Format: Hardback, 231 pages, height x width: 235x155 mm, 11 Illustrations, color;
4 Illustrations, black and white; XIV, 231 p. 15 illus., 11 illus. in color.
Series: Mathematical Physics Studies
Pub. Date: 20-May-2025
ISBN-13: 9783031823183
This book offers a comprehensive exploration of contemporary intersections between geometry, topology, and theoretical physics, emphasizing their mathematical foundations and applications. Originating from lectures presented by experts during two summer schools held in Villa de Leyva, Colombia, the book reflects the synergy between global analysis, operator algebras, and their role in modern physics.
The chapters present state-of-the-art developments on a wide range of topics: the geometry and topology of foliations, affine manifolds, C*-algebras, and the pseudo-differential calculus of boundary value problems. These are enriched by applications to the theory of topological quantum matter.
The book is suitable for graduate students and researchers, offering detailed introductions to advanced topics such as the longitudinal index theorem for foliations, the geometry of the Poincare half-space in a C*-algebra, and mathematical frameworks for topological matter. With a balance of foundational material and novel insights, it serves as both a learning resource and a reference for advanced studies at the intersection of mathematics and physics.
Geometric structures, invariants and their uses in physics by A. Cardona
and A.F. Reyes-Lega.- . Lectures on the Euler characteristic of affine
manifolds by Camilo Arias-Abad and Sebastian Velez-Vasquez.- Elliptic Curves
by Philip Candelas.- The arithmetic of Calabi-Yau varieties, by Xenia de la
Ossa.- Foliations and operator algebras by Georges Skandalis.-
Pseudo-differential operators on groups and nonharmonic analysis, by Michael
Ruzhansky.- Mathematical Foundations of Topological Matter, by Manuel Asorey.
Format: Hardback, 556 pages, height x width: 235x155 mm, X, 556 p., 1 Hardback
Series: Infosys Science Foundation Series
Pub. Date: 27-Mar-2025
ISBN-13: 9789819628179
This book attempts to present a comprehensive survey of the geometry of CR-submanifolds. The theory of submanifolds is one of the most interesting topics in differential geometry. The topic is introduced by Aurel Bejancu as a generalization of holomorphic and totally real submanifolds of almost Hermitian manifolds, in 1978. Afterward, the study of CR-submanifolds became a very active research subject.
Organized into 22 chapters, the book starts with basic knowledge of Riemannian manifolds and submanifolds, almost Hermitian manifolds and their subclasses, Hopf fibration, symmetric spaces, and a general inequality for submanifolds in complex space forms (in Chaps. 1 and 2). Later, it presents the main results on CR-submanifolds in Kaehler manifolds, the basic inequalities associated with CR-submanifolds in Kaehler manifolds, and several theories and results related to Kaehler manifolds (in Chaps. 311). Further, the book discusses the basics of almost-contact metric manifolds and their subclasses, CR-submanifolds of Sasakian, trans-Sasakian and quasi-Sasakian manifolds, with a particular attention on the normal CR-submanifolds (in Chap. 12). It also investigates the contact CR-submanifolds of S-manifolds, the geometry of submersions of CR-submanifolds, and the results on contact CR-warped product submanifolds (in Chaps. 1618, 20). In Chapter 19, we discuss submersions of CR-submanifolds. The book also presents some recent results concerning CR-submanifolds of holomorphic statistical manifolds. In particular, it gives the classification of totally umbilical CR-statistical submanifolds in holomorphic statistical manifolds, as well as a ChenRicci inequality for such submanifolds (Chapter 21). In the last chapter, we present results on CR-submanifolds of indefinite Kaehler manifolds and their applications to physics.
Chapter 1 Basics on Manifolds and Submanifolds.-
Chapter 2 Basics on almost Hermitian manifolds and their subclasses.
Chapter 3 CR-submanifolds of KOahler manifolds.
Chapter 4 Inequalities for CR-submanifolds in Kahler manifolds.-
Chapter 5 CR-warped products in Kahler manifolds.
Chapter 6 CR-submanifolds of locally conformal Kahler manifolds.
Chapter 7 CR-submanifolds of quaternion Kahler manifolds.
Chapter 8 CR-submanifolds of nearly Kahler manifolds.
Chapter 9 CR-submanifolds of quasi-Kahler manifolds.
Chapter 10 Generic submanifolds of nearly Kahler manifolds.-
Chapter 11 Generic submanifold of locally conformal Kahler manifolds.-
Chapter 12 Basics of almost contact metric manifolds and their subclasses.-
Chapter 13 Contact CR-submanifolds of trans-Sasakian manifolds.-
Chapter 14 CContact CR-submanifolds of nearly Sasakian manifolds.-
Chapter 15. Contact CR-submanifolds of nearly trans-Sasakian manifolds.
Chapter 16 Contact CR-submanifolds of quasi-Sasakian manifolds.-
Chapter 17 Contact CR-submanifolds of ??-manifolds.
Chapter 18. Generic submanifolds of manifolds equipped with almost contactmetric structures.
Chapter 19. Submersion of CR-submanifolds.
Chapter 20 Contact CR-warped product submanifolds.
Chapter 22 CR-submanifolds of indefinite KOahler manifolds and applications.
Format: Hardback, 222 pages, height x width: 240x168 mm, 39 Illustrations, color;
1 Illustrations, black and white; XVI, 222 p. 40 illus., 39 illus. in color.,
Series: Synthesis Lectures on Mathematics & Statistics
Pub. Date: 16-Apr-2025
ISBN-13: 9783031819230
This Second Edition is an essential guide to understanding, modeling, and predicting complex dynamical systems using new methods with stochastic tools. Expanding upon the original book, the author covers a unique combination of qualitative and quantitative modeling skills, novel efficient computational methods, rigorous mathematical theory, as well as physical intuitions and thinking. The author presents mathematical tools for understanding, modeling, and predicting complex dynamical systems using various suitable stochastic tools. The book provides practical examples and motivations when introducing these tools, merging mathematics, statistics, information theory, computational science, and data science. The author emphasizes the balance between computational efficiency and modeling accuracy while equipping readers with the skills to choose and apply stochastic tools to a wide range of disciplines. This second edition includes updated discussion of combining stochastic models with machine learning and addresses several additional topics, including importance sampling, regression, and maximum likelihood estimate. The author also introduces a new chapter on optimal control.
Stochastic Toolkits.- Introduction to Information Theory.- Basic
Stochastic Computational Methods.- Simple Gaussian and Non-Gaussian SDEs.-
Data Assimilation.- Optimal Control.- Prediction.- Data-Driven Low-Order
Stochastic Models.- Conditional Gaussian Nonlinear Systems.- Parameter
Estimation with Uncertainty Quantification.- Combining Stochastic Models with
Machine Learning.- Instruction Manual for the MATLAB Codes.
Format: Paperback / softback, 221 pages, height x width: 235x155 mm,
43 Illustrations, black and white; VIII, 221 p. 43 illus.,
Series: Compact Textbooks in Mathematics
Pub. Date: 16-Apr-2025
ISBN-13: 9783031825088
This textbook is designed for a first course in ring theory, module theory and category theory. Written following several decades of teaching experience, it stands out with its clear and engaging style, featuring thorough explanations and attention to detail. Carefully selected exercises encourage active learning and problem-solving.
The textbook integrates elementary category theory with basic concepts and examples developed throughout the course. Although the primary focus is on rings and modules, relevant notions for other algebraic structures, such as groups and semigroups, are also discussed. Thus, this book aims at introducing students to noncommutative rings and modules within a broader algebraic context.
Aimed at advanced undergraduates or master students in mathematics, this textbook is suitable both for use in the classroom and self-study. Whereas the first part of the book covers a basic course in ring and module theory, the latter part includes optional deepening topics.
- 1. Basic Notions.- 2. Some Classes of Modules.- 3. Right Artinian
Rings.- 4. Local Rings, Injective Modules, Flat Modules.- 5. Additive
Categories, Abelian Categories.- 6. Appendices.
Format: Hardback, 201 pages, height x width: 254x178 mm, 191 Illustrations, color;
123 Illustrations, black and white; XVII, 201 p. 314 illus., 191 illus. in color.,
Pub. Date: 04-Apr-2025
ISBN-13: 9783031777677
This book examines Florence Nightingale David's life, contributions, and relationships throughout her life, as well as her subsequent legacy. Florence Nightingale David (1909-1993) was the first woman professor in the world's first academic statistics department, served in various British ministries during the war from 1939-1945, and was one of the first women to chair a statistics department in a research university.
In this biography, the life stories of David are used as a vehicle to explore a variety of questions surrounding culture and engagement in the statistical sciences. What does it take to succeed in an environment that is not inclusive of your demographic? How can stories be used to bring technical material to life for students and other learners? And how can a nontraditional leader succeed in challenging boundaries and moving an enterprise forward?
Introduction.- Part I At the Glass Ceiling.
Chapter 1 Deserving 1955-1957).- Part II Up the Hill.
Chapter 2 Growing (1909-1928).
Chapter 3 Learning (1928-1931).- Part III In the Trenches.
Chapter 4 Rising (1931-1938).
Chapter 5 Serving (1939-1946).- Part IV Up the Ladder.
Chapter 6 Renewing (1946-1957).
Chapter 7 Transitioning (1957-1967).- Part V In the New World.
Chapter 8 Arriving (1967-1974).
Chapter 9 Leading (1973-1977).-Part VI Down the Memory Lane.
Chapter 10 Remembering.
Chapter 11 Ending (1977-).- Part VII Over the Lifetime.
Chapter 12 Summarizing.
Format: Hardback, 442 pages, height x width: 235x155 mm, 53 Illustrations, color;
33 Illustrations, black and white; XXV, 442 p. 86 illus., 53 illus. in color.,
Pub. Date: 04-May-2025
ISBN-13: 9789819620036
This book contains select chapters on a range of topics in directional statistics, multivariate statistical inference, financial statistics, statistical machine learning and reliability inference. At the 43rd Annual Convention of the Indian Society for Probability and Statistics (ISPS) held in Prayagraj (formerly Allahabad), Uttar Pradesh, India, from 68 February 2024, attribute was paid to Prof. Ashis SenGupta on the occasion of his 70th birthday. He has pioneered research on directional statistics in the modern era in India and enhanced it worldwide and contributed significantly to the advancement of the following topics:
Highly flexible distributions on manifolds Statistical machine learning in data science Big data on manifolds Optimal multiparameter, multivariate statistical inference Reliability inference and stress-dependent-strength models Directional statistics for highly volatile financial models Cylindrical, spherical and toroidal regression analysis Innovative applications of emerging real-life directional data
This book contains select chapters on a range of topics in directional statistics, multivariate statistical inference, financial statistics, statistical machine learning and reliability inference. At the 43rd Annual Convention of the Indian Society for Probability and Statistics (ISPS) held in Prayagraj (formerly Allahabad), Uttar Pradesh, India, from 68 February 2024, attribute was paid to Prof. Ashis SenGupta on the occasion of his 70th birthday. He has pioneered research on directional statistics in the modern era in India and enhanced it worldwide and contributed significantly to the advancement of the following topics:
Chapter 1 Circular Data Diagnostics in Regression and Time Series Models.
Chapter 2 The Weighting Approach on the Circle.
Chapter 3 Isotonic Regression Estimators for Simultaneous Estimation of Order Restricted
Location/Scale Parameters of a Bivariate Distribution: A Unified Study.