The main classes of inverse problems for equations of mathematical physics and their numerical solution methods are considered in this book which is intended for graduate students and experts in applied mathematics, computational mathematics, and mathematical modelling.

The book addresses mathematicians and physicists, including graduate students, who are interested in quantum dynamical systems and applications of operator algebras and ergodic theory. It is the only monograph on this topic. Although the authors assume a basic knowledge of operator algebras, they give precise definitions of the notions and in most cases complete proofs of the results which are used.

The stability problem for approximate homomorphisms, or the Ulam stability problem, was posed by S. M. Ulam in the year 1941. The solution of this problem for various classes of equations is an expanding area of research. In particular, the pursuit of solutions to the Hyers-Ulam and Hyers-Ulam-Rassias stability problems for sets of functional equations and ineqalities has led to an outpouring of recent research.

This volume, dedicated to S. M. Ulam, presents the most recent results on the solution to Ulam stability problems for various classes of functional equations and inequalities. Comprised of invited contributions from notable researchers and experts, this volume presents several important types of functional equations and inequalities and their applications to problems in mathematical analysis, geometry, physics and applied mathematics.

"Functional Equations in Mathematical Analysis" is intended for researchers and students in mathematics, physics, and other computational and applied sciences.

This volume collects the edited and reviewed contribution presented in the 7th iTi Conference in Bertinoro, covering fundamental and applied aspects in turbulence. In the spirit of the iTi conference, the volume is produced after the conference so that the authors had the opportunity to incorporate comments and discussions raised during the meeting. In the present book, the contributions have been structured according to the topics: I Theory II Wall bounded flows III Pipe flow IV Modelling V Experiments VII Miscellaneous topics

The aim of this proceeding is addressed to present recent developments of the mathematical research on the Navier-Stokes equations, the Euler equations and other related equations. In particular, we are interested in such problems as: 1) existence, uniqueness and regularity of weak solutions2) stability and its asymptotic behavior of the rest motion and the steady state3) singularity and blow-up of weak and strong solutions4) vorticity and energy conservation5) fluid motions around the rotating axis or outside of the rotating body6) free boundary problems7) maximal regularity theorem and other abstract theorems for mathematical fluid mechanics.

The past decade has witnessed the rapid development of a new mathematical tool, called wavlet analysis, for analyzing complex signals. It has begin to play a serious role in applications ranging from communications to geophysics, and from simulations to image processing. Like Fourier analysis (of which it is a generalization), or musical notation, wavelet analysis provides a method for representing a set of complex phenomena in a simpler, more compact, and thus more efficient manner. This text introduces the ideas and methods of wavelet analysis, relates them to previously known methods in mathematics and engineering, and shows how to apply wavelet analysis to digital signal processing. It begins by describing the multiscale (sometimes called "fractal") nature of information in many aspects of thereal world; it then turns to the algebra and analysis of wavelet matrices, scaling and wavelet functions, and the corresponding analysis of square-integrable functins on a space. The discussion then turns from the continuous to the discrete and shows how a properly selected set of wavelets can be used to represent -- and even differentiate -- a wide range of signls efficiently and effectively. The last part of the book presents a wide variety of applications of wavelets to probllems in data compression and telecommunications.

to the English Translation This is a concise guide to basic sections of modern functional analysis. Included are such topics as the principles of Banach and Hilbert spaces, the theory of multinormed and uniform spaces, the Riesz-Dunford holomorphic functional calculus, the Fredholm index theory, convex analysis and duality theory for locally convex spaces. With standard provisos the presentation is self-contained, exposing about a h- dred famous "named" theorems furnished with complete proofs and culminating in the Gelfand-Nalmark-Segal construction for C*-algebras. The first Russian edition was printed by the Siberian Division of "Nauka" P- lishers in 1983. Since then the monograph has served as the standard textbook on functional analysis at the University of Novosibirsk. This volume is translated from the second Russian edition printed by the Sobolev Institute of Mathematics of the Siberian Division of the Russian Academy of Sciences. in 1995. It incorporates new sections on Radon measures, the Schwartz spaces of distributions, and a supplementary list of theoretical exercises and problems. This edition was typeset using AMS-'lEX, the American Mathematical Society's 'lEX system. To clear my conscience completely, I also confess that: = stands for the definor, the assignment operator, signifies the end of the proof."

The Complex Variable Boundary Element Method (CVBEM) has an important role to play in a number of technical engineering situations and can be a tremendous help to scholars and practitioners preoccupied with solving problems in areas such as heat transport, structural mechanics and river hydraulics. As well as describing the extremely useful applications of this method, the authors explain the mathematical background to the CVBEM, which is vital to understanding the subject as a whole. Advances in the Complex Variable Boundary Element Method is the most comprehensive of books on this subject, bringing together ten years of work and boasting the latest news in CVBEM technology. It will be of particular interest to those concerned with solving technical engineering problems - scientists, graduate students, computer programmers and those working in industry may all find the book helpful.

This collection of original articles and surveys addresses the recent advances in linear and nonlinear aspects of the theory of partial differential equations. The key topics include operators as "sums of squares" of real and complex vector fields, nonlinear evolution equations, local solvability, and hyperbolic questions.

This book discusses the latest advances in algorithms for symbolic summation, factorization, symbolic-numeric linear algebra and linear functional equations. It presents a collection of papers on original research topics from the Waterloo Workshop on Computer Algebra (WWCA-2016), a satellite workshop of the International Symposium on Symbolic and Algebraic Computation (ISSAC'2016), which was held at Wilfrid Laurier University (Waterloo, Ontario, Canada) on July 23-24, 2016. This workshop and the resulting book celebrate the 70th birthday of Sergei Abramov (Dorodnicyn Computing Centre of the Russian Academy of Sciences, Moscow), whose highly regarded and inspirational contributions to symbolic methods have become a crucial benchmark of computer algebra and have been broadly adopted by many Computer Algebra systems.

The present book is the second of the two volume Proceedings of the Mark Krein International Conference on Operator Theory and Applications. This conference, which was dedicated to the 90th Anniversary of the prominent mathematician Mark Krein, was held in Odessa, Ukraine from 18-22 August, 1997. The conference focused on the main ideas, methods, results, and achievements of M. G. Krein. This second volume is devoted to operator theory and related topics. It opens with the bibliography of M. G. Krein and a number of survey papers about his work. The main part of the book consists of original research papers presenting the state of the art in operator theory and its applications. The first volume of these proceedings, entitled Differential Operators and related Topics, concerns the other aspects of the conference. The two volumes will be of interest to a wide-range of readership in pure and applied mathematics, physics and engineering sciences. Table of Contents Preface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Bibliography of Mark Grigorevich Krein . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix Review papers: M. G. Krein's Contributions to Prediction Theory H. Dym M. G. Krein's Contribution to the Moment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 AA Nudelman Research Papers: Solution of the Truncated Matrix Hamburger Moment Problem according to M. G. Krein . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Y. M. Adamyan and I. M. Tkachenko Extreme Points of a Positive Operator Ball . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 T. Ando M-accretive Extensions of Sectorial Operators and Krein Spaces . . . . . . . . . 67 Y. M. Arlinskii A Simple Proof of the Continuous Commutant Lifting Theorem . . . . . . . . . . 83 R. Bruzual and M.

This monograph presents a collection of results, observations, and examples related to dynamical systems described by linear and nonlinear ordinary differential and difference equations. In particular, dynamical systems that are susceptible to analysis by the Liapunov approach are considered. The naive observation that certain "diagonal-type" Liapunov functions are ubiquitous in the literature attracted the attention of the authors and led to some natural questions. Why does this happen so often? What are the spe cial virtues of these functions in this context? Do they occur so frequently merely because they belong to the simplest class of Liapunov functions and are thus more convenient, or are there any more specific reasons? This monograph constitutes the authors' synthesis of the work on this subject that has been jointly developed by them, among others, producing and compiling results, properties, and examples for many years, aiming to answer these questions and also to formalize some of the folklore or "cul ture" that has grown around diagonal stability and diagonal-type Liapunov functions. A natural answer to these questions would be that the use of diagonal type Liapunov functions is frequent because of their simplicity within the class of all possible Liapunov functions. This monograph shows that, although this obvious interpretation is often adequate, there are many in stances in which the Liapunov approach is best taken advantage of using diagonal-type Liapunov functions. In fact, they yield necessary and suffi cient stability conditions for some classes of nonlinear dynamical systems."

This volume consists of eight papers on new advances in interpolation theory for matrix functions and completion theory for matrices and operators. Much emphasis is placed on different interpolation and completion problems when the interpolant is estimated in two different norms. The book also focusses on the study of the spectra of different completions of 2 x 2 block matrices when originally all entries are specified except the lower left corner. A third theme concerns two-sided tangential interpolation problems for real rational matrix functions, and also for the time varying case. A tangential moment problem is also analyzed. All papers deal with related problems of modern matrix analysis, operator theory, complex analysis and system theory and will appeal to a wide group of mathematicians and engineers. The material can be used for advance courses and seminars. Contents: Editorial Introduction ? D. Alpay/P. Loubaton: The tangential trigonometric moment problem on an interval and related topics ? M. Bakonyi/V.G. Kaftal/G. Weiss/H.J. Woerdeman: Maximum entropy and joint norm bounds for operator extensions ? J.A. Ball/I. Gohberg/M.A. Kaashoek: Bitangential interpolation for input-output operators of time varying systems: the discrete time case ? J.A. Ball/I. Gohberg/L. Rodman: Two-sided tangential interpolation of real rational matrix functions ? H. Du/C. Gu: On the spectra of operator completion problems ? C. Foias/A.E. Frazho/W.S. Li: The exact H2 estimate for the central H interpolant ? A.E. Frazho/s.M. Kherat: On mixed H2 - H tangential interpolation ? I. Gohberg/C.Gu: On a completion problem for matrices

The book constructs explicitly the fundamental solution of the sub-Laplacian operator for a family of model domains in Cn+1. This type of domain is a good point-wise model for a Cauchy-Rieman (CR) manifold with diagonalizable Levi form. Qualitative results for such operators have been studied extensively, but exact formulas are difficult to derive. Exact formulas are closely related to the underlying geometry and lead to equations of classical types such as hypergeometric equations and Whittaker's equations.

Functional Equations, Inequalities and Applications provides an extensive study of several important equations and inequalities, useful in a number of problems in mathematical analysis. Subjects dealt with include the generalized Cauchy functional equation, the Ulam stability theory in the geometry of partial differential equations, stability of a quadratic functional equation in Banach modules, functional equations and mean value theorems, isometric mappings, functional inequalities of iterative type, related to a Cauchy functional equation, the median principle for inequalities and applications, Hadamard and Dragomir-Agarwal inequalities, the Euler formulae and convex functions and approximate algebra homomorphisms. Also included are applications to some problems of pure and applied mathematics.

This book will be of particular interest to mathematicians and graduate students whose work involves functional equations, inequalities and applications.

This monograph, addressing researchers as well as engineers, is devoted to nonclassical thermoelastic modelling of the nonlinear dynamics of shells. Differential equations of different dimensionality and different type have to be combined and nonlinearities of different geometrical, physical or elasto-plastic categories are addressed. Special emphasis is given to the Bubnov--Galerkin method. It can be applied to many problems in the theory of plates and shells, even those with very complex geometries, holes and various boundary conditions. The authors made every effort to keep the text intelligible for both practitioners and graduate students, although they offer a rigorous treatment of both purely mathematical and numerical approaches presented so that the reader can understand, analyse and track the nonlinear dynamics of spatial systems (shells) with thermomechanical behaviours.

Pedagogical insights gained through 30 years of teaching applied mathematics led the author to write this set of student-oriented books. Topics such as complex analysis, matrix theory, vector and tensor analysis, Fourier analysis, integral transforms, ordinary and partial differential equations are presented in a discursive style that is readable and easy to follow. Numerous clearly stated, completely worked out examples together with carefully selected problem sets with answers are used to enhance students' understanding and manipulative skill. The goal is to help students feel comfortable and confident in using advanced mathematical tools in junior, senior, and beginning graduate courses.

This text explains how advances in wavelet analysis provide new means for multiresolution analysis and describes its wide array of powerful tools. The book covers such topics as: the variations of the windowed Fourier transform; constructions of special waveforms suitable for specific tasks; the use of redundant representations in reconstruction and enhancement; applications of efficient numerical compression as a tool for fast numerical analysis; and approximation properties of various waveforms in different contexts.

Beginning with the works of N.N.Krasovskii [81, 82, 83], which clari fied the functional nature of systems with delays, the functional approach provides a foundation for a complete theory of differential equations with delays. Based on the functional approach, different aspects of time-delay system theory have been developed with almost the same completeness as the corresponding field of ODE (ordinary differential equations) the ory. The term functional differential equations (FDE) is used as a syn onym for systems with delays 1. The systematic presentation of these re sults and further references can be found in a number of excellent books [2, 15, 22, 32, 34, 38, 41, 45, 50, 52, 77, 78, 81, 93, 102, 128]. In this monograph we present basic facts of i-smooth calculus ~ a new differential calculus of nonlinear functionals, based on the notion of the invariant derivative, and some of its applications to the qualitative theory of functional differential equations. Utilization of the new calculus is the main distinction of this book from other books devoted to FDE theory. Two other distinguishing features of the volume are the following: - the central concept that we use is the separation of finite dimensional and infinite dimensional components in the structures of FDE and functionals; - we use the conditional representation of functional differential equa tions, which is convenient for application of methods and constructions of i~smooth calculus to FDE theory.

The main theme is the integration of the theory of linear PDE and the theory of finite difference and finite element methods. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods. The chapters on elliptic equations are preceded by a chapter on the two-point boundary value problem for ordinary differential equations. Similarly, the chapters on time-dependent problems are preceded by a chapter on the initial-value problem for ordinary differential equations. There is also one chapter on the elliptic eigenvalue problem and eigenfunction expansion. The presentation does not presume a deep knowledge of mathematical and functional analysis. The required background on linear functional analysis and Sobolev spaces is reviewed in an appendix. The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering.

JeanVaillant L'oeuvre de Jean Leray est originale et profonde; ses theoremes et ses theories sont au coeur des recherches mathematiques actuelles: la beaute de chacun de ses travaux ne se divise pas. Son cours de Princeton, sous forme de notes en anglais (et d'une traduction en russe) en est une belle illustration: ce cours presente les equations aux derivees partielles a partir de la transformation de Laplace et du theoreme de Cauchy-Kowaleska et contient l'essentiel de nombreusesrecherchesmodernes. Lerayavaitpourbutderesoudreunprobleme, souvent d'origine mecanique ou physique - qui se pose, et non qu'on se pose -, de demontrer un theoreme; il construit alors son oeuvre de facon complete et essentiellement intrinseque. En fait, Leray construit une theorie dont l'extension tient a son origine naturelle, l'acuite, la perfection, la profondeur d'esprit de son auteur;enmemetempsildominelescalculs,qu'ilmeneavecplaisiretelegance: "Il n'y a pas de mathematiques sans calculs" disait-il. La science etait au centre de la vie de Jean Leray. Il s'inquietait de sa sauvegarde. Rappelons quelques phrases de ses textes de 1974: "D'ailleurs la science ne s'apprend pas: elle se comprend. Elle n'est pas lettre morte et les livres n'assurent pas sa perennite; elle est une pensee vivante. Pour la maitriser notre esprit doit, habilement guide, la redecouvrir de meme que notre corps a du revivre dans le sein mat- nel, toute l'evolution qui crea notre espece. Aussi n'y a-t-il qu'une facon ef?cace d'enseigner les sciences et les techniques: transmettre l'esprit de recherche.

This comprehensive book presents a rigorous and state-of-the-art treatment of variational inequalities and complementarity problems in finite dimensions. This class of mathematical programming problems provides a powerful framework for the unified analysis and development of efficient solution algorithms for a wide range of equilibrium problems in economics, engineering, finance, and applied sciences. New research material and recent results, not otherwise easily accessible, are presented in a self-contained and consistent manner. The book is published in two volumes, with the first volume concentrating on the basic theory and the second on iterative algorithms. Both volumes contain abundant exercises and feature extensive bibliographies. Written with a wide range of readers in mind, including graduate students and researchers in applied mathematics, optimization, and operations research as well as computational economists and engineers, this book will be an enduring reference on the subject and provide the foundation for its sustained growth.

This reference work deals with important topics in general topology and their role in functional analysis and axiomatic set theory, for graduate students and researchers working in topology, functional analysis, set theory and probability theory. It provides a guide to recent research findings, with three contributions by Arhangel'skii and Choban.

This volume collects the edited and reviewed contribution presented in the 9th iTi Conference that took place virtually, covering fundamental and applied aspects in turbulence. In the spirit of the iTi conference, the volume is produced after the conference so that the authors had the opportunity to incorporate comments and discussions raised during the meeting. In the present book, the contributions have been structured according to the topics: I Experiments II Simulations and Modelling III Data Processing and Scaling IV Theory V Miscellaneous topics

Since the early 1960s, the mathematical theory of variational inequalities has been under rapid development, based on complex analysis and strongly influenced by 'real-life' application. Many, but of course not all, moving free (Le., a priori un known) boundary problems originating from engineering and economic applica tions can directly, or after a transformation, be formulated as variational inequal ities. In this work we investigate an evolutionary variational inequality with a memory term which is, as a fixed domain formulation, the result of the application of such a transformation to a degenerate moving free boundary problem. This study includes mathematical modelling, existence, uniqueness and regularity results, numerical analysis of finite element and finite volume approximations, as well as numerical simulation results for applications in polymer processing. Essential parts of these research notes were developed during my work at the Chair of Applied Mathematics (LAM) of the Technical University Munich. I would like to express my sincerest gratitude to K. -H. Hoffmann, the head of this chair and the present scientific director of the Center of Advanced European Studies and Research (caesar), for his encouragement and support. With this work I am fol lowing a general concept of Applied Mathematics to which he directed my interest and which, based on application problems, comprises mathematical modelling, mathematical and numerical analysis, computational aspects and visualization of simulation results."