Hellmut Kneser
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Hellmut Kneser
Hellmuth Kneser (16 April 1898 – 23 August 1973) was a Baltic German mathematician, who made notable contributions to group theory and topology. His most famous result may be his theorem on the existence of a prime decomposition for 3-manifolds. His proof originated the concept of normal surface, a fundamental cornerstone of the theory of 3-manifolds. He was born in Dorpat, Russian Empire (now Tartu, Estonia) and died in Tübingen, Germany. He was the son of the mathematician Adolf Kneser and the father of the mathematician Martin Kneser. He assisted Wilhelm Süss in the founding of the Mathematical Research Institute of Oberwolfach and served as the director of the institute from 1958 to 1959. He was an editor of Mathematische Zeitschrift, Archiv der Mathematik and Aequationes Mathematicae. Kneser formulated the problem of non-integer iteration of functions and proved the existence of the entire Abel function of the exponential; on the base of this Abel function ...
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Baltic German
Baltic Germans (german: Deutsch-Balten or , later ) were ethnic German inhabitants of the eastern shores of the Baltic Sea, in what today are Estonia and Latvia. Since their coerced resettlement in 1939, Baltic Germans have markedly declined as a geographically determined ethnic group. However, it is estimated that several thousand people with some form of (Baltic) German identity still reside in Latvia and Estonia. Since the Middle Ages, native German-speakers formed the majority of merchants and clergy, and the large majority of the local landowning nobility who effectively constituted a ruling class over indigenous Latvian and Estonian non-nobles. By the time a distinct Baltic German ethnic identity began emerging in the 19th century, the majority of self-identifying Baltic Germans were non-nobles belonging mostly to the urban and professional middle class. In the 12th and 13th centuries, Catholic German traders and crusaders (''see '') began settling in the eastern ...
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Dorpat
Tartu is the second largest city in Estonia after the Northern Europe, Northern Europe, European country's political and financial capital, Tallinn. Tartu has a population of 91,407 (as of 2021). It is southeast of Tallinn and 245 kilometres (152 miles) northeast of Riga, Latvia. Tartu lies on the Emajõgi river, which connects the two largest lakes in Estonia, Lake Võrtsjärv and Lake Peipus. From the 13th century until the end of the 19th century, Tartu was known in most of the world by variants of its historical name Dorpat. Tartu, the largest urban centre of southern Estonia, is often considered the "intellectual capital city" of the country, especially as it is home to the nation's oldest and most renowned university, the University of Tartu (founded in 1632). Tartu also houses the Supreme Court of Estonia, the Ministry of Education and Research (Estonia), Ministry of Education and Research, the Estonian National Museum, and the oldest Estonian-language theatre, Vane ...
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Abel Function
The Abel equation, named after Niels Henrik Abel, is a type of functional equation of the form :f(h(x)) = h(x + 1) or :\alpha(f(x)) = \alpha(x)+1. The forms are equivalent when is invertible. or control the iteration of . Equivalence The second equation can be written :\alpha^(\alpha(f(x))) = \alpha^(\alpha(x)+1)\, . Taking , the equation can be written ::f(\alpha^(y)) = \alpha^(y+1)\, . For a known function , a problem is to solve the functional equation for the function , possibly satisfying additional requirements, such as . The change of variables , for a real parameter , brings Abel's equation into the celebrated Schröder's equation, . The further change into Böttcher's equation, . The Abel equation is a special case of (and easily generalizes to) the translation equation, :\omega( \omega(x,u),v)=\omega(x,u+v) ~, e.g., for \omega(x,1) = f(x), :\omega(x,u) = \alpha^(\alpha(x)+u).     (Observe .) The Abel function further provides the canonical coordi ...
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Aequationes Mathematicae
''Aequationes Mathematicae'' is a mathematical journal. It is primarily devoted to functional equations, but also publishes papers in dynamical systems, combinatorics, and geometry. As well as publishing regular journal submissions on these topics, it also regularly reports on international symposia on functional equations and produces bibliographies on the subject. János Aczél founded the journal in 1968 at the University of Waterloo, in part because of the long publication delays of up to four years in other journals at the time of its founding. It is currently published by Springer Science+Business Media, with Zsolt Páles of the University of Debrecen as its editor in chief. János Aczél remains its honorary editor in chief. it was listed as a second-quartile mathematics journal by SCImago Journal Rank The SCImago Journal Rank (SJR) indicator is a measure of the prestige of scholarly journals that accounts for both the number of citations received by a journal and th ...
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Archiv Der Mathematik
'' Archiv der Mathematik'' is a peer-reviewed mathematics journal published by Springer, established in 1948. Abstracting and indexing The journal is abstracted and indexed in:
Springer. 2022
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Mathematische Zeitschrift
''Mathematische Zeitschrift'' (German for ''Mathematical Journal'') is a mathematical journal for pure and applied mathematics published by Springer Verlag. It was founded in 1918 and edited by Leon Lichtenstein together with Konrad Knopp, Erhard Schmidt, and Issai Schur. Past editors include Erich Kamke, Friedrich Karl Schmidt, Rolf Nevanlinna, Helmut Wielandt, and Olivier Debarre Olivier Debarre (born 1959) is a French mathematician who specializes in complex algebraic geometry.Debarr ...
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* * Mathematics journals Publications established in 1918 {{math ...
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Mathematical Research Institute Of Oberwolfach
The Oberwolfach Research Institute for Mathematics (german: Mathematisches Forschungsinstitut Oberwolfach) is a center for mathematical research in Oberwolfach, Germany. It was founded by mathematician Wilhelm Süss in 1944. It organizes weekly workshops on diverse topics where mathematicians and scientists from all over the world come to do collaborative research. The Institute is a member of the Leibniz Association, funded mainly by the German Federal Ministry of Education and Research and by the state of Baden-Württemberg. It also receives substantial funding from the ''Friends of Oberwolfach'' foundation, from the ''Oberwolfach Foundation'' and from numerous donors. History The Oberwolfach Research Institute for Mathematics (MFO) was founded as the ''Reich Institute of Mathematics'' (German: ''Reichsinstitut für Mathematik'') on 1 September 1944. It was one of several research institutes founded by the Nazis in order to further the German war effort, which at that ...
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Wilhelm Süss
Wilhelm Süss (7 March 1895 – 21 May 1958) was a German mathematician. He was founder and first director of the Oberwolfach Research Institute for Mathematics. Biography He was born in Frankfurt, Germany, and died in Freiburg im Breisgau, Germany. Süss earned a Ph.D. degree in 1922 from Goethe University Frankfurt, for a thesis written under the direction of Ludwig Bieberbach. In 1928 he took a lecturing position at the University of Greifswald, and in 1934 he became a Professor at the University of Freiburg. Wilhelm Süss was a member of the Nazi Party and the National Socialist German Lecturers League; he joined Stahlhelm to avoid being automatically enrolled in Sturmabteilung but later he, with all Stahlhelm members, became members of Sturmabteilung. The extent to which he worked with Nazis or only cooperated as little as possible is a matter of debate among historians. In 1936–1940, he was an editor of the journal ''Deutsche Mathematik ''Deutsche Mathematik'' (Ger ...
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Martin Kneser
Martin Kneser (21 January 1928 – 16 February 2004) was a German mathematician. His father Hellmuth Kneser and grandfather Adolf Kneser were also mathematicians. He obtained his PhD in 1950 from Humboldt University of Berlin with the dissertation: ''Über den Rand von Parallelkörpern''. His advisor was Erhard Schmidt. His name has been given to Kneser graphs which he studied in 1955. He also gave a simplified proof of the Fundamental theorem of algebra. Kneser was an Invited Speaker of the ICM in 1962 at Stockholm. His main publications were on quadratic forms and algebraic groups. See also * Approximation in algebraic groups * Betke–Kneser theorem * Kneser–Tits conjecture *Kneser's theorem (combinatorics) In the branch of mathematics known as additive combinatorics, Kneser's theorem can refer to one of several related theorems regarding the sizes of certain sumsets in abelian groups. These are named after Martin Kneser, who published them in 1953 ... * Kneser g ...
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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 ...
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Germany
Germany,, officially the Federal Republic of Germany, is a country in Central Europe. It is the second most populous country in Europe after Russia, and the most populous member state of the European Union. Germany is situated between the Baltic and North seas to the north, and the Alps to the south; it covers an area of , with a population of almost 84 million within its 16 constituent states. Germany borders Denmark to the north, Poland and the Czech Republic to the east, Austria and Switzerland to the south, and France, Luxembourg, Belgium, and the Netherlands to the west. The nation's capital and most populous city is Berlin and its financial centre is Frankfurt; the largest urban area is the Ruhr. Various Germanic tribes have inhabited the northern parts of modern Germany since classical antiquity. A region named Germania was documented before AD 100. In 962, the Kingdom of Germany formed the bulk of the Holy Roman Empire. During the 16th ce ...
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Tübingen
Tübingen (, , Swabian: ''Dibenga'') is a traditional university city in central Baden-Württemberg, Germany. It is situated south of the state capital, Stuttgart, and developed on both sides of the Neckar and Ammer rivers. about one in three of the 90,000 people living in Tübingen is a student. As of the 2018/2019 winter semester, 27,665 students attend the Eberhard Karls University of Tübingen. The city has the lowest median age in Germany, in part due to its status as a university city. As of December 31, 2015, the average age of a citizen of Tübingen is 39.1 years. The city is known for its veganism and environmentalism. Immediately north of the city lies the Schönbuch, a densely wooded nature park. The Swabian Alb mountains rise about (beeline Tübingen City to Roßberg - 869 m) to the southeast of Tübingen. The Ammer and Steinlach rivers are tributaries of the Neckar river, which flows in an easterly direction through the city, just south of the medieval old t ...
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