Описание: This book deals with the analysis of linear operators from a quasi-Banach function space into a Banach space. The central theme is to extend the operator to as large a (function) space as possible, its optimal domain, and to take advantage of this in analyzing the original operator.
Описание: Presents a survey of some aspects of extension problems in Complex Analysis and Geometry. Recalling the preliminary and necessary notions of complex analysis, this title presents a survey that focuses on extension of holomorphic functions on the reflection principle, on extension results via cohomology vanishing, and on the boundary problem.
Описание: This volume is an introductory text in several complex variables, using methods of integral representations and Hilbert space theory. It investigates mainly the
studies of the estimate of solutions of the Cauchy-Riemann equations in pseudoconvex domains and the extension of holomorphic functions in submanifolds of pseudoconvex domains
which were developed in the last 50 years. We discuss the two main results mentioned above by two different methods: the integral formulas and the Hilbert space
The theorems concerning general pseudoconvex domains are analyzed using Hilbert space theory, and the proofs for theorems concerning strictly pseudoconvex
domains are solved using integral representations. This volume is written in a self-contained style, so that the proofs are easily accessible to beginners. There are exercises featured at
the end of each chapter to aid readers to better understand the materials of this volume.
Fairly detailed hints are articulated to solve these exercises.
Pocket Book of Integrals and Mathematical Formulas, 5th Edition covers topics ranging from precalculus to vector analysis and from Fourier series to statistics, presenting numerous worked examples to demonstrate the application of the formulas and methods. This popular pocket book is an essential source for students of calculus and higher mathematics courses. It also provides an easy-to-use, accessible reference for mathematicians, engineers, scientists, and others seeking vital mathematical formulas, concepts, and definitions.
Enlarging the type without sacrificing special topics involving financial mathematics and number theory, this 5th Edition:
Includes several classic calculus applications that illustrate the power and practical use of calculus
Discusses an interesting offshoot of Fermat's last theorem, namely, "near misses"
Reformats and revises the table of integrals for improved clarity and accuracy
Through careful selection of topics and detail, Pocket Book of Integrals and Mathematical Formulas, 5th Edition remains a portable yet comprehensive resource for students and professionals, containing the most important mathematical formulas for engineering and scientific applications.
Описание: This book presents fundamentals and important results of vector optimization in a general setting. The theory developed includes scalarization, existence theorems, a generalized Lagrange multiplier rule and duality results. Applications to vector approximation, cooperative game theory and multiobjective optimization are described. The theory is extended to set optimization with particular emphasis on contingent epiderivatives, subgradients and optimality conditions. Background material of convex analysis being necessary is concisely summarized at the beginning.
Описание: S.L. Sobolev (1908вЂ“1989) was a great mathematician of the twentieth century. His selected works included in this volume laid the foundations for intensive development of the modern theory of partial differential equations and equations of mathematical physics, and they were a gold mine for new directions of functional analysis and computational mathematics.The topics covered in this volume include SobolevвЂ™s fundamental works on equations of mathematical physics, computational mathematics, and cubature formulas. Some of the articles are generally unknown to mathematicians because they were published in journals that are difficult to access.
Автор: Chentsov A.G., Morina S.I. Название: Extensions and Relaxations ISBN: 1402005792 ISBN-13(EAN): 9781402005794 Издательство: Springer Рейтинг: Цена: 10284 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: In this book a general topological construction of extension is proposed for problems of attainability in topological spaces under perturbation of a system of constraints. This construction is realized in a special class of generalized elements defined as finitely additive measures. A version of the method of programmed iterations is constructed. This version realizes multi-valued control quasistrategies, which guarantees the solution of the control problem that consists in guidance to a given set under observation of phase constraints.Audience: The book will be of interest to researchers, and graduate students in the field of optimal control, mathematical systems theory, measure and integration, functional analysis, and general topology.
Описание: This book offers a comprehensive treatment of the exercises and case studies as well as summaries of the chapters of the book "Linear Optimization and Extensions" by Manfred Padberg. It covers the areas of linear programming and the optimization of linear functions over polyhedra in finite dimensional Euclidean vector spaces.Here are the main topics treated in the book: Simplex algorithms and their derivatives including the duality theory of linear programming. Polyhedral theory, pointwise and linear descriptions of polyhedra, double description algorithms, Gaussian elimination with and without division, the complexity of simplex steps. Projective algorithms, the geometry of projective algorithms, Newtonian barrier methods. Ellipsoids algorithms in perfect and in finite precision arithmetic, the equivalence of linear optimization and polyhedral separation. The foundations of mixed-integer programming and combinatorial optimization.
Описание: DLP denotes a dynamic-linear modeling and optimization approach to computational decision support for resource planning problems that arise, typically, within the natural resource sciences and the disciplines of operations research and operational engineering. It integrates techniques of dynamic programming (DP) and linear programming (LP) and can be realized in an immediate, practical and usable way. Simultaneously DLP connotes a broad and very general modeling/ algorithmic concept that has numerous areas of application and possibilities for extension. Two motivating examples provide a linking thread through the main chapters, and an appendix provides a demonstration program, executable on a PC, for hands-on experience with the DLP approach.
This monograph deals with the mathematics of extending given partial data-sets obtained from experiments;
Experimentalists frequently gather spectral data when the observed data is limited, e.g., by the precision of instruments; or by other limiting external factors. Here the limited information is a restriction, and the extensions take the form of full positive definite function on some prescribed group. It is therefore both an art and a science to produce solid conclusions from restricted or limited data.
While the theory of is important in many areas of pure and applied mathematics, it is difficult for students and for the novice to the field, to find accessible presentations which cover all relevant points of view, as well as stressing common ideas and interconnections. We have aimed at filling this gap, and we have stressed hands-on-examples.
Автор: Rabinowitz Название: Extensions of Moser–Bangert Theory ISBN: 0817681167 ISBN-13(EAN): 9780817681166 Издательство: Springer Рейтинг: Цена: 10284 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This monograph presents extensions of the Moser–Bangert approach that include solutions of a family of nonlinear elliptic PDEs on Rn and an Allen–Cahn PDE model of phase transitions. After recalling the relevant Moser–Bangert results, Extensions of Moser–Bangert Theory pursues the rich structure of the set of solutions of a simpler model case, expanding upon the studies of Moser and Bangert to include solutions that merely have local minimality properties. Subsequent chapters build upon the introductory results, making the monograph self contained.The work is intended for mathematicians who specialize in partial differential equations and may also be used as a text for a graduate topics course in PDEs.
Описание: Concentration compactness is an important method in mathematical analysis which has been used in mathematical research. This book aims to combine a concise formulation of the method, a range of applications to variational problems, and background material concerning manifolds, non-compact transformation groups and functional spaces.
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