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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| 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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| Pubblicazione: | Providence, Rhode Island : , : American Mathematical Society, , 2014 |
| ©2014 | |
| Descrizione fisica: | 1 online resource (300 p.) |
| Disciplina: | 516.3/5 |
| Soggetto topico: | Tropical geometry |
| Geometry, Algebraic | |
| Idempotents | |
| Soggetto genere / forma: | Electronic books. |
| Persona (resp. second.): | LitvinovG. L <1944-> (Grigoriĭ Lazarevich) |
| SergeevS. N. <1981-> | |
| Note generali: | Description based upon print version of record. |
| Nota di bibliografia: | Includes bibliographical references at the end of each chapters. |
| Nota di contenuto: | ""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 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"" | |
| Titolo autorizzato: | Tropical and idempotent mathematics and applications |
| ISBN: | 1-4704-1684-0 |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9910480532703321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |
Serie:
Contemporary mathematics (American Mathematical Society) ; ; 616.