Takayuki Furuta, Department of Applied Mathematics, Faculty of Science,
Space University of Tokyo, Japan
Introduction to Linear Operators
From Matrix to Bounded Linear Operators on a Hilbert Space
This introductory text is an essential guide to linear operators, clearly explaining the most up-to-date research and fundamental results on linear operators based on matrix theory. Important topics, such as Hilbert spaces, fundamental properites of bounded linear operators, and further devlopment of bounded linear operators are presented.
Contents: Chapter I: Hilbert Spaces ・ Inner Product Spaces and Hilbert Spaces ・ Jordon-Neumann Theorem ・ Orthogonal Decomposition of Hilbert Space ・ Gram-Schmidt Orthonormal Procedure and its Applications ・ Chapter II: Fundamental Properties of Bounded Linear Operators ・ Bounded Linear Operators on a Hilbert Space ・ Partial Isometry Operator and Polar Decomposition of an Operator ・ Polar Decomposition of an Operator and its Applications ・ Spectrum of an Operator ・ Numerical Range of an Operator ・ Relations among Several Classes of Non-normal Operators ・ Characterizations of Convexoid Operators and Related Examples ・ Chapter III: Further Development of Bonded Linear Operators Young Inequality and Hder-McCarthy Inequality ・ Lowner-Heinz Inequality and Furuta Inequality ・ Chaotic Order and the Relative Operator Entropy ・ Aluthge Transformation on p-Hyponormal Operators and log-Hyponormal Operators ・ A Subclass of Paranormal Operators Including log-Hyponormal Operators and Several Related Classes ・ Operator Inequalities Associated with Kantorovich Inequality and Holder-McCarthy Inequality ・ Some Properties on Partial Isometry, Quasinormality and Paranormality ・ Weighted Mixed Schwarz Inequality and Generalized Schwarz Inequality ・ Selberg Inequality ? An Extension of Heinz-Kato Inequality ・ Norm Inequalities Equivalent to Lowner-Heinz Inequality
Norm Inequalities Equivalent to Heinz Inequality
Readership: Undergraduates and graduates in mathematics and physics.
November, 2001 / 254 pp / Paper / 0-415-26799-4
Yoshiyuki Hino, Professor of Mathematics and Informatics, Chiba University, Japan,
T. Naito, Professor of Mathematics, The University of Electro-Communications, Japan,
Nguyen Van Minh, Associate Professor of Mathematics, Hanoi University,
Jong Son Shin, Professor of Mathematics, Korea University, Korea
Almost Periodic Solutions of Differential Equations in Banach Spaces
The authors present recent developments in investigating spectral conditions for the existence of periodic and almost periodic solutions of inhomogenous equations in Banach spaces. Many of the results represent significant advances in this area. In particular, a new approach based on the so-called evolution semigroups with an original decomposition technique is systematically presented.
The monograph also includes extensions of classical methods, such as fixed points and stability methods, to abstract functional differential equations with applications to partial functional differential equations.
Contents: Preliminaries ・ Strongly Continuous Semigroups of Operators ・ Evolution Equations ・ Spectral Theory ・ Spectral Criteria ・ Evolution Semigroups & Periodic Equations ・ Sums of Commuting Operators ・ Decomposition Theorem ・ Fixed Point Theorems and Fredholm Operators ・ Discrete Systems ・ Semilinear Equations ・ Nonlinear Evolution Equations ・ Notes ・ Stability Methods ・ Skew Product Flows ・ Existence Theorems of Almost Periodic Integrals ・ Processes and Quasi-processes ・ BC-stabilities and p-stabilities ・ Existence of Almost Periodic Solutions
Readership: Researchers, post-graduates, working professionals and those interested in applied mathematics, differential equations and applications.
Series Part: Stability and Control: Theory, Methods and Applications, Volume 15
Sep, 2001 / 258 pp / Cloth / 0-415-27266-1
Vladimir P. Krainov, Moscow Institute of Physics and Technology
Selected Mathematical Methods in Theoretical Physics
Selected Mathematical Methods in Theoretical Physics is intended as a supplementary text book for advanced university students in theoretical physics. It will enrich the knowledge of students who already have a solid grounding in mathematical analysis.
The author aims to show how a scientist, knowing the answer to a problem intuitively or through experiment, can develop a mathematical method to obtain the required answer. The approach adopted here involves two procedures: firstly the formulation of differential or integral equations for describing the physical procession the basis of more general physical laws, and then the approximate solution of these equations using small dimensionless physical parameters, or by using numerical parameters for the objects under consideration.
The eleven chapters of the book, which can be read in sequence or studied independently of each other, contain many examples of simple physical models, as well as problems for students to solve.
Contents: Calculation of Integrals ・ Continual Integrals ・ Calculation of Green's Functions ・ The Whittaker Method ・ Intense Perturbations ・ Inverse Problems ・ The Self-Consistent Approximation ・ Soliton Solutions ・ Dynamic Chaos ・ Prey-Predator Population Models ・ Random Processes
Readership: Advanced undergraduate and postgraduate students in physics and theoretical physics.
Sep. 2001 / 216 pp / Cloth / 0-415-27234-3
Sep. 2001 / 216 pp / Paper / 0-415-27239-4
Patricia Melin and Oscar Castillo, both Adjunct Professors, San Diego State University, USA
Modelling, Simulation and Control of Non-linear Dynamical Systems
An Intelligent Approach Using Soft Computing and Fractal Theory
This book presents a unified view of mathematical modeling, simulation and control of complex non-linear dynamical systems using soft computing techniques and fractal theory. Firstly, a new fuzzy-fractal approach to automated mathematical modeling of non-linear dynamical systems is presented and illustrated with examples in the PROLOG programming language. Secondly, a new fuzzy-genetic approach to automated simulation of dynamical systems is presented and illustrated with examples in the MATLAB programming language. Thirdly, a new method for model-based adaptive control using a neuro-fuzzy-fractal approach combined with the methods mentioned above is presented and illustrated using MATLAB. Finally, applications of these new methods for modeling, simulation and control of real dynamical systems are presented. The applications contained in this book are from a wide range of areas such as biochemical processes, robotic systems, manufacturing, food industry and chemical processes.
Contents: Introduction to Modeling, Simulation and Control of Non-Linear Dynamical Systems ・ Fuzzy Logic for Modeling ・ Neural Networks for Control ・ Genetic Algorithms and Fractal Theory for Modeling and Simulation ・ Fuzzy-Fractal Approach for Automated Mathematical Modelling ・ Fuzzy-Genetic Approach for Automated Simulation ・ Neuro-Fuzzy Approach for Adaptive Model-Based Control ・ Advanced Applications of Automated Mathematical and Simulation ・ Advanced Applications of Adaptive Model-Based Control
Readership: Advanced undergraduate, researchers and working professionals.
Series Part: Numerical Insights, Volume 2
Oct. 2001 / 272 pp / Cloth / 0-415-27236-X
A. D. Polyanin, ,Institute for Problems in Mechanics, Russian Acadmey of Science, Moscow,
V. F. Zaitsev, Research Institute of Numerical Mathematics and Control Problems, St Petersberg, Russia, A. Moussiaux, Charge d'Enseignement a la Faculte des Sciences (dept Physiques) des F.U.N (Facultes Universitaires de Namur) Belguim
Handbook of First-Order Partial Differential Equations
The book contains a concise and systematic demonstration of about 3000 first order partial differential equations presenting the solutions in a clear way. In the process, many new and exact solutions to linear and nonlinear equations are detailed. Thus, several times more equations are contributed here than ever before.
This handbook is presented in chapters, sections and subsections to aid the reader. Within each subsection the equations are arranged in order of increasing complexity. The extensive table of contents allows the reader rapid access to the desired equation or family of equations. Each chapter opens with preliminary remarks outlining the basic analytical methods for solving the equations and with some methods given in a schematic and simplified manner the handbook has a straight-forward approach for readers.
This text pays special attention to equations of the general form, showing their dependence upon arbitrary functions. It presents equations and their applications; these include differential geometry, nonlinear mechanics, gas dynamics, heat and mass transfer, wave theory and much more. Later chapters outline methods for solving first order partial differential equations and presents examples which show how the methods can be applied to specific equations. Other equations contain one or more free parameters (dealing with families of differential equations) which allows the reader to fix these parameters while solving the equations.
Contents: PART I: Linear Equations with Two Independent Variables ・ PART II: Linear Equations with Three of More Independent Variables ・ PART III: Nonlinear Equations ・ Equations with Two Independent Variables Quadratic in Derivatives ・ Nonlinear Equations With Two Independent Variables or General Form ・ Nonlinear Equations with Three of More Independent Variables ・ Supplement Solution of Differential Equations Through the CONVODE Software
Readership: Researchers, lecturers and engineers who have studied to graduate level and beyond, also students studying applied mathematics, mechanics, control theory, physics and engineering science.
Dec. 2001 / 520 pp / Cloth / 0-415-27267-X