Download or read book Methods of Intermediate Problems for Eigenvalues Theory and Ramifications written by A. Weinstein and published by Elsevier. This book was released on 1972-06-23 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering
Download or read book Operator Theory in Krein Spaces and Nonlinear Eigenvalue Problems written by Karl-Heinz Förster and published by Springer Science & Business Media. This book was released on 2006-03-16 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of recent original research papers in operator theory in Krein spaces, on generalized Nevanlinna functions, which are closely connected with this theory, and on nonlinear eigenvalue problems. Key topics include: spectral theory for normal operators; perturbation theory for self-adjoint operators in Krein spaces; and, models for generalized Nevanlinna functions.
Download or read book Numerical Verification Methods and Computer Assisted Proofs for Partial Differential Equations written by Mitsuhiro T. Nakao and published by Springer Nature. This book was released on 2019-11-11 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last decades, various mathematical problems have been solved by computer-assisted proofs, among them the Kepler conjecture, the existence of chaos, the existence of the Lorenz attractor, the famous four-color problem, and more. In many cases, computer-assisted proofs have the remarkable advantage (compared with a “theoretical” proof) of additionally providing accurate quantitative information. The authors have been working more than a quarter century to establish methods for the verified computation of solutions for partial differential equations, mainly for nonlinear elliptic problems of the form -∆u=f(x,u,∇u) with Dirichlet boundary conditions. Here, by “verified computation” is meant a computer-assisted numerical approach for proving the existence of a solution in a close and explicit neighborhood of an approximate solution. The quantitative information provided by these techniques is also significant from the viewpoint of a posteriori error estimates for approximate solutions of the concerned partial differential equations in a mathematically rigorous sense. In this monograph, the authors give a detailed description of the verified computations and computer-assisted proofs for partial differential equations that they developed. In Part I, the methods mainly studied by the authors Nakao and Watanabe are presented. These methods are based on a finite dimensional projection and constructive a priori error estimates for finite element approximations of the Poisson equation. In Part II, the computer-assisted approaches via eigenvalue bounds developed by the author Plum are explained in detail. The main task of this method consists of establishing eigenvalue bounds for the linearization of the corresponding nonlinear problem at the computed approximate solution. Some brief remarks on other approaches are also given in Part III. Each method in Parts I and II is accompanied by appropriate numerical examples that confirm the actual usefulness of the authors’ methods. Also in some examples practical computer algorithms are supplied so that readers can easily implement the verification programs by themselves.
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1969 with total page 736 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Many Body Methods in Quantum Chemistry written by Uzi Kaldor and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume contains the text of the invited lectures presented at the Symposium on Many Body Methods in Quantum Chemistry, held on the campus of Tel Aviv University in August 1988. The Symposium was a satellite meeting of the Sixth International Congress on Quantum Chemistry held in Jerusalem. The development and application of many-body methods in Quantum chemistry have been on the rise for a number of years. This is therefore a good time for an interim report on the state of the field. It is hoped that such a report is hereby provided, though it may not be complete. The Symposium was held under the auspices of Tel Aviv University, Raymond and Beverly Sackler Faculty of Exact Sciences, School of Chemistry. Other sponsors were the Israeli Academy of Sciences and Humanities, and the Israeli Ministry of Science and Development. Many thanks go to all of them. Finally, I would like to thank all the speakers and participants for making the meeting the enjoyable and (I hope) profitable experience it was. Tel Aviv, Israel Uzi Kaldor TESTS AND APPLICATIONS OF COMPLETE MODEL SPACE QUASIDEGENERATE MANY-BODY PERTURBATION THEORY FOR MOLECULES Karl F. Freed The James Franck Institute and Department of Chemistry The University of Chicago, Chicago, DUnois 60637 U.S.A.
Download or read book Numerical Solution of Ordinary Differential Equations written by and published by Academic Press. This book was released on 1971-03-31 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering
Download or read book Dynamic Programming and Its Application to Optimal Control written by and published by Elsevier. This book was released on 1971-10-11 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering
Download or read book Vibrations and Waves in Continuous Mechanical Systems written by Peter Hagedorn and published by John Wiley & Sons. This book was released on 2007-10-22 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of vibrations is of fundamental importance in engineering and technology. Discrete modelling is sufficient to understand the dynamics of many vibrating systems; however a large number of vibration phenomena are far more easily understood when modelled as continuous systems. The theory of vibrations in continuous systems is crucial to the understanding of engineering problems in areas as diverse as automotive brakes, overhead transmission lines, liquid filled tanks, ultrasonic testing or room acoustics. Starting from an elementary level, Vibrations and Waves in Continuous Mechanical Systems helps develop a comprehensive understanding of the theory of these systems and the tools with which to analyse them, before progressing to more advanced topics. Presents dynamics and analysis techniques for a wide range of continuous systems including strings, bars, beams, membranes, plates, fluids and elastic bodies in one, two and three dimensions. Covers special topics such as the interaction of discrete and continuous systems, vibrations in translating media, and sound emission from vibrating surfaces, among others. Develops the reader’s understanding by progressing from very simple results to more complex analysis without skipping the key steps in the derivations. Offers a number of new topics and exercises that form essential steppingstones to the present level of research in the field. Includes exercises at the end of the chapters based on both the academic and practical experience of the authors. Vibrations and Waves in Continuous Mechanical Systems provides a first course on the vibrations of continuous systems that will be suitable for students of continuous system dynamics, at senior undergraduate and graduate levels, in mechanical, civil and aerospace engineering. It will also appeal to researchers developing theory and analysis within the field.
Download or read book Variational Calculations in Quantum Field Theory written by L Polley and published by World Scientific. This book was released on 1988-07-01 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contributions in this conference proceeding present an alternative approach to solving the Quantum Field Theory problem using the variational approach. Many different issues are visited using this approach — Yang Mills Theory, going beyond the Guassian Approximation, in QCD and QED. Contents:A Variational Approach to QCD Bound States (J Greensite)Vacuum and Excited States in Truncated-Mode Coulomb-Gauge Yang-Mills Theory (R E Cutkosky and K C Wang)Difficulties in Applying the Variational Principle to Quantum Field Theories (R P Feynman)Schrodinger Approach to Ground State Wavefunctionals (W A Bardeen)Computer Measurement of the Yang-Mills Vacuum (and String) Wavefunctionals (J Greensite)The Magnetic Instability of the Perturbative Yang-Mills Vacuum (G Preparata)A Step Beyond the Gaussian Approximation in Yang-Mills Theory (L Polley and U Ritschel)Dynamical Symmetry Breaking in QCD and Quark Masses (R Casalbuoni)Zero Temperature Quark Matter Equation of State (F Grassi)λΦ43+1 λ > 0, with Spontaneous Symmetry Breaking (R Tarrach)Gaussian Approximations and Renormalization of Effective Potentials in 1 + 1 vs Higher Dimensions (J Wudka)Covariant Gaussian Approximation: Formalism (A Kovner and B Rosenstein)Covariant Gaussian Approximation: Applications (B Rosenstein and A Kovner)Variational Methods in Large N Supersymmetric Models (O Eyal)Variational Calculations of Particle Masses in Quantum Field Theory: Beyond the Simplest Gaussian Ansatz (J W Darewych, M Horbatsch and R Koniuk)Bound State Wavefunctions in Strongly' Coupled QED (W Dykshoorn, R Koniuk and J W Darewych)Feynman's Polaron Theory: Translation into Hamiltonian Language (K Yamazaki)Asymptotics of Classical Yang-Mills Fields (C Cronstrom)Variational Calculation of Instanton-Based Yang-Mills Vacuum at Finite Temperature (T Kanki)The Structure of Gauge Field Theories within Different Regularization Schemes and Aspects of Confinement (P Besting, J Neubauer and D Schiitte)The Deconfined Phase of QCD (J E Mandula and M Ogilvie)Spectral Estimates for Hamiltonian Lattice Theory (A Duncan)Testing Variational Ground States Against Conformal Invariance (A Patkos)The t-Expansion in Lattice QCD (D Horn)Ground State of Lattice SU(2) QCD with Finite Chemical Potential (E G Klepfish and A Krasnitz) Readership: Graduate students and researchers interested in quantum field theory. Keywords:Variational Techniques;Quantum Field Theory;Yang–Mills Theory;Gaussian Approximation;Symmetry Breaking in QCD;Quantum Chromodynamics;Quantum Electrodynamics;Gauge Field Theory
Download or read book A Course in Mathematical Physics 3 written by Walter Thirring and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this third volume of A Course in Mathematical Physics I have attempted not simply to introduce axioms and derive quantum mechanics from them, but also to progress to relevant applications. Reading the axiomatic litera ture often gives one the impression that it largely consists of making refined axioms, thereby freeing physics from any trace of down-to-earth residue and cutting it off from simpler ways of thinking. The goal pursued here, however, is to come up with concrete results that can be compared with experimental facts. Everything else should be regarded only as a side issue, and has been chosen for pragmatic reasons. It is precisely with this in mind that I feel it appropriate to draw upon the most modern mathematical methods. Only by their means can the logical fabric of quantum theory be woven with a smooth structure; in their absence, rough spots would . inevitably appear, especially in the theory of unbounded operators, where the details are too intricate to be comprehended easily. Great care has been taken to build up this mathematical weaponry as completely as possible, as it is also the basic arsenal of the next volume. This means that many proofs have been tucked away in the exercises. My greatest concern was to replace the ordinary cal culations of uncertain accuracy with better ones having error bounds, in order to raise the crude manners of theoretical physics to the more cultivated level of experimental physics.
Download or read book Quantum Mathematical Physics written by Walter Thirring and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a new edition of Volumes 3 and 4 of Walter Thirring’s famous textbook on mathematical physics. The first part is devoted to quantum mechanics and especially to its applications to scattering theory, atoms and molecules. The second part deals with quantum statistical mechanics examining fundamental concepts like entropy, ergodicity and thermodynamic functions.
Download or read book Industrial Mathematics written by and published by . This book was released on 1973 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Spectral Approximation of Linear Operators written by Francoise Chatelin and published by SIAM. This book was released on 2011-05-26 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published: New York: Academic Press, 1983.
Download or read book Principles of Combinatorics written by Berge and published by Academic Press. This book was released on 1971-04-20 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: Berge's Principles of Combinatorics is now an acknowledged classic work of the field. Complementary to his previous books, Berge's introduction deals largely with enumeration. The choice of topics is balanced, the presentation elegant, and the text can be followed by anyone with an interest in the subject with only a little algebra required as a background. Some topics were here described for the first time, including Robinston-Shensted theorum, the Eden-Schutzenberger theorum, and facts connecting Young diagrams, trees, and the symmetric group.
Download or read book Transversal Theory written by L. Mirsky and published by Academic Press. This book was released on 1971-04-20 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Transversal Theory
Download or read book Integer Programming written by and published by Academic Press. This book was released on 1971-05-14 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering
Download or read book System Identification written by James L Melsa and published by Academic Press. This book was released on 1971-06-26 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: System Identification
