|
Cohn-Vossen
Stefan Cohn-Vossen (28 May 1902 – 25 June 1936) was a mathematician, who was responsible for Cohn-Vossen's inequality and the Cohn-Vossen transformation is also named for him. He proved the first version of the splitting theorem. He was also known for his collaboration with David Hilbert on the 1932 book ''Anschauliche Geometrie'', translated into English as '' Geometry and the Imagination''. He was born in Breslau (then a city in the Kingdom of Prussia; now Wrocław in Poland). He wrote a 1924 doctoral dissertation at the University of Breslau (now the University of Wrocław) under the supervision of Adolf Kneser. He became a professor at the University of Cologne in 1930. He was barred from lecturing in 1933 under Nazi racial legislation, because he was Jewish.. In 1934 he emigrated to the USSR, with some help from Herman Müntz. While there, he taught at Leningrad University. He died in Moscow from pneumonia. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cohn-Vossen Transformation
Stefan Cohn-Vossen (28 May 1902 – 25 June 1936) was a mathematician, who was responsible for Cohn-Vossen's inequality and the Cohn-Vossen transformation is also named for him. He proved the first version of the splitting theorem. He was also known for his collaboration with David Hilbert on the 1932 book ''Anschauliche Geometrie'', translated into English as '' Geometry and the Imagination''. He was born in Breslau (then a city in the Kingdom of Prussia; now Wrocław in Poland). He wrote a 1924 doctoral dissertation at the University of Breslau (now the University of Wrocław) under the supervision of Adolf Kneser. He became a professor at the University of Cologne in 1930. He was barred from lecturing in 1933 under Nazi racial legislation, because he was Jewish.. In 1934 he emigrated to the USSR, with some help from Herman Müntz. While there, he taught at Leningrad University. He died in Moscow from pneumonia. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cohn-Vossen's Inequality
In differential geometry, Cohn-Vossen's inequality, named after Stefan Cohn-Vossen, relates the integral of Gaussian curvature of a non-compact surface (differential geometry), surface to the Euler characteristic. It is akin to the Gauss–Bonnet theorem for a compact space, compact surface. A divergent path within a Riemannian manifold is a smooth curve in the manifold that is not contained within any compact space, compact subset of the manifold. A complete manifold is one in which every divergent path has infinite arc length, length with respect to the Riemannian metric on the manifold. Cohn-Vossen's inequality states that in every complete Riemannian 2-manifold ''S'' with finite total curvature and finite Euler characteristic, we haveRobert Osserman, ''A Survey of Minimal Surfaces'', Courier Dover Publications, 2002, page 86. : \iint_S K \, dA \le 2\pi\chi(S), where ''K'' is the Gaussian curvature, ''dA'' is the element of area, and ''χ'' is the Euler characteristic. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Splitting Theorem
In the mathematical field of differential geometry, there are various splitting theorems on when a pseudo-Riemannian manifold can be given as a metric product. The best-known is the Cheeger–Gromoll splitting theorem for Riemannian manifolds, although there has also been research into splitting of Lorentzian manifolds. Cheeger and Gromoll's Riemannian splitting theorem Any connected Riemannian manifold has an underlying metric space structure, and this allows the definition of a ''geodesic line'' as a map such that the distance from to equals for arbitrary and . This is to say that the restriction of to any bounded interval is a curve of minimal length which connects its endpoints. In 1971, Jeff Cheeger and Detlef Gromoll proved that, if a geodesically complete and connected Riemannian manifold of nonnegative Ricci curvature contains any geodesic line, then it must split isometrically as the product of a complete Riemannian manifold with . The proof was later simplified by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry And The Imagination
''Geometry and the Imagination'' is the English translation of the 1932 book by David Hilbert and Stefan Cohn-Vossen. The book was based on a series of lectures Hilbert made in the winter of 1920–21. The book is an attempt to present some then-current mathematical thought to "contribute to a more just appreciation of mathematics by a wider range of people than just the specialists." It differentiates between two tendencies in mathematics and any other scientific research: on the one hand, toward abstraction and logical relations, correlating the subject matter in a systematic and orderly manner, and on the other hand an intuitive approach, which moves toward a more immediate grasp of and a "live rapport" with the same material. Further he asserts that intuitive understanding actually plays a major role for the researcher as well as anyone who wishes to study and appreciate Geometry. Contents Topics covered by the chapters in the book include the Leibniz formula for , c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Herman Müntz
250px (Chaim) Herman Müntz (28 August 1884, in Łódź – 17 April 1956, in Sweden) was a German mathematician, now remembered for the Müntz approximation theorem. Biography He was born in Łódź (then in the Piotrków Governorate of the Russian Empire, now in Poland) in a secular Jewish family, who had adopted a German spelling of the surname ''Minc''. He was educated there and at the Friedrich-Wilhelms-Universität in Berlin, graduating in 1906. He wrote a doctoral dissertation there on partial differential equations and the Plateau problem, in 1910, supervised by H. A. Schwarz. In 1911 he moved to Munich. In the following years he published on projective geometry, iterative methods, and approximation theory. In 1914 he took a teaching position in a school near Heppenheim, and a year later another in Hochwaldhausen. He became a German citizen in 1919. At around that time he suffered a breakdown, and moved back to Poland with his wife. He shortly began publishing mat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David Hilbert
David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician, one of the most influential mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory, the calculus of variations, commutative algebra, algebraic number theory, the foundations of geometry, spectral theory of operators and its application to integral equations, mathematical physics, and the foundations of mathematics (particularly proof theory). Hilbert adopted and defended Georg Cantor's set theory and transfinite numbers. In 1900, he presented a collection of problems that set the course for much of the mathematical research of the 20th century. Hilbert and his students contributed significantly to establishing rigor and developed important tools used in modern mathematical physics. Hilbert is known as one of the founders of proof theory and mathematical logic. Life Early life and edu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Wrocław
, ''Schlesische Friedrich-Wilhelms-Universität zu Breslau'' (before 1945) , free_label = Specialty programs , free = , colors = Blue , website uni.wroc.pl The University of Wrocław ( pl, Uniwersytet Wrocławski, UWr; la, Universitas Wratislaviensis) is a public university, public research university in Wrocław, Poland. It is the largest institution of higher learning in Lower Silesian Voivodeship, with over 100,000 graduates since 1945, including some 1,900 researchers, among whom many have received the highest awards for their contributions to the development of scientific scholarship. Renowned for its high quality of teaching, it was placed 44th by ''QS World University Rankings'': EECA 2016, and is situated on the same campus as the former University of Breslau, which produced 9 Nobel Prize winners. The university was founded in 1945, replacing the previous German University of Breslau. Following the territorial changes of Poland immediately a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adolf Kneser
Adolf Kneser (19 March 1862 – 24 January 1930) was a German mathematician. He was born in Grüssow, Mecklenburg, Germany and died in Breslau, Germany (now Wrocław, Poland). He is the father of the mathematician Hellmuth Kneser and the grandfather of the mathematician Martin Kneser. Kneser is known for the first proof of the four-vertex theorem that applied in general to non-convex curves. Kneser's theorem on differential equations is named after him, and provides criteria to decide whether a differential equation is oscillating. He is also one of the namesakes of the Tait–Kneser theorem on osculating circle In differential geometry of curves, the osculating circle of a sufficiently smooth plane curve at a given point ''p'' on the curve has been traditionally defined as the circle passing through ''p'' and a pair of additional points on the curve i ...s. Selected publications * *; *; * * References External links * * 1862 births 1930 deaths 19th-century ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Göttinger Digitalisierungszentrum
The Center for Retrospective Digitization in Göttingen (german: Göttinger DigitalisierungsZentrum, GDZ) is an online system for archiving academic journals maintained by the University of Göttingen The University of Göttingen, officially the Georg August University of Göttingen, (german: Georg-August-Universität Göttingen, known informally as Georgia Augusta) is a public research university in the city of Göttingen, Germany. Founded .... See also * JSTOR * List of retrodigitized Mathematics Journals and Monograph References External linksOfficial website (German only) German digital libraries Academic publishing Göttingen {{database-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Law For The Restoration Of The Professional Civil Service
The Law for the Restoration of the Professional Hitler Service (german: Gesetz zur Wiederherstellung des Berufsbeamtentums, shortened to ''Berufsbeamtengesetz''), also known as Civil Service Law, Civil Service Restoration Act, and Law to Re-establish the Civil Service, was a law passed by the Nazi regime of Germany on 7 April 1933, two months after Adolf Hitler had attained power and two weeks after the promulgation of the Enabling Act. It was one of the first anti-Semitic and racist laws to be passed in Germany. Articles of the law Article 1 of the Law claimed that in order to re-establish a "national" and "professional" civil service, members of certain groups of tenured civil servants were to be dismissed. Civil servants who were not of Aryan descent were to retire. Non-Aryans were defined as someone descended from non-Aryans, especially those descended from Jewish parents, or grandparents. Members of the Communist Party, or any related or associated organisation were to be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Encyclopedia Of Mathematics
The ''Encyclopedia of Mathematics'' (also ''EOM'' and formerly ''Encyclopaedia of Mathematics'') is a large reference work in mathematics. Overview The 2002 version contains more than 8,000 entries covering most areas of mathematics at a graduate level, and the presentation is technical in nature. The encyclopedia is edited by Michiel Hazewinkel and was published by Kluwer Academic Publishers until 2003, when Kluwer became part of Springer. The CD-ROM contains animations and three-dimensional objects. The encyclopedia has been translated from the Soviet ''Matematicheskaya entsiklopediya'' (1977) originally edited by Ivan Matveevich Vinogradov and extended with comments and three supplements adding several thousand articles. Until November 29, 2011, a static version of the encyclopedia could be browsed online free of charge online. This URL now redirects to the new wiki incarnation of the EOM. ''Encyclopedia of Mathematics'' wiki A new dynamic version of the encyclopedia is now ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1902 Births
Nineteen or 19 may refer to: * 19 (number), the natural number following 18 and preceding 20 * one of the years 19 BC, AD 19, 1919, 2019 Films * ''19'' (film), a 2001 Japanese film * ''Nineteen'' (film), a 1987 science fiction film Music * 19 (band), a Japanese pop music duo Albums * ''19'' (Adele album), 2008 * ''19'', a 2003 album by Alsou * ''19'', a 2006 album by Evan Yo * ''19'', a 2018 album by MHD * ''19'', one half of the double album ''63/19'' by Kool A.D. * ''Number Nineteen'', a 1971 album by American jazz pianist Mal Waldron * ''XIX'' (EP), a 2019 EP by 1the9 Songs * "19" (song), a 1985 song by British musician Paul Hardcastle. * "Nineteen", a song by Bad4Good from the 1992 album '' Refugee'' * "Nineteen", a song by Karma to Burn from the 2001 album ''Almost Heathen''. * "Nineteen" (song), a 2007 song by American singer Billy Ray Cyrus. * "Nineteen", a song by Tegan and Sara from the 2007 album '' The Con''. * "XIX" (song), a 2014 song by Slipkn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
