LEADER 04531nam 2200637 450 001 9910480532703321 005 20180731045123.0 010 $a1-4704-1684-0 035 $a(CKB)3150000000020198 035 $a(EBL)3114303 035 $a(SSID)ssj0001234692 035 $a(PQKBManifestationID)11790790 035 $a(PQKBTitleCode)TC0001234692 035 $a(PQKBWorkID)11222458 035 $a(PQKB)10838523 035 $a(MiAaPQ)EBC3114303 035 $a(PPN)19710259X 035 $a(EXLCZ)993150000000020198 100 $a20150416h20142014 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aTropical and idempotent mathematics and applications $eInternational Workshop on Tropical and Idempotent Mathematics, August 26-31, 2012, Independent University, Moscow, Russia /$fG. L. Litvinov, S. N. Sergeev, editors 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2014. 210 4$dİ2014 215 $a1 online resource (300 p.) 225 1 $aContemporary Mathematics,$x1098-3627 ;$v616 300 $aDescription based upon print version of record. 311 $a0-8218-9496-X 320 $aIncludes bibliographical references at the end of each chapters. 327 $a""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"" 327 $a""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"" 327 $a""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"" 327 $a""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"" 327 $a""On the mathematical foundations of classical thermodynamics"" 410 0$aContemporary mathematics (American Mathematical Society) ;$v616. 606 $aTropical geometry$vCongresses 606 $aGeometry, Algebraic$vCongresses 606 $aIdempotents$vCongresses 608 $aElectronic books. 615 0$aTropical geometry 615 0$aGeometry, Algebraic 615 0$aIdempotents 676 $a516.3/5 702 $aLitvinov$b G. L$g(Grigorii? Lazarevich),$f1944- 702 $aSergeev$b S. N.$f1981- 712 12$aInternational Workshop on Tropical and Idempotent Mathematics 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910480532703321 996 $aTropical and idempotent mathematics and applications$92018562 997 $aUNINA