Описание: The need for developing a better understanding of the behaviour of small samples by observing experiments presents a problem far beyond purely academic interest. This monograph describes the character of incomplete fuzzy information, and proposes and proves the principle of information diffusion. The focus lies in changing a traditional sample-point into a fuzzy set to partly fill the gap caused by incomplete data, so that the recognition of relationships between input and output can be improved. Part 1 examines the origins of the principle of information diffusion and describes the mathematical concepts and proofs. Topics covered include: information matrix, demonstration of information distribution, and the kernel function in terms of information diffusion. Part 2 covers applications such as earthquake engineering and risk assessment of flood, and demonstrates that the new theory is useful for studying practical cases.
Описание: This volume contains a wealth of results and methodologies applicable to a wide range of problems arising in reaction-diffusion theory. The first part is concerned with obtaining the complete structure of the large-time solution of scalar reaction diffusion equations, and systems of reaction-diffusion equations. The second part is concerned with the analysis of a class of singular reaction-diffusion equations. In this detailed analysis, use is made of the method of matched asymptotic expansions, dynamical systems theory, and comparison theorems, which provide a powerful combination of techniques for the detailed analysis of this broad class of reaction-diffusion equations. The monograph can be viewed both as a handbook, and as a detailed description of the methodology. Researchers in reaction-diffusion theory, and scientists applying reaction-diffusion theory to such areas as chemical kinetics, biological systems, epidemiology and population dynamics, will find it a popular addition to the literature.
Описание: This book describes numerical methods for partial differential equations (PDEs) coupling advection, diffusion and reaction terms, encompassing methods for hyperbolic, parabolic and stiff and nonstiff ordinary differential equations (ODEs). The emphasis lies on time-dependent transport-chemistry problems, describing e.g. the evolution of concentrations in environmental and biological applications. Along with the common topics of stability and convergence, much attention is paid on how to prevent spurious, negative concentrations and oscillations, both in space and time. Many of the theoretical aspects are illustrated by numerical experiments on models from biology, chemistry and physics. A unified approach is followed by emphasizing the method of lines or semi-discretization. In this regard this book differs substantially from more specialized textbooks which deal exclusively with either PDEs or ODEs. This book treats integration methods suitable for both classes of problems and thus is of interest to PDE researchers unfamiliar with advanced numerical ODE methods, as well as to ODE researchers unaware of the vast amount of interesting results on numerical PDEs.
Описание: This book develops a unified mathematical framework for treating a wide variety of diffusion-related periodic phenomena in such areas as heat transfer, electrical conduction and light scattering. The presentation is largely in the form of case studies directly applicable in a wide range of experimental methodologies.
Описание: This book surveys a wide variety of mathematical models of diffusion in the ecological context. It is written with the primary intent of providing scientists, particularly physicists but also biologists, with some background in the mathematics and physics of diffusion, and shows how they can be applied to ecological problems. The secondary intent is to provide a specialized textbook for graduate students who are interested in mathematical ecology. The reader is assumed to have a basic knowledge of probability and differential equations. Each chapter in this new edition has been substantially updated by appropriate leading researchers in the field, and contains much new material covering developments in the field in the last 20 years.
Описание: Now available in paperback, this celebrated book has been prepared with readers’ needs in mind, remaining a systematic treatment of the subject whilst retaining its vitality. The second volume follows on from the first, concentrating on stochastic integrals, stochastic differential equations, excursion theory and the general theory of processes. Much effort has gone into making these subjects as accessible as possible by providing many concrete examples that illustrate techniques of calculation, and by treating all topics from the ground up, starting from simple cases. Many of the examples and proofs are new; some important calculational techniques appeared for the first time in this book. Together with its companion volume, this book helps equip graduate students for research into a subject of great intrinsic interest and wide application in physics, biology, engineering, finance and computer science.
Описание: The monograph is devoted mainly to the analytical study of the differential, pseudo-differential and stochastic evolution equations describing the transition
probabilities of various Markov processes. These include (i) diffusions (in particular,degenerate diffusions), (ii) more general jump-diffusions, especially stable jump-diffusions driven by
stable Levy processes, (iii) complex stochastic Schrodinger equations which correspond to models of quantum open systems. The main results of the book concern the existence,
two-sided estimates, path integral representation, and small time and semiclassical asymptotics for the Green functions (or fundamental solutions) of these equations, which represent the
transition probability densities of the corresponding random process.
The boundary value problem for Hamiltonian systems and some spectral asymptotics ar also discussed.
Readers should have an elementary knowledge of probability, complex and functional analysis, and calculus.
Автор: L. C. G. Rogers Название: Diffusions, Markov Processes, and Martingales ISBN: 0521775949 ISBN-13(EAN): 9780521775946 Издательство: Cambridge Academ Рейтинг: Цена: 8490 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Now available in paperback, this celebrated book has been prepared with readers’ needs in mind, remaining a systematic guide to a large part of the modern theory of Probability, whilst retaining its vitality. The authors’ aim is to present the subject of Brownian motion not as a dry part of mathematical analysis, but to convey its real meaning and fascination. The opening, heuristic chapter does just this, and it is followed by a comprehensive and self-contained account of the foundations of theory of stochastic processes. Chapter 3 is a lively and readable account of the theory of Markov processes. Together with its companion volume, this book helps equip graduate students for research into a subject of great intrinsic interest and wide application in physics, biology, engineering, finance and computer science.
Автор: Bass Название: Diffusions and Elliptic Operators ISBN: 0387983155 ISBN-13(EAN): 9780387983158 Издательство: Springer Цена: 17897 р. Наличие на складе: Поставка под заказ.
Описание: Serve as a reference book for graduate students and researchers in probability theory or partial differential equations who want to learn more about the interplay of these two areas.
Автор: G. George Yin; Chao Zhu Название: Hybrid Switching Diffusions ISBN: 1441911049 ISBN-13(EAN): 9781441911049 Издательство: Springer Рейтинг: Цена: 19056 р. Наличие на складе: Поставка под заказ.
Описание: Focusing on switching diffusion processes that involve both continuous dynamics and discrete events, this comprehensive study moves from basic properties such as Feller and strong Feller to the numerical solutions of switching diffusions and stability.
Автор: Kallianpur Gopinath Название: Stochastic Analysis and Diffusion Processes ISBN: 0199657076 ISBN-13(EAN): 9780199657070 Издательство: Oxford Academ Рейтинг: Цена: 6984 р. Наличие на складе: Поставка под заказ.
Описание: Beginning with the concept of random processes and Brownian motion and building on the theory and research directions in a self-contained manner, this book provides an introduction to stochastic analysis for graduate students, researchers and applied scientists interested in stochastic processes and their applications.
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