Theory of Extremal Problems
Author | : |
Publisher | : Elsevier |
Total Pages | : 473 |
Release | : 2009-06-15 |
Genre | : Mathematics |
ISBN | : 0080875270 |
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Theory of Extremal Problems
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Author | : |
Publisher | : Elsevier |
Total Pages | : 473 |
Release | : 2009-06-15 |
Genre | : Mathematics |
ISBN | : 0080875270 |
Theory of Extremal Problems
Author | : Peter Frankl |
Publisher | : American Mathematical Soc. |
Total Pages | : 234 |
Release | : 2018-08-15 |
Genre | : Extremal problems |
ISBN | : 1470440393 |
One of the great appeals of Extremal Set Theory as a subject is that the statements are easily accessible without a lot of mathematical background, yet the proofs and ideas have applications in a wide range of fields including combinatorics, number theory, and probability theory. Written by two of the leading researchers in the subject, this book is aimed at mathematically mature undergraduates, and highlights the elegance and power of this field of study. The first half of the book provides classic results with some new proofs including a complete proof of the Ahlswede-Khachatrian theorem as well as some recent progress on the Erdos matching conjecture. The second half presents some combinatorial structural results and linear algebra methods including the Deza-Erdos-Frankl theorem, application of Rodl's packing theorem, application of semidefinite programming, and very recent progress (obtained in 2016) on the Erdos-Szemeredi sunflower conjecture and capset problem. The book concludes with a collection of challenging open problems.
Author | : I. V. Girsanov |
Publisher | : Springer Science & Business Media |
Total Pages | : 142 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642806848 |
The author of this book, Igor' Vladimirovich Girsanov, was one of the first mathematicians to study general extremum problems and to realize the feasibility and desirability of a unified theory of extremal problems, based on a functional analytic approach. He actively advocated this view, and his special course, given at the Faculty of Mechanics and Mathematics of the Moscow State University in 1963 and 1964, was apparently the first systematic exposition of a unified approach to the theory of extremal problems. This approach was based on the ideas of Dubovitskii and Milyutin [1]. The general theory of extremal problems has developed so intensely during the past few years that its basic concepts may now be considered finalized. Nevertheless, as yet the basic results of this new field of mathematics have not been presented in a form accessible to a wide range of readers. (The profound paper of Dubovitskii and Milyutin [2] can hardly be recommended for a first study of the theory, since, in particular, it does not contain proofs of the fundamental theorems. ) Girsanov's book fills this gap. It contains a systematic exposition of the general principles underlying the derivation of necessary and sufficient conditions for an extremum, in a wide variety of problems. Numerous applications are given to specific extremal problems. The main material is preceded by an introductory section in which all prerequisites from functional analysis are presented.
Author | : Vladimir Mikhailovich Tikhomirov |
Publisher | : |
Total Pages | : 136 |
Release | : 1986 |
Genre | : |
ISBN | : |
Author | : Stanislav V. Emelyanov |
Publisher | : Walter de Gruyter |
Total Pages | : 317 |
Release | : 2011-12-22 |
Genre | : Mathematics |
ISBN | : 3110893010 |
This monograph provides a thorough treatment of parameter-dependent extremal problems with local minimum values that remain unchanged under changes of the parameter. The authors consider the theory as well the practical treatment of those problems, both in finite-dimensional as well as in infinite-dimensional spaces. Various applications are considered, e.g., variational calculus, control theory and bifurcations theory. Thorough treatment of parameter-dependent extremal problems with local minimum values. Includes many applications, e.g., variational calculus, control theory and bifurcations theory. Intended for specialists in the field of nonlinear analysis and its applications as well as for students specializing in these subjects.
Author | : Vladimir Mikhaĭlovich Tikhomirov |
Publisher | : |
Total Pages | : 144 |
Release | : 1986-11-17 |
Genre | : Mathematics |
ISBN | : |
This monograph deals with the general principles of the theory of extremal problems. The author discusses Lagrange's principle, the duality principle, the complete elimination of restrictions, the Hamilton-Jacobi principle, the extension of extremal problems, and the invariance principle.
Author | : Konstantin Ivanovich Babenko |
Publisher | : American Mathematical Soc. |
Total Pages | : 348 |
Release | : 1975 |
Genre | : Mathematics |
ISBN | : 9780821830017 |
Discusses univalent functions and extremal problems.
Author | : Bela Bollobas |
Publisher | : Courier Corporation |
Total Pages | : 512 |
Release | : 2013-07-02 |
Genre | : Mathematics |
ISBN | : 0486317587 |
The ever-expanding field of extremal graph theory encompasses a diverse array of problem-solving methods, including applications to economics, computer science, and optimization theory. This volume, based on a series of lectures delivered to graduate students at the University of Cambridge, presents a concise yet comprehensive treatment of extremal graph theory. Unlike most graph theory treatises, this text features complete proofs for almost all of its results. Further insights into theory are provided by the numerous exercises of varying degrees of difficulty that accompany each chapter. Although geared toward mathematicians and research students, much of Extremal Graph Theory is accessible even to undergraduate students of mathematics. Pure mathematicians will find this text a valuable resource in terms of its unusually large collection of results and proofs, and professionals in other fields with an interest in the applications of graph theory will also appreciate its precision and scope.
Author | : |
Publisher | : |
Total Pages | : |
Release | : 1979 |
Genre | : Calculus of variations |
ISBN | : |
Author | : Mark Grigorʹevich Kreĭn |
Publisher | : American Mathematical Soc. |
Total Pages | : 430 |
Release | : |
Genre | : Mathematics |
ISBN | : 9780821886717 |
In this book, an extensive circle of questions originating in the classical work of P. L. Chebyshev and A. A. Markov is considered from the more modern point of view. It is shown how results and methods of the generalized moment problem are interlaced with various questions of the geometry of convex bodies, algebra, and function theory. From this standpoint, the structure of convex and conical hulls of curves is studied in detail and isoperimetric inequalities for convex hulls are established; a theory of orthogonal and quasiorthogonal polynomials is constructed; problems on limiting values of integrals and on least deviating functions (in various metrics) are generalized and solved; problems in approximation theory and interpolation and extrapolation in various function classes (analytic, absolutely monotone, almost periodic, etc.) are solved, as well as certain problems in optimal control of linear objects.