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Entropy2016,18, 386 95. DeSaxcĂ©,G.;VallĂ©e,C.Bargmanngroup,momentumtensorandGalilean invarianceofClausius-Duhem Inequality. Int. J.Eng. Sci. 2012,50, 216–232. [CrossRef] 96. DeSaxcĂ©,G. Entropyand structure for the thermodynamic systems. InGeometric Science of Information, Second International Conference GSI 2015 Proceedings; Nielsen, F., Barbaresco, F., Eds.; LectureNotes in ComputerScience;Springer: Berlin/Heidelberg,Germany,2015;Volume9389,pp.519–528. 97. Kapranov,M.Thermodynamicsandthemomentmap. 2011;arXiv:1108.3472v1. 98. Pavlov,V.P.;Sergeev,V.M.Thermodynamics fromthedifferentialgeometrystandpoint.Theor.Math. Phys. 2008,157, 1484–1490. [CrossRef] 99. Cartier,P.;DeWitt-Morette,C.Functional Integration. ActionandSymmetries;CambridgeUniversityPress: Cambridge,UK,2004. 100. Libermann,P.;Marle,C.M.SymplecticGeometryandAnalyticalMechanics; SpringerScience&BusinessMedia: Berlin/Heidelberg,Germany,1987. 101. Lichnerowicz,A.EspaceshomogĂšnesKĂ€hleriens. InColloquedeGĂ©omĂ©trieDiffĂ©rentielle;CNRSP:Paris,France, 1953;pp.171–184. (InFrench) 102. Lichnerowicz,A.ReprĂ©sentationCoadjointeQuotient etEspacesHomogĂšnesdeContact, coursduCollĂšgedeFrance; Springer: Berlin/Heidelberg,Germany,1986. (InFrench) 103. Balian, R.; Valentin, P.Hamiltonian structure of thermodynamicswith gauge. Eur. Phys. J. B 2001, 21, 269–282. [CrossRef] 104. Marle,C.M.OnHenriPoincaré’snote“SuruneformenouvelledesĂ©quationsde lamĂ©canique”. J.Geom. SymmetryPhys. 2013,29, 1–38. 105. PoincarĂ©,H. Sur une formenouvelle des Ă©quationsde laMĂ©canique. C.R.Acad. Sci. 1901, 7, 369–371. (InFrench) 106. Sternberg,S.Symplectichomogeneousspaces.Trans.Am.Math. Soc. 1975,212, 113–130. [CrossRef] 107. Bourguignon, J.P.CalculVariationnel;EcolePolytechnique: Paris,France,2007. (InFrench) 108. Dedecker,P.Apropertyofdifferential formsinthecalculusofvariations.Pac. J.Math. 1957,7, 1545–1549. [CrossRef] 109. Marle,C.M.Onmechanical systemswithaLiegroupasconïŹgurationspace. In JeanLeray ’99Conference Proceedings;DeGosson,M.,Ed.;Springer: Berlin/Heidelberg,Germany,2003;pp.183–203. 110. Marle,C.M.SymmetriesofHamiltoniansystemsonsymplecticandpoissonmanifolds. InSimilarity and SymmetryMethods; Springer: Berlin/Heidelberg,Germany,2014;pp.185–269. 111. Kirillov,A.A.Meritsanddemeritsof theorbitmethod.Bull. Am.Math. Soc. 1999,36, 433–488. [CrossRef] 112. Cartan, E. La structure des groupes de transformations continus et la thĂ©orie du triĂšdre mobile. Bull. Sci.Math.1910,34, 250–284. (InFrench) 113. Cartan,E.Leçons sur les Invariants IntĂ©graux;Hermann: Paris,France,1922. (InFrench) 114. Cartan,E.LesrĂ©centesgĂ©nĂ©ralisationsde lanotiond’espace.Bull. Sci.Math. 1924,48, 294–320. (InFrench) 115. Cartan, E. Le rĂŽle de la ThĂ©orie des Groupes de Lie dans L’évolution de la GĂ©omĂ©trie Modern; C.R. CongrĂšs International:Oslo,Norway,1936;Volume1,pp.92–103. (InFrench) 116. Libermann, P. La gĂ©omĂ©trie diffĂ©rentielle d’Elie Cartan Ă  Charles Ehresmann et AndrĂ© Lichnerowicz. InGĂ©omĂ©trie auXXesiĂšcle, 1930-2000:Histoire etHorizons;Hermann: Paris,France,2005. (InFrench) 117. Koszul, J.L.Sur la formehermitiennecanoniquedesespaceshomogĂšnescomplexes.Can. J.Math. 1955,7, 562–576. (InFrench) [CrossRef] 118. Koszul, J.L.ExposĂ©s sur lesEspacesHomogĂšnesSymĂ©triques;PublicaçãodaSociedadedeMatematicadeSĂŁo Paulo: SĂŁoPaulo,Brazil, 1959. (InFrench) 119. Koszul, J.L. Domaines bornĂ©es homogĂšnes et orbites de groupes de transformations afïŹnes. Bull. Soc. Math.Fr. 1961,89, 515–533. (InFrench) 120. Koszul, J.L.Ouverts convexes homogĂšnes des espaces afïŹnes. Math. Z. 1962, 79, 254–259. (In French) [CrossRef] 121. Koszul, J.L.VariĂ©tĂ©s localementplatesetconvexitĂ©.Osaka J.Math. 1965,2, 285–290. (InFrench) 122. Koszul, J.L.LecturesonGroupsofTransformations;TataInstituteofFundamentalResearch: Bombay, India,1965. 123. Koszul, J.L.DĂ©formationsdesvariĂ©tĂ©s localementplates.Ann. Inst. Fourier1968,18, 103–114. (InFrench) [CrossRef] 124. Koszul, J.L.TrajectoiresconvexesdegroupesafïŹnesunimodulaires. InEssaysonTopologyandRelatedTopics; Springer: Berlin,Germany,1970;pp.105–110. 115
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Differential Geometrical Theory of Statistics
Titel
Differential Geometrical Theory of Statistics
Autoren
Frédéric Barbaresco
Frank Nielsen
Herausgeber
MDPI
Ort
Basel
Datum
2017
Sprache
englisch
Lizenz
CC BY-NC-ND 4.0
ISBN
978-3-03842-425-3
Abmessungen
17.0 x 24.4 cm
Seiten
476
Schlagwörter
Entropy, Coding Theory, Maximum entropy, Information geometry, Computational Information Geometry, Hessian Geometry, Divergence Geometry, Information topology, Cohomology, Shape Space, Statistical physics, Thermodynamics
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Differential Geometrical Theory of Statistics