From e37aec65e2bcbd80c4e541c8a85446befd29ba6e Mon Sep 17 00:00:00 2001 From: =?utf8?q?J=C3=A9r=C3=B4me=20Benoit?= Date: Tue, 9 Oct 2018 12:05:14 +0200 Subject: [PATCH] initial import of the latex document. MIME-Version: 1.0 Content-Type: text/plain; charset=utf8 Content-Transfer-Encoding: 8bit Signed-off-by: Jérôme Benoit --- .gitignore | 9 + CE.PNG | Bin 0 -> 59939 bytes ProjetOptimRO.tex | 400 +++++++++++++++++++++++++++++++++++++++++++++ amu.jpg | Bin 0 -> 271670 bytes index2.png | Bin 0 -> 4086 bytes stdlib_sbphilo.bib | 281 +++++++++++++++++++++++++++++++ 6 files changed, 690 insertions(+) create mode 100644 .gitignore create mode 100644 CE.PNG create mode 100644 ProjetOptimRO.tex create mode 100644 amu.jpg create mode 100644 index2.png create mode 100644 stdlib_sbphilo.bib diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..f6af9d9 --- /dev/null +++ b/.gitignore @@ -0,0 +1,9 @@ +*.aux +*.bbl +*.blg +*.fdb_latexmk +*.fls +*.log +*.pdf +*.synctex.gz +*.toc \ No newline at end of file diff --git a/CE.PNG b/CE.PNG new file mode 100644 index 0000000000000000000000000000000000000000..a67b857c56111af91537a8e0347f04fe99c088a8 GIT binary patch literal 59939 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+\documentclass[12pt,oneside,a4paper]{book} + + +%%%%%Packages + +\usepackage{latexsym} +\usepackage{amssymb} +\usepackage[utf8]{inputenc} +\usepackage[francais]{babel} +\usepackage{color} +\usepackage{geometry} +\usepackage{graphicx} +\usepackage{amsfonts} +\usepackage[T1]{fontenc} +\usepackage{multirow} +\usepackage{fancyhdr} +\usepackage{tocbibind} +\usepackage{lmodern} + + +%%%%%Marges & en-t\^etes + +\geometry{hmargin=2.3cm, vmargin=3cm} +\fancyhf{} % supprime les en-t\^etes et pieds pr\'ed\'efinis +\fancyhead[FC]{\bfseries\thepage} % N∞page centre bas +\fancyhead[HC]{\footnotesize\leftmark} % chapitre centre haut +\renewcommand{\headrulewidth}{0.2pt} % filet en haut +\addtolength{\headheight}{0.5pt} % espace pour le filet +\renewcommand{\footrulewidth}{0.2pt} %filet en bas + + +%%%%%Th\'eor\`eme et d\'efinitions + +\newtheorem{Def}{D\'efinition} +\newtheorem{Not}[Def]{Notation} +\newtheorem{Th}{Th\'eor\`eme} +\newtheorem{Prop}[Th]{Proposition} +\newtheorem{Cor}[Th]{Corollaire} +\newtheorem{Rmq}{Remarque} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{document} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%Page de garde + +\begin{center} + + %\includegraphics[scale=0.5]{logo_sciences_rvb.png}\\ + \includegraphics[scale=0.5]{index2.png}\\ + + \vspace*{0.5cm} + + \footnotesize{ + \large \bf D\'epartement d'Informatique, Réseaux et Multimédia\\ + \large \bf 5ème année\\ + } + + \vspace*{0.5cm} + + %\large{Master 2 Professionnel\\ + %Math\'ematiques et Informatique des Nouvelles Technologies\\} + + \large{Projet \\ en \\ Optimisation et Recherche Opérationnelle \\} + + \vspace*{0.7cm} + + \begin{tabular}{c} + \hline + ~\\ + \huge\textbf { Titre du Projet} \\ + \huge\textbf {en}\\ + \huge\textbf {} \\ + ~\\ + \hline + \end{tabular} + + \vspace*{0.7cm} + + \includegraphics[scale=0.4]{CE.PNG}\\ + + \vspace*{0.5cm} + + \large par\\ + + %\large \bsc{}\\ + %\normalsize{M\'emoire encadr\'e par :} \large St\'ephane \bsc{Ballet}\\ + + \vspace*{0.2cm} + \large {\bf Prénom \bsc{Nom}}\\ + + %\vspace*{0.1cm} + + % \large sous la direction de \\ + + %\vspace*{0.1cm} + + %Eric Audureau et Thierry Masson + + %\vspace*{1cm} + + \vspace*{1cm} + + %\normalsize{Licence de Mathématiques 3ème année} + \normalsize{Année 2018-2019} + +\end{center} + +\thispagestyle{empty} + +\newpage + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +\pagestyle{plain} +\frontmatter + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + + +%%%%%Table des mati\`eres + +\tableofcontents + +\begin{figure}[!b] + \begin{center} + %\includegraphics{logo_fac2} + \includegraphics[scale=0.04]{amu} + \end{center} +\end{figure} + +\newpage + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +\mainmatter +\pagestyle{fancy} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\chapter{Introduction générale} + +%I – INTRODUCTION GENERALE + +\vspace{.5em} + +\section{Qu'est-ce que la recherche opérationnelle?} + +\section{Qu'est-ce que l'optimisation?} + +Dans cette section nous prenons appui sur l'ouvrage {\it Optimisation et contrôle des systèmes linéaires} \cite{Berg} de Maïtine Bergounioux \footnote{Maïtine Bergounioux, {\it Optimisation et contrôle des systèmes linéaires}, Dunod, 2001.}. +Nous utiliserons aussi l'ouvrage de Francis Filbet\footnote{Francis Filbet, {\it Analyse numérique - Algorithme et étude mathématique}, Dunod, 2009.}, {\it Analyse numérique - Algorithme et étude mathématique} \cite{Filb}. + + +%{\it La relativité}, Que sais-je?, 4ème édition, puf, 2000, \cite{Mavr}; +%ainsi que Jean Hladik, {\it La relativité selon Einstein}, L'esprit des sciences, Ellipses, 2000, \cite{Hlad}. + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\chapter{Sujets d'étude en travaux dirigés} + +\section{Cahier des charges} + +Il s'agit de travailler en binôme ou bien seul sur des sujets complémentaires et d'approfondissement du cours. Le travail en question effectué durant les TDs consistera +à effectuer un dossier sur un thème. Le dossier devra être tapé en Latex ou Tex puisque il peut y avoir des formules de mathématiques ou de physiques. Il pourra aussi comporter une partie "implémentation effective" d'algorithmes (en annexe). + +\vspace{.5em} + +Sur la fond, toutes les sources de connaissance utilisées devront être citées. En particulier, la méthodologie universitaire sera privilégiée +(citations en note de bas de page et dans le corps du document, liste des références en fin de document dans la bibliographie, etc...). +Wikipédia pourra être utilisé mais cela devra être mentionné en tant que référence (note de bas de page ou citation dans le corps du document). +L'accent sera essentiellement mis sur la démarche scientifique utilisée à égal niveau avec le contenu acquis des connaissances. + +\vspace{.5em} + +Plusieurs sources devront être croisées afin de prétendre au maximum de vraisemblance +et d'objectivité scientifique. Le document ne devra pas excéder 10 pages. +On privilégiera les qualités de synthèse, d'organisation ainsi que du contenu du document. + +\section{Proposition de sujets} + +\subsection{Analyse numérique} + +\vspace{.5em} + +1) Méthode des moindres Carrés (cas général, cas pondéré, cas des équations non linéaires). + +\vspace{.5em} + +2) Méthode de Newton-Raphson (cas d'une variable, cas de deux variables) - Application: extrema d'une fonction à deux variables. + +\vspace{.5em} + +3) Autres méthodes: méthode de Jacobi, de Gauss-Seidel, etc.... + +\vspace{.5em} + + +\subsection{Optimisation} + +\vspace{.5em} + +\subsubsection{Optimisation sans contrainte} + +{\bf A- Algorithmes déterministes} + +\vspace{.5em} + +1) Régression linéaire sans contrainte (pré-requis: Méthode des moindres carrés). + +\vspace{.5em} + +2) Méthodes de descente: la méthode du gradient (à pas constant ou à pas variable ou à pas optimal). + +\vspace{.5em} + +3) Méthode de Newton (ou méthode dite de la tangente) et application à la recherche d'extrema. + +\vspace{.5em} + +4) Méthodes de descente: méthode du gradient conjugué (cas linéaire et cas général) + +\vspace{.5em} + +5) Méthode de relaxation + +\vspace{.5em} + +{\bf B- Algorithmes probabilistes ou dit stochastiques} + +\vspace{.5em} + +1) Dynamique de métropolis (prérequis: chaines de Markov) + +\vspace{.5em} + +2) Recuit simulé sur un ensemble fini et application au problème du voyageur de commerce (prérequis: dynamique de métropolis) + +\vspace{.5em} + +\subsubsection{Optimisation ou minimisation avec contraintes} + +\vspace{.5em} + +1) Régression linéaire avec contraintes (prérequis: méthode des moindres carrés, conditions ou équations dites de Karush-kuhn-Tucker (KKT)) . + +\vspace{.5em} + +2) Cas de la programmation linéaire (prérequis: Lagrangien et multiplicateurs de Lagrange, conditions de KKT). + +\vspace{.5em} + +3) Algorithmes: méthode du gradient projeté, méthode de Lagrange-Newton pour des contraintes en égalité, +méthode de Newton projetée pour des contraintes de bornes, méthodes de pénalisation, +méthodes de programmation quadratique successive (SQP Sequential Quadratic Programming), +méthode de dualité (méthode d'Uzawa, prérequis: théorie de la dualité convexe) etc... + +\vspace{.5em} + + +\subsection{Recherche opérationnelle} + +\vspace{.5em} + +\subsubsection{La programmation linéaire (cas particulier de l'optimisation avec contraintes)} + +1) Méthode d'énumération. + +\vspace{.5em} + +2) Méthode du simplexe. + +\vspace{.5em} + +3) Application à des problèmes de R.O: + +\vspace{.5em} + +\hspace{.3em} 3.1) Fêtes de Pâques: A l'approche des fêtes de Pâques, un artisan chocolatier décide de confectionner des oeufs en chocolats. En allant inspecter ses réserves, il constate qu'il lui reste 18 kg de cacao, 8 kg de noisettes et 14 litres de lait. Ce chocolatier a deux spécialités: l'oeuf {\it extra} et l'oeuf {\it sublime}. Un oeuf {\it extra} nécessite 1kg de cacao, 1 kg de noisettes et 2 litres de lait tandis qu'un oeuf {\it sublime} nécessite 3 kg de cacao, 1 kg de noisettes et 1 litre de lait. Il fera un bénéfice de 20 euros en vendant un oeuf {\it extra}, et de 30 euros en vendant un oeuf {\it sublime}. + +\vspace{.5em} + +\hspace{.6em} a) \'Ecrire ce problème sous la forme d'un problème de programmation linéaire. + +\vspace{.5em} + +\hspace{.6em} b) Combien d'oeufs extra et sublime doit-il fabriquer pour faire le plus grand bénéfice? + +\vspace{.5em} + +\hspace{.3em} 3.2) Organisation du travail: La fabrication d'une pièce $P_1$ a un prix de revient de 150 euros et celle d'une pièce $P_2$ coûte 100 euros. Chaque pièce est traitée successivement dans trois ateliers. Le nombre d'heures-machines par pièce est indiqué dans le tableau suivant : + +\vspace{.5em} + +\begin{center} +$ +\begin{array}{|c|c|c|c|} +\hline + Atelier & A & B & C\\ + \hline + Pièce 1 & 3 h & 5 h & 2 h\\ + \hline + Pièce 2 & 1 h & 3 h & 3 h\\ + \hline + \end{array} +$ +\end{center} + +\vspace{.5em} + +Pour éviter le chômage technique, l'atelier A doit obligatoirement fournir 1200 heures machines, l'atelier B doit obligatoirement fournir 3000 heures machines et l'atelier C doit obligatoirement fournir 1800 heures machines. + +\hspace{.6em} a) \'Ecrire ce problème sous la forme d'un problème de programmation linéaire. + +\vspace{.5em} + +\hspace{.6em} b) Combien faut-il fabriquer de pièces $P_1$ et $P_2$ pour minimiser le coût de revient de l'ensemble de la production et pour assurer le fonctionnement des trois ateliers excluant tout chômage technique? + +\vspace{.5em} + + +\bibliographystyle{plain} +\bibliography{stdlib_sbphilo} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\end{document} + + +\begin{thebibliography}{6}\input{MemoireM2Ballet6.synctex.gz(busy)} + + + %\bibitem[1]{BL} Jean-Pierre \bsc{Bourguignon} et David \bsc{Langlois}, Cours de M1, Module Relativité Générale, + %Ecole Polytechnique, ParisTech, 2011.\\ + + %\bibitem[2]{G} Gilles \bsc{Cohen-Tannoudji}, Einstein et la refondation relativiste de la physique, 2005.\\ + + %\bibitem[3]{D} Pierre \bsc{Duhem}, La théorie physique, son objet, sa structure, Vrin, 2007.\\ + + %\bibitem[4]{E1} Albert \bsc{Einstein}, Die formale grundlage der allgemeinen Relativittstheorie. Kniglich Preussische + %Akademie der Wissenschaften (Berlin),Sitzungsberichte: pp 1030-1085. \\ + + %\bibitem[5]{G} Christian \bsc{Godin}, Dictionnaire de philosophie, Fayard Edition du temps, 2004.\\ + + %\bibitem[6]{H} Jean \bsc{Hladik}, La Relativité selon Einstein, L'Esprit des Sciences, Ellipses.\\ + + %\bibitem[7]{IS} \bsc{Iftime} and \bsc{Stachel}, The hole argument for covariant theories, arKiv:gr-qc/0512021v2, 8 avril 2006.\\ + + %\bibitem[8]{K} \bsc{Kant}, Critique de la raison pure, Traduction, présentation, notes par Alain Renaut, GF-Flammarion, 2006.\\ + + %\bibitem[9]{K2} \bsc{Kant}, Prolégomènes à toute métaphysique future, Traduction de Louis Guilermit, Vrin, 1986.\\ + + %\bibitem[10]{KU} Thomas \bsc{Kuhn}, La structure des révolutions scientifiques, Flammarion Champs Sciences, 2008. + + %\bibitem[11]{L} Marc \bsc{Lachièze-Rey}, Initiation à la cosmologie, 3ème édition, Dunod, 2000.\\ + + %\bibitem[12]{Mas} Thierry \bsc{Masson}, Cours de géométrie différentielle, groupe et algèbre de Lie, fibrés et connexions, 2010.\\ + + %\bibitem[13]{Poi} Henri \bsc{Poincaré}, La Science et L'Hypothèse, Flammarion, Paris, 1968.\\ + + %\bibitem[14]{Mav} Stamatia \bsc{Mavridès}, La Relativité, Que sais-je, 4ème édition, PUF, 2000.\\ + + %\bibitem[15]{R} Robert \bsc{Rynasiewicz}, The Lessons of the Hole Argument, The British Journal of the Philosophy of Science, + %vol; 45 (2), 407-436, Oxford University Press, Oxford Journals, 1994. \\ + + %\bibitem[16]{S} Standford Encyclopedia of Philosophy.\\ + + %\bibitem[17]{W} Wikipedia.\\ + + %\bibitem[1]{Bachtold} {\bf Manuel Bächtold}, L'interprétation de la mécanique quantique, une approche pragmatique, Collection vision des sciences, Hermann, 2008 .\\ + %\bibitem[2]{Aspect} {\bf Alain Aspect}, Présentation naïve des inégalités de Bell, 2004.\\ + \bibitem[3]{Basda} {\bf Jean-Louis Basdevant et Manuel Joffre}, Mécanique Quantique, Les éditions de l'Ecole Polytechnique, 2006.\\ + %\bibitem[4]{Diu} {\bf Bernard Diu}, Le congrès de Solvay de 1927: petite chronique d'un grand évènement, Bibnum.\\ + + + + %\bibitem[1]{B} \bsc{Aristote}, Métaphysique, traduction J.Tricot, Vrin, 1974.\\ + + +\end{thebibliography} + + + diff --git a/amu.jpg b/amu.jpg new file mode 100644 index 0000000000000000000000000000000000000000..95af6a405bae40fc79e656ad947e223f74748fd9 GIT binary patch literal 271670 zcmeFa3EbRNxj$aTi!9d#mHi@RRY==RCd*_>TbzB#WG0hYG6@JbGf8H$OeV=>mZYHf z{sr}3LA?m&3Q~Xk6tE(T>}9o3W97R$iDs0%)D*iPK)?bFTWN$e3<6V zob%+I=lPyzJ4@dD)tgVvTfnqBZl~MoSo6_Efq7&!L+|j^ywT^Q^HzZG_ksUr{(bYo zpI9x|wHCv$*y5B<;E~IASu$KaY+G&F73UAzhS^;_TzcS`_+oH9x(y#V ze_X`XmmU}yJ#~JKX6DB_jyxY*6kHTs*a#5ld>mbb;z$U^7t9X^0wf#=!NK4{gj|du zi;>{`na_dCb^%vQ97$Qs#*;G-1b;0(aHeO2!C=tVM-N*6neXtZqG)Ko|Kx!mvuzO51n=Y z?f3<7v7TX@h1}+t3@W8EZP1~=gw-ajwwoLC8q`}%1Gq_|E5=1vUKR`>!G!^Up->qK zE=KUhXb1`*ivxir@Frzv31a+PM^Y7U6Dk0SfC?$h5ZF*?s(Q?kK?63azL`eMD!Dlt z9jDys7|SN3CSw@AuIq?y$C)21VUtFT3Ct9mqEK%2+I3S@jqW=6OMC+5}mGG 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diff --git a/stdlib_sbphilo.bib b/stdlib_sbphilo.bib new file mode 100644 index 0000000..facedae --- /dev/null +++ b/stdlib_sbphilo.bib @@ -0,0 +1,281 @@ + +%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Bibliographie philosophique +%%%%%%%%%%%%%%%%%%%%%%%%%%% + +@ARTICLE{Aspe, +author="Alain Aspect", +title="Présentation naïve des inégalités de Bell", +journal="", +volume=" ", +number="", +pages="", +publisher="", +year="2004", +} + +@BOOK{Bach, +author="Manuel Bächtold", +title="L'interprétation de la mécanique quantique, une approche pragmatique", +volume="Collection vision des sciences", +publisher="Hermann", +year="2008", +} + +@BOOK{Berg, +author="Maïtine Bergounioux", +title="Optimisation et contrôle des systèmes linéaires", +volume="", +publisher="Dunod", +year="2001", +} + + + +@ARTICLE{Bohr, +author="Niels Bohr", +title="Le principe de complémentarité", +journal="Nature", +volume=" ", +number="121", +pages="580-591", +publisher="", +year="1928", +} + + +@ARTICLE{Diu, +author="Bernard Diu", +title="Le congrès de Solvay de 1927: petite chronique d'un grand évènement", +journal="Bibnum", +volume=" ", +number="", +pages="", +publisher="", +year="", +} + +@BOOK{Duhe, +author="Pierre Duhem", +title="La théorie physique, son objet, sa structure", +volume="", +publisher="Vrin", +year="2007", +} + + + +@BOOK{Eins1, +author="Albert Einstein", +title="Sur l’\'electrodynamique des corps en mouvement", +volume="Les Grands Classiques Gauthier-Villards", +publisher="Editions Jacques Gabay", +year="1925", +} + +@BOOK{Eins2, +author="Albert Einstein", +title="L’\'ether et la th\'eorie de la relativit\'e", +volume="Les Grands Classiques Gauthier-Villards", +publisher="Editions Jacques Gabay", +year="1925", +} + +@BOOK{Eins3, +author="Albert Einstein", +title="La G\'eom\'etrie et l’Exp\'erience", +volume="Les Grands Classiques Gauthier-Villards", +publisher="Editions Jacques Gabay", +year="1925", +} + +@BOOK{Eins4, +author="Albert Einstein", +title="La Relativit\'e ", +volume="", +publisher="Petite Bibliothèque Payot", +year="1963", +} + +@BOOK{EinsOC2, +author="Albert Einstein", +title="Oeuvres choisies, Relativités I: Relativités restreinte et générale", +volume="2", +publisher="Sources du savoir, Seuil CNRS ", +year="1993", +} + +@BOOK{EinsOC3, +author="Albert Einstein", +title="Oeuvres choisies, Relativités II: Relativités restreinte et générale", +volume="3", +publisher="Sources du savoir, Seuil CNRS ", +year="1993", +} + +@BOOK{Filb, +author="Francis Filbet", +title="Analyse numérique - Algorithme et étude mathématiques", +volume="", +publisher="Dunod", +year="2009", +} + + + + +@BOOK{Godi, +author="Christian Godin", +title="Dictionnaire de philosophie", +volume="", +publisher="Fayard Edition du temps", +year="2004", +} + + +@BOOK{Hlad, +author="Jean Hladik", +title="La relativité selon Einstein", +volume="L'esprit des sciences", +publisher="Hermann", +year="Ellipses", +} + +@ARTICLE{IfSt, +author=" Mihaela Iftime and John Stachel", +title="The hole argument for covariant theories", +journal="General Relativity and Gravitation", +volume=" ", +number="38", +pages="1241-1252", +publisher="", +year="2006", +} + +@BOOK{Kant1, +author=" Emmanuel Kant", +title="Critique de la raison pure", +volume="Traduction, présentation, notes par Alain Renaut", +publisher="GF-Flammarion", +year="2006", +} + +@BOOK{Kant2, +author=" Emmanuel Kant", +title="Prolégomènes à toute métaphysique future", +volume="Traduction de Louis Guillermit", +publisher="Vrin", +year="1986", +} + +@BOOK{Kuhn, +author=" Thomas Kuhn", +title="La structure des révolutions scientifiques", +volume=" ", +publisher="Flammarion", +year="2008 (1ère édition 1962)", +} + + +@BOOK{Lach, +author=" Marc Lachièze-Rey", +title=" Initiation à la cosmologie", +volume="", +publisher="Dunod", +year="3ème édition, 2000", +} + +@BOOK{Leco, +author=" Dominique Lecourt", +title="La philosophie des sciences", +volume="", +publisher="PUF", +year="2ème édition, 2000", +} + + +@BOOK{Mass, +author=" Thierry Masson", +title="Cours de géométrie différentielle, groupe et algèbre de Lie, fibrés et connexions", +volume="", +publisher="", +year="2010", +} + + +@BOOK{Mavr, +author="Stamatia Mavridès", +title="La Relativit\'e ", +volume="", +publisher="Que sais-je, 4ème édition, PUF", +year="2000", +} + +@BOOK{Newt, +author="Isaac Newton", +title="Principes mathématiques de la philosophie naturelle (Philosophiae naturalis principia mathematica)", +volume="", +publisher="document numérisé par Jean-Marc Simonet, Les classiques des sciences sociales, Bibliothèque Paul-Emile Boulet de l'Université du Québec", +year="2010", +} + +@BOOK{Niet, +author="Friedrich Nietzsche", +title="La naissance de la tragédie", +volume="tr. de l'allemand par Hans Hildenbrand et Laurent Valette, Présentaion, notes et lexique de Pierre Héber-Suffrin.", +publisher="Christian Bourgois éditeur", +year="1991", +} + + +@BOOK{Nor1, +author=" John Norton", +title="Standford Encyclopedia of Philosophy", +volume="", +publisher="Copyright", +year="1999, 20004", +} + +@BOOK{PascEG, +author="Blaise Pascal", +title="De l'esprit géométrique", +volume="", +publisher="GF-Flammarion", +year="1985", +} + + + +@BOOK{Poin, +author="Henri Poincaré", +title="La science et l'hypothèse", +volume="", +publisher="Flammarion", +year="1968", +} + + +@ARTICLE{Ryna, +author="Robert Rynasiewicz", +title="The Lessons of the Hole Argument", +journal="The British Journal of the Philosophy of Science ", +volume="vol; 45 ", +number="2", +pages="407--436", +publisher="Oxford University Press, Oxford Journals", +year="Oxford University Press, Oxford Journals, 1994", +} + +@BOOK{Sain, +author="Saint Augustin", +title="Les Confessions", +volume="", +publisher="GF-Flammarion", +year="1964", +} + + + + + + -- 2.34.1