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Georges Humbert
Marie Georges Humbert (7 January 1859 Paris, France – 22 January 1921 Paris, France) was a French mathematician who worked on Kummer surfaces and the Appell–Humbert theorem and introduced Humbert surfaces. His son was the mathematician Pierre Humbert. He won the Poncelet Prize of the Académie des Sciences in 1891. He studied at the École Polytechnique. He was the brother-in-law of Charles Mangin. WorksApplication de la théorie des fonctions fuchsiennes à l'étude des courbes algébriques Journal de mathematiques pure et appliquées, 4th Series, Vol. 2, 1886, pp. 239–328Online, pdf*Pierre Humbert, Gaston Julia Gaston Maurice Julia (3 February 1893 – 19 March 1978) was a French Algerian mathematician who devised the formula for the Julia set. His works were popularized by French mathematician Benoit Mandelbrot; the Julia and Mandelbrot fractals are ... (Editor): Georges Humbert- Oeuvres, Gauthier-Villars 1929 *Cours d'Analyse, 2 volumes, Gauthier-Villars 19 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pierre Humbert (mathematician)
Pierre Humbert (13 June 1891, Paris – 17 November 1953, Montpellier) was a French mathematician who worked on the theory of elliptic functions and introduced Humbert polynomials. He was the son of the mathematician Georges Humbert and married the daughter of Henri Andoyer. Pierre Humbert was an Invited Speaker of the ICM in 1928 in Bologna. See also * Humbert series PublicationsIntroduction à l'études des fonctions elliptiques, à l'usage des étudiants des facultés des sciences Paris, Hermann 1922 *with Henri Andoyer: Histoire de la Nation Française. Tome XIV, Histoire des Sciences en France; première partie, Histoire des Mathématiques, de la Mécanique et de l'Astronomie. Paris 1924 *Calcul Symbolique, Paris, Hermann 1934 *with Serge Colombo: Le calcul symbolique et ses applications à la physique mathématique, Paris, Gauthier-Villars 1949, 2nd edn. 1965 *Potentiels et Prepotentiels, Gauthier-Villars 1937 *Exercises numeriques d´ astronomie, Paris 1933 *L´Oeuvre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kummer Surface
In algebraic geometry, a Kummer quartic surface, first studied by , is an irreducible nodal surface of degree 4 in \mathbb^3 with the maximal possible number of 16 double points. Any such surface is the Kummer variety of the Jacobian variety of a smooth hyperelliptic curve of genus 2; i.e. a quotient of the Jacobian by the Kummer involution ''x'' ↦ −''x''. The Kummer involution has 16 fixed points: the 16 2-torsion point of the Jacobian, and they are the 16 singular points of the quartic surface. Resolving the 16 double points of the quotient of a (possibly nonalgebraic) torus by the Kummer involution gives a K3 surface with 16 disjoint rational curves; these K3 surfaces are also sometimes called Kummer surfaces. Other surfaces closely related to Kummer surfaces include Weddle surfaces, wave surfaces, and tetrahedroids. Geometry of the Kummer surface Singular quartic surfaces and the double plane model Let K\subset\mathbb^3 be a quartic surface with an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Appell–Humbert Theorem
In mathematics, the Appell–Humbert theorem describes the line bundles on a complex torus or complex abelian variety. It was proved for 2-dimensional tori by and , and in general by Statement Suppose that T is a complex torus given by V/\Lambda where \Lambda is a lattice in a complex vector space V. If H is a Hermitian form on V whose imaginary part E = \text(H) is integral on \Lambda\times\Lambda, and \alpha is a map from \Lambda to the unit circle U(1) = \, called a semi-character, such that :\alpha(u+v) = e^\alpha(u)\alpha(v)\ then : \alpha(u)e^\ is a 1- cocycle of \Lambda defining a line bundle on T. For the trivial Hermitian form, this just reduces to a character. Note that the space of character morphisms is isomorphic with a real torus\text_(\Lambda,U(1)) \cong \mathbb^/\mathbb^if \Lambda \cong \mathbb^ since any such character factors through \mathbb composed with the exponential map. That is, a character is a map of the form\text(2\pi i \langle l^*, -\rangle )for s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
