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Record Nr. |
UNINA9910480532703321 |
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Titolo |
Tropical and idempotent mathematics and applications : International Workshop on Tropical and Idempotent Mathematics, August 26-31, 2012, Independent University, Moscow, Russia / / G. L. Litvinov, S. N. Sergeev, editors |
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Pubbl/distr/stampa |
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Providence, Rhode Island : , : American Mathematical Society, , 2014 |
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©2014 |
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ISBN |
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Descrizione fisica |
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1 online resource (300 p.) |
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Collana |
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Contemporary Mathematics, , 1098-3627 ; ; 616 |
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Disciplina |
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Soggetti |
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Tropical geometry |
Geometry, Algebraic |
Idempotents |
Electronic books. |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references at the end of each chapters. |
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Nota di contenuto |
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""Preface""; ""In Memory of Grigory Litvinov""; ""Tropical Cramer determinants revisited""; ""1. Introduction""; ""2. Semirings with a symmetry and a modulus""; ""3. Combinatorial properties of semirings""; ""4. Elimination in semirings and Cramer theorem""; ""5. Existence of solutions of tropical linear systems""; ""6. Homogeneous systems: the generalized Gondran-Minoux theorem""; ""7. Systems of balances and intersections of signed hyperplanes""; ""8. Computing all Cramer Permanents: tropical Jacobi versus transportation approach""; ""9. Computing determinants""; ""Acknowledgment"" |
""References""""An approximation of Hopf-Lax type formula via idempotent analysis""; ""1. Introduction""; ""2. Basic notions of idempotent analysis""; ""3. Approximation formulas to solutions of Hamilton-Jacobi equations""; ""References""; ""Ideals of MV-semirings and MV-algebras""; ""1. Introduction""; ""2. Preliminaries""; ""3. Ideals, congruences and quotients""; ""4. The frame of radical ideals of an MV-semiring""; ""5. The frame of radical ideals of an MV-algebra""; ""6. The frames of open sets of \Spec( ) and of \Spec( )""; ""7. The frame of |
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open sets of \Max( )""; ""References"" |
""2. Optimal solution""""3. Approximate solution""; ""4. Conclusions""; ""References""; ""Algebraic structures of tropical mathematics""; ""1. Introduction""; ""2. Algebraic background""; ""3. The layered structure""; ""4. Matrices and linear algebra""; ""5. Identities of semirings, especially matrices""; ""References""; ""Parametric dequantization, tropical reduction of hyperfields and steady states of AC electrical networks""; ""1. Introduction""; ""2. Real tropical polynomials over a semifield""; ""3. Parametric limits of polynomials with various conditions on their coefficients"" |
""4. Complex tropical polynomials over hyperfield and tropical reduction""""5. The power balance equations in AC network""; ""6. Tropical reduction of the power balance equations, Foster coefficients and minimal spanning trees""; ""7. Concluding remarks""; ""References""; ""A constrained tropical optimization problem: Complete solution and application example""; ""1. Introduction""; ""2. Preliminary definitions and results""; ""3. Linear inequalities""; ""4. An optimization problem""; ""5. Applications to optimal scheduling""; ""Acknowledgments""; ""References"" |
""On the mathematical foundations of classical thermodynamics"" |
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