Solvable

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Representations of Solvable Lie Groups

Didier Arnal,Bradley Currey
Representations of Solvable Lie Groups Book PDF

Author : Didier Arnal,Bradley Currey
Publisher : Cambridge University Press
Page : 464 pages
File Size : 47,8 Mb
Release : 2020-04-08
Category : Mathematics
ISBN : 9781108651936

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Representations of Solvable Lie Groups by Didier Arnal,Bradley Currey Pdf

The theory of unitary group representations began with finite groups, and blossomed in the twentieth century both as a natural abstraction of classical harmonic analysis, and as a tool for understanding various physical phenomena. Combining basic theory and new results, this monograph is a fresh and self-contained exposition of group representations and harmonic analysis on solvable Lie groups. Covering a range of topics from stratification methods for linear solvable actions in a finite-dimensional vector space, to complete proofs of essential elements of Mackey theory and a unified development of the main features of the orbit method for solvable Lie groups, the authors provide both well-known and new examples, with a focus on those relevant to contemporary applications. Clear explanations of the basic theory make this an invaluable reference guide for graduate students as well as researchers.

Quasi-Exactly Solvable Models in Quantum Mechanics

A.G Ushveridze
Quasi Exactly Solvable Models in Quantum Mechanics Book PDF

Author : A.G Ushveridze
Publisher : CRC Press
Page : 480 pages
File Size : 46,9 Mb
Release : 2017-07-12
Category : Science
ISBN : 9781351420327

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Quasi-Exactly Solvable Models in Quantum Mechanics by A.G Ushveridze Pdf

Exactly solvable models, that is, models with explicitly and completely diagonalizable Hamiltonians are too few in number and insufficiently diverse to meet the requirements of modern quantum physics. Quasi-exactly solvable (QES) models (whose Hamiltonians admit an explicit diagonalization only for some limited segments of the spectrum) provide a practical way forward. Although QES models are a recent discovery, the results are already numerous. Collecting the results of QES models in a unified and accessible form, Quasi-Exactly Solvable Models in Quantum Mechanics provides an invaluable resource for physicists using quantum mechanics and applied mathematicians dealing with linear differential equations. By generalizing from one-dimensional QES models, the expert author constructs the general theory of QES problems in quantum mechanics. He describes the connections between QES models and completely integrable theories of magnetic chains, determines the spectra of QES Schrödinger equations using the Bethe-Iansatz solution of the Gaudin model, discusses hidden symmetry properties of QES Hamiltonians, and explains various Lie algebraic and analytic approaches to the problem of quasi-exact solubility in quantum mechanics. Because the applications of QES models are very wide, such as, for investigating non-perturbative phenomena or as a good approximation to exactly non-solvable problems, researchers in quantum mechanics-related fields cannot afford to be unaware of the possibilities of QES models.

Maximal nilpotent subalgebras II: A correspondence theorem within solvable associative algebras. With 242 exercises

Sven Bodo Wirsing
Maximal nilpotent subalgebras II A correspondence theorem within solvable associative algebras With 242 exercises Book PDF

Author : Sven Bodo Wirsing
Publisher : Anchor Academic Publishing
Page : 193 pages
File Size : 54,6 Mb
Release : 2017-11-09
Category : Mathematics
ISBN : 9783960676966

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Maximal nilpotent subalgebras II: A correspondence theorem within solvable associative algebras. With 242 exercises by Sven Bodo Wirsing Pdf

Within series II we extend the theory of maximal nilpotent substructures to solvable associative algebras, especially for their group of units and their associated Lie algebra. We construct all maximal nilpotent Lie subalgebras and characterize them by simple and double centralizer properties. They possess distinctive attractor and repeller characteristics. Their number of isomorphic classes is finite and can be bounded by Bell numbers. Cartan subalgebras and the Lie nilradical are extremal among all maximal nilpotent Lie subalgebras. The maximal nilpotent Lie subalgebras are connected to the maximal nilpotent subgroups. This correspondence is bijective via forming the group of units and creating the linear span. Cartan subalgebras and Carter subgroups as well as the Lie nilradical and the Fitting subgroup are linked by this correspondence. All partners possess the same class of nilpotency based on a theorem of Xiankun Du. By using this correspondence we transfer all results to maximal nilpotent subgroups of the group of units. Carter subgroups and the Fitting subgroup turn out to be extremal among all maximal nilpotent subgroups. All four extremal substructures are proven to be Fischer subgroups, Fischer subalgebras, nilpotent injectors and projectors. Numerous examples (like group algebras and Solomon (Tits-) algebras) illustrate the results to the reader. Within the numerous exercises these results can be applied by the reader to get a deeper insight in this theory.

New Trends in Integrability and Partial Solvability

A.B. Shabat,A. González-López,M. Mañas,L. Martínez Alonso,M.A. Rodríguez
New Trends in Integrability and Partial Solvability Book PDF

Author : A.B. Shabat,A. González-López,M. Mañas,L. Martínez Alonso,M.A. Rodríguez
Publisher : Springer Science & Business Media
Page : 297 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400710238

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New Trends in Integrability and Partial Solvability by A.B. Shabat,A. González-López,M. Mañas,L. Martínez Alonso,M.A. Rodríguez Pdf

Proceedings of the NATO Advanced Research Workshop, held in Cadiz, Spain, from 12 to 16 June 2002

Foundations of Galois Theory

M.M. Postnikov
Foundations of Galois Theory Book PDF

Author : M.M. Postnikov
Publisher : Elsevier
Page : 123 pages
File Size : 49,7 Mb
Release : 2014-07-10
Category : Mathematics
ISBN : 9781483156477

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Foundations of Galois Theory by M.M. Postnikov Pdf

Foundations of Galois Theory is an introduction to group theory, field theory, and the basic concepts of abstract algebra. The text is divided into two parts. Part I presents the elements of Galois Theory, in which chapters are devoted to the presentation of the elements of field theory, facts from the theory of groups, and the applications of Galois Theory. Part II focuses on the development of general Galois Theory and its use in the solution of equations by radicals. Equations that are solvable by radicals; the construction of equations solvable by radicals; and the unsolvability by radicals of the general equation of degree n ? 5 are discussed as well. Mathematicians, physicists, researchers, and students of mathematics will find this book highly useful.

Solvable

Arnaud Chevallier,Albrecht Enders
Solvable Book PDF

Author : Arnaud Chevallier,Albrecht Enders
Publisher : Pearson UK
Page : 246 pages
File Size : 44,5 Mb
Release : 2022-05-11
Category : Electronic
ISBN : 9781292374277

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Solvable by Arnaud Chevallier,Albrecht Enders Pdf

A 3-step process for solving complex problems of any kind: Frame, Ideate, Decide. Solvable offers practical tools that are both evidence-based and presented in an accessible and visual way to help you improve all aspects of problem solving at work and home.

Solvability Theory of Boundary Value Problems and Singular Integral Equations with Shift

Georgii S. Litvinchuk
Solvability Theory of Boundary Value Problems and Singular Integral Equations with Shift Book PDF

Author : Georgii S. Litvinchuk
Publisher : Springer Science & Business Media
Page : 388 pages
File Size : 41,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401143639

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Solvability Theory of Boundary Value Problems and Singular Integral Equations with Shift by Georgii S. Litvinchuk Pdf

The first formulations of linear boundary value problems for analytic functions were due to Riemann (1857). In particular, such problems exhibit as boundary conditions relations among values of the unknown analytic functions which have to be evaluated at different points of the boundary. Singular integral equations with a shift are connected with such boundary value problems in a natural way. Subsequent to Riemann's work, D. Hilbert (1905), C. Haseman (1907) and T. Carleman (1932) also considered problems of this type. About 50 years ago, Soviet mathematicians began a systematic study of these topics. The first works were carried out in Tbilisi by D. Kveselava (1946-1948). Afterwards, this theory developed further in Tbilisi as well as in other Soviet scientific centers (Rostov on Don, Ka zan, Minsk, Odessa, Kishinev, Dushanbe, Novosibirsk, Baku and others). Beginning in the 1960s, some works on this subject appeared systematically in other countries, e. g. , China, Poland, Germany, Vietnam and Korea. In the last decade the geography of investigations on singular integral operators with shift expanded significantly to include such countries as the USA, Portugal and Mexico. It is no longer easy to enumerate the names of the all mathematicians who made contributions to this theory. Beginning in 1957, the author also took part in these developments. Up to the present, more than 600 publications on these topics have appeared.

Approximation-solvability of Nonlinear Functional and Differential Equations

Wolodymyr V. Petryshyn
Approximation solvability of Nonlinear Functional and Differential Equations Book PDF

Author : Wolodymyr V. Petryshyn
Publisher : Routledge
Page : 227 pages
File Size : 51,7 Mb
Release : 2017-11-22
Category : Mathematics
ISBN : 9781351465700

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Approximation-solvability of Nonlinear Functional and Differential Equations by Wolodymyr V. Petryshyn Pdf

This reference/text develops a constructive theory of solvability on linear and nonlinear abstract and differential equations - involving A-proper operator equations in separable Banach spaces, and treats the problem of existence of a solution for equations involving pseudo-A-proper and weakly-A-proper mappings, and illustrates their applications.;Facilitating the understanding of the solvability of equations in infinite dimensional Banach space through finite dimensional appoximations, this book: offers an elementary introductions to the general theory of A-proper and pseudo-A-proper maps; develops the linear theory of A-proper maps; furnishes the best possible results for linear equations; establishes the existence of fixed points and eigenvalues for P-gamma-compact maps, including classical results; provides surjectivity theorems for pseudo-A-proper and weakly-A-proper mappings that unify and extend earlier results on monotone and accretive mappings; shows how Friedrichs' linear extension theory can be generalized to the extensions of densely defined nonlinear operators in a Hilbert space; presents the generalized topological degree theory for A-proper mappings; and applies abstract results to boundary value problems and to bifurcation and asymptotic bifurcation problems.;There are also over 900 display equations, and an appendix that contains basic theorems from real function theory and measure/integration theory.

Introduction to Abstract Algebra

Benjamin Fine,Anthony M. Gaglione,Gerhard Rosenberger
Introduction to Abstract Algebra Book PDF

Author : Benjamin Fine,Anthony M. Gaglione,Gerhard Rosenberger
Publisher : JHU Press
Page : 583 pages
File Size : 45,5 Mb
Release : 2014-07
Category : Mathematics
ISBN : 9781421411767

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Introduction to Abstract Algebra by Benjamin Fine,Anthony M. Gaglione,Gerhard Rosenberger Pdf

Presents a systematic approach to one of math's most intimidating concepts. Avoiding the pitfalls common in the standard textbooks, this title begins with familiar topics such as rings, numbers, and groups before introducing more difficult concepts.

Lie Algebras of Bounded Operators

Daniel Beltita,Mihai Sabac
Lie Algebras of Bounded Operators Book PDF

Author : Daniel Beltita,Mihai Sabac
Publisher : Springer Science & Business Media
Page : 240 pages
File Size : 47,6 Mb
Release : 2001-04-01
Category : Mathematics
ISBN : 3764364041

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Lie Algebras of Bounded Operators by Daniel Beltita,Mihai Sabac Pdf

In several proofs from the theory of finite-dimensional Lie algebras, an essential contribution comes from the Jordan canonical structure of linear maps acting on finite-dimensional vector spaces. On the other hand, there exist classical results concerning Lie algebras which advise us to use infinite-dimensional vector spaces as well. For example, the classical Lie Theorem asserts that all finite-dimensional irreducible representations of solvable Lie algebras are one-dimensional. Hence, from this point of view, the solvable Lie algebras cannot be distinguished from one another, that is, they cannot be classified. Even this example alone urges the infinite-dimensional vector spaces to appear on the stage. But the structure of linear maps on such a space is too little understood; for these linear maps one cannot speak about something like the Jordan canonical structure of matrices. Fortunately there exists a large class of linear maps on vector spaces of arbi trary dimension, having some common features with the matrices. We mean the bounded linear operators on a complex Banach space. Certain types of bounded operators (such as the Dunford spectral, Foia§ decomposable, scalar generalized or Colojoara spectral generalized operators) actually even enjoy a kind of Jordan decomposition theorem. One of the aims of the present book is to expound the most important results obtained until now by using bounded operators in the study of Lie algebras.

American Journal of Mathematics

Anonim
American Journal of Mathematics Book PDF

Author : Anonim
Publisher : Unknown
Page : 424 pages
File Size : 52,8 Mb
Release : 1886
Category : Electronic journals
ISBN : UOM:39015085207010

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American Journal of Mathematics by Anonim Pdf

The American Journal of Mathematics publishes research papers and articles of broad appeal covering the major areas of contemporary mathematics.

Non-Associative Algebra and Its Applications

Lev Sabinin,Larissa Sbitneva,Ivan Shestakov
Non Associative Algebra and Its Applications Book PDF

Author : Lev Sabinin,Larissa Sbitneva,Ivan Shestakov
Publisher : CRC Press
Page : 558 pages
File Size : 49,5 Mb
Release : 2006-01-13
Category : Mathematics
ISBN : 0824726693

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Non-Associative Algebra and Its Applications by Lev Sabinin,Larissa Sbitneva,Ivan Shestakov Pdf

With contributions derived from presentations at an international conference, Non-Associative Algebra and Its Applications explores a wide range of topics focusing on Lie algebras, nonassociative rings and algebras, quasigroups, loops, and related systems as well as applications of nonassociative algebra to geometry, physics, and natural sciences. This book covers material such as Jordan superalgebras, nonassociative deformations, nonassociative generalization of Hopf algebras, the structure of free algebras, derivations of Lie algebras, and the identities of Albert algebra. It also includes applications of smooth quasigroups and loops to differential geometry and relativity.

Exercises in Algebra

AlexandraI. Kostrikin
Exercises in Algebra Book PDF

Author : AlexandraI. Kostrikin
Publisher : Routledge
Page : 474 pages
File Size : 54,9 Mb
Release : 2019-01-22
Category : Mathematics
ISBN : 9781351449366

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Exercises in Algebra by AlexandraI. Kostrikin Pdf

This text contains more than 2000 exercises in algebra. These exercises are currently used in teaching a fundamental course in algebra in the Department of Mechanics and Mathematics at Moscow State University. The text is divided into three parts, which correspond to three semesters of study. Each section contains not only standard exercises, but also more difficult exercises at the end of some sections, these more challenging exercises being marked with asterisks. At the end of the book, results of calculations, a list of notations and basic definitions are given.

Crystallographic Groups and Their Generalizations

Paul Igodt,Herbert Abels,Yves Félix,Fritz Grunewald
Crystallographic Groups and Their Generalizations Book PDF

Author : Paul Igodt,Herbert Abels,Yves Félix,Fritz Grunewald
Publisher : American Mathematical Soc.
Page : 310 pages
File Size : 40,7 Mb
Release : 2000
Category : Science
ISBN : 9780821820018

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Crystallographic Groups and Their Generalizations by Paul Igodt,Herbert Abels,Yves Félix,Fritz Grunewald Pdf

This volume contains articles written by the invited speakers and workshop participants from the conference on 'Crystallographic Groups and Their Generalizations', held at Katholieke Universiteit Leuven, Kortrijk (Belgium). Presented are recent developments and open problems. Topics include the theory of affine structures and polynomial structures, affine Schottky groups and crooked tilings, theory and problems on the geometry of finitely generated solvable groups, flat Lorentz 3-manifolds and Fuchsian groups, filiform Lie algebras, hyperbolic automorphisms and Anosov diffeomorphisms on infra-nilmanifolds, localization theory of virtually nilpotent groups and aspherical spaces, projective varieties, and results on affine appartment systems. Participants delivered high-level research mathematics and a discussion was held forum for new researchers. The survey results and original papers contained in this volume offer a comprehensive view of current developments in the field.

Solvable Models in Quantum Mechanics

Sergio Albeverio,Friedrich Gesztesy,Raphael Hoegh-Krohn,Helge Holden
Solvable Models in Quantum Mechanics Book PDF

Author : Sergio Albeverio,Friedrich Gesztesy,Raphael Hoegh-Krohn,Helge Holden
Publisher : Springer Science & Business Media
Page : 458 pages
File Size : 41,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642882012

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Solvable Models in Quantum Mechanics by Sergio Albeverio,Friedrich Gesztesy,Raphael Hoegh-Krohn,Helge Holden Pdf

Next to the harmonic oscillator and the Coulomb potential the class of two-body models with point interactions is the only one where complete solutions are available. All mathematical and physical quantities can be calculated explicitly which makes this field of research important also for more complicated and realistic models in quantum mechanics. The detailed results allow their implementation in numerical codes to analyse properties of alloys, impurities, crystals and other features in solid state quantum physics. This monograph presents in a systematic way the mathematical approach and unifies results obtained in recent years. The student with a sound background in mathematics will get a deeper understanding of Schrödinger Operators and will see many examples which may eventually be used with profit in courses on quantum mechanics and solid state physics. The book has textbook potential in mathematical physics and is suitable for additional reading in various fields of theoretical quantum physics.