Format: Paperback / softback, 432 pages, height x width: 235x155 mm, 21 Tables,
color; 24 Illustrations, color; 6 Illustrations, black and white; X, 432 p. 30 ill., 24 ill. en couleurs.
Series: Mathematiques et Applications 88
Pub. Date: 31-Oct-2022
ISBN-13: 9783031128004
The book provides a pedagogic and comprehensive introduction to homogenization theory with a special focus on problems set for non-periodic media. The presentation encompasses both deterministic and probabilistic settings. It also mixes the most abstract aspects with some more practical aspects regarding the numerical approaches necessary to simulate such multiscale problems. Based on lecture courses of the authors, the book is suitable for graduate students of mathematics and engineering. Cet ouvrage est une introduction pedagogique a la theorie de l'homogeneisation, et aux approches numeriques associees, pour la comprehension et la simulation des problemes a plusieurs echelles. La presentation est axee sur les differentes hypotheses possibles pour mettre en oeuvre la theorie, selon que le milieu ambiant a une geometrie periodique ou non. Le public vise est celui des cycles M et D des universites ainsi que celui des ecoles d'ingenieurs et formations equivalentes.
1 La dimension "zero".- 2 Homogeneisation en dimension 1.- 3 Dimension 2 : Les cas "simples" : abstrait ou periodique.- 4 Dimension 2 : Des cas explicites au-dela du periodique.- 5 Approches numeriques.- 6 Au-dela de l'equation de diffusion et sujets varies.
Format: Paperback / softback, 290 pages, height x width: 235x155 mm, X, 290 p.
Series: UNITEXT 140
Pub. Date: 23-Oct-2022
This book, the second of two volumes, contains approximately 350 exercises in Algebra which have featured exam questions for the Algebraic Structure and Algebra I courses taught by the authors at the University of Pisa. Each exercise is presented together with one or more solutions, carefully written with consistent language and notation. A distinguishing feature of this book is the fact that each exercise is unique and requires some creative thinking to be solved. The themes covered in this volume are: group theory and Sylow theorems, commutative rings with an emphasis on unique factorisation, Gaussian integers, field extensions and Galois theory. The book includes a detailed section recalling relevant theory that can be used as a reference for study and revision. A list of preliminary exercises introduces the main techniques to be applied in solving the proposed exam questions. This volume is aimed at second year students in Mathematics and Computer science.
Format: Hardback, 540 pages, height x width: 235x155 mm, 30 Tables, color; 27 Illustrations,
color; 12 Illustrations, black and white; X, 540 p. 39 illus., 27 illus. in color.
Series: Operator Theory: Advances and Applications 289
Pub. Date: 29-Nov-2022
ISBN-13: 9783031138508
This volume is dedicated to the memory of Harold Widom (1932?2021), an outstanding mathematician who has enriched mathematics with his ideas and ground breaking work since the 1950s until the present time.
It contains a biography of Harold Widom, personal notes written by his former students or colleagues, and also his last, previously unpublished paper on domain walls in a Heisenberg?Ising chain. Widom's most famous contributions were made to Toeplitz operators and random matrices. While his work on random matrices is part of almost all the present-day research activities in this field, his work in Toeplitz operators and matrices was done mainly before 2000 and is therefore described in a contribution devoted to his achievements in just this area.
The volume contains 18 invited and refereed research and expository papers on Toeplitz operators and random matrices. These present new results or new perspectives on topics related to Widom's work.
Part I: Harold Widom's Life, Work, and Last Paper.- Biography of Harold Widom.- Domain walls in the Heisenberg-Ising Spin-1/2 chain.- Harold Widom's Contributions to the Spectral Theory and Asymptotics of Toeplitz Operators and Matrices.- Visualizations of two functions emerging in connection with Toeplitz determinants.- Part II: Personal Notes.- A remarkable advisor, mentor, and friend.- My Encounters with Harold Widom.- Memories of Harold Widom.- Personal Reflection on Harold Widom.- Part III: Invited Contributions.- Loops in SU(2) and factorization, II.- Opennes of regular regimes of complex random matrix models.- Focusing nonlocal nonlinear Schrodinger equation with asymmetric boundary conditions: large-time behavior.- Algebras of commuting differential operators for integral kernels of Airy type.- A random walk on the Rado graph.- Widom factors and Szeg}o-Widom asymptotics, a review.- Some recent progress on the stationary measure for the open KPZ equation.- Probability of two large gaps in the bulk and at the edge of the spectrum of random matrices.- Multiplicative properties of infinite block Toeplitz and Hankel matrices.- Toeplitz and related operators on polyanalytic Fock spaces.- Strong Szego theorem on a Jordan curve.- Toeplitz operators with non-trivial kernels and non-dense ranges on weak Hardy spaces.- Renyi entropies of the free Fermi gas in multi-dimensional space at high temperature.- Spectral asymptotics for Toeplitz matrices having certain piecewise continuous symbols.- Global and local scaling limits for linear eigenvalue statistics of Jacobi -ensembles.- On the limit of some variable-coeffcient Toeplitz-like determinants.- On diagonalizable quantum weighted Hankel matrices.- On the product formula for Toeplitz and related operators.
Format: Paperback / softback, 603 pages, height x width: 235x155 mm,
36 Illustrations, color; 35 Illustrations, black and white; X, 603 p. 71 illus., 36 illus. in color.
Series: Lecture Notes in Mathematics 2313
Pub. Date: 01-Nov-2022
ISBN-13: 9783031122439
This volume is an original collection of articles by 44 leading mathematicians on the theme of the future of the discipline. The contributions range from musings on the future of specific fields, to analyses of the history of the discipline, to discussions of open problems and conjectures, including first solutions of unresolved problems. Interestingly, the topics do not cover all of mathematics, but only those deemed most worthy to reflect on for future generations. These topics encompass the most active parts of pure and applied mathematics, including algebraic geometry, probability, logic, optimization, finance, topology, partial differential equations, category theory, number theory, differential geometry, dynamical systems, artificial intelligence, theory of groups, mathematical physics and statistics.
Format: Hardback, 212 pages, height x width: 235x155 mm, X, 212 p., 1 Hardback
Series: Algebra and Applications 30
Pub. Date: 22-Nov-2022
ISBN-13: 9783031122873
This book offers an original introduction to the representation theory of algebras, suitable for beginning researchers in algebra. It includes many results and techniques not usually covered in introductory books, some of which appear here for the first time in book form.
The exposition employs methods from linear algebra (spectral methods and quadratic forms), as well as categorical and homological methods (module categories, Galois coverings, Hochschild cohomology) to present classical aspects of ring theory under new light. This includes topics such as rings with several objects, the Harada?Sai lemma, chain conditions, and Auslander?Reiten theory. Noteworthy and significant results covered in the book include the Brauer?Thrall conjectures, Drozdfs theorem, and criteria to distinguish tame from wild algebras.
This text may serve as the basis for a second graduate course in algebra or as an introduction to research in the field of representation theory of algebras. The originality of the exposition and the wealth of topics covered also make it a valuable resource for more established researchers.
1 Introduction and First Examples.- 2 A Categorical Approach.- 3 Constructive Methods.- 4 Spectral Methods in Representation Theory.- 5 Group Actions on Algebras and Module Categories.- 6 Reflections and Weyl Groups.- 7 Simply Connected Algebras.- 8 Degenerations of Algebras.- 9 Further Comments.
Format: Paperback / softback, 320 pages, height x width: 235x155 mm, 2 Tables, color;
3 Illustrations, color; 8 Illustrations, black and white; X, 320 p. 11 illus., 3 illus. in color.,
Series: Lecture Notes in Mathematics 2317
Pub. Date: 23-Nov-2022
ISBN-13: 9783031128790
Providing the first comprehensive account of the widely unknown cooperation and friendship between Emmy Noether and Helmut Hasse, this book contains English translations of all available letters which were exchanged between them in the years 1925-1935. It features a special chapter on class field theory, a subject which was completely renewed in those years, Noether and Hasse being among its main proponents.
These historical items give evidence that Emmy Noether's impact on the development of mathematics is not confined to abstract algebra but also extends to important ideas in modern class field theory as part of algebraic number theory. In her letters, details of proofs appear alongside conjectures and speculations, offering a rich source for those who are interested in the rise and development of mathematical notions and ideas. The letters are supplemented by extensive comments, helping the reader to understand their content within the mathematical environment of the 1920s and 1930s.