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

• 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
• Classificazione: 15A8016Y6005C2014T0552A3035F2190C4865H2092C4282B30
• 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.: 9910788257003321
• Lo trovi qui: Univ. Federico II
• Serie: Contemporary mathematics, ; 616 . 0271-4132