Edited by Bipan Hazarika, Edited by Santanu Acharjee, Edited by Dragan S. Djordjevic

Advances in Topology, Dynamical Systems and Interdisciplinary Applications

Format: Hardback, 246 pages, height x width: 235x155 mm, 73 Illustrations,
color; 2 Illustrations, black and white; XIV, 246 p. 75 illus., 73 illus. in color.,
Series: Industrial and Applied Mathematics
Pub. Date: 01-May-2025
ISBN-13: 9789819619603

Description

This book contains selected chapters on topology and dynamical systems and their interdisciplinary applications. Targeting researchers in interdisciplinary areas, the book covers contemporary interdisciplinary topics in topology and dynamical systems, such as closure functions, Partially Negative Dimensional Product (PNDP) manifolds, Khalimsky topological subspaces, neutrosophic topological space, ideal topological spaces, relator spaces, predator?prey symbiosis, cosmological models, and nanofluids.

Table of Contents

Chapter 1 Closure Functions Induced by * and psi Operators.
Chapter 2 PNDP Manifolds.
Chapter 3 A Unified Study of Normal Spaces.

Boris Buffoni, John Toland

Connected Sets in Global Bifurcation Theory

Format: Paperback 104 pages, height x width: 235x155 mm, 10 Illustrations, black and white; VI, 104 p. 10 illus.,
Series: SpringerBriefs in Mathematics
Pub. Date: 02-May-2025
ISBN-13: 9783031870507

Description

This book explores the topological properties of connected and path-connected solution sets for nonlinear equations in Banach spaces, focusing on the distinction between these concepts. Building on Rabinowitz's dichotomy and classical results on Peano continua, the authors introduce "congestion points"where connected sets fail to be weakly locally connectedand examine the extent to which their presence is compatible with path-connectedness. Through rigorous analysis and examples, the book provides new insights into global bifurcations.

Structured into seven chapters, the book begins with an introduction to global bifurcation theory and foundational concepts in set theory and metric spaces. Subsequent chapters delve into connectedness, local connectedness, and congestion points, culminating in the construction of intricate examples that highlight the complexities of solution sets. The authors' careful selection of material and fluent writing style make this work a valuable resource for PhD students and experts in functional analysis and bifurcation theory.

Table of Contents

1. Introduction.-
2. Set Theory Foundations.-
3. Metric Spaces.-
4. Types of Connectedness.-
5. Congestion Points.-
6. Decomposable and Indecomposable Continua.-
7. Pathological Examples.

Alexander Iksanov, Alexander Marynych, Ihor Samoilenko, Andrey Pilipenko

Locally Perturbed Random Walks

Format: Paperback, 224 pages, height x width: 240x168 mm, 2 Illustrations, color;
3 Illustrations, black and white; X, 224 p. 5 illus., 2 illus. in color.,
Series: Frontiers in Mathematics
Pub. Date: 12-May-2025
ISBN-13: 9783031839184

Description

This monograph provides a comprehensive overview of locally perturbed random walks, tools used for their analysis, and current research on their applications. The authors present the material in a self-contained manner, providing strong motivation in Chapter One with illustrative examples of locally perturbed random walks and an introduction of the mathematical tools that are used throughout the book. Chapter Two shows the construction of various stochastic processes that serve as scaling limits for locally perturbed random walks, particularly focusing on reflected and skewed processes. In Chapter Three, the authors prove various limit theorems for these perturbed random walks. The final chapter serves as an appendix that collects essential background material for readers who wish to understand the arguments more deeply. Locally Perturbed Random Walks will appeal to researchers interested in this area within modern probability theory. It is also accessible to students who have taken a second course in probability.

Table of Contents

Chapter 1: Introduction.
Chapter 2: LLevy-type processes with singularities.
Chapter 3: Functional limit theorems for locally perturbed random walks.
Chapter 4: Auxiliary results.

Alexander Marynych, Alexander Iksanov, Andrey Pilipenko, Ihor Samoilenko

Locally Perturbed Random Walks

Format: Paperback / softback, 224 pages, height x width: 240x168 mm,
2 Illustrations, color; 3 Illustrations, black and white; X, 224 p. 5 illus., 2 illus. in color.
Series: Frontiers in Mathematics
Pub. Date: 12-May-2025
ISBN-13: 9783031839184

Description

This monograph provides a comprehensive overview of locally perturbed random walks, tools used for their analysis, and current research on their applications. The authors present the material in a self-contained manner, providing strong motivation in Chapter One with illustrative examples of locally perturbed random walks and an introduction of the mathematical tools that are used throughout the book. Chapter Two shows the construction of various stochastic processes that serve as scaling limits for locally perturbed random walks, particularly focusing on reflected and skewed processes. In Chapter Three, the authors prove various limit theorems for these perturbed random walks. The final chapter serves as an appendix that collects essential background material for readers who wish to understand the arguments more deeply. Locally Perturbed Random Walks will appeal to researchers interested in this area within modern probability theory. It is also accessible to students who have taken a second course in probability.

Table of Contents

Chapter 1: Introduction.
Chapter 2: LLevy-type processes with singularities.
Chapter 3: Functional limit theorems for locally perturbed random walks.
Chapter 4: Auxiliary results.

S. P. Mukherjee, Asok K. Nanda

Probability Models in Reliability Analysis

Format: Hardback, 363 pages, height x width: 235x155 mm, 26 Illustrations,
color; 2 Illustrations, black and white; XV, 363 p. 28 illus., 26 illus. in color.
Series: University Texts in the Mathematical Sciences
Pub. Date: 16-May-2025
ISBN-13: 9789819630486

Description

This book delves into the fundamental theoretical aspects of reliability analysis, focusing on various probabilistic models. These models are essential for representing random variations in underlying variables such as time-to-failure, the number of failures between consecutive repairs and similar metrics. The calculation, estimation and prediction of reliability all hinge on using appropriate probability models. The book introduces various models beneficial for researchers in the field of reliability. It also provides a comprehensive overview of the available models, highlighting their distinctive features and practical applications in a narrative format. The content of the book is designed to appeal to a broad readership. Students and researchers in the field of reliability analysis will find a comprehensive yet easily understandable summary of models applicable to their data sets of interest. It should be noted, however, As stated clearly in the preface, this book does not illustrate applications of the models discussed in terms of real-life data.

Table of Contents

1. Introduction.-
2. Properties of Life Distributions.-
3. Univariate Continuous Distributions.-
4. Some Discrete Distributions.-
5. Distributions Derived from the Parent Distribution.-
6. Finite Range Life Distributions.-
7. Ordering among Life Distributions .-
8. Classes of Life Distributions .-
9. Characterizations of Life Distributions .-
10. Distributions of Special Interest .-
11. Using an Appropriate Probability Model.


Gabriel Nguetseng

Homogenization Algebras and Applications:
A Deterministic Homogenization Theory

Format: Hardback, 411 pages, height x width: 235x155 mm, XXII, 411 p., 1 Hardback
Series: Springer Monographs in Mathematics
Pub. Date: 08-May-2025
ISBN-13: 9783031847042

Description

The book presents a deterministic homogenization theory intended for the mathematical analysis of non-stochastic multiscale problems, both within and beyond the periodic setting. The main tools are the so-called homogenization algebras, the classical Gelfand representation theory, and a class of actions by the multiplicative group of positive real numbers on numerical spaces. The basic approach is the Sigma-convergence method, which generalizes the well-known two-scale convergence procedure. Numerous problems are worked out to illustrate the theory and highlight its broad applicability. The book is primarily intended for researchers (including PhD students) and lecturers interested in periodic as well as non-periodic homogenization theory.

Table of Contents

1. Preliminaries. -
2. Homogenization Algebras on RN.-
3. -Convergence: The Periodic Setting.-
4. -Convergence: The General Setting.-
5. Homogenization of Elliptic Operators.-
6. Homogenization of Parabolic Operators I.-
7. Homogenization Of Parabolic Operators II.-
8. Reiterated Homogenization.


Victor H. L. Rocha, Josiney A. Souza

Lyapunov Stability of Transformation Semigroups

Format: Hardback, 228 pages, height x width: 235x155 mm, 14 Illustrations,
black and white; XVIII, 228 p. 14 illus.,
Series: Latin American Mathematics Series
Pub. Date: 06-May-2025
ISBN-13: 9783031857607

Description

This book presents recent research results on Lyapunov stability and attraction for semigroup actions in a pedagogical format, providing the reader with numerous modern ideas and mathematical formulations for dynamical concepts in the transformation group theory.

In recent decades, many fundamental concepts of dynamical systems have been extended to the general framework of transformation semigroups. Limit sets, attractors, isolated invariant sets, prolongational limit sets, and stable sets now have semigroup theoretical analogues. This monograph consolidates recent advancements in this field in a way that makes it accessible to graduate students. An effort was made to relate the presented results to important recurrence notions, for contextual clarity.

A rudimentary understanding of group theory and topology, including the concepts of semigroup action, orbit, fiber bundle, compactness, and connectedness, is a prerequisite for reading this text. As a valuable resource for research projects and academic dissertations on topological dynamics, geometry, and mathematical analysis, this work can potentially open new avenues for further research.

Table of Contents

Preface.- Introduction.- Semigroup actions.- Attraction and Lyapunov
stability.- Orbital maps.- Lyapunov stability on fiber bundles.- Fenichels
uniformity lemma.- Stability and controllability.- Higher stability and
generalized recurrence.- Fiber bundles.- References.- Index.