Evolution Equations With A Complex Spatial Variable

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Evolution Equations with a Complex Spatial Variable

Author : Ciprian G Gal
Publisher : World Scientific
ISBN 13 : 9814590614
Total Pages : 204 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Evolution Equations with a Complex Spatial Variable by : Ciprian G Gal

Download or read book Evolution Equations with a Complex Spatial Variable written by Ciprian G Gal and published by World Scientific. This book was released on 2014-03-18 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Contents:Historical Background and MotivationHeat and Laplace Equations of Complex Spatial VariablesHigher-Order Heat and Laplace Equations with Complex Spatial VariablesWave and Telegraph Equations with Complex Spatial VariablesBurgers and Black–Merton–Scholes Equations with Complex Spatial VariablesSchrödinger-Type Equations with Complex Spatial VariablesLinearized Korteweg–de Vries Equations with Complex Spatial VariablesEvolution Equations with a Complex Spatial Variable in General Domains Readership: Graduates and researchers in partial differential equations and in classical analytical function theory of one complex variable. Key Features:For the first time in literature, the study of evolution equations of real time variable and complex spatial variables is madeThe study includes some of the most important classes of partial differential equations: heat, Laplace, wave, telegraph, Burgers, Black–Merton–Scholes, Schrodinger and Korteweg–de Vries equationsThe book is entirely based on the authors' own workKeywords:Evolution Equations of Complex Spatial Variables;Semigroup of Linear Operators;Complex Convolution Integrals;Heat;Laplace;Wave;Telegraph;Burgers;BlackâMertonâScholes;Schrodinger;Kortewegâde Vries Equations

Introduction to Fractional and Pseudo-Differential Equations with Singular Symbols

Author : Sabir Umarov
Publisher : Springer
ISBN 13 : 3319207717
Total Pages : 434 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Introduction to Fractional and Pseudo-Differential Equations with Singular Symbols by : Sabir Umarov

Download or read book Introduction to Fractional and Pseudo-Differential Equations with Singular Symbols written by Sabir Umarov and published by Springer. This book was released on 2015-08-18 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Bloch-type Periodic Functions: Theory And Applications To Evolution Equations

Author : Yong-kui Chang
Publisher : World Scientific
ISBN 13 : 9811254370
Total Pages : 209 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Bloch-type Periodic Functions: Theory And Applications To Evolution Equations by : Yong-kui Chang

Download or read book Bloch-type Periodic Functions: Theory And Applications To Evolution Equations written by Yong-kui Chang and published by World Scientific. This book was released on 2022-07-13 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph aims to provide for the first time a unified and homogenous presentation of the recent works on the theory of Bloch periodic functions, their generalizations, and their applications to evolution equations. It is useful for graduate students and beginning researchers as seminar topics, graduate courses and reference text in pure and applied mathematics, physics, and engineering.

An Exponential Function Approach To Parabolic Equations

Author : Lin Chin-yuan
Publisher : World Scientific
ISBN 13 : 9814616400
Total Pages : 176 pages
Book Rating : 4.8/5 (146 download)

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Book Synopsis An Exponential Function Approach To Parabolic Equations by : Lin Chin-yuan

Download or read book An Exponential Function Approach To Parabolic Equations written by Lin Chin-yuan and published by World Scientific. This book was released on 2014-08-08 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Frontiers in Approximation Theory

Author : George A Anastassiou
Publisher : World Scientific
ISBN 13 : 9814696110
Total Pages : 228 pages
Book Rating : 4.8/5 (146 download)

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Book Synopsis Frontiers in Approximation Theory by : George A Anastassiou

Download or read book Frontiers in Approximation Theory written by George A Anastassiou and published by World Scientific. This book was released on 2015-06-23 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Contents:Fractional Monotone ApproximationRight Fractional Monotone Approximation Theory Univariate Left Fractional Polynomial High Order Monotone Approximation Theory Univariate Right Fractional Polynomial High Order Monotone Approximation TheorySpline Left Fractional Monotone Approximation Theory Using Left Fractional Differential OperatorsSpline Right Fractional Monotone Approximation Theory Using Right Fractional Differential OperatorsComplete Fractional Monotone Approximation TheoryLower Order Fractional Monotone Approximation TheoryApproximation Theory by Discrete Singular OperatorsOn Discrete Approximation by Gauss–Weierstrass and Picard Type Operators Approximation Theory by Interpolating Neural NetworksApproximation and Functional Analysis Over Time Scales Readership: Graduate students and researchers in approximation theory. Key Features:Presents new research in approximation theoryAn extensive list of references is given in every chapterIt is about fractional approximation, neural networks and singular integrals approximationsImportant to applications in applied mathematicsKeywords:Fractional Approximation;Neural Networks;Singular Integrals

Functional Equations and Inequalities

Author : John Michael Rassias
Publisher : World Scientific Publishing Company
ISBN 13 : 9813147628
Total Pages : 396 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis Functional Equations and Inequalities by : John Michael Rassias

Download or read book Functional Equations and Inequalities written by John Michael Rassias and published by World Scientific Publishing Company. This book was released on 2017-03-20 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Request Inspection Copy

Differential Sheaves And Connections: A Natural Approach To Physical Geometry

Author : Mallios Anastasios
Publisher : World Scientific
ISBN 13 : 981471948X
Total Pages : 304 pages
Book Rating : 4.8/5 (147 download)

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Book Synopsis Differential Sheaves And Connections: A Natural Approach To Physical Geometry by : Mallios Anastasios

Download or read book Differential Sheaves And Connections: A Natural Approach To Physical Geometry written by Mallios Anastasios and published by World Scientific. This book was released on 2015-09-17 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Frontiers in Time Scales and Inequalities

Author : George A Anastassiou
Publisher : World Scientific
ISBN 13 : 9814704458
Total Pages : 288 pages
Book Rating : 4.8/5 (147 download)

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Book Synopsis Frontiers in Time Scales and Inequalities by : George A Anastassiou

Download or read book Frontiers in Time Scales and Inequalities written by George A Anastassiou and published by World Scientific. This book was released on 2015-08-06 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Contents:Foundations of Right Delta Fractional Calculus on Time ScalesPrinciples of Right Nabla Fractional Calculus on Time ScalesAbout Right Delta Discrete FractionalityAbout Right Nabla Discrete Fractional CalculusRepresentations and Ostrowski Inequalities over Time ScalesLandau Inequalities on Time ScalesGrüss and Comparison of Means Inequalities over Time ScalesAbout Integral Operator Inequalities over Time ScalesAbout Vectorial Integral Operator Inequalities Using Convexity over Time ScalesGeneral Grüss and Ostrowski Inequalities Using s-ConvexityEssential and s-Convexity Ostrowski and Grüss Inequalities Using Several FunctionsGeneral Fractional Hermite–Hadamard Inequalities Using m-Convexity and (s, m)-ConvexityAbout the Reduction Method in Fractional Calculus and Fractional Ostrowski Inequalities Readership: Advanced graduate students and researchers interested in time scales, inequalities and difference/differential equations. Key Features:Presents new research on time scales and related inequalitiesMaterials are crucially related to difference/differential equationsSelf-contained chapters that can be read independentlyAn extensive list of references is given in each chapterThe topics covered are diverseKeywords:Time Scale;Fractional Derivative;Difference Equation;Fractional Inequality

Nonlinear Evolution Equations And Dynamical Systems Needs '94

Author : Vladimir G Makhankov
Publisher : World Scientific
ISBN 13 : 9814549428
Total Pages : 406 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Nonlinear Evolution Equations And Dynamical Systems Needs '94 by : Vladimir G Makhankov

Download or read book Nonlinear Evolution Equations And Dynamical Systems Needs '94 written by Vladimir G Makhankov and published by World Scientific. This book was released on 1995-04-26 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Stochastic Models With Applications To Genetics, Cancers, Aids And Other Biomedical Systems (Second Edition)

Author : Wai-yuan Tan
Publisher : World Scientific
ISBN 13 : 9814397210
Total Pages : 524 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis Stochastic Models With Applications To Genetics, Cancers, Aids And Other Biomedical Systems (Second Edition) by : Wai-yuan Tan

Download or read book Stochastic Models With Applications To Genetics, Cancers, Aids And Other Biomedical Systems (Second Edition) written by Wai-yuan Tan and published by World Scientific. This book was released on 2015-10-28 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Emerging Concepts in Evolution Equations

Author : Carolyn Murphy (Writer on mathematics)
Publisher : Nova Science Publishers
ISBN 13 : 9781536108736
Total Pages : 105 pages
Book Rating : 4.1/5 (87 download)

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Book Synopsis Emerging Concepts in Evolution Equations by : Carolyn Murphy (Writer on mathematics)

Download or read book Emerging Concepts in Evolution Equations written by Carolyn Murphy (Writer on mathematics) and published by Nova Science Publishers. This book was released on 2017 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reviews new research and analyzes emerging concepts in evolution equations. Chapter One discusses the evolution equation of Lie-type for finite deformations, and its time-discrete integration. Chapter Two presents a review of recent results on group analysis of nonlinear evolution equations in one spatial variable. Chapter Three addresses the problem of exponential stabilization of a class of 1-D PDEs with Dirichlet boundary control. (Imprint: Novinka)

Discrete Approximation Theory

Author : George A Anastassiou
Publisher : World Scientific
ISBN 13 : 9813145854
Total Pages : 348 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis Discrete Approximation Theory by : George A Anastassiou

Download or read book Discrete Approximation Theory written by George A Anastassiou and published by World Scientific. This book was released on 2016-09-29 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph, we present the authors' recent work of the last seven years in Approximation Theory. Chapters are self-contained and can be read independently and advanced courses can be taught out of this book. Here our generalized discrete singular operators are of the following types: Picard, Gauss–Weierstrass and Poisson–Cauchy operators. We treat both the unitary and non-unitary, univariate and multivariate cases of these operators, which are not necessarily positive operators. The book's results are expected to find applications in many areas of pure and applied mathematics, and statistics. As such, it is suitable for researchers, graduate students, and seminars of related subjects, and serves well as an invaluable resource for all science libraries.

A Concise Guide To Semigroups And Evolution Equations

Author : Belleni-morante Aldo
Publisher : World Scientific
ISBN 13 : 9813104570
Total Pages : 180 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis A Concise Guide To Semigroups And Evolution Equations by : Belleni-morante Aldo

Download or read book A Concise Guide To Semigroups And Evolution Equations written by Belleni-morante Aldo and published by World Scientific. This book was released on 1994-05-18 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a simple and concise introduction to the theory of semigroups and evolution equations, both in the linear and in the semilinear case. The subject is presented by a discussion of two standard boundary value problems (from particle transport theory and from population theory), and by showing how such problems can be rewritten as evolution problems in suitable Banach spaces.Each section of the book is completed by some notes, where the relevant notions of functional analysis are explained. Some other definitions and theorems of functional analysis are discussed in the Appendices (so that the only prerequisites to read the book are classical differential and integral calculus).

A Nonlinear Progress to Modern Soliton Theory

Author : Colin Rogers
Publisher : Cambridge Scholars Publishing
ISBN 13 : 1527591557
Total Pages : 166 pages
Book Rating : 4.5/5 (275 download)

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Book Synopsis A Nonlinear Progress to Modern Soliton Theory by : Colin Rogers

Download or read book A Nonlinear Progress to Modern Soliton Theory written by Colin Rogers and published by Cambridge Scholars Publishing. This book was released on 2022-12-06 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Evolution Equations and Lagrangian Coordinates

Author : Anvarbek M. Meirmanov
Publisher : Walter de Gruyter
ISBN 13 : 311087444X
Total Pages : 329 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Evolution Equations and Lagrangian Coordinates by : Anvarbek M. Meirmanov

Download or read book Evolution Equations and Lagrangian Coordinates written by Anvarbek M. Meirmanov and published by Walter de Gruyter. This book was released on 2011-07-20 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich and Z. Janko, Groups of Prime Power Order, Volume 6 (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

Handbook of Evolution Equations

Author : Gaston M. N'Guérékata
Publisher :
ISBN 13 : 9781616684297
Total Pages : 0 pages
Book Rating : 4.6/5 (842 download)

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Book Synopsis Handbook of Evolution Equations by : Gaston M. N'Guérékata

Download or read book Handbook of Evolution Equations written by Gaston M. N'Guérékata and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents current mathematical research in the study of evolution equations. Topics discussed include the complexity of evolutionary dynamics; variational hyperbolic inequality in spatial variables; the superposition of functions; evolutionary dynamics equations and the information law of evolution and time periodic solutions for quasigeostrophic motion and their stability.

Sojourns in Probability Theory and Statistical Physics - I

Author : Vladas Sidoravicius
Publisher : Springer Nature
ISBN 13 : 9811502943
Total Pages : 338 pages
Book Rating : 4.8/5 (115 download)

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Book Synopsis Sojourns in Probability Theory and Statistical Physics - I by : Vladas Sidoravicius

Download or read book Sojourns in Probability Theory and Statistical Physics - I written by Vladas Sidoravicius and published by Springer Nature. This book was released on 2019-10-17 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.