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

368 Pages·2002·28.02 MB·English

by  Noel G. Barton (auth.)

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 1s t 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 ofA pplied 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 e-ISBN-13: 978-1-4613-0263-6
DOT: 10.1007/978-1-4613-0263-6
Published by Kluwer Academic Publishers,
P.O. Box 17, 3300AA Dordrecht, The Netherlands.
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© 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
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This book is dedicated to
P. Butzer and M.Z. Nashed
for their life-long
contributions to
applied mathematics.
Contents
Preface ix
Contributing Authors xix
A Perspective on Industrial Mathematics Work in Recent Years 1
Noel G. Barton
Part I Sampling Theorems
The Sampling Theorem of Signal Processing 23
Paul L. Butzer
The 'Riesz Basis Method' for Deriving Sampling Series: An Overview and some
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
vii
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 219
Graeme Fairweather, Morrakot Khebchareon
Low Cost Control Problems 251
S. Kesavan, J. Saint Jean Paulin
The Importance of Strange Attractors for Industrial Mathematics 275
Rene Lozi
Sufficient Optimality in a Parabolic Control Problem 305
Hans D. Mittelmann, Fredi Troltzsch
Finite Element Approximations to an Evolutionary Variational Inequality with a
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. How
ever, 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 in
stitutions and between institutions. The scope of professional mathematicians
should not be limited to academic institutions but should find place in emerg
ing 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 inspira
tion 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 under
stand 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,
IX
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 pric
ing. Professor P. L. Butzer, Technical University Aachen, Germany, an author
ity 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 di
verse physical phenomena, though stochastic in nature. Professor P. Toint,
University of Namur, Belgium and Dr. N. I. Gould, Rutherford Appleton Lab
oratory, Oxford, world leaders of the algorithmic optimization, presented their
current research which is applied to solve very effectively mathematical pro
gramming 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. Profes
sor 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. Pro
fessor 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 work
ing 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