04487nam 2200601 450 991081289010332120220819054651.01-4704-1684-0(CKB)3150000000020198(EBL)3114303(SSID)ssj0001234692(PQKBManifestationID)11790790(PQKBTitleCode)TC0001234692(PQKBWorkID)11222458(PQKB)10838523(MiAaPQ)EBC3114303(RPAM)17921355(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 ;6160271-4132Description 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,6160271-4132Tropical geometryCongressesGeometry, AlgebraicCongressesIdempotentsCongressesTropical geometryGeometry, AlgebraicIdempotents516.3/515A8016Y6005C2014T0552A3035F2190C4865H2092C4282B30mscLitvinov G. L(Grigoriĭ Lazarevich),1944-Sergeev S. N.1981-International Workshop on Tropical and Idempotent MathematicsMiAaPQMiAaPQMiAaPQBOOK9910812890103321Tropical and idempotent mathematics and applications4019931UNINA