Format: Hardback, 424 pages, height x width: 235x155 mm, Approx. 425 p., 1 Hardback
Series: Latin American Mathematics Series UFSCar subseries
Pub. Date: 27-Aug-2025
ISBN-13: 9783031962813
This textbook explores differential geometrical aspects of the theory of completely integrable Hamiltonian systems. It provides a comprehensive introduction to the mathematical foundations and illustrates it with a thorough analysis of classical examples.
This book is organized into two parts. Part I contains a detailed, elementary exposition of the topics needed to start a serious geometrical analysis of complete integrability. This includes a background in symplectic and Poisson geometry, the study of Hamiltonian systems with symmetry, a primer on the theory of completely integrable systems, and a presentation of bi-Hamiltonian geometry.
Part II is devoted to the analysis of three classical examples of integrable systems. This includes the description of the (free) n-dimensional rigid-body, the rational Calogero-Moser system, and the open Toda system. In each case, ths system is described, its integrability is discussed, and at least one of its (known) bi-Hamiltonian descriptions is presented.
Part I: Preliminary material.- Symplectic Geometry.- Elements of Poisson
Geometry.- Hamiltonian G-actions and the Marsden-Weinstein-Meyer reduction.-
Lagrangian fibrations and integrable systems.- Elements of Bi-Hamiltonian
Geometry.- Bibliographical Notes.- Part II: A Sample of Classical Integrable
Systems.- Rigid bodies.- The Toda System.- Calogero-Moser Systems.- Appendix
A: Elements of Symplectic Linear Algebra.- Appendix B: Elements of
Differential Geometry.- Appendix C: Lie Groups, Lie Algebras, and Fiber
Bundles.- Appendix D: Cotangent Lifts.- Bibliography.- Index.
Format: Hardback, 325 pages, height x width: 235x155 mm, 76 Illustrations, color; 5 Illustrations, black and white; XII, 325 p. 81 illus., 76 illus. in color., 1 Hardback
Series: Trends in Mathematics
Pub. Date: 12-Sep-2025
ISBN-13: 9783031905094
This volume features selected contributions from participants of the 17th African Conference on Research in Computer Science and Applied Mathematics (CARI 2024), held at the University of Beja?a, Algeria, from November 23-26, 2024. The topics covered include mathematical modelling, stochastic methods, and related fields.
A Note on Additive Model Building for Spatial Functional Regression.-
Quadratic Programming Problems with Preprocessing and a Diagonally Dominant
M-matrix.- Beta Prime Kernel Availability Density Estimation of a Repairable
Series System.- Imperfect maintenance of series systems.- Performance
Evaluation of a Web services.- Modeling and analysis of Covid19 patients
hospitalization dynamic reliability by a semi-Markovian model.- Combinatorial
optimization of banana clean reliance.- Adaptive Refined Descriptive Sampling
Algorithm for Dependent.- variables using Iman and Conover method in Monte
Carlo simulation.- Linear Control Design for Synchronization of Fractional
Predator-Prey.- Systems with Group Defense and Harvesting.- Fractional
dynamics of a Cholera model with Atangana-Baleanu operator.- Fractional-order
dynamics of a Typhoid epidemic model.- A model of plasmid-bearing,
plasmid-free competition in a chemostat.- On a slow-fast SEIRS Model
structured in age.- Global asymptotic stability for a predator-prey model.-
The operating diagram of an SIS model in the chemostat.- On a competition
model of two toxin-producing species in the chemostat.
Format: Hardback, 225 pages, height x width: 235x155 mm, Approx. 225 p., 1 Hardback
Series: Applied and Numerical Harmonic Analysis
Pub. Date: 27-Aug-2025
ISBN-13: 9783031955501
Over the course of his distinguished career, Edward Saff has made a number of groundbreaking contributions in the fields of approximation theory, potential theory, and complex analysis. The chapters in this volume ? compiled on the occasion of his 80th birthday ? are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements
Ed Saff at 80: Career and Distinguished Scientific Contributions.
.- Exponential bases on modified domains.
.- Positive definite singular kernels on two-point homogeneous spaces.
.- HOormander and Bernhardssons extremal function I.
.- Absolute Minima of Potentials of a Certain Class of Spherical Designs.
.- Logarithmic and Riesz Energy on the Sphere: Better Bounds via elementary
Methods.
.- Energy of codes with forbidden distances in 48 dimensions.
.- Frequency-dependent stability for Gabor frames.
.- A nonnegative even kernel arising from extremal sine polynomials.
.- The number of real zeros of polynomials with constrained coefficients.
.- Approximate orthogonality, Bourgains pinned distance theorem, and
exponential frames.
.- Application of Sparse Grids to Approximation and Optimization.
.- Shape preserving approximation of periodic functionsA survey.
.- Spaces of trigonometric series and the Wiener algebra.
.- Variational Conditions on Extremal Orthonormal Polynomials for Restricted
Measures.
.- Behavior of bounded solutions, ??(??, ??), to the
heat equation in R?? × (0, )as ?? .
.- Weighted equilibrium and the flow of derivatives of polynomials.
.- A linear programming bound in a sign-alternating case.
.- Approximation by Fourier sums on the classes of generalized Poisson
integrals.
.- On Linear Spaces with Ideal Complements.
.- On Analytic Functions with Taylor Coefficients Taken from a Finite Set.
Format: Paperback / softback, 251 pages, height x width: 235x155 mm, 4 Illustrations, black and white; X, 251 p. 4 illus., 1 Paperback / softback
Series: Universitext
Pub. Date: 04-Sep-2025
ISBN-13: 9783031962950
This textbook offers an elementary introduction to noncommutative rings and algebras. Beginning with the classical theory of finite-dimensional algebras, it then develops a more general structure theory of rings, grounded in modules and tensor products. The final chapters cover free algebras, polynomial identities, and rings of quotients.
Many results are presented in a simplified form rather than in full generality, with an emphasis on clear and understandable exposition. Prerequisites are kept to a minimum, and new concepts are introduced gradually and carefully motivated. Introduction to Noncommutative Algebra is thus accessible to a broad mathematical audience, though it is primarily intended for beginning graduate students and advanced undergraduates encountering the subject for the first time.
This new edition includes several additions and improvements, while preserving the original texts character and approach.
Chapter 1. Finite Dimensional Division Algebras.
Chapter 2. Structure of Finite Dimensional Algebras.
Chapter 3. Modules and Semisimple Rings.-
Chapter 4. Structure of Rings.
Chapter 5. Tensor Products in Noncommutative Algebra.
Chapter 6. Noncommutative Polynomials.
Chapter 7. Rings of Quotients and Structure of PI-Rings.
Format: Hardback, 413 pages, height x width: 235x155 mm, 11 Illustrations, color; 12 Illustrations, black and white; X, 413 p. 23 illus., 11 illus. in color., 1 Hardback
Series: Trends in the History of Science
Pub. Date: 10-Sep-2025
ISBN-13: 9783031957765
This volume explores the profound impact of Felix Klein on the evolution of mathematics beyond Germany, particularly in number theory, algebra, geometry, analysis, and the application of mathematics in scientific and technical fields, as well as mathematics education. The various essays in it highlight the often-overlooked contributions of mathematicians from diverse backgrounds, including Czech, Greek, Hungarian, Japanese, Polish, Russian, and Ukrainian scholars who studied under Klein. By examining the protocols of Klein's seminars from 1872 to 1912, this book uncovers how his teachings shaped their careers. Additionally, it explores Klein's collaborative efforts with David Hilbert and their influence on international mathematical communication.
This volume is essential reading for historians of mathematics and researchers interested in the development of science and mathematics at the turn of the 20th century.
Chapter 1. Felix Kleins Vision: A School for Mathematical Productivity Regardless of Nationality, Gender, and Area of Research.-
Chapter 2. About Polish students of Felix Klein.
Chapter 3. Mathematicians from the Czech lands and Felix Klein.
Chapter 4. I have to tell you about England!: Felix Kleins influence on the research of young British mathematicians.
Chapter 5. Foreign inspiration and domestic tradition: the Gottingen-speaking mathematicians in Turin.
Chapter 6. Mellen Woodman Haskell in Leipzig and Gottingen.
Chapter 7. From Naples to Pavia, passing from Gottingen. The scientific trajectory of Ernesto Pascal and his relationship with Felix Klein.
Chapter 8. Wilhelm Wirtinger and his publications on Abelian functions, in particular theta functions.
Chapter 9. Felix Klein and his relations with Greek mathematicians as they appear in their letters.
Chapter 10. Felix Kleins first female doctoral student Grace Emily Chisholm Young A livelong connection concerning mathematical research and more.
Chapter 11. From St Petersburg to Gottingen. About Helena Bortkiewicz and Aleksandra Stebnicka.
Chapter 12. Bridging Gottingen and Tokyo: Oral Culture and the Dynamics of Mathematical Knowledge.
Chapter 13. Felix Kleins mature distance student, Encyklopadie contributor and self-declared heir: the Austrian Richard von Mises.
Chapter 14. The presence of Felix Klein in the process of modernization and internationalization of mathematical culture in Spain and Argentina.
Chapter 15. Kleins Seminars on Probability.
Chapter 16. Foreign Students in Felix Kleins Seminars.
Format: Hardback, 194 pages, height x width: 240x168 mm, 3 Illustrations, color; 3 Illustrations, black and white; X, 194 p. 6 illus., 3 illus. in color., 1 Hardback
Series: Classic Texts in the Sciences
Pub. Date: 12-Sep-2025
ISBN-13: 9783031914881
This book presents William Clifford’s English translation of Bernhard Riemann’s seminal text, accompanied by detailed mathematical, historical, and philosophical commentary. It explores Riemann’s revolutionary ideas on space, placing them within the broader framework developed by later thinkers such as Helmholtz, Ricci, Weyl, and Einstein. A historical introduction situates Riemann’s work in its 19th-century context, while subsequent chapters trace the evolution of the concept of space across philosophy, physics, and mathematics, and examine its enduring influence up to modern research.
The second edition includes expanded mathematical commentary, a new section on metric geometry and machine learning, a systematic bibliography, and numerous updates throughout.
Appealing to mathematicians, historians, and readers with an interest in physics or philosophy, this book provides a comprehensive perspective on Riemann’s groundbreaking contributions and their lasting impact.
Introduction.- Historical background.- Riemann's habilitation.-
Presentation of the texts.- Reception and impact on history.- Modern
research.- Bibliography.