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[null,"1.","Record Nr.",null,"UNINA9910349323203321"]
[null,null,"Autore",null,"Zaslavski Alexander J"]
[null,null,"Titolo",null,"Turnpike Conditions in Infinite Dimensional Optimal Control  / / by Alexander J. Zaslavski"]
[null,null,"Pubbl/distr/stampa",null,"Cham : , : Springer International Publishing : , : Imprint : Springer, , 2019"]
[null,null,"ISBN",null,"3-030-20178-3"]
[null,null,"Edizione",null,"[1st ed. 2019.]"]
[null,null,"Descrizione fisica",null,"1 online resource (578 pages)"]
[null,null,"Collana",null,"Springer Optimization and Its Applications, , 1931-6828 ; ; 148"]
[null,null,"Disciplina",null,"629.8312"]
[null,null,"Soggetti",null,"Calculus of variations"]
[{"$nulls":4},"Differential equations, Partial"]
[{"$nulls":4},"Functional analysis"]
[{"$nulls":4},"Group theory"]
[{"$nulls":4},"Calculus of Variations and Optimal Control; Optimization"]
[{"$nulls":4},"Partial Differential Equations"]
[{"$nulls":4},"Functional Analysis"]
[{"$nulls":4},"Group Theory and Generalizations"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,"Nota di contenuto",null,"Preface -- 1. Introduction -- 2. Discrete-time autonomous problems -- 3. Discrete-time nonautonomous problems on half-axis -- 4. Discrete-time nonautonomous problems on axis -- 5. Continuous-time autonomous problems -- 6. Continuous-time nonautonomous problems on half-axis -- 7. Continuous-time nonautonomous problems on axis."]
[null,null,null,"Sommario/riassunto","This book provides a comprehensive study of turnpike phenomenon arising in optimal control theory. The focus is on individual (non-generic) turnpike results which are both mathematically significant and have numerous applications in engineering and economic theory. All results obtained in the book are new. New approaches, techniques, and methods are rigorously presented and utilize research from finite-dimensional variational problems and discrete-time optimal control problems to find the necessary conditions for the turnpike phenomenon in infinite dimensional spaces. The semigroup approach is employed in the discussion as well as PDE descriptions of continuous-time dynamics. The main results on sufficient and necessary conditions for the turnpike property are completely proved "]
[{"$nulls":4},"and the numerous illustrative examples support the material for the broad spectrum of experts. Mathematicians interested in the calculus of variations, optimal control and in applied functional analysis will find this book a useful guide to the turnpike phenomenon in infinite dimensional spaces. Experts in economic and engineering modeling as well as graduate students will also benefit from the developed techniques and obtained results."]
[null,"2.","Record Nr.",null,"UNINA9910960442103321"]
[null,null,"Autore",null,"Bredon Glen E"]
[null,null,"Titolo",null,"Sheaf Theory / / by Glen E. Bredon"]
[null,null,"Pubbl/distr/stampa",null,"New York, NY : , : Springer New York : , : Imprint : Springer, , 1997"]
[null,null,"ISBN",null,"1-4612-0647-2"]
[null,null,"Edizione",null,"[2nd ed. 1997.]"]
[null,null,"Descrizione fisica",null,"1 online resource (XI, 504 p.)"]
[null,null,"Collana",null,"Graduate Texts in Mathematics, , 2197-5612 ; ; 170"]
[null,null,"Disciplina",null,"512"]
[null,null,"Soggetti",null,"Algebra"]
[{"$nulls":4},"Algebraic topology"]
[{"$nulls":4},"Algebraic Topology"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","Bibliographic Level Mode of Issuance: Monograph"]
[null,null,null,"Nota di bibliografia","Includes bibliographical references and index."]
[null,null,"Nota di contenuto",null,"I Sheaves and Presheaves -- Definitions -- 2 Homomorphisms, subsheaves, and quotient sheaves -- 3 Direct and inverse images -- 4 Cohomomorphisms -- 5 Algebraic constructions -- 6 Supports -- 7 Classical cohomology theories -- Exercises -- II Sheaf Cohomology -- 1 Differential sheaves and resolutions -- 2 The canonical resolution and sheaf cohomology -- 3 Injective sheaves -- 4 Acyclic sheaves -- 5 Flabby sheaves -- 6 Connected sequences of functors -- 7 Axioms for cohomology and the cup product -- 8 Maps of spaces -- 9 ?-soft and ?-fine sheaves -- 10 Subspaces -- 11 The Vietoris mapping theorem and homotopy invariance -- 12 Relative cohomology -- 13 Mayer-Vietoris theorems -- 14 Continuity -- 15 The Künneth and universal coefficient theorems -- 16 Dimension -- 17 Local connectivity -- 18 Change of supports; local cohomology groups -- 19 The transfer homomorphism and the Smith sequences -- 20 Steenrod’s cyclic reduced powers -- 21 The Steenrod operations -- Exercises -- III Comparison with Other Cohomology Theories.-1 Singular cohomology -- 2 Alexander-Spanier cohomology -- 3 de Rham cohomology -- 4 ?ech cohomology -- Exercises -- IV Applications of Spectral Sequences -- 1 The spectral sequence of a differential sheaf -- 2 The fundamental theorems of sheaves -- 3 Direct image relative to a support family -- 4 The Leray sheaf -- 5 Extension of a support family by a family on the base space -- 6 The Leray spectral sequence of a map -- 7 Fiber bundles -- 8 Dimension -- 9 The spectral sequences of Borel and Cartan -- 10 Characteristic classes -- 11 The spectral sequence of a filtered differential sheaf -- 12 The Fary spectral sequence -- 13 "]
[{"$nulls":4},"Sphere bundles with singularities -- 14 The Oliver transfer and the Conner conjecture -- Exercises -- V Borel-Moore Homology -- 1 Cosheaves -- 2 The dual of a differential cosheaf -- 3 Homology theory -- 4 Maps of spaces -- 5 Subspaces and relative homology -- 6 The Vietoris theorem, homotopy, and covering spaces -- 7 The homology sheaf of a map -- 8 The basic spectral sequences -- 9 Poincaré duality -- 10 The cap product -- 11 Intersection theory -- 12 Uniqueness theorems -- 31 Uniqueness theorems for maps and relative homology -- 14 The Künneth formula -- 15 Change of rings -- 16 Generalized manifolds -- 17 Locally homogeneous spaces -- 18 Homological fibrations and p-adic transformation groups -- 19 The transfer homomorphism in homology -- 20 Smith theory in homology -- Exercises -- VI Cosheaves and ?ech Homology -- 1 Theory of cosheaves -- 2 Local triviality -- 3 Local isomorphisms -- 4 Cech homology -- 5 The reflector -- 6 Spectral sequences -- 7 Coresolutions -- 8 Relative ?ech homology -- 9 Locally paracompact spaces -- 10 Borel-Moore homology -- 11 Modified Borel-Moore homology -- 12 Singular homology -- 13 Acyclic coverings -- 14 Applications to maps -- Exercises -- A Spectral Sequences -- 1 The spectral sequence of a filtered complex -- 2 Double complexes -- 3 Products -- 4 Homomorphisms -- B Solutions to Selected Exercises -- Solutions for Chapter I -- Solutions for Chapter II -- Solutions for Chapter III -- Solutions for Chapter IV -- Solutions for Chapter V -- Solutions for Chapter VI -- List of Symbols -- List of Selected Facts."]
[null,null,null,"Sommario/riassunto","This book is primarily concerned with the study of cohomology theories of general topological spaces with \"general coefficient systems.\" Sheaves play several roles in this study. For example, they provide a suitable notion of \"general coefficient systems.\" Moreover, they furnish us with a common method of defining various cohomology theories and of comparison between different cohomology theories. The parts of the theory of sheaves covered here are those areas impor­tant to algebraic topology. Sheaf theory is also important in other fields of mathematics, notably algebraic geometry, but that is outside the scope of the present book. Thus a more descriptive title for this book might have been Algebraic Topology from the Point of View of Sheaf Theory. Several innovations will be found in this book. Notably, the con­cept of the \"tautness\" of a subspace (an adaptation of an analogous no­tion of Spanier to sheaf-theoretic cohomology) is introduced and exploited throughout the book. The factthat sheaf-theoretic cohomology satisfies 1 the homotopy property is proved for general topological spaces. Also, relative cohomology is introduced into sheaf theory. Concerning relative cohomology, it should be noted that sheaf-theoretic cohomology is usually considered as a \"single space\" theory."]