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Duality Ii
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Download or read book Duality Ii written by David Cupples and published by David Cupples. This book was released on 2006-09 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mike and Chris are two lonely soul, era]individuals in search of the one elusive thing that we all seek, yet few of us really ever findaourselves. In this case, however, they do find themselvesaleading to a journey, to discoveries the likes of which neither of them could have dreamed. Not the least of which is that they are reincarnated persons from millennia back called the Duality, and that they are the son, the creation, of the Greek god Apollo. They have been pre-ordained to participate in a quest wherein few facts are made known to them. They are also gifted with a companion who is shrouded in mystery. You have to watch yourselves on this one; do you ever feel like someone is watching you? What is too much information?
Book Synopsis Duality Principles in Nonconvex Systems by : David Yang Gao
Download or read book Duality Principles in Nonconvex Systems written by David Yang Gao and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: Motivated by practical problems in engineering and physics, drawing on a wide range of applied mathematical disciplines, this book is the first to provide, within a unified framework, a self-contained comprehensive mathematical theory of duality for general non-convex, non-smooth systems, with emphasis on methods and applications in engineering mechanics. Topics covered include the classical (minimax) mono-duality of convex static equilibria, the beautiful bi-duality in dynamical systems, the interesting tri-duality in non-convex problems and the complicated multi-duality in general canonical systems. A potentially powerful sequential canonical dual transformation method for solving fully nonlinear problems is developed heuristically and illustrated by use of many interesting examples as well as extensive applications in a wide variety of nonlinear systems, including differential equations, variational problems and inequalities, constrained global optimization, multi-well phase transitions, non-smooth post-bifurcation, large deformation mechanics, structural limit analysis, differential geometry and non-convex dynamical systems. With exceptionally coherent and lucid exposition, the work fills a big gap between the mathematical and engineering sciences. It shows how to use formal language and duality methods to model natural phenomena, to construct intrinsic frameworks in different fields and to provide ideas, concepts and powerful methods for solving non-convex, non-smooth problems arising naturally in engineering and science. Much of the book contains material that is new, both in its manner of presentation and in its research development. A self-contained appendix provides some necessary background from elementary functional analysis. Audience: The book will be a valuable resource for students and researchers in applied mathematics, physics, mechanics and engineering. The whole volume or selected chapters can also be recommended as a text for both senior undergraduate and graduate courses in applied mathematics, mechanics, general engineering science and other areas in which the notions of optimization and variational methods are employed.
Book Synopsis Complementarity, Duality and Symmetry in Nonlinear Mechanics by : David Yang Gao
Download or read book Complementarity, Duality and Symmetry in Nonlinear Mechanics written by David Yang Gao and published by Springer Science & Business Media. This book was released on 2012-11-08 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complementarity, duality, and symmetry are closely related concepts, and have always been a rich source of inspiration in human understanding through the centuries, particularly in mathematics and science. The Proceedings of IUTAM Symposium on Complementarity, Duality, and Symmetry in Nonlinear Mechanics brings together some of world's leading researchers in both mathematics and mechanics to provide an interdisciplinary but engineering flavoured exploration of the field's foundation and state of the art developments. Topics addressed in this book deal with fundamental theory, methods, and applications of complementarity, duality and symmetry in multidisciplinary fields of nonlinear mechanics, including nonconvex and nonsmooth elasticity, dynamics, phase transitions, plastic limit and shakedown analysis of hardening materials and structures, bifurcation analysis, entropy optimization, free boundary value problems, minimax theory, fluid mechanics, periodic soliton resonance, constrained mechanical systems, finite element methods and computational mechanics. A special invited paper presented important research opportunities and challenges of the theoretical and applied mechanics as well as engineering materials in the exciting information age. Audience: This book is addressed to all scientists, physicists, engineers and mathematicians, as well as advanced students (doctoral and post-doctoral level) at universities and in industry.
Book Synopsis Cones and Duality by : Charalambos D. Aliprantis
Download or read book Cones and Duality written by Charalambos D. Aliprantis and published by American Mathematical Soc.. This book was released on 2007-06-12 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ordered vector spaces and cones made their debut in mathematics at the beginning of the twentieth century. They were developed in parallel (but from a different perspective) with functional analysis and operator theory. Before the 1950s, ordered vector spaces appeared in the literature in a fragmented way. Their systematic study began around the world after 1950 mainly through the efforts of the Russian, Japanese, German, and Dutch schools. Since cones are being employed to solve optimization problems, the theory of ordered vector spaces is an indispensable tool for solving a variety of applied problems appearing in several diverse areas, such as engineering, econometrics, and the social sciences. For this reason this theory plays a prominent role not only in functional analysis but also in a wide range of applications. This is a book about a modern perspective on cones and ordered vector spaces. It includes material that has not been presented earlier in a monograph or a textbook. With many exercises of varying degrees of difficulty, the book is suitable for graduate courses. Most of the new topics currently discussed in the book have their origins in problems from economics and finance. Therefore, the book will be valuable to any researcher and graduate student who works in mathematics, engineering, economics, finance, and any other field that uses optimization techniques.
Book Synopsis Unity from Duality: Gravity, Gauge Theory and Strings by : Constantin P. Bachas
Download or read book Unity from Duality: Gravity, Gauge Theory and Strings written by Constantin P. Bachas and published by Springer Science & Business Media. This book was released on 2008-01-26 with total page 674 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contributions to this volume of the famous summer school in Les Houches cover the recent developments in supersymmetric string theory, the gauge theory/string theory correspondence and string duality. The book is a comprehensive introduction to the recent developments in string/M-theory and quantum gravity.
Book Synopsis Generalized Preinvexity and Second Order Duality in Multiobjective Programming by : Xinmin Yang
Download or read book Generalized Preinvexity and Second Order Duality in Multiobjective Programming written by Xinmin Yang and published by Springer. This book was released on 2018-09-27 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces readers to several new generalized preinvex functions and generalized invariant monotone functions. It begins by describing the main properties of these functions and various relations. Several examples are then presented to illustrate various interesting relationships among preinvex functions and the properly inclusive relations among the generalized invariant monotonicities. In addition, several second order and higher order symmetric duality models are provided for multi-objective nonlinear programming problems. Lastly, weak and strong duality theorems under generalized convexity assumptions are provided. The book offers a well-synthesized, accessible, and usable treatment for students, researchers and practitioners in the areas of OR, optimization, applied mathematics and engineering, and all those working on a wide range of related problems, which include financial institutions, logistics, transportation, traffic management, etc.
Book Synopsis Linear Optimization and Duality by : Craig A. Tovey
Download or read book Linear Optimization and Duality written by Craig A. Tovey and published by CRC Press. This book was released on 2020-12-15 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear Optimization and Dualiyy: A Modern Exposition departs from convention in significant ways. Standard linear programming textbooks present the material in the order in which it was discovered. Duality is treated as a difficult add-on after coverage of formulation, the simplex method, and polyhedral theory. Students end up without knowing duality in their bones. This text brings in duality in Chapter 1 and carries duality all the way through the exposition. Chapter 1 gives a general definition of duality that shows the dual aspects of a matrix as a column of rows and a row of columns. The proof of weak duality in Chapter 2 is shown via the Lagrangian, which relies on matrix duality. The first three LP formulation examples in Chapter 3 are classic primal-dual pairs including the diet problem and 2-person zero sum games. For many engineering students, optimization is their first immersion in rigorous mathematics. Conventional texts assume a level of mathematical sophistication they don’t have. This text embeds dozens of reading tips and hundreds of answered questions to guide such students. Features Emphasis on duality throughout Practical tips for modeling and computation Coverage of computational complexity and data structures Exercises and problems based on the learning theory concept of the zone of proximal development Guidance for the mathematically unsophisticated reader About the Author Craig A. Tovey is a professor in the H. Milton Stewart School of Industrial and Systems Engineering at Georgia Institute of Technology. Dr. Tovey received an AB from Harvard College, an MS in computer science and a PhD in operations research from Stanford University. His principal activities are in operations research and its interdisciplinary applications. He received a Presidential Young Investigator Award and the Jacob Wolfowitz Prize for research in heuristics. He was named an Institute Fellow at Georgia Tech, and was recognized by the ACM Special Interest Group on Electronic Commerce with the Test of Time Award. Dr. Tovey received the 2016 Golden Goose Award for his research on bee foraging behavior leading to the development of the Honey Bee Algorithm.
Book Synopsis Duality in Vector Optimization by : Radu Ioan Bot
Download or read book Duality in Vector Optimization written by Radu Ioan Bot and published by Springer Science & Business Media. This book was released on 2009-08-12 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents fundamentals and comprehensive results regarding duality for scalar, vector and set-valued optimization problems in a general setting. One chapter is exclusively consecrated to the scalar and vector Wolfe and Mond-Weir duality schemes.
Book Synopsis Duality in Optimization and Variational Inequalities by : C.j. Goh
Download or read book Duality in Optimization and Variational Inequalities written by C.j. Goh and published by CRC Press. This book was released on 2002-05-10 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive volume covers a wide range of duality topics ranging from simple ideas in network flows to complex issues in non-convex optimization and multicriteria problems. In addition, it examines duality in the context of variational inequalities and vector variational inequalities, as generalizations to optimization. Duality in Optimizati
Download or read book Basic Number Theory written by Andre Weil and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Poincaré Duality Algebras, Macaulay's Dual Systems, and Steenrod Operations by : Dagmar M. Meyer
Download or read book Poincaré Duality Algebras, Macaulay's Dual Systems, and Steenrod Operations written by Dagmar M. Meyer and published by Cambridge University Press. This book was released on 2005-08-18 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: A monograph demonstrating remarkable and unexpected interdisciplinary connections in the areas of commutative algebra, invariant theory and algebraic topology.
Book Synopsis Fields, Strings, and Duality by : Brian Greene
Download or read book Fields, Strings, and Duality written by Brian Greene and published by World Scientific. This book was released on 1997 with total page 1089 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The past year has witnessed truly remarkable developments in our understanding of string theory. Fields, Strings and Duality - TASI 96 is an invaluable collection of review papers on the subject, contributed by the most prominent researchers in the field. This volume is a scientific treasure for graduate students, researchers and all others who are interested in the progress of theoretical physics."--Publisher's website
Book Synopsis Kac Algebras and Duality of Locally Compact Groups by : Michel Enock
Download or read book Kac Algebras and Duality of Locally Compact Groups written by Michel Enock and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the theory of Kac algebras and their dual ity, elaborated independently by M. Enock and J . -M. Schwartz, and by G. !. Kac and L. !. Vajnermann in the seventies. The sub ject has now reached a state of maturity which fully justifies the publication of this book. Also, in recent times, the topic of "quantum groups" has become very fashionable and attracted the attention of more and more mathematicians and theoret ical physicists. One is still missing a good characterization of quantum groups among Hopf algebras, similar to the character ization of Lie groups among locally compact groups. It is thus extremely valuable to develop the general theory, as this book does, with emphasis on the analytical aspects of the subject instead of the purely algebraic ones. The original motivation of M. Enock and J. -M. Schwartz can be formulated as follows: while in the Pontrjagin duality theory of locally compact abelian groups a perfect symmetry exists between a group and its dual, this is no longer true in the various duality theorems of T. Tannaka, M. G. Krein, W. F. Stinespring . . . dealing with non abelian locally compact groups. The aim is then, in the line proposed by G. !. Kac in 1961 and M. Takesaki in 1972, to find a good category of Hopf algebras, containing the category of locally compact groups and fulfilling a perfect duality.
Book Synopsis Conjugate Duality in Convex Optimization by : Radu Ioan Bot
Download or read book Conjugate Duality in Convex Optimization written by Radu Ioan Bot and published by Springer Science & Business Media. This book was released on 2009-12-24 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: The results presented in this book originate from the last decade research work of the author in the ?eld of duality theory in convex optimization. The reputation of duality in the optimization theory comes mainly from the major role that it plays in formulating necessary and suf?cient optimality conditions and, consequently, in generatingdifferent algorithmic approachesfor solving mathematical programming problems. The investigations made in this work prove the importance of the duality theory beyond these aspects and emphasize its strong connections with different topics in convex analysis, nonlinear analysis, functional analysis and in the theory of monotone operators. The ?rst part of the book brings to the attention of the reader the perturbation approach as a fundamental tool for developing the so-called conjugate duality t- ory. The classical Lagrange and Fenchel duality approaches are particular instances of this general concept. More than that, the generalized interior point regularity conditions stated in the past for the two mentioned situations turn out to be p- ticularizations of the ones given in this general setting. In our investigations, the perturbationapproachrepresentsthestartingpointforderivingnewdualityconcepts for several classes of convex optimization problems. Moreover, via this approach, generalized Moreau–Rockafellar formulae are provided and, in connection with them, a new class of regularity conditions, called closedness-type conditions, for both stable strong duality and strong duality is introduced. By stable strong duality we understand the situation in which strong duality still holds whenever perturbing the objective function of the primal problem with a linear continuous functional.
Book Synopsis Osiris and the Egyptian Resurrection by : Sir Ernest Alfred Wallis Budge
Download or read book Osiris and the Egyptian Resurrection written by Sir Ernest Alfred Wallis Budge and published by . This book was released on 1911 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Encyclopaedia of Religion and Ethics: Indexes by : James Hastings
Download or read book Encyclopaedia of Religion and Ethics: Indexes written by James Hastings and published by . This book was released on 1927 with total page 778 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Encyclopaedia of Religion and Ethics by : James Hastings
Download or read book Encyclopaedia of Religion and Ethics written by James Hastings and published by Edinburgh : T. & T. Clark. This book was released on 1927 with total page 792 pages. Available in PDF, EPUB and Kindle. Book excerpt:
