As a relatively new area in mathematics, stochastic partial differential equations (PDEs) are still at a tender age and have not yet received much attention in the mathematical community. Filling the void of an introductory text in the field, Stochastic Partial Differential Equations introduces PDEs to students familiar with basic probability theory and Ito's equations, highlighting several computational and analytical techniques.
Without assuming specific knowledge of PDEs, the text includes many challenging problems in stochastic analysis and treats stochastic PDEs in a practical way....

Unlike the classical Sturm theorems on the zeros of solutions of second-order ODEs, Sturm's evolution zero set analysis for parabolic PDEs did not attract much attention in the 19th century, and, in fact, it was lost or forgotten for almost a century. Briefly revived by Polya in the 1930's and rediscovered in part several times since, it was not until the 1980's that the Sturmian argument for PDEs began to penetrate into the theory of parabolic equations and was found to have several fundamental applications.
Geometric Sturmian Theory of Nonlinear Parabolic Equations and Applications...

To keep pace with and further advance the rapidly developing field of applied control technologies, this book provides systematic training in the analytic theory and rigorous design of fuzzy systems. Almost entirely self-contained, it establishes a brief, yet sufficient foundation for designing and analyzing fuzzy intelligent and control systems. It clearly explains fuzzy sets, fuzzy logic, fuzzy inference, approximate reasoning, fuzzy rule base, basic fuzzy PID control systems, and more. This handy reference guide includes teaching examples as well as problem exercises, and it can easily be...

Despite remarkable developments in the field, a detailed treatment of non-Kerr law media has not been published. Introduction to non-Kerr Law Optical Solitons is the first book devoted exclusively to optical soliton propagation in media that possesses non-Kerr law nonlinearities.
After an introduction to the basic features of fiber-optic communications, the book outlines the nonlinear Schrodinger equation (NLSE), conserved quantities, and adiabatic dynamics of soliton parameters. It then derives the NLSE for Kerr law nonlinearity from basic principles, the inverse scattering transform,...

Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics is the first book to provide a systematic construction of exact solutions via linear invariant subspaces for nonlinear differential operators. Acting as a guide to nonlinear evolution equations and models from physics and mechanics, the book focuses on the existence of new exact solutions on linear invariant subspaces for nonlinear operators and their crucial new properties.
This practical reference deals with various partial differential equations (PDEs) and models that exhibit...

Research and development in the pioneering field of quantum computing involve just about every facet of science and engineering, including the significant areas of mathematics and physics. Based on the firm understanding that mathematics and physics are equal partners in the continuing study of quantum science, Mathematics of Quantum Computation and Quantum Technology explores the rapid mathematical advancements made in this field in recent years.
Novel Viewpoints on Numerous Aspects of Quantum Computing and Technology
Edited by a well-respected team of experts, this volume compiles...