Commutability Of Gamma Limits In Problems With Multiple Scales
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Commutability Of Gamma Limits In Problems With Multiple Scales
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Author : Martin Jesenko
language : en
Publisher: Logos Verlag Berlin GmbH
Release Date : 2017
Commutability Of Gamma Limits In Problems With Multiple Scales written by Martin Jesenko and has been published by Logos Verlag Berlin GmbH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Mathematics categories.
In the calculus of variations, the goal is to explore extrema of a given integral functional. From origins of the problem, it might be expected that the functional can be adequately simplified by neglecting some small quantities. A way to rigorously justify such an approximation is the Γ-convergence that ensures convergence of corresponding (global) extrema. The main motivation of this work is to investigate properties of doubly indexed integral functionals that Γ-converge for one index fixed. In other words, for two possible approximations we would like to determine whether we may perform them consecutively and if they commute. Our examples are taken from material science with homogenization being one of these two processes. In the first part we are considering a setting related to the elastic regime. However, our assumptions are fairly general and allow for applications in different areas. The second part is devoted to problems in the Hencky plasticity. They are considerably different due to special growth properties of the density.
Dilations Linear Matrix Inequalities The Matrix Cube Problem And Beta Distributions
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Author : J. William Helton
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-02-21
Dilations Linear Matrix Inequalities The Matrix Cube Problem And Beta Distributions written by J. William Helton and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-21 with Mathematics categories.
An operator C on a Hilbert space H dilates to an operator T on a Hilbert space K if there is an isometry V:H→K such that C=V∗TV. A main result of this paper is, for a positive integer d, the simultaneous dilation, up to a sharp factor ϑ(d), expressed as a ratio of Γ functions for d even, of all d×d symmetric matrices of operator norm at most one to a collection of commuting self-adjoint contraction operators on a Hilbert space.
Noncommutative Geometry Quantum Fields And Motives
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Author : Alain Connes
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-03-13
Noncommutative Geometry Quantum Fields And Motives written by Alain Connes and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-13 with Mathematics categories.
The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role: space-time, where the guiding principle is the problem of developing a quantum theory of gravity, and the space of primes, where one can regard the Riemann Hypothesis as a long-standing problem motivating the development of new geometric tools. The book stresses the relevance of noncommutative geometry in dealing with these two spaces. The first part of the book deals with quantum field theory and the geometric structure of renormalization as a Riemann-Hilbert correspondence. It also presents a model of elementary particle physics based on noncommutative geometry. The main result is a complete derivation of the full Standard Model Lagrangian from a very simple mathematical input. Other topics covered in the first part of the book are a noncommutative geometry model of dimensional regularization and its role in anomaly computations, and a brief introduction to motives and their conjectural relation to quantum field theory. The second part of the book gives an interpretation of the Weil explicit formula as a trace formula and a spectral realization of the zeros of the Riemann zeta function. This is based on the noncommutative geometry of the adèle class space, which is also described as the space of commensurability classes of Q-lattices, and is dual to a noncommutative motive (endomotive) whose cyclic homology provides a general setting for spectral realizations of zeros of L-functions. The quantum statistical mechanics of the space of Q-lattices, in one and two dimensions, exhibits spontaneous symmetry breaking. In the low-temperature regime, the equilibrium states of the corresponding systems are related to points of classical moduli spaces and the symmetries to the class field theory of the field of rational numbers and of imaginary quadratic fields, as well as to the automorphisms of the field of modular functions. The book ends with a set of analogies between the noncommutative geometries underlying the mathematical formulation of the Standard Model minimally coupled to gravity and the moduli spaces of Q-lattices used in the study of the zeta function.
An Introduction To Quantum Field Theory
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Author : Michael E. Peskin
language : en
Publisher: CRC Press
Release Date : 2018-05-04
An Introduction To Quantum Field Theory written by Michael E. Peskin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-04 with Science categories.
An Introduction to Quantum Field Theory is a textbook intended for the graduate physics course covering relativistic quantum mechanics, quantum electrodynamics, and Feynman diagrams. The authors make these subjects accessible through carefully worked examples illustrating the technical aspects of the subject, and intuitive explanations of what is going on behind the mathematics. After presenting the basics of quantum electrodynamics, the authors discuss the theory of renormalization and its relation to statistical mechanics, and introduce the renormalization group. This discussion sets the stage for a discussion of the physical principles that underlie the fundamental interactions of elementary particle physics and their description by gauge field theories.
Method Validation In Pharmaceutical Analysis
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Author : Joachim Ermer
language : en
Publisher: John Wiley & Sons
Release Date : 2006-03-06
Method Validation In Pharmaceutical Analysis written by Joachim Ermer and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-06 with Science categories.
Adopting a practical approach, the authors provide a detailed interpretation of the existing regulations (GMP, ICH), while also discussing the appropriate calculations, parameters and tests. The book thus allows readers to validate the analysis of pharmaceutical compounds while complying with both the regulations as well as the industry demands for robustness and cost effectiveness. Following an introduction to the basic parameters and tests in pharmaceutical validation, including specificity, linearity, range, precision, accuracy, detection and quantitation limits, the text focuses on a life-cycle approach to validation and the integration of validation into the whole analytical quality assurance system. The whole is rounded off with a look at future trends. With its first-hand knowledge of the industry as well as regulating bodies, this is an invaluable reference for analytical chemists, the pharmaceutical industry, pharmaceutists, QA officers, and public authorities.
The Cauchy Problem For Convolution Equations
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Author : Leonid Romanovich Volevich
language : en
Publisher:
Release Date : 1994
The Cauchy Problem For Convolution Equations written by Leonid Romanovich Volevich and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Cauchy problem categories.
Spectral Methods
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Author : Jie Shen
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-08-25
Spectral Methods written by Jie Shen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-25 with Mathematics categories.
Along with finite differences and finite elements, spectral methods are one of the three main methodologies for solving partial differential equations on computers. This book provides a detailed presentation of basic spectral algorithms, as well as a systematical presentation of basic convergence theory and error analysis for spectral methods. Readers of this book will be exposed to a unified framework for designing and analyzing spectral algorithms for a variety of problems, including in particular high-order differential equations and problems in unbounded domains. The book contains a large number of figures which are designed to illustrate various concepts stressed in the book. A set of basic matlab codes has been made available online to help the readers to develop their own spectral codes for their specific applications.
Formalized Music
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Author : Iannis Xenakis
language : en
Publisher: Pendragon Press
Release Date : 1992
Formalized Music written by Iannis Xenakis and has been published by Pendragon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Juvenile Nonfiction categories.
Pendragon Press is proud to offer this new, revised, and expanded edition of Formalized Music, Iannis Xenakis's landmark book of 1971. In addition to three totally new chapters examining recent breakthroughs in music theory, two original computer programs illustrating the actual realization of newly proposed methods of composition, and an appendix of the very latest developments of stochastic synthesis as an invitation to future exploration, Xenakis offers a very critical self-examination of his theoretical propositions and artistic output of the past thirty-five years. This edition of Formalized Music is an essential tool for understanding the man and the thought processes of one of this century's most important and revolutionary musical figures.
Elasticity And Geometry
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Author : Basile Audoly
language : en
Publisher: Oxford University Press
Release Date : 2010-06-24
Elasticity And Geometry written by Basile Audoly and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-24 with Mathematics categories.
We experience elasticity everywhere in everyday life. This book covers several modern aspects of the established field of elasticity theory, applying general methods of classical analysis including advanced nonlinear aspects to derive detailed solutions to specific problems. It can serve as an introduction to nonlinear methods in science.
Fractional Signals And Systems
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Author : Manuel Duarte Ortigueira
language : en
Publisher: ISSN
Release Date : 2022-01-31
Fractional Signals And Systems written by Manuel Duarte Ortigueira and has been published by ISSN this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-31 with Mathematics categories.
The book illustrates the theoretical results of fractional derivatives via applications in signals and systems, covering continuous and discrete derivatives, and the corresponding linear systems. Both time and frequency analysis are presented. Some