|
Henri Paul Cartan
Henri Paul Cartan (; 8 July 1904 – 13 August 2008) was a French mathematician who made substantial contributions to algebraic topology. He was the son of the mathematician Élie Cartan, nephew of mathematician Anna Cartan, oldest brother of composer , physicist and mathematician , and the son-in-law of physicist Pierre Weiss. Life According to his own words, Henri Cartan was interested in mathematics at a very young age, without being influenced by his family. He moved to Paris with his family after his father's appointment at Sorbonne in 1909 and he attended secondary school at Lycée Hoche in Versailles. available also at In 1923 he started studying mathematics at École Normale Supérieure, receiving an agrégation in 1926 and a doctorate in 1928. His PhD thesis, entitled ''Sur les systèmes de fonctions holomorphes a variétés linéaires lacunaires et leurs applications'', was supervised by Paul Montel. Cartan taught at Lycée Malherbe in Caen from 1928 to 1929, at Uni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nancy, France
Nancy ; Lorraine Franconian: ''Nanzisch'' is the Prefectures in France, prefecture of the northeastern Departments of France, French department of Meurthe-et-Moselle. It was the capital of the Duchy of Lorraine, which was Lorraine and Barrois, annexed by France under King Louis XV in 1766 and replaced by a Provinces of France, province, with Nancy maintained as capital. Following its rise to prominence in the Age of Enlightenment, it was nicknamed the "capital of Eastern France" in the late 19th century. The metropolitan area of Nancy had a population of 511,257 inhabitants at the 2018 census, making it the 16th-largest functional area (France), functional urban area in France and Lorraine's largest. The population of the city of Nancy proper is 104,885. The motto of the city is , —a reference to the thistle, which is a symbol of Lorraine. Place Stanislas, a large square built between 1752 and 1756 by architect Emmanuel Héré under the direction of Stanislaus I of Poland to lin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cartan's Lemma (potential Theory)
In potential theory, a branch of mathematics, Cartan's lemma, named after Henri Cartan, is a bound on the measure and complexity of the set on which a logarithmic Newtonian potential is small. Statement of the lemma The following statement can be found in Levin's book.B.Ya. Levin, ''Lectures on Entire Functions'' Let ''μ'' be a finite positive Borel measure In mathematics, specifically in measure theory, a Borel measure on a topological space is a measure that is defined on all open sets (and thus on all Borel sets). Some authors require additional restrictions on the measure, as described below. F ... on the complex plane C with ''μ''(C) = ''n''. Let ''u''(''z'') be the logarithmic potential of ''μ'': :u(z) = \frac\int_\mathbf \log, z-\zeta, \,d\mu(\zeta) Given ''H'' ∈ (0, 1), there exist discs of radii ''r''''i'' such that :\sum_i r_i < 5H and : for all ''z'' outside the union of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Los Angeles Times
The ''Los Angeles Times'' (abbreviated as ''LA Times'') is a daily newspaper that started publishing in Los Angeles in 1881. Based in the LA-adjacent suburb of El Segundo since 2018, it is the sixth-largest newspaper by circulation in the United States. The publication has won more than 40 Pulitzer Prizes. It is owned by Patrick Soon-Shiong and published by the Times Mirror Company. The newspaper’s coverage emphasizes California and especially Southern California stories. In the 19th century, the paper developed a reputation for civic boosterism and opposition to labor unions, the latter of which led to the bombing of its headquarters in 1910. The paper's profile grew substantially in the 1960s under publisher Otis Chandler, who adopted a more national focus. In recent decades the paper's readership has declined, and it has been beset by a series of ownership changes, staff reductions, and other controversies. In January 2018, the paper's staff voted to unionize and final ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Academie Des Sciences
The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research. It was at the forefront of scientific developments in Europe in the 17th and 18th centuries, and is one of the earliest Academies of Sciences. Currently headed by Patrick Flandrin (President of the Academy), it is one of the five Academies of the Institut de France. History The Academy of Sciences traces its origin to Colbert's plan to create a general academy. He chose a small group of scholars who met on 22 December 1666 in the King's library, near the present-day Bibliothèque Nationals, and thereafter held twice-weekly working meetings there in the two rooms assigned to the group. The first 30 years of the Academy's existence were relatively informal, since no statutes had as yet been laid down for the institution. In contrast to its British ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Le Monde
''Le Monde'' (; ) is a French daily afternoon newspaper. It is the main publication of Le Monde Group and reported an average circulation of 323,039 copies per issue in 2009, about 40,000 of which were sold abroad. It has had its own website since 19 December 1995, and is often the only French newspaper easily obtainable in non-French-speaking countries. It is considered one of the French newspapers of record, along with '' Libération'', and ''Le Figaro''. It should not be confused with the monthly publication '' Le Monde diplomatique'', of which ''Le Monde'' has 51% ownership, but which is editorially independent. A Reuters Institute poll in 2021 in France found that "''Le Monde'' is the most trusted national newspaper". ''Le Monde'' was founded by Hubert Beuve-Méry at the request of Charles de Gaulle (as Chairman of the Provisional Government of the French Republic) on 19 December 1944, shortly after the Liberation of Paris, and published continuously since its first edit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Topology
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariant (mathematics), invariants that classification theorem, classify topological spaces up to homeomorphism, though usually most classify up to Homotopy#Homotopy equivalence and null-homotopy, homotopy equivalence. Although algebraic topology primarily uses algebra to study topological problems, using topology to solve algebraic problems is sometimes also possible. Algebraic topology, for example, allows for a convenient proof that any subgroup of a free group is again a free group. Main branches of algebraic topology Below are some of the main areas studied in algebraic topology: Homotopy groups In mathematics, homotopy groups are used in algebraic topology to classify topological spaces. The first and simplest homotopy group is the fundamental group, which records information about loops in a space. Intuitively, homotopy gro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heinz R
The H. J. Heinz Company is an American food processing company headquartered at One PPG Place in Pittsburgh, Pennsylvania. The company was founded by Henry J. Heinz in 1869. Heinz manufactures thousands of food products in plants on six continents, and markets these products in more than 200 countries and territories. The company claims to have 150 number-one or number-two brands worldwide. Heinz ranked first in ketchup in the US with a market share in excess of 50%; the Ore-Ida label held 46% of the frozen potato sector in 2003. Since 1896, the company has used its " 57 Varieties" slogan; it was inspired by a sign advertising 21 styles of shoes, and Henry Heinz chose the number 57 even though the company manufactured more than 60 products at the time, because "5" was his lucky number and "7" was his wife's. In February 2013, Heinz agreed to be purchased by Berkshire Hathaway and the Brazilian investment firm 3G Capital for $23billion. On March 25, 2015, Kraft announced its m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wolf Prize In Mathematics
The Wolf Prize in Mathematics is awarded almost annually by the Wolf Foundation in Israel. It is one of the six Wolf Prizes established by the Foundation and awarded since 1978; the others are in Agriculture, Chemistry, Medicine, Physics and Arts. According to a reputation survey conducted in 2013 and 2014, the Wolf Prize in Mathematics is the third most prestigious international academic award in mathematics, after the Abel Prize and the Fields Medal. Until the establishment of the Abel Prize, it was probably the closest equivalent of a "Nobel Prize in Mathematics", since the Fields Medal is awarded every four years only to mathematicians under the age of 40. Laureates Laureates per country Below is a chart of all laureates per country (updated to 2022 laureates). Some laureates are counted more than once if have multiple citizenship. Notes See also * List of mathematics awards References External links * * * Israel-Wolf-Prizes 2015Jerusalempost Wolf Prizes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Émile Picard Medal
The Émile Picard Medal (or Médaille Émile Picard) is a medal named for Émile Picard awarded every 6 years to an outstanding mathematician by the Institut de France, Académie des sciences. This rewards a mathematician designated by the Academy of Sciences every six years. The first medal was awarded in 1946. Recipients The Émile Picard Medal recipients are * Maurice Fréchet (1946) * Paul Lévy (1953) * Henri Cartan (1959) * Szolem Mandelbrojt (1965), * Jean-Pierre Serre (1971) * Alexandre Grothendieck (1977) * André Néron (1983) * François Bruhat (1989) * Jean-Pierre Kahane (1995) * Jacques Dixmier (2001) * Louis Boutet de Monvel (2007) * Luc Illusie (2012) * Yves Colin de Verdière (2018) See also * List of mathematics awards This list of mathematics awards is an index to articles about notable awards for mathematics. The list is organized by the region and country of the organization that sponsors the award, but awards may be open to mathematicians from around th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peccot Lectures
The Peccot Lecture (''Cours Peccot'' in French) is a semester-long mathematics course given at the Collège de France. Each course is given by a mathematician under 30 years old who has distinguished themselves by their promising work. The course consists in a series of conferences during which the laureate exposes their recent research works. Being a Peccot lecturer is a distinction that often foresees an exceptional scientific career. Several future recipients of the Fields Medal, Abel Prize, members of the French Academy of Sciences, and professors at the Collège de France are among the laureates. Some of the most illustrious recipients include Émile Borel and the Fields medalists Laurent Schwartz, Jean-Pierre Serre, or Alain Connes. Some Peccot lectures may additionally be granted – exceptionally and irregularly – the Peccot prize or the Peccot–Vimont prize. History The Peccot lectures are among several manifestations organized at the Collège de France which are fun ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weak Dimension
In abstract algebra, the weak dimension of a nonzero right module ''M'' over a ring ''R'' is the largest number ''n'' such that the Tor group \operatorname_n^R(M,N) is nonzero for some left ''R''-module ''N'' (or infinity if no largest such ''n'' exists), and the weak dimension of a left ''R''-module is defined similarly. The weak dimension was introduced by . The weak dimension is sometimes called the flat dimension as it is the shortest length of a resolution of the module by flat modules. The weak dimension of a module is at most equal to its projective dimension. The weak global dimension of a ring is the largest number ''n'' such that \operatorname_n^R(M,N) is nonzero for some right ''R''-module ''M'' and left ''R''-module ''N''. If there is no such largest number ''n'', the weak global dimension is defined to be infinite. It is at most equal to the left or right global dimension of the ring ''R''. Examples *The module \Q of rational numbers over the ring \Z of integers ha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
