Format: Hardback, 320 pages
Pub. Date: 14-Apr-2024
ISBN-13: 9789811290404
This monograph offers a comprehensive exposition of the theory surrounding time-fractional partial differential equations, featuring recent advancements in fundamental techniques and results. The topics covered encompass crucial aspects of the theory, such as well-posedness, regularity, approximation, and optimal control. The book delves into the intricacies of fractional Navier-Stokes equations, fractional Rayleigh-Stokes equations, fractional Fokker-Planck equations, and fractional Schrodinger equations, providing a thorough exploration of these subjects. Numerous real-world applications associated with these equations are meticulously examined, enhancing the practical relevance of the presented concepts.The content in this monograph is based on the research works carried out by the author and other excellent experts during the past five years. Rooted in the latest advancements, it not only serves as a valuable resource for understanding the theoretical foundations but also lays the groundwork for delving deeper into the subject and navigating the extensive research landscape. Geared towards researchers, graduate students, and PhD scholars specializing in differential equations, applied analysis, and related research domains, this monograph facilitates a nuanced understanding of time-fractional partial differential equations and their broader implications.
Preface
About the Author
Introduction
Preliminaries
Fractional Navier?Stokes Equations
Fractional Rayleigh?Stokes Equations
Fractional Fokker?Planck Equations
Fractional Schrodinger Equations
Bibliography
Index
Format: Hardback, 164 pages
Pub. Date: 11-May-2024
ISBN-13: 9789811288883
Paperback
SBN-13: 9789811290251
This is a concise book that introduces students to the basics of logical thinking and important mathematical structures that are critical for a solid understanding of logical formalisms themselves as well as for building the necessary background to tackle other fields that are based on these logical principles. Despite its compact and small size, it includes many solved problems and quite a few end-of-section exercises that will help readers consolidate their understanding of the material.This textbook is essential reading for anyone interested in the logical foundations of Informatics, Computer Science, Data Science, Artificial Intelligence, and other related areas. Written with undergraduate students in these disciplines in mind, this book can very well serve the needs of interested and curious readers who wish to get a grasp of the logical principles upon which these fields are built. This book does not require readers to possess math skills beyond those learned in high school.
Preface
Acknowledgments
Introduction
Propositional Logic
Set Theory
Predicate Logic
Mathematical Induction
Functions and Relations
Graph Theory and Its Applications
Appendix A Translation to Propositional Logic
Appendix B Translation to Predicate Logic
Index
Format: Hardback, 300 pages
Pub. Date: 30-Jun-2024
ISBN-13: 9789811287206
Paperback
SBN-13: 9789811287428
The series is edited by the head coaches of China's IMO National Team. Each volume, catering to different grades, is contributed by the senior coaches of the IMO National Team. The Chinese edition has won the award of Top 50 Most Influential Educational Brands in China.The series is created in line with the mathematics cognition and intellectual development levels of the students in the corresponding grades. All hot mathematics topics of the competition are included in the volumes and are organized into chapters where concepts and methods are gradually introduced to equip the students with necessary knowledge until they can finally reach the competition level.In each chapter, well-designed problems including those collected from real competitions are provided so that the students can apply the skills and strategies they have learned to solve these problems. Detailed solutions are provided selectively. As a feature of the series, we also include some solutions generously offered by the members of Chinese national team and national training team.
Ingenious Computation of Rational Numbers
Absolute Value
First Degree Equation with One Variable
System of First Degree Equations
Application of a System of First Degree Equations
Set up (Systems of) Equations to Solve Word Problems
(System of) First Degree Inequalities
Multiplication and Division of Polynomials with Integer Coefficients
Line Segments
Angle
Sum of the Interior Angles of a Triangle
Parallel Lines
Assign a Variable Unnecessary to be Solved
Undetermined Coeffiffifficients
Synthetic Division and Polynomial Remainder Theorem
Simplify and Evaluate an Algebraic Formula
Logical Inference I
Logical Inference II
Divisibility
Odd Numbers and Even Numbers
Prime Numbers and Composite Numbers
The Rule of Sum and the Rule of Product
Number of Divisors
Positional Notation
Modular Arithmetic
First Degree Diophantine Equation with Two Unknowns
The Drawer Principle
Format: Hardback, 284 pages
Pub. Date: 19-May-2024
ISBN-13: 9789811290435
The primary focus of the book is to explore the asymptotic behavior of problems formulated within cylindrical structures. Various physical applications are discussed, with certain topics such as fluid flows in channels being particularly noteworthy. Additionally, the book delves into the relevance of elasticity in the context of cylindrical bodies.In specific scenarios where the size of the cylinder becomes exceptionally large, the material's behavior is determined solely by its cross-section. The investigation centers around understanding these particular properties.Since the publication of the first edition, several significant advancements have been made, adding depth and interest to the content. Consequently, new sections have been incorporated into the existing edition, complemented by a comprehensive list of references.
Introduction
The Dirichlet Problem in Some Unbounded Domains
The Pure Neumann Problem
Periodic Problems
Anisotropic Singular Perturbation Problems
Eigenvalue Problems
Elliptic Systems
The Stokes Problem
Variational Inequalities
Calculus of Variations
Format: Hardback, 764 pages
Pub. Date: 14-Jun-2024
ISBN-13: 9789811291715
The Fourier transform is a 'tool' used in engineering and computer vision to model periodic phenomena. Starting with the basics of measure theory and integration, this book delves into the harmonic analysis of locally compact abelian groups. It provides an in-depth tour of the beautiful theory of the Fourier transform based on the results of Gelfand, Pontrjagin, and Andre Weil in a manner accessible to an undergraduate student who has taken linear algebra and introductory real analysis.Highlights of this book include the Bochner integral, the Haar measure, Radon functionals, the theory of Fourier analysis on the circle, and the theory of the discrete Fourier transform. After studying this book, the reader will have the preparation necessary for understanding the Peter-Weyl theorems for complete, separable Hilbert algebras, a key theoretical concept used in the construction of Gelfand pairs and equivariant convolutional neural networks.
Preface
Introduction
Function Spaces Often Encountered
The Riemann Integral
Measure Theory; Basic Notions
Integration
The Fourier Transform and Cotransform on ??n, ?n, ?n
Radon Measures on Locally Compact Spaces
The Haar Measure and Convolution
Normed Algebras and Spectral Theory
Analysis on Locally Compact Groups
Appendices:
Topology
Vector Norms and Matrix Norms
Basics of Groups and Group Actions
Hilbert Spaces
Well-Ordered Sets, Ordinals, Cardinals, Alephs
Bibliography
Symbol Index
Index
Format: Hardback, 330 pages
Series: Trends in Abstract and Applied Analysis
Pub. Date: 29-May-2024
ISBN-13: 9789811287473
State continuous dynamic models can be reformulated into discrete state processes. This process generates numerical schemes that lead theoretical iterative schemes. This type of method of stochastic modelling generates three basic problems. First, the fundamental properties of solution, namely, existence, uniqueness, measurability, continuous dependence on system parameters depend mode of convergence. Second, the basic probabilistic and statistical properties mean, variance, moments of qualitative/quantitative behaviour of solutions are directly described as concept of solution process or via probability distribution or density functions either. Finally, deterministic versus stochastic modelling of dynamic processes is to what extent the stochastic mathematical model differs from the corresponding deterministic model in the absence of random disturbances or fluctuations and uncertainties.Most literature in this subject was developed in the 1950s, and focussed on the theory of systems of continuous and discrete-time deterministic; however, continuous-time and its approximation schemes of stochastic differential equations faced the problems outlined above and made slow progress in developing problems as a result. This monograph addresses these problems by presenting an account of stochastic versus deterministic issues in discrete state dynamic systems in a systematic and unified way.
Stochastic Systems of Difference Equations with Random Parameters Methods
Stochastic Systems of Difference Equations of Ito-Type-Methods
Stochastic Systems of Difference Equations: Qualitative Analysis
Random Polynomials
Numerical Schemes for Systems of Differential Equations with Random Parameters
Numerical Schemes for Systems of Difference Equations of Ito-Type
Discrete-Time Probabilistic, Stochastic Dynamic Modeling and Statistical Data Analyses
Appendices:
Stochastic
Ordinary Differential Equations with Random Parameters
Boundary Value Problems
Format: Hardback, 394 pages
Pub. Date: 04-Jul-2024
ISBN-13: 9781800615571
Paperback
SBN-13: 9781800615601
Problems and Solution in Stochastic Calculus exposes readers to distinct simple ideas and proofs in stochastic calculus and its applications. It is intended as a companion to the successful original title Introduction to Stochastic Calculus with Applications (3rd Edition) by Fima Klebaner. The current book is authored by three active researchers in the fields of probability, stochastic processes, and their applications in financial mathematics, mathematical biology, and more. The book features problems rooted in their ongoing research. Mathematical finance and biology feature pre-eminently, but the ideas and techniques can equally apply to fields such as engineering and economics.The problems set forth are accessible to students new to the subject, with most of the problems and their solutions centring on a single idea or technique at a time to enhance the ease of learning. While the majority of problems are relatively straightforward, more complex questions are also set in order to challenge the reader as their understanding grows. The book is suitable for either self-study or for instructors, and there are numerous opportunities to generate fresh problems by modifying the ones presented, facilitating a deeper grasp of the material.
Introduction
Preliminaries from Calculus
Concepts of Probability Theory
Basic Stochastic Processes
Brownian Motion Calculus
Stochastic Differential Equations
Diffusion Processes
Martingales
Semi-martingales
Pure Jump processes
Change of Probability Measure
Applications in Finance
Applications in Biology