Copyright Year 2023
ISBN 9781032384375
November 17, 2022 Forthcoming by CRC Press
426 Pages
This book surveys some of the important research work carried out by Indian scientists in the field of pure and applied probability, quantum probability, quantum scattering theory, group representation theory and general relativity.
It reviews the axiomatic foundations of probability theory by A.N. Kolmogorov and how the Indian school of probabilists and statisticians used this theory effectively to study a host of applied probability and statistics problems like parameter estimation, convergence of a sequence of probability distributions, and martingale characterization of diffusions.
It will be an important resource to students and researchers of Physics and Engineering, especially those working with Advanced Probability and Statistics.
1. Classical and Quantum Probability 2. Quantum Scattering Theory 3. Linear Algebra and Operator Theory 4. Group Theory in Statistical Signal Processing and Control 5. Statistical Aspects of EEG Signal Analysis and Image Processing in the Medical Science 6. Electromagnetism and Quantum Field Theory 7. Some Aspects of Superstring Theory 8. Superconductivity 9. Some Aspects of Large Deviation Theory 10. Contributions of Some Indian Scientists 11. Applied Differential Equations 12. Quantum Signal Processing 13. Aspects of Circuit Theory and Device Physics 14. Index on the Contents and Notes
Copyright Year 2023
ISBN 9781032302478
December 5, 2022 Forthcoming by Chapman & Hall
456 Pages 25 B/W Illustrations
A conceptually clear induction to fundamental analysis theorems, a tutorial for creative approaches for solving problems, a collection of modern challenging problems, a pathway to undergraduate research, all these desires gave life to the pages here.
This book exposes students to stimulating and enlightening proofs and hard problems of classical analysis mainly published in the Mathematical Association of America Monthly.
The author presents proofs as a form of exploration rather than just a manipulation of symbols. Drawing on the papers from the MAA journals, numerous conceptually clear proofs are offered. Each proof provides either a novel presentation of a familiar theorem or a lively discussion of a single issue, sometimes with multiple derivations.
The book collects and presents problems to promote creative techniques for problem-solving and undergraduate research and offers instructors an opportunity to assign these problems as projects. This book provides a wealth of opportunities for these projects.
Each problem is selected for its natural charm?the connection with an authentic mathematical experience, the origination from the ingenious work of professionals, and ready developments into well-shaped results of broader interest.
Preface
Chapter1: Sequences
Chapter2: Infinite Numerical Series
Chapter 3: Continuity
Chapter 4: Differentiation
Chapter 5: Integration
Chapter 6: Sequences and Series of Functions
Chapter 7: Improper and Parametric Integration
Appendix A: A List of Problems from MAA
Bibliography
Index
Copyright Year 2023
ISBN 9781032390178
December 23, 2022 Forthcoming by CRC Press
608 Pages 290 B/W Illustrations
This book introduces differential geometry and cutting-edge findings from the discipline by incorporating both classical approaches and modern discrete differential geometry across all facets and applications, including graphics and imaging, physics and networks.
With curvature as the centerpiece, the authors present the development of differential geometry, from curves to surfaces, thence to higher dimensional manifolds; and from smooth structures to metric spaces, weighted manifolds and complexes, and to images, meshes and networks. The first part of the book is a differential geometric study of curves and surfaces in the Euclidean space, enhanced while the second part deals with higher dimensional manifolds centering on curvature by exploring the various ways of extending it to higher dimensional objects and more general structures and how to return to lower dimensional constructs. The third part focuses on computational algorithms in algebraic topology and conformal geometry, applicable for surface parameterization, shape registration and structured mesh generation.
The volume will be a useful reference for students of mathematics and computer science, as well as researchers and engineering professionals who are interested in graphics and imaging, complex networks, differential geometry and curvature.
Section I Differential Geometry, Classical and Discrete 1. Curves 2. Surfaces: Gauss Curvature ? First Definition 3. Metrization of Gauss Curvature 4. Gauss Curvature and Theorema Egregium 5. The Mean and Gauss Curvature Flows 6. Geodesics 7. Geodesics and Curvature 8. The Equations of Compatibility 9. The Gauss-Bonnet Theorem and the Poincare Index Theorem 10. Higher Dimensional Curvatures 11. Higher Dimensional Curvatures 12. Discrete Ricci Curvature and Flow 13. Weighted Manifolds and Ricci Curvature Revisited Section II Differential Geometry, Computational Aspects 14. Algebraic Topology 15. Homology and Cohomology Group 16. Exterior Calculus and Hodge Decomposition 17. Harmonic Map 18. Riemann Surface 19. Conformal Mapping 20. Discrete Surface Curvature Flows 21. Mesh Generation Based on Abel-Jacobi Theorem Section III Appendices 22. Appendix A 23. Appendix B 24. Appendix C
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Copyright Year 2023
ISBN 9781032363615
362 Pages
The subjects described in this book are BCC-algebras and an even wider class of weak BCC-algebras. The aim of the book is to summarize the achievements to date in the subject and to present them in the form of a logically created theory. Through appropriate grading and a precise description of the steps of the proofs, this theory is easily assimilated, and it should not take too long for the reader to learn about it.
We begin with the motivation for their creation, many examples and basic results used later in the book. Then we deal with the constructions of BCC-algebras and calculate the numbers of their subalgebras.
The author describes the so-called solid weak BCC-algebras. They have some properties of BCI-algebras, but this requires completely new, often difficult, proofs. The important subclasses of weak BCC-algebras and the relationships between them are presented with many examples.
BCC-Algebras is intended for researchers dealing with abstract algebra and for logicians working on the border between logic and algebra. The book is also of interest to students interested in the theory of (weak) BCC-algebras or simply in abstract algebra.
The structure of the book makes it possible to discover topics that require further research, which, depending on the degree of difficulty, may be completed with a thesis or dissertation.
Preface
1 BCC-Algebras - Introduction
1.1 Basic Definitions and Facts
1.2 Constructions of BCC-Algebras
1.3 Estimating the Number of Subalgebras
2 Special Objects in Weak BCC-Algebras
2.1 Atoms
2.2 Branches
2.3 BCC-
2.4 Congruences
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ISBN: 978-1-119-69695-7
November 2022
288 Pages
A rigorous presentation of different expansion and semi-analytical methods for fractional differential equations
Fractional differential equations, differential and integral operators with non-integral powers, are used in various science and engineering applications. Over the past several decades, the popularity of the fractional derivative has increased significantly in diverse areas such as electromagnetics, financial mathematics, image processing, and materials science. Obtaining analytical and numerical solutions of nonlinear partial differential equations of fractional order can be challenging and involve the development and use of different methods of solution.
Computational Fractional Dynamical Systems: Fractional Differential Equations and Applications presents a variety of computationally efficient semi-analytical and expansion methods to solve different types of fractional models. Rather than focusing on a single computational method, this comprehensive volume brings together more than 25 methods for solving an array of fractional-order models. The authors employ a rigorous and systematic approach for addressing various physical problems in science and engineering.
Covers various aspects of efficient methods regarding fractional-order systems
Presents different numerical methods with detailed steps to handle basic and advanced equations in science and engineering
Provides a systematic approach for handling fractional-order models arising in science and engineering
Incorporates a wide range of methods with corresponding results and validation
Computational Fractional Dynamical Systems: Fractional Differential Equations and Applications is an invaluable resource for advanced undergraduate students, graduate students, postdoctoral researchers, university faculty, and other researchers and practitioners working with fractional and integer order differential equations.