-ul-Islam, M Sayeki, Hidemitsu Schraut, K C Selmer, Ernst S Saeki, Sadahiro Sayre, John E Schreiber, Bert M Seltzer, Stanley E Sh~ga, :u:: ... YtD Saff, Edward B Scalzo, Richard C Sh1h, ;..Oi Schreiber, Morris Semmes, Shih, SbaJ Sagan, Bruce E Scaramuzzi, Roberto Schreiner, Erik A Stephen William

656 h Fellowship Fund (Continued) AMsResearc

Siu, By run B Son~. Sung- Ye~l Stasheff, James D Straubing, Howard Siu. Man-Keung ~on~. Ku~um K Staton. William A III Straughan, Brian Siu. Yum Ton

657 AMS Research Fellowship Fund (Continued) s~abo, Manfred Egan Terrae, Riho Torres de Squire, Turyn, Richard J Szalajka, Walter S Terwilliger, Paul M Maria L Tutte, W T Van Deueater Szarek, Stanislaw J Terzuoli, Andrew J Torres, Euclides Tuvell, Walter E llook w ' Szczarba, Robert H Teaser, Steven B Torres, M VanEck, II N Tuzhilin, Avgustin Szczyrba, Igor Tewfick, Torres, Waldo A Vaa Eerde.re Sze, Alexander Ahmed Hisham Tosques, Mario Tymchatyn, Edward D Paul 14 c~· Szekeres, George Textorius, Bjorn 0 B Totaro, Burt J Tyrl, Paul Van Geem.en, Ben Szeto, Mabel Thelen, Brian J Tousley, Horace W Tysk, Johan Van Lint J Vao l

658 F Uowship Fund (Continued) ,A)IS aesearch e Jeffrey Allen washburn, Werschulz, Arthur G Williams, Peter David Wright, Robert B Jr Wessel, W Roy Williams, Wright, Joseph S Richard R Jr Wright, Marcus W A Washburn, Sherwood West, Dennis E \'tfl'· 0~:~d Williams, Robert F Wright, Mary H f~kli•· Washington, West, Donald C ¥ .,N Bruce Edwin West, James E Williams, Ronald 0 Wright, Ron P Williams, Sarah Wright, Steve J n;-Jarnes A Washington, Westbrook, Edwin Lawrence C Westbury, Williams, Wright, . Christopher Grey Scott Warner Thomas Perrin Jr """"V~· J~.,ard R Wass, Noel Christopher Western, DW Williams, Vincent C Wschebor, Mario ~:;·. L Ya Charles K Wu, Ching-mu Wasserman, Arthur G Westman, Joel J Williamson, Clifton J Wu, Hung-Hsi pr paul F Wasserman, RichardS Westphal-Schmidt, u Williamson, Francis U Wu, TC ~~~ 'HidekaZU Watanabe, ShOji Westwater, M John Williamson, JgpiO Jack Wurfel, Tilmann ..... Watatani, Yasuo Westwood, Derek J Williamson, ...... Shushan Lal E Marie A Waterhouse, Wetzel, John E Williamson, Richard Wurster, Jr filll:'~k. Lucien William C Wexler, D Wills, Jorg M Wylie, Clarence R J Walter w.n tdichael L Waterman, Daniel Wheeler, Charles H III Willson, Stephen Wyss, fiatt• Raymond Waterman, MichaelS Wheeler, John A Wilson, James B fill'1"' Daniel F Daoxing Waterman, Peter L Wheeler, Robert F Wilson, John H Xi a, Jingbo :::~~r David H Watkins, DavidS White, Alvin M Wilson, Leslie C Xi a, Zhen Xiang er Diane M Watkins, Joseph C White, Arthur T Wilson, Paul R Xiong, B B Yuan :::er: Gretchen Watkins, Mark E White, Benjamin S Wilson, Raymond Xu, fiaper, R W Watkins, Murray S White, Brian Cabell Wilson, Robert Lee fiaper, Richard C Morris Watkins, White, Charles M Wilson, Robert R Yachter, 'l'a&O•"· Joh_n. B William Thomas White, Denis A Wilson, Terence E Yadin, Micha 0 wacreicb, Phahp Watkinson, Anthony White, Donald B Windham, Yadin, Micha Wap&aff, Samuel S Jr Watnick, Richard M White, George N Jr Michael Parks Yahya, SM Wakl, John J Watson, Harry A Jr White, John T Wine, James D Yajima, Yukinobu WaiDler, Steph~n Watson, James D White, Lee Wayne Wing, G Milton Yale, I Keith Waiawrilht, Erac Watson, Martha F White, Myron E Wingler, Eric J Yale, Paul B John WaiiW'tilbt, Stephen White, NeilL Winker, Steven K Yamada, Miyuki Waiveril, Charles F Watson, John J White, Stevan Russell Winslow, Dennis N Yamada, Shinichi Wajaryb, Bronislaw Wavrik, Arthur K Whitehart, FE Winston, Kenneth Yamada, Toshihiko wUaaa, Kaoru Wayman, Alan Whitehead, George W Winters, Robert Yamaguchi, ltaru Wake •. Bob Alan Wayne, Weaver, George E Whitehead, Wintrobe, F Yamaguchi, Jinsei wu1man, Peter R Kathleen B Wirszup, lzaak Yamaguchi, Keizo Walawander, Weaver, James Whiteman, Albert L Wise, Gary Lamar Yamakawa, Mineo CJDthia A Weaver, Wiskott, Bettina Yamaki, Hiroyoshi Walcaak, Hubert R Robert Wooddell Whites, Keith W Wm Douglas Yamanoshita, Tsuneyo Walde, Ralph E Webster, Sidney M Whitfield, John H M Withers, KJ Yamaoka, Kenya WU., David B Wechsler, Martin T Whitley, Robert J Witsch, Yamasaki, Masayuki Walker, Carol L Wedel, Arnold M Whitley, W Thurmon Witsenhausen, Hans S Minoru Walker, Elbert A Weening, Joseph S Whitman, Andrew P Witt, Donald M Yanagawa, Kenjiro Walker, Homer F Wefelscheid, Heinrich Whitman, Philip M Witt, Michael B Yanagi, Walker, James Edward Wegener, Delano P Whitney, D Ransom Witte, DavidS Yanagiwara, Hiraki Walker, James S Wegner, Udo Whitney, Ronald F Witte, Franklin P Yang, Chung-Tao Walker, James W Wehausen, John V Whitney, Stephen Witten, Louis Yang, Jeong Sheng Walker, Julia A Wehlen, Joseph A Jr Whitson, Kim J Woan, Wen-Jin Yang, Kung-Wei Walker, Larry R Weibel, John L Whitt, Lee B Wochele, Mark D Yang, Zhanbo Walker, Marshall Wei!, Clifford E Whittaker, James V Woeppel, James J Yano, Ken taro Will, Charles T C Weiler, Jerome T Whittall, Gerald B Woess, Wolfgang Yanowitch, Michael Will, Curtias E Weill, Lawrence R Whittlesey, Emmet F Woldar, Andrew J Yao, Andrew Chi-Chih W~l. G E Weiner, Brian L Why burn, Clifton T Wolf, Edwin M Yap, HP Wlllace, David A R Weiner, Jerome H Why burn, Lucille E Wolf, Frantisek Yap, Leonard Y H Wallace, David Robert Weinitschke, Wickelgren, Wayne A Wolf, Thomas R Yaqub, Fawzi M W~l .., C J Hubertus J Wicker, Fletcher D Wolfe, Michael David Yarmush, David L WII.Jn, Lawrence J Weinkam, James J Wickerhauser, Wolk, Elliot S Yasue, Kunia Wlllin, Hans E Weinstein, AlanD Mladen Victor Wolkowicz, Gail S K Yasuhara, Ann W&lli1, Walter D Weinstein, DavidS Widman, Kjell-Ove H Wolpert, Scott A Yasuhara, Mitsuru Wallcbap, Gerard E Weinstein, Jack Widom, Harold Wong, Alex Cheuk W Yau, Stephen S-T Wlilb, John B Weinstein, Michael I Wiegand, Roger A Wong, James S W Yeager, Dorian P John J Wlilb, Weis, Dennis G Wiegand, Wong, Kwok Chi Yebra, Wallh, John Thomas Weis, Lutz Sylvia Margaret Wong, Jose Luis Andres Wlilb, Mary L We is, RansomeD Wiegmann, Philip Pit-Wang Yee, GeorgeS Walter, Gilbert G Weisner, Louis Klaus Werner Wong, Raymond Y Yeh, Kwanching Eleanor B Walter~, Weiss, Asia lviC Wielenberg, Norbert J Wong, Yeh, Neng-Che Walter•, Peter Weiss, David M Wiener, Howard W Roman Woon-Ching Yen, David H Y Waltman, Paul Weiss, Shau-King L Yhap, Waltota, Jay R Guido L Wightman, ArthurS Wong, Weiss, EP Wong, Sherman K Ernesto Franklin l'aa, Zhe.Xian Norman J Wigner, Weiss, Volker Wong, Warren J Yntema, Mary K WaabJ, Goran Richard M Wihstutz, Weiss, WilliamW Yo he, James M Waas, Cecilia y Robert J Wik, Anders Wong, Yokoi, Hideo Waa1, Derming Weiss, Winfried R E Wik, Ingemar L Wong, Yuen-Fat Weissler, Norman J Wong, Yung-Chow Yomdin, Yosef N :Ill, Edward T H Frederic B Wild berger, Weitkamp, L Andrew J Wood, Geoffrey V Yoneda, Kaoru 'ti .... Hwai·Chiuan Galen Wiles, Welch, Lloyd R Wilker, Peter Wood, John C Yoneguchi, Hajimu -~·· Kwang·Shang Wellner, Jon A Wilkerson, Wood, John W Yood, Bertram ,:•· L~ke Wells, Charles F Clarence W Wood, Thomas E Yoon, Byung Jun \'arc~ Yang Hsiung Wells, Michael B Yoshida, Masaaki W all, Henry A David M Wilkinson, Steven V Woodroofe, 'I; lld, Harold N Wells, R 0 Jr Willard, Stephen Woodrow, Yoshida, Zensho w. &td, John T Wells, Robert Williams, Bennie B Robert Edward Yoshimura, Jin Genji t;ltd, JOsephine A Welmers, Everett T Williams, Charles W Woodruff, William M Yoshino, 'live, Buck Welters, GE Williams, Dana P Woods, Alan C Yoshino, Takashi Wendel, A Dale Yoshizawa, Taro Robert B J r James G Williams, David Woods, w:~:d, D Young, Barry H lillDe a, Gregory T Wendland, Wolfgang L Williams, Dorothy J Woods, Jerry It • Ranson J Wendroff, Burton Williams, Francis D Woods, R Grant Young, David M Jr _.:;:. Frank W III Wendt, Dieter W F Williams, George K Woodward, Gordon S Young, Donald F \ '• S.th L Wene, Gregory P Williams, Gerald W Woolf, William B Young, Elmer Lorne Wenger, Ronald H Williams, Hugh C Wouk, Arthur Young, Lael M -:::· L B~tt~ Wente, Hugh M WoyczyD.ski, Wojbor A Young, '&rtit~ieW llharn E Henry C Williams, Wenzl, Hans Williams, Lawrence R Wrench, John W Jr MacDonald Burritt Alfred E ~lrlcb.,..:ki Werfel, Scott Williams, Lynn R Wright, Charles R B Young, Paul M 'v.i, Sh • Stefan E &ukat A.li Wermer, John Williams, Margaret A Wright, David G Young, Sam Wayne Werner, Peter Williams, Mark Wright, David J Young, Virginia Ruth

659 AMS Research Fellowship Fund (Continued)

Young, Wo-Sang Zahreddine, Ziad Zeller, Mike Ziobro, John M Younger, Daniel H Zajac Edward E Zelmer, Graham Zippo, Siro ZaidO, L&~IJ6 Younis, Zalcman, Lawrence A Zemanek, Janice R Zipse, Philip W ~ucker, Stevea M Rahman Mahmoud Zalik, R A Zemmer, Joseph L Jr Zirilli, Francesco uckerberg II Yovanovich, Zama, Nobuo Zhou, Zhiming Zitron, Norman R Zuckerman' G'/I.Ja. L M Michael Zarnbrini, Jean-Claude Zhu. Jianchao Zitzler, Siham Braidi Zuckerman' 'Mtete J Zuckerman' p &rtit '­ Yu, Jing Zamfirescu. Zia. Lee L Zivaljevic, Rade T Yu, Lucille Chieh Christina M Ziege, Roland W Zizi, Khelifa Zw('~bel, J~hn&~llt Yui, Noriko Zanolin, Fabio Ziegler, H J \V Zizler. Vaclav ~w~lfel, Paul F Zw1ck, 0 Yung, Mordechai M Zarantonello, Sergio E Ziegler, Zvi Zlatev, Zahari Zaring, Wilson M Zierau, Roger Craig Zo, Felipe J Zwier, Paul J Zabrodsky, Alexander Zaslavsky, Thomas Zierler, Neal Zoch, Richmond T Zacharia, Dan Zechar, Corwin S Ziesenhenne, Zoercher, C Z Anonymoua (79) Zacharias, Gail Zeheb, Ezra Linda Curtis Zomorrodian, Reza Zacks, Shelemyahu Zehnder, Eduard J Ziller, Wolfgang Zoreda-Lozano, Juan J Zadeh, Lotfi A Zeigler, Fredrick J Zilmer, Delbert E Zorn, Paul Zaharopol, Radu Zelinsky, Daniel Zimmerman. Jay J Zoroa, P Zahid, Zelie, Joseph Zink, Robert E Zorzitto, Frank A Muhammad Ishaq Zeller, Karl Zinn, J Zou, Hung Bin

ICM-86

Abotteen, Essam A Bshouty, Daoud Edgar, Hugh Maxwell Hag, Per Kwasik, Stawomir Adler, George Burghelea, Dan Wallace Hahn, Marjorie G Adolphson. Alan C Bustelo, Julia Ana Eiseman, Peter R Hamilton, Lalli, Bikkar S Aguiar, Glenn E El Carnal, Abbas David Howard Lam, Thu Uc Aizenman, Michael Calder bank, Robert Elliott, Joanne Hamilton, Howard B Landon, Michele B Akylas, Cardenas, Humberto T Enayat, Ali Hartig, Donald Lange, Charita G Triant<1phyllos R Carey, A L Ericson, Lars Hatori, Asako Lee, Chung N Al-Dhahir, M W Caricato, Gaetano Everitt. William N Hayashi, Mikihiro Lee, John Chin Allan, Robert Boyd Carlson, John R Hector, J Gilbert Lehrer, Gustav I Allinger, Deborah F Carrington, Walter A Fadell, Albert G Hempel, J A Lichtenstein, Walter D Anantharaman- Carson, Mark Erwin Fadell, Edward R Henkin, Douglas W Lightbourne, Delaroche, Claire Castro, Alfonso Fahy, Michael A Hepp, Klaus James HIll Celestin. Higgins, John R Faour, Nazih S Lin, Charles S C Anderson, James A Lennox Isidore Hoare, A Howard M Lin, Fenson, Eitan M Jer-Yan Jerry Anderson, Mary J Chan, Beda Hofmann, Lindstrom, Tom L Ferguson, David R Andersson, Rolf L Chan, Jean B Mark Challis Liu, Shih-Chao Ferry. Steven C Anichini, Giuseppe Chan, Ming Kam Holme, Audun Lluis, Emilio R Fine, Benjamin Anton, Jose Manuel Chan, Yun K Hopkins, Mark R Lobo, Natividadt A Finley, Joel F Arlinghaus, Sandra L Chao, J A Hornung, L'lrich Loeb!, Richard I Fischer, Arnold, Timothy K Chazin, Robert Louis BPrnd Horwitz, Judy A Lorentz, Rudolph A Fitzgibbon, Assadi, Amir Hossein Chicks, Charles H William E Hsieh, Wan-Chen Lucas, Thomas G Atzmon, Aharon Chidume, Fitzpatrick, Ben G Hughes, C Bruce Lyons, Richard~ Charles Ejike Fleishman, Bernard A Hurley. Charles Rory Lynn~>, Baartmans, Chipman, J Curtis Floyd, William ,J Huthnance, Edward D William Kimbel Alphonse H Christ, F Michael Forsythe, Keith W Baillieul, John B Chu, Tienchen Francis. George K lves, Robert T Macdonald, I G Baillon, Jean-Bernard Cochrane, Todd E Franco, Salvatore S Iwahori, Nagayoshi Madden, Jamea Jottp~. Balkema, A A Coggins, Friedlander, Susan J Mallio!;, Anastal!U08 Sandler, Wyllis Porter Eldridge III Friedman, Charles N Jacobs, Glenn K Manders, Kenneth L Banks, John A Cohen, Haskell Frohman, Charles D Jacobson, Marcel Mansour, Mohamed Banning, Charles L Cohen, Marvin N Fu, Yen-Tzu James, Willard D Marcus, Michael B Barajas, Alberto Cole, Floyd B Ill Furth. Dave Jenkins, Joe Wiley Markis, Loui&e Leon Barcellos, Anthony Conlon, Samuel B Jensen, Ulla Kurstein Marlin, Joe A Marsden, Edwin L Jr Bauer, Frances B Connett, William C Gale, Deborah Nelson JoffP, Peter Martindale, Becker, James C Connoly, Frank X Galliher, Herbert P Johnson. Gordon G Wallace S III Behncke, Horst Conrad, Allen F Galloway, Johnson, Beissinger, Cook. Edith A Steven Darrel Masih, Samuel A Gregory James Massey, William Janet Simpson Cook, Thurlow A .Jones, G A Garcia, Sonia M F Matthies, Karl H Belair, Luc Coolsaet, Arnold A Gardner, Merritt P Jones, Kathryn A Bell, Wayne C Coste, Alain Jones, Marsha Finkel Mauceri, G C .d G Gerber, Marlies McDowell, Davl Bellin, Gianluigi Cowen, Michael J Jordan. Steven L Ghosh, Parimal K McKiern~n, ~r~d ~ Bellow. Alexandra Gillett, Calvin C Joseph, Deborah A Bennett, James H Daaboul, Mouaffak Joyce, David E ~lc:"/erney, G Mark~ Glass, Michael S MN~rschaert, M Berg, John Richard Darko, Denis F Judson, Thomas W Gluck, Herman R Melvin, Paul .:~ Berg, Joseph Dauxois, J Jurdjevic, Velimir Godfrey, William A Berge, John Orrin Davis, James J Mendelsoh~, ~~~~ Godsil, Chris Men g. C Berglund, John F De Canniere, Jean Kalas, Ivan K Chlng~cel Goeters, Herman P Mewborn, A d W Berstein, Israel DeLeon, Morris Jack Kaminker, Jerry Goldman, Malcolm Bertram, Edward A Demilio, Richard A Kaneko, Tetsuo Miller, D~n; el J Goldsteifn, Max Miller, M•c a N Block, Richard E Derzko, N A Karp, L Goodman, Miller, Ro~ert • Bojars, Juris A De Sapia, Rodolfo V Sue E Kawohl, Bernhard Milner, CKioU Boland, James M Deshpande, Goyal, Sulbha Kay, Joseph A E~:~ Graham, Victor W Milnor, Tl a A Bozeman, Robert E Janardan V Keough, Gerard E Mingo. Jatnetl Braunschweiger, DeVault, John L Gray, Cary G Kevorkian, Aram K Gray, George A Mischenko, Chris C Devos, Robert M Khazal, Peter Andr~:.,b Bray, William 0 Di Paola, Robert A Green, Mark L Rey adh Rashed Mishra, sw:~~ 1d Brickell, Ernest F Domic, Antun Greig-Smith, N H Kilambi, Mitchell, K Brickman, Jacob Doss, Said Griess, Srinivasacharyulu ~ark Mitchell. R N Brockett, Roger W Dostal, Milos A Robert Louis .J r Kim, Moon W Mobapatra,nnY J Grivel, Pierre P Brodnax, Drbohlav, Karel Kimura, Tosihusa Moore, Oa Rebecca Martin Drams, Carl G Grow, David E Kinsey, L Christine Brown, Duff, George F D Gundnzalp, Yavuz Kline, Niall W Mo~=bert Laure~• Charles Franklin Duntsch, Iva Gunnarsson, Knorrer, Horst JaJP" Brungs, Hana H Durst, Lincoln K Thomas E W Krieger, Henry A ~~;~:~: Jobn W Bruter, Claude P Dwyer, William G Guthrie. Joe A Kushner, Alberto Leon

660 ~~-S6 (Continued)

Patterson. Larry A Scattone, Francesco Suen, Ching-Yun Walsh, John B Gr~gory J Payne, Thomas H Schell, Emil D Sun, Jiayong Walter, Charles N ...... GeorgeR Perez. Jose Jesus Schiff, Joel L Suter, Ueli Wardlaw, William P ,..,.... J(eilh W Perry, Peter Anton Schneider, Hans ,...... Lee D Swanson, David L Wasserman, Robert H Pettet, Martin R Schuett, Werner Sylvester, John Wattenberg, Frank A ~· Masanori .,_. ... Phelps, Kevin T Seda, Anthony Karel Wee, In-Suk Segal, Sanford L Phillips, Richard E Tan, Soo Tang Weidner, John F ,.--;;:f~Y Cbamba, Plumeri. Charles John Segnari, T James Tang, Ping T Weiner, Joel L James~ Pogorzelski, Sehgal, Virindra M ,..Jdo'Wil~homas G Tavares, Geovan Weinzweig, Avrum I Henry Andrew Shafii-Mousavi, Tavernini, Lucio Wells, James H ::;:·aarn M Portinari, Joao C Morteza Wells, Robert Prest, Michael Y Shamble, John P Theilheimer, Feodor Thieleker, Ernest A Welstead, \:aftal~ich. ~~rion Prince, Deborah E Shank, Herbert S Stephen Thomas Thomas, Scott D ~~~a~o: Tad R Pugh, David L Shapiro, David Eden Wheeler, Robert L sapraJaD· K Thorpe, Alice C Puttaswamy, T K Shapiro, Dawn M White, Brian Cabell JuDI ~~~~. W~n Shatz, Stephen S To, Ting On \Vhite, Myron E ~ 1011111 , Adil Raddatz, William D Sherif, Nagwa Tondra, Richard J ·. lrr David R Wild berger, Norman J Radford, David E Shields, Allen L Towsley, Gary W ~ntis. Stylianos Wilf, Herbert S Ramaley, James F Shochat. David D Toyoshima, S,...an. Rogers J Witsch, K J Rao, Ranga R Shores, Thomas S Tetsunosuke \,_.011 , Paul K Witsenhausen, Hans S Rao, Veldanda V Shpuntoff, Albert F Tracewell, Theodore N "tt~litld. Susan B Wong, James C S Reed, Michael C Siemon, Helmut Trushin, David \oi. Sun Sook Wong, William W Rehmer. Karl 0 So1r1. Taka8hi Silverman, Edward Tsagas, Grigorios F Wood, Derick Reicher, Israel R Singh, Sankatha P Tucker, Charles T Wright, J D Maitland O'Connor, M Lesley Reid, Les Singmaster, David B Tunnell, Jerrold B Wymore, A Wayne Reilly, I van L ()doll>. R W K Sipe, Patricia Lilaine Turner, Philip H Oflia, Daniel Clyde Richter, Wayne H Sirao, Tunekiti Turner, T Rolf Yamaguchi, Seiichi Opt. Arthur Riley, Siu, Byron B Tymchatyn, Edward D Yang, Ting Obaru, Shinnosuke Geoffrey William Skarda, Ralph V Jr Yeh, Susan M T Roberts, Joseph B Skjelbred, Tor ()sat, Emin T Ukegawa, Takasaburo Yomdin, Yosef N O'Seill, Barrett Robinson, Smith, Justin R Umegaki, Hisaharu Yoshida, Zensho Qocood. Brad G Raymond G Jr Smith, Roger R Urenko, John B Younglove, James N Ouuki. T Rochon, Donna F Smythe, Neville F Ursini, Aldo Younis, Ottmbacher, Peter Romero-Fuster, Sneddon, Ian N Rahman Mahmoud ()uydin, Murad Maria Carmen Srinivasan, T P Vamos, Peter Rose, David A Srivastava, Jaya N Zame, Alan Van Arkel, Nicolaas A Pakula, Lewis I Rosen, Lon M Srivastava, Kailash N Zaslove, Barry L Palmer, John Bergin Ryan, Michael D Stanek, Peter F G Vanderbei, Robert Parchment, Osborne C Ryan, Raymond A Stanford, David P Van Meter, Robert G Anonymous (6) Puier, Ellen Maycock Stanton, Robert J Van Rossum, Herman PatiODI, Charles D Sabharwal, Ranjit S Stern, Venkataraman, Pucucci, Richard S Salcido, Lynnell Elizabeth Rangachari Pathak, Rogelio Carrillo Stevens, Gary E Vincenzi, Antonio Vijay Oamodar Sankappanavar, H P Stewart, James D Viswanathan, B Patterson, David B Sant, Lino Street, Anne Penfold Vourtsanis, Yiannis

Contents: b.-methods in group rings; The GROUP RINGS, CROSSED Jacobson radical of group rings; Zero divisors PRODUCTS AND GALOIS in group rings; Polycyclic group rings; Crossed products of finite groups; Crossed THEORY products of infinite groups; Computing the symmetric ring of quotients; Galois theory DonaldS. Passman and crossed products; Galois theory of prime rings; Rings and fixed rings. For readers with a basic graduate level background in algebra, this book provides 1980 Mathematics Sub;ect Classification: 16 a readable introduction to three major ISBN 0-8218-0714-5. LC 86-1177 ISSN 0160-7642 Interrelated subjects of noncommutative 80 pages (softcover), May 1986 algebra. The theme is the interplay List price $12, all individuals $7 betY:'een group theory and ring theory, To order, please specify CBMS/64NA deahng specifically with group rings, crossed products and the Galois theorv of · ' J . nngs. The author has carefully Shipping/Handling: 1st book $2, each tncl~ded most definitions, to keep the add'! $1, $25 max. By air, 1st book $5, each req.lilred background minimal. Each article c t · . add'! $3, $100 max. the .- on au~s a s~lectwn of results on Prepayment required. Order from AMS, glven top1c, a hmited number of P.O. Box 1571, Annex Station, Providence, proofs or sketches, and at least a few RI 02901-9930, or call 800-556-7774 to use open Problems. VISA or MasterCard.

661 Journal of the American Mathematical Society

Editors

Michael Artin, MIT H. Blaine Lawson, Jr., SUNY at Stony Brook Richard Melrose, MIT Wilfried Schmid, Harvard University Robert E. Tarjan, Princeton University and AT&T Bell Labs

Associate Editors

James G. Arthur Joe Harris Peter Bickel Hendrik W. Lenstra, Jr. Gerd Faltings Andrew Majda Charles L. Fefferman Hugh L. Montgomery Michael H. Freedman Paul H. Rabinowitz Daniel Friedan Karen Uhlenbeck Ronald L. Graham

The Journal of the American Mathematical Society will be published quart.erl~, b~ ginning in January 1988. It will contain research articles of the highest quality 111 areas of pure and applied mathematics. Authors are requested to include introduc­ tions which will be accessible to research mathematicians in all fields.

There are no page charges for this journal.

Manuscripts may be submitted to any of the editors. The journal will be se~ :; AMS, using the JIMS- TEX macro package developed to simplify the use of . an mathematics. If the manuscript is prepared using JIMS-TEX, the tapes or floppies c be used directly without need for further proofreading. 1987 AMS Elections ~ Council Nominations for Vice-Presidents and Members-at-Large JORDAN ALGEBRAS IN . 'dents and five members-at-large of ANALYSIS, OPERATOR two vice-~rlesi. 11 be elected by the Society in a the Colli!Cl WI f 8 7 THEORY, AND ed I ction in the fall o 19 . cooteSt ~ e residents will serve for a term of QUANTUM MECHANICS The vice-p Th C 'I ars effective January 1, 1988. e ~u?ci 1110 ye · ted three candidates for the pos1t10n. Harald U pmeier bas nomma TheY are: This book is based on the CBMS Regional James G. Glimm William P. Thurston Conference held at the University of BarrY Simon California, Irvine, on July 15-19, 1985. In The five members-at-large will serve for a recent years Jordan algebras have found term of three years. The Council nominated interesting applications in seemingly such seven candidates. They are: unrelated areas of mathematics as operator theory, the foundations of Richard W. Beals Diana Frost Shelstad quantum mechanics, complex analysis Johnny E. Brown Donald Soli tar in finite and infinite dimensions, and Lawrence Craig Evans Harold M. Stark harmonic analysis on homogeneous Albert Marden spaces. The author describes some The Council plans to name a fourth candidate relevant results and puts them in a for vice-president and additional candidates for general framework, based on the concepts and J B* -triple. member-at-large to bring their number to at least of J B-algebra ten. Contents: J B-algebras and J B• -triples; The deadline for petitions proposing addi­ Bounded symmetric domains and tional nominations is July 6. Such proposals will J B•-triples; Siegel domains and Cayley not reach the Council for action by mail ballot transformations; Geometry of Jordan IIDtil after that date. structures and quantum mechanics; Derivations and dynamical systems; Kernel President's Candidates functions and harmonic analysis; Hannonic functions and Hua operators; Toeplitz Cor the Nominating Committee operators and Toeplitz c· -algebras; Index 1988 and 1989 theory for multivariable Toeplitz operators; Quantization of curved phase spaces. Four members of the Nominating Committee are fall of 1987. Continuing 1980 Mathematics SubJect Classifications: to be elected in the 17, 32, 46, 47, 43, 58, 81 lllelllbers are: ISBN 0-8218-0717-X, LC 86-28794 M. Salah Baouendi Carl Pomerance ISSN 0160-7642 Paul C. Fife 96 pages (softcover). January 1987 William P. Ziemer List price $13, all individuals $8 ,,_ ~reshident G. D. Mostow has named four of To order, please specify CBMS/67NA ""'e1g t d'd 1'1.-. can I ates for the other four places. "'"1 are: Shipping/Handling: 1st book $2, each $5, each Griess add'] $1, $25 max. By air, 1st book ~~~~Dwork Robert Louis add'! $3, $100 max. If no · ~ Leonard L. Scott Prepayment required. Order from AMS, t.ingmg ~nations by petition have not appeared P.O. Box 1571, Annex Station, Providence, to use eight number of candidates to at RI 02901-9930, or call 800-556-7774 fast ~t to~al VISA or MasterCard. ~dent. ' 1 will be brought up to eight by the

Bttluehem p Everett Pitcher ' ennsylvania Secretary

663 1987 AMS Elections Nominations by Petition

Vice-President or Member-at-Large Two positions of vice-president and member of the Rules and Procedures . Council ex officio for a term of two years are to be filled in the election of 1987. The Council intends Use separate copies of the form for each . I for vice-president, member-at-large 0 caadicl.te to nominate four candidates. Nominations by the Nominating Committee. ' r llleJDber fi petition as described in the box are acceptable. 1. To be considered, petitions m t Five positions of member-at-large of the dressed to Everett Pitcher, Secretary u;.; ld- Council for a term of three years are to be 6248, Providence, Rhode Island 02940 ~· IIOl filled in the same election. Nominations by pe­ arrive by July 6, 1987. ' - tition in the manner described in the box are 2. The name of the candidate must be · IIWDa acceptable. The Council has stated its intent to It. . appears h m t e Gom b. d'ne Membership Liat. Hlbe have at least ten candidates and will bring the name does not appear in ~he list, as in the eue fi a number up to ten if the nominations by petition new member or by error, It must be as it appean. do not do so. the mailing lists, for example on the mailing label: the QD. to the Council, which, the Notices. If the name does not identify Petitions are presented didate uniquely, append the member code wllili according to Section 2 of Article VII of the may be obtained from the candidate's ~label bylaws, makes the nominations. The Council of or the Providence office. 23 January 1979 stated the intent of the Council 3. The petition for a single candidate m&yta~­ of nominating all persons on whose behalf there sist of several sheets each bearing the statemem fi were valid petitions. The Council of 20 January the petition, including the name of the position, IIIII 1987 established a policy that, beginning with the signatures. The name of the candidate must beer· interval1987-1996, the Council intends to approve actly the same on all sheets. no more than two nominations by petition of the 4. On the facing page is a sample form b pe­ from the Semary; individual in any ten year period. titions. Copies may be obtained same however, petitioners may make and use pholooopils Prior to presentation to the Council, peti­ or reasonable facsimiles. tions in aid of a candidate for the position of 5. A signature is valid when it is clearly !ball vice-president or of member-at-large of the Coun­ of the member whose name and address is given iD cil must have at least 50 valid signatures and the left-hand column. must conform to several rules and operational 6. The signature may be in the style ch011e11 bJ' considerations, which are described in the box. the signer. However, the printed name and addle~ I will be checked against the Combined Membmilil List and the mailing lists. No attempt will be mad! The Nominating Committee for 1988 to match variants of names with the form of Dllllf neither in the CML 11(1 111 The name of a candidate for member of the in the CML. A name the mailing lists is not that of a member.~ may be placed on the Nominating Committee ple: The name Everett Pitcher is that of a ote ~ ballot by petition. The candidate's assent and The name E. Pitcher appears. not to be. N rl petitions bearing at least 100 valid signatures are the mailing label of the Not1ces can be peeled ri required for a name to be placed on the ballot. and affixed to the petition as a convenient 'IIIII In addition, several other rules and operational presenting the printed name c~rrectly.) arioUt If' considerations which are described in the box 7. When a petition meetmg th~e~theCit' should be followed. quirements appears, the Secretary w~l a,melll.­ didate whether he is willing. ~o have his ~ocedure IJf ballot. Petitioners can fac!li~ate t~e P dstateiJIIII' accompanying the petitions with a s1gne from the candidate giving his consent.

664 NOMINATION PETITION FOR 1987 ELECTION . ned members of the American Mathematical The undersig Society propose the name of

d·date for the position of (check one): asacan I

D Vice-President D Member-at-Large of the Council D Member of the Nominating Committee

lithe American Mathematical Society for a term beginning January 1, 1988.

~Name and Address (printed or typed, or Notices mailing label)

Signature

Signature

Signature

Signature ~------

Signature ~------~

Signature

665 JOURNALS OF DISTINCTION

• MATHEMATICAL REVIEWS Since 1940, Mathematical Reviews has been the recognized reviewing and ab­ stracting journal covering published mathematical research literature. Over 40,000 reviews or abstracts, by 12,000 international reviewers, are published each year. The reviews in each issue are arranged according to the 1980 Math­ ematics Subject Classification (1985 Revision). Subscriptions include annual author and subject indexes. Published monthly. 1987 subscription rate: Either paper or microfiche subscriptions: List $2950; Inst member $2360; Indiv member $354*; MR Reviewer $236* Postage surcharge: India $153; other foreign $60 Combination paper and microfiche subscriptions: List $3924; Inst member $3139 $200 late charge applies Optional delivery: First class $70; airmail $190 *Add $10 for subscriptions in the US; $60 for subscriptions outside the US . • CURRENT MATHEMATICAL PUBLICATIONS This current awareness journal, which is published every three weeks, is a sub­ ject index of recent and forthcoming mathematical publications which have been classified by the editors of Mathematical Reviews. (The classification scheme used is the 1980 Mathematics Subject Classification (1985 Revision), published in the most recent annual index of Mathematical Reviews.) Each issue contains an author and key index; author and key indexes covering a half year are in­ cluded in issues 9 and 17. Each issue contains a list of the serials represented in that issue and a separate listing of serial additions and changes, as well as a section containing the tables of contents of certain journals. Volume 19 is the 1987 volume. 1987 subscription rate: List $233; Inst member $186; Indiv $140; MR Reviewer $93 Postage surcharge: India $38; other foreign $25 Optional delivery: First class $30; airmail $60 10% late charge applies. . . ns are not Subscriptions are sold only on a calendar year basis; split year and multiple year subscnptlD uarY accepted. Subscription orders received from nonmember institutions and organizations after Ja~murn 1 of the subscription year will be sold at list price plus a 10% late charge (rounded); the maXI late charge for any subscription is $200. . before Microfiche Subscriptions: Microfiche editions of subscriptions are mailed (first class or airmall~uction the issue is sent by the printer. All fiche are negative, 105mm by 148mm, have a 24 to 1 re ratio, and contain 98 frames per fiche. ,....

PREPAYMENT REQUIRED. Send orders to: American Mathematical Society, P.O. ~~he 1571, Annex Station, Providence, Rhode Island 02901-9930 USA, or call 800-556-77741n continental US to use VISA or MasterCard. June 20. Pacific Lutheran University raconta, . _.,- f r the 835th Meetzng program o

Registration d l al 1d thirtv-fifth meeting of the . ht hun re< J . Thr rig \I thematic a! ~'":rety·wtll be held_ at Pa- The meeting registration desk will be located in .\_mrncan · a l' ivcr,;itv in Tacoma. Washmgton, thr lobby of the Rieke Science Center. The . Lutheran n . l . . 'II c~c_ , June 20. EJ87. T ns rneetmg wr desk will be open from 9:00 a.m. to 11:00 ,,n ·'aturda;. . · ]·unction wtth· t 1Je p an'fi c 1'or"' th - a.m. on Friday and from 8:00 a.m. to 10:00 · held lil con 1 A · · f "" · f the \!at bcmatica ssocratron o a.m. on Saturday. The registration fees are wr;t ;ectwn o $10 for members of the AMS or MAA. $16 for America. nonmembers, and $5 for students or unemployed mathematicians. Invited Addresses

Br invitation of the Commi~tee. to Select !_lour Petition Table · · ak ~ for Far Western Sect ronal Meetmgs. A petition table will be set up in the registration ~pr e,.. · · d l h. :here will be one mnted one-hour a cress. T e area. Additional information can be found in a •praker is: box on page 526 in the Salt Lake City meeting . BRA:'iKO GRl'.:'iBAl'\1. l:niversity of Wash- announcement in the April issue of Notices. :ngton. The geometry of polyhedra, Saturday, 10:45 a.m. Accommodations A block of dormitory rooms has been reserved on campus for participants. Rates are $8.65 per Special Sessions person per night, double occupancy and $12.65 per Br invitation of the sanw committee, there will person per night. single occupancy. Participants ~one special session of ,;elected twenty-minute should make reservations by writing to: Kenneth papers. The topic of thi" session, the organizer, E. Batker, Department of Mathematics, Pacific and final list of speakers i,- Lutheran University, Tacoma, WA 98447. The Polyhedral and planar graphs, MOSHE deadline for receipt of reservations is June 5, 1987. ROSE:\FELD, Pacific Lutheran l:'niversity, Sat­ Participants who prefer off-campus accom­ urday. 1:30 p.m. The ,;peakers are David W. modations should make their own reservations Barnette. Peter Gritzmar;n, Branko Griinbaum. directly with the hotel/motel of their choice. A ;,ora_A. Hartsfield. Vict<1r L. Klee, Dragoslav listing of area motels, the distance from the uni­ c.ubJc. Mtchael D. Plummer, and Moshe Rosen­ versity, and current rates are as follows. Rates do fPid not include local taxes and are subject to change. Apple Inn (6 blocks) 1811 South 76th Street, Tacoma, WA 98499 Contributed Papers Telephone: 206-473-7100 There will also be om• "<~ssion for contributed Single: $29 Double: $34 ·m-minute papers. Best Western Lakewood Motor Inn (6 blocks) 6125 Motor S. W., Tacoma, WA 98499 Telephone: 206-584-2212 MAA Program Single: $38 Double: $40 ;The ·'-HA · program on Thursday with a ~ort course D · . . . . . Butler's Heritage Inn (6 blocks) " . on zsc rrtr /l;c;thematzcs uszng dzffer- 'ce equatz h · . 6802 South Sprague, Tacoma, WA 98499 in on.s. c ilii'PO t1y J A.\1ES T. SANDEFUR ' Georgetow r · Telephone: 206-4 75-5900 •r,urse co . n lllvrr:.;Jt~ On Friday the short Single: $29 Double: $34 ''"o c ntmu,es. and 0CJ'·-ALD 13U'SHAW Wash- ... ,, n ~tate r ...... c ' Nendel's Motel (5 blocks) ·'<'ture tit! d Rnn <'I sHy. wlll present an afternoon 8702 South Hosmer, Tacoma, WA 98499 :11h fi e ejlectwn., nn discrete mathematics e rst two ye . -. ·\ . . . Telephone: 206-535-3100 :Jet Lein h ld m ·'· c tthe Fnday evemng ban- Double: $45 ';ILL~!A} ,; . at tlw ~':'I wood Inn, LEONARD Single: $39 ?:e;·d · · umven;ny Cli Texas at Aust1·n and Quality Inn ( 4 blocks) . •'. 1 ent of the . . . . ' :ed Pi . "-lAA. Will dehver an address 9920 South Tacoma Way, Tacoma. WA 98499 ,. . ea.santrzes '. ::versitv C · ·"'-' '' noon luncheon in the Telephone: 206-588-5241 HoBERT· J e-~~~r C;Jtfc·" Shoppe on Saturday, Single: $28 Double: $31 '\Will n E\\u r. \\p,tc-rn Washington Univer- Tacoma South Travelodge ( 4 blocks) s,eak on · Sessi . a topic io be announced. 9915 South Tacoma Way, Tacoma, WA 98499 . F ons for co t .. ;., ridav f 11 nt,:cted papers will be held Telephone: 206-588-6615 · a t ernoon - 1 , . • dnu 'ctturday ·.nornmg. Single: $28 Double: $32

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00 00 85 85 Food Service arriving by bus. the terminal is in downtown . in the rniversity Center will be Tacoma; take bus #45 to the University. should take 1'bt cafe:enaboth days of the meeting as well ~s Persons driving to the meeting to Tacoma. take exit 127 and open dunn~ the rniversity Center and Columbia Interstate route I-5 5DJCk Bars ~dition. a listing of. local restaurants travel east on Highway 512 to Pacific Avenue and Center. In] ble at the registratwn desk. (Parkland/Mount Rainier exit), turn south ,ill be avai a continue approximately 12 blocks to 121st Street Travel and Local Information or Garfield Street. The campus is two blocks west · erved bv all major airlines. The of Pacific A venue . .,.,aco !!18 IS ·rportS is •situated approximately. 30 ·racai c• '. Parking ~a- th of Tacoma The Capital Aeroporter miles nor . There are regular visitor parking lots on campus. ·ides round-trip shuttle service to Tac~ma. Reserved lots p!OI t'ons are required and may be obtamed close to the Rieke Science Center. 1 may be used by visitors 5:00 p.m. to 7:00 a.m. Resealrvla g 206-572-9544. The one-way fare is $14 ~c m d . and on weekends. · person or $25 roun tn P. p6 Passengers traveling by train will arrive at Weather at 1001 Pu_Yallup Avenue, the AMTRAK station The weather in the Puget Sound area should be where buses are avmlable for travel Pierce Transit mild, sunny, and dry in June, affording spectacular there, transfer to bus #45 to downtown. From views of Mount Rainier. which stops at Pacific Lutheran University. If

Joint Mathelllatics Meetings

August 5-8, 1987 University of Utah Salt Lake City, Utah

669 Program of the Sessions

In t . . The tim~ limi~ f?r e~h contribute? paper in_ the AMS _ge?-eral s~ssions is ten minutes. hmtt vanes from sesston to sesston and wtthm sesstons. To maintain the schedhe ~ sesstons, the ttme liate limits will be strictly enforced. ule, . Abstracts of papers presented in AMS sessions at this meeting will be found in the June 1987 to the American Mathematical Society, ordered according to the nM~~ Abstracts of papers presented 0 parentheses following the listings below. -..... ID papers with more than one author, an asterisk follows the name of the author who plans to For Pl!leltt the paper at the meeting.

Thursday, June 18, 1987, 3:00 p.m.

MAA Short Course Rieke Science Center, Room S.t(l

Friday, June 19, 1987, 9:00 a.m.

MAA Short Course Rieke Science Center, Room s.u~

Friday, June 19, 1987, 11:00 a.m.

MAA Business Meeting Rieke Science Center, Leraas Lecture Hall

Friday, June 19, 1987, 1:10 p.m. Hall MAA Invited Address Rieke Science Center, Leraas Lecture BUSHAW, Washingtoo 1:10- 2:10 Reflections on discrete mathematics in the first two years. DONALD State University

Friday, June 19, 1987, 2:20 p.m. Science Center, Leraas Lecture Hall MAA Panel Rieke

Friday, June 19, 1987, 3:30p.m. Faculty House, Downstairs Loungt MAA Contributed Papers

Friday, June 19, 1987, 6:00 p.m. Stillwood Inn, facolll& Banquet and MAA Special Address 6:00- No host reception 7:00- Pleasantries. LEONARD GILLMAN, University of Texas, Austin

June 20, 1987, 9:00 a.m. Saturday, RoODI s-r.!!i Rieke Science Center, MAA Contributed Papers

Saturday, June 20, 1987, 11:00 a.m. !lail aas J,eeturt AMS Invited Address Rieke Science Center, Ler (sa&-5t.o51 11:00-11:50 (1) The geometry of polyhedra. BRANKO GRUNBAUM, University of Washington

Saturday, June 20, 1987, 12:00 p.m. C aee Shop!!' . C ter Oil' UniversitY en . •ty Luncheon and MAA Special Address e Un•vers1 Reserv 12:00- Title to be announced. ROBERT JEWITT, Western Washington

670 Saturday, June 20, 1987, 1:30 p.m.

P I hedral and Planar Graphs Rieke Science Center, Leraas Lecture Hall o-ionon oY d . Sptdll """: (2) Some comments on the -step conJecture. VICTOR KLEE, University of Washington Ill- 1:5J (835-99-15) , . . . . , ) A twisted quadrangulated torus. DRAGOSLAV LJUBIC, Umver8Ity of Washmgton (835-52-08) 2:00 2:Z5 ~!) Minimal quadrangulations. :'\ORA HARTSFIELD* and GERHARD RINGEL, University of 2:11 2:55 California, Santa Cruz (835-05-03) (Sponsored by Gerhard Ringel) (5) The toroidal analogue to Eberhard's theorem. PETER GRITZMANN, University of Washington 3:00· 3:25 and Universitaet Siegen, Federal Republic of Germany (835-52-09) (6) Edge-transitive planar graphs. B RANKO G RUNBAUM*, University of Washington, and 311- 3:55 G. C. SHEPHARD, University of East Anglia, England (835-05-07) (7) Coloring, covering and matching in. 3-polytopal graphs. Some recent results. MICHAEL t:OO- 4'25 PLUMMER, \'anderbilt Umvers1ty (835-05-01) 4:11 4: 55 (8) Two factors of simple 3-polytopes. MOSHE ROSENFELD, Pacific Lutheran University (835-05-06) (Sponsored by!\. Christian Meyer, Jr.) • (9) Title to be announced. DAVID W. BARNETTE, University of California, Davis (835-99-16) 5ffl· 5: 2J Saturday, June 20, 1987, 2:00 p.m. s.ioD 00 Contributed Papers Rieke Science Center, Room S-109 lffl- 2:10 (10) On the computation of the Baker-Hausdorf-Campbell formula in terms of an alternate basis system. FRANCIS Mt:RRAY, Duke University (83.5-99-14) 21.\- 2:25 (11) Calculating power residues using multiplicative groups (mod M) w. Idempotent identities. W. L. FORSYTHE, Ellensburg, Washington (835-11-11) 2:30" 2:40 (12) A proportwnality principle for partitioning problems. Preliminary report. THEODORE P. HILL, Georgia Institute of Technology (835-28-10) 2:45" 2:55 (13) The shape of the strongest column is arbitrarily chse to the shape of the weakest column. DAVID C. BARNES, Washington State University (835-34-12) 3:00 3:10 (14) Trace-class valued increasing functions. Preliminary report. PARFENY P. SAWOROTNOW, Catholic University of America (8:3.5-46-04) .1:15. 3:25 (15) Probabilistic advantages in high sum wins contests . .JOHN HILGERS, Michigan Technological University (835-60-13)

Hugo Rossi ~~Lake City. Utah Associate Secretary

Presenters of Papers Numbers following the names indicate the speakers' positions on the program. •AMS Invited lecturer *Special session speaker

Barnes, D. C., 13 • Griinbaum. B .. 1 Hill, T. P., 12 *Plummer. M .. 7 'Barnette, D. w 9 , F0!1ythe, W. L.',' 11 * Griinbaum. B .. 6 * Klee. V., 2 *Rosenfeld, M., 8 Gntzma.nn, P., 5 * Hartsfield, N., 4 * Ljubic, D., 3 Saworotnow, P. P., 14 Hilgers, J., 15 Murray, F., 10

671 Salt Lake City Meetings, August 5-8, 1987 Supplement to Announcement in April Notices

Please refer to the Preliminary Announcement for this meeting which appears on pages 519-543 IMPORTANT DEADL;;----. of the April 1987 issue of Notices. The table AMS Abstracts of contents for the preliminary announcement is For consideration for special sessions reproduced below for convenience. Of contributed papers MAA Abstracts Of contributed papers WHERE TO FIND IT PAGE Preregistration and Housing MAA Minicourse Preregistration PREREGISTRATION AND HOUSING 520 Summer List of Applicants Motions for AMS Business Meeting SUMMER MEETING OF THE AMS 519 Housing Cancellations (90% refund) Colloquium Lectures, Prizes, Invited Addresses, Special MAA Banquet (50% refund) Sessions, Contributed Papers, Council, Business Preregistration cancellations (50% refund) Meeting Snowbird Outing (50% refund) SUMMER MEETING OF THE MAA 521 Hedrick Lectures, Invited Addresses, Minicourses, Contributed Papers, Student Papers, Business Meeting, AMS Special Sessions Board of Governors, Section Officers, Banquet for The deadline for submission of abstracts ipt­ 25-year Members for cial sessions was changed to May 8. JOINT AMS-MAA SESSIONS 525 OTHER ORGANIZATIONS 525 AMS Contributed Papers AWM, ICEMAP, JPBM, liME, NSF TIMETABLE 531 The deadline for submission of abstracts for coo­ tributed papers has been changed to Mar 21. OTHER EVENTS OR ITEMS OF INTEREST 525 Book Sales, Exhibits, Information Table, Summer List of Applicants, Petition Table MAA Invited Address ACCOMMODATIONS 526 The title of the invited address to be giftll University Housing and Food Services, Motels by PAUL J . 8 TEINHARDT has been changed to REGISTRATION AT THE MEETINGS 532 Quasicrystals: A new state of matter. Fees, Dates, Locations, Times, Services MISCELLANEOUS INFORMATION 534 Athletic Facilities, Book Stores, Camping, Child Care, The Preregistration/Housing Form, SUIIIIIlff Crib Rental, Handicapped, Libraries, Local List of Applicants Form, with instructions, and Information, Medical Services, Parking, Social Events, the Minicourse Preregistration Form can be Tours, Travel, Weather found at the back of this issue. MAPS 528-529 Hugo Rossi Salt Lake City, Utah Associate SecntarY

semisimple Lie algebras by W. Bohro, LIE ALGEBRAS AND a course on Kac-Moody Lie algebras~ RELATED TOPICS I. G. Macdonald, and a course on fo groups by M. Hazewinkel. D. J. Britten, F. W. Lemire, and R. V. Moody, Editors 1980 Mathematics Subject ClassifiatioiiS' 17, 22 ISBN 0-8218-6009-7. LC 8!>-26BlS As the Proceedings of the 1984 Canadian ISSN 0731-1036 S6 Mathematical Society's Summer Seminar, 392 pages (softcover), February ~ 9 S44 these papers focus on some recent Individual member 126. List proce ' advances in the theory of semisimple Institutional member S35 /SNA Lie algebras and some direct outgrowths To order, please specify CMSAMS of that theory. Of particular interest are notes for several courses presented 2 each add'l Sl, S25 at the meeting: an important survey Shipping/Handling: 1st book $ ~dd'l $3, S100 111.X· max. By air, 1st book $5, each AMS p.O. 80% article by R. Block and R. Wilson on Prepayment required. Ord~r fr:: Rl o290t-9930• or restricted simple Lie algebras, a survey 1571, Annex Station, Provtden 'MasterCard· of universal enveloping algebras of call 800-556-7774 to use VISA or

672 30- November 1, University of Nebraska [JJeOID, Octo ber ~Announcement of the 837th Meeting first

d d and thirty-seventh meeting Most of the papers to be presented at these 'fbt eight h~ re Mathematical Society will be special sessions will be by invitation. However. rJ the AJnenUc~ rsity of Nebraska in Lincoln. anyone submitting an abstract for the meeting L-LI t the mve ~ d d liE"' a Friday afternoon. ~atur ay an who feels that his or her paper would be particu­ 0 ~· ~ 8 October 30- November 1. 1987. larly appropriate for one of these special sessions SaDd&Y mornmg ' should indicate this clearly on the abstract form Invited Addresses and submit it by July 27, 1987, three weeks before . . · of the Committee to Select Hour the deadline for contributed papers. in order that 111 IJIVltaf~~entral Sectional Meetings. there will it may be considered for inclusion. Participants ~invited one-hour addresses. The speakers, are reminded that a charge of $16 is imposed for ~affiliations and titles, where avmlable, are as retyping abstracts that are not in camera-ready form. iJI)orls: p . . t f p CAROLYN S. GORDON, _vmversl yo en:l- qlvania and Washington Umvers1ty, St. Loms. Contributed Papers W/1 you can't hear the shape of a manifold. There will also be sessions for contributed ten­ ~AVID GRIFFEATH. University of Wisconsin. minute papers. Abstracts should be prepared Madison title to be announced. on the standard AMS form available from the · DAVID W. MASSER, University of Michigan. AMS office in Providence or in the Departments Ann Arbor, Transcendence without transcendental of Mathematics. Abstracts should be sent to the nmbtrs. Editorial Department. American Mathematical DAN VOICULESCU. University of California, Society, Post Office Box 6248, Providence, Rhode Berkeley, title to be announced. Island 02940, so as to arrive before the August 17, 1987. abstract deadline. Participants are Special Sessions reminded that a charge of $16 is imposed for By invitation of the same committee. there will be retyping abstracts that are not in camera-ready lml'8l special sessions of selected twenty-minute form. Late papers will not be accommodated. papers. The topics of the sessions, and the names llld affiliations of the organizers, are as follows: Registration Operator algebras and operator theory, The registration desk will be open on Friday FRANKL. G!LFEATHER. Universitv of Nebraska. afternoon. October 30 and Saturday, October Lincoln. · • 31, at hours to be announced. The registration Transformation groups in geometry, CAR­ fees are $30 for members of the AMS, $45 for OLYN S. GORDON and QUO-SHIN CHI, Wash­ nonmembers. and $10 for students or unemployed lll(ton University. mathematicians. Cellular automata and nonlinear dynamics. ERICA_ JEN, Los Alamos National Laboratory. . Petition Table S Fmite geometries and combinatorial design, A petition table will be set up in the registration _T0S D. MAGLIVERAS. EARL S. KRAMER. area. Additional information can be found in a ... 0ALEM . . ~ U ESNER, Department of Computer box in the Salt Lake City meeting announcement ce, . Diversity of Nebraska, Lincoln. on page 526 of the April issue of Notices . .; ~eml-groups and connections with automata Travel and Local Information STUA~m~ languages, JOH~ C .. MEAKIN and liocoin. · MARGOLIS, Umvers1ty of Nebraska, Information concerning travel, housing accommo­ dations, food service. etc. will appear in the Dioph t · UJiive · an me problems, ROBERT E. TUBBS. August issue of Notices. Ctsity of Colorado, Boulder. Robert M. Fossum "'JJ;ER•~ ommutative A W al ge bra d an algebraic geometry, Urbana. Illinois Associate Secretary UJiiversity .of NIEbGAND and BRIAN HARBOURNE, e raska, Lincoln.

673 Los Angeles, November 14-15, University of California, Los A First Announcement of the 838th Meeting ~

The eight hundred and thirty-eighth meeting Contributed Papers of the American Mathematical Society will be There will also be sessions for cont 'b held at the University of California on Friday minute papt>rs. Abstracts should ~ uted lea. and Saturday, November 14-15, 1987. This on the standard A.Ms form available ~ meeting will be held in conjunction with the AMS office m Providence or in the ~ Southern California section of the Mathematical of Mathematics. Abstracts should be se 1 Association of America. Editorial Departnwnt, American Mathn to .lht Invited Addresses Society, Pm;t Officp Box 62~8, Providenc~ Island 02940. so as to arnve before the A By invitation of the Committee to Select Hour 18, 1987, abstract deadline. ParticipantB Speakers for Far Western Sectional Meetings, wa: remir:ded that a charge of $16 is imposed b there will be three invited one-hour addresses retypmg ab,;tracts that are not in camera-l!ady including: form. HENRYK HECHT, University of Utah, title It appPars unlikely that late papers can lit to be announced. accommodate-d. PAUL YANG, University of Southern Califor­ nia, title to be announced. MAA Program Special Sessions The MAA pro~mm will take place on Saturdav and will include a luncheon. Additional inf~. By invitation of the same committee, there will be mation will be- included in the August ~e of several special sessions of selected twenty-minute Notices. papers. The topics of the sessions, and the names and affiliations of the organizers, are as follows: Petition Table Differential geometry, ROBERT GREENE, A petition tab!(' will be set up in the registration University of California, Los Angeles, and H.-Y. area. Addition a! information can be found in a CHOI, University of Utah. box in the Salt Lake City meeting announcement Game theory. WILLIAM LUCAS, Claremont on page 526 of the April issue of Notices. Graduate School. Stochastic processes, SIDNEY PORT, Uni­ Travel and Local Information versity of California, Los Angeles, and RUTH InformatioH coHrerning accommodations, food WILLIAMS, University of California, San Diego. service, and transportation will be included m Geometric Topology, JOHN WALSH, Univer­ the August i,;onP of Notices. sity of California, Riverside. Most of the papers to be presented at these Hugo Rossi . special sessions will be by invitation. However, Salt Lake City. Uah Associate Secretarl anyone submitting an abstract for the meeting who feels that his or her paper would be particu­ larly appropriate for one of these special sessions, should indicate this clearly on the abstract form and submit it by July 28, 1987, three weeks before the deadline for contributed papers, in order that it may be considered for inclusion. Participants are reminded that a charge of $16 is imposed for retyping abstracts that are not in camera-ready form.

674 October 1987 Meeting in Lincoln Invited Speakers Central Section Deadline for organizers: Expired IJJd Special Sessions Deadline for consideration: July 27, 1987 Invited Speakers at AMS Meetings Frank Gilfeather, Operator algebras and operator theory Tht individuals listed belo:V have accepted invi­ Carolyn Gordon and Quo-Shin Chi, Transforma­ tJtiODS to address the Society at the times and tion groups in geometry ~ indicated. For some meetings, the list of Erica Jen, Cellular automata and nonlinear dy­ !ptakers is incomplete. namzcs Salt Lake City, August 1987 Spyros D. Magliveras, Earl Kramer, and Dale Mesner, Finite geometries and combinatorial J)onald G. Aronson Michael Starbird design (AMS-MAA) John C. Meakin and Stuart W. Margolis, Semi­ Robert Finn Vogtmann (AM8-MAA) Karen groups and connections with automata and Edward W. Formanek Brian C. White formal language David Jerison Robert Lee Wilson Robert Tubbs, Diophantine problems Stephen Kerchoff Edward Witten Roger Wiegand and Brian Harbourne, Commuta­ Paul C. Roberts (Colloquium tive algebra and algebraic geometry Lecturer)

Lincoln, October 1987 November 1987 Meeting in Los Angeles Section David W. Masser Far Western Carolyn S. Gordon Deadline for organizers: Expired David Griffeath Dan Voiculescu Deadline for consideration: July 28, 1987 Robert Greene, Differential geometry Los Angeles, November 1987 William Lucas, Game theory Henryk Hecht Sidney Port and Ruth Williams, Stochastic processes Atlanta, January 1988 John Walsh, Geometric topology Constantine M. Dafermos David P. Ruelle Fall1987 Meeting Philip J. Hanlon (Gibbs Lecturer) Dusa McDuff Peter Clive Sarnak Eastern Section Roger D. Nussbaum Stephen W. Semmes No meeting will be held

Organizers and Topics Fall1987 Meeting of Special Sessions Southeastern Section TJ!e !ist below contains all the information about No meeting will be held t 1al Sessions at meetings of the Society avail­ t~e a~ the time this issue of Notices went to January 1988 Meeting in Atlanta ..:~ter. Th~ section below entitled Infor­ ann ~r Organizers describes the timetable for Associate Secretary: W. Wistar Comfort ouncmg the existence of Special Sessions. Deadline for organizers: Expired Deadline for consideration: To be announced Marlow Anderson and Todd Feil, Ordered alge­ August l987 Meeting in Salt Lake City braic systems Associate Secretary: Hugo Rossi Alfred D. Andrew and John H. Elton, Banach Deadline - Deadl" 1or organzzers: Expired space theory Donald G. A.:~for conSideration: May 8, 1987 Jean Bevis, George Davis, Frank Hall, Fred A. evolutio nson and Hans Othmer, Nonlinear Massey, and Valerie Miller, Modern trends in ~eth S n equatzons matrix analysis and applications t · h . theory · Brown ' c eome TIC met ads zn group Jack B. Brown and R. Daniel Mauldin, Measure E"4ward W. Form . theory and descriptive set theory J theory anek, Rzng theory and invariant Shui-nee Chow and Roger D. Nussbaum, Nonlin­ atob Goodm ear differential delay equations geornetr an and Erwin Lutwak, Discrete Lewis A. Coburn, Toeplitz operators and geometry lohn M Y and convexity of differential and integra­ · Lee c Saber Elaydi, Stability p manifolds' eometry and analysis on CR differential equations auJ C. Roberts C Herbert Freedman and Paul Waltman, Applica­ braic geo ' ommutative algebra and alge­ tions of differential equations to population metry ecology

675 Robert B. Gardner and Clyde Martin, Geometry in Notices early enough to allow an of nonlinear control systems Society who wishes to do so to subm~t mei!Iber li ~ Paul Hill, Abelian groups consideration fo: presentation in th~ ;;:~ .. Theodore P. Hill and Robert Kertz, Discrete-time before the deadhne for such consider t' ial ~ 'a] S . a IOU optimal stopping theory Spect esswns are effective at Sec ·. Henryk Iwaniek and Peter Clive Sarnak, Analytic ings and can usually be accommodat dtlOQaJ Mt.t. theory of automorphic forms and applications arranged by the Associate Secretary un~ · They lit Michael S. Jacobson and Ronald Gould, Graph vision o~ the Com_m~ttee to Select Hour~ the 8\iper. theory the sectwn. The !mutation on the numb let er Peakenof...... __ H. W. Lenstra, Jr., Algebraic number theory and depe~d? on the space _and time available. n;-" algorithms restnctwn as for natwnal meetings a li Iaiii! Stephen R. Mahaney, Structural complexity theory deadline for announcing Special Session~p tes to_ th. Lynn McLinden and JayS. Treiman, Optimization meetings: no Special Session may be a a llett~ . PProved toe Roger D. Nussbaum, Nonlinear differential delay Iate £or 1ts announcement to appear in time to allot. equations reasonable interval for members to prepare and ·1 A. G. Ramm, Multidimensional inverse scattering, ml. t t h.e1r a b stracts pnor . to the special earl deadlmt11lb- related problems in analysis and applications set for consideration of papers for Special S:.,. Dennis Stanton, Combinatorics and group repre­ The Soc_iety_ reserves the right of first ~ sentations for .the pubhcatwn o~ proceedings of any specia; R. A. Zalik, Total positivity and applications sesswn. These proceedmgs appear in the book~ Contemporary Mathematics. · Information for Organizers Information for Speakers Special Sessions at Annual and Summer Meetings are held under the general supervision of the Program A great many of the papers presented in Spec;~ Committee. They are administered by the Associate Sessions at meetings of the Society are invited paJ>fl' Secretary in charge of the meeting with staff assistance but any member of the Society who wishes to d( from the Society office in Providence. so may submit an abstract for consideration for Some Special Sessions arise from an invitation presentation in a Special Session, provided it > to a proposed organizer issued through the Associate received in Providence prior to the special earl! Secretary. Others are spontaneously proposed by deadline announced above and in the announcement; interested organizers or participants. Such proposals of the meeting at which the Special Session has beet are welcomed by the Associate Secretaries. scheduled. Contributors should know that there;; The number of Special Sessions at a Summer or a limitation in size of a single special session. " Annual Meeting is limited to twelve. Proposals, in­ that it is sometimes true that all places are filled~ vited or offered, that are received at least nine months invitation. Papers not accepted for a Special Seslioo prior to the meeting are screened for suitability of are considered as ten-minute contributed papers. the topic and of the proposed list of speakers, and Abstracts of papers submitted for considera· for possible overlap or conflict with other proposals. tion for presentation at a Special Session must bf (Specific deadlines for requesting approval for Special received by the Providence office (Editorial Depart· Sessions at national meetings are given above.) If ment American Mathematical Society, Post ~~~ ' 'alor"'· necessary, the numerical limitation is enforced. Box 6248. Providence, RI 02940) by the spect :eet; Proposals for Special Sessions should be submit­ line for Special Sessions, which is u~ually three~. for ted directly to the Associate Secretary in charge of the earlier than the deadline for contributed papers . '] h decreed that ll< meeting (at the address given in the accompanying the same meeting. The Counc1 as hi' 1, 1 ~ box). If such proposals are sent to the Providence paper, whether invited or contributed, ~ay unl~ a:: office, addressed to Notices, or directed to anyone in the program of a meeting of the_ Soc:~rovidt'tlf' other than the Associate Secretary, they will have abstract of the paper has been receiVed to be forwarded and may not be received before the prior to the deadline. quota is filled. In accordance with an action of the Executive Committee of the Council, no Special Session may be arranged so late that it may not be announced

676 :!;:;:;;:;;;;:;;;;:;::;:;:;::::::::::::::::::!i:::H:::!ii::n:nn:nnn:::::::: THE BIEBERBACH CONJECTURE: Proceedings Is for Special Sessions to the of the Symposium on the Occasion of the Proof c ...d Proposa . "'".. Associate Secretaries Albert Baernstein. David Drasin, Peter Duren and Albert Marden. Editors , of sectional meetings. are arr~nged by the {Mathematical Surveys and Monographs. Volume 21) Tht progra!ll· for the sectiOn m questiOn . . te Secret&rY . For 70 years. the Bieberbach conjecture has intrigued .~ 13 • (Pacific and Mountam) western SectiOn the mathematical world. In 1977. Louis de Branges far Rossi, Associate Secretary of Purdue University took up the challenge of this Hugo t of MathematiCS Oepartmen famous unsolved problem. He will be recognized . . rsity of Utah lnlve · UT 84112 as the mathematician who proved Bieberbach's Salt Lake C1ty, conjecture. And more importantly. his method came (Telephone 801-581- 8159) from totally unexpected sources: operator theory and C ntral Section special functions. t " Fossum Associate Secretary Robert ;vt. ' . This book. based on the Symposium on the Occasion Department of ~a~hematics of the Proof. tells the story behind this fascinating rniversity of Ilhnms 1409 West Green Street proof and offers insight into the nature of the t:rbana. IL 61801 conjecture. its history and its proof. A special and (Telephone 217- 333-3975) unusual feature of the book is the enlightened personal accounts of the people involved in the exciting events Eastern Section W. Wistar Comfort, Associate Secretary surrounding the proof. Especially attractive are the Department of Mathematics photographs of mathematicians who have made Wesleyan University significant contributions to univalent functions. the ~iddletown, CT 06457 area of complex analysis which provides the setting iTelephone 203-347-9411) for the Bieberbach conjecture. Southeastern Section Research mathematicians. especially analysts. are Frank T. Birtel, Associate Secretary sure to enjoy the articles in this volume. Most Department of Mathematics articles require only a basic knowledge of real and 1\Ilane University complex analysis. The survey articles are accessible :\ew Orleans, LA 70118 to non-specialists. and the personal accounts of all !Telephone 504-865- 5646) who have played a part in this important discovery As a general rule, members who anticipate orga­ will fascinate any reader. nizing Special Sessions at AMS meetings are advised to 1980 Mathematics Subject Classifications: 30, 47 !lek approval at least nine months prior to the sched­ ISBN 0-8218-1521-0. LC 86-10843. ISSN 0076-5376 nled date of the meeting. No Special Sessions can be 260 pages (hardcover). 1986 approved too late to provide adequate advance notice to List price $45, Institutional member $36, Individual member $27 Code SURV/21NA ~embm who wish to participate. 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, Rl 02901-9930, or call 800-556-7774 to use VISA or MasterCard.

scientists interested in exploring the field APPROXIMATION for possible applications to their own fields. The book is best understood by THEORY those with a standard first graduate course in real and complex analysis. but Carl de Boor, Editor some of the presentations are accessible with the minimal requirements of The papers in this book, first presented advanced calculus and linear algebra. at a ~986 AMS Short Course, give a lmef Introduction to approximation 1980 Mathemattcs Subjert Classtficattons: theory and some of its current areas 41.30.65 ISBN 0-821~-0098-1. LC 86-10846 of active research, both theoretical and ISSN 0160-7634 ~jplied. The first lecture describes and 144 pages. August 1986 ~ ustrates the basic concerns of the field. Hardcover: List price $26. Institutional . 0Plcs highlighted in the other lectures memhE'r $21. Individual mf'mber $16 :~elude the following: approximation in Softcover: List price $22. Institutional e complex domain, N-width. optimal mE:'mber $18, Individual member $13 To order. please specify PSAPM/36NA recovery, interpolation, algorithms for (hardcover). PSAPMS/36NA (softcover) :PProximation, and splines, with a strong t~P1has1s on a multivariate setting for Shipping/Handling: 1st book $2. each r ast three topics. add'l $1. $25 max. By air. 1st book $5. each add'l $3. $100 max. ·Thebook·. Is anne d at mat h ematiCians.. Prepayment requtred. Order from AMS. Interest d . P.O. Box 1571. Annex Station. Providence. ru e m an introduction to areas of Rl 02901-99:JO. or call 8DO-!i56-7774 to use trent research and to engineers and \'ISA or MasterCard

677 Call For Topics For 1989 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 1989. The deadlines for receipt of these Recent Conferences suggestions, as well as some relevant information about each of the conferences, are outlined below. AMS Summer Institute An application form to be used when submitting 1985- Algebraic geom_etry, . organized by suggested topic(s) for any of these conferences EISEN BUD of Brandeis Umversity. DAVID (except the Short Course Series) may be obtained 1986- Representations of finite groups nd by writing to the Meetings Department, American topics, organized by JONATHAN L. A~p ~flaw Mathematical Society, P.O. Box 6248, Providence, the University of Chicago. ERIN II Rhode Island 02940, or telephoning 401-272-9500. 1987- Theta functions, organized by L Individuals willing to serve as organizers EHRENPREIS of Yeshiva University and ROBEON should be aware that the professional meeting GUNNING of Princeton University. EllT staff in the Society's Providence office will provide 1988- Operator theory/Operator algebras and fiPIIIi. full support and assistance before, during, and cations, organized by WILLIAM B. ARVESON 11 after each of these conferences. Organizers should University of California, Berkeley, and RONALD also note that for all conferences, except Summer G. DOUGLAS ofStateUniversityofNewYorkat Research Conferences, it is required that the Stony Brook. proceedings be published by the Society, and that AMS-SIAM Symposium on Some proceedings of Summer Research Conferences are Mathematical Questions in BlolOI)' frequently published. A member of the Organizing Committee must be willing to serve as editor of 1985- Plant biology, organized by ROBERT M. MIURA of the University of British Columbia. the proceedings. 1986- Modeling circadian rhythms, organized by All suggestions must include (1) the names GAIL A. CARPENTER of Northeastern Uniwr­ and affiliations of proposed members and chair­ sity. man of the Organizing Committee; (2) a two- or 1987- Models in population biology, organized by three-page detailed outline of the subject(s) to be ALAN HASTINGS of the University of Califomia. covered, including the importance, timeliness of Davis. the topic, and estimated attendance; (3) a list 1988 - Dynamics of excitable media, organized by of the recent conferences in the same or closely HANS G. 0THMER of the University of Utah. related areas; (4) a tentative list of names and affiliations of the proposed principal speakers; (5) AMS-SIAM Summer Seminar a list of likely candidates who would be invited 1984- Nonlinear systems of PDE in applied matlle­ to participate and their current affiliations; and matics, organized by BASIL NICOLAENKO of Lc» (6) any other observations which may affect the Alamos National Laboratories. size of the conference and the amount of support 1985-Reacting flows: Combustion and chemical If· required. Any suggestions as to sites and dates actors, organized by G. S. S. LUDFORD of()ornell should be made as early as possible in order to University. . PIA allow adequate time for planning. By action of 1987- Computational Aspects of VLSI D~Mgll . the AMS Board of Trustees, the Meetings De­ an Emphasis on Semiconductor Device Sllll~ partment of the Society is responsible for the final organized by RANDOLPH BANK of the Uru-ve!Si selection of the site for each conference and for of California, San Diego. · . 8J8kflll all negotiations with the host institution. Indi­ 1988- Computational solution of nonllnea~oW£11 viduals submitting suggestions for the conferences of equations, organized by EUGENE AL listed below are requested to recommend sites or of Colorado State University. geographic areas which would assist the Meetings Department in their search for an appropriate site. In the case of Joint Summer Research Conferences in the Mathematical Sciences, a one-, two-, or three-week conference may be proposed. Refer to the accompanying box titled Topics of Current and Recent Conferences for lists of topics.

678 AMS Summer Institute t98 9 . Call for Topics for . t s are intended to prov1de an 1989 AMS Short Course Series · 5utu e ~er tn resentation of the state of the art • andab 1e p . h . The AMS Short Courses consist of a series of intro­ IJil(le~ . field of research m pure mat ematJcs, ductory survey lectures and discussions ordinarily iJllllactJVe. extend over a three-week period. extending over a period of one and one-half days not overlap and usually urnmer institute must starting immediately prior to the Joint Mathemat­ 5 [)all'S for~ Society's summer meeting, which ics Meetings held in January and August each year. tlJo;t of tee of this printing have not yet been Each theme is a specific area of applied mathematics at the tl: there should be a period of at least or mathematics used in the study of a specific sub­ 111 dttt1 Ul btween them. Proceedings are pub­ ject or collection of problems in one of the physical, in the series # week 1 ~ Society as volumes biological or social sciences. technology or business. ~ed dby ef Symposia in Pure Mathematics. ~~ mgs o Topics in recent years have been 111 aments in 111 athe­ [)eadline For Suggestions: August 15, 1987 matics (January 1987), Approximation Theory (Jan­ uary 1986), Actuarial Mathematics (August 1985), AMS-SIAM Summer Seminar Fair Allocation (January 1985), Environmental and 1989 Natural Resource Mathematics (August 1984). Pro­ al Of the summer seminar is to provide an ceedings are published by the Society as volumes in Tb . 1" d h . ego· runent and program m app 1e mat emat1cs the series Proceedings of Symposia in Applied Mathe­ envt~ch experts can exchange the latest ideas and matics, with the approval of the Editorial Commit­ lD wcomers can learn about the field. Proceedings tee. ::published by the Society as volumes in the Deadline for Suggestions: Suggestions for the !tries Lectures in Applzed M athematzcs. January 1989 course should be submitted by for the August 1989 Deadline For Suggestions: August 15, 1987 July 1. 1987: suggestions course should be submitted by December 1. 1987. 1989 Joint AMS-IMS-SIAM Summer Submit suggestions to: Professor Stefan A. Burr, Research Conferences in the Chairman, AMS Short Course Subcommittee. De­ Mathematical Sciences partment of Computer Sciences. CUNY, City Col­ lege, New York, New York 10031. These conferences are similar in structure to those held at Oberwolfach, and represent diverse areas ofmathematical activity, with emphasis on areas currently especially active. Careful attention ~paid to subjects in which there is important interdisciplinary activity at present. Topics for the sixth series of one-week conferences, being held COMBINATORICS AND ORDERED SETS lll 1987, are Categories in computer science and Ivan Rival. Editor Mathematics. Volume 57) /ogle, Hamiltonian dynamical systems, Graphs and (Contemporary algonthms, Geometry of group representations, For the mathematician interested in discrete The connection between infinite dimensional and mathematics. from the senior undergraduate to the professional level. this volume provides f~rst-rate fintte dtmensional dynamical systems Geometry surveys of the important combinatorics themes 1n of rando t · ' ~ . m. mo wn, Crystal growth and pattern ordered sets dormatron m phase transitions. Complex analytic These expository lectures. given at a 1985 Joint l'!amtcs, and Statistical inference from stochastic Summer Research Conference. cover a wide range of Soc·PTOcesses · If procee d mgs· are pubhshed. by the topics. which include: the three-machine problem to C tety, they will appear as volumes in the series illustrate the ordeHheoretic aspects of scheduling ontemporary Mathematics. theory: the techniques used in settling the '"matching conjecture·· the decomposition of ordered sets Deadline For Suggestions: February 1, 1988 into few chains: the reorientation of graphs: the varied occurrences of the meet-distribution property, surveys techniques used in settling binary sorting problems: the formulation of a general view point for retraction: the survey of cutsets: and the role played by subdiagrams in ordered sets 1980 Mathematics Subject Classifications 06, 05 ISBN 0-8218-5051-2, LC 86-8006, ISSN 0271 4132 304 pages (soft cover), 1986 List price $29, lnstituttonal member $23. Individual member $17 Code CONM/57 NA

Shipping/Handling: 1st book $2. each add"! $1. $25 max. By air. 1st book $5. each add"! $3. $100 max. Prepayment required. Order from AMS. P 0 Box 1571. Annex Station. Providence. Rl 02901-9930. or call 800-556-7774 to use VISA or MasterCard.

679 Special Meetings

THIS SECTION contains announcements of meetings of interest to some segment of mathematical public, including ad hoc, local, or regional meetings, and meetings or ~ dev?ted to ~peciali~ed topics, as ~ell as an~wu?'cements of r~gularly scheduled me:::JlOiia natwnal or mternatwnal mathematical organ1zatwns. InformatiOn on meetings of the ~~ol. and on meetings sponsored by the Society, will be found both in this section and on th~· front cover. All meetings listed here, to the best of our knowledge, are open meetings~~ public is invited to attend. AN. ANNOUNCE~ENT will be published in Notices if it cont~ins the place, date, and the subJeCt (when apphcable); a second full announcement w•ll be pubhshed only if there are change. or. necessary additional inforn:a~ion. Once an announcement has .appear~d, the event will be bnefly noted m each 1ssue untli •t has been held and a reference wlil be g1ven 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 ;rogram) deadlines for abstracts or contributed papers, and source of further information. Meetings heJci outside the North American area may carry more detailed information. In any case, if there ia 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.

1986-1987. Academic Year Devoted to Algebraie Geome­ 27-30. Fifth Biennial Conference of the A.clllar. try, Mittag-Leffler Institute, Djursholm, Sweden. (January Christians in the Mathematical Scleneee, Calm a.., 1986, p. 130) Grand Rapids, Michigan. (January 1987, p. 133) 1986-1987. Speeial Year in Combinatories and Complex­ 27-30. Seventh Great Plains Operator TbearJ ...... ity, University of Illinois at Chicago, Chicago, Illinois. University of Kansas, Lawrence, Kansas. (FelmiarJ 1117, (April 1987, p. 548) p. 360) 1986-1987. Speeial Year in Modern Analysis, University of 28-29. Downeast Conference on Graphs, Colbr a.., Illinois at Urbana-Champaign, Urbana, Illinois. (October Waterville, Maine. (April 1987, p. 549) 1986, p. 840) 28-30. Annual Summer Meeting of the Cuadlall6 1986-1987. Workshop for Academic Year, University of ematical Soeiety, Queen's University, Kingatoa, OIUiD. Arizona, Tucson, Arizona. (January 1987, p. 131) Canada. (February 1987, p. 360) 1987-1988. Academic Year Devoted to Several Complex 28-June 1. Fourth Southeast Asian C~a116 Variables, Mittag-Leffler Institute, Djursholm, Sweden. ematical Education, Singapore. (August 1986, P. eM) (January 1987, p. 131) 31-June 3. 1987 Annual Meeting, StatiaticiiSICillr If October 12, 1986-December 13, 1987. Mathematisches Canada, Quebec City, Canada. (November 1986, P. 91'1) Forschungsinstitut Oberwolfach (Weekly Conferences), Federal Republic of Germany. (October 1986, p. 840) JUNE 1987 January 12, 1987-June 20, 1987. Research Program on Different Aspects of the Mathematical Theory of Evolution 1-4. Second International Tampere CODf'enDCtllllllllt Equations, University and the Scuola Normale Superiore, tics, Tampere, Finland. (November 1986, P· 962) II Pisa, Italy. (January 1987, p. 131) 1-5. National Seience Foundation-eoorer.r;.,.::,. September 14, 1987-June 25, 1988. Program on Applied Combinatorics, Institute for Mathematics and its Appli­ the Mathematical Seiences on ~auge ~eoryT 550) University Saint Louis, Missoun. (Aprli 198 • P· -' cations, University of Minnesota, Minneapolis, Minnesota. , Di1tllil1• (April 1987, p. 548) 1-5. Ramanl.\ian Centenary Conferen~ (felllllf Illinois at Urbana-Champaign, Urbana, ' January-July 1988. Symposium on Representation Theory and Group Theory, Manchester, England. (April 1987, 1987, p. 360) J981, p. 548) 1--6. Theorie de Hodge, Marseille, France. (FebnJIIJ p. 360) -- 1-10. Second Annual Meeting of~he ~J'(IVIIik-l(lplli. ****** shop in Analysis and Its Applicattons, u Yugoslavia. (October 1986, p. 843) IJIIIJ.IIIIIf' MAY 1987 2-4. Artifieial Intelligence, Expert ~yateo;-pain. 26-~28. Multiple-valued Logic, University of Massachusetts, in Modelling and Simulation, Bare~ ont.stitute rl ~ Boston, Massachusetts. (January 1987, p. 133) Information: Symposium Secretar•a~arcelon& 14. ~ 26-28. Workshop on Nonlinear Hyperbolic Waves, Math­ netics, Diagonal, 647, 2a planta, f Computer~ ematical Sciences Research Institute, Berkeley, California. or C. Kulikowski, Department .0k NeW Jfll(#/ (August 1986, p. 654) Rutgers University, New Brunsw•c ' ~ . t' in 27-29. Differential Equations Meeting, Dublin, Ireland. 4-6. Computer Exper1menta .•on . N~.-1111·uri. (J-· (February 1987, p. 359) University of Missouri, Columb1a, M•SSO 27~-29. Institute of Mathematical Statistics Eastern Re­ p. 133) in.....-::, gional Meeting, Virginia Polytechnic Institute and State 4-6. Congress on Educational C~rnr;t:arY 1981• P. University, Blacksburg, Virginia. (February 1987, p. 359) Universita di Roma I, Roma, Itaha. e

680 t · Oberwolfach, Federal Republic 17-19. NASECODE V Conference: The Fifth International GeoJIM r1e, Conference on the Numerical Analysis of Semiconductor 1-~ ~ bruarY 1987, P· 360) Devices and Integrated Circuits, Trinity College, Dublin, -~Y· ~Evolution and Chaotic Phenomena, Noto, Ireland. (October 1986, p. 843) ·18 !fGGIID 1987, P· 360) ~-(FebruarY • and the Microcomputer, Salisbury 17-21. Third International Conference on Discrete Mathe­ A~,Nalh~bt•c• Maryland. (February 1987, p. 360) matics: Graph Theory and Discrete Geometry, Dortmund, f 12 · SaiiB ury, . Federal Republic of Germany. (February 1987, p. 361) ~c.,uegt· d Systemes Codes, Marseille, France. · • -'tbJDI!Iique eo 17-23. Symmetry Methods in Differential Equations, Utah ; 13- ,,.. 1987 p. 360) . State University, Logan, Utah. (February 1987, p. 361) lfbrUilY .. Group Conference Theory, National ; 19. SIDPpore re Republic of Singapore. (March 18-20. 835th Meeting of the AMS, Tacoma, Washington. •. .ersitY of Smgapo , Information: For further details, see the Meetings section lDI 370) of this issue of Notices. !9116- P· Noolinear Hyperbolic Equations for ~IJ. WorkJbop ~rino Italy. (January 1987, p. 133) 19-August 15. Joint Summer Research Conference in the . __.... Sciences. ' . . Mathematical Sciences, Cornell University, Ithaca. - on Educational Computmg m Mathe- Information: For further details, see the Meetings section 1113· (;oDgl'eBIIItaly (February 1987, p. 360) .,a.. Rome, · of the February 1987 issue of Notices . · b Pacific Coast Resource Modeling Confer- 22-25. Second Annnal Symposium on Logie in Computer 1113·. Sixt .1 f British Columbia, Vancouver, Canada. - umversl y 0 Science, Cornell University, Ithaca, New York. (November Jill;.., 1987. p. 133) 1986, p. 962) Coaference on Operator Theory and Functional ~-Phoenix, Arizona. (February 1987, p. 360) 22-27. Mathematiques et Sciences Humaines, Marseille, France. (February 1987, p. 361) !I-ll. Number Theory, Trace Formulas and Discrete (;nlpl. Oslo. Norway. (January 1987, p. 133) 22-27. Paul Levy Conference on Stochastic Processes, Ecole Polytechnique, Palaiseau, France. (February 1987, -:IS. Jolat Summer Research Conference in the Mathe- p. 361) !uw Sciences, University of Colorado, Boul'_ler. . l•/"""•tion: For further deta1ls, see the Meetmgs sectwn 22-28. 2nd Korea Institute of Technology Mathematics of the Febuary 1987 issue of Notzces. Workshop, Taejon, Korea. Program: The program will consist of a series of lectures 1;16. NASECODE V SHORT COURSE: The Interfaces IIIIIJiecralion of Process, Device and. Circuit Models­ by the invited speakers and some one hour special talks .b illroduetion, Trinity College, Dubhn, Ireland. (Octo­ on Geometry and Analysis . Invited Speakers: P. Ahern, J. Burbea, R. Greene, A. ber 1986. p. 843) Gray, K. Grove, K. Hahn, and P. Pflug. 1; 19. Conference on Combinatoric• and Complexity, Call for Papers: Papers are solicited in all areas of [Diversity of Illinois at Chicago, Chicago, Illinois. (Febru­ geometry or analysis. The deadline is June 15, 1987. IIY 1987, p. 360) Information: Y. Oh, Director, Mathematics Research Cen­ 1;.19. Conference on Maximum Principles and Eigenvalue ter, Korea Institute of Technology, 400 Kusongdong PIGblemo in Partial Dlfl'erential Equations, University of Taejon, Korea 300-31. Knoxville, Tennessee. (February 1987, p. 360) T'"""""'· 22-July 2. NSF Workshop on Extremes of Random 1;·19. Conference on Parallel Architectures and Lan- Processes in Applied Probability, University of California, 1111'1 Europe, Eindhoven, The Netherlands. (February Santa Barbara, California. (April 1987, p. 550) l~i. p. 360) 22-July 3. Symposium on Banach Algebras and Automatic IH9. Mathematical ABBociation of America's North Continuity, Leeds, England. ~ Section Summer Seminar on Graph Theory and Information: H. Dales, School of Mathematics, University Liloor Algebra, University of Minnesota, Duluth, Min­ of Leeds, Leeds LS2 9JT, England. ll!liOta. (January 1987, p. 133) 23-26. Dundee Biennial Conference on Numerical Analy­ ~ 19. National Science Foundation-Conference Board sis, Dundee, Scotland. 1M Sciences Regional Conference on Mat~ematical Information: The Organising Secretaries, Biennial Con­ ~ichig· IDvariance Applications in Statistics, University of ference on Numerical Analysis, Department of Mathe­ ·• an, Ann Arbor, Michigan. (April 198 7, p. 550) matical Sciences, The University, Dundee, DD1 4HN, 1 ~19. OR M th · llUry S ' . 8 emat1cs and the Microcomputer Salis- Scotland, United Kingdom. P l«Jiate College, Salisbury, Maryland. (Februar; 1987, 23-26. Sixth IMACS International Symposium on Com­ !; 19. Research puter Methods for PDE's, Lehigh University, Bethlehem, 11 ~-·· • Conference on Probabilistic Analysis Pennsylvania. (January 1986, p. 134) . """"'lllatona) Optimiz t · p . I Diversity Bait' a Jon roblems, .Johns Hopkms IH S · ~more, Maryland. (February 1987, p. 361) 23-27. International Conference on Generalized Func­ 9 tions, Convergence Structures and Their Applications, lll ~P;~wn ~n Mathematical Theory of Networks Dubrovnik, Yugoslavia. (June 1986, p. 560) 1; 26 ' oemx, Arizona. (February 1987, p. 361) · Workshop d Sh 24-26. 1987 National Educational Computing Conference, "-b. Univers't fan . o~t Course on Stochastic Net- Philadelphia, Pennsylvania. (April 1987, p. 550) lily 1987, p. 1' ~)0 WJsconsm, Madison, Wisconsin. (Jan- 3 26-27. Meeting on Domain Theory, Leeds, England. (April !; July 3. Micro 1987, p. 551) ~kal &ienc:~am on Commutative Algebra, Math- 1~r i98S, p. ;~arch Institute, Berkeley, California. 28-July 3. Bonn Workshop on Foundations of Comput­ 6 ing, Bonn, Federal Republic of Germany. (February 1987, ~y 24 · Workah0 p. 361) r-"· Institute ~ P on Molecular Structure and Dy­ ~...,ity of M' or Mathematics and its Applications 28-July 4. Harmonische Analyse und Darstellungstheorie ""· 198 7, J>. 36l)mnesot a, M'mneapohs, . Mmnesota. . (Febru-' Topologischer Gruppen, Oberwolfach, Federal Republic of l& 19 Germany. (February 1987, p. 361) ...... : Second AnnUal ":-1\ 1'heory C Conference on Structure in Com- 29-July 3. Premiere Conference Internationale sur lee oven.'- · ornel! U · · uer 1986 'p. 96 2) mvers1ty, Ithaca, New York . Mathematiques Appliquee& et Industrielles, Paris, France. (August 1986, p. 654)

681 29--July 4. First Joint International Conference on Indus­ 14-24. Durham Symposium on Rep trial and Applied Mathematics, Paris, France. (February Algebraic Groups and Related Fini~ ~ 1987, p. 361) England. . . G...... :. 29--July 4. Fonctions Automorphes, Marseille, France. Informat.on: S. Donkm, School of Math . (February 1987, p. 361) Queen Mary College, Mile End Road~~ England. ' on Ei 4NS. 3G-July 4. Third International Seminar on Random Graphs and Probabilistic Methods in Combinatoric&, 1.9--24. Conference on Potential Theo s1ty, Prague, Czechoslovakia. (June ~· Charles Uaht,. Poznan, Poland. (October 1986, p. 844) 1 , p. 560) 2G-24. Workshop on Topological Markov QL,.. JULY 1987 Ia ted Systems, Heidelberg, Federal Re bl'.._.. .. I. (April 1987, p. 551) pu IC of~ July-August. Low Dimensional Topology Symposium, University of Sussex, Brighton, Great Britain. (August 2G-25. 1987 European Summer Meeting of tile Colloquium 1987, University of Granada, S ~L,J.eatr 1986, p. 654) 1987, p. 551) P&in. (APriJ 1-18. Dix-septieme Ecole d'Ete de Calcul des Probabilites, Saint-Flour (Cantal), France. (February 1987, p. 361) 2G-25. Second International Congr- of the'"'-~ . Fuzzy Systems Association, Tokyo, Japan. -­ 2-12. Durham Symposium on Operator Algebras, Durham, Informatwn: Second IFSA Congre88 Secretariat England. Society of Instrument and Control En!!ioeen' ~/o 'lit Information: R. Plymen, Department of Mathematics, 303, Hongo, Bunkyo-ku, Tokyo 113, Japan. ' ~28- University of Manchester, Oxford Road, Manchester M13 9PL, England. 2G-25. United States - United Kingdom Joial s.r.. on Operator Algebras, Coventry, England, (April 1987 5-18. Conference Internationale de Theorie des Nombres p. 551) •. (CITN), Universite Laval, Quebec, Canada. (February 1987, p. 361) 27-29. SLU-GTE Conference on Commuta&M U..... Analysis, Saint Lawrence University, Canton, New Ycrl 5-25. Research Workshop on Banach Space Theory, (April 1987, p. 551) University oflowa, Iowa City, Iowa. (February 1987, p. 361) 27-31. International Symposium on 1nfwma1iaa .. 6-8. Martin Beale Memorial Symposium, London, Eng­ Coding Theory, State University of Campinas, Campiaao. land. Brazil. (January 1987, p. 134) Information: B. Peberdy, Scicon Limited, Wavendon Tower, Wavendon, Milton Keynes MK17 8LX, England. 27-August 1. Second Siegen Topology S)'llllllllima, Sie&oa. Federal Republic of Germany. (February 1987, p. 362) 6-10. Interdisciplinary Conference on Mathematical Logic and Related Subjects, Durban, South Africa. 27-August 8. K-theory and its Applicatloaa, lbadan. Information: C. Brink, Department of Mathematics, Uni- Nigeria. (February 1987, p. 362) versity of Cape Town, Rondebosch 7700, South Africa, 31-August 3. Boston Workshop for Matbemllla fit. or J. Heidema, Department of Mathematics, Rand ulty, Wellesley College, Wellesley, Massachusetts. (Janllll)" Afrikaans University, Post Office Box 524, Johannes­ 1987, p. 134) burg 2000, South Africa. 6-10. Third Gregynog Symposium on Differential Equa­ AUGUST 1987 tions, University of Wales, United Kingdom. (October 1986, p. 844) 1-5. Symposium on Dependence in Statlstla md ,_, 6-16. A Research Symposium in Complex Analysis, bility, Laurel Highlands, Pennsylvania. . lJt. Imperial College, South Kensington, London, England. Information: H. Block, A. Sampson~ ~r T. ~VI~ rJ (October 1986, p. 844) partment of Mathematics and StatiSIICS, Umvenaly Pittsburgh, Pittsburgh, Pennsylvania. 6-24. Summer Research Institute on Theta Functions, Bowdoin College, Brunswick, Maine. 1-6. Fifth Conference on Graph Theory of Claiaa, Peoplr"s Information: For further details, see the Meetings section Republic of China. (August 1986, p. 654) . of this issue of Notices. 3-7. Georgia Topology Conference, University of GeoiPL 1G-ll. Logic and Linguistics Conference, Stanford Uni­ Athens, Georgia. (January 1987, p. 134) versity, Stanford, California. (January 1987, p. 134) ':.--7. Second Howard University Sym~-:::= 12-16. Seventh Inter-American Conference on Mathemat­ Semigroups, Partial Differential Equa~l~ rColwalJia. ics Education, Santo Domingo, Dominican Republic. tors, Howard University, Washington, D1stnct 0 Information: VII CIAEM, Centro de Investigaciones, Uni- (February 1987, p. 362) lA versidad Cat6lica Madre y Maestra, Apdo. Postal 822, 3-21. Mathematical and Statistical ~· Santiago de los Caballeros, Dominican Republic. Evolutionary Theory, Universite de Mont ' 13-17. Automata, Languages, and Programming, Karl­ Canada. (January 1987, p. 134) . '--r.lallt- sruhe, Federal Republic , Institute 1"' of Germany. (August 1986, p. 654) 3-28. Four-week Program on Ro b ot .1cs, . of !diDDfliOIL 13-17. Eleventh British Combinatorial Conference, Lon­ ematics and its Applications, Umverslty :162) don, United Kingdom. (November 1986, p. 962) Minneapolis, Minnesota. (February 1987, P· . -""" 13-17. Inequalities: Fifty Years on From Hardy, Little­ 4-7. Sixth International Cowerene-~ eon &lYe M•~ ,.... wood and Polya, University of Birmingham, Birmingham, Modelling: An Interdisciplinary In~~ ~ England. (October 1986, p. 844) Researchers and Educators in EngJD iallod ,pt6 Set 13-17. National Science Foundation-Conference Board of Biological, Medical, Environmental, S~ MissOuri· (fe!P the Mathematical Sciences Regional Conference on Group ences, Washington University, St. Louis, Actions on Manifolds, Virginia Polytechnic Institute and ary 1987, p. 362) ~ u-4 lA State University, Blacksburg, Virginia. (April1987, p. 551) 4-8. National Science Foundat~on-C ~ Ill AJ. 13-17. Sixth National Conference on Artificial Intelli­ the Mathematical Sciences Reg1Dnalad SpriJigS• ~ gence, Seattle, Washington. (February 1987, p. 362) gorithms, Colorado College, Color 0 (April 1987, p. 552) f "~~"-'"' ~ 13-23. Group Actions on Manifolds, Virginia Polytech­ aJDilies o • ...- nic Institute and State University, Blacksburg, Virginia. 5-7. Workshop on Generic F 362) (February 1987, p. 362) Montreal, Canada. (February 1987, P·

682 ties Meetings, Salt Lake C:ity, Utah. which may be useful for future work on this and related .~ Jilll>llfatbeJDll h details, see the Meetmgs sectiOn problems. r- . . For fnrt er Information: G. Benkart or J. Osborn, Department of ~- of Notices. Mathematics, University of Wisconsin, Madison, Wis­ J8SUe SUIJIIIler Conference, Extending the J Ibis consin 53706. • .a 9blll AonoU ters in Education, University of r-- )lfiad: Compu 24-27. International Conference on Computational Tech­ ..... e Oregon. . . Sydney, Australia. ~· EugeD · ters in Education, Umvers1ty of Ore­ niques and Applications, ; ..:....tion: CompuCenter 1553 Moss Street, Eugene, Information: C. Fletcher, Computational Techniques and Ill"''"-:- · uauon ' ,.. (Data Analysis Based on the L 1 -Norm and Related ...._;ll-~ latOlllat"onaiI co ...-· erence on Computational Tech- Methods, University of Neuchatel, Neuchatel, Switzerland. l98'/, p.~) Applications, Sydney, Australia. (February (January 1987, p. 135) 31-September 6. Workshop on Artificial Intelligence for 17 na1 ....-~ Iaternar H b 10 conference on Rings, Modules, and Natural Sciences, Torino, Italy. ' 0 art, Tasmania. (June 1986 p 560) Call for Papers: Send title and extended abstract to the 17-~ 1987 J . ' . address below. ~- Oint Statistical Meetings, San Francisco, Ia. (April 1987, p. 552) Information: M. Rasetti, Institute for Scientific Inter­ 17-21. Second In . change, Villa Gualino, 10133 Torino, Italy. Telephone: tiJ, Debrec H ternabonal Colloquium on Group The­ 39-11-6502679. "'onr.a . en, ungary. bon: E Szab' L · con. Pf. 12 H. 40 °• aJos Kossuth University, Debre- SEPTEMBER 1987 17_22 , ' - 10, Hungary...... lichth lnt t' 1-5. Conference on Mathematical Quantum Field The­ ~ llld Phll ernahy Io~I Congress of Logie, Method- 0 Universite de Montreal, Quebec, ~ Repu:"' (J f Science, Moscow, Union of Soviet ory and Related Topics, 17-22 cs. anuary 1987, p. 134) Canada. A..L., • Meeting on G Invited Speakers: I. Affieck, T. Balaban, G. Battle, D. ;;::; eometry of Banach Spaces, Mons, Brydges, P. Federbush, J. Feldman, L. Gross, J. Hamad, · · !ion: C. Finet I · J. Imbrie, R. Jackiw, A. Jaffe, T. Kennedy, J. Patera, V. ~~del'Etat · M ' nstitut de Mathematique Univer- Rivasseau, L. Rosen, G. Semenoff, I. Sigal, A. Wightman, -.iUJn. a ons, 15 avenue Maistriau 7000 Mons and P. Wittwer. , ''-21 • ' Information: F. Clarke, Director, Centre de recherches .&-..:. • Third Collferen ~~lion Theo ee. on Numerical Methods and mathematiques, Universite de Montreal, Cartes Postale ~ 1987, p. 13~· Umversity of Nis, Nis, Yugoslavia. 6128-A, Montreal, Quebec, Canada H3C 3J7. U-29. WorL-• 3-5. Satellite Meeting to the 46th Session of the Inter­ ~ &llll?PonLieAI . , , A.... · ty of Wiscono· gebras of Prime Characteristic national Statistical Institute, Kyoto, Japan. (April 1987, . ..,.,,. Th ·~m Madi w· · ' p. 552) the~ e worksho' . son, Isconsm. ol...i hlelli of c1 . P. Will survey recent progress on 7-9. Summer Conference on Category Theory and Com­ f · 3Ssifymg sim 1 fi · · · · -..was 0 Prune ch P e mte dimensional Lte puter Science, University of Edinburgh, Edinburgh, Scot­ aracteristic and will explore topics land. (January 1987, p. 135)

683 7-11. International Symposium on Harmonic Analysis, 9-10. Fifteenth Annual Mathematics and 8 Centre Universitaire de Luxembourg, Luxembourg. (Febru­ ference, Miami University, Oxford Oh' '-tll&lc. Cas. ary 1987, p. 363) p. 553) ' 10· (APriJ li87. 8-11. Third International Conference on the Teaching 9-1~. Sixth A?Jlual Midwest Statlatica CoDlt of Mathematical Modelling and Applications, University vers1ty of Illm01s, Urbana-Champaign, lllinoia ..._, Ulli­ of Kassel, Kassel, Federal Republic of Germany. (January Informatwn: S. Portnoy, Program Chai 0.:...._ 1987, p. 135) Statistics, University of Illinois, 1409 w~-G"'lfflt II Urbana, Illinois 61801. 8-16. Forty-sixth Biennial Session of the International reensu-. Statistical Institute, Tokyo, Japan. 9-10. Thirteenth Annual Student CoDlt . Information: International Statistical Institute Permanent University, Oxford, Ohio. (April 1987, p. 5~' !.liaiai Office, 428 Prinses Beatrixlaan, Post Office Box 950, 2270 10. Tenth Conference on Probability and 8 AZ Voorburg, Netherlands. Atmospheric Science, Alberta, Canada. (April!~ ia 9-11. Seventh Gesellschaft fiir Angewandte Mathematik 16-17. Third Eastern Small College Computlac 'p. 5531 und Mechanik Conference on Numerical Methods in Fluid ence, Marist College, Poughkeepsie, New York. (F~ Mechanics, Louvain-la-Neuve, Belgium. (February 1987, 1987, p. 363) --~ p. 363) 19-23. 20th International Conference on the APPilalla. 9-11. Twelfth Symposium on Operations Research, Uni­ of Computers and Mathematics in the Mineral ~ versity of Passau, Passau, Federal Republic of Germany. Johannesburg, South Africa. · (February 1987, p. 363) Info~mation: The Conference Secretary (C.31), Mintek Pr1vate Bag X3015, Randberg 2125, South Africa. · 9-12. Internationale Konferenz iiber Anwendungen und 2Q-22. Fourth International Conference on Text p,_, Modellbildung im Mathematikunterricht, Kassel, Federal ing Systems {PROTEXT IV), Boston, Massachusetts Republic of Germany. (June 1986, p. 560) Information: Conference Management Services, Port or. 9-12. Sixth Aachen Symposium on Signal Theory: Multi­ fice Box 5, 51 Sandycove Road, Dun Laoghaire Co dimensional Signals and Image Processing, Aachen, Fed­ Dublin, Ireland. Telephone: ( +353-1) 452081 or (f353- eral Republic of Germany. (February 1987, p. 363) 1) 808025 if no reply. 10--12. Advances in Computational Modelling and Nu­ 23-24. Combined Midwest-Southeast Difl'erealiallqa­ merical Analysis, University of Chicago, Chicago, Illinois. tions Conference, Vanderbilt University, Nashville, Tea­ (February 1987, p. 363) nessee. Program: Lectures will be given by L. Evans, Univmitym 13-19. Journees Arithmetiques 1987, Ulm, Federal Re­ Maryland, J. Hale, Brown University, and H. Hethccle. public of Germany. (June 1986, p. 560) University of Iowa, and there will also he sesaiooa lor 14-18. National Science Foundation-Conference Board short contributed talks. of the Mathematical Sciences Regional Conference on Information: G. Webb, Mathematics Department, Van­ Fractal Geometry, University of Cincinnati, Cincinnati, derbilt University, Nashville, Tennessee 37235, 61[).322. Ohio. (April 1987, p. 552) 4162. 14-18. Workshop on Polyhedral Combinatoric• and Ge­ 25-28. Joint National Meeting ofthe Operatloaaa-dl ometric Complexity, Institute for Mathematics and its Society of America and the Institute of ~ Applications, University of Minnesota, Minneapolis, Min­ Sciences, Saint Louis, Missouri. nesota. (February 1987, p. 363) Information: V. Sauter, School of Business, ~nivenily of Missouri, 8001 Natural Bridge Road, Samt Louil. 17-19. International Association of Statistical Computing, First Satellite Meeting, Tokyo, Japan. Missouri 63121-4499, 314-553-6281. Information: C. Hayashi, 23-11, Inokasira, 2-Tyome, 25-31. International Conference on Populatloa....,. Mitaka-Sei, Tokyo, Japan. matic:s, Schwerin, German Democratic Republic. Ge8ell· Information: The Secretariat ICPM 87, ~- Ko~~der 2Q-26. DMV-Jahrestagung 1987, Berlin, Federal Republic schaft fiir physikalische und math~tlsche B1o ~ of Germany. (June 1986, p. 560) Deutschen Demokratischen Repubhk_. Am Kupr:.,rik. 21-24. 1987 Conference on Software Maintenance, Austin, 7, Berlin 1080, Deutschen DemokratlSChen Rep Lack Texas. 26--30. Third Asian Conference in MathematiCil · Information: R. Martin, National Bureau of Standards, Beijing, China. . f Softwart· Building 225, Room B266, Gaithersburg, Maryland Information: Y. Dongping, Institute ~.. ~ 20899, 301-921-3545. Academia Sinica, Post Office Box 8718, B<~J~ 28--30. International Conference on Linear Algebra and 26--31. Mathematical Methods in OperatiOIII Applications, Valencia, Spain. Sofia, Bulgaria. (January 1987, p. 135) oplDC (;Gat' Information: V. Hernandez, Escuela Tecnica Superior de 27-30. Computer Communication for Devel lngenieros Industriales, Universidad Politecnica, Apart­ tries '87, New Delhi, India. . am (;oolJDit· ado 2012, 46071 Valencia, Spain. Information: S. Ramani, Cha1rman, Pro~opinC CoUll' 29-0ctober 2. Fifth International Symposium on Data tee on Computer Communication for D~olocY• Gui­ Analysis and Informatics, Versailles, France. (February tries'87, National Center for Software B baY 400 ()19. 1987, p. 363) mohar Cross Road, Number 9, Juhu, om India. AMS Ljnc

684 DECEMBER 1987 30-Junc 3. International Conference on Numerical Math­ ematics. Kent Ridge. Republic of Singapore. (April 1987. p. 553) 22_24_ Eleventh National System~_Conference _ 1987. KuruJ

'· Filth Caribbean Conference, in Combinatorics and h> . l'niversJtv of the \\est Indies. Cave HilL JfTNE 1988 ()lllpUIIDg. ! • BarbaddosS. kcrs: R. Read (l'nivcrsity of Waterloo) and 20-24. Fifth International Conference on Boundary and lnVII< pea . . . f (' d'lf) R. Churchhouse ( l mverRlty o _.ar I . Interior Layers: Computational and Asymptotic Methods. CaHfor Papen Participants w1shmg to present papers are Shanghai. China. asked 10 submit abstrac;,s with completed registratiOn Call for Papers: Submit one page types~t or typ~written cards by August 31. I 98•. For more mformat10n. wnte abstract ( 500 words rnaxinunn) on any topic of rdf'vance to the address below. . to the conference by September 30. 1987. Authors work­ Information: C. Cadogan. Department of Mathematics. ing outside of China should send abstracts to J. :\1iller. Cniversity of the West Indies, Post Office Box 64. Numerical Analysis Group. Trinity College. Dublin 2. Bridgetown. Barbados, West Indies. Ireland (telephone +35:i-1 6B749). Those working in abstracts to G. Ben-yu. Depart­ &-9. Joint Mathematics Meetings, Atlanta, Georgia. (April China should send their nlCnt of Mathernatics. Scir-IH'f' and Technology Univer~it~' !!187, p. 553) of Shanghai, Shanghai, China. Information: H. Daly. American Mathematical Society. Meetings Departmellt, Post Office Box 6248. Providence. Information: Outside of China: P. McKeever. Conference Office Box .5, 51 Sandycove Rhode Island 02940. Managernent Services, Post Road, Dun Laoghaire. C:o" Dublin. Ireland. Telephmw: !l-!5. National Science Fomtda•ion-Conference Board of ( +353-1) 452081. In China: P. Zhong-xiong, Department 1M Mathematical Sciences Regional Conference on Kaluza­ of Mathematics, Science and Technology Cniversily of llliD Theory, University of New Mexico, Albuquerque. Shanghai. Shanghai. China. Telephorw: 9529:32. ~ewMexico. (Aprill987. p. 55:3) 20 24. International Algebra Conference. Lisbon. Portu­ Summer Research Insti­ »-February 5. Twenty-eighth gal. (February 1987. p. 364) lllf of the Australian Mathematical Society, Shortland. -'U81ralia. 27 July 15. Microprogram on the Structure of Banach Information: R. Eggleton, Department of Mathematics. Spaces. Mathematical Sciences Research Institute. Bf'rkP­ Stat~tics and Computer Science, University of Newcas­ ley. California. tle, Rankin Drive, Shortland. :\'ew South Wales 2308, Information: Mathcn1atical Sciencf'E Research Instit utf'. All8tralia. 1000 Centennial Drive. Berkeley, California 94720.

FEBR/'ARY 1988 JI'LY 198/i

1988 Australian Applied Mathematics Conference, ~- 10 10. Representation Theory and Group Theory. :'v1anch­ ~Australia. (February 1987. p. 363) ester. England. (February 1987. p. :i64) 13--20. Edinburgh Mathematical Society's 1988 Saint An­ MARCH 1988 drews Colloquium, St. Andrews. Fife. Scotland. (February ll-!8. Seco d · 1987. p. 364) l'r.bl.ma n InternatiOnal Conference on Hyperbolic ary l!l87 · Aachen, Federal Republic of Germany. ( Febru- 17-27. Ninth Congress of the International Association . p. 363) of Mathematical Physics. Swans~a. Wales. (Ff'bruar~· 1987, p. 364) APRIL 1988 18 22. Twelfth IMACS World Congress on Scientific Computation. Paris. FrancP. (February 1987. p. :l64) l7-30. l'he Firs . . r...... Banff ~~Canadian Number Theory Society Con­ 23-August :3. Sixth International Congress on Mathe­ 1987, p. 364) ,' lberta. Canada. (February matical Education, Budapest. Hungary. (February 1987, p. 364) MAY 1988 lft.'ln ., 1988 M: ~ General ~he~atical Sciences Congress and 32nd AI'GUSJ' 198fi /""'l'· Canb eetJng of the Australian Mathematical \f""'•hon'ga. AUstralia. 8 -12. AMS Centennial Celebration. Provid~nce. Rhod~ ·;Ustralian ti , Heyde, Department of Statistics. lAS, Island. (April 1987. p. 5,5:3) · C'r 26o1 Aauonal l:mversity. GPO Box 4. Canberra, Informatwn: H. Daly, American Mathematical Society. l:l-1; · Ustralia Meetings Department. Post Office Box 6248. PrO\·idetJce. 'C.nrerenc Rhode Island 02940 1,1 · Chiangrn • on Mathematical Methods and Appli- t"!)]•hon: S. ;•· Thctiland. 9 12. International Symposium in Real Analysis. lTHi­ ~'ersily, B anglllanee. Faculty of Science, Kasetsart versity of Ulster. Colerairw. :'

685 14-27. Harmonic Analysis on Reductive Groups, Bowdoin College, Brunswick, Maine. Program: The Conference will explore recent advances in harmonic analysis on both real and p-adic reductive GENERALIZED DYSON groups. The two week duration of the conference will SERIES, GENERALIZED allow for many valuable discussions and informal work sessions. FEYNMAN DIAGRAMS Invited Speakers: J. Bernstein, Harvard University, R. Howe, Yale University, W. Schmid, Harvard University, THE FEYNMAN INTE-' and D. Vogan, Massachusetts Institute of Technology. GRAL AND FEYNMAN'S Information: W. Barker, Chairman, Harmonic Analysis on Reductive Groups, Department of Mathematics, Bow­ OPERATIONAL doin College, Brunswick, Maine 04011, 207-725-3571 or CALCULUS 207-725-3567. 2Q-26. Groups, Pusan, Republic of Korea. Information: A. Kim, Department of Mathematics, The Pusan National University, Pusan 607, Republic of Ko­ Gerald W. Johnson and Miehel rea. L. Lapidus 21-27. Seventeenth International Congress of Theoretical and Applied Mechanics, Grenoble, France. (January 1987, Th~ authors study generalized DyiiOn p. 135) senes a:nd their representation by 22-25. 1988 Joint Statistical Meetings, New Orleans, generalized Feynman diagrams as Louisiana. well as the closely related topic of Information: American Statistical Association, 806 15th Feynman 's time-ordered operational Street Northwest, Washington, District of Columbia calculus for noncommuting operators. 20005, 202-393-3253. They obtain these perturbation series by replacing ordinary Lebesgue measure JANUARY 1989 in the time integration involved in the Feynman-Kac functional by an arbitrarv 8-11. First Caribbean Conference on Fluid Dynamics, Lebesgue-Stieltjes measure. They then· Saint Augustine, Trinidad, West Indies. calculate the Weiner and Feynman path Invited Speakers: C. Brebbia, H. Brenner, S. Davis, H. Giesekus, and H. Phelps. integrals of the corresponding functional. Call for Papers: Abstracts of about 500 words should be These Dyson series provide a means of sent by January 31, 1988, to the Editorial Committee, is CACOFD 89, Department of Mathematics, University carrying out the "disentangling" that a of West Indies, Saint Augustine, Trinidad, West Indies. crucial element of Feynman's operational Information: Additional information may be obtained calculus. The authors are able to treat from the Conference Chairman, H. Ramkissoon, at the far more general functionals than the above address. traditional exponential function; in fact, 11-14. Joint Mathematics Meetings, Phoenix, Arizona. the class of functionals dealt with lo11D8 (April 1987, p. 553) a rather large commutative Banach Information: H. Daly, American Mathematical Society, algebra. The theory is of interest in i_ta Meetings Department, Post Office Box 6248, Providence, relation to several areas of mathematical Rhode Island 02940. physics. i980 Mathemattcs Subject Classificali...,: JULY 1989 81, 05, 28. 47, 58, 01 ISBN 0-8218-2413-9, LC 86-14154 5--19. Microprogram on Noncommutative Rings, Mathe­ ISSN 0065-9266 matical Sciences Research Institute, Berkeley, California. 88 pages (softcover), July !986 19 Information: Mathematical Sciences Research Institute, List price $11. Institutional member ' 1000 Centennial Drive, Berkeley, California 94720. Individual member $7 O/J5INA To order, please speCify MEM AUGUST 1989 ------28-September 1. Third International Conference on the Shipping/Handlingo 1st book $2, •:~5 each Theory of Groups and Related Topics, Canberra, Australia. add'l $1, $25 max. By air, lst boo ' Information: J. Cossey, Mathematics Department, Faculty add'! $3, $100 max. r from AMS, of Science, Australian National University, GPO Box 4, Prepayment requtred · Or de . ProvideD«• Canberra, ACT 2601, Australia. P.O. Box 1571. Annex Statwn, 7774 to u,. RI 02901-9930. or call 800·556- VISA or MasterCard. JANUARY 1990

17-20. Joint Mathematics Meetings, Louisville, Kentucky. (April 1987, p. 553) Information: H. Daly, American Mathematical Society, Meetings Department, Post Office Box 6248, Providence, Rhode Island 02940.

686 NEW AMS PUBLICA liONS

where he served as a Lecturer between 1965-1967. His ...... ,-,,, . current research interests are in the areas of combinatorial group theory, and he has published several papers :E GROUP RINGS on Burnside groups. Fox subgroups. and dimension Narain Gupta subgroups. Narain Gupta is a Fellow of the Royal Society Porary Mathematics, Volume 66) of Canada and he currently holds a Killam Research j(OIItem Fellowship from the Canada Council. Th. book deals with some aspects of linear Contents ~ ·ques in combinatorial group theory havmg Magnus embeddings and free differential calculus t~n~rigin in the work of Wilhelm Magnus in the :9~- The central theme is the identification Applications of Magnus embedding those subgroups of free groups and properties of Fox subgroups of free groups which are induced by certam rdeals of the mtegral group rings of free groups. This subject has Dimension subgroups been developed extensively, and the author seeks Generalized Magnus embeddings to present, in contemporary style, a systematic and comprehensive account of some of its 1980 Mathematics Subject Classifications· 20H25, 20F99, the book are a solution 20C05, 20C07, 20F05. 20F26. developments. Included in 20F14, 16A26, 16A27, 20015, 20F10, 20F12 of the Fox subgroup problem and an up-to-date ISBN 0-8218-5072-5, LC 87-12427 development of the dimension subgroup problem. ISSN 0271-4132 Aimed at graduate students and researchers in 144 pages (softcover), June 1987 Individual member S13, List price $22, combinatorial group theory, the book requires a Institutional member $18 familiarity with the general terminology of free To order, please specify CONM/ 66N groups and group rings. ~~------

CURRENT TRENDS IN ARITHMETICAL ALGEBRAIC GEOMETRY Kenneth A. Ribet, Editor (Contemporary Mathematics, Volume 67)

This volume contains papers presented at the AMS-IMS-SIAM Joint Summer Research Conference on Current Trends in Arithmetical Algebraic Geometry, held in August 1985 at Humboldt State University in Arcata, California. The conference focused on hyperbolic geometry, Arakelov theory, and connections between etale cohomology and crystalline cohomology. The book is accessible to both graduate students and mathematicians interested in current topics in arithmetical geometry, particularly those readers in neighboring fields who wish to acquire an overview is now intensely BiOGRAPHy of some topics in which research be ~araln G active. Some of the introductory papers will Uo . UPta is p f '~s,ty of M . ro essor of Mathematics at the of interest to the nonspecialists, while others are "liCe l967. He arnltoba. Canada. where he has taught directed at researchers and advanced graduate ~ees fro'll Ali:~~ved his M. A. and LL.B. {1959) students familiar with the area. Portions of this 5) fro'll the A Un,vers1ty. India. and his Ph.D. book are likely to become fundamental references ustral,an National University. Canberra . and will be of permanent value to researchers. ! order • · 'orm rn the back of this issue or call 800-556-7774 to use VISA or MasterCard. Shipping and handling charges will be added.

687 Contents Introduction NOETHERIAN RINGS AND A. Beilinson, Height pairing between algebraic THEIR APPLICATIONS cycles Lance W. Small, Editor Pierre Deligne, Dale Husemoller, Survey of (Mathematical Surveys and Monographs, Drinfef d modules Volume 24) Jean-Marc Fontaine, William Messing, p-adic periods and p-adic etale cohomology Researchers in ring theory or allied topic Henri Gillet, An introduction to higher dimensional the representation theory of finite dimenss: suclh as I b ·11 · · 1onaLie Arakelov theory a ge ras, w1 apprec1ate th1s collection of ex . lect~res. on recent advances in ring theory=~~ Serge Lang, Diophantine problems in complex apphcat1ons to other areas. Five of the lect hyperbolic analysis ~ere delivered at a co~ference on Noetheria~es Ron Livm!, Cubic exponential sums and Galois nngs at the Mathemat1sches Forschungsinstitut representations Oberwolfach, in January 1983, and the sixth ' was delivered at a London Mathematical Society J.-P. Serre, Lettre a J.-F. Mestre D~rham conference ~n July 1983. The study of the Joseph H. Silverman, A survey of the theory of pnme and pnm1t1ve 1deal spectra of various classes height functions of rings forms a common theme in the lectures, and Lucien Szpiro, Presentation de Ia theorie t~ey touch on such topic_s as the structure of group d'Arakelov nngs of polycycl1c-by-f1mte groups, localization in noncommutative rings, and rings of differential 1980 Mathematics Subject Classifications: 11G, 14F, 19E, 32H operators. The lectures require the background of ISBN 0-8218-5074-1, LC 87-11506 an advanced graduate student in ring theory and ISSN 0271-4132 may be used in seminars in ring theory at this level. 304 pages {softcover), June 1987 Individual member US. List price $30, Contents Institutional member $24 To order. please specify CONM/67N J. T. Stafford, The Goldie rank of a module Daniel R. Farkas, Noetherian group rings: An exercise in creating folklore and intuition CUMULATIVE INDEX TO J. C. Jantzen, Primitive ideals in the enveloping MATHEMATICS OF algebra of a semisimple Lie algebra COMPUTATION, 1970-84 Thomas J. Enright, Representation theory of semisimple Lie algebras This index is a sequel to the Cumulative Index to Mathematics of Computation 1943-1969. It is a Jan-Erik Bjork, Filtered Noetherian rings compilation by author and subject of all material R. Rentschler. Primitive ideals in enveloping appearing in Mathematics of Computation during algebras the years 1970-1984 (volumes 24-43). The author 1980 Mathematics Subject Classifications: index gives full bibliographic information on all 16A33. 16A03. 16A08: 17B35, 17B10. 20C07 of the items including classification numbers. ISBN 0-8218-1525-3 The Mathematical Reviews number and reviewer ISSN 0076-5376 name have also been provided when available. 230 pages {hardcover). June 1987 Individual member 132. List price $54. The subject index is changed from the 1943-1969 Institutional member $43 subject index and now includes title, language, and To order, please specify SURV /24N MR number {when available) as well as author name. The codes found in the previous index are retained. 1980 Mathematics Subject Classification: 00 ISBN 0-8218-0093-0. LC gs45-54 500 pages {softcover), July 1987 Individual member 131. List price $52. Institutional member $42 To order, please specify MCOMIN/2N

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688 IV The general H= optimization problem Nonlinear H= optimization

$ RATOR THEORY, ANALYTIC 1980 Mathematics Subject Classifications. MATRICES, AND 47-01. 46-01. 93-XX. 22-XX. 30-XX, 42-XX, OP~CTIONS, 49-XX ENGINEERING ISBN 0-8218-0718-8, LC 87-1192 ~~ECTRICAL ISSN 0160-7642 William Helton 152 pages (softcover), June 1987 J. h the assistance of Joseph A. Ball, All individuals Sll, List price $19 To order, please specify CBMS/68N Wit 1 R Johnson, and John N. Palmer Char~sRegional Conference ~eries, Numbe.r 68 ICBM ed by the National SCience Foundat1on) SuppOrt ded for functional analysts, control theorists, PROCEEDINGS OF THE 1985 ~:possibly researche~s in Lie gr~ups, ~his book MONTREAL CONFERENCE IN presents some interes.tmg .conne_cth1ons e 1t~een NUMBER THEORY mathematics and engmeenng w1t out r_e ymg H. an engineering background. It prov1des a Kisilevsky and J. Labute, Editors (Conference Proceedings of the Canadian :Oilied approach to deriving _basic resul~s in . Mathematical Society, Volume 7) several seemingly diverse top1~s: Nev~nlmna-P1ck interpolation, H00 approx1mat1on, Wemer-H~pf factorization with vanous symmetry constramts, This volume contains the proceedings of the commutant lifting, and the Kdv equation. The Canadian Mathematical Society's Summer Seminar first three of these topics play a substantial role in Number Theory, held in June 1985 at the in the engineering problem of designing systems Loyola Campus of Concordia University. Directed to meet frequency domain specifications. Several at advanced graduate students and research of the chapters introduce this problem from the mathematicians, this book requires a background point of view of functional analysis and then of graduate study in number theory and modular proceed to the modern subject of robust control. functions and will provide readers with a survey Other topics treated are certain types of matrix of current research topics in number theory. The approximation and optimization of very general papers range over a variety of areas, including local nonlinear sup-norm objective functions over H00 • and global number fields, L-series, modular forms, The book requires a background in functional lwasawa theory, and arithmetic algebraic geometry. analysis and complex analysis equivalent to a first Included are papers by H. Stark and B. Gross course in these subjects. based on lectures they gave at the conference. Contents In his paper, Stark presents a new point of view I Engineering motivation regarding modular forms and Dirichlet series. Gross's paper presents a geometric approach to Engineering background Engineering problems Eichler's arithmetic theory of definite quaternion algebras and to Waldspurge's results on the central 11 Analytic function theory critical values of L-series. Fr . act•onal maps and Grassmannians Contents Repr~se~ting shift invariant subspaces T. Chinberg, Intersection theory and capacity Apphc~tlon~ to factorization, interpolation, and theory on arithmetic surfaces approx1mat1on R. Crew, L-functions of p-adic characters and a Further applications Matrix ana'o d . . geometric "main conjecture" ' gs an generalizations E. de Shalit, Making class field theory explicit Ill Matrices P. Feit, The poles and residues of Eisenstein series Some matrix bl · . . on symmetric domains Opt' . . pro ems m engmeenng •m1zat1on t · · R. Gold, Kida's theorem and p-adic L-functions completions • rna nx mequalities, and matrix B. Gordon, Algebraic cycles of higher weight and The spectru f modular forms algebra m 0 a matrix with respect to an D. Goss, Analogies between global fields

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689 the special values of Distinguished by the breadth o;-;------ts B. H. Gross, Heights and . . persn..r.~- an d b y 1ts treatment of appliCations th' ~~u~ L-series 15 R. Gupta, M. R. Murty, and V. K. Murty, The contains nearly 50 papers on param' t . ~ume Euclidean algorithm for 5-integers a~~ nonlinear differential equations. e{~~ed ~~~ was into tw book IS D. Hayes, Real quadratic function fields d1v1ded. as the conference .h fhS · 0 Partso..­ J. Minardi, lwasawa modules for Z~-extensions of 1. m onor o t e turm sesquicenten · 1 • '«t and oscillation ·~~Is number fields with spectral theory th~la or hnear M. R. Murty and V. K. Murty, A variant of the second order equations, eigenvalue probryl h . . . 1 d' emsanc~ Bombieri- Vinogradov theorem t e1r extens1ons. me u mg Hamiltonian T. Orloff. Another proof of the Kronecker limit Part 2 is devoted to nonlinear differentia~ystems. problems in multiparametequations formulae and addresses er b.f . h P. Philippon. Independence et groupes algebriques 1 urcat1on t eory, normal forms, invariant t · · d · S I onanc~ D. Ramakrishnan, Arithmetic of Hilbert­ c haot1c ynamKs. evera of the papers de 1 '. equations. a with Blumenthal surfaces bifurcations in delay-differential Elliptic curves and values of D. Rohrlich. In addition, both parts of the book present L -functions significant applications of recent theoretical Fourier series and special values of M. Rosen, advances to such diverse fields as population L-functions Heeke dynamics, chemical reactions, geology, and p-adic L-functions and descent on K. Rubin, mechanical engineering. In this way, these elliptic curves non-CM proceedings reflect the dynamics of the conference Modular forms and related objects H. M. Stark, which fostered mutually beneficial interactions ' Canonical liftings of formal L. Tatevossian, between linear and nonlinear theory as well as modules between theory and applications. 0. Taussky, Integral matrices in algebraic number theory Requiring a basic knowledge of the qualitative of differential equations, this book is 1980 Mathematics Subject Classifications: theory 11F55, 11R, 11F41, 11F30, 12A70. 11G05, aimed at mathematicians and students working 11G40, 11S31, 14L05 in any area of differential equations, as well as 87-1307 ISBN 0-8218-6012-7, LC researchers interested in applying recent results ISSN 0731-1036 theory to other 472 pages (softcover). June 1987 in oscillation and bifurcation Individual member 132, List price $54, disciplines. Readers will gain a broad perspective Institutional member $43 on current research in this area from both the order, please specify CMSAMS/7N To Sturm ian and dynamical systems points of view. as well as an understanding of new results useful for application and of directions for future research.

1980 Mathematics Subject Classifications: PROCEEDINGS OF THE 1986 34, 58; 35, 70, 92. and others SEMINAR ON ISBN 0-8218-6013-5, LC 87-11402 ANNUAL ISSN 0731-1036 OSCILLATION, BIFURCATION, 740 pages (softcover). June 1987 Individual member 145, List price $75, AND CHAOS Institutional member $60 F. V. Atkinson, W. F. Langford, and A. B. To order, please specify CMSAMS/8N Mingarelli, Editors (Conference Proceedings of the Canadian Volume 8) 3 •·:·•·- Mathematical Society, THEORY AND APPLICATIONS The year 1986 marked the sesquicentennial of OF DIFFERENTIABLE the publication in 1836 of J. Sturm's classic FUNCTIONS OF SEVERAL memoir on boundary value problems for second order equations. In July 1986, the Canadian VARIABLES Mathematical Society sponsored the International 5. M. Nikol'skii, Editor . Volume 1701 Steklov Institute. Conference on Oscillation, Bifurcation. and Chaos. (Proceedings of the This volume held at the University of Toronto. I .th various contains the proceedings of this conference. This collection of papers dea s WI. ble functiofiS problems on the theory of differentia

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690 -----~riables and its application to FaTn, B. l., Extension of functions in anisotropic al rea va T · "d d rJ sever. . I equations. opiCS conS I ere Sobolev spaces parti~l dlffe~~~tlatheorems. applications for 1980 Mathematics Subject Classifications: ,e: unbed g eparation theorems, denseness 26. 30, 33. 35. 40. 41. 42,46. 54; 47,53 ,_..,J.,y spaces. s d f . ISBN 0-8218-3101-1 )1111""" pactly supporte unctions, smooth _com umbers for imbedding operators, ISSN 0081-5438 rJ 300 pages (softcover). June 1987 IJIPIOX~matlo~~nd singular operators, as well Individual member 172. List price $120. (alderOII-ZY~ 5 of a variety of boundary value Institutional member $96 the solut1on To order, please specify STEKL0/170N ~ms and Cauchy problems. Contents 'd' v B. L., On an analogue of the first ~ 10:1~e problem for elliptic equations with FOURTEEN PAPERS bOU aryacy~ The method of bilinear forms ttegene~ . TRANSLATED FROM THE aesov. 0. V.. Integral representations of functions. RUSSIAN and imbedding theorems l. A. Aksent'ev et al. aesov. 0. V.. The Littlewood-Paley theorem for a {American Mathematical Society Translations, mixed norm Series 2, Volume 136) BoTmatov, K. Kh., Separation theorems. weighted spaces and their applications The papers in this collection range over a variety of topics, including integral representations, complex Bugrov. Ya. S., Linear means of Fo~rier series and analysis, differential equations, and functional Fourier integrals. and the rate of thetr con vergence analysis. Gol'dman, M. L., Imbedding theorems for Contents anisotropic NikoY skii-Besov spaces with moduli of l. A. Aksent'ev and I. R. Nezhmetdinov, cootinuity of general form Sufficient conditions for univalence of certain Kazaryan, G. G., Weak solutions of the Dirichlet integral transforms problem for a quasilinear equation with lower terms N. V. Zabolotskii, Some relations for the Kal'neT, S. G., On a lower estimate of the Nevanlinna characteristics of li-subharmonic Lebesgue function of linear means of Fourier-Jacobi functions of order less than 1 series V. S. Vladimirov, Functions of several complex Karapetyan, G. A., Solution of semi-elliptic variables in mathematical physics equations in a half-space A. E. Etkin, Some boundary value problems with The Cauchy Kipriyanov, I. A. and Ivanov, l. A., a spectral parameter in the boundary conditions problem for the Euler-Poisson-Darboux equation in a homogeneous symmetric Riemannian space. I T. N. Arutyunyan, The inverse problem for the Dirac system on a semiaxis. with discrete spectrum Kryuchkov, V. S., Differential properties of the symbol of a Calder6n-lygmund singular integral V. E. Katsnel'son, Continuous analogues of the operator Hamburger-Nevanlinna theorem and fundamental matrix inequalities of classical problems. I K~havtsev, L. D., On equivalent norms in lllelg ted spaces V. E. Katsnel'son, Continuous analogues of the ~.~t-avtsev, N. L., On approximation of Hamburger-Nevanlinna theorem and fundamental '"'II:IDnsb · ~ · matrix inequalities of classical problems. II and . Y e~ttre •uncttons of exponential type on tmbeddmg theorems in a mixed norm V. E. Katsnel'son, Continuous analogues of the KUZnetsov y densene 'f u._ _V •• On the question of the Hamburger-Nevanlinna theorem and fundamental ss 0 mftnttely differentiable functions in matrix inequalities of classical problems. Ill Beso v spaces V. E. Katsnel'son, Continuous analogues of the lizorkin, P. I. a d 0 . oftheappro. ". telbaev, M. 0., Esttmates Hamburger-Nevanlinna theorem and fundamental Oflerator for ~tmatton numbers of an imbedding matrix inequalities of classical problems. IV ~ilcol' .. spaces of Sobolev type with weights M. I. Ostrovskii, On properties of the opening . sku, Yu S I dtlf~ntiabl ~· ·· ntegral estimates for and related closeness characterizations of Banach e unctions on unbounded domains spaces

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691 S. Ya. Novikov, E. M. Semenov and E. V. Tokarev, On the structure of subspaces of the spaces Ap (fl) Andreana S. Madgerova, Isomorphisms of AND RESIDUES homogeneous function algebras on the torus POLES V. A. Kasimov, A property of Hilbert modules OF EISENSTEIN SERIES and Fredholm operators over C* -algebras FOR SYMPLECTIC AND Al'gis Morkelyunas [Aigis Morkeliiinas), On UNITARY GROUPS two choice rules similar to the plurality rule and Paul Feit Borda's rule

1980 Mathematics Subject Classifications This book evaluates Dirchlet series which 30, 31, 32, 34, 39, 42, 44, 46, 47 anse m st udymg Founer coefficients ISBN 0-8218-3112-7, LC 87-12578 of certain Eisenstein series for a wide ISSN 0065-9290 variety of groups. The author uses this 144 pages (hardcover). July 1987 Individual member 128, List price $47, technical calculation to prove many Institutional member $38 theorems about automorphic forms, To order, please specify TRANS2/136N finding generalizations of the classical theorems for series of small weights. He also locates all of the poles of an Eisenstein series of arbitrary weight. Directed at specialists in the theory of automorphic forms in several variables the book demonstrates that for cert.W: algebraic groups, there is a family of Eisenstein series whose Fourier expansions can be thoroughly described. Thus it suggests that such a "good" family of Eisenstein series must exist for other groups as well.

1980 Mathematics Subject Classification: II John Harer, Arnold Kas, and ISBN 0-8218-2347-7. LC 86-3386 Robion Kirby ISSN 0065-9266 93 pages (Roftcover). :'vlay 1986 $12, Institutional member SlO, This book gives handlebody descriptions List price Individual member $7 of the elliptic surfaces over P 1 , including To order. pleaRP specify MEM0/346NA the Kiimmer surface. The authors derive handlebody decompositions of Shipping/Handling: 1st book $2, each the surfaces obtained by performing add 'l $1, $25 max. By air, 1st book $5, eecb logarithmic transforms to these elliptic add'l $3. $100 max. surfaces. They pay special attention to Prepayment required. Order from AMS, the Dolgachev surfaces D(p. q). P.O. Box 1571, Annex Station, Providence, 1980 Mathematics Subject Classifications: Rl 02901-9930, or call 800-556-7774 to use 57. 14 VISA or MasterCard. ISBN 0-8218-2:l51-5. LC 86-17451 JSSN 0065-9266 l02 pageR (softcover), July 1986 List price $12, Institutional member $10, Individual member $7 To order, please specify MEM0/350NA

Shipping/Handling: 1st book $2, each add'\ $1, $2E:i max. By air. 1st book $5, t.~ach add'\ $3. $100 max. Prepayment required. Order from AMS, P.O. Box 1571, Annex Station. Providence. RI 02901-9930, or call 800-556-7774 to ww \'ISA or MasterCard.

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692 New Members

Mathematical Society of Japan ()rdina1'Y Makoto Masumoto 5h\'lllala B Dason Izumi Takagi · 8513 A Greenbelt Road Greenbelt, Maryland Societe Mathematique Suisse Andrea Giovanni Clivio Billy L Foster University of Montana Societe Mathematique de France Missoula, Montana Christian Mauduit Ralph E Howard . Jacques J P Vauthier University of South Carohna Columbia, South Carolina Unione Matematica ltaliana Tadeusz Iwaniec Marco Biroli Syracuse University Syracuse, New York ~K Mohler Nominee University of Alabama in Birmingham Birmingham, Alabama California Polytech State University ~atthew P Rickey Donald W Gallaher St Olaf College Vivienne M Gerard Northfield, Minnesota Kevin R Reynier Sidney C Scull York University Calvin College Downsview (M3J 1P3), Ontario, Canada Deborah Lynn Blouw Arjen Sevensten Mark E Hamstra ~orth Holland Publishing Company Richard Hsung (1000 B2) Amsterdam, Netherlands Rodney A Tjoelker Jagraj Singh Case Western Reserve University ~vernment Girls High School DISh (F2R), India Mahalakshmi Jayaraman Shuzo Takahashi Cornell University 227 Durham Street William J Gay Menlo Park, California Robert Torop Georgetown University Springer-Verlag Scott M Auerbach - N~w York, New York John M Teske ~

693 Oberlin College University of California, Riverside Elizabeth LaFond Joycelyn G Del Mundo Ohio State University, Columbus University of Georgia J Ignacio Alarcon Chin-Cheng Lin Hua Chen University of Houston-University p k Michael J Donahue Michael F Gran ado ar Alan Hunter Forrest Manuel O'Ryan University of Illinois at Urbana-Ch . Karin B Reinhold-Larsson William R Harris am1Nitgn Qi Wang University of Saskatchewan Oregon State University Leslie J Walter Marc R Goulet Western Kentucky University Springer- Verlag New York Joel D Haywood Ruediger J Gebauer St Louis University Institutional Jean A McCann St Louis University Swarthmore College St Louis, Missouri Matthew H Katinsky Texas Tech University Sivanandan Balakumar An-Gwo Bian Dafeng Chen Kendall Clyde Richards Mark Stamp Joseph T Tahsoh

PATH FUNCTIONS AND GENERALIZED BASIC HYPERGEOMETRIC FUNCTIONS Kevin W. J. Kadell 1980 Mathemattcs SubJect Classificatiofl8: 33, 05, 11, :19, 41 ISBN 0-8218-2420-1, LC 86-28866 In this book the author obtains path ISSN 0065-9266 functions and their basic properties 60 pages (softcover), January 1987 by extending the constructive theory List price $10, Institutional member SS, of partition generating functions Individual mf"rnber $6 NA developed by Sylvester, Durfee, Andrews, To order, please specify MEM0/360 and others. Giving infinite families of generalizations of some basic hypergeometric summation formulas, he Shipping/Handling: 1st book $2, eac:5 each add'! $1, $25 max. By air, 1st book ' provides an interesting trade-off between add'! $3, $100 max. MS complexity and rate of convergence. He Prepayment requtred. Order. from A vid~nce, adds one free parameter to the q-analog P.O. Box 1571, Annex Statwn, Pro use of the limiting form of Jackson's theorem RI 02901-9930, or call 800-556-7774 to to generalize that result. VISA or MasterCard.

694 Personal Items ,1Gromov of the School of Mathemat­ ~ d H utes Etudes, Bures-Sur-Yvette, THE LEGACY OF SONYA .,. Jnstltut es ~nted as the initial holder of the was app 01 · R KOVALEVSKAYA FraJ!Cf· 'd w. Richardson Fou~dat~on egents ~odinSMathematics at the Umvers1ty of Texas Linda Keen, Editor ('ball' . f m AprillO to May 1, 1987. at ~ustlll ro Sonya Kovalevskaya was a distinguished · dB Sawyer was elected an Honorary mathematician and considered by !)eSmfotnhe New Zealand Mathematical Society \ltiDber o 1 her contemporaries to be among the ~ J986. best of her generation. Her work, KOaakU Yosida was a~ar~ed the Mauro. Pi- ideas and approach to mathematics are still relevant today, while her !Oilt' Prize by the Facolta d1. SCJ~n~e Ma~ematJ:h~ F' ·bee Naturali della Umvers1ta degh Stud1 d1 accomplishments continue to inspire women mathematicians. ~·La Sapienza" in 1986. The academic year 1985-86 marked Deaths the 15th anniversary of the Association for Women in Mathematics and the Jacob Benson, of Asbury Park, New Jersey, 25th anniversary of the Mary Ingraham died November 21, 1986, at the age of 65. He was Bunting Institute of Radcliffe College, a member of the Society for 37 years. Harvard University- both organizations that have enhanced women's role in Julian Blau, Professor Emeritus of Antioch mathematics. These two occasions College. Ohio, died March 10, 1987, at the age of provided a framework for a Kovalevskaya 69. He was a member of the Society for 49 years. celebration, which included a symposium John 0. Chellevold, Professor Emeritus of at Radcliffe College, and special sessions Wartburg College, Waverly, Iowa, died December at the the AMS meeting in Amherst, :Kl. 1986, at the age of 80. He was a member of Massachusetts, both in October 1985. The papers in this collection were drawn the Society for 39 years. from those two events. Harold Grad, Professor at New York Univer­ sity. Courant Institute, died November 17, 1986, The first group of papers contains back­ at the age of 63. He was a member of the Society ground material about Kovalevskaya's for 39 years. life and work, including a discussion of how she has been perceived by the .. Pet_er Henrid, Professor at North Carolina mathematical community over the lmvers1ty and at the Eidgenossische Technische last century. The rest of the papers Hocl!schu!e, Zurich, died March 13 1987 at the contain new mathematics and cover a l(fof63 · He was a member of the 'Society ' for 33 wide variety of subjects in geometry, )!ars. analysis, dynamical systems and applied mathematics. They all involve in one M ~ S. Johnson, Washington DC, died form or another Kovalevskaya's main ~arc I, 1987, at the age of n.' He was a areas of interest, differential equations mber of the Society for 31 years. and mathematical questions arising from Clarence B L' d . t f W . physical phenomena. died Febru ' lD QUJS , o ashmgton, DC, 2 lllember of~ • 1~87, at the age of 73. He was a 1980 Mathematics Subject Classifications: e Soc1etv for 4 7 years William • . 00. OJ ISBN 0-8218-5067-9 ISSN 0271-4132 htt 14. 1986 ~t McNabb, of Dallas, died Septem­ 286 pages (soft cover), January 1987 li the Societ' r the age of 71. He was a member List price $29. Institutional member $23, Y •or 20 years. Individual member $17 Charles H Rand To order. please specify CONM/64NA !idiusetts A 'h all, of the University of Mas- lgtofsg ·H m erst, died March 10 1987 at the · e was ' ' Shipping/Handling: 1st book $2, each add'l $1, ~. a member of the Society for 24 $25 max. By air, 1st book $5, each add 'I $3, $100 max. Prepayment required. Order from AMS, P.O. Box J...._A!exander Zab d 0 1571, Annex Station, Providence, RI 02901-9930, ~·usatem. Isra ~ sky, of Hebrew University, or call 800-556-7774 to use VISA or MasterCard. ~gt of 49 H el, died November 20 1986 at the ""-'""~. · e was a member of the Society' ' for 22

695 Visiting Mathematicians

The list of visiting mathematicians includes both foreign mathematicians visiting in the United St tea Americans visiting abroad. Note that there are two separate lists. a 8lld C...., IIi

American Mathematicians Visiting Abroad Name and Home Country Host Institution Field of S11ecial Interest Assmus, Edward F., Jr. University of Birmingham, Combinatorics ~ (U.S.A.) England 5/87 ·IOJt. Beasley, Leroy (U.S.A.) University College, Ireland Matrix Theory Bhattacharyya, Gouri Gadja Mada University, Statistics 8/87. 1;81 (U.S.A.) Indonesia; 6/87. 9,t, Indian Statistical Institute, India 10/87. I.!! Cummings, Larry (Canada) University of Paris, France Pure Mathematics 9/87. 6.•1! Davidson, Mark G. (U.S.A.) University of Iceland Group Representations 8/87. 1.!! Drazin, Michael P. (U.S.A.) University College, England Algebra 7/87. 7;81 Geddes, Keith (Canada) Universite de Grenoble, France Computer Science 9/87. &ill Gottlieb, Dan (U.S.A.) I.H.E.S., France Topology 7/87. 7/11 Jackson, Peter L. (Canada) Katholieke Universiteit, Production and Inventory 9/87. 611! Belgium Control Klotz, Jerome (U.S.A.) Gadja Mada University, Statistics 1/87. 7.@: Indonesia McCleary, John (U.S.A.) University of Sydney, Australia Algebraic Topology 6/87. s;r. Milner, Fabio A. (U.S.A.) University of Rome, Italy Numerical Analysis 1/88- 8/1! Protter, Philip (U.S.A.) Universite Paris VI, France Probability 5/87. 1{8: Puri, Prem S. (U.S.A.) Indian Statistical Institute, Applied Probability and 6/87. 6/1! India Stochastic Processes Weintraub, Steven H. University of Bayreuth, West Algebraic Topology 8/87 · II!! (U.S.A.) Germany Weitsman, Allen (U.S.A.) University of York, England Complex Variables 1/88· 1,!!

Visiting Foreign Mathematicians Ali, M. A. (Jordan) University of Connecticut Mathematical Statistics and 9/87. l/8! Design of Experiments Barrera, Pablo (Mexico) University of New Mexico Numerical Analysis 10/86· 718: Ben-Artzi, Matania (Israel) Northwestern University Functional Analysis 6/87. 9!87 Bjorch, Ake (Sweden) University of Tennessee Numerical Analysis 5/88· 7181 Bose, Arup (India) Purdue University Statistics and Probability 1/87. 6/l! 7/87 -12/S: Bruss, Thomas (Belgium) University of California, Santa Applied Probability Barbara 9/87 -12ir. Cellina, Arrigo (Italy) University of California, Santa Optimization and Control Theory Barbara 8/87. 1.!! Chang, Kung Ching (China) University of Equations Wisconsin-Madison 7/87. 6 ii Chen, Chen-Hsin (Republic Harvard University Biostatistical Science of China) 9/87. 6!! Chen, Guiqiang (China) New York University, Courant Nonlinear Partial Differential Institute Equations and Their Applications 4/88• iii Chipot, Michal (France) University of California, Santa Variational Inequalities, Barbara Nonlinear Problems in P.D.E's. 9/87· 6 ~ Deshpande, Jayant (India) University of California, Santa Mathematical Statistics Barbara 8/87. 8ii Elduque, Alberto (Spain) University of Lie Algebra Wisconsin-Madison 10/87. 12 ~ Eremenko, A. E. (U.S.S.R.) Purdue University Complex Analysis, Iteration 8/87. l Farnsteiner, Rolf (Germany) University of Lie Algebra Wisconsin-Madison 8/81· 8 Feng, Youhe (China) Southern Illinois University, Functional Differential Equations - Carbondale 9/~- ,r Fryer, John (England) University of North Carolina, Survivorship Analysis, Time Chapel Hill Series

696 Host Institution Field of Special Interest Period of Visit Horne Com!lfv University of Missouri Functional Analysis 8/87- 7/88 .~ . Gilles l France) Cornell University Combinatorial Optimization 3/87- 8/87 ~·Martin (West (;er!Da.nY) New York University, Courant Constructive Field Theory 9/87- 6/88 TakaS hi l Japan I Institute JWa. University of Toronto Combinatorics 9/87- 6/88 fWU""'· A (Israel l University of North Carolina, Differential Geometry 9/87- 12/87 Ernst (West fktDU"· Chapel Hill (;er!DaJlYl University of Statistics 8/87- 5/88 [lorVJih· Lajos (Hungary) Wisconsin-Madison University of Statistics 9/87- 5/88 llfYt&nd. Arnljot (Norway) Wisconsin-Madison University of Statistics 9/87- 5/88 Hfrl&nd. Liv (Norway) Wisconsin-Madison University of Utah Differential Equations 9/87- 7/88 HUUOO· Vivian C. L. [England) . . Algebraic Topology 1/87 - 12/87 ;;.ru. Oluferni S. ( N•gena) Howard University Numerical Analysis 1/88- lltbt. Yasuhiko (Japan) University of Utah 4/88 Juhaoz. Istvan (Hungary) University of Set Theoretic Topology 8/87- 1/88 Wisconsin-Madison Kennedy. Douglas (Great Georgia Institute of Technology Probability 9/87- 6/88 Britain) !ilchenassaiDY· Satyanad New York University, Courant Nonlinear Elliptic P.D.E. 9/87- 5/89 (Ftanee) Institute Ko ...Iski. Marek (Poland) University of Utah Numerical Analysis 9/87- 6/88 liMo. Rainer (West University of Delaware Integral Equations 9/87 - 12/87 G

697 N arne and Home Country Host Institution Field of SQecial Interest P· Thistlethwaite, Morwen University of California, Santa Knot Theory, Low Dimensional ~ (Great Britain) Barbara Topology 8/87. Tfll Torunczyk, Henryk University of Tennessee Geometric Topology (Poland) 9/87. ll/87 Trotter, Leslie (West Cornell University Combinatorial Optimization Germany) 8/87. 8;8l Tserpes, Nicolas (Greece) Wayne State University Probability and Statistics Tsuda, K. (Japan) University of Toronto Algebraic Topology 8/87. Sill Tzifriri, Lior (Israel) Louisiana State University Functional Analysis 10/87. 6/!l van Mill, Jan (Netherlands) Wesleyan University Point-Set and Geometric 8/87. S/!l Topology 7/87. 9ft. Viterbo, Claude M. New York University, Courant Hamiltonian Systems and (France) Institute Nonlinear Analysis 9/87. 6/118 Walter, Wolfgang Utah State University; Differential Equations (Germany) University of Connecticut 9/87. l/118 Watanabe, Osamu (Japan) University of California, Santa Theoretical Computer Science 1/88. S;l! Barbara 8/87. 8/8! Welters, Geraldo E. (Spain) University of Utah Algebraic Geometry 1/88. 4/811 Wen, Li (China) University of Analysis Wisconsin-Madison 8/87. l/118 Wisniewski, Jaroslaw Johns Hopkins University Algebraic Geometry (Poland) 7/87. 6;111i Xue, Kefu (China) Medical University of South Engineering 7/87. 6,8! Carolina Yang, Shangjun (People's University of Missouri-Kansas Matrix Theory 8/87. 12!8: Republic of China) City Ye, Yangbo (China) Johns Hopkins University Group Representations 7/87. 6/llli Zhang, Nien-Fan (China) Southern Methodist University Mathematical Statistics and 6/87 · S;Sil Time Series Analysis Zwicker, John (England) Dalhousie University Mathematical Physics 7/87. 9/87

many of which are discussed in these MULTIPARAMETER papf:rs. The articles also describe theoretical and experimental studies BIFURCATION THEORY of chemical reactors, which provide many situations in which to test the Martin Golubitsky and John M. mathematical ideas. Other test areas Guckenheimer, Editors arc found in fluid dynamics, particularly in studying the routes to chaos in two This 1985 A'v!S Summer Research laboratory systems, Taylor-Couette Conference brought together flow between rotating cylinders and mathematicians interested in Rayleigh-Benard convection in a fluid rnultipararneter bifurcation with layer. scientists working on fluid instabilitics and chemical reactor dynamics. This proceedings volunw demonstrates the 1980 Mathemattcs Subject Classificahons: mutuallv beneficial interactions between 58. 34, 76 ISBN 0-8218-5060-1, LC 86-8106 the rnat.hcmatical analysis, based on ISSN 0271-4132 86 genericity. and experimental studies in 408 pages (softcover), August 19 $27 t hcsc fields. Various papers study steady List. price $34, Institutional member ' state bifurcation. Hopf bifurcation to Individual membe~ $20 'M ,56NA periodic solutions, interactions between To order, please specify COl\. I modes, dvnarnic bifurcations, and tlH' role of sy.mmetries in such systems. A . , . b k $2 each section of abstracts at the end of the Slnppmg/Hand!mg: 1st 00 ' k $S each add'! $1, $25 max. By air, 1st boo ' volume provides guides and pointers to the literature. add'! $3, $100 max. from AMS, Prepayment requ.red, Order p ovidence, The mathematical study of multipa­ P.O. Box 1571, Annex Statwn. r 4 to use rameter bifurcation leads to a number RI 02901-9930, or call S00-556-777 of theoretical and practical difficulties, VISA or MasterCard.

698 MS Reports and Communications ~ Recent Appointments University of Hawaii. The speakers were Patrick Ahern, Sheldon Axler, George Csordas, Carl H. Fitzgerald, Simon Hellerstein, Aimo Hinkkanmen, bers · terms of office on standing Keiji Izuchi, Boris Korenblum, Frank D. Lesley, cGIJllllittee me~ on December 31 of the year ·uees expire . Joseph Miles, Bruce Palka, John Rossi, Donald (diiiDl_ theses following their names, . m paren . Sarason, W. Schneider, Joel H. Shapiro, Daniel :::: otherwise specified. Shea, Wayne Smith, Charles S. Stanton, Kenneth Stephenson, David C. Ullrich, and Richard S. Mackey (1989) has been appo!nted Varga. )libael eM Rinzel (1989) has been reappo~nte_d Rings and modules, KENT R. FULLER, Uni­ 11!11 J~MS-SIAM Committee on Mathematzcs zn versity of Iowa. The speakers were Gene Abrams, 10 thei e Sciences by Presidents G. D. Most ow Goro Azumaya, John A. Beachy, Douglas G. ~\1~/'and Charles William Gear (SIAM). Other Burkholder, John Dauns, Vlastimil Dlab, Joe IAl rs of the committee are Kenneth L. Lange W. Fisher, K. R. Goodearl, Robert Gordon, E. =Hans G. Othmer (1988), Alan S. Perelson L. Green, T. Lenagan, W. K. Nicholson, James (t!I8T). and Richard E. Plant (1988). Osterburg, Mark L. Teply, and Birge Zimmerman­ Huisgen. Past Meetings Combinatorics, JERROLD J. GRIGGS, Uni­ Reports of versity of South Carolina, Columbia. The speak­ The March 1987 Meeting in Honolulu ers were Brian Alspach, R. L. Graham, Katherine Heinrich, Pavol Hell, I. D. MacDonald, Bojan The eight hundred and thirty-second meeting of Mohar, J. B. Nation, W. T. Trotter, and Victor the American Mathematical Society was held at K. Wei. the University of Hawaii in Honolulu, March Set theory and its applications, THOMAS ~28. 1987. JECH, Pennsylvania State University. The speak­ Invited Addresses. By invitation of the ers were James E. Baumgartner, Andreas R. Blass, Committee to Select Hour Speakers for Far West­ Matthew Foreman, Marcia J. Groszek, Alexander liD Sectional Meetings, there were two invited S. Kechris, Richard Laver, D. A. Martin, Karel addresses. MARTIN SCHARLEMANN of the Uni­ Prikry, and W. Hugh Woodin. tmity of California, Santa Barbara, spoke on Differential geometry, PETER LI, University .4pplications of naive graph theory to the topology of Utah, RICHARD M. SCHOEN, and S .-T. of S-manifolds; he was introduced by Terry Law­ YAU, University of California, San Diego. The !1lll. EDWARD A. BERTRAM of the University speakers were Robert L. Bryant, Hyeong I. Choi, of Hawaii spoke on Some combinatorial problems Robert E. Greene, Karsten Grove, R. Hamilton, ~-groups; he was introduced by Ronald L. Meinhard E. Mayer, Mario J. Micallef, Frank Morgan, S. Walter Wei, Brian White, and S.-T. S!*ial Sessions. By invitation of the same Yau. :::Wttee, there were seven special sessions of There were also two sessions for contributed ~ed t:-venty-minute papers. The topics of ten-minute papers, of seven and four papers _sessiOns, the names and affiliations of the respectively. lrpnizersAI · an d rIsts of the speakers are as follows: The undersigned associate secretary would gebra!c topology. CHRISTOPHER J ALL- like to thank R. Torretto of the MAA for sug­ DAY and R LIT . . !Jlfakers · TLE. Umversity of Hawaii. The gesting this meeting and Adolf Mader of the Y. Hsianwere Bohu~il Cenkl, James F. Davis, W. University of Hawaii who served very effectively l\" " g. S. Kwasik, Mikiya Masuda William as the local organizer. · ·'~enasco J h ' Low-di~ 0 n 0 prea, and S. Warer. Hugo Rossi STEVEN BLEILER, ~niversityof~~f:f~a/ topolo~y, Salt Lake City, Utah Associate Secretary :ifhnan Akb 1 s Columbia. The speakers were 0: Gillman.t~ut, Mladen Bestvina, P. M. Gilmer, llilden, Osam~ ~c~. ~ordon, John Hempel, M. The Council Meeting in Newark ~- Martin L a~Imizu, Terry Lawson, Darren ~.:iakanichi uRs~Igh, Kenneth C. Millett, Yasu- The Council met on 25 April 1987 at 7:00 PM ..,___"V

699 from the Committee on Science Policy published Committee to Monitor ProbleDIS in the Notices for April on p. 448. These in Commu~icati~n Richard S. Palaia recommendations concerned themselves with the The Counc1l rece1ved the resian~t· . . "'"' !On of R..1.. two motions entertained by the Business Meeting D. Edwards from the Ed1tonal Comnt"t ·"''J!!t of 22 January 1987 as detailed in the Notices for Transactions and Memoirs and from t~ tee of the February on pp. 398-399. The Council adopted The Council elected James W e Co1111til_ . C•n~...... on. a plan that is enunciated on p. 615 of this June place as Editor of the Transactions and M m.~ issue. The Council adjourned at midnight. emo1rs. The Council agreed that the Society ad­ minister two prizes from the Fredkin Foundation Bethlehem, Pennsylvania Everett PltGer concerned with automatic theorem proving [ATP], Secretary known as the Milestone Prize "for foundational work in ATP" and the Current Prize "for ongoing work [in ATP] that shows promise." Statistics on Women Mathematieiana The Council changed the name of the research fellowship awarded by the Society to the Ameri­ Compiled by the AMS can Mathematical Society Centennial Fellowships, effective beginning in 1988. At its August 1985 meeting, the Council of tht AMS approved a motion to regularly assembl! The Council noted that each paper in the and report in Notices information on the relatm Proceedings will carry a notation of the name of numbers of men versus women in at least tht the editor who accepts it. following categories: membership in the AMS: The Council received the information that invited hour addresses at AMS meetings; speakm Irwin Kra had been elected to the Executive at special sessions at AMS meetings; and mem~ Committee for a term of four years. of editorial boards of AMS journals. The Council received a request to rescind its It was subsequently decided that this infor· statement of intent not to entertain more than two mation would be gathered by determining the sei nominations by petition of the same individual in of the individuals in the above categories based on any ten year period. The Council did not rescind name identification and that additional informa­ its previous action. tion on the number of Ph.D.'s granted to women The Council nominated William Browder as would also be collected using the AMS Annual candidate for the position of president-elect in the Survey. Since name identification was used, thf election of 1987. information for some categories necessitated thf The Council nominated candidates for vice­ use of four classifications: president and member-at-large in the_ same ele~­ Male - names that were obviously male; tion. Election to these offices carnes Counc1l Female - names that were obviously female: membership. See p. 663 for the names and Unknown- names that could not be i~ent~ related issues. as clearly male or female (I.e., "'"1 The Council nominated the following can­ initials given); and bf didates for positions in uncontested election in Foreign - foreign names that could ~~ 1987. identified as clearly male or . ~ Associate Secretary Andy Roy Magid The following is the second re~rt:e. Lance W. Small this information. Updated reports will Trustee Frederick W. Gehring annually in Notices.

Editorial Committees Bulletin Roger E. Howe 0 din In the u.s. Colloquium Raoul H. Bott Members of the AMS Res! g G4% Mathematical Reviews Hans F. Weinberger Male: 10,904 13% Mathematical Surveys M. Susan Montgomery Female: 2,134 14% Unknown: 2•295 9% Mathematics of Computation 1,582 Donald Goldfarb Foreign: Total checked: 16,91~ Proceedings Frederick R. Cohen Barbara L. Keyfitz ------George C. Papanicolaou Speake~'~ Jonathan M. Rosenberg Invited Hour Address 1986) James E. West at AMS Meetings (1977- s'l% Warren J. Wong Male: 326 3% Transactions and Memoirs Female: 12 1% James E. Baumgartner Unknown: 3~ 9% Foreign: 9 Roger D. Nussbaum Total checked: 37 Carl Pomerance

700 k 8 at Special Sessions Trustees and Council Members Sp~;rMeetings (1982-1986) 1986 1985 1984 1983 at A 2,926 75% Total: 65 71 70 63 Male: 224 6% Male: 56 86% 61 86% 62 89% 55 87% Felllale: 530 14% Female: 9 14% 10 14% 8 11% 8 13% UnknoWn: 226 5% Foreign: 3 906 Total checked: '

Members of Editorial Boards of AMS Journals _!WL._ ___l[[L_ 1985 ~ ~ ~ ~ ~ ~ ~ 85 82 82 67 59 flL 102 93 90 83 !09 79 93% 77 94% 78 95% 64 96% 56 95% 1\JIIl: 94 92% 85 91% 84 93% 77 93% !04 95% 7% 5 6% 4 5% 3 4% 3 5% )lale: 8 8% 8 9% 6 7% 6 7% 6 renaie: 5 5%

Ph.D.'s Granted to U.S. Citizens 1981 1980 1979 1978 1977 !986 1985 1984 1983 1982 567 578 596 634 689 433 455 519 TrAaJ· ~ ~ 491 85% 503 84% 545 86% 602 87% Yale: 304 79% 315 80% 346 80% 366 80% 431 83% 465 82% 102 18% 87 15% 93 16% 89 14% 87 13% F~e: 82 21% 81 20% 87 20% 89 20% 88 17%

NONCOMMUTATIVE HARMONIC ANALYSIS Michael E. Taylor

This book explores some basic roles of Lie groups value problems for domains with simple shapes. '~mear analysis. with particular emphasis on the that exhibit noncommutative groups of symmetries. & erahzat1ons of the Fourier transform and the study Also. the book contains detailed work. which has not of Part,al differential equations It began as lecture previously been published. on the harmonic analysis of notes for a one-se . auth . mester graduate course g1ven by the the Heisenberg group and harmonic analysis on cones. 1 a 1°r n noncommutative harmonic analysis. It is va uable resou rc f b lac It e or oth graduate students and Contents ana~y:i·s andd requires only a background with Fourier Some basic concepts of Lie group representation theory. The Heisenberg group: The unitary group: Compact few ch an bas1c functional analysis plus the first apters of a st d . · Lie groups: Harmonic analysis on spheres: Induced T an ard text on L1e groups. representations. systems of imprimitivity. and semidirect he basic meth d f analysis a 0 0 noncommutative harmonic products: Nilpotent Lie groups: Harmonic analysis on synthesi.ze generalization of Fourier analysis. is to cones: SL(2. R): SL(2. C). and more general Lorentz operators . . groups: Groups of conformal transform,ations: The croup has a . 0 n a space on wh1ch a L1e "~ucible unitary representation from operators on symplectic group and the metaplectic group: Spinors: represent t' Semisimple Lie groups Study is far f a IOn spaces Though the general deal of the rom complete. this book covers a great 1980 Mathematics Subject Classifications: 43, 35, 22 ISBN 0-8218-1523-7. LC 86-10924, ISSN 0076-5376 classes of togress that has been made on important 344 pages (hardcover). 1986 Unii le groups. L•st price $68, Institutional member S54, Individual member $41 boo ke rnany other b Code SURV /22NA k focuses on the ooks on harmonic analysis. this lllalys,s and P . relat1onsh1p between harmonic Shipping/Handling: 1st book $2. each add'l $1. $25 tonsiQ art1al diffe · ers man 1 rent1al equations. The author max. By air. 1st book $5. each add'l $3. $100 max. Y c assical PDEs. particularly boundary Prepayment required. Order from AMS. P 0. Box 1571. Annex Station. Providence. Rl 02901-9930, or call 800-556-7774 to use VISA or MasterCard.

701 MATHEMATICAL REVIEWS ASSOCIATE EDITORS

The Mathematical Reviews Editorial than special skill, is sought. A reading Committee invites applications and rec­ ~n?wledge of two main foreign languages ommendations for two-year appointments 1s Important, but not essential. (Russian as Associate Editor of MR, to commence and Chinese are especially desirable.) as soon as possible, but no later than Those interested in combining a sab­ the summer of 1987. Applications will be batical or other leave with a part-time welcomed from persons taking leave from or full-time appointment as an Associate other positions, and in particular from Editor should write for further details. tenured faculty members who could take The twelve-month salary is negotiable, leave to come to MR for two years. and will be commensurate with the ex­ The MR office is located in Ann Ar­ perience applicants bring to the position. bor, Michigan, adjacent to the campus Retirement, insurance plans, and other of the University of Michigan, and the fringe benefits are similar to those in editors enjoy many faculty privileges at universities. Of special importance is a the university. At present, MR employs policy providing a study leave after at eleven editors, about a dozen consul­ least two years. This amounts to three tants, and over fifty noneditorial person­ months of full pay for each two years nel. It produces Mathematical Reviews spent as Editor. and Current Mathematical Publications Applications (including curriculum vitae, and various indexes, as well as the online bibliography, data on experience, and names and addresses service Math\Sci. The responsibilities of three refer­ of Associate Editors fall primarily in the ences) and recommendations sh~uld be sent to Dr. R. G. Bartle, Execut1ve day-to-day operations of classifying arti­ Ed­ itor cles and books, assigning these items to Mathematical Reviews, P. 0. Box 8604 Ann Arbor MI 48107. Telephone reviewers, and editing the reviews when 313-996-5250. interested in they are returned. Other responsibilities Th~se app~y­ ing for this position are urged to inquire evolve in accordance with the individual's experience and capabilities. At this time, immediately. . . ual 18 no particular area of mathematical spe­ Mathematical Remews an eq cialization is sought, although strength opportunity employer. in applied areas is desirable. Consid­ erable breadth in mathematics, rather 'f' d Advertisements Classrr~re~:::.:~------usEs for classified advertising are books or lecture notes for sale. books being sought. positions SIJGGESiED e or rental of houses. and typing services. ~· exchang $ 75 per word with a minimum of $37.50. The same ad in 7 consecutive issues is $4 00 per word. ¢RATE !Solid unless centering and spacmg are requested. A centered lme of any length or the equivalent in white T~"ill be sets dis defined as a group of characters w1th space at each end. Prepayment IS requ~red of md1v1duals ~~ 1s $7.00. A wors For an additional $10.00 charge. announcements can be placed anonymously. Correspondence 1101 of institution . bill forwarded .. be l'sted on the inside front cover. OLINES are ' ...... oEA PROHIBIT discnmmat1on m employment on the bas1s of color. age, sex. race. relig1on or nat1onal u.s. LAWS Available" advertisements from institutions outside the U. S. cannot be published unless they are ~· "Pos,~on: statement that the institution does not discriminate on these grounds whether or not it is subject ~pamed yDetails and specifiC wordmg may be found followmg the Class1f1ed Advertisements m the January and uslaws . to . t .issues of the Notices. A&CUS ONS WANTED ADVERTISEMENTS from involuntarily unemployed mathematicians are accepted smJAil. conditions for free publication. Call toll-free 800-556-7774 and speak to Wahlene Siconio for further "*' certam .,/ormation NO AD AND CHECK TO: Advertising Department. AMS .. P. 0. Box 6248, Providence. Rhode Island 02940. :Viduals are requested to pay in advance. mst1tut1ons are not requ~red to do so.

POSITIONS AVAILABLE McGill University Department of Mathematics and Statistics SOUTHERN ILLINOIS UNIVERSITY The Department of Mathematics and Statistics at AT EDWARDSVILLE McGill University wishes to sponsor a strong candidate for Chair, Mathematics and Statistics the Natural Sciences and Engineering Research Council of Applications and nominations are invited for the po­ Canada (NSERC) 1987-88 University Research Fellowship SI!IOO of Chair of the Department of Mathematics and Competition. These Fellowships are five year research Statistics. Applicants should have a doctorate in Mathe­ positions (with a review in the third year). in the nature of rnatKs or Statistics. a record of successful teaching and Research Assistant Professorships. and carry a teaching research in Mathematics or Statistics. strong leadership load of at most one course throughout the academic year. llldcommunication skills. and a commitment to promoting Applicants should have shown some substantial research research. teaching. and other creative activities. ability beyond their doctoral thesis. They should be The Department of Mathematics and Statistics is part Canadian Citizens or landed immigrants by November 1. d the School of Sciences. which includes departments 1987.

703 POSITIONS AVAILABLE THE AUSTRALIAN NATIONAL ~ Applications are invited from suitabl UNIVe~ and men for appointment to the Y QUalified THE UNIVERSITY OF VERMONT ~ DEPARTMENT OF MATHEMATICS DOCTORAL FELLOW /RESEARCH ~~~lion of PosT AND STATISTICS CHAIR PARTMENT OF MATHEMATIC LOWintheD£: SCHOOL OF PHYSICAL SCIENCES \h RESEAR(~ Applications are invited for the position of Chairperson of Mathematics (Head: Professor D. wR e. [)epa~ of the Department of Mathematics and Statistics at carries out research in several areas · oblnSOn (~IJ the University of Vermont. The university is seeking Algebras; Semigroups and Mathemati n~mely ~ a mathematician or statistician with a strong esearch tial Differential Equations and Geome~a . PhYSICs: Par. background. a record of leadership and a commitment Lie Groups and Algebraic Groups· Ordy: Foundations · r 1nary l\ilr___ - to excellence in teaching. The new chairperson will tial Equations and Control Theory; Functio - .. ._ be instrumental in shaping research mathematics. both Group Theory. Closing date: 31 July 19~;1 Ana~s.s within the university and in the State of Vermont. by 9.4.1. Salary will be in accordance with Ret: PS developing the existing strengths of the department as and experience within the range: Postdociuabfication; well as fostering interaction with the other scientific and Grade 1 (at a fixed point A$24,013-A$27 SO~ral l'tllo, engineering groups in the university, the medical school search Fellow A$27.859--A$35.600 p.a.; APPoin/'a. Re. and industry. This task is expected to include the be: Research Fellow normally up to three yea"":;,1"'" implementation of a Ph.D. program and building in the the poss1b1llty of extensiOn to maximum of five Inti! areas of analysis and applied mathematics. Postdoctoral Fellow normally two years. with the'1&5 The University of Vermont. established in 1791. is sibility of extension to maximum of three years ~ located in Burlington. situated between the Green and perannuat1on. matern1ty leave and assistance with Adirondack Mountains on the shores of Lake Champlain. available. The University reserves the right not 1 tra.t~ The greater Burlington area supports a concentration . k Omaie an appomtment or to rna e an appointment by inv~~a- of hi-tech industries. The University currently enrolls tlon at any t1me. Applicants should quote the rei . approximately 8.150 undergraduates and 1.075 graduates. ence number when submitting applications to R.V. ou: It has a strong reputation for undergraduate education Registrar. GPO Box 4. Canberra. ACT. 2601 Australia and is committed to further developing its graduate and THE UNIVERSITY IS AN EQUAL OPPORTUNITY research programs. EMPLOYER. Candidates must possess a doctorate in Mathematics or Statistics. and although all fields of specialization are welcome. preference will be given to candidates in areas Institute for Computer Applications In Science best suited to enhance the department's development as and Engineering {ICASE). A limited number of vis­ outlined above. Salary is competitive and will be commen­ iting appointments are available for both junior- and surate with the candidate's experience. Nominations of. senior-level researchers at the Institute for Computer Ap. and applications from. qualified female and minority candi­ plications in Science and Engineering (!CASE) which ~ dates are especially invited. The position will be available operated by the Universities Space Research Association beginning June 1. 1988. The target date for receiving I CASE serves as a center for interaction between lancle! applications is August 31. 1987; however. applications will Research Center staff and the academic community m be accepted until the position is filled. Nominations and the areas of applied and numerical mathematics. applied applications (including a resume listing names. addresses. computer science. and development of mathematical mod­ and phone numbers of at least three references) should els in a variety of application areas. Applications for be submitted to: partial support while on sabbatical leave are encoul3gtd as are applications from Ph.D.'s for two-year renewable Professor Kenneth I. Golden. Chair appointments. Inquiries should be addressed to the ~ Mathematics and Statistics Search Committee rector. !CASE. Mailstop 132C. NASA Langley Researc Office of the Dean. College of Engineering and Center. Hampton. Virginia 23665. An Equal Opportunity Mathematics Employer. 123 Votey Building University of Vermont Burlington. VT 05405 Department of Mathematics The University of Vermont is an Equal Opportunity. University of Alberta Affirmative Action Employer. Edmonton, Alberta, Canada .. . track 10111 Applications are inv1ted for two tenure- lessorpos~ lelti in Numerical Analysis at the Assistant Pro Ph 0 Applications are invited from Greek-speaking mathe­ R . ements are a maticians who are also Greek citizens. holding the Ph.D starting September 1. 1987. eqwr . 1for researd' and proven ability or demonstrated pote~t~erential eQtll' degree. for a position at the level of associate profes­ 1 sor. The position is for people working in the area of and teaching in either numencal partl~l 'th exper;ence partial differential equations and their applications. Ap­ tions and computational fluid dynamiCSh WI positionS) (II plicants should contact Prof. S. Pnevmatikos. University in scientific computing (for one of~ ery and splineS of Thessaloniki, School of Technology, Division of Math. computational algorithms. operator ~ ~ range is 1J0111 Sciences. Thessaloniki. Greece. (for the other position). Current s~ang upon qualifiCJ' $31.612 (Canadian) per annum depen :etters of refere"U tions. Send vitae and arrange for threeman Acting Chi< Two faculty positions at assistant professor rank begin­ to be sent to: Professor H · I.. Fr~nive~itY of ,UJeiP ning Fall Semester. 1987-88. Ph.D. (or near completion) man. Department of MathematiC\ UniversitY rJ ~ in mathematics or statistics required. Duties include 12 Edmonton. Canada. T6G 2G1. Thbut in acco~antf hours of undergraduate teaching and customary participa­ is an equal opportumty employer. rioritY wdl be::: tion in departmental functions, curriculum development. Canadian Immigration requ~rements. t residents. C filr and advising of students. Send resume. transcripts and to Canadian citizens and perman~ Please refer 10 three letters of recommendation by June 15. 1987. to date for applications is July 31. 19 d~ertisement. David W. Bange. Department of Mathematics. University AMD-11 when responding to thiS a ~ of Wisconsin - La Crosse. La Crosse. WI 54601. An AA/EOE employer.

704 Foundations of Semiological Theory of Numbers ,.-p0siTIONS AVAILABLE H. A. Pogorzelski and W. J. Ryan Volume 1 {1982). General Semiology, 597 pp .. $29.95 ~nlversltY of VIctoria . . Volume 2 (1985), Semio. Functions. 695 pp., $34.95 f Mathematics at the Umversoty (Ten Volumes Projected) .... oepartmen~ 0 strong candidates for the 1987- UMO Press. Univ. of Maine. Orono. ME 04469 ,.~ . seekong h. . . V"oetoria os . . Research Fellows op competotoon. (Post free within US if check included) ~ NSERC Unove;:ships have an initial term of up to TTII5f research awarded on a competotove basos by f~e Math/Stats Library: List from R. Chesters. Suite 1900. 2 ~ ,ears and aces and Engineering Research Councol of First Canadian Place. Toronto. Canada M5X 1E3. dlt Natural Sc~nties of a University Research Fellow woll ~- The uone course per term on Mathematocs and .etude teachong h graduate program. Areas of research · ttO. non t e · h · NOTES ON ABSTRACT AND pllie1pa. De artment include doscrete mat ematocs, LINEAR ALGEBRA SIJtlll!h on theE' p mathematical physocs. and operator .,..tineilr PO son E. H. Connell These notes are written with the philosophy that ab­ diii'Y·. nts should submit. not later than August 1. stract algebra should precede linear algebra. and that a Aji!IIIC3 · 1 m vitae and the names of at least 3 1987. a currocu u course in abstract and linear algebra should stand along ~to: . with calculus at the base of the curriculum. The present Or C R. Miers. Chaorman courses in cookbook linear algebra and discrete mathemat­ oepartment of Mathematocs ics are educational disasters. and would best be replaced University of Voctoroa by a year course which presents a coherent theory. These Victoria. B.C. VSW 2Y2 notes are not designed to teach the course. but rather to The University of Victoria offers equal employment give a tightly organized presentation of the basic material. ·t·es to qualified male and female applicants. They are intended for students in mathematics. science, opportum 1 • • • R h Fel NSERC regulations requore that U~oversoty esearc .- and computer science. and may be used as a text or as loWShip nominees be Canadian cotozens or landed ommo­ a supplement to a conventional text. There are chapters pts at the time of nomonatoon. on groups. rings. matrices. and linear algebra. For course use. they may be reproduced at your local Kinko's. To order. send $7.75 to Kinko's. 1212 South Dixie. Coral PURDUE UNIVERSITY CALUMET Gables. FL 33146. HAMMOND, INDIANA 46323 Department of Mathematical Sciences HELDERMANN VERLAG. Nassauische Str. 26. Assistant Professor. beginning August 24. 1987. tenure­ D-1000 Berlin-West 31. Just published: W. H. Cornish. track upon completion of Ph.D. Requirements: Ph.D. or Antimorphic action. Categories of algebraic structures A.B.D. in Mathematics or Computer Science. Statistics with involutions or anti-endomorphisms. $24. W. Tay­ bidcground and teaching experience preferred. Applica­ lor. The clone of a topological space. $20. S. Wolfenstein lioll deadline is July 1. 1987. Send letter of application, {ed). Algebra and order. Proc. First Int. Symp. Ordered lila. and three letters of recommendation to: Richard L. Algebraic Structures. Luminy-Marseilles 1984. $36. YilteS, Search Committee Chairperson. at the above ad­ dless. Purdue University Calumet is an Equal Opportunity. Affirmative Action Employer. UNIVERSITY OF WATERLOO PRESS Nonlinear Optimization Bibliography, edited by Ger­ MERTON COLLEGE, OXFORD ald Berman. 1985. 312 pp. $50.00. ISBN 0-88898-063-9. Fellowship and Tutorship In Mathematics Graph Theory Bibliography, edited by Gerald Ber­ The College proposes to elect an Official Fellow and man. 1984. 2 volumes. $65.00. ISBN 0-88898-046-9. Tutor in Mathematics. with effect from 1st October 1988 Order from University of Waterloo Press. University of or possibly earlier, by arrangement. The person appointed Waterloo. Waterloo ON Canada N2L 3G1. {No shipping : ~ requored to give tuition in Pure Mathematics for charges) Hh.;nal Honour Schools of Mathematics. Mathematics rJ U'. 050Phy and Mathematics & Computation. The title llle :rsoty Lecturer (C.U.F.) may be conferred upon lith sue~' of the fellowship; the full stipend associated ,.,_ a lecturership will be met by the College The ""'may at a late d ( . . · COinmitm t r ate though the Unoversoty has no ,,_ ___ iten to do so) be converted into a stipendiary -·~ YPOSt. Applications sho ld b rlcareer and bl" u e sent to the Warden. with details '-r than Fri~~ •cations and names of three referees. not lilly be obt~ f25 September 1987. Further particulars -- n rom the Warden's secretary . ...__ FOR SALE I.IATH SCI P ~Jordan Rd 6 RESS. Robert Hermann. Director. ~ THe CL~~~klme. MA 02146. 617-738-0307. ~TRy OF C ICAL DIFFERENTIAL GE­ ::""'Kes Valiron t URVES AND SURFACES. by ~Series. ~ol ra~slated by James Glazebrook {Lie llilnics. and contr~l t;). $50 39 titles in mathematics. -.....____:: eory on print: Write for catalog.

705 Collected Works of Niels Henrik Abel (Oeuvres complete de Niels Henrik Abel)

The Norwegian Mathematical Society now offers for sale a limited number of copies of the 0 .. edition {in French) of Abels Collected Works. These copies have been stored for over 100 Ye ngl~ail881 Archives in Oslo and are of considerable historical and mathematical interest. ars In the Stite

The collected works consist of two volumes edited by the two outstanding mathematicians L 5 S. Lie. The papers range from the delightful "Note sur un memoire de M. L. Olivier,-" in which. A~low and that there exists no function 'P(n) such that 'P(n)an--+ 0 if and only if :Ean converges (easily und el Proves . ) . . erstood by any good f1rst year undergraduate student , to some of the h1ghl1ghts of the mathematics of the 191h Abel's proof of the unsolvability of the general quintic equation, his pioneering work on elliptic func _century: well as more general algebraic functions, culminating in the famous Abel theorem. In addition the tions 35 • re are ex- tensive editors' notes on Abel's papers. Also included are several letters from Abel to Crelle, Legendre and Norwegian mathematicians. Sylow and Lie end the preface with these words: "Abel a eu de grands successeurs; mais pour qui veut continuer dans Ia voie frayee par lui, il sera toujours profitable de remonter a Ia source meme: les immortellcs Oeuvres d'Abel". ("Abel has had great successors, but for those who want to continue on the road which he has paved, it will always be profitable to go back to the sources: the immortal works of Abel"). To order Abels Collected Works, send a cheque or an international money order for the amount of $100 (which includes postages and handling) to Abels Collected Works, The Norwegian Mathematical Society Postbox 1053 Blindern 0316 Oslo 3

by Monique Hakina, Nessim Sibony, Erik NEW CONSTRUCTIONS L0w and Paula Russo. Some of these are OF FUNCTIONS new even in one variable. HOLOMORPHIC IN THE An appreciation of techniques not previously used in the context of several UNIT BALL OF en complex variables will reward the reader who is reasonably familiar with Walter Rudin holomorphic functions of one complex variable and with some functional The starting point for the research analysis. presented in this book is A. B. Aleksandrov's proof that nonconstant 32 inner functions exist in the unit ball B of 1980 Mathemattcs Subject ClasStfication: en. The construction of such functions ISBN 0-8218-0713-7, LC 86-1205 ISSN 0160-7642 has been simplified by using certain 96 pages (softcover), May 1986 homogeneous polynomials discovered List price $13, all individuals $8 by Ryll and Wojtaszczyk; this yields To order, please specify CBMS/63NA solutions to a large number of problems. ------The lectures, presented at a CBMS Regional Conference held in 1985, Shipping/Handling: 1st book $2, eac~ ach are organized into a body of results add'] $1, $25 max. By air, 1st book 5, e discovered in the preceding four years in add'] $3, $100 max. S Prepayment requtred. Order from AM d' ce this field, simplifying some of the proofs 1'.0. Box 1571, Annex Station, ProVI ens.' and generalizing some results. The book RI 02901-9930, or call 800-556-7774 to u also contains results that were obtained VISA or MasterCard. . Ill -be rcnltil"~uN \. pmn'rJit!, 1 •-.unJ z to ,:.',h/e eas_\ tr' use, and en/(' ~·able 1 r.. · -Dr. Michael Ecker The College Mathematics Journal

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The Joy of T£X is the user-friendly user's the finished product, even novice technical guide for AMS- 'I'E;X, an extension of '!EX, typists will find the manual easy to use in Donald Knuth's revolutionary program for helping them produce beautiful technical typesetting technical material. .4)v(S -'lEX 'JEXt. 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)v(S -'lEX 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 types:tting technical text, especially text countered text and mathematics. "Sauces contaming 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, comparahle to the work of the finest tionary of special JEXniques. Prtnters. Exercises sprinkled generously through Most importantly, 'lEX's capabilities are each chapter encourage the reader to sit not available only to 'JEXperts. While down at a terminal and learn through ex­ mathem t. · . a 1cmns and experienced technical perimentation. Appendixes list summaries typi~ts will find that 1EX allows them to of frequently used and more esoteric sym­ ~PeCify mathematical formulas with greater bols as well as answers to the exercises. accuracy d . an st1 1I have great control over ~ "''1~L~,~ ----.c::::I::::S'::::::::::::::::::::::::::::::::=::::::::======.. 'c, BN 0-8218-2999-8 LC 85-7506 PREPAYMENT REQUIRED. Order from ~·~ ~~~' \._ 290 pages, April 19B6 American Mathematical Society \\S;~;~-· A~1S lndiv. Memb. $24, AMS lnst. PO Box 1571 , ~ :;J ~emb. $28, List price $32 Annex Station 'I'~_ -- /dt-, To order specify JOYT /NA Providence, RI 02901-9930 \om'""" Sh· or call 800-556-7774 to use VISA or MasterCard. 1PPing/Handling: 1st book $2 each adcl'l $1 $2 . ' $5 • max. 5; by a1r, 1st book ·each add'l $3, max. $100 PROBABILITY THEORY SUBJECT INDEXES FROM MATHEMATICAL REVIEWS 1980-84, 1973-79, 1959-72, 1940-58 .\!any mathematicians have expressed a desire to have a compilation of articles, books and confer proceedings that have been reviewed in Mathematical Reviews available by subject area. Together wit~~~ companion index on statistics listed below, this volume is the first such compilation. e This volume gives a listing of author names and review numbers of all the items having primary or classifications in probability theory for the entire 45-year span of Mathematical Rev,ews from 1940 throu ~~ndary conveniently collected in one volume. The titles are also given for items beginning in 1959. Full bibliogr;ph' !184, information is not provided here. but can readily be obtained using the information given here by consultin IC 'the the appropriate author indexes, the issues of MR, or .\lath\Sci (for items beginning in 1959). The classificat~el 1 schemes used during these years are also included at the end of the index. 100 This convenient index should be of great value to researchers working in the area of probability, or persons who need to consult the literature in this active field.

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STATISTICS SUBJECT INDEXES FROM MATHEMATICAL REVIEWS 1980-84, 1973-79, 1959-72, 194o-58 This volume is a companion to the volume of Probability Theory Subject Indexes mentioned above. It gives a listing of author names and review numbers of all the items having primary or secondary classifications in statistics for the entire 45-year span of Mathematical Re1•iews from 1940 through 1984, conveniently collected in one volume. The titles are also given for items beginning in 1959. Full bibliographic information is not provided here, but can readily be obtained using the information given here by consulting either the appropriate author indexes, the issues of MR, or Math\Sci (for items beginning in 1959). The claBsification schemes used during these years are also included at the end of the index. This convenient index should be of great value to n•searchers working in the area of statistics, or persons who need to consult the literature in this important field. ISBN 0-8218-0107-4, LC 86-26460 500 pages, March 1987 List $67, Inst. mem. $54, lndiv. mem. $40. Reviewer $34 To order, please specify STATIN/40/84NA

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Probability Theory Subject Indexes from Mathematical Reviews, 1940-84 Statistics Subject Indexes from Mathematical Reviews, 1940-84 Two volume set price: ' ' List: $115, lnst. mem. $92, lndiv. mem. $69, Reviewer $58 To order, please specify STAPI:-1/40/84 NA -, \,. ' Order from: . al SocietY PREPAYMENT REQUIRED. Adrl shipping American MathematiC and handling: $2 first book. $! each add'l, max $25 by air $5 first book, Annex Station ! : $3 each add'l, max $100 P.O. Box 1571 gg30 Providence. RI 02901- oo-556-71'14 ~~~ Call 401-272-9500 or 8 ard I i--~ to use VISA or MasterC ~ 111 illr-~------NOW AVAILABLE AUTHOR AND SUBJECT INDEXES OF MATHEMATICAL REVIEWS, 1980-84

This comprehrnsive 12--volumr srt contains both author and subjrct listings for all of the reviews that appeared in Mathematical Reviews during the years 1980 to 198-1. Containing approximatrly 9.600 pagrs. it is an important addition to any mathematics library

With this set of indexes at hand. rmders ran

• access fully by both author and subject arra. the mathematical litrrature of thr past five yrars

• discover listings for approximatrly 20!LOOO paprrs. books. and cmtfermcr procrrd­ ings all the itnns revirwrd in Mathematical Reviews during thesr yrars

• obtain information about approximatrly 8.000 additional itrms that were not n•• virwrd individually. but which arr fully classifird and cross-rrfermced in thrse indrxe:-;

• find complete bibliographic information for rach article undrr any author a:;soci­ atrd with the article. and cross-references for the names of rditors. translators. and othrr prrsons associated with an itrm

• arrpss via a key index. all those publications that do not havr namPd authors or Pditors

• locate_ under rach subject index heading. all items having this cla:;sification as either a primary or a secondary classification

ISBN 0-8218-0105-08 LC 42-4:221 December 1986_ 9.600 pages Ltst $1875 lnst. mrni. $1500 To order_ plrase sprcify MREVIN /80/84NA ' '

Atn - PREPAYMENT REQL'IRED. Order from ertran MatiH•rnatical Soci!'ty_ Annex Station_ P 0 Box 1.571. Providrnce RI 02901-99:lO Telephone (401) 272-9.500 or (800) 556-7774 -~-- - WHEN MATH\SCI IS ONLINE MATHEMATICS IS ON THE SCREEN 800,000 Entries in Seconds Math\Sci is the online database that finds, in a matter of seconds, any informa­ tion published in Mathematical Reviews (MR), Current Mathematical Publications (CMP), Current Index to Statistics (CIS), and the Index to Statistics and Proba­ bility by John Tukey and lan Ross. These combined sources give you over 800,000 entries in all areas of the mathematical sciences. Monthly Updates Math\Sci is updated monthly, with over 3,700 new entries from MR and 4,000from CMP; also quarterly updates of 750 new entries from CIS. Easy Fingertip Access When can you use Math\Sci? Anytime ... 24 hours a day. Now you can search for all the information from MR. CMP, CIS and the Tukey Index when you want it and need it. From your office. From your home. Anywhere you can connect a modem to a microcomputer (or terminal) and dial a local number. Where to Get Online with Math\Sci Math\Sci is produced by the American Mathematical Society, a source of mathema~ ical materials for nearly 100 years. Math\Sci can be accessed on BR ' DIALOG, CompuServe, EasyNet, and the European Space Agency (ESA). Tole;;~ more about Math\Sci, contact Taissa Kusma at the AMS by calling SQ0-556-7 in the continental United States. / ~~- American Mathematical Society CI P.O. Box 6248 r-----r----- ~:{\lEMA 1,..... Providence. Rl 02940 ~ __ ..-- .~i~ !·j: TPHTOI""·.- ~ ~..-- _(J~/ c • ; ... 401-272-9500 _...---...... - "' ~ 0 --""""F=--+--+--+-+--+-+---+--t- ~ < M ~92~-- ~ SUBJECT INDEX OF MATHEMATICAL REVIEWS, 1959-1972 J. L. Selfridge, Editor

This subject index fills the last remaining gap to provide complete author and subject indexes for the entire run of Mathematical Reviews from its beginnings in 1940 up through 1984. With this index together with the 198Q-84 author and subject indexes. readers will now be able to access fully. by both author and subject. the mathematical literature of the past 45 years. Readers recognized the value of subject indexing with the publication of the Author and Subject Index of Mathematical Reviews 1973-1979. This initiated a retrospective subject indexing project now completed with the four-volume Subject Index of Mathematical Reviews 1959-72. This index is ordered by the subject classification scheme in effect during 1968-72. with the 1962-67 articles having been reclassified as necessary. Under each heading. the subject index lists all items reviewed with either primary or secondary classification in the given area. Beside the first author's name are listed the title of the book or article. the language in which it was written. and its MR review number. Cross-references to these entries are provided for secondary authors. A list of entries and references by key words follows the authors in each classification. To locate a given item. this subject index may be used in conjunction with the appropriate. previously published author indexes. which provide full bibliographic information as well as the reviewer's name.

1980 Mathematics Subject Classification: 00 ISBN 0-8218-0095-7, LC 42-4221, ISSN 0025-5629 2516 pages, December 1985 List price $1177, Institutional member $942, Individual member $1177, Reviewer $1177 To order, please specify MREVIN/59/72NA

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. Rl 02901-9930, or call 800-556-7774 to use VISA or MasterCard. Summer List of Applicants Instructions for Applicant Form on facing The form. Forms submitted by job applican~ INTEGRAL GEOMETRY attend the August meetings in Salt Lake City wmbo posted. The first 1mpress1on a prospective emp~ Robert L. Bryant, Vict~r has of an apphcant may be based on the apj>ear Guillemin, Sigurdur Helgason, of this form. ~ The forms should be carefully typed using a freah and R. 0. Wells, Jr., Editors black ribbon. The best res~lts ~re obtained with a carbon-coated polyethyle?"e film nbbon, but satisfac_ The topic of integral geometry is not as tory results may be obtamed usmg a ribbon made of well known as its counterpart, differential nylon or other woven fahnc 1f smtable care is exer­ geometry. However, research in integral cised. It is important that the keys be clean and maR geometry has indicated that this field a sharp, clear impression. Use a correcting typewriter may yield as equally deep insights or correction tape or fluid if necessary. Submit the as differential geometry has into the original typed version only. Hand lettered forms are global and local nature of manifolds acceptable if prepared carefully. and the functions on them. In 1984, an The summary strip. Information provided here will AMS-IMS-SIAM joint summer research be used to prepare a printed list of applicants for dis. conference on integral geometry was held tribution to employers. Please supply all information at Bowdoin College. This volume consists requested, and confine your characters to the boxl'! of papers presented there. provided. Use the codes below. Circled letters iden­ The papers range from purely expository tify corresponding items on the form and the strip. to quite technical and represent a good Address forms to the Mathematics Meetings Hous­ survey of contemporary work in integral ing Bureau, P. 0. Box 6887, Providence, RI 02940 geometry. Three major areas are covered: The deadline for rece1pt IS June 1, 1987. the classical problems of computing geometric invariants by statistical @ Specialties averaging procedures; the circle of ideas concerning the Radon transform, AL = Algebra AN = Anal)'!i! going back to the seminal work of BI = Biomathematics BS = Biostatistics Funck and Radon around 1916-1917; CB = Combinatorics CM = Communicatioo and integral-geometric transforms CN = Control CS = Computer Sciew DE = Differential EquatKIII! which are now being used in the study CT = Circuits EC = Economics ED = Mathematical Educatl JSSN 0271-4132 NT = Number Theory OR SA ! S stems Ana!Y"' 360 pages (soft cover), January 1987 PR = Probability • - ~0 = Topo~ List price $33, Institutional member $26, ST = Statistics Individual member $20 To order, please specify CONM/63NA @ Career Objectives A ademic Teachinl Shipping/Handling: 1st book $2, each AR = Academic Research AT= c onsultllll NC = Nonacad. C add'! $1, $25 max. By air, 1st book $5, each NR = Nonacademic R&D add'! $3, $100 max. NS = Nonacademic Supervision Prepayment required. Order from AMS, G) Duties P.O. Box 1571, Annex Station, Providence, ® to use RI 02901-9930, or call 800-556-7774 u 0' underr~ VISA or MasterCard. T =Teaching R=llf"'·- G =Graduate - Administ~ A- o-Indtl!l~ C = Consulting IN - rocesiP! S = Supervision DP =Data p GOY = Government Location

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718 Summer List of Applicants Mathematical Sciences Employment Register August 1987 Salt Lake City, Utah . structions on facing page) IPlea!t see tn

APPLICANT: Name'------­ Mailing address (include zip code) ------

@Specialties . @Career objectives and accomplishments ACADEMIC: 0 Research, D Teaching SON-ACADEMIC: D Research and Development, D Consulting, D Supervision Near-term career goals1------

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Available mo / ~ ·--yr.__ Location______Salary____ _ !\! References (N arne and Institution)

yes D noD

~ltV STRIP Family Name First Name Mailing Address ~(torat'd.) [I I I I I I I I I I I I. I I I I I I I I I. ,-,-I1~1 ;:....,I 1--.-1..,..--,1 1---..-1--,-1 ,-,-1 1~1 ~I 1--.-1..,..--,1 1----..-1--,-,1 I. Address (cont'd.) State & Zip Code 0 Specialties . [ I I I I I I I I I I I I I I I. I I I I I I I I I. ITJ ITJ ITJ ITJ ITJ. @ Highest@ @ r.:::.. @ C:.. @ rn Degree C Yr. C Institution \QI E '\!} G Most recent employer .ITIJJ. ITJ. I I I I I I I I I I 1. ITJ. ITJ. ITJ. I I I I I I I I I I I. f.\ D · . 0 Available (.'\ r.;., ctiJj"ed dut•es J mo./y•. \!,) 1M/ Sessions . DIIJ. ITJ/ITJ. D. D D 0 0

719 MAA MINICOURSE PREREGISTRATION FORM, Salt Lake City, Utah August 5-8, 1987

Please complete this form and return it WITH YOUR PAYMENT to:

John Gilliland Mathematical Association of America 1529 Eighteenth Street, N.W. Washington, DC 20036 Telephone: 202-387-5200

(Please print) Surname First Middle - City State Street address Z1p -

IMPORTANT NOTES:

1. Deadline for Minicourse preregistration: June 1, 1987 2. Deadline for 50% refund: July 31, 1987 3. Registration for the Joint Meetings is a requirement in order to participate in the Minicoune1. Complete I the Preregistration/Housing Form included in the meeting announcement and return it to Providence with t::.e applicable Joint Meetings preregistration fee. DO NOT SEND MINICOURSE FORI! 01 IllS TO PROVIDEN~;E. 4. Each participant must fill out a separate Minicourse form. 5. Enrollment is limited to tw~ Minicourses, subject to availability. 6. Please complete the following and send both form and payment to John Gilliland at the above addrua:

a. I would like to attend Minicourse

2 Minicourses

b. Please enroll me in MAA Minicourse(s): 11 __ and II

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7. PAYMENT:

a. Check enclosed:

b. Credit card type: ) MasterCard ) VISA

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Number Minicourse Organizer -~-.-- Appl~ed -mathematics via classroom e~periments Herbert R. Bailey 2. Using computer spreadsheet programs in calculus, differential equations, and combinatorics Donald R. Snow 3. A microcomputer linear algebra course using Linear-Kit Howa1·d Anton 4. A survey of educational software David p. Kraines Vivian Kraines Joan p. Wyzkoski 5. Introduction to computer graphics A calculus lab course using MicroCalc Har 1 ey Fl anderfs kel 6. Solomon A. Gar un 7. For all practical purposes · ,I MAA MlUl·cour••(~ P­ I plan on preregistering for the Joint Meetings only in order to attend the . 11 d full~ indicated above. It is my understanding that, should the course(s) of my choice be fl e ' the Joint Meetings preregistration fee will be made.

720 PREREGISTRATION AND HOUSING FORI' I, SALT LAKE CITY, liT All August S-8, 1987

~lUST BE RECEIVED IN PROVIDENCE NO LATER THAN JUNE 1987 Please complete this form and return it with your payment to ~bthematics ~~etings Housing Bureau

0 Box 6887, Providence, Rhode Island 02940 - Telephone 401-272-9500, Ext. 290 Telex: 797192 P. • Preregistration June 1 ~: Residence Hall Room Payments June 1 SOl Refund on Prereg1strat10n August 4 * 901 Refund on Residence Jlall Room August ~ SOl Refund on MAA Banqu

REGISTRATION FEES Pregistratwn At ~~eting SbY mail prior to 6/1) JOINT MATHEMATICS MEETINC',S Member of ~IS, MAA, IIME $59 $ 77 • Student, Unemployed or Emeritus $16 $ 21 Nonmember $90 $117

•.Ul full-time students currently working toward a degree or diploma qualify for the student registration fees regardless of income. The unemployed st<:'tus refers to any l?erson currently unemployed, acti:'ely seek­ .•loyment and who is not a student. It 1s not mtended to mclude persons who have voluntanly :ipd fran their latest position. The emeritus status refers to any person who has been a member of the .tfiorMAA for twenty years or more and is retired on account of age from his or her latest ···------position.

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721 PREREGISTRATION AND HOUSING REQUEST FORM (continued)

(Please read sections on housing and room rates in meeting announcement.)

UNIVERSITY HOUSING SECTION: (Please complete Sections I through IV below.)

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722 Application for Membership 1987 le AN MATHEMATICAL SOCIETY Date. 19. A-ER

.....-- verse srcte of this form to determine what member­ Fields of Interest ;>ease read there are eligible for. Then fill out this application and If you w1sh to be on the mailing lists to receive information about publications m f1elds of mathematics in which you ;•O c•tegory ~o:s poss1ble. Your name will be added to our mailing '!ll!m 11 as 500 ceJpt of your completed application, and payment for have an mterest. please consult the list of major headings !s:l upOn our re of the 1980 Mathematics Subject Class1ficatton below -emoerduesrons to the Notices and the Bulletin (New Series) are Select no more than five category numbers and fill 1n the Subscnpp.~rt of your membership. numbers where indicated on the left. These categones will "{iuded as be added to your computer record so that you will be informed of new publications or special sales in the fields you have indicated First Middle ..... >tase~ndlcate- below the way your name should appear in the Combined Mem- 00 General 01 History and biography :ri''P ust 03 Mathematical logic and foundations 04 Set theory First Middle or Initial 05 Combinatorics ..... 06 Order. lattices, ordered algebraic structures - 08 General mathematical systems >ace of B1rth Zip/Country City State 11 Number theory 12 Field theory and polynomials 13 Commutative rings and algebras Jate o! 81r1h Year DIY Month 14 Algebraic geometry 15 Linear and multilinear algebra; matrix •'ormerly a member of AMS, please indicate dates theory 16 Associative rings and algebras :oeck here 1f you are now a member of either MAA or SIAM 0 17 Nonassociative rings and algebras 18 Category theory. homological algebra :.qrees w1th InStitutions and dates 19 K-theory 20 Group theory and generalizations 22 Topological groups. Lie groups 26 Real functions 28 Measure and integration 30 Functions of a complex variable 31 Potential theory 32 Several complex variables and analytic spaces 33 Special functions

State Zip,...Country 34 Ordinary differential equations 35 Partial differential equations '••ds of Interest (choose fiVe from the list at right) 39 Finite differences and functional equations 40 Sequences. series. summability 41 Approximations and expansions 42 Fourier analysis 43 Abstract harmonic analysis ~ress for all mall 44 Integral transforms. operational calculus 45 Integral equations 46 Functional analysis 4 7 Operator theory 49 Calculus of variations and optimal control; optimization 51 Geometry 52 Convex sets and related geometric topics 53 Differential geometry 54 Genera I topology 55 Algebraic topology 57 Manifolds and cell complexes 58 Global analysis, analysis on manifolds 60 Probability theory and stochastic processes 62 Statistics --- 65 Numerical analysis Pre,aym~eth 68 Computer science ads and Mailing Addresses 70 Mechanics of particles and systems Str,o Chetk 73 Mechanics of solids ;.~ s, money ord 76 Fluid mechanics -"'~Po Box 157 ers, UNESCO coupons to American Mathematical 78 Optics. electromagnetic theory 1 1 Annex Stat1on, Providence, Rl 02901-1571. ouse VISA 80 Classical thermodynamics. heat transfer ~a,, or Masterca d Quantum mechanics emat~eat Soc,et r · f1ll 1n 1nformat1on requested and mail to Amencan 81 82 Statistical physics. structure of matter ~Or y. P 0 Box 6248, Providence, Rl 02940. _ Foreig 83 Relativity ''oo n Bank Tran 85 Astronomy and astrophysics e Island H . slers: The name and address of the AMS bank IS ~~ osp,tal T 86 Geophysics a,TrustPiaza P rust Nat1onal Bank, Account #000-753-111, One 90 Economics. operations research. · rov,dence, Rl 02903 u sA liSA- , . programming. games 92 Biology and behavioral sciences J MasterCard 93 Systems theory; control 94 Information and communication. circuits Expiration date M7NO Membership Categories Reciprocating Societies Please read the followmg to determrne ---- what membershrp category you are elrgr­ Allahabad MathematiCal S ble for. and then rndrcate below the category for whrch you are applyrng ocrety Asocracron Matematrca Espanola Austral ran Mathematrcal Socrety Berlrner Mathematische G For ordinary members whose annual professional income is below _ essellschaft e $26,000, the dues are $64; for those whose annual professiOnal Calcutta Mathematrcal Socrety , income is $26,000 or more. the dues are $84 Dansk Matematrsk Forenrng For a joint family membership, one pays ordinary dues. based on Deutsche Mathematrker-Vere his or her income, and the other pays ordinary dues based on his or her rnrgung e v :drnburgh Mathematical Socrety mcome, less $20. (Only the member paying full dues will receive the Gesellschaft fur Angewandte Notrees and the Bulletin as a privilege of membership, but both Mathematrk und Mechanrk members will be accorded all other privileges of membership.) Minimum dues for contributing members are $126. Glasgow Mathematrcal Assocratron For either students or unemployed individuals, dues are $21, and lndran Mathematrcal Socrety annual verification is required. lranran Mathematrcal Socrety The annual dues for reciprocity members who reside outside the lsrenzka Staerdfraedafelagrd U.S. and Canada are $42. To be eligible for this classification, members Israel Mathematrcal Unron must belong to one of those foreign societies w1th which the AMS has established a reciprocity agreement. and annual venf1cat10n is Korean Mathematrcal Socrely required. Reciprocity members who res1de in the U.S or Canada must London Mathematrcal Socrety pay ordinary member dues ($64 or $84) Malaysran Mathematrcal Socrety The annual dues for external members, those who reside in devel­ Mathematrcal Socrety of Japan oping countries which do not have any mathematical society, are $45. Mathematrcal Socrety of the Phrlrppmes Members can purchase a multi-year membership by prepaymg their current dues rate for either two, three, four or five years. This opt10n Mathematrcal Socrety of the Republrc ot is not available to either unemployed or student members. Chrna New Zealand Mathematrcal Socrety N,gerran Mathematrcal Socrely 1987 Dues Schedule Norsk Matematrsk Forenrng Osterrerchrsche Mathematrsche For any category of membershrp where two dues prrces are grven. the hrgher Gesellschaf1 one rs to be pard by persons whose annual professronai rncome rs $26.000 or more Pulsk1e Towarzystwo Matematyczne Punjab Mathematical Socrety Real Sacred ad Matematrca Espanola Ordrnary member $64 $84 Socredad Colombrana de Matemi!lrca

Jorntfamily member (full rate) $64 $84 Socredad de Matematrca de Chrle Socredad Matematrcadela Jomt famrly member (reduced rate) $44 $64 Republrca Domrnrcana Soc1edad Matematrca Mexrcana Contrrbuting member (mmrmum $126) Soc1edade Brasile1ra de Matematica Student member (please verrfy)' $21 Socredade Brasrlerra de Matematrca

i\pl 1cada e Computac1onal Unemployed member (please verrfy)' $21 Socredade Paranaense de Matematrca Reciprocrty member (please venfyl' $42 $64 $84 oOC'edade Portuguesa de Matematrca Socret«t Catalana de Crencres Frsrques External member $45 Clurmrques' Matematrques Socrete de Mathematrques Appltquees Multr-year membership $ for years P-t lndustnelles Soc,ete Mathematrque de Belgrque

1 Student Verification (srgn below) Societe Mathematique de France ..::;oclete Mathematique Suisse t I am a full-t1me student at Southeast Asran Mc.thematrcal soon c;, Jomen Matemaattrnen Yhdrstys currently workmg toward a degree ~~ecska M3tematrkersamfundet

, jn 1 on Matem8t1ca Argentina 2 Unemployed Verification (srgn below) I am currently unemployed and Unlone Matematlca ltaliana actively seekmg employment My unemployment status 1s not a result of volun­ VIJnana Pan shad of India tary res1gnat1on or of retirement from my last pos1t1on Wrskundrg GenootschaP

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Fasten PAY1HENT secur Geometry of Numbers A. Haar Memorial Conference Second Edition Edited by J. Szabados and K. Tandori By P.M. Gruber and C.G. Lekkerkerker Colloquia Mathematica Societatis Janos Bolyai, 49 North-Holland Mathematical Library, To mark the centenary of the birth of one of the greatest Hungarian 37 Mathematicians, Alfred Haar, the Janos Bolyai Mathematical Society and The 1969 first edition was published as Volume VIII in the series the Hungarian Academy of Sciences organized this memorial Bibliotheca Mathematica conference in Budapest, August 1985. This second edition contains a rather complete picture of the geometry 152 mathematicians from all parts of the world took part in the of numbers, including relaUons to other branches of mathemaUcs such conference. The subjects covered were mostly those areas of as analytic number theory, diophantine approximation, coding and mathematics in which Alfred Haar created outstanding and fundamental numerical analysis. The authors have retained the existing text (with results, such as approximation theory, orthogonal series (in particular minor corrections) while adding to each chapter supplementary sections Haar series), Haar measure and its applications. on the more recent developments. While this method may have 19871018 pages (in 2 vols.) Price: US $170.75/Dfl. 350.00 drawbacks, it has the advantage of showing clearly where recent ISBN 0-444-70095-1 progress has taken place and in what areas interesUng results may be expected in the future. 1987 xvi+ 724 pages Price: US $105.001011. 215.00 Differential Equations: ISBN 0·444· 70152-4 Qualitative Theory Edited by B. Sz.-Nagy and L Hatvani Saks Spaces and Applications Colloquia Mathematica Societatis Janos Bolyai, 47 to Functional Analysis This volume contains selected papers from the Second Colloquium on Qualitative Theory of Differential Equations held in Szeged, Hungary. Second Revised Edition The majority of the papers included here deal with asymptotic properties and stability problems of solutions of ordinary and functional differenUal By J.B. Cooper equations. The reader will find articles on the bifurcation of solutions, on boundary value problems, the existence of periodic solutions, and North-Holland Mathematics Studies, 139 papers concerned with applications in mechanics, physics and biology. The first edition of this monograph appeared in 1978. In view of the 19871172 pages (in 2 vols.) Price: $175.501011.360.00 progress made in the intervening years, the original text has been ISBN 0-444-70093-5 revised, several new sections have been added and the list of references has been updated. The book presents a systematic treatment of the theory of Saks Spaces, i.e. vector space with a norm and related, Goodness-of-Fit subsidiary locally convex topology. Applications are given to space of bounded, continuous functions, to measure theory, vector measures, Edited by P. Revesz, K. Sarkadit and P.K. Sen spaces of bounded measurable functions, spaces of bounded analytic functions, and to W'-algebras. Colloquia Mathematica Societatis Janos Bolyai, 45 1987 x +372 pages Price: US $83.001011. 17.0.00 The 36 papers collected in this volume were originally presented at the ISBN 0-444-70219-9 Colloquium on Goodness-of-Fit, held in Debrecen, Hungary. The subject of the Colloquium was the main research area of the organizer of the meeting, the late Karoly Sarkadi. The speakers, from 14 countries, referred frequently to his work and influence. Foundations of Analysis over 1987 624 pages Price: US $131.751Dfl. 270.00 Surreal Number Fields ISBN 0-444-70087-0 ByN.L.AIIing North-Holland Mathematics Studies, 141 In this fairly self-contained volume, a tower of surreal number fields is defined, each being a real-closed field having a canonical formal power North-Holland series structure and many other higher order properties. Formal versions In the U.S.A. and Canada: of such theorems as the Implicit Function Theorem hold over such fields. Elsevier Science Publishing Co. Inc. The Main Theorem states that every formal power series in a finite P.O. Box 1663, Grand Central Station number of variables over a surreal field has a positive radius of hyper­ New York, NY 10163, U.S.A. convergence within which it may be evaluated. AnalyUc functions of several surreal and surcomplex variables can then be defined and In all other countries: studied. A primer on Conway's field of surreal numbers is Elsevier Science Publishers also given. Book Order Department 1987 xvi + 37 4 pages Price: US $73.25/Dfl. 150.00 P.O. Box 211 ISBN 0-444-70226-1 1000 AE Amsterdam, The Netherlands

US $prices are valid only in the USA and Canada. In all other countries the Dutch Guilder (Of/.) price is definitive. Customers in the Netherlands, please add 6% B. T. W. In New York State applicable sales tax should be added. All prices are subject to change without prior notice.

NH/MATH/BK/0963 Geometry of Numbers A. Haar Memorial Conference Second Edition Edited by J. Szabados and K. Tandori By P.M. Gruber and C.G. Lekkerkerker Colloquia Mathematica Societatis Janos Bolyai, 49 North-Holland Mathematical Library, To mark the centenary of the birth of one of the greatest Hungarian 37 Mathematicians, Alfred Haar, the Janos Bolyai Mathematical Society and The 1969 first edition was published as Volume VIII in the series the Hungarian Academy of Sciences organized this memorial Bibliotheca Mathematica conference in Budapest, August 1985. This second edition contains a rather complete picture of the geometry 152 mathematicians from all parts of the world took part in the of numbers, including relaUons to other branches of mathemaUcs such conference. The subjects covered were mostly those areas of as analytic number theory, diophantine approximation, coding and mathematics in which Alfred Haar created outstanding and fundamental numerical analysis. The authors have retained the existing text (with results, such as approximation theory, orthogonal series (in particular minor corrections) while adding to each chapter supplementary sections Haar series), Haar measure and its applications. on the more recent developments. While this method may have 19871018 pages (in 2 vols.) Price: US $170.75/Dfl. 350.00 drawbacks, it has the advantage of showing clearly where recent ISBN 0-444-70095-1 progress has taken place and in what areas interesUng results may be expected in the future. 1987 xvi+ 724 pages Price: US $105.001011. 215.00 Differential Equations: ISBN 0·444· 70152-4 Qualitative Theory Edited by B. Sz.-Nagy and L Hatvani Saks Spaces and Applications Colloquia Mathematica Societatis Janos Bolyai, 47 to Functional Analysis This volume contains selected papers from the Second Colloquium on Qualitative Theory of Differential Equations held in Szeged, Hungary. Second Revised Edition The majority of the papers included here deal with asymptotic properties and stability problems of solutions of ordinary and functional differenUal By J.B. Cooper equations. The reader will find articles on the bifurcation of solutions, on boundary value problems, the existence of periodic solutions, and North-Holland Mathematics Studies, 139 papers concerned with applications in mechanics, physics and biology. The first edition of this monograph appeared in 1978. In view of the 19871172 pages (in 2 vols.) Price: $175.501011.360.00 progress made in the intervening years, the original text has been ISBN 0-444-70093-5 revised, several new sections have been added and the list of references has been updated. The book presents a systematic treatment of the theory of Saks Spaces, i.e. vector space with a norm and related, Goodness-of-Fit subsidiary locally convex topology. Applications are given to space of bounded, continuous functions, to measure theory, vector measures, Edited by P. Revesz, K. Sarkadit and P.K. Sen spaces of bounded measurable functions, spaces of bounded analytic functions, and to W'-algebras. Colloquia Mathematica Societatis Janos Bolyai, 45 1987 x +372 pages Price: US $83.001011. 17.0.00 The 36 papers collected in this volume were originally presented at the ISBN 0-444-70219-9 Colloquium on Goodness-of-Fit, held in Debrecen, Hungary. The subject of the Colloquium was the main research area of the organizer of the meeting, the late Karoly Sarkadi. The speakers, from 14 countries, referred frequently to his work and influence. Foundations of Analysis over 1987 624 pages Price: US $131.751Dfl. 270.00 Surreal Number Fields ISBN 0-444-70087-0 ByN.L.AIIing North-Holland Mathematics Studies, 141 In this fairly self-contained volume, a tower of surreal number fields is defined, each being a real-closed field having a canonical formal power North-Holland series structure and many other higher order properties. Formal versions In the U.S.A. and Canada: of such theorems as the Implicit Function Theorem hold over such fields. Elsevier Science Publishing Co. Inc. The Main Theorem states that every formal power series in a finite P.O. Box 1663, Grand Central Station number of variables over a surreal field has a positive radius of hyper­ New York, NY 10163, U.S.A. convergence within which it may be evaluated. AnalyUc functions of several surreal and surcomplex variables can then be defined and In all other countries: studied. A primer on Conway's field of surreal numbers is Elsevier Science Publishers also given. Book Order Department 1987 xvi + 37 4 pages Price: US $73.25/Dfl. 150.00 P.O. Box 211 ISBN 0-444-70226-1 1000 AE Amsterdam, The Netherlands

US $prices are valid only in the USA and Canada. In all other countries the Dutch Guilder (Of/.) price is definitive. Customers in the Netherlands, please add 6% B. T. W. In New York State applicable sales tax should be added. All prices are subject to change without prior notice.

NH/MATH/BK/0963 Bool{s for Orthogonality and Spacetime Geometry the Serious R. Goldblatt This book examines the geometrical notion of orthogonality, and shows how to use it Student as the primitive concept on which to base a metric structure in affine geometry. Exam­ from Springer-Verlag ples involve Minkowskian geometry and its various sub-geometries. 19871Approx. 189 pp./126 illus./Paper $26.00 Projective Geometry Universitext ISBN 0-387-96519-X H.S.M. Coxeter The first Springer edition of this classic text features enhanced discussions of Veblen's Power Series from a notation, and of Desargue's configuration as a "complete 5-point" in space, in its Computational ana logic relation to Pappus' configuration, and as interpreted by von Staudt's proof. Point of View 19871Approx. 162 pp.ICioth $29.00 (tent.) K.T. Smith ISBN 0-387-96532-7 Contents include: Taylor Polynomials, Se­ quences and Series, Power Series and Complex Differentiability, Local Analytic Topological and Uniform Functions, Analytic Continuation, and a section of problems. Spaces 19871Approx. 144 pp./Paper $23.00 I.M.James Universitext A discussion of both the topological theory ISBN 0-387-96516~5 and the uniform theory stressing the rela­ tion between the two. Numerous exercises are featured after each chapter. Moduli of Smoothness 19871163 pp./19 illus./Cioth $36.00 z. Ditzian and V. Totik Undergraduate Texts in Mathematics An introduction to a new way of measuring ISBN 0-387-96466-5 smoothness. The results are new and com­ plete proofs are given. Will be of interest to mathematicians working in approximation Geometry I and D theory, interpolation of spaces, numerical M. Berger analysis, and real analysis. Translated from the French by M. Cole 19871Approx. 300 pp./Cioth $54.90 (tent.) and S. Levy Springer Series in Computational Mathematics, Vol. 9 This two-volume textbook is the long­ ISBN 0-387-96536-X awaited translation of the French book ~ Geometrie, originally published in five vol­ Q LU 0 umes. It gives a detailed treatment of ge­ N 0'1 ~ ometry in the classical se(lse. Examines N To order, send a check or money order to a:' 8Ill such topics as crystallographic 0 groups, af­ Springer-Verlag New York, Inc., Attn: G. N ..J fine, 0 Euclidean and non-Euclidean spher­ Kiely, 175 Fifth Avenue, New York, NY < 0!: ical 8 and hyperbolic geometries, projective 10010. To order by phone, call TOLL FREE u OJ~ geometry and many others. z i= u 1-800-526-7254 (in NJ, 201-348-4033). For Ill c < "0 Volume I mail orders, please include $2.50 for ship­ Ill :E ~ .. 19871428 pp./426 illus./Paper $39.00 ping and sales tax if you are a NY, NJ, orCA LU ·;; .. -Ill ::1: ...0 c.. Universitext resident. :E 1- Q.. .. ISBN 0-387-11658-3 ..:I < < otf 1.!) Volume II OJ :E ..c "'='"N &'. 19871406 pp./364 illus./Paper $39.00 Springer-Verlag ... z ID '+- ~ Universitext New York Berlin Heidelberg 0 < >( Q u a."' ISBN 0-387-17015-4 0 London Paris Tokyo "'OJ ii2 ' u LU = E ... :I 0 :E 0 .. z < c::..: ~