Infobox scientist name Camille Jordan image Jordan 4.jpeg birth date birth date 1838 01 05 birth place Lyon death date death date and age 1922 01 22 1838 01 05 death place Paris nationality France French fields Mathematics workplaces alma mater cole polytechnique doctoral advisor academic advisors Victor Puiseux and Joseph Alfred Serret doctoral students known for awards Marie Ennemond Camille Jordan January 5, 1838 &ndash January 22, 1922 was a France French mathematician , known both for his foundational work in group theory and for his influential Cours d analyse . He was born in Lyon and educated at the cole polytechnique . He was an engineer by profession later in life he taught at the cole polytechnique and the Coll ge de France , where he had a reputation for eccentric choices of notation. He is remembered now by name in a number of foundational results The Jordan curve theorem , a topological result required in complex analysis The Jordan normal form and the Jordan matrix in linear algebra In mathematical analysis , Jordan measure or Jordan content is an area measure that predates measure theory . In group theory the Composition series Jordan H lder theorem on composition series is a basic result. Jordan s theorem on finite linear groups Jordan s work did much to bring Galois theory into the mainstream. He also investigated the Mathieu group s, the first examples of sporadic group s. His Trait des substitutions , on permutation group s, was published in 1870. The asteroid 25593 Camillejordan and Institute of Camille Jordan are named in his honour. Camille Jordan is not to be confused with the geodesist Wilhelm Jordan geodesist Wilhelm Jordan Gauss Jordan elimination or the physicist Pascual Jordan Jordan algebra s . Books by C. Jordan Cours d analyse de l Ecole Polytechnique 1 Calcul diff rentiel Gauthier Villars, 1909 Cours d analyse de l Ecole Polytechnique 2 Calcul int gral Gauthier Villars, 1909 Cours d analyse de l Ecole Polytechnique 3 quations di ... more details
Cergy Pontoise is a New town France new town in France , in the Val d Oise d partement in France d partement , northwest of Paris on the Oise River . It owes its name to two of the commune in France communes that it covers, Cergy and Pontoise . Population 2003 183,430 Area is 77.74 km Population density 2,360 hab. km Administration As of 2005 , Cergy Pontoise is a communaut d agglom ration consisting of twelve commune in France communes Boisemont, Val d Oise Boisemont Cergy Courdimanche ragny sur Oise Jouy le Moutier Menucourt Neuville sur Oise Osny Pontoise Puiseux Pontoise Saint Ouen l Aum ne Vaur al Population Historical populations align right 1962 34050 1968 41576 1975 69546 1982 102967 1990 159168 1999 178656 2003 183430 Since the establishment of the new agglomeration, the population has quadrupled over forty years. History In the 1960s, faced by the fast development of Paris and its suburbs, it was decided to control and balance it by creating several new cities around Paris . To the north, the choice was made on the surroundings of Pontoise. The old city was to be integrated in a much larger unit, whose center would be Cergy , at the time not more than a village. From 1965, the establishment of the new city was to be done in several stages April 16, 1969 creation of the publicly owned tablissement public d am nagement EPA 1971 creation of the Syndicat communautaire d am nagement SCA . August 11, 1972 official creation of the new city of Cergy Pontoise, gathering fifteen communes the eleven current ones, and Boisemont, Val d Oise Boisemont , Boissy l Aillerie , M ry sur Oise and Pierrelaye . 1983 the law Rocard amended the new cities. 1984 Syndicat d agglom ration nouvelle SAN replaces the SCA, four communes left the structure the four mentioned above December 31, 2002 end of the mission and dissolution of the EPA, following the completion of the new city. January 1, 2004 transformation of the SAN into a communaut d agglom ration . 2004 Boisemont becomes ... more details
cite book author Puiseux Dao S year 1970 title Acetabularia and Cell Biology publisher Springer Verlag ... Sea.. In Developmental Biology of Acetabularia. Bonotto, S., Kefeli, V. & Puiseux Dao, S. Eds ..., M. & Puiseux Dao, S. 1984 . The effects of blue and red light on the transcellular electric potential ... more details
411 BC Ptolemaeus lunar crater Ptolemaeus align right 164 km Ptolemy circa 87 150 Puiseux crater Puiseux align right 24 km Pierre Puiseux 1855 1928 Pupin crater Pupin align right 2 km ... more details
In mathematics , the Newton polygon is a tool for understanding the behaviour of polynomial s over local field s. In the original case, the local field of interest was the field of formal Laurent series in the indeterminate X , i.e. the field of fractions of the formal power series ring K nowiki X nowiki , over K , where K was the real number or complex number field. This is still of considerable utility with respect to Puiseux expansion s. The Newton polygon is an effective device for understanding the leading terms aX sup r sup of the power series expansion solutions to equations P F X 0 where P is a polynomial with coefficients in K X , the polynomial ring that is, implicit function implicitly defined algebraic function s. The exponents r here are certain rational number s, depending on the branch of a function branch chosen and the solutions themselves are power series in K nowiki Y nowiki with Y X sup 1 d sup for a denominator d corresponding to the branch. The Newton polygon gives an effective, algorithmic approach to calculating d . After the introduction of the p adic number s, it was shown that the Newton polygon is just as useful in questions of ramification for local fields, and hence in algebraic number theory . Newton polygons have also been useful in the study of elliptic curve s. Definition A priori, given a polynomial over a field, the behaviour of the roots assuming it has roots will be unknown. Newton polygons provide one technique for the study of the behaviour of the roots. Let math K math be a local field with discrete valuation math v K math and let math f x a nx n cdots a 1x a 0 in K x math with math a 0 a n ne 0 math . Then the Newton polygon of math f math is defined to be the lower convex hull of the set of points math P i left i,v K a i right , math ignoring the points with math a i 0 math . Restated geometrically, plot all of these points P sub i sub on the xy plane. Let s assume that the points indices increase from left to right P sub 0 ... more details
Image Pierre Janssen.jpg thumb Jules Janssen The Prix Jules Janssen is the highest award of the Soci t astronomique de France French Astronomical Society . Created in 1897 and awarded annually, it is usually given in alternate years to a French astronomer, and to an astronomer of another nationality. It is distinct from the Janssen Medal French Academy of Sciences Janssen Medal created 1886 , which is awarded by the French Academy of Sciences France Academy of Sciences . Both awards are named for the French astronomer Pierre Janssen 1824 1907 better known as Jules Janssen . Laureates 1897 Camille Flammarion 1898 Samuel Pierpont Langley 1899 Auguste Charlois 1900 Pierre Puiseux 1901 Joseph Joachim Landerer , Thomas David Anderson , and Henri Chr tien 1902 Sylvie Camille Flammarion 1903 Michel Giacobini 1904 Percival Lowell 1905 Josep Comas Sol 1906 Edward Emerson Barnard 1907 Milan Rastislav tef nik 1908 Edward Charles Pickering 1909 William Henry Pickering 1910 Philip Herbert Cowell and Andrew Crommelin 1911 Jean Bosler 1912 Max Wolf 1913 Alphonse Borrelly 1914 Annibale Ricc 1915 not awarded 1916 not awarded 1917 George Ellery Hale 1918 G. Raymond 1919 Guillaume Bigourdan 1920 Henri Alexandre Deslandres 1921 Ren Jarry Desloges 1922 Albert Abraham Michelson 1923 Aymar de la Baume Pluvinel 1924 George Willis Ritchey 1925 Eug ne Michel Antoniadi 1926 Walter Sydney Adams 1927 Gustave Auguste Ferri 1928 Arthur Stanley Eddington 1929 Charles Fabry 1930 Robert Esnault Pelterie 1931 Albert Einstein 1932 Bernard Lyot 1933 Harlow Shapley 1934 Willem de Sitter 1935 Ernest Esclangon 1936 Georges Lema tre 1937 Giorgio Abetti 1938 Jules Baillaud 1939 A. Arnulf 1940 not awarded 1941 not awarded 1942 not awarded 1943 not awarded 1944 not awarded 1945 Harold Spencer Jones 1946 Charles Maurain , Fernand Baldet 1947 Jan Hendrik Oort 1948 Lucien Henri d Azambuja 1949 Bertil Lindblad 1950 Andr Louis Danjon 1951 Gerard Peter Kuiper 1952 Frederick John Marrian Stratton 1953 Andr C ... more details
Use dmy dates date May 2011 Infobox French commune name Cergy image coat of arms Blason ville fr Cergy Val d Oise .svg image Mairie cergy.JPG caption Town hall map size 270px adjustable map Cergy map.png map caption Location in red within Paris inner and outer suburbs latitude 49.0361 longitude 2.0631 region le de France department Val d Oise arrondissement Pontoise canton INSEE 95127 postal code 95000 mayor Dominique Lefebvre term 2001 2008 intercommunality Cergy Pontoise elevation m 25 elevation min m 21 elevation max m 121 area km2 11.68 population 58265 population date 2006 Cergy IPA fr s . i is a Communes of France commune in the northwestern suburbs of Paris, France. It is located convert 27.8 km mi abbr on from the Kilometre Zero France center of Paris , in the new town France new town of Cergy Pontoise , created in the 1960s, of which it is the central and most populated commune. Although neighboring Pontoise is the official pr fecture capital of the Val d Oise d partement in France d partement , the pr fecture building and administration, as well as the department council conseil g n ral , are located inside the commune of Cergy, which is regarded as the de facto capital of Val d Oise. The sous pr fecture building and administration, on the other hand, are located inside the commune of Pontoise. Name The name Cergy comes from Medieval Latin Sergiacum , meaning estate of Sergius , a Gallo Roman landowner. Administration Image Cergy pr fecture quartiers.jpg 270px thumb left Map of the quarters of Cergy. Cergy is the chief town of two cantons The canton of Cergy Nord is made of part of Cergy and communes of Boissy l Aillerie , Osny , Puiseux Pontoise 53,779 inhabitants The canton of Cergy Sud is made of part of Cergy and the commune of ragny, Val d Oise ragny 32,969 inhabitants . Twin towns and sister cities Flagicon USA Columbia, Maryland Columbia , Maryland, United States. Flagicon Germany Erkrath , Germany. Flagicon People s Republic of China Liaoyang , ... more details
for non archimedean analytic spaces Berkovich space An analytic space is a generalization of an analytic manifold that allows singularity mathematics singularities . An analytic space is a space that is local property locally the same as an analytic variety . They are prominent in the study of several complex variables , but they also appear in other contexts. Definition Fix a field k with a valuation. Assume that the field is complete and not discrete with respect to this valuation. For example, this includes R and C with respect to their usual absolute values, as well as fields of Puiseux series with respect to their natural valuations. Let U be an open subset of k sup n sup , and let f sub 1 sub , ..., f sub k sub be a collection of analytic functions on U . Denote by Z the common vanishing locus of f sub 1 sub , ..., f sub k sub , that is, let Z x f sub 1 sub x ... f sub k sub x 0 . Z is an analytic variety. Suppose that the structure sheaf mathematics sheaf of V is math mathcal O V math . Then Z has a structure sheaf math mathcal O Z mathcal O V mathcal I Z math , where math mathcal I Z math is the ideal generated by f sub 1 sub , ..., f sub k sub . In other words, the structure sheaf of Z consists of all functions on V modulo the possible ways they can differ outside of Z . An analytic space is a locally ringed space math X, mathcal O X math such that around every point x of X , there exists an open neighborhood U such that math U, mathcal O U math is isomorphic as locally ringed spaces to an analytic variety with its structure sheaf. Such an isomorphism is called a local model for X at x . An analytic mapping or morphism of analytic spaces is a morphism of locally ringed spaces. This definition is similar to the definition of a scheme mathematics scheme . The only difference is that for a scheme, the local models are spectrum of a ring spectra of rings , whereas for an analytic space, the local models are analytic sets. Because of this, the basic theories of ... more details
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