Trends in Industrial and Applied Mathematics

Applied Optimization

Volume 72

Series Editors:

Panos M. Pardalos University of Florida, U.S.A.

Donald Hearn University of Florida, U.S.A.

The titles published in this series are listed at the end of this volume.

Trends in Industrial and Applied Mathematics Proceedings of the 1 st International Conference on Industrial and Applied Mathematics of the Indian Subcontinent

Edited by

Abul Hasan Siddiqi Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia

and

Michal Kocvara Institute of Applied Mathematics, University of Erlangen, Erlangen, Germany

KLUWER ACADEMIC PUBLISHERS DORDRECHT I BOSTON I LONDON

A c.I.P. Catalogue record for this book is available from the Library of Congress.

ISBN-13: 978-1-4613-7967-6 DOT: 10.1007/978-1-4613-0263-6

e-ISBN-13: 978-1-4613-0263-6

Published by Kluwer Academic Publishers, P.O. Box 17, 3300AA Dordrecht, The Netherlands.

Sold and distributed in North, Central and South America by Kluwer Academic Publishers, 101 Philip Drive, Norwell, MA 02061, U.S.A.

In all other countries, sold and distributed by Kluwer Academic Publishers, P.O. Box 322, 3300 AH Dordrecht, The Netherlands.

Printed on acidjree paper

All Rights Reserved © 2002 Kluwer Academic Publishers Reprint of the original edition <2002>

No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work.

This book is dedicated to P. Butzer and M.Z. Nashed

for their life-long contributions to

applied mathematics.

Contents

Preface

Contributing Authors

A Perspective on Industrial Mathematics Work in Recent Years

Noel G. Barton

Part I Sampling Theorems

The Sampling Theorem of Signal Processing

Paul L. Butzer

The 'Riesz Basis Method' for Deriving Sampling Series: An Overview and some

ix

xix

1

23

Applications 63

1.R. Higgins

Sampling and Quasi-Sampling in Rotation Invariant Paley-Wiener Spaces 77

B. Ohligs, R.L. Stens

Part II Wawelets

Wavelet Based Computer Simulation of some Meteorological Parameters 95

AH. Siddiqi, Z. Asian, A Tokgozlu

A New Fast DCT based Digital Watermarking Technique 117

M.A Suhail, AH. Siddiqi, S. /pson

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viii TRENDS IN INDUSTRIAL AND APPLIED MATHEMATICS

Part III Mathematical Programming and Applications

A Derivative-Free Algorithm for Sparse Unconstrained Optimization Problems 131

Benoit Colson, Philippe L. Toint

Numerical Methods for Large-Scale Non-Convex Quadratic Programming 149

Nicholas l. M. Gould, Philippe L. Toint

Free Material Optimization: An Overview 181

Michal Kocvara, Jochem Zowe

Part IV Numerical Methods and Control

Numerical Methods for Schrodinger-Type Problems

Graeme Fairweather, Morrakot Khebchareon

Low Cost Control Problems

S. Kesavan, J. Saint Jean Paulin

The Importance of Strange Attractors for Industrial Mathematics

Rene Lozi

Sufficient Optimality in a Parabolic Control Problem

Hans D. Mittelmann, Fredi Troltzsch

Finite Element Approximations to an Evolutionary Variational Inequality with a

219

251

275

305

Volterra Term 317

Pradeepa Nair, Amiya K. Pani

On some Recent Developments concerning Moreau's Sweeping Process 339

A.H. Siddiqi, P. Manchanda, M. Brokate

Preface

An important objective of the study of mathematics is to analyze and visualize phenomena of nature and real world problems for its proper understanding. Gradually, it is also becoming the language of modem financial instruments. To project some of these developments, the conference was planned under the joint auspices of the Indian Society of Industrial and Applied mathematics (ISlAM) and Guru Nanak Dev University (G.N.D.U.), Amritsar, India. Dr. Pammy Manchanda, chairperson of Mathematics Department, G.N.D. U., was appointed the organizing secretary and an organizing committee was constituted.

The Conference was scheduled in World Mathematics Year 2000 but, due one reason or the other, it could be held during 22.-25. January 2001. How­ever, keeping in view the suggestion of the International Mathematics union, we organized two symposia, Role of Mathematics in industrial development and vice-versa and How image of Mathematics can be improved in public. These two symposia aroused great interest among the participants and almost everyone participated in the deliberations. The discussion in these two themes could be summarized in the lengthy following lines: "Tradition of working in isolation is a barrier for interaction with the workers in the other fields of science and engineering, what to talk of non-academic areas, specially the private sector of finance and industry. Therefore, it is essential to build bridges within in­stitutions and between institutions. The scope of professional mathematicians should not be limited to academic institutions but should find place in emerg­ing industry, like bioinformatics, communication technology. Mathematicians should not thrive only on the intrinsic beauty of mathematics and should not carry it as an esthetic and intellectual activity. In fact, the should take inspira­tion from Galileo, Newton, Euler, Gauss, Riemann, Poincare, and others who integrated mathematics with the physical world. The mathematics syllabus and its method of teaching from early stages should be designed in such a way, that learners realize that besides its own beauty, it could be very useful to under­stand intricacies of nature and to resolve real world problems." It may not be out of place to mention that similar views were expressed by Professor Phillip A. Griffiths, Director of the Institute for Advanced Study, Princeton, New Jersey,

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x TRENDS IN INDUSTRIAL AND APPLIED MATHEMATICS

in his talk Trends for Science and mathematics in the 21 st Century in an event of the WMY2000 in Cairo.

The invited speakers covered a wide range of topics varying from algorithmic optimization, variational methods, numerical methods, wavelets, to financial mathematics, homogenization, control and sampling theorems. In addition, there were many excellent papers and some stimulated discussion sessions. Besides academic program the participants also enjoyed cultural program along with the excellent hospitality extended in Amritsar, Delhi and in the city of Taj Mahal, Agra.

In this talk Dr. Noel Barton, Director of ICIAM 2003, Sydney, Australia, presented his experience of working with industrial problems in Australia and indicated his recent work on simulation of Black-Scholes model of option pric­ing. Professor P. L. Butzer, Technical University Aachen, Germany, an author­ity on approximation theory and semi group methods discussed his life long experience and contribution in the area of communication technology. In two technical lectures Professor M. Z. Nashed, Delaware University, USA, and the editor of the Pure and Applied Mathematics series of Marcel Dekker, New York, explained the current trends in variational inequality which models di­verse physical phenomena, though stochastic in nature. Professor P. Toint, University of Namur, Belgium and Dr. N. I. Gould, Rutherford Appleton Lab­oratory, Oxford, world leaders of the algorithmic optimization, presented their current research which is applied to solve very effectively mathematical pro­gramming problems involving up to half a million unknowns and constraints. Professor Hans Mittelmann, Arizona State University, who is widely known for his work on variational methods for partial differential equations, discusses his current results. Professor S. Kesavan, a celebrated Indian Mathematician, Math. Science, Chennai, explained elegantly some control problems related to homogenization along with applications to industrial problems.

Professor Vidar Thomee, Chalmers University of Technology, Goteborg, Sweden, the world leader of numerical methods for parabolic partial differential equations, talked about the current development in his specialization. Profes­sor G. Fairweather, Chairmen of the Department of Mathematics and Computer Science, Colorado School of Mines, USA, discussed applications of Galerkin finite element methods to solve various forms of Schrodinger equations. Pro­fessor J. R. Higgins, UK, devoted his talk to sampling theorems. Professor R. Lozi, Director of Institute of Mathematics, Nice, France, who is popular for his attractors, talked about the role of dynamical systems in problems of industry. Professor A. K. Pani, lIT Bombay, India, explained his experience in work­ing with industrial problems given to him by industrial institutions in Bombay (Mumbai). Prof. R. L. Stens of Aachen University, Germany, presented his recent contribution in the field of Approximation theory. Prof. Zafar AsIan, Vice-Rector of Beykent University, Istanbul, Turkey, talked about applications

PREFACE xi

of wavelet methods in data processing with special reference to meteorological data of Isparata, Turkey. This methodology could be very vital for accurate prediction of climate changes. Prof. P. N. Shivakumar, University Manitoba, Winnipeg, Canada, and Prof. N. Rudraiah, Banglore University, discussed sev­eral industrial applications of their current results.

MK talked about methods, algorithms and computer programs which would allow one to design automatically real world mechanical structures. This re­search is supported by a special program of German Ministry of Development and Technologies which promotes cooperation of mathematical departments at universities with industrial companies. In his talk AHS provided current infor­mation on image processing and variational techniques. Black-Scholes model for which Scholes and Merton fetched Nobel Price in 1997 was referred many times by different speakers. Due to limitation of space and time constraints, many invited talks could not be included in the proceeding.

In the end, we like to thank Dr. John Martindale, Scientific Editor, Kluwer Academic Publishers, Boston, for his cooperation.

Abul Hasan Siddiqi, Dhahran, September 2001

Organization and Ackowledgment

The conference was jointly organized by the Indian Society of Industrial and Applied Mathematics (ISlAM) and Guru Nanak Dev University (GNDU), Amritsar, India. In the first place we are grateful to the following organizations for providing generous financial assistance:

• Abdus Salam International Centre for Theoretical Physics, Trieste, Italy • All India Council of Technical Education, HRD, Govt. of India, Delhi • National Board of Higher Mathematics, India • Council of Scientific and Industrial Research, India • The Duty Society, AM.U., Aligarh, India.

Organizing Committee

Prof. J. N. Kapur EN.ASc., EASe., EN.A, President ISlAM

Prof. U. P. Singh Former Vice Chancellor, Purvanchal University, Jaunpur

Prof. A H. Siddiqi KFUPM, Saudi Arabia, Secretary ISlAM

Prof. N. K. Gupta I.I.T., Delhi

Prof. V. P. Saxena Vice Chancellor, Jiwaji University, Gwalior

Prof. Karmeshu J.N.U. Delhi

Prof. P. Achutan I. I. T. Madras

Prof. C. Mohan Roorkee University, Roorkee

Dr. P. Manchanda (Organizing Secretary) GNDU, Amritsar

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XIV TRENDS IN INDUSTRIAL AND APPLIED MATHEMATICS

Prof. P. N. Srivastava, fonner General President of Indian Science Congress, former Vice Chancellor of JNU, and former member of Planning Commis­sion was the Chief Guest and inaugurated the Conference. In his address he highlighted the role of Mathematics in Science and Technology.

The inaugural function was presided over by Dr. H. S. Soch, Vice Chancellor, GNDU Prof. J. N. Kapur, President of ISlAM, delivered key note address. He also gave a technical talk. Prof. A. H. Siddiqi, Secretary ofISIAM, presented the activities of the Society. Dr. Noel Barton, Director of ICIAM 2003 in Sydney, briefed about the progress in the arrangements of ICIAM 2003 and extended invitation to the participants to attend the Congress. Dr. R. S. Bawa, Registrar GNDU, thanked the participants and the audience.

Two awards, one instituted by the Duty Society AMU, called Zakir Husain Prize, and the other instituted by the Mathematics Trust, C-766, New Friends Colony, New Delhi, were awarded to Prof. J. N. Kapur and Prof. A. K. Pani, respectively. The Vice Chancellor of GNDU honoured all invited speakers and Prof. V. P. Saxena, Vice Chancellor, Jiwaji University, Gwalior, Prof. Rudraiah, former Vice Chancellor of Gulbarga University, Prof. U. P. Singh, Former Vice Chancellor, Purvanchal University, Jaunpur, by presenting shawls to them.

I take this opportunity to thank Prof. M. A. Virasoro, Director of Abdus Salam International Centre for Theoretical Physics, for his generous financial support.

I would also like to thank Prof. A. H. Siddiqi and Dr. M. Kocvara for agreeing to edit the proceedings of the Conference.

List of the participants is given at the end.

Pammy Manchanda Organizing Secretary

and Chairperson Department of Mathematics GNDU, Amritsar, India

Contributing Authors

z. AsIan, Beykent University, Faculty of Sciences and Letters, Department of Mathematics and Computing, Istanbul 34900, Turkey zaslan @beykent.edu.tr

Noel G. Barton, CSIRO Mathematical and Information Sciences, Locked Bag 17, North Ryde NSW 1670, Australia Noel. Barton @cmis.csiro.au

M. Brokate, Zentrum Mathematik, Technical University Munich, 80290 Mu­nich, Germany brokate@appl-math.tu-muenchen.de

Paul L. Butzer, Lehrstuhl A fUr Mathematik, RWTH Aachen, 52056 Aachen, Germany

Benoit Colson, Department of Mathematics, FUNDP, Rempart de la Vierge, 8, B-5000 Namur, Belgium bc@math.fundp.ac.be

Graeme Fairweather, Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, Colorado 80401, U.S.A. gfairwea@mines.edu

Nicholas I. M. Gould, Computational Science and Engineering Department, Rutherford Appleton Laboratory, Chilton, Oxfordshire, OX11 OQX, England n.gould@rl.ac.uk

J.R. Higgins, I.H.P, 4 Rue du Bary, 11250 Montclar, France. rhiggins@wanadoo.fr

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xx TRENDS IN INDUSTRIAL AND APPLIED MATHEMATICS

S. Ipson, University of Bradford, Bradford, UK

S. Kesavan, The Institute of Mathematical Sciences, C. 1. T. Campus, Taramani, Chennai-600 113, India kesh@ imsc.ernetin

Morrakot Khebchareon, Department of Mathematical and Computer Sciences Colorado School of Mines, Golden, Colorado 80401, U.S.A. mkhebcha@mines.edu

Michal Koevara, Institute of Applied Mathematics, University of Erlangen, Martensstr. 3, 91058 Erlangen, Germany kocvara@am.uni-erlangen.de

P. Manchanda, Department of Mathematics, GNDU, Amritsar-143005, India kmanch@jla.vsnl.netin

Hans D. Mittelmann, Department of Mathematics, Arizona State University, Box 871804, Tempe, AZ 85287-1804, U.S.A. mittelmann @asu.edu

Pradeepa Nair, Department of Mathematics, Indian Institute of Technology, Bombay, Powai, Mumbai-400 076, India pradeepa@math.iitb.ac.in

B. Ohligs, Lehrstuhl A fUr Mathematik, RWTH-Aachen, D-52056 Aachen, Germany bernd@mathA.rwth-aachen.de

Amiya K. Pani, Department of Mathematics, Indian Institute of Technology, Bombay, Powai, Mumbai-400 076, India akp@math.iitb.ac.in

J. Saint Jean Paulin, Departement de Mathematiques, Universite de Metz, Ile du Sau1cy 57045 Metz Cedex 01, France sjpaulin @poncelet.sciences.univ-metz.fr

Contributing Authors xxi

A.H. Siddiqi, King Fahd University of Petroleum & Minerals, P.O. Box 1274, Dhahran 31261, Saudi Arabia ahasan@kfupm.edu.sa

R.L. Stens, Lehrstuhl A flir Mathematik, RWTH-Aachen, D-52056 Aachen, Germany stens@mathA.rwth-aachen.de

M.A. Suhail, King Fahd University of Petroleum & Minerals, P.O. Box 1274 Dhahran 31261, Saudi Arabia

Philippe L. Toint, Department of Mathematics, FUNDP, Rempart de la Vierge, 8, B-5000 Namur, Belgium pht@math.fundp.ac.be

A. Tokgozlu, Stileyman Demirel University, Faculty of Science, Department of Geography, Isparta, Turkey tokgozlu@fef.sdu.edu.tr

Fredi Troitzsch, Technische Universitat Berlin, Fakultat II - Mathematik und Naturwissenschaften, Sekretariat Ma 4-5, Str. des 17. Juni 136, D-10623 Berlin, Germany. troeltz@math.tu-berlin.de

Jochem Zowe, Institute of Applied Mathematics, University of Erlangen, Mar­tensstr. 3, 91058 Erlangen, Germany zowe@am.uni-erlangen.de