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OF THE AMERICAN MATHEMATICAL SOCIETY VOLUME 13, NUMBER 4 ISSUE N0.90 JUNE, 1966 cAfotiaiJ OF THE AMERICAN MATHEMATICAL SOCIETY Edited by John W. Green and Gordon L. \\.alker CONTENTS MEETINGS Calendar of Meetings • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 420 Program of the June Meeting in British Columbia...... • • . • • • • • • • • 421 Abstracts for the Meeting- Pages 4720478 PRELIMINARY ANNOUNCEMENT OF MEETING. • • • • • • . • • • • • • • • • • • • • 425 DOCTORATES CONFERRED IN 1965............................. 431 RECENT POLICIES CONCERNING FEDERAL RESEARCH GRANTS. • • • • • • • • 450 NEWS ITEMS AND ANNOUNCEMENTS •••••••••••••.••• , • 424, 451, 452,468 MEMORANDA TO MEMBERS Request for Visiting Foreign Mathematicians • • • • • • • . • • • • • • • • • . • • 456 The Employment Register. • • • • • • • • • • • • • • • • • . • • • • • • • • • • • • • • 456 PERSONAL ITEMS. • • • • • • • • • • • • • • • • • • • • • • • • • • • . • • • • • • • • • • • 457 ACTIVITIES OF OTHER ASSOCIATIONS..... • • • • • • • • • . • • • • • • • • • • • • 459 NEW AMS PUBLICATIONS.. • • • • • • • • • • • • • • • • • • . • . • • • • • • • • • • • • • 460 SUPPLEMENTARY PROGRAM- Number 39........................ 464 ABSTRACTS OF CONTRIBUTED PAPERS.......................... 469 ERRATA. • • • • • • • • • • • • • • • • • • • • • • • • • • • • . • • . • • • • • • • • • • • . • • • 513 INDEX TO ADVERTISERS • • • • • • • • • • • • • • • • • • • • . • • • • . • • • • • • • • • 525 RESERVATION FORMS...................................... 526 MEETINGS Calendar of Meetings NOTE: This Calendar lists all of the meetings which have been approved by the Council up to the date at which this issue of the cJforicei) 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·* 636 August 2-9-September 2, 1966 New Brunswick, New Jersey July 8 13 637 October 29, 1966 Philadelphia, Pennsylvania Sept. Sept. 28 638 November 11' 1966 Tampa, Florida 28 639 November 19, 1966 Los Angeles, California Sept. 28 640 November 25-26, 1966 Mexico City, Mexico Sept. January 23-27, 1967 Houston, Texas August 28-September 1, 1967 Toronto, Ontario, Canada January, 1968 San Francisco, California *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 the by title abstracts are .July 1, and September 6, 1966. The c.Noti.ceJJ 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 $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 (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. Authorization is granted under the authority 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©. 1966 by the American Mathematical Society Printed in the United States of America 420 Six Hundred Thirty-Fifth Meeting University ofVictoria and Canadian Services College, Royal Roads June 18,1966 PROGRAM The six hundred thirty-fifth meeting ROOM RESERVATIONS of the American Mathematical Society will be held at the University of Victoria in A limited amount of residence ac­ Victoria, Br~tish Columbia, on June 18, commodation will be available on campus 1966, in conjunction with meetings of the for the nights of June 16, 17, 18. The daily Pacific Northwest Section of the Mathemati­ adult rates for rooms without meals are cal Association of America and the Society $5.00 for single $4.00 per person in a for Industrial and Applied Mathematics. double room; children under age 10, $1.00. The Society will meet on Saturday, and the Reservations for residence accommodation Association and SIAM will hold their regu­ should be sent as soon as possible to Pro­ lar sessions on Friday, June 17. There will fessor Phoebe Noble, Department of Mathe­ be special sessions of the Association for matics, University of Victoria, Victoria, members of mathematics departments of B.C. Requests should include the number two year colleges, junior colleges, and and names of adults and children, dates community colleges during the morning and and times of arrival and departure, and afternoon of Saturday, June 18. check or money order for pre-payment of By invitation of the Committee to room. (If payment is made in American Select Hour Speakers for Far Western money, rates are $4.75, $3.80, $0.95.} Sectional Meetings, the Society will be ad­ As a major tourist center, Victoria dressed at 11:00 A.M. on Saturday by Pro­ abounds in motels and motor hotels. For a fessor P. Emery Thomas of the University list of motels or further information con­ of California, Berkeley. The title of the cerning motels or ferry timetables write talk by Professor Thomas is "Vectorfields to Phoebe Noble at the given address. on manifolds." It will be given in Elliott Many hotels are available in Victoria 168. although none are located close to the Sessions for contributed papers will Gordon Head Campus of the University. be held on Saturday at 9:00A.M. and 2:00 Below is a partial list of downtown hotels. P.M. Late papers may be added to these (Minimum rates are quoted.) sessions. A supplementary program listing Anyone who wishes to stay in a hotel changes and late papers will be available should write directly to the hotel for re­ at the registration desk. All sessions of servations. These hotels are approximately the meeting will be held in the Lecture 3 miles from the campus. Room annex of the Elliott Building. The Dominion Hotel 759 Yates Street REGISTRATION Single Double Twin $7.00-10.00 $7.00-11.00 $10.00-15.00 The registration desk will be in the lobby of this building, and it will be open The Douglas Hotel from 8:30A.M. to 5:30 P.M. on Friday and 1450 Douglas Street Saturday, June 17, and 18. $6.00-8.00 $8.00-10.00 $10.00-12.00 421 The Empress Hotel 5:00P.M. on Saturday, June 18, at Canadian 721 Government Street Services College, Royal Roads. Tea will $13.00 $19.00 $19.00 be served, and there will be an opportunity The Strathcona Hotel to explore the gardens and grounds of the 919 Douglas Street College. All persons attending the meet­ $8.00 $9.50 $10.50 ings are invited to this reception. Trans­ portation will be provided from the Gordon ENTERTAINMENT Head Campus of the University of Victoria to Royal Roads for those who need it. A beer party will be held in the Invitations should be picked up at the time Student Union Building at 8:30 P.M. on the of registration. evening of June 17. All persons attending the meetings are invited as guests of the Victoria is served by Air Canada departments of mathematics at the Univer­ from Seattle to Vancouver. There is also sity of Victoria and Canadian Services a direct bus service from downtown Van­ College, Royal Roads. A complimentary couver to downtown Victoria via the B.C. luncheon, through the courtesy of the British Government Ferries and a bus service from Columbia Centennial Committee, will be downtown Seattle to Port Angeles, Wash­ held in the cafeteria on the Gordon Head ington, via the Hood Canal Bridge which Campus of the University of Victoria be­ connects directly with the Port Angeles­ tween 12:00 noon and 2:00P.M. on Saturday, Victoria ferry. Members who are able to June 18. There will be an informal recep­ do so are advised to come to Victoria by tion from noon until 12:30 P.M. in the cafe­ private car since only in this way can one teria, followed by the luncheon. Tickets take full advantage of the scenic beauties for this luncheon may be picked up at the of the Victoria area. There is an excellent registration desk. Since it may be necessary car ferry service from Tsawwassen to to limit attendance at this luncheon, those Swartz Bay, twenty miles north ofVictoria; persons who wish to attend are urged to from Anacortes, Washington, to Sidney, obtain their complimentary tickets when British Columbia; and from Port Angeles, they register. A reception will be held at Washington, to downtown Victoria. PROGRAM OF THE SESSIONS The time limit for each contributed paper is ten minutes. To maintain the schedule the time limit will be strictly enforced. • -- SATURDAY, 9:00 A.M. General Session, Room 060, Elliott Building 9:00-9:10 ( 1) Totally positive matrices whose entries are permanental functions of a given matrix Dr. D. W.Sasser and Dr.M.L. Slater*, Sandia C-orporation, Albuquerque, New Mexico (635-7) 9:15-9:25 (2) On error bounds for generalized inverses Professor Adi Ben-Israel, University of Illinois at Chicago (635-6) 9:30-9:40 (3) An example of a Julia line which is not a Milloux line Professor W. J. Schneider, Syracuse University (635-14) *For papers with more than one author, an asterisk follows the name of the author who plans to present the paper at the meeting. 422 9:45-9:55 (4) Reduction of Fredholm integral equations with Green's function kernels to Volterra equations Mr. S. K. Aalto, Oregon State University (635-15) 10:00-10:10 ( 5) Singular perturbations of a nonlinear system of ordinary differential equations Professor J. W. Macki, University of Alberta (635-8) 10:15-10:25 (6) On the behavior of the solutions of some nonlinear differential equations Professor D.
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  • On Families of Mutually Exclusive Sets

    On Families of Mutually Exclusive Sets

    ANNALS OF MATHEMATICS Vol. 44, No . 2, April, 1943 ON FAMILIES OF MUTUALLY EXCLUSIVE SETS BY P . ERDÖS AND A. TARSKI (Received August 11, 1942) In this paper we shall be concerned with a certain particular problem from the general theory of sets, namely with the problem of the existence of families of mutually exclusive sets with a maximal power . It will turn out-in a rather unexpected way that the solution of these problems essentially involves the notion of the so-called "inaccessible numbers ." In this connection we shall make some general remarks regarding inaccessible numbers in the last section of our paper . §1. FORMULATION OF THE PROBLEM . TERMINOLOGY' The problem in which we are interested can be stated as follows : Is it true that every field F of sets contains a family of mutually exclusive sets with a maximal power, i .e . a family O whose cardinal number is not smaller than the cardinal number of any other family of mutually exclusive sets contained in F . By a field of sets we understand here as usual a family F of sets which to- gether with every two sets X and Y contains also their union X U Y and their difference X - Y (i.e. the set of those elements of X which do not belong to Y) among its elements . A family O is called a family of mutually exclusive sets if no set X of X of O is empty and if any two different sets of O have an empty inter- section. A similar problem can be formulated for other families e .g .