MATHEMATICAL EDITED BY

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1 MAY 1990 VOLUME 109 NUMBER 1 WHOLE NUMBER 371 Proceedings JL OFTHE AMERICAN MATHEMATICAL EDITED BY William Adams J Marshall Ash Maurice Auslander Andreas R Blass Andrew M Bruckner Dennis Burke Frederick R Cohen William J Davis, Managing Editor Clifford J Earle, Jr Lawrence F Gray Palle E T Jorgensen Jeffry N Kahn Barbara L Keyfitz Kenneth R Meyer Paul S Muhly George C Papanicolaou Louis J Ratliff, Jr Jonathan M Rosenberg James E West Warren J Wong PROVIDENCE,RHODEISLAND USA ISSN SOCIETY

2 Proceedings of the American Mathematical Society This journal is devoted entirely to research in pure and applied mathematics Editorial Policy To be published in the Proceedings, a paper must be correct, new, nontrivial and significant Further, it must be well written and of interest to a substantial number of mathematicians Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication Proceedings Editors shall solicit, and encourage publication of, worthy papers of length not exceeding 15 typed pages Very short notes not to exceed two printed pages are also accepted, and appear under the heading Shorter notes Items deemed suitable include an elegant new proof of an important and well-known theorem, an Illuminating example or counterexample, or a new viewpoint on familiar results New results, if of a brief and striking character, might also be acceptable, though in general a paper which is merely very short will not be suitable for the Shorter notes department On January 23, 1979, the Council of the American Mathematical Society abolished blind refereeing as a policy for the Proceedings, but decided that any author who so requests and who provides a blind copy of a manuscript will have the manuscript refereed blind Two copies of a manuscript should be submitted If blind refereeing is intended, one should be complete and one blind, and then the latter will be sent to the referee without disclosure of the author's name or institution SUBSCRIPTION INFORMATION PROCEEDINGS OF THE AMERICAN MATHEMATI- CAL SOCIETY is published monthly Subscription prices for Volumes (1990) are $432 list; $346 institutional member; $259 individual member A late charge of 10% of the subscription price will be imposed upon orders received from nonmembers after January 1 of the subscription year Subscribers outside the United States and India must pay a postage surcharge of $25: subscribers in India must pay a postage surcharge of $38 Expedited delivery to destinations in North America $30; elsewhere $67 Combination paper and microfiche subscription prices are $575 list; $460 institutional member Microfiche of each issue will be mailed the fastest way possible before the camera copy is sent to the printer Microfilm subscriptions may be purchased from University Microfilms International, 300 North Zeeb Road, Ann Arbor, Michigan BACK NUMBER INFORMATION Back number prices per volume are for Volumes 1-89, $117 list $93 institutional; for Volumes 90-92, $134 list; $107 institutional member; for Volumes 93-95, $179 list; $143 institutional member; for Volumes 96-98, $198 list; $158 institutional members; for Volumes , $209 list; $168 institutional member; for Volumes , $214 list; $171 institutional member Subscriptions and orders for publications of the American Mathematical Society should be addressed to American Mathematical Society P O Box 1571, Annex Station, Providence, R I All orders must be accompanied by payment Other correspondence should be addressed to P O Box 6248, Providence, R I PROCEEDINGS of the American Mathematical Society is published monthly by the American Mathematical Society at 201 Charles Street Providence, R I Second-class postage is paid at Providence, Rhode Island Postmaster: Send address changes to PROCEEDINGS, American Mathematical Society, P O Box 6248, Providence, R I Copyright 1990 American Mathematical Society All rights reserved Printed in the United States of America Information on Copying and Reprinting can be found at the back of this journal The paper used in this journal is acid-free and falls within the guidelines established to ensure permanence and durability This publication was typeset using iî^s-tgx, the American Mathematical Society's TpX macro system I

3 Manuscript Information 1 Articles submitted for publication should be typewritten, double spaced, and no more than 15 (8j" x 11 ") pages long The Manual for Authors, available from the Society, should be consulted for symbols and style conventions Authors should take the greatest possible care in preparing the original manuscript Hand drawn symbols are satisfactory, if clearly done; directions to the printer should be included where necessary on a separate sheet Authors must keep complete copies of their manuscripts, and editors will acknowledge receipt To encourage the submission of manuscripts in electronic form using TgX and the 4A45-TgX macro package, the Executive Committee of the Council has adopted a policy that allows for accelerating the publication date of such manuscripts by as much as 20 weeks, which is approximately equal to the time normally needed by the Society for copyediting, typesetting, and proofreading an average manuscript 2 The first page should consist of a descriptive title, followed by an abstract which summarizes the article in language suitable for workers in the general field (algebra, analysis, etc) The descriptive title should be short, but informative; useless or vague phrases such as "some remarks about" or "concerning" should be avoided The abstract should be at least one complete sentence, and at most 150 words Included with the footnotes to the paper, but placed before the first footnote, there should be first the 1980 Mathematics Subject Classification ( 1985 Revision) representing the primary and secondary subjects of the article This may be followed by a list of key words and phrases describing the subject matter of the article and taken from it A list of the numbers may be found in the annual subject index of Mathematical Reviews, published with the December issue starting in A Copyright Transfer Agreement is required before a paper will be published in the Proceedings A copy of the form is sent with the acknowledgement of receipt of manuscript from the Providence office of the Society Authors are urged to return the forms immediately to prevent delays in processing and publishing of the manuscript OFFPRINTS AND ADDRESS CHANGES Any inquiries concerning a paper which has been accepted for publication, including information regarding offprints or changes of address for mailing proof, should be sent directly to the Editorial Department, American Mathematical Society, PO Box 6248, Providence, Rhode Island GALLEY PROOF When a paper with more than one author has been accepted for publication, only one set of galley proof will be sent Joint authors should, therefore, indicate on the original manuscript which of them should receive galley proof in the event that the manuscript is accepted for publication BACKLOG 150 pages Papers currently being accepted by the editors will be published in months COPYING AND REPRINTING Individual readers of this publication, and nonprofit libraries acting for them are permitted to make fair use of the material, such as to copy an article for use in teaching or research Permission is granted to quote brief passages from this publication in reviews provided the customary acknowledgement of the source is given Republication, systematic copying, or multiple reproduction of any material in this publication (including abstracts) is permitted only under license from the American Mathematical Society Requests for such permission should be addressed to the Executive Director, American Mathematical Society, PO Box 6248, Providence, Rhode Island The appearance of the code on the first page of an article in this journal indicates the copyright owner's consent for copying beyond that permitted by Sections 107 or 108 of the US Copyright Law, provided that the fee of $100 plus $25 per page for each copy be paid directly to Copyright Clearance Center, Inc, 27 Congress Street, Salem, Massachusetts This consent does not extend to other kinds of copying, such as copying for general distribution, for advertising or promotion purposes, for creating new collective works, or for resale

4 Submission of Manuscript Send papers directly to one of the editors listed under the subject field of the paper The numbers in parentheses are the first two digits of major classification from the 1980 Mathematics Subject Classification (1985 Revision) and describe the fields being handled by the editor LOGIC AND FOUNDATIONS (03 04) Andreas R Blass, Department of Mathematics, University of Michigan, Ann Arbor Michigan COMBINATORICS, COMPUTER SCIENCE AND INFORMATION THEORY ( ) Jeffry N Kahn, Department of Mathematics, Rutgers University, New Brunswick New Jersey COMMUTATIVE ALGEBRA ( ) Louis J Ratliff, Jr, Department of Mathematics, University of California, Riverside, California GENERAL ALGEBRA ( ) Maurice Auslander, Department of Mathematics, Brandeis University, PO Box 9110, Waltham, Massachusetts GROUP THEORY (20) Warren J Wong, Department of Mathematics, University of Notre Dame, Notre Dame Indiana ALGEBRAIC AND DIFFERENTIAL TOPOLOGY ( ) Frederick R Cohen, Department of Mathematics, University of Rochester, Rochester, New York REAL VARIABLES ( ) Andrew M Bruckner, Department of Mathematics, University of California, Santa Barbara California COMPLEX VARIABLES ( ) Clifford J Earle Jr, Cornell University, White Hall, Ithaca, New York NUMBER THEORY (11) William Adams, Department of Mathematics University of Maryland, College Park, Maryland ORDINARY DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS ( ) Kenneth R Meyer, Department of Mathematical Sciences, University of Cincinnati, Cincinnati Ohio PARTIAL DIFFERENTIAL EQUATIONS (35 49) Barbara L Keyfitz, Department of Mathematics, University of Houston, Houston, Texas GENERAL ANALYSIS ( ) J Marshall Ash Department of Mathematics, DePaul University, Chicago, Illinois FUNCTIONAL ANALYSIS AND OPERATOR THEORY (46 47) Palle E T Jorgensen, University of Iowa, Iowa City, Iowa FUNCTIONAL ANALYSIS AND CONVEXITY (46 52) William J Davis, Department of Mathematics, Ohio State University, Columbus, Ohio COMPLEX VARIABLES, FUNCTIONAL ANALYSIS, AND OPERATOR THEORY ( ) Paul S Muhly, Department of Mathematics University of Iowa, Iowa City, Iowa L7E GROUPS AND GEOMETRY ( ) Jonathan M Rosenberg, Department of Mathematics, University of Maryland, College Park, Maryland GENERAL TOPOLOGY (54) Dennis Burke, Department of Mathematics, Miami University of Ohio, Oxford, Ohio James E West, Department of Mathematics, Cornell University, Ithaca, New York PROBABILITY AND CERTAIN OTHER FIELDS (60-94 inclusive) Lawrence F Gray, Department of Mathematics University of Minnesota Minneapolis Minnesota George C Papanicolaou, Applied Mathematics Division, New York University-Courant Institute, 251 Mercer Street New York, New York All other communications should be addressed to the Managing Editor William J Davis, at the above address

5 CONTENTS Continued from back cover On Rhoades' open questions By Shih-sen Chang and Qi-chun Zhong 269 Large compact separable spaces may all contain ßN By Alan Dow 275 H COMBINATORICS A partition theorem for [0, 1] By H J Prömel and B Voigt 281

6 PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY CONTENTS Whole No 371 May 1990 Vol 109, No 1 A ALGEBRA AND NUMBER THEORY By Daniel Cass and Pasquale J Arpaia Matrix generation of Pythagorean «-tuples Filtrations of rational representations of reductive groups of semisimple rank 1 By Stephen Doty By Dieter Jungnickel On the number of self-dual bases of GF(q'") over GF(q) Alfred J Menezes, and Scott A Vanstone By Ronghui Ji On the smoothed Toeplitz extensions and A'-theory By Jan Okniñski and Mohan S Putcha PI semigroup algebras of linear semigroups By J Vukman Commuting and centralizing mappings in prime rings By James K Devenev and Joe Yanik Rationality of some genus 0 extensions of K(X) By Robert I Campbell Notes on the Baumslag-Solitar nonresidually finite examples E Graham Evans, By Hara Charalambous Betti numbers for modules of finite length Miller and Matthew B ANALYSIS Kj is uniformly Kadec-Klee By Chris Lennard By Daniel M Oberlin A linearization of the circular maximal operator By Andreas Wannebo Hardy inequalities By Antonio Suárez Granero Stable unit balls in Orlicz spaces The existence of absolutely continuous invariant measures for C'l+,: Jablonski transformation By You-Shi Lou in R" Properties on the unit circle of polynomials with unimodular coefficients By Donald J Newman and André Giroux By Akihito Uchiyama On the characterization of HP(R") in terms of Fourier multipliers By José Mendoza Copies of /^c in D'(p;X) Convolution in the harmonic Hardy class h'' with 0 < p < 1 By Miroslav Pavlovic By Ralph Howard and Anton R Schep Norms of positive operators on ''-spaces By KJ Brown, Principal eigenvalues for problems with indefinite weight function on Ry C Cosner, and J Fleckinger By Peter Lindqvist On the equation div( Vw ''~:ViO + k\u\l'~1u = 0 By Juan Arias-de-Reyna On the theorem of Frullani On eigenvalue problems of the /;-Laplacian with Neumann boundary conditions By Yin Xi Huang A note on exponential intcgrability and pointwise estimates of Littlewood-Paley functions By Mark Leckband By Andrei Verona and Maria Elena Verona Locally efficient monotone operators D GEOMETRY By Sueli 1 Rodrigues Costa On closed twisted curves On the sectional curvature of compact hypersurfaces Yoe Itokawa 205 By Leslie Coghlan and 215 G TOPOLOGY By Masayuki Yamasaki Maps between orbifolds Restrictions of open mappings of continua By Witold D Bula and E D Tymchatyn By Katsuya Eda First countability and local simple connectivity of one point unions By John Franks and Micha-l Misiurewicz Rotation sets of toral flows By Eva Butkovicová Decreasing chains without lower bounds in the Rudin-Frolik order By Roy A Johnson, Eliza Wajch, and Three cardinal functions similar to net weight WtADYSLAW 261 WlLCZYÑSKI (Continued on inside back cover)