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Jakob Nielsen (mathematician)
Jakob Nielsen (15 October 1890 in Mjels, Als (island), Als – 3 August 1959 in Helsingør) was a Danish mathematician known for his work on automorphisms of surface (mathematics), surfaces. He was born in the village Mjels on the island of Als Island, Als in North Schleswig, in modern-day Denmark. His mother died when he was 3, and in 1900 he went to live with his aunt and was enrolled in the Realgymnasium. In 1907 he was expelled for being a member of an illicit student club. Nevertheless, he matriculated at the University of Kiel in 1908. Nielsen completed his doctoral dissertation in 1913. Soon thereafter, he was drafted into the German Imperial Navy. He was assigned to coastal defense. In 1915 he was sent to Constantinople as a military adviser to the Ottoman Empire, Turkish Government. After the war, in the spring of 1919, Nielsen married Carola von Pieverling, a German medical doctor. In 1920 Nielsen took a position at the Technical University of Breslau. The next ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nielsen Theory
Nielsen theory is a branch of mathematical research with its origins in topological fixed-point theory. Its central ideas were developed by Danish mathematician Jakob Nielsen, and bear his name. The theory developed in the study of the so-called ''minimal number'' of a map ''f'' from a compact space to itself, denoted ''MF'' 'f'' This is defined as: :\mathit = \min \, where ''~'' indicates homotopy of mappings, and #Fix(''g'') indicates the number of fixed points of ''g''. The minimal number was very difficult to compute in Nielsen's time, and remains so today. Nielsen's approach is to group the fixed-point set into classes, which are judged "essential" or "nonessential" according to whether or not they can be "removed" by a homotopy. Nielsen's original formulation is equivalent to the following: We define an equivalence relation In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric, and transitive. The equipollence relation betwee ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jakob Nielsen (born 1991), Danish footballer
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Jacob or Jakob Nielsen may refer to: * Jacob Nielsen, Count of Halland (died c. 1309), great grandson of Valdemar II of Denmark * , Norway (1768-1822) * Jakob Nielsen (mathematician) (1890–1959), Danish mathematician known for work on automorphisms of surfaces * Jakob Nielsen (usability consultant) (born 1957), Danish web usability consultant * Jakob Axel Nielsen (born 1967), Danish lawyer and politician * Jakob Nielsen (actor) (1900-1978) * Jacob Nielsen (cyclist) (born 1978), Danish cyclist * Jakob Ahlmann Nielsen Jakob Ahlmann Nielsen (born 18 January 1991) is a retired Danish professional association football, footballer who played as a left-back and current scout at AaB Fodbold, AaB. He has played three matches for the Denmark national football team. Cl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Technical University Of Denmark
The Technical University of Denmark (), often simply referred to as DTU, is a polytechnic university and school of engineering. It was founded in 1829 at the initiative of Hans Christian Ørsted as Denmark's first polytechnic, and it is today ranked among Europe's leading engineering institutions. It is located in the town Kongens Lyngby, north of central Copenhagen, Denmark. Along with École Polytechnique in Paris, École Polytechnique Fédérale de Lausanne, Eindhoven University of Technology, Technical University of Munich and Technion – Israel Institute of Technology, DTU is a member of EuroTech Universities Alliance. History DTU was founded in 1829 as the "College of Advanced Technology" (Danish: Den Polytekniske Læreanstalt). The Physicist Hans Christian Ørsted, at that time a professor at the University of Copenhagen, was one of the driving forces behind this initiative. He was inspired by the École Polytechnique in Paris, France which Ørsted had visited as a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1890 Births
Events January * January 1 – The Kingdom of Italy establishes Eritrea as its colony in the Horn of Africa. * January 2 – Alice Sanger becomes the first female staffer in the White House. * January 11 – 1890 British Ultimatum: The United Kingdom demands Portugal withdraw its forces from the land between the Portuguese colonies of Portuguese Mozambique, Mozambique and Portuguese Angola, Angola (most of present-day Zimbabwe and Zambia). * January 15 – Ballet ''The Sleeping Beauty (ballet), The Sleeping Beauty'', with music by Pyotr Ilyich Tchaikovsky, Tchaikovsky, is premiered at the Mariinsky Theatre, Imperial Mariinsky Theatre in Saint Petersburg, St. Petersburg, Russia. * January 25 ** The United Mine Workers of America is founded. ** American journalist Nellie Bly completes her round-the-world journey in 72 days. February * February 5 – The worldwide insurance and financial service brand Allianz is founded in Berlin, Germany. * February 18 – The National Americ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nielsen Realization Problem
The Nielsen realization problem is a question asked by about whether finite subgroups of mapping class groups can act on surfaces, that was answered positively by . Statement Given an oriented surface, we can divide the group Diff(''S''), the group of diffeomorphisms of the surface to itself, into isotopy classes to get the mapping class group π0(Diff(''S'')). The conjecture asks whether a finite subgroup of the mapping class group of a surface can be realized as the isometry group of a hyperbolic metric on the surface. The mapping class group acts on Teichmüller space. An equivalent way of stating the question asks whether every finite subgroup of the mapping class group fixes some point of Teichmüller space. History asked whether finite subgroups of mapping class groups can act on surfaces. claimed to solve the Nielsen realization problem but his proof depended on trying to show that Teichmüller space (with the Teichmüller metric) is negatively curved. pointed out a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nielsen–Thurston Classification
In mathematics, Thurston's classification theorem characterizes homeomorphisms of a compact orientable surface. William Thurston's theorem completes the work initiated by . Given a homeomorphism ''f'' : ''S'' → ''S'', there is a map ''g'' isotopic to ''f'' such that at least one of the following holds: * ''g'' is periodic, i.e. some power of ''g'' is the identity; * ''g'' preserves some finite union of disjoint simple closed curves on ''S'' (in this case, ''g'' is called ''reducible''); or * ''g'' is pseudo-Anosov. The case where ''S'' is a torus (i.e., a surface whose genus is one) is handled separately (see torus bundle) and was known before Thurston's work. If the genus of ''S'' is two or greater, then ''S'' is naturally hyperbolic, and the tools of Teichmüller theory become useful. In what follows, we assume ''S'' has genus at least two, as this is the case Thurston considered. (Note, however, that the cases where ''S'' has boundary or is not orie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nielsen Transformation
In mathematics, especially in the area of modern algebra known as combinatorial group theory, Nielsen transformations are certain automorphisms of a free group which are a non-commutative analogue of row reduction and one of the main tools used in studying free groups . Given a finite basis of a free group F_n, the corresponding set of elementary Nielsen transformations forms a finite generating set of \mathrm(F_n). This system of generators is analogous to elementary matrices for GL_n(\Z) and Dehn twists for mapping class groups of closed surfaces. Nielsen transformations were introduced in to prove that every subgroup of a free group is free (the Nielsen–Schreier theorem). They are now used in a variety of mathematics, including computational group theory, k-theory, and knot theory. Definitions Free groups Let F_n be a finitely generated free group of rank n. An elementary Nielsen transformation maps an ordered basis _1,\ldots, x_n/math> to a new basis _1,\ldots,y ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fenchel–Nielsen Coordinates
In mathematics, Fenchel–Nielsen coordinates are coordinates for Teichmüller space introduced by Werner Fenchel and Jakob Nielsen. Definition Suppose that ''S'' is a compact Riemann surface of genus ''g'' > 1. The Fenchel–Nielsen coordinates depend on a choice of 6''g'' − 6 curves on ''S'', as follows. The Riemann surface ''S'' can be divided up into 2''g'' − 2 pairs of pants by cutting along 3''g'' − 3 disjoint simple closed curves. For each of these 3''g'' − 3 curves γ, choose an arc crossing it that ends in other boundary components of the pairs of pants with boundary containing γ. The Fenchel–Nielsen coordinates for a point of the Teichmüller space of ''S'' consist of 3''g'' − 3 positive real numbers called the lengths and 3''g'' − 3 real numbers called the twists. A point of Teichmüller space is represented by a hyperbolic metric on ''S''. The leng ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
UNESCO
The United Nations Educational, Scientific and Cultural Organization (UNESCO ) is a List of specialized agencies of the United Nations, specialized agency of the United Nations (UN) with the aim of promoting world peace and International security, security through international cooperation in education, arts, sciences and culture. It has 194 Member states of UNESCO, member states and 12 associate members, as well as partners in the Non-governmental organization, non-governmental, Intergovernmental organization, intergovernmental and private sector. Headquartered in Paris, France, UNESCO has 53 regional field offices and 199 National Commissions for UNESCO, national commissions. UNESCO was founded in 1945 as the successor to the League of Nations' International Committee on Intellectual Cooperation.English summary). UNESCO's founding mission, which was shaped by the events of World War II, is to advance peace, sustainable development and human rights by facilitating collaboratio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harald Bohr
Harald August Bohr (22 April 1887 – 22 January 1951) was a Danish mathematician and footballer. After receiving his doctorate in 1910, Bohr became an eminent mathematician, founding the field of almost periodic functions. His brother was the Nobel Prize-winning physicist Niels Bohr. He was on the Denmark national team for the 1908 Summer Olympics, where he won a silver medal. Biography Bohr was born in 1887 to Christian Bohr, a professor of physiology, from a Lutheran background, and Ellen Adler Bohr, a woman from a wealthy Jewish family of local renown. Harald had a close relationship with his elder brother, which ''The Times'' likened to that between Captain Cuttle and Captain Bunsby in Charles Dickens' '' Dombey and Son''. Mathematical career Like his father and brother before him, in 1904 Bohr enrolled at the University of Copenhagen, where he studied mathematics, obtaining his master's degree in 1909 and his doctorate a year later. Among his tutors were Hieronymus Geo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Copenhagen
The University of Copenhagen (, KU) is a public university, public research university in Copenhagen, Copenhagen, Denmark. Founded in 1479, the University of Copenhagen is the second-oldest university in Scandinavia, after Uppsala University. The University of Copenhagen consists of six different Faculty (division), faculties, with teaching taking place in its four distinct campuses, all situated in Copenhagen. The university operates 36 different departments and 122 separate research centres in Copenhagen, as well as a number of museums and botanical gardens in and outside the Danish capital. The University of Copenhagen also owns and operates multiple research stations around Denmark, with two additional ones located in Greenland. Additionally, University of Copenhagen Faculty of Health and Medical Sciences, The Faculty of Health and Medical Sciences and the public hospitals of the Capital Region of Denmark, Capital and Region Zealand, Zealand Region of Denmark constitute the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nazis
Nazism (), formally named National Socialism (NS; , ), is the far-right politics, far-right Totalitarianism, totalitarian socio-political ideology and practices associated with Adolf Hitler and the Nazi Party (NSDAP) in Germany. During Hitler's rise to power, it was frequently referred to as Hitler Fascism () and Hitlerism (). The term "neo-Nazism" is applied to other far-right groups with similar ideology, which formed after World War II, and after Nazi Germany collapsed. Nazism is a form of fascism, with disdain for liberal democracy and the parliamentary system. Its beliefs include support for dictatorship, fervent antisemitism, anti-communism, anti-Slavism, anti-Romani sentiment, scientific racism, white supremacy, Nordicism, social Darwinism, homophobia, ableism, and the use of eugenics. The ultranationalism of the Nazis originated in pan-Germanism and the ethno-nationalist ''Völkisch movement, Völkisch'' movement which had been a prominent aspect of German nationa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
