Language: English
Published/Copyright: 2025
The book includes recent articles on various topics studied recently in Banach algebras and abstract harmonic analysis. On the Banach algebra side, the reader will find idempotents and socle of a Banach algebra; closed subspaces of a Banach space, including the classical sequence spaces, which are realized as the kernel of a bounded operator; the connection between the stable rank one and Dedekind-finite property of the algebra of operators on a Banach space; spectral synthesis properties in convolution Sobolev algebras on the real line.
The harmonic analysis side includes a generalization of the famous Beurling theorem; groups with few finite-dimensional unitary representations; relations between ideals of the Figa-Talamanca Herz algebra of a locally compact group and ideals of Figa-Talamanca Herz algebra of its closed subgroup; the tame functionals on Banach algebras and in harmonic analysis; and cancellation, factorization, and isometries in algebras on a locally compact group.
The book also includes four surveys written by leaders in the area of full sheaf cohomology theory for noncommutative C - algebras; one-parameter semigroups of bounded operators on a Banach space which are weakly continuous in the sense of Arveson.
The book offers insights from leading mathematicians on how Banach algebras and abstract harmonic analysis have developed over the last decade.
The book will be useful to mathematicians and students in many areas of mathematics.
Frontmatter
Publicly Available I
Preface V
Publicly Available VII
Kernels of bounded operators on the classical transfinite Banach sequence spaces
Max Arnott and Niels Jakob Laustsen 1
Beurling’s theorem on locally compact Abelian groups
Ali Baklouti and Mahmoud Filali 13
On idempotents and the socle of a Banach algebra
Rudi Brits, Muhammad Hassen and Francois Schulz 17
Fréchet algebras with a dominating Hilbert algebra norm
Tomasz Ciaś 29
Relations between ideals of the Figà-Talamanca Herz algebra A p ( G ) of a locally compact group G and ideals of A p ( H ) of a closed subgroup
Antoine Derighetti 59
The composition of conditional expectation and multiplication operators
Y. Estaremi 71
On the generation of Arveson weakly continuous semigroups
Jean Esterle 81
The semigroup algebra of a foundation semigroup with locally convex topologies and its Arens regularity
R. Farokhzad and M. Filali 119
Bohr compactification and Chu duality of non-Abelian locally compact groups
María V. Ferrer and Salvador Hernández 131
ℓ 1 -bases in Banach algebras and Arens irregularities in harmonic analysis
Mahmoud Filali and Jorge Galindo 143
Right cancellation, factorization, and right isometries
Mahmoud Filali and Pekka Salmi 177
On spectral synthesis in convolution Sobolev algebras on the real line
José E. Galé, María M. Martínez and Pedro J. Miana 187
Projective and free matricially normed spaces
A. Ya. Helemskii 205
Banach spaces whose algebras of operators are Dedekind-finite but they do not have stable rank one
Bence Horváth 219
Invariant complementation property and fixed-point sets on power bounded elements in the group von Neumann algebra
Anthony To-Ming Lau 229
Subspaces that can and cannot be the kernel of a bounded operator on a Banach space
Niels Jakob Laustsen and Jared T. White 241
Towards a sheaf cohomology theory for C ∗ -algebras
Martin Mathieu 249
Tame functionals on Banach algebras
Michael Megrelishvili 265
Left ideals of Banach algebras and dual Banach algebras
Jared T. White 279
Index
This book aims to highlight the latest developments in fixed point theory and functional analysis by presenting insights from renowned scientists, physicists, and mathematicians worldwide.
The book offers a comprehensive overview of the latest advancements in the field, featuring original contributions and surveys. Readers will find a wealth of useful tools and techniques to deepen their understanding of recent advances in mathematical and functional analysis, as well as their applications in physics and engineering. Each chapter highlights new research avenues, making this book an ideal resource for graduate students, faculty, and researchers seeking to expand their knowledge of fixed point theory and functional analysis, as well as their practical applications. The computational aspects in Banach and Hilbert spaces are well explored. Only a basic knowledge of analysis, topology, basic computation, and functional analysis is required to fully appreciate the material.
Explores modern tools in the theory
It has an interdisciplinary nature
It provides future trends in the area
Frontmatter
Publicly Available I
Preface V
Contents
Publicly Available VII
About the Editors
1 From Banach to Rus–Hicks–Rhoades: A history of contraction nappings
Sehie Park 1
2 On the fixed points of Hardy–Rogers and Ćirić–Reich–Rus-type interpolative cyclic contraction in b-metric spaces and rectangular b-metric spaces
Jyoti Saikia and Pradip Debnath 41
3 Hybrid-type fixed-point results on S-metric spaces
Nihal Taş and Elif Kaplan 51
4 Refinements and reverses of Jensen tensorial inequality for twice differentiable functions of selfadjoint operators in Hilbert spaces
Silvestru Sever Dragomir 69
5 Summation formulas as modular relations
N.-L. Wang, T. Kuzumaki and S. Kanemitsu 93
6 Some geometric properties on Banach lattices
Halimeh Ardakani, Yeol Je Cho and Madjid Eshaghi Gordji 109
7 The nonlinear principles and fixed-point theorems for non-self F contraction and non-expansive set-valued mappings by applying Caristi fixed-point theorem in locally complete convex spaces
George Xianzhi Yuan, Yuanlei Luo and Yeol Je Cho 149
8 On the order of convergence of a Traub-type method
Santhosh George 179
9 Some fixed-point results for expansive mappings in G-metric spaces
Nora Fetouci and Stojan Radenović 193
10 Extended Kantorovich’s results on Newton’s method for solving generalized equations on Hilbert space
Ioannis K. Argyros and Santhosh George 207
11 Integral-type Berezin radius inequalities
Vuk Stojiljković and Mehmet Gürdal 215
12 Local convergence analysis of a hybrid Gauss–Newton method under a majorant condition
Ioannis K. Argyros and Santhosh George 235
13 Extended convergence region for a family of King–Traub methods for solving nonlinear equations
Ioannis K. Argyros, Stepan Shakhno, Samundra Regmi and Halyna Yarmola 245
14 New integral inequalities for Atangana–Baleanu fractional integrals via ( h , m )-convex functions
Juan E. Nápoles Valdés and Bahtiyar Bayraktar 263
15 Analysis of fixed-point theory in the setting of non-Archimedean fuzzy-b-metric spaces
Nabanita Konwar 283
16 Fixed points of set-valued generalized rational graphic ϕ-contractive operators in semi-metric spaces
Talat Nazir and Mujahid Abbas 291
17 A new generalization of Kannan’s fixed-point theorem via simple F-contraction
Kallol Bhuyan and Pradip Debnath 307
Index 321
Bibliograph
Published ahead of schedule, this book is part of the 2026 MEMS collection and may become open access under our Subscribe to Open programme in 2026.
In this memoir, we prove the local-in-time well-posedness of thick spray equations in Sobolev spaces, for initial data satisfying a Penrose-type stability condition. This system is a coupling between particles described by a kinetic equation and a surrounding fluid governed by compressible Navier–Stokes equations. In the thick spray regime, the volume fraction of the dispersed phase is not negligible compared to that of the fluid. We identify a suitable stability condition bearing on the initial data that provides estimates without loss, ensuring that the system is well posed. This condition coincides with a Penrose condition appearing in earlier works on singular Vlasov equations. We also rely on crucial new estimates for averaging operators. Our approach allows us to treat many variants of the model, such as collisions in the kinetic equation, non-barotropic fluid or density-dependent drag force.
Pages: 350
ISBN: 978-1-80061-835-0 (hardcover)
ISBN: 978-1-80061-848-0 (softcover)
The Embodied Mind provides an overview of important developments in technology, medicine, and the sciences, whose comprehension is necessary for individuals to achieve a harmonious relationship with their environment. In addition, the critical importance of the Arts and Letters is emphasized.
The book consists of five parts. The six chapters of the first part provide an in-depth analysis of AI. The second part reviews the recent remarkable advances in immunology, cancer, and gene editing; it also presents a unified approach to the treatment of several conditions, such as heart attacks and strokes. The five chapters of the third part summarize breakthroughs in physics (without using any equations); from the huge contributions of Einstein to the discovery of the Higgs particle. The fourth part discusses fundamental unconscious processes, the critical impact of sleep, and techniques for mapping the brain. The last part uses examples of a variety of diverse areas, from space cells and schizophrenia to literature and philosophy to illustrate the importance of key concepts introduced in Ways of Comprehending.
No other book matches The Embodied Mind in its combination of breadth, depth, and interdisciplinary focus. Postgraduate researchers in each field will find cutting-edge discoveries presented with due intensity, while general readers and high school learners will be able to understand the nuances and complexities of each subject part.
Part I: Artificial Intelligence:
Artificial Intelligence
The Impact of AI on Medicine
Opportunities and Challenges
The Impact of Cognition of the Body Proper and of the Brain's Laterization
The Vital Importance of Glia Cells in Mental Functions
AI versus Human Thought
Part II: Medical Breakthroughs:
Breakthroughs in Immunology
Clinical Implications of Immunological Breakthroughs
Breakthroughs in the Fight Against Cancer
Novel Approaches to Cancer Treatment
A Unified Approach to Etiology and Treatment in Medicine
Gene Editing
Part III:
Associations and the Striking Inventiveness of Einstein
Generalization, Mathematization, Unification, and Quantum Electrodynamics
Dismantling the Atom and the Astonishing Contributions of the Cavendish Laboratory
Co-operation and the Primacy of Experimental Physics
Interdisciplinarity and the Huge Impact of Particle Physics
Part IV:
The Time-Lag in Conscious Sensory Perception and Free Will
The Impact on Health of Largely Unknown Unconscious Processes
The Crucial Importance of Sleep
Mapping the Brain
Epilogue
This book is intended for advanced undergraduate and graduate students specializing in mathematics and the mathematical sciences.
Pages: 250
ISBN: 978-1-80061-838-1 (hardcover)
ISBN: 978-1-80061-855-8 (softcover)
This book offers both a theoretical and practical introduction to Differential Calculus of several real variables, tailored for students embarking on their first semester of study in the subject. Designed especially for those in Mathematical and Physical Sciences, as well as Engineering disciplines, it assumes only a foundational understanding of single-variable calculus and basic linear algebra.
The book begins with a study of finite-dimensional Euclidean spaces, including geometry, metrics, convergence, compactness, and convexity. It then progresses to continuous and differentiable functions, exploring directional derivatives, the chain rule, vector fields, and Fréchet and Gâteaux differentials. Further chapters address higher-order derivatives, Taylor's formula, and the conditions for local extrema, before delving into essential theorems such as the Inverse and Implicit Function Theorems. The final chapter introduces differentiable manifolds and constrained optimization using Lagrange multipliers.
Each topic is supported by a selection of thoughtfully designed problems that reinforce both conceptual understanding and practical skills. Complete solutions are provided at the end of the book, making it a valuable resource for classroom use and self-study alike. This is a clear and rigorous foundation for anyone beginning their journey into multivariable calculus.
Preface
Notations
Finite-Dimensional Euclidean Spaces
Continuous Functions of Several Variables
Differentiable Functions
Higher-Order Derivatives, Maxima and Minima
The Inverse and Implicit Function Theorems
Manifolds and Constrained Extremes: Lagrange Multipliers
Solutions of the Problems
Bibliography
Index
This book is intended for undergraduate and graduate students in Mathematics,
Physics, and Engineering who are beginning their study of differential
calculus of several real variables.
This is the second edition of the popular textbook published in German (1996) and English (1999), with 10000+ citations
Sets the mathematical foundations of Formal Concept Analysis, with applications to data analysis or knowledge processing
Presents, in a compact exposition, numerous examples at play, complementing each chapter with notes and references
Formal Concept Analysis is a field of applied mathematics based on the mathematization of concept and conceptual hierarchy. It thereby activates mathematical thinking for conceptual data analysis and knowledge processing. The underlying notion of “concept” evolved early in the philosophical theory of concepts and still has effects today. In mathematics it played a special role during the emergence of mathematical logic in the 19th century. Subsequently, however, it had virtually no impact on mathematical thinking. It was not until 1979 that the topic was revisited and treated more thoroughly.
Since then, Formal Concept Analysis has fully emerged, sparking a multitude of publications for which the first edition of this textbook established itself as the standard reference in the literature, with a total of 10000+ citations. This is the second edition, revised and extended, of the textbook published originally in German (1996) and translated into English (1999), giving a systematic presentation of the mathematical foundations while also focusing on their possible applications for data analysis and knowledge processing. In times of digital knowledge processing, formal methods of conceptual analysis are gaining in importance. The book makes the basic theory for such methods accessible in a compact form, and presents graphical methods for representing concept systems that have proved themselves essential in communicating knowledge.
The textbook complements each chapter with further notes, references and trends, putting the work in modern context and highlighting potential directions for further research. Additionally, the book contains an entirely new chapter on contextual concept logic, including a section on description logics and relational concept analysis. As such, it should be a valuable resource for students, instructors and researchers at the crossroads of subject areas like Applied and Discrete Mathematics, Logics, Theoretical Computer Science, Knowledge Processing, Data Science, and is meant to be used both for research and in class, as a teaching resource.
Front Matter
Pages i-xii
Download chapter PDF
Order-theoretic foundations
Bernhard Ganter, Rudolf Wille
Pages 1-21
Concept lattices of formal contexts
Bernhard Ganter, Rudolf Wille
Pages 23-75
Determination and representation
Bernhard Ganter, Rudolf Wille
Pages 77-115
Parts, factors, and bonds
Bernhard Ganter, Rudolf Wille
Pages 117-162
Decompositions of concept lattices
Bernhard Ganter, Rudolf Wille
Pages 163-214
Constructions of concept lattices
Bernhard Ganter, Rudolf Wille
Pages 215-248
Properties of concept lattices
Bernhard Ganter, Rudolf Wille
Pages 249-281
Context comparison and conceptual measurement
Bernhard Ganter, Rudolf Wille
Pages 283-309
Contextual concept logic
Bernhard Ganter, Rudolf Wille
Pages 311-334
Back Matter
Pages 335-370
The new edition includes advanced stochastic gradient descent algorithms
Covers detailed applications to finance
Based on years of teaching and research experience
Part of the book series: Universitext (UTX)
Now in a thoroughly revised and expanded second edition, this textbook offers a comprehensive and self-contained introduction to numerical methods in probability, with particular emphasis on stochastic optimization and its applications in financial mathematics.
The volume covers a broad range of topics, including Monte Carlo simulation techniques—such as the simulation of random variables, variance reduction strategies, quasi-Monte Carlo methods—and recent advancements like the multilevel Monte Carlo paradigm. It further discusses discretization schemes for stochastic differential equations and optimal quantization methods. A rigorous treatment of stochastic optimization is provided, encompassing stochastic gradient descent, including Langevin-based gradient descent algorithms, new to this edition. Detailed applications are presented in the context of numerical methods for pricing and hedging financial derivatives, the computation of risk measures (including value-at-risk and conditional value-at-risk), parameter implicitation, and model calibration.
Intended for graduate students and advanced undergraduates, the textbook includes numerous illustrative examples and over 200 exercises, rendering it well-suited for both classroom use and independent study.
Front Matter
Pages i-xxiii
Download chapter PDF
Simulation of Random Variables
Gilles Pagès
Pages 1-26
The Monte Carlo Method and Applications to Option Pricing
Gilles Pagès
Pages 27-47
Variance Reduction
Gilles Pagès
Pages 49-102
The Quasi-Monte Carlo Method
Gilles Pagès
Pages 103-142
Optimal Quantization Methods I: Cubatures
Gilles Pagès
Pages 143-183
Stochastic Optimization and Applications to Finance
Gilles Pagès
Pages 185-286
Discretization Scheme(s) of a Brownian Diffusion
Gilles Pagès
Pages 287-376
The Diffusion Bridge Method: Application to Path-Dependent Options (II)
Gilles Pagès
Pages 377-394
Biased Monte Carlo Simulation, Multilevel Paradigm
Gilles Pagès
Pages 395-485
Back to Sensitivity Computation
Gilles Pagès
Pages 487-522
Optimal Stopping, Multi-Asset American/Bermudan Options
Gilles Pagès
Pages 523-553
Langevin Gradient Descent Algorithms
Gilles Pagès
Pages 555-583
Miscellany
Gilles Pagès
Pages 585-610
Back Matter
Pages 611-636
Unified framework for the numeircal solution of PDEs on curved domains
Practical implementation with high-order numerical schemes in MATLAB and C++
Designed for accessibility and visualization of geometric concepts
Part of the book series: Springer Asia Pacific Mathematics Series (SAPACM, volume 7)
This book presents a comprehensive and geometrical approach to solving partial differential equations (PDEs) on complex curved domains using orthonormal moving frames. Rooted in Élie Cartan’s classical theory but adapted for computational practicality, the framework aligns local basis vectors with the intrinsic geometry and anisotropy of the domain, enabling accurate and efficient discretization without requiring explicit metric tensors or Christoffel symbols. Topics include the construction of moving frames on general manifolds, covariant derivatives via connection 1-forms, and frame-based formulations of gradient, divergence, curl, and Laplacian operators. Extensive MATLAB and C++ implementations (via Nektar++) are provided for benchmark problems in diffusion-reaction systems, shallow water equations, and Maxwell’s equations on complex surfaces such as the sphere, pseudosphere, and atrial tissue. Emphasizing clarity and accessibility, the book blends theory, visualization, and numerical practice, making it an essential resource for graduate students and researchers in scientific computing, applied mathematics, and engineering disciplines dealing with PDEs on non-Euclidean domains.
Table of contents
Front Matter
Pages i-xvii
Download chapter PDF
Introduction to Moving Frames for Curved and Anisotropic Domains
Sehun Chun
Pages 1-27
Constructing Moving Frames for Curved Geometries
Sehun Chun
Pages 29-58
Covariant Derivatives on Curved Surfaces via Moving Frames
Sehun Chun
Pages 59-94
Differential Operators in Moving Frames
Sehun Chun
Pages 95-132
Applications to PDEs on Curved Surfaces
Sehun Chun
Pages 133-206
Relative Acceleration and the Riemann Curvature Tensor
Sehun Chun
Pages 207-233
Back Matter
Pages 235-248
Comprehensive overview of hoop theory
Numerous examples
A resource for researchers and students
Part of the book series: Frontiers in Mathematics (FM)
This book offers a comprehensive and in-depth exploration of hoop theory, a fascinating branch of algebra with deep connections to logic and other areas of mathematics. Among algebraic structures, hoops stand out as a rich subject of study, bridging the worlds of residuated lattices, BL-algebras, MV-algebras, and related systems.
Starting with fundamental concepts of algebraic and lattice-theoretical structures, the book gradually delves into the core theory of hoops, investigating their algebraic structure, properties, and relationships with other algebraic systems. Significant attention is also devoted to the lattice-theoretical properties of hoops, and the interplay between algebraic and logical perspectives is emphasized.
This book is intended for advanced undergraduates with a background in algebra and logic, Ph.D. students, and researchers. Featuring a number of examples and exercises, it serves as a valuable resource for those seeking a comprehensive and in-depth understanding of hoop theory and its applications.