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Author: C. Constantinescu
Publisher: Springer
ISBN: 3540392750
Category : Mathematics
Languages : en
Pages : 202
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Book Description
Author: C. Constantinescu
Publisher: Springer
ISBN: 3540392750
Category : Mathematics
Languages : en
Pages : 202
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Book Description
Author: Corneliu Constantinescu
Publisher:
ISBN:
Category :
Languages : en
Pages : 94
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Book Description
Author: J. S. Milne
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 440
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Book Description
Here, published for the first time, are the complete proofs of the fundamental arithmetic duality theorems that have come to play an increasingly important role in number theory and arithmetic geometry. The text covers these theorems in Galois cohomology, ,tale cohomology, and flat cohomology and addresses applications in the above areas. The writing is expository and the book will serve as an invaluable reference text as well as an excellent introduction to the subject.
Author: Allen Altman
Publisher: Springer
ISBN: 3540363092
Category : Mathematics
Languages : en
Pages : 188
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Book Description
Author: David Yang Gao
Publisher: Springer
ISBN: 3319580175
Category : Mathematics
Languages : en
Pages : 374
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Book Description
This book on canonical duality theory provides a comprehensive review of its philosophical origin, physics foundation, and mathematical statements in both finite- and infinite-dimensional spaces. A ground-breaking methodological theory, canonical duality theory can be used for modeling complex systems within a unified framework and for solving a large class of challenging problems in multidisciplinary fields in engineering, mathematics, and the sciences. This volume places a particular emphasis on canonical duality theory’s role in bridging the gap between non-convex analysis/mechanics and global optimization. With 18 total chapters written by experts in their fields, this volume provides a nonconventional theory for unified understanding of the fundamental difficulties in large deformation mechanics, bifurcation/chaos in nonlinear science, and the NP-hard problems in global optimization. Additionally, readers will find a unified methodology and powerful algorithms for solving challenging problems in complex systems with real-world applications in non-convex analysis, non-monotone variational inequalities, integer programming, topology optimization, post-buckling of large deformed structures, etc. Researchers and graduate students will find explanation and potential applications in multidisciplinary fields.
Author: Peter D. T. A. Elliott
Publisher: Cambridge University Press
ISBN: 9780521560887
Category : Mathematics
Languages : en
Pages : 368
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Book Description
Deals with analytic number theory; many new results.
Author: Paolo Aluffi
Publisher: American Mathematical Soc.
ISBN: 147046571X
Category : Education
Languages : en
Pages : 713
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Book Description
Algebra: Chapter 0 is a self-contained introduction to the main topics of algebra, suitable for a first sequence on the subject at the beginning graduate or upper undergraduate level. The primary distinguishing feature of the book, compared to standard textbooks in algebra, is the early introduction of categories, used as a unifying theme in the presentation of the main topics. A second feature consists of an emphasis on homological algebra: basic notions on complexes are presented as soon as modules have been introduced, and an extensive last chapter on homological algebra can form the basis for a follow-up introductory course on the subject. Approximately 1,000 exercises both provide adequate practice to consolidate the understanding of the main body of the text and offer the opportunity to explore many other topics, including applications to number theory and algebraic geometry. This will allow instructors to adapt the textbook to their specific choice of topics and provide the independent reader with a richer exposure to algebra. Many exercises include substantial hints, and navigation of the topics is facilitated by an extensive index and by hundreds of cross-references.
Author: Vladimir Kadets
Publisher: Springer
ISBN: 3319920049
Category : Mathematics
Languages : en
Pages : 553
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Book Description
Written by an expert on the topic and experienced lecturer, this textbook provides an elegant, self-contained introduction to functional analysis, including several advanced topics and applications to harmonic analysis. Starting from basic topics before proceeding to more advanced material, the book covers measure and integration theory, classical Banach and Hilbert space theory, spectral theory for bounded operators, fixed point theory, Schauder bases, the Riesz-Thorin interpolation theorem for operators, as well as topics in duality and convexity theory. Aimed at advanced undergraduate and graduate students, this book is suitable for both introductory and more advanced courses in functional analysis. Including over 1500 exercises of varying difficulty and various motivational and historical remarks, the book can be used for self-study and alongside lecture courses.
Author: Rolf Färe
Publisher: Springer Science & Business Media
ISBN: 9401106517
Category : Business & Economics
Languages : en
Pages : 178
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Book Description
Our original reason for writing this book was the desire to write down in one place a complete summary of the major results in du ality theory pioneered by Ronald W. Shephard in three of his books, Cost and Production Functions (1953), Theory of Cost and Produc tion Functions (1970), and Indirect Production Functions (1974). In this way, newcomers to the field would have easy access to these important ideas. In adg,ition, we report a few new results of our own. In particular, we show the duality relationship between the profit function and the eight equivalent representations of technol ogy that were elucidated by Shephard. However, in planning the book and discussing it with colleagues it became evident that such a book would be more useful if it also provided a number of applications of Shephard's duality theory to economic problems. Thus, we have also attempted to present exam ples of the use of duality theory in areas such as efficiency measure ment, index number theory, shadow pricing, cost-benefit analysis, and econometric estimation. Much of our thinking about duality theory and its uses has been influenced by our present and former collaborators. They include Charles Blackorby, Shawna Grosskopf, Knox Lovell, Robert Russell, and, not surprisingly, Ronald W. Shephard. We have also benefit ted over the years from many discussions with W. Erwin Diewert.
Author: Michael Makkai
Publisher: American Mathematical Soc.
ISBN: 0821825658
Category : Mathematics
Languages : en
Pages : 122
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Book Description
We develop a duality theory for small Boolean pretoposes in which the dual of the [italic capital]T is the groupoid of models of a Boolean pretopos [italic capital]T equipped with additional structure derived from ultraproducts. The duality theorem states that any small Boolean pretopos is canonically equivalent to its double dual. We use a strong version of the duality theorem to prove the so-called descent theorem for Boolean pretoposes which says that category of descent data derived from a conservative pretopos morphism between Boolean pretoposes is canonically equivalent to the domain-pretopos. The descent theorem contains the Beth definability theorem for classical first order logic. Moreover, it gives, via the standard translation from the language of categories to symbolic logic, a new definability theorem for classical first order logic concerning set-valued functors on models, expressible in purely syntactical (arithmetical) terms.
