Format: Paperback 218 pages, height x width: 235x155 mm,
1 Illustrations, black and white; IX, 218 p. 1 illus.,
Series: Lecture Notes in Mathematics 2302
Pub. Date: 23-Apr-2022
ISBN-13: 9783030959555
Author Biography
Goodreads reviews
<div><div>This book gives a proof of Cherlin’s conjecture for finite binary primitive permutation groups. Motivated by the part of model theory concerned with Lachlan’s theory of finite homogeneous relational structures, this conjecture proposes a classification of those finite primitive permutation groups that have relational complexity equal to 2. </div><div><br></div><div>The first part gives a full introduction to Cherlin’s conjecture, including all the key ideas that have been used in the literature to prove some of its special cases. The second part completes the proof by dealing with primitive permutation groups that are almost simple with socle a group of Lie type. A great deal of material concerning properties of primitive permutation groups and almost simple groups is included, and new ideas are introduced. </div><div><br></div><div>Addressing a hot topic which cuts across the disciplines of group theory, model theory and logic, this book will be of interest to a wide range of readers. It will be particularly useful for graduate students and researchers who need to work with simple groups of Lie type.</div></div><div><br></div>
Introduction. - Preliminary results for groups of Lie type. - Exceptional Groups. - Classical Groups.
Format: Hardback, 192 pages, height x width: 235x155 mm, 107 Illustrations,
color; 13 Illustrations, black and white; VIII, 192 p. 120 illus., 107 illus. in color.,
Series: Association for Women in Mathematics Series 30
Pub. Date: 10-May-2022
ISBN-13: 9783030955182
<div><div>This second volume of Research in Computational Topology is a celebration and promotion of research by women in applied and computational topology, containing the proceedings of the second workshop for Women in Computational Topology (WinCompTop) as well as papers solicited from the broader WinCompTop community. The multidisciplinary and international WinCompTop workshop provided an exciting and unique opportunity for women in diverse locations and research specializations to interact extensively and collectively contribute to new and active research directions in the field. The prestigious senior researchers that signed on to head projects at the workshop are global leaders in the discipline, and two of them were authors on some of the first papers in the field. </div><div><br></div><div>Some of the featured topics include topological data analysis of power law structure in neural data; a nerve theorem for directional graph covers; topological or homotopical invariants for directed graphs encoding connections among a network of neurons; and the issue of approximation of objects by digital grids, including precise relations between the persistent homology of dual cubical complexes.</div></div><div><p></p><p></p></div>
The Persistent Homology of Dual Digital Image Constructions (V. Robins).- Morse-based Fibering of the Persistence Rank Invariant (C. Landi).- Local Versus Global Distances for Zigzag and Multi Parameter Persistence Modules (E. Gasparovic).- Tile-transitive tilings of the Euclidean and hyperbolic planes by ribbons (V. Robins).- Graph Pseudometrics from a Topological Point of View (J. Tan).- Nerve theorems for fixed points of neural networks (C. Curto).- Combinatorial Conditions for Directed Collapsing (T. Fasy).- Lions and contamination, triangular grids, and Cheeger constants (L. Gibson).- A Topological Approach for Motion Track Discrimination (S. Tymochko).- Persistent topology of protein space (W. Hamilton).- Mappering Mecklenburg County: Exploring Census data for potential communities of interest (M. Thatcher).- Stitch Fix for Mapper and Topological Gains (B. Wang).
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Format: Hardback, 553 pages, height x width: 235x155 mm, 11 Illustrations, color;
2 Illustrations, black and white; XV, 553 p. 13 illus., 11 illus. in color.
ISBN-13: 9789811698644
The book serves as a primary textbook of partial differential equations (PDEs), with due attention to their importance to various physical and engineering phenomena. The book focuses on maintaining a balance between the mathematical expressions used and the significance they hold in the context of some physical problem. The book has wider outreach as it covers topics relevant to many different applications of ordinary differential equations (ODEs), PDEs, Fourier series, integral transforms, and applications. It also discusses applications of analytical and geometric methods to solve some fundamental PDE models of physical phenomena such as transport of mass, momentum, and energy.
As far as possible, historical notes are added for most important developments in science and engineering. Both the presentation and treatment of topics are fashioned to meet the expectations of interested readers working in any branch of science and technology. Senior undergraduates in mathematics and engineering are the targeted student readership, and the topical focus with applications to real-world examples will promote higher-level mathematical understanding for undergraduates in sciences and engineering.
Classical Vector Analysis.- Ordinary Differential Equations.- Partial Differential Equation Models.- Partial Differential Equations.- General Solution and Complete Integral.- Method of Characteristics.- Separation of Variables.- Method of Eigenfunctions Expansion.- Fourier Transforms.- Laplace Transform.
Format: Hardback, height x width: 235x155 mm, Approx. 290 p.
Series: Developments in Mathematics 70
Pub. Date: 30-May-2022
ISBN-13: 9783030950873
In 1922, Harald Bohr and Johannes Mollerup established a remarkable characterization of the Euler gamma function using its log-convexity property. A decade later, Emil Artin investigated this result and used it to derive the basic properties of the gamma function using elementary methods of the calculus. Bohr-Mollerup's theorem was then adopted by Nicolas Bourbaki as the starting point for his exposition of the gamma function.<br><br>This open access book develops a far-reaching generalization of Bohr-Mollerup's theorem to higher order convex functions, along lines initiated by Wolfgang Krull, Roger Webster, and some others but going considerably further than past work. In particular, this generalization shows using elementary techniques that a very rich spectrum of functions satisfy analogues of several classical properties of the gamma function, including Bohr-Mollerup's theorem itself, Euler's reflection formula, Gauss' multiplication theorem, Stirling's formula, and Weierstrass' canonical factorization.<br><br>The scope of the theory developed in this work is illustrated through various examples, ranging from the gamma function itself and its variants and generalizations (q-gamma, polygamma, multiple gamma functions) to important special functions such as the Hurwitz zeta function and the generalized Stieltjes constants.<br> <br>This volume is also an opportunity to honor the 100th anniversary of Bohr-Mollerup's theorem and to spark the interest of a large number of researchers in this beautiful theory.
Preface.- List of main symbols.- Table of contents.
Chapter
1. Introduction.
Chapter
2. Preliminaries.
Chapter
3. Uniqueness and existence results.
Chapter
4. Interpretations of the asymptotic conditions.
Chapter
5. Multiple log-gamma type functions.
Chapter
6. Asymptotic analysis.-
Chapter
7. Derivatives of multiple log-gamma type functions.
Chapter
8. Further results.
Chapter
9. Summary of the main results.
Chapter
10. Applications to some standard special functions.
Chapter
11. Definining new log-gamma type functions.
Chapter
12. Further examples.
Chapter
13. Conclusion.- A. Higher order convexity properties.- B. On Krull-Webster's asymptotic condition.- C. On a question raised by Webster.- D. Asymptotic behaviors and bracketing.- E. Generalized Webster's inequality.- F. On the differentiability of \sigma_g.- Bibliography.- Analogues of properties of the gamma function.- Index.
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Format: Hardback, 1226 pages, height x width: 235x155 mm, XIV, 1226 p.,
Series: Grundlehren der mathematischen Wissenschaften 359
Pub. Date: 24-May-2022
ISBN-13: 9783030940546
This book provides a coherent, self-contained introduction to central topics of <i>Analytic Partial Differential Equations</i> in the natural geometric setting. The main themes are the analysis in phase-space of analytic PDEs and the Fourier?Bros?Iagolnitzer (FBI) transform of distributions and hyperfunctions, with application to existence and regularity questions.<div><br></div><div>The book begins by establishing the fundamental properties of analytic partial differential equations, starting with the Cauchy?Kovalevskaya theorem, before presenting an integrated overview of the approach to hyperfunctions via analytic functionals, first in Euclidean space and, once the geometric background has been laid out, on analytic manifolds. Further topics include the proof of the Lojaciewicz inequality and the division of distributions by analytic functions, a detailed description of the Frobenius and Nagano foliations, and the Hamilton?Jacobi solutions of involutive systems of eikonal equations. The reader then enters the realm of microlocal analysis, through pseudodifferential calculus, introduced at a basic level, followed by Fourier integral operators, including those with complex phase-functions (<i>a la</i> Sjostrand). This culminates in an in-depth discussion of the existence and regularity of (distribution or hyperfunction) solutions of analytic differential (and later, pseudodifferential) equations of principal type, exemplifying the usefulness of all the concepts and tools previously introduced. The final three chapters touch on the possible extension of the results to systems of over- (or under-) determined systems of these equations?a cornucopia of open problems.<div><p>This book provides a unified presentation of a wealth of material that was previously restricted to research articles. In contrast to existing monographs, the approach of the book is analytic rather than algebraic, and tools such as sheaf cohomology, stratification theory of analytic varieties and symplectic geometry are used sparingly and introduced as required. The first half of the book is mainly pedagogical in intent, accessible to advanced graduate students and postdocs, while the second, more specialized part is intended as a reference for researchers.</p></div></div>