Theory and Computation of Tensors

Theory and Computation of Tensors
Author: Yimin Wei,Weiyang Ding
Publsiher: Academic Press
Total Pages: 148
Release: 2016-08-28
ISBN 10: 0128039809
ISBN 13: 9780128039809
Language: EN, FR, DE, ES & NL

Theory and Computation of Tensors Book Review:

Theory and Computation of Tensors: Multi-Dimensional Arrays investigates theories and computations of tensors to broaden perspectives on matrices. Data in the Big Data Era is not only growing larger but also becoming much more complicated. Tensors (multi-dimensional arrays) arise naturally from many engineering or scientific disciplines because they can represent multi-relational data or nonlinear relationships. Provides an introduction of recent results about tensors Investigates theories and computations of tensors to broaden perspectives on matrices Discusses how to extend numerical linear algebra to numerical multi-linear algebra Offers examples of how researchers and students can engage in research and the applications of tensors and multi-dimensional arrays

Theory and Computation of Complex Tensors and its Applications

Theory and Computation of Complex Tensors and its Applications
Author: Maolin Che,Yimin Wei
Publsiher: Springer Nature
Total Pages: 250
Release: 2020-04-01
ISBN 10: 9811520593
ISBN 13: 9789811520594
Language: EN, FR, DE, ES & NL

Theory and Computation of Complex Tensors and its Applications Book Review:

The book provides an introduction of very recent results about the tensors and mainly focuses on the authors' work and perspective. A systematic description about how to extend the numerical linear algebra to the numerical multi-linear algebra is also delivered in this book. The authors design the neural network model for the computation of the rank-one approximation of real tensors, a normalization algorithm to convert some nonnegative tensors to plane stochastic tensors and a probabilistic algorithm for locating a positive diagonal in a nonnegative tensors, adaptive randomized algorithms for computing the approximate tensor decompositions, and the QR type method for computing U-eigenpairs of complex tensors. This book could be used for the Graduate course, such as Introduction to Tensor. Researchers may also find it helpful as a reference in tensor research.

Theory and Computation of Tensors

Theory and Computation of Tensors
Author: Yimin Wei,Weiyang Ding
Publsiher: Academic Press
Total Pages: 148
Release: 2016-09-01
ISBN 10: 9780128039533
ISBN 13: 0128039531
Language: EN, FR, DE, ES & NL

Theory and Computation of Tensors Book Review:

"Theory and Computation of Tensors: Multi-Dimensional Arrays" investigates theories and computations of tensors to broaden perspectives on matrices. Data in the Big Data Era is not only growing larger but also becoming much more complicated. Tensors (multi-dimensional arrays) arise naturally from many engineering or scientific disciplines because they can represent multi-relational data or nonlinear relationships. Provides an introduction of recent results about tensorsInvestigates theories and computations of tensors to broaden perspectives on matricesDiscusses how to extend numerical linear algebra to numerical multi-linear algebraOffers examples of how researchers and students can engage in research and the applications of tensors and multi-dimensional arrays

Tensors for Data Processing

Tensors for Data Processing
Author: Yipeng Liu
Publsiher: Academic Press
Total Pages: 596
Release: 2021-10-21
ISBN 10: 0323859658
ISBN 13: 9780323859653
Language: EN, FR, DE, ES & NL

Tensors for Data Processing Book Review:

Tensors for Data Processing: Theory, Methods and Applications presents both classical and state-of-the-art methods on tensor computation for data processing, covering computation theories, processing methods, computing and engineering applications, with an emphasis on techniques for data processing. This reference is ideal for students, researchers and industry developers who want to understand and use tensor-based data processing theories and methods. As a higher-order generalization of a matrix, tensor-based processing can avoid multi-linear data structure loss that occurs in classical matrix-based data processing methods. This move from matrix to tensors is beneficial for many diverse application areas, including signal processing, computer science, acoustics, neuroscience, communication, medical engineering, seismology, psychometric, chemometrics, biometric, quantum physics and quantum chemistry. Provides a complete reference on classical and state-of-the-art tensor-based methods for data processing Includes a wide range of applications from different disciplines Gives guidance for their application

Computation of Nonlinear Structures

Computation of Nonlinear Structures
Author: Debabrata Ray
Publsiher: John Wiley & Sons
Total Pages: 992
Release: 2015-12-14
ISBN 10: 111899695X
ISBN 13: 9781118996959
Language: EN, FR, DE, ES & NL

Computation of Nonlinear Structures Book Review:

Comprehensively introduces linear and nonlinear structural analysis through mesh generation, solid mechanics and a new numerical methodology called c-type finite element method Takes a self-contained approach of including all the essential background materials such as differential geometry, mesh generation, tensor analysis with particular elaboration on rotation tensor, finite element methodology and numerical analysis for a thorough understanding of the topics Presents for the first time in closed form the geometric stiffness, the mass, the gyroscopic damping and the centrifugal stiffness matrices for beams, plates and shells Includes numerous examples and exercises Presents solutions for locking problems

Tensor Spaces and Numerical Tensor Calculus

Tensor Spaces and Numerical Tensor Calculus
Author: Wolfgang Hackbusch
Publsiher: Springer Nature
Total Pages: 605
Release: 2019-12-16
ISBN 10: 3030355543
ISBN 13: 9783030355548
Language: EN, FR, DE, ES & NL

Tensor Spaces and Numerical Tensor Calculus Book Review:

Special numerical techniques are already needed to deal with n × n matrices for large n. Tensor data are of size n × n ×...× n=nd, where nd exceeds the computer memory by far. They appear for problems of high spatial dimensions. Since standard methods fail, a particular tensor calculus is needed to treat such problems. This monograph describes the methods by which tensors can be practically treated and shows how numerical operations can be performed. Applications include problems from quantum chemistry, approximation of multivariate functions, solution of partial differential equations, for example with stochastic coefficients, and more. In addition to containing corrections of the unavoidable misprints, this revised second edition includes new parts ranging from single additional statements to new subchapters. The book is mainly addressed to numerical mathematicians and researchers working with high-dimensional data. It also touches problems related to Geometric Algebra.

Atomic and Molecular Nonlinear Optics Theory Experiment and Computation

Atomic and Molecular Nonlinear Optics  Theory  Experiment and Computation
Author: G. Maroulis,T. Bancewicz,B. Champagne
Publsiher: IOS Press
Total Pages: 544
Release: 2011-05-27
ISBN 10: 1607507420
ISBN 13: 9781607507420
Language: EN, FR, DE, ES & NL

Atomic and Molecular Nonlinear Optics Theory Experiment and Computation Book Review:

The papers collected in this volume in honor of the late Stanisław Kielich cover an impressive range of modern subjects in molecular science. These subjects include, among others, the nonlinear optics of molecules, new approaches to the electronic structure of large molecules, the properties of carbon nanotubes, fluorescence polarization spectroscopy, computational studies of systems of fundamental interest to collision-induced spectroscopy, the simulation of fluids, NLO materials, chemical bonding in complex molecules, the NLO properties of functionalized DNA and the magnetic properties of molecular assemblies. Written by eminent specialists, the papers should offer valuable guidance to a wide community of graduate students and researchers.

Tensor Analysis

Tensor Analysis
Author: Liqun Qi,Ziyan Luo
Publsiher: SIAM
Total Pages: 318
Release: 2017-04-19
ISBN 10: 1611974755
ISBN 13: 9781611974751
Language: EN, FR, DE, ES & NL

Tensor Analysis Book Review:

Tensors, or hypermatrices, are multi-arrays with more than two indices. In the last decade or so, many concepts and results in matrix theory?some of which are nontrivial?have been extended to tensors and have a wide range of applications (for example, spectral hypergraph theory, higher order Markov chains, polynomial optimization, magnetic resonance imaging, automatic control, and quantum entanglement problems). The authors provide a comprehensive discussion of this new theory of tensors. Tensor Analysis: Spectral Theory and Special Tensors is unique in that it is the first book on these three subject areas: spectral theory of tensors; the theory of special tensors, including nonnegative tensors, positive semidefinite tensors, completely positive tensors, and copositive tensors; and the spectral hypergraph theory via tensors.

Tensors

Tensors
Author: J. M. Landsberg
Publsiher: American Mathematical Soc.
Total Pages: 439
Release: 2011-12-14
ISBN 10: 0821869078
ISBN 13: 9780821869079
Language: EN, FR, DE, ES & NL

Tensors Book Review:

Tensors are ubiquitous in the sciences. The geometry of tensors is both a powerful tool for extracting information from data sets, and a beautiful subject in its own right. This book has three intended uses: a classroom textbook, a reference work for researchers in the sciences, and an account of classical and modern results in (aspects of) the theory that will be of interest to researchers in geometry. For classroom use, there is a modern introduction to multilinear algebra and to the geometry and representation theory needed to study tensors, including a large number of exercises. For researchers in the sciences, there is information on tensors in table format for easy reference and a summary of the state of the art in elementary language. This is the first book containing many classical results regarding tensors. Particular applications treated in the book include the complexity of matrix multiplication, P versus NP, signal processing, phylogenetics, and algebraic statistics. For geometers, there is material on secant varieties, G-varieties, spaces with finitely many orbits and how these objects arise in applications, discussions of numerous open questions in geometry arising in applications, and expositions of advanced topics such as the proof of the Alexander-Hirschowitz theorem and of the Weyman-Kempf method for computing syzygies.

Computational Tensor Analysis of Shell Structures

Computational Tensor Analysis of Shell Structures
Author: Steve Naomis,Paul C.M. Lau
Publsiher: Springer Science & Business Media
Total Pages: 309
Release: 2012-12-06
ISBN 10: 3642842437
ISBN 13: 9783642842436
Language: EN, FR, DE, ES & NL

Computational Tensor Analysis of Shell Structures Book Review:

This book presents a method which is capable of evaluating the deformation characteristics of thin shell structures A free vibration analysis is chosen as a convenient means of studying the displacement behaviour of the shell, enabling it to deform naturally without imposing any particular loading conditions. The strain-displacement equations for thin shells of arbitrary geometry are developed. These relationships are expressed in general curvilinear coordinates and are formulated entirely in the framework of tensor calculus. The resulting theory is not restricted to shell structures characterized by any particular geometric form, loading or boundary conditions. The complete displacement and strain equations developed by Flugge are approximated by the curvilinear finite difference method and are applied to computing the natural frequencies and mode shapes of general thin shells. This approach enables both the displacement components and geometric properties of the shell to be approximated numerically and accurately. The selection of an appropriate displacement field to approximate the deformation of the shell within each finite difference mesh is discussed in detail. In addition, comparisons are made between the use of second and third-order finite difference interpolation meshes.

Tensors Asymptotic Geometry and Developments 2016 2018

Tensors  Asymptotic Geometry and Developments 2016   2018
Author: J.M. Landsberg
Publsiher: American Mathematical Soc.
Total Pages: 144
Release: 2019-07-05
ISBN 10: 1470451360
ISBN 13: 9781470451363
Language: EN, FR, DE, ES & NL

Tensors Asymptotic Geometry and Developments 2016 2018 Book Review:

Tensors are used throughout the sciences, especially in solid state physics and quantum information theory. This book brings a geometric perspective to the use of tensors in these areas. It begins with an introduction to the geometry of tensors and provides geometric expositions of the basics of quantum information theory, Strassen's laser method for matrix multiplication, and moment maps in algebraic geometry. It also details several exciting recent developments regarding tensors in general. In particular, it discusses and explains the following material previously only available in the original research papers: (1) Shitov's 2017 refutation of longstanding conjectures of Strassen on rank additivity and Common on symmetric rank; (2) The 2017 Christandl-Vrana-Zuiddam quantum spectral points that bring together quantum information theory, the asymptotic geometry of tensors, matrix multiplication complexity, and moment polytopes in geometric invariant theory; (3) the use of representation theory in quantum information theory, including the solution of the quantum marginal problem; (4) the use of tensor network states in solid state physics, and (5) recent geometric paths towards upper bounds for the complexity of matrix multiplication. Numerous open problems appropriate for graduate students and post-docs are included throughout.

Theoretical and Computational Research in the 21st Century

Theoretical and Computational Research in the 21st Century
Author: Nazmul Islam
Publsiher: CRC Press
Total Pages: 282
Release: 2014-10-28
ISBN 10: 1771880333
ISBN 13: 9781771880336
Language: EN, FR, DE, ES & NL

Theoretical and Computational Research in the 21st Century Book Review:

This book focuses mainly on the recent developments of all types of theoretical, mathematical, and computational conceptions, as well as modelling and simulation of specific research themes covering all scientific and technical disciplines from chemistry, physics, and engineering to biology and medicine. The book contains timely reviews and research covering fundamental and applied research aspects in all disciplines of natural sciences, including their historical representations and philosophical perspectives. The book discusses the fact that the largest and smallest values of the fukui function and local softness do not necessarily correspond to the softness and hardness regions of the molecules such as porphyrins. The authors have adopted two popular calculation procedures for this venture. One is the very old Hückel molecular orbital calculation, and the other is one of best semi-empirical AM-1 procedures for such systems. Our finding is that neither the fukui functions nor the local softnesses can predict the preferred donor sites of porphyrins toward metal ions.

TENSORS

TENSORS
Author: AHSAN, ZAFAR
Publsiher: PHI Learning Pvt. Ltd.
Total Pages: 240
Release: 2015-05-21
ISBN 10: 812035088X
ISBN 13: 9788120350885
Language: EN, FR, DE, ES & NL

TENSORS Book Review:

The principal aim of analysis of tensors is to investigate those relations which remain valid when we change from one coordinate system to another. This book on Tensors requires only a knowledge of elementary calculus, differential equations and classical mechanics as pre-requisites. It provides the readers with all the information about the tensors along with the derivation of all the tensorial relations/equations in a simple manner. The book also deals in detail with topics of importance to the study of special and general relativity and the geometry of differentiable manifolds with a crystal clear exposition. The concepts dealt within the book are well supported by a number of solved examples. A carefully selected set of unsolved problems is also given at the end of each chapter, and the answers and hints for the solution of these problems are given at the end of the book. The applications of tensors to the fields of differential geometry, relativity, cosmology and electromagnetism is another attraction of the present book. This book is intended to serve as text for postgraduate students of mathematics, physics and engineering. It is ideally suited for both students and teachers who are engaged in research in General Theory of Relativity and Differential Geometry.

EPR of Free Radicals in Solids I

EPR of Free Radicals in Solids I
Author: Anders Lund,Masaru Shiotani
Publsiher: Springer Science & Business Media
Total Pages: 414
Release: 2012-12-12
ISBN 10: 9400748930
ISBN 13: 9789400748934
Language: EN, FR, DE, ES & NL

EPR of Free Radicals in Solids I Book Review:

EPR of Free Radicals in Solids: Trends in Methods and Applications, 2nd ed. presents a critical two volume review of the methods and applications of EPR (ESR) for the study of free radical processes in solids. Emphasis is on the progress made in the developments in EPR technology, in the application of sophisticated matrix isolation techniques and in the advancement in quantitative EPR that have occurred since the 1st edition was published. Improvements have been made also at theoretical level, with the development of methods based on first principles and their application to the calculation of magnetic properties as well as in spectral simulations. EPR of Free Radicals in Solids I focuses on the trends in experimental and theoretical methods to extract structural and dynamical properties of radicals and spin probes in solid matrices by continuous wave (CW) and pulsed techniques. It presents simulation techniques and software for CW and pulsed EPR as well as studies of quantum effects at low temperature. The chapters dealing with quantum chemistry methods for the theoretical interpretation of hyperfine coupling tensors and g-tensors have been much extended in this edition and a new chapter on the calculation of zero-field splitting tensors has been added. This new edition is a valuable resource to experimentalists and theoreticians in research involving free radicals, as well as for students of advanced courses in physical chemistry, chemical physics, materials science, biophysics, biochemistry and related fields. This new edition is a valuable resource to experimentalists and theoreticians in research involving free radicals, as well as for students of advanced courses in physical chemistry, chemical physics, materials science, biophysics, biochemistry and related fields.

Algebraic and Computational Aspects of Real Tensor Ranks

Algebraic and Computational Aspects of Real Tensor Ranks
Author: Toshio Sakata,Toshio Sumi,Mitsuhiro Miyazaki
Publsiher: Springer
Total Pages: 108
Release: 2016-03-18
ISBN 10: 4431554599
ISBN 13: 9784431554592
Language: EN, FR, DE, ES & NL

Algebraic and Computational Aspects of Real Tensor Ranks Book Review:

This book provides comprehensive summaries of theoretical (algebraic) and computational aspects of tensor ranks, maximal ranks, and typical ranks, over the real number field. Although tensor ranks have been often argued in the complex number field, it should be emphasized that this book treats real tensor ranks, which have direct applications in statistics. The book provides several interesting ideas, including determinant polynomials, determinantal ideals, absolutely nonsingular tensors, absolutely full column rank tensors, and their connection to bilinear maps and Hurwitz-Radon numbers. In addition to reviews of methods to determine real tensor ranks in details, global theories such as the Jacobian method are also reviewed in details. The book includes as well an accessible and comprehensive introduction of mathematical backgrounds, with basics of positive polynomials and calculations by using the Groebner basis. Furthermore, this book provides insights into numerical methods of finding tensor ranks through simultaneous singular value decompositions.

Theoretical and Computational Acoustics 2001

Theoretical and Computational Acoustics 2001
Author: Er-Chang Shang,Qihu Li,T. F. Gao
Publsiher: World Scientific
Total Pages: 676
Release: 2002
ISBN 10: 9812380124
ISBN 13: 9789812380128
Language: EN, FR, DE, ES & NL

Theoretical and Computational Acoustics 2001 Book Review:

This book contains 67 papers presented at ICTCA2001. It includes three keynote addresses surveying the frontier developments in computational and theoretical acoustics. The papers cover aero-, seismo- and ocean acoustics, as well as ultrasonics. Computational methods, numerical simulation, theoretical analysis and experimental results are emphasized by different papers.

Handbook of Computational Chemistry

Handbook of Computational Chemistry
Author: Jerzy Leszczynski
Publsiher: Springer Science & Business Media
Total Pages: 1427
Release: 2012-01-14
ISBN 10: 940070710X
ISBN 13: 9789400707108
Language: EN, FR, DE, ES & NL

Handbook of Computational Chemistry Book Review:

This handbook is a guide to current methods of computational chemistry, explaining their limitations and advantages and providing examples of their applications. The first part outlines methods, the balance of volumes present numerous important applications.

Nonlinear Hyperbolic Equations Theory Computation Methods and Applications

Nonlinear Hyperbolic Equations     Theory  Computation Methods  and Applications
Author: Josef Ballmann,Rolf Jeltsch
Publsiher: Springer Science & Business Media
Total Pages: 718
Release: 2013-03-08
ISBN 10: 3322878694
ISBN 13: 9783322878694
Language: EN, FR, DE, ES & NL

Nonlinear Hyperbolic Equations Theory Computation Methods and Applications Book Review:

On the occasion of the International Conference on Nonlinear Hyperbolic Problems held in St. Etienne, France, 1986 it was decided to start a two years cycle of conferences on this very rapidly expanding branch of mathematics and it·s applications in Continuum Mechanics and Aerodynamics. The second conference toolc place in Aachen, FRG, March 14-18, 1988. The number of more than 200 participants from more than 20 countries all over the world and about 100 invited and contributed papers, well balanced between theory, numerical analysis and applications, do not leave any doubt that it was the right decision to start this cycle of conferences, of which the third will be organized in Sweden in 1990. ThiS volume contains sixty eight original papers presented at the conference, twenty two cif them dealing with the mathematical theory, e.g. existence, uniqueness, stability, behaviour of solutions, physical modelling by evolution equations. Twenty two articles in numerical analysis are concerned with stability and convergence to the physically relevant solutions such as schemes especially deviced for treating shoclcs, contact discontinuities and artificial boundaries. Twenty four papers contain multidimensional computational applications to nonlinear waves in solids, flow through porous media and compressible fluid flow including shoclcs, real gas effects, multiphase phenomena, chemical reactions etc. The editors and organizers of the Second International Conference on Hyperbolic Problems would lilce to thanlc the Scientific Committee for the generous support of recommending invited lectures and selecting the contributed papers of the conference.

High field EPR Spectroscopy on Proteins and Their Model Systems

High field EPR Spectroscopy on Proteins and Their Model Systems
Author: Klaus Möbius,Anton Savitsky
Publsiher: Royal Society of Chemistry
Total Pages: 375
Release: 2009-01-01
ISBN 10: 0854043683
ISBN 13: 9780854043682
Language: EN, FR, DE, ES & NL

High field EPR Spectroscopy on Proteins and Their Model Systems Book Review:

Understanding the major factors determining the specificity of transmembrane transfer processes in proteins is now a hot topic in molecular bio-science. Advanced electron paramagnetic resonance (EPR) at high magnetic fields is a powerful technique for characterizing the transient states of proteins in action. High-Field EPR Spectroscopy on Proteins and their Model Systems: characterization of Transient Paramagnetic States offers a comprehensive overview of experimental techniques in, and paradigmatic examples of, the application of high-field EPR spectroscopy in biology and chemistry. The book's focus is on the use of the technique in conjunction with site-specific mutation strategies and advanced quantum-chemical computation methods to reveal protein structure and dynamics. This yields new insights into biological processes at the atomic and molecular level. The theoretical and instrumental background of high-field EPR is described and examples of paradigmatic protein systems, such as photosynthetic reaction centres, are discussed in the light of recent investigations. Aspects of structure dynamics-function relations that are revealed by studying site-specific mutants are highlighted, thereby combining high-field EPR with genetic engineering techniques. The information obtained complements that obtained from protein crystallography, solid-state NMR, infrared and optical spectroscopy. The book documents both background knowledge and results of the latest research in the field. Unique features include comparisons of information content of EPR, ENDOR, Triple resonance, ESEEM and PELDOR taken at different microwave frequencies and magnetic fields. Coherent treatment of the subject by the leading Berlin high-field EPR laboratory covers the theoretical background as well as state-of-art research both in terms of instrumentation and application to biological systems. The book provides an outlook to future developments and references for further reading and is essential reading for postdoctoral scientists, professionals, academics and graduate students working in this field.

The Eleventh Marcel Grossmann Meeting

The Eleventh Marcel Grossmann Meeting
Author: Anonim
Publsiher: Unknown
Total Pages: 135
Release: 2022
ISBN 10: 9814470031
ISBN 13: 9789814470032
Language: EN, FR, DE, ES & NL

The Eleventh Marcel Grossmann Meeting Book Review: