Format: Hardback, 560 pages
Pub. Date: 07-Feb-2025
ISBN-13: 9789811298509
Partial Differential Equations (PDEs) are fundamental in fields such as physics and engineering, underpinning our understanding of sound, heat, diffusion, electrostatics, electrodynamics, thermodynamics, fluid dynamics, elasticity, general relativity, and quantum mechanics. They also arise in areas like differential geometry and the calculus of variations.This book focuses on recent investigations of PDEs in Sobolev and analytic spaces. It consists of twelve chapters, starting with foundational definitions and results on linear, metric, normed, and Banach spaces, which are essential for introducing weak solutions to PDEs. Subsequent chapters cover topics such as Lebesgue integration, LpLpLp spaces, distributions, Fourier transforms, Sobolev and Bourgain spaces, and various types of KdV equations. Advanced topics include higher order dispersive equations, local and global well-posedness, and specific classes of Kadomtsev-Petviashvili equations.This book is intended for specialists like mathematicians, physicists, engineers, and biologists. It can serve as a graduate-level textbook and a reference for multiple disciplines.
Preliminaries
Lebesgue Integration
The Lp Spaces
Distributions. The Fourier Transform
Sobolev Spaces. Analytic Spaces
Original Method for the KdV Equation in Hs(R)
Fifth-Order Shallow Water Equation
Higher Order Nonlinear Dispersive Equation
Kadomtsev-Petviashvili in Analytic Spaces
Generalized Kadomtsev-Petviashvili I Equation
Coupled System of KdV Equations in Gevrey Spaces
System of Generalized KdV Equations
This book is addressed to a wide audience of specialists such as mathematicians, physicists, engineers and biologists. It can be used as a textbook at the graduate level and as a reference book for several disciplines. It is suitable for researchers in PDEs, mathematics, physics, biology, chemistry and informatics.
Format: Hardback, 270 pages
Pub. Date: 09-Feb-2025
ISBN-13: 9789811297212
This book provides an introduction to the mathematical theory of games using both classical methods and optimization theory. Employing a theorem-proof-example approach, the book emphasizes not only results in game theory, but also how to prove them.Part 1 of the book focuses on classical results in games, beginning with an introduction to probability theory by studying casino games and ending with Nash's proof of the existence of mixed strategy equilibria in general sum games. On the way, utility theory, game trees and the minimax theorem are covered with several examples. Part 2 introduces optimization theory and the Karush-Kuhn-Tucker conditions and illustrates how games can be rephrased as optimization problems, thus allowing Nash equilibria to be computed. Part 3 focuses on cooperative games. In this unique presentation, Nash bargaining is recast as a multi-criteria optimization problem and the results from linear programming and duality are revived to prove the classic Bondareva-Shapley theorem. Two appendices covering prerequisite materials are provided, and a 'bonus' appendix with an introduction to evolutionary games allows an instructor to swap out some classical material for a modern, self-contained discussion of the replicator dynamics, the author's particular area of study.
Format: Hardback, 200 pages
Pub. Date: 20-Feb-2025
ISBN-13: 9789811297380
Can the limitations of the Riemann integral be overcome? What is its relationship with modern analysis The theory of Lebesgue integration is a crucial component in the development of modern analysis. This book is an in-depth real analysis textbook, which introduces the basic theory of modern analysis and the basic skills of analysis. Based on the knowledge of real analysis, the theory of interpolation of operators and the Fourier transform theory are further introduced systematically. The main contents include: abstract measures and integrals, measure and topology, Lebesgue integration on Rn, the interpolation of operators on Lp(Rn), Hardy-Littlewood maximal function, convolution and the Fourier transform. They play an important role in harmonic analysis, partial differential equations, probability and numerical analysis. This book is moderately difficult and detailed, focusing on the combination of abstract and concrete, and training readers to skillfully use modern analysis.This textbook is an excellent reference book for readers studying the fields of Harmonic analysis and partial differential equations. It is intended for advanced undergraduate and graduate students in university mathematics, as well as mathematicians and physicists in general.
Abstract Measure and Integral
Measure and Topology
Lebesgue Integration on Rn
The Interpolation of Operators on Lp(Rn)
Hardy-Littlewood Maximal Function
Convolution
The Fourier Transform
Advanced undergraduate and graduate students, mathematicians and physicists.
Format: Hardback, 225 pages
Series: Problem Solving in Mathematics and Beyond
Pub. Date: 08-Feb-2025
ISBN-13: 9789811296987
There is little opportunity in classrooms today for teachers to explore the amazing applications of mathematics outside the curriculum. This book is intended to show how mathematics manifests itself in areas that most people are unaware of. One can even revel in the history of how our number system evolved and how that has enabled us to define the beauty in mathematics as well as in art, architecture, nature, and beyond.The first two chapters of this book introduce the Fibonacci numbers and investigate their amazing relationships and applications in our general environment. The following four chapters focus on the Golden Ratio and the Golden Rectangle, exploring how they manifest all around us, often hiding in plain sight: in everything from architectural wonders such as the Taj Mahal to coin design, and from Greek vases to petal formation. We conclude our enjoyable journey through these mathematical wonders by considering conic sections and how they explain many aspects of everyday life, such as radar dishes, headlight reflectors, and whispering halls. This exposure to aspects of mathematics that are usually bypassed in the school curriculum will provide high school students, teachers, and general readers with an opportunity to truly appreciate the power and beauty of mathematics.
Format: Hardback, 504 pages
Pub. Date: 05-Mar-2025
ISBN-13: 9789811298479
Over the past two decades, the method of fundamental solutions (MFS) has attracted great attention and has been used extensively for the solution of scientific and engineering problems. The MFS is a boundary meshless collocation method which has evolved from the boundary element method. In it, the approximate solution is expressed as a linear combination of fundamental solutions of the operator in the governing partial differential equation.One of the main attractions of the MFS is the simplicity with which it can be applied to the solution of boundary value problems in complex geometries in two and three dimensions. The method is also known by many different names in the literature such as the charge simulation method, the de-singularization method, the virtual boundary element method, etc.Despite its effectiveness, the original version of the MFS is confined to solving boundary value problems governed by homogeneous partial differential equations. To address this limitation, we introduce various types of particular solutions to extend the method to solving general inhomogeneous boundary value problems employing the method of particular solutions.This book consists of two parts. Part I aims to provide theoretical support for beginners. In the spirit of reproducible research and to facilitate the understanding of the method and its implementation, several MATLAB codes have been included in Part II.This book is highly recommended for use by post-graduate researchers and graduate students in scientific computing and engineering.
Fundamentals:
Introduction
Fundamental Solutions
Basis Functions
Particular Solutions
Solving Partial Differential Equations
Method of Fundamental Solutions
Advanced Topics:
Solution of Elliptic BVPs
Method of Particular Solutions
Matrix Decomposition Algorithms for Axisymmetric BVPs
Localized Method of Fundamental Solutions
Inverse Problems
Geometric Modeling Using MFS
Numerical modelers, researchers in scientific computing for science and engineering, and numerical methods for partial differential equations. Design engineers, graduate students in applied mathematics and engineering, academic faculty and researchers in numerical methods.
Format: Hardback, 300 pages
Pub. Date: 07-Mar-2025
ISBN-13: 9789819801718
This book was written for advanced undergraduate math or science majors. Its initial purpose was to illustrate the elementary mathematical theory of ordinary differential equations and their diverse and powerful applications. Historically these have been decisive in many physical problems, some of which have philosophically challenged and indeed altered our civilization's concepts. Because of the importance of the subject, the book is also suitable for a one-semester course for graduate students. The book consists of 12 chapters and six appendices.
Format: Hardback, 220 pages
Pub. Date: 30-Apr-2025
ISBN-13: 9789811296703
This volume consists of several papers written by the main participants of the 7th International Colloquium on Differential Geometry and its Related Fields (ICDG2023). Readers will find some papers that cover geometric structures on manifolds, such as quaternionic structures, Kaehler structures, Einstein structures, contact structures and so on, as well as other papers that deal with probability theory and discrete mathematics.In this volume, the authors present their recent research in differential geometry and related fields, offering a comprehensive overview for researchers not only within differential geometry but also across various areas of mathematics and theoretical physics. They aim for this volume to serve as a valuable guide for young scientists beginning their studies and research careers in the related fields. Together with previous proceedings, readers will gain insight into the progress of research on geometric structures in Riemannian manifolds.
Nonorientable Minimal Surfaces with Various Types of Ends
The SO(3,1)-Orbits in the Light Cone of the 2-Fold Exterior Power of the Minkowski 4-Space
On Sectional Curvatures of Some Einstein
Einstein-Like Metrics on Flag Manifolds
Representation of the Complex Structure of the T^{2} Fibre Bundle over the Hirzebruch Surface CP^{2} #CP^{2}}
Non-horocyclic Unbounded Trajectories on a Complex Hyperbolic Space are Not Expressed by Those on Real Hypersurfaces of Type (A)
On Instability of F-Yang?Mills Connections
Two Weight Projective Codes and Some Combinatorial Objects
Kaehler Graphs Whose Principal Graphs are of Tensor Product Type
Biconservative Hypersurfaces in E_{s}^{5}
Canonical Form Theory in Geometry ? Foundations and Applications
An overview on *-Ricci Solitons
Graduate students and researchers in the field of differential geometry and also in a wide area of mathematics. Young scientists will find it a good