Kategoria BISAC: Mathematics >> Differential Equations - General

The first edition of Stochastic Partial Differential Equations: A Modeling, White Noise Functional Approach, gave a comprehensive introduction to SPDEs. In this, the second edition, the authors build on the theory of SPDEs driven by space-time Brownian motion, or more generally, space-time Levy process noise. Applications of the theory are emphasized throughout. The stochastic pressure equation for fluid flow in porous media is treated, as are applications to finance.

Graduate students in pure and applied mathematics as well as researchers in SPDEs, physics, and engineering...

Schrodinger Equations and Diffusion Theory addresses the question What is the Schrodinger equation? in terms of diffusion processes, and shows that the Schrodinger equation and diffusion equations in duality are equivalent. In turn, Schrodinger s conjecture of 1931 is solved. The theory of diffusion processes for the Schrodinger equation tells us that we must go further into the theory of systems of (infinitely) many interacting quantum (diffusion) particles.

The method of relative entropy and the theory of transformations enable us to construct severely singular diffusion...

Classical mechanics is one of those special occurrences in science where interdisciplinary contributions have come together in a perfect blend, providing a most elegant and penetrating example of "modeling" in science. Following Lagrangrian principles, the author employs mathematics not only as a "unifying" language, but also to exemplify its role as a catalyst behind new concepts and discoveries, such as the d'Alembert principle, complex systems dynamics, and Hamiltonian mechanics. Today, these same dynamics are now being focused to address other interdisciplinary areas of research in...

This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applications such as stochastic resonance, Brownian motion in periodic potentials and Brownian motors are...

This book introduces a variety of neural network methods for solving differential equations arising in science and engineering. The emphasis is placed on a deep understanding of the neural network techniques, which has been presented in a mostly heuristic and intuitive manner. This approach will enable the reader to understand the working, efficiency and shortcomings of each neural network technique for solving differential equations.The objective of this book is to provide the reader with a sound understanding of the foundations of neural networks and a comprehensive introduction to...