AMERICAN MATHEMATICAL SOCIETY VOLUME 8, NUMBER 5 ISSUE NO. 56 OCTOBER 1961 THE AMERICAN MATHEMATICAL SOCIETY oticeiJ Edited by GORDON L. WALKER CONTENTS MEETINGS Calendar of Meetings . • . • • • • • . • • • . • • .. • • • . • • • . • . • . • • • . • . 3 92 Program of the Five Hundred Eighty-third Meeting in Cambridge, Massachusetts •.•.•.•. 393 Abstracts of the Meeting- pages 423-436 PRELIMINARY ANNOUNCEMENTS OF MEETINGS •••••••..••••..••.... 398 ACTIVITIES OF OTHER ASSOCIATIONS .•.•.••••..•....•••..•.... , • 402 FELLOWSHIP AND RESEARCH OPPORTUNITIES •.•••..•....•...••..•. 403 lHE ANNUAL SALARY SURVEY ••.•.••••.•••.•....•.•••.•.•.•.•.. 406 STARTING SALARIES FOR MATHEMATICIANS WITH A PH.D •••..•.••.•••. 409 NEWS ITEMS AND ANNOUNCEMENTS • . • • . • • • . • . • . • . • . • . • • • . 410 PERSONAL ITEMS .•....•.•••..•.•.........•.•••.•.••..•.••.. 412 MEMORANDA TO MEMBERS Australian Mathematical Society Summer Research Institute .•••..•.•.. 401 Proceedings Editorial Committee .••..•..•.•........•••.•.•.•. 420 Two Volumes of Mathematical Reviews in 1962 •.••••••••.••.•.•.•. 420 Berliner Mathematische Gesellschaft e. V. .•.•...•••.•••••.... 4ZO Dmtsche Mathematiker Vereinigung ••...•.•••••...•.•...•...•. 420 Union Matematica Argentina ......••.•••••.••..••..•.•. , • • . • . 420 SUPPLEMENTARY PROGRAM N0.6 .••••..•••••.•••.•...•.......•• 421 ABSTRACTS OF CONTRIBUTED PAPERS ..•.••..•.....•••.•.•...•.. 423 INDEX OF ADVERTISERS ••••....••.•••.•....••.....•••••••.•.• 459 MEETINGS CALENDAR OF MEETINGS Note: This Calendarlists all of the meetings which have been approved by the Council up to the date ·at ·which 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 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* 584 November 17-18, 1961 Milwaukee, Wisconsin Oct. 3 585 November 17-18, 1961 Gainesville, Florida Oct. 3 586 November 18, 1961 Santa Barbara, California Oct. 3 587 January 22-26, 1962 Cincinnati, Ohio Nov. 17 (68th Annual Meeting) 588 February 22, 1962 New York, New York Jan. 9 (Emphasis on Finite Groups and Continuous Groups) 589 April 12-14, 1962 Chicago, Illinois Feb. 27 590 April 16-19, 1962 Atlantic City, New Jersey Feb. 27 591 April 25, 1962 Monterey, California Feb. 27 592 August 27-31, 1962 Vancouver, British Columbia (67th Summer Meeting) January 24-28, 1963 Berkeley, California (69th Annual Meeting) August 26-30, 1963 Boulder, Colorado (68th Summer Meeting) January 20-24, 1 964 Miami, Florida (70th Annual Meeting) August, 1965 Ithaca, New York August, 1966 New Brunswick, New Jersey * 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 deadline dates for by title abstracts are November 10 and January 2nd. The NOTICES of the American Mathematical Society is published by the Society seven times a year, in February, April, June, August, October, November, and December. Price per annual vol­ ume is $7 .00. Price per copy, $2.00. Special price for copies sold at registration desks of meetings of the Society, $1.00 per copy. Subscriptions, orders for back numbers (none available before 1958), and inquiries should be addressed to the American Mathematical Society, 1350 Main Street, Ann Arbor, Michigan, or to 190 Hope Street, Providence 6, Rhode Island. Second-class postage paid at Ann Arbor, Michigan. Authorization is granted under the author­ ity of the act of August 24, 1912, as amended by the act of August 4, 1947 (Sec. 34.21, P. L. and R.). Accepted for mailing at the special rate of postage provided for in section 34.40, paragraph (d). Copyright © 1961 by the American Matbematical Society Printed in the United States of America Five Hundred Eighty-Third Meeting Massachusetts Institute of Technology Cambridge, Massachusetts October 28, 1961 PROGRAM The five hundred eighty-third meet­ Technology is located on the Cambridge ing of the American Mathematical Society side of the Charles River approximately will be held on Saturday, October 28, 1961, one to two miles from the various railway at the Massachusetts Institute of Technol­ stations in Boston. It is easily accessible ogy. All times given below are Eastern by automobile, subway, trackless trolley Standard Time. or taxicab. There will be ample free park­ By invitation of the Committee to ing space in the East Parking Lot of the Select Hour Speakers for Eastern Sec­ Institute grounds for those traveling by tional Meetings, Professor Michel Ker­ automobile. The entrance to this parking vaire of New York University will deliver lot is at the corner of Main and Vassar an address at 2:00 P.M. on Saturday in Streets. The sessions will be held in Room 26-100. His title is "Some results Buildings 2,4,6 and 26. The most conven­ and problems in differential topology." ient entrance for those coming by automo­ The lecture room is the auditorium of the bile or subway is the entrance at the Karl Taylor Compton Laboratories, to the Northwest corner of the Hayden Memo­ north of the main building and easily ac­ rial Library. It is a seven to ten minute cessible by connecting corridors. walk from the Kendall Square station of There will be sessions for contri­ the Cambridge-Dorchester subway. This buted papers on Saturday morning, at Subway may be boarded at various points 10:00 A.M., and on Saturday afternoon at including South Station, Boston, and Har­ 3:15 P.M. in rooms 2-190, 2-390, 4-270 vard Square, Cambridge. Those coming by and 6-120. taxicab or trackless trolley should enter There will be a registration desk on at the main entrance, 77 Massachusetts the first floor of Building 2. The Mathe­ Avenue. Most of the entrances except the matics Common Room, 2-290, and a class­ two mentioned above are closed on Satur­ room, 2-131, near the registration desk, day. will be available for conversation rooms Lunch will be served in an M.l. T. and may be used as coat rooms. cafeteria, and a list of nearby restaurants The Massachusetts Institute of in Boston and Cambridge will be available. PROGRAM OF THE SESSIONS The time limit for each contributed paper is ten minutes. The contributed papers are scheduled at 15 minute intervals so that listeners can circulate between the differ­ ent sessions. To maintain this schedule, the time limit will be strictly enforced. SATURDAY, 10:00 A.M. General Session, Room 2-190 10:00 - 10:10 (l) Geometric properties of polynomial surfaces and hypersurfaces Professor Robert Osserman, Stanford University (583- 44) 393 10:15 - 10:Z5 (Z) Weak:* closure of functions of absolute value one Professor R. R. Goldberg* and Professor A, B. Simon, Northwestern University (583-6) 10:30 - 10:40 (3) Harmonic analysis on a Hilbert space Professor Leonard Gross, Cornell University (583-Z6) 10:45 - 10:55 (4) Analytic continuation of polyharmonic functions Mr. S. R. Kraft, University of Maryland (583 -1) 11:00 - 11:10 (5) A remark concerning the solution of the Dirichlet problem by finite differ­ ences Professor Bernard Epstein, Yeshiva University (583-ZZ) 11:15- 11:Z5 (6) On the global existence of solutions of nonlinear parabolic equations Mr. Stanley Kaplan, New York University (583-Z9) 11:30 - 11:40 (7) A reduction to an integral equation of an inhomogeneous, singular Cauchy problem in harmonic space Mr. B. A. Fusaro, University of Maryland and University of Oklahoma (583-38) 11:45 - 11:55 (8) Convergence of operator averages Professor R. V. Chacon, Brown University (583-30) SATURDAY, 10:00 A.M. Session on Applied Mathematics, Room Z-390 10:.00 - 10:10 (9) On the geometry of the vorticity tensor and the ·vorticity vector in the rela­ tivistic hydrodynamics Dr. E. R. Suryanarayan, University of Rhode Island (583 -7) 10:15 - 10:Z5 (10) Solution of the space charge problem for a pulsed Townsend discharge Dr. j. A. Morrison* and Dr. D. Edelson, Bell Telephone Laboratories, Incorporated, Murray Hill, New jersey (583-9) 10:30 - 10:40 (11) Holor algebra Professor D. E. Spencer, University of Connecticut (583-15) 10:45 - 10:55 (lZ) The roots of polynomial surfaces Mr. L. j. Cohen, Applied Data Research, Incorporated, Princeton, New jersey (583-ZO) 11:00 - 11:10 (13) On rational Tchebycheff approximation. Preliminary report Dr. E. W. Cheney, Iowa State University and Mr. H. L. Loeb*, Syste·m Development Corporation, Santa Monica, California (583 -19) 11:15- 11:Z5 (14) Solutions of a class of linear partial differential equations with variable co­ efficients Professor W. F·. Ames and Mr. Hernando de la Cuesta*, University of Delaware (583-Z1) * For papers with more than one author, an asterisk follows the name of the author who plans to present the paper at the meeting. 394 11:30 - 11:40 (15) Pattern recognition by moments Dr. F. L. Alt, National Bureau of Standards, Washington, D. C. (583-40) 11:45 - 11:55 (16) Channels which transmit letters of unequal duration Professor R. M. Krause, Armour Research Foundation of Illinois Insti­ tute of Technology (583-43) SATURDAY, 10:00 A.M. General Session, Room 6-120 10:00 - 10: 10 (17) Hierarchic algebra. II Mrs. M. B. Prestrud, The Rand Corporation, Santa Monica, California (583-3) 10:15 - 10:25 (18) Increasing rates of convergence with summability methods Professor G. G. Bilodeau, Boston College (583 -13) 10:30 - 10:40 (19) A theorem on partially ordered sets. Preliminary report Professor Kurt Bing, Rensselaer Polytechnic Institute (583-17) 10:45 - 10:55 (20) Algebraic structure of groups of provable permutations Mr. C. F. Kent, Massachusetts Institute of Technology (583-10) 11:00 - 11:10 (21) A note on bounded-truth-table reducibility. Preliminary report Mr. P. C. Fischer, Massachusetts Institute of Technology (583-5) 11:15- 11:25 (22) WITHDRAWN 11:30- 11:40 (23) The fundamental operator of a stationary Markov process.