Part of Cambridge Series in Statistical and Probabilistic Mathematics
Not yet published - available from February 2024
FORMAT: Hardback ISBN: 9781107174009
Complex networks are key to describing the connected nature of the society that we live in. This book, the second of two volumes, describes the local structure of random graph models for real-world networks and determines when these models have a giant component and when they are small-, and ultra-small, worlds. This is the first book to cover the theory and implications of local convergence, a crucial technique in the analysis of sparse random graphs. Suitable as a resource for researchers and PhD-level courses, it uses examples of real-world networks, such as the Internet and citation networks, as motivation for the models that are discussed, and includes exercises at the end of each chapter to develop intuition. The book closes with an extensive discussion of related models and problems that demonstratemodern approaches to network theory, such as community structure and directed models.
Features many exercises on the theory of networks and properties of network models
Gives the simplest possible proofs for the key results, demonstrating the beauty of the field and the methods used
The first text on local convergence of networks, a key notion in the analysis of sparse random graphs
'Even before its publication, the second volume of 'Random graphs and complex networks' has become a classic for anyone working in random graph theory. Remco van der Hofstad manages to treat in detail a very large extent of this fascinating theory, while staying extremely pedagogical and accessible to a broad audience. It covers in depth the local convergence and small-world properties of scale-free random graphs. Together with the first volume, these are among the essential books every probabilist should have on their shelf!' Nicolas Curien, Universite Paris-Saclay
'This is a wonderful book, covering major topics at the forefront of modern random graph theory and its application to the modelling and description of real-world complex networks. Whereas Volume 1 covers basic models, ideas and techniques, Volume 2 focusses on two key topics - connected components and small world properties ? for three different classes of random graphs - inhomogeneous random graphs, configuration models, preferential attachment models. At the basis is the notion of local convergence, which is powerful tool to describe large sparse random graphs. Suitable for researchers at the level of PhD and above, the two volumes will become a landmark in network science.' Frank den Hollander, Leiden University
Preface
Possible course outline
Part I. Preliminaries:
1. Introduction and preliminaries
2. Local convergence of random graphs
Part II. Connected Components in Random Graphs:
3. Connected components in general inhomogeneous random graphs
4. Connected components in configuration models
5. Connected components in preferential attachment models
Part III. Small-world Properties of Random Graphs:
6. Small-world phenomena in inhomogeneous random graphs
7. Small-world phenomena in configuration models
8. Small-world phenomena in preferential attachment models
Part IV. Related Models and Problems:
9. Related models
Appendix
Glossary
References
Index.
Copyright 2024
Hardback
ISBN 9781032670171
200 Pages 92 B/W Illustrations
April 12, 2024 by CRC Press
Ario and Zawidzki show readers how to handle symmetric structures in engineering using group-theoretic bifurcation theory as a mathematical tool for the finite element analysis of symmetric structures.
They guide the reader from the initial mathematical concepts through to application examples. Readers will gain a solid theoretical grounding in group theory and strong working knowledge of the use of computational frameworks for structural analysis using mathematical representations of symmetry and physical symmetry. First, the authors elaborate an outline of symmetric structures in engineering and then describe the representation of symmetry and group theory. They then discuss block diagonalization theory and finite element analysis models. This provides readers with the base knowledge needed for Chapter 6, which is based on numerical analysis examples of invariant, static FEM model systems and dynamic model systems of the dihedral group. This unique approach is a vital method that will enable readers to reduce the time and computation needed for accurate analysis so that they can better design such structures. The focus on finite element methods and practical examples and case studies throughout provides a strong practical foundation for anyone studying or working in this field.
The book is a valuable resource for undergraduate and postgraduate students on various courses such as civil and mechanical engineering, architecture, structural engineering, applied mathematics, and physics. Additionally, it describes vital practical solutions for structural engineers, structural system manufacturers, fabricators of prefabricated elements, and developers of computational mechanics and so on.
Part 1: This is fundamental part 1. Introduction 2. Symmetry and its representation 3. Group Theory and Structural Mechanics 4. Basics of the finite element method Part 2: This is the application of group theory to symmetric structures 5. Block Diagonalization Theory for Dihedral Groups 6. Numerical Analysis of Dihedral Group Invariant Systems 7. Numerical Efficiency Evaluation of Parallel Computing Method 8. Group products A D3. invariant plate element B D2. invariant bending plate element
Copyright 2024
Hardback
ISBN 9781032599021
Paperback
ISBN 9781032595986
318 Pages 54 B/W Illustrations
April 8, 2024 by Chapman & Hall
This book introduces readers to the art of doing mathematical proofs. Proofs are the glue that holds mathematics together. They make connections between math concepts and show why things work the way they do. This book teaches the art of proofs using familiar high school concepts, such as numbers, polynomials, functions, and trigonometry. It retells math as a story, where the next chapter follows from the previous one.
Readers will see how various mathematical concepts are tied, will see mathematics is not a pile of formulas and facts, but has an orderlyandbeautifuledifice.
The author begins with basic rules of logic, and then progresses through the topics already familiar to the students: numbers, inequalities, functions, polynomials, exponents, and trigonometric functions. There are also beautiful proofs for conic sections, sequences, and Fibonacci numbers. Each chapter has exercises for the reader.
gI find the book very impressive. The choice and sequence of topics is excellent, and it is wonderful to have all of these things together in one volume. Theorems are clearly stated, and proofs are accurate.h -- Michael Comenetz
The thoroughness of the narrative is one of the main strengths of the book. The book provides a perfect illustration of mathematical thinking. Each step of a given derivation is precise and clear.-- Julie Gershunskaya
Draganovfs book stands out from the many competing books. Draganovfs goal is to show that mathematics depends on the notion of proof. Unlike other transitions books, he addresses mathematical topics at an accessible level rather than topics studied later in the university curriculum. ?Ken Rosen
Copyright 2024
Hardback
ISBN 9781032560090
210 Pages
April 11, 2024
The theory of the measure of noncompactness has proved its significance in various contexts, particularly in the study of fixed-point theory, differential equations, functional equations, integral and integrodifferential equations, optimization, and others. This edited volume presents the recent developments in the theory of the measure of noncompactness and its applications in pure and applied mathematics. It discusses important topics such as measures of noncompactness in the space of regulated functions, application in nonlinear infinite systems of fractional differential equations, and coupled fixed point theorem.
? Explains numerical solution of functional integral equation through coupled fixed point theorem, measure of noncompactness and iterative algorithm.
? Showcases applications of the measure of noncompactness and Petryshynfs fixed point theorem functional integral equations in Banach algebra.
? Explores the existence of solutions of the implicit fractional integral equation via extension of the Darbofs fixed point theorem.
? Discusses best proximity point results using measure of noncompactness and its applications.
? Includes solvability of some fractional differential equations in the holder space and their numerical treatment via measures of noncompactness.
This reference work is for scholars and academic researchers in pure and applied mathematics.
1. The existence and numerical solution of functional integral equation via coupled fixedpoint theorem, measure of non-compactness and iterative algorithm
Reza Arab and Mohsen Rabbani
2. Applications of measure of non-compactness and Petryshyn's fixed--point theorem for a class of functional integral equations in a Banach algebra
Amar Deep, Parul Saini, and Deepika Saini
3. Some Darbo fixed point theorems and solutions of the implicit fractional integral equation
Bhuban Chandra Deuri and Anupam Das
4. A survey on recent best proximity point results using measure of noncompactness and applications
Inzamamul Haque and Javid Ali
5. A Petryshyn based approach to the existence of solutions for Volterra functional integral equations with Hadamard-type fractional integrals
Satish Kumar, Manochehr Kazemi, and Soniya Singh
6. Coupled fixed point theorem and measure of noncompactness for existence of solution of functional integral equations system and iterative algorithm to solve it
Mohsen Rabbani and Reza Arab
7. Optimum solution of integral equation via measure of noncompactness
Mallika Sarmah and Anupam Das
8. Approximate finite dimensional additive mappings in modular spaces by fixed-point method
K. Tamilvanan, N. Revathi, and A. Charles Sagayaraj
9. Ulam stability results of the quadratic functional equation in Banach space and multi-normed space by using direct and fixed point methods
K. Tamilvanan, N. Revathi, K. Sethukumarasamy, and A. Charles Sagayaraj
10. Solution of simultaneous nonlinear integral equations by generalized contractive condition
Shiv Kant Tiwari, Laxmi Rathour, and Vishnu Narayan Mishra
11. Compactness via Hausdor measure of non-compactness on q-Pascal difference sequence spaces
Taja Yaying and S. A. Mohiuddine
Copyright 2024
Hardback
ISBN 9781032489230
200 Pages 15 B/W Illustrations
April 4, 2024 by Chapman & Hall
E The book Graph Theory and Decomposition covers major areas of the decomposition of graphs.
E It is a three-part reference book with nine chapters that is aimed at enthusiasts as well as research scholars.
E It comprehends historical evolution and basic terminologies.
E It deliberates on decompositions into cyclic graphs, such as cycle, digraph, and K4-e decompositions.
E In addition to determining the pendant number of graphs, it has a discourse on decomposing a graph into acyclic graphs like general tree, path, and star decompositions.
E It summarises another recently developed decomposition technique, which decomposes the given graph into multiple types of subgraphs.
E Major conjectures on graph decompositions are elaborately discussed.
E It alludes to a comprehensive bibliography that includes over 514 monographs and journal articles.
E It includes 510 theorems, 101 definitions, 56 conjectures, 40 open problems, and an algorithm.
E The index section facilitates easy access to definitions, major conjectures, and named theorems.
E Thus, the book Graph Theory and Decomposition will be a great asset, we hope, in the field of decompositions of graphs and will serve as a reference book for all who are passionate about graph theory.
1. Decompositions of Graphs: An introduction. 2. Cycle Decompositions 3. Digraph Decompositions 4. K4-e Decompositions 5. Tree Decompositions 6. Path Decompositions 7. Star Decompositions 8. Pendant Number of Graphs 9. Multiple Decompositions of Graphs 10. Bibliography 11. Index
Volume 12 in the series Fractional Calculus in Applied Sciences and Engineering
This book is devoted to the existence and uniqueness results for various classes of problems with periodic conditions. All of the problems in this book deal with fractional differential equations and some fractional derivatives such as the Riemann-Liouville, Caputo and Hilfer fractional derivatives. Classical fixed point theorems as well as the coincidence degree theory of Mawhin are employed as tools.
Includes new results using Mawhin's coincidence degree theory
Each chapter ends with a section devoted to remarks and bibliographical suggestions
All abstract results are substantiated with illustration
Preface
Mouffak Benchohra, Soufyane Bouriah, Abdelkrim Salim and Yong Zhou
Publicly Available VII
Contents
Publicly Available IX
1 Introduction 1
2 Preliminary background 9
3 Caputo-type fractional differential equations 26
4 Õ-Caputo fractional integro-differential equations 66
5 Nonlinear fractional pantograph differential equations with Õ-Caputo derivative 95
6 Nonlinear Õ-Caputo fractional pantograph coupled systems 138
7 Nonlinear fractional differential equations with Õ-Hilfer fractional derivative 157
8 Õ-Hilfer fractional pantograph-type differential equations 201
9 Nonlinear Õ-Hilfer fractional coupled systems 233
10 k-Generalized Õ-Hilfer fractional differential equations with periodic conditions 260
11 Nonlinear implicit k-generalized Õ-Hilfer fractional coupled systems 276
Bibliography 311
Index