edited by Michael Beaney and Erich H. Reck

Gottlob Frege: Critical Assessments of Leading Philosophers 4vols.

August 2005
Pages c. 1680 pp. (4 volumes)
ISBN 0-415-30601-9 (set)
0-415-30602-7 (Vol. I)
0-415-30603-5 (Vol. II)
0-415-30604-3 (Vol. III)
0-415-30605-1 (Vol. IV)

Volume I: Frege’s Philosophy in Context
Volume II: Frege’s Philosophy of Logic
Volume III: Frege’s Philosophy of Mathematics
Volume IV: Frege’s Philosophy of Thought and Language

General Introduction

George F. Carrier, Max Krook, and Carl E. Pearson

Functions of a Complex Variable: Theory and Technique

[This volume] is a classic textbook and reference on the subject of complex variables. It established a gold standard against which all other texts in applied mathematics should be judged・ As the authors intended, the theory part is concise and quickly leads the reader from an introduction to complex numbers to useful and powerful techniques, with applications to integral representation of special functions, transform and asymptotic methods in the complex plane, and integral equations, just to name a few. It is in the application of these techniques where the authors devoted most of the efforts. These were done masterfully. This book remains a relevant and must-read book for applied mathematicians today.-・K.K. Tung, Professor and Chair of Applied Mathematics, University of Washington.

[This] is a book for those looking for applications of complex variables above and beyond what is found in standard elementary texts. I know of no single source where one finds such advanced topics as asymptotics, transforms, the Wiener-Hopf method, and dual and singular integral equations treated with such insight, thoroughness, and flair or where one finds such a rich, non-trivial collection of examples and exercises. Here is the power of complex variables as a practical tool on full display.-・Jim Simmonds, Emeritus Professor of Civil Engineering, University of Virginia.

Functions of a complex variable are used to solve applications in various branches of mathematics, science, and engineering. Functions of a Complex Variable: Theory and Technique is a book in a special category of influential classics because it is based on the authors・extensive experience in modeling complicated situations and providing analytic solutions. The book makes available to readers a comprehensive range of these analytical techniques based upon complex variable theory.

Proficiency in these techniques requires practice. The authors provide many exercises, incorporating them into the body of the text. By completing a substantial number of these exercises, the reader will more fully benefit from this book.

Audience

Based on graduate courses in applied mathematics, Functions of a Complex Variable: Theory and Technique is intended for applied mathematicians, scientists, engineers, and senior or graduate-level students who have advanced knowledge in calculus and are interested in such subjects as complex variable theory, function theory, mathematical methods, advanced engineering mathematics, and mathematical physics.

Contents

Preface; Erratum; Chapter 1: Complex Numbers And Their Elementary Properties; Chapter 2: Analytic Functions; Chapter 3: Contour Integration; Chapter 4: Conformal Mapping; Chapter 5: Special Functions; Chapter 6: Asymptotic Methods; Chapter 7: Transform Methods; Chapter 8: Special Techniques; Index.

July 2005 / xiv + 438 pages / Softcover / ISBN 0-89871-595-4

R.M.M. Mattheij, S.W. Rienstra, J.H.M. ten Thije Boonkkamp

Partial Differential Equations: Modeling, Analysis, Computation

Partial differential equations (PDEs) are used to describe a large variety of physical phenomena, from fluid flow to electromagnetic fields, and are indispensable to such disparate fields as aircraft simulation and computer graphics. While most existing texts on PDEs deal with either analytical or numerical aspects of PDEs, this innovative and comprehensive textbook features a unique approach that integrates analysis and numerical solution methods and includes a third component?modeling?to address real-life problems. The authors believe that modeling can be learned only by doing; hence a separate chapter containing 16 user-friendly case studies of elliptic, parabolic, and hyperbolic equations is included and numerous exercises are included in all other chapters.

Partial Differential Equations: Modeling, Analysis, Computation enables readers to deepen their understanding of a topic ubiquitous in mathematics and science and to tackle practical problems. The advent of fast computers and the development of numerical methods have enabled the modern engineer to use a large variety of packages to find numerical approximations to solutions of PDEs. Problems are usually standard and a thorough knowledge of a well-chosen subset of analytical and numerical tools and methodologies is necessary when dealing with real-life problems. When one is dealing with PDEs in practice, it becomes clear that both numerical and analytical treatments of the problem are needed.

Audience

This comprehensive book is intended for graduate students in applied mathematics, engineering, and physics and may be of interest to advanced undergraduate students. Mathematicians, scientists, and engineers also will find the book useful.

Contents

List of Figures; List of Tables; Notation; Preface; Chapter 1: Differential and difference equations; Chapter 2: Characterization and classification; Chapter 3: Fourier theory; Chapter 4: Distributions and fundamental solutions; Chapter 5: Approximation by finite differences; Chapter 6: The Equations of continuum mechanics and electromagnetics; Chapter 7: The art of modeling; Chapter 8: The analysis of elliptic equations; Chapter 9: Numerical methods for elliptic equations; Chapter 10: Analysis of parabolic equations; Chapter 11: Numerical methods for parabolic equations; Chapter 12: Analysis of hyperbolic equations; Chapter 13: Numerical methods for scalar hyperbolic equations; Chapter 14: Numerical methods for hyperbolic systems; Chapter 15: Perturbation methods; Chapter 16: Modeling, analyzing, and simulating problems from practice; Appendices: Useful definitions and properties; Bibliography; Index.

2005 / xxxiii + 665 pages / Softcover / ISBN 0-89871-594-6

Albrecht Bottcher and Sergei M. Grudsky

Spectral Properties of Banded Toeplitz Matrices

This is a wonderful book, full of the latest material on Toeplitz matrices and operators, including norms, spectra, pseudospectra, fields of values, and polynomial hulls. The notes at the end of the chapters are especially interesting and the exercises are challenging. The writing is careful and precise but also entertaining. --Anne Greenbaum, Professor of Mathematics, University of Washington.

This book is a tremendous resource for all aspects of the spectral theory of banded Toeplitz matrices. It will be the first place I turn when looking for many results in this field, and given this book's amazing breadth and depth, I expect to find just what I need. -- Mark Embree, Assistant Professor of Computational and Applied Mathematics, Rice University.

This self-contained introduction to the behavior of several spectral characteristics of large Toeplitz band matrices is the first systematic presentation of a relatively large body of knowledge. Covering everything from classic results to the most recent developments, Spectral Properties of Banded Toeplitz Matrices is an important resource. The spectral characteristics include determinants, eigenvalues and eigenvectors, pseudospectra and pseudomodes, singular values, norms, and condition numbers. Toeplitz matrices emerge in many applications and the literature on them is immense. They remain an active field of research with many facets, and the material on banded ones until now has primarily been found in research papers.

The book may serve both as a text for introducing the material and as a reference. The approach is based on the know-how and experience of the authors in combining functional analytical methods with hard analysis and in applying operator theoretical methods to matrix theory, which reveals the essence of several phenomena and leads to significant improvements in existing results. All basic results presented in the book are precisely stated as theorems and accompanied by full proofs.

Audience

This book is written for applied mathematicians, engineers, and scientists who encounter Toeplitz matrices in their research. It also will be of interest to mathematicians in the fields of operator theory, numerical analysis, structured matrices, or random matrix theory, and physicists, chemists, biologists, and economists who deal with stationary statistical and stochastic problems. Parts of the book are suitable for use as a graduate-level text on Toeplitz matrices or analysis.

Contents

Preface; Chapter 1: Infinite Matrices; Chapter 2: Determinants; Chapter 3: Stability; Chapter 4: Instability; Chapter 5: Norms; Chapter 6: Condition Numbers; Chapter 7: Substitutes for the Spectrum; Chapter 8: Transient Behavior; Chapter 9: Singular Values; Chapter 10: Extreme Eigenvalues; Chapter 11: Eigenvalue Distribution; Chapter 12: Eigenvectors and Pseudomodes; Chapter 13: Structured Perturbations; Chapter 14: Impurities; Bibliography; Index.

2005 / x + 411 pages / Softcover / ISBN 0-89871-599-7

Editors Wataru Takahashi, Tamaki Tanaka

Nonlinear Analysis and Convex Analysis.
3rd Int'l. Conference Tokyo 2003, JAPAN

ISBN 4-946552-15-4 Hardcover pp. 591

Contents;

Koji Aoyama
A survey: An inverse of the Berge maximum theorem

Sachiko Atsushiba
Strong convergence theorems for finite nonexpansive mappings in Banach spaces

Xiaosong Ding, Love Ekenberg, and Mats Danielson A fast bilinear optimization algorithm

Jun Ichi Fujii and Masatoshi Fujii
Jensen's Inequalities on any interval for operators

Kiyoko Furuya
Approximation of semigroups generated by $-i\partial \Tilde{\Psi}$

Pando Gr. Georgiev
Random critical points

Ryusuke Hohzaki
A search game with several types of false contacts

Masayuki Horiguchi and Masami Kurano
Stopped semi-Markov decision processes with multiple constraints

Takanori Ibaraki and Wataru Takahashi
Convergence of regularized solutions of ill-posed problem with monotone operators in a Banach space

Shigeru Iemoto, Tomonari Suzuki, and Wataru Takahashi
Nadler's fixed point theorem with a vector-valued distance

Hideaki Iiduka and Wataru Takahashi
Strong and weak convergence theorems by a hybrid steepest descent method in a Hilbert space

H.C. Jimbo, A. Ouentcheu, and R.E. Bozeman
Portfolio optimization with the growth model

Shoji Kamimura
The proximal point algorithm in a Banach space

Jun Kawabe
The portmanteau theorem for Dedekind complete Riesz space-valued measures

Hidefumi Kawasaki
A game-theoretic aspect of conjugate sets for a nonlinear programming problem

Kazuo Kido
A nonlinear approximation of the nucleolus

Gang Eun Kim and Hirobumi Kiuchi
Strong convergences of Ishikawa iterations for asymptotically quasi-nonexpansive mappings in the intermediate sense

Kenji Kimura and Tamaki Tanaka
Existence result for vector-valued saddle-point problem by using convex envelope

Yasunori Kimura
Mosco convergence and maximal monotone operators in Banach spaces

Fumiaki Kohsaka and Wataru Takahashi
Weak and strong convergence theorems for minimax problems in Banach spaces

Naoto Komuro
Domination property of the set of upper bounds in ordered linear spaces

Masamichi Kon
On fuzzy multicriteria location problems

Masami Kurano, Masami Yasuda, Jun-ichi Nakagami, and Yuji Yoshida
A fuzzy stopping problem with the concept of perception: The finite and infinite horizon cases

Anthony To-Ming Lau and Wataru Takahashi
Submeans and nonlinear analysis

Yukihiro Maruyama
Associative sequential decision process

Takashi Matsuhisa
Communication leading to Nash equilibrium without acyclic condition

Takashi Matsuhisa, Ryuichiro Ishikawa, and Yoshiaki Hoshino
Core equivalence in economy under generalized information

Mitsutaka Matsumoto and Satoshi Fuchimoto
An evolutionary game approach to sanctioning problems

Shin-ya Matsushita and Wataru Takahashi
An iterative algorithm for relatively nonexpansive mappings by a hybrid method and applications

Hiromichi Miyake
A fixed point theorem for asymptotically nonexpansive mappings in metric spaces with convex structure

Atsushi Moritani, Tetsuzo Tanino, Kojiro Kuroki, and Keiji Tatsumi
Cooperative fuzzy games with restrictions on coalitions

Yoshiaki Muroya and Emiko Ishiwata
Global stability for nonlinear difference equations with variable delay

Natalia Nadezhkina and Wataru Takahashi
Modified extragradient method for solving variational inequalities in real Hilbert spaces

Koichiro Naito
Recurrent dimensions of quasi-periodic orbits with multiple frequencies: Extended common multiples and Diophantine conditions

K. Nakajo, K. Shimoji, and W. Takahashi
A weak convergence theorem by products of mappings in Hilbert spaces

Rabia Nessah and Moussa Larbani
g-maximum equality

Toshihiko Nishishiraho
The degree of convergence of equi-uniform approximation processes of integral operators in Banach spaces

Ichiro Nishizaki, Masatoshi Sakawa, Hideki Katagiri, and Yoshio Uemura
Cost allocation based on the solution concept from fuzzy cooperative games for a production and transportation problem ---a case study---

Ryohei Nozawa and Werner Oettli
The polarization principle in dynamic optimization

Tetsuya Nuriya and Daishi Kuroiwa
An observation of approximate saddle points

Hideho Ogasawara
A factorized form of the Broyden family of updates from the preconvex class

Sehie Park
Fixed points, Roberts spaces, and the compact AR problem

Leon A. Petrosjan
Cooperation in games with incomplete information

Seiji Saito
Boundary value problems of fuzzy differential equations

Siegfried Schaible and Jianming Shi
Recent developments in fractional programming: Single-ratio and max-min case

Yoshiyuki Sekiguchi
Necessary optimality conditions for general mathematical programming with continuous constraints

Tomoo Shimizu
The almost fixed point property for multivalued nonexpansive mappings of a metric space with some kind of convexity

Tomonari Suzuki
Krasnoselskii and Mann's type sequences and Ishikawa's strong convergence theorem

M. Tsukada, T. Miura, S. Wada, Y. Takahashi, and S.-E. Takahasi
On Wirtinger-Beesack type integral inequalities

Hiroshi Yabe
Global convergence of conjugate gradient methods for unconstrained minimization

Isao Yamada and Nobuhiko Ogura
Adaptive projected subgradient method and its applications to signal processing problems

Takeshi Yoshimoto
On non-integral orders of strong ergodicity in nonlinear ergodic theory