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E. Witt
Ernst Witt (26 June 1911 – 3 July 1991) was a German mathematician, one of the leading algebraists of his time. Biography Witt was born on the island of Alsen, then a part of the German Empire. Shortly after his birth, his parents moved the family to China to work as missionaries, and he did not return to Europe until he was nine. After his schooling, Witt went to the University of Freiburg and the University of Göttingen. He joined the NSDAP (Nazi Party) and was an active party member. Witt was awarded a Ph.D. at the University of Göttingen in 1934 with a thesis titled: "Riemann-Roch theorem and zeta-Function in hypercomplexes" (Riemann-Rochscher Satz und Zeta-Funktion im Hyperkomplexen) that was supervised by Gustav Herglotz with Emmy Noether suggesting the top for the doctorate. He qualified to become a lecturer and gave guest lectures in Göttingen and Hamburg. He became associated with the team led by Helmut Hasse who led his habilitation. In June 1936 gave his habil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nice
Nice ( , ; Niçard: , classical norm, or , nonstandard, ; it, Nizza ; lij, Nissa; grc, Νίκαια; la, Nicaea) is the prefecture of the Alpes-Maritimes department in France. The Nice agglomeration extends far beyond the administrative city limits, with a population of nearly 1 millionDemographia: World Urban Areas , Demographia.com, April 2016 on an area of . Located on the , the southeastern coast of France on the , at the foot of the |
Bourbaki–Witt Theorem
In mathematics, the Bourbaki–Witt theorem in order theory, named after Nicolas Bourbaki and Ernst Witt, is a basic fixed point theorem for partially ordered sets. It states that if ''X'' is a non-empty chain complete poset, and f : X \to X such that f (x) \geq x for all x, then ''f'' has a fixed point. Such a function ''f'' is called ''inflationary'' or ''progressive''. Special case of a finite poset If the poset ''X'' is finite then the statement of the theorem has a clear interpretation that leads to the proof. The sequence of successive iterates, : x_=f(x_n), n=0,1,2,\ldots, where ''x''0 is any element of ''X'', is monotone increasing. By the finiteness of ''X'', it stabilizes: : x_n=x_, for ''n'' sufficiently large. It follows that ''x''∞ is a fixed point of ''f''. Proof of the theorem Pick some y \in X. Define a function ''K'' recursively on the ordinals as follows: :\,K(0) = y :\,K( \alpha+1 ) = f( K( \alpha ) ). If \beta is a limit ordinal, then b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
World War II
World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposing military alliances: the Allies and the Axis powers. World War II was a total war that directly involved more than 100 million personnel from more than 30 countries. The major participants in the war threw their entire economic, industrial, and scientific capabilities behind the war effort, blurring the distinction between civilian and military resources. Aircraft played a major role in the conflict, enabling the strategic bombing of population centres and deploying the only two nuclear weapons ever used in war. World War II was by far the deadliest conflict in human history; it resulted in 70 to 85 million fatalities, mostly among civilians. Tens of millions died due to genocides (including the Holocaust), starvation, ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Helmut Hasse
Helmut Hasse (; 25 August 1898 – 26 December 1979) was a German mathematician working in algebraic number theory, known for fundamental contributions to class field theory, the application of ''p''-adic numbers to local class field theory and diophantine geometry (Hasse principle), and to local zeta functions. Life Hasse was born in Kassel, Province of Hesse-Nassau, the son of Judge Paul Reinhard Hasse, also written Haße (12 April 1868 – 1 June 1940, son of Friedrich Ernst Hasse and his wife Anna Von Reinhard) and his wife Margarethe Louise Adolphine Quentin (born 5 July 1872 in Milwaukee, daughter of retail toy merchant Adolph Quentin (b. May 1832, probably Berlin, Kingdom of Prussia) and Margarethe Wehr (b. about 1840, Prussia), then raised in Kassel). After serving in the Imperial German Navy in World War I, he studied at the University of Göttingen, and then at the University of Marburg under Kurt Hensel, writing a dissertation in 1921 containing the Hasse–Minkowsk ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gustav Herglotz
Gustav Herglotz (2 February 1881 – 22 March 1953) was a German Bohemian physicist best known for his works on the theory of relativity and seismology. Biography Gustav Ferdinand Joseph Wenzel Herglotz was born in Volary num. 28 to a public notary Gustav Herglotz (also a Doctor of Law) and his wife Maria née Wachtel. The family were Sudeten Germans. He studied mathematics and astronomy at the University of Vienna in 1899, and attended lectures by Ludwig Boltzmann. In this time of study, he had a friendship with his colleagues Paul Ehrenfest, Hans Hahn and Heinrich Tietze. In 1900 he went to the LMU Munich and achieved his Doctorate in 1902 under Hugo von Seeliger. Afterwards, he went to the University of Göttingen, where he habilitated under Felix Klein. In 1904 he became Privatdozent for Astronomy and Mathematics there, and in 1907 Professor extraordinarius. In 1908 he became Professor extraordinarius in Vienna, and in 1909 at the University of Leipzig. From 1925 (until becom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sturmabteilung
The (; SA; literally "Storm Detachment") was the original paramilitary wing of the Nazi Party. It played a significant role in Adolf Hitler's rise to power in the 1920s and 1930s. Its primary purposes were providing protection for Nazi rallies and assemblies, disrupting the meetings of opposing parties, fighting against the paramilitary units of the opposing parties, especially the ''Roter Frontkämpferbund'' of the Communist Party of Germany (KPD) and the '' Reichsbanner Schwarz-Rot-Gold'' of the Social Democratic Party of Germany (SPD), and intimidating Romani, trade unionists, and especially Jews. The SA were colloquially called Brownshirts () because of the colour of their uniform's shirts, similar to Benito Mussolini's blackshirts. The official uniform of the SA was the brown shirt with a brown tie. The color came about because a large shipment of Lettow- shirts, originally intended for the German colonial troops in Germany's former East Africa colony, was purcha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oswald Teichmüller
Paul Julius Oswald Teichmüller (; 18 June 1913 – 11 September 1943) was a German mathematician who made contributions to complex analysis. He introduced quasiconformal mappings and differential geometric methods into the study of Riemann surfaces. Teichmüller spaces are named after him. He was a supporter of the Nazi regime. Born in Nordhausen, Teichmüller attended the University of Göttingen, where he graduated in 1935 under the supervision of Helmut Hasse. His doctoral dissertation was on operator theory, though this was his only work on functional analysis. His next few papers were algebraic, but he switched his focus to complex analysis after attending lectures given by Rolf Nevanlinna. In 1937, he moved to the University of Berlin to work with Ludwig Bieberbach. Bieberbach was the editor of ''Deutsche Mathematik'' and much of Teichmüller's work was published in the journal, which made his papers hard to find in modern libraries before the release of his collected works ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nazi Party
The Nazi Party, officially the National Socialist German Workers' Party (german: Nationalsozialistische Deutsche Arbeiterpartei or NSDAP), was a far-right politics, far-right political party in Germany active between 1920 and 1945 that created and supported the ideology of Nazism. Its precursor, the German Workers' Party (; DAP), existed from 1919 to 1920. The Nazi Party emerged from the Extremism, extremist German nationalism, German nationalist, racism, racist and populism, populist paramilitary culture, which fought against the communism, communist uprisings in post–World War I Germany. The party was created to draw workers away from communism and into nationalism. Initially, Nazi political strategy focused on anti–big business, anti-bourgeoisie, bourgeois, and anti-capitalism, anti-capitalist rhetoric. This was later downplayed to gain the support of business leaders, and in the 1930s, the party's main focus shifted to Antisemitism, antisemitic and Criticism of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Freiburg
The University of Freiburg (colloquially german: Uni Freiburg), officially the Albert Ludwig University of Freiburg (german: Albert-Ludwigs-Universität Freiburg), is a public university, public research university located in Freiburg im Breisgau, Baden-Württemberg, Germany. The university was founded in 1457 by the House of Habsburg, Habsburg dynasty as the second university in Austrians, Austrian-Habsburg territory after the University of Vienna. Today, Freiburg is the List of universities in Germany#Universities by date of establishment, fifth-oldest university in Germany, with a long tradition of teaching the humanities, social sciences and natural sciences and technology and enjoys a high academic reputation both nationally and internationally. The university is made up of 11 faculty (division), faculties and attracts students from across Germany as well as from over 120 other countries. Foreign students constitute about 18.2% of total student numbers. The University of Fr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
China
China, officially the People's Republic of China (PRC), is a country in East Asia. It is the world's most populous country, with a population exceeding 1.4 billion, slightly ahead of India. China spans the equivalent of five time zones and borders fourteen countries by land, the most of any country in the world, tied with Russia. Covering an area of approximately , it is the world's third largest country by total land area. The country consists of 22 provinces, five autonomous regions, four municipalities, and two Special Administrative Regions (Hong Kong and Macau). The national capital is Beijing, and the most populous city and financial center is Shanghai. Modern Chinese trace their origins to a cradle of civilization in the fertile basin of the Yellow River in the North China Plain. The semi-legendary Xia dynasty in the 21st century BCE and the well-attested Shang and Zhou dynasties developed a bureaucratic political system to serve hereditary monarchies, or dyna ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Als (island)
Als (, german: Alsen) is a Danish island in the Baltic Sea. Geography Als lies to the east of the Jutland peninsula, across from the Danish town of Sønderborg, and north of the coast of Southern Schleswig, Germany. Covering an area of 321 km2 (124 sq. miles), the island has a total population of 51,322 as of 1 January 2010."Danmarks Statistik." Retrieved 28 June 2010. It is administered as part of the as of 1 January 2007. To the north and east of the island are the waters of the , to the south is [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abstract Algebra
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The term ''abstract algebra'' was coined in the early 20th century to distinguish this area of study from older parts of algebra, and more specifically from elementary algebra, the use of variables to represent numbers in computation and reasoning. Algebraic structures, with their associated homomorphisms, form mathematical categories. Category theory is a formalism that allows a unified way for expressing properties and constructions that are similar for various structures. Universal algebra is a related subject that studies types of algebraic structures as single objects. For example, the structure of groups is a single object in universal algebra, which is called the ''variety of groups''. History Before the nineteenth century, algebra meant ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
