OF THE AMERICAN MATHEMATICAL SOCIETY VOLUME 16, NUMBER 3 ISSUE NO. 113 APRIL, 1969 OF THE AMERICAN MATHEMATICAL SOCIETY Edited by Everett Pitcher and Gordon L. Walker CONTENTS MEETINGS Calendar of Meetings ..................................... 454 Program for the April Meeting in New York ..................... 455 Abstracts for the Meeting - Pages 500-531 Program for the April Meeting in Cincinnati, Ohio ................. 466 Abstracts for the Meeting -Pages 532-550 Program for the April Meeting in Santa Cruz . ......... 4 73 Abstracts for the Meeting- Pages 551-559 PRELIMINARY ANNOUNCEMENT OF MEETING ....................•.. 477 NATIONAL REGISTER REPORT .............. .. 478 SPECIAL REPORT ON THE BUSINESS MEETING AT THE ANNUAL MEETING IN NEW ORLEANS ............•................... 480 INTERNATIONAL CONGRESS OF MATHEMATICIANS ................... 482 LETTERS TO THE EDITOR ..................................... 483 APRIL MEETING IN THE WEST: Some Reactions of the Membership to the Change in Location ....................................... 485 PERSONAL ITEMS ........................................... 488 MEMORANDA TO MEMBERS Memoirs ............................................. 489 Seminar of Mathematical Problems in the Geographical Sciences ....... 489 ACTIVITIES OF OTHER ASSOCIATIONS . 490 SUMMER INSTITUTES AND GRADUATE COURSES ..................... 491 NEWS ITEMS AND ANNOUNCEMENTS ..... 496 ABSTRACTS OF CONTRIBUTED PAPERS .................•... 472, 481, 500 ERRATA . • . 589 INDEX TO ADVERTISERS . 608 MEETINGS Calendar of Meetings NOn:: This Calendar lists all of the meetings which have been approved by the Council up to the date at which this issue of the c;Noticei) was sent to press. The summer and annual meetings are joint meetings of the Mathematical Association of America and the American Mathematical Society. The meeting dates which fall rather far in the future are subject to change. This is particularly true of the meetings to which no numbers have yet been assigned. Meet­ Deadline ing Date Place for No. Abstracts• May 1, 1969** 667 August 25-29, 1969 (74th Summer Meeting) Eugene, Oregon July 1, 1969 668 O·:tober 2 5, 1969 Cambridge, Massachusetts Sept. 9, 196 November 21-22, 1969 Baton Rouge, Louisiana November 29, 1969 Ann Arbor, Michigan January 22-26, 1970 Miami, Florida (76th Annual Meeting) August 24-28, 1970 Laramie, Wyoming (75th Sum mer Meeting) january 21-25, 1971 Atlantic City, New Jersey (77th Annual Meeting) *The abstracts of papers to be presented in person at the meetings must be received in the Head­ quarters Offices of the Society in Providence, Rhode Island, on or before these deadlines. The dead­ lines also apply to news items. The next two deadlines for by-title abstracts will be April 25 and June 24, 1969. **Deadline for the cJVoticeiJfor the June issue; no meeting is scheduled in June. ··~~~~··--·-····--- The cAfofiai) of the American Mathematical Society is published by the Society in January, February, April, June, August, October, November and December. Price per annual volume is $10.00. Price per copy $3.00. Special price for copies sold at registration desks of meetings of the Society, $1.00 per copy. Subscriptions, orders for back numbers (back issues of the last two years only are available) and inquiries should be addressed to the American Mathematical Society, P.O. Box 6248, Providence, Rhode Island 02904. Second-class postage paid at Providence, Rhode Island, and additional mailing offices. Copyright©, 1969 by the American Mathematical Society Printed in the United States of America 454 Six Hundred Sixty-Fourth Meeting Americana of New York New York, New York Apri12-5, 1969 The six hundred sixty-fourth meet­ ing Committee which consists of Dr. ing of the American Mathematical Society W. A. Blackwell, Dr. Frank Branin, Dr. will be held at the Americana of New York Robert Brayton, Professor Frank Harary, in New York City on April 2-5, 1969. and Professor Herbert S. Wilf(chairmar:). By invitation of the Committee to The hour speakers at the symposium will Select Hour Speakers for Eastern Sec­ be Professor J. W. T. Youngs, University tional Meetings, the following four ad­ of California, Santa Cruz; Dr. Robert dresses will be presented: Professor Brayton, IBM Corporation; Dr. D. C. David Shale, University of Pennsylvania, Youla, Brooklyn Polytechnic Institute; will speak on "Some probabilistic ideas and Professor R. J. Duffin, Carnegie­ in mathematical physics" at 11:00 a.m. on Mellon University. In addition, there will Friday, April4; Professor Cathleen Mora­ be twelve half-hour addresses. The sym­ wetz, New York University, will speak on posium will be held in the Regency Ball­ "Energy flow: wave motion and geometri­ room on Wednesday, April 2, and in the cal optics" at 2:00 p.m. on Friday, April4; Georgian Ballroom A on Thursday, April3. Professor Katsumi Nomizu, Brown Uni­ versity, will speak on" Differential geome­ REGISTRATION try of complex hyper surfaces" at 11:00 a.m. on Saturday, April 5; Professor The registration desk will be in William Browder, Princeton University, Loire Suites 4 and 5. It will be open from will speak at 2:00 p.m. on Saturday, 9:00 a.m. to 5:00 p.m. on Wednesday April 5, on "Invariants of manifolds." All through Saturday, April 2-5. four addresses will be presented in the Georgian Ballroom A. EXHIBITS There will be sessions for ten­ minute contributed papers both mornings A joint book exhibit will be on dis­ and afternoons of Friday and Saturday. play in Vendome Suite 10 from 9:00 a.m. There will be provision for late papers. to 5:00 p.m. on each of the four days. The Council of the Society will meet on Friday, April 4, at 5:00 p.m. in ACCOMMODATIONS the Versailles Terrace. There will be an in term is sion for dinner. Persons intending to stay at the Americana should make their own reser­ SYMPOSIUM ON vations with the hotel. A reservation blank MATHEMATICAL ASPECTS OF and a listing of room rates can be found ELECTRICAL NETWORK THEORY on page 452 of the February issue of these cffofiaiJ. With the support of the Air Force Office of Scientific Research and the U.s. MAIL ADDRESS Army Research Office (Durham), there will be a symposium on Mathematical Aspects Registrants at the meeting mayre­ of Electrical Network Theory on April 2 ceive mail addressed in care of the Ameri­ and April 3. The AMS -SIAM Committee on can Mathematical Society, Americana of Applied Mathematics chose the topic of New York, 801 7th Avenue (and 52nd the symposium and appointed the Organiz- Street), New York, New York 10019. 455 SYMPOSIUM ON MATHEMATICAL ASPECTS OF ELECTRICAL NETWORK THEORY WEDNESDAY, 2:00P.M. First Session, Regency Ballroom 10:00-10:50 Kirchhoff's laws and map-coloring problems Professor j.W.T. Youngs, University of California, Santa Cruz 11:00-11:20 A new perturbation theory for nonlinear network synthesis Professor Roger W. Brockett, Massachusetts Institute of Technology Second Session, Regency Ballroom 2:00-2:50 Network models Professor Richard Duffin, Carnegie-Mellon University 3:00-3:20 Successive secants in the solution of nonlinear network equations Professor Ronald A. Rohrer, University of California, Berkeley 3:30-3:50 Electrical network analysis, network-programming, and matroid theory Professor George Minty, Indiana University 4:00-4:20 Existence of solution to electrical network problem via homology sequences Dr. j. Paul Roth, IBM, T. j. Watson Research Center 4:30-4:50 An algebraic-topological overview of network analogies, the vector calculus, and Maxwell's equations Dr. Franklin H. Branin, Jr., IBM, Kingston, New York THURSDAY, 10:00 A.M. Third Session, Georgian Ballroom A 10:00-10:50 Nonlinear RLC Networks Dr. Robert Brayton, IBM, T. j. Watson Research Center 11:00-11:20 Equivalent nonlinear electrical networks Professor P. P. Varaiya, University of California, Berkeley 11:30-11:50 Numerical techniques for fast and accurate transient analysis of nonlinear networks Professor D. A. Calahan, University of Michigan Fourth Session, Georgian Ballroom A 2:00-2:50 Some recent developments in the synthesis of multivariable positive-real matrices Dr. Dante C. Youla, Brooklyn Polytechnic Institute 3:00-3:20 Some properties of a nonlinear model for synchronizing digital transmission networks Dr. Irvin Sandberg, Bell Laboratories 3:30-3:50 Some formulation aspects of electrical network theory Professor Myril B. Reed, Colorado State University 456 4:00-4:20 Graph theory and its applications in circuit theory ProfessorS. Park Chan, University of Santa Clara 3:30-4:50 Some applications in electrical network theory of a linear graph theorem by Berge and Ghouila- Houri Dr. Dan Wolaver, Massachusetts Institute of Technology PROGRAM OF THE SESSIONS The time limit for each contributed paper is 10 minutes. The contributed papers are scheduled at 15 minute intervals. To maintain this sched'Jle, the time limit will be strictly enforced. FRIDAY, 9:00 A.M. Session on Logic and Foundations I, Vendome ll-12 9:00-9:10 (1) Completeness theorems for the propositional calculus of kind W. Preliminary report Mr. Donald j. Brown, Stevens Institute of Technology (664-33) (Introduced by Professor Stephen L. Bloom) 9: 15-9:25 (2) Intermediate theories with respect to Keisler's ultraproduct ordering Mr. L. Taylor Ollmann and Professor Ani! Nerode*, Cornell University (664-7) 9:30-9:40 (3) A completeness theorem for theories of kind W Professor Stephen L. Bloom, Stevens Institute of Technology (664-24) 9:45-9:55 (4) Consistency of some non-Fregean theory Professor Roman Suszko, Stevens Institute of Technology (664-23) (Introduced by Professor Stephen L. Bloom) 10:00-10: lO (5) Variant forms of quantification of the predicate of use in analysis Professor Ira Rosenbaum, University of Miami (664-72) 10:15-10:25 (6) Representation theorems for context sensitive languages Professor Leonard H. Haines, University of California, Berkeley (664-88) (Introduced by Professor Michael A. Harrison) FRIDAY, 9:00 A.M. Session on Differential equations, Chambord 14-15 9:00-9:10 (7) A theorem on contractive stability Dr.