A Variational Theory Of Convolution Type Functionals

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A Variational Theory Of Convolution Type Functionals

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Author : Roberto Alicandro
language : en
Publisher: Springer Nature
Release Date : 2023-05-02

A Variational Theory Of Convolution Type Functionals written by Roberto Alicandro and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-02 with Mathematics categories.

This book provides a general treatment of a class of functionals modelled on convolution energies with kernel having finite p-moments. A general asymptotic analysis of such non-local functionals is performed, via Gamma-convergence, in order to show that the limit may be a local functional representable as an integral. Energies of this form are encountered in many different contexts and the interest in building up a general theory is also motivated by the multiple interests in applications (e.g. peridynamics theory, population dynamics phenomena and data science). The results obtained are applied to periodic and stochastic homogenization, perforated domains, gradient flows, and point-clouds models. This book is mainly intended for mathematical analysts and applied mathematicians who are also interested in exploring further applications of the theory to pass from a non-local to a local description, both in static problems and in dynamic problems.

Thermodynamics And Kinetic Theory Proceedings Of The 5th Bilateral Polish Italian Meeting

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Author : W Kosinski
language : en
Publisher: World Scientific
Release Date : 1992-03-27

Thermodynamics And Kinetic Theory Proceedings Of The 5th Bilateral Polish Italian Meeting written by W Kosinski and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-03-27 with categories.

This book gives a comprehensive review of the current status of the theory of the pion-two-nucleon systems at intermediate energies. It also makes an extensive comparison of the theoretical prediction with the corresponding data obtained recently from the major meson factories.

Geometric And Analytic Aspects Of Functional Variational Principles

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Author : Rupert Frank
language : en
Publisher: Springer Nature
Release Date : 2024-11-19

Geometric And Analytic Aspects Of Functional Variational Principles written by Rupert Frank and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-19 with Mathematics categories.

This book is dedicated to exploring optimization problems of geometric-analytic nature, which are fundamental to tackling various unresolved questions in mathematics and physics. These problems revolve around minimizing geometric or analytic quantities, often representing physical energies, within prescribed collections of sets or functions. They serve as catalysts for advancing methodologies in calculus of variations, partial differential equations, and geometric analysis. Furthermore, insights from optimal functional-geometric inequalities enhance analytical problem-solving endeavors. The contributions focus on the intricate interplay between these inequalities and problems of differential and variational nature. Key topics include functional and geometric inequalities, optimal norms, sharp constants in Sobolev-type inequalities, and the regularity of solutions to variational problems. Readers will gain a comprehensive understanding of these concepts, deepening their appreciation for their relevance in mathematical and physical inquiries.

Applied Theory Of Functional Differential Equations

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Author : V. Kolmanovskii
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Applied Theory Of Functional Differential Equations written by V. Kolmanovskii 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 2012-12-06 with Mathematics categories.

This volume provides an introduction to the properties of functional differential equations and their applications in diverse fields such as immunology, nuclear power generation, heat transfer, signal processing, medicine and economics. In particular, it deals with problems and methods relating to systems having a memory (hereditary systems). The book contains eight chapters. Chapter 1 explains where functional differential equations come from and what sort of problems arise in applications. Chapter 2 gives a broad introduction to the basic principle involved and deals with systems having discrete and distributed delay. Chapters 3-5 are devoted to stability problems for retarded, neutral and stochastic functional differential equations. Problems of optimal control and estimation are considered in Chapters 6-8. For applied mathematicians, engineers, and physicists whose work involves mathematical modeling of hereditary systems. This volume can also be recommended as a supplementary text for graduate students who wish to become better acquainted with the properties and applications of functional differential equations.

Introduction To Functional Differential Equations

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Author : Jack K. Hale
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-21

Introduction To Functional Differential Equations written by Jack K. Hale 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 2013-11-21 with Mathematics categories.

The present book builds upon an earlier work of J. Hale, "Theory of Func tional Differential Equations" published in 1977. We have tried to maintain the spirit of that book and have retained approximately one-third of the material intact. One major change was a complete new presentation of lin ear systems (Chapters 6~9) for retarded and neutral functional differential equations. The theory of dissipative systems (Chapter 4) and global at tractors was completely revamped as well as the invariant manifold theory (Chapter 10) near equilibrium points and periodic orbits. A more complete theory of neutral equations is presented (see Chapters 1, 2, 3, 9, and 10). Chapter 12 is completely new and contains a guide to active topics of re search. In the sections on supplementary remarks, we have included many references to recent literature, but, of course, not nearly all, because the subject is so extensive. Jack K. Hale Sjoerd M. Verduyn Lunel Contents Preface............................................................ v Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . 1. Linear differential difference equations . . . . . . . . . . . . . . 11 . . . . . . 1.1 Differential and difference equations. . . . . . . . . . . . . . . . . . . . 11 . . . . . . . . 1.2 Retarded differential difference equations. . . . . . . . . . . . . . . . 13 . . . . . . . 1.3 Exponential estimates of x( ¢,f) . . . . . . . . . . . . . . . . . . . . . 15 . . . . . . . . . . 1.4 The characteristic equation . . . . . . . . . . . . . . . . . . . . . . . . 17 . . . . . . . . . . . . 1.5 The fundamental solution. . . . . . . . . . . . . . . . . . . . . . . . . . 18 . . . . . . . . . . . . 1.6 The variation-of-constantsformula............................. 23 1. 7 Neutral differential difference equations . . . . . . . . . . . . . . . . . 25 . . . . . . . 1.8 Supplementary remarks. . . . . . . . . . . . . . . . . . . . . . . . . . . 34 . . . . . . . . . . . . . 2. Functional differential equations: Basic theory . . . . . . . . 38 . . 2.1 Definition of a retarded equation. . . . . . . . . . . . . . . . . . . . . . 38 . . . . . . . . . 2.2 Existence, uniqueness, and continuous dependence . . . . . . . . . . 39 . . . 2.3 Continuation of solutions . . . . . . . . . . . . . . . . . . . . . . . . . . 44 . . . . . . . . . . . .

Energy Minimization Methods In Computer Vision And Pattern Recognition

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Author : Xue-Cheng Tai
language : en
Publisher: Springer
Release Date : 2015-01-07

Energy Minimization Methods In Computer Vision And Pattern Recognition written by Xue-Cheng Tai and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-07 with Computers categories.

This volume constitutes the refereed proceedings of the 10th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition, EMMCVPR 2015, held in Hong Kong, China, in January 2015. The 36 revised full papers were carefully reviewed and selected from 45 submissions. The papers are organized in topical sections on discrete and continuous optimization; image restoration and inpainting; segmentation; PDE and variational methods; motion, tracking and multiview reconstruction; statistical methods and learning; and medical image analysis.

Poroelastic Structures

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Author : G. Cederbaum
language : en
Publisher: Elsevier
Release Date : 2000-07-12

Poroelastic Structures written by G. Cederbaum and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-07-12 with Technology & Engineering categories.

Poroelasticity is a continuum theory for the analysis of a porous media consisting of an elastic matrix containing interconnected fluid-saturated pores. In physical terms the theory postulates that when a porous material is subjected to stress, the resulting matrix deformation leads to volumetric changes in the pores. This book is devoted to the analysis of fluid-saturated poroelastic beams, columns and plates made of materials for which diffusion in the longitudinal direction(s) is viable, while in the perpendicular direction(s) the flow can be considered negligible because of the micro-geometry of the solid skeletal material. Many microstructures and fabrication schemes could be imagined, which would produce bulk materials with the postulated behavior. The book provides a methodology and a theoretical basis for investigating the mechanical behaviors of the structural elements made of such materials. It is recognized that the response of the poroelastic structural element to loading is sensitive to the properties of the fluid and to the diffusion boundaries, which can be easily altered in practice. Therefore, such structural elements and thus their features are potentially controllable. In other words, it could be possible to convert such elements into intelligent or smart structures. If this is so, it would be interesting that such structural elements could work as both sensors and actuators, e.g. the fluid can "feel" the change of the temperature by changing its viscosity and this results in a change of the behavior of the structure. The present book is the first of its kind; there does not exist in the professional literature any book which deals with this subject.Chapter 1 is a general introduction and overview. The governing equations for beams are presented in Chapter 2. Chapter 3 then presents analytical solutions for the quasi-static bending problem. Series solutions are found for normal loading with various mechanical and diffusion boundary conditions. The finite element method is developed and employed for the quasi-static beams and columns with small deflections in Chapter 4. In Chapter 5 solutions are found for free and forced vibrations of poroelastic beams. Chapter 6 deals with large deflections of beams. The stability of poroelastic columns is investigated in Chapter 7. Three problems are considered: buckling, post-buckling, and dynamic stability. Formulations are found in Chapter 8 for fluid-saturated poroelastic plates consisting of a material, for which the diffusion is possible in the in-plane directions only, both for bending and for in-plane loading. This book attempts to constitute a reasonably self-contained presentation of a wide spectrum of problems related to the analysis of the type of poroelastic structure considered.

Concrete Functional Calculus

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Author : R. M. Dudley
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-03

Concrete Functional Calculus written by R. M. Dudley 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 2010-11-03 with Mathematics categories.

Concrete Functional Calculus focuses primarily on differentiability of some nonlinear operators on functions or pairs of functions. This includes composition of two functions, and the product integral, taking a matrix- or operator-valued coefficient function into a solution of a system of linear differential equations with the given coefficients. For nonlinear integral equations with respect to possibly discontinuous functions having unbounded variation, existence and uniqueness of solutions are proved under suitable assumptions. Key features and topics: * Extensive usage of p-variation of functions * Applications to stochastic processes. This work will serve as a thorough reference on its main topics for researchers and graduate students with a background in real analysis and, for Chapter 12, in probability.

Encyclopaedia Of Mathematics

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Author : Michiel Hazewinkel
language : en
Publisher: Springer
Release Date : 2013-12-20

Encyclopaedia Of Mathematics written by Michiel Hazewinkel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-20 with Mathematics categories.

Method Of Variation Of Parameters For Dynamic Systems

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Author : V. Lakshmikantham
language : en
Publisher: Routledge
Release Date : 2019-09-10

Method Of Variation Of Parameters For Dynamic Systems written by V. Lakshmikantham and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-10 with Mathematics categories.

Method of Variation of Parameters for Dynamic Systems presents a systematic and unified theory of the development of the theory of the method of variation of parameters, its unification with Lyapunov's method and typical applications of these methods. No other attempt has been made to bring all the available literature into one volume. This book is a clear exposition of this important topic in control theory, which is not covered by any other text. Such an exposition finally enables the comparison and contrast of the theory and the applications, thus facilitating further development in this fascinating field.