Evolution Equations With A Complex Spatial Variable
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Evolution Equations With A Complex Spatial Variable
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Author : Ciprian G Gal
language : en
Publisher: World Scientific
Release Date : 2014-03-18
Evolution Equations With A Complex Spatial Variable written by Ciprian G Gal and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-18 with Mathematics categories.
This book investigates several classes of partial differential equations of real time variable and complex spatial variables, including the heat, Laplace, wave, telegraph, Burgers, Black-Merton-Scholes, Schrödinger and Korteweg-de Vries equations.The complexification of the spatial variable is done by two different methods. The first method is that of complexifying the spatial variable in the corresponding semigroups of operators. In this case, the solutions are studied within the context of the theory of semigroups of linear operators. It is also interesting to observe that these solutions preserve some geometric properties of the boundary function, like the univalence, starlikeness, convexity and spirallikeness. The second method is that of complexifying the spatial variable directly in the corresponding evolution equation from the real case. More precisely, the real spatial variable is replaced by a complex spatial variable in the corresponding evolution equation and then analytic and non-analytic solutions are sought.For the first time in the book literature, we aim to give a comprehensive study of the most important evolution equations of real time variable and complex spatial variables. In some cases, potential physical interpretations are presented. The generality of the methods used allows the study of evolution equations of spatial variables in general domains of the complex plane.
Introduction To Fractional And Pseudo Differential Equations With Singular Symbols
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Author : Sabir Umarov
language : en
Publisher: Springer
Release Date : 2015-08-18
Introduction To Fractional And Pseudo Differential Equations With Singular Symbols written by Sabir Umarov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-18 with Mathematics categories.
The book systematically presents the theories of pseudo-differential operators with symbols singular in dual variables, fractional order derivatives, distributed and variable order fractional derivatives, random walk approximants, and applications of these theories to various initial and multi-point boundary value problems for pseudo-differential equations. Fractional Fokker-Planck-Kolmogorov equations associated with a large class of stochastic processes are presented. A complex version of the theory of pseudo-differential operators with meromorphic symbols based on the recently introduced complex Fourier transform is developed and applied for initial and boundary value problems for systems of complex differential and pseudo-differential equations.
An Exponential Function Approach To Parabolic Equations
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Author : Chin-yuan Lin
language : en
Publisher: World Scientific
Release Date : 2014-08-08
An Exponential Function Approach To Parabolic Equations written by Chin-yuan Lin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-08 with Mathematics categories.
This volume is on initial-boundary value problems for parabolic partial differential equations of second order. It rewrites the problems as abstract Cauchy problems or evolution equations, and then solves them by the technique of elementary difference equations. Because of this, the volume assumes less background and provides an easy approach for readers to understand.
Sojourns In Probability Theory And Statistical Physics I
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Author : Vladas Sidoravicius
language : en
Publisher: Springer Nature
Release Date : 2019-10-17
Sojourns In Probability Theory And Statistical Physics I written by Vladas Sidoravicius and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-17 with Mathematics categories.
Charles M. (Chuck) Newman has been a leader in Probability Theory and Statistical Physics for nearly half a century. This three-volume set is a celebration of the far-reaching scientific impact of his work. It consists of articles by Chuck’s collaborators and colleagues across a number of the fields to which he has made contributions of fundamental significance. This publication was conceived during a conference in 2016 at NYU Shanghai that coincided with Chuck's 70th birthday. The sub-titles of the three volumes are: I. Spin Glasses and Statistical Mechanics II. Brownian Web and Percolation III. Interacting Particle Systems and Random Walks The articles in these volumes, which cover a wide spectrum of topics, will be especially useful for graduate students and researchers who seek initiation and inspiration in Probability Theory and Statistical Physics.
Frontiers In Approximation Theory
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Author : George A Anastassiou
language : en
Publisher: World Scientific
Release Date : 2015-06-23
Frontiers In Approximation Theory written by George A Anastassiou and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-23 with Mathematics categories.
This monograph presents the author's work of the last five years in approximation theory. The chapters are self-contained and can be read independently. Readers will find the topics covered are diverse and advanced courses can be taught out of this book.The first part of the book is dedicated to fractional monotone approximation theory introduced for the first time by the author, taking the related ordinary theory of usual differentiation at the fractional differentiation level with polynomials and splines as approximators. The second part deals with the approximation by discrete singular operators of the Favard style, for example, of the Picard and Gauss-Weierstrass types. Then, it continues in a very detailed and extensive chapter on approximation by interpolating operators induced by neural networks, a connection to computer science. This book ends with the approximation theory and functional analysis on time scales, a very modern topic, detailing all the pros and cons of this method.The results in this book are expected to find applications in many areas of pure and applied mathematics. So far, very little is written about fractional approximation theory which is at its infancy. As such, it is suitable for researchers, graduate students, and performing seminars as well as an invaluable resource for all science libraries.
Functional Equations And Inequalities Solutions And Stability Results
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Author : John Michael Rassias
language : en
Publisher: World Scientific Publishing Company
Release Date : 2017-03-20
Functional Equations And Inequalities Solutions And Stability Results written by John Michael Rassias and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-20 with Mathematics categories.
This volume covers the topic in functional equations in a broad sense and is written by authors who are in this field for the past 50 years. It contains the basic notions of functional equations, the methods of solving functional equations, the growth of functional equations in the last four decades and an extensive reference list on fundamental research papers that investigate the stability results of different types of functional equations and functional inequalities. This volume starts by taking the reader from the fundamental ideas to higher levels of results that appear in recent research papers. Its step-by-step expositions are easy for the reader to understand and admire the elegant results and findings on the stability of functional equations.
Differential Sheaves And Connections A Natural Approach To Physical Geometry
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Author : Anastasios Mallios
language : en
Publisher: World Scientific
Release Date : 2015-09-17
Differential Sheaves And Connections A Natural Approach To Physical Geometry written by Anastasios Mallios and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-17 with Mathematics categories.
This unique book provides a self-contained conceptual and technical introduction to the theory of differential sheaves. This serves both the newcomer and the experienced researcher in undertaking a background-independent, natural and relational approach to 'physical geometry'. In this manner, this book is situated at the crossroads between the foundations of mathematical analysis with a view toward differential geometry and the foundations of theoretical physics with a view toward quantum mechanics and quantum gravity. The unifying thread is provided by the theory of adjoint functors in category theory and the elucidation of the concepts of sheaf theory and homological algebra in relation to the description and analysis of dynamically constituted physical geometric spectrums.
Stochastic Models With Applications To Genetics Cancers Aids And Other Biomedical Systems Second Edition
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Author : Wai-yuan Tan
language : en
Publisher: World Scientific
Release Date : 2015-10-28
Stochastic Models With Applications To Genetics Cancers Aids And Other Biomedical Systems Second Edition written by Wai-yuan Tan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-28 with Mathematics categories.
This book presents a systematic treatment of Markov chains, diffusion processes and state space models, as well as alternative approaches to Markov chains through stochastic difference equations and stochastic differential equations. It illustrates how these processes and approaches are applied to many problems in genetics, carcinogenesis, AIDS epidemiology and other biomedical systems.One feature of the book is that it describes the basic MCMC (Markov chain and Monte Carlo) procedures and illustrates how to use the Gibbs sampling method and the multilevel Gibbs sampling method to solve many problems in genetics, carcinogenesis, AIDS and other biomedical systems.As another feature, the book develops many state space models for many genetic problems, carcinogenesis, AIDS epidemiology and HIV pathogenesis. It shows in detail how to use the multilevel Gibbs sampling method to estimate (or predict) simultaneously the state variables and the unknown parameters in cancer chemotherapy, carcinogenesis, AIDS epidemiology and HIV pathogenesis. As a matter of fact, this book is the first to develop several state space models for many genetic problems, carcinogenesis and other biomedical problems.To emphasize special applications to medical problems, in this new edition the book has added a new chapter to illustrate how to develop biologically-supported stochastic models and state space models of carcinogenesis in human beings. Specific examples include hidden Markov models and state space models for human colon cancer, human liver cancer and some human pediatric cancers such as retinoblastoma and hepatoblastoma. The book also gives examples to illustrate how to develop procedures to assess cancer risk of environmental agents through initiation-promotion protocols.
Frontiers In Time Scales And Inequalities
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Author : George A Anastassiou
language : en
Publisher: World Scientific
Release Date : 2015-08-06
Frontiers In Time Scales And Inequalities written by George A Anastassiou and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-06 with Mathematics categories.
This monograph contains the author's work of the last four years in discrete and fractional analysis. It introduces the right delta and right nabla fractional calculus on time scales and continues with the right delta and right nabla discrete fractional calculus in the Caputo sense. Then, it shows representation formulae of functions on time scales and presents Ostrowski type inequalities, Landau type inequalities, Grüss type and comparison of means inequalities, all these over time scales. The volume continues with integral operator inequalities and their multivariate vectorial versions using convexity of functions, again all these over time scales. It follows the Grüss and Ostrowski type inequalities involving s-convexity of functions; and also examines the general case when several functions are involved. Then, it presents the general fractional Hermite-Hadamard type inequalities using m-convexity and (s, m)-convexity. Finally, it introduces the reduction method in fractional calculus and its connection to fractional Ostrowski type inequalities is studied.This book's results are expected to find applications in many areas of pure and applied mathematics, especially in difference equations and fractional differential equations. The chapters are self-contained and can be read independently, and advanced courses can be taught out of it. It is suitable for researchers, graduate students, seminars of the above subjects, and serves well as an invaluable resource for all science libraries.
A Nonlinear Progress To Modern Soliton Theory
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Author : Colin Rogers
language : en
Publisher: Cambridge Scholars Publishing
Release Date : 2022-12-06
A Nonlinear Progress To Modern Soliton Theory written by Colin Rogers and has been published by Cambridge Scholars Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-06 with Mathematics categories.
This book provides a historical account of the discovery in 1834 of a remarkable singular wave that was ultimately to lead to the development of modern soliton theory with its diverse physical applications. In terms of associated geometry, the classical work of Bäcklund and Bianchi and its consequences is recounted, notably with regard to nonlinear superposition principles, which later were shown to be generic to soliton systems and which provide the analytic description of complex multi-soliton interaction. Whereas the applications of modern soliton in certain areas of physics are well-documented, deep connections between soliton theory and nonlinear continuum mechanics have had a separate development. This book describes wide applications in such disparate areas as elastostatics, elastodynamics, superelasticity, shell theory, magnetohydrostatics and magnetohydrodynamics, and will appeal to research scientists and advanced students with an interest in integrable systems in nonlinear physics or continuum mechanics.