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Stochastic Cauchy Problems in Infinite Dimensions
Stochastic Cauchy Problems in Infinite Dimensions: Generalized and Regularized Solutions presents stochastic differential equations for random processes with values in Hilbert spaces. Accessible to non-specialists, the book explores how modern semi-group and distribution methods relate to the methods of infinite-dimensional stochastic analysis. It also shows how the idea of regularization in a broad sense pervades all these methods and is useful for numerical realization and applications of the theory. The book presents generalized solutions to the Cauchy problem in its initial form with white noise processes in spaces of distributions. It also covers the "classical" approach to stochastic problems involving the solution of corresponding integral equations. The first part of the text gives a self-contained introduction to modern semi-group and abstract distribution methods for solving the homogeneous (deterministic) Cauchy problem. In the second part, the author solves stochastic problems using semi-group and distribution methods as well as the methods of infinite-dimensional stochastic analysis.
War Secrets in the Ether
"The story of German 'code-breaking' successes and radio-espionage during and between the world wars"--Cover.
Nonlinear PDEs
The emphasis throughout the present volume is on the practical application of theoretical mathematical models helping to unravel the underlying mechanisms involved in processes from mathematical physics and biosciences. It has been conceived as a unique collection of abstract methods dealing especially with nonlinear partial differential equations (either stationary or evolutionary) that are applied to understand concrete processes involving some important applications related to phenomena such as: boundary layer phenomena for viscous fluids, population dynamics,, dead core phenomena, etc. It addresses researchers and post-graduate students working at the interplay between mathematics and ot...
Resistance to Belief Change
This book examines the human proclivity to resist changing our beliefs. Drawing on psychological, neurological, and philosophical research, and integrating topics as wide ranging as emotion, cognition, social (and physical) context, and learning theory, Lao and Young explore why this resistance to change impedes our learning and progression. They also suggest that failure to adapt our beliefs to available and informed evidence can incur costs that may be seen in personal growth, politics, science, law, medicine, education, and business. Resistance to Belief Change explores the various manifestations of resistance, including overt, discursive, and especially inertial forms of resistance. As w...
Current Catalog
First multi-year cumulation covers six years: 1965-70.
Mathematical Reviews
None
Historical Abstracts
Vols. 17-18 cover 1775-1914.
Nonlocal Diffusion and Applications
Working in the fractional Laplace framework, this book provides models and theorems related to nonlocal diffusion phenomena. In addition to a simple probabilistic interpretation, some applications to water waves, crystal dislocations, nonlocal phase transitions, nonlocal minimal surfaces and Schrödinger equations are given. Furthermore, an example of an s-harmonic function, its harmonic extension and some insight into a fractional version of a classical conjecture due to De Giorgi are presented. Although the aim is primarily to gather some introductory material concerning applications of the fractional Laplacian, some of the proofs and results are new. The work is entirely self-contained, and readers who wish to pursue related subjects of interest are invited to consult the rich bibliography for guidance.
