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Author : Arif Salimov
Publisher : Unknown
Page : 200 pages
File Size : 52,7 Mb
Release : 2013
Category : Tensor algebra
ISBN : 1622571045
Author : Liqun Qi,Haibin Chen,Yannan Chen
Publisher : Springer
Page : 329 pages
File Size : 48,8 Mb
Release : 2018-03-30
Category : Mathematics
ISBN : 9789811080586
This book offers an introduction to applications prompted by tensor analysis, especially by the spectral tensor theory developed in recent years. It covers applications of tensor eigenvalues in multilinear systems, exponential data fitting, tensor complementarity problems, and tensor eigenvalue complementarity problems. It also addresses higher-order diffusion tensor imaging, third-order symmetric and traceless tensors in liquid crystals, piezoelectric tensors, strong ellipticity for elasticity tensors, and higher-order tensors in quantum physics. This book is a valuable reference resource for researchers and graduate students who are interested in applications of tensor eigenvalues.
Author : Raul Curto,Martin Mathieu
Publisher : Springer Science & Business Media
Page : 156 pages
File Size : 40,5 Mb
Release : 2011-02-24
Category : Mathematics
ISBN : 9783034800372
This volume contains solicited articles by speakers at the workshop ranging from expository surveys to original research papers, each of which carefully refereed. They all bear witness to the very rich mathematics that is connected with the study of elementary operators, may it be multivariable spectral theory, the invariant subspace problem or tensor products of C*-algebras.
Author : L. C. Biedenharn,M. A. Lohe
Publisher : World Scientific
Page : 305 pages
File Size : 43,7 Mb
Release : 1995
Category : Science
ISBN : 9789810223311
Quantum groups are a generalization of the classical Lie groups and Lie algebras and provide a natural extension of the concept of symmetry fundamental to physics. This monograph is a survey of the major developments in quantum groups, using an original approach based on the fundamental concept of a tensor operator. Using this concept, properties of both the algebra and co-algebra are developed from a single uniform point of view, which is especially helpful for understanding the noncommuting co-ordinates of the quantum plane, which we interpret as elementary tensor operators. Representations of the q-deformed angular momentum group are discussed, including the case where q is a root of unity, and general results are obtained for all unitary quantum groups using the method of algebraic induction. Tensor operators are defined and discussed with examples, and a systematic treatment of the important (3j) series of operators is developed in detail. This book is a good reference for graduate students in physics and mathematics.
Author : Brian L. Silver
Publisher : Academic Press
Page : 248 pages
File Size : 45,9 Mb
Release : 2013-09-17
Category : Mathematics
ISBN : 9781483191812
Irreducible Tensor Methods: An Introduction for Chemists explains the theory and application of irreducible tensor operators. The book discusses a compact formalism to describe the effect that results on an arbitrary function of a given set of coordinates when that set is subjected to a rotation about its origin. The text also explains the concept of irreducible tensor operators, particularly, as regards the transformation properties of operators under coordinate transformations, and, in a special way, the group of rotations. The book examines the systematic construction of compound tensor operators from simple operators to classify the behavior of any operator under coordinate rotations. This classification is a significant component of the irreducible tensor method. The text explains the use of the 6-j and 9-j symbols to complete theoretical concepts that are applied in irreducible tensor methods dealing with problems of atomic and molecular physics. The book describes the matrix elements in multielectron systems, as well as the reduced matrix elements found in these systems. The book is suitable for nuclear physicists, molecular physicists, scientists, and academicians in the field of quantum mechanics or advanced chemistry.
Author : Quddus Khan
Publisher : Misha Books
Page : 578 pages
File Size : 55,5 Mb
Release : 2020-12-29
Category : Mathematics
ISBN : 9789389055320
This book is intended to serve as a Textbook for Undergraduate and Post - graduate students of Mathematics. It will be useful to the researchers working in the field of Differential geometry and its applications to general theory of relativity and other applied areas. It will also be helpful in preparing for the competitive examinations like IAS, IES, NET, PCS, and UP Higher Education exams. The text starts with a chapter on Preliminaries discussing basic concepts and results which would be taken for general later in the subsequent chapters of this book. This is followed by the Study of the Tensors Algebra and its operations and types, Christoffel's symbols and its properties, the concept of covariant differentiation and its properties, Riemann's symbols and its properties, and application of tensor in different areas in part – I and the study of the Theory of Curves in Space, Concepts of a Surface and Fundamental forms, Envelopes and Developables, Curvature of Surface and Lines of Curvature, Fundamental Equations of Surface Theory, Theory of Geodesics, Differentiable Manifolds and Riemannian Manifold and Application of Differential Geometry in Part –II. KEY FEATURES: Provides basic Concepts in an easy to understand style; Presentation of the subject in a natural way; Includes a large number of solved examples and illuminating illustrations; Exercise questions at the end of the topic and at the end of each chapter; Proof of the theorems are given in an easy to understand style; Neat and clean figures are given at appropriate places; Notes and remarks are given at appropriate places.
Author : Francisco Bulnes
Publisher : BoD – Books on Demand
Page : 142 pages
File Size : 43,7 Mb
Release : 2020-09-09
Category : Mathematics
ISBN : 9781839625558
This book brings together recent advances in tensor analysis and studies of its invariants such as twistors, spinors, kinematic tensors and others belonging to tensor algebras with extended structures to Lie algebras, Kac-Moody algebras, and enveloping algebras, among others. Chapters cover such topics as classical tensors and bilinear forms, tensors for exploring space–time, tensor applications in geometry and continuum media, and advanced topics in tensor analysis such as invariant theory, derived categories, hypercohomologies, k-modules, extensions of kinematic tensors, infinite dimensional operators, and more.
Author : Shi-Ju Ran,Emanuele Tirrito,Cheng Peng,Xi Chen,Luca Tagliacozzo,Gang Su,Maciej Lewenstein
Publisher : Springer Nature
Page : 160 pages
File Size : 43,6 Mb
Release : 2020-01-27
Category : Science
ISBN : 9783030344894
Tensor network is a fundamental mathematical tool with a huge range of applications in physics, such as condensed matter physics, statistic physics, high energy physics, and quantum information sciences. This open access book aims to explain the tensor network contraction approaches in a systematic way, from the basic definitions to the important applications. This book is also useful to those who apply tensor networks in areas beyond physics, such as machine learning and the big-data analysis. Tensor network originates from the numerical renormalization group approach proposed by K. G. Wilson in 1975. Through a rapid development in the last two decades, tensor network has become a powerful numerical tool that can efficiently simulate a wide range of scientific problems, with particular success in quantum many-body physics. Varieties of tensor network algorithms have been proposed for different problems. However, the connections among different algorithms are not well discussed or reviewed. To fill this gap, this book explains the fundamental concepts and basic ideas that connect and/or unify different strategies of the tensor network contraction algorithms. In addition, some of the recent progresses in dealing with tensor decomposition techniques and quantum simulations are also represented in this book to help the readers to better understand tensor network. This open access book is intended for graduated students, but can also be used as a professional book for researchers in the related fields. To understand most of the contents in the book, only basic knowledge of quantum mechanics and linear algebra is required. In order to fully understand some advanced parts, the reader will need to be familiar with notion of condensed matter physics and quantum information, that however are not necessary to understand the main parts of the book. This book is a good source for non-specialists on quantum physics to understand tensor network algorithms and the related mathematics.
Author : G Lumer
Publisher : CRC Press
Page : 534 pages
File Size : 52,9 Mb
Release : 2000-11-08
Category : Medical
ISBN : 0824790103
This volume presents a collection of lectures on linear partial differntial equations and semigroups, nonlinear equations, stochastic evolutionary processes, and evolution problems from physics, engineering and mathematical biology. The contributions come from the 6th International Conference on Evolution Equations and Their Applications in Physical and Life Sciences, held in Bad Herrenalb, Germany.
Author : J A Tuszynski
Publisher : World Scientific
Page : 332 pages
File Size : 44,8 Mb
Release : 1990-08-06
Category : Electronic
ISBN : 9789814506816
This book contains introductory comments concerning the definitions, the symmetry properties and the basic formulae for matrix elements of tensor operators. The main body of text consists of tables of reduced matrix elements of double tensor operators within pn,dn and fn configurations, i.e. all the principal pure configurations of the atomic and nuclear structure. These tables are complete which means that the author has run through all the states of the following configurations: p2, p3, d2, d3, d4, d5, f2, f3, f4, f5, f6, f7 for multiparticle systems with central symmetry. Double tensor operators wk1k2 have been chosen in these calculations, for a number of reasons. First of all, they are the most general type of spherical tensor operators and, since they are normalized, they are the most convenient to use. Secondly, they have been very frequently used in many areas of physics, most notably in nuclear, atomic, molecular and solid state physics. There are also tabulated conversion factors to enable the use of these tables for other types of definitions of tensor operators. Contents: IntroductionTablesReferencesTables of Reduced Matrix Elements Readership: Atomic and mathematical physicists. Keywords:Tensor Operators;Reduced Matrix Elements
Author : Asim Orhan Barut,Ryszard R?czka
Publisher : World Scientific
Page : 750 pages
File Size : 52,8 Mb
Release : 1986
Category : Mathematics
ISBN : 9971502178
Lie!algebras - Topological!groups - Lie!groups - Representations - Special!functions - Induced!representations.
Author : Robert S. Doran,Efton Park
Publisher : American Mathematical Soc.
Page : 267 pages
File Size : 51,6 Mb
Release : 2016-07-28
Category : Operator algebras
ISBN : 9781470419486
his volume contains the proceedings of the AMS Special Session Operator Algebras and Their Applications: A Tribute to Richard V. Kadison, held from January 10–11, 2015, in San Antonio, Texas. Richard V. Kadison has been a towering figure in the study of operator algebras for more than 65 years. His research and leadership in the field have been fundamental in the development of the subject, and his influence continues to be felt though his work and the work of his many students, collaborators, and mentees. Among the topics addressed in this volume are the Kadison-Kaplanksy conjecture, classification of C∗-algebras, connections between operator spaces and parabolic induction, spectral flow, C∗-algebra actions, von Neumann algebras, and applications to mathematical physics.
Author : Nazrul Islam
Publisher : New Age International
Page : 6 pages
File Size : 51,5 Mb
Release : 2006-12
Category : Tensor algebra
ISBN : 9788122418385
The Book Is Written Is In Easy-To-Read Style With Corresponding Examples. The Main Aim Of This Book Is To Precisely Explain The Fundamentals Of Tensors And Their Applications To Mechanics, Elasticity, Theory Of Relativity, Electromagnetic, Riemannian Geometry And Many Other Disciplines Of Science And Engineering, In A Lucid Manner. The Text Has Been Explained Section Wise, Every Concept Has Been Narrated In The Form Of Definition, Examples And Questions Related To The Concept Taught. The Overall Package Of The Book Is Highly Useful And Interesting For The People Associated With The Field.
Author : Peter A. Fillmore,James A. Mingo
Publisher : American Mathematical Soc.
Page : 338 pages
File Size : 42,7 Mb
Release : 2024-06-28
Category : Mathematics
ISBN : 0821871218
The study of operator algebras, which grew out of von Neumann's work in the 1920s and the 1930s on modelling quantum mechanics, has in recent years experienced tremendous growth and vitality. This growth has resulted in significant applications in other areas - both within and outside mathematics. The field was a natural candidate for a 1994-1995 program year in Operator Algebras and Applications held at The Fields Institute for Research in the Mathematical Sciences. This volume contains a selection of papers that arose from the seminars and workshops of the program. Topics covered include the classification of amenable C*-algebras, the Baum-Connes conjecture, E[subscript 0] semigroups, subfactors, E-theory, quasicrystals, and the solution to a long-standing problem in operator theory: Can almost commuting self-adjoint matrices be approximated by commuting self-adjoint matrices?
Author : Edoardo Angelo Di Napoli,Paolo Bientinesi,Jiajia Li,André Uschmajew
Publisher : Frontiers Media SA
Page : 192 pages
File Size : 42,5 Mb
Release : 2022-11-08
Category : Science
ISBN : 9782832504253
