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Jan Jaworowski
Jan W. Jaworowski (March 2, 1928 in Augustów, Poland – April 10, 2013 in Bloomington, Indiana) was a Polish and American mathematician, topologist. Biography His father was Jan Leonard Jaworowski, and his mother—Helena (maiden name Heybowicz). Jaworowski graduated with a master's degree from the mathematics department of the University of Warsaw. He got his Ph.D. from the Polish Academy of Sciences in 1955, in Algebraic topology, under Karol Borsuk. He generalized the Borsuk–Ulam theorem about antipodes. He taught at University of Warsaw, University of Ljubljana, and for years at The Indiana University Bloomington. He published 64 papers during his 57-years official career (and another 12 after his retirement in 1995). He was a promoter of at least 11 doctoral theses. He was a member of the Institute for Advanced Study The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jerse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Augustów
Augustów is a town in north-eastern Poland. It lies on the Netta River and the Augustów Canal. It is the seat of Augustów County and of Gmina Augustów in the Podlaskie Voivodeship. Augustów has an area of , and as of June 2022 it has a population of 29,305. In 1970, Augustów became officially recognized as a health and relaxation (psychology), relaxation resort. In 1973, surrounding settlements were named a part of it, forming a popular resort town. History A settlement in the area was first mentioned in 1496. Augustów was established around 1540 by Bona Sforza and granted Magdeburg rights in 1557 by Sigismund II Augustus, after whom it was also named. It was laid out in a very regular manner, with a spacious market-place. Until 1569 Augustów belonged to the Grand Duchy of Lithuania. In 1569 it became part of the Crown of the Kingdom of Poland, while its cemetery was left in the Grand Duchy, both countries formed the Polish–Lithuanian Commonwealth as a result of the U ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Antipodal Point
In mathematics, two points of a sphere (or n-sphere, including a circle) are called antipodal or diametrically opposite if they are the endpoints of a diameter, a straight line segment between two points on a sphere and passing through its center. Given any point on a sphere, its antipodal point is the unique point at greatest distance, whether measured intrinsically (great-circle distance on the surface of the sphere) or extrinsically ( chordal distance through the sphere's interior). Every great circle on a sphere passing through a point also passes through its antipodal point, and there are infinitely many great circles passing through a pair of antipodal points (unlike the situation for any non-antipodal pair of points, which have a unique great circle passing through both). Many results in spherical geometry depend on choosing non-antipodal points, and degenerate if antipodal points are allowed; for example, a spherical triangle degenerates to an underspecified lune if t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1928 Births
Events January * January – British bacteriologist Frederick Griffith reports the results of Griffith's experiment, indirectly demonstrating that DNA is the genetic material. * January 1 – Eastern Bloc emigration and defection: Boris Bazhanov, Joseph Stalin's personal secretary, crosses the border to Iran to defect from the Soviet Union. * January 17 – The OGPU arrests Leon Trotsky in Moscow; he assumes a status of passive resistance and is exiled with his family. * January 26 – The volcanic island Anak Krakatau appears. February * February – The Ford River Rouge Complex at Dearborn, Michigan, an automobile plant begun in 1917, is completed as the world's largest integrated factory. * February 8 – Scottish-born inventor John Logie Baird broadcasts a transatlantic television signal from London to Hartsdale, New York. * February 11 – February 19, 19 – The 1928 Winter Olympics are held in St. Moritz, Switzerland, the first as a separate event. Sonja Henie of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transformation Groups
In mathematics, the automorphism group of an object ''X'' is the group consisting of automorphisms of ''X'' under composition of morphisms. For example, if ''X'' is a finite-dimensional vector space, then the automorphism group of ''X'' is the group of invertible linear transformations from ''X'' to itself (the general linear group of ''X''). If instead ''X'' is a group, then its automorphism group \operatorname(X) is the group consisting of all group automorphisms of ''X''. Especially in geometric contexts, an automorphism group is also called a symmetry group. A subgroup of an automorphism group is sometimes called a transformation group. Automorphism groups are studied in a general way in the field of category theory. Examples If ''X'' is a set with no additional structure, then any bijection from ''X'' to itself is an automorphism, and hence the automorphism group of ''X'' in this case is precisely the symmetric group of ''X''. If the set ''X'' has additional structure, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Institute For Advanced Study
The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Einstein, J. Robert Oppenheimer, Emmy Noether, Hermann Weyl, John von Neumann, Michael Walzer, Clifford Geertz and Kurt Gödel, many of whom had emigrated from Europe to the United States. It was founded in 1930 by American educator Abraham Flexner, together with philanthropists Louis Bamberger and Caroline Bamberger Fuld. Despite collaborative ties and neighboring geographic location, the institute, being independent, has "no formal links" with Princeton University. The institute does not charge tuition or fees. Flexner's guiding principle in founding the institute was the pursuit of knowledge for its own sake.Jogalekar. The faculty have no classes to teach. There are no degree programs or experimental facilities at the institute. Research ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indiana University Bloomington
Indiana University Bloomington (IU Bloomington, Indiana University, IU, IUB, or Indiana) is a public university, public research university in Bloomington, Indiana, United States. It is the flagship university, flagship campus of Indiana University and its largest campus, with over 48,000 students. Established as the state's seminary in 1820, the name was changed to "Indiana College" in 1829 and to "Indiana University" in 1838. Indiana University is a member of the Association of American Universities and is Carnegie Classification of Institutions of Higher Education, classified among "R1: Doctoral Universities – Very high research activity". Its schools and programs include the Jacobs School of Music, Kelley School of Business, Indiana University School of Education, School of Education, Indiana University School of Informatics, Luddy School of Informatics, O'Neill School of Public and Environmental Affairs, Indiana University School of Public Health-Bloomington, School of Pu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Ljubljana
The University of Ljubljana (, , ), abbreviated UL, is the oldest and largest university in Slovenia. It has approximately 38,000 enrolled students. The university has 23 faculties and three art academies with approximately 4,000 teaching and research staff, assisted by approximately 2,000 technical and administrative staff. The University of Ljubljana offers programs in the humanities, sciences, and technology, as well as in medicine, dentistry, and veterinary science. The university was founded in the centre of Ljubljana, where the central university building and the majority of its faculties are located. Since then, newer buildings have been constructed in the suburbs of the city. History Beginnings Although certain academies (notably of philosophy and theology) were established as Jesuit higher education in what is now Slovenia as early as the seventeenth century, the first university was founded in 1810 under the ''Écoles centrales'' of the First French Empire, French impe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Borsuk–Ulam Theorem
In mathematics, the Borsuk–Ulam theorem states that every continuous function from an ''n''-sphere into Euclidean ''n''-space maps some pair of antipodal points to the same point. Here, two points on a sphere are called antipodal if they are in exactly opposite directions from the sphere's center. Formally: if f: S^n \to \R^n is continuous then there exists an x\in S^n such that: f(-x)=f(x). The case n=1 can be illustrated by saying that there always exist a pair of opposite points on the Earth's equator with the same temperature. The same is true for any circle. This assumes the temperature varies continuously in space, which is, however, not always the case. The case n=2 is often illustrated by saying that at any moment, there is always a pair of antipodal points on the Earth's surface with equal temperatures and equal barometric pressures, assuming that both parameters vary continuously in space. The Borsuk–Ulam theorem has several equivalent statements in terms o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poland
Poland, officially the Republic of Poland, is a country in Central Europe. It extends from the Baltic Sea in the north to the Sudetes and Carpathian Mountains in the south, bordered by Lithuania and Russia to the northeast, Belarus and Ukraine to the east, Slovakia and the Czech Republic to the south, and Germany to the west. The territory has a varied landscape, diverse ecosystems, and a temperate climate. Poland is composed of Voivodeships of Poland, sixteen voivodeships and is the fifth most populous member state of the European Union (EU), with over 38 million people, and the List of European countries by area, fifth largest EU country by area, covering . The capital and List of cities and towns in Poland, largest city is Warsaw; other major cities include Kraków, Wrocław, Łódź, Poznań, and Gdańsk. Prehistory and protohistory of Poland, Prehistoric human activity on Polish soil dates to the Lower Paleolithic, with continuous settlement since the end of the Last Gla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
