Table Of ContentPerspectives in
Mathematical Sciences
INTERDISCIPLINARY MATHEMATICAL SCIENCES
Series Editor: Jinqiao Duan (Illinois Inst. of Tech., USA)
Editorial Board: Ludwig Arnold, Roberto Camassa, Peter Constantin,
Charles Doering, Paul Fischer, Andrei V. Fursikov, Sergey V. Lototsky,
Fred R. McMorris, Daniel Schertzer, Bjorn Schmalfuss, Yuefei Wang,
Xiangdong Ye, and Jerzy Zabczyk
Published
Vol. 1: Global Attractors of Nonautonomous Dissipative Dynamical Systems
David N. Cheban
Vol. 2: Stochastic Differential Equations: Theory and Applications
A Volume in Honor of Professor Boris L. Rozovskii
eds. Peter H. Baxendale & Sergey V. Lototsky
Vol. 3: Amplitude Equations for Stochastic Partial Differential Equations
Dirk Blömker
Vol. 4: Mathematical Theory of Adaptive Control
Vladimir G. Sragovich
Vol. 5: The Hilbert–Huang Transform and Its Applications
Norden E. Huang & Samuel S. P. Shen
Vol. 6: Meshfree Approximation Methods with MATLAB
Gregory E. Fasshauer
Vol. 7: Variational Methods for Strongly Indefinite Problems
Yanheng Ding
Vol. 8: Recent Development in Stochastic Dynamics and Stochastic Analysis
eds. Jinqiao Duan, Shunlong Luo & Caishi Wang
Vol. 9: Perspectives in Mathematical Sciences
eds. Yisong Yang, Xinchu Fu & Jinqiao Duan
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Interdisciplinary Mathematical Sciences – Vol. 9
Perspectives in
Mathematical Sciences
Editors
Yisong Yang
Polytechnic Institute of New York University, USA
Xinchu Fu
Shanghai University, China
Jinqiao Duan
Illinois Institute of Technology, USA
World Scientific
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UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
PERSPECTIVES IN MATHEMATICAL SCIENCES
Interdisciplinary Mathematical Sciences — Vol. 9
Copyright © 2010 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
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ISBN-13 978-981-4289-30-6
ISBN-10 981-4289-30-2
Printed in Singapore.
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November10,2009 15:3 WorldScientificReviewVolume-9.75inx6.5in PerspectivesMath
Professor Youzhong Guo
Novemb er 10, 2009 15:3 World Scientific Review Volume - 9.75in x 6.5in Persp ectives Math
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Editorial Foreword
This volume of Interdisciplinary Mathematical Sciences collects invited contribu-
tions giving timely surveys on a diverse range of topics of contemporary research
activities, including applications of analytic functions in periodic elastic mechan-
ical problems, bifurcation and chaos in microelectromechanical systems, random
dynamical systems and stochastic differential equations, epidemic disease propaga-
tion dynamics, inverse problems for equations of parabolic type, chaotic behavior
ofatwo-componentBose–Einsteinsystem,thep-Laplacianproblemswithalinking
geometric structure, progress in chaos control, chaos synchronization and complex
networks,mathematicalmodelingofcoldplasmabypartialdifferentialequationsof
mixed type, gravitatingYang–Millsfields in arbitrarydimensions,the Hamiltonian
constraint and Mandelstam identities in quantum gravity study, the lattice Boltz-
mann simulation and application to a nonlinear Schro¨dinger equation, stability of
nonlocaltime-delayedBurgersequation,bifurcationanalysisoftheSwift-Hohenberg
equation,anewglobal-localcomputationalmethodfordifferentialequations,anda
review onrepresentingtopologicalclasses by harmonic quantities with applications
in quantum field theory. The ordering of the chapters follows the alphabetic order
of the last names of the first authors of the contributions.
Wearegratefultoalltheauthorsfortheircontributionstothis volume. Special
thanks are due to Professor Zhenting Hou and Dr. Han-ping Chin, authors of
PrefaceandPostscript,respectively,whichprovidevividintroductions to Professor
Youzhong Guo for the reader. We would also like to thank Dr. Rajesh Babu,
Production Specialist at World Scientific Publishing, for his professional editorial
assistance.
We are privileged and honored to dedicate this volume to Professor Youzhong
Guo, our teacher and life-long friend, on the occasion of his 75th birthday and 55
years of career in mathematical sciences.
Yisong Yang, Polytechnic Institute of New York University
Xinchu Fu, Shanghai University
Jinqiao Duan, Illinois Institute of Technology
August 10, 2009
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Preface
This festschrift volume is dedicated to Professor Youzhong Guo on the occasion of
his 75th birthday and 55 years of scientific career.
Born in Hangzhou, China, on October 25, 1935, and graduated from Nanjing
University of Technology in 1955, Guo was recruited to Institute of Mathematical
Sciences (Wuhan), Academia Sinica, as a research assistant to work with mathe-
matician, Professor Guoping Li, academician of Academia Sinica. Since then, Guo
has been engagedinmathematical sciences researchand made many achievements.
He published over one hundred articles ranging in pure and applied mathematics,
especially in mathematical physics, system science, and mathematical economics.
Guo’sinfluencethroughhispublications,lectures,andserviceshasbenefitedpeople
far beyond his fields.
In 1979, Guo was appointed Professor and Executive Vice-Director of Institute
of Mathematical Sciences and Chairman of the Institute’s Academic Committee.
In 1987, Guo was appointed Chairman of Wuhan Municipal Commission of Sci-
ence and Technology and became Director of Institute for Industry and Applied
Mathematics. Afterwards he was elected as Vice-Chairman of Chinese Society of
IndustrialandAppliedMathematics,ChairmanofRationalMechanicsandModern
Mathematics Commission of Chinese Society of Mechanics. Among his other past
and present positions and responsibilities are: Editor-in-Chief/Editor of Lecture
Notes for Mathematics, Acta Mathematica Scientia, Structural Analysis Systems
and Engineering Analysis International, Director of System Engineering Society of
China.
In the 1950’s, Guo contributed in the approximation theory of functions, an-
alytical theory of differential equations, variational principles, error estimates of
solutions of differential equations in the Sobolev spaces. Guo also designed Wuhan
Laboratory of Electrostatic Acceralator, Academia Sinica. Taking a cooperative
research task with the Academy of Sciences of Soviet Union and working with
GuopingLi, Guostudiedthe theoryandapplicationsofautomorphicfunctions and
the Minkowski–Denjoy functions for a long time. Their results were published as
the first monograph of its kind in the world in 1978.
In the 1960’s, Guo worked on field theory and the Three-Gorge Project. He
developed the principles of transformations of fiber bundles for general relativistic
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