The Calculus of Variations in the Large

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Publisher : American Mathematical Soc.
ISBN 13 : 0821810189
Total Pages : 384 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Calculus of Variations in the Large by : Marston Morse

Download or read book The Calculus of Variations in the Large written by Marston Morse and published by American Mathematical Soc.. This book was released on 1934-12-31 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Morse theory is a study of deep connections between analysis and topology. In its classical form, it provides a relationship between the critical points of certain smooth functions on a manifold and the topology of the manifold. It has been used by geometers, topologists, physicists, and others as a remarkably effective tool to study manifolds. In the 1980s and 1990s, Morse theory was extended to infinite dimensions with great success. This book is Morse's own exposition of his ideas. It has been called one of the most important and influential mathematical works of the twentieth century. Calculus of Variations in the Large is certainly one of the essential references on Morse theory.

Mathematical Reviews

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Publisher :
ISBN 13 :
Total Pages : 1208 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 2007 with total page 1208 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Extremal Problems for the Möbius Function

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Publisher :
ISBN 13 :
Total Pages : 200 pages
Book Rating : 4.3/5 (129 download)

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Book Synopsis Extremal Problems for the Möbius Function by : Margaret A. Readdy

Download or read book Extremal Problems for the Möbius Function written by Margaret A. Readdy and published by . This book was released on 1993 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Variational Analysis

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Publisher : Courier Corporation
ISBN 13 : 0486153223
Total Pages : 276 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Variational Analysis by : Marston Morse

Download or read book Variational Analysis written by Marston Morse and published by Courier Corporation. This book was released on 2013-02-27 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents extended separation, comparison, and oscillation theorems that replace classical analysis. Its analysis of related quadratic functionals shows how critical extremals can substitute for minimizing extremals. 1973 edition.

Computing and Combinatorics

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Publisher : Springer Science & Business Media
ISBN 13 : 3540405348
Total Pages : 573 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Computing and Combinatorics by : Tandy Warnow

Download or read book Computing and Combinatorics written by Tandy Warnow and published by Springer Science & Business Media. This book was released on 2003-07-09 with total page 573 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in this volume were presented at the 9th Annual International C- puting and Combinatorics Conference (COCOON 2003), held July 25–28, 2003, in Big Sky, MT, USA. The topics cover most aspects of theoretical computer science and combinatorics related to computing. Submissionstotheconferencethisyearwereconductedelectronically.Atotal of 114 papers were submitted, of which 52 were accepted. The papers were evaluated by an international program committee consisting of Nina Amenta, Tetsuo Asano, Bernard Chazelle, Zhixiang Chen, Francis Chin, Kyung-Yong Chwa, Robert Cimikowski, Anne Condon, Michael Fellows, Anna Gal, Michael Hallett,DanielHuson,NaokiKatoh,D.T.Lee,BernardMoret,BrendanMumey, Gene Myers, Hung Quang Ngo, Takao Nishizeki, Cindy Phillips, David Sanko?, Denbigh Starkey, Jie Wang, Lusheng Wang, Tandy Warnow and Binhai Zhu. It is expected that most of the accepted papers will appear in a more complete form in scienti?c journals. The submitted papers were from Canada (6), China (7), Estonia (1), F- land (1), France (1), Germany (8), Israel (4), Italy (1), Japan (11), Korea (22), Kuwait (1), New Zealand (1), Singapore (2), Spain (1), Sweden (2), Switzerland (3), Taiwan (7), the UK (1) and the USA (34). Each paper was evaluated by at least three Program Committee members, assisted in some cases by subre- rees. In addition to selected papers, the conference also included three invited presentations by Jon Bentley, Dan Gus?eld and Joel Spencer.

Lectures on the Calculus of Variations and Optimal Control Theory

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Author :
Publisher : American Mathematical Soc.
ISBN 13 : 9780821826904
Total Pages : 354 pages
Book Rating : 4.8/5 (269 download)

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Book Synopsis Lectures on the Calculus of Variations and Optimal Control Theory by : Laurence Chisholm Young

Download or read book Lectures on the Calculus of Variations and Optimal Control Theory written by Laurence Chisholm Young and published by American Mathematical Soc.. This book was released on 2000 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is divided into two parts. The first addresses the simpler variational problems in parametric and nonparametric form. The second covers extensions to optimal control theory. The author opens with the study of three classical problems whose solutions led to the theory of calculus of variations. They are the problem of geodesics, the brachistochrone, and the minimal surface of revolution. He gives a detailed discussion of the Hamilton-Jacobi theory, both in the parametric and nonparametric forms. This leads to the development of sufficiency theories describing properties of minimizing extremal arcs. Next, the author addresses existence theorems. He first develops Hilbert's basic existence theorem for parametric problems and studies some of its consequences. Finally, he develops the theory of generalized curves and "automatic" existence theorems. In the second part of the book, the author discusses optimal control problems. He notes that originally these problems were formulated as problems of Lagrange and Mayer in terms of differential constraints. In the control formulation, these constraints are expressed in a more convenient form in terms of control functions. After pointing out the new phenomenon that may arise, namely, the lack of controllability, the author develops the maximum principle and illustrates this principle by standard examples that show the switching phenomena that may occur. He extends the theory of geodesic coverings to optimal control problems. Finally, he extends the problem to generalized optimal control problems and obtains the corresponding existence theorems.

An Introduction to Extremal Kahler Metrics

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Publisher : American Mathematical Soc.
ISBN 13 : 1470410478
Total Pages : 210 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis An Introduction to Extremal Kahler Metrics by : Gábor Székelyhidi

Download or read book An Introduction to Extremal Kahler Metrics written by Gábor Székelyhidi and published by American Mathematical Soc.. This book was released on 2014-06-19 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: A basic problem in differential geometry is to find canonical metrics on manifolds. The best known example of this is the classical uniformization theorem for Riemann surfaces. Extremal metrics were introduced by Calabi as an attempt at finding a higher-dimensional generalization of this result, in the setting of Kähler geometry. This book gives an introduction to the study of extremal Kähler metrics and in particular to the conjectural picture relating the existence of extremal metrics on projective manifolds to the stability of the underlying manifold in the sense of algebraic geometry. The book addresses some of the basic ideas on both the analytic and the algebraic sides of this picture. An overview is given of much of the necessary background material, such as basic Kähler geometry, moment maps, and geometric invariant theory. Beyond the basic definitions and properties of extremal metrics, several highlights of the theory are discussed at a level accessible to graduate students: Yau's theorem on the existence of Kähler-Einstein metrics, the Bergman kernel expansion due to Tian, Donaldson's lower bound for the Calabi energy, and Arezzo-Pacard's existence theorem for constant scalar curvature Kähler metrics on blow-ups.

Hyperbolic Complex Spaces

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Publisher : Springer Science & Business Media
ISBN 13 : 3662035820
Total Pages : 480 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Hyperbolic Complex Spaces by : Shoshichi Kobayashi

Download or read book Hyperbolic Complex Spaces written by Shoshichi Kobayashi and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the three decades since the introduction of the Kobayashi distance, the subject of hyperbolic complex spaces and holomorphic mappings has grown to be a big industry. This book gives a comprehensive and systematic account on the Carathéodory and Kobayashi distances, hyperbolic complex spaces and holomorphic mappings with geometric methods. A very complete list of references should be useful for prospective researchers in this area.

OAR Quarterly Index of Current Research Results

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Publisher :
ISBN 13 :
Total Pages : 576 pages
Book Rating : 4.E/5 ( download)

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Book Synopsis OAR Quarterly Index of Current Research Results by : United States. Air Force. Office of Aerospace Research

Download or read book OAR Quarterly Index of Current Research Results written by United States. Air Force. Office of Aerospace Research and published by . This book was released on 1965 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lectures on the Calculus of Variations and Optimal Control Theory

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Author :
Publisher : American Mathematical Society
ISBN 13 : 1470479001
Total Pages : 353 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Lectures on the Calculus of Variations and Optimal Control Theory by : L. C. Young

Download or read book Lectures on the Calculus of Variations and Optimal Control Theory written by L. C. Young and published by American Mathematical Society. This book was released on 2024-10-30 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is divided into two parts. The first addresses the simpler variational problems in parametric and nonparametric form. The second covers extensions to optimal control theory. The author opens with the study of three classical problems whose solutions led to the theory of calculus of variations. They are the problem of geodesics, the brachistochrone, and the minimal surface of revolution. He gives a detailed discussion of the Hamilton-Jacobi theory, both in the parametric and nonparametric forms. This leads to the development of sufficiency theories describing properties of minimizing extremal arcs. Next, the author addresses existence theorems. He first develops Hilbert's basic existence theorem for parametric problems and studies some of its consequences. Finally, he develops the theory of generalized curves and ?automatic? existence theorems. In the second part of the book, the author discusses optimal control problems. He notes that originally these problems were formulated as problems of Lagrange and Mayer in terms of differential constraints. In the control formulation, these constraints are expressed in a more convenient form in terms of control functions. After pointing out the new phenomenon that may arise, namely, the lack of controllability, the author develops the maximum principle and illustrates this principle by standard examples that show the switching phenomena that may occur. He extends the theory of geodesic coverings to optimal control problems. Finally, he extends the problem to generalized optimal control problems and obtains the corresponding existence theorems.

Theory of Extremal Problems

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Author :
Publisher : Elsevier
ISBN 13 : 0080875270
Total Pages : 473 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis Theory of Extremal Problems by :

Download or read book Theory of Extremal Problems written by and published by Elsevier. This book was released on 2009-06-15 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theory of Extremal Problems

Quadrature Domains and Their Applications

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Publisher : Springer Science & Business Media
ISBN 13 : 3764373164
Total Pages : 298 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Quadrature Domains and Their Applications by : Peter Ebenfelt

Download or read book Quadrature Domains and Their Applications written by Peter Ebenfelt and published by Springer Science & Business Media. This book was released on 2006-03-10 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quadrature domains were singled out about 30 years ago by D. Aharonov and H.S. Shapiro in connection with an extremal problem in function theory. Since then, a series of coincidental discoveries put this class of planar domains at the center of crossroads of several quite independent mathematical theories, e.g., potential theory, Riemann surfaces, inverse problems, holomorphic partial differential equations, fluid mechanics, operator theory. The volume is devoted to recent advances in the theory of quadrature domains, illustrating well the multi-facet aspects of their nature. The book contains a large collection of open problems pertaining to the general theme of quadrature domains.

Interpolation Theory and Its Applications

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Publisher : Springer Science & Business Media
ISBN 13 : 9400900597
Total Pages : 215 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Interpolation Theory and Its Applications by : Lev A. Sakhnovich

Download or read book Interpolation Theory and Its Applications written by Lev A. Sakhnovich and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Interpolation problems play an important role both in theoretical and applied investigations. This explains the great number of works dedicated to classical and new interpolation problems ([1)-[5], [8), [13)-[16], [26)-[30], [57]). In this book we use a method of operator identities for investigating interpo lation problems. Following the method of operator identities we formulate a general interpolation problem containing the classical interpolation problems (Nevanlinna Pick, Caratheodory, Schur, Humburger, Krein) as particular cases. We write down the abstract form of the Potapov inequality. By solving this inequality we give the description of the set of solutions of the general interpolation problem in the terms of the linear-fractional transformation. Then we apply the obtained general results to a number of classical and new interpolation problems. Some chapters of the book are dedicated to the application of the interpola tion theory results to several other problems (the extension problem, generalized stationary processes, spectral theory, nonlinear integrable equations, functions with operator arguments). 2. Now we shall proceed to a more detailed description of the book contents.

U.S. Government Research Reports

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Publisher :
ISBN 13 :
Total Pages : 712 pages
Book Rating : 4.3/5 (243 download)

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Book Synopsis U.S. Government Research Reports by :

Download or read book U.S. Government Research Reports written by and published by . This book was released on 1964 with total page 712 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to Enumerative and Analytic Combinatorics

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Publisher : CRC Press
ISBN 13 : 1482249103
Total Pages : 555 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Introduction to Enumerative and Analytic Combinatorics by : Miklos Bona

Download or read book Introduction to Enumerative and Analytic Combinatorics written by Miklos Bona and published by CRC Press. This book was released on 2015-09-18 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Enumerative and Analytic Combinatorics fills the gap between introductory texts in discrete mathematics and advanced graduate texts in enumerative combinatorics. The book first deals with basic counting principles, compositions and partitions, and generating functions. It then focuses on the structure of permutations, graph enumerat

Introduction to Chemical Graph Theory

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Publisher : CRC Press
ISBN 13 : 0429833997
Total Pages : 271 pages
Book Rating : 4.4/5 (298 download)

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Book Synopsis Introduction to Chemical Graph Theory by : Stephan Wagner

Download or read book Introduction to Chemical Graph Theory written by Stephan Wagner and published by CRC Press. This book was released on 2018-09-05 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Chemical Graph Theory is a concise introduction to the main topics and techniques in chemical graph theory, specifically the theory of topological indices. These include distance-based, degree-based, and counting-based indices. The book covers some of the most commonly used mathematical approaches in the subject. It is also written with the knowledge that chemical graph theory has many connections to different branches of graph theory (such as extremal graph theory, spectral graph theory). The authors wrote the book in an appealing way that attracts people to chemical graph theory. In doing so, the book is an excellent playground and general reference text on the subject, especially for young mathematicians with a special interest in graph theory. Key Features: A concise introduction to topological indices of graph theory Appealing to specialists and non-specialists alike Provides many techniques from current research About the Authors: Stephan Wagner grew up in Graz (Austria), where he also received his PhD from Graz University of Technology in 2006. Shortly afterwards, he moved to South Africa, where he started his career at Stellenbosch University as a lecturer in January 2007. His research interests lie mostly in combinatorics and related areas, including connections to other scientific fields such as physics, chemistry and computer science. Hua Wang received his PhD from University of South Carolina in 2005. He held a Visiting Research Assistant Professor position at University of Florida before joining Georgia Southern University in 2008. His research interests include combinatorics and graph theory, elementary number theory, and related problems

Geometry and Light

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Publisher : Courier Corporation
ISBN 13 : 0486134903
Total Pages : 290 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Geometry and Light by : Ulf Leonhardt

Download or read book Geometry and Light written by Ulf Leonhardt and published by Courier Corporation. This book was released on 2012-07-06 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Suitable for advanced undergraduate and graduate students of engineering, physics, and mathematics and scientific researchers of all types, this is the first authoritative text on invisibility and the science behind it. More than 100 full-color illustrations, plus exercises with solutions. 2010 edition.