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Nikolaus Hofreiter
Nikolaus Hofreiter (8 May 1904 – 23 January 1990) was an Austrian mathematician who worked mainly in number theory. Biography Hofreiter went to school in Linz and studied from 1923 in Vienna with Hans Hahn (mathematician), Hans Hahn, Wilhelm Wirtinger, Emil Müller at the Technische Universität Wien on descriptive geometry, and Philipp Furtwängler, with whom he obtained his doctorate in 1927 on the reduction theory of quadratic forms (''Eine neue Reduktionstheorie für definite quadratische Formen''). In 1928 he passed the Lehramtsprüfung examination and completed the probationary year as a teacher in Vienna, but then returned to the university (first as a scientific assistant at the TU Vienna) where in 1929 he was assistant to Furtwängler and then habilitated in 1933. He was even then an excellent teacher, and gave lectures not only in Vienna but also in Graz. His dissertation and habilitation thesis dealt with the reduction theory of quadratic forms, which Gauss, Charles H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charles Hermite
Charles Hermite () FRS FRSE MIAS (24 December 1822 – 14 January 1901) was a French mathematician who did research concerning number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra. Hermite polynomials, Hermite interpolation, Hermite normal form, Hermitian operators, and cubic Hermite splines are named in his honor. One of his students was Henri Poincaré. He was the first to prove that '' e'', the base of natural logarithms, is a transcendental number. His methods were used later by Ferdinand von Lindemann to prove that π is transcendental. Life Hermite was born in Dieuze, Moselle, on 24 December 1822, with a deformity in his right foot that would impair his gait throughout his life. He was the sixth of seven children of Ferdinand Hermite and his wife, Madeleine née Lallemand. Ferdinand worked in the drapery business of Madeleine's family while also pursuing a career as an artist. The drapery business relocate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Definite Integral
In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration. Along with differentiation, integration is a fundamental, essential operation of calculus,Integral calculus is a very well established mathematical discipline for which there are many sources. See and , for example. and serves as a tool to solve problems in mathematics and physics involving the area of an arbitrary shape, the length of a curve, and the volume of a solid, among others. The integrals enumerated here are those termed definite integrals, which can be interpreted as the signed area of the region in the plane that is bounded by the graph of a given function between two points in the real line. Conventionally, areas above the horizontal axis of the plane are positive while areas below are negative. Integrals also refer to the concept of an a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indefinite Integrals
In calculus, an antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral of a function is a differentiable function whose derivative is equal to the original function . This can be stated symbolically as . The process of solving for antiderivatives is called antidifferentiation (or indefinite integration), and its opposite operation is called ''differentiation'', which is the process of finding a derivative. Antiderivatives are often denoted by capital Roman letters such as and . Antiderivatives are related to definite integrals through the second fundamental theorem of calculus: the definite integral of a function over a closed interval where the function is Riemann integrable is equal to the difference between the values of an antiderivative evaluated at the endpoints of the interval. In physics, antiderivatives arise in the context of rectilinear motion (e.g., in explaining the relationship between position, velocity and accelera ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Josef Laub , a Japanese manufacturer of musical instruments
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Josef may refer to * Josef (given name) * Josef (surname) * ''Josef'' (film), a 2011 Croatian war film *Musik Josef Musik Josef is a Japanese manufacturer of musical instruments. It was founded by Yukio Nakamura, and is the only company in Japan specializing in producing oboe The oboe ( ) is a type of double reed woodwind instrument. Oboes are usually ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ernst Peschl
Ernst Ferdinand Peschl (1 September 1906 – 9 June 1986) was a German mathematician. Early life Ernst Peschl came from a family of brewery owners. He was born to Eduard Ferdinand Peschl and his wife, Ulla (née Adler) in 1906. Education and academic appointments After finishing secondary school in 1925 in Passau, Peschl started studying mathematics, physics, and astronomy in Munich. He received his doctorate in 1931 from the University of Munich under the supervision of Constantin Carathéodory with a dissertation titled ''Über die Krümmung von Niveaukurven bei der konformen Abbildung einfachzusammenhängender Gebiete auf das Innere eines Kreises; eine Verallgemeinerung eines Satzes von E. Study'' ("On the curvature of level curves of the conformal mapping of simply connected domains to the interior of a circle: A generalization of a theorem of Eduard Study"). This was followed by some years spent working as an assistant with Robert König in Jena and Heinrich Behnke ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bernhard Baule
Bernhard is both a given name and a surname. Notable people with the name include: Given name *Bernhard of Saxe-Weimar (1604–1639), Duke of Saxe-Weimar *Bernhard, Prince of Saxe-Meiningen (1901–1984), head of the House of Saxe-Meiningen 1946–1984 *Bernhard, Count of Bylandt (1905–1998), German nobleman, artist, and author * Prince Bernhard of Lippe-Biesterfeld (1911–2004), Prince Consort of Queen Juliana of the Netherlands *Bernhard, Hereditary Prince of Baden (born 1970), German prince *Bernhard Frank (1913–2011), German SS Commander * Bernhard Garside (born 1962), British diplomat * Bernhard Goetzke (1884–1964), German actor * Bernhard Grill (born 1961), one of the developers of MP3 technology *Bernhard Heiliger (1915–1995), German sculptor * Bernhard Langer (born 1957), German golfer *Bernhard Maier (born 1963), German celticist *Bernhard Raimann (born 1997), Austrian American football player *Bernhard Riemann (1826–1866), German mathematician *Bernhard Sieb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wolfgang Gröbner
Wolfgang Gröbner (11 February 1899 – 20 August 1980) was an Austrian mathematician. His name is best known for the Gröbner basis, used for computations in algebraic geometry. However, the theory of Gröbner bases for polynomial rings was developed by his student Bruno Buchberger in 1965, who named them for Gröbner. Gröbner is also known for the Alekseev-Gröbner formula, which is actually proven by him. Early life Gröbner was born in Gossensaß, which at that time was in part of the County of Tyrol of the Austro-Hungarian Empire and is now part of Italy. Gröbner first studied engineering at the University of Technology in Graz, Austria, but switched in 1929 to mathematics. Career He wrote his dissertation ''Ein Beitrag zum Problem der Minimalbasen'' in 1932 at the University of Vienna; his advisor was Phillip Furtwängler. After his promotion, he did further studies at the University of Göttingen under Emmy Noether, in what is now known as commutative algebra. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Braunschweig
Braunschweig () or Brunswick ( , from Low German ''Brunswiek'' , Braunschweig dialect: ''Bronswiek'') is a city in Lower Saxony, Germany, north of the Harz Mountains at the farthest navigable point of the river Oker, which connects it to the North Sea via the rivers Aller and Weser. In 2016, it had a population of 250,704. A powerful and influential centre of commerce in medieval Germany, Brunswick was a member of the Hanseatic League from the 13th until the 17th century. It was the capital city of three successive states: the Principality of Brunswick-Wolfenbüttel (1269–1432, 1754–1807, and 1813–1814), the Duchy of Brunswick (1814–1918), and the Free State of Brunswick (1918–1946). Today, Brunswick is the second-largest city in Lower Saxony and a major centre of scientific research and development. History Foundation and early history The date and circumstances of the town's foundation are unknown. Tradition maintains that Brunswick was created through the merge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Berlin
Berlin ( , ) is the capital and largest city of Germany by both area and population. Its 3.7 million inhabitants make it the European Union's most populous city, according to population within city limits. One of Germany's sixteen constituent states, Berlin is surrounded by the State of Brandenburg and contiguous with Potsdam, Brandenburg's capital. Berlin's urban area, which has a population of around 4.5 million, is the second most populous urban area in Germany after the Ruhr. The Berlin-Brandenburg capital region has around 6.2 million inhabitants and is Germany's third-largest metropolitan region after the Rhine-Ruhr and Rhine-Main regions. Berlin straddles the banks of the Spree, which flows into the Havel (a tributary of the Elbe) in the western borough of Spandau. Among the city's main topographical features are the many lakes in the western and southeastern boroughs formed by the Spree, Havel and Dahme, the largest of which is Lake Müggelsee. Due to its l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diophantine Approximation
In number theory, the study of Diophantine approximation deals with the approximation of real numbers by rational numbers. It is named after Diophantus of Alexandria. The first problem was to know how well a real number can be approximated by rational numbers. For this problem, a rational number ''a''/''b'' is a "good" approximation of a real number ''α'' if the absolute value of the difference between ''a''/''b'' and ''α'' may not decrease if ''a''/''b'' is replaced by another rational number with a smaller denominator. This problem was solved during the 18th century by means of continued fractions. Knowing the "best" approximations of a given number, the main problem of the field is to find sharp upper and lower bounds of the above difference, expressed as a function of the denominator. It appears that these bounds depend on the nature of the real numbers to be approximated: the lower bound for the approximation of a rational number by another rational number is larger than ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry Of Numbers
Geometry of numbers is the part of number theory which uses geometry for the study of algebraic numbers. Typically, a ring of algebraic integers is viewed as a lattice in \mathbb R^n, and the study of these lattices provides fundamental information on algebraic numbers. The geometry of numbers was initiated by . The geometry of numbers has a close relationship with other fields of mathematics, especially functional analysis and Diophantine approximation, the problem of finding rational numbers that approximate an irrational quantity. Minkowski's results Suppose that \Gamma is a lattice in n-dimensional Euclidean space \mathbb^n and K is a convex centrally symmetric body. Minkowski's theorem, sometimes called Minkowski's first theorem, states that if \operatorname (K)>2^n \operatorname(\mathbb^n/\Gamma), then K contains a nonzero vector in \Gamma. The successive minimum \lambda_k is defined to be the inf of the numbers \lambda such that \lambda K contains k linearly independ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
