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Paul Koebe
Paul Koebe (15 February 1882 – 6 August 1945) was a 20th-century German mathematician. His work dealt exclusively with the complex numbers, his most important results being on the uniformization of Riemann surfaces in a series of four papers in 1907–1909. He did his thesis at Berlin, where he worked under Hermann Schwarz. He was an extraordinary professor at Leipzig from 1910 to 1914, then an ordinary professor at the University of Jena before returning to Leipzig in 1926 as an ordinary professor. He died in Leipzig. He conjectured the Koebe quarter theorem on the radii of disks in the images of injective functions, in 1907. His conjecture became a theorem when it was proven by Ludwig Bieberbach in 1916, and the function f(z)=z/(1-z)^2 providing a tight example for this theorem became known as the Koebe function. Awards * 1922, Ackermann–Teubner Memorial Award See also * Koebe groups *Midsphere *Riemann mapping theorem In complex analysis, the Riemann mapping theorem st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Luckenwalde
Luckenwalde (; Upper and dsb, Łukowc) is the capital of the Teltow-Fläming district in the German state of Brandenburg. It is situated on the Nuthe river north of the Fläming Heath, at the eastern rim of the Nuthe-Nieplitz Nature Park, about south of Berlin. The town area includes the villages of Frankenfelde and Kolzenburg. Overview The former Slavic settlement of ''Lugkin'' was conquered by Margrave Conrad Wettin of Meissen in the course of the 1147 Wendish Crusade. ''Lukenwalde'' Castle was first mentioned in a 1216 deed as a burgward of the Bishopric of Brandenburg, it was acquired by Zinna Abbey in 1285. Together with Zinna it remained under the rule of the Archbishopric of Magdeburg and its successor, the Prussian Duchy of Magdeburg until it was attached to the Margraviate of Brandenburg in 1773. Originating in the 17th century, Luckenwalde's cloth and wool factories did not spring up till the reign of King Frederick II of Prussia and soon were among the most e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
People From Luckenwalde
A person ( : people) is a being that has certain capacities or attributes such as reason, morality, consciousness or self-consciousness, and being a part of a culturally established form of social relations such as kinship, ownership of property, or legal responsibility. The defining features of personhood and, consequently, what makes a person count as a person, differ widely among cultures and contexts. In addition to the question of personhood, of what makes a being count as a person to begin with, there are further questions about personal identity and self: both about what makes any particular person that particular person instead of another, and about what makes a person at one time the same person as they were or will be at another time despite any intervening changes. The plural form "people" is often used to refer to an entire nation or ethnic group (as in "a people"), and this was the original meaning of the word; it subsequently acquired its use as a plural form of per ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1945 Deaths
1945 marked the end of World War II and the fall of Nazi Germany and the Empire of Japan. It is also the only year in which Nuclear weapon, nuclear weapons Atomic bombings of Hiroshima and Nagasaki, have been used in combat. Events Below, the events of World War II have the "WWII" prefix. January * January 1 – WWII: ** Nazi Germany, Germany begins Operation Bodenplatte, an attempt by the ''Luftwaffe'' to cripple Allies of World War II, Allied air forces in the Low Countries. ** Chenogne massacre: German prisoners are allegedly killed by American forces near the village of Chenogne, Belgium. * January 6 – WWII: A German offensive recaptures Esztergom, Kingdom of Hungary (1920–1946), Hungary from the Russians. * January 12 – WWII: The Soviet Union begins the Vistula–Oder Offensive in Eastern Europe, against the German Army (Wehrmacht), German Army. * January 13 – WWII: The Soviet Union begins the East Prussian Offensive, to eliminate German forces in East Pruss ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1882 Births
Year 188 (CLXXXVIII) was a leap year starting on Monday of the Julian calendar. At the time, it was known in the Roman Empire as the Year of the Consulship of Fuscianus and Silanus (or, less frequently, year 941 ''Ab urbe condita''). The denomination 188 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years. Events By place Roman Empire * Publius Helvius Pertinax becomes pro-consul of Africa from 188 to 189. Japan * Queen Himiko (or Shingi Waō) begins her reign in Japan (until 248). Births * April 4 – Caracalla (or Antoninus), Roman emperor (d. 217) * Lu Ji (or Gongji), Chinese official and politician (d. 219) * Sun Shao, Chinese general of the Eastern Wu state (d. 241) Deaths * March 17 – Julian, pope and patriarch of Alexandria * Fa Zhen (or Gaoqing), Chinese scholar (b. AD 100) * Lucius Antistius Burrus, Roman politician (executed) * Ma Xiang, Chi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Riemann Mapping Theorem
In complex analysis, the Riemann mapping theorem states that if ''U'' is a non-empty simply connected space, simply connected open set, open subset of the complex plane, complex number plane C which is not all of C, then there exists a biholomorphy, biholomorphic mapping ''f'' (i.e. a bijective function, bijective holomorphic function, holomorphic mapping whose inverse is also holomorphic) from ''U'' onto the open unit disk :D = \. This mapping is known as a Riemann mapping. Intuitively, the condition that ''U'' be simply connected means that ''U'' does not contain any “holes”. The fact that ''f'' is biholomorphic implies that it is a conformal map and therefore angle-preserving. Such a map may be interpreted as preserving the shape of any sufficiently small figure, while possibly rotating and scaling (but not reflecting) it. Henri Poincaré proved that the map ''f'' is essentially unique: if ''z''0 is an element of ''U'' and φ is an arbitrary angle, then there exists precis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Midsphere
In geometry, the midsphere or intersphere of a polyhedron In geometry, a polyhedron (plural polyhedra or polyhedrons; ) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices. A convex polyhedron is the convex hull of finitely many points, not all on ... is a sphere which is tangent to every Edge (geometry), edge of the polyhedron. That is to say, it touches any given edge at exactly one point. Not every polyhedron has a midsphere, but for every convex polyhedron there is a combinatorially equivalent polyhedron, the canonical polyhedron, that does have a midsphere. The radius of the midsphere is called the midradius. Examples The uniform polyhedron, uniform polyhedra, including the regular polyhedron, regular, Quasiregular polyhedron, quasiregular and Semiregular polyhedron, semiregular polyhedra and their Dual polyhedron, duals all have midspheres. In the regular polyhedra, the inscribed sphere, midsphere, and circumscribe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kleinian Group
In mathematics, a Kleinian group is a discrete subgroup of the group (mathematics), group of orientation-preserving Isometry, isometries of hyperbolic 3-space . The latter, identifiable with PSL(2,C), , is the quotient group of the 2 by 2 complex number, complex matrix (mathematics), matrices of determinant 1 by their center (group theory), center, which consists of the identity matrix and its product by . has a natural representation as orientation-preserving conformal transformations of the Riemann sphere, and as orientation-preserving conformal transformations of the open unit ball in . The group of Möbius transformation, Möbius transformations is also related as the non-orientation-preserving isometry group of , . So, a Kleinian group can be regarded as a discrete subgroup group action, acting on one of these spaces. History The theory of general Kleinian groups was founded by and , who named them after Felix Klein. The special case of Schottky groups had been studied a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ludwig Bieberbach
Ludwig Georg Elias Moses Bieberbach (; 4 December 1886 – 1 September 1982) was a German mathematician and Nazi. 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'' (german: Theorie der automorphen Funktionen). 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 work on dynamics in several complex variables, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Koebe Quarter Theorem
In complex analysis, a branch of mathematics, the Koebe 1/4 theorem states the following: Koebe Quarter Theorem. The image of an injective analytic function f:\mathbf\to\mathbb from the unit disk \mathbf onto a subset of the complex plane contains the disk whose center is f(0) and whose radius is , f'(0), /4. The theorem is named after Paul Koebe, who conjectured the result in 1907. The theorem was proven by Ludwig Bieberbach in 1916. The example of the Koebe function shows that the constant 1/4 in the theorem cannot be improved (increased). A related result is the Schwarz lemma, and a notion related to both is conformal radius. Grönwall's area theorem Suppose that :g(z) = z +b_1z^ + b_2 z^ + \cdots is univalent in , z, >1. Then :\sum_ n, b_n, ^2 \le 1. In fact, if r > 1, the complement of the image of the disk , z, >r is a bounded domain X(r). Its area is given by : \int_ dx\,dy = \int_\overline\,dz = \int_\overline\,dg=\pi r^2 - \pi\sum n, b_n, ^2 r^. Since the area i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ordinary Professor
Academic ranks in Germany are the titles, relative importance and power of professors, researchers, and administrative personnel held in academia. Overview Appointment grades * (Pay grade: ''W3'' or ''W2'') * (''W3'') * (''W2'') * (''W2'', only in ''Baden-Württemberg'') – although paid like a professor appointed at level W2, lecturers in this position do not have a professor title; the term was formerly used in all states for senior lecturer positions with research and teaching responsibilities (''C2'', being phased out since 2002) * (not tenured, only rarely with tenure track) (''W1'') * (not tenured) (''W1'', only in ''Baden-Württemberg'') * or (''A13'', ''A14'', ''A15'') * (''TVöD 13/14/15'', ''TvL 13/14/15'') * (''TVöD'', ''TvL'' ''A13 a. Z.'') * (''TVöD'', only in ''Baden-Württemberg'') * (''TdL'') * (''TdL'') Non-appointment grades * * – conferred, in some German states, to a ''Privatdozent'' who has been in service for several years, without forma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extraordinary Professor
Academic ranks in Germany are the titles, relative importance and power of professors, researchers, and administrative personnel held in academia. Overview Appointment grades * (Pay grade: ''W3'' or ''W2'') * (''W3'') * (''W2'') * (''W2'', only in ''Baden-Württemberg'') – although paid like a professor appointed at level W2, lecturers in this position do not have a professor title; the term was formerly used in all states for senior lecturer positions with research and teaching responsibilities (''C2'', being phased out since 2002) * (not tenured, only rarely with tenure track) (''W1'') * (not tenured) (''W1'', only in ''Baden-Württemberg'') * or (''A13'', ''A14'', ''A15'') * (''TVöD 13/14/15'', ''TvL 13/14/15'') * (''TVöD'', ''TvL'' ''A13 a. Z.'') * (''TVöD'', only in ''Baden-Württemberg'') * (''TdL'') * (''TdL'') Non-appointment grades * * – conferred, in some German states, to a ''Privatdozent'' who has been in service for several years, without forma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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