Published: 31 October 2023
Publisher: International Press of Boston, Inc.
Paperback
178 pages
This book is based upon the first in a series of lecture notes written by the author for his courses in mathematical physics at Qiuzhen College of Tsinghua University, Beijing. Its purpose is to explain the key physical elements of Lagrangian and Hamiltonian mechanics, and their relationship to modern developments in geometry. Heavy emphasis is placed on different faces of concrete examples that illustrate the bridge between mathematics and physics.
Si Li received his PhD in mathematics at Harvard University, and is currently professor in the Department of Mathematical Sciences at Tsinghua University. His specialty is mathematical physics, especially the interplay between quantum field theory and geometry/topology. He is the winner of the 2016 Morningside Gold Medal, for his construction of the quantum B-twisted string field theory, and for his solution to the Landau?Ginzburg Mirror Symmetry Conjecture. He was an invited plenary speaker at the String-Math conference in 2018 (Japan) and in 2021 (Brazil).
Published: 15 October 2023
Publisher: International Press of Boston, Inc.
Paperback
180 pages
This book is based upon a series of lecture notes written by the author for his courses in mathematical physics at Qiuzhen College of Tsinghua University. The essence of this book is to explain both the physical and the geometric aspects of modern electromagnetism, as well as the bridge between these two viewpoints. The first part of this book explains key ingredients of electromagnetic fields and their classical dynamics. The second part explains Maxwell theory in terms of the geometry of
fiber bundle. We use the language of differential forms throughout this book to illustrate the geometric and topological natures of Maxwell’s equations.
Si Li received his PhD in mathematics at Harvard University, and is currently professor in the Department of Mathematical Sciences at Tsinghua University. His specialty is mathematical physics, especially the interplay between quantum field theory and geometry/topology. He is the winner of the 2016 Morningside Gold Medal, for his construction of the quantum B-twisted string field theory, and for his solution to the Landau?Ginzburg Mirror Symmetry Conjecture. He was an invited plenary speaker at the String-Math conference in 2018 (Japan) and in 2021 (Brazil).
Format: Hardback, 1200 pages, height x width: 254x178 mm, 12 Illustrations, color; 65 Illustrations,
black and white; XX, 1200 p. 77 illus., 12 illus. in color. In 2 volumes, not available separately., 2 hardbacks
Series: Cornerstones
Pub. Date: 07-Apr-2024
ISBN-13: 9783031505065
Other books in subject:
This text gives a comprehensive introduction to the “common core” of convex geometry. Basic concepts and tools which are present in all branches of that field are presented with a highly didactic approach. Mainly directed to graduate and advanced undergraduates, the book is self-contained in such a way that it can be read by anyone who has standard undergraduate knowledge of analysis and of linear algebra. Additionally, it can be used as a single reference for a complete introduction to convex geometry, and the content coverage is sufficiently broad that the reader may gain a glimpse of the entire breadth of the field and various subfields. The book is suitable as a primary text for courses in convex geometry and also in discrete geometry (including polytopes). It is also appropriate for survey type courses in Banach space theory, convex analysis, differential geometry, and applications of measure theory. Solutions to all exercises are available to instructors who adopt the text for coursework.
Most chapters use the same structure with the first part presenting theory and the next containing a healthy range of exercises. Some of the exercises may even be considered as short introductions to ideas which are not covered in the theory portion. Each chapter has a notes section offering a rich narrative to accompany the theory, illuminating the development of ideas, and providing overviews to the literature concerning the covered topics. In most cases, these notes bring the reader to the research front. The text includes many figures that illustrate concepts and some parts of the proofs, enabling the reader to have a better understanding of the geometric meaning of the ideas. An appendix containing basic (and geometric) measure theory collects useful information for convex geometers.
Preface.-
1. Convex functions.-
2. Convex sets.-
3. A first look into polytopes.-
4. Volume and area.-
5. Classical inequalities.-
6. Mixed volumes-
7. Mixed surface area measures.-
8. The Alexandrov-Frechel inequality.-
9. Affine convex geometry Part 1.-
10. Affine convex geometry Part 2.-
11. Further selected topics.-12. Historical steps of development ofconvexity as a field.- A. Measure theory for convex geometers.- References.-
Index.
Format: Paperback / softback, 133 pages, height x width: 235x155 mm, 1 Illustrations, black and white; X, 133 p. 1 illus.,
Series: SpringerBriefs in Mathematics
Pub. Date: 11-Apr-2024
This book presents the reader with a streamlined exposition of the notions and results leading to the construction of normal forms and, ultimately, to the construction of smooth conjugacies for the perturbations of tempered exponential dichotomies. These are exponential dichotomies for which the exponential growth rates of the underlying linear dynamics never vanish. In other words, its Lyapunov exponents are all nonzero. The authors consider mostly difference equations, although they also briefly consider the case of differential equations. The content is self-contained and all proofs have been simplified or even rewritten on purpose for the book so that all is as streamlined as possible. Moreover, all chapters are supplemented by detailed notes discussing the origins of the notions and results as well as their proofs, together with the discussion of the proper context, also with references to precursor results and further developments. A useful chapter dependence chart is included in the Preface. The book is aimed at researchers and graduate students who wish to have a sufficiently broad view of the area, without the discussion of accessory material. It can also be used as a basis for graduate courses on spectra, normal forms, and smooth conjugacies.
The main components of the exposition are tempered spectra, normal forms, and smooth conjugacies. The first two lie at the core of the theory and have an importance that undoubtedly surpasses the construction of conjugacies. Indeed, the theory is very rich and developed in various directions that are also of interest by themselves. This includes the study of dynamics with discrete and continuous time, of dynamics in finite and infinite-dimensional spaces, as well as of dynamics depending on a parameter. This led the authors to make an exposition not only of tempered spectra and subsequently of normal forms, but also briefly of some important developments in those other directions. Afterwards the discussion continues with the construction of stable and unstable invariant manifolds and, consequently, of smooth conjugacies, while using most of the former material.
The notion of tempered spectrum is naturally adapted to the study of nonautonomous dynamics. The reason for this is that any autonomous linear dynamics with a tempered exponential dichotomy has automatically a uniform exponential dichotomy. Most notably, the spectra defined in terms of tempered exponential dichotomies and uniform exponential dichotomies are distinct in general. More precisely, the tempered spectrum may be smaller, which causes that it may lead to less resonances and thus to simpler normal forms. Another important aspect is the need for Lyapunov norms in the study of exponentially decaying perturbations and in the study of parameter-dependent dynamics. Other characteristics are the need for a spectral gap to obtain the regularity of the normal forms on a parameter and the need for a careful control of the small exponential terms in the construction of invariant manifolds and of smooth conjugacies.
Preface.-
1. Spectra and Examples.-
2. Asymptotic Behavior.-
3. Resonances and Normal Forms.-
4. Parameter-Dependent Dynamics.-
5. The Case of Differential Equations.-
6. Infinite-Dimensional Dynamics.-
7. Stable and Unstable Foliations.-
8. Construction of Smooth Conjugacies.- References
Format: Hardback, 545 pages, height x width: 235x155 mm, 29 Tables, color;
30 Illustrations, color; 6 Illustrations, black and white; XIII, 545 p. 36 illus., 30 illus. in color.
Series: Springer Series in Statistics
Pub. Date: 25-Mar-2024
ISBN-13: 9783031516085
This volume provides a comprehensive survey that covers various modern methods used for detecting and estimating change points in time series and their models. The book primarily focuses on asymptotic theory and practical applications of change point analysis. The methods discussed in the book go beyond the traditional change point methods for univariate and multivariate series. It also explores techniques for handling heteroscedastic series, high-dimensional series, and functional data. While the primary emphasis is on retrospective change point analysis, the book also presents sequential "on-line" methods for detecting change points in real-time scenarios. Each chapter in the book includes multiple data examples that illustrate the practical application of the developed results. These examples cover diverse fields such as economics, finance, environmental studies, and health data analysis. To reinforce the understanding of the material, each chapter concludes with several exercises. Additionally, the book provides a discussion of background literature, allowing readers to explore further resources for in-depth knowledge on specific topics. Overall, "Change Point Analysis for Time Series" offers a broad and informative overview of modern methods in change point analysis, making it a valuable resource for researchers, practitioners, and students interested in analyzing and modeling time series data.
Cumulative Sum Processes.- Change Point Analysis of the Mean.- Variance
Estimation, Change Points in Variance, and Heteroscedasticity.- Regression
Models.- Parameter Changes in Time Series Models.- Sequential
Monitoring.- High-dimensional and Panel Data.- Functional Data.
Format: Hardback, 276 pages, height x width: 235x155 mm, 9 Illustrations, black and white; XII, 276 p. 9 illus.
Pub. Date: 02-Apr-2024
ISBN-13: 9783031516047
The main goal of this book is to describe various aspects of the theory of joint spectra for matrices and linear operators. It is suitable for a graduate-level topic course in spectral theory and/or representation theory. The first three chapters can also be adopted for an advanced course in linear algebra. Centered around the concept of projective spectrum, the book presents a coherent treatment of fundamental elements from a wide range of mathematical disciplines, such as complex analysis, complex dynamics, differential geometry, functional analysis, group theory, and Lie algebras. Researchers and students, particularly those who aspire to gain a bigger picture of mathematics, will find this book both informative and resourceful.
1 Characteristic Polynomial in Several Variables.- 2 Finite Dimensional Group Representations.- 3 Finite Dimensional Lie Algebras.- 4 Projective Spectrum in Banach Algebras.- 5 The C?-algebra of the Infinite Dihedral Group.- 6 The Maurer-Cartan Form of Operator Pencils.- 7 Hermitian Metrics on the Resolvent Set.- 8 Compact Operators and Kernel Bundles.- 9 Weak Containment and Amenability.- 10 Self-similarity and Julia Sets.- References.
Format: Hardback, 370 pages, height x width: 235x155 mm, 1 Illustrations,
black and white; XVIII, 370 p. 1 illus
Series: Springer Proceedings in Mathematics & Statistics 443
Pub. Date: 11-Apr-2024
ISBN-13: 9783031507946
The book intends to be a collection of research papers on algebra and related topics, most of which were presented at the international "Workshop on Associative Rings and Algebras with additional structures (WARA22)". The purpose of the workshop WARA22 was to present the current state of the art both in the Theory of Lie structures of associative rings and algebras and in the Theory of functional identities in rings. The conference has emerged as a powerful forum offering researchers the opportunity to meet, get to know each other and discuss advances in ring theory, inspiring further research directions. The main topics covered refer to rings with involution, Lie and Jordan structures, rings and algebras arising under various constructions, modules, bimodules and ideals in associative algebras, behavior of derivations, automorphisms and other kinds of additive maps in rings and algebras. All the contributing authors are leading international academicians and researchers in their respective fields. The papers cover a wide range of topics in ring theory, group theory, matrix algebra and graph theory. The book will serve both the specialist looking for the latest results and the novice looking for the appropriate references to access the study and understanding of the results presented here.
G. S. Sandhu, B. Dhara, S. Ghosh , A note on multiplicative
(generalized)-derivations and left sided ideals in semiprime rings.- Nirbhay
Kumar, Avanish Kumar Chaturved, On weekly generalized reversible rings.- Sk
Aziz, Om Prakash, Additivity of multiplicative b-generalized (skew)
derivations.- M. O. Alshammari, F. Ali, Specht Modules and Representations of
Symmetric Group.- B. Dhara, S. Kar, K. Singh, Commutativity Theorems on Prime
Rings with Generalized Derivations.- A. Abbasi, M. R. Mozumder, Commutativity
of -prime rings with generalized derivation.- M. S. Pandey, A. Pandey, A
note on b-generalized skew derivations on prime rings.- N. ur Rehman, S. A.
Mir, M. Nazim, Analysis of some topological indices over the weakly
zero-divisor graph of the ring Zp × Zq × Zr.- Md Arshad Madni, M. S. Akhtar,
M. R. Mozumder, A study of central identities equipped with skew Lie product
involving generalized derivations.- M. R. Mozumder, N. Parveen, W. Ahmed,
Some results on left-sided ideals of semiprime rings with Symmetric (, )
n-derivations.- A. Ali, K. Kumar, M. Tasleem, Central power values of
generalized derivation and structure of unital Banach algebra.- A. Pandey, B.
Prajapati, Generalized skew derivations of order 2 in prime rings with
multilinear polynomials.- Zhi-Cheng Deng, F. Wei, Local and 2-local Lie-type
Derivations of Operator Algebras on Banach Spaces.- F. Wei, Jing-Xiong Xu,
The Noncommutative Singer-Wermer Conjecture and Generalized Skew
Derivations.- M. Ashraf, M. A. Ansari, Md Shamim Akhter, Non-global
multiplicative Lie triple derivations on rings.- A. Z. Ansari, F. Shujat,
Algebraic identities on prime and semiprime rings.- G. Scudo, Generalized
derivations with periodic values on prime rings.- L. Carini, V. De Filippis,
On a functional identity involving power values of generalized skew
derivations on Lie ideals.- M. Andaloro, Generalized Skew Derivations with
periodic values on Lie ideals.- M. Bera, B. Dhara, Generalized
skew-derivations acting on multilinear polynomials in prime rings.- M.
Salahuddin Khan, S. Ali, A. Nadim Khan, M. Ayedh, Results on b-generalized
derivations in rings.- F. Shujat, A. Z. Ansari, Results on generalized skew
bi-semiderivation in prime rings.- F. Ammendolia, Commuting iterates of
generalized derivations on Lie ideals.- M. A. Raza, T. Al-Sobhi, Non-linear
mappings preserving product m n + n m on factor von Neumann algebras.- F.
Rania, A commutativity condition for semiprime rings with generalized skew
derivations.- Faez A. Alqarni, Nadeem ur Rehman, Hafedh M. Alnoghashi,
Results on Generalized Derivations in Prime Rings with Involution.- M.
Ashraf, N. Khan, W. Rehman, G. Mohammad, Quantum codes over an extension of
Z4.- N. Parveen, Product of Traces of Permuting n-Derivations on Prime and
Semiprime Ideals of a Ring.