04531nam 2200637 450 991048053270332120180731045123.01-4704-1684-0(CKB)3150000000020198(EBL)3114303(SSID)ssj0001234692(PQKBManifestationID)11790790(PQKBTitleCode)TC0001234692(PQKBWorkID)11222458(PQKB)10838523(MiAaPQ)EBC3114303(PPN)19710259X(EXLCZ)99315000000002019820150416h20142014 uy 0engur|n|---|||||txtccrTropical 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, editorsProvidence, Rhode Island :American Mathematical Society,2014.©20141 online resource (300 p.)Contemporary Mathematics,1098-3627 ;616Description based upon print version of record.0-8218-9496-X Includes bibliographical references at the end of each chapters.""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""Contemporary mathematics (American Mathematical Society) ;616.Tropical geometryCongressesGeometry, AlgebraicCongressesIdempotentsCongressesElectronic books.Tropical geometryGeometry, AlgebraicIdempotents516.3/5Litvinov G. L(Grigoriĭ Lazarevich),1944-Sergeev S. N.1981-International Workshop on Tropical and Idempotent MathematicsMiAaPQMiAaPQMiAaPQBOOK9910480532703321Tropical and idempotent mathematics and applications2018562UNINA