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Commutability Of Gamma Limits In Problems With Multiple Scales
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Book Synopsis Commutability of Gamma-limits in problems with multiple scales by : Martin Jesenko
Download or read book Commutability of Gamma-limits in problems with multiple scales written by Martin Jesenko and published by Logos Verlag Berlin GmbH. This book was released on 2017 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Dilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta Distributions by : J. William Helton
Download or read book Dilations, Linear Matrix Inequalities, the Matrix Cube Problem and Beta Distributions written by J. William Helton and published by American Mathematical Soc.. This book was released on 2019-02-21 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis An Introduction To Quantum Field Theory by : Michael E. Peskin
Download or read book An Introduction To Quantum Field Theory written by Michael E. Peskin and published by CRC Press. This book was released on 2018-05-04 with total page 866 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Geometric Flows on Planar Lattices by : Andrea Braides
Download or read book Geometric Flows on Planar Lattices written by Andrea Braides and published by Springer Nature. This book was released on 2021-03-23 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the reader to important concepts in modern applied analysis, such as homogenization, gradient flows on metric spaces, geometric evolution, Gamma-convergence tools, applications of geometric measure theory, properties of interfacial energies, etc. This is done by tackling a prototypical problem of interfacial evolution in heterogeneous media, where these concepts are introduced and elaborated in a natural and constructive way. At the same time, the analysis introduces open issues of a general and fundamental nature, at the core of important applications. The focus on two-dimensional lattices as a prototype of heterogeneous media allows visual descriptions of concepts and methods through a large amount of illustrations.
Book Synopsis Theory of Translation Closedness for Time Scales by : Chao Wang
Download or read book Theory of Translation Closedness for Time Scales written by Chao Wang and published by Springer. This book was released on 2021-05-20 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph establishes a theory of classification and translation closedness of time scales, a topic that was first studied by S. Hilger in 1988 to unify continuous and discrete analysis. The authors develop a theory of translation function on time scales that contains (piecewise) almost periodic functions, (piecewise) almost automorphic functions and their related generalization functions (e.g., pseudo almost periodic functions, weighted pseudo almost automorphic functions, and more). Against the background of dynamic equations, these function theories on time scales are applied to study the dynamical behavior of solutions for various types of dynamic equations on hybrid domains, including evolution equations, discontinuous equations and impulsive integro-differential equations. The theory presented allows many useful applications, such as in the Nicholson`s blowfiles model; the Lasota-Wazewska model; the Keynesian-Cross model; in those realistic dynamical models with a more complex hibrid domain, considered under different types of translation closedness of time scales; and in dynamic equations on mathematical models which cover neural networks. This book provides readers with the theoretical background necessary for accurate mathematical modeling in physics, chemical technology, population dynamics, biotechnology and economics, neural networks, and social sciences.
Book Synopsis Formalized Music by : Iannis Xenakis
Download or read book Formalized Music written by Iannis Xenakis and published by Pendragon Press. This book was released on 1992 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Topics on Concentration Phenomena and Problems with Multiple Scales by : Andrea Braides
Download or read book Topics on Concentration Phenomena and Problems with Multiple Scales written by Andrea Braides and published by Springer Science & Business Media. This book was released on 2006-08-14 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of variational problems showing multi-scale behaviour with oscillation or concentration phenomena are a challenging topic of very active research. This volume includes lecture notes devoted to the asymptotic analysis of such problems when the multi-scale behaviour derives from scale separation in the passage from atomistic systems to continuous functionals, from competition between bulk and surface energies, from various types of homogenization processes (random, in perforated domains, on fractals), and to concentration effects in Ginzburg-Landau energies and in subcritical growth problems.
Book Synopsis Atoms, Molecules and Photons by : Wolfgang Demtröder
Download or read book Atoms, Molecules and Photons written by Wolfgang Demtröder and published by Springer. This book was released on 2019-02-09 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to Atomic and Molecular Physics explains how our present model of atoms and molecules has been developed over the last two centuries both by many experimental discoveries and, from the theoretical side, by the introduction of quantum physics to the adequate description of micro-particles. It illustrates the wave model of particles by many examples and shows the limits of classical description. The interaction of electromagnetic radiation with atoms and molecules and its potential for spectroscopy is outlined in more detail and in particular lasers as modern spectroscopic tools are discussed more thoroughly. Many examples and problems with solutions are offered to encourage readers to actively engage in applying and adapting the fundamental physics presented in this textbook to specific situations. Completely revised third edition with new sections covering all actual developments, like photonics, ultrashort lasers, ultraprecise frequency combs, free electron lasers, cooling and trapping of atoms, quantum optics and quantum information.
Book Synopsis Free Discontinuity Problems by : Nicola Fusco
Download or read book Free Discontinuity Problems written by Nicola Fusco and published by Springer. This book was released on 2017-02-02 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a series of lectures on three of the best known examples of free discontinuity problems: the Mumford-Shah model for image segmentation, a variational model for the epitaxial growth of thin films, and the sharp interface limit of the Ohta-Kawasaki model for pattern formation in dyblock copolymers.
Book Synopsis The Analytical Theory of Heat by : Jean-Baptiste-Joseph Fourier
Download or read book The Analytical Theory of Heat written by Jean-Baptiste-Joseph Fourier and published by . This book was released on 1878 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Signal Processing for Communications by : Paolo Prandoni
Download or read book Signal Processing for Communications written by Paolo Prandoni and published by Collection Savoir suisse. This book was released on 2008-06-17 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: With a novel, less classical approach to the subject, the authors have written a book with the conviction that signal processing should be taught to be fun. The treatment is therefore less focused on the mathematics and more on the conceptual aspects, the idea being to allow the readers to think about the subject at a higher conceptual level, thus building the foundations for more advanced topics. The book remains an engineering text, with the goal of helping students solve real-world problems. In this vein, the last chapter pulls together the individual topics as discussed throughout the book into an in-depth look at the development of an end-to-end communication system, namely, a modem for communicating digital information over an analog channel.
Book Synopsis Gamma-Convergence for Beginners by : Andrea Braides
Download or read book Gamma-Convergence for Beginners written by Andrea Braides and published by Clarendon Press. This book was released on 2002-07-25 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of Gamma-convergence is commonly recognized as an ideal and flexible tool for the description of the asymptotic behaviour of variational problems. Its applications range from the mathematical analysis of composites to the theory of phase transitions, from Image Processing to Fracture Mechanics. This text, written by an expert in the field, provides a brief and simple introduction to this subject, based on the treatment of a series of fundamental problems that illustrate the main features and techniques of Gamma-convergence and at the same time provide a stimulating starting point for further studies. The main part is set in a one-dimensional framework that highlights the main issues of Gamma-convergence without the burden of higher-dimensional technicalities. The text deals in sequence with increasingly complex problems, first treating integral functionals, then homogenisation, segmentation problems, phase transitions, free-discontinuity problems and their discrete and continuous approximation, making stimulating connections among those problems and with applications. The final part is devoted to an introduction to higher-dimensional problems, where more technical tools are usually needed, but the main techniques of Gamma-convergence illustrated in the previous section may be applied unchanged. The book and its structure originate from the author's experience in teaching courses on this subject to students at PhD level in all fields of Applied Analysis, and from the interaction with many specialists in Mechanics and Computer Vision, which have helped in making the text addressed also to a non-mathematical audience. The material of the book is almost self-contained, requiring only some basic notion of Measure Theory and Functional Analysis.
Book Synopsis Evaluation of Biomarkers and Surrogate Endpoints in Chronic Disease by : Institute of Medicine
Download or read book Evaluation of Biomarkers and Surrogate Endpoints in Chronic Disease written by Institute of Medicine and published by National Academies Press. This book was released on 2010-06-25 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many people naturally assume that the claims made for foods and nutritional supplements have the same degree of scientific grounding as those for medication, but that is not always the case. The IOM recommends that the FDA adopt a consistent scientific framework for biomarker evaluation in order to achieve a rigorous and transparent process.
Book Synopsis Method Validation in Pharmaceutical Analysis by : Joachim Ermer
Download or read book Method Validation in Pharmaceutical Analysis written by Joachim Ermer and published by John Wiley & Sons. This book was released on 2006-03-06 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Lectures On Phase Transitions And The Renormalization Group by : Nigel Goldenfeld
Download or read book Lectures On Phase Transitions And The Renormalization Group written by Nigel Goldenfeld and published by CRC Press. This book was released on 2018-03-08 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering the elementary aspects of the physics of phases transitions and the renormalization group, this popular book is widely used both for core graduate statistical mechanics courses as well as for more specialized courses. Emphasizing understanding and clarity rather than technical manipulation, these lectures de-mystify the subject and show precisely "how things work." Goldenfeld keeps in mind a reader who wants to understand why things are done, what the results are, and what in principle can go wrong. The book reaches both experimentalists and theorists, students and even active researchers, and assumes only a prior knowledge of statistical mechanics at the introductory graduate level.Advanced, never-before-printed topics on the applications of renormalization group far from equilibrium and to partial differential equations add to the uniqueness of this book.
Book Synopsis Measurement Uncertainty in Chemical Analysis by : Paul De Bièvre
Download or read book Measurement Uncertainty in Chemical Analysis written by Paul De Bièvre and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is now becoming recognized in the measurement community that it is as important to communicate the uncertainty related to a specific measurement as it is to report the measurement itself. Without knowing the uncertainty, it is impossible for the users of the result to know what confidence can be placed in it; it is also impossible to assess the comparability of different measurements of the same parameter. This volume collects 20 outstanding papers on the topic, mostly published from 1999-2002 in the journal "Accreditation and Quality Assurance." They provide the rationale for why it is important to evaluate and report the uncertainty of a result in a consistent manner. They also describe the concept of uncertainty, the methodology for evaluating uncertainty, and the advantages of using suitable reference materials. Finally, the benefits to both the analytical laboratory and the user of the results are considered.
Book Synopsis Introduction to Mathematical Economics by : Anthony L. Ostrosky
Download or read book Introduction to Mathematical Economics written by Anthony L. Ostrosky and published by . This book was released on 1979-01-01 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt:
