This volume is not an ordinary proceedings volume assembling papers submitted but a collection of prestigious survey papers on various subjects studied enthusiastically by experts all over the world. The reader will uncover profound, new research problems as well as numerous signposts for future direction.
Contents:
Convolutions of the von Mangoldt Function and Related Dirichlet Series (S Egami & K Matsumoto)
Constructing New Non-Congruent Numbers by Graph Theory (K Feng & Y Xue)
Distribution of Units of an Algebraic Number Field Modulo an Ideal (Y Kitaoka)
Sign Changes of Fourier Coefficients and Eigenvalues of Cusp Forms (W Kohnen)
Shifted Convolution Sums of Fourier Coefficients of Cusp Forms (Y-K Lau et al.)
Two Expositions on Arithmetic of Cubics (K Miyake)
Distribution of Points on Modular Hyperbolas (I E Shparlinski)
A Survey of Problems and Results on Restricted Sumsets (Z-W Sun)
A General Modular Relation in Analytic Number Theory (H Tsukada)
L-Functions of Function Fields (D Wan)
Readership: Graduate students and researchers in mathematics.
268pp Pub. date: Jul 2007
ISBN 978-981-270-810-6
981-270-810-3
This seminal book unites three different areas of modern science: the micromechanics and nanomechanics of composite materials; wavelet analysis as applied to physical problems; and the propagation of a new type of solitary wave in composite materials, nonlinear waves. Each of the three areas is described in a simple and understandable form, focusing on the many perspectives of the links among the three.
All of the techniques and procedures are described here in the clearest and most open form, enabling the reader to quickly learn and use them when faced with the new and more advanced problems that are proposed in this book. By combining these new scientific concepts into a unitary model and enlightening readers on this pioneering field of research, readers will hopefully be inspired to explore the more advanced aspects of this promising scientific direction. The application of wavelet analysis to nanomaterials and waves in nanocomposites can be very appealing to both specialists working on theoretical developments in wavelets as well as specialists applying these methods and experiments in the mechanics of materials.
Contents:
Wavelets and Wavelet Analysis
Materials with Internal Structure
Analysis of Waves in Materials
Analysis of Simple and Solitary Waves in Materials
Computer Analysis of Solitary Elastic Waves
Readership: Advanced undergraduate and graduate students as well as experts in mathematical modeling, engineering mechanics and mechanics, physics; specialists in wavelet and wave analysis as tools for mathematical modeling.
450pp (approx.) Pub. date: Scheduled Fall 2007
ISBN 978-981-270-784-0
981-270-784-0
Dimensional analysis is a magical way of finding useful results with almost no effort. It makes it possible to bring together the results of experiments and computations in a concise but exact form, so that they can be used efficiently and economically to make predictions. It takes advantage of the fact that phenomena go their way independently of the units we measure them with, because the units have nothing to do with the underlying physics. This simple idea turns out to be unexpectedly powerful.
Students often fail to gain from dimensional analysis, because bad teaching has led them to suppose it cannot be used to derive new results, and can only confirm results that have been secured by some other route. That notion is false. This book demonstrates what can be done with dimensional analysis through a series of examples, starting with Pythagoras・theorem and the simple pendulum, and going on to a number of practical examples, many from the author痴 experience in ocean engineering. In parallel, the book explains the underlying theory, starting with Vaschy痴 elegant treatment, whilst avoiding unnecessary complexity. It also explores the use and misuse of models, which can be useful but can also be seriously misleading.
Contents:
Introduction and Motivation
Numbers and Units
Dimensions, Dimensionless Groups and Variables
Dimensional Analysis
Similarity and Intelligent Experimentation
Equations in Non-Dimensional Form
Models
Solutions to Problems
Readership: Undergraduate and graduate (MSc) students interested in dimensional analysis.
180pp (approx.) Pub. date: Scheduled Winter 2007
ISBN 978-981-270-818-2
981-270-818-9
ISBN 978-981-270-819-9(pbk)
981-270-819-7(pbk
This textbook comprehensively introduces students and researchers to the application of continuous symmetries and their Lie algebras to ordinary and partial differential equations. Covering all the modern techniques in detail, it relates applications to cutting-edge research fields such as Yang?Mills theory and string theory.
Aimed at readers in applied mathematics and physics rather than pure mathematics, the material is ideally suited to students and researchers whose main interest lies in finding solutions to differential equations and invariants of maps.
A large number of worked examples and challenging exercises help readers to work independently of teachers, and by including SymbolicC++ implementations of the techniques in each chapter, the book takes full advantage of the advancements in algebraic computation.
Twelve new sections have been added in this edition, including: Haar measure, Sato's theory and sigma functions, universal algebra, anti-self dual Yang?Mills equation, and discrete Painleve equations.
Contents:
Groups
Lie Groups
Lie Transformation Groups
Infinitesimal Transformations
Lie Algebras
Introductory Examples
Differential Forms and Tensor Fields
Lie Derivative and Invariance
Invariance of Differential Equations
Lie?Backlund Vector Fields
Differential Equation for a Given Lie Algebra
A List of Lie Symmetry Vector Fields
Recursion Operators
Backlund Transformations
Lax Representations
Conservation Laws
Symmetries and Painleve Test
Ziglin’s Theorem and Integrability
Lie Algebra Valued Differential Forms
Bose Operators and Lie Algebras
Maps and Invariants
Computer Algebra
Differential Manifolds
Readership: Students, teachers and researchers in theoretical and mathematical physics, quantum classical mechanics, computational physics and numerical and computational methods.
472pp Pub. date: Jul 2007
ISBN 978-981-270-809-0
981-270-809-X US