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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). He graduated (got master's degree) from the mathematical 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 and was a promoter of at least 11 doctoral theses. He was a member of the Institute for Advanced Study during the 1960/61. Jaworowski specialized in the 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Augustów
Augustów (; lt, Augustavas, formerly known in English as ''Augustovo'' or ''Augustowo'')" is a city in north-eastern Poland with 29,729 inhabitants as of December 2021. It lies on the Netta River and the Augustów Canal. It is situated in the Podlaskie Voivodeship (since 1999), having previously been in Suwałki Voivodeship (1975–1998). It is the seat of Augustów County and of Gmina Augustów. In 1970, Augustów became officially recognized as a health and 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, wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Antipodal Point
In mathematics, antipodal points of a sphere are those diametrically opposite to each other (the specific qualities of such a definition are that a line drawn from the one to the other passes through the center of the sphere so forms a true diameter). This term applies to opposite points on a circle or any n-sphere. An antipodal point is sometimes called an antipode, a back-formation from the Greek loan word ''antipodes'', meaning "opposite (the) feet", as the true word singular is ''antipus''. Theory In mathematics, the concept of ''antipodal points'' is generalized to spheres of any dimension: two points on the sphere are antipodal if they are opposite ''through the centre''; for example, taking the centre as origin, they are points with related vectors v and −v. On a circle, such points are also called diametrically opposite. In other words, each line through the centre intersects the sphere in two points, one for each ray out from the centre, and these two poi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1928 Births
Nineteen or 19 may refer to: * 19 (number), the natural number following 18 and preceding 20 * one of the years 19 BC, AD 19, 1919, 2019 Films * ''19'' (film), a 2001 Japanese film * ''Nineteen'' (film), a 1987 science fiction film Music * 19 (band), a Japanese pop music duo Albums * ''19'' (Adele album), 2008 * ''19'', a 2003 album by Alsou * ''19'', a 2006 album by Evan Yo * ''19'', a 2018 album by MHD * ''19'', one half of the double album '' 63/19'' by Kool A.D. * ''Number Nineteen'', a 1971 album by American jazz pianist Mal Waldron * ''XIX'' (EP), a 2019 EP by 1the9 Songs * "19" (song), a 1985 song by British musician Paul Hardcastle. * "Nineteen", a song by Bad4Good from the 1992 album '' Refugee'' * "Nineteen", a song by Karma to Burn from the 2001 album ''Almost Heathen''. * "Nineteen" (song), a 2007 song by American singer Billy Ray Cyrus. * "Nineteen", a song by Tegan and Sara from the 2007 album '' The Con''. * "XIX" (song), a 2014 song by Slipkno ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polish Mathematicians
Polish may refer to: * Anything from or related to Poland, a country in Europe * Polish language * Poles Poles,, ; singular masculine: ''Polak'', singular feminine: ''Polka'' or Polish people, are a West Slavic nation and ethnic group, who share a common history, culture, the Polish language and are identified with the country of Poland in C ..., people from Poland or of Polish descent * Polish chicken * Polish brothers (Mark Polish and Michael Polish, born 1970), American twin screenwriters Polish may refer to: * Polishing, the process of creating a smooth and shiny surface by rubbing or chemical action ** French polishing, polishing wood to a high gloss finish * Nail polish * Shoe polish * Polish (screenwriting), improving a script in smaller ways than in a rewrite See also * * * Polonaise (other) {{Disambiguation, surname Language and nationality disambiguation pages ... [...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 stru ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Institute For Advanced Study
The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholars, including J. Robert Oppenheimer, Albert Einstein, Hermann Weyl, John von Neumann, 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 is never contract ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indiana University Bloomington
Indiana University Bloomington (IU Bloomington, Indiana University, IU, or simply Indiana) is a public research university in Bloomington, Indiana. It is the flagship campus of Indiana University and, with over 40,000 students, its largest campus. Indiana University is a member of the Association of American Universities and is classified among "R1: Doctoral Universities – Very high research activity". It has numerous schools and programs, including the Jacobs School of Music, the Luddy School of Informatics, Computing, and Engineering, the O'Neill School of Public and Environmental Affairs, the Kelley School of Business, the School of Public Health, the School of Nursing, the School of Optometry, the Maurer School of Law, the School of Education, the Media School, and the Hamilton Lugar School of Global and International Studies. The university is home to an extensive student life program, with more than 750 student organizations on campus and with around 17 percent o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Ljubljana
The University of Ljubljana ( sl, Univerza v Ljubljani, , la, Universitas Labacensis), often referred to as UL, is the oldest and largest university in Slovenia. It has approximately 39,000 enrolled students. 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 French imperial administration of the Illyrian provinces. The chancellor of the university in Ljubljana during the French period was Joseph Walland (a.k.a. , 1763–1834), born in Upper Carniola. That university was disbanded in 1813, when Austria regained territorial control and reestablished the Imperial Royal Lyceum of Ljubljana as a higher-education institution. Quest for a national university During the second half of the 19th century, several political claims for the establishment of a Slovene-language ... [...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. 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 of odd functions. Recall that S^n is the ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poland
Poland, officially the Republic of Poland, is a country in Central Europe. It is divided into 16 administrative provinces called voivodeships, covering an area of . Poland has a population of over 38 million and is the fifth-most populous member state of the European Union. Warsaw is the nation's capital and largest metropolis. Other major cities include Kraków, Wrocław, Łódź, Poznań, Gdańsk, and Szczecin. Poland has a temperate transitional climate and its territory traverses the Central European Plain, extending from Baltic Sea in the north to Sudeten and Carpathian Mountains in the south. The longest Polish river is the Vistula, and Poland's highest point is Mount Rysy, situated in the Tatra mountain range of the Carpathians. The country is 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. It also shares maritime boundaries with Denmark a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
