|
Wilhelm Blaschke
Wilhelm Johann Eugen Blaschke (13 September 1885 – 17 March 1962) was an Austrian mathematician working in the fields of differential and integral geometry. Education and career Blaschke was the son of mathematician Josef Blaschke, who taught geometry at the Landes Oberrealschule in Graz. After studying for two years at the Technische Hochschule in Graz, he went to the University of Vienna, and completed a doctorate in 1908 under the supervision of Wilhelm Wirtinger. His dissertation was ''Über eine besondere Art von Kurven vierter Klasse''. After completing his doctorate he spent several years visiting mathematicians at the major universities in Italy and Germany. He spent two years each in positions in Prague, Leipzig, Göttingen, and Tübingen until, in 1919, he took the professorship at the University of Hamburg that he would keep for the rest of his career. His students at Hamburg included Shiing-Shen Chern, Luis Santaló, and Emanuel Sperner. In 1933 Blaschke signed th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graz
Graz (; sl, Gradec) is the capital city of the Austrian state of Styria and second-largest city in Austria after Vienna. As of 1 January 2021, it had a population of 331,562 (294,236 of whom had principal-residence status). In 2018, the population of the Graz larger urban zone (LUZ) stood at 652,654, based on principal-residence status. Graz is known as a college and university city, with four colleges and four universities. Combined, the city is home to more than 60,000 students. Its historic centre ('' Altstadt'') is one of the best-preserved city centres in Central Europe. In 1999, the city's historic centre was added to the UNESCO list of World Heritage Sites and in 2010 the designation was expanded to include Eggenberg Palace (german: Schloss Eggenberg) on the western edge of the city. Graz was designated the Cultural Capital of Europe in 2003 and became a City of Culinary Delights in 2008. Etymology The name of the city, Graz, formerly spelled Gratz, most likely stems ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vow Of Allegiance Of The Professors Of The German Universities And High-Schools To Adolf Hitler And The National Socialistic State
Bekenntnis der Professoren an den Universitäten und Hochschulen zu Adolf Hitler und dem nationalsozialistischen Staat officially translated into English as the Vow of allegiance of the Professors of the German Universities and High-Schools to Adolf Hitler and the National Socialistic State was a document presented on 11 November 1933 at the Albert Hall in Leipzig. It had statements in German, English, Italian, and Spanish by selected German academics and included an appendix of signatories. The purge to remove academics and civil servants with Jewish ancestry began with a law being passed on 7 April 1933. This document was signed by those that remained in support of Nazi Germany. Martin Heidegger in his inaugural lecture in May 1933 as ''Rektor'', and who was later in October appointed "Führer of the university", said (translated): "The much celebrated "academic freedom" is being banished from the German university; for this freedom was not genuine, since it was only negative. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Blaschke Conjecture
In mathematics—specifically, in Riemannian geometry—a Wiedersehen pair is a pair of distinct points ''x'' and ''y'' on a (usually, but not necessarily, two-dimensional) compact Riemannian manifold (''M'', ''g'') such that every geodesic through ''x'' also passes through ''y'', and the same with ''x'' and ''y'' interchanged. For example, on an ordinary sphere where the geodesics are great circles, the Wiedersehen pairs are exactly the pairs of antipodal points. If every point of an oriented manifold (''M'', ''g'') belongs to a Wiedersehen pair, then (''M'', ''g'') is said to be a Wiedersehen manifold. The concept was introduced by the Austro-Hungarian mathematician Wilhelm Blaschke and comes from the German term meaning "seeing again". As it turns out, in each dimension ''n'' the only Wiedersehen manifold (up to isometry) is the standard Euclidean ''n''-sphere. Initially known as the Blaschke conjecture, this result was established by combined works ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hilbert%27s Fourth Problem
In mathematics, Hilbert's fourth problem in the 1900 list of Hilbert's problems is a foundational question in geometry. In one statement derived from the original, it was to find — up to an isomorphism — all geometries that have an axiomatic system of the classical geometry ( Euclidean, hyperbolic and elliptic), with those axioms of congruence that involve the concept of the angle dropped, and `triangle inequality', regarded as an axiom, added. If one assumes the continuity axiom in addition, then, in the case of the Euclidean plane, we come to the problem posed by Jean Gaston Darboux: "To determine all the calculus of variation problems in the plane whose solutions are all the plane straight lines." There are several interpretations of the original statement of David Hilbert. Nevertheless, a solution was sought, with the German mathematician Georg Hamel being the first to contribute to the solution of Hilbert's fourth problem. A recognized solution was given by Ukrainian m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Blaschke Condition
In complex analysis, the Blaschke product is a bounded analytic function in the open unit disc constructed to have zeros at a (finite or infinite) sequence of prescribed complex numbers :''a''0, ''a''1, ... inside the unit disc, with the property that the magnitude of the function is constant along the boundary of the disc. Blaschke products were introduced by . They are related to Hardy spaces. Definition A sequence of points (a_n) inside the unit disk is said to satisfy the Blaschke condition when :\sum_n (1-, a_n, ) <\infty. Given a sequence obeying the Blaschke condition, the Blaschke product is defined as : with factors : provided ''a'' ≠ 0. Here is the |
Blaschke Sum
In convex geometry and the geometry of convex polytopes, the Blaschke sum of two polytopes is a polytope that has a facet parallel to each facet of the two given polytopes, with the same measure. When both polytopes have parallel facets, the measure of the corresponding facet in the Blaschke sum is the sum of the measures from the two given polytopes. Blaschke sums exist and are unique up to translation, as can be proven using the theory of the Minkowski problem for polytopes. They can be used to decompose arbitrary polytopes into simplices, and centrally symmetric polytopes into parallelotopes. Although Blaschke sums of polytopes are used implicitly in the work of Hermann Minkowski, Blaschke sums are named for Wilhelm Blaschke, who defined a corresponding operation for smooth convex sets. The Blaschke sum operation can be extended to arbitrary convex bodies, generalizing both the polytope and smooth cases, using measures on the Gauss map. Definition For any d-dimensional pol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Blaschke–Lebesgue Theorem
In plane geometry the Blaschke–Lebesgue theorem states that the Reuleaux triangle has the least area of all curves of given constant width. In the form that every curve of a given width has area at least as large as the Reuleaux triangle, it is also known as the Blaschke–Lebesgue inequality. It is named after Wilhelm Blaschke and Henri Lebesgue, who published it separately in the early 20th century. Statement The width of a convex set K in the Euclidean plane is defined as the minimum distance between any two parallel lines that enclose it. The two minimum-distance lines are both necessarily tangent lines to K, on opposite sides. A curve of constant width is the boundary of a convex set with the property that, for every direction of parallel lines, the two tangent lines with that direction that are tangent to opposite sides of the curve are at a distance equal to the width. These curves include both the circle and the Reuleaux triangle, a curved triangle formed from arcs of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
VEB Deutscher Verlag Der Wissenschaften
(DVW) (English: ''German Publisher of Sciences'') was a scientific publishing house in the former German Democratic Republic (GDR/). Situated in Berlin, DVW was founded as (VEB) on 1 January 1954 as the successor of the main department of "university literature" of the publisher (VWV). During the first ten years, DVW, for the most part, published mathematical and scientific literature aimed at university education. About 780 titles were introduced with a total print run of some 3.7 million books. In 1964, DVW took over parts of the programme of and also published textbooks on topics of philosophy, history and sociology. DVW was among the publishers of the (MSB). Whilst more than a third of the production was distributed into Western foreign countries, the publisher still did not make a profit due to the fixed low book prices, politically motivated so called ' (PAOs) dictated by the East German government. In 1988, with a turnaround of 8.4 million East German mark, DVW los ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Credit (creative Arts)
In general, the term credit in the artistic or intellectual sense refers to an acknowledgment of those who contributed to a work, whether through ideas or in a more direct sense. Credit in the arts In the creative arts, credits are an acknowledgment of those who participated in the production. They are often shown at the end of movies and on CD jackets. In film, video, television, theater, etc., ''credits'' means the list of actors and behind-the-scenes staff who contributed to the production. Non-fiction In non-fiction writing, especially academic works, it is generally considered important to give credit to sources of information and ideas. Failure to do so often gives rise to charges of plagiarism, and "piracy" of intellectual rights such as the right to receive a royalty for having written. In this sense the financial and individual meanings are linked. Academic papers generally contain a lengthy section of footnotes or citations. Such detailed crediting of sources provides ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convex Set
In geometry, a subset of a Euclidean space, or more generally an affine space over the reals, is convex if, given any two points in the subset, the subset contains the whole line segment that joins them. Equivalently, a convex set or a convex region is a subset that intersects every line into a single line segment (possibly empty). For example, a solid cube is a convex set, but anything that is hollow or has an indent, for example, a crescent shape, is not convex. The boundary of a convex set is always a convex curve. The intersection of all the convex sets that contain a given subset of Euclidean space is called the convex hull of . It is the smallest convex set containing . A convex function is a real-valued function defined on an interval with the property that its epigraph (the set of points on or above the graph of the function) is a convex set. Convex minimization is a subfield of optimization that studies the problem of minimizing convex functions over convex se ... [...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] |
German Mathematical Society
The German Mathematical Society (german: Deutsche Mathematiker-Vereinigung, DMV) is the main professional society of German mathematicians and represents German mathematics within the European Mathematical Society (EMS) and the International Mathematical Union (IMU). It was founded in 1890 in Bremen with the set theorist Georg Cantor as first president. Founding members included Georg Cantor, Felix Klein, Walther von Dyck, David Hilbert, Hermann Minkowski, Carl Runge, Rudolf Sturm, Hermann Schubert, and Heinrich Weber. The current president of the DMV is Ilka Agricola (2021–2022). Activities In honour of its founding president, Georg Cantor, the society awards the Cantor Medal. The DMV publishes two scientific journals, the ''Jahresbericht der DMV'' and ''Documenta Mathematica''. It also publishes a quarterly magazine for its membership the ''Mitteilungen der DMV''. The annual meeting of the DMV is called the ''Jahrestagung''; the DMV traditionally meets every four y ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
