Format: Hardback, 346 pages, height x width: 235x155 mm, 10 Illustrations, black and white; XIII, 346 p. 10 illus.
Series: Applied Mathematical Sciences 211
Pub. Date: 02-Nov-2022
ISBN-13: 9783031127618
This book is intended to provide graduate students and researchers in graph theory with an overview of the elementary methods of graph Ramsey theory. It is especially targeted towards graduate students in extremal graph theory, graph Ramsey theory, and related fields, as the included contents allow the text to be used in seminars. It is structured in thirteen chapters which are application-focused and largely independent, enabling readers to target specific topics and information to focus their study. The first chapter includes a true beginner's overview of elementary examples in graph Ramsey theory mainly using combinatorial methods. The following chapters progress through topics including the probabilistic methods, algebraic construction, regularity method, but that's not all. Many related interesting topics are also included in this book, such as the disproof for a conjecture of Borsuk on geometry, intersecting hypergraphs, Turan numbers and communication channels, etc.
Existence.- Small Ramsey Numbers.- Basic Probalistic Method.- Random Graph.- Lovasz Local Lemma.- Constructive Lower Bounds.- Turan Number and Related Ramsey Number.- Communication Channels.- Dependent Random Choice.- Quasi-Random Graphs.- Regularity Lemma and van der Waerden Number.- More Ramsey Linear Functions.- Various Ramsey Problems.
Format: Hardback, 192 pages, height x width: 235x155 mm, 3 Tables, color; 3 Illustrations,
color; 4 Illustrations, black and white; VIII, 192 p. 7 illus., 3 illus. in color.
Series: Tutorials, Schools, and Workshops in the Mathematical Sciences
Pub. Date: 22-Nov-2022
ISBN-13: 9783031142673
This volume presents an accessible overview of mathematical control theory and analysis of PDEs, providing young researchers a snapshot of these active and rapidly developing areas. The chapters are based on two mini-courses and additional talks given at the spring school "Trends in PDEs and Related Fields" held at the University of Sidi Bel Abbes, Algeria from 8-10 April 2019. In addition to providing an in-depth summary of these two areas, chapters also highlight breakthroughs on more specific topics such as: Sobolev spaces and elliptic boundary value problems Local energy solutions of the nonlinear wave equation Geometric control of eigenfunctions of Schroedinger operators Research in PDEs and Related Fields will be a valuable resource to graduate students and more junior members of the research community interested in control theory and analysis of PDEs.
Sobolev Spaces and Elliptic Boundary Values Problems (Cherif Amrouche).- Survey on the decay of the local energy for the solutions of the nonlinear wave equations (Ahmed Bchatnia).- A spectral numerical method to approximate the boundary controllability of the wave equation with variable coefficients (Carlos Castro).- Aggregation equation and collapse to singular measure (Taoufik Hmidi, Dong Li).- Geometric Control of Eigenfunctions of Schrodinger Operators (Fabricio Macia).- Stability of a graph of strings with local Kelvin-Voigt damping (Kais Ammari, Zhuangyi Liu, Farhat Shel).
Format: Hardback, 492 pages, height x width: 242x170 mm, 231 Illustrations, black and white; XIV, 492 p. 231 illus.
Series: Vladimir I. Arnold - Collected Works 6
Pub. Date: 12-Nov-2022
ISBN-13: 9783031048005
This volume 6 of the Collected Works comprises 27 papers by V.I.Arnold, one of the most outstanding mathematicians of all times, written in 1991 to 1995. During this period Arnold's interests covered Vassiliev’s theory of invariants and knots, invariants and bifurcations of plane curves, combinatorics of Bernoulli, Euler and Springer numbers, geometry of wave fronts, the Berry phase and quantum Hall effect.
The articles include a list of problems in dynamical systems, a discussion of the problem of (in)solvability of equations, papers on symplectic geometry of caustics and contact geometry of wave fronts, comments on problems of A.D.Sakharov, as well as a rather unusual paper on projective topology. The interested reader will certainly enjoy Arnold’s 1994 paper on mathematical problems in physics with the opening by-now famous phrase “Mathematics is the name for those domains of theoretical physics that are temporarily unfashionable.”
The book will be of interest to the wide audience from college students to professionals in mathematics or physics and in the history of science. The volume also includes translations of two interviews given by Arnold to the French and Spanish media. One can see how worried he was about the fate of Russian and world mathematics and science in general.
1 Bernoulli-Euler updown numbers associated with function singularities, their combinatorics and arithmetics.- 2 Congruences for Euler, Bernoulli and Springer numbers of Coxeter groups.- 3 The calculus of snakes and the combinatorics of Bernoulli, Euler and Springer numbers of Coxeter groups.- 4 Springer numbers and Morsification spaces.- 5 Polyintegrable flows.- 6 Bounds for Milnor numbers of intersections in holomorphic dynamical systems.- 7 Some remarks on symplectic monodromy of Milnor fibrations.- 8 Topological properties of Legendre projections in contact geometry of wave fronts [ On topological properties of Legendre projections in contact geometry of wave fronts].- 9 Sur les proprietes topologiques des projections lagrangiennes en geometrie symplectique des caustiques [ On topological properties of Lagrangian projections in symplectic geometry of caustics].- 10 Plane curves, their invariants, perestroikas and classifications (with an appendix by F. Aicardi).- 11 Invariants and perestroikas of plane fronts.- 12 The Vassiliev theory of discriminants and knots.- 13 The geometry of spherical curves and the algebra of quaternions.- 14 Remarks on eigenvalues and eigenvectors of Hermitian matrices, Berry phase, adiabatic connections and quantum Hall effect.- 15 Problems on singularities and dynamical systems.- 16 Sur quelques problemes de la theorie des systemes dynamiques [ On some problems in the theory of dynamical systems].- 17 Mathematical problems in classical physics.- 18 Problemes resolubles et problemes irresolubles analytiques et geometriques [ Solvable and unsolvable analytic and geometric problems].- 19 Projective topology.- 20 Questions a V.I. Arnold (an interview with M. Audin and P. Iglesias) [ Questions to V.I. Arnold].- 21 En todo matematico hay un angel y un demonio (an interview with Marimar Jimenez) [ In every mathematician, there is an angel and a devil].- 22 Will Russian mathematics survive?.- 23 Will mathematics survive? Report on the Zurich Congress.- 24 Why study mathematics? What mathematicians think about it.- 25 Preface to the Russian translation of the book by M.F. Atiyah "The Geometry and Physics of Knots".- 26 A comment on one of A.D. Sakharov's "Amateur Problems".- 27 Comments on two of A.D. Sakharov's "Amateur Problems".- Acknowledgements.
Format: Paperback / softback, 217 pages, height x width: 235x155 mm, X, 217 p.,
Series: Universitext
Pub. Date: 20-Nov-2022
ISBN-13: 9783031118210
This book gives an introduction to discrete-time Markov chains which evolve on a separable metric space.
The focus is on the ergodic properties of such chains, i.e., on their long-term statistical behaviour. Among the main topics are existence and uniqueness of invariant probability measures, irreducibility, recurrence, regularizing properties for Markov kernels, and convergence to equilibrium. These concepts are investigated with tools such as Lyapunov functions, petite and small sets, Doeblin and accessible points, coupling, as well as key notions from classical ergodic theory. The theory is illustrated through several recurring classes of examples, e.g., random contractions, randomly switched vector fields, and stochastic differential equations, the latter providing a bridge to continuous-time Markov processes.
The book can serve as the core for a semester- or year-long graduate course in probability theory with an emphasis on Markov chains or random dynamics. Some of the material is also well suited for an ergodic theory course. Readers should have taken an introductory course on probability theory, based on measure theory. While there is a chapter devoted to chains on a countable state space, a certain familiarity with Markov chains on a finite state space is also recommended.
1 Markov Chains.- 2 Countable Markov Chains.- 3 Random Dynamical Systems.- 4 Invariant and Ergodic Probability Measures.- 5 Irreducibility.- 6 Petite Sets and Doeblin points.- 7 Harris and Positive Recurrence.- 8 Harris Ergodic Theorem.
Format: Hardback, 208 pages, height x width: 235x155 mm, VIII, 208 p., 1 Hardback
Series: Infosys Science Foundation Series in Mathematical Sciences
Pub. Date: 27-Nov-2022
ISBN-13: 9783031136696
Other books in subject:
This book is a self-contained advanced monograph on inequalities involving the numerical radius of bounded linear operators acting on complex Hilbert spaces. The study of numerical range and numerical radius has a long and distinguished history starting from the Rayleigh quotients used in the 19th century to nowadays applications in quantum information theory and quantum computing.
This monograph is intended for use by both researchers and graduate students of mathematics, physics, and engineering who have a basic background in functional analysis and operator theory. The book provides several challenging problems and detailed arguments for the majority of the results. Each chapter ends with some notes about historical views or further extensions of the topics. It contains a bibliography of about 180 items, so it can be used as a reference book including many classical and modern numerical radius inequalities.
Chapter
1. Preliminaries.
Chapter
2. Fundamental numerical radius inequalities.
Chapter
3. Bounds of the numerical radius using Buzano's inequality.
Chapter
4. p-numerical radius inequalities of an n-tuple of operators.
Chapter
5. Numerical radius inequalities of product of operators.
Chapter
6. Numerical radius of operator matrices and applications.
Chapter
7. Operator space numerical radius of 2 x 2 block matrices.
Chapter
8. A-numerical radius inequalities of semi-Hilbertian spaces.
Chapter
9. Research Problems
Format: Hardback, 300 pages, height x width: 235x155 mm, 6 Illustrations, black and white; X, 300 p. 6 illus.
Series: Springer Monographs in Mathematics
Pub. Date: 09-Nov-2022
ISBN-13: 9783031138720
This monograph adopts an operational and functional analytic approach to the following problem: given a short exact sequence (group extension) 1 ? N ? G ? H ? 1 of finite groups, describe the irreducible representations of G by means of the structure of the group extension. This problem has attracted many mathematicians, including I. Schur, A.H. Clifford, and G. Mackey and, more recently, M. Isaacs, B. Huppert, Y.G. Berkovich & E.M. Zhmud, and J.M.G. Fell & R.S. Doran.
The main topics are, on the one hand, Clifford Theory and the Little Group Method (of Mackey and Wigner) for induced representations, and, on the other hand, Kirillov’s Orbit Method (for step-2 nilpotent groups of odd order) which establishes a natural and powerful correspondence between Lie rings and nilpotent groups. As an application, a detailed description is given of the representation theory of the alternating groups, of metacyclic, quaternionic, dihedral groups, and of the (finite) Heisenberg group.
The Little Group Method may be applied if and only if a suitable unitary 2-cocycle (the Mackey obstruction) is trivial. To overcome this obstacle, (unitary) projective representations are introduced and corresponding Mackey and Clifford theories are developed. The commutant of an induced representation and the relative Hecke algebra is also examined. Finally, there is a comprehensive exposition of the theory of projective representations for finite Abelian groups which is applied to obtain a complete description of the irreducible representations of finite metabelian groups of odd order.
Preliminaries.- Clifford Theory.- Abelian Extensions.- The Little Group Method for Abelian Extensions.- Examples and Applications.- Central Extensions and the Orbit Method.- Unitary Representations of Finite Group Extensions.- Induced projective representations.- Clifford Theory for Projective Representations.- Projective representations of finite Abelian groups with applications.- Appendices.