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Charles Ehresmann Et Commentées
Charles Ehresmann œuvres complètes et commentées CATÉGORIES STRUCTURÉES ET QUOTIENTS PARTIE III - 1 commentée par Andrée CHARLES EHRESMANN AMIENS 1980 CHARLES EHRESMANN 19 Avril 1905 - 22 Septembre 1979 «... Le mathématicien est engagé dans la poursuite d'un rêve sans fin, mais la traduction de ce rêve en formules précises exige un effort extraordinaire. Chaque problème résolu pose de nouvelles questions de plus en plus nombreuses.Mais qui d'en• tre nous ne se surprend pas quelquefois à se poser la question dangereuse : a quoi bon tout cet effort? On a dit que les Mathéma- tiques sont «le bulldozer de la Physique ». Bien que personne ne puisse douter de l'efficacité des Mathématiques dans les appli• cations pratiques, je ne crois pas qu'un mathématicien voie dans cette efficacité la justification de ses efforts car le vrai but de son rêve perpétuel est de comprendre la structure de toute chose». Extrait du discours fait par Charles EHRESMANN en 1967, pour remercier l'Université de Bologna de l'avoir nommé Docteur Honoris Causa. Tous droits de traduction, reproduction et adaptation réservés pour tous pays LISTE DES PUBLICATIONS DE CHARLES EHRESMANN 1. TRAVAUX DE RECHERCHE. 1. Les invariants intégraux et la topologie de l'espace proj ectif réglé, C. R. A. S. Paris 194 ( 1932 ), 2004-2006. 2. Sur la topologie de certaines variétés algébriques, C.R.A.S. Paris 196 ( 1933 ), 152-154. 3- Un théorème relatif aux espaces localement proj ectifs et sa généralisa• tion, C. R. A. S. Paris 196 (1933), 1354- 1356. 4. Sur la topologie de certains espaces homogènes, Ann. -
The Works of Charles Ehresmann on Connections: from Cartan
********************************** BANACH CENTER PUBLICATIONS, VOLUME 76 INSTITUTE OF MATHEMATICS POLISH ACADEMY OF SCIENCES WARSZAWA 2007 THE WORKS OF CHARLES EHRESMANN ON CONNECTIONS: FROM CARTAN CONNECTIONS TO CONNECTIONS ON FIBRE BUNDLES CHARLES-MICHEL MARLE Institut de Math´ematiques, Universit´ePierre et Marie Curie, 4, place Jussieu, 75252 Paris c´edex 05, France E-mail: [email protected] Abstract. Around 1923, Elie´ Cartan introduced affine connections on manifolds and defined the main related concepts: torsion, curvature, holonomy groups. He discussed applications of these concepts in Classical and Relativistic Mechanics; in particular he explained how parallel transport with respect to a connection can be related to the principle of inertia in Galilean Mechanics and, more generally, can be used to model the motion of a particle in a gravitational field. In subsequent papers, Elie´ Cartan extended these concepts for other types of connections on a manifold: Euclidean, Galilean and Minkowskian connections which can be considered as special types of affine connections, the group of affine transformations of the affine tangent space being replaced by a suitable subgroup; and more generally, conformal and projective connections, associated to a group which is no more a subgroup of the affine group. Around 1950, Charles Ehresmann introduced connections on a fibre bundle and, when the bundle has a Lie group as structure group, connection forms on the associated principal bundle, with values in the Lie algebra of the structure -
Cartan Connections to Connections on fibre Bundles, and Some Modern Applications
The works of Charles Ehresmann on connections: from Cartan connections to connections on fibre bundles, and some modern applications Charles-Michel Marle Universite´ Pierre et Marie Curie Paris, France The works of Charles Ehresmann on connections: from Cartan connections to connections on fibre bundles, and some modern applications – p. 1/40 Élie Cartan’s affine connections (1) Around 1923, Élie Cartan [1, 2, 3] introduced the notion of an affine connection on a manifold. That notion was previously used, in a less general setting, by H. Weyl [16] and rests on the idea of parallel transport due to T. Levi-Civita [11]. The works of Charles Ehresmann on connections: from Cartan connections to connections on fibre bundles, and some modern applications – p. 2/40 Élie Cartan’s affine connections (1) Around 1923, Élie Cartan [1, 2, 3] introduced the notion of an affine connection on a manifold. That notion was previously used, in a less general setting, by H. Weyl [16] and rests on the idea of parallel transport due to T. Levi-Civita [11]. A large part of [1, 2] is devoted to applications of affine connections to Newtonian and Einsteinian Mechanics. Cartan show that the principle of inertia (which is at the foundations of Mechanics), according to which a material point particle, when no forces act on it, moves along a straight line with a constant velocity, can be expressed locally by the use of an affine connection. Under that form, that principle remains valid in (curved) Einsteinian space-times. The works of Charles Ehresmann on connections: from Cartan connections to connections on fibre bundles, and some modern applications – p. -
Bibliography
Bibliography [AK98] V. I. Arnold and B. A. Khesin, Topological methods in hydrodynamics, Springer- Verlag, New York, 1998. [AL65] Holt Ashley and Marten Landahl, Aerodynamics of wings and bodies, Addison- Wesley, Reading, MA, 1965, Section 2-7. [Alt55] M. Altman, A generalization of Newton's method, Bulletin de l'academie Polonaise des sciences III (1955), no. 4, 189{193, Cl.III. [Arm83] M.A. Armstrong, Basic topology, Springer-Verlag, New York, 1983. [Bat10] H. Bateman, The transformation of the electrodynamical equations, Proc. Lond. Math. Soc., II, vol. 8, 1910, pp. 223{264. [BB69] N. Balabanian and T.A. Bickart, Electrical network theory, John Wiley, New York, 1969. [BLG70] N. N. Balasubramanian, J. W. Lynn, and D. P. Sen Gupta, Differential forms on electromagnetic networks, Butterworths, London, 1970. [Bos81] A. Bossavit, On the numerical analysis of eddy-current problems, Computer Methods in Applied Mechanics and Engineering 27 (1981), 303{318. [Bos82] A. Bossavit, On finite elements for the electricity equation, The Mathematics of Fi- nite Elements and Applications IV (MAFELAP 81) (J.R. Whiteman, ed.), Academic Press, 1982, pp. 85{91. [Bos98] , Computational electromagnetism: Variational formulations, complementar- ity, edge elements, Academic Press, San Diego, 1998. [Bra66] F.H. Branin, The algebraic-topological basis for network analogies and the vector cal- culus, Proc. Symp. Generalised Networks, Microwave Research, Institute Symposium Series, vol. 16, Polytechnic Institute of Brooklyn, April 1966, pp. 453{491. [Bra77] , The network concept as a unifying principle in engineering and physical sciences, Problem Analysis in Science and Engineering (K. Husseyin F.H. Branin Jr., ed.), Academic Press, New York, 1977. -
1 Portraits Leonhard Euler Daniel Bernoulli Johann-Heinrich Lambert
Portraits Leonhard Euler Daniel Bernoulli Johann-Heinrich Lambert Compiled and translated by Oscar Sheynin Berlin, 2010 Copyright Sheynin 2010 www.sheynin.de ISBN 3-938417-01-3 1 Contents Foreword I. Nicolaus Fuss, Eulogy on Leonhard Euler, 1786. Translated from German II. M. J. A. N. Condorcet, Eulogy on Euler, 1786. Translated from French III. Daniel Bernoulli, Autobiography. Translated from Russian; Latin original received in Petersburg in 1776 IV. M. J. A. N. Condorcet, Eulogy on [Daniel] Bernoulli, 1785. In French. Translated by Daniel II Bernoulli in German, 1787. This translation considers both versions V. R. Wolf, Daniel Bernoulli from Basel, 1700 – 1782, 1860. Translated from German VI. Gleb K. Michajlov, The Life and Work of Daniel Bernoullli, 2005. Translated from German VII. Daniel Bernoulli, List of Contributions, 2002 VIII. J. H. S. Formey, Eulogy on Lambert, 1780. Translated from French IX. R. Wolf, Joh. Heinrich Lambert from Mühlhausen, 1728 – 1777, 1860. Translated from German X. J.-H. Lambert, List of Publications, 1970 XI. Oscar Sheynin, Supplement: Daniel Bernoulli’s Instructions for Meteorological Stations 2 Foreword Along with the main eulogies and biographies [i, ii, iv, v, viii, ix], I have included a recent biography of Daniel Bernoulli [vi], his autobiography [iii], for the first time translated from the Russian translation of the Latin original but regrettably incomplete, and lists of published works by Daniel Bernoulli [vii] and Lambert [x]. The first of these lists is readily available, but there are so many references to the works of these scientists in the main texts, that I had no other reasonable alternative. -
Women Mathematicians in France in the Mid-Twentieth Century Introduction
* Women mathematicians in France in the mid-twentieth century Yvette Kosmann-Schwarzbach * To appear in the BSHM Bulletin: Journal of the British Society for the History of Mathematics (2015) DOI 10.1080/17498430.2014.976804 A short outline of the French system of “Écoles normales supérieures” and “agrégations” serves as the introduction to our account of the careers of the five women who completed a doctorate in mathematics in France before 1960 and became internationally known scientists: Marie-Louise Dubreil-Jacotin (1905-1972), Marie-Hélène Schwartz (1913-2013), Jacqueline Ferrand (1918-2014), Paulette Libermann (1919-2007) and Yvonne Choquet-Bruhat (b. 1923). This is followed by a more general description of the place of women on the mathematical scene in France between 1930 and 1960, together with a brief sketch of the accomplishments of some other women and the identification of all those who were active in research before 1960 and became professors in the French university system. Introduction The intersection of the fields of history of mathematics and history of women is notoriously small. From Hypatia of Alexandria to Emmy Noether, very few women are known to have contributed to the development of mathematics, and the number of those born in France is even smaller. Were there any before Gabrielle-Émilie Le Tonnelier de Breteuil, marquise Du Châtelet-Lomond (1706-1749), the little-known Nicole-Reine Étable de Labrière Lepaute (1723-1788) and the even lesser known Marie Anne Victoire Pigeon d’Osangis (1724-1767)?Were there any between Sophie Germain (1776-1831) and those whose names and accomplishments will appear in this article? There were two French lady scientists working with the astronomer Jérôme de Lalande, Louise du Pierry (1746-1806) and Jeanne Lefrançais de Lalande (1769-1832). -
Quelques Souvenirs Des Années 1925-1950 Cahiers Du Séminaire D’Histoire Des Mathématiques 1Re Série, Tome 1 (1980), P
CAHIERS DU SÉMINAIRE D’HISTOIRE DES MATHÉMATIQUES GEORGES DE RHAM Quelques souvenirs des années 1925-1950 Cahiers du séminaire d’histoire des mathématiques 1re série, tome 1 (1980), p. 19-36 <http://www.numdam.org/item?id=CSHM_1980__1__19_0> © Cahiers du séminaire d’histoire des mathématiques, 1980, tous droits réservés. L’accès aux archives de la revue « Cahiers du séminaire d’histoire des mathématiques » im- plique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pé- nale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ - 19 - QUELQUES SOUVENIRS DES ANNEES 1925-1950 par Georges de RHAM Arrivé à la fin de ma carrière, je pense à son début. C’est dans ma année 1. en 1924, que j’ai décidé de me lancer dans les mathématiques. En 1921, ayant le bachot classique, avec latin et grec, attiré par la philosophie, j’hésitais d’entrer à la Facul- té des Lettres. Mais finalement je me décidai pour la Faculté des Sciences, avec à mon programme l’étude de la Chimie, de la Physique et surtout, pour finir, la Biologie. Je ne songeais pas aux Mathématiques, qui me semblaient un domaine fermé où je ne pourrais rien faire. Pourtant, pour comprendre des questions de Physique, je suis amené à ouvrir des livres de Mathématiques supérieures. J’entrevois qu’il y a là un domaine immense, qui ex- cité ma curiosité et m’intéresse à tel point qu’après cinq semestres à l’Université, j’ abandonne la Biologie pour aborder résolument les Mathématiques. -
Urs Stammbach, ETH-Zürich List of Publications A. Papers
Urs Stammbach, ETH-Z¨urich List of Publications A. Papers [1] Anwendungen der Homologietheorie der Gruppen auf Zentralreihen und auf Invari- anten von Pr¨asentierungen, Math. Z. 94 (1966), 155 - 177. [2] (with M.-A. Knus) Anwendungen der Homologietheorie der Liealgebren auf Zentral- reihen und auf Pr¨asentierungen, Comment. Math. Helv. 42 (1967), 297 - 306. [3] Ein neuer Beweis eines Satzes von Magnus, Proc. Cambridge Phil. Soc. 63 (1967), 929 - 930. [4] Uber¨ freie Untergruppen gegebener Gruppen, Comment. Math. Helv. 43 (1968), 132 - 136. [5] (with B. Eckmann) Homologie et diff´erentielles. Suites exactes, C. R. Acad. Sci. Paris 265 (1967), 11 - 13. [6] (with B. Eckmann) Homologie et diff´erentielles. Basses dimensions, cas sp´eciaux,C. R. Acad. Sci. Paris 265 (1967), 46 - 48. [7] (with B. Eckmann) On exact sequences in the homology of groups and algebras, Illinois J. Math. 14 (1970), 205 - 215. [8] On the weak homological dimension of the group algebra of solvable groups, J. London Math. Soc. (2) 2 (1970), 567 - 570. [9] Homological methods in group varieties, Comment. Math. Helv. 45 (1970), 287 - 298. [10] Varietal homology and parafree groups, Math. Z. 128 (1972), 153 - 167. [11] (with B. Eckmann and P.J. Hilton) On the homology theory of central group exten- sions. I. The commutator map and stem extensions, Comment. Math. Helv. 47 (1972), 102 -122. [12] (with B. Eckmann and P.J. Hilton) On the homology theory of central group exten- sions. II. The exact sequence in the general case, Comment. Math. Helv. 47 (1972), 171 -178. [13] (with B. Eckmann and P.J. -
Constrained Optimization on Manifolds
Constrained Optimization on Manifolds Von der Universit¨atBayreuth zur Erlangung des Grades eines Doktors der Naturwissenschaften (Dr. rer. nat.) genehmigte Abhandlung von Juli´anOrtiz aus Bogot´a 1. Gutachter: Prof. Dr. Anton Schiela 2. Gutachter: Prof. Dr. Oliver Sander 3. Gutachter: Prof. Dr. Lars Gr¨une Tag der Einreichung: 23.07.2020 Tag des Kolloquiums: 26.11.2020 Zusammenfassung Optimierungsprobleme sind Bestandteil vieler mathematischer Anwendungen. Die herausfordernd- sten Optimierungsprobleme ergeben sich dabei, wenn hoch nichtlineare Probleme gel¨ostwerden m¨ussen. Daher ist es von Vorteil, gegebene nichtlineare Strukturen zu nutzen, wof¨urdie Op- timierung auf nichtlinearen Mannigfaltigkeiten einen geeigneten Rahmen bietet. Es ergeben sich zahlreiche Anwendungsf¨alle,zum Beispiel bei nichtlinearen Problemen der Linearen Algebra, bei der nichtlinearen Mechanik etc. Im Fall der nichtlinearen Mechanik ist es das Ziel, Spezifika der Struktur zu erhalten, wie beispielsweise Orientierung, Inkompressibilit¨atoder Nicht-Ausdehnbarkeit, wie es bei elastischen St¨aben der Fall ist. Außerdem k¨onnensich zus¨atzliche Nebenbedingungen ergeben, wie im wichtigen Fall der Optimalsteuerungsprobleme. Daher sind f¨urdie L¨osungsolcher Probleme neue geometrische Tools und Algorithmen n¨otig. In dieser Arbeit werden Optimierungsprobleme auf Mannigfaltigkeiten und die Konstruktion von Algorithmen f¨urihre numerische L¨osungbehandelt. In einer abstrakten Formulierung soll eine reelle Funktion auf einer Mannigfaltigkeit minimiert werden, mit der Nebenbedingung -
HOMOTECIA Nº 4-16 Abril 2018
HOMOTECIA Nº 4 – Año 16 Lunes, 2 de Abril de 2018 1 Sobre la descapitalización intelectual y profesional actual en Venezuela. En la última década del siglo XX se realizaron investigaciones sobre educación que arrojaron como resultados, que en Venezuela se estaba produciendo una descapitalización intelectual la cual se definía como la disminución del número de individuos capaces intelectualmente, con destrezas y habilidades propias que puedan generar soluciones óptimas en la resolución significativa de los problemas nacionales primordiales, y que como consecuencia de esto, se le restaba a la nación potencial humano útil para implementar un proceso de desarrollo; todo ello en el contexto de la improductividad de la Educación Media Diversificada y Profesional como consecuencia directa de la deficiente realidad práctica que se vivía en la Educación Básica. La interpretación que se le daba a lo anterior era señalar que aunque los egresados de los estudios secundarios en número se correspondían con la masificación impulsada en el sector por los gobiernos de turno, el devenir de la mayoría de estos egresados en los estudios universitarios sería de transcurrir lento y no muy brillante, es decir tardarían en graduarse en más tiempo del que se estipulaba para ello y con pocos méritos que destacar, haciendo parecer la inversión de recursos económicos en educación como poco exitosa y productora de pérdidas para la nación. Pero aun así, sin que dependiera de la época histórica del momento que se vivía, en el transcurrir de la línea temporal se pudo detectar que los egresados en cada cohorte presentaban un perfil suficientemente satisfactorio que los llevaba, al realizar un mejor esfuerzo posterior, obtener loables méritos, camino válido para alcanzar convertirse a futuro en excelentes profesionales. -
Rudi Mathematici
Rudi Mathematici x4-8188x3+25139294x2-34301407052x+17549638999785=0 Rudi Mathematici January 53 1 S (1803) Guglielmo LIBRI Carucci dalla Sommaja Putnam 1999 - A1 (1878) Agner Krarup ERLANG (1894) Satyendranath BOSE Find polynomials f(x), g(x), and h(x) _, if they exist, (1912) Boris GNEDENKO such that for all x 2 S (1822) Rudolf Julius Emmanuel CLAUSIUS f (x) − g(x) + h(x) = (1905) Lev Genrichovich SHNIRELMAN (1938) Anatoly SAMOILENKO −1 if x < −1 1 3 M (1917) Yuri Alexeievich MITROPOLSHY 4 T (1643) Isaac NEWTON = 3x + 2 if −1 ≤ x ≤ 0 5 W (1838) Marie Ennemond Camille JORDAN − + > (1871) Federigo ENRIQUES 2x 2 if x 0 (1871) Gino FANO (1807) Jozeph Mitza PETZVAL 6 T Publish or Perish (1841) Rudolf STURM "Gustatory responses of pigs to various natural (1871) Felix Edouard Justin Emile BOREL 7 F (1907) Raymond Edward Alan Christopher PALEY and artificial compounds known to be sweet in (1888) Richard COURANT man," D. Glaser, M. Wanner, J.M. Tinti, and 8 S (1924) Paul Moritz COHN C. Nofre, Food Chemistry, vol. 68, no. 4, (1942) Stephen William HAWKING January 10, 2000, pp. 375-85. (1864) Vladimir Adreievich STELKOV 9 S Murphy's Laws of Math 2 10 M (1875) Issai SCHUR (1905) Ruth MOUFANG When you solve a problem, it always helps to (1545) Guidobaldo DEL MONTE 11 T know the answer. (1707) Vincenzo RICCATI (1734) Achille Pierre Dionis DU SEJOUR The latest authors, like the most ancient, strove to subordinate the phenomena of nature to the laws of (1906) Kurt August HIRSCH 12 W mathematics. -
Stefanie Ursula Eminger Phd Thesis
CARL FRIEDRICH GEISER AND FERDINAND RUDIO: THE MEN BEHIND THE FIRST INTERNATIONAL CONGRESS OF MATHEMATICIANS Stefanie Ursula Eminger A Thesis Submitted for the Degree of PhD at the University of St Andrews 2015 Full metadata for this item is available in Research@StAndrews:FullText at: http://research-repository.st-andrews.ac.uk/ Please use this identifier to cite or link to this item: http://hdl.handle.net/10023/6536 This item is protected by original copyright Carl Friedrich Geiser and Ferdinand Rudio: The Men Behind the First International Congress of Mathematicians Stefanie Ursula Eminger This thesis is submitted in partial fulfilment for the degree of PhD at the University of St Andrews 2014 Thesis Declaration 1. Candidate’s declarations: I, Stefanie Eminger, hereby certify that this thesis, which is approximately 78,500 words in length, has been written by me, and that it is the record of work carried out by me, or principally by myself in collaboration with others as acknowledged, and that it has not been submitted in any previous application for a higher degree. I was admitted as a research student in September 2010 and as a candidate for the degree of PhD in September 2010; the higher study for which this is a record was carried out in the University of St Andrews between 2010 and 2014. Date ……………… Signature of candidate …………………………………… 2. Supervisor’s declaration: I hereby certify that the candidate has fulfilled the conditions of the Resolution and Regulations appropriate for the degree of PhD in the University of St Andrews and that the candidate is qualified to submit this thesis in application for that degree.