Mathematics and the 21st Century: Proceedings of the International Conference, Cairo, Egypt, 15-20 January 2000 PDF
Preview Mathematics and the 21st Century: Proceedings of the International Conference, Cairo, Egypt, 15-20 January 2000
[js i/jismaitonaJ Confarsnc;: Mathematics and the 21st Century Editors A. A. Ashour & A.-S. F. Obada World Scientific Mathematics and the 21st Century Proceedings of the International Conference Mathematics and the 21st Century Cairo, Egypt 15-20 January 2000 Editors A. A. Ashour Department of Ivlathematics, Cairo University, Egypt A.-S. F. Obada Department of Mathematics, Al-Azhar University, Egypt V f e World Scientific « • Singapore *New Jersey London* Hong Kong Published by World Scientific Publishing Co. Pte. Ltd. P O Box 128, Fairer Road, Singapore 912805 USA office: Suite IB, 1060 Main Street, River Edge, NJ 07661 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE Library of Congress Cataloging-in-Publication Data Mathematics and the 21st century : proceedings of the international conference, Cairo, Egypt, 15-20 January 2000 / edited by A.A. Ashour, A.-S.F. Obada. p. cm. ISBN 9810245483 (alk. paper) 1. Mathematics--Congresses. I. Ashour, A.A. II.Obada, A.-S.F. III. International Conference on Mathematics and the 21st century (2000 : Cairo, Egypt) QA1 .M83245 201 0-068520 510-dc21 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. Copyright © 2001 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. Printed in Singapore by Uto-Print The International Organizing Committee A. A. Ashour (Egypt) (Chairman) F. Abi-Khuzam (Lebanon) N. Balahrishnan (Canada) P. Griffiths (USA) (General Secretary of IMU) A. Hamoui (Kuwait) M. Ismail (USA) I. Khalil (Morocco) J. Palis (Brazil) (President of IMU) P. Sarnak (USA) Local Organizing Committee G. M. Abd Al-Kader (Al-Azhar University) E. K. Al-Hussaini (Assiut University) A. H. Azzam (Suez Canal University) S. El-Gindy (Assiut University) H. El-Hosseiny (Cairo University) H. M. El-Oweidy (Al-Azhar University) H. N. Ismail (Benha High Institute) I. F. Mikhail (Ain Shams University) A.-S. F. Obada (Al-Azhar University) vii Preface The Conference on "Mathematics and the 21st Century" was held in Cairo, Egypt during the period 15-20 January 2000. The Conference was an event of the WMY2000 initiative launched by the International Mathematical Union. The Conference was hosted in the Tiba Rose Hotel in Cairo with its good facilities, where most of the foreign participants were lodged. The following organizations are acknowledged for their financial support: The International Mathematical Union (IMU). The Abdus Salam Interna- tional Center for Theoretical Physics (ICTP), Trieste, Italy. The Third World Academy of Science (TWAS). UNESCO's Regional Office for Science and Tech- nology for the Arab States (ROSTAS). Ministry of International Cooperation, Egypt. The Egyptian Academy for Scientific Research Technology (ASRT). The International Committee for WMY2000 is acknowledged for making their web site available to distribute information about the conference. The Egyp- tian Mathematical Society helped in the organization of the conference. The Conference was opened by an address from H. E. Prof. Dr. Mofeed Shehab, Egyptian Minister of Scientific Research. In addition, Prof. M. Yosry President of the ASRT, Prof. Jacob Palis, President of IMU, and also repre- senting TWAS, Prof. M. El-Deek, Head of ROSTAS addressed the conference. A message of good wishes from Prof. M. Verasoro Director of ICTP was delivered by Prof. A. Ashour chairman of the conference who also gave a wel- coming speach. The opening session was followed by the Millennium lecture, "A Thousand Years of Mathematics" delivered by Sir Michael Atiyah. The conference's sessions consisted of plenary lectures and topical sessions. Some of the plenary lectures covered general fields such as: Rewriting the his- tory of mathematics (Rashed); Education of mathematics (Ebeid); Relation between mathematics and sciences (Griffiths); Mathematical aspects of trans- portation (Groetschel). General reviews of the recent research and standing problems were also delivered. In this aspect the following lectures are relevant: A global view of dynamical systems (Palis); Einstein's theory of space-time and gravitation (Ehlers); A geometrical theory for the unification of all fun- damental forces (El-Naschie); Transfer of energy from low frequency to high frequency modes (Nayfeh); Stratification of algebras (Dlab); Multivariate sta- tistical distributions (Balakrishnan). The invited topical lectures covered: Finite groups (Bolinches & Assad); Radical theory (Wiegandt); Enumerative geometry (Procesi); Moduli problems viii in geometry (Narasimhan); Asymptotic behaviour of solutions of evolution equations (Basit); Instability of nonlinear evolution equations (Debnath); Non- smooth dynamical systems (Kuepper); On approximations of functions (H. Ismail); On a semi-analytic method for the solution of some elliptic B.V.P (Ghaleb); On robust layer resolving methods for computing numerical approx- imations (Miller); Eigen values for fractal drums (Fleckinger); Electrostatic models and orthogonal polynomials (M. Ismail); On the developments on the- ory of functions of several complex variables (Fadlalla); Invertibility preserv- ing linear maps (Sourour); Entire functions sections (Abi Khuzan); Optical solitons (Bullough); Non-classical properties of intermediate states (Obada); On the relativistic 2-body problem (Komy); Singularities in general relativ- ity (Buchner); Linear geometry of light cone (Abdel-Megied); Advances and new results in prediction (Al-Hassaini); and Theory of accelerated experiments (Nikouline). The plenary and invited topical lectures covered a broad spectrum of research in mathematics and its applications together with the history of math- ematics and mathematics education. More than 90 research papers related to different fields of mathematics were delivered in the topical sessions. The Conference was attended by 132 participants, coming from 19 coun- tries, including 11 invited plenary speakers and 24 invited topical speakers. In the closing ceremony, Prof. Narasimhan, the Director of Mathematics in ICTP gave a short speech and Prof. Ali H. Nayfeh of Virginia Polytech., USA spoke for the invited speakers and Prof. Ashour chairman of the conference gave some concluding remarks. The Conference offered a unique opportunity for mathematicians from Egypt, and nearby countries to have an overview of the actual status of re- search in many areas of the mathematical sciences and to tighten connections with their colleagues in other countries. The organizing committee requested all the lecturers who delivered the plenary and the invited lectures to present the texts of their contributions. The following volume comprises the texts of the plenary and invited topical lectures that have been provided by the contributors. A. A. Ashour Cairo A.-S. F. Obada October 2000 IX Contents Organizing Comite v Preface vi Milenium Lecture - Cairo, 15 January 20 1 Sir Michael Atiyah Trends for Science and Mathematics in the 21st Century 3 Phillip A. Griffiths Arabic Mathematics and Rewriting the History of Mathematics 13 Roshdi Rashed The Paradigm Shift in Mathematics Education: A Scenario for Change 27 William Ebeid Einstein's Theory of Spacetime and Gravity 41 Jurgen Ehlers Moduli Problems in Geometry 53 M. S. Narasimhan Enumerative Geometry from the Greks to Strings 59 C. Procesi Optical Solitons: Twenty-Seven Years of the Last Millennium and Thre More Years of the New? 69 R. K. Bullough Concepts for Non-smoth Dynamical Systems 123 Tassilo Kiipper Radical Theory: Developments and Trends 141 Richard Wiegandt On Minimal Subgroups of Finite Groups 153 M. Asaad Totaly and Mutualy Permutable Products of Finite Groups 159 A. Ballester-Bolinches Asymptotic Behaviour of Solutions of Evolution Equations 169 Bolis Basit
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