Format: Hardback, 450 pages, height x width: 235x155 mm, 1 Illustrations, black and white; X, 450 p. 1 illus., 1 Hardback
Pub. Date: 04-Sep-2025
ISBN-13: 9783031953682
This book offers several topics of mathematical analysis which are closely connected with significant properties of real-valued functions of various types (such as semi-continuous functions, monotone functions, convex functions, measurable functions, additive and linear functionals, etc.). Alongside with fairly traditional themes of real analysis and classical measure theory, more profound questions are thoroughly discussed in the book appropriate extensions and restrictions of functions, oscillation functions and their characterization, discontinuous functions on resolvable topological spaces, pointwise limits of finite sums of periodic functions, some general results on invariant and quasi-invariant measures, the structure of non-measurable sets and functions, the Baire property of functions on topological spaces and its connections with measurability properties of functions, logical and set-theoretical aspects of the behavior of real-valued functions.
Chapter 1. Unary and Binary Relations.
Chapter 2. Partial Functions and Functions.
Chapter 3. Elementary Facts on Cardinal Numbers.
Chapter 4. Some Properties of the Continuum.
Chapter 5. The Oscillation of a Real-valued Function at a Point.
Chapter 6. Points of Continuity and Discontinuity of Real-valued Functions.
Chapter 7. Real-valued Monotone Functions.
Chapter 8. Real-valued Convex Functions.
Chapter 9. Semicontinuity of a Real-valued Function at a Point.
Chapter 10. Semicontinuous Real-valued Functions on Quasi-compact Spaces.
Chapter 11. The BanachSteinhaus Theorem.
Chapter 12. A Characterization of Oscillation Functions.
Chapter 13. Semicontinuity versus Continuity.
Chapter 14. The Outer Measures.
Chapter 15. Finitely Additive and Countably Additive Measures.
Chapter 16. Extensions of Measures.
Chapter 17. Caratheodorys and Marczewskis Extension Theorems.-
Chapter 18. Positive Linear Functionals.
Chapter 19. The Nonexistence of Universa Countably Additive Measures.
Chapter 20. Radon Measures.
Chapter 21. Invariant and Quasi-invariant Measures.
Chapter 22. Pointwise Limits of Finite Sums of Periodic Functions.
Chapter 23. Absolutely Nonmeasurable Setsin Commutative Groups.
Chapter 24. Radon Spaces.
Chapter 25. Nonmeasurable Sets with respect to Radon Measures.
Chapter 26. The RadonNikodym Theorem.
Chapter 27. Decompositions of Linear Functionals.-
Chapter 28. Linear Continuous Functionals and Radon Measures.
Chapter 29. Linear Continuous Functionalson a Real Hilbert Space.
Chapter 30. Baire Property in Topological Spaces.
Chapter 31. The StoneWeierstrass Theorem.-
Chapter 32. More on the Function Space C(X).
Chapter 33. Uniformization of Plane Sets by Relatively Measurable Functions.
Format: Hardback, 424 pages, height x width: 235x155 mm, 112 Illustrations, color; 5 Illustrations, black and white; XVI, 424 p. 117 illus., 112 illus. in color., 1 Hardback
Pub. Date: 12-Sep-2025
ISBN-13: 9783031936265
This book offers a first step towards getting machines to understand history in terms of analysing historical narratives. It uses computational intelligence and history texts as keys to ask different questions than have been asked about our human history so far.
The book is divided into three main parts. The first part discusses the mathematical language of history, the second part uses simple models to analyse historical laws written in mathematical language, and the third part discusses the impact of general Large Language Models (LLMs) on the study of history.
Introduction.- Asymptotics in Digital Humanities.- Function Diagrams in
Digital Humanities.- History of War.- History Through Clocks.- Networks and
Macrohistory.- Networks Microhistory.- What Is a Computational Model for
History.- History through the Core.- History after the Death of the
Witnesses.- History while the Witnesses are Still Alive.- Propaganda in
History.- Stochastic terrorism.- Historian Machine.- Information and
History.- Machine Learning and History.- Representing Historical
Information.- Fake Histor
Format: Hardback, 275 pages, height x width: 235x155 mm, 83 Illustrations, black and white; X, 275 p. 83 illus., 1 Hardback
Series: University Texts in the Mathematical Sciences
Pub. Date: 08-Sep-2025
ISBN-13: 9789819692583
This book systematically develops the theory of Metric Spaces while serving as a connection between classical Real Analysis and General Topology. It is designed for senior undergraduate and graduate students, providing formal definitions, theorems, proofs, examples, remarks, exercises, and explanatory notes. Instructors can use the numerous examples and miscellaneous results to structure their teaching approach. The book contains seven chapters, first of which lists primary results (without proofs) from the undergraduate Real Analysis course. Each subsequent chapter builds on cues from previous levels, adapting them to the context of Metric Spaces.Additionally, the book includes four appendix chapters. The first three are included to maintain the flow of discussion in the main chapters, relegating less relevant proofs to the appendices. The fourth appendix on the Cantor set is included to provide insight into this notable mathematical concept.
Chapter 1. Recollections.
Chapter 2. Basic Notions.
Chapter 3. Topology of Metric Spaces
Chapter 4. Completeness.
Chapter 5. Continuity.-
Chapter 6. Compactness.
Chapter 7. Connectedness.
Format: Hardback, 722 pages, height x width: 235x155 mm, 89 Illustrations, black and white; XVI, 722 p. 89 illus., 1 Hardback
Series: Springer Asia Pacific Mathematics Series 2
Pub. Date: 17-Oct-2025
ISBN-13: 9789819685691
This book is designed for graduate students to acquire knowledge of simplicial complexes, Dimension Theory, ANR Theory (Theory of Retracts), and related topics. These theories are connected with various elds in Geometric Topology, Algebraic Topology as well as General Topology. Except for the second half of the last chapter, this book is entirely self-contained. To make the ideas of proofs easier to understand, many proofs are illustrated with gures or diagrams. While exercises are not explicitly included, some results are provided with only sketches of proofs. Completing the proofs in detail is a good exercise for the reader. Researchers will also nd this book very helpful, as it contains many important results not presented in usual textbooks, such as dim X ~ I = dim X + 1 for a metrizable space X; the difference between small and large inductive dimensions; a hereditarily innite-dimensional space; the ANR property of locally contractible countable-dimensional metrizable spaces; an innite-dimensional space with nite cohomological dimension; a dimension-raising cell-like map; and a non-AR metric linear space. The last three subjects are linked to each other, demonstrating how deeply related the two theories are. Simplicial complexes are very useful in various elds of Topology and are indispensable for studying theories of dimension and ANR. Many textbooks deal with simplicial complexes, but none discuss in detail what is non-locally nite. For example, J.H.C. Whitehead's theorem on small subdivisions is very important, but its proof cannot be found in any other book. The homotopy type of simplicial complexes is discussed in textbooks on Algebraic Topology using CW complexes, but geometrical arguments using simplicial complexes are relatively easy. Many contents have been added to this edition to make it more comprehensive.
Preliminaries.- Metrizability, Paracompactness, and Related Properties.-
Topology of Linear Spaces and Convex Sets.- Simplicial Complexes and
Polyhedra.- Dimensions of Spaces.- Retracts and Extensors.- Cell-Like Maps
and Related Topics.
Format: Paperback / softback, 94 pages, height x width: 235x155 mm, 3 Illustrations, color; 1 Illustrations, black and white; XII, 94 p. 4 illus., 3 illus. in color., 1 Paperback / softback
Series: SpringerBriefs in Statistics
Pub. Date: 15-Sep-2025
ISBN-13: 9789819682799
This book provides a self-contained lecture on a Malliavin calculus approach to asymptotic expansion and weak approximation of stochastic differential equations (SDEs) as well as numerical methods for computing parabolic partial differential equations (PDEs). Particularly, Malliavinfs integration by parts is effectively applied to the computation schemes combined with deep learning methods. Constructions of asymptotic expansion and weak approximation are given in detail with the theoretical convergence analysis. The schemes enable efficient computation for high-dimensional SDEs and fast spatial approximation for high-dimensional parabolic PDEs without suffering from the curse of dimensionality. Moreover, the algorithms and Python codes are available with numerical examples for finance, physics, and statistics. Readers including graduate-level students, researchers, and practitioners can understand both theoretical and applied aspects of recent developments of asymptotic expansion and weak approximation.
Chapter 1. Introduction.
Chapter 2. It? calculus.
Chapter 3. Malliavin calculus.
Chapter 4. Asymptotic expansion.
Chapter 5. Weak approximation.-
Chapter 6. Application: Deep learning-based weak approximation.
Format: Hardback, 191 pages, height x width: 235x155 mm, 47 Illustrations, color; 14 Illustrations, black and white; X, 191 p. 61 illus., 47 illus. in color., 1 Hardback
Series: Trends in Mathematics 14
Pub. Date: 07-Sep-2025
ISBN-13: 9783031978562
This volume is a collection of extended abstracts authored by women mathematicians in Latin America. The contributions included span key areas such as analysis, partial differential equations, algebraic geometry, and combinatorics. Beyond the technical content, the volume reflects on the impact of women in mathematics in Latin America and forms part of the broader initiative led by the International Community of Mathematicians from Latin America (ICMAM) to foster visibility of researchers in Latin America.
This volume celebrates the role of women in advancing mathematics in Latin America.
Chapter 1. A quick dive into Celestial Mechanics.
Chapter 2. The Cage and Diameter Problems for Bipartite Biregular Graphs.
Chapter 3. A measure of financial technologies usage: A proposal for Mexico.
Chapter 4. Some theoretical foundation for protein identification through cyclic codes.-
Chapter 5. Uniqueness of the star central configuration in the 5-body problem.
Chapter 6. Uniform temperature distribution induced by an optimal domain shape.
Chapter 7. Toeplitz subshifts, equicontinuous systems and residually finite groups.
Chapter 8. Slowly non-dissipative reactiondiffusion equations with a jumping nonlinearity.
Chapter 9. A computational framework for the calculation of a polynomial invariant in spatial graphs.
Chapter 10. The Search for Rainbow 3-term arithmetic progressions: An Inspirational Journey.
Chapter 11. Dividing lines among fields.
Chapter 12. Frames in shift invariant spaces of weighted mixed Lebesgue spaces Lp,q.
Chapter 13. Cremona transformations of P3 stabilizing quartic surfaces.
Chapter 14. The density of Gabor systems in expansible locally Compact Abelian groups.
Chapter 15. Fourier optimization and consequences of the generalized Riemann hypothesis.
Chapter 16. Quantile regression in the analysis of the distribution of total monthly income.-
Chapter 17. The k-Yamabe Flow and its solitons.
Chapter 18. The continuity problem of Lyapunov exponents for measures with noncompact support.
Chapter 19. Degree conditions for trees in undirected and directed graphs.