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You searched IISERK - Title: Atkins' molecules / Peter Atkins.
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Call Number
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515.35
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Author
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Cârjă, Ovidiu.
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Title
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Viability, invariance and applications [electronic resource] / Ovidiu Cârjă, Mihai Necula, Ioan I. Vrabie.
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Publication
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Amsterdam ; Boston : Elsevier, 2007.
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Material Info.
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xii, 344 p. : ill. ; 25 cm.
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Series
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North-Holland mathematics studies, 0304-0208 ; 207
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Summary Note
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The book is an almost self-contained presentation of the most important concepts and results in viability and invariance. The viability of a set K with respect to a given function (or multi-function) F, defined on it, describes the property that, for each initial data in K, the differential equation (or inclusion) driven by that function or multi-function) to have at least one solution. The invariance of a set K with respect to a function (or multi-function) F, defined on a larger set D, is that property which says that each solution of the differential equation (or inclusion) driven by F and issuing in K remains in K, at least for a short time. The book includes the most important necessary and sufficient conditions for viability starting with Nagumos Viability Theorem for ordinary differential equations with continuous right-hand sides and continuing with the corresponding extensions either to differential inclusions or to semilinear or even fully nonlinear evolution equations, systems and inclusions. In the latter (i.e. multi-valued) cases, the results (based on two completely new tangency concepts), all due to the authors, are original and extend significantly, in several directions, their well-known classical counterparts. - New concepts for multi-functions as the classical tangent vectors for functions - Provides the very general and necessary conditions for viability in the case of differential inclusions, semilinear and fully nonlinear evolution inclusions - Clarifying examples, illustrations and numerous problems, completely and carefully solved - Illustrates the applications from theory into practice - Very clear and elegant style.
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Notes
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Includes bibliographical references (p. 325-333) and indexes.
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Notes
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Preface -- Chapter 1. Generalities -- Chapter 2. Specific preliminary results -- Ordinary differential equations and inclusions -- Chapter 3. Nagumo type viability theorems -- Chapter 4. Problems of invariance -- Chapter 5. Viability under Caratȟodory conditions -- Chapter 6. Viability for differential inclusions -- Chapter 7. Applications -- Part 2 Evolution equations and inclusions -- Chapter 8. Viability for single-valued semilinear evolutions -- Chapter 9. Viability for multi-valued semilinear evolutions -- Chapter 10. Viability for single-valued fully nonlinear evolutions -- Chapter 11. Viability for multi-valued fully nonlinear evolutions -- Chapter 12. Caratȟodory perturbations of m-dissipative operators -- Chapter 13. Applications -- Solutions to the proposed problems -- Bibliographical notes and comments -- Bibliography -- Name Index -- Subject Index -- Notation.
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Notes
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Electronic reproduction. Amsterdam : Elsevier Science & Technology, 2007.
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ISBN
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9780444527615
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ISBN
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0444527613
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Subject
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Differential equations.
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Subject
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Set theory.
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Subject
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Symmetry (Mathematics)
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Subject
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Electronic books.
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Added Entry
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Necula, Mihai.
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Added Entry
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Vrabie, I. I. (Ioan I.), 1951-
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Added Entry
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ScienceDirect (Online service)
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Date
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Year, Month, Day:01405141
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Link
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An electronic book accessible through the World Wide Web; click for information ScienceDirect
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