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Functional Inequalities Markov Semigroups and Spectral Theory
In this book, the functional inequalities are introduced to describe:(i) the spectrum of the generator: the essential and discrete spectrums, high order eigenvalues, the principle eigenvalue, and the spectral gap;(ii) the semigroup properties: the uniform intergrability, the compactness, the convergence rate, and the existence of density;(iii) the reference measure and the intrinsic metric: the concentration, the isoperimetic inequality, and the transportation cost inequality.
Analysis for Diffusion Processes on Riemannian Manifolds
Stochastic analysis on Riemannian manifolds without boundary has been well established. However, the analysis for reflecting diffusion processes and sub-elliptic diffusion processes is far from complete. This book contains recent advances in this direction along with new ideas and efficient arguments, which are crucial for further developments. Many results contained here (for example, the formula of the curvature using derivatives of the semigroup) are new among existing monographs even in the case without boundary. Contents:PreliminariesDiffusion Processes on Riemannian Manifolds without BoundaryReflecting Diffusion Processes on Manifolds with BoundaryStochastic Analysis on Path Space over...
Harnack Inequalities for Stochastic Partial Differential Equations
In this book the author presents a self-contained account of Harnack inequalities and applications for the semigroup of solutions to stochastic partial and delayed differential equations. Since the semigroup refers to Fokker-Planck equations on infinite-dimensional spaces, the Harnack inequalities the author investigates are dimension-free. This is an essentially different point from the above mentioned classical Harnack inequalities. Moreover, the main tool in the study is a new coupling method (called coupling by change of measures) rather than the usual maximum principle in the current literature.
Dirichlet Forms and Stochastic Processes
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Two-Dimensional Nanomaterials for Fire-Safe Polymers
This book provides an overview of the latest scientific developments and technological advances in two-dimensional (2D) nanomaterials for fire-safe polymers. It summarizes the preparation methods for diverse types of 2D nanomaterials and their polymer composites and reviews their flame-retardant properties, toxic gas and smoke emission during combustion, and inhibition strategies. Covers fundamental aspects like influence of size and dispersion of 2D nanomaterials to help readers develop efficient, multi-functional, and ecofriendly fire-safe polymer composites for a wide range of applications Discusses new-emerging 2D nanomaterials for fire-safe polymer applications, including MXenes, graphitic carbon nitride, boron nitride, and black phosphorus Introduces basic modes of flame retardant action of 2D nanomaterials, including smoke and toxic gas suppression, and the role of 2D nanomaterials in promoting char formation This book is suitable for both scholars and engineers in the fields of polymer science and engineering. It is also aimed at graduate students in chemistry, materials, and safety science and engineering.
Distribution Dependent Stochastic Differential Equations
Corresponding to the link of Itô's stochastic differential equations (SDEs) and linear parabolic equations, distribution dependent SDEs (DDSDEs) characterize nonlinear Fokker-Planck equations. This type of SDEs is named after McKean-Vlasov due to the pioneering work of H P McKean (1966), where an expectation dependent SDE is proposed to characterize nonlinear PDEs for Maxwellian gas. Moreover, by using the propagation of chaos for Kac particle systems, weak solutions of DDSDEs are constructed as weak limits of mean field particle systems when the number of particles goes to infinity, so that DDSDEs are also called mean-field SDEs. To restrict a DDSDE in a domain, we consider the reflection boundary by following the line of A V Skorohod (1961).This book provides a self-contained account on singular SDEs and DDSDEs with or without reflection. It covers well-posedness and regularities for singular stochastic differential equations; well-posedness for singular reflected SDEs; well-posedness of singular DDSDEs; Harnack inequalities and derivative formulas for singular DDSDEs; long time behaviors for DDSDEs; DDSDEs with reflecting boundary; and killed DDSDEs.
Qing Xiang
According to legend, "Dark Sink" is an ancient book, which is divided into two volumes: Qingxiang and Suxiang. It is dry, profound and abstruse. However, the author claims that the fairy myth recorded in it is true. The person who wrote this book can no longer be tested, but the word "fish" remains on the title page of the book. According to "Dark Sink", at the beginning of heaven and earth, at the beginning of everything, yin and yang are unpredictable. The unforeseen events of yin and yang are called gods, and the gods stand and China decides. Differentiation of the three realms, adhering to heaven, reincarnation of life and death.
