LEADER 01148nam--2200385---450- 001 990001731840203316 005 20050617164856.0 035 $a000173184 035 $aUSA01000173184 035 $a(ALEPH)000173184USA01 035 $a000173184 100 $a20040607d1974----km-y0itay0103----ba 101 0 $aeng 102 $aGB 105 $aa|||||||001yy 200 1 $aMarxist perspectives in the sociology of education$fMaurice Levitas 210 $aLondon [etc.]$cRoutledge & Kegan Paul$d1974 215 $aVIII, 208 p.$cill.$d21 cm 410 0$12001 454 1$12001 461 1$1001-------$12001 606 0 $aEducazione$xConcezione marxista 606 0 $aCultura$xConcezione marxista 606 0 $aSociologia$xConcezione marxista 676 $a371 700 1$aLEVITAS,$bMaurice$0562697 801 0$aIT$bsalbc$gISBD 912 $a990001731840203316 951 $aII.5. 2494(XV A 1)$b19753 L.M.$cXV A 959 $aBK 969 $aUMA 979 $aSIAV5$b10$c20040607$lUSA01$h1423 979 $aCOPAT1$b90$c20050617$lUSA01$h1648 996 $aMarxist perspectives in the sociology of education$9946939 997 $aUNISA LEADER 01117nam--2200361---450- 001 990003485830203316 005 20110119102800.0 035 $a000348583 035 $aUSA01000348583 035 $a(ALEPH)000348583USA01 035 $a000348583 100 $a20110119d1976----km-y0itay50------ba 101 $aspa 102 $aES 105 $a||||||||001yy 200 1 $a<> emancipacion de la mujer romana en el siglo I D.C.$fArcadio del Castillo 210 $aGranada$cUniversidad de Granada$d1976 215 $a303 p.$d21 cm 225 2 $aColeccion monografica Universidad de Granada$v42 410 0$12001$aColeccion monografica Universidad de Granada$v42 454 1$12001 461 1$1001-------$12001 606 0 $aDonne$xPosizione sociale$yRoma antica$7ba$8ita$2BNCF 676 $a937 700 1$aDEL CASTILLO,$bArcadio$0609236 801 0$aIT$bsalbc$gISBD 912 $a990003485830203316 951 $aHS 315$b549 DSA 959 $aBK 969 $aDSA 979 $aDSA$b90$c20110119$lUSA01$h1028 996 $aEmancipacion de la mujer romana en el siglo I D.C$91110767 997 $aUNISA LEADER 05590nam 2200529 450 001 996466414703316 005 20231110233030.0 010 $a3-030-72162-0 035 $a(CKB)4100000011984432 035 $a(MiAaPQ)EBC6682762 035 $a(Au-PeEL)EBL6682762 035 $a(OCoLC)1261380181 035 $a(PPN)269149260 035 $a(EXLCZ)994100000011984432 100 $a20220411d2021 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aLectures on optimal transport /$fLuigi Ambrosio, Elia Brue?, and Daniele Semola 210 1$aCham, Switzerland :$cSpringer,$d[2021] 210 4$d©2021 215 $a1 online resource (250 pages) 225 1 $aUnitext ;$vv.130 311 $a3-030-72161-2 320 $aIncludes bibliographical references. 327 $aIntro -- Preface -- Contents -- Lecture 1: Preliminary Notions and the Monge Problem -- 1 Notation and Preliminary Results -- 2 Monge's Formulation of the Optimal Transport Problem -- Lecture 2: The Kantorovich Problem -- 1 Kantorovich's Formulation of the Optimal Transport Problem -- 2 Transport Plans Versus Transport Maps -- 3 Advantages of Kantorovich's Formulation -- 4 Existence of Optimal Plans -- Lecture 3: The Kantorovich-Rubinstein Duality -- 1 Convex Analysis Tools -- 2 Proof of Duality via Fenchel-Rockafellar -- 3 The Theory of c-Duality -- 4 Proof of Duality and Dual Attainment for Bounded and Continuous Cost Functions -- Lecture 4: Necessary and Sufficient Optimality Conditions -- 1 Duality and Necessary/Sufficient Optimality Conditions for Lower Semicontinuous Costs -- 2 Remarks About Necessary and Sufficient Optimality Conditions -- 3 Remarks About c-Cyclical Monotonicity, c-Concavity and c-Transforms for Special Costs -- 4 Cost=distance2 -- 5 Cost=Distance -- 6 Convex Costs on the Real Line -- Lecture 5: Existence of Optimal Maps and Applications -- 1 Existence of Optimal Transport Maps -- 2 A Digression About Monge's Problem -- 3 Applications -- 4 Iterated Monotone Rearrangement -- Lecture 6: A Proof of the Isoperimetric Inequality and Stability in Optimal Transport -- 1 Isoperimetric Inequality -- 2 Stability of Optimal Plans and Maps -- Lecture 7: The Monge-Ampe?re Equation and Optimal Transport on Riemannian Manifolds -- 1 A General Change of Variables Formula -- 2 The Monge-Ampe?re Equation -- 3 Optimal Transport on Riemannian Manifolds -- Lecture 8: The Metric Side of Optimal Transport -- 1 The Distance W2 in P2(X) -- 2 Completeness of Square Integrable Probabilities -- 3 Characterization of Convergence in the Space of Square Integrable Probabilities. 327 $aLecture 9: Analysis on Metric Spaces and the Dynamic Formulation of Optimal Transport -- 1 Absolutely Continuous Curves and Their Metric Derivative -- 2 Geodesics and Action -- 3 Dynamic Reformulation of the Optimal Transport Problem -- Lecture 10: Wasserstein Geodesics, Nonbranching and Curvature -- 1 Lower Semicontinuity of the Action A2 -- 2 Compactness Criterion for Curves and Random Curves -- 3 Lifting of Geodesics from X to P2(X) -- Lecture 11: Gradient Flows: An Introduction -- 1 lambda-Convex Functions -- 2 Differentiability of Absolutely Continuous Curves -- 3 Gradient Flows -- Lecture 12: Gradient Flows: The Bre?zis-Komura Theorem -- 1 Maximal Monotone Operators -- 2 The Implicit Euler Scheme -- 3 Reduction to Initial Conditions with Finite Energy -- 4 Discrete EVI -- Lecture 13: Examples of Gradient Flows in PDEs -- 1 p-Laplace Equation, Heat Equation in Domains, Fokker-Planck Equation -- 2 The Heat Equation in Riemannian Manifolds -- 3 Dual Sobolev Space H-1 and Heat Flow in H-1 -- Lecture 14: Gradient Flows: The EDE and EDI Formulations -- 1 EDE, EDI Solutions and Upper Gradients -- 2 Existence of EDE, EDI Solutions -- 3 Proof of Theorem 14.7 via Variational Interpolation -- Lecture 15: Semicontinuity and Convexity of Energies in the Wasserstein Space -- 1 Semicontinuity of Internal Energies -- 2 Convexity of Internal Energies -- 3 Potential Energy Functional -- 4 Interaction Energy -- 5 Functional Inequalities via Optimal Transport -- Lecture 16: The Continuity Equation and the Hopf-Lax Semigroup -- 1 Continuity Equation and Transport Equation -- 2 Continuity Equation of Geodesics in the Wasserstein Space -- 3 Hopf-Lax Semigroup -- Lecture 17: The Benamou-Brenier Formula -- 1 Benamou-Brenier Formula -- 2 Correspondence Between Absolutely Continuous Curves in the Probabilities and Solutions to the Continuity Equation. 327 $aLecture 18: An Introduction to Otto's Calculus -- 1 Otto's Calculus -- 2 Formal Interpretation of Some Evolution Equations as Wasserstein Gradient Flows -- 3 Rigorous Interpretation of the Heat Equation as a Wasserstein Gradient Flow -- 4 More Recent Ideas and Developments -- Lecture 19: Heat Flow, Optimal Transport and Ricci Curvature -- 1 Heat Flow on Riemannian Manifolds -- 2 Heat Flow, Optimal Transport and Ricci Curvature -- References. 410 0$aUnitext 606 $aMathematical optimization 606 $aOptimització matemàtica$2thub 608 $aLlibres electrònics$2thub 615 0$aMathematical optimization. 615 7$aOptimització matemàtica 676 $a519.6 700 $aAmbrosio$b Luigi$044009 702 $aBrue?$b Elia 702 $aSemola$b Daniele 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466414703316 996 $aLectures on Optimal Transport$92175022 997 $aUNISA LEADER 00963nam0 22002531i 450 001 UON00204767 005 20231205103308.242 100 $a20030730d1974 |0itac50 ba 101 $aita 102 $aIT 105 $a|||| ||||| 200 1 $a Mussolini$euna biografia$fLaura Fermi$gprefazione di Ugoberto Alfassio Grimaldi 210 $aMilano$cBompiani$d1974. VI$d476 p. ; 21 cm. 316 $aSMARRITO$5IT-UONSI III STORIAEURD B/0047 606 $aMUSSOLINI, BENITO$3UONC037882$2FI 620 $aIT$dMilano$3UONL000005 700 1$aFERMI$bLaura$3UONV122653$046745 712 $aBompiani$3UONV246238$4650 801 $aIT$bSOL$c20240220$gRICA 899 $aSIBA - SISTEMA BIBLIOTECARIO DI ATENEO$2UONSI 912 $aUON00204767 950 $aSIBA - SISTEMA BIBLIOTECARIO DI ATENEO$dSI III STORIAEUR D B 0047 $eSI SS 2048 5 0047 SMARRITO 996 $aMussolini$9218100 997 $aUNIOR