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Ludwig Bieberbach
Ludwig Georg Elias Moses Bieberbach (; 4 December 1886 – 1 September 1982) was a German mathematician and leading representative of National Socialist German mathematics (" Deutsche Mathematik"). Biography Born in Goddelau, near Darmstadt, he studied at Heidelberg and under Felix Klein at Göttingen, receiving his doctorate in 1910. His dissertation was titled ''On the theory of automorphic functions'' (). He began working as a Privatdozent at Königsberg in 1910 and as Professor ordinarius at the University of Basel in 1913. He taught at the University of Frankfurt in 1915 and the University of Berlin from 1921–45. Bieberbach wrote a habilitation thesis in 1911 about groups of Euclidean motions – identifying conditions under which the group must have a translational subgroup whose vectors span the Euclidean space – that helped solve Hilbert's 18th problem. He worked on complex analysis and its applications to other areas in mathematics. He is known for his wor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Goddelau
Riedstadt (), with its municipal area of 73.76 km2 is Groß-Gerau district's biggest town by land area. It lies in Hesse, Germany, about 12 km southwest of Darmstadt. Geography Location Riedstadt is shaped not only by its preserved rural structure, but also by being near several cities, namely Frankfurt am Main, Darmstadt, Wiesbaden, Mainz, and Mannheim. As its name suggests, it lies in the Hessisches Ried, the northeastern section of the Rhine rift. The community practises the structured settlement of environmentally friendly business operations. Local recreation sites near the community include the Kühkopf-Knoblochsaue nature reserve, the Bergstraße, the Odenwald, and the Taunus. Neighbouring communities Riedstadt borders in the north on the community of Trebur and the town of Groß-Gerau, in the east on the towns of Griesheim and Pfungstadt (both in Darmstadt-Dieburg), in the south on the town of Gernsheim and the communities of Biebesheim and Stockstadt a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bieberbach Conjecture
In complex analysis, de Branges's theorem, or the Bieberbach conjecture, is a theorem that gives a necessary condition on a holomorphic function in order for it to map the open unit disk of the complex plane injectively to the complex plane. It was posed by and finally proven by . The statement concerns the Taylor coefficients a_n of a univalent function, i.e. a one-to-one holomorphic function that maps the unit disk into the complex plane, normalized as is always possible so that a_0=0 and a_1=1. That is, we consider a function defined on the open unit disk which is holomorphic and injective ('' univalent'') with Taylor series of the form :f(z)=z+\sum_ a_n z^n. Such functions are called ''schlicht''. The theorem then states that : , a_n, \leq n \quad \textn\geq 2. The Koebe function (see below) is a function for which a_n=n for all n, and it is schlicht, so we cannot find a stricter limit on the absolute value of the nth coefficient. Schlicht functions The normalization ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hilbert's Eighteenth Problem
Hilbert's eighteenth problem is one of the 23 Hilbert problems set out in a celebrated list compiled in 1900 by mathematician David Hilbert. It asks three separate questions about lattices and sphere packing in Euclidean space. Symmetry groups in dimensions The first part of the problem asks whether there are only finitely many essentially different space groups in n-dimensional Euclidean space. This was answered affirmatively by Bieberbach. Anisohedral tiling in 3 dimensions The second part of the problem asks whether there exists a polyhedron which tiles 3-dimensional Euclidean space but is not the fundamental region of any space group; that is, which tiles but does not admit an isohedral (tile- transitive) tiling. Such tiles are now known as anisohedral. In asking the problem in three dimensions, Hilbert was probably assuming that no such tile exists in two dimensions; this assumption later turned out to be incorrect. The first such tile in three dimensions was found b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Group (mathematics)
In mathematics, a group is a Set (mathematics), set with an Binary operation, operation that combines any two elements of the set to produce a third element within the same set and the following conditions must hold: the operation is Associative property, associative, it has an identity element, and every element of the set has an inverse element. For example, the integers with the addition, addition operation form a group. The concept of a group was elaborated for handling, in a unified way, many mathematical structures such as numbers, geometric shapes and polynomial roots. Because the concept of groups is ubiquitous in numerous areas both within and outside mathematics, some authors consider it as a central organizing principle of contemporary mathematics. In geometry, groups arise naturally in the study of symmetries and geometric transformations: The symmetries of an object form a group, called the symmetry group of the object, and the transformations of a given type form a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Humboldt University Of Berlin
The Humboldt University of Berlin (, abbreviated HU Berlin) is a public research university in the central borough of Mitte in Berlin, Germany. The university was established by Frederick William III on the initiative of Wilhelm von Humboldt, Johann Gottlieb Fichte and Friedrich Daniel Ernst Schleiermacher as the University of Berlin () in 1809, and opened in 1810. From 1828 until its closure in 1945, it was named the (Royal) Friedrich Wilhelm University of Berlin (FWU Berlin; ). During the Cold War, the university found itself in East Berlin and was ''de facto'' split in two when the Free University of Berlin opened in West Berlin. The university received its current name in honour of Alexander and Wilhelm von Humboldt in 1949. The university is divided into nine faculties including its medical school shared with the Freie Universität Berlin. The university has a student enrollment of around 35,000 students, and offers degree programs in some 171 disciplines from un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Basel
The University of Basel (Latin: ''Universitas Basiliensis''; German: ''Universität Basel'') is a public research university in Basel, Switzerland. Founded on 4 April 1460, it is Switzerland's oldest university and among the world's oldest universities. The university is traditionally counted among the leading institutions of higher learning in the country. The associated Basel University Library is the largest and among the most important libraries in Switzerland. The university hosts the faculties of theology, law, medicine, humanities and social sciences, science, psychology, and business and economics, as well as numerous cross-disciplinary subjects and institutes, such as the Biozentrum for biomedical research and the Institute for European Global Studies. In 2020, the university had 13,139 students and 378 professors. International students accounted for 27 percent of the student body. In its over 500-year history, the university has been home to Erasmus of Rotterdam, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Königsberg
The University of Königsberg () was the university of Königsberg in Duchy of Prussia, which was a fief of Poland. It was founded in 1544 as the world's second Protestant Reformation, Protestant academy (after the University of Marburg) by Duke Albert, Duke of Prussia, Albert of Prussia and charted by the King Sigismund II Augustus. It was commonly known as the Albertina and served as a Protestant counterpart to the Catholic Jagiellonian University in Kraków. Following World War II, the city of Königsberg was transferred to the Soviet Union according to the 1945 Potsdam Agreement, and renamed Kaliningrad in 1946. The Albertina was closed and the remaining German population Flight and expulsion of Germans (1944–1950), expelled, by the terms of the Potsdam Agreement. Today, the Immanuel Kant Baltic Federal University in Kaliningrad claims to maintain the traditions of the Albertina. History Albert, former Grand Master of the Teutonic Order and first Duchy of Prussia, Duke of P ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Privatdozent
''Privatdozent'' (for men) or ''Privatdozentin'' (for women), abbreviated PD, P.D. or Priv.-Doz., is an academic title conferred at some European universities, especially in German-speaking countries, to someone who holds certain formal qualifications that denote an ability (''facultas docendi'') and permission to teach ('' venia legendi'') a designated subject at the highest level. To be granted the title Priv.-Doz. by a university, a recipient has to fulfill the criteria set by the university which usually require excellence in research, teaching, and further education. In its current usage, the title indicates that the holder has completed their habilitation and is therefore granted permission to teach and examine students independently without having a full professorship (chair). With respect to the level of academic achievement, the title of ''Privatdozent'' is comparable to that of an Associate Professor (United States), Senior Lecturer (United Kingdom), or ''maître de con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Darmstadt
Darmstadt () is a city in the States of Germany, state of Hesse in Germany, located in the southern part of the Frankfurt Rhine Main Area, Rhine-Main-Area (Frankfurt Metropolitan Region). Darmstadt has around 160,000 inhabitants, making it the fourth largest city in the state of Hesse after Frankfurt am Main, Wiesbaden, and Kassel. Darmstadt holds the official title "City of Science" () as it is a major centre of scientific institutions, universities, and high-technology companies. The European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT) and the European Space Agency's European Space Operations Centre (ESA ESOC) are located in Darmstadt, as well as Gesellschaft für Schwerionenforschung, GSI Centre for Heavy Ion Research, where several chemical elements such as bohrium (1981), meitnerium (1982), hassium (1984), darmstadtium (1994), roentgenium (1994), and copernicium (1996) were discovered. The existence of the following elements was also confirmed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deutsche Mathematik
''Deutsche Mathematik'' (German Mathematics) was a mathematics journal founded in 1936 by Ludwig Bieberbach and Theodor Vahlen. Vahlen was publisher on behalf of the German Research Foundation (DFG), and Bieberbach was chief editor. Other editors were , Erich Schönhardt, Werner Weber (mathematician), Werner Weber (all volumes), Ernst August Weiß (volumes 1–6), , Wilhelm Süss (volumes 1–5), Günther Schulz (mathematician), Günther Schulz (:de:Günther Schulz (Mathematiker), de), (volumes 1–4), Georg Feigl, Gerhard Kowalewski (volumes 2–6), , Willi Rinow, (volumes 2–5), and Oswald Teichmüller (volumes 3–7). In February 1936, the journal was declared the official organ of the German Student Union (DSt) by its ''Reichsführer'', and all local DSt mathematics departments were requested to subscribe and actively contribute. In the 1940s, issues appeared increasingly delayed and bunched; the journal ended with a triple issue (due Dec 1942) in June 1944. ''Deutsche Mathe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nazism
Nazism (), formally named National Socialism (NS; , ), is the far-right totalitarian socio-political ideology and practices associated with Adolf Hitler and the Nazi Party (NSDAP) in Germany. During Hitler's rise to power, it was frequently referred to as Hitler Fascism () and Hitlerism (). The term " neo-Nazism" is applied to other far-right groups with similar ideology, which formed after World War II, and after Nazi Germany collapsed. Nazism is a form of fascism, with disdain for liberal democracy and the parliamentary system. Its beliefs include support for dictatorship, fervent antisemitism, anti-communism, anti-Slavism, anti-Romani sentiment, scientific racism, white supremacy, Nordicism, social Darwinism, homophobia, ableism, and the use of eugenics. The ultranationalism of the Nazis originated in pan-Germanism and the ethno-nationalist '' Völkisch'' movement which had been a prominent aspect of German ultranationalism since the late 19th centu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
