Nonlinear Theory of Generalized Functions (Research Notes in Mathematics Series)

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Published by Chapman & Hall/CRC .

Written in English

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Subjects:

  • Applied mathematics,
  • Differential equations,
  • Functional Analysis,
  • Geometry,
  • Theory of distributions (Funct,
  • Mathematics,
  • Nonlinear Programming,
  • Science/Mathematics,
  • Research,
  • Mathematical Analysis,
  • Mathematics / Differential Equations,
  • Theory of distributions (Functional analysis),
  • Congresses,
  • Nonlinear theories

Edition Notes

Book details

ContributionsMichael Oberguggenberger (Editor), Michael Grosser (Editor), Michael Kunzinger (Editor), Gunther Hormann (Editor)
The Physical Object
FormatPaperback
Number of Pages400
ID Numbers
Open LibraryOL8258711M
ISBN 100849306493
ISBN 109780849306495

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Nonlinear Theory of Generalized Functions - CRC Press Book Questions regarding the interplay of nonlinearity and the creation and propagation of singularities arise in a variety of fields-including nonlinear partial differential equations, noise-driven stochastic partial differential equations, general relativity, and geometry with singularities.

This book provides a simple introduction to a nonlinear theory of generalized functions introduced by J.F. Colombeau, which gives a meaning to any multiplication of distributions. This theory extends. This book provides a simple introduction to a nonlinear theory of generalized functions introduced by J.F.

Colombeau, which gives a meaning to any multiplication of distributions. This theory extends from pure mathematics (it presents a faithful generalization of the classical theory of C. A workshop held at the Erwin-Schrödinger International Institute for Mathematical Physics in Vienna investigated these questions and culminated in this volume of invited papers from experts in the fields of nonlinear partial differential equations, structure theory of generalized functions, geometry and general relativity, stochastic partial.

An introduction to a nonlinear theory of generalized functions introduced by J F Colombeau, which gives a meaning to any multiplication of distributions. It is suitable for.

With a focus on applications, this books provides a compilation of recent approaches to the problem of singularities in nonlinear models.

The theory of differential algebras of generalized functions serves as the central theme of the project, along with its interrelations with classical : Paperback. This book provides a simple introduction to a nonlinear theory of generalized functions introduced by J.F.

Colombeau, which gives a meaning to any multiplication of distributions. This theory extends from pure mathematics (it presents a faithful generalization of the classical theory of C. functions and provides a synthesis of most existing Cited by: Get this from a library.

A nonlinear theory of generalized functions. [Hebe A Biagioni] -- This book provides a simple introduction to a nonlinear theory of generalized functions introduced by J.F. Colombeau, which gives a meaning to any multiplication of distributions. This theory extends. The purpose of this article is to present an overview of a branch of nonlinear analysis that has taken up rapid development during the past decade: the theory of “multiplication of distributions” or better the “nonlinear theory of generalized functions”, as it goes far beyond the former topic by by: When discussing the case of non-smooth profile function a we will also employ the nonlinear theory of generalized functions in the sense of Colombeau, standard references are [9,10,20,15].

Download Distribution Theory (Generalized Functions) Notes Download free online book chm pdf. The aim of this note is to give an introduction to nonlinear Fourier analysis from a harmonic analyst’s point of view.

This book focuses on the material analysis based on Fourier transform theory. The book chapters are related to FTIR and the. This book provides a discussion of nonlinear problems that occur in four areas, namely, mathematical methods, fluid mechanics, mechanics of solids, and transport phenomena.

Organized into 15 chapters, this book begins with an overview of some of the fundamental ideas of two mathematical theories, namely, invariant imbedding and dynamic programming. This paper lays the foundations for a nonlinear theory of differential geometry that is developed in a subsequent paper which is based on Colombeau algebras of.

Introduction to Fourier Analysis by Nati Linial. This lecture note describes the following topics: Classical Fourier Analysis, Convergence theorems, Approximation Theory, Harmonic Analysis on the Cube and Parseval’s Identity, Applications of Harmonic Analysis, Isoperimetric Problems, The Brunn-Minkowski Theorem and Influences of Boolean Variables, Influence of variables on boolean functions.

Appendix Fundamental Properties of Generalized Functions A.1 Definition of generalized functions First of all, let us give some material from mathematics, which is necessary for defining the concept of a generalized function.

Let us consider the following linear functional: T[ϕ(x)] = f(x)ϕ(x)dx. (A.1)File Size: KB. that “there will never exist a theory of generalized functions adapted to nonlinear calculations.” For the theory and applications of scalar valued nonlinear generalized func-tions, see the recent introductions in [3, 4, 14], the survey [5] and the book [10] on their use in continuum mechanics, and the survey [21] and the book [13] on.

that “there will never exist a theory of generalized functions adapted to nonlinear calculations.” For the theory and applications of scalar valued nonlinear generalized func-tions, see the recent introductions in [3, 4, 15], the survey [5] and the book [10] on their use in continuum mechanics, and the survey [22] and the book [14] onCited by: 3.

Laser theory of Fabry-Perot (FP) semiconductor lasers proves to be nonlinear, since the gain, the refractive index and the loss coefficient are the functions of energy nonlinear theory made it possible to explain a number of experiments some of which could not even be explained (for example, natural linewidth), much less modeled, on the basis of other theoretical models; this suggests.

Presented in two sections, part one describes Generalized Functions and Operator Theory, part two addresses Operator Theory and Dynamical Systems.

The interplay between mathematics and physics is now more necessary than ever-and more difficult than ever, given the. The chapter describes generalized monotonicity. It also presents several criterion functions f for which f-monotonicity corresponds to different concepts used in optimization theory.

The book is self-contained, all results are proven very rigorously, and where appropriate, the evolution of results is explained and framed in the historical context. I recommend this book very warmly and without any reservations to anyone interested in nonlinear Perron–Frobenius theory.' Bjorn S.

Ruffer Source: Mathematical Reviews. Over the past few years a certain shift of focus within the theory of algebras of generalized functions (in the sense of J. Colombeau) has taken place. Originating in infinite dimensional analysis and initially applied mainly to problems in nonlinear partial differential equations involving.

Week 6: Lyapunov stability theory for time-varying nonlinear systems, comparison functions, uniform stability, exponential stability (Section).

Week 7: Time-varying systems and linearization (Section ), and Converse Theorems (Section ). Week 8. Input-state feedback linearization and input-output linearization (Chapter 14).

Week 9. Book Description. The success of the first edition of Generalized Linear Models led to the updated Second Edition, which continues to provide a definitive unified, treatment of methods for the analysis of diverse types of data.

Today, it remains popular for its clarity, richness of content and direct relevance to agricultural, biological, health, engineering, and other applications. Overview of Generalized Nonlinear Models in R Linear and generalized linear models Examples: I binary logistic regressions I rate models for event counts I log-linear models for contingency tables (including multinomial logit models) I multiplicative models for durations and other positive measurements I hazard models for event history data etc., Size: KB.

Generalized Linear Models: With Applications in Engineering and the Sciences, Second Edition continues to provide a clear introduction to the theoretical foundations and key applications of generalized linear models (GLMs).

Maintaining the same nontechnical approach as its predecessor, this update has been thoroughly extended to include the. The goal of this book is to present the main ideas and techniques in the field of continuous smooth and nonsmooth optimization.

Starting with the case of differentiable data and the classical results on constrained optimization problems, and continuing with the topic of nonsmooth objects involved in optimization theory, the book concentrates on both theoretical and practical Pages: A Nonlinear Theory of Generalized Functions An introduction to a Nonlinear theory of generalized functions introduced by J F Colombeau, which gives a meaning to any multiplication of distributions.

It is suitable for mathematicians, physicists and engineers. the specifications that cannot be expressed as linear functions. There are numerous nonlinear specifications considered in empirical applications. A flexible nonlinear specification is y t = α+β xγ t −1 γ +e t, where (xγ t −1)/γ is the so-called Box-Cox transform of x t, which yields different func-tions, depending on the value Size: KB.

Generalizations of convex functions to pseudoconvex and quasiconvex functions are given and then used to obtain generalized optimality conditions and duality results in the presence of nonlinear equality constraints. The book has four useful self-contained appendices on vectors and matrices, topological properties of n-dimensional real space.

The fields of optimization theory and nonlinear analysis continue to be very active. This book presents not only the wide spectrum and diversity of the results, but also their manifold connections to other areas, such as differential equations, functional analysis, operator theory, calculus of variations, numerical analysis, and mathematical.

Some stability definitions we consider nonlinear time-invariant system x˙ = f(x), where f: Rn → Rn a point xe ∈ R n is an equilibrium point of the system if f(xe) = 0 xe is an equilibrium point ⇐⇒ x(t) = xe is a trajectory suppose xe is an equilibrium point • system is globally asymptotically stable.

Nonlinear Fourier analysis is based upon a generalization of linear Fourier analysis referred to as the inverse scattering transform, the fundamental building block of which is a generalized Fourier series called the Riemann theta function.

Elucidating the art and science of implementing these functions in the context of physical and time. simple, reasonably general, nonlinear system theory could be developed.

Hand in hand with this viewpoint was the feeling that many of the approaches useful for linear systems ought to be extensible to the nonlinear theory. This is a key point if the theory is to.

This book deals with the theory and algorithms related to solving nonlinear programming problems. The book is divided into three parts. The first part begins by providing important discussion on modelling and on formulating nonlinear programs from the viewpoint of favorably influencing the performance of algorithms that will ultimately be used.

This is perhaps the first book containing biographical information of Sir James Lighthill and his major scientific contributions to the different areas of fluid mechanics, applied mathematics, aerodynamics, linear and nonlinear waves in fluids, geophysical fluid dynamics, biofluiddynamics, aeroelasticity, boundary layer theory, generalized.

Optimization Theory and Methods: Nonlinear Programming - Ebook written by Wenyu Sun, Ya-Xiang Yuan. Read this book using Google Play Books app on your PC, android, iOS devices. Download for offline reading, highlight, bookmark or take notes while you read Optimization Theory and Methods: Nonlinear Programming.

Linear, Nonlinear, Ordinary, Partial to the theory of generalized functions. The advantage of this approach is that a The second part of the book is concerned with nonlinear problems and more advanced techniques.

Although we have used a lot of the material in Chapters 9. The GSVD is applied to solve the generalized eigenvalue problem which is formulated in the feature space defined by a nonlinear mapping through kernel functions. Our GSVD-based kernel discriminant analysis is theoretically compared with other kernel-based nonlinear discriminant analysis by: analysis of control systems.

Linear control theory treats systems for which an underlying linear model is assumed, and is a relatively mature subject, complete with firm theoret-ical foundations and a wide range of powerful and applicable design methodologies; see e.g., Anderson & Moore (), Kailath ().

In contrast, nonlinear control theoryFile Size: KB. COMPREHENSIVE COVERAGE OF NONLINEAR PROGRAMMING THEORY AND ALGORITHMS, THOROUGHLY REVISED AND EXPANDED Nonlinear Programming: Theory and Algorithms—now in an extensively updated Third Edition—addresses the problem of optimizing an objective function in the presence of equality and inequality constraints.

Many realistic problems cannot be adequately .After presenting the main shock-fitting ideas in the context of a simple scalar equation, the author applies Colombeau's theory of generalized functions to the Euler equations to demonstrate how the theory recovers well-known results and to provide an in-depth understanding of the nature of jump conditions.

The book also presents the theory of factorization and composition structure of integral operators associated with the generalized associated Legendre function, the fractional integro-differential properties of the functions P m,n κ (z) and Q m,n κ (z), the classes of dual and triple integral equations associated with the function P m,n-1/2.

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