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ematical Society

< 2. c 3 II> J~ cz 3 i"... w Calendar of AMS Meetings

THIS CALENDAR lists all meetings which have been approved by the Council prior to the date this issue of the Notices was sent to press. The summer and annual meetings are joint meetings of the Mathematical Association of America and the Ameri· can 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 second 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 meet­ ing. Abstracts should be submitted on special forms which are available in many departments of mathematics and from the office of the Society in Providence. 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 ab· stracts submitted for consideration for presentation at special sessions is usually three weeks earlier than that specified below. For additional information consult the meeting announcement and the list of organizers of special sessions.

MEETING ABSTRACT NUMBER DATE PLACE DEADLINE ISSUE

795 june 18-19, 1982 Bellingham, Washington APRIL 19, 1982 june 796 August 23-26, 1982 Toronto, Ontario, Canada JUNE 7, 1982 August (86th Summer Meeting) November 12-13, 1982 East Lansing, Michigan November 19-20, 1982 Monterey, California january 5-9, 1983 Denver, Colorado (89th Annual Meeting) April14-15, 1983 New York, New York August 8-12, 1983 Albany, New York (87th Summer Meeting) january 25-29, 1984 Louisville, Kentucky (90th Annual Meeting) january 9-13, 1985 Anaheim, California (91 st Annual Meeting) January 21-25, 1987 San Antonio, Texas (93rd Annual Meeting)

DEADLINES: Advertising: (june issue} April 29 (August issue} june 23 News/Special Meetings: (june issue} April 12 (August issue} June 7

Other Events Sponsored by the Society. june 6-july 17, 1982, AMS Summer Research Conferences, University of New Hampshire, Durham. january issue, page 73. june 28-july 16, 1982, AMS-ASL Summer Research Institute on Recursion Theory, Cornell University, Ithaca, New York. February issue, page 194. july 6-16, 1982, AMS-SIAM Summer Seminar on Applications of Group Theory in Physics and Mathematical Physics, University of Chicago. February issue, page 194. August 21-22, 1982, AMS Short Course: Statistical Data Analysis, Toronto, Canada. This issue, page 276.

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 from time to time in the Notices (e.g. June 1980, page 378). Send change of address notices to the Society at Post Office Box 6248, Providence, RI 02940. [Notices is published eight times a year (January, February, April, June, August, October, November, December) by the American Mathematical Society at 201 Charles Street, Providence, RI 02904. Second class postage paid at Providence, RI and additional mailing offices. POSTMASTER: Send address change notices to Membership and Sales Department, American Mathematical Society, Post Office Box 6248, Providence, RI 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. The street address should never be used by correspondents, unless they plan to deliver their messages by hand. Members are strongly urged to notify the Society themselves of address changes (in the manner described above), since (as explained above) reliance on the postal service change-of-address forms is liable to cause delays in processing such requests in the AMS office. Notices of the American Mathematical Society

Volume 29, Number 3, April 1982

EDITORIAL COMMITTEE Ralph P. Boas, Ed Dubinsky Richard ). Griego, Susan Montgomery Mary Ellen Rudin, Bertram Walsh Everett Pitcher {Chairman) MANAGING EDITOR Lincoln K. Durst ASSOCIATE EDITORS Hans Samelson, Queries 234 Support of Mathematical Research in the U. S. Ronald L. Graham, Special Articles L Structure and Magnitude, K. M. Hoffman SUBSCRIPTION ORDERS 238 NSF Budget for Fiscal 1983 Subscription for Vol. 29 (1982): $36 list, $18 member. The subscription 245 Polish Prisoners and the price for members is included in the International Congress in Warsaw annual dues. Subscriptions and orders for AMS publications should be 247 News and Announcements addressed to the American Mathematical 249 NSF Mathematical Sciences Section Society, P. 0. Box 1571, Annex Station, 1982 AMS Elections (Nominations by Petition) Providence, Rl 02901. All orders must 250 be prepaid. 252 Queries ORDERS FOR AMS BOOKS AND 253 Letters to the Editor INQUIRIES ABOUT SALES, SUBSCRIP­ 256 Assistant Executive Director, AMS TIONS, AND DUES may be made by calling Carol-Ann Blackwood at 257 Future Meetings of the Society 800-556-7774 (toll free in U.S.) between Madison, April 16-77, 257; Bellingham, 8:00a.m. and 4:15p.m. eastern time, june 78-79, 270; Toronto, August 23-26, 273; Monday through Friday. See page 17. Synopses, Short Course on Statistical Data CHANGE OF ADDRESS. To avoid Analysis, 291; Topics: 1984 Symposium, 272; interruption in service please send Invited Speakers, 272; Special Sessions, 272 address changes four to six weeks in advance. It is essential to include the 293 Special Meetings member code which appears on the 298 New AMS Publications address label with all correspondence Miscellaneous regarding subscriptions. 302 Personal Items, 302; Deaths, 302; INFORMATION ABOUT ADVERTISING Assistantships and Fellowships (Supplement), 303; in the Notices may be obtained from New Doctorates (Supplement), 304 Virginia Biber at 401-272-9500. 305 AMS Reports and Communications CORRESPONDENCE, including changes of the of address should be sent to American Recent Appointments, 305; Officers Mathematical Society, P.O. Box 6248, Society, 1981 and 1982, 306 Providence, Rl 02940. 307 Advertisements Second class postage paid at 315 Registration Forms Providence, Rl, and additional mailing Preregistration and Housing offices. Copyright © 1982 by the Toronto American Mathematical Society. Reservation Form, 315, 316; Printed in the United States of America. Summer List of Applicants, 318, 319 The Support of Mathematical Research in the United States I. Structure and Magnitude by Kenneth M. Hoffman

A Working Paper prepared for the AMS Committee on Science Policy

This document was written in January 1982, • A prestigious national committee has been as an outgrowth of discussions within the AMS set up by the National Research Council to Committee on Science Policy aimed at developing review the health and support of research a major Society statement on the appropriate scale in the mathematical sciences in the United and use of extra-university funds for the support States. of the national research effort in mathematics The details of our circumstances as we start (broadly defined). It was intended to be a 1982 would seem to argue even more strongly framework for discussion, not a treatise with fully­ for development of a consistent rationale for the detailed arguments. The principal theses of the support of mathematics. paper, beyond the essential fact that the funding Consider first our political or procedural cir­ level has been markedly too low for many years, cumstances. There has been considerable con­ are that we must realize that the proper support of troversy in the mathematical community over mathematics involves much more than the support the (originally one and now two) new research in­ of individual mathematicians and that both we stitutes. It has gone on for years. The debate over and the funding agencies must behave accordingly. the intrinsic merits of the institute idea-some­ At an immediate practical level, these mean that what along the lines of the European model-has -in our efforts to seek additional resources as always been heavily influenced by concerns over well as in our planning for the use of existing the use of scarce resources to support experiments resources-it is important that we get away from in such directions-how many research grants such heavy reliance on the model of small grants will be lost?-and by concerns about process­ which contain summer salaries and little else and has the mathematical community been properly move toward patterns of support which properly consulted? It seems best to answer these questions reflect the variety of activities important to the now by saying "Opinions still vary." But one health of the mathematical research enterprise. thing we should be able to agree on is that, as The publication of this working paper is one of a result of a prolonged and sometimes heated a series of steps which the Committee on Science Policy intends to take to involve the broader KENNETH M. HOFFMAN (Massachusetts Institute mathematical community in its deliberations. We of Technology) is Chairman of the Society's will welcome your comments. Committee on Science Policy. Other members of the The general circumstances in which the math­ Committee are Hyman Bass (Columbia University), ematicians of this country now find themselves Felix E. Browder (University of Chicago), Frederick point to the need for us to design a coherent W. Gehring (University of Michigan), Andrew M. plan for the development and use of mathematical Gleason (Harvard University), William J. LeVeque research funds: (Executive Director, AMS), George D. Mostow • The mathematical community has just come (Yale University), Ralph S. Phillips (Stanford out of one of the most lively and controversial University), Julia B. Robinson (University of debates about resources it has ever had-the California, Berkeley), Linda Preiss Rothschild debate over the research institutes (MSRis). (University of Wisconsin, Madison), Isadore M. Singer (University of Ca!iforPia, Berkeley), James D. • We are in a time of tight money and will no Stasheff (University of North Carolina, Chapel Hill), doubt continue to face some difficult choices. Elias M. Stein (Princeton University), and Hans F. • A significant change has begun in the pattern Weinberger (University of Minnesota). Comments of support at the Mathematical Sciences on this working paper, which is not a statement Section of the National Science Foundation, of a formal Society position, may be addressed with the use of a somewhat smaller percentage to the Committee: AMS Committee on Science of its funds for summer salaries and a bit Policy, Room 2-280, Massachusetts Institute of more for what the Section has called coherent Technology, Cambridge, Massachusetts 02139. modes of support (including the MSRis).

234 debate, we are a bit tired-a bit fractured, in step in that process is to realize that we are in a the eyes of others-yet it is essential that we difficult situation but that we do have a choice. pull ourselves together and ensure that our policy­ We can stand in the pit forever, debating about making machinery works more effectively in the the chain of events which brought us to where we future. are, hoping that some nameless force will come And what about our financial circumstances? to pull us out. Or, we can formulate a plan and Quite naturally, our minds turn first to recent begin to climb out. One role of the Committee on events. To the continuing tightness of university Science Policy is to lead in the latter direction. We budgets has been added a new squeeze on must pull the mathematical community together government funding. When the federal budgetary around a plan, a plan on the basis of which we dust finally settled for the current year (FY 1982), can (i) sensibly tell the supporters of science what support of applied mathematics through the usual it is that we need resources for, and (ii) argue sorts of contracts with the Department of Defense forcefully that those resources should be provided. and the Department of Energy did not keep pace The rudiments of such a plan can be seen by with inflation. There were nice increases at the reviewing in more detail the problems we face and military agencies, but much of the added money is some of the changes in funding patterns which for targeted purposes. The major non-university have been occurring. supporter of academic research in mathematics, The three principal problems we face regarding the Mathematical Sciences Section of NSF, also the support of basic mathematical research in the fared pretty well from a general point of view, United States are these. getting a 3 million dollar increase over its FY 1981 1. There has been a substantial lack of (extra­ budget of $28.2 million. Viewed from 'inside'­ university) funding for research in the core* areas that is, seeing how other fields fared in the climate of mathematics for a number of years. This has of general budget cuts-one would probably even been recognized by a number of mathematicians say that the MSS fared very well this year. for some time. Ironically, it has been difficult But the view from 'outside' is hardly something to persuade many people in the science support to cheer about. The NSF funds did keep up establishment, in part because funding is so far with inflation, but inflation's toll, together with from appropriate levels (conservatively, off by the costs of the 'coherent modes' and maybe a factor of 2) that it is difficult for them to some enrichment of grants, will probably mean believe that any field could have gotten into that over 100 fewer mathematicians will have such a fix. It is even difficult now to persuade 'standard' grants (summer salaries) than the 1,400 some mathematicians, because they seem to have who had them last year. This impact will be felt in a mathematical community which is getting forgotten what contracts and grants are supposed increasingly nervous about its future. The wisdom to look like, forgotten what the things are that of directing resources away from summer salaries need to be supported. will be seriously questioned; and, no doubt, 2. The Mathematical Sciences Section of the debates about the institutes and other aspects of National Science Foundation has become almost how we got into such a fix will be rekindled. If the sole extra-university supporter of research in the FY 1983 federal budget process follows the the core* areas of mathematics. There is virtually roller coaster pattern of this year, it will no doubt no support from the private sector. Since the mid add its own complications to our discussions. 1960s-when a new emphasis on direct mission Throughout these discussions, it will be important relevance began-the Department of Defense has to remember that we stand monetarily just about phased out nearly all of its once very substantial where we stood last year and that the most serious support of core areas of mathematics, and the aspects of our financial circumstances have little resources have not been added to the NSF budget to do with recent events-they have to do with to compensate. (Of government support of events which have occurred over a long period of academic research in the mathematical sciences­ time. excluding 'computer science'- NSF is responsible A series of actions and inactions over many for about 65%; in pure mathematics, the figure is years has placed the research mathematicians of 97%.) this country in a financial pit, with extremely 3. The pattern of support by the Mathematical scarce resources and with most of those resources Sciences Section at NSF was until recently that of devoted to summer salaries; the shortage of extra­ small research grants which consisted of summer university resources makes it very difficult to salaries and very little else. It is still true that sustain the intellectual vitality of our enterprise summer salaries (including indirect costs) account now that the financial squeeze is on the univer­ for about 80% of the Section's budget. This sities; the support pattern complicates asking for is roughly because of the following. Growth help because it inadvertently projects to others in the number of outstanding mathematicians the image that either we don't need support for *The term 'core' is used here in a somewhat broader things beyond summer salaries or, worse yet, that sense than in NSF parlance. We intend the term to we are just plain greedy. This is a pit from which encompass not only pure mathematics but a good deal of we must begin to extricate ourselves. The first fundamental applied mathematics as well.

235 and the need to pick up people whom DOD incremental advantage for the mathematicians once would have supported strained the resources over their fellow scientists or to get them a larger of the Section dramatically over the past 10 share of the pie. What is being said is that or 15 years. During many of these same something is dramatically wrong, because the pie years, the fraction of NSF resources devoted to is (and has been) too small. The correction of mathematics decreased. For reasons we shall things may require a different shape of pie or even comment upon later-reasons which we don't a change of bakery staff, but the issue of chronic think had anything to do with the selfishness under-funding for mathematics must be faced by of mathematicians-summer salaries stayed and those involved in setting science policy. virtually everything else disappeared from grants: Awareness of the mathematicians' plight is graduate students, postdoctoral fellows, research growing. The Assembly of Mathematical and associates, secretaries, publication costs. Physical Sciences of the National Research Coun­ It is vital to the long-term health of the cil has appointed an ad hoc Committee on mathematical research enterprise in this country Resources for the Mathematical Sciences under that something substantial be done about each of the Chairmanship of Dr. Edward E. David, Jr., these three problems and accordingly that all efforts President of Exxon Research and Engineering, to to improve the support picture for mathematics be review the support and health of our research en­ made with three inter-related objectives in mind: terprise, not only in core mathematics, but across • significantly increase the resources available the whole spectrum of the mathematical sciences. for the support of mathematical research This review was stimulated largely by preliminary • increase the number of major sources of evidence regarding inadequate support for core support areas of mathematics (pure and applied), but its • modify the pattern of support properly to scope will be much broader. Five government reflect the categories of people and things agencies and seven industrial concerns have joined which are vital to the health of the research with the American Mathematical Society and enterprise. other professional organizations to support that One brief comment about each problem. The Committee's work. research universities have tried to compensate for Awareness also has grown within the Founda­ loss of support for graduate students, postdoctoral tion, and actions have been taken. The National fellows, research associates, travel, etc., but, Science Board, the governing board of the Founda­ because of their own financial problems, they tion, initiated a Postdoctoral Fellowship program have not been able to sustain the effort and the which now funds 30 such fellowships in mathe­ resultant pressures on us are now extreme; we matics. As it eventually turned out, these were are in serious trouble, with scant academic job funded by MSS resources and did not (as far as we opportunities, collapsing graduate programs and can see) add to the resources available to support no financial flexibility with which to respond. mathematics. But the creation of the fellowships The burden of being (almost) the sole funding was interpreted by many in the mathematical agency for core mathematics is too great for the community as a first signal of awareness and, as Mathematical Sciences Section, because it places such, a sign of hope that the underlying support the Section in the inappropriate de facto position question might be addressed. of making policy for the national mathematical The more tangible effect of the Postdoctoral community; this is one reason the debate over Fellowship program was to re-direct part of the the 'institutes' was so tortuous. The continuation resources for mathematics to support a vital of the 'summer salary plus a dribble' pattern research need which was critically underfunded. obscures the need for other things to be supported One might say that it marked the opening of a and creates the illusion we referred to before: that new effort to change support patterns to reflect all the mathematicians care about is their own more accurately how the research enterprise in summer salaries. This is a costly kind of non­ mathematics functions. luxury, doubly so because it asks the people who A second major step in this direction has been make large-scale funding decisions about science taken by the development of the set of 'new' to believe that there are important categories of initiatives which has been under discussion the people or things for which we need support when last couple of years, consisting principally of the we are unwilling to place these categories high on MSRis at Berkeley and Minneapolis and the AMS our operational priority lists-unwilling to insist "Oberwohlfach" conferences, but including as well that reasonable fractions of them be supported support for the Research Center at Madison out of existing research funds. and the postdoctoral program at Courant plus One further word about the problem of the increased support for the Institute for Advanced general support level. We are not alone in having Study and modification of the NSF Postdoctoral funding problems. It must always be emphasized Fellowship Program. that our primary concern has nothing to do with A third NSF step to change support patterns some kind of one-upmanship relative to other to reflect the range of things important to the fields of science. It is not voiced to gain some conduct of mathematical research, a step which

236 The National Research Council's COMMITTEE grants, somewhat along the lines of the Canadian ON RESOURCES FOR THE MATHEMATI­ model, with recipients selected by NSF and the CAL SCIENCES consists of William Browder rest of the administrative chores handled by AMS. (Mathematics, Princeton University), Edward Under this program, some 100 mathematicians E. David, Jr. (President of Exxon Research each year would be given two-year grants of about and Engineering, formerly Science Advisor to 912,000 per year to be used for non-salary items President Nixon), Gerard Debreu (Economics, needed in their research. The most significant Stanford University), Gerald P. Dinneen (Vice item is probably professional travel. It is felt that President, Science and Technology, Honeywell, the ability to travel to meetings and conferences or Inc., formerly Principal Deputy Under Secretary to visit major centers is important to the research of_ Defense in the Carter Administration), of increasingly many active mathematicians who Rtchard C. DiPrima (Mathematical Sciences, do not have larger contracts or grants, and that Rensselaer Polytechnic Institute), Bradley Efron the need for some special program to make such (Statistics, Stanford University), Michael Fisher travel possible will increase as we struggle through (Chemistry and Physics, Cornell University), the next few years. The second proposal asks Marvin L. Goldberger (President, Califor­ for NSF support of part of the cost of publishing nia Institute of Technology), Phillip A. Mathematical Reviews. The financial burden of Griffiths (Mathematics, Harvard University), this important publication, which is used by all Robert Herman (Operations Science, Univer­ professional mathematicians in the world, has sity of Texas), Arthur M. Jaffe (Mathematics been carried by its small set of subscribers and and Physics, Harvard University), Peter D. the AMS, with contributions from individuals Lax (Courant Institute of the Mathematical and sponsoring organizations amounting to about Sciences, New York University), Brockway one percent of the annual deficits which the McMillan (Vice President, Bell Laboratories, Society bears. Recently, dramatic price increases Retired), George D. Mostow (Mathematics, Yale have been necessary to help reduce the perennial University), William A. Nierenberg (Director, deficits. No doubt subscribers will thus be lost Scripps Institution of Oceanography), James and the deficits will continue-unless major help B. Serrin (Mathematics, University of Min­ is forthcoming. The proposal does not ask NSF to nesota), I. M. Singer (Mathematics, Univer­ absorb AMS deficits; it asks for recognition that sity of California, Berkeley), Guido L. Weiss the cost of publishing Mathematical Reviews is (Mathematics, Washington University), Jerome primarily a cost of the national research enterprise Wiesner (Institute Professor, Massachusetts In­ in mathematics and for a determination of the stitute of Technology, formerly President of appropriate share of that cost to be borne by the M.I. T. and Science Advisor to Presidents Ken­ Foundation. nedy and Johnson). Ralph E. Gomory (Vice If there is a philosophy behind these recent President and Director of Research, IBM) serves and proposed changes, it is the one described in as Advisor to the Committee. The Committee's the introduction, that the support of mathematics staff is under the direction of Kenneth M. involves more than the support of individual Hoffman (Mathematics, Massachusetts Institute mathematicians' salaries, as important as such of Technology), Executive Director. salary support is. The changes provide increased support for national programs, increased support may be taken this year, is under discussion for major research centers, and the enrichment in the Advisory Panel to the Mathematical of grants to pay for the variety of people and Sciences Section: A reduction of the number activities which are important to research in of standard research project grants (SRPS) to mathematics. The theme of this paper is that enrich somewhat the remaining grants-here and although the merits of each proposed change there to provide support for a graduate student, a should be considered very carefully, these are the research associate, secretarial help or whatever. general directions in which we must continue to The American Mathematical Society will submit move, that only in this way can our true needs two important proposals to the National Science be seen, that only in this way do we have a Foundation in 1982, which if funded will further fighting chance of getting something done about modify the pattern of use of resources. The our chronic under-funding. This may be very first proposal calls for the establishment of a painful until available resources grow. But what limited program of small non-salary research is the alternative?

237 National Science Foundation Budget for Fiscal 1983

The current administration in Washington Table I reflects the recently improved treatment submitted its budget request for FY 1983 to of the mathematical sciences at NSF: for the Congress on February 8, 1982. Parts of the first time in recent history, funds (in current Administration's request concerning the budget dollars) being spent on the mathematical sciences for the National Science Foundation are described increased (line {1)), while those for research in this article, which continues a series begun ten support in other areas (line {2)) dropped. The that the $2.9 million years ago in the Notices. The most recent report careful observer will notice from 1981 to 1982 for mathematics just series appeared in the June 1981 issue, increase in this offset the $2.9 million decrease for other research pages 325ff. support in the same period. The FY1983 budget This report continues the practice of printing the request, however, suggests that the ''trend" begun usual Tables I, IT, ill (below and opposite), which last year may not last very long, since the depict (respectively) the part of the entire NSF percentage growth in the funds requested for budget allocated to the mathematical sciences, mathematics is less than it has been for some the fraction of the budget for the Division of time, while for other research support it is greater. the Mathematical and Physical Sciences devoted Table IT shows that changes in the division of to the mathematical sciences, and the effects of the fiscal pie for the Division of the Mathematical inflation on the NSF budget. and Physical Sciences continue to be small. The signs of Following the tables on the facing page is slice for Computer Research shows some growth, apparently at the expense of Materials an excerpt from the FY 1983 Budget Request Research. sent to Congress by the Administration in Tables illa and llib present a ten-year view February; the excerpt, titled ''Mathematical of the effects of inflation on the NSF budget: NSF section Sciences Subactivity", is part of the although the increases in current dollars appear to of the submission to Congress. Information on the be large, the amount of money spent on research plight of the education programs at NSF is given continues to decline when reckoned in constant in a box on page 242. dollars.

TABLE L NATIONAL SCIENCE FOUNDATION BUDGET (Millions of Dollars)

1979 1980 1981 1982 1983 Actual Change Actual Change Actual Change Plan Change Request 1/28/80 (79-80) 1/15/81 {80-81) 2/8/82 {81-82) 2/8/82 {82-83) 2/8/82

(1)Mathematical Sciences Research Support $ 22.8 9.6% $ 25.0 13.2% $ 28.3 10.3% $ 31.2 8.7% $ 33.9 (2)0ther Research Support (Note A) 761.0 7.5% 817.7 6.8% 873.7 -0.3% 870.8 9.5% 953.4 (3)Education, Information, Foreign Currency Program (Note B) 88.4 7.9% 95.4 -15.5% 80.6 -61.9% 30.7 -27.0% 22.4 (4)Program Development and Management ("Overhead") (Note C) 54.7 6.4% 58.2 1.7% 59.2 7.3% 63.5 -0.6% 63.1

(5)Totals $926.9 7.5% $996.3 4.6% $1041.8 -4.4% $996.2 7.7% $1072.8 (6)(1) as % of (1) and (2) 2.91% 2.97% 3.14% 3.46% 3.43% (7)(1) as % of (5) 2.46% 2.51% 2.72% 3.13% 3.16%

NOTE A. Scientific research and facilities (excluding mathematics and science information). National and special research programs, and national research centers. Support for mathematics has been excluded, cf. items (1) and (3). NOTE B. The programs in this group are ones in which there is some support for projects in every field, including mathematics. The foreign currency program involves both cooperative scientific research and the dissemination and translation of foreign scientific publications. Foreign currencies in excess of the normal requirements of the U.S. are used. NOTE C. This heading covers the administrative expenses of operating the Foundation; the funds involved are not considered to constitute direct support for individual projects.

238 TABLE IT. DMSION OF MATHEMATICAL AND PHYSICAL SCIENCES (Millions of Dollars)

Section 1979 Actual 1980 Actual 1981 Actual 1982 Plan 1983 Request Mathematical Sciences $ 22.8 (10.91%) $ 25.0 (11.01%) $ 28.3 (11.03%) $ 31.2 (11.43%) $ 33.9 (11.35%) Computer Research 16.8 ( 8.04%) 18.5 ( 8.15%) 22.3 ( 8.69%) 25.7 ( 9.42%) 29.3 ( 9.81%) Physics 61.7 (29.54%) 63.4 (27.93%) 72.1 (28.11%) 75.3 (27 .59%) 88.5 (29.63%) Chemistry 45.2 (21.64%) 51.4 (22.64%) 57.6 (22.46%) 60.7 (22.24%) 66.1 (22.13%) Materials Research 62.4 (29.87%) 68.7 (30.26%) 76.2 (29.71%) 80.0 (29.31 %) 80.9 (27.08%) Total $208.9 $227.0 $256.5 $272.9 $298.7

TABLE IDa. TEN-YEAR COMPILATION OF THE NSF BUDGET (Millions of Dollars) Current dollars are converted to 1967 dollars using the wholesale/producer index

1974 1975 1976 1977 1978 1979 Actual Actual Actual Actual Actual Actual (1) Mathematical Sciences Research Support $ 14.5 $ 16.4 $ 17.3 $ 20.1 $ 21.4 $ 22.8 1967 dollars 9.1 9.4 9.4 10.4 10.0 9.7 (2) Other Research Support 491.5 551.9 592.1 642.9 702.8 761.0 1967 dollars 908.2 915.7 929.9 991.1 926.8 922.7 (3) Education, Information, Foreign Currency Program 104.4 83.0 72.8 83.3 84.3 88.4 1967 dollars 65.5 47.5 99.7 42.9 99.2 97.5 (4) Program Development and Management ("Overhead") 35.2 37.9 42.2 45.5 48.7 54.7 1967 dollars 22.1 21.7 29.0 29.4 22.6 29.2 (5) Totals $645.6 $693.2 $724.4 $791.8 $857.2 $926.9 1967 dollars 404.8 996.5 995.5 407.8 998.6 999.0

TABLE Illb. TEN-YEAR COMPILATION (Continued)

1980 1981 1982 1983 Increase Increase Actual Actual Plan Request 1974-1981 1974-1983

(1) Mathematical Sciences Research Support $ 25.0 $ 28.3 $ 31.2 $ 33.9 95% 134% 1967 dollars 9.9 10.4 14% (2) Other Research Support 817.7 873.7 870.8 953.4 78% 94% 1967 dollars 904.2 920.6 4% (3) Education, Information, Foreign Currency Program 95.4 80.6 30.7 22.4 -23% -79% 1967 dollars 95.5 29.6 -55% (4) Program Development and Management ("Overhead") 58.2 59.2 63.5 63.1 68% 79% 1967 dollars 21.7 21.7 -1.8% (5) Totals $996.3 $1041.84 $996.2 1072.8 61% 66% 1967 dollars 970.6 982.9 -5.6%

239 Mathematieal Seienees Subaetivity results from one field to explore another field and its applications. (Millions of dollars) A brief description of research areas supported Actual Plan Request under the Mathematical Sciences subactivity FY1981 FY1982 FY1983 follows: • Classical Analysis concerns the study of real Classical Analysis $3.6 $3.1 $3.3 and complex functions, their approximation, Modern Analysis 3.7 3.2 3.5 Geometric Analysis -0- 3.0 3.2 and their interrelations as solutions of or­ Topology, Geometry dinary and partial differential equations, es­ & Foundations 6.0 -0- -0- sential tools for the description of physical Topology & Foundations -0- 4.0 4.3 phenomena. Algebra & Number Theory 4.9 5.0 5.4 Applied Mathematics 4.0 3.8 4.1 • Modern Analysis centers on the study of Statistics & Probability 3.1 3.3 3.5 classes of functions endowed with special Special Projects 2.9 5.6 6.6 abstract geometric and algebraic properties. Total $28.3 $31.2 $33.9 Typical areas of study are the abstract operators of mathematical physics and er­ Objectives and Description godic theory. The objectives of the Foundation's Mathemati­ • Geometric Analysis covers a broad spectrum cal Sciences program are to foster the creation of geometry and analysis and their strong of new mathematical knowledge and promote the and growing interconnections. This research use of mathematical methods and techniques for includes differential equations, representation the better understanding of physical, biological, theory, functions of several complex variables, and social phenomena. and minimal surfaces. Mathematics involves the discovery and study • Topology and Foundations: Topology studies of the formal, abstract structures underlying the in a formal and abstract manner those world and human activities in that world. Em­ properties of geometric objects which persist phasis is on those structures of broad intellectual after deformation by stretching, shrinking, applicability and those reflecting fundamental and twisting without tearing or cutting. aspects of the real world. Mathematics is the Foundations research involves the study of natural language with which to describe the ac­ the logical structure and basic concepts which tivities and laws of nature, and therefore provides undergird mathematics. an indispensable undergirding of science. • Algebra and Number Theory: Algebra deals Mathematics is constantly used in a variety of with abstract mathematical structures such applications; in turn the applications motivate the as groups, rings, and fields. Algebraic struc­ study of abstract structures which are pervasive tures constitute a fertile field for applications. in applications. For example, abstract algebraic Number theory is the study of the structure concepts permitted the development of linear and properties of number systems. Results in programming, the optimization technique that, this area have recently and successfully been when computerized, is used thousands of times applied to the design of cryptographic codes. every day in a wide range of industrial and • Applied Mathematics centers on the use of military contexts. In turn, the desire and need mathematics for the modeling, analysis, and to solve optimization problems motivated the explanation of real world phenomena. This study of novel abstract mathematical structures. broad field includes work in such diverse areas These studies have resulted in the development of as fluid dynamics, continuum mechanics, new mathematical techniques such as the Kalman mathematical biology, systems theory, and filter, an optimal predictor widely used in aircraft optimization. guidance systems, industrial assembly lines, and • Statistics and Probability: Statistics is the economic forecasting models. study of methods for the collection, organiza­ The structure of mathematical ideas is an tion, and analysis of data for the purpose elaborate development of interlocking patterns of of uncovering fundamental mathematical abstraction, each mathematical notion tied to its relationships among various variables. Prob­ empirical origins in multiple ways. The concepts ability theory provides useful mathematical and their interrelationships are abstract, but their models, and is the basic element in statistical relevance to the physical world, coupled with their reasoning. It deals with phenomena that are abstractness, provides the needed tools for the random in the sense of combining long-term description and understanding of the fundamental regularity with short-term unpredictability. properties of the world. Such tools are essential The spread of epidemics through a popula­ to the advancement of science and technology. tion, claims against an insurance company, An exciting recent development is the increasing and the level of demand on a communication interaction among different fields of mathematics. network exhibit characteristics of random­ There is frequent use of ideas, techniques, and ness.

240 • Special Projects focuses on those research Major Programmatic Topics activities which cut across more than one • Classical statistical procedures depend field of mathematics. Included in Special heavily on stringent assumptions concerning Projects are postdoctoral research fellow­ the data. If it is suspected that these assump­ ships, research conferences and workshops, tions are not met, how should the statistical research institutes, and computational equip­ analyses be carried out? How do these new ment. analyses perform when compared to their In addition to standard research grants in classical counterparts? all of the above areas, significant attention is • To what extent can one make use of human paid to fostering the increasingly fruitful interac­ visual abilities and computer display devices tions among different mathematical subfields and in analyzing data? their areas of application. In particular, the • Hyperbolic non-euclidean geometry appears two recently established mathematical sciences to be the most promising new technique research institutes at Berkeley and Minnesota for understanding the topology of curved provide groups of researchers, including recent three-dimensional spaces. In particular, will recipients of the doctorate, with opportunities the last remaining case of the 80-year-old to work intensively in specific areas of abstract Poincare Conjecture, which deals with three­ and applied mathematics. Together with the dimensional spheres, finally yield to this Mathematical Sciences Postdoctoral Research Fel­ approach? lowship program, the institutes provide research • Will the limits of provability continue to be positions for junior investigators. Additionally, illuminated by the coming together of insights problems related to the increasing use and need for from abstract recursion theory (mathematical computational facilities for mathematical sciences logic) and from the theory of algorithms research are being addressed through a program (computer science)? which allows a limited number of awards for the • Mysterious and surprising connections with purchase of special-purpose computing equipment. automorphic forms continue to be uncovered NSF Role by mathematicians working in such diverse areas as representation theory, algebraic Research in the mathematical sciences is funded geometry, and number theory. Most recently, by the NSF, the Department of Defense (DOD), in the construction of the largest of the the Department of Energy (DoE), the National sporadic finite simple groups, numerical Institutes of Health (NIH), and the National invariants of the group coincided exactly Aeronautics and Space Administration (NASA). with other numerical invariants of a certain Of these agencies, the NSF is the only one type of automorphic form. The research with responsibility for support across the entire areas of group theory and automorphic forms spectrum of the discipline. Other federal programs were thought to be totally unrelated, but are focused on areas determined to be related to the numbers involved are large (the first is specific agency missions. 196883) and the relationship cannot possibly The role of NSF in support of academic basic be coincidental. Can we unlock the secret research in the mathematical sciences is a pivotal of these complex analytic functions and one. It provides virtually all of the federal determine why their influence is so pervasive? funding for basic mathematics research in algebra, • Do the chaotic motions of low-dimensional number theory, geometric analysis, topology, and approximations to the Navier-Stokes equa­ foundations. Current estimates indicate that in tions, the equations of motion of a fluid, FY 1981 it provided approximately 85 percent really represent turbulence? of the support for research in Modem Analysis • Can one realistically describe biological sys­ and Classical Analysis with the balance provided tems with mathematical models involving a by DOD and DOE. In Applied Mathematics small number of unspecified parameters which and in Statistics and Probability the other may be determined from a limited number of federal agencies support only about 50 percent laboratory experiments, and can one rely on of all research conducted at academic institutions. these models to predict the outcome of more However, these areas are of considerable interest complicated laboratory and field situations? to those agencies because of possible applications • What are the connections between completely in the near term. integrable, infinite-dimensional, Hamiltonian NSF coordinates its support of research in the systems and the underlying physical processes mathematical sciences with its counterpart federal which they approximately describe? In agencies through the Interagency Committee for particular, is the Korteweg-de Vries equation Extramural Mathematics Programs. This group really a good model for waves in shallow meets regularly to share information on policies of water? support and to discuss areas of emphasis and of • Recent studies of contact surfaces arising in unusual scientific opportunity. liquid-air and liquid-liquid phenomena have

241 proven highly successful through the appli­ cation of powerful new variational methods. Education Programs at the To what extent can these techniques be National Science Foundation exploited in analyzing the smoothness and The Administration's program for phasing out the stability of interfaces between other immis­ Foundation's activities concerned with education, is cible liquids in equilibrium? displayed in the table below showing how each line of the Education Directorate's budget has been eliminated • Can exploiting the geometric content of (with the single exception of the Graduate Research Fel­ relativity and gauge field theory continue lowship program, where fellowships previously awarded to provide methods for handling the difficult have been allowed to continue). According to a report published in the Chronicle of Higher Education, March partial differential equations involved, such as 3, 1982, the director of the Foundation has announced the Yang-Mills field equations? that the Education Directorate is being abolished, on the grounds that "ten persons is hardly enough to Significant Recent Achievements staff a directorate." Some Congressmen have criticized Optimal Statistical Designs. A statistical both the budget reduction and the action to dissolve the Directorate. Representative Robert N. Shamansky, experiment is often designed to maximize the Democrat of Ohio, was quoted by the Chronicle as information in the data that will be obtained. observing that "the approach of this Administration to Recently several new optimal designs have been science education is equivalent to the Chinese Cultural Revolution." Representative Doug Walgren, Democrat constructed in the area of regression analysis. of Pennsylvania, chairman of the Subcommittee on In a regression setting, a dependent variable is Science, Research, and Technology, was reported to expressed as a random error plus a function have said that the decision to abolish the directorate of the independent variables and the unknown is "appalling," especially as the announcement came before Congress had an opportunity to evaluate and parameters. The key design elements are the respond to the budget-reduction request. levels of the independent variables at which the dependent variable is to be observed. Z. Galil and Science and Engineering Education (Millions of dollars) J. Kiefer, working at the University of California, Actual Plan Request Berkeley, simplified the task of obtaining such FY 1981 FY 1982 FY 1983 optimal designs for linear regression settings. Personnel Improvement Using a computer search routine, they constructed Faculty Improvement $10.2 $ 0.8 -0- a design for situations with twelve or fewer Graduate Research Fellowships 14.0 15.0 15.0 parameters. Prior to their work such complete Student Oriented Programs 5.7 -0- -0- knowledge was available only for cases in which Minorities, Women and the the number of parameters did not exceed five. Physically Handicapped 3.5 1.0 -0- Primality Testing. Mathematicians and com­ Subtotal $33.4 $16.8 $15.0 puter scientists have revitalized the close ties between the two fields, in part through work on Science Education Resouree Improvement computational complexity; that is, how difficult it Comprehensive Assistance to is to make a computation and how fast can it be Undergraduate Science done. For example, number theory and theoretical Education (CAUSE) $8.9 -0- -0- computer science alike are interested in finding Undergraduate Instructional Improvement 6.2 -0- -0- fast methods of determining whether or not a given Resource Centers for Science large number is prime. For the number theorist, and Engineering 2.8 -0- -0- this is a classical problem which has long resisted -- solution; for the computer scientist, interest has Subtotal $17.8 -0- -0- been focused by a recently developed method Science Education of public key encryption (coding) based on the Development and Research ability to find very large {50 digit or more) prime Development in Science Education $6.2 $1.7 -0- numbers quickly and the simultaneous inability Research in Science to factor large numbers quickly. This common Education 4.7 0.5 -0- problem has recently found a partial solution, -- with a fast computer algorithm for primality Subtotal $10.9 $ 2.2 -0- testing which uses some very deep mathematical Science Education properties. The results were announced in late Communication 1980 by L. Adleman of the University of Southern Public Understanding of Science $4.3 $1.2 -0- California and R. Rumely and Carl Pomerance of Information Dissemination the University of Georgia. for Science Education 1.2 -0- -0- Four-Dimensional Poincare Conjecture. In Other Programs (STIA) $3.1 -0- -0- -- August 1981, Michael H. Freedman of the Subtotal $ 8.6 $ 1.2 -0- University of California, San Diego, announced the solution of one of the two most famous NSB Commission on Pre-College Education -0- $ 0.7 -0- outstanding problems in topology, the Four­ Dimensional Poincare Conjecture. This concerns Total Science and the four-dimensional analogue of a conjecture Engineering Education $70.7 $20.9 $15.0 about three-dimensional spheres that has resisted

242 all attacks since Henri Poincare formulated it Littlewood conjectured that for frequencies which at the turn of the century. Now only the are composed of fundamental harmonics each original three-dimensional case remains. All other making the same contribution to the whole, dimensions have been settled. the average amplitude always exceeds a fixed, What is at issue is whether a sphere is the computable bound. This bound depends only on unique possessor of certain simple topological the number of harmonics, not their frequencies. characteristics. No one has found any other The conjecture was studied over the course of topological structures with these characteristics, several decades. Partial results continued to add to but neither has anyone been able to rule out the credibility of the conjecture. Finally, in 1981, the possibility of their existence for dimension three mathematicians succeeded in showing that three (and dimension four until now). Freedman Littlewood was indeed correct. They are Brent P. proved that there are no such objects in the Smith, California Institute of Technology, Louis four-dimensional case. If there are such objects, Pigno, Kansas State University, and 0. Carruth as yet unknown in the three-dimensional case, McGehee, Louisiana State University. Despite that points to a very fundamental gap in our the distinguished history of this conjecture, its understanding of topology. That gap has been final proof is entirely self-contained and not halved by Freedman's achievement. explicitly dependent on earlier work. It is Dispenive Systems. Many physical systems striking in its simplicity and has already inspired are modeled by equations which exhibit the further valuable contributions to the field of following important characteristics: disturbances analysis, contributions applicable to problems of propagate with finite speed, they are nonlinear, mechanical and electrical oscillations. and they are dispersive, in that the speed of Changes Between FY1982 Budget Request propagation depends on the wave length of the and FY 1982 Current Plan motion. The prototype and perhaps best studied The FY 1982 Current Plan represents a decrease of all such equations is the Korteweg-de Vries of $2.5 million below the FY 1982 Request of $33.7 (Knv) equation, an equation which describes, at million. This decrease results from a combination least on certain scales, phenomena ranging from of Congressional actions and NSF's responses to free surface waves in shallow water, plasma flows, budget reductions by the Administration. and the spread of infectious diseases. Research The Current Plan is $2.9 million or 10 percent over the past fifteen years has shown that the over the FY 1981 obligation. It represents modest KDV equation, though nonlinear, exhibits three real growth which will be used to implement the remarkable properties: (i) it may be solved exactly first full year of operation of a dual system of just as a linear equation, (ii) it obeys an asymptotic support in the Mathematical Sciences. A key role superposition principle which guarantees that in this system is played by the coherent modes coherent wave forms decouple as time proceeds activities of the Special Projects Program. These to minus and plus infinity, and (iii) it has an activities include two research institutes, a variety infinite number of conservation laws. An open of research workshops, postdoctoral and visitor problem has been to characterize those dispersive support, and computer equipment acquisition for wave equations with the above properties. Some coordinated research efforts. The coherent modes had conjectured that, if a given dispersive system activities will be increased from $3.4 million to $4.3 could be approximately described by one with the million in order to provide the solid foundation aforementioned properties, then the former might necessary for their development. itself be endowed with those same properties. • In May 1981, the Foundation approved the es­ Recently, Peter Olver of the University of tablishment of two mathematical sciences re­ Minnesota and T. Brooke Benjamin of Oxford search institutes. In FY 1982, the Mathemati­ University have shown that this conjecture was cal Sciences Research Institute at Berkeley overly optimistic. They analyzed one specific will be funded at $1.6 million and the Institute system, namely the "exact" equations which for Mathematics and its Applications at the describe free surface waves in shallow water, and University of Minnesota will be funded at showed that they have only seven conservation $0.8 million. laws associated with them rather than the • In accordance with a recommendation of infinite number of such laws associated with the the Advisory Subcommittee for Mathematical approximating KDV equation. This result opens Sciences in June, 1981, a new computer many new lines of research. instrumentation activity will be funded at The Littlewood Conjecture. The complicated $0.7 million. phenomenon of one-dimensional vibrations, or • Scientific Research Project Support (sRPS) periodic motion, can be described in terms of will decrease $4.0 million, from $29.6 million the superposition of fundamental frequencies: in the FY 1982 Budget Request to $25.6 mil­ harmonics. Any displacement from a rest position, lion in the FY 1982 Current Plan. This the amplitude, may be represented as the sum of decrease will be distributed among the Math­ the displacements of the contributing harmonics. ematical Sciences program elements in a way The distinguished British mathematician J. E. consistent with changing needs among fields.

243 In order to maintain effective grant size, the University of Wisconsin, and the Courant Institute number of senior investigators supported will of Mathematical Sciences at New York University have to be decreased. will be increased by $0.1 million to a total of $1.1 • In order to meet increased interest in million. geometry and its applications to physics • The Mathematical Sciences Postdoctoral and mathematical physics, portions of the Research Fellowship program will be Topology, Geometry, and Foundations, Clas­ strengthened by extending from two years to sical Analysis, and Modern Analysis programs three years the term over which a fellowship have been combined into a new program in may be held. The option, introduced in FY Geometric Analysis. 1982, to hold either a full-time research fel­ FY 1983 Budget Highlights lowship or a half-time research instructorship Explanation of Jnereases, Deueases will be retained. Support for these fellowships and Continuing Emphases increases from $0.6 million to $0.8 million in FY1983. The FY 1983 Budget Request of $33.9 million • FY 1983 is the second year of a thrust to is $2.7 million, or 8.7 percent, above the FY1982 provide funds for instrumentation. These $1.0 Current Plan. Of this increase, million will funds will increase by $0.3 million above the be used to enhance the development of activities, FY 1982 level to a total of $1 million, to serve including coherent modes, in the Special Projects the computational equipment needs of several Program. These activities will be followed with groups of investigators in departments in the great care as preliminary evaluations are made of mathematical sciences. their effectiveness. • Participants in the six American Mathemati­ • Support for Scientific Research Project Sup­ cal Society summer research workshops to be 6.6 port programs will increase by percent supported in FY 1983 [sic] will do research in to a total of $27.2 million. As this is below probabilistic computational complexity; er­ constant level of effort, increased grant size godic theory and applications; nonlinear par­ will require a decrease in the number of senior tial differential equations; values of L-series investigators supported. at special points; four-manifold theory; and • The two research institutes will be allowed quantum fields, probability, and geometry. modest growth of $0.3 million or 12.5 per­ Percentage increases for the eight program ele­ to a total of $2.7 million to allow cent ments from FY 1982 to FY 1983 are as follows: some strengthening of support for junior in­ vestigators. The Mathematical Sciences Re­ Increases, FY 1982 to FY 1983 $ Millions Percent search Institute in Berkeley, California, will concentrate on research in nonlinear partial Classical Analysis $0.2 6.7% differential equations and in adaptive and Modern Analysis 0.2 6.8 robust estimation in statistics. The Institute Geometric Analysis 0.2 6.6 for Mathematics and its Applications at the Topology & Foundations 0.3 6.4 Algebra & Number Theory 0.3 6.6 University of Minnesota will concentrate on Applied Mathematics 0.3 6.8 research in statistical and thermodynamic Statistics & Probability 0.2 6.7 approaches to phase transition phenomena. Special Projects 1.0 17.9 • Visitor and postdoctoral support at the Total Mathematical Sciences $2.7 8.7% Institute for Advanced Study in Princeton, the Mathematics Research Center at the

244 Polish Prisoners and the International Congress in Warsaw

The administrative office of the American Math­ lists are incomplete, and some of the names on one ematical Society in Providence has received reports list appear to have variant spellings on others of from four different sources of the imprisonment the lists. Tentative additional identifications have of Polish mathematical scientists by the military been made using information in the rues of the regime in Poland. Each report contained a list editorial office of Mathematical Reviews in Ann of names. One mathematician, Boleslaw Gleieh­ Arbor. gewieht, was reported to be in hiding (the report asserted that a warrant had been issued for his Three reviewers for Mathematical Reviews are arrest); another, Stanislaw Hartman, was reported included on the lists: to have been arrested and later released. The four lists include a total of thirty names, nine of which Roman Duda, of Wroclaw has been a reviewer appear on two of the lists, four appear on three, for Mathematical Reviews since 1963 and has and three on all four. reviewed seventeen papers since 1979 alone; Although the names of the individuals who since 1972 he has had nine of his own papers transmitted each of the reports to the Providence reviewed in Mathematical Reviews, in the areas of staff are known to the editors of the Notices, general topology, algebraic topology, and global no information about the original source of any analysis/analysis on manifolds. of the lists is available at present. Names and Stanislaw Hartman, also of Wroclaw, has been a identifications of many of the individuals on the reviewer for Mathematical Reviews since 1967 and has reviewed six papers since 1979; since 1972 he Statement by G. D. Mostow has had fourteen of his own papers reviewed in Mathematical Reviews, in the areas of abstract Chairman, U. 8. National Committee for Mathematics harmonic analysis, history and biography, and Fourier analysis. He is a member of the Institute March 4, 1982 of Mathematics of the Polish Academy of Sciences, Lennart Carleson, president of the IMU, Wroclaw. accompanied by Jacques-Louis Lion, secretary of the IMU, and Olli Lehto, chairman of the Jan Waszkiewicz, of the Technical University of 1978 International Congress of Mathematicians Wroclaw, served as a reviewer for Mathematical in Helsinki, visited Poland on February 8, 9 and Reviews from 1971 to 1980; he has had six of 10 in order to ascertain the feasibility of holding his own papers reviewed in Mathematical Reviews the 1982 International Congress in Warsaw, as since 1972, in the areas of mathematical logic and scheduled. statistics. There was general agreement that the Con­ Others, reported to have been arrested, whose gress could not be held under the conditions mathematical works have been reviewed in Math­ then prevailing. The visitors were, however, ematical Reviews during the period covered by the deeply impressed by the fervent desire of all most recent cumulative index (1973 to 1979) or Polish mathematicians that the Congress be later are: held in August. President Carleson submitted to the Polish Konrad BieliD.ski of Kielce who has published government a list of assurances that would be a papers in mathematical logic. prerequisite for the Congress to be held. These Krzysztof Chmiel of the Institute of Control include, among other stipulations, Engineering of the Technical University of Poznan. (1) the free circulation of mathematicians One of his papers in computer science was reviewed seeking to attend the Congress, by Mathematical Reviews in 1980. (2) the release from jail of the mathemati­ Elibieta Dudek, of the Silesian University of cians under arrest, Katowice, has had two papers in mathematical (3) the lifting of the 11 p.m. to 5 a.m. logic and foundations reviewed, the most recent curfew. in 1981. The Executive Committee of the IMU will meet in Paris on April2, 1982. At that meeting, Boleslaw Gleiehgewieht has written papers on a decision is expected on how to proceed with group theory and generalizations which have been the Congress. reviewed in Mathematical Reviews, and listed in the latest cumulative index.

245 Kowalski of Warsaw. One of the lists contained Andrzej Zaraeh of the Institute of Mathematics a D. Kowalski, another an S. Kowalski (both of of the Technical University of Wroclaw has had Warsaw). Records at the Mathematical Reviews seven papers reviewed in Mathematical Reviews office in Ann Arbor include information on one since 1972, in the areas of logic and set theory. S. Kowalski of Olsztyn (100 miles from Warsaw) who has published in functional analysis, and Other names on the lists are: one Stanislaw Kowalski of L6dz (75 miles from J. Bartosiewicz of Warsaw, a student at the Warsaw), who has published in computer science. Technical University. Janusz Onyszkiewiez of Warsaw was on all four J. Chomieki of Warsaw, an assistant at the lists. Professor Onyszkiewicz, a member of the University Institute of Mathematics of the Polish Academy of Sciences, has published papers in mathematical J. Dubikajtis of Katowice, a student. logic and the foundations of mathematics. M. Frybes, a university student in Warsaw. Ryszard Rubinsztein, also a member of the M. Gogulski, a university student in Warsaw. Institute of Mathematics of the Polish Academy (A second list included M. Gugulski of Warsaw, of Sciences, has published papers in algebraic possibly the same person.) topology and in manifolds and cell complexes. M. Grudzinski of Warsaw. Marian Srebrny, of Warsaw, is a logician whose name was on all four lists; he has nad thirteen Tadeusz Huskowski, a differential geometer of of his papers reviewed in Mathematical Reviews Wroelaw. since 1972 (in history and biography, logic, and S. Kawalee of Warsaw. set theory). On one of the lists, he is reported to Kozlowski of the Institute of Computers, Warsaw. be at the Academy. D. Kupieeki of Warsaw. Andrzej Tye of the Institute of Mathematics of the Polish Academy of Sciences, Torwi, has published J. Lity:D.ski of Warsaw. eight papers reviewed in Mathematical Reviews M. Michalik, a numerical analyst, Institute of since 1972, in the areas of commutative rings and Education, L6dz. algebras, algebraic topology, and manifolds and cell complexes. His name appears on two of the Z. Romaszewska of Warsaw. lists. A. Siuda, a teacher in L6dz. Andrzej Wronski, of the department of logic of K. Tunyliski, a logician in Torwi. Jagiellonian University of Krakow, had forty-three papers reviewed in Mathematical Reviews between Mrs. X, an assistant at the Technical University 1972 and 1980. in Radom.

SELECTED TABLES IN MATHEMATICAL STATISTICS Managing Editor, f. M. Davenport Each volume of this series contains one or more Mathematical Statistics. The purpose of the series is sets of extensive tables of interest to statisticians and to provide an outlet for tables of high quality and users of statistical methods. The introductory material utility which are too long to be published in a tech- for each set discusses method of computation, accu- nical journal. Each table is carefully checked for racy, methods of interpolation (when required), and accuracy before it is accepted. applications, and gives numerical examples of the use The editors for volume 7 are R. E. Odeh and of the tables. This series is edited by the Institute of W. J. Kennedy. THE PRODUCT OF TWO NORMALLY DISTRIBUTED RANDOM VARIABLES by William Q. Meeker, jr., Larry W. Cornwell, and Leo A. Aroian This volume contains tables of percentiles of the will be a useful addition to statistical, technical, and distribution of two (possibly correlated) normally scientific libraries. distributed random variables. Theoretical properties are reviewed, numerical methods are described, and Volume 7, viii + 256 pages (hard cover) a number of references are provided. This distribu­ List price $12.40, institutional member $9.30, individual member of AMS or IMS $6.20 tion has applications in the fields of physical, engi­ ISBN 0-8218-1907-0; LC 74-6283 neering, biomedical, and social sciences as well as in Publication date: April 1981 auditing and other business applications. This volume To order, please specify TABLES/7N Prepayment is required for all AMS publications. Order from AMS, P.O. Box 1571, Annex Station, Providence, Rl 02901, or call toll free 800-556-7774 to charge with Visa or MasterCard.

246 News and Announcements

AMS Postdoctoral Research Fellowship The awards are made to United States citizens or nationals. Selections are made on the One AMS Postdoctoral Research Fellowship was basis of ability of the applicant and the likely awarded in 1982. The recipient is Nicholas J. improvement of his or her future in science. Kuhn, who took his Ph.D. under Peter May at A panel of mathematical scientists, chosen by the University of Chicago in 1980. His thesis the American Mathematical Society, the Institute was entitled Structure of James-Hopf maps. He for Mathematical Statistics, and the Society for was a Lecturer at the University of Chicago from Industrial and Applied Mathematics, evaluated 1978 to 1980. From 1980 to 1982 he has been 100 applications; final selections were made by an Acting Assistant Professor at the University of NSF. Washington. It is his plan to spend his fellowship The Postdoctoral Fellowships have been year of 1982-1983 at Princeton University and modified this year to provide increased flexibility Northwestern University. for the recipients. The stipend of $26,000 provides The AMS Research Fellowship Fund was estab­ support for a nine-month academic year and lished in 1973 in response to the need for funds two two-month summers. Recipients have the for postdoctoral research. The fellowships are option of receiving the academic-year support awarded on the basis of mathematical merit to full-time for one academic year or half-time for recent recipients of Ph.D.'s (regardless of their two academic years. age) who are citizens or permanent residents of The recipients are listed below with current a country in North America. The awards are affiliation in parentheses, followed by the name of intended to support research fellows for a period the fellowship institution: of one year, and at present carry a stipend of $22,000 each, with an expense allowance of $1,000. Malcolm R. Adams (Massachusetts Institute of The competition was under the supervision of the Technology), University of California, Berkeley; Society's Committee on Postdoctoral Fellowships, Jim Agler (University of Virginia), Univer­ consisting of Benedict Gross, Richard H. Karp, sity of California, San Diego; David E. Bar­ Daniel J. Kleitman, Paul H. Rabinowitz, Donald rett (University of Chicago), Princeton Univer­ E. Sarason, and Robert I. Soare (chairman). sity; Patricia Bauman (University of Minnesota), There were many strong candidates among the Courant Institute, New York University; Howard 109 applicants. The fellowship is financed by the S. Becker (University of Wisconsin), Califor­ generous contributions of supporters of mathe­ nia Institute of Technology; F. Michael Christ matical research, supplemented with Society funds (University of Chicago), Princeton University; appropriated according to a matching formula. James Wesley Cogdell (University of Maryland), The continuation of the AMS Research Fellowship Cornell University; John Brian Conrey (University program depends on contributions the Society of illinois), University of Texas, Austin; Kevin R. receives. Every member of the Society is urged Coombes (University of Chicago), Harvard Univer­ to contribute to the Fund. Contributions are, of sity; Aaron Fogelson (Courant Institute, New course, tax deductible. Checks should be made York University), National Institutes of Health; payable to the American Mathematical Society, Matthew Foreman (University of California, Los clearly marked "AMS Research Fellowship Fund" Angeles), University of Colorado; Solomon Fried­ and sent to the American Mathematical Society, berg (University of Chicago), Harvard Univer­ Post Office Box 1571, Annex Station, Providence, sity; Devra Garfinkle (Massachusetts Institute of Rhode Island 02901. Technology), Massachusetts Institute of Technol­ ogy; Joseph Glover (University of Rochester), NSF Announces Mathematical Sciences University of California, San Diego; Glen R. Postdoctoral Research Fellowships Hall (University of Minnesota), University of Wis­ consin; David Harbater (University of Pennsyl­ Thirty recent recipients of doctoral degrees vania), University of Pennsylvania; Jim E. Hoste in the mathematical sciences have been offered (University of Utah), University of California, fellowship awards designed to contribute to Berkeley; Robert A. Indik (Princeton University), the future vitality of the Nation's scientific Massachusetts Institute of Technology; Nicholas effort. The awards will be made under the Na­ J. Kuhn (University of Washington), Northwes­ tional Science Foundation's (NSF) Mathematical tern University; John M. Lee (Massachusetts Sciences Postdoctoral Research Fellowship pro­ Institute of Technology), University of Michigan; gram, now in its fourth year. They will permit David Leep (University of Chicago), University recipients to choose research environments that of California, Berkeley; Randall J. LeVeque will have the greatest benefit to their scientific (Stanford University), Courant Institute, New development. York University; John Alan McDonald (Stanford

247 University), Stanford Linear Accelerator Cen­ which are primes). Certain conditions are specified ter; David R. Morrison (Princeton University), in the announcement of the prize. For example, Princeton University; Judith A Packer {Harvard the published proof must be in English, it must University) University of California, Berkeley; appear in one of a number of journals specified by Randolph J. Schilling (University of Arizona), the donor, and a copy of the journal containing Courant Institute, New York University; Steven the proof must be delivered by certified mail to T. Schwarz {University of Chicago), Harvard wcs {address above). The prize is to be awarded University; Thomas M. Sellke (Stanford Univer­ one year after the date of publication, if during sity), University of Michigan; Lloyd N. Trefethen that time the proof has not been refuted. The (Stanford University), University of Wisconsin; offer expires March 31, 1985. The prize is to be and David J. Wright {Harvard University), Johns divided if more than one valid proof is produced Hopkins University. during the time period in question and all the conditions mentioned are satisfied in each case. Gordon Thomas Whybum Professonhip Readers interested in a more detailed specification of the conditions are urged to correspond with University of Virginia the firm offering the prize. Inquiries should Primoff, vice-president, The Rector and Visitors of the University of be addressed to Eugene Services, Inc., at the address Virginia have announced the establishment of Worldwide Computer 201-694-8876). a Chair to be known as the Gordon Thomas given above {telephone Whyburn Professorship in Mathematics. Professor Whyburn was a member of the faculty 1983-1984 Advaneed Research from 1934 until his death in 1969. He was Fellowships in India chairman of the department from 1934 until1966 and then became the first member of the Center Twelve long-term (six to ten months) and nine for Advanced Studies in the Sciences at the short-term (two to three months) research awards, University of Vrrginia. without restriction as to field, are offered for He served the Society and the mathematical 1983-1984 by the Indo-U.S. Subcommission on community in many ways, for instance as a Education and Culture. Applicants must be member of the committee responsible for the U.S. citizens at the postdoctoral or equivalent establishment of Mathematical Reviews, as a professional level. The fellowship program seeks member of the War Policy Committee (ad hoc to open new channels of communication between predecessor of the Conference Board of the academic and professional groups in the United Mathematical Sciences), and as a member and States and India and to encourage a wider range of chairman of the Editorial Committee of the research activity between the two countries than Transactions. He was President of the Society in now exists. Therefore, scholars and professionals 1953 and 1954 and a Trustee for a number of years who have limited or no experience in India are thereafter. especially encouraged to apply. Professor Whyburn was the author of 149 papers Fellowship terms include: $1,200-$1,500 per and books. In 1940 he presented the Society's month, depending on academic/professional Colloquium Lectures, which were subsequently achievement and seniority, $350 per month pay­ published in his book Analytic Topology, AMS able in dollars and the balance in rupees; an Colloquium Publications, volume 28. allowance for books and study/travel in India; He was elected to the National Academy of and international travel for the grantee. In addi­ Sciences in 1951. In 1968 he received the Thomas tion, long-term fellows receive international travel Jefferson Award from the University of Virginia. for dependents; a dependent allowance of $100- For his paper "On the structure of continua," $250 per month in rupees; and a supplementary to 34,000 rupees. This which appeared in the AMS Bulletin in 1936, research allowance up Subcom­ he was awarded the MAA's Chauvenet Prize for program is sponsored by the Ind

248 National Science Foundation Report from the Mathematical Sciences Section

In accordance with a decision of the National Science Board, the policy-making body of the Meetings of the Advisory Subcommittee National Science Foundation, we have started for Mathematical Sciences sending copies of reviews of a proposal to principal The Advisory Subcommittee for Mathemati­ investigators after final action has been taken cal Sciences usually meets twice a year-late on the proposal. The practice up until this spring and late autumn-and most of the meet­ time was to send reviews only to those principal ings are open. The program oversight reviews investigators who requested them. We shall are closed since they involve inspection and continue to delete references, usually used for discussion of particular proposals. Those parts comparisons to persons not in the proposal. of the Advisory Subcommittee meetings which However ' the sheer volume of reviews flowing.. refer to proposals or to future budgets are also through the Section will preclude our contmwng closed. the practice of typing handwritten reviews. We Although the dates for meetings of t_he shall also begin to use multi-copy review forms Advisory Subcommittee are generally set q~te so that the copy to the principal investigator far in advance the agenda for these meetmgs may simply be pulled off, saving our secretaries are generally n~t completed before the deadline the work of duplicating reviews. The ad hoc for publication in the Federal Register. mail review process which the Section has used since its beginnings is, as you are all well aware, A spring meeting was scheduled for June 8 the foundation of our review, evaluation, and and 9, 1982, which, unfortunately, has been decision process. This is an appropriate place to cancelled because of a lack of operating funds. thank all the mail reviewers who give so much of The autumn meeting is scheduled for October their time and energy to providing information to 29 and 30, 1982; the closed program ~ersight program directors in their review and evaluation reviews will be on the two days preceding that of proposals. All of us in the Section are deeply meeting. W.G.R. appreciative of your assistance and look forward [EDITORS' NOTE. The names of the members of to your continuing cooperation. the Advisory Subcommittee will be found on page The Section is now actively recruiting for five 639 of the November 1981 issue of the Notices.] program director positions to be filled on. a support of somewhat fewer investigators by this rotational basis, preferably for two years, starting mechanism. this coming August. These are in Classical The NSF's FY 1983 budget request to the Analysis, Modern Analysis, Applied Mathematics, Congress, which was sent to the Congres_s .on Statistics and Probability, and a new program in Geometric Analysis. We are also seeking February 8, contains a request of $33.9 ~on for the Mathematical Sciences. There 1s, of an associate program director for the Applied course a long path from the budget request to Mathematics program. Applicants should have the appropriation. Any eventual increase a Ph.D. or equivalent experience and training in fi~al over FY 1982 would be spread over all Section an appropriate field, plus six years of successful activities. The emphasis begun in FY 1982 on scientific research experience in the field. A Special Projects and on the need to increase grant broad general knowledge of the field and some size in order to allow reasonable flexibility has administrative experience are also required. I would appreciate receiving your inquiries or enhanced total funds while decreasing the number of investigators receiving support through SRPS; recommendations. Filling these positions with it is impossible now to estimate the size of the the best people is clearly of great importance to decrease. the mathematical sciences research community. The Section's current operating number for The NSF International Travel Grant program was discontinued last fall. All applications Fiscal Year 1982 (starting October 1, 1981) is $31.2 for international travel now compete with all million, compared to $28.2 million in FY 1981, so FY 1982 will be neither as threatening as we had other research proposals for program funds. For once feared nor as promising as we would prefer. the most part, only requests to support travel We plan to fund the new computing research by groups of mathematicians to international equipment acquisition activity, the postdoctoral meetings will receive consideration. Individual fellowships, the AMS summer conferences, regular awards will not be made except in the most conferences, regional conferences, and the research unusual circumstances. institutes essentially as scheduled. Funds for William G. Rosen, Head the usual Scientific Research Project Support Mathematical Sciences Section (SRPS) awards are essentially fiat, resulting in the

249 1982 AMS ELECTIONS Nominations by Petition

Viee-President or Member-a~ Large Rules and Proeedures One position of vice-president and member of the Council ex officio for a term of two years is to be Use separate copies of the form for (a) filled in the election of 1982. The Council intends candidates for vice-president, (b) candidates to nominate two candidates, whose names may be for member-at-large, (c) candidates for the expected to appear in the June issue of the Notices, Nominating Committee. which is scheduled to be mailed by the printer on May 1. To be considered, petitions must be ad­ 21. Nominations by petition in the manner described dressed to Everett Pitcher, Secretary, Box 6248, below are acceptable. Providence, Rhode Island 02940, and must Five positions of member-at-large of the Council arrive by July 10, 1982. for a term of three years are to be filled in the 2. The name of the candidate must be given same election. The Council intends to nominate seven as it appears in the Combined Membership List. candidates, whose names may be expected to appear If the name does not appear in the list, as in the June Notices. Nominations by petition in the in the case of a new member or by error, it manner described below are acceptable. The Council must be as it appears in the mailing lists, for has stated its intent to have at least ten candidates example on the mailing label of the Notices. and will bring the number up to ten if the nominations If the name does not identify the candidate by petition do not do so. uniquely, append the member code, which may Petitions are presented to the Council, which, be obtained from the candidate's mailing label according to Section 2 of Article VII of the bylaws, or the Providence office. makes the nominations. The Council of 23 January 3. The petition for a single candidate may 1979 stated the intent of the Council of nominating all consist of several sheets each bearing the persons on whose behalf there were valid petitions. statement of the petition, including the name Prior to presentation to the Council, petitions in aid of the position, and signatures. The name of of a candidate for the position of vice-president or of the candidate must be exactly the same on all member-at-large of the Council must have at least 50 sheets. valid signatures and must conform to several rules and operational considerations, which are described in the 4. On the facing page is a sample form for box. petitions. Copies may be obtained from the Secretary; however, petitioners may make and The Nominating Committee for 1983 use photocopies or reasonable facsimiles. 5. A signature is valid when it is clearly that The Council has approved the continuation of of the member whose name and address is given the procedure of filling places on the Nominating in the left-hand column. Committee by election. There will be four continuing 6. The signature may be in the style chosen members of the Nominating Committee, namely by the signer. However, the printed name and David Mumford address will be checked against the Combined Ralph S. Phillips Membership List and the mailing lists. No Linda Preiss Rothschild attempt will be made to match variants of George W. Whitehead names with the form of name in the CML. A There will be four places filled by election in a name neither in the CML nor on the mailing preferential ballot. The President will name six lists is not that of a member. (Example: The candidates for these four places. The names may be name Everett Pitcher is that of a member. The expected to appear in the June issue of the Notices. name E. Pitcher appears not to be. Note that Nominations by petition, in the manner described in the mailing label of the Notices can be peeled the box, will be accepted. Should the final number of oft' and affixed to the petition as a convenient candidates be less than eight, the President will bring way of presenting the printed name correctly.) it up to eight. The name of a candidate for member of the 7. When a petition meeting these various Nominating Committee may be placed on the ballot by requirements appears, the Secretary will ask the petition. The candidate's assent and petitions bearing candidate whether he is willing to have his name on the ballot. Petitioners can facilitate the at least 100 valid signatures are required for a name to procedure by accompanying the petitions with a be placed on the ballot. In addition, several other rules and operational considerations which are described in signed statement from the candidate giving his consent. the box should be followed.

250 NOMINATION PETITION FOR 1982 ELECTION The undersigned members of the American Mathematical Society propose the name of

as a candidate for the position of (check one):

0 Viee-President o Member-at-Large ofthe Council o Member of the Nominating Committee

of the American Mathematical Society for a term beginning January 1, 1983.

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

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251 Queries Edited by Hans Samelson QUESTIONS WELCOMED from AMS members regarding mathematical matters such as details of, or references to, vaguely remembered theorems, sources of exposition of folk theorems, or the state of current knowledge concerning published or unpublished conjectures. REPLIES from readers will be edited, when appropriate, into a composite answer and published in a subsequent column. All answers received will ultimately be forwarded to the questioner. QUERIES and RESPONSES should be typewritten if at all possible and sent to Professor Hans Samelson, American Mathematical Society, P. 0. Box 6248, Providence, Rhode Island 02940

Problem List all eigenvalues of £ 0 in an admissible module do not belong to a ray {they always lie on a line), then all the Kae-Mood.y Lie Theory multiplicities are 1? The following is a list of open questions submitted to 3. {Victor Kac). Is it true that the Hilbert completion the special session on Kac-Moody Lie theory held at of an admissible unitarizable {with respecj; to the the AMS meeting in Amherst, Massachusetts, October antilinear anti-involution w(L.;) = L-i), W-module 16-18, 1981. can be integrated to a (unitary) representation of 1. (Victor Kac). Classify all Z-graded Lie algebras the universal central extension of the group of g = EB;ezB; with no nontrivial graded ideals and of dift'eomorphisms of the circle? finite Gelfand-Kirillov dimension. Is it true that there 4. (Yictor Kac). Let G be a simple compact Lie group, are only three possibilities with dim 9; = 1 for all j: let G (resp. ~) be the universal central extension of the 2 affine Lie algebras ~l) and 4 ), and the Lie algebra group of polynomial {reap. C 00) maps from the unit W with basis L;, j E Z, and commutation relations circle to G. Is it true that the (unitary) representation [L.;,L;] = (i- j)L.;+;? of

MATHEMATICAL SURVEYS applications to other areas of mathematics; for ex­ ample, in the simulation of transcendental functions APPROXIMATION BY POLYNOMIALS on computers. In most computers, fixed point arith­ WITH INTEGRAL COEFFICIENTS metic is faster than f1 oating point arithmetic and it by Le Baron 0. Ferguson may be possible to take advantage of this fact in the Results in the approximation of functions by evaluation of integral polynomials to create more polynomials with coefficients which are integers efficient simulations. Another promising area for have been appearing since that of Pal in 1914. The applications of this research is in the design of digital body of results has grown to an extent which seems filters. A central step in the design procedure is the to justify the present book. The intention here is to approximation of a desired system function by a make these results as accessible as possible. polynomial or rational function. Since only finitely The book addresses essentially two questions. many binary digits of accuracy actually can be The first is the question of what functions can be realized for the coefficients of these functions in any approximated by polynomials whose coefficients are real filter the problem amounts (to within a scale integers and the second question is how well are they factor) to approximation by polynomials or rational approximated {Jackson type theorems). For example, functions with integral coefficients. a continuous function f on the interval -1,1 can be This book should make the task of finding out uniformly approximated by polynomials with integral what is known in this field significantly easier as it coefficients if and only if it takes on integral values presents an introduction to most of the known re­ at -1, 0 and +1 and the quantity f(1) + f(O) is divisi­ sults in the area of approximation by polynomials ble by 2. The results regarding the second question with integral (integer) coefficients and pointers to the are very similar to the corresponding results regarding literature for the rest. It is accessible to students at approximation by polynomials with arbitrary co­ the graduate level and above_ efficients. In particular, nonuniform estimates in Volume 17, xi + 160 pages (hard cover) terms of the modules of continuity of the approxi­ List price $28.80, institutional member $21.60, mated function are obtained. individual member $14.40 ISBN 0-8218-1517-2; LC 79-20331 Aside from the intrinsic interest to the pure Publication date: February 1980 mathematician, there is the likelihood of important To order, please specify SU RV/17 N

Prepayment is required for all AMS publications. Order from AMS, P. 0. Box 1571, Annex Station, Providence, Rl 02901, or call toll free 800-556-7774 to charge with Visa or MasterCard. 252 Letters to the Editor

Circular A-21 Mcintyre and Stockman, like the letter from President Giamatti of Yale on 14 June 1978; letters from Richard I submit a resolution passed unanimously by the Atkinson, Director of NSF {also on 14 June 1978), and Yale Mathematics Department and the text referred to Lewis Branscomb, Chairman of the National Science Board in the resolution. (16 May 1980) to Mcintyre; several articles in Science by S. MacLane (Mathematics, University of Chicago) on 10 Robert Szczarba, Chairman October 1980, Giamatti on 28 November 1980, Kenneth Department of Mathematics Brown (UCSF School of Medicine) on 24 April1981, Herb Yale University Gutowsky (Chemistry, University of illinois) on 8 May 1981; editorials in Science by the editor Philip Abelson Reaolution by the Yale Mathematiea Department on 25 April 1980 and by Branscomb {who is also Chief on P8l'IODDel Activity Reporta Scientist at IBM on 8 August 1980; resolutions from at The following resolution was passed unanimously at least 24 academic senates or equivalent faculty bodies the 22 January 1982 meeting of the Yale Mathematics throughout the country; requests for suspension not only Department. in many of the above statem6Ilts (e.g. Branscomb's letter) The Yale Administration has asked us to fill out but also in a letter of 13 June 1980 to Mcintyre ~ Personnel Activity Reports, commonly known as "effort behalf of AAU, NAB, the Delegation for Basic Biomedical reports." We .endorse the Faeulty Penpeetive1 on Circular Research, and the Council of Scientific Society Presidents; A-21 dated 16 November 1981. Specifically, we do numerous letters from CBBP itself {24 November 1980, not accept the fundamental assumption that accounting 6 March 1981, 29 April 1981, for instance); numerous of sponsored research in universities must stem from a letters from individual professors. percentage description of activity, effort, time, or any Our own opinions are in basic agreement with the other similar notion, devoted to separately identifiable perspectives documented above. Therefore we regret that activities such as teaching, research, or administration. OMB has rejected many essential points of view expressed Percentages under any of these names are meaningless in these statements, and also has rejected proposals based and artificial. The important thing is the result of on them or similar views. research, not the relative amount of (whatever) devoted 1. We do not accept the fundamental assumption of to it. The base itself from which the percentage is OMB and HHB that accounting of sponsored research in derived is impossible to determine. Requirements of such universities must stem from a percentage description of percentages cause professors or administrators to draw activity, effort, time, or any other similar notion like and testify to artificial and meaningless distinctions. energy, devoted to separately identifiable activities such If the government bases its accounting for sponsored as teaching, research, or administration. The multiplicity research in universities on spurious categories, then not of names arose from attempts to find appropriate notions only is the accounting of dubious value, but the universities which might satisfy accountants. But percentages under become vulnerable to harmful changes designed to any of these names are meaningless and artificial. The make the spurious distinctions real. These changes important thing is the result of research, not the relative may profoundly alter relationships of faculties toward amount of {whatever) devoted to it. The base itself administrators and toward their academic responsibilities from which the percentage is derived is impossible to by ratifying a change of status from that of "independent determine. Requirements of such percentages cause thinker, partially subsidized so as to have the leisure to professors or administrators to draw and testify to artificial think, to that of a professional, employed to do a job" and meaningless distinctions. A professor working in his (Mackey, letter to Science, 2 September 1966). laboratory with a graduate student is both instructing and For these reasons, the Department of Mathematics doing research. continues to find effort reports offensive intrusive If the government bases its accounting for sponsored meaningless, and contrary to the spirit of sclentific and research in universities on spurious categories, then not academic enquiry. Those of us who agree to complete only is the accounting of dubious value, but the universities these reports do so only because of the possibility that the become vulnerable to harmful changes designed to University Administration will not accept grant awards for make the spurious distinctions real. These changes those who refuse, as reported in Science, 15 January 1982 may profoundly alter relationships of faculties toward in connection with Lang's grant. • The University is forced administrators and toward their academic responsibilities into this position by the threat that federal auditors may by ratifying a change of status from that of "independent at a later date disallow awards to those who refuse to thinker, partially subsidized so as to have the leisure to complete these reports. We find the situation depressing. think, to that of a professional, employed to do a job" (Mackey, letter to Science, 2 September 1966). Even if an Some Faeulty Perspectives on Circular A-21' administrator signs forms for each faculty member, giving 16 November 1981 percentages of half a dozen activities, "it is a sham for the department head to pretend to have firsthand knowledge Faculty perspectives concerning Circular A-21 have and even more of a sham if he should leave the actual been stated many times. Such perspectives are reflected determination of those percentages to an administrative in the 1968 Report of the Goode Task Force, comprised assistant. Government requirements of sham certification of representatives of BOB, DOD, GAO, NSF, HEW, who fill up paper, promote cynicism, and invite future conflicts" contacted faculty members directly; the resolution of the {Mac Lane, letter to Science, 9 October '1.981). National Academy of Sciences {22 April 1980); the Report 2. Percentage proportions estimated in a government of the National Commission on Research; the resolutions supported project proposal are themselves coarse estimates of the AAU Committees on Graduate Education, Research designed to give peer reviewers a general notion of how Management, and Science and Research {20 April 1980); the grant fits into a larger scheme. In "Remarks" to letters from university presidents to OMB Directors the National Commission on Research on 16 March 1979 *Lang proposes instead to sign the following statement: David Goodstein rightly states: "The existing system of "I certify that all expenditures reported herein have been proposals and grants is based on the notion that what made in accordance with the appropriate purposes set happens is that specific ideas for research lead to very forth in the application and award document." (Editors] well-defined projects which then can be supported with

253 a specific amount of money for a specific amount of 1981), thus creating an adversary atmosphere against tl time until that project is finished. That idea is not universities, which in turn is taken as reason for imposu only false but totally pernicious. The only way I know more regulations and ''tight controls." The universiti• of to conduct research is to maintain a certain level are not equipped to deal with this kind of assault on then of expertise in a scientific field, and to follow whatever 5. Once regulations concerning cost transfers or salai new ideas and directions come up as they come up." support are in place, the audits based on meaningless an When academic scientists deal with their counterparts in artificial regulations lead to further misunderstanding government granting agencies, neither side gives too much further adversary proceedings, and further waste of tim' credence to the percentage estimates. When auditors from effort, activity, energy, and money (both governmer HHS impute accounting precision to these estimates, they money and university money needed to contest sue cause scientific harm (unwittingly, but harm nevertheless). audits, which has already happened in the case of COl 3. Some auditors' point of view is that "accomplishing transfers). a research goal or objective does not mean there has been 6. Many scientists (notably Kenneth Brown in h a successful research effort. . . The real test is whether Science article) have expressed the viewpoint that overhea the research effort went through a gauntlet of controlled costs drawn by universities are excessive and detract fun( administrative mechanisms that minimized the risk at from scientific research. The problem of determinin every step of a long haul. This should be management's overhead costs is complicated, and the issue is so techniCJ honest criteria [sic] . . . We can conclude that the process that there is no consensus here. The upward spiral c itself should be the major criterion in measuring past indirect cost rates has triggered aggressive audits of tl research efforts or in the administrative evaluation of the indirect cost components, the largest of which contair proposals for research funding." • "faculty administrative effort." We reject this view. For one thing, it misses 7. The introduction of fictional accounting precisio the difference between creativity and, say, industrial in an environment which is intentionally and beneficial] production; for another, it places the auditors in opposition imprecise will insure continuing disagreements betwee not only to science but to the scientific granting agencies universities and the government. It will hamper researcl of the government. As Atkinson states in his letter: "The divert funds from academic and scientific work t arms length relationship between a federal purchaser and administrative, bureaucratic purposes; place faculties i a contractor is not the same as the federal/university adversary positions to administrators; bury, not reveal, tb relationship ... Yet the proposed changes in A-21 move us few genuine instances of improper use of federal mone~ farther in the direction of converting our grants into cost­ We do not feel that the imposition of inappropriat reimbursement contracts." The National Science Board accounting requirements can be offset by the gener1 and many others have suggested "that the provisions [of A- warning: 21] ... represent the 'procurement' approach, rather than In the use of any methods for apportioning salarie, the 'assistance' approach ..." it is recognized that, in an academic setting, r1 In addition, pressures from several sources, including search, service, and administration are inextricabl the audit agencies, result in grants getting more and intermingled. A precise assessment of factors thf more specific and more and more detailed, thus hurting contribute to costs is not feasible, nor is it expected. the fundamental purpose of government assistance to 'This view is correct, but contradicts what is expecte research (which the scientists want to do anyhow, not for later in the AAU Proposal. (A similar contradictio the government but for society): to make available an exists in the current version of Circular A-21.) It allOVI environment where this research can flourish. Again from government agencies like OMB and HHS to point to sue the Atkinson letter: "Federal audits of universities have a paragraph for public relations purposes when dealin been increased. Practices which were countenanced by. with Congress and the press, as evidence of OMS's an federal auditors for years have now been spotlighted HHS's reasonableness; while audit agencies enforce til and questioned, and as a result, costs have been other paragraphs to the letter when dealing with tb disallowed. Greater and greater emphasis has been universities. Such contradictions have indeed been use placed on recordkeeping and documentation ..." in the past precisely in this fashion. Fred Richards, i The harm done by the separation of the audit and his letter to John Lordan (Chief, Financial Managemer granting processes has been noted by the National Branch of OMB) concerning the latter's testimony of 2 Commission on Research. Scientific granting agencies March 1980 to the House Committee on Science an are considering possibilities already recommended in the Technology, writes: Goode Task Force Report, that "faculty support be As you note, in introducing this document [revise expressed as a lump sum dollar amount without being Circular A-21] roughly a year ago, Mr. Maclntyr related to an accompanying fraction of the investigator's referred to the ''tight new rules" that ''will brin time or effort." We support this trend, and that recom­ uniformity to university accounting and will narr01 mendation. We support the NCR recommendations 4 and the range of accounting alternatives available t 5, both of which address themselves to the "reasonable­ universities." These marvelous things are all t ness, from a research standpoint, of the expenditures be accomplished while "reducing the administrativ for personnel." The key words here and elsewhere are burdens on the university." Two such statemen1 "reasonable" and "fair," distinct from "percentages." following one after the other start an aura of unrealij and 'doublethink' which continues 4. Existing regulations concerning cost transfers already to build. put serious constraints on the use of research funds. Gutowsky in his Science article points out that th For example, several different government agencies may regulatory problems which he has catalogued are coii support a research project together. The science program pounded by what he calls the "bureaucratic syndrome. directors understand the scientific validity of cost transfers He appropriately quotes Scott's words: ''Well-intentione among related projects, but regulations imposed by people will pursue their own bureau's objectives moe earnestly, ignoring auditing agencies hamper scientifically valid use of the the consequences of their actions eve: when those actions funds. Researchers cannot compartmentalize their work conflict with other values protected b government or harm the institutions they are designed in that fashion. Accountants may see "abuse" when none t assist." exists according to the soundest research practices. They communicate these so-called "abuses" to the Congress and We hope there will be people in the government i to the press (as in the Jack Anderson column of 28 August a position to reverse the momentum of the accountant! and to accept a fundamentally different point of vie1 *Philip Kropatkin {Deputy Assistant Inspector General from the one now prevailing to draft audit regulation~ for Auditing at HEW) "Basic research audits," The Internal Otherwise, we see only more trouble ahead, stemming fror Auditor, April 1979. requirements that are impossible to verify satisfactorily.

254 Faculty members who have contributed a significant part of themselves reacting to the impositions of Circular Poliey on Letters to Editor A-21 feel considerable distress at this diversion from scientific and academic achievements. We recognize that Readers who wish to respond to letters published many of our colleagues, perhaps most, fearful of the in this issue are urged to do so before June 1, 1982. possible waste of themselves in "fighting windmills," so Responses received by that date may be edited to reduce destructive of their work, have reacted in the way described repetition and will be considered for publication in the in the Goode Task Force Report: October 1982 issue. On balance, [faculty] attitude is expressed thus: "We Letters submitted for publication in the Notices are think effort reporting is meaningless and useless. It reviewed by the Editorial Committee, whose task is is a waste of time, but if the Government sees a to determine which ones are suitable for publication. real need for it as a requirement for funding, we The publication schedule requires from two to four will cooperate, especially if you make it as simple as months between receipt of the letter in Providence and possible and preferably have someone else do it." publication of the earliest issue of the Notices in which We hope new attitudes in the government will prevail and it could appear. will make such cynicism unnecessary. Publication decisions are ultimately made by majority Our society is beginning to realize the economic vote of the Editorial Committee, with ample provision and human costs of the psychology of ''tight controls" for prior discussion by committee members, by mail or applied with well-intentioned but narrow perspective. at meetings. Because of this discussion period, some The National Administration itself has expressed its letters may require as much as seven months before a commitment to avoid ''unnecessary requirements which final decision is made. interfere with productive research carried out by colleges and universities with public funds." Our perspectives, like The committee reserves the right to edit letters. those in Part ill of the AAU Proposal, are presented not The Notices does not ordinarily publish complaints so much "on behalf of the faculty but on behalf of the about reviews of books or articles, although rebuttals general good of science and the avoidance of needless and and correspondence concerning reviews in the Bulletin encumbering paperwork which threatens to compromise of the American Mathematical Society will be considered seriously scientific research in universities." for publication. Originally signed by: Kenneth Brown (Physiology, Letters should be mailed to the Editor of the UCSF School of Medicine); Irvin Child (Psychology, Notices, American Mathematical Society, Post Office Yale); C. S. Foote (Chemistry, UCLA); David Box 6248, Providence, Rhode Island 02940, and will be Goodstein (Physics, Caltech); H. S. Gutowsky acknowledged on receipt. (Chemistry, University of lllinois); Barclay Kamb (Geology, Caltech); S. Lang (Mathematics, Yale); Calvin Moore (Mathematics, Berkeley); Ray Or­ bach (Physics, UCLA); Fred Richards (Molecular Biophysics, Yale); John Walsh (UCLA School of Medicine). C. Lowell Harriss (Professor Emeritus of Economics, Columbia) was in the Far East on 16 November, and signed the day of his return on 25 November 1981.

LECTURES IN APPLIED MATHEMATICS

NONLINEAR OSCILLATIONS IN BIOLOGY (California Institute of Technology), F. C. Hoppen­ edited by Frank C. Hoppensteadt steadt (University of Utah), P. Waltman (University This seminar, sponsored jointly by the American of Iowa), and A. S. Winfree (Purdue University). Mathematical Society and the Society for Industrial This book is an unusual and useful collection of and Applied Mathematics, was held at the University applied and theoretical articles geared toward intro­ of Utah from june 12 to june 23,1978, and intended ducing the reader to a wide variety of methods in as an introduction to the theory and methods of non­ nonlinear oscillations. It will be of interest to applied linear oscillations and how they are used to study mathematicians, bioengineers, and biophysicists who oscillatory phenomena in the life sciences. A core have a background of undergraduate mathematics series of lectures by L. N. Howard, in-depth case studies (calculus, differential equations), and some graduate by A. S. Winfree and C. Steele and background lectures mathematics (diffusion processes, fluid mechanics). on mathematical topics by j. Guckenheimer, j. K. Hale, It contains summaries of some recent applications of F. C. Hoppensteadt, D. Ludwig and 0. E. Rossler are re­ nonlinear oscillations methods in life sciences. The produced in these proceedings. Additional lectures papers are directed at introducing mathematically on cell metabolism, population dynamics, perturba­ adept scientists to recent methods and results. tion theory, neural sciences, epidemiology and reac­ Volume 17, x + 253 pages tion-diffusion systems were given but without written List price $36.00, institutional member $27.00, record. The program for the seminar was organized individual member $18.00 ISBN 0-8218-1117-7; LC 79-26469 by W. S. Childress (Courant Institute of Mathemati­ Publication date: November 1979 cal Sciences, New York University), D. S. Cohen To order, please specify LAM/17 N Prepayment is required for all AMS publications. Order from AMS, P.O. Box 1571, Annex Station, Providence, Rl 02901, or call toll free 800-556-7774 to charge with Visa or MasterCard.

255 Position Open Assistant Executive Director AMERICAN MATHEMATICAL SOCIETY Providence, Rhode Island The Society intends to employ a mathematical scientist in the above-named position, to assist in the management of the Society's affairs. The initial appointment will be for three years, with the possibility of reappointment thereafter on a term or continuing basis. Qualifications: The ideal candidate would have received a Ph.D. in one of the mathematical sciences within the past ten years (so as to be familiar with the language and trends of contemporary American research mathematics), would have good command of the English language and be capable of writing well and easily, would have both an interest and previous experience (at least at the departmental committee level) in administration, and would have an equable temperament and be able to work harmoniously with mathematicians and nonmathematicians alike. Some previous experience with computers (as word or data processors), editorial procedures or printing would be desirable but is of secondary importance. Responsibility: About 125 people work at the Society's Providence office, and about half of them are concerned with publishing (editorial processing, translation, composition, printing/binding, promotion and order fulfillment). In addition there are departments concerned with meeting arrangements, budgeting and fiscal records, membership services, computer programming and operations, and staff/building services. The person filling this new position will assist the Executive Director and Deputy Executive Director in administering the work of this staff, and in executing the decisions of the Board of Trustees and the Council. Sensitivity for the concerns of the mathematical community is essential since an important part of the job is to facilitate communication between members of the staff and the Trustees, the Council, editorial and other AMS committees, government agencies, and the general mathematical community. Some travel will be involved. Applications and nominations should be sent to Dr. W. J. LeVeque, Executive Director American Mathematical Society P. 0. Box 6248 Providence, RI 02940 Completed applications, including appropriate letters of reference, received by 1 May 1982 will be assured of consideration. The Society is an equal opportunity employer, and has a generous fringe benefit program, including TIAA/CREF. Salary for this position will be commensurate with the background of the appointee.

The name of the chairman of the editorial committee for Mathematical Surveys is incorrectly listed in the 1982 edition of the Mathematical Sciences Administrative Directory. Jane Cronin Scanlon is chairman of the committee.

256 Madison, Aprill6-17, 1982, University of Wisconsin Program for the 794th Meeting

The seven hundred ninety-fourth meeting of the Richard A. Askey, A.O.L. Atkin, R. Balasubramanian, American Mathematical Society will be held at the Bruce C. Berndt, William H. Burge, S. Chowla, University of Wisconsin, Madison, on Friday and P .D. T .A. Elliott, Basil Gordon, Marvin Knopp, Carlos Saturday, April 16-17, 1982. The Association for J. Moreno, K. G. Ramanathan, Robert A. Rankin, Symbolic Logic will also meet on Friday and Saturday. Mark Sheingorn, Dennis Stanton, and Samuel S. Registration and most sessions will be held in the Wagstaff, Jr. Wisconsin Center, located at the corner of Langdon Asymptotic solutions of ordinary differential and Lake Streets. equations, Po-FANG HSIEH, Western Michigan The meeting will be preceded by a Symposium on University. The speakers will be Donatus U. Anyanwu, Several Complex Variables, to be held Monday through H. Gingold, Leon M. Hall, B. J. Harris, P. F. Thursday, April12-15, in the Wisconsin Center. Partial Hsieh, David Ching-Her Lin, D. A. Lutz, R. E. support is anticipated under a grant from the National Meyer, Robert E. O'Malley, Jr., Seymour V. Parter, Science Foundation. The topic for the symposium was T. K. Puttaswamy, W. H. Reid, Maxwell Rosenlicht, selected by the 1980 Committee to Select Hour Speakers Reinhard Schiifke, and Charles Tier. for Western Sectional Meetings, whose members were Paul T. Bateman, William H. Jaco (chairman), Albert Applications of cohomology in number theory, Marden, Mary E. Rudin, and Paul J. Sally, Jr. [See JOHN M. MASLEY, University of Illinois, Chicago page 210 of the February Notices.) The Organizing Circle and University of Notre Dame. The speakers Committee for the symposium, responsible for selecting will be Walter L. Baily, Jr., Robert J. Bond, Gary the speakers and arranging the program, consists Cornell, H. Kisilevsky, William Messing, Dinakar· of Robert C. Gunning, F. Reese Harvey, Raghavan Ramakrishnan, Michael J. Razar, Michael I. Rosen, Narasimhan, Walter Rudin, Yum-Tong Siu (chairman), William Sinnott, and S. Sperber. Wilhelm F. Stoll, and Shing-Tung Yau. Partial differential equations, PAUL H. Invited Addresses RABINOWITZ, University of Wisconsin, Madison. The speakers will be Felix E. Browder, E. DiBenedetto, By invitation of the 1981 Committee to Select Hour Lawrence C. Evans, Ronald Gariepy, Robert Jensen, Speakers for Central Sectional Meetings, there will be Carlos E. Kenig, S. Klainerman, Alan C. Lazer, Paul E. four invited one-hour addresses. The speakers, their Sacks, M. Slemrod, Joel A. Smoller, Bruce Turkington, titles, and the scheduled times of presentation are as and William P. Ziemer. follows: MICHAEL G. CRANDALL, University of Wiscon­ Classical real analysis; DANIEL WATERMAN, sin, Madison, Generalized solutions of Hamilton­ Syracuse University. The speakers will be Peter Bullen; Jacobi equations, 11:00 a.m. Friday. Richard B. Darst, Henry Fast, James Foran, K. M. CASPER GOFFMAN, Purdue University, Some Garg, Paul ·o. Humke, Lee Larson, Cheng-Ming Lee, uses of Sobolev spaces and of Cesari spaces, 1:45 David A. Legg, Jan Marik, C. J. Neugebauer, Togo p.m. Friday. Nishiura, R. J. O'Malley, Michael Schramm, B. S. JAMES S. MILNE, University of Michigan, Ann Thomson, C. E. Wei!, and Robert E. Zink. Arbor, Arithmetic varieties, 11:00 a.m. Saturday. Topics in the theory of functions of a single YASUTAKA SIBUYA, University of Minnesota, complex variable, JACK WILLIAMSON, University Minneapolis, Gevrey expansions and cohomological of Hawaii, Honolulu, and· University of Wisconsin, methods in the theory of asymptotic solutions, 1:45 Madison. The speakers will be Albert Baernstein II, p.m. Saturday. Johnny E. Brown, Albert Edrei, Matts Essen, Stephen All four talks will be given in the auditorium of the D. Fisher, Robert M. Gethner, Bruce Hanson, John Wisconsin Center. Lewis, Joseph Miles, Rao Nagisetty, Richard Rochberg, Special Sessions John Rossi, Li-Chien Shen, Charles S. Stanton, Allen Weitsman, Thomas H. Wolff, and Jang-Mei Wu. By invitation of the same committee, there will be the following seven sessions of selected twenty-minute Contributed Papers papers: There will be seven sessions for contributed ten­ Minimal manifolds, RICHARD L. BISHOP, minute papers. University of Illinois, Urbana-Champaign. The speakers Audio-Visual Equipment will be Josef Bemelmans, Robert Gulliver, Robert Hardt, Nicholas J. Korevaar, Johannes C. C. Nitsche, All session rooms will be equipped with an Philippe Tondeur, Karen K. Uhlenbeck, and Ai-Nung overhead projector and screen. A blackboard will Wang. also be available. Equipment for the preparation The legacy of Srinivasa Ramanujan, DAVID of transparencies will be located at the meeting M. BRESSOUD, Pennsylvania State University, Uni­ registration desk Monday through Friday, but will not versity Park. The speakers will be George E. Andrews, be available on Saturday.

257 Central Madison

1. The Concourse 6. Madison Inn 2. Edgewater Hotel 7. Memorial Union 3. Howard Johnson's 8. Town and Campus Motel Motor Lodge 9. Wisconsin Center 4. Inn on the Park 10. Van Vleck Hall 5. Lowell Hall (Dept. of Math.)

~ = Public Parking

LAHE mononA

258 The Association for Symbolic Logie Single $30-40 Double $40 The Association for Symbolic Logic will meet on Town & Campus Best Westem Motel Friday and Saturday, April16-17, in Room 224 of the State at Frances Street, Madison, WI 53703 Telephone: 608-257-4881 or 800-528-1234 Wisconsin Center. The ASL program will include the Single $36 Double $44 following four invited addresses: C. WARD HENSON, University of Illinois, Urbana­ Food Service Champaign, Banach space model theory, 9:00 a.m. A cafeteria located in the basement of the Wisconsin Friday. Center is open Monday through Friday from 7:30 to DAVID KUEKER, University of Maryland, Some 11:00 a.m. for continental breakfast, and from 11:30 model-theoretic conjectures and stability, 1:45 p.m. a.m. to 12:30 p.m. for lunch; it is not open Saturday Friday. or Sunday. A wider variety of food can be purchased at the Lakeside Cafeteria MENACHEM MAGIDOR, Hebrew University, on the first floor (northeast corner} of the Memorial Union. Jerusalem, Title to be announced, 9:00am. Saturday. The Lakeside cafeteria is open Monday through Friday from 7:00a.m. to 3:00 JOHN STEEL, University of California, Los p.m. and 4:45 to 6:30 p.m., and Sunday from 9:00 a.m. Angeles, Determinacy in the Mitchell models, 1:45 to 1:30 p.m. It ia closed on Saturday. The Tripp p.m. Saturday. Commons, which is on the floor above the Lakeside In addition, the ASL program will include sessions of Cafeteria, specializes in a salad bar where salad is co~tributed twenty- minute papers on Friday morning, paid for by the ounce. Tripp Commons is open only Friday afternoon, and Saturday morning. Monday through Friday from 11:45 a.m. to 1:00 p.m. Registration Also in the Memorial Union is the Ratskeller which serves beer, hamburgers, and sandwiches; it is open The registration desk will be open from 8:30 a.m. Monday through Friday from 7:30a.m. until9:30 p.m., until 4:00 p.m. Monday through Friday, and from Saturday from 8:00 a.m. to 9:30 p.m., and Sunday from 8:30 a.m. until noon on Saturday in the lobby of the 11:30 a.m. to 9:30 p.m. Wisconsin Center. Registration fees for the symposium . Many restaurants are to be found and meeting are: within walking distance of the Wisconsin Center, and a list will be Symposium Only available at the registration desk. Nonmember S15 Parking Members of AMS or ASL $10 Student/Unemployed $ 5 All of the hotels or motels listed above, including Meeting Only Lowell Hall, offer parking for their guests. There is a public parking ramp only a block and a half from the Nonmember $16 Wisconsin Center on Lake Street, between State Street Members of AMS or ASL $10 and University Avenue. Student/Unemployed $ 5 Symposium and Meeting Travel Nonmember $31 Madison is located 150 miles northwest of Chicago Members of AMS or ASL S20 (via Route 1-90} and 80 miles west of Milwaukee (via Student/Unemployed $10 Route 1-94). The Dane County Regional Airport is located five miles northeast of Madison Registration fees only partially cover expenses of and is served by Frontier, Mississippi Valley, Northwest, Ozark, holding meetings. All mathematicians who wish to and Republic Airlines. Transportation between attend sessions are expected to register. the airport and all points in Madison is provided by Bender's Accommodations Limousine Service and Union Cab Company. The trip Blocks of rooms are being held for participants at from the airport takes approximately 20 minutes and the following area motels. Individuals should have the cost per person for the limousine is $2.75, while the made their own reservations prior to the cut-off date of taxi service costs about $6.50 regardless of the number March 15. Rates listed do not include the 4 percent of passengers. Wisconsin State or the 6 percent City of Madison The Alco Bus Company operates buses between taxes, and are subject to possible ..:hange. O'Hare Airport and Madison. Buses are scheduled Howard Johneon's Motor Lodge to depart from O'Hare daily at 9:30 and 11:00 a.m., 525 W. Johnson Street, Madison, WI 53703 2:00, 5:00, 7:00 and 10:00 p.m., and return daily Telephone: 608-251-5511 or 800-654-2000 from Madison at 7:00 and 10:00 a.m., 1:00, 2:30, Single $34 (1 queen bed, 1 person) and 5:30 p.m. The trip in either direction takes Double $39 (1 queen bed, 2 people) approximately 3 hours and costs $10 per person. In Double $43 (2 double beds, 2 people) Madison the Alco buses arrive at and depart from the Lowell Ball (Wisconsin Center Guest House) front entrance of the Memorial Union. Up-to-date 610 Langdon Street, Madison, WI 53706 information may be obtained by calling Alco Bus in Telephone: 608-256-2621 Madison at 608-257-5593. Single $22 Double $26 Ma_dison is also served by Greyhound and Trailways Madison Inn bus hnes, and by the major rental car companies. 601 Langdon Street, Madison WI 53703 The closest Amtrak service is to or from Columbus Telephone: 608-257-4391 ' Wisconsin, located 30 miles northeast of Madison. '

259 PROGRAM FOR THE SYMPOSIUM ON SEVERAL COMPLEX VARIABLES

All sessions will be held in the auditorium of the Wisconsin Center, unless indicated otherwise

MONDAY, APRIL 12 9:00-10:00 Complex Morse theory. HANS GRAUERT, University of Gottingen, Federal Republic of Germany 10:15-10:45 Some properties of the automorphism groups of domains. ROBERT E. GREENE, University of California, Los Angeles 10:15-10:45 Boundary behavior of holomorphic functions in weakly pseudoconvex domains. ALEXANDER NAGEL, University of Wisconsin, Madison (Room 224) 11:00-11:30 Automorphism groups of strongly pseudoconvex domains. STEVEN G. KRANTZ, Pennsylvania State University 11:00-11 :30 Fully integrable Pfaffian systems. MICHAEL B. FREEMAN, University of Kentucky (Room 224) 11 :45-12:15 Stability of the Mange-Ampere foliation. PIT-MANN WONG, University of Notre Dame 11 :45-12:15 A Stein tnanifold topologically but not holomorphically equivalent to a domain in en. WILLIAM R. ZAME, State University of New York, Buffalo (Room 224) 2:00- 2:30 An intrinsic characterization of Kahler manifolds. H. BLAINE LAWSON, JR., State University of New York, Stony Brook 2:00- 2:30 Intrinsic distances. LASZLO LEMPERT, Eotvos University, Budapest, Hungary (Room 224) 2:45- 3:15 Geometry of domains In en. PAUL C. YANG, Indiana University 2:45- 3:15 Polynomial interpolation of analytic functions. THOMAS BLOOM, University of Toronto (Room 224) 3:30- 4:00 The Levi forms and CR extension. ALBERT BOGGESS, University of Michigan, Ann Arbor 3:30- 4:00 Carleson measures and applications. SUN-YUNG A. CHANG, University of California, Los Angeles (Room 224) 4:15- 4:45 The geometry of a complex tangent. SIDNEY M. WEBSTER, University of Minnesota, Minneapolis 4:15- 4:45 A survey of results and open problems for real submanifolds of en with CR singularity GARY A. HARRIS, Texas Tech University (Room 224)

TUESDAY, APRIL 13 9:00-10:00 A survey of the a-Neumann problem. JOSEPH j. KOHN, Princeton University 10:15-10:45 Riemann-Roch theorems. DOMINGO TOLEDO, University of Utah 10:15-10:45 Proper holomorphic self maps of weakly pseudoconvex domains. STEVEN R. BELL, Princeton University (Room 224) 11:00-11:30 Harmonic forms dual to geodesic cycles. YU LIN L. TONG, Institute for Advanced Study 11:00-11:30 Boundary regularity of proper maps. DAVID E. CATLIN, Princeton University (Room 224) 11 :45-12:15 Applications of Kiihler-E/nstein-Calabl- You metrics to algebraic geometry. ANDRE I N. TODOROV, Institute for Advanced Study 11:45-12:15 Geometry of real hypersurfaces. JOHN P. D'ANGELO, University of Illinois, Urbana­ Champaign (Room 224) 2:00- 2:30 Moduli algebra and its applications. STEPHEN SHING-TOUNG Y AU, University of Illinois, Chicago Circle 2:00- 2:30 The heat equation for D. NANCY K. STANTON, University of Notre Dame (Room 224) 2:45- 3:15 Birational theory of hyperplane sections of projective three folds. ANDREW SOMMESE, University of Notre Dame 2:45- 3:15 Some topological restrictions on holomorphic mappings. ERIC D. BEDFORD, Princeton University (Room 224)

260 3:30- 4:00 A class of compact complex surfaces with negative curvature. BUN WONG, Institute for Advanced Study 3:30- 4:00 Plurlsubharmonic functions that vanish on the boundary. NORBERTO KERZMAN, University of North Carolina, Chapel Hill (Room 224) 4:15- 4:45 The Poincare-Lelong equation on complete Kiihler manifolds. NGAIMING MOK, Princeton University 4:15- 4:45 Integral representations of differentiable forms: Some recent developments. R. MICHAEL RANGE, State University of New York, Albany (Room 224)

WEDNESDAY, APRIL 14 9:00-10:00 Extension of closed positive currents. HENRI SKODA, University of Paris VI, France 10:.10-10:40 Inner functions in the ball. WALTER RUDIN, University of Wisconsin, Madison 10:50-11:20 Hilbert spaces of analytic functions. HUGO ROSSI, University of Utah 11 :30-noon Some remarks on q-completeness. HUNG-HSI WU, University of California, Berkeley 1:45- 2:45 How many equations are needed to describe a variety in projective or affine space? MICHAEL SCHNEIDER, University of Bayreuth, Federal Republic of Germany 2:55- 3:25 The Schwarz lemma in several complex variables. HALSEY L. ROYDEN, Stanford University 3:35- 4:05 Defect relations for meromorphic functions on en. BERNARD SHIFFMAN, johns Hopkins University 4:15- 4:45 The 3-Neumann problem on the ball in en. JOHN POLKING, Rice University 4:55- 5:25 Extensions of holomorphlc vector bundles and coupled field equations. R. 0. WELLS, JR., Rice University

THURSDAY, APRIL 15 9:00-10:00 A survey on recent development in differential geometry of Kiihler manifolds. SHING­ TUNG YAU, Institute for Advanced Study 10:10-10:40 Embedding theorem for strongly pseudoconvex CR structure. MASATAKE KURANISHI, Columbia University 10:50-11:20 Peak sets for A .. (D). JOHN E. FORNAESS, Princeton University 11 :30-noon Properties of parabolic manifolds. WILHELM STOLL, University of Notre Dame 1:45- 2:15 Curvature and stability for vector bundles. SHOSHICHI KOBAYASHI, University of California, Berkeley 2:25- 2:55 Highly noncontinuable functions. EDGAR LEE STOUT, University of Washington 3:05- 3:35 Plurisubharmonic functions and capacities. B. A. TAYLOR, University of Michigan, Ann Arbor 3:45- 4:15 Boundary asymptotics of Kiihler-Einsteln metrics. DANIEL M. BURNS, j R., University of Michigan, Ann Arbor 4:25- 5:25 Title not available. G. HENKIN, Academy of Sciences of the USSR, Moscow PROGRAM OF THE AMS SESSIONS

The time limit for each contributed paper in the AMS general sessions is ten minutes. In the special sessions the time varies from session to session and within sessions. To maintain the schedule, the time limits will be strictly enforced. Abstracts for papers presented in AMS sessions at this meeting will be found in the April 1982 issue of Abstracts of papers presented to the American Mathematical Society, ordered according to the num· bers in parentheses following the listings below. For papers with more than one author, an asterisk follows the name of the author who plans to pre­ sent the paper at the meeting.

FRIDAY, 8:00A.M. Special Session on The Legacy of Srinivasa Ramanujan. I, Room 227, Wisconsin Center 8:00- 8:20 ( 1) Mock theta functions and Ramanujan's "lost" notebook. Professor GEORGE E. ANDREWS, Pennsylvania State University, University Park (794-10-54) 8:30- 8:50 2) Ramanujan as a patient. Professor ROBERT A. RANKIN, University of Glasgow, Scotland (794-01-11) 9:00- 9:20 3) Ramanujan's quarterly reports. Professor BRUCE C. BERNDT, University of Illinois, Urbana-Champaign (794-44-14) 9:30- 9:50 4) Some integrals of Ramanujan and extensions, and why we care about them. Pre­ liminary report. Professor RICHARD A. ASKEY, University of Wisconsin, Madison (794-33-2) 10:00-10:20 5) Ramanujan's continued fractions. K. G. RAMANATHAN, Tata Institute of Funda­ mental Research, Bombay, India, and Institute for Advanced Study (794-1 0-82) (Introduced by Professor George E. Andrews) 10:30-10:50 6) Ramanujan's "proof" of the von Staudt-Ciausen theorem. Professor SAMUEL S. WAGSTAFF, JR., University of Georgia (794-10-18)

FRIDAY, 8:00A.M. Session on Several Complex Variables, Room 316, Wisconsin Center 8:00- 8:10 ( 7) Topological type of complex varieties of codimension greater than one. Preliminary report. Professor DENIS BLACKMORE, New jersey Institute of Technology (794-32-76) 8:15- 8:25 8) Analytic equivalence relations. Preliminary report. Professor HANS GRAUERT, University of Giittingen, Federal Republic of Germany (794-32-77) (Introduced by Professor Yum Tong Siu)

FRIDAY; 8:00 A. M. Session on Differential Equations, Auditorium, Wisconsin Center 8:00- 8:10 ( 9) Uniform asymptotic expansions of Whittaker functions. Preliminary report. N. SHAWAGFEH* and Dr. M. L. GLASSER, Clarkson College (794-34-103) (In­ troduced by Professor Mark J. Ablowitz) 8:15- 8:25 ( 1 0) Periodic travelling waves for singularly perturbed predator-prey equations via the Conley index. Professor JOEL A. SMOLLER, University of Michigan, Ann Arbor (794-34-9) 8:30- 8:40 ( 11) An extension of Rockland's hypoel/ipticity theorem to pseudodifferential operators. KENNETH G. MILLER, Wichita State University (794-35-102) 8:45- 8:55 ( 12) Geometry of second order linear partial differential operators. Preliminary report. Dr. GREGORY A. FREDRICKS, Texas Tech University (794-35-12) FRIDAY, 8:30A.M. Special Session on Topics in the Theory of Functions of a Single Complex Variable. I, Room 316, Wisconsin Center 8:30- 8:50 ( 13) Distribution of zeros of holomorphic functions on the unit disc. BRUCE HANSON, University of Wisconsin, Madison (794-30-86) (Introduced by Professor Daniel Shea) 9:00- 9:20 ( 14) Problems about integral means of derivatives of univalent functions. Preliminary report. Professor ALBERT BAERNSTEIN II, Washington University (794-30-34) 9:30- 9:50 ( 15) Meromorphic univalent functions whose ranges contain a fixed disk. jOHNNY E. BROWN, Purdue University (794-30-22)

262 10:00-10:20 ( 16) Starlikeness of a class of holomorphic functions. Professor JOHN LEWIS, Univer­ sity of Kentucky (794-30-88) 10:30-10:50 ( 17) Eigen-values for holomorphic functions. Preliminary report. Professor STEPHEN D. FISHER, Northwestern University (794-30-57}

FRIDAY, 9:00A.M. Session on Analysis and Applied Mathematics, Room 226, Wisconsin Center 9:00- 9:10 ( 18} Bessel functions on Pn. Dr. THOMAS E. BENGTSON, Miami University, Oxford (794-33-78} 9:15- 9:25 ( 19) A simple definition of the Feynman integral with applications. Professor R.H. CAMERON* and Professor D. A. STORVICK, University of Minnesota, Minneapolis (794-28-100} 9:30- 9:40 ( 20} A theory of interval iteration. Professor L. B. RALL, University of Wisconsin, Madison (794-65-5} 9:45- 9:55 ( 21} On one integral equation involved in non-isotropic elasticity. Dr. V.I. FABRIK­ ANT* and Professor T. S. SANKAR, Concordia University (794-73-3) (Introduced by Professor E. Galperin}

FRIDAY, 9:00A.M. Special Session on Classical Real Analysis. I, Room 311, Wisconsin Center 9:00- 9:20 ( 22) Path derivatives: A unified view of certain generalized derivatives. Professor R. J. O'MALLEY*, A. M. BRUCKNER and B. S. THOMSON, University of Wisconsin, Milwaukee (794-26-96} 9:30- 9:50 ( 23} On the level set structure of a continuous function. B.S. THOMSON, Simon Fraser University (794-26-43} 1 0:00-10:20 ( 24) On generalized Peano derivatives. Preliminary report. Professor CHENG-MING LEE, University of Wisconsin, Milwaukee (794-26-16) 10:30-10:50 ( 25) The symmetric derivative. LEE LARSON, Western Illinois University (794-26-59)

FRIDAY, 9:00A.M. Special Session on Partial Differential Equations. I, Auditorium, Wisconsin Center 9:00- 9:20 ( 26) Variants of the Palais-Smale condition in strongly nonlinear elliptic problems. Professor FELIX E. BROWDER, University of Chicago (794-35-92} 9:30- 9:50 ( 27} Some asymptotic problems in fully nonlinear elliptic equations and stochastic con­ trol. Final report. Professor ROBERT JENSEN*, University of Kentucky, and Professor PIERRE LOUIS LIONS, University of Paris, France (794-35-98} 10:00-10:20 ( 28) The exterior Dirichlet problem for a class of degenerate elliptic equations, with applications to geometry. Preliminary report. CARLOS E. KENIG*, and WEI­ MING Nl, University of Minnesota, Minneapolis (794-35-41) 10:30-10:50 ( 29} Application of a Sturm/an theorem for parabolic operators with periodic coeffi­ cients. Preliminary report. Professor ALAN C. LAZER, University of Cincinnati and Univeristy of Miami (794-35-53}

FRIDAY, 10:00 A. M. Session on History and Education, Room 226, Wisconsin Center 10:00-10:10 ( 30} Quadrature and cubature in medieval Near Eastern mathematics. Preliminary re- port. Dr. All A. AL-DAFFA* and Dr. JOHN J. STROYLS, University of Petro­ leum and Minerals, Saudi Arabia (794.()1-7} 10:15-10:25 ( 31} Rules of algebra applied to exponentiation. Preliminary report. DENNIS G. COLLINS, Valparaiso University (794-26-114} 10:30-10:40 ( 32} One prospect for right-brain education in mathematics. PRESTON C. HAMMER*, Grand Rapids, Michigan, and KATE HAMMER KERMAN, Hesperia, Michigan (794-96-117}

FRIDAY, 11:00 A.M. Invited Address, Auditorium, Wisconsin Center 11 :00-12:00 ( 33} Generalized solutions of Hamilton-jacobi equations. Professor MICHAEL G. CRANDALL, University of Wisconsin, Madison (794-35-94}

263 FRIDAY, 1:45 P.M. Invited Address, Auditorium, Wisconsin Center 1:45- 2:45 ( 34) Some uses of Sobolev spaces and of Cesari spaces. Professor CASPER GOFFMAN, Purdue University, West Lafayette (794-28-4)

FRIDAY, 3:00P.M. Special Session on The Legacy of Srinivasa Ramanujan. II, Room 227, Wisconsin Center 3:00- 3:20 ( 35) Poincare series and the vanishing of Ramanujan's function r(n). MARVIN KNOPP, Temple University (794-1 0-25) 3:30- 3:50 ( 36) The value distribution of the differences of additive arithmetic functions. Professor P. D. T. A. ELLIOTT, University of Colorado, Boulder (794-10-47) 4:00- 4:20 ( 37) Congruence properties of modular forms studied by Glaisher and Ramanujan. Pre­ liminary report. Professor BASIL GORDON, University of California, Los Angeles (794-10-65) (Introduced by Professor David M. Bressoud) 4:30- 4:50 ( 38) The Rogers-Ramanujan identities and q-Lagrange inversion. DENNIS STANTON*, University of Minnesota, Minneapolis, and IRA GESSEL, Massachusetts Institute of Technology (794-05-46) 5:00- 5:20 ( 39) Combinatorial interpretations of some identities of the Rogers-Ramanujan type. Dr. WILLIAM H. BURGE, IBM T. J. Watson Research Center (794-05-48) (Intro­ duced by Professor David M. Bressoud)

FRIDAY, 3:00P.M. Special Session on Classical Real Analysis. II, Room 311, Wisconsin Center 3:00- 3:20 ( 40) Thunsdorff's integral inequality for a class of monotone functions. Professor TOGO NISHIURA, Wayne State University (794-26-63) 3:30- 3:50 ( 41) Riemann-Stieltjes integrals of functions of generalized bounded variation. Prelimi­ nary report. MICHAEL SCHRAMM, Syracuse University (794-26-61) 4:00- 4:20 ( 42) Weak-star convergence in the dual of the continuous functions on the n-cube, 1 .;;;; n .;;;; =. Professor RICHARD B. DARST, Stanford University (794-46-97)

4:30- 4:50 ( 43) Best best L~ approximation. Professor DAVID A. LEGG, Indiana University­ Purdue University, Fort Wayne (794-41-74) 5:00- 5:20 ( 44) Schauder bases for LP [0, 1] derived from subsystems of the Schauder system. Preliminary report. Professor ROBERT E. ZINK, Purdue University, West Lafayette (794· 26-1 06) 5:30- 5:50 ( 45) Weighted iterates of the Hardy-Littlewood maximal operator. Preliminary report. Dr. M.A. LECKBAND and Professor C. J. NEUGEBAUER*, Purdue University, West Lafayette (794-43-30)

FRIDAY, 3:00P.M. Special Session on Topics in the Theory of Functions of a Single Complex Variable. II, Room 316, Wiscon· sin Center 3:00- 3:20 ( 46) A remark on the Nevanlinna deficiency. Professor JOSEPH MILES, University of Illinois, Urbana-Champaign (794-30-89) 3:30- 3:50 ( 47) The minimum modulus of meromorphic functions of lower order less than one. Dr. MATTS ESSEN, Uppsala University, Sweden, Dr. JOHN ROSSI*, Purdue Uni· versity, West Lafayette, and Dr. DANIEL SHEA, University of Wisconsin, Madison (794-30-15) 4:00- 4:20 ( 48) Zeros of partial sums of Taylor expansions of entire functions. Professor ALBERT EDREI, Syracuse University (794-30-90) 4:30- 4:50 ( 49) A Polya "shire" theorem for entire functions. ROBERT M. GETHNER, University of Wisconsin, Madison (794-30-87) 5:00- 5:20 ( 50) On a classification of a class of meromorphic functions by their derivatives. Pre­ liminary report. Dr. LI-CHIEN SHEN, California Institute of Technology (794-30-113)

FRIDAY, 3:00P.M. Special Session on Asymptotic Solutions of Ordinary Differential Equations. I, Room B1, Lowell Hall 3:00- 3:20 ( 51) On the swirling flow between rotating coaxial disks: A survey. Professor SEYMOUR V. PARTER, University of Wisconsin, Madison (794-34-32)

264 3:30- 3:50 ( 52} Uniformly valid asymptotic solutions of the Orr-Sommerfeld equation. Professor W. H. REID, University of Chicago (794-34-31} 4:00- 4:20 ( 53} &nach spaces of functions analytic in polydiscs. Professor L. J. GRIMM, University of Missouri, Rolla, and Professor LEON M. HALL*, University of Nebraska, Lincoln (794-32-50} 4:30- 4:50 ( 54} Bounds for functions in Hardy fields. Preliminary report. MAXWELL ROSEN- LICHT, University of California, Berkeley (794-41-36} 5:00- 5:20 ( 55} Global simplification of o singularly perturbed linear ordinary differential system. Professor P. F. HSIEH*, Western Michigan University, and Professor H. GINGOLD, West Virginia University (794-34-75}

FRIDAY, 3:00P.M. Special Session on Partial Differential Equations. II, Auditorium, Wisconsin Center 3:00- 3:20 ( 56} Stability and bifurcation of steady-state solutions for predator-prey equations with diffusion. Professor JOEL A. SMOLLER*, University of Michigan, Ann Arbor, E. CONWAY, Tulane University, and R. GARDNER, University of Massachusetts, Am­ herst (794-35-8} 3:30- 3:50 ( 57} A singular limit arising in steady vortex flow. Preliminary report. BRUCE TURKING- TON, Mathematics Research Center, University of Wisconsin, Madison (794-35-66} 4:00- 4:20 ( 58} The viscosity-capillarity admissibility criterion. Preliminary report. Professor M. SLEMROD, Rensselaer Polytechnic Institute and Mathematics Research Center, Uni­ versity of Wisconsin, Madison (794-35-44} 4:30- 4:50 ( 59} The incompressible limit in nonlinear elasticity. Preliminary report. ProfessorS. KLAINERMAN*, and Professor R. V. KOHN, Courant Institute of Mathematical Sciences, New York University (794-35-93} FRIDAY, 3:00P.M. Session on Combinatorics and Algebra, Room 226, Wisconsin Center 3:00- 3:10 ( 60} Interpolation theorem for the number of endvertices of spanning trees. Professor SEYMOUR SCHUSTER, Carleton College (794-05-1} 3:15- 3:25 ( 61} On the number ofregular configurations. Preliminary report. Dr. YUN-SHYONG CHOW, Brown University (794-06-72} (Introduced by Professor Donald E. McClure} 3:30- 3:40 ( 62} Signso/vobility revisited. VICTOR KLEE*, RICHARD LADNER and RACHEL MANBER, University of Washington (794-15-56} 3:45- 3:55 ( 63} Representations of semigroup actions. Preliminary report. Dr. WALTER S. SIZER, Moorhead State University (794-20-38} 4:00- 4:15 ( 64} Withdrawn

SATURDAY, 8:00A.M. Special Session on Asymptotic Solutions of Ordinary Differential Equations. II, Room 212, Wisconsin Center 8:00- 8:20 ( 65} A new asymptotic decomposition method applied to multi turning point problems with piecewise smooth coefficients. Preliminary report. Professor H. GINGOLD, West Virginia University (794-34-40} (Introduced by Professor Po-Fang Hsieh} 8:30- 8:50 ( 66} Very irregular points. Dr. R. E. MEYER*, University of Wisconsin, Madison, and Dr. j. F. PAINTER, Lawrence Livermore Laboratory, California (794-34-55} (Intro­ duced by Professor Po-Fang Hsieh} 9:00- 9:20 ( 67} Uniform asymptotic solutions of second order linear ordinary differential equations with singular points. Dr. DONATUS U. ANY ANWU, University of Nigeria (794-41-6} (Introduced by Professor Joseph B. Keller} 9:30- 9:50 ( 68} A two point connection problem for o certain nth order differential equation of W. B. Ford's type. Professor T. K. PUTIASWAMY, Ball State University (794-34-20} 10:00-10:20 ( 69} A connection problem foro regular and on irregular singular point of complex ordi­ nary differential equations. Dr. REINHARD SCHAFKE, University of Essen, Federal Republic of Germany, and University of Wisconsin, Milwaukee (794-34-52} (Intro­ duced by Professor D. A. Lutz} 10:30-10:50 ( 70} Shock and transition foyers for nonlinear singularly perturbed systems. Preliminary report. Professor ROBERT E. O'MALLEY, JR., Rensselaer Polytechnic Institute (794-34-27} 26S SATURDAY, 8:00A.M. Session on Number Theory, Room 227, Wisconsin Center 8:00- 8:10 ( 71) Construction of amicable pairs. Preliminary report. Professor DALE WOODS, North- east Missouri State University (794-1 0-21) 8:15- 8:25 ( 72) p-adic continued fractions. Dr. PATRICK J. C. LAMONT, Western Illinois University (794-1 0-71)

SATURDAY, 8:00A.M. Session on Functions of a Complex Variable, Room 316, Wisconsin Center 8:00- 8:10 ( 73) Operators on spaces of analytic functions. Dr. GEORGE A. BRAUER, University of Minnesota, Minneapolis (794-46-1 01) 8:15- 8:25 ( 74) On the oscillations of differential transforms: The Bernstein problem for Hermitian and Laguerre expansions. Preliminary report. CARL PRATHER, Virginia Polytechnic Institute and State University (794-30-35) 8:30- 8:40 ( 75) Extreme points of convex sets ofpotentials. Professor MAYNARD ARSOVE*, Uni­ veristy of Washington, and Professor HEINZ LEUTWILER, Universitat Erlangen­ Ni.irnberg, Federal Republic of Germany (794-31-19)

SATURDAY, 8:30A.M. Special Session on The Legacy of Srinivasa Ramanujan. II I, Room 227, Wisconsin Center 8:30- 8:50 ( 76) On the distribution of the values of certain arithmetical functions. Professor CARLOS J. MORENO, University of Illinois, Urbana-Champaign (794-1 0-1 OS) 9:00- 9:20 ( 77) Ramanujan in Teichmiiller space. Professor L. ALAYNE PARSON, Ohio State Uni­ versity, Columbus, and Professor MARK SHEINGORN*, Baruch College, City Uni­ versity of New York (794-1 0-26) 9:30- 9:50 ( 78) On Ramanujan's function. R. BALASUBRAMANIAN*, University of Illinois, Urbana­ Champaign, and M. RAMMURTY, Tata Institute of Fundamental Research, Bombay, India (794-10-104) 10:00-10:20 ( 79) Ramanujan's modular intuition. Dr. A. 0. L. ATKIN, University of Illinois, Chicago Circle (794-01-45) 10:30-10:50 ( 80) On Pel/'s equation. Preliminary report. ProfessorS. CHOWLA, Institute for Advanced Study (794-1 0-107)

SATURDAY, 8:30A.M. Special Session on Applications of Cohomology in Number Theory. I, Room 138, Wisconsin Center 8:30- 8:50 ( 81) The Riemann-Hurwitz genus formula in the theory of ZP-extensions. Professor WARREN M. SINNOTT, Rutgers University, New Brunswick (794-12-99) 9:00- 9:20 ( 82) The norm map on jacobians. Preliminary report. Professor MICHAEL I. ROSEN, Brown University (794-14-1 09) 9:30- 9:50 ( 83) Cohomologyofgroupsandthecapitulationproblem. Professor ROBERT j. BOND, Boston College (794-12-119) 10:00-10:20 ( 84) The semi-simplicity of certain lwasawa modules. Professor H. KISI LEVSKY, Concordia University (794-12-118) 10:30-10:50 ( 85) Higher regulators and values of zeta functions of curves. Preliminary report. Dr. DINAKAR RAMAKRISHNAN, University of Chicago (794-12-120)

SATURDAY, 8:30A.M. Special Session on Partial Differential Equations. Ill, Auditorium, Wisconsin Center 8:30- 8:50 ( 86) Removable singularities of nonlinear parabolic equations. Preliminary report. Profes­ sor WILLIAM P. ZIEMER, Mathematics Research Center, University of Wisconsin, Madison (794-35-68) 9:00- 9:20 ( 87) c1 +a local regularity for weak solutions of certain degenerate elliptic equations. Pre­ liminary report. Professor E. Dl BENEDETTO, Indiana University, Bloomington (794-35-69) 9:30- 9:50 ( 88) Filtration in a partially saturated porous medium. Preliminary report. Professor EMMANUELE Dl BENEDETTO, Indiana University, Bloomington, and Professor RONALD GARIEPY*, University of Kentucky (794-35-83)

266 10:00-10:20 ( 89} Regularity properties for solutions of certain degenerate PDE. Professor LAWRENCE C. EVANS, University of Maryland, College Park (794-35-13) 10:30-10:50 ( 90} Some existence and nonexistence theorems for solutions of degenerate parabolic equations. Dr. PAUL E. SACKS* and Dr. HOWARD A. LEVINE, Iowa State Uni­ versity (794-35-17} SATURDAY, 9:00A.M. Special Session on Classical Real Analysis. Ill, Room 311, Wisconsin Center 9:00- 9:20 ( 91) Multiplication and transformation of derivatives. Preliminary report. Professor JAN MARIK, Michigan State University (794-26-64} (Introduced by Professor Clifford E. Weil} 9:30- 9:50 ( 92) Some properties of an approximately continuous integral. Dr. PETER BULLEN, University of British Columbia (794-26-42} 10:00-10:20 ( 93} The structure of continuous functions which satisfy Lusin's condition (N}. Pro­ fessor JAMES FORAN, University of Missouri, Kansas City (794-26-39} 10:30-10:50 ( 94} Pseudopotentials with singular support-uniqueness questions. Professor HENRY FAST, Wayne State University (794-26-122} SATURDAY, 9:00 A. M. Special Session on Topics in the Theory of Functions of a Single Complex Variable. Ill, Room 316, Wiscon­ sin Center 9:00- 9:20 ( 95} Approximation of subharmonic functions in Rm with small Riesz mass. Prelimi- nary report. CHARLES S. STANTON, University of Wisconsin, Madison (794-31-84} 9:30- 9:50 ( 96} Subharmonic functions of finite order in space. Professor RAO NAGISETTY*, University of Toledo, and Professor DANIEL SHEA, University of Wisconsin, Mad- ison (794-31-85} 10:00-10:20 ( 97} Covering properties of certain exceptional sets in a half-space. Dr. MATTS ESSEN*, University of Uppsala, Sweden, Professor HOWARD JACKSON, McMaster University, and Dr. PHIL RIPPON, University College, Cork, Ireland (794-31-10} 10:30-10:50 ( 98} Subharmonic functions in c1 +<>domains. JANG-MEI WU, University of Illinois, Urbana-Champaign (794-30-91)

SATURDAY, 9:00A.M. Special Session on Minimal Manifolds. I, Room 109, Wisconsin Center 9:00- 9:20 ( 99} Tori of prescribed mean curvature and the rotating drop. Preliminary report. Pro­ fessor ROBERT GULLIVER, University of Minnesota, Minneapolis (794-49-67} 9:30- 9:50 (1 00} A variational approach to closed, nonparametric surfaces of prescribed mean curva­ ture. Dr. JOSEF BEMELMANS, University of Minnesota, Minneapolis (794-49-73} (Introduced by Professor Robert D. Gulliver} 10:00-10:20 (101) Partition of a convex body by a surface of stationary area. Professor JOHANNES C. C. NITSCHE, University of Minnesota, Minneapolis (794-53-111} 10:30-10:50 (1 02) Convex solutions to nonlinear elliptic boundary value problems. Professor NICHOLAS J. KOREVAAR, Mathematics Research Center, University of Wiscon­ sin, Madison (794-35-29} SATURDAY, 11:00 A.M. Invited Address, Auditorium, Wisconsin Center 11:00-12:00 (103) Arithmetic varieties. Professor JAMES S. MILNE, University of Michigan, Ann Arbor (794-1 0-24}

SATURDAY, 1:45 P.M. Invited Address, Auditorium, Wisconsin Center 1 :45- 2:45 (1 04} Gevrey expansions and cohomological methods in the theory of asymptotic solu­ tions. Professor YASUTAKA Sl BUYA, University of Minnesota, Minneapolis (794-34-95}

267 SATURDAY, 3:00P.M. Special Session on Applications of Cohomology in Number Theory. II, Room 138, Wisconsin Center 3:00- 3:20 (105) Arithmetic groups commensurable with the Hilbert modular group. Preliminary re- port. Professor WALTER L. BAILY, JR., University of Chicago (794-10-81) 3:30- 3:50 (106) Twisted Kloosterman sums and p-adic Bessel functions. Preliminary report. Pro­ fessor A. ADOLPHSON, University of Washington, and ProfessorS. SPERBER*, University of Minnesota, Minneapolis (794-10-115) 4:00- 4:20 (1 07) The f-rank of the real class group of cyclotomic fields. Preliminary report. Profes­ sor GARY CORNELL*, University of Connecticut, Storrs, and Professor MICHAEL I. ROSEN, Brown University (794-12-11 0) 4:30- 4:50 (108) Cocycles associated with Eisenstein series. Dr. MICHAEL J. RAZAR, University of Maryland, College Park (794-12-121) (Introduced by Professor John M. Masley) 5:00- 5:20 (1 09) Cohomologica/ constructs for varieties defined over a local field. Professor WILLIAM MESSING, University of Minnesota, Minneapolis (794-14-116) SATURDAY, 3:00P.M. Special Session on Classical Real Analysis. IV, Room 311, Wisconsin Center 3:00- 3:20 (110) Baire one, null functions. Professor A.M. BRUCKNER, University of California, Santa Barbara, and Professor J. MARIK and Professor C. E. WElL*, Michigan State University (794-26-60) 3:30- 3:50 (111) Properties of functions in terms of bilateral derivates. K. M. GARG, University of Alberta (794-26-58) 4:00- 4:20 (112) Symmetric and a-porous: a characterization. Professor PAUL D. HUMKE*, St. Olaf College, and Professor BRIAN S. THOMSON, Simon Fraser University (794-26-62) SATURDAY, 3:00P.M. Special Session on Topics in the Theory of Functions of a Single Complex Variable. IV, Room 316, Wis­ consin Center 3:00- 3:20 {113) Applications of Baernstein's *-function to the Fredholm equation. Preliminary re- port. Dr. ALLEN WEITSMAN, Purdue University, West Lafayette (794-30-33) 3:30- 3:50 {114) Interpolation sequences in the Bergman space. RICHARD ROCHBERG, Washing­ ton University (794-30-28) 4:00- 4:20 (115) Restrictions of BMO functions. Preliminary report. THOMAS H. WOLFF, Univer­ sity of Chicago (794-26-70) (Introduced by Professor David Leep) SATURDAY, 3:00P.M. Special Session on Asymptotic Solutions of Ordinary Differential Equations. Ill, Room 212, Wisconsin Center 3:00- 3:20 (116) Asymptotic integration of some second order differential equations. Preliminary report. Professor D. A. LUTZ, University of Wisconsin, Milwaukee (794-34-51) 3:30- 3:50 (117) The sufficiency of Matkowsky-condition in the problem of resonance. DAVID CHING-HER LIN, University of Minnesota, Minneapolis (794-34-37) 4:00- 4:20 (118) Bounds for the eigenvalues of Sturm-Liouville equations. Professor B. J. HARRIS, Northern Illinois University (794-34-49) 4:30- 4:50 (119) Asymptotic solution of stochastically perturbed ordinary differential equations. Professor BERNARD J. MATKOWSKY, Northwestern University, Professor CHARLES TIER*, Northwestern University, and Professor ZEEV SCHUSS, Tel Aviv University, Israel (794-34-80) SATURDAY, 3:00 P. M. Special Session on Minimal Manifolds. II, Room 109, Wisconsin Center 3:00- 3:20 (120) Isotropic minimal surfaces In SU(N ). Preliminary report. Professor KAREN K. UHLENBECK, University of Illinois, Chicago Circle (794-53-123) 3:30- 3:50 (121) Some remarks on a model problem for plasticity. Preliminary report. Professor ROBERT HARDT* and Professor DAVID KINDERLEHRER, University of Min­ nesota, Minneapolis (794-35-112)

268 4:00- 4:20 (122) Curvature properties of harmonic foliations. FRANZ W. KAMBER and PHILIPPE TONDEUR*, University of Illinois, Urbana-Champaign (794-57-23) 4:30- 4:50 (123) Minimal surfaces in R4 as holomorphic curves. Preliminary report. AI-NUNG WANG, Michigan Technological University (794-53-79) Paul T. Bateman Urbana, Illinois Associate Secretary

PRESENTERS OF PAPERS AT AMS SESSIONS

Following each name is the number corresponding to the speaker's position on the program • Invited one-hour lecturers * Special session speakers

AI-Daffa, A. A. 30 Fabrikant, V. I. 21 *Lee, C.-M. 24 *Rossi, j. 47 *Andrews, G. E. 1 *Fast, H. 94 *Legg, D. A. 43 *Sacks, P. E. 90 *Anyanwu, D. U. 67 *Fisher, S. D. 17 *Lewis, j. 16 *Schafke, R. 69 Arsove, M. 7 5 *Foran, j. 93 *Lin,D.C.-H. 117 *Schramm, M. 41 *Askey, R. A. 4 Fredricks, G. A. 1 2 *Lutz, D. A. 116 Schuster, S. 60 *Atkin, A. 0. L. 79 *Garg, K. M. 111 Marik, j. 91 Shawagfeh, N. 9 * Baernstei n, A., II 1 4 *Gariepy, R. 88 *Messing, W. 109 *Sheingorn, M. 77 *Baily, W. L., Jr. 1 OS *Gethner, R. M. 49 *Meyer, R. E. 66 *Shen, L.-C. 50 *Balasubramanbn, R. 78 *Gingold, H. 65 *Miles, j. 46 •Sibuya, Y. 1 04 *Bemelmans, j. 100 •Goffman, C. 34 Miller, K. G. 11 *Sinnott, W. M. 81 Bengtson, T. E. 18 *Gordon, B. 37 •Milne, j. S. 103 Sizer, W. S. 63 *Berndt, B. C. 3 Grauert, H. 8 *Moreno, C. J. 76 *Siemrod, M. 58 Blackmore, D. 7 *Gulliver, R. 99 * Nagisetty, R. 96 *Smaller, j. A. 1 0, 56 *Bond, R. j. 83 *Hall, L. M. 53 *Neugebauer, C. j. 45 *Sperber, S. 1 06 Brauer, G. A. 73 Hammer, P. C. 32 *Nishiura, T. 40 *Stanton, C. S. 95 *Browder, F. E. 26 *Hanson, B. 13 *Nitsche, j. C. C. 1 01 *Stanton, D. 38 *Brown, j. E. 15 *Hardt, R. 121 *O'Malley, R. E., Jr. 70 *Thomson, B. S. 23 *Bullen, P. 92 *Harris, B. j. 118 *O'Malley, R. j. 22 *Tier, C. 119 *Burge, W. H. 39 *Hsieh, P. F. 55 *Parter, S. V. 51 *Tondeur, P. 122 Cameron, R. H. 19 *Humke, P. D. 112 Prather, C. 74 *Turkington, B. 57 Chow, Y.-S. 61 *jensen, R. 27 *Puttaswamy, T. K. 68 *Uhlenbeck, K. K. 120 *Chawla, S. 80 * Kenig, C. E. 28 Rail, L. B. 20 *Wagstaff, S. S., j r. 6 Collins, D. G. 31 *Kisilevsky, H. 84 * Ramakrishnan, D. 85 *Wang, A.-N. 123 *Cornell, G. 1 07 * Klainerman, S. 59 *Ramanathan, K. G. 5 *Wei I, C. E. 11 0 •Crandall, M. G. 33 Klee, V. 62 *Rankin, R. A. 2 *Weitsman, A. 113 *Darst, R. B. 42 *Knopp, M. 35 *Razar, M. j. 108 *Wolff, T. H. 115 *Di Benedetto, E. 87 * Korevaar, N. j. 1 02 *Reid, W. H. 52 Woods, D. 71 *Edrei, A. 48 Lamont, P. j. C. 72 * Rochberg, R. 114 *Wu, j.-M. 98 *Elliott, P.D.T.A. 36 *Larson, L. 25 *Rosen, M. I. 82 *Ziemer, W. P. 86 *Essen, M. 97 *Lazer, A. C. 29 *Rosen Iicht, M. 54 *Zink, R. E. 44 *Evans, L. C. 89

AMS TRANSLATIONS-SERIES 2

TWELVE PAPERS IN ANALYSIS B. S. Mitjagin, The structure of subspaces of an The papers and authors are as follows: infinite Hilbert scale S. A. Vinogradov, Properties of multipliers of Couchy­ I. S. Belov, The homotopy type of the linear group Stieltjes integrals and some factorization problems of the Banach space C(rm w 1) for analytic functions V. P. Glusko and 0. M. SmeljanskiT, Coercive solv­ E. M. Dyn'kin, Pseudo-analytic extension of smooth ability of a boundary value problem for a complete functions. The uniform scale degenerate second order differential equation in A. E. Tumanov and G. M. Henkin, Interpolation sub­ Hilbert space manifolds of pseudoconvex manifolds M. M. Malamud and E. R. Cekanovskii, On the linear S. V. Hruscev, Singularities of linear operators in equivolence of Volterra operators in Banach spaces spaces of analytic functions T. V. Paskova, On the completeness of peak-shaped V. M. FaivysevskiT, Structure of ideals in some Schauder systems Banach algebras satisfying a generalized Ditkin condition Volume 115, v + 202 pages (hard cover) List price $35.20, institutional member $26.40, B. S. Pavlov, Dilation theory and spectral analysis of individual member $17.60 nonselfodjoint differential operators ISBN 0-8218-3065-1; LC 80-20715 M. A. Pekker, Resonances in the scatter(ng of acoustic Publicatlon date: November 1980 waves by a spherical inhomogeneity of the density To order, please specify TRANS2/115Q Prepayment is required for all AMS publications. Order from AMS, P.O. Box 1571, Annex Station, Providence, Rl 02901, or call toll free 800-556-7774 to charge with Visa or MasterCard.

269 Bellingham, June 18-19, 1982, Western Washington University Second Announcement of the 795th Meeting

The seven hundred ninety-fifth meeting of the F. H. Hildebrand, K. Tiahrt, and R. L. Jay. The American Mathematical Society will be held at Western second, Topics in mathematics, will be presided over Washington University, Bellingham, Washington, on by E. Newell of the Highline Community College; the Friday and Saturday, June 18-19, 1982. This meeting speakers are E. Zemgalis, L. A. Hinrichs, L. E. Bobisud, will be held in conjunction with a meeting of the and K. 0. Gamon. Mathematical Association of America (MAA). All There will also be two panel discussions, one of which sessions will take place in Bond Hall. is Mathematics and computer science, moderated by P. C. Gilmore of the University of British Columbia; Invited Addresses the panelists include J. Clavert, S. Hedetniemi, and By invitation of the Committee to Select Hour L. G. Stucki. The second panel discussion, Trends Speakers for Far Western Sectional Meetings, there will in graduate programs, will be moderated by R. be two invited one-hour addresses. The speakers, and Kauffman of Western Washington University and the the titles of their talks, are as follows: participants will be D. Bushaw, W. L. Cook, H. E. MICHAEL FREEDMAN, University of California, Reinhardt, and R. M. Schori. San Diego, Bing topology, infinite procedures, and There will be a demonstration by C. Long of the Poincare conjecture in dimension four. Washington State University of video cassettes and MARINA RATNER, University of California, of a project book developed by MAA to answer the Berkeley, Some interactions between ergodic theory high school students' question about mathematics: But and topological geometry. what will I ever use it for? Special Sessions Open House, Banquet and Luneheon By invitation of the same committee, there will be Participants arriving by Thursday evening, June two special sessions of selected twenty-minute papers. 17, are cordially invited to attend an open house at The topics of these special sessions and names of the the home of Betty and John Reay of the Western organizers are: Washington University Department of Mathematics Continuum theory, LEWIS E. WARD, JR., and Computer Science. The Reay residence is located University of Oregon. at 117 Hawthorne Road in Bellingham. Several complex variables, JOHN SCHERK, An open house and display of teaching materials will University of Alberta. be held Friday afternoon in the Mathematics Resource Most of the papers to be presented at these special Laboratory and at the Computer Center. sessions will be by invitation. However, anyone sub­ A social hour at 6:00 p.m. Friday evening, will be mitting an abstract for the meeting who feels that his followed by a banquet at 7:00 p.m. at which salmon or her paper would be particularly appropriate for one will be served as the entree. The featured speaker will of the special sessions should indicate this clearly on be EDWIN HEWITT of the University of Washington; the abstract form and submit it by March 29, 1982, his talk is entitled, Even mathematicians are odd. three weeks before the deadline for contributed papers. The cost of the banquet is $10 per person. There will be a luncheon at noon on Saturday, Contributed Papers at which the featured speaker will be MARCIA P. There will also be sessions for contributed ten­ SWARD, Associate Director of the MAA; the title of minute papers. Abstracts should be sent to the her talk is Like 55, mathematics saves lives. The American Mathematical Society, P. 0. Box 6248, cost for the luncheon is $4.50 per person. Providence, Rhode Island 02940, so as to arrive prior Participants wishing to make reservations for the to the deadline of April 19. Abstracts should be banquet and/or luncheon must do so by writing prepared on the standard form available from the AMS to Dorothy Telles, Department of Continuing Educa­ office in Providence or in departments of mathematics. tion, Western Washington University, Bellingham, Late papers will be accepted for presentation at the Washington 98225. A check or money order must be meeting, but will not appear in the printed program. enclosed and sent so as to arrive not later than Other Organizations June 10. The MAA program will include an invited address Registration by JAMES A COCHRAN of Washington State The registration desk will be located outside of University, entitled A potpourri of eigenvalue results Room 105 in Bond Hall. It will be open from 8:30 -the exploitation of analogies. · a.m. to noon and 1:00 to 4:30 p.m. on Friday, and There will be two MAA special sessions. The from 8:30 to 11:00 a.m. on Saturday. The registration first is Different methods of teaching mathematics, fees will be $6 for members of the AMS or MAA, $8 presided over by Brian Hogan of the Highline for nonmembers, and $2 for students or unemployed Community College; the sp.eakers are M. M. Enneking, mathematicians.

270 Accommodations Evergreen Motel 1015 Samish Way, Bellingham 98225 Housing accommodations and/or meal service will Telephone: 206-734-7671 be available on the campus of Western Washington Single $22 Double $26-$28 University on a prepaid reservation basis as follows: Motel Six A full room and meal plan (cost $45 per person 3701 Byron, Bellingham 98225 double occupancy, or $51 for single occupancy) includes Telephone: 206-734-6940 lodging for two nights (Thursday and Friday, June 17 Single $14.45 Double $18.45 and 18); breakfast, lunch, social hour and banquet Quadruple $21.45 on Friday, June 18; breakfast and buffet luncheon on Park Motel Saturday, June 19. Rooms are located in Ridgeway 101 N. Samish Way, Bellingham 98225 Omega Residence Hall. Each has two single beds, and Telephone: 206-733-8280 all linens are provided, but there is no television or Single $22 Double $24 telephone service. NOTE: A minimum of two nights Double $28 (two queen-sized beds} lodging is required. Pony Soldier Motor Inn Participants not planning to reside on campus 215 N. Samish Way, Bellingham 98225 may reserve individual meals at the following prices, Telephone: 206-734-8830 which include applicable tax. Friday, June 18: 800-732-1249 (Washington) Breakfast $2, lunch $3.50, social hour and banquet $10. 800-426-1028 (Idaho, Nevada, Saturday, June 19: Breakfast $2; buffet luncheon Northern California, Oregon) $4.50. Breakfast on Friday and Saturday will be served Single $28.50 Double $31.50 from 7:15 to 8:15 a.m., and lunch on Friday will be (one queen-sized bed} served from noon to 1:00 p.m. (Times for the Friday Camping is available at the following campgrounds: evening banquet and Saturday luncheon are included Larrabee State Park in the section, Open House, Banquet and Luncheon 245 Chuckanut Drive, Bellingham 98225 on the preceding page.) All meals will be served in Telephone: 206-676-2093 Ridgeway Omega Dining Hall. Bayview State Park Participants who wish to register for the full 1093 Bayview Edison Road, Mt. Vernon, WA 98273 room and meal plan, or for individual meals only, Telephone: 206-757-0227 must send reservations (including specific dates and Birch Bay State Park meals desired) to Dorothy Telles, Department of 5105 Helwig Road, Blaine, WA 98230 Continuing Education, Western Washington University, Telephone: 206-366-5944 Bellingham, Washington 98225, along with a check or Travel money order to cover the cost of the reservations Bellingham is situated 90 miles north of Seattle requested, so as to arrive not later than June 10. All and 50 miles south of Vancouver, British Columbia; reservations will be acknowledged, and will include a both cities have international airports served by major campus map and other relevant information. Written airlines. Two commuter airlines offer several daily requests for refunds will be honored if received prior to flights to Bellingham from Seattle, but there is no June 10. airline service from Vancouver. Passengers arriving in The following area motels are all within a short Bellingham by plane must call a taxi from the airport; drive from the campus, and individuals should make the taxi fare to the campus is approximately $10. reservations directly with the motel of their choice. Greyhound Bus Lines provides several trips each Rates shown do not include tax, and are subject to day from both Seattle and Vancouver. Participants change. arriving at the Greyhound Bus Terminal will find taxis available for the two-mile ride to the campus. Aloha Motel Participants arriving by car should take the Samish 315 N. Samish Way, Bellingham 98225 Way exit from Interstate 5, and follow the signs to Telephone 206-733-4900 the campus. Drivers should stop at the Parking and Single $22 Double $24-$28 Transportation office, located at 21st and West College (one bed} Way, between the hours of 7:00 a.m. and 5:00 p.m. to Coaehman Inn obtain a permit for free parking on campus. 120 N. Samish Way, Bellingham 98225 Telephone: 206-671-9000 Hugo Rossi Single $32.50 Double $36.50 Salt Lake City, Utah Associate Secretary

271 Jacob Goodman, Discrete and computational Invited Speakers geometry and Special Sessions Saul Gorn, Computing theory C. V. Jones, History of mathematics Invited Speakers at AMS Meetings Arne Magnus, Pade approximations and continued fractions The individuals listed below have accepted invita­ N. F. G. Martin, Ergodic theory tions to address the Society at the times and places Jill Mesirov and Robert Bryant, Nonlinear partial indicated. For some meetings, the list of speakers is differential equations in physics and geometry incomplete. Thomas Saaty, Mathematics of complexity and Bellingham, June 1982 noncausal thinking Michael Freedman Marina Ratner S. P. Singh and S. Thomeier, Fixed point theory and applications Toronto, August 1982 H. Tropp, History of computing David W. Boyd Joel L. Lebowitz H. Wilf, Bijective proofs in generalized partition Sun-Yung Alice Chang John W. Milnor theory and enumerative combinatorics Barish-Chandra Brent Pendleton Smith Morris W. Hirsch W. T. Tutte November 1982 Meeting in Monterey (Colloquium Lecturer) Shmuel Winograd DeCidline for considerlltion: To be Clnnounced biology East Lansing, November 1982 Frank C. Hoppensteadt, Mathematical William T. Eaton Jeffrey B. Rauch Simon Hellerstein Monterey, November 1982 David Gieseker Call For Topics Organizers and Topics of Special Sessions 1984 AMS-SIAM SYMPOSIUM Names of organizers of special sessions to be held Some Mathematieal Questions in Biology at meetings of the Society are listed below, along with the topic of the session. Most of the papers presented Suggestions for topics for the May 1984 Symposium at special sessions are by invitation. Other papers will Some Mathematical Questions in Biology should be considered at the request of the author provided be submitted to the AMS-SIAM Committee on that this is indicated clearly on the abstract form and Mathematics in the Life Sciences before the end the abstract is submitted by the deadlines given below. of' May 1982. These deadlines are usually three weeks earlier than The Symposium is held in conjunction with the the normal abstract deadlines for meetings. Papers Annual Meeting of the AAAS in May. The not selected for special sessions will automatically be Chairman of the committee is Robert M. Miura, considered for regular sessions unless the author gives Department of Mathematics, University of British specific instructions to the contrary. Columbia, Vancouver, British Columbia, Canada V6T June 1982 Meeting in Bellingham 1 Y4; other members of the committee are H. Thomas Deadline for considerCition: MCirch B9 Banks, Brown University; Joel E. Cohen, Rockefeller University; Frank C. Hoppensteadt, University of John Scherk, Several complex variables Utah; Joseph B. Keller, Stanford University; Donald Lewis E. Ward, Jr., Continuum theory A. Ludwig, University of British Columbia; Garrett M. August 1982 Meeting in Toronto Odell, Rensselaer Polytechnic Institute; and Charles S. Deadline for considerCition: MCiy 17 Peskin, New York University. Richard A. Askey, The mathematical legacy of Some recent topics in these annual symposia Gabor Szego have been Theoretical and experimental studies in David W. Boyd, Number theory cellular, developmental and population biology (1980), biology Sun-Yung Alice Chang, Classical harmonic analysis Biomechanics and models in developmental (1981), and Neurobiology, the study of the nervous Harvey Friedman, Applications of logic to mathe- (1982). The 1983 Symposium will matics and computer science systems of organisms be on Muscle Physiology.

272 Toronto Meetings, August 21-26, 1982 First Announcement

The August 1982 Joint Mathematics Meetings, The Toronto meetings will be joint meetings including the 86th summer meeting of the AMS, the in a stronger sense than before. AMS and MAA 62nd summer meeting of the Mathematical Association sessions will run concurrently and simultaneously. of America, and the 1982 annual meeting of Pi Mu In addition, the two organizations are sponsoring a Epsilon, will be held August 23-26, 1982 (Monday­ special Joint Session; details about the Joint Session Thursday), at the University of Toronto. The meetings appear later on in this announcement. will be preceded by the AMS Short Course on August 21 and 22 (Saturday and Sunday), 1982. Sessions will The members of the AMS/MAA Joint Program take place on the campus of the University of Toronto. Committee for the Toronto Meeting are Raymond G. Ayoub, Edward J. Barbeau, Jr., Ronald L. Graham, The members of the Local Arrangements Committee Leonard Gillman (chairman), Richard K. Guy, Hugh are Morton Abramson, James G. Arthur, Raymond G. L. Montgomery, George D. Mostow, Everett Pitcher, Ayoub (ex officio), Edward J. Barbeau, Jr. (publicity and Gerald J. Porter. director), L. Terrell Gardner, William J. LeVeque (ex officio), James McCool, Stephen J. Pierce (chairman), 86TH SUMMER MEETING OF THE AMS David P. Roselle (ex officio), Annette Sunter, James R. Vanstone, and John B. Wilker. August 23-26, 1982 Colloquium Leeturea WHERE TO FIND IT PAGE There will be a series of four Colloquium Lectures SUMMER MEETING OF THE AMS 273 presented by MORRIS W. HIRSCH of the University Colloquium Lectures, Primes, Invited Addresses, of California, Berkeley. The title of the lecture series Special Sessions, Contributed Papers, Council will be announced later. The lectures will be given at and Business Meetings, Other AMS Sessions, 1:00 p.m. Monday through Thursday, August 23-26. Joint AMS/MAA Sessions AMS SHORT COURSE 276 Steele Prizes PREREGISTRATION AND HOUSING 274 The 1982 Leroy P. Steele Prizes will be awarded at a session at 4:30p.m. on Wednesday, August 25. TIMETABLE 277 OTHER ORGANIZATIONS 278 Invited Addreaaea AWM, MAA, nME By invitation of the AMS Program Committee, there OTHER EVENTS OF INTEREST 280 will be eight invited one-hour addresses. The list of Book Sales, Summer List of Applicants, speakers and some of the titles follow: Exhibits, Second-hand Book Exchange DAVID W. BOYD, University of British Columbia, INFORMATION FOR PARTICIPANTS 282 Vancouver; SUN-YUNG ALICE CHANG, University University Housing, Food Services, Hotel of California, Los Angeles, HP -spaces in one and Accommodations, Registration at Meetings several variables; BARISH-CHANDRA, Institute CAMPUS MAP 284 for Advanced Study, On the theory of the Whittaker REGISTRATION DESK SERVICES 288 integral; JOEL L. LEBOWITZ, Rutgers University; AMS/MAA Information, Audio-Visual Aid, Assistance, Comments and Complaints, Baggage and Coat Check, Check Cashing, Lost and Found, Local Information, Mail, Personal and Telephone Messages, Transparencies, Visual Index MISCELLANEOUS INFORMATION 288 Athletic Facilities, Book Stores, Camping, Child Care, Crib Rental, Libraries, Local Infonnation, Medical Services, Parking, Social Events, Travel, Weather

IMPORTANT DEADLINES Abltraet., For eomiderati.on for special aealliona May17 or ecmtributed papen June 7 Summer List or Applic:anta July 9 Preregiltration 11nd Bouaing July 9 BouliDg IIIUleellationl (refund or depolit) July 15 Seeond-hand Book Exelumge July 19 Motion• for Buaine11 Meeting July 26 Preregistration IIIUleellationa (50% reftm.d) Auguat 20 Due• credit for noamemben September 26 Morris W. Hirsch, Colloquium Lecturer

273 PREREGISTRATION AND HOUSING -MATHEMATICS MEETINGS HOUSING BUREAU

Those who preregister for either the Joint Mathematics At the suggestion of the AMS Board of Trustees, Meetings or the MAA Minicourses or both will be able to the AMS/MAA Joint Meetings Committee authorized pick up their badges and other material in Toronto after an experimental agreement with a travel service in an 4:00 p.m. on Sunday, August 22, 1982, during the hours attempt to assist participants in obtaining the best the Joint Mathematics Meetings registration desk is open. airline fares possible to and from Toronto. This travel Summer List of Applicants. The AMS will publish service (which has an 800 number) is described on the a Summer List of mathematical scientists seeking following page. All participants are urged to consider employment for distribution at the Toronto meeting in this organization for their airline and hotel reservations. August 1982. This experiment will be evaluated in order to determine To be included in the list, applicants should complete whether it can provide a useful service for members. the special applicant preregistration form form found at the back of this issue of the Notices The completed form Prwegilltration. Preregistration for these meetings must should be mailed with the meeting preregistration form. be eompleted by July 9, 1982. All those wishing to The deadline for receipt of applicant forms is the same as preregister must complete the form which appears at the for the Joint Meetings (July 9, 1982). See the section on back of this issue and submit it along with the appropriate OTHER EVENTS OF INTEREST for more details. preregistration fee(s) to the Mathematics Meetings Housing Mathematics Meetings Housiug Bureau. The form for Bureau in Providence by July 9. requesting university residence hall accommodations will Preregistration fees do not represent an advance be found at the back of this issue. The use of the deposit for lodgings. One must, however, preregister services offered by the Mathematics Meetings Housing for the meetings in order to obtain confirmed residence B·Jre&u requires preregistration for the meetings. Persons hall accommodations through the Maih.,IL

274 The Toronto Meetings Travel Hotline - Call 800-556-6882 In Rhode Island and outside the continental U.S. call 401-884-9500 or Telex 952165 CONVENIENCE, SAVINGS, IMMEDIATE CONFIRMATION ON HOTEL & AIRLINE ARRANGEMENTS Hours of Operation: 9 a.m.-8 p.m. Eastern Time Monday through Thursday, Fridays until 6 p.m. Another Member Service to Assist you if You're Attending the Toronto Meetings and Use a Major Credit Card. One free call answers all your travel questions and supplies you with all your needs, including hotel rooms and/or reduced-rate airline arrangements. Meeting preregistration can only be done through the Mathematics Meetings Housing Bureau, which can not be reached through this 800 number. See facing page for detailed information on how to preregister and obtain university accommodations. THE SUPERSERVICE: Discount travel arrangements, including special fare check service. - Whenever possible savings up to 55 percent. - Guaranteed lowest possible airfare for your itinerary. - Comparison of individual travel plans to discounted fares. - Unbiased selection of airlines so the best arrangements can be made. - Fare check: A special review 30 days prior to your trip and again 15 days prior to insure that you are getting the lowest available airline fare. You will be automatically reticketed if fares drop below your original ticket cost. - Ground transfers. HOTEL: - Immediate confirmation of hotel, room type and rate. - No mail-in forma, no waiting. N.B.: University accommodations must be obtained through the Mathematics Meetings Housing Bureau. THE NECESSITIES: - You must use VISA, MASTERCARD or AMERICAN EXPRESS to utilioe the travel hotline. Please have your card number and expiration date ready when you call. - Remember, you can use this convenient service to purchase your airline tickets and ground transfers, and to make your hotel room reservation. THE GUARANTEE: The loweot fareo, immediate confirmation and individualioed peroonal oervlce. If you have any questions regarding this service, call the Toronto Meetings Travel Hotline - 800-556-6882

JOHN W. MILNOR, Institute for Advanced Study; and Thursday; Nonlinear partial differential equa­ BRENT PENDLETON SMITH, California Institute tions in physics and geometry, JILL MEsmov, In­ of Technology; W. T. TUTTE, University of Waterloo; stitute for Defense Analyses and ROBERT BRYANT, and SHMUEL WINOGRAD, IBM Watson Research Rice University, Wednesday and Thursday; Math­ Center. ematics of complexity and noncausal thinking, Special Sessions THOMAS SAATY, University of Pittsburgh, Monday By invitation of the same committee, there will and Tuesday; Fixed point theory and applications, S. be fourteen special sessions of selected twenty-minute P. SINGH and S. THOMEIER, Memorial University papers. The titles of these special sessions, the names of of Newfoundland, Wednesday and Thursday; History the mathematicians arranging them, and the tentative of computing, H. TROPP, University of Toronto, days they will meet are as follows: Monday and Tuesday; Bijective proofs in generalized The mathematical legacy of Gabor Szeg6, partition theory and enumerative combinatorics, RICHARD A. AsKEY, University of Wisconsin, H. WILF, University of Pennsylvania, Wednesday and Madison, Monday and Tuesday; Number theory, Thursday. DAVID W. BOYD, University of British Columbia, Most of the papers to be presented at these Vancouver, Monday and Tuesday; Classical harmonic special sessions will be by invitation; however, anyone analysis, SUN-YUNG ALICE CHANG, University contributing an abstract for the meeting who feels of California, Los Angeles, Monday and Tuesday; that his or her paper would be particularly appropriate Applications of logic to mathematics and com­ for one of these sessions should indicate this clearly puter science, HARVEY FRIEDMAN, Ohio State on the abstract, and should submit it by May University, Tuesday and Wednesday; Discrete and 17, three weeks earlier than the normal deadline computational geometry, JACOB GOODMAN, City for eontributed papers, in order that it may be College (CUNY), Wednesday and Thursday; Comput­ considered for inclusion. ing theory, SAUL GORN, University of Pennsylvania, Monday and Tuesday; History of mathematics, C. Contributed Papers V. JONES, University of Toronto, Monday and Tues­ day; Pade approximations and continued fractions, There will be sessions for contributed papers on ARNE MAGNUS, Colorado State University, Wednes­ Monday afternoon after 2:00 p.m., Tuesday morning day and Thursday; Ergodic theory, N. F. G. MAR­ untilll:OO a.m., Wednesday afternoon, and Thursday TIN, University of Virginia, Charlottesville, Wednesday morning and afternoon. Abstracts should be prepared

275 American Mathematical Society Short Course Series Statistieal Data Analysis August 21-22,1982 The American Mathematical Society, in conjunction with its eighty-sixth summer meeting, will present a one and one-half day short course entitled Statistical Data Analysis on Saturday and Sunday, August 21 and 22, 1982, at the University of Toronto. The program is under the direction of Ram Gnanadesikan, and will include lectures by Ram Gnanadesikan, Paul A. Tukey, Colin L. Mallows, Joseph B. Kruskal, and Jon R. Kettenring, all from Bell Laboratories, Murray Hill. Statistical data analysis includes a wide variety of methods for analyzing data, both to answer specific questions posed before the data are available, and also to discover significant features of the data which were not anticipated ahead of time. Useful methods range from extremely simple to mathematically sophisticated. Work in this field ranges from straightforward applications, through ingenious applications and special adaptation of existing methods, to the development of totally new methods. Many bodies of data do not yield up their secrets to standard methods, so applied statisticians find it important to stay in contact with new methodology. Useful new methods often result from the challenge posed by a puzzling set of data, so methodologists find it important to stay in contact with applications. Often methodological innovation and penetrating insight into substantive problems go hand in hand. The ultimate goal of statistical theory is the analysis of data, but for several decades attention has been focused on mathematical solutions to some rather limited intermediate goals. The emerging field of "data analysis" pays renewed attention to the ultimate goals. Recent developments have made major contributions to everyday statistical practice and have provided many new intermediate goals worthy of attention. This course will discuss several of these developments. The course will consist of a 30-minute introduction, six 75-minute lectures, and a 45-minute summary and open discussion. Ram Gnanadesikan will present the introduction and summary, Paul Tukey will speak about graphical techniques, Colin Mallows about robust methods, Joseph Kruskal about multilinear models, and Jon Kettenring will present a case study. For further information, see the synopses of the talks or browse through some of the carefully selected references in this issue of the Notices on pages 291-292. Some acquaintance with classical statistics will be presumed, including basic probability theory and the ideas of estimation, hypothesis testing, regression analysis, analysis of variance, and correlation. The short course was recommended by the Society's Committee on Employment and Educational Policy, whose members are Lida K. Barrett (chairman), Irwin Kra, Robert W. McKelvey, Donald C. Rung, Robert J. Thompson, and Barnet M. Weinstock. The short course series is under the direction of the CEEP Short Course Subcommittee, whose members are Stefan A. Burr, Ronald L. Graham, Robert W. McKelvey, Cathleen S. Morawetz, Barbara L. Osofsky, and Philip D. Straffin, Jr. The short course is open to all who wish to participate upon payment of the registration fee. There are reduced fees for students and unemployed individuals. Please refer to the section entitled INFORMATION FOR PARTICIPANTS for details.

276 TIMETABLE The purpose of this timetable is to provide assistance to registrants in the selection of arrival and departure dates. The program, as outlined below, is based on information available at press time.

AMERICAN MATHEMATICAL SOCIETY SHORT COURSE SERIES

SATURDAY, August 21 STATISTICAL DATA ANALYSIS 11:00 a.m. - 4:00p.m. REGISTRATION 2:00p.m. - 2:30p.m. Introduction and summary Ram Gnanadesikan 2:30p.m. - 3:45p.m. Graphical methods Paul A. Tukey 3:45p.m. - 4:15 p.m. Break 4:15p.m. - 5:30p.m. Graphical methods Paul A. Tukey

SUNDAY, August 22

8:00a.m. - 2:00p.m. REGISTRATION 9:00a.m. - 10:15 a.m. Robust methods Colin L. Mallows 10:15 a.m. - 10:45 a.m. Break 10:45 a.m. - noon Robust methods Colin L. Mallows noon - 1:30 p.m. Lunch 1:30 p.m. - 2:45p.m. Multilinear models Joseph B. Kruskal 2:45p.m. - 3:15p.m. Break 3:15p.m. - 4:30p.m. A case study Jon R. Kettenring 4:30 p.m. - 5:15p.m. Summary and open discussion Ram Gnanadesikan and audience

JOINT MATHEMATICS MEETINGS

SUNDAY, August 22 American Mathematical Society Mathematical Association of America 9:00 a.m. - 4:00p.m. Board of Governors Meeting 9:00a.m. - 5:00p.m. Minicourse iH 4:00p.m. - 8:00p.m. REGISTRATION 4:00p.m. - 8:00 p.m. AMS Book Sale MAA Book Sale 5:00 p.m. - 10:00 p.m. Council Meeting 7:00p.m. - 10:00 p.m. Minicourse #2

MONDAY, August 23 AMS MAA 8:00 a.m. - 4:30p.m. REGISTRATION 8:00a.m. - 4:30p.m. AMS Book Sale IMAA Book Sale 8:30a.m. - 8:35 a.m. WELCOME ADDRESS 8:40a.m. - 9:40a.m. Invited Address Title to be announced John w. Milnor 8:40a.m. - noon Contributed Paper Sessions 9:50a.m. - 10:50 a.m. Invited Address On the theory of the Whittaker integral Harish-Chandra 11:00 a.m. - noon Invited Address Hp spaces in one and several variables Sun-Yung Alice Chang 1:00 p.m. - 2:00p.m. Colloquium Lecture I Title to be announced Morris W. Hirsch 1:00 p.m. - 5:00 p.m. EXHffiiTS I

277 on the standard AMS form available from the AMS who is to vote at a meeting is thereby identifying office in Providence or in departments of mathematics, himself as and claiming to be a member of the and should be sent to the American Mathematical American Mathematical Society. For additional Society, Post Office Box 6248, Providence, Rhode information on the Business Meeting, please refer to Island 02940, so as to anive by the abstract the announcement titled Committee on the Agenda for deadline of June 7. Members are reminded that a Business Meetings. charge of $12 is imposed for retyping abstracts that are not in camera-ready form. ACTMTIES OF OTHER ORGANIZATIONS Late papen will not be accepted. The Mathematical Association of America (MAA) will hold its 62nd summer meeting August Audio-Visual Equipment 23-26 (Monday-Thursday). The Business Meeting of Rooms where special sessions and contributed paper the MAA will take place at 4:30 p.m. on Tuesday, sessions will be held will be equipped with an overhead August 24, at which the Carl B. Allendoerfer, Lester projector, screen, and blackboard. R. Ford, and George P6lya awards will be presented. Presenters of ten- or twenty-minute papers are A series of three Earle Raymond Hedrick Lectures strongly urged to use the overhead projector rather will be given by JAMES W. CANNON of the than the blackboard for their presentation in order University of Wisconsin, Madison. The title of this to obtain maximum visibility by all members of the series of three lectures will be announced later. audience of the material being presented. The MAA will schedule sessions for contributed papers. There will be four sessions, on the following Other AMS Seasions topics: At the invitation of the AMS Program Committee, The undergraduate mathematics curriculum; ETTORE F. INFANTE, Division Director of the Special concerns: remediation, articulation, and Mathematical and Computer Sciences Section of the math anxiety; National Science Foundation, will speak at 8:30 p.m. The 'USe of computers in undergraduate mathe­ on Wednesday, August 25. matics instruction; Classroom notes. Joint AMS/MAA Sessions Papers submitted for these sessions will be refereed. The AMS and MAA are jointly sponsoring a series To submit a paper, send the following information of one-hour addresses on topics in the history of before June 7, 1982 to the Mathematical Association mathematics. The speakers and the titles of their talks of America, 1529 18th Street, N.W., Washington, DC are: 20036: title; intended session; a one-paragraph abstract C. TRUESDELL, Johns Hopkins University, The influence of elasticity on analysis. Committee on the Agenda for Bullneas Meetings J. BARKLEY ROSSER, Mathematics Research The Society has a Committee on the Agenda for Center, University of Wisconsin, Madison, Mathe­ Business Meetings. The purpose is to make Business matics and mathematicians in World War II. Meetings orderly and effective. The committee does not have legal or administrative power. It is intended GEORGE W. WHITEHEAD, Massachusetts In­ that the committee consider what may be called "quasi­ stitute of Technology, Homotopy theory: the first political" motions. The committee has several possible twenty-five years. courses of action on a proposed motion, including but JEAN A DIEUDONNE, Nice, France. The work not restricted to of Bourbaki during the past thirty years. (a) doing nothing; to arrive Courant Institute of Mathe­ (b) conferring with supporters and opponents PETER D. LAX, at a mutually accepted amended version to be circulated matical Sciences, New York University, The 1982 in advance of the meeting; International Congress of Mathematicians. (e) recommending and planning a format for debate Report on the winners of the 1982 Fields Medals. to suggest to a Business Meeting; (Speakers to be announced.) (d) recommending referral to a committee; (e) recommending debate followed by referral to a Council Meeting committee. The Council of the Society will meet at 5:00 p.m. on There is no mechanism that requires automatic Sunday, August 22, in the Governing Council Chamber submission of a motion to the committee. However, if a of Simcoe Hall. motion has not been submitted through the committee, it may be thought reasonable by a Business Meeting to Businesa Meeting refer it rather than to aet on it without benefit of the advice of the committee. The Business Meeting of the Society will take The committee consists of Everett Pitcher (chairman), place immediately following the Steele Prize Session Marian B. Pour-El, David A. Sanchez, and Guido L. on Wednesday, August 25, in the Medical Sciences Weiss. Auditorium. The secretary notes the following In order that a motion for the Business Meeting of resolution of the Council: Each person who attends a August 25, 1982, receive the service offered by the it should be in the Society shall be willing and committee in the most eft'eetive manner, Business Meeting of the hands of the secretary by July 26, 1982. able to identify himself as a member of the Society~ Everett Pitcher, Secretary In further explanation, it is noted that each person

278 TIMETABLE MONDAY, August 23 American Mathematical Society I Mathematical Association of America 2:10 p.m. - 5:30 p.m. AMS/MAA JOINT SESSION ON THE HISTORY OF MATHEMATICS 2:10p.m. The influence of elasticity on analysis C. Truesdell 3:20p.m. Mathematics and mathematicians in World War II J. Barkley Rosser 4:30p.m. Homotopy theory: the first twenty-five years George W. Whitehead 2:10p.m. - 5:30 p.m. Special Sessions Sessions for Contributed Papers I AMS/MAA JOINT SESSION ON THE HISTORY OF MATHEMATICS 7:30 p.m. - 8:30p.m. The work of Bourbaki during the past thirty years JeanA. Dieudonn~ 8:45 p.m. BEER PARTY TUESDAY, August 24 AMS I Other Organizations 8:30a.m. - 4:30 p.m. REGISTRATION 8:30a.m. - 4:30 p.m. AMS Book Sale \IVIAA Book Sale 8:30 a.m. - 4:30 p.m. EXHIBITS 8:40 a.m. - 9:40 a.m. MAA - Invited Address 8:00 a.m. - 10:50 a.m. Special Sessions Sessions for Contributed Papers 9:50 a.m. - 10:50 a.m. MAA - Invited Address 11:00 a.m. - noon MAA - Hedrick Lecture I Title to be announced James W. Cannon 1:00 p.m. - 2:00 p.m. Colloquium Lecture II Title to be announced Morris W. Hirsch 2:10p.m. - 3:10 p.m. MAA - Invited Address 2:10 p.m. - 3:10 p.m. Sessions for Contributed Papers 3:20p.m. - 4:20 p.m. Invited Address MAA - Contributed Paper Sessions Title to be announced David W. Boyd 4:30 p.m. - 5:30 p.m. MAA - Business Meeting 7:00 p.m. - 10:00 p.m. Pi Mu Epsilon - Reception 7:00 p.m. - 10:00 p.m. MAA - Minicourse 112 7:30 p.m. - 10:30 p.m. AMS/MAA JOINT SESSION 7:30p.m. The 1982 International Congress of Mathematicians Peter D. Lax 8:30p.m. Report on the Winners of the 1982 Fields Medals

WEDNESDAY, August 25 AMS Other Organizations

7:45 a.m. - 8:30 a.m. Association for Women in Mathematics Breakfast and Membership Meeting 8:30 a.m. - 4:30 p.m. REGISTRATION 8:30 a.m. - 4:30 p.m. AMS Book Sale I MAA Book Sale 8:30 a.m. - 4:30 p.m. EXHIBITS 8:40 a.m. - 9:40 a.m. Invited Address Title to be announced Shmuel Winograd 8:40a.m. - 9:40 a.m. A '-''M - Panel Discussion 8:40 a.m. - 10:50 a.m. MAA - Contributed Paper Sessions 9:00 a.m. - 11:30 a.m. liME - Contributed Paper Session 9:50 a.m. - 10:50 a.m. Invited Address Title to be announced W. T. Tutte

279 (for distribution at the meeting); a one-page outline; the notebooks at no charge. Books for sale must be and a list of special equipment required. Late papers listed on separate pages from books wanted (as many will not be aeeepted. of either per page as one wishes), and the lists made The MAA is also planning two minicourses. The up on 8.5 inch by 11 inch pages. first will be held all day on Sunday, August 22, and the Please include the information below: second from 7:00 p.m. to 10:00 p.m. Sunday evening, Books Offered: Name, address, telephone, will or August 22, and Tuesday evening, August 24. Further will not be at the meeting. Author, title, publisher, details are not yet available. year of publication, condition of book (for example The minicourses are open only to persons who have slightly used, annotated lightly or heavily, like registered for the Joint Mathematics Meetings and paid new), price or books wanted in trade. the registration fee. The minicourses have separate Books Wanted: Name, address, telephone, will or registration fees of $15 each, and are limited to 30 will not be at the meeting. Author, title, publisher, participants each. edition, price one is willing to pay. The MAA is planning a banquet for individuals who Lists may be sent to the Promotion Department of have been members of the Association for twenty-five the Society until July 19, or may be brought to the years or more. The banquet will take place Wednesday meeting. If brought to the meeting, two copies of each evening, August 25. Details will appear in a later issue. page should be supplied so that duplicate notebooks Pi Mu Epsilon (liME) will hold its annual meeting can be maintained. on Wednesday and Thursday, August 25 and 26. The Please send your lists to: Promotion Department, J. Sutherland Frame Lecture will be given at 8:30 p.m. AMS, Post Office Box 6248, Providence, Rhode Island on Wednesday. 02940. Make checks payable to the AMS. If you The Association for Women in Mathematics have questions, call Phoebe Murdock, 401-272-9500, (AWM) will hold a panel discussion at 8:40 a.m. extension 237. on Wednesday, August 25. The AWM membership meeting will take place in conjunction with a breakfast Summer List of Applicants at 7:45a.m. on Wednesday. At the direction of the AMS-MAA-SIAM Committee on Employment Opportunities, which is charged with OTHER EVENTS OF INTEREST operation of the Employment Register and with Book Sales the publication Employment Information in the Books published by the AMS and the MAA will Mathematical Sciences, the Society will publish be sold for cash prices somewhat below the usual a Summer List of mathematical scientists seeking prices when these same books are sold by mail. employment, for distribution at the Toronto meeting These discounts will be available only to registered in August 1982. participants wearing the official meeting badge. VISA Copies of the 1982 summer list will be available at and MASTERCARD credit cards will be accepted the Transparencies section of the registration desk for for book sale purchases at the meeting. The book $2. Following the meeting, they may be purchased sales will be open the same days and hours as the from the AMS Office in Providence for $3. This list Joint Mathematics Meetings registration desk, and are should prove useful to employers who have last minute located in the meeting registration area. openings in the latter part of the summer or in the fall. Exhibits The applicant preregistration resume at the back of this issue of the Notices is supplemented by a The book and educational media exhibits will be coded strip summarizing the information contained in open from 1:00 p.m. to 5:00p.m. on Monday, August it. Please be sure to fill in the summary strip in 23, and from 8:30 a.m. to 4:30 p.m. on Tuesday addition to completing the resume form itself, which and Wednesday, August 24-25. All participants are will be posted at the meeting. The strip provides an encouraged to visit the exhibits during the meeting. abbreviated version of the information on the form Second-hand Book and Journal Exchange and is used to prepare a computer-printed list of At the Joint Books and Journals display in the preregistered applicants called the Summer List of exhibit area, notebooks will be available with lists of Applicants. books on mathematics for sale or being sought. There Great care should be taken in preparing the coded will be separate notebooks of books for sale and books strip as well as the resume form in order to assure that wanted with names and addresses of the owners (or the listings are readable. Please study the instructions seekers). The details of the transactions themselves carefully before filling out the form. are to be arranged by the participants, and the AMS The deadline for receipt of applicant forms is will not accept responsibility for settling disputes if July 9, 1982. arrangements go awry. The applicant preregistration resume form and the It is necessary to charge a small fee to cover the cost preregistration form for the Joint Meetings will be of preparing the notebooks. Each person participating reprinted in the May 1982 issue of the publication who will not be at the meeting is asked to pay $2 for Employment Information in the Mathematical the first page, and $1 for each additional page (one Sciences. side is one page). Those who will attend the meeting Instead of an Employment Register at the Summer may bring their lists with them and insert them into Meeting in Toronto, there will be an opportunity for

280 TIMETABLE

WEDNESDAY, August 25 American Mathematical Society Other Organizations 11:00 a.m. - noon MAA - Hedrick Lecture II Title to be announced James W. Cannon noon - 1:00 p.m. liME - Council Luncheon 1:00 p.m. - 2:00 p.m. Colloquium Lecture III Title to be announced Morris W. Hirsch 1:00 p.m. - 4:20 p.m. Special Sessions Sessions for Contributed Papers 2:10p.m. - 3:10 p.m. MAA - Invited Address 3:20p.m. - 4:20p.m. MAA - Invited Address 4:30 p.m. - 6:00 p.m. Steele Prize Session and Business Meeting 5:30p.m. - 8:30 p.m. MAA - Banquet for 25-Year Members 6:30p.m. - 8:15 p.m. liME - Banquet 7:00p.m. - 10:00 p.m. MAA - Section Officers Meeting 8:30p.m. - 9:30 p.m. liME - J. Sutherland Frame Lecture 8:30 p.m. - 9:30 p.m. Title to be announced Ettore F. Infante

THURSDAY, August 26 AMS Other Organizations

8:00 a.m. - 9:00 a.m. liME - Dutch Treat Breakfast 8:30 a.m. - 1:30 p.m. ASSISTANCE & INFORMATION DESK 8:40 a.m. - 9:40 a.m. MAA - Invited Address 8:00a.m. - noon Special Sessions Sessions for Contributed Papers 9:10 a.m. - noon IIME - Contributed Paper Session 9:50 a.m. - 10:50 a.m. MAA - Invited Address 11:00 a.m. - noon MAA - Hedrick Lecture III Title to be announced James W. Cannon 1:00 p.m. - 2:00 p.m. Colloquium Lecture IV Title to be announced Morris W. Hirsch 1:00 p.m. - 2:00p.m. MAA - Contributed Paper Sessions 2:10p.m. - 3:10 p.m. MAA - Invited Address 2:10p.m. - 3:10p.m. Sessions for Contributed Papers

3:20 p.m. - 4:20p.m. Invited Address Title to be announced Brent Pendleton Smith 3:20p.m. - 5:20 p.m. MAA - Contributed Paper Sessions 3:30 p.m. - 5:00 p.m. IIME - Contributed Paper Session 4:30p.m. - 5:30 p.m. Invited Address Title to be announced Joel L. Lebowitz

281 posting of both applicant resume forms and employers at Knox College at a special rate are limited to one announcements of open positions in or near the main large room containing 7 single beds. (See Types of meeting registration area. There will be no special Accommodations on the facing page.) room set aside for interviews. No provisions will be There are three types of accommodations available made by the Society for interviews: arrangements will for participants at the University of Toronto: air­ be the responsibility of each employer and applicant. conditioned rooms, non-air-conditioned rooms, and Messages may be left in the message box located in the family units at Scarborough College, a half-hour's to registration area. one hour's drive by auto, or one hour's to one-hour­ Special applicant and employer forms will be avail­ and-a-half's ride on public transportation at the height able at the Transparencies section of the registra­ of the rush hours (7:00 a.m. to 9:30 a.m. and 3:30 p.m. tion desk both for applicants to post resumes and to 6:30p.m.). for employers to post forms announcing positions. Scarborough College is located about 17 miles from Employers who do not plan to attend, but who wish to the University of Toronto in a rural area just south of display literature only, may do so at no charge. This route 401. There is free parking for participants near material must, however, be received in the Providence the town house units on campus. There are eleven office no later than July 9, 1982. Information cannot units; each unit is fully equipped for housekeeping. be taken over the telephone, either in Providence after There is no maid service provided. The town houses July 9, or at the meeting. contain 4 or 6 single beds, or 2 singles and 2 doubles Applicants who submit an applicant form, but do for a total of 6 occupants. Parents may bring cribs for not plan to attend the meeting will be listed on the infants; however, cribs may also be rented. (See section for printed list only. There is no provision made on Crib Rental.) Bed linen is provided, as are towels, the posting resumes for participants who do not attend face cloths, and soap for those participants paying a meeting. daily rate; however, towels, face cloths and soap INFORMATION FOR PARTICIPANTS are not included in the weekly rates. (See Types of Accommodations.) It may also be advisable to Univenity Housing bring coat hangers. Scarborough College is northeast Please refer to the map of the campus included in of Toronto and can be reached from route 401 east this meeting announcement for location of the following or west by taking exit 61. Go south on Morningside residences: Wetmore, Wilson, Whitney, Devonshire, Sir Avenue and turn left on Military Trail. The campus Daniel Wilson, and Margaret Addison Halls, as well as is located south of Ellesmere Road on right. For those those in Knox, Trinity and St. Michael's Colleges. arriving from the U.S. either from Buffalo or Niagara Participants desiring confirmed reservations for on­ Falls, take the Queen Elizabeth Way (QEW). Stay on campus housing must preregister prior to the July 9, the QEW through Toronto to Don Valley Parkway to 1982 deadline. Rooms may be available for those who route 401. Proceed east to exit 61 and go south on do not preregister, but this cannot be guaranteed. Morningside Avenue as stated above. No university residence halls may be occupied prior The famous Metropolitan Toronto Zoo is located to August 20, with the exception of Scarborough within a bus ride of the Scarborough campus, as is the College, where families or groups may take up Ontario Science Center. Please note that the exact residence on August 19. Rates for some residence fare of 75 cents is required for bus and subway fare. halls include breakfast; others do not. Rooms in St. The university and the respective residence halls are Michael's College may not be occupied until August 21; not responsible for articles left behind after check-out. therefore, participants in the AMS Short CoU1"8e The university regrets that it is unable to provide or othen are advised to choose from among the porters to assist participants with their luggage. other residence halls listed below if they plan to In each residence hall (with the exception of Knox arrive on August 20. All participants must be checked College which does not supply towels, face cloths out of the residence halls in St. Michael's College, or soap), two sheets, a pillow, one pillowcase and Trinity College, New College, Scarborough College, blanket are provided for each bed occupied, as well as Daniel Wilson Halls and Whitney, Devonshire and Sir a set of towels, soap and drinking glass. No face cloths The exceptions are by noon on Friday, August 27. are supplied. It is also suggested that the participant residing in Knox College and in those participants bring clothes hangers in the event there are none in the residence halls in Victoria University who may check room assigned. Housekeeping will clean rooms daily, out a day later at noon on August 28. Check-out but will not make the beds. Rooms are equipped with times on other days is also noon, and anyone failing to desks, chairs, dressers, and lamps, and have either one check out by this time will be charged an additional or two single beds. There are elevators serving each night's lodging by the university. Breakfasts are not floor in the high-rise dormitories. All residence halls included in room rates at Scarborough College, or smoke alarms. in rates charged for children occupying mattresses in have Whitney Hall or cots in Victoria University (Margaret No pets are allowed in the residence halls. Alcoholic Addison Hall). Children's meals may be purchased beverages are not prohibited; however, residents are a Ia carte in the cafeterias. (See section on Food required to exercise moderation. Services.) Students may obtain accommodations in There will be no telephone service in any of the Trinity College at a reduced rate. Facilities for students residence hall rooms, but there are pay telephones and

282 Types of Accommodations Family Town Bouse Units: (not air-conditioned - no deposit required; available nights of 8/19 through 8/26 (check-out must be 8/27]; rates do not include NOTE: All rates include tax. breakfast). NOTE: For accommodations marked with an asterisk, weekly rate does not include towels, face Air-conditioned Rooms: (available 8/20 through 8/26) cloths, or soap. Males: Wetmore - (includes breakfast for occupancy on Scarborough College - 11 units available nights of 8/22 through 8/26) (#32 on map) 2 units/4 singles each $16.05 per person per night or $21.50 Single/per person per night $176.55 weekly* $15.50 Double/per person per night 2 units/6 singles each $16.05 per person per night or Wetmore - (no breakfast for occupancy on nights of $214.00 weekly * 8/20 and 8/21) 7 units/2 singles and 2 doubles $20.00 Single/per person per night $16.05/single/per person per night $13.50 Double/per person per night $13.91/double/person per night Females: $214.00 weekly * Wilson - (includes breakfast for occupancy on nights $10.17 per child under 12 per night if occupying a bed. of 8/22 through 8/26) (#32a on map) $21.50 Smglefper person per night Wilson- (no breakfast for occupancy on nights of Cheek-in Times and Loeationa 8/20 and 8/21) $20.00 Single/per person per night of Reaidenee Halla and Scarborough College Non-air-conditioned Rooms: (available 8/20 through 8/26 or 8/27) Whitney Ball, St. George Street and Hoskins Avenue Malea: (#13 on map) Devonshire - (includes breakfast for occupancy on 11:00 a.m. - 11:00 p.m. nights of 8/22 through 8/26) (#12 on map) Porter on duty 24 hours $20.50 S"inglefper person per night Wilson Hall, New College, Willcocks Street and Huron Devonshire- (no breakfast for occupancy on nights Street (#32a on map) of 8/20 and 8/21) 11:00 a.m. -11:00 p.m. $19.00 Single/per person per night Porter on duty 24 hours St. Hilda's College, Trinity College - (does not Sir Daniel Wileon, St. George Street (next to Whitney) include breakfast) (#608 on map) (#29 on map) $18.73 Single/per person per night 11:00 a.m. - 11:00 p.m. $12.31 Double/per person per night Porter on duty 24 hours $16.59 Student single nightly rate Wetmore Ball, Classic Avenue and Huron Street (#32 St. Michael's College- (available 8/21 through 8/26; on map) does not include breakfast) (#401-432 on map) 11:00 a.m. - 11:00 p.m. $18.73 Single/per person per night After 11:00 p.m., go to Wilson Hall for key. $12.31 Double/per person per night Devonahire Ball, Devonshire Place and Hoskin Avenue Knox College- (available 8/20 through 8/27; does (#12 on map) not include breakfast) (#575 on map) 11:00 a.m. - 11:00 p.m. $16.05 Single/per person per night After 11:00 p.m., go to Whitney Hall for key. $12.84 Student single nightly rate St. Hilda's College, Trinity College, 44 Devonshire Place Co-ed: Whitney (#13 on map) and Sir Daniel Wilson (#608 on map) Halls (#29 on map) are available nights of 8/20 through 9:00a.m. -5:00p.m. 8/26; rates include breakfast for occupancy on nights of After.S:OO p.m., porter is on duty 8/22 through 8/26. Margaret Addison Hall at Victoria Knox College, St. George Street and Willcocks Street University (#508 on map) available nights of 8/20 (#575 on map) through 8/27; rates include breakfast for occupancy on 9:00 a.m. - 4:00p.m. nights of 8/20 through 8/26. $20.50 Single/per person per night Check-in at Bursar's Office, East Academic Wing, 59 $14.50 Double/per person per night George Street. After 4:00 p.m., pick up key from don The following rates do not include breakfast in on duty (aka resident). Whitney and Sir Daniel Wilson Halls for nights of 8/20 St. Michael'• College, 81 St. Mary Street and Bay Street and 8/21: (#401-432 on map) $19.00 Single/per person per day 8:00 a.m. - 8:00 p.m. $12.50 Double/per person per day Check-in at Porter's Office, lower Elmsley Hall at Mail Room. After 8:00 p.m. go to switchboard at 50 Children'• Ratea: (applicable to rooms in Whitney Hall and Victoria University only) St. Joseph Street located in Clover Hill Wing east of church. $7.49 - Daily mattress charge payable on arrival for children ages 10-14 in Whitney Hall in room Margaret Addison Ball, Victoria University - Charles with parents. Children's meals are not included in Street West at University Avenue (#508 on map) mattress charge but may be purchased a la carte. 24 hour check-in at desk in Child of age 15 or over must occupy a bed and pay Margaret Addison Hall adult single rate which includes breakfast. Scarborough College (Block A), Military Trail, West $5.35 - Daily cot charge for children ages 4 to Hill, Ontario (south of route 401) 12 in Victoria University (Margaret Addison Hall); Check-in will be handled on an individual basis if breakfast is not included in cot charge. Child of 12 arrival time is given on housing form, or go to residence or over must occupy bed and pay adult single rate trailer next to Block A, which is open on weekdays from which includes breakfast. 9:00 a.m. to 5:00 p.m.

283 University of Toronto

Numerical directory and 81 St. George Grad. Residence [3A] location guide 63 254-56 McCaul St. [3El 64 91 St. George St. [3B] 1 University College [3CJ 88 industrial Relations Centre [3AJ 2 Hart House I 4C] 89 Admissions Ofiice [3Al 3 Sigmund Samuel Library Bldg. [40 1 90 88 College St. [6EJ 4 McMurrich Building [401 91 Studio Theatre [2B] 5 Medical Sciences Building [401 95 43 Queen's Park Cres. E. [SCI 6 John P. Robarts Research Ub. [2BI 96 47 Queen's Park Cres. E. (SCI 6a Library Science Building [2BJ 97 39 Queen's Park Cres. E. [SCI 6b Thomas Fisher Rare Book Lib. [2Bl 97a Culture & Technology Centre 7 Mining Building [3EJ [SCI 8 Wallberg Building [3E] 99 121 St. Joseph St. ISCI Sa Metallurgy Building [3EJ 103 Sch. of Continuing Studies (2AI 9 Sandford Fleming Labs. [3EJ 104 Institute for Policy Analysis [2AI 10 Simcoe Hall [30! 110 MediaCentre[3AI lOa Convocation Hall [30! 1 1 1 246 Bloor St West [3A I 1 1 Botany Building [4EJ 113 651 SpadinaAve. (Vladimir 12 Devonshire House [3BJ House) liB[ 13 Whitney Hall [3C! 115 97St.GeorgeSt.[3B[ 14 Faculty of Education [2AJ 1 17 W. B. MacMurray Field House 15 Lillian Massey Building [SAl [1BI 16 Banting Institute [5EJ 120 Old Observatory (SAC)[ 4C I 19 U. ofT. Press/Bookroom [30] 125 703 SpadinaAve.(IAI 20 Rosebrugh Building [4EJ 132 Innis College [2B[ 21 Engineering Annex [3E] 138 370 Huron St. [2B[ 22 Mechanical Engineering Bldg. [3E[ 141 Margaret Fletcher Day Care 23 Women's Union [3C] Centre[3A[ 24 Haultain Building [4EJ 170 167CollegeSt. [3E[ 25 FitzGerald Building [4E] 171 455SpadinaAve.[1EI 26 Cumberland House [3El 172 MacDonald-Mowat House [301 27 Forestry Building [3D 1 174 203 College St. [3EI 28 Architecture Building [2El 178 342-44BioorSt.W.[1AI 29 Sir Daniel Wilson Residence [3C I 180 Faculty of Educ. Registrar [2AI 30 Varsity Stadium [3AJ 181 Ontlnst.forStudiesinEduc.[3A[ 30a Varsity Arena [4A] 401-432 St. Michael's Collage 31 16 Hart House Circle [4Cl 501-524 Victoria University 32 New College (Wetmore Hall) [2CJ 550 Toronto Sch. of Theology [SA] Hall)[! C] 32a New College (Wilson 575 Knox Collage [3D] Sidney Smith Hall [2CJ 33 600-608 Trinity College 34 Massey College [3B] 675 Wycllfla Collage [4C] 35 Royal Conservatory of Music [4AJ !below) 36 Nursing Building [20] Teaching Hospitals Hospital 37 David Dunlap Observatory (below) 961 Toronto Western 38a Woodsworth College [3Al 962 Princess Margaret Hospital 38b Drill Hall [3A] 963 Wellesley Hospital 39 49 St. George st. [30] 964 St. Michael's Hospital 40 Flavelle House [4BJ 966 Hospital for Sick Children 43 School of Graduate Studies [30] 966 Sunnybrook Medical Centre 45 Infirmary [20] 967 Mt. Sinai Hospital 46 44 St. George St. [20] 968 Women's College Hospital 49 Aerospace Building (below] 969 Toronto General Hospital 50 Falconer Hall [4BJ 970 Clarke Institute of Psychiatry 51 Edward Johnson Building [4B] 971 Addiction Research Clinical lnst. 52 Best Institute [5E] 972 Lyndhurst Hospital 53 Institute of Child Study (below) 54 1 SpadinaCrescent[IDJ 56 Graduate Students' Union [20] 57 Textbook Store [20] 58 Hea~h Service [20] Alphabetical directory 59 Bancroft Hall [20] 61 South Borden Building [20] Addison {Marg.) Hall {Victoria) 508 Borden Building [20] 61a North Brannan Hall (St. MichHI's) 411 [tC] 63 631 SpadinaAve. Devonshire House 12 65 Dentistry Building (below) {Marg.) Day Care Ctr. 141 67 215 Huron Street [2EJ Fletcher 68 Benson Building [2C] Knox Collage 575 68a Athletic Complex Medical Sciences lnst. 5 (proposed)[ I CJ St. Michael's College 400's 69 AiumniHouse[tDJ Sidney Smith Hall 33 70 Galbrahh Building [3E] Simcoe Hall 10 71 92 College St [BEl Trinity College 600 72 Ramsay Wright Zoological Labs. Victoria University 501 [2C] Watmore Hall (New Collage) 32 73 Lash Miller Chemical Labs. [20] Whitney Hall 13 74 581 SpadinaAve. [1 OJ Wilson Hall (Now Collage) 32a 75 Faculty Club [20] Wilson (Sir Daniel) Residence 29 76 Information Services Dept. [1 OJ 77 Sussex Court [2B] 78 McLennan Physical Labs. [20] @ = Park Plaza Hotel Burton Tower 79 Hughes Pharmacy Bldg [20] @ = Subway station

284 St. George Campus

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285 campus telephones available in the public lobby areas All those who request university housing in advance and about the campus. will receive a written confirmation from the Mathe­ There are coin-operated vending machines (with the matics Meetings Housing Bureau. This confirmation exception of Trinity College) and laundromats in each should be presented to the university clerk at time of hall; however, participants are advised to bring their check-in. The remainder due for the duration of each own detergent. Irons and ironing boards are available participant's stay as originally requested on his or in some of the residence halls. her preregistration/housing form is due in full at Temporary parking outside residence hall check-in time of check-in. Cash, personal checks and travelers' points will be allowed for 10-15 minutes. See the checks in Canadian funds will be accepted. U.S. section on Parking for further information. funds will be taken at par. Credit cards will not be Checks must be made payable to either the No more than two adults may occupy a room at accepted. of Toronto or to the college or university to the same time. Only one child may occupy the same University which the participant has been assigned. room with its parents. Rules regarding children vary in the three residences set aside for families: Victoria Refundable key deposits of $3 to $5 are mandatory be forfeited if a University, Whitney Hall, and Scarborough College. at check-in; however, this deposit will Please refer to the section below for information on key is lost. All keys open doors to rooms, and, in some accommodations for families. No cribs for children are residences, will open outer doors also. available from the university. (See the section on Crib Individuals who fail to preregister and obtain Rental.) confirmed university accommodations must go to desk (Housing section) in Room rates for the nights of August 22 through the meeting registration lobby Sidney Smith Hall (#33 on map) 26 will include breakfast in the cafeteria in Wilson the or St. George Street in order to receive a room Hall, New College for those participants residing in on assignment, if rooms are still available. It is Wetmore, Wilson, Whitney, Devonshire and Sir Daniel suggested that these individuals bring a set of towels, Wilson Halls. Rates for occupancy in these halls for face cloths, soap, and clothes hangers in the event they the nights of August 20 and 21 are prorated since are assigned to Knox College. Since the number of that cafeteria is closed on weekends and breakfast not rooms being held for latecomers is limited, everyone is available. Room rates for adult participants residing in urged to preregister and obtain housing in advance in Margaret Addison Hall in Victoria University include order to avoid disappointment. Again, no guarantee breakfast in Burwash Hall across the street (#504 on can be made that the university will be able to make map). It is expected that this cafeteria will be open rooms available for last-minute arrivals. on weekends; however, should there .be a change in this plan, reimbursement will be made by Victoria Food Services University for the amount charged for the breakfast(s). Breakfast for those participants staying in Wetmore, Please note that mattress and cot rates for children Wilson, Whitney, Sir Daniel Wilson, and Devonshire residing in either Whitney or Margaret Addison Halls Halls will be served in the cafeteria located in Wilson do not include breakfast as indicated in the following Hall, New College beginning on Monday, August 23, section. and ending on Friday, August 27. No meals will be Those preregistering and requesting university hous­ served in the Wilson Hall, New College cafeteria on ing before the July 9 deadline must include a $15 weekends. Participants staying in Margaret Addison room deposit (nonrefundable after July 15) for all Hall, Victoria University, will use the cafeteria in residences except Scarborough College. (Details are Brennan Hall (#411 on campus map). It is anticipated given below.) The deposit must be submitted at the that this cafeteria will be open on the weekend prior to same time as the preregistration/housing form. Forms the Joint Meetings. Participants staying in residence received without the deposit will be returned. halls on campus whose room rates include breakfast NOTE: Should it be necessary for participants to will be issued vouchers at check-in as proof of payment. cancel their preregistration and housing, they should Children's room rates (if not occupying a bed) do not be aware that the housing deposits can be refunded include breakfast. only up to July 15. Those wishing to cancel It is likely that those attending the AMS Short should write or telephone the Mathematics Meetings Course on August 21-22 or still on campus on Saturday, Housing Bureau (401-272-9500, ext. 239) before August 28, must eat off-campus. The University of this deadline. No refunds of housing deposits can Toronto campus is surrounded by many restaurants be made after these monies have been turned over within easy walking distance and in the moderate price to the university. As has been the custom, 50 percent range. of the preregistration fee(s) will be refunded if the Breakfast will be served in the cafeterias from 7:30 Mathematics Meetings Housing Bureau is notified of a.m. to 9:00 a.m.; lunch from noon to 1:30 p.m.; the cancellation prior to the deadline date of August and dinner from 5:00 p.m. to 6:30 p.m. A typical 20. Any changes in arrival and departure dates breakfast consists of 2 eggs, 2 slices bacon/ham, 2 must be made with the Mathematics Meetings slices toast/jam, 2 beverages and one fruit. The lunch Housing Bureau until August 20 (401-272-9500, and dinner meals may be purchased a Ia carte. Lunch ext 239). After 4:00 p.m. on August 22, please call would include soup and salad, one entree, roll, butter, Mary A. Coeeoli at the Telephone Message Center 2 beverages and one dessert. A typical dinner would be in Toronto. soup and salad, one entree, potato and vegetable, roll,

286 butter, 2 beverages, one fruit and one dessert. Coffee is for $6 per day; the Carlton Inn has underground unlimited if selected as choice of beverage. No seconds parking for $2.50 per day. are allowed. The cost of breakfast in the cafeterias for those not Registration at the Meetings on the breakfast plan is $2.50-$2.75, and for those Meeting preregistration and registration fees only participants and their families who prefer to take their partially cover expenses of holding meetings. All meals in the cafeteria, the cost of lunch is $3.90-$4.10, mathematicians who wish to attend sessions are and dinner $5.00-$5.50. expected to register, and should be prepared to show Scarborough College provides full food service a Ia their meeting badge, if so requested. The fees for carte in their cafeteria which is open Monday through registration at the meetings, which are 30 percent more Friday from 9:00 a.m. to 4:00 p.m. than the preregistration fees, are listed below: Hotel Accommodations AMS Short Course Blocks of rooms have been set aside for use by Student/Unemployed $10 participants at the hotels listed below. Participants All Other Participants $30 should make their own reservations early, either One-day Fee (Second Day Only) $15 directly with the hotels, or with the Toronto Meetings Travel Hotline when booking airline reservations. In Joint Mathematics Meetings either case, participants should identify themselves as Member of AMS, MAA, liME $48 participants in the Joint Mathematics Meetings. The Emeritus Member of AMS, MAA $12 rates listed below are subject to change, and to a Nonmember $74 7 percent Ontario Sales Tax; all rates are quoted in Student/Unemployed $12 Canadian dollars. MAA Minicourses #1 and #2 The following codes apply: AC = Air Conditioned; All Participants $15 each CL = Cocktail Lounge; FP = Free Parking; RT = Restaurant; SP = Swimming Pool; TV = Television. Registration fees may be paid at the meetings in The age limit for children below which there is no cash, by personal or travelers' checks, or by VISA or charge, providing a cot is not required and they are MASTERCARD credit cards. in the same room as a parent, is shown in parentheses There will be no extra charge for members of on the same line as the charge for an extra person in the families of registered participants, except that the room. In all cases "Single" refers to one person in all professional mathematicians who wish to attend one bed; "Double" refers to two persons in one bed; sessions must register independently. "Twin" refers to two persons in two beds. A rollaway All full-time students currently working toward a cot for an extra person can be added to double or twin degree or diploma qualify for the student registration rooms only. Participants will be advised of deposit fees, regardless of income. requirements by the hotels at time of confirmation. The unemployed status refers to any person currently Park Plama Hotel (A on campus map) unemployed, actively seeking employment, and who is 4 Avenue Road, Toronto, Ontario (M5R 2E8) not a student. It is not intended to include persons who Telephone: (416) 924-5471 have voluntarily resigned or retired from their latest Single: $85 Double: $95 position. Extra person in room: $10 (15 years) The emeritus status refers to any person who has Code: AC, TV (in-home movies), CL, RT been a member of the AMS or MAA for twenty years The deadline for reservations is July 26. or more, and is retired on account of age from his or Royal York (20-30 minute walk) her latest position. 100 Front Street West, Toronto, Ontario (M5J 1E3) Nonmembers who register at the meetings and pay Telephone: (416) 368-2511 the $7 4 nonmember registration fee are entitled to Single: $76 Twin: $91 a discount of the difference between the member Extra person in room: $16 (15 years) registration fee of $48 and the nonmember registration Code: AC, TV, CL, RT fee of $7 4 as a $26 credit against dues in either the AMS The deadline for reservations is July 28. or MAA or both, provided they join before September Carlton Inn (20-30 minute walk) 26, 1982. 30 Carlton Street, Toronto, Ontario (M5B 2E9) Nonmember students who register at the meetings Telephone: (416) 977-6655 and pay the $12 registration fee are also entitled Single: $39 to a discount of the difference between the student Extra person in room: $7 (13 years) preregistration fee of $8 and the registration fee of $12 Code: AC, TV, CL, RT, SP, sauna, small as a $4 credit against dues in either the AMS or MAA refrigerator in each room or both, provided they join before September 26, 1982. The deadline for reservations is August 1. Nonmembers and nonmember students who thus The Park Plaza Hotel has underground parking for qualify may join at the meetings, or by mail afterwards $5.75 for 24 hours; the Royal York has sheltered parking up to the deadline.

287 Registration Dates and Times future meetings. Comments on all phases of the reply is desired, AMS Short Course meeting are welcome. If a written participants should furnish their name and address. Medical Sciences Building Outside Room 3153, Participants with problems of an immediate nature Saturday, August 21 11:00 a.m. to 4:00 p.m. requiring action at the meeting should see the meeting Sunday, August 22 8:00a.m. to 2:00p.m. manager, who will try to assist them. Joint Mathematics Meetings Local Information MAA Minicourses (until filled)] [and This section of the desk will be staffed by members Entrance Lobby, Sidney Smith Hall of the Local Arrangements Committee and other Sunday, August 22 4:00p.m. to 8:00p.m. volunteers from the Toronto mathematical community. Monday, August 23 8:00 a.m. to 4:30 p.m. Lost and Found Tuesday, August 24, and 8:30 a.m. to 4:30 p.m. See the meeting cashier. Wednesday, August 25 Mail Assistance and Information Desk All mail and telegrams for persons attending the Outside Medical Sciences Auditorium meetings should be addressed to the participant, Thursday, August 26 8:30a.m. to 1:30 p.m. c/o Joint Mathematics Meetings, Department of Mathematics, University of Toronto, Toronto, Ontario, Please note that the Joint Mathematics Meetings Canada M5S 1Al. Mail and telegrams so addressed registration desk will not be open on Thursday, August may be picked up at the mailbox in the registration 26, and that the telephone message center will not be area during the hours the registration desk is open. in operation that day. Other services provided during First class mail not picked up will be forwarded the meeting at the registration desk will also no longer after the meeting to the mailing address given on the be available (see section below on REGISTRATION participant's registration record. DESK SERVICES). There will, however, be a small desk set up outside the Auditorium in the Personal Messages Medical Sciences Building where local information will Participants wishing to exchange messages during be available and where a staff member will provide the meetings should use the mailbox mentioned above. limited assistance to participants. No registration or Message pads and pencils are provided. It is regretted cash transactions will be possible at this desk. that such messages left in the box cannot be forwarded to participants after the meeting is over. REGISTRATION DESK SERVICES Telephone Messages AMS/MAA Information A telephone message center will be located in Information on the publications and activities of the registration area to receive incoming calls for both organizations may be obtained at this section of participants. The center will be open from August the registration desk. 22-25 only, during the same hours as the Joint Mathematics Meetings registration desk. Messages will Audio-Visual Aid be taken and the name of any individual for whom A member of the AMS staff will be available to a message has been received will be posted until the advise or consult with speakers on their audio-visual message has been picked up at the message center. requirements. The telephone number of the message center will be Baggage and Coat Cheek announced in the August issue of the Notices. Participants may leave baggage, parcels, coats, etc., Transparencies for safekeeping at the registration desk during the Speakers wishing to prepare transparencies in hours it is open, provided these items are picked up advance of their talk will find the necessary materials before the desk closes for the day. Articles left after and copying machines at this section of the registration closing time cannot be reclaimed until the following desk. A member of the staff will assist and advise morning. Articles not picked up when registration speakers on the best procedures and methods for closes at 4:30 p.m. on Wednesday, August 25, will be preparation of their material. There is a modest charge turned over to the Department of Mathematics. for these materials. Cheek Cashing Visual Index The meeting cashier will cash personal or travelers' Alphabetical lists of registered participants, including checks up to $50, upon presentation of the official local addresses, arrival and departure dates, is meeting registration badge, provided there is enough maintained in the registration area. cash on hand. MISCELLANEOUS INFORMATION Assistance, Comments and Complaints A log for registering participants' comments or com­ Athletic Facilities plaints about the meeting is kept at the Transparencies Meeting participants may use the swimming pool Section of the registration desk. All participants are and track for a $5 guest fee. Upon proof of meeting encouraged to use this method of helping to improve registration, guest cards will be issued at the Booking

288 Office in the Athletic Center. As this is the maintenance of Montreal will not cash personal checks. Their week for the facility, squash and tennis will not be hours of operaion are from 10:00 a.m. to 3:00 p.m. available, and the towel service may not be operating. Monday through Thursday, and from 10:00 a.m. to Book Stores 6:00 p.m. on Friday. It is suggested that participants with confirmed housing reservations on campus plan There are three book stores located on campus. The on paying for their accommodations at check-in time U of T Bookroom, located on Kings College Circle, and in Canadian funds, since U.S. funds will be accepted the U of T Textbook Store, located on Huron Street, by the university housing clerks at par. are both open from 8:45 a.m. to 4:30 p.m., Monday The Toronto Transit Commission operates subways, through Friday. The Student Christian Movement streetcars, trolley buses, and suburban buses. All fares Bookstore, located on the edge of campus at the corner of Bloor and St. George, is open 9:00 a.m. to 6:00 p.m., are 75 cents each, or eight for $5. Monday through Friday, and 10:00 a.m. to 6:00 p.m. Taxi rates are SUO at flag drop and 20 cents each Saturday. additional 1/8 mile. In addition to the activities listed under the section Camping titled Social Events, Toronto has many other sights There are no suitable camping sites located near and attractions, such as the Royal Ontario Museum, the university. Those persons wishing to camp should the CN Tower, Casa Lorna, Toronto Islands, Old Fort contact their local KOA office for the current issue of York, Ontario Place, and The Art Gallery of Ontario Handbook and Directory for Campers. in Grange Park. Further information can be obtained Child Care on these places at the Local Information section of the meeting registration desk. Daycare may be arranged by interested individuals by contacting the director of the Margaret Fletcher Medical Services Daycare Centre, who will take children on a first­ The University Health Service is open from 9:00 a.m. come, first-served basis. Write to Ms. Mercedes to 4:30 p.m. daily for medical attention. Emergencies Chacin de Fuchs, Margaret Fletcher Daycare Centre, occuring during the evening or weekends can be 100 Devonshire Place, University of Toronto, Toronto, handled at the Emergency Department of any of the Ontario, Canada M5S 2C9. local hospitals: Toronto General Hospital, College at Crib Rental University; Women's College Hospital, 76 Grenville Street (College at Bay); the Hospital for Sick Children, Cribs are available for $2.50 per day, plus 7 percent 555 University Avenue. In addition, the Academy provincial sales tax, and a $10 total delivery and pick­ of Medicine can advise of local doctors who are on up charge. Strollers, high chairs, and infant (under emergency call. Their telephone number is 922-1134. 20 lbs.) car seats are also available; rates on request. Dental service can be arranged through the University Those persons wishing to rent any of these items should write to the undernamed as soon as possible, giving Health Centre. dates required. In the case of cribs, full payment Parking must be enclosed in Canadian funds: Annette Sunter, Parking throughout the university is extremely Department of Mathematics, University of Toronto, limited as the campus was not designed for motor Toronto, Ontario, Canada M5S 1A7. traffic. Parking stickers for pay lots will be available Libraries at the meeting registration desk for $3 per day. A The Mathematics Department Library, located on 400 car parking lot on St. George Street will be open the second floor of Sidney Smith Hall, will be open from Monday through Friday, for which a $3 parking fee, 9:00 a.m. to 9:00 p.m. for the duration of the meetings. payable on site, is charged. There are also several areas Information concerning books located in other libraries where on-street parking is free from 9:00 a.m. to 4:00 is available from the Department Library. The main p.m. and 6:00 p.m. to 7:00 a.m. Metered parking is collection of books is in the Science and Medicine also available. Maps indicating these parking areas will Library, located on Kings College Circle. The Robarts also be available at the registration desk. Participants Library houses the Humanities collection. Summer are urged to drive as little as possible between the hours for the university libraries are: dormitories and the meeting areas. Robarts 8:30a.m. to 11:00 p.m. Monday-Thursday Participants attending the AMS Short Course on 8:30 a.m. to 6:00 p.m. Friday Saturday and Sunday August 21-22, or the MAA 9:00 a.m. to 5:00 p.m. Saturday Minicourses on Sunday, August 22, will find free Sci-Med 8:30a.m. to 9:00p.m. Monday-Thursday parking for the weekend only on King's College Circle 8:30 a.m. to 5:00 p.m. Friday and Hart House Circle. 9:00 a.m. to 5:00 p.m. Saturday Social Events Local Information The Department of Mathematics is planning enter­ The Bank of Montreal, 262 Bloor Street West at St. tainment for mathematicians and their families during George, will exchange U.S. currency for participants at the meeting. At 8:45 p.m. on Monday, August 23, no charge, provided either cash or recognized travelers' there will be an evening beer party at Wetmore Hall checks are presented. Canadian funds can also be Cafeteria, New College. Tickets to this event will obtained through MASTERCARD; however, the Bank be sold in advance at the Transparencies section of

289 the meeting registration desk. More information will where VIA provides six trains daily to Toronto. Both appear in the June issue. .AMTRAK and VIA provide daily New York-Toronto During the week of the meeting, there will be services. many entertainment events in Toronto and vicinity. A From all U.S. points, routes lead directly to number of theatres will be giving regular performances Toronto on Highway 401. To get to the main (St. at this time. At Niagara-on-the-Lake there is the George) University of Toronto campus from 401, take Shaw Festival, and at Stratford a Shakespeare festival. exit 52 (Avenue Road). Take Avenue Road south Both of these places are relatively close to Toronto, approximately five miles, where it becomes University and return transportation for any evening is easy to Avenue after crossing Bloor Street. Then, see the arrange. In addition to theatrical events, Toronto has campus map. a wide variety of musical events during the summer. Entering Canada is usually no problem for U.S. The Canadian National Exhibition will be in progress citizens, and involves nothing more than answering the week of the meeting, and is easily accessible questions about where they were born, where they from the university by public transportation. Tours are going, and how long they will stay, and showing can be arranged during the daytime to such local some form of proof of citizenship such as a voter's places of interest as the Ontario Science Centre, the or birth certificate. Permanent U.S. residents who McMichael Collection, and the large Metropolitan Zoo. are not citizens are required to bring their alien Participants interested in these events should check registration receipt card (U.S. form 1-151 or 1-551). with the Local Information section of the meeting Entry requirements vary for people coming to Canada registration desk. from countries other than the United States. As a Travel general rule, the visitor should have a valid national passport. In August, Toronto is on Eastern Standard Time. There is regular airline service to Toronto International Weather Airport by several major airline carriers. The normal daytime high temperature during this The airport in Toronto is approximately 18 miles period is 79"F. Normal night-time low is 61°F. Rainfall from city center, and the trip takes between 25 and in August averages 2.65 inches, with a 30 percent 60 minutes. A taxi costs S18-$20; limousine $20; the average daily probability of precipitation. Humidity Airport Express bus to Islington Subway station $2, ranges from a daytime high of 67 percent to a then 75 cents to the city; the bus to York Mills station night-time low of 55 percent. The record high and $2.50, then 75 cents to the city; and the Charterways low temperatures for August are 102°F and 39"F Bus to downtown (stops at Royal York and Sheraton respectively. Light sweaters and jackets are advised Centre) $5.50. None of these services, except the taxi for evening wear. Temperatures in Canada are given in or limousine, will bring one directly to the university the Celsius scale, so the preceding temperatures would campus. Participants are advised to utilize cab service read: normal high 26, normal low 16, record high 39, for the last leg of the trip. Most major car rental record low 4. agencies maintain desks at the airport. VIA has eight trains daily from Montreal to Toronto, Raymond G. Ayoub and one a day from Vancouver. One can take University Park, Pennsylvania Associate Secretary AMTRAK to Detroit, and then the bus to Windsor,

MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY

ODD PRIMARY INFINITE FAMILIES IN STABLE HOMOTOPY THEORY by Rolph L. Cohen In this paper new infinite families in each odd Contents primary part of the stable homotopy groups of 1. Odd primary Brown-Gitler spectra spheres are constructed. Along the way to obtaining 2. H*(U2sn) as a module over the Steenrod algebra these elements there is a detailed study of the stable 3. The odd primary stable homotopy type of n,2s2+n homotopy type of the double loop space of a sphere, 4. Applications to the stable homotopy groups of n,2sn. This study includes an explicit computation spheres of its cohomology as a module over the Steenrod 5. Applications of the Adams-Novikov spectral algebra, the construction of odd primary analogues of sequence-more infinite families in prr! Brown-Gitler spectra, and a demonstration of how Memoir Number 242, viii + 92 pages (soft cover) these spectra can be used to describe the stable homo­ List price $5.60, institutional member $4.20, topy type of n,2sn. Finally, applications of the individual member $2.80 ISBN 0-8218-2242-X; LC 80-28537 Adams-Novikov spectral sequence based on the Brown­ Publication date: March 1981 Peterson spectrum are discussed. To order, please specify M EM0/242N Prepayment is required for all AMS publications. Order from AMS, P.O. Box 1571, Annex Station, Providence, Rl 02901, or call toll free 800-556-7774 to charge with Visa or MasterCard.

290 American Mathematical Society Short Course Series

Statistical Data Analysis (August 21 and 22, 1982) Synopses and Reading Lists

Introduction and Summary (Ram Gnanadesikan). specifications rather than optimum performance under To set the stage for the lecture series, the concerns and one specification. The underlying idea is to identify characteristics of data analysis will be described. These observations which are deviant, and to reduce their aspects will be compared with the more familiar ones influence (in a rigorous way, and without excessive of mathematical statistics, to which they correspond, computation). After a review of the general concepts, and the differences will be clearly brought out. At the practical methods will be explained for several areas, end of the series, a summary will be given, focussing including estimation of basic quantities, estimation. of on the common strands which thread through all the the coefficients of a regression equation, and smoothing different lecture topics. of functions. 1. J. W. Tukey and M. B. Wilk, Data analysis 1. F. Hampel, Robust estimation: a condensed and statistics: an expository overview, AFIPS Con­ partial survey, Zeitschrift fiir Wahrscheinlichkeits­ ference Proceedings, Fall Joint Computer Conference theorie und Verwandte Gebiete 27 (1973), 87-104. 29 (1966), 695-709. 2. P. J. Huber, Robust statistics, Wiley, New York, 2. R. Gnanadesikan and M. B. Wilk, Data analytic 1981. methods in multivariate statistical analysis, Multi­ 3. R. L. Launer and G. N. Wilkinson (editors), variate Analysis II (P.R. Krishnaiah, editor), Academic Robustness in statistics, Academic Press, New York, Press, New York, 1969, pages 593-638. 1979, especially chapters by Hogg, Huber, Tukey, Martin and Box. Graphical Methods (Paul A. Tukey). Numerical 4. C. L. Mallows, Robust methods-some ex­ methods for data analysis usually require some prior amples of their use, American Statistician 33 knowledge or belief about the kinds of relationships (November 1979), 179-184. in a set of data. By contrast, graphical displays 5. C. L. Mallows, Some theory of nonlinear can provide effective initial insight into the data and smoothers, Annals of Statistics 8 (1980), 695-715. reveal unexpected features. Sometimes a graphical analysis by itself will suffice; in other cases, graphs Multilinear Models (Joseph B. Kruskal). Linear can aid the choice of suitable models. Plots also models underlie most numerical methods for analyzing provide important diagnostic information to accompany data, such as regression and analysis of variance. numerical analyses. The talk will present graphical data Models that are exactly or approximately bilinear, displays for exploratory use, for assessing distributional however, underlie several important methods such as models, for aiding regression modeling, and for looking principal components analysis, factor analysis, multi­ at higher-dimensional data. dimensional scaling, and others. Trilinear models 1. J. W. Tukey, Exploratory data analysis, Chap­ underlie at least two significant methods, including ters 1 and 2, Addison-Wesley, Reading, Massachusetts, PARAFAC, and models of even higher order find 1977. occasional use. Many multilinear models have geomet­ rical meaning. After a brief introduction to these 2. P. A. Tukey and J. W. Tukey, Graphical display ideas, some topics will be discussed in greater detail, of data sets in 3 or more dimensions, Interpreting including the most basic bilinear and trilinear models, Multivariate Data (V. Barnett, editor), Chapters 10- the analogy between them, the Singular Value De­ Wiley, London, 12, 1981. composition, and particularly PARAFAC, which will 3. P. F. Velleman and D. C. Hoaglin, ABCs of receive the greatest attention. EDA, Chapters 1, 3, 4 and 6, Duxbury, Boston, 1981. 1. J. B. Kruskal, Multilinear models for data 4. M. B. Wilk and R. Gnanadesikan, Probabiity analysis, Behaviormetrika 10 (July 1981), 1-20. plotting methods for the analysis of data, Biometrika 55 (1968), 1-17. 2. J. B. Kruskal, Factor analysis and principal components: bilinear methods, International En­ Robust Methods (Colin L. Mallows). Methods cyclopedia of Statistics (W. H. Kruskal and J. M. for estimating unknown quantities are a major part Tanur, editors), Macmillan and Free Press, New York, of statistics and data analysis. The majority of 1978, pages 307-330. methods in wide use today were selected because they 3. R. A. Harshman and Sheri Berenbaum, Basic perform optimally (in some sense) if the data are concepts underlying the PARAFAC-CANDECOMP generated according to some specified random process. three-way factor analysis model and its application In practice, however, the generating process is seldom to longitudinal data, Present and Past in Middle Life known, so robust methods seem a better choice: (D. Eichorn eta!., editors), Academic Press, New York, these provide reasonable performance under a range of 1981.

291 4. J. Douglas Carroll and J. B. Kruskal, Scal­ graphical displays, analysis of variance, singular value ing, multidimensional, International Encyclopedia of decomposition, and PARAFAC. The data are a three­ Statistics (W. H. Kruskal and J. M. Tanur, editors), way array giving corporate revenues broken down by Macmillan and Free Press, New York, 1978, pages 892 year, by category, and by subsidiary (of a single parent -907. company). The main goal of the analysis is to reveal the underlying structure of the data. A Case Study (Jon R. Kettenring). The previous material dealt with several methods used in data 1. J. Mandel, A new analysis of variance model analysis. This case study illustrates the actual for nonadditive data, Technometrics 13 (1911), 1- process of data analysis with a real example, using 18.

PROCEEDINGS OF THE INTERNATIONAL CONGRESS OF MATHEMATICIANS, HELSINKI 1978* edited by 01/i Lehto The Proceedings of the International Congress of A. N. Shiryaev, Absolute continuity and singularity Mathematicians held in Helsinki, August 15-23, 1978, of probability measures in functional spaces are in two volumes. Volume 1 contains an account of A. Wei I, History of mathematics: why and how the Congress, the list of members, presentations of 5.-T. Yau, The role of partial differential equations the works of the Fields medallists, the plenary one­ in differential geometry. hour addresses, and the invited addresses in sections In addition there were 120 invited forty-five­ 1-5. Volume 2 contains the invited addresses in sec­ minute addresses divided into nineteen sections. The tions 6-19. A complete index is included in both sections follow: volumes. 1. Mathematical logic and foundations of mathematics On the decision of the Fields Medals Committee, 2. Algebra the works of the Fields medallists were presented as 3. Number theory follows: 4. Geometry 5. Topology N. M. Katz: The work of Pierre De/igne 6. Algebraic geometry L. Carleson: The work of Charles Fefferman 7. Lie groups, algebraic groups, automorphic functions j. Tits: The work of Gregori Aleksandrovitch Margulis 8. Real and functional analysis I. M. james: The work of Daniel Quillen 9. Complex analysis The invited one-hour plenary addresses included 10. Operator algebras and group representations follow: 11. Probability and mathematical statistics L. V. Ahlfors, Quasiconformal mappings, Teichmiiller 12. Partial differential equations spaces, and Kleinian groups 13. Ordinary differential equations and dynamical A. P. Calderon, Commutators, singular integrals on systems and applications Lipschitz curves 14. Control theory and optimization problems Connes, von Neumann algebras A. 15. Mathematical physics and mechanics R. D. Edwards, The topology of manifolds and cell­ 16. Numerical analysis like maps 17. Discrete mathematics and mathematical aspects D. The classification of finite simple Gorenstein, of computer science groups 18. Mathematics in the social and biological sciences M. Kashiwara, Micro-local analysis 19. History and Education. N. N. Krasovskii, Control under incomplete informa­ Part I, 506 pages; Part II, 516 pages (hard cover) tion and differential games Price $70.00 for 2 volumes. R. P. Langlands, L-functions and automorphic ISBN 951-41-0352-1 representations Pub: :ation date: March 1980 ju. I. Manin, Modular forms and number theory To order, please specify PICMI78 N 5. P. Novikov, Linear operators and integrable Hamiltonian systems *These proceedings were published for the 1978 Interna­ R. Penrose, The complex geometry of the natural tional Congress of Mathematicians with the cooperation of world Academia Scientiarum Fennica and are being distributed by W. Schmid, Representations of semisimple Lie groups the AMS.

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

292 Special Meetings

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

1981-1982. Distinguilhed Lecture Series in Applied 13-16. Sixth European Meeting on Cybernetics and Mathematics, Chicago, Illinois. (February 1982, p. 196) Systems Researeh, Vienna, Austria. (February 1982, p. 197) 1981-1982. Special Program in Algebraic Number Theory and Algebra, University of Illinois at Urbana-Champaign, 13-16. GAMM-Tagung 1982, Budapest, Hungary. Urbana, Illinois. (October 1981, p. 546) (October 1981, p. 547) Stochastic Calculus on 1981-1982. Academic Year Devoted to Mathematical 13-27. Semimartingales and Manifolds, Centre Recherche Mathematiques Appliquees, Problema in Theoretical Physics, The Mittag-Leffler Universite de Montreal, Montreal, Canada. (February Institute, Djursholm, Sweden. (February 1981, p. 177) 1982, p. 201) 1982-1983. Special Year in Lie Group Representations, 15-17. John B. Barrett Memorial Lectures in Dift'erential University of Maryland, College Park, Maryland. Equations, University of Tennessee, Knoxville, Tennessee. Program: There will be advanced courses and lecture series (January 1982, p. 75) concentrated in the following areas: algebraic aspects 16-17. Pacific Coast Conference on Mathematical Modeling of semisimple theory; arithmetic groups, automorphic of Renewable Resources, Humboldt State University, representations, automorphic forms, L-groups, base Arcata, California. (February 1982, p. 197) change, orbital integrals, adelic and local theory; analytic aspects of semisimple theory; orbit method; 16-17. Fifteenth Annual Small College Computing Sym­ and applications. posium, North Dakota State University, Fargo, North Organizing Committee: Rebecca Herb, Ray Johnson, Steve Dakota. (January 1982, p. 75) Kudla, Ron Lipsman (Chairman), Jonathan Rosenberg. 16-17. A Hundred Yean of Algebra 1830-1930, Oxford, Information: Ronald L. Lipsman, Chairman, Organizing England. (January 1982, p. 76) Committee, Department of Mathematics, University of 16-20. Conference on Representation Theory of Reductive Maryland, College Park, Maryland 20742. Groups, Park City, Utah. (February 1982, p. 197) January 3-0ctober 2, 1982. Mathematisehes Fonehungs­ 17. Twenty-Fourth Algebra Day, Carleton University, institut Oberwoltaeh, (Weekly Conferences), Federal Ottawa, Canada K1S 5B6. Republic of Germany. (January 1982, p. 74) Speakers: B. Hartley, C. Processi, D. Solitar. September 1, 1982-Augnst 31, 1983. Statistical and Information: M. Chacron, Department of Mathematics Continuum Approaehes to Phase Transition, Institute and Statistics, Carleton University, Ottawa, Canada for Mathematics and its Applications, University of K1S 5B6. Minnesota, Minneapolis, Minnesota. (January 1982, p. 74) 19-21. Operations Research Society of America and The Institute of Management Sciences Joint National Meeting, Detroit, Michigan. APRIL 1982 Information: Seth Bonder, Vector Research, Inc., P. 0. Box 1506, Ann Arbor, Michigan 48106. 2-3. Discrete Geometry and Convexity Days, New York Academy of Sciences and Courant Institute of 22-23. Thirteenth Annual Pittsburgh Conference on Mathematical Sciences, New York, New York. (January Modeling and Simulation, University of Pittsburgh, 1982, p. 75; February 1982, p. 196) Pittsburgh, Pennsylvania. (October 1981, p. 547) 23-25. Joumees Relativistes, Lyon, France. (February Number Theory Conference, Illinois State 3. Illinois 1982, p. 197) University, Normal, Illinois. (February 1982, p. 196) 24. Conference on Mathematics Learning and Teaching, 3-4. Eleventh Midwest Partial Dift'erential Equations Rutgers University, Newark, New Jersey. (February 1982, Conference, University of Illinois, Chicago Circle. p. 197) (February 1982, p. 197) 26-28. Society for Industrial and Applied Mathematics 6-8. Fifth International Symposium on Programming, Special Conference on Linear Algebra and Applications, Torino, Italy. (February 1982, p. 197) Raleigh, North Carolina. (October 1981, p. 547)

293 26-29. Joum&s d'Aualyse Harmonique, Lyon, France. JUNE 1982 InformatiOfl: G. Arsae or J. Braeonnier, Departement de Mathematiques, Universite C. Bernard, 43 boulevard 2-4. Conference on Computer Architecture and Computa­ 11 Novembre 1918, 69622 Villeurbanne Cedex, Lyon, tional Mathematics, University of Minnesota, Minneapolis, France. Minnesota. 26-29. Soei.ety for JnduatriaJ. and Applied Mathematiea Speakers: Mark Kae, H. T. Kung, Richard McGehee, Speeial. Conference on Applied Linear Algebra, Raleigh, Steve Orazag, Jacob T. Schwartz, Daniel Blatnik, James North Carolina. (October 1981, p. 547; January 1982, p. Thornton, and James Wilkinson. 76) . Organil:ing Committee: G. H. Golub, R. Franta, P. Lax, 26-30. NSF-CBMS Conference on AutomorphiiDl Groupa N. C. Metropolis, J. B. Rosen, and Y. Shimamoto. of von Neumann Algebraa and the Strueture of Facton, Information: George R. Sell, Institute for Mathematics University of Iowa, Iowa City, Iowa. (October 1981, p. 547) and its Applications, 514 Vincent Hall, 206 Church 29-30. Deei.aion Problema in Mathematiea and Computer Street S.E., Minneapolis, Minnesota 55455. Sei.ence, Bowling Green State University, Bowling Green, Ohio. (February 1982, p. 197) 3-5. Statistieal Soei.ety of Canada 1982 Annual Meeting, University of Ottawa, Canada. (February 1982, p. 198} MA¥1982 6-11. Conference on Approximation Theory, University 5-7. Fourteenth Annual ACM Sympoaium on the Theory of Alberta, Edmonton, Canada. (November 1981, p. 644; of Computing, San Francisco, California. (October 1981, January 1982, p. 76} p. 548) 7-10. National Computer Conference, New York, New 7. Sixth Symposium on the Unification of Finite Elements, Finite Dift'erencea and Calculua of Variation, University of York. Connecticut, Storrs, Connecticut. (February 1982, p. 197) Information: AFIPS, P. 0. Box 9658, 1815 North Lynn 10--14. Twenty-Sixth Annual Meeting of the Aultralian Street, Suite 800, Arlington, Virginia 22209. Mathematieal Soei.ety, Newcastle, Australia. (January 7-11. Joum&a aur lea Equations aux Deriv&s Partiellea, 1982, p. 76) Saint-Jean-de-Monts, France. 13-14. Optimisation Days 1982, Universite de Montreal, Information: Pham The Lai, 28 rue de Ia Caillette, 44100 Montreal, Canada. (January 1982, p. 76) Nantes, France. 13-15. Midwest Dynamieal Systema Spring Seminar, Case 7-17. Seventh International Conference on Operator Western Reserve University, Cleveland, Ohio. Theory, Timisoara-Herculana, Romania. (February 1982, Program: There will be 9 one-hour talks in differentiable p. 198} dynamical systems and related areas. Information: Mike Hurley, Department of Mathematics 7-18. Workshop on Mea1ure Theory and ita Applications, and Statistics, Case Western Reserve University, Universite de Sherbrooke, Sherbrooke, Quebec, Canada. Cleveland, Ohio 44106. (February 1982, p. 198} 16-28. NATO AdVIUlced Study Institute on Nonlinear 8-11. Conference in Modern .Analyaia and Probability (in Stochastic Problems, Algarve, Portugal. (January 1982, honor of Shisuo Kakutani}, New Haven, Connecticut. p. 76) (January 1982, p. 76} 17-19. Fourth Symposium on Mathematieal Programming with Data Perturbation~, Marvin Center, George 8-11. 1982 Short Courae on Teaching Computer Sei.ence Washington University, Walhington, D. C. (January 1982, in a Mathematics Department, Denison University, p. 76) Granville, Ohio. (January 1982, p. 76} 17-19. Seventeenth New Zealand Mathematics Colloquium, 14-16. Firat American Control Conference, Sheraton University of Otago, Dunedin, New Zealand. (January National Hotel, Arlington, Virginia. 1982, p. 76) InformatiOfl: M Rabins, Department of Mechanical 17-21. Conference on Mathematieal Models for Equitable Engineering, Wayne State University, Detroit, Michigan Allocationa, The Citadel, Charleston, South Carolina. 48202, (313}577-3843. (February 1982, p. 197) 14-18. Gordon Research Conference on Theoretieal 17-June 5. Second Franco-Southeast Aaian Mathematieal Biology and Biomathematics, Tilton School, Tilton, Conference, Quezon City, Philippines. (January 1982, p. 76) New Hampshire. Purpose: The purpose of the Gordon Research Conferences 24-27. Journ&s de Statiatique, Brussels, Belgium. is to foster and promote education and science by (February 1982, p. 197) organizing and operating meetings of research scientists 24-28. International Forecasting Conference, Valencia, with common interests in the fields of chemistry or Spain. (October 1981, p. 548) related sciences for the purpose of discussions and the 24-29. Joum&a Complexes 1982, Nancy, France. free exchange of ideas. The complete program for InformatiOfl: D. Barlet, Jnstitut E. Cartan, Universite the 1982 Gordon Research Conferences iB published in Nancy-I, Case officielle 140, 54037 Nancy Cedex, France. Science, March 5, 1982. 25-27. Twelfth International Symposium on Multivalued Co-chairmen: Arthur Winfree and John J. Tyson. Logie, Paris, France. (February 1982, p. 198) Program: There will be lectures on the following 26-28. AdVIUlced Seminar on the Theory of Diapened topics: the human sleep-wake cycle; biochemical Multiphase Flow, Mathematics Research Center, Univer­ control mechanisms; cardiae arrhythmias; economics sity of Wisconsin, Madison, Wisconsin 53706. (February of renewable resources; and the evolution of animal 1982, p. 198) behavior. 27. Trends and Applicationa1982: AdVIUleea in Information Speakers: M. Allessie, C. Clark, C. Czeisler, L. Glass, M. Technology, National Bureau of Standards, Gaithersburg, Guevara, J. Hale, W. Hamilton, J. Jalife, J. Keener, R. Maryland. (January 1982, p. 76} Kronauer, R. May, J. Maynard-Smith, P. Painter, P. 30--June 1. Canadian Mathematieal Soei.ety Summer Rapp, S. Scott, M. Sobel, J. Swierzbinski, R. Wever, A. Meeting, Carleton University, Ottawa, Ontario, Canada. Winfree, E. C. Zeeman. (February 1982, p. 198} InformatiOfl: Alexander M. Cruickshank, Director, Gordon Invited Speakers: (Additional). L. Ehrenpreis (Yeshiva Research Conferences, Pastore Chemical Laboratory, University), A. Friedman (Northwestern University), M. Schechter (Yeshiva University). University of Rhode Island, Kingston, Rhode Island 02881, (401}783-4011 or 3372. 30--June 2.1982 Joint Meeting of the Clauiflcation Soei.ety and the Psychometric Soei.ety, Universite du Quebec a 14-18. Meeting on Symbolic Computation, Salisbury Montreal, Montreal, Quebec, Canada. (February 1982, p. State College, Salisbury, Maryland. (February 1982, p. 198} 198}

294 14--18. Special Conference in Honor of Professor H. pollution, and occupational exposure to toxic substances. Za11enhau1, Ohio State University, Columbus, Ohio. Statistical methodologies examined at the conference Topics: Combinatoric&, group theory, homogeneous forms, will include cohort, panel, and case-control studies. number theory and the theory of orders. Co-chairmen: Ross L. Prentice (University of Washington Deadline for Contributions: May 15, 1982. and Fred Hutchinson Cancer Research Center, Seattle), Information: Surinder Sehgal, Department of Mathematics, and Alice S. Whittemore (Stanford University Medical The Ohio State University, 231 West 18th Avenue, School). Conference Director is Donald L. Thomsen, Jr. Columbus, Ohio 43210. (SIMS). Information: SIAM Institute for Mathematics and 14--18. MAA Worklhop for Case Study Course in Applied Society (RAC-8), 97 Parish Road South, New Canaan, Mathematics, University of Maine, Orono, Maine. Connecticut 06840, (203)966-1008. Program: The workshop will include demonstration of a case-study teaching technique, interaction with industry 28-July 2. Ninth Prague Conference on Information representatives, experience in developing a classroom Theory, Statistical Decisions and Random Proee11es, problem from a real-world situation, discussion of Prague, Czechoslovakia. (February 1982, p. 199) ways in which problems from industry may be used 28-July 2. Second Bad Honnef Worklhop on Stochastic in the classroom, examples of problems which have Dift'erential System•, Bonn, Federal Republic of Germany. been obtained from and which use undergraduate (February 1982, p. 199) mathematics. The workshop will be conducted by Jeanne Agnew and Marvin Keener of Oklahoma State 28-July 2. Differential Geometric Control Theory, University. Michigan Technological University, Houghton, Michigan. Information: Grattan Murphy, Department of Mathe­ (January 1982, p. 77) matics, University of Maine at Orono, Orono, Maine 28-July 2. Eleventh Conference on Stoeha1tic Proce1ses 04469; or Don Small, Department of Mathematics, and their Applications, University of Clermont-Ferrand, Colby College, Waterville, Maine 04901. France. (October 1981, p. 548) 14--18. Fifth Interuational Conference on Trends in 28-July 3. Second World Conference on Mathematics at Theory and Pracd.ce of Nonlinear Dill'erential Equation•, the Service of Man, Las Palmas (Canary Islands), Spain. Department of Mathematics, University of Texas at (October 1981, p. 548) Arlington, Arlington, Texas 76019. (January 1982, p. 77) '29-July 2. Third Sym.polium on Control of Distributed 15-17. Worklhop on Low-Probability/Bigh-Comequence Parameter Systems, Toulouse, France. (February 1982, p. Riak AIUIJ.yli•, Hyatt Regency, Arlington, Virginia. 199) (February 1982, p. 198) 15-28. Conference on Finite Groups, Montreal, Canada. JULY 1982 (February 1982, p. 198) 16-18. Second Interuational Conference on Boundary and 5-11. Conference on Ordered Set• and Applications, Lyon, Interior Layen-Computational and .A.ymptotic Method• France. (February 1982, p. 199) (BAIL II), Dublin, Ireland. (November 1981, p. 644) 12-14. EURO V: Fifth European Congre•• on Operation~ 17-18. New Direction• for Risk AIUIJ.ylii-Seeond Annual Rele&rCb, Lausanne, Switzerland. (February 1982, p. 199) Meeting of the Society for Risk AIUIJ.yli•, Hyatt Regency, 12-14. Joint Meeting of Operation• Rele&rCb Society Arlington, V~rginia. (February 1982, p. 198) of America and The Institute of Management Sciences, 20-July 2. Combinatorial Methods in Topology and Lausanne, Switzerland. (February 1982, p. 199) Algebraic Geometry, University of Rochester, Rochester, 12-16. CBMS Regional Conference on Competition Models New York 14627. (February 1982, p. 198) in Ecology, Utah State University, Logan, Utah. (February 21. Journee Arithmetique, Orsay, France. 1982, p. 199) Information: D. Bertrand or M. Waldschmidt, Institut 14--17. Third Geometry Symposium, Siegen, Federal Henri Poincare, 11 rue P. et M. Curie, 75231 Paris Republic of Germany. (February 1982, p. 200) Cedex 05, France. 19-21. 1982 Summer Computer Simulation Conference, 21-25. Queueing Networkl and Applications, Johns Marriott City Center Hotel, Denver, Colorado. Hopkins University, Baltimore, Maryland. (February 1982, p. 199) Program: The conference will cover all aspects of simulation methodology and applications. There will 21-25. Problem Solving, Salisbury State College, be technical sessions on mathematical methods, model Salisbury, Maryland. (February 1982, p. 199) design, simulation languages, validation techniques and 21-25. IEEE Interuational Sym.polium on Information the use of equipment and processor configurations. The Theory, Lea Arcs, France. (October 1981, p. 548) program will emphasize applications of simulation to engineering design and analysis; physical, environmental 21-25. Ninth U. S. National Congre11 of Applied and industrial processes; energy systems operation and Meehanic1, Cornell University, Ithaca, New York. (August control; economics, management and planning, and 1981, p. 438) simulators for research and training. 22-30. International Conference on Population Biology, Information: Marvin F. Anderson, Department of University of Alberta, Edmonton, Alberta, Canada. Electrical and Computer Engineering, University of (February 1982, p. 199) Colorado, 1100 Fourteenth Street, Denver, Colorado 80202, (303)629-2685. 2~0. 1982 National Educational Computing Conference, Kansas City, Missouri. (November 1981, p. 644) 19-23. SIAM Thirtieth Annivenary Meeting, Stanford 28-July 1. Symposium on Random Walks and their University, Stanford, California. (February 1982, p. 200) Application to the Phylical and Biological Sciences, 25-August 7. Joint NATO /London Mathematical Society Gaithersburg, Maryland. (February 1982, p. 199) Advanced Study lnltitute on Systems of Nonlinear 28-July 2. Eighth Re1eareh Application Conference on Partial Dill'erential Equation•, Oxford, United Kingdom. Human Riak Alaea~ment, Alta, Utah. (November 1981, p. 644) Sponsor: SIAM Institute for Mathematics and Society. 26-August 13. Interuational Seminar on Data Anaiyli•, Program: The conference will consider a wide variety Universite de Montreal, Montreal, Canada. (February of environmental health risks, including radiation, air 1982, p. 200)

295 AUGUST 1982 SEPTEMBER 1982

August 1982. International Conference on Finite Element 1-10. International Institute on Stoehastics and Optimisa­ Methods, Beijing, China. (January 1982, p. 77) tion, University of Milan, Gargnano, Italy. modeling, algorithm 2-6. International Seminar on Functional Analysis, Program: Sessions will consider of the algorithm. Holomorphy and Approximation Theory, State Univer­ design, and analysis of the performance point processes, sity of Campinas, Brazil. (November 1981, p. 644.) Specialized topics include Poisson Gaussian processes, Monte Carlo methods, sampling ***(These dates have been changed from those previously methods, heuristics for NP-hard problems, and quasi­ announced.)*** enumerative methods. There will be invited and 2-6. Third Conference on Topology of Manifolds and contributed lectures, and discussion sessions. Homotopy Theory, Rio de Janeiro, Brasil. (February Information: M. Speranza, International Institute on 1982, p. 200) Stochastics and Optimization, c/o IAMI, Via Cicognara 3-10. Meeting on Binary Systems and Ring Theoretic 7, 20129 Milan, Italy. Methods in Universal Algebra, Czechoslovakia. (January 15-17. IFAC Symposium on Computer Aided Design of 1982, p. 77) Multi:variable Teehnologieal Sylltems, Purdue University, 8-13. Tenth IMACS World Congress on Systems Simulation West Lafayette, Indiana. and Scientific Computation, Montreal, Canada. (June Information: Gary Leininger, Purdue University, 1981, p. 348) IFAC/CAD, School of Mechanical Engineering, West Program: There will be symposia on specialized topics Lafayette, Indiana 47907. such as modeling and simulation of biological systems; modeling and simulation of energy systems; parallel OCTOBER 1982 computation; computer methods for ordinary and partial differential equations; computer arithmetics; evaluation October-November 1982. Workshop on Teaehing of of computer systems performance; discrete systems Graduate and Undergraduate Mathematics, Chiangmai, simulation; applications of scientific computation in the Thailand. (January 1982, p. 77) engineering sciences. 1-2. Tenth Annual Mathematics and Statistics Conference, 8-13. First International Conference on Teaehing of Miami University, Oxford, Ohio. Statisties, Sheffield, England. (January 1982, p. 77) Invited Speakers; Harold Abelson (Massachusetts Institute (Ohio State 9-10. International Conference on Philosophy and Foun­ of Technology); William Buttelmann University); James T. Fey (University of Maryland); dations ofMathematies, Warsaw, Poland. (February 1982, Stephen C. Kleene (University of Wisconsin); Bruce p. 200) Weide (Ohio State University). 11-19. International Congress of Mathematicians, Warsaw, Call for Papers: The theme of the conference will be Poland. (August 1981, p. 426; February 1982, p. 152) "Mathematics and Computing". Contributed papers 16-19. Institute of Mathematieal Statisties Annual Meet­ relating to the theme are welcome. Of particular interest ing, Cincinnati, Ohio. (February 1982, p. 200) will be papers dealing with the use of computers in the teaching of mathematics. 19-21. Third Ameriean Time Series Meeting, Cincinnati, Deadline for Abstracts; Abstracts should be sent by June Ohio. (February 1982, p. 200) 1, 1982, to the address below. 19--27. Eighth Conference on Analytie Funetions, Information: Don Koehler or Fred Schuurmann, Blazejewko, Poland. (August 1981, p. 438) Department of Mathematics and Statistics, Miami University, Oxford, Ohio 45056. 22-September 8. :xneme Ecole d'Ete de Calcul des Probabilites, Saint-Flour, Cantal, France. 17-21. International Conference on Mathematiea, Univer­ Invited Speakers: R. M. Dudley (Massachusetts Institute sity of Riyadh, Riyadh, Saudi Arabia. (February 1982, p. of Technology), H. Kunita (Kyushu University), F. 200) Ledrappier (Universite Paris VI). 25-27. Splll'lle Matrix Symposium, Fairfield Glade, Information: P. L. Hennequin, Departement de Tennessee. (February 1982, p. 200) Mathematiques Appliquees, Universite de Clermont, B. P. 45, 63170 Aubiere, France. NOVEMBER 1982 23-27. Tenth Australian Conference on Combinatorial Mathematies, University of Adelaide, Adelaide, South 2--4. SIAM Conference on Numerieal Simulation of VLSI Australia. Devices, Boston, Massachusetts. Program: Contributed papers are sought in all Sponsors: Society for Industrial and Applied Mathematics, areas of combinatorics, pure and applied, including Institute for Electrical and Electronic Engineers. combinatorial computing. There will be invited lectures. Program: The major emphasis of the conference will be The fourth annual general meeting of the Combinatorial directed towards the numerical solution of the coupled Mathematics Society of Australasia will be held at the two- and three-dimensional systems of partial differential conference. equations used to describe the process steps and device Information: L. R. A. Casse, Director, Combinatorial behavior. Device-related aspects of circuit design and Mathematics Society of Australasia, Department of simulation of system layout will also be considered. Mathematics, University of Adelaide, North Terrace, Call for Papers: Contributors should submit ten copies Adelaide, South Australia, 5001. of a 50-word descriptive abstract, and a single-page 300-500 word summary of a 20-minute presentation by 23-27. Eleventh International Symposium on Mathemati­ June 1, 1982, to Donald J. Rose, Room 2C-283, Bell eal Programming, University of Bonn, Bonn, West Laboratories, 600 Mountain Avenue, Murray Hill, New Germany. (February 1982, p. 200) Jersey 0797 4, (201 )582-4355. 23-28. Equadiff 82, Wiirzburg, Federal Republic of Information: Hugh B. Hair, SIAM Services Manager, 1405 Germany. (January 1982, p. 77) Architects Building, 117 South 17th Street, Philadelphia, Pennsylvania 19103, (215)564-2929. 30-September 3. Eleventh International Symposium on Mathematieal Foundations of Computer Science, Gdansk, 3-5. Twenty-third Annual IEEE Symposium on Founda­ Poland. ***(This meeting has been cancelled. See tions of Computer Science, Chicago, lllinois. (February February 1982, p. 201.)*** 1982, p. 201)

296 16-December 10. Autumn Courae on Mathematical 14-18. NSF-CBMS Regional Conference on Mathematical Ecology, International Centre for Theoretical Physics, Theory of Laminar Combustion, Colorado State University, Trieste, Italy. Fort Collins, Colorado. Program: The first two weeks of the course will emphasize Principal Lecturer: G. S. S. Ludford, Cornell University. the foundations of mathematical ecology and will focus Information: J. W. Thomas, Department of Mathematics, on deterministic and stochastic models of populations Colorado State University, Fort Collins, Colorado 80523. and communities. The second portion of the course 22-26. NSF-CBMS Regional Research Conference on Non­ will feature research seminars on current developments and applications. Special emphasis will be on resource linear Waves and Integrable Systems, East Carolina Univer­ sity, Greenville, North Carolina. management, population biology and infectious diseases, Principal Lecturer: Alan C. Newell, University of Arizona. transport processes and biological oceanography. Program: The Conference is intended to bring researchers Speakers: R. Anderson (England), J. Beddington together who are interested in the mathematical theory and (England), C. Clark (Canada), J. Cohen (U.S.A.), K. application of nonlinear wave phenomena. The lectures will Dietz (West Germany), J. Frauenthal (U.S.A.), L. Gross cover broad research-expository topics including nonlinear (U.S.A.), T. Hallam (U.S.A.), A. Hastings (U.S.A.), S. oscillators, wave-trains and methods used in their analysis, Levin (U.S.A.), D. Ludwig (Canada), R. May (U.S.A.), derivation of the canonical nonlinear evolution equation, A. Okubo (U.S.A.), T. Platt (Canada), L. Ricciardi Korteweg-de Vries, nonlinear Schrodinger, Sine-Gordon, (Italy), L. Segel (Israel), F. Scudo (Italy), and M. Turelli inverse scattering theory, Hamiltonian structure, solitons (U.S.A.). . under perturbation, and solitons in physics. Some additional Support: Some support is available from ICTP. Deadlme invited lectures and informal seminars will also be included for application for support is May 31, 1982. in the conference program. Information: T. G. Hallam, Department of Mathematics, Support: NSF support, for travel and living expenses, is University of Tennessee, Knoxville, Tennessee 37996; available for conference participants. Simon Levin, Ecology and Systematics, Cornell Univer­ Deadline for applications: Application for participation and sity, Ithaca, New York 14853; or ICTP, P. 0. Box 586, possible support should be made on or before May 7, 1982. 1-34100 Trieste, Italy. Late applications will be considered as space permits. In­ clusion of a statement of interests with emphasis on current LATE ENTRIES research and publications will be helpful for selection of June 1982 funded participants. 7-11. NSF Conference on Large Deviations, Southern Information: Lokenath Debnath, Department of Mathematics. lllinois University, Carbondale, Illinois. East Carolina University, Greenville, North Carolina 27834, Principal Speaker: S. R. S. V aradhan of Courant Institute (919)757-6715 or 6879. will give ten lectures. Topics: The Vencel-Freidlin theory of small random per­ July 1982 turbations of dynamical systems, large deviation problems connected with the ergodic theory of Markov processes, 12-16. Conference on Partial Differential Equations (in and applications to various problems in statistical mechanics. Honor of Ralph Phillips), Stanford University, Stanford, Support: Funding is available for 25 participants. . California. Information: P. Feinsilver or Tom Paine, Mathematics Sponsor: National Science Foundation. Department, Southern Illinois University, Carbondale, Information: Helen Schawlow, Department of Mathematics, Illinois 62901. Stanford University, Stanford, California 94305.

CONTEMPORARY MATHEMATICS PROCEEDINGS OF THE CONFERENCE ON state-of-the art flavor, the book contains several re­ INTEGRATION, TOPOLOGY, AND GEOMETRY search articles devoted to topics as diverse as spectral IN LINEAR SPACES theory (by N. Dunford) and weak and strong com­ pactness in spaces of Pettis integrable functions (by edited by William H. Graves ). Brooks and N. Dinculeanu). This book contains survey articles contributed The book gives an overview of the current state by speakers at a conference held at the University of of affairs in the study of measure and integration in North Carolina in Chapel Hill in the spring of 1979 linear spaces and applications thereof. Those who and organized around contributions of the late B. ) . will enjoy these papers are workers in functional Pettis to the development of measure and integration analysis with an interest in measure and integration in linear spaces and the role of general linear spaces in linear spaces, especially the many delighted readers in measure-theoretic considerations. Topics covered of Diestel and Uhl's Vector Measures (Amer. Math. include strict topologies in topological measure theory Soc. Mathematical Surveys, Volume 15). (by H. Collins), the Dunford-Pettis property (by ) . Diestel), the Radon-Nikodym property (by R. Huff), the Orlicz-Pettis phenomenon (by N. Kalton), appli- Volume 2, x + 269 pages (soft cover) List price $16.00, institutional member $12.00, cations of measure and integration in linear spaces individual member $8.00 (by I. Kluvanek), and the role of the Pettis measur- ISBN o-8218-5002-4; LC 80-25417 ability theory (by).). Uhl, Jr.). In addition to these Publication date: November 1980 survey articles which impart both a historical and a To order, please specify CONM/2•N Prepayment is required for all AMS publications. Order from AMS, P.O. Box 1571, Annex Station, Providence, Rl 02901,.or call toll free 800-556-7774 to charge with Visa or MasterCard.

297 New AMS Publications

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CONTEMPORARY MATHEMATICS This book contains a representative sample of (ISSN 0271-4132) current research by experts from many countries. There are two outstanding contributions. First the ORDERED FIELDS AND REAL book represents the first broadly international con­ ference on its topic, and, above all, it contains prob­ ALGEBRAIC GEOMETRY ably the greatest break-through yet in commutative edited by Donald W. Dubois and Tomas Recio algebra, with a brilliant array of applications in real The contents of this book comprise, with only algebraic geometry. This is the paper of Coste and minor editorial changes, papers submitted by those Roy where the theory of the spectre reel is given its mathematicians who accepted an invitation to first full exposition. speak at the American Mathematical Society's There are other papers of unusual significance. Special Session on Ordered Fields and Real Alge­ Pfister applies his famous quadratic form theory to a braic Geometry in San Francisco, January 1981. study of Abelian varieties. Delfs and Knebusch add C. Andradas, Normal decompositions of semi­ another chapter to their semi-algebraic topology in algebraic sets varieties over real-closed fields. Lam and Shapiro add G. Brumfiel, Some open problems to their fine contributions in quadratic form theory. Michel Coste and Marie-Fran~oise Roy, La topologie There are outstanding contributions from several du spectre reel young mathematicians, notably Andradas, Delzell, H. Delfs and M. Knebusch, Semialgebraic topology Harman, Merzel, Recio and Schiilting. over a real closed field Potential readers require above all a good back­ C. Delzell, A finiteness theorem for open semi-alge­ ground in commutative algebra (especially the real braic sets, with applications to Hilbert's 17th kind). Most papers require basic knowledge of affine problem algebraic varieties. Some require sheaf theory, or L. Brocker, Andreas Dress and R. Scharlau, An cohomology theory or quadratic form theory. (almost) trivia/local-global principle for the repre­ sentation of -1 as a sum of squares in an arbi­ 1980 Mathematics Subject Classlflcatlons:12D15, 12]15, 32C05, 10C04, 13j25. trary commutative ring Volume 8, viii + 368 pages (soft cover) G. Efroymson, The Nash ring of a real surface List price $18.80, institutional member $14.1 0, R. Gilmer, Extension of an order to a simple trans' individual member $9.40 cendental extension ISBN 0-8218-5007-5; LC 82·3951 D. Gondard, Theorie des modeles et fonctions de­ Publication date: April 1982 finies positives sur les var!etes algebriques reeles To order, please specify CONM/8N J. Harman, Chains of higher level orderings M. Henriksen and F. Smith, Some properties of positive derivations on f-rings PAPERS IN ALGEBRA, J. Merzel, Quadratic forms over fields with finitely ANALYSIS AND STATISTICS many orderings edited by Rudolf Lid/ B. Glastad and J. Mott, Finitely generated groups of divisibility The papers collected in this volume are modified A. Pfister, On quadratic forms and Abelian varieties versions of invited lectures and some contributed over function fields specialist session papers presented at the 21st Sum­ D. Dubois and T. Recio, Order extensions and real mer Research Institute of the Australian Mathemati­ algebraic geometry cal Society held at the University of Tasmania from H. Schiilting, Real points and real places 12th January until 6th February 1981. N. Schwartz, The strong topology on real algebraic The 21st Summer Research Institute covered a varieties wide range of topics in pure and applied algebra, D. Shapiro and T. Lam, The square class invariant analysis and statistics. Most of the invited lectures for Pythagorean fields were of a survey nature and each week of the Insti­ A. Tognoli, Coherent algebraic sheaves In real alge­ tute was devoted to different subject areas. Invited braic geometry lectures reproduced in this volume are: A. Engler and T. Viswanathan, Digging holes in C. W. Curtis and G. I. Lehrer, Homology representa­ algebraic closures aIa Artin-11 tions of finite groups of Lie type

298 R. Delbourgo, Matrix correlation functions CONTENTS D. Elliott, Some aspects of singular integral equa- 1. Imbedded, intermediate, and interpolation tions-A numerical analyst's viewpoint Banach spaces F. Hirzebruch, Some examples of algebraic surfaces 2. Interpolation in spaces of measurable functions I. G. Macdonald, Lie groups and combinatorics 3. Scales of Banach spaces M. Mendes- France, Paper folding, space-filling curves 4. Interpolation methods and Rudin-Shapiro sequences 5. (By S. G. Krein). Interpolation in spaces of G. Pilz, Near-rings: What they are and what they smooth functions (This chapter is not included are good for in the Soviet edition.) T. J. Rivl in, The optimal recovery of functions 1980 Mathematics Subject Classifications: 46E30, 46E35; N. J. A. Sloane, Recent bounds for codes, sphere 44A15, 42C10. packings and related problems obtained by linear Volume 54, xii + 376 pages programming and other methods List price $71.20, institutional member $53.40, of individual member $35.60 G. S. Watson, Three aspects of the statistics ISBN 0-8218-4504-7; LC 81-20637 directions Publication date: February 1982 E. C. Zeeman, Bifurcation and catastrophe theory To order, please specify MMON0/54N Twenty-two of the contributed papers are also in­ cluded in this volume on specialist topics in algebra, analysis and statistics. OF THE One of the main strengths of this book is the PROCEEDINGS introductory and survey nature of some papers, STEKLOV INSTITUTE OF MATHEMATICS especially Hirzebruch, Pilz, Rivlin, Sloane, Watson, (ISSN 0081-5438) Zeeman. Articles of high research value are Curtis and Lehrer, Macdonald, Sloane. The papers by THEORY AND APPLICATIONS OF Delbourgo, Elliott, Mendes-France concentrate on a DIFFERENTIABLE FUNCTIONS OF narrower topic than the other invited papers. Some SEVERAL VARIABLES. VII papers contain expository work (e.g. Pilz, Rivlin, Zeeman), but the main emphasis is on surveying a edited by S.M. Nikol'skiT given topic. translated by J. szacs Individuals might gain an insight into a new ABSTRACT. In the papers of this collection imbed­ field due to the introductory nature of some of the ding and extension theorems are established for various papers. They will also get to know the frontiers of function spaces, existence conditions and properties current research in some topics. of traces of functions are found, and the behavior of for bound­ 1980 Mathematics Subject Classifications: OOA 10; 05-06, functions at infinity is studied. Conditions 14-06,16-06,41-06,62-06,94-06 edness and compactness of an imbedding in weighted Volume 9, xvi + 400 pages (soft cover) spaces are found. On the basis of a new integral List price $20.80, institutional member $15.60, representation of functions the rate of decrease of the individual member $10.40 error in cubature formulas is estimated. Boundary ISBN 0-8218-5009-1; LC 82-1826 value problems for elliptic equations with degeneracy Publication date: April 1982 To order, please specify CONM/9N are studied. A difference method of solving the Dirichlet problem for the Laplace and Poisson equa­ tions in a polyhedron is proposed. Some comparative properties of general differential operators with con­ stant coefficients are studied and some conditions TRANSLATIONS OF for hypoellipticity are obtained. MATHEMATICAL MONOGRAPHS The preceding parts of this series were published (ISSN 0065-9282) in volumes 77 (1965), 89 (1967), 105 (1969), 117 (1972), 131 (1974), and 140 (1976). INTERPOLATION OF LINEAR OPERATORS CONTENTS by S. G. KreTn, ju. I. Petunin, and E. M. Semenov 0. V. Besov and V. P. II 'in, Projection representations translated by }. Szucs of functions by means of differences ABSTRACT. This book is devoted to an important 0. V. Besov, Error estimates for cubature formulas in direction in functional analysis: interpolation theory terms of smoothness of functions for linear operators. The main methods for construc­ V. I. Burenkov, On partitions of unity ting interpolation spaces are expounded and their V. I. Burenkov and M. L. Gol'dman, On extension properties are studied. These methods allow one to of LP-functions look at a number of theorems and inequalities of V. I. Burenkov and B. L. Fain, On the extension of classical analysis from a new standpoint. Interpola­ functions in anisotropic spaces with preservation tion theory for operators has numerous applications of class in Fourier series, approximation theory, partial differ­ E. A. Volkov, On the smoothness of solutions of the ential equations, etc. Some of them are developed in Dirichlet problem and the composite mesh method the book. on polyhedra

299 M. L. Gol' dman, The description of traces for certain 1980 Mathematics Subject Classifications: 55P35, 55P40, function spaces 55S 12, 55T15. G. G. Kazarjan and V. N. Markarjan, Criteria for Number 258, viii + 228 pages (soft cover) hypoellipticity in terms of power and strength of List price $12.80, institutional member $9.60, individual member $6.40 operators ISBN 0-8218-2258-6; LC 81-20515 G. G. Kazarjan, Comparison of powers of polynomials Publication date: March 1982 and their hypoellipticlty To order, please specify MEMOI258N G. A. Kaljabin, Description of traces for anisotropic Tr/ebei-L/zorkin classes REFERENCE WORK P. I. Lizorkin, The behavior at Infinity of functions In a Liouville class. On Riesz potentials of arbitrary MATHFILE USER'S GUIDE order MATHFILE is the Society's new computer-search­ N. V. Miro~in, The exterior Dirichlet problem for a able version of Mathematical Reviews (the cumulative degenerate elliptic operator index covering 1973 to 1979, as well as the contents S. M. Nikol'skii~ A variational problem for an equa­ of issues published in 1980 and since, including for tion of elliptic type with degeneration on the the latter texts of the reviews themselves). For infor­ boundary mation on MATHFILE see the February 1982 Notices, ju. S. Nikol'skii, Inequalities between different semi­ page 169. norms of differentiable functions of several vari­ A user's guide has been prepared by the Society ables to make searching MATHFILE easier, more effective M. Otelbaev, Imbedding theorems for weighted and faster. The Guide includes: spaces and their applications in the study of the Instructions. How to get started on the vendors' sys­ spectrum of the Schrodinger operator tems, an explanation of the file and suggestions on A. P. Terehin, Mixed q-lntegral p-var/ation and equiv­ search techniques. alence and Imbedding theorems for classes of Abbreviations. journal name abbreviations used by functions with mixed moduli of smoothness Mathematical Reviews, and the full titles as defined 1980 Mathematics Subject Classifications: 26, 35, 41, 46, by the Library of Congress, the ISSN, Coden, and 47, 65. useful publishing information. Number 150, vii + 325 pages (soft cover) Subject Classification Systems. A correlated four­ List price $88.00, institutional member $66.00, column display of the two Individual member $44.00 (1970 and 1980) slightly ISBN 0-8218-3047-3; LC 68·1677 different systems, the Library of Congress system, Publication date: February 1982 and an inversion of the list showing LC numbers To order, please specify STEKL0/150N and corresponding AMS classification codes. Index of terms occurring in the subject classification. Alphabetic listing of subject words from the 1980 Mathematics Subject Classification with the corre­ MEMOIRS OF THE AMS sponding class numbers given for each. This list will (ISSN 0065-9266} be very helpful to searchers unfamiliar with the 1980 Mathematics Subject Classification. THE UNSTABLE ADAMS SPECTRAL SEQUENCE Title words of entries reviewed from 1973 to 1979, FOR FREE ITERATED LOOP SPACES arranged alphabetically with class numbers under by Robert j. Wellington which the entries occurred and frequency of occur­ This monograph is concerned with making the rence of each word in each section. unstable Adams spectral sequence an effective tool Inversion of the title word list, arranged by classifi­ for studying the homotopy groups of suspension cation number, showing which title words occurred spaces ~n X. The analysis focuses on the free iterated in each section and with what frequency. This will loop spaces Q,n ~n X, n > 0. Included is a descrip­ be useful in finding the right words to search on a tion of the mod p homology of rzn ~n X as an un­ specific subject. stable coalgebra over the Steenrod algebra A, with 1980 Mathematics Subject Classification: 00 the primitive elements receiving particular attention. The Dyer-Lashof homology operations are related Approximately 350 pages, Three-ring Binder List price $50.00, institutional member $37.50, to the Lambda operations, which is useful in com­ individual member $37.50 puting the unstable Ext groups associated with the ISBN 0-8218..()216-X spaces rzn ~n X A discussion of various algebraic Publication date: May 1982 EHP sequences is presented and the results of the inductive calculations are tabulated. The monograph CORRECTION concludes with an explanation of a procedure for On page 171, of the February issue of Notices, computing the £ 2 term of the unstable Adams the name of Walter Schempp, author of Complex spectral sequence for rzn ~n X The spectral se­ contour Integral representation of cardinal spline quence and its differentials are displayed through a functions, Volume 7 of Contemporary Mathematics, range for the example rznsn+k. was misspelled.

300 SOME RECENT REPRINTS ALGEBRAIC GEOMETRY AND THETA FUNCTIONS AUTOMATA ON INFINITE OBJECTS by Arthur B. Coble AND CHURCH'S PROBLEM Colloquium Publications, Volume 10 by Michael Rabin (ISBN 0-8218-1010-3) 282 pages (soft cover} CBMS Regional Conference Series in Mathematics 1929; reprinted with corrections 1961; reprinted 1982 Number 13, 22 pages (ISBN 0-8218-1663-2) List price $18.80, institutional member $14.10, 1972; reprinted 1982 (soft cover) individual member $9.40 List price $8_80, individual $4.40 To order, please specify COLL/10N To order, please specify CBMS/13N THE THEORY OF APPROXIMATION ANALYSIS ON LIE GROUPS by D. jackson HOMOGENEOUS SPACES Colloquium Publications, Volume 11 by Sigurdur Helgason (ISBN 0-8218-1011-1} 178 pages (soft cover) CBMS Regional Conference Series in Mathematics 1930; reprinted 1982 Number 14, 64 pages (ISBN 0-8218-1664-0) List price $18.80, institutional member $14.10, 1972; reprinted with corrections 1982 (soft cover) individual member $9.40 List price $8.80, individual $4.40 To order, please specify COLL/11 N To order, please specify CBMS/14N FOURIER TRANSFORMS DIFFERENTIAL GAMES IN THE COMPLEX DOMAIN by A vner Friedman by R. E. A. C. Paley and N. Wiener CBMS Regional Conference Series in Mathematics Colloquium Publications, Volume 19 Number 18, 66 pages (ISBN 0-8218-1668-3) (ISBN 0-8218-1019-7} 183 pages (soft cover) 1974; reprinted 1982 (soft cover) 1934; reprinted 1982 List price $9.60, individual $4.80 List price $27.60, institutional member $20.70, To order, please specify CBMS/18N individual member $13.80 To order, please specify COLL/19N UNITARY DILATIONS OF HILBERT SPACE OPERATORS ORTHOGONAL POLYNOMIALS AND RELATED TOPICS by Gabor Szego by Bela Sz.-Nagy Colloquium Publications, Volume 23 CBMS Regional Conference Series in Mathematics (ISBN 0-8218-1023-5) 430 pages (soft cover) Number 19,54 pages (ISBN 0-8218-1669-1) 1939; fourth edition 1975; reprinted 1981 1974; reprinted with corrections 1982 (soft cover) List price $30.40, institutional member $22.80, List price $9.60, individual $4.80 individual member $15.20 To order, please specify CBMS/19N To order, please specify COLL/23N

INTRODUCTION TO SOME METHODS TOPOLOGICAL DYNAMICS OF ALGEBRAIC K-THEORY by W. H. Gottschalk and G. A. Hedlund by Hyman Bass Colloquium Publications, Volume 36 CBMS Regional Conference Series in Mathematics (ISBN 0-8218-1 036-7) 167 pages (soft cover) Number 20,68 pages (ISBN 0-8218-1670-5) 1955; reprinted 1982 1974; reprinted 1982 (soft cover) List price $24.80, institutional member $18.60, List price $8.20, individual $4.1 0 individual member $12.40 To order, please specify CBMS/20N To order,- please specify COLL/36N

ISOLATED INVARIANT SETS LECTURES IN STATISTICAL MECHANICS AND THE MORSE INDEX by G. Uhlenbeck, G. W. Ford, and E. W. Montro/1 by Charles C. Conley Lectures in Applied Mathematics CBMS Regional Conference Series in Mathematics Volume 1,181 pages (ISBN 0-8218-1101-0) Number 38,89 pages (ISBN 0-8218-1688-8) 1963; reprinted 1982 (soft cover) 1978; reprinted 1982 (soft cover} List price $23.20, institutional member $17.40, List price $12.80, individual $6.40 individual member $11.60 To order, please specify CBMS/38N To order, please specify LAM/1 N

THE PROBLEM OF MOMENTS LECTURES ON FLUID MECHANICS by}. A. Shohat and j. D. Tamarkin by 5. Goldstein Mathematical Surveys, Number 1 Lectures in Applied Mathematics (ISBN 0-8218-1501-6), 144 pages (soft cover) Volume 2A, 311 pages (ISBN 0-8218-0048-5} 1943; revised edition 1950; reprinted 1982 1960; reprinted 1982 {soft cover) List price $25.60, institutional member $19.20, List price $36.00, institutional member $27.10, individual member $12.80 individual member $18.00 To order, please specify SURV/1 N To order, please specify LAM/2.1

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301 MISCELLANEOUS

Personal Items J. Dwight Daugherty of Clearwater, Florida, Emeritus Professor of Kutztown State College, died on Peter W. Bates of Texas A&M University will be December 24, 1981, at the age of 81. He was a member a visiting mathematician at Heriot-Watt University, of the Society for 18 years. Scotland, for 1981-1982. J. M. Gandhi of Northern Illinois University died David E. Blair of Michigan State University will be on January 23, 1982, at the age of 49. He was a a visiting mathematician at the University of Liverpool, member of the Society for 13 years. England, for 1981-1982. Frank G. Krupansky of Miami, Florida, an Robert A. Blumenthal of St. Louis University has electrical engineer for Coulter Electronics, died on been appointed to an associate professorship at that November 14, 1981, at the age of 32. He was a member university. of the Society for 7 years. Biswa Nath Datta of Northern Illinois University Demetrio& G. Magiros of Philadelphia, Pennsyl­ has been appointed to a professorship at that university. vania, a mathematical consultant with General Electric Space and Environmental Studies Division, died on Subhash C. Saxena of New Delhi, India, will be January 19, 1982, at the age of 69. He was a member a visiting mathematician at the Indian Institute of of the Society for 31 years. Technology, for 1981-1982. Milton A. Nelson of Great Neck, New York, died Deaths on April 29, 1981, at the age of 67. He was a member of the Society for 14 years. Homer Vmeent Craig of Del Rio, Texas, Emeritus John W. Riner of Ohio State University died on Professor of the University of Texas, Austin, died on January 26, 1982, at the age of 57. He was a member November 30, 1981, at the age of 81. He was a member of the Society for 26 years. of the Society for 56 years.

MATHEMATICAL SCIENCES 1982 administrative directory

PROFESSIONAL MATHEMATICAL ASSOCIATIONS ACADEMIC INSTITUTIONS-DEPARTMENTS IN THE MATHEMATICAL SCIENCES AND OTHER FACILITIES in the U.S., Canada, Central America, and the Caribbean, coded according to the highest degree offered MATHEMATICAL UNITS IN NONACADEMIC ORGANIZATIONS HEADS AND KEY PERSONNEL of a selected group of government agencies EDITORS OF JOURNALS in the mathematical sciences OFFICERS AND COMMITIEE MEMBERS in more than 25 professional mathematical organizations AN INDEX OF ACADEMIC INSTITUTIONS

$12.60 Publication date: February 15, 1982 Code: ADMDIR82- Prepayment Required american mathematical society p. o. box 1571, annex station, providence, r. i. 02901

302 Assistantships and Fellowships in the Mathematical Sciences in 1982-1983 Supplementary List

The entries below supplement the December 1981 Special Issue of the Notices. The first supplement appeared on pages 204-209 of the February 1982 Notices (see page 204 for an explanation of the abbrevia­ tions used).

TYPE OF ASSISTANCE STIPEND FEES SERVICE REQUIRED DEGREES AWARDED (number anticipated paid to student paid by hours type Academic year 1982-1983) dollars months student ($) per week of service 1980-1981

CANADA University of Waterloo, Waterloo, Ontario N2L 3G1 DEPARTMENT OF APPLIED MATHEMATICS Applications due: 7/31/82 Bachelor's by inst. 2697 C. F. A. Beaumont, Chairman Faculty 21; Published 17 Bachelor's by dept. 20 Master's by dept. 8 Teaching Assistantship (60) 4 760-6520 9 * 5·1 0 Grading, tutoring Ph.D. (78/81) AM 5. Total: 5 Research Assistantship (17) 6900 12 * Research Scholarship (13)** * Other (14)** 600-2400 12 * Research *Canadian or landed immigrant: $1059.69 for 12 months; student visa: $2436.69 for 12 months. **See University Calendar for details. DEPARTMENT OF COMBINATORICS AND OPTIMIZATION Applications due: 4/30/82 Bachelor's by inst. 2697 J. Adrian Bondy, Chairman Faculty 21; Published 18 Bachelor's by dept. 22 Master's by dept. 6 Teaching Assistantship {26) 4760-6520 9 * 5·1 0 Grading, tutoring Ph.D. (78/81) OR 1, Other 15. Research Assistantship (18) 6900 12 * Research Total: 16 Scholarship (4)** * Other (8)** 600-2400 12 * Research *Canadian or landed immigrant: $1059.69 for 12 months; student visa: $2436.69 for 12 months. **See University Calendar for details. DEPARTMENT OF COMPUTER SCIENCE Applications due: 4/82 Bachelor's by inst. 2697 ]. A. Brzozowski, Chairman Faculty 33; Published 33 Bachelor's by dept. 83 Master's by dept. 28 Teaching Assistantship (65) 4760-6520 9 * 5·10 Grading, tutoring Ph.D. (78/81) CS 16. Total: 16 Research Assistantship (32) 6900 12 * Research Scholarship (20)** * Other (12)** 600-2400 12 * Research *Canadian or landed immigrant: $1059.69 for 12 months; student visa: $2436.69 for 12 months. **See University Calendar for details. DEPARTMENT OF PURE MATHEMATICS Applications due: 5/1/82 Bachelor's by inst. 2697 G. E. Cross, Chairman Faculty 24; Published 19 Bachelor's by dept. 1 0 Master's by dept. 3 Teaching Assistantship (14) 4760-6520 9 * 5-10 Grading, tutoring Ph.D. (78/81) ANT 1, GT 1. Research Assistantship (1 0) 6900 12 * Research Total: 2 Scholarship (1 )** * Other (2)** 600-2400 12 * Research *Canadian or landed immigrant: $1059.69 for 12 months; student visa: $2436.69 for 12 months. **See University Calendar for details. DEPARTMENT OF STATISTICS Applications due: 4/1/82 Bachelor's by inst. 2697 ]. F. Lawless, Chairman Faculty 30; Published 20 Bachelor's by dept. 26 Master's by de pt. 7 Teaching Assistantship (23) 4760-6520 9 * 5-10 Grading, tutoring Ph.D. (78/81) S 10. Total: 10 Research Assistantship (20) 6900 12 * Research Scholarship (1 0)** * Other (12)** 600-2400 12 * Research *Canadian or landed immigrant: $1059.69 for 12 months; student visa: $2436.69 for 12 months. **See University Calendar for details.

303 Doctorates Conferred in 1980-1981 (Supplementary List)

The following Jist supplements the NEW YORK CANADA list of thesis titles published in the November 1981 Notices (see page 619 Cornell University Carleton University for an explanation of the numbers in {9;8,1,0,0,0,0,0) {3;1,2,0,0,0,0,0) parentheses). MATHEMATICS MATHEMATICS AND STATISTICS DISTRICT OF COLUMBIA Beichl, Isabel Marie, Computations in Aly, Emad Eldin, Quantile process, group cohomology for finite groups. spacings and goodness-of-fit. American University Blank, Brian Evan, Boundary behavior of Cotterill, Derek, On the limiting dis­ (1;0,1,0,0,0,0,0) limits of discrete series representatives. tribution of and critical values for Brady, Stephen, Recursive aspects of the the Hoeffding-Blum-Kiefer-Rosenblatt in­ MATHEMATICS, STATISTICS AND COMPUTER SCIENCE theory of real closed fields. dependence criterion. Birgitta, £-func­ Iscoe, Ian, The man-hour process as­ Mitchell, Keith, A study of ridge regres­ Brattstrom, Gudrun tions of Jacobi-Sum Heeke characters. sociated with measure valued branching sion and some examples of its application The classical random motions in Rd. in multivariate analysis. Donald, Matthew James, limits of P( )2 qt~antum field theories. ll..LINOIS Gatsonis, Constantine Achilleos, Es­ timation of the posterior density of a Northwestern University location parameter. (4;0,0,0,0,4,0,0) Immerman, Neil, First order expressibility as a new complexity measure. ENGINEERING SCIENCE AND APPLIED MATHEMATICS Lo, Martin W., Isometric embeddings and Bryant, Michael, Some aspects of elastic deformations of surfaces with boundary 3 bodies in contact. inR . Dunayevsky, Victor, Dynamic effects of Nag, Subhashis, On some geometrical fracture of elastic-plastic material3. problems in Teichmii.ller and Torelli spaces. Lederer, Philip, Location-price games. Malon, David, Germ-Markov processes. SUNY at Albany {2;2,0,0,0,0,0,0) NEBRASKA MATHEMATICS AND STATISTICS University of Nebraska Ryczaj, Jerzy, ck -estimates for the {3;3,0,0,0,0,0,0) Cauchy-Riemann eqt~ations on certain weakly pseudoconvex domains. MATHEMATICS AND STATISTICS Samotij, Krzysztof, Some properties of Right focal point Henderson, Johnny, harmonic functions with restrictions on boundary value problems for ordinary growth. differential equations. Krauter, William W. ill, Combinatorial Yeshiva University properties of algebraic sets. (1;0,1,0,0,0,0,0) Sastry, A Siva Sankara, Vector integrals MATHEMATICS and products of vector measures. Kushner, Howard Burt, Wishart expecta­ tion operators and invariant differential operators.

304 AMS Reports and Communications

Recent Appointments the Audit Committee. The continuing member is Cathleen S. Morawetz. Committee members' terms of office on standing Alex Rosenberg, as chairman of the Board of committees expire on December 31 of the year Trustees, is now a member of the Investment given in parentheses following their names, unless Committee. The other members of the Committee are otherwise specified. Franklin P. Peterson, chairman, and Steve Armentrout. The terms of the members of the Committee on The Committee on Affirmative Action Proce­ Science Policy have been adjusted to establish ·a dures has been discharged with the thanks of the reasonable size and practical rotation. The members Council. are Hyman Bass (1984), Felix E. Browder (1984), The Committee on Legal Aid has been discharged Frederick W. Gehring (1982), Andrew M. Gleason (ex with the thanks of the Council. This act accomplishes officio), Kenneth Hoffman, chairman (1984), William J. only a change in the line of reporting of the Committee, LeVeque (ex officio), George D. Mostow (1983), Ralph not its dissolution. The Committee is now a Committee S. Phillips (1982), Julia B. Robinson (ex officio), Linda of the Board of Trustees. Preiss Rothschild (1983), I. M. Singer (1984), James Steve Armentrout has been appointed by Alex D. Stasheff (1983), Elias M. Stein (1982), Hans F. Rosenberg, chairman of the Board of Trustees, to Weinberger (1982).

MATHEMATICAL SURVEYS

ESSENTIALS OF BROWNIAN MOTION Absorption and the Dirichlet problem. Space-time AND DIFFUSION process and the heat equation. Killed processes, by Frank B. Knight Green functions, and the distributions of additive This work was first-drafted five years ago at the functionals. Time-change theorem (classical case), invitation of the editors of the Encyclopedia of parabolic equations and their solution semigroups, Mathematics and its Applications. However, it was some basic examples, distribution of passage times. 5. Local time: construction by random walk found to contain insufficient physical applications embedding. Local time processes. Trotter's theorem. for that series, hence it has finally come to rest at The Brownian flow. Brownian excursions. The zero the doorstep of the American Mathematical Society. The first half of the work is little changed from the set and Levy's equivalence theorem. Local times of classical diffusions. Sample path properties. original, a fact which may partly explain both the allusions to applications and the elementary approach. 6. Boundary conditions for Brownian motion. It was written to be understood by a reader having The general boundary conditions. Construction of minimal familiarity with continuous time stochastic the processes using local time. Green functions and processes. The most advanced prerequisite is a dis­ eigenfunction expansions (compact case). crete parameter martingale convergence theorem. 7. This chapter is a "finale" on nonsingular General summary and outline: diffusion. The generators ( d / dm) ( d+ I dx+) are char­ 0. Introduction. Some gratuitous generalities on acterized. The diffusions on open intervals are con­ scientific method as it relates to diffusion theory. structed. The conservative boundary conditions are 1. Brownian motion is defined by the character­ obtained and their diffusions are constructed. The ization of P. Levy. Then it is constructed in three general additive functionals and nonconservative basic ways and these are proved to be equivalent in diffusions are developed and expressed in terms of the appropriate sense. Uniqueness theorem. Brownian motions. 2. Projective invariance and the Brownian bridge The audience for this survey is anyone who presented. Probabilistic and absolute properties are desires an introduction to Markov processes with distinguished. Among the former: the distribution of continuous paths which is both coherent and ele­ the maximum, first pas~age time distributions, and mentary. The approach is from the particular to the hitting probabilities. Among the latter: law of general. Each method is first explained in the simplest iterated logarithm, quadratic variation, Holder conti­ case and supported by examples. Therefore, the book nuity, non-recurrence for r ;;;. 2. should be readily understandable to anyone with a 3. General methods of Markov processes adapted first course in measure-theoretic probability. to diffusion. Analytic and probabilistic methods are distinguished. Among the former: transition functions, Number 18, xiii + 201 pages (hard cover) semigroups, generators, resolvents. Among the latter: List price $34.40, institutional member $25.80, individual member $17.20 Markov properties, stopping times, zero-or-one laws, ISBN 0-8218-151 8-0; LC 80-29504 Dynkin's formula, additive functionals. Publication date: May 1981 4. Classical modifications of Brownian motion. To order, please specify SURV/1 8N Prepayment is required for all AMS publications. Order from AMS, P. 0. Box 1571, Annex Station, Providence, Rl 02901, or call toll free 800-556-7774 to charge with Visa or MasterCard.

305 Officers of the Society, 1981 and 1982 Except for the Members-at-Large of the Council, the month and year of the first term and the end of the present term are given. For Members-at-Large of the Council, the last year of the present term is listed. COUNCIL President: Andrew M. Gleason 1/81-12/82 Associate Secretaries Ex-president: Peter D. Lax 1/81-12/81 Raymond G. Ayoub 1/77-12/82 President-elect: Julia B. Robinson 1/82-12/82 Paul T. Bateman 1/67-12/83 Vice Presidents Frank T. Birtel 1/77-12/82 Michael Artin 1/82-12/83 Kenneth A. Ross 1/71-12/81 Hyman Bass 1/80-12/81 Hugo Rossi 1/82-12/83 Pau I R. Hal mos 1/81-12/82 Treasurer Mary Ellen Rudin 1/80-12/81 Franklin P. Peterson 8/73-12/82 Elias M. Stein 1/82-12/83 Associate Treasurer Secretary: Everett Pitcher 1/67-12/82 Steve Armentrout 7/77-12/82 Members-at-1 arge All terms are for 3 years and expire on December 31 of the given year 1981 1982 Chandler Davis Frederick W. Gehring Donald L. Burkholder Peter A. Fillmore Robert P. Gilbert Lee Lorch Alan J. Hoffman Melvin Hochster Ronald L. Graham* Richard S. Millman Linda Keen Robert P. Langlands Johan H. B. Kemperman Marian B. Pour-El 0. Carruth McGehee Susan Montgomery Karen Uhlenbeck Mary Ellen Rudin* Paul J. Sally, Jr. Hector J. Sussman Daniel H. Wagner David A. Sanchez I. M. Singer* *Member-at·large, as provided for in Article 7, Section 4 (last sentence) of the Bylaws of the Society.

Publications and Communications Committees Bulletin Editorial Committee Proceedings Editorial Committee Felix E. Browder 1/78-12/83 Thomas H. Brylawski 1/80-12/84 Meyer Jerison 1/80-12/82 David Eisenbud 1/78-12/81 Calvin C. Moore 1/82-12/84 David M, Goldschmidt 1/82-12/85 I. M. Singer 1/79-12/81 William E. Kirwan II 1/80-12/83 Colloquium Editorial Committee David J. Lutzer 1 /80-12/83 John W. Milnor 1/79-12/84 Robert R. Phelps 1/78-12/81 Stephen Smale 1/78-12/83 Reinhard E. Schultz 1/80-12/83 Elias M. Stein 1/77-12/82 J. Jerry Uhl, Jr. 1/82-12/85 Mathematical Reviews Editorial Committee Lawrence A. Zalcman 1/79-12/82 Paul T. Bateman 9/77-12/82 Representatives on American Journal of Mathematics Elwyn R. Berlekamp 1/79-12/81 Victor W. Guillemin 1/78-12/83 Morton Lowengrub 1/82-12/84 Richard G. Swan 5/77-12/82 Carl M. Pearcy 3/78-12/83 Transactions and Memoirs Editorial Committee Mathematical Surveys Editorial Committee Michael Artin 1/79-12/82 Donald W. Anderson 1/79-12/84 William B. Johnson 1/82-12/85 R. James Milgram 1/77-12/82 W.A.J. Luxemburg 4/77-12/81 Jane Cronin Scanlon 1/78-12/83 Jan Mycielski 1/80-12/83 Mathematics of Computation Editorial Committee Walter David Neumann 1/82-12/85 James H. Bramble 1/73-12/83 Steven Orey 1 /79-12/82 Carl de Boor 1/77-12/82 Paul H. Rabinowitz 1/80-12/83 Morris Newman 1/81-12/83 James D. Stasheff 1/78-12/81 Daniel Shanks 1/79-12/84 R. 0. Wells, Jr. 1/79-12/82 Chairman, Committee to Monitor Problems in Communication Robert G. Bartle 1/81-12/84 BOARD OF TRUSTEES Steve Armentrout (ex officio) 7/77-12/82 Richard S. Palais 1/72-12/81 Andrew M. Gleason {ex officio) 1/81-12/82 Franklin P. Peterson Ronald L. Graham 1/82-12/86 (ex officio) 8/73-12/82 Joseph J. Kohn 1/78-12/82 Alex Rosenberg 1/74-12/83 Cathleen S. Morawetz 1/76-12/85 P. Emery Thomas 1/80-12/84

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307 POSITIONS AVAILABLE Southampton College of Long Island University. Mathematics Faculty opening Fall 1982. Rank and salary dependent on experience and qualifications. Small liberal arts college with SOUTHERN TECHNICAL INSTITUTE distinguished science program. Rural seashore location Mathematics Department Marietta, Georgia 30060 ninety miles from New York City. Please send resume to Professor R. A. Melter, Department of Mathematics, One or more tenure-track positions as instructor or Southampton College, Southampton, New York 11968. Assistant Professor, teaching primarily service courses Telephone inquiries to 516-283-4000. through second-quarter calculus. M.S. will be considered, Ph.D. expected for tenure. Background in technology pre­ ferred. Begins Fall 1982. Salary competitive for this type of LOS ALAMOS NATIONAL LABORATORY position. Send resume, three references, and transcripts of APPLIED MATHEMATICS: The Center for Nonlinear all graduate and undergraduate work to S. A. Stricklen, Studies (CNLS) and the Mathematical Analysis Group at Mathematics Search Committee. Los Alamos are seeking qualified applicants for a permanent staff position in mathematics, starting in September 1982. THE AUSTRALIAN NATIONAL UNIVERSITY invites Candidates must show excellent achievements or outstanding applications for POSTDOCTORAL FELLOW OR RESEARCH promise in research in DYNAMICAL SYSTEMS and/or FELLOW in MATHEMATICS RESEARCH SCHOOL OF GLOBAL ANALYSIS. This staff member will be closely in­ PHYSICAL SCIENCES. The Department of Mathematics in volved with the CNLS interdisciplinary research theme on the Research School (Head: Professor D. W. Robinson) has chaos and coherence in physical systems. This research pro­ an academic staff complement of 17 and is carrying out re­ gram unifies the efforts of mathematicians, theoretical search in the following areas: Operator Algebras and Mathe­ physicists and experimentalists. Required qualifications in­ matical Physics, Partial Differential Equations and Geometry, clude: a Ph.D. in mathematics or closely related field; a viz. Group Theory, Lie Groups and Algebraic Groups, demonstrated research excellence; a willingness to interact Global Analysis, Ordinary Differential Equations and Control with physicists and other applied scientists. Consideration Theory, and Foundations. Appointment will be from late will be given to both senior and junior applicants. Fringe 1982. Salary in accordance with qualifications and experience benefits are those of the University of California System. within the ranges: Research Fellow $20,963-$27,539 p.a.; Operated by the University of California for the Depart­ Postdoctoral Fellow Grade 2 $20,963-$27,539 p.a.; Post­ ment of Energy, the laboratory provides excellent working doctoral Fellow Grade 1 $18,068-$20,699 p.a. Current ex­ conditions and opportunities for advanced research. change rate $A1 = $US1.07 = UK58P. Appointment will be: Resumes should be sent to: Research Fellow up to 3 years with the possibility of ex­ B. Nicolaenko and A. C. Scott tension, after review, to 5 years; Postdoctoral Fellow up to Center for Nonlinear Studies, MS-B258 2 years with possibility of extension to 3 years. Reasonable Los Alamos National Laboratory appointment expenses are paid; superannuation; assistance los Alamos, NM 87545 with housing. The University reserves the right not to make Los Alamos National laboratory is an Equal Opportunity/ an appointment or to make an appointment by invitation at Affirmative Action Employer. U.S. Citizenship or Permanent any time. Applicants may obtain further particulars from Resident Visa Required. The Registrar, The Australian National University, P. 0. Box 4, Canberra, Australia, with whom applications close on 30 JUNE 1982. DEPARTMENT OF MATHEMATICS KANSAS STATE UNIVERSITY One tenure-track position starting july 1, 1982, at the level of assistant professor, preferably in the area of Applied Tenure-track position at Full Professor level for academic Mathematics. Ph.D. required. Duties include research. Three year 1982-1983. Salary approximately $33-35,000 for letters of reference to be sent to: J. W. Macki, Chairman, 9-month appointment. Candidates must have demonstrated Department of Mathematics, University of Alberta, research ability in harmonic analysis, along with a broad Edmonton, Alberta T6G 2G1. The University is an equal knowledge of probability theory and operator algebras. opportunity employer. Deadline for submission of applica­ Commitment to excellence in teaching expected. Ph.D. or tions is April 15, 1982. Canadian citizens and permanent equivalent in mathematics required. residents of Canada will be given preference. Tenure-track position at Assistant Professor level for academic year 1982-83. Salary approximately $20-22,000 SLIPPERY ROCK STATE COLLEGE for nine-month appointment. Candidates must have demon­ strated research ability in algebra and have training broad Mathematics instructor or assistant professor (tenure-track): enough to teach a variety of graduate courses in this field. To teach and coordinate basic mathematics courses at Of special interest would be candidates whose research college freshman level. Master's degree required, doctorate interests are either in representation theory or algebraic preferred. Successful teaching experience is required. A geometry. Commitment to excellence in teaching expected. specialty in developing instructional techniques for college­ Ph.D. in mathematics or equivalent required. level remedial mathematics courses desired. Experience in testing and computer-aided instruction is especially valued. Starting date: 08/16/82 Please send transcripts, three letters of recommendation, Closing date: 05/01/82 vitae and letter of application to: Screening Committee, Contact: Department Head Department of Mathematics and Computer Science, Slippery Rock State College, Slippery Rock, PA 16057. Department of Mathematics Salary Range: instructor $15,135-$20, 125; assistant profes­ Kansas State University sor $18,280-$24,358. Starting date August 27, 1982. Manhattan, KS 66506 Application deadline April 20, 1982. Affirmative Action/ 913-532-67 50 Equal Opportunity Employer. KSU is an AA/EOE

308 POSITIONS AVAILABLE PUBLICATIONS

CLAREMONT MCKENNA COLLEGE is seeking a The 1982 March issue of the INTERNATIONAL qualified person for a three-year visiting assistant professor­ JOURNAL OF MATHEMATICS AND MATHEMATICAL ship teaching mathematics and computing. Applicants SCIENCES has just been published. The JOURNAL is a should have a Ph.D. in computer science, mathematics or a quarterly journal devoted to publication of original research closely related field, have a strong commitment to teaching, papers, research notes, research-expository and survey and show promise in research. Background and interest in articles with emphasis on unsolved problems and open ques­ numerical analysis, mathematical modelling, data base tions. All areas listed on the cover of MATHEMATICAL design, or statistics would be especially appropriate. REVIEWS-such as pure and applied mathematics, mathe­ Claremont McKenna College (formerly Claremont Men's matical physics, theoretical mechanics, probability and College) is a coeducational, liberal arts college with a cur­ mathematical statistics, theoretical biology-are included ricular emphasis on economics and political science and is within Mathematics and Mathematical Sciences. one of the Claremont Colleges. The standard teaching load Information about the journal can be obtained from is five courses per year ranging from freshman introductory Lokenath Debnath, Mathematics Department, East Carolina courses to advanced undergraduate courses. The College University, Greenville, NC 27834. shares a VAX 11 with three other Claremont Colleges and students have access via twelve ports. FREE Resumes and letters of recommendation should be sent to: For free. Unbound BULL. AMS, 1954- and A. M. Monthly, Professor James B. Lucke, Chairman 1934- a few months missing. You pay shipping. D. V. Department of Mathematics Widder, Harvard. Qaremont McKenna College Claremont, California 91711 FOR SALE Claremont McKenna College is an Equal Opportunity/ Affirmative Action Employer. Unbound A mer. Math. Monthly vols. 72 (1965)-88 (1981), Bulletin AMS vols. 73 (1967)-83 (1977). Best offer. R. SITUATIONS WANTED Stoll, Math. Dept., Cleveland State U, Cleveland, OH 4411 S.

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DYNAMIC, FLEXIBLE Ph.D. mathematician, 27, seeks non­ academic employment, e.g. in mathematical modelling or MATH SCI PRESS, 53 Jordan Rd., Brookline, MA 02146. scientific software. One year statistical consultancy experience 617-738-0307. Publisher (32 titles) of cross-disciplinary (London) plus two previous postdoctoral positions in work between geometry and Lie groups (history and fron­ Germany and the U.S. Good communication and software tiers), physics and systems. Translations of Klein, Lie, Ricci skills. Background in stochastic mathematics. Write to and Levi-Civita. Discounts to scholars, students and to 'Richard,' 3584 Broadway, Boulder, CO 80302; tel. libraries for large or standing orders. 303-447-9121. WANTED TO BUY MEETING ANNOUNCEMENT The Addelman·Semple Resource Centre of the Department NSF-CBMS Regional Conference on Mathematical Theory of Mathematics and Statistics, Carleton University, Ottawa, of Laminar Combustion to be held at Colorado State Uni­ Ontario, Canada K1 S 5B6, is interested in purchasing com­ versity, Fort Collins, Colorado, June 14-18, 1982. The plete volumes of back issues of certain mathematical jour­ principal lecturer is G. S. S. Ludford of Cornell University. nals (not Mathematical Reviews). Please send a list giving For information contact J. W. Thomas, Department of volume, year, title, price wanted, to Dr. K. S. Williams at Mathematics, Colorado State University, Fort Collins, the above address. Colorado 80523.

309 UNIVERSITY OF MARYLAND COLLEGE PARK, MD 20742 PROFESSOR OF APPLIED MATHEMATICS Applications are invited for a research professorship in Applied Mathematics to be held jointly in the Department of Mathe­ matics and the Institute for Physical Science and Technology. Applicants should have an o~tstanding record of research in a field of applied mathematics such as numerical analysis, fluid mechanics, solid mechanics, etc., and should be able to interact effec­ tively with other faculty members. The A computer-animated 12-minute color sound film teaching load consists of one graduate course per semester. The salary is negotia­ Honored at scientific and technical film festivals: Prix de Ia recherche fondamentale, Brussels ble. All inquiries will be treated confiden­ Diploma of Honour, Tokyo tially. Applications, which should include a Banchoff /Strauss Productions, Inc. curriculum vitae, should be sent to Profes­ P.O. Box 2430 Providence, R.I. 02906 sorS. S. Antman or Professor F. W. J. Olver; those received by 1 May, 1982 will Price $240. Other titles available upon request. be assured full consideration. The University of Maryland is an Equal Opportunity/Affirmative Action Employer.

~~8~~~88~~8~~~8~8

PROCEEDINGS OF SYMPOSIA IN PURE MATHEMATICS

THE SANTA CRUZ CONFERENCE ON FINITE GROUPS edited by Bruce Cooperstein and Geoffrey Mason

In the last year or so there have been widespread just come of age. This conference was partially sup­ rumors that group theory is finished, that there is ported by a grant from the National Science Founda- nothing more to be done. It is not so. tion. -from the Preface by G. Mason While it is true that we are tantalizingly close to that pinnacle representing the classification of finite There are 90 papers in this book by almost as simple groups, one should remember that only by many authors. The major divisions of the book are: reaching the top can one properly look back and 1. Classification theory of finite simple groups, survey the neighboring territory. It was the task of 2. General theory of groups, the Santa Cruz conference not only to describe the 3. Properties of the known groups, tortuous route which brings us so close to the sum­ 4. Representation theory of groups of Lie-type, mit of classification, but also to chart out more 5. Character theory of finite groups, accessible paths-ones which might someday be open 6. Combinatorics, to the general mathematical public. 7. Computer applications, A third concern was the elucidation of topics in 8. Connections with number theory and other fields. related fields, and it is to one of these three areas The table of contents includes so many mathe­ that the papers in this volume are devoted. maticians well known and active in the field that it just a quick glance at the table of contents [too would be unfair to list a sample. lengthy to be included here] will reveal a wide variety of topics with which the modern group theorist must Volume 37, xviii + 634 pages (hard cover) contend. Some of these, for example the connections List price $39.60, institutional member $29.70, individual member $19.80 with the theory of modular functions, have very re- ISBN 0-8218-1440-0; LC 80-26879 cent origins, but they leave us with the clear impres- Publication date: january 1981 sion that, far from being dead, group theory has only To order, please specify PSPUM/37N Prepayment is required for all AMS publications. Order from AMS, PO Box 1571, Annex Station Providence, Rl 02901, or call toll free 800-556-7774 to charge with Visa or MasterCard.

310 311 Recent Titles in Mathematics

Zero-Symmetric An Introduction to Graphs Applied Optimal Control Trivalent Graphical Regular Representations GREG KNOWLES of Groups A Volume in the MATHEMATICS IN SCIENCE H. S. M. COXETER, ROBERTO FRUCHT, and AND ENGINEERING Series DAVID L. POWERS Treats optimal control theory and emphasizes its The authors describe and use various methods application to problems in science, engineer­ for obtaining zero-symmetric graphs in an at­ ing, and business. Included are a large number tempt to compute a census of those having not of solved problems. more than 120 vertices. 1981, 192 pp., $19.50 ISBN: 0-12-416960-0 1981, 184 pp., $17.50 ISBN: 0-12-194580-4

The Theory of Mathematical Positional Games Perspectives With Applications in Economics Essays on Mathematics and Its Historical Development IOSIF A. KRASS and SHAWKAT M. HAMMOUDEH EDITED BY JOSEPH W. DAUBEN A Volume in the ECONOMIC THEORY, A collection of essays dedicated to the distin­ ECONOMETRICS, AND MATHEMATICAL guished historian of mathematics, K. R. Bier­ ECONOMICS Series mann. The authors are all recognized authori­ Krass and Hammoudeh examine some basic ties in their disciplines, making this work a val­ mathematical aspects of positional games and uable addition to the libraries of all mathemati­ provide economic applications of the theory. cians and historians of science. 1981, 240 pp., $37.00 ISBN: 0..12-425920-0 1981, 288 pp., $34.00 ISBN: 0-12-204050-3

Applied Iterative Quantum Mechanics Methods in Hilbert Space LOUIS A. HAGEMAN and DAVID M. YOUNG Second Edition A Volume in the COMPUTER SCIENCE AND EDUARD PRUGOVECKI APPLIED MATHEMATICS Series A Volume in the PURE AND APPLIED This volume considers the practical utilization MATHEMATICS Series of iterative methods for solving large, sparse This valuable work provides a rigorous mathe­ systems of linear algebraic equations. The au­ matical treatment of the basic aspects of non­ thors present the underlying computational and relativistic quantum mechanics. A self-contained theoretical principles of certain general meth­ book, it presupposes only a general knowledge ods, and show how these principles can be used of calculus and linear algebra. to select effective iterative solution methods. 1981, 688 pp., $39.50 ISBN: 0-12-566060-X 1981, 416 pp., $39.50 ISBN: 0-12-313340-8

312 from Academic Press .••

Foundations of Mathematical Analysis Stochastic Analysis and Applications

M. M. RAO EDITED BY LEOPOLDO NACHBIN A Volume in the PROBABILITY AND These volumes contain a collection of mathe­ MATHEMATICAL ST ATIST/CS Series matical writings in honor of Laurent Schwartz This book thoroughly covers the fundamentals on the occasion of his 65th birthday, March 5, of stochastic processes and emphasizes impor­ 1980. tant applications. Each chapter includes a sec­ PART A tion on problems and complements (with Advances in Mathematics Supplementary sketches of proofs) that provide additional val­ Studies, Volume 7 A uable material (e.g., entropy and information). 1981, 432 pp., $51.00 ISBN: 0-12-512801-0 1981,320 pp., $39.50 ISBN: 0-12-580850-X PART 8 Advances in Mathematics Supplementary The Theory of Studies, Volume 7B 1981, 416 pp., $49.00 ISBN: 0-12-512802-9 Eisenstein Systems M. SCOTT OSBORNE and GARTH WARNER A Volume in the PURE AND APPLIED MATHEMATICS Series Elliptic Problem Let G be a reductive Lie group, f a nonuniform Solvers lattice in G. Then the central problem in the theory of automorphic forms relative to the pair EDITED BY MARTIN SCHULTZ (G, f) is the spectral decomposition of L2 (G/f). This important volume covers various aspects of This volume identifies the continuous spectrum the numerical solution of elliptic partial differ­ in L2 (G/f), utilizing the Selberg-Langlands the­ ential equations. Vividly demonstrates current ory of Eisenstein series. advances in developing elliptic problem solvers 1981, 400 pp., $55.00 ISBN: 0-12-529250-3 and analyzing their performance. 1981, 456 pp., $31.50 ISBN: 0-12-632620-7

Ordinary Send payment with order and save postage and Differential handling. Equations Prices are in U.S. dollars and are subject to change without notice. RICHARD K. MILLER and ANTHONY N. MICHEL An excellent text for a first graduate course in Academic Press, Inc. differential equations for students in mathemat­ A Subsidiary of ics, engineering, and the sciences. Covers fun­ Harcourt Brace Jovanovich, Publishers damental theory and includes examples of dif­ New York • London • Toronto • Sydney ferential equations that arise in science and en­ San Francisco gineering. 111 FIFTH AVENUE, NEW YORK, N.Y. 10003 1981, 376 pp., $34.50 ISBN: 0-12-497280-2

313 FINITE SIMPLE GROUPS An Introduction to Their Classification by Daniel Goren8tein1 Rutgers, The State University ofNew Jersey Provides the reader with a considerable insight into simple group theory and, in particular, the overall picture of the fundamental four-part subdivision of the classification proof, the group theoretic origins, definitions of each of the known simple groups, and the methods that have been developed for the study of simple groups. An excellent preparatory guide to the classification proof. Includes definitions of every term used in the book. A volume in The University Series in Mathematics. approx. 325 pp., illus., 1982 $29.50

CONTROL, IDENTIFICATION, AND INPUT OPTIMIZATION by Robert Kalaba, University ofSouthern California, Los Angeles and Karl Spingarn, Hughes Aircraft Company, Los Angeles Provides a self-contained, plenary introduction to the numerical determination of optimal inputs. For the upper division undergraduate and graduate student, as well as for engineers and scientists in industry, who require the analytical and computational tools necessary to compute optimal inputs for systems identification. Volume 25 in Mathematical Concepts and Methods in Science and Engineering. approx. 425 pp., illus., 1982 $39.50

APPLIED PROBJlBILIT\' by Frank A. Haight, The Pennsylvania State University Designed for students with some experience in mathematics, but no prior knowledge of probability, this volume provides a quick yet rigorous introduction to the standard mathematics of probability and stochastic processes. Volume 23 in Mathematical Concepts and Methods in Science and Engineering. 302 pp., illus., 1981 $35.00

THE CALCULUS OF VARIATIONS AND OPTIMAL CONTROL An Introduction by George Leitmann, University of California, Berkeley "This book covers the basic theory of the calculus of variations and optimal control.... contains a rigorous mathematical presentation of the basic theoretical results ... it is very clearly written and easy to learn from and to teach with. Numerous illustrative examples and figures are interspersed through it making it even more attractive to the reader." -Daniel Tabak, Ben-Gurion University, Beer Sheva, Israel Volume 24 in Mathematical Concepts and Methods in Science and Engineering. 328 pp., illus., 1981 $35.00

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DEADLINES: PREREGISTRATION: july 9, 1982 for preregistration fee(s) RESIDENCE HALL ROOM DEPOSIT: july 9, 1982 (NOT REFUNDABLE AFTER JULY 15) CANCELLATIONS: Preregistrations may be cancelled until August 20 by writing or calling the Mathematics Meetings Housing Bureau (see above). SO% of the preregistration fee(s) will be refunded if notification is received by this date. Confirmed residence hall reservations may be cancelled until july 1 S when deposit will be refunded; however, after that date, no refunds will be allowed. CHANGES: Changes in arrival and departure dates must be made with the Mathematics Meetings Housing Bureau by August 20 (See ad­ dress and number above.). Please refer to meeting announcement for number to call after this date. REGISTRATION FEES Preregistration (by mail prior to 7/9) At Meeting JOINT MATHEMATICS MEETINGS Member of AMS, MAA, llME $34 $48 *Student, Unemployed or Emeritus $ 8 $12 Nonmember $52 $74 AMS Short Course Please affix AMS or MAA label here. Member/Nonmember $25 $30 If none, complete 1-3 below. *Student or Unemployed $ 5 $10 MAA MINICOURSE #1 $15 $15 .J MAA MINICOURSE #2 L $15 $15 *All full·time students currently working toward a degree or diploma qualify for the student registration fees, regardless of Income. The unemployed status refers to any person currently unemployed, actively seeking employment, and who is not a student. It is not intended to include persons who have voluntarily resigned from their latest position. The emeritus status refers to ~ who has been a member of the AMS or MAA for twenty years or more, and is retired on account of age from his or her latest position.

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315 PREREGISTRATION AND HOUSING RESERVATION REQUEST FORM (continued) UNIVERSITY HOUSING SECTION [ ] I WILL NOT REQUIRE A ROOM. Please read section on 11 Types of Accommodations" in meeting announcement. Please reserve the following residence hall accommodations: (Rates are given in Canadian dollars and include Provincial Sales Tax.) AIR-CONDITIONED ROOMS - PLEASE CIRCLE NIGHT(S) OF OCCUPANCY: MALES: $20.00 Wetmore - Single Night(s) of 8/20 21 (no breakfast) $21.50 Wetmore - Single Night(s) of 8/22 23 24 25 26 (breakfast included) $13.50 Wetmore - Double/per person Night(s) of 8/20 21 (no breakfast) $15.50 Wetmore - Double/per person Night(s) of 8/22 23 24 25 26 (breakfast included) FEMALES: $21.50 Wilson -· Single Night(s) of 8/20 21 (no breakfast) $20.00 Wilson - Single Night(s) of 8/22 23 24 25 26 (breakfast included)

NON-AIR-CONDITIONED ROOMS- PLEASE CIRCLE NIGHT(S) OF OCCUPANCY: MALES: $19.00 Devonshire - Single Night(s) of 8/20 21 (no breakfast) $20.50 Devonshire - Single Night(s) of 8/22 23 24 25 26 (breakfast included) $18.73 Trinity - Single Night(s) of 8/20 21 22 23 24 25 26 (no breakfast) $12.31 Trinity - Double/per person Night(s) of 8/20 21 22 23 24 25 26 (no breakfast) $16.59 Trinity (Student) - Single Night(s) of 8/20 21 22 23 24 25 26 (no breakfast) $18.73 St. Michael's - Single Night(s) of 8/21 22 23 24 25 26 (no breakfast) $12.31 St. Michael's- Double/per person Night(s) of 8/21 22 23 24 25 26 (no breakfast) $16.05 Knox - Single Night(s) of 8/20 21 22 23 24 25 26 27 (no breakfast) $12.84 Knox (Student) - Single Night(s) of 8/20 21 22 23 24 25 26 27 (no breakfast) CO-ED and FAMILIES: $19.00 Sir Daniel Wilson - Single Night(s) of 8/20 21 (no breakfast) $20.50 Sir Daniel Wilson - Single Night(s) of 8/22 23 24 25 26 (breakfast included) $19.00 Whitney - Single Night(s) of 8/20 21 (no breakfast) $20.50 Whitney - Single Night(s) of 8/22 23 24 25 26 (breakfast included) $12.50 Whitney - Double/per person Night(s) of 8/20 21 (no breakfast) $14.50 Whitney - Double/per person Night(s) of 8/22 23 24 25 26 (breakfast included) $20.50 Victoria (Margaret Addison) - Single Night(s) of 8/20 21 22 23 24 25 26 (breakfast included) $14.50 Victoria (Margaret Addison) - Double/per person Night(s) of 8/20 21 22 23 24 25 26 (breakfast included)

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316 - ExPOSITIONES CALL FOR ) PAPERS MATHEMATICAE I -

International Journal for Pure and Applied Mathematics Managing Editor Objectives S.D. Chatterji The keyword for our journal is ,exposition": expository and survey Ecole Polytechnique Federale articles as well as informative book reviews in all branches of de Lausanne mathematics are our main objectives. A second aim is to give rapid publication to a certain number of short research announcements Editorial Board and mathematical notes. Finally, through our reports on important S. Albeverio mathematical events and letters to the editor, we intend to bring Universitiit Bochurn about a fruitful debate in the international mathematical H. Bauer community. Universitiit Erlangen Scope P. Cartier Ecole Polytechnique de Paris Surveys: Expository and survey articles written at the level of beginning research students (20-50 printed pages). RE. Edwards Australian National University, Mathematical Notes: Interesting new proofs, novel points of view Canberra and conjectures (up to 4 printed pages). B. Fuglede Research Announcements: Main concepts and results of significant Copenhagen University research (4 printed pages). P. J. Hilton Book Reviews: Detailed analysis of selected books in the form of Battelle Research Center, Seattle informative essays. R V.Kadison Miscellanea: Important current events, biographical and auto­ University of Pennsylvania, biographical accounts, mathematical education and research etc. Philadelphia Letters to the Editor: Columns open to all for discussion. D. G. Kendall University of Cambridge (U.K) Call for Papers M.Mlak Expositiones Mathematicae will publish articles in English, French PAN, Krakow and German. All mathematical articles and correspondence should P. Ribenboim be sent to the Managing Editor: Queens University, Kingston Prof. S. D. Chatterji, EPFL, Departement de mathematiques, (Canada) 61, av. de Cour, CH-1007 Lausanne, Switzerland V. S. Varadarajan University of California, r------Los Angeles 1 An: Bibliographisches lnstitut AG, Postfach 311, D-6800 Mannheim 1 Order Form I Subscription information: D Please send me a sample copy (presumably 1982, Sep.) 4 issues per volume: approx. US $ 100.00 (220.- DM) D Please enter my subscription starting with volume 1 per volume.

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1 Date/Signature Summer List of Applicants CONTEMPORARY MATHEMATICS hutruetions for Applicant Form on facing page (ISSN 0271-4132) The form. Forms submitted by job applicants who attend the August meetings in Toronto will be posted. UMBRAL CALCULUS AND HOPF ALGEBRAS The first impression a prospective employer has of an edited by Robert Morris applicant may be based on the appearance of this form. CONTENTS: The forms should be carefully typed using a fresh S. A. joni and G.-C. Rota, Coalgebras and bialge­ black ribbon. The best results are obtained with a bras in combinatorics carbon-coated polyethylene film ribbon, but satisfac­ Warren Nichols and Moss Sweedler, Hopf algebras tory results may be obtained using a ribbon made of and comblnatorics nylon or other woven fabric if suitable care is exer­ This book represents a unique blending of two cised. It is important that the keys be clean and make fields only recently recognized as related. On one a sharp, clear impression. Use a correcting typewriter hand lies the field of combinatorics with roots (at or correction tape or fluid if necessary. Submit the least immediately traceable via generating functions original typed version only. Hand lettered forms are to umbra) calculus, the speciality at hand) in the acceptable if prepared carefully. 19th century writings of Boole on operator calculus. The IUIIlDllll"f strip. Information provided here will Both the foundations and much of the history of be used to prepare a printed list of applicants for dis­ the umbra) calculus are explored in great clarity in tribution to employers. Please supply all information .previous papers by Rota and others. On the other requested, and confine your characters to the boxes hand is the field of Hopf algebras, which is usually provided. Use the codes below. Circled letters identify traced to a paper of Milnor and Moore but whose corresponding items on the form and the strip. first general exposition by Sweedler is little more Address forms to the Mathematics Meetings Hous­ than a decade old. ing Bureau, P. 0. Box 6887, Providence, RI 02940. Both Rota and Sweedler were pleased when the The deadline for receipt is July 9, 1982. See pages 274 University of Oklahoma was able to support their and 280 for more information. joint appearance at a conference funded by the j. C. Karcher Foundation in May, 1978. The confer­ ence centered on lectures they gave, with S. A. joni @ Specialties assisting Rota. Sweedler lectured first on elementary coalgebra theory aimed at combinatorists, Rota on AI.. = Algebra AN = Analysis BI = Biomathematics BS = Biostatistics elementary combinatorics aimed at the algebraists. CB = Combinatorics CM = Co=unication Both lectures converged toward those who were or CN = Control CS = Computer Science would work at the intersection. Sweedler and Warren CT = Circuits DE = Differential Equations Nichols prepared notes of Sweedler's talks and joni EC = Economics ED = Mathematical Education and Rota of Rota's and a mimeographed version was FA = Functional Analysis Fl = Financial Mathematics circulated by the Oklahoma Mathematics Department. FL = Fluid Mechanics GE = Geometry The present volume makes these more accessible. HM = Histocy of Math LO = Logic The Sweedler notes here are essentially unchanged MB = Mathematical Biology ME = Mechanics from those distributed by Oklahoma. They aim, in a MO = Modelling MP = Mathematical Physics direct and elementary way, to give the reader suffi­ MS = Management Science NA = Numerical Analysis NT = Number Theory OR = Operations Research cient knowledge of coalgebra theory to understand PR = Probability SA = Systems Analysis the coalgebra formulation of special sequences of ST = Statistics TO = Topology polynomials. The Rota notes are reproduced from Studies in @ Career Objectives Applied Mathematics, volume 61, and represent a reworking of the original, with corrections and a AR = Academic Research AT = Academic Teaching few additions. They contain detailed applications NR = Nonacademic R&D NC = Nonacad. Consulting not only to umbral calculus, but to partition stud­ NS = Nonacademic Supervision ies, incidence algebras, lattice theory, and other traditional spheres of combinatoric interest. The notes form a broad survey for anyone who would ® (!) Duties like detailed and concrete examples of the areas already known to be amenable to a coalgebraic ap­ T =Teaching U = Undergraduate G =Graduate R =Research proach. C = Consulting A = Administration 1980 Mathematics Subiect Classifications: 16A24, 05820, S = Supervision IND = Industry 05-02, 16A20 GOY = Government DP = Data Processing Volume 6, viii + 84 pages (soft cover) List price $7.60, institutional member $5.70, Location individual member $3.80 ISBN 0·8218-5003-2; LC 81-22756 Publication date: February 1982 E =East S =South To order, please specify CONM/6N C =Central M=Mountain W=West 0 = Outside U.S. I = Indifferent Prepayment is required for all AMS publications. Order from AMS, PO Box 1571, Annex Station, © U.S. Citizenship Status Providence, Rl 02901, or call 800-556-7774 to charge with VISA or MasterCard. C = U.S. Citizen P = Permanent Resident T =Temporarily in U.S. N = Non-U.S. Citizen

318 APPLICANT FORM MATHEMATICAL SCffiNCES EMPLOYMENT REGISTER AUGUST 1982 TORONTO, ONTARIO, CANADA

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@ Specialtie"'------­ @ Career objectives and accomplishments ACADEWC: 0 Research, 0 Teaching NON-ACADEWC: 0 Research and Development, 0 Consulting, 0 Supervision Near-~rmcareergoal~------

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@Degree Year Institution ------@No. of abstracts, in~rnal report..______------@No. of papers accepte:u______------®No. of books and patent...______EMPLOYMENT IDSTORY: Present Previous Previous @Employer ------­ Position @Duties Years ______to ______to•------_____to·----- DESffiED POSITION: ______(!)Duties______(])Available mo. __ fyr.__ Locatio,,______Salary______@References (Nwne and Institution)

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Family Name Firat Name Mailing Addre .. SUMMARY STRIP I Ill II II I II I I, Ill I I Ill 1, II I II II I I II II I I I I Ill 1, Addreaa (cont'd.) Address (cont'd.) State & Zip Code @ 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 I I I I I I 1, I I I I I I I I 1, OJ OJ OJ [1] [I], @ Career objectives @M~\~::t @Yr. @ Institution @ @ ® @Moat recent employer [I] [I] OJ OJ rn. ITTIJ, OJ, I I I I I I I I I I 1, [I], OJ, OJ, I I I I I I I I I I 1, @ Present duties (!) De aired duties 0 !,~~~~r~le @ 11111111 I II, CIIII rrrr1 OJ/rn. o

319 When You Need Information That Counts Turn To ... PROGRESS IN MATHEMATICS A timely. in-depth monographic series that explores the varied paths of modern mathematics. Each volume offers a close look at a different aspect of mathematics, reporting on research developments that combine original results with an expository treatment of the particular subject area. Vol. 16: Rational Homotopy Theory and Differential forms Philip A. Griffiths, Harvard University and John Morgan. Columbia University (1981/253 pp./Hardcover/$17.50 ISBN 3-7643-3041-4) Vol. 17: Triangular Products of Group Representation and Their Applications S.M. Vovsi, Riga Polytechnic Institute. USSR (1982/135 pp./Hardcover/$12.50 ISBN 3-7643-3062-7) Vol. 18: Geometrie Analytique Rigide et Applications Jean fresnel, UER Mathematique et lnformatique, Talence, France, and Marius van der Put. Mathematish lnstituut, Groningen, The Netherlands (1981/227 pp./hardcover/$15.00 ISBN 3-7643-3069-4) Vol. 19: Periods of Hilbert Modular Surfaces Takayuki Oda, Hokkaido University. Sapporo. Japan (1982/140 pp./Hardcover/$10.00 ISBN 3-7643-3084-8)

A New Journal For All Mathematicians SELECTA MATHEMATICA SOVIETICA Managing Editor: A.V. Balakrishnan, University of California at Los Angeles Selecta Mathematica Sovietica offers important work from Soviet mathematicians that, to date. has had limited exposure in English. Covering a wide variety of subjects, the journal is a significant contribution to the international exchange of scientific information. Vol. 2 (4 issues) 1982 $98.00 (prices subject to change.)

Birkhauser Boston, Inc. 380 Green Street P.O. Box 2007 Cambridge, MA 02139

320 Numerical Solutions of Partial Differential Equations Proceedings of the 1981 Conference on the commonly occurring partial differential equations. Numerical Solutions of Differential Equations held There are also two survey articles on the numerical at Queen's College, Melbourne University, Australia, solutions of sets of large sparse linear algebraic 23-27 August, 1981 equations, one describing iterative techniques and the other describing direct methods. These sets of edited by JOHN NOVE equations occur in each of the four methods men­ tioned above. In addition, twenty papers are in­ 1982. xii + 648 pages. Price: US $93.00/Dfl. 200.00 cluded in the work in which recent refinements of ISBN 0-444-86356-7 the various numerical techniques used to solve The work contains surveys of finite difference, partial differential equations were described, or finite-element, Galerkin and boundary integral experiences in applying these methods to solve equation methods, all under one cover. The meth· problems in engineering physics, oceanography, ods described are illustrated with solutions to hydrology or meteorology were reported.

Biomathematics in 1980 edited by LUIGI RICCIARDI and ALWYN SCOTI papers published clearly demonstrate the viability of the field. Topics covered range from theoretical NORTH-HOLLAND MATHEMATICS STUDIES, Vol. 58 to experimental in neuroscience, pattern formation, 1982. xiv + 298 pages. Price: US $55.75/Dfl. 120.00 population dynamics, self-organizing systems, ISBN 0-444-86355-9 senescence and cardiovascular modelling. The coupled nonlinear diffusion system emerges in This work brings together a diverse collection of a several chapters as a useful model in neuro­ selection of research studies in modern bio­ dynamics, pattern formation, population diffusion mathematics presented at the workshop. The and synergetics.

Mathematical Logic In computer Science edited by B. DOMOLKI and T. GERGELY Colloquium include: -model theoretical, universal algebra and category COLLOQUIA MATHEMATICA SOCIETATIS JANOS theoretical approaches to program semantics; BOLYAI, Vol. 26 - logical and model theoretical approaches to 1981. 758 pages. Price: US $116.25/Dfl. 250.00 program-verification, data representation and ISBN 0-444-85440·1 problem specification; - logical and model theoretical approaches to This volume contains 31 papers prepared for the theorem proving, automatic programming and Colloquium on Mathematical Logic in Programming automatic problem solving; that was held on September 10-15, 1978, in -very high level, logically based programming Salg6tarjan, Hungary. Main topics of the languages.

Applications of variational Inequalities In stochastic control by ALAIN BENSOUSSAN and JACQUES-LOUIS This volume is devoted to the study of stopping LIONS time and control problems for systems governed by stochastic differential equations, which play an STUDIES IN MATHEMATICS AND ITS important role in numerous applications. It uses APPLICATIONS, Vol. 12 intensively the theory of partial differential 1982. xii + 564 pages. Price: US $81.50/Dfl. 175.00 equations and variational inequalities to solve ISBN 0·444-86358-3 problems of stochastic control; these methods are also useful in very remote fields like free boundary Translation of "Applictions des lnequations Varia­ problems in Mechanics and Physics. tionelles en ContrOie Stochastique", published by Dunod, Paris, 1978

North-Holland Publishing Company P.O. Box 211 - 1000 AE Amsterdam- The Netherlands In the U.S.A. & Canada: Elsevier Science Publishing Co., Inc.- 52 Vanderbilt Avenue- New York, N.Y. 10017

The Dutch guilder price is definitive. US$ prices are subject to exchange rate fluctuations. 0814 NH ------A Brief on Tensor Analysis James G. Simmonds This volume was written for advanced under­ graduates in engineering, physics, mathemat­ ics, and applied sciences. A main feature of this Springer for text is the development of the tools for manipu­ lating the field equations of continuum me­ chanics. The book's informal style is enhanced Matheinatics by worked-out problems, exercises, and a stress on physical applications. A basic knowl­ edge of calculus, linear algebra, mechanics, and geometry is assumed. l982/130pp. approx./28 Illus. approx./Cloth Lectures from Markov $18.80 Undergraduate Texts In Mathematics Processes to Brownian ISBN 0-387-90639-8 Motion Geometry: A Metric Kai Lai Chung These lectures tie together large quantities of Approach with Models classical and new material to form a basic text Richard S. Millman and George D. Parker on the accomplishments of modern probability Using Birkhoff's metric approach, this text of­ of theory. Covering basic results and a number fers a vivid development of classical and Eu­ topics which are not readily accessible in other clidean geometries. By integrating models with texts, this book is written in a clear, unclut­ theory, the authors have presented abstract ap­ tered style using many exercises which will systems quite accessibly. Axioms and examples peal to both students and teachers. are supplemented by examples which nurture 198l/256pp. approx./3 Illus. approx./Cloth intuition and computational skills. $34.00 l981/355pp. /259 Illus./Cioth $29.80 Grundlehren der mathematischen Wissen­ Undergraduate Texts In Mathematics schaften Vol. 249 ISBN 0-387-90610-X ISB~ 0-387-90618-5 Introduction to Coming Soon! Springer-Verlag is preparing to publish a new exhaustive study of quantum physics, Tm: Cyclotomic Fields and >-1- HISTORICAL DEVELOPMENT Ot' Qt'A:IIT\'M Tllt:OHY. 1.1.1 Lawrence C. Washington 0 0 Written by Jagdish Mehra, with assistance N u '< u 0 OJ 01:: al "'u ·;:; 1.1.1 0 ::;: d z <( c.: