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Feodor Deahna
Heinrich Wilhelm Feodor Deahna (8 July 1815 – 8 January 1844) was a German mathematician.. He is known for providing proof of what is now known as Frobenius theorem in differential topology, which he published in Crelle's Journal in 1840.. Deahna was born near Bayreuth on July 8, 1815, and was a student at the University of Göttingen in 1834. In 1843 he became an assistant mathematics teacher at the Fulda Fulda () (historically in English called Fuld) is a city in Hesse, Germany; it is located on the river Fulda and is the administrative seat of the Fulda district (''Kreis''). In 1990, the city hosted the 30th Hessentag state festival. Histor ... Gymnasium, but he died soon afterwards in Fulda, on January 8, 1844. Selected works * Deahna, F. "Über die Bedingungen der Integrabilitat ....", ''J. Reine Angew. Math.'' 20 (1840) 340-350. References 1815 births 1844 deaths 19th-century German mathematicians Differential geometers Mathematicians from the Kingdom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Allgemeine Deutsche Biographie
(ADB; ) is one of the most important and comprehensive biographical reference works in the German language. It was published by the Historical Commission of the Bavarian Academy of Sciences between 1875 and 1912 in 56 volumes, printed in Leipzig by Duncker & Humblot. The ADB contains biographies of about 26,500 people who died before 1900 and lived in the German language Sprachraum of their time, including people from the Netherlands before 1648. Its successor, the , was started in 1953 and is planned to be finished in 2023. The index and full-text articles of ADB and NDB are freely available online via the website ''German Biography'' ('' Deutsche Biographie''). Notes References * * External links * ''Allgemeine Deutsche Biographie'' – full-text articles at German Wikisource Wikisource is an online wiki-based digital library of free-content source text, textual sources operated by the Wikimedia Foundation. Wikisource is the name of the project as a whole; it i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frobenius Theorem (differential Topology)
In mathematics, Frobenius' theorem gives necessary and sufficient conditions for finding a maximal set of independent solutions of an overdetermined system of first-order homogeneous linear partial differential equations. In modern differential geometry, geometric terms, given a family of vector fields, the theorem gives necessary and sufficient integrability conditions for the existence of a foliation by maximal integral manifolds whose tangent bundles are spanned by the given vector fields. The theorem generalizes the Picard–Lindelöf theorem, existence theorem for ordinary differential equations, which guarantees that a single vector field always gives rise to integral curves; Frobenius gives compatibility conditions under which the integral curves of ''r'' vector fields mesh into coordinate grids on ''r''-dimensional integral manifolds. The theorem is foundational in differential topology and Differentiable manifold, calculus on manifolds. Contact geometry studies 1-forms ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Topology
In mathematics, differential topology is the field dealing with the topological properties and smooth properties of smooth manifolds. In this sense differential topology is distinct from the closely related field of differential geometry, which concerns the ''geometric'' properties of smooth manifolds, including notions of size, distance, and rigid shape. By comparison differential topology is concerned with coarser properties, such as the number of holes in a manifold, its homotopy type, or the structure of its diffeomorphism group. Because many of these coarser properties may be captured algebraically, differential topology has strong links to algebraic topology. The central goal of the field of differential topology is the classification of all smooth manifolds up to diffeomorphism. Since dimension is an invariant of smooth manifolds up to diffeomorphism type, this classification is often studied by classifying the ( connected) manifolds in each dimension separately: * In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crelle's Journal
''Crelle's Journal'', or just ''Crelle'', is the common name for a mathematics journal, the ''Journal für die reine und angewandte Mathematik'' (in English: ''Journal for Pure and Applied Mathematics''). History The journal was founded by August Leopold Crelle (Berlin) in 1826 and edited by him until his death in 1855. It was one of the first major mathematical journals that was not a proceedings of an academy. It has published many notable papers, including works of Niels Henrik Abel, Georg Cantor, Gotthold Eisenstein, Carl Friedrich Gauss and Otto Hesse. It was edited by Carl Wilhelm Borchardt from 1856 to 1880, during which time it was known as ''Borchardt's Journal''. The current editor-in-chief is Daniel Huybrechts ( Rheinische Friedrich-Wilhelms-Universität Bonn). Past editors * 1826–1856: August Leopold Crelle * 1856–1880: Carl Wilhelm Borchardt * 1881–1888: Leopold Kronecker Leopold Kronecker (; 7 December 1823 – 29 December 1891) was a Germa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayreuth
Bayreuth ( or ; High Franconian German, Upper Franconian: Bareid, ) is a Town#Germany, town in northern Bavaria, Germany, on the Red Main river in a valley between the Franconian Jura and the Fichtel Mountains. The town's roots date back to 1194. In the 21st century, it is the capital of Upper Franconia and has a population of 72,148 (2015). It hosts the annual Bayreuth Festival, at which performances of operas by the 19th-century German composer Richard Wagner are presented. History Middle Ages and Early Modern Period The town is believed to have been founded by the counts of County of Andechs, Andechs probably around the mid-12th century,Mayer, Bernd and Rückel, Gert (2009). ''Bayreuth – Tours on Foot'', Heinrichs-Verlag, Bamberg, p.5, . but was first mentioned in 1194 as ''Baierrute'' in a document by Bishop Otto VI of Andechs, Otto II of Bishopric of Bamberg, Bamberg. The syllable ''-rute'' may mean ''Rodung'' or "clearing", whilst ''Baier-'' indicates immigrants from ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Göttingen
The University of Göttingen, officially the Georg August University of Göttingen (, commonly referred to as Georgia Augusta), is a Public university, public research university in the city of Göttingen, Lower Saxony, Germany. Founded in 1734 by George II of Great Britain, George II, King of Great Britain and Electorate of Hanover, Elector of Hanover, it began instruction in 1737 and is recognized as the oldest university in Lower Saxony. Recognized for its historic and traditional significance, the university has affiliations with 47 Nobel Prize winners by its own count. Previously backed by the German Universities Excellence Initiative, the University of Göttingen is a member of the U15 (German Universities), U15 Group of major German research universities, underscoring its strong research profile. It is also a part of prominent international and European academic networks such as Guild of European Research-Intensive Universities, The Guild, the ENLIGHT alliance, and the Hek ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fulda
Fulda () (historically in English called Fuld) is a city in Hesse, Germany; it is located on the river Fulda and is the administrative seat of the Fulda district (''Kreis''). In 1990, the city hosted the 30th Hessentag state festival. History Middle Ages In 744 Saint Sturm, a disciple of Saint Boniface, founded the Benedictine monastery of Fulda as one of Boniface's outposts in the reorganization of the church in Germany. The initial grant for the abbey was signed by Carloman, Mayor of the Palace in Austrasia (in office 741–47), the son of Charles Martel. The support of the Mayors of the Palace, and later of the early Pippinid and Carolingian rulers, was important to Boniface's success. Fulda also received support from many of the leading families of the Carolingian world. Sturm, whose tenure as abbot lasted from 747 until 779, was most likely related to the Agilolfing dukes of Bavaria. Fulda also received large and constant donations from the Etichonids, a lea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gymnasium (Germany)
''Gymnasium'' (; German plural: ''Gymnasien''), in the German education system, is the most advanced and highest of the three types of German secondary schools, the others being ''Hauptschule'' (lowest) and ''Realschule'' (middle). ''Gymnasium'' strongly emphasizes academic learning, comparable to the British grammar school system or with university preparatory school, prep schools in the United States. A student attending ''Gymnasium'' is called a ''Gymnasiast'' (German plural: ''Gymnasiasten''). In 2009/10 there were 3,094 gymnasia in Germany, with students (about 28 percent of all precollegiate students during that period), resulting in an average student number of 800 students per school.Federal Statistical office of Germany, Fachserie 11, Reihe 1: Allgemeinbildende Schulen – Schuljahr 2009/2010, Wiesbaden 2010 Gymnasia are generally public, state-funded schools, but a number of parochial and private gymnasia also exist. In 2009/10, 11.1 percent of gymnasium students ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1815 Births
Events January * January 2 – Lord Byron marries Anna Isabella Milbanke in Seaham, county of Durham, England. * January 3 – Austria, Britain, and Bourbon-restored France form a secret defensive alliance treaty against Prussia and Russia. * January 8 – Battle of New Orleans: American forces led by Andrew Jackson defeat British forces led by Sir Edward Pakenham. American forces suffer around 60 casualties and the British lose about 2,000 (the battle lasts for about 30 minutes). * January 13 – War of 1812: British troops capture Fort Peter in St. Marys, Georgia, the only battle of the war to take place in the state. * January 15 – War of 1812: Capture of USS ''President'' – American frigate , commanded by Commodore Stephen Decatur, is captured by a squadron of four British frigates. February * February 3 – The first commercial cheese factory is founded in Switzerland. * February 4 – The first Dutch student association, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1844 Deaths
In the Philippines, 1844 had only 365 days, when Tuesday, December 31 was skipped as Monday, December 30 was immediately followed by Wednesday, January 1, 1845, the next day after. The change also applied to Caroline Islands, Guam, Marianas Islands, Marshall Islands and Palau as part of the Captaincy General of the Philippines; these became the first places on Earth to redraw the International Date Line. Events January–March * January 4 – The first issue of the Swedish-languaged ''Saima'' newspaper founded by J. V. Snellman is published in Kuopio, Finland. * January 15 – The University of Notre Dame, based in the city of the same name, receives its charter from Indiana. * February 27 – The Dominican Republic gains independence from Haiti. * February 28 – A gun on the USS ''Princeton'' explodes while the boat is on a Potomac River cruise, killing U.S. Secretary of State Abel Upshur, U.S. Secretary of the Navy Thomas Walker Gilmer and four other people. Pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
19th-century German Mathematicians
The 19th century began on 1 January 1801 (represented by the Roman numerals MDCCCI), and ended on 31 December 1900 (MCM). It was the 9th century of the 2nd millennium. It was characterized by vast social upheaval. Slavery was abolished in much of Europe and the Americas. The First Industrial Revolution, though it began in the late 18th century, expanded beyond its British homeland for the first time during the 19th century, particularly remaking the economies and societies of the Low Countries, France, the Rhineland, Northern Italy, and the Northeastern United States. A few decades later, the Second Industrial Revolution led to ever more massive urbanization and much higher levels of productivity, profit, and prosperity, a pattern that continued into the 20th century. The Catholic Church, in response to the growing influence and power of modernism, secularism and materialism, formed the First Vatican Council in the late 19th century to deal with such problems and confirm ce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Geometers
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of single variable calculus, vector calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Lobachevsky. The simplest examples of smooth spaces are the plane and space curves and surfaces in the three-dimensional Euclidean space, and the study of these shapes formed the basis for development of modern differential geometry during the 18th and 19th centuries. Since the late 19th century, differential geometry has grown into a field concerned more generally with geometric structures on differentiable manifolds. A geometric structure is one which defines some notion of size, distance, shape, volume, or other rigidifying structu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
