Language: English
Publication date: 2006 Size: 185x260mm
Number of Pages: 181 pages Binding: Hardcover
Subject(s): Mathematics
ISBN: 7807340207
This book is concerned with Cauchy problem for the first order quasilinear hyperbolic systems, some basic concepts of quasilinear hyperbolic systems and basic methods for studying classical solutions are given. In this book, we discussed single quasilinear hyperbolic equation, classical solutions to reducible quasilinear hyperbolic systems, dissipation and relaxation problem, singularities caused by the eigenvectors, and quasilinear hyperbolic systems in linearly degenerate type.
CONTENTS
Preface
Chapter 1 Introduction
Chapter 2 The Single Quasilinear Hyperbolic Systems
Chapter 3 Quasilinear Hyperbolic Systems in Diagonal Form
Chapter 4 Discontinuous Intitial Value Problem for Quasilinear Hyperbolic Systems
Chapter 5 Singularities Caused by the Eigenvectors
Chapter 6 Quasilinear Hyperbolic Systems with Dissipative Term
Chapter 7 Quasilinear Hyperbolic Systems with Relaxation
Chapter 8 Cauchy Problem for Quasilinear Hyperbolic Systems in Linearly
Bibliography
Language: English
Publication date: 2007 Size: 170mm×240mm
Number of Pages: 410 pages Binding: Paperback
Subject(s): Mathematics
ISBN: 978-7-03-018888-5
Chapter 0 Integers, Number Fields and Polynomials
PartⅠ General Theory of Systems of Linear Equations
Introduction
Setting-up of Systems of Linear Equations and Method of Elimination
Chapter 1 Algebra of Matrices
Chapter 2 The Determinant Method for a Special Class of Linear Equations (Cramer’s Rule)
Chapter 3 General Theory of Systems of Linear Equations
Chapter 4 Linear Spaces and Systems of Linear Equations
Chapter 5 Symmetric Bilinear Metric Spaces and Systems of Linear Equations
PartⅡ The Principal Axes Problem of Real Quadratic Forms
Introduction
Geometric Origin of the Principal Axes Problem of Quadratic Forms
Chapter 6 Linear Transformations on Linear Spaces
Chapter 7 A Class of Direct Sum Decompositions of Linear Spaces Relative to Linear Transformations
Chapter 8 Two Classes of Linear Transformations on Euclidean Spaces and the Principal Axes Problem of Quadratic Forms
Chapter 9 Further Development?Similarity Canonical Forms of Matrices
Language: English
Publication date: 2007 Size: 175×245mm
Number of Pages: 254 Binding: Paperback
Subject(s): Mathematics
ISBN: 7-03-016832-1
Besides showing basic concepts and principles on partial differential equations, the focus of attention in this book is discussing main methods and techniques for solving basic definite problems.
Contents
Chapter 1 Introduction
Chapter 2 Mathematical models and problems for defining solutions
Chapter 3 Classification and simplification for linear partial differential equations of second order
Chapter 4 Integral method on characteristics
Chapter 5 The method of separating variables on finite region
Chapter 6 Eigenvalue problems and special functions
Chapter 7 Multidimensional boundary value problems
Chapter 8 Integral transformations
Chapter 9 Basic properties of harmonic functions
Chapter 10 Green function and their application to PDEs
(Mathematics Monograph Series 7)
Language: English
Publication date: 2007 Size: 170×245mm
Number of Pages: 243 Binding: Hardcover
Subject(s): Mathematics
ISBN: 978-7-03-018835-9
The aim of this book is to give a more systematic account for the bifurcation theory method of dynamical systems to find traveling wave solutions with an emphasis on singular waves and understand their dynamics for some classes of the well-posedness of nonlinear partial differential equations.
Contents
Chapter1 Traveling Wave Equations of Some Physical Models
Chapter2 Basic Mathematical Theory of the Singular Traveling Wave Systems
Chapter3 Bifurcations of Traveling Wave Solutions of Nonlinear Elastic Rod Systems
Chapter4 Bifurcations of Traveling Wave Solutions of Generalized Camassa-Holm Equation
Chapter5 Bifurcations of Traveling Wave Solutions of Higher Order Korteweg-De Vries Equations
Chapter6 The Bifurcations of the Traveling Wave Solutions of K(m,n) Equation
Chapter7 Kink Wave Solution Determined by a Parabola Solution of Planar Dynamical Systems
Chapter8 Traveling Wave Solutions of Coupled Nonlinear Wave Equations
Chapter9 Solitary Waves and Chaotic Behavior for a Class of Coupled Field Equations
Chapter10 Bifurcations of Breather Solutions of Some Nonlinear Wave Equations
Chapter11 Bounded Solutions of (n+1)-Dimensional Sine- and Sinh-Gordon Equations
Chapter12 Exact Explicit Traveling Wave Solutions for Two Classes of (n+1)-Dimensional Nonlinear Wave Equations
References
Language: English
Publication date: 2007 Size: 180×250mm
Number of Pages: 291 Binding: Hardcover
Subject(s): Mathematics
ISBN: 978-7-03-018608-9
Our purpose of writing this book is to help the readers to better understand Kac’s book. This book was written based on my lecture notes in Kac-Moody algebras taught in Chinese Academy of Mathematics and System Sciences in 2005,2006. We have tried to give the details that Kac’s book lacks and correct some mistakes.
Contents
Chapter 1 Structure of Kac-Moody Algebras
Chapter 2 Affine Kac-Moody Algebas
Chapter 3 Representation Theory
Chapter 4 Representations of Affine and Virasoro Algebas
Chapter 5 Related Modular Forms
Chapter 6 Realizations of Modules
Bibliography
Index
Language: English
Publication date: 2007 Size:
Number of Pages: 533 Binding: Paperback
Subject(s): Mathematics
ISBN: 9787040221527
Features
● Reflecting the latest progress in mathematics; introducing the latest research issues in mathematics;
● Great importance is attached to the historical background of the issues in mathematics; an overall view of the current situation of each particular field of mathematics is given in the series;
● The series provides first hand resources for those interested in new research topics in mathematics and the latest research achievements in interdisciplinary fields;
● Each volume is either a monograph or a collection of research papers regarding these mathematical issues.
Language: English
Publication date: 2007 Size: 155mm×230mm
Number of Pages: 409 Binding: Paperback
Subject(s): Mathematics
ISBN: 978-7-03-018931-8/O.2744
The aim of this book is to provide an introduction to current advances of preserver problems on matrices and present the basic methods of studying preserver problems. In order to ensure that the content is self-contained, we took some conclusions and their proofs from other books or papers, which will be convenient to the readers. It is also intended to offer a collection of references on preserver problems on matrices.
Contents
Preface
Notation
Chapter1 Introduction to preserver problems
Chapter2 Preservers of the smallest nonzero rank
Chapter3 Additive rank-additivity preservers and applications
Chapter4 Additive preservers of rank equivalence and applications
Chapter5 Linear square-zero preservers on spaces of square matrices
Chapter6 Preservers of k-power/k-potent
Chapter7 Preservers of inverses of matrices
Chapter8 Preservers of generalized inverses of matrices
Chapter9 Linear preservers of involutory matrices
Chapter10 Additive adjoint preservers
Chapter11 Preservers of multiplication
Appendix A Fitting decomposition of a matrix
Appendix B Canonical form of a rank-additive matrix pair
Appendix C Canonical form of a matrix triple
Appendix D Adjoint matrices
Bibliography
Index