Format: Paperback / softback, 496 pages, height x width: 235x155 mm, 1 Illustrations, color; 3 Illustrations, black and white
Series: Lecture Notes in Mathematics
Pub. Date: 08-Nov-2026
ISBN-13: 9783032271020
This volume develops the structural theory of oneparameter semigroups of positive operators on ordered Banach spaces, addressing the fundamental problem of characterizing their generators, spectral properties, and asymptotic behavior. Such semigroups form a central analytical framework for models arising in partial differential equations, probability theory, ergodic theory, and mathematical physics.
Since its first publication in 1986, the book has become a foundational reference, offering a rigorous and unified treatment of positivity, Banach lattices, and semigroup theory. The exposition covers Banach spaces, Banach lattices, C(X) spaces, and operator algebras, with a systematic focus on generator theory, spectral analysis, and longtime behavior.
This second edition preserves the original conceptual framework and organization while presenting the entire text in a fully revised and professionally typeset form. Misprints have been corrected, references updated, and a new chapter of notes surveys key developments of the past four decades, placing the original results in a modern context without compromising their historical coherence. The book remains an essential resource for researchers and advanced graduate students in operator theory and functional analysis.
Part I. One-parameter Semigroups on Banach Spaces.
Chapter 1. Basic results on Semigroups on Banach Spaces.
Chapter 2. Characterization of Semigroups on Banach Spaces.
Chapter 3. Spectral Theory.
Chapter 4. Asymptotics of Semigroups on Banach Spaces.- Part II. Positive
Semigroups on Spaces C0 (X).
Chapter 5. Basic results on Spaces C0 (X).
Chapter 6 Characterization of Positive Semigroups on C0 (X).
Chapter 7. Spectral Theory of Positive Semigroups on C0 (X).
Chapter 8. Asymptotics of Positive Semigroups on C0 (X).- Part III. Positive
Semigroups on Banach Lattices.-
Chapter 9. Basic Results on Banach Lattices and Positive Operators.
Chapter 10. Characterization of Positive Semigroups on Banach Lattices.
Chapter 11 Spectral Theory on Banach Lattices.
Chapter 12. Asymptotics of Positive Semigroups on Banach Lattices.- Part
IV. Positive Semigroups on C*- and W*-Algebras.
Chapter 13. Basic Results on Semigroups and Operator Algebras.-
Chapter 14. Characterization of Positive Semigroups on W*-Algebras.
Chapter 15. Spectral theory of Positive Semigroups on W*-algebras and their
Preduals.
Chapter 16. Asymptotics of Positive Semigroups on C*-and W*-Algebras.
Format: Paperback / softback, 158 pages, height x width: 240x168 mm, VIII, 158 p.
Series: Frontiers in Mathematics
Pub. Date: 09-Sep-2026
ISBN-13: 9789819215683
This book presents a comprehensive and focused attempt to derive key properties of multidimensional, or multi-index, Chebyshev polynomials by using generalized Hermite polynomials as a foundational tool. It demonstrates how multi-index Hermite polynomials can be employed to construct multidimensional Chebyshev polynomials of both the first and second kinds. Through symbolic and integral techniques, including a formal treatment of the Laplace transform, the book investigates various generalizations of these polynomial families. Emphasizing multi-index formulations, it explores these polynomials through a symbolic framework involving suitable integral transforms by leveraging the Laplace transforms. Key operational techniques are developed and applied to deepen conceptual understanding and navigate the formal structures underpinning various derived relationships.
The discussion is highlighted in applications inspired by real-world physical problems. Multi-index Hermite polynomials are examined in the context of quantum optics to model both coherent and incoherent radiation field distributions. Multidimensional systems coupled through electromagnetic radiation are addressed, alongside related wave propagation phenomena. Higher-order Laguerre polynomials are utilized to compute statistical moments of chaotic radiation, while multidimensional Bessel functions are explored for their role in laser theory. Traditional applications of Chebyshev polynomials in approximation theory are also revisited, providing a bridge between classic and contemporary mathematical approaches.
The content of the book is designed into three parts, each addressing a distinct facet of the subject. Part I is devoted to the algebraic theory of general set-theoretic solutions to the YangBaxter equation, with particular emphasis on skew left braces and RotaBaxter groups. Part II presents a detailed treatment of the algebraic theory of racks and quandles. Part III, the most advanced part of the book, is concerned with the homology and cohomology theories associated with solutions to the YangBaxter equation. From the point of view of logical dependency, Parts I and II are largely self-contained and may be read independently, while Part III builds upon foundational concepts introduced in the earlier parts.
Chapter 1 Generalized Two-variable Hermite Polynomials.
Chapter 2 Multi-index Hermite Polynomials.
Chapter 3 Orthogonal Hermite Functions.-
Chapter 4 Chebyshev Polynomials and Integral Representations.
Chapter 5 Generalized Two-variable Chebyshev Polynomials.
Chapter 6 Chebyshev-like Polynomials.
Format: Hardback, 257 pages, height x width: 235x155 mm, IV, 257 p.
Series: Association for Women in Mathematics Series
Pub. Date: 14-Sep-2026
ISBN-13: 9783032292940
This book assembles new research from the field of computational topology, a cutting-edge area emerging on the boundary between computer science and mathematics. Topics range over the breadth of the discipline, from surface reconstruction to persistent homology and its applications. Chapters are accessible to a broad range of researchers, both in the field of computational topology as well as in other related disciplines (e.g., statistics, computational biology, machine learning).
This book highlights research that was initiated at WinCompTop 2023, a workshop held in July 2023 at the EPFL, where 25 women in the field of computational topology gathered to work on research problems. Additional contributions were also solicited from the broader Women in Computational Topology network.
Preface.- Introduction.- Decompositions of the persistent homology
transform.- Multilevel sparsification of higher-order data.- Studying
self-similarity of complex networks with persistent magnitude.- Probabilistic
Behavior of Prefalence-Augmented Barcodes.- Connections between dynamic
programming and directed topology.- Bibliography.- Index.
Format: Paperback / softback, 541 pages, height x width: 235x155 mm, 1 Illustrations, black and white
Series: Mathematics Study Resources
Pub. Date: 09-Sep-2026
ISBN-13: 9783662738245
This book is a guide for self-study of mathematics as a scientific discipline. It addresses a diverse audience: young people interested in gaining a deeper understanding of the material presented in school, teachers who run math clubs and are looking for material that connects to the school curriculum, university members curious about an alternative perspective on mathematics as a field of study, professionals from other disciplines who have a basic mathematical background and wish to deepen their understanding of mathematics.
This book assumes an intuitive grasp of natural numbers and solid mastery of the calculation techniques taught in lower secondary school. Starting from elementary problems in enumerative combinatorics, it first offers a systematic description of the natural numbers. Considerations on solving equations then lead, step by step, to the introduction of real numbers. This enables the development of powerful concepts for modeling distances and other quantities such as areas and volumes. The study of systems of equations further introduces the concepts of vector space and linearization, which allow computations through linear approximation.
In this way, this book conveys the fundamental content of the first three to four semesters of a mathematics degree program. It deliberately avoids the usual division into separate subjects such as Linear Algebra, Analysis, or Probability. Instead, the problems arise from questions about mathematical modeling or from interesting mathematical ideas.
This book is a translation of the original German edition, enriched with exercises and solutions. The translation was done with the help of an artificial intelligence machine translation tool. A subsequent human revision was done primarily in terms of content, so that this book may read stylistically differently from a conventional translation.
Counting and Numbers.- Linear Computation.- Distance and
Neighborhoods.- Measures and Integrals.- Linear Approximation.
Format: Hardback, 454 pages, height x width: 235x155 mm, 11 Illustrations, color; 1 Illustrations, black and white
Series: Mathematics in Mind
Pub. Date: 09-Sep-2026
ISBN-13: 9783032307200
This text, structured in two parts, presents a distinctive pedagogical approach to the foundations of mathematics by treating the subject as a formal language to be learned. Its central thesis is that mastery of modern mathematics, logic, and computer science requires fluency in a precise and structured mode of thinkingan architecture of thought grounded in a rigorous and expressive language. The book develops a method for learning mathematical language in a way aligned with contemporary foreign language pedagogy, enabling readers to interpret mathematical texts with clarity and precision while gaining insight into their underlying patterns, structures, capabilities, and limitations. In doing so, it bridges the gap between intuitive understanding and formal rigor, complementing standard courses in logic, set theory, algebra, and philosophy.
The text includes approximately 190 exercises of varying difficulty, each accompanied by detailed solutions to support independent study and self-assessment. It also explicitly connects the formal language of mathematics with the operational logic of artificial intelligence. Undergraduate students in mathematics, computer science, philosophy, and linguisticsas well as graduate students seeking a clear and structured review of foundational conceptswill find the book a valuable contribution to their understanding of mathematical formalism. Those interested in the logical principles underlying computer science and AI will likewise find it an engaging resource for deepening their grasp of formal structures.
Part I, The Ascent, serves as a conceptual and intuitive guide, using the metaphor of language acquisition levels (A1 to C1) to develop understanding from the basic syntax of mathematical expressions (the Matryoshka principle) to advanced ideas in formal logic and set theory, enriched by analogies, historical context, and philosophical motivation. Part II, Proof-Theoretical Basis, provides the rigorous definitions and proofs underpinning these concepts, completing the transition from intuition to formal precision.
Preface.- List of Key Theorems.- I The Ascent.- Survival.- The Threshold
of logic.- Formal Logic.- The Foundations of Mathematics.- A mathematician's
paradise.- II Proof-Theoretical Basis.- Language.- Logic.- Arithmetic.- Set
Theory.- Answers to exercises.- References.- List of Notations.- Index.
Format: Hardback, 249 pages, height x width: 235x155 mm, XVI, 249 p.
Series: Springer Series in Computational Mathematics
Pub. Date: 15-Aug-2026
ISBN-13: 9789819213344
This book provides an accessible yet rigorous introduction to the mathematical analysis of finite element methods (FEMs), which serve as powerful computational tools supported by solid mathematical foundations. FEMs are built on weak or variational formulations of differential equations and on piecewise polynomial approximations, making them particularly effective for boundary value problems of elliptic partial differential equations.
While many books address the mathematical theory of FEMs, they are often written at a level that is difficult for beginners, especially students in engineering. This book aims to bridge that gap by presenting the most essential and fundamental aspects of FEM analysis in a concise and self-contained manner without compromising mathematical depth. To maintain clarity and focus, the discussion is limited to one- and two-dimensional differential equations, and the finite elements considered are among the simplest. The bibliography is deliberately selective, referring mainly to classical and representative works.
The first part of the book introduces the mathematical foundations of FEMs through the analysis of the two-dimensional Poisson equation. These chapters are suitable for undergraduate students and are designed to provide a clear overview of the subject. Chap. 1 offers a short introductory course from a strict mathematical viewpoint, giving readers a broad perspective on the field.
The subsequent chapters develop weak formulations of 2D Poisson boundary value problems, their simplest finite element approximations, and corresponding error estimates. In the later part of the volume, the focus shifts to saddle-point type approximation problems, which play important roles in areas such as fluid mechanics, solid mechanics, and electromagnetism. Topics on hypercircle method and eigenvalue estimation are also included to enrich the reader's understanding.
Finally, the appendices present essential notations and theorems used throughout the book, often in their simplest and most illustrative forms. This structure enables beginners to approach FEMs with confidence while still offering specialists a mathematically sound and meaningful treatment.
Part 1 Fundamentals.
Chapter 1 Analysis of FEM for 1D model problem.-
Chapter 2 Weak formulations of 2D Poisson's boundary value problems.
Chapter 3 Analysis of P_1 and Q_1 finite elements.- Part 2 Advanced study of FEM's.-
Chapter 4 Non-conforming FEM.
Chapter 5.- Mixed methods based on saddle-point type weak formulation.
Chapter 6 Eigenvalue problems for Laplace operator.- Part 3 Miscellaneous topics.
Chapter 7 Finite elements for incompressible or nearly incompressible media.
Chapter 8 Edge element approximation for computational electromagnetism.
Chapter 9 Quasi-hypercircle method for Poisson's equation.
Format: Hardback, 362 pages, height x width: 235x155 mm, 1 Illustrations, color; 1 Illustrations, black and white
Pub. Date: 29-Aug-2026
ISBN-13: 9789819212347
Analysis on manifolds has become one of the most dynamic and influential areas of modern mathematics, driving breakthroughs in geometry, partial differential equations, and mathematical physics, while increasingly shaping fields such as statistics, data science, and artificial intelligence. This book offers a clear and engaging introduction to the powerful analytic and geometric techniques that have defined the subjectfrom Yaus gradient estimates and the LiYau differential Harnack inequality to the SacksUhlenbeck blowup method and contemporary geometric flows.
Spanning seven cohesive chapters, the book blends foundational theory with modern developments, guiding readers through heat kernel analysis, harmonic map theory, minimal surfaces, and geometric flows. The final chapters showcase new results arising from the authors recent collaborations, highlighting cuttingedge progress on symplectic critical surfaces and mean curvature flows.
Accessible yet rigorous, this book is ideal for researchers and advanced students seeking both a solid grounding in geometric analysis and a window into current research at the forefront of the field.
Elliptic equations on Riemannian manifolds.- Heat kernel on Riemannian
manifolds and its applications.- Harmonic maps.- Heat flows.- Minimal
surfaces.- -symplectic critical surfaces.- Mean curvature flows.-
AppendixComparison theorems in Riemannian geometry.
Format: Hardback, 190 pages, height x width: 235x155 mm, 60 Illustrations, color; 3 Illustrations, black and white
Series: Springer INdAM Series
Pub. Date: 16-Sep-2026
ISBN-13: 9789819211210
The volume aims at creating a closer connection for the researchers devoted to the mathematical and numerical study of the vascular and cardiac systems in order to provide a scientific exchange of the recent developments on such topics, including modern emerging ones like scientific machine learning and high performance computing. The volume contains contributions from leading experts in computational physiology, numerical analysis, applied mathematics, and scientific computing, with the objective of reviewing recent advances in cardiovascular modeling and exploring new methodological frontiers. The chapters included here reflect the scientific quality and interdisciplinary breadth of the discussions that took place during the meeting. The works collected in this volume highlight the essential role of mathematical and numerical modeling in understanding cardiovascular dynamics, improving computational methods for physiological simulation, and supporting clinically relevant applications. The contributions range across reduced-order modelling, data assimilation, boundary conditions in haemodynamics, cardiac electrophysiology, heterogeneous tissue modelling, high-performance computing simulation, and patient-specific computational methodologies.
A Review of Equation-Based and Data-Driven Reduced Order Models
featuring a Hybrid cardiovascular application.- Predicting Boundary
Conditions in Hemodynamic Models via Stochastic Filtering Techniques.- On the
choice of proper outlet boundary conditions for numerical simulation of
cardiovascular flows.- Twins in Coronary Artery Disease: A Mathematical
Roadmap.- Advanced Bidomain Framework for Drug Testing in Heterogeneous
Cardiac hiPSC Tissues.- A comparison of parallel algebraic multigrid solvers
for the cardiac EMI model.- Computerized Modeling of Electrophysiology and
Pathoelectrophysiology of the Atria How Much Detail is needed?.- Numerical
Modeling and Simulation of Transcatheter Aortic Valve Implantation.- A
Scalable and Efficient Parallel Simulation Framework for Patient-Specific
Brugada Syndrome Arrhythmia Modeling.