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https://en.wikipedia.org/wiki/Piopio%2C%20New%20Zealand
Piopio is a small town in the Waitomo District. It is situated on approximately 23 km from Te Kūiti. Demographics Statistics New Zealand describes Piopio as a rural settlement, which covers and had an estimated population of as of with a population density of people per km2. The settlement is part of the larger Aria statistical area. Piopio had a population of 465 at the 2018 New Zealand census, an increase of 69 people (17.4%) since the 2013 census, and a decrease of 3 people (−0.6%) since the 2006 census. There were 171 households, comprising 234 males and 234 females, giving a sex ratio of 1.0 males per female, with 120 people (25.8%) aged under 15 years, 93 (20.0%) aged 15 to 29, 177 (38.1%) aged 30 to 64, and 78 (16.8%) aged 65 or older. Ethnicities were 69.0% European/Pākehā, 49.0% Māori, 1.3% Pacific peoples, and 1.3% Asian. People may identify with more than one ethnicity. Although some people chose not to answer the census's question about religious affiliation, 56.8% had no religion, 23.9% were Christian, 5.2% had Māori religious beliefs, 1.3% were Buddhist and 2.6% had other religions. Of those at least 15 years old, 33 (9.6%) people had a bachelor's or higher degree, and 99 (28.7%) people had no formal qualifications. 30 people (8.7%) earned over $70,000 compared to 17.2% nationally. The employment status of those at least 15 was that 153 (44.3%) people were employed full-time, 72 (20.9%) were part-time, and 18 (5.2%) were unemployed. Marae There are marae in the area, affiliated with the hapū of Ngāti Maniapoto: Mōkau Kohunui Marae and Ko Tama Tāne meeting house are affiliated with Apakura, Ngāti Kinohaku and Waiora Napinapi Marae and Parekahoki meeting house are affiliated with Ngāti Matakore and Pare te Kawa Te Paemate Marae and meeting house are affiliated with Paemate Mangarama Mara and Rongorongo meeting house are affiliated with Apakura. Education Piopio College provides high school education for Year 7 to 13 students, with a roll of Piopio School provides primary education for new entrants and Year 1 to 6 students, with a roll of . Both schools are coeducational. Rolls are as of Notable people Hannah Osborne (born 1994), Olympic rower Merv Smith (1933–2018), broadcaster References External links Waitomo District Council Populated places in Waikato Waitomo District
https://en.wikipedia.org/wiki/Thomas%20Kempe%20%28footballer%29
Thomas Kempe (born 17 March 1960) is a German retired professional footballer who played as a defensive midfielder. His sons Dennis and Tobias are also professional footballers. Career statistics References External links 1960 births Living people German men's footballers Men's association football midfielders Germany men's B international footballers Germany men's under-21 international footballers MSV Duisburg players VfB Stuttgart players VfL Bochum players Bundesliga players German football managers Tauro F.C. managers 20th-century German people West German men's footballers People from Wesel (district) Footballers from Düsseldorf (region)
https://en.wikipedia.org/wiki/Walter%20Oswald
Walter Oswald (born 8 October 1955) is a German former professional footballer who played as a midfielder or defender. Career statistics References External links 1955 births Living people Footballers from Linz German men's footballers Men's association football defenders Men's association football midfielders FC Gütersloh players FC St. Pauli players VfL Bochum players VfL Bochum II players Bundesliga players 2. Bundesliga players West German men's footballers People from Gütersloh Footballers from Detmold (region) Austrian emigrants to Germany
https://en.wikipedia.org/wiki/Michael%20Rzehaczek
Michael Rzehaczek (born 17 January 1967) is a retired German football midfielder. He was forced to retire due to knee injuries. Career Statistics References External links 1967 births Living people People from Recklinghausen Footballers from Münster (region) German men's footballers VfL Bochum players VfL Bochum II players Bundesliga players Men's association football midfielders West German men's footballers
https://en.wikipedia.org/wiki/Uwe%20Leifeld
Uwe Leifeld (born 24 July 1966) is a retired German football forward, who works as a scout with VfL Bochum . Career Statistics References External links 1966 births Living people German men's footballers VfL Bochum players FC Schalke 04 players SC Preußen Münster players Bundesliga players Germany men's under-21 international footballers Footballers from Münster Men's association football forwards West German men's footballers
https://en.wikipedia.org/wiki/Josef%20Nehl
Josef "Jupp" Nehl (born 13 June 1961) is a German former professional footballer who played as a striker or midfielder. Career statistics References External links 1961 births Living people German men's footballers Footballers from Cologne Men's association football midfielders Bundesliga players VfL Bochum players Bayer 04 Leverkusen players FC Viktoria Köln players West German men's footballers
https://en.wikipedia.org/wiki/Dixmier%20trace
In mathematics, the Dixmier trace, introduced by , is a non-normal trace on a space of linear operators on a Hilbert space larger than the space of trace class operators. Dixmier traces are examples of singular traces. Some applications of Dixmier traces to noncommutative geometry are described in . Definition If H is a Hilbert space, then L1,∞(H) is the space of compact linear operators T on H such that the norm is finite, where the numbers μi(T) are the eigenvalues of |T| arranged in decreasing order. Let . The Dixmier trace Trω(T) of T is defined for positive operators T of L1,∞(H) to be where limω is a scale-invariant positive "extension" of the usual limit, to all bounded sequences. In other words, it has the following properties: limω(αn) ≥ 0 if all αn ≥ 0 (positivity) limω(αn) = lim(αn) whenever the ordinary limit exists limω(α1, α1, α2, α2, α3, ...) = limω(αn) (scale invariance) There are many such extensions (such as a Banach limit of α1, α2, α4, α8,...) so there are many different Dixmier traces. As the Dixmier trace is linear, it extends by linearity to all operators of L1,∞(H). If the Dixmier trace of an operator is independent of the choice of limω then the operator is called measurable. Properties Trω(T) is linear in T. If T ≥ 0 then Trω(T) ≥ 0 If S is bounded then Trω(ST) = Trω(TS) Trω(T) does not depend on the choice of inner product on H. Trω(T) = 0 for all trace class operators T, but there are compact operators for which it is equal to 1. A trace φ is called normal if φ(sup xα) = sup φ( xα) for every bounded increasing directed family of positive operators. Any normal trace on is equal to the usual trace, so the Dixmier trace is an example of a non-normal trace. Examples A compact self-adjoint operator with eigenvalues 1, 1/2, 1/3, ... has Dixmier trace equal to 1. If the eigenvalues μi of the positive operator T have the property that converges for Re(s)>1 and extends to a meromorphic function near s=1 with at most a simple pole at s=1, then the Dixmier trace of T is the residue at s=1 (and in particular is independent of the choice of ω). showed that Wodzicki's noncommutative residue of a pseudodifferential operator on a manifold M of order -dim(M) is equal to its Dixmier trace. References Albeverio, S.; Guido, D.; Ponosov, A.; Scarlatti, S.: Singular traces and compact operators. J. Funct. Anal. 137 (1996), no. 2, 281—302. See also Singular trace Von Neumann algebras Hilbert spaces Operator theory Trace theory
https://en.wikipedia.org/wiki/List%20of%20things%20named%20after%20Alfred%20Tarski
In the history of mathematics, Alfred Tarski (1901–1983) is one of the most important logicians. His name is now associated with a number of theorems and concepts in that field. Theorems Łoś–Tarski preservation theorem Knaster–Tarski theorem (sometimes referred to as Tarski's fixed point theorem) Tarski's undefinability theorem Tarski–Seidenberg theorem Some fixed point theorems, usually variants of the Kleene fixed-point theorem, are referred to the Tarski–Kantorovitch fixed–point principle or the Tarski–Kantorovitch theorem although the use of this terminology is limited. Tarski's theorem Other mathematics-related work Bernays-Tarski axiom system Banach–Tarski paradox Lindenbaum–Tarski algebra Łukasiewicz-Tarski logic Jónsson–Tarski duality Jónsson–Tarski algebra Gödel–McKinsey–Tarski translation The semantic theory of truth is sometimes referred to as Tarski's definition of truth or Tarski's truth definitions. Tarski's axiomatization of the reals Tarski's axioms for plane geometry Tarski's circle-squaring problem Tarski's exponential function problem Tarski–Grothendieck set theory Tarski's high school algebra problem Tarski–Kuratowski algorithm Tarski monster group Tarski's plank problem Tarski's problems for free groups Tarski–Vaught test Tarski's World Other 13672 Tarski, a main-belt asteroid Tarski
https://en.wikipedia.org/wiki/Uwe%20Fabig
Uwe Fabig (born 17 October 1961) was a professional ice hockey player. He captained the Krefeld Pinguine team in 1991. Career statistics References 1961 births Living people German ice hockey defencemen Kassel Huskies players Krefeld Pinguine players Sportspeople from Krefeld
https://en.wikipedia.org/wiki/Kenji%20Takahashi%20%28footballer%2C%20born%201985%29
is a former Japanese football player. Club statistics References External links 1985 births Living people Ritsumeikan University alumni Association football people from Osaka Prefecture People from Takatsuki, Osaka Japanese men's footballers J2 League players Tokushima Vortis players FC Osaka players Men's association football midfielders
https://en.wikipedia.org/wiki/Kazuma%20Irifune
is a former Japanese football player. Club statistics References External links 1986 births Living people Association football people from Miyazaki Prefecture Japanese men's footballers J1 League players J2 League players Sanfrecce Hiroshima players Tokushima Vortis players Men's association football defenders People from Miyazaki (city)
https://en.wikipedia.org/wiki/Taiji%20Furuta
is a former Japanese football player. Club statistics References External links 1982 births Living people Osaka University of Health and Sport Sciences alumni Association football people from Nara Prefecture Japanese men's footballers J2 League players Tokushima Vortis players Men's association football goalkeepers
https://en.wikipedia.org/wiki/William%20J.%20LeVeque
William Judson LeVeque (August 9, 1923 – December 1, 2007) was an American mathematician and administrator who worked primarily in number theory. He was executive director of the American Mathematical Society during the 1970s and 1980s when that organization was growing rapidly and greatly increasing its use of computers in academic publishing. Life and education LeVeque was born August 9, 1923, in Boulder, Colorado. He received his Bachelor of Arts degree from the University of Colorado in 1944, and a master's degree in 1945 and a Ph.D. in 1947 from Cornell University. He was an instructor at Harvard University from 1947 to 1949, then started at University of Michigan as an instructor and rose to professor. In 1970 he moved to the Claremont Graduate School. In 1977 he became executive director of the American Mathematical Society and remained there until his retirement in 1988. After retirement LeVeque and his wife, Ann, took up sailing and lived on their sailboat for three years while they traveled from Narragansett Bay to Grenada. They then moved to Bainbridge Island, Washington, where he kept active in volunteer activities for the rest of his life. He died December 1, 2007. His son Randall J. LeVeque is a well known applied mathematician. Work LeVeque's research interest was number theory, specifically transcendental numbers, uniform distribution, and Diophantine approximation. He wrote a number of number theory textbooks and reference books, which influenced the development of number theory in the United States. A long-term project was to update Leonard Eugene Dickson's History of the Theory of Numbers. This project eventually produced a six-volume collection titled Reviews in Number Theory. The Special Libraries Association's Physics-Astronomy-Mathematics Division awarded LeVeque its Division Award in 1978 for his contributions to the bibliography of mathematics. The American Mathematical Society grew rapidly during LeVeque's time as executive director (1977–1988). Revenues tripled from $5 million in 1977 to $14.9 million in 1988. The Society began computerizing at a rapid rate during this period, with Mathematical Reviews first becoming available electronically through existing academic dial-up services; this system later evolved into MathSciNet. Most of the headquarters staff received computer terminals for use in the new operations. Selected publications (6 volumes) Further reading A retrospective by LeVeque of his work at the American Mathematical Society. Notes External links 1923 births 2007 deaths 20th-century American mathematicians Cornell University alumni Harvard University Department of Mathematics faculty Harvard University faculty Number theorists University of Colorado alumni University of Michigan faculty
https://en.wikipedia.org/wiki/Koji%20Kataoka
is a former Japanese football player. He won the 1999 Bangabandhu Cup with the Japan Football League XI. Club statistics References External links 1977 births Living people Association football people from Fukuoka Prefecture Japanese men's footballers J2 League players Japan Football League (1992–1998) players Japan Football League players Tokushima Vortis players Men's association football midfielders
https://en.wikipedia.org/wiki/Kim%20Jeong-hyun%20%28footballer%2C%20born%201988%29
Kim Jeong-hyun (김정현; born May 16, 1988) is a South Korean football player who since 2007 has played for Incheon United. Club career statistics External links 1988 births Living people Men's association football forwards South Korean men's footballers Incheon United FC players K League 1 players
https://en.wikipedia.org/wiki/Asher%20Kravitz
Asher Kravitz (; born 1969), is an Israeli author and lecturer on physics and mathematics at the Academic College of Engineering in Jerusalem and at the Open University. He is a noted animal rights activist and wildlife photographer. Biography Kravitz was born in Jerusalem and raised in a traditional Jewish home. He studied electronics at Kiryat Noar, a vocational yeshiva high-school, and at the Djanogly High School in Jerusalem. His military service in the Israeli Army began in the Commando Brigade of Armored Corps. Toward the end of his service, he served as an instructor of Krav Maga. Kravitz completed his bachelor's degree in Physics at the Hebrew University and his master's degree at the Technion. While studying at the Technion, he joined the Israeli Police Force and served as an investigator in the National Unit for the Investigation of Serious Crimes. After leaving the Police Force, he taught two years at the High School of Arts and Sciences. Since the year 2000, Kravitz has been teaching courses in mathematics and physics at the Academic College of Engineering in Jerusalem and at the Open University of Israel. He also lectured on literature at the Hebrew University School for Overseas Students. Photography and documentation of wildlife Since 1997, Kravitz has worked intensively on documenting through photography wildlife both in Israel and in Africa. During the 2000s, a number of his articles on animal rights and wellbeing have been published. Kravitz documented his many excursions to Africa with extensive photography of its wildlife and also participated in an Israeli mission to set up a haven for orphaned gorillas in Cameroon. Books His first two books, Magic Square (G'vanim, 2002) and Boomerang (Keter, 2003) are humorous whodunits with plots built around complex criminal cases. His third book, I'm Mustafa Rabinowitz (Kibbutz M'uhad, 2005), is a story about a soldier fighting in an anti-terrorist unit in the Israeli army and the moral dilemmas that he faces. His fourth book, The Jewish Dog (Yediot Books, 2007), is the post mortem autobiography of Koresh, a dog born into the household of a German Jewish family during the pre-Holocaust period in Germany, and his lifelong travails. This last novel was awarded a "Diamond Citation" by the Book Publishers Association of Israel. References External links , website of The Institute for Translation of Hebrew Literature Asher Kravitz, The Lexicon of Modern Hebrew Literature The first chapter of I'm Mustafa Rabinowitz, website of Yediot Books 1969 births Living people Israeli animal rights activists Israeli humorists Israeli mathematicians Israeli novelists Israeli physicists Jewish physicists
https://en.wikipedia.org/wiki/Jayanta%20Kumar%20Ghosh
Jayanta Kumar Ghosh (Bengali: জয়ন্ত কুমার ঘোষ, 23 May 1937 – 30 September 2017) was an Indian statistician, an emeritus professor at Indian Statistical Institute and a professor of statistics at Purdue University. Education He obtained a B.S. from Presidency College, then affiliated with the University of Calcutta, and subsequently a M.A. and a Ph.D. from the University of Calcutta under the supervision of H. K. Nandi. He started his research career in the early 1960s, studying sequential analysis as a graduate student in the department of statistics at the University of Calcutta. Research Among his best-known discoveries are the Bahadur–Ghosh–Kiefer representation (with R. R. Bahadur and Jack Kiefer) and the Ghosh–Pratt identity along with John W. Pratt. His research contributions fall within the fields of: Bayesian inference Asymptotics Modeling and model selection High dimensional data analysis Nonparametric regression and density estimation Survival analysis Statistical genetics Awards and honors Elected member of the International Statistical Institute Advisory editor, Journal of Statistical Planning and Inference Fellow of the Institute of Mathematical Statistics Fellow of the Indian National Science Academy Life member and director of the Calcutta Statistical Association Fellow of the Indian Academy of Sciences Japanese Society for Promotion of Sciences Fellowship, 1978 Shanti Swarup Bhatnagar Prize for Science and Technology, 1981 President, Statistics Section of the Indian Science Congress Association, 1991 President, International Statistical Institute, 1993 Mahalanobis Gold Medal of Indian Science Congress Association, 1998 Invited speaker of the International Congress of Mathematicians, 1998 P. V. Sukhatme Prize for Statistics, 2000 Mahalanobis Memorial Lecture, State Science and Technology Congress, W. Bengal, 2003 D.Sc. (h.c.), B.C. Roy Agricultural University, W. Bengal, India, 2006 International Indian Statistical Association (IISA) Lifetime Achievement Award, 2010 Padma Shree (2014) by the Government of India Bibliography He has published over 50 research papers. He has also published four books, which are: Invariance in Testing and Estimation (Lecture Notes), 1967, published by Indian Statistical Institute, Calcutta. Higher Order Asymptotics (based on CBMS-NSF lecture), published jointly by Institute of Mathematical Statistics and American Statistical Association, 1994. (with R.V. Ramamoorthi) Bayesian Nonparametrics (Springer 2003). (with Mohan Delampady and Tapas Samanta) An Introduction to Bayesian Analysis - Theory and Methods, Springer 2006. References External links Indian Statistical Institute Statistics Department homepage Dr. Ghosh's profile at Purdue University Dr. Ghosh's webpage at the Statistics Department of Purdue University A biography of Dr. Ghosh written by Professor Anirban Dasgupta 1937 births 2017 deaths Scientists from Kolkata Indian statisticians Purdue University fa
https://en.wikipedia.org/wiki/Ji%C5%99%C3%AD%20Matou%C5%A1ek%20%28mathematician%29
Jiří (Jirka) Matoušek (10 March 1963 – 9 March 2015) was a Czech mathematician working in computational geometry and algebraic topology. He was a professor at Charles University in Prague and the author of several textbooks and research monographs. Biography Matoušek was born in Prague. In 1986, he received his Master's degree at Charles University under Miroslav Katětov. From 1986 until his death he was employed at the Department of Applied Mathematics of Charles University, holding a professor position since 2000. He was also a visiting and later full professor at ETH Zurich. In 1996, he won the European Mathematical Society prize and in 2000 he won the Scientist award of the Learned Society of the Czech Republic. In 1998 he was an Invited Speaker of the International Congress of Mathematicians in Berlin. He became a fellow of the Learned Society of the Czech Republic in 2005. Matoušek's paper on computational aspects of algebraic topology won the Best Paper award at the 2012 ACM Symposium on Discrete Algorithms. Aside from his own academic writing, he has translated the popularization book Mathematics: A Very Short Introduction by Timothy Gowers into Czech. He was a supporter and signatory of the Cost of Knowledge protest. Matoušek died in 2015, aged 51. In 2021, a lecture hall at the Faculty of Mathematics and Physics, Charles University, was named after him. Books Invitation to Discrete Mathematics (with Jaroslav Nešetřil). Oxford University Press, 1998. . Translated into French by Delphine Hachez as Introduction aux Mathématiques Discrètes, Springer-Verlag, 2004, . Geometric Discrepancy: An Illustrated Guide. Springer-Verlag, Algorithms and Combinatorics 18, 1999, . Lectures on Discrete Geometry. Springer-Verlag, Graduate Texts in Mathematics, 2002, . Using the Borsuk-Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry. Springer-Verlag, 2003. . Topics in Discrete Mathematics: Dedicated to Jarik Nešetřil on the Occasion of His 60th Birthday (with Martin Klazar, Jan Kratochvíl, Martin Loebl, Robin Thomas, and Pavel Valtr). Springer-Verlag, Algorithms and Combinatorics 26, 2006. . Understanding and Using Linear Programming (with B. Gärtner). Springer-Verlag, Universitext, 2007, . Thirty-three miniatures — Mathematical and algorithmic applications of linear algebra. American Mathematical Society, 2010, . Approximation Algorithms and Semidefinite Programming (with B. Gärtner). Springer Berlin Heidelberg, 2012, . Mathematics++: Selected Topics Beyond the Basic Courses (with Ida Kantor and Robert Šámal). American Mathematical Society, 2015, . See also Ham sandwich theorem Discrepancy theory Kneser graph References External links Jiri Matousek home page 1963 births 2015 deaths Mathematicians from Prague Charles University alumni Czech mathematicians Researchers in geometric algorithms Academic staff of Charles University Academic staff of ETH Zurich Combinatorialists Topologists
https://en.wikipedia.org/wiki/Kim%20Sang-rok
Kim Sang-Rok (born February 25, 1979) is a South Korean football player who currently plays for Bucheon FC 1995 in the K League. Club career statistics External links 1979 births Living people Men's association football midfielders South Korean men's footballers Pohang Steelers players Gimcheon Sangmu FC players Jeju United FC players Incheon United FC players Busan IPark players Ulsan Hyundai Mipo Dockyard FC players Bucheon FC 1995 players K League 1 players Korea National League players K League 2 players Korea University alumni
https://en.wikipedia.org/wiki/An%20Jae-jun
An Jae-jun (; born 8 February 1986) is a South Korean football centre-back, who plays for Army United. Club career statistics External links 1986 births Living people Men's association football defenders South Korean men's footballers Incheon United FC players Jeonnam Dragons players Asan Mugunghwa FC players Seongnam FC players Daejeon Hana Citizen players An Jae-jun K League 1 players K League 2 players
https://en.wikipedia.org/wiki/Kwon%20Chan-soo
Kwon Chan-Soo (born May 30, 1974) is a South Korean former football player. His previous club is K-League side Seongnam Ilhwa Chunma and Incheon United. Club career statistics External links 1974 births Living people Men's association football goalkeepers South Korean men's footballers Seongnam FC players Incheon United FC players K League 1 players Dankook University alumni
https://en.wikipedia.org/wiki/Lee%20Sang-don%20%28footballer%29
Lee Sang-don (born August 12, 1985) is a South Korean football player who currently plays for Goyang Hi FC. His younger brother Lee Sang-ho is also a footballer. Career statistics References 1985 births Living people South Korean men's footballers Suwon Samsung Bluewings players Ulsan Hyundai FC players Gangwon FC players Goyang Zaicro FC players K League 1 players K League 2 players Men's association football midfielders
https://en.wikipedia.org/wiki/Al-Sahel
Al-Sahel (, also transliterated As-Sahel and As-Sehel) is a Syrian village in the An-Nabek District of the Rif Dimashq Governorate. According to the Syria Central Bureau of Statistics (CBS), al-Sahel had a population of 5,677 in the 2004 census. Its inhabitants are predominantly Sunni Muslims. Nearby cities and towns Weather References Bibliography External links Al-Sahel Page Al-Sahel Site Populated places in An-Nabek District
https://en.wikipedia.org/wiki/Lee%20Jin-ho
Lee Jin-Ho (; born 3 September 1984) is a former South Korean football player. Club career statistics Honours Club Ulsan Hyundai K-League: 2005 References 1984 births Living people Footballers from Ulsan Men's association football forwards South Korean men's footballers Ulsan Hyundai FC players Pohang Steelers players Gimcheon Sangmu FC players Daegu FC players Jeju United FC players Gwangju FC players Lee Jin-ho Korea National League players K League 1 players K League 2 players Expatriate men's footballers in Thailand South Korean expatriate men's footballers South Korean expatriate sportspeople in Thailand 21st-century South Korean people
https://en.wikipedia.org/wiki/Dietrich%20Barfurth
Karl Dietrich Gerhard Barfurth (25 January 1849 – 23 March 1927) was a German anatomist and embryologist born in Dinslaken. He studied mathematics and sciences at the University of Göttingen, and medicine (1879–1882) at the University of Bonn. In 1882 he earned his medical doctorate, and in 1883 received his habilitation in anatomy. In 1888 he worked as prosector under Friedrich Sigmund Merkel (1845–1919) in Göttingen. From 1889 to 1896 he was a professor of anatomy, embryology and histology at the University of Dorpat, and afterwards was professor of anatomy at the University of Rostock and director of the institute of anatomy. Barfurth is remembered for regeneration research of body parts (tissues, limbs, organs, etc.) in animals at the embryonic, larval and adult stages of life. He was the author of the following works on regeneration: Regeneration und Transplantation (1917) Methoden zur Erforschung der Regeneration bei Tieren (Methods for the Study of Regeneration in Animals) (1920) References Catalogus Professorum Rostochiensium (biography) A History of Regeneration Research by Charles E. Dinsmore 1849 births 1927 deaths German embryologists German anatomists People from Wesel (district) Academic staff of the University of Rostock Academic staff of the University of Tartu 20th-century German zoologists 19th-century German zoologists Members of the Göttingen Academy of Sciences and Humanities
https://en.wikipedia.org/wiki/Kaplansky%27s%20theorem%20on%20quadratic%20forms
In mathematics, Kaplansky's theorem on quadratic forms is a result on simultaneous representation of primes by quadratic forms. It was proved in 2003 by Irving Kaplansky. Statement of the theorem Kaplansky's theorem states that a prime p congruent to 1 modulo 16 is representable by both or none of x2 + 32y2 and x2 + 64y2, whereas a prime p congruent to 9 modulo 16 is representable by exactly one of these quadratic forms. This is remarkable since the primes represented by each of these forms individually are not describable by congruence conditions. Proof Kaplansky's proof uses the facts that 2 is a 4th power modulo p if and only if p is representable by x2 + 64y2, and that −4 is an 8th power modulo p if and only if p is representable by x2 + 32y2. Examples The prime p = 17 is congruent to 1 modulo 16 and is representable by neither x2 + 32y2 nor x2 + 64y2. The prime p = 113 is congruent to 1 modulo 16 and is representable by both x2 + 32y2 and x2+64y2 (since 113 = 92 + 32×12 and 113 = 72 + 64×12). The prime p = 41 is congruent to 9 modulo 16 and is representable by x2 + 32y2 (since 41 = 32 + 32×12), but not by x2 + 64y2. The prime p = 73 is congruent to 9 modulo 16 and is representable by x2 + 64y2 (since 73 = 32 + 64×12), but not by x2 + 32y2. Similar results Five results similar to Kaplansky's theorem are known: A prime p congruent to 1 modulo 20 is representable by both or none of x2 + 20y2 and x2 + 100y2, whereas a prime p congruent to 9 modulo 20 is representable by exactly one of these quadratic forms. A prime p congruent to 1, 16 or 22 modulo 39 is representable by both or none of x2 + xy + 10y2 and x2 + xy + 127y2, whereas a prime p congruent to 4, 10 or 25 modulo 39 is representable by exactly one of these quadratic forms. A prime p congruent to 1, 16, 26, 31 or 36 modulo 55 is representable by both or none of x2 + xy + 14y2 and x2 + xy + 69y2, whereas a prime p congruent to 4, 9, 14, 34 or 49 modulo 55 is representable by exactly one of these quadratic forms. A prime p congruent to 1, 65 or 81 modulo 112 is representable by both or none of x2 + 14y2 and x2 + 448y2, whereas a prime p congruent to 9, 25 or 57 modulo 112 is representable by exactly one of these quadratic forms. A prime p congruent to 1 or 169 modulo 240 is representable by both or none of x2 + 150y2 and x2 + 960y2, whereas a prime p congruent to 49 or 121 modulo 240 is representable by exactly one of these quadratic forms. It is conjectured that there are no other similar results involving definite forms. Notes Theorems in number theory Quadratic forms
https://en.wikipedia.org/wiki/Yuki%20Ishida
is a former Japanese football player. Club statistics References External links 1980 births Living people Seisa Dohto University alumni Association football people from Sapporo Japanese men's footballers J2 League players Japan Football League players Shonan Bellmare players Tokushima Vortis players Matsumoto Yamaga FC players Fujieda MYFC players Men's association football forwards
https://en.wikipedia.org/wiki/Kazuyuki%20Mugita
is a former Japanese football player. Club statistics References External links 1984 births Living people Osaka University of Health and Sport Sciences alumni Association football people from Ishikawa Prefecture Japanese men's footballers J2 League players Tokushima Vortis players Men's association football midfielders
https://en.wikipedia.org/wiki/Satoshi%20Koizumi
is a former Japanese football player. Club statistics References External links 1985 births Living people National Institute of Fitness and Sports in Kanoya alumni Association football people from Tokyo Metropolis People from Akishima, Tokyo Japanese men's footballers J2 League players Tokushima Vortis players Men's association football midfielders
https://en.wikipedia.org/wiki/Kota%20Sugawara
is a Japanese football player who played for Kochi United SC of the Shikoku Soccer League, scoring 49 goals in 3 seasons. Club statistics Updated to 20 February 2016. References External links 1985 births Living people Kokushikan University alumni Association football people from Hokkaido Japanese men's footballers J2 League players Japan Football League players Tokushima Vortis players Iwate Grulla Morioka players Reilac Shiga FC players Zweigen Kanazawa players FC Osaka players Kochi United SC players Men's association football forwards People from Muroran, Hokkaido
https://en.wikipedia.org/wiki/Ryosuke%20Sasagaki
is a former Japanese football player. His brother is Takuya Sasagaki. Club statistics References External links 1985 births Living people Osaka Gakuin University alumni Association football people from Shizuoka Prefecture Japanese men's footballers J2 League players Ehime FC players Men's association football forwards
https://en.wikipedia.org/wiki/Yoichi%20Kamimaru
is a former Japanese football player. Club statistics References External links 1984 births Living people Chukyo University alumni Association football people from Aichi Prefecture Japanese men's footballers J2 League players Ehime FC players Men's association football midfielders
https://en.wikipedia.org/wiki/Manabu%20Wakabayashi
is a Japanese football player. He plays for Tochigi Uva FC. Club statistics References External links 1979 births Living people Association football people from Tochigi Prefecture Japanese men's footballers J1 League players J2 League players Japan Football League players Tochigi City FC players Tochigi SC players Omiya Ardija players Ehime FC players Men's association football forwards
https://en.wikipedia.org/wiki/Eigo%20Sekine
is a former Japanese football player. Club statistics References External links 1981 births Living people Association football people from Saitama Prefecture Japanese men's footballers J2 League players Japan Football League players Ehime FC players Men's association football defenders
https://en.wikipedia.org/wiki/Shuichi%20Akai%20%28footballer%29
is a former Japanese football player. he currently assistant manager J3 League club of Ehime FC Club statistics Updated to 23 February 2016. References External links 1981 births Living people Sendai University alumni Japanese men's footballers J2 League players Japan Football League players Ehime FC players Men's association football midfielders Association football people from Sapporo
https://en.wikipedia.org/wiki/Alistair%20Sinclair
Alistair Sinclair (born 1960) is a British computer scientist and computational theorist. Sinclair received his B.A. in mathematics from St. John’s College, Cambridge in 1979, and his Ph.D. in computer science from the University of Edinburgh in 1988 under the supervision of Mark Jerrum. He is professor at the Computer Science division at the University of California, Berkeley and has held faculty positions at University of Edinburgh and visiting positions at DIMACS and the International Computer Science Institute in Berkeley. Sinclair’s research interests include the design and analysis of randomized algorithms, computational applications of stochastic processes and nonlinear dynamical systems, Monte Carlo methods in statistical physics and combinatorial optimization. With his advisor Mark Jerrum, Sinclair investigated the mixing behaviour of Markov chains to construct approximation algorithms for counting problems such as the computing the permanent, with applications in diverse fields such as matching algorithms, geometric algorithms, mathematical programming, statistics, physics-inspired applications and dynamical systems. This work has been highly influential in theoretical computer science and was recognised with the Gödel Prize in 1996. A refinement of these methods led to a fully polynomial time randomised approximation algorithm for computing the permanent, for which Sinclair and his co-authors received the Fulkerson Prize in 2006. Sinclair's initial forms part of the name of the GNRS conjecture on metric embeddings of minor-closed graph families. References British computer scientists Theoretical computer scientists Gödel Prize laureates Alumni of the University of Edinburgh Living people UC Berkeley College of Engineering faculty 1960 births Alumni of St John's College, Cambridge
https://en.wikipedia.org/wiki/Shinsaku%20Mochidome
is a former Japanese football player. Club statistics References External links 1988 births Living people Association football people from Osaka Prefecture Japanese men's footballers J2 League players Japan Football League players Ehime FC players V-Varen Nagasaki players Kamatamare Sanuki players SP Kyoto FC players Men's association football defenders
https://en.wikipedia.org/wiki/Ryota%20Takasugi
is a Japanese football player currently playing for Tochigi SC. Club career statistics Updated to 28 February 2020. 1Includes Promotion Playoffs to J1. References External links 1984 births Living people Meiji University alumni Association football people from Yamaguchi Prefecture Japanese men's footballers J1 League players J2 League players FC Machida Zelvia players Ehime FC players V-Varen Nagasaki players Tochigi SC players Men's association football midfielders
https://en.wikipedia.org/wiki/Thomas%20Stratos
Thomas Stratos (born 9 October 1966) is a German-Greek football coach and a former player. Career statistics As of 25 October 2022 References 1966 births Living people German men's footballers Bundesliga players 2. Bundesliga players Arminia Bielefeld players Hamburger SV players 1. FC Saarbrücken players FC Gütersloh players German football managers FC Gütersloh managers SSV Jahn Regensburg managers Berliner FC Dynamo managers 3. Liga managers Men's association football defenders Men's association football midfielders German people of Greek descent German expatriate sportspeople in Saudi Arabia German expatriate sportspeople in Greece
https://en.wikipedia.org/wiki/Vector%20space%20model
Vector space model or term vector model is an algebraic model for representing text documents (and any objects, in general) as vectors of identifiers (such as index terms). It is used in information filtering, information retrieval, indexing and relevancy rankings. Its first use was in the SMART Information Retrieval System. Definitions Documents and queries are represented as vectors. Each dimension corresponds to a separate term. If a term occurs in the document, its value in the vector is non-zero. Several different ways of computing these values, also known as (term) weights, have been developed. One of the best known schemes is tf-idf weighting (see the example below). The definition of term depends on the application. Typically terms are single words, keywords, or longer phrases. If words are chosen to be the terms, the dimensionality of the vector is the number of words in the vocabulary (the number of distinct words occurring in the corpus). Vector operations can be used to compare documents with queries. Applications Relevance rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as a vector with same dimension as the vectors that represent the other documents. In practice, it is easier to calculate the cosine of the angle between the vectors, instead of the angle itself: Where is the intersection (i.e. the dot product) of the document (d2 in the figure to the right) and the query (q in the figure) vectors, is the norm of vector d2, and is the norm of vector q. The norm of a vector is calculated as such: Using the cosine the similarity between document dj and query q can be calculated as: As all vectors under consideration by this model are element-wise nonnegative, a cosine value of zero means that the query and document vector are orthogonal and have no match (i.e. the query term does not exist in the document being considered). See cosine similarity for further information. Term frequency-inverse document frequency weights In the classic vector space model proposed by Salton, Wong and Yang the term-specific weights in the document vectors are products of local and global parameters. The model is known as term frequency-inverse document frequency model. The weight vector for document d is , where and is term frequency of term t in document d (a local parameter) is inverse document frequency (a global parameter). is the total number of documents in the document set; is the number of documents containing the term t. Advantages The vector space model has the following advantages over the Standard Boolean model: Simple model based on linear algebra Term weights not binary Allows computing a continuous degree of similarity between queries and documents Allows ranking documents according to their possible relevance Allows partial m
https://en.wikipedia.org/wiki/Roland%20Glowinski
Roland Glowinski (9 March 1937 – 26 January 2022) was a French-American mathematician. He obtained his PhD in 1970 from Jacques-Louis Lions and was known for his work in applied mathematics, in particular numerical solution and applications of partial differential equations and variational inequalities. He was a member of the French Academy of Sciences and held an endowed chair at the University of Houston from 1985. Glowinski wrote many books on the subject of mathematics. In 2012, he became a fellow of the American Mathematical Society. Selected publications with Jacques-Louis Lions and Raymond Trémolières: Numerical Analysis of variational inequalities, North Holland 1981 2011 pbk edition Numerical methods for nonlinear variational problems, Springer Verlag 1984, 2008; 2013 pbk edition with Michel Fortin: Augmented Lagrangian methods : applications to the numerical solution of boundary-value problems, North Holland 1983 with Patrick Le Tallec: Augmented Lagrangian and operator-splitting methods in nonlinear mechanics, Society for Industrial and Applied Mathematics 1989 with Jacques-Louis Lions and Jiwen He: Exact and approximate controllability for distributed parameter systems: a numerical approach, Cambridge University Press 2008 References External links homepage short biography 1937 births 2022 deaths 20th-century American mathematicians 21st-century American mathematicians French mathematicians Mathematical analysts Members of the French Academy of Sciences Fellows of the Society for Industrial and Applied Mathematics Fellows of the American Mathematical Society University of Houston faculty
https://en.wikipedia.org/wiki/%C4%8Cech-to-derived%20functor%20spectral%20sequence
In algebraic topology, a branch of mathematics, the Čech-to-derived functor spectral sequence is a spectral sequence that relates Čech cohomology of a sheaf and sheaf cohomology. Definition Let be a sheaf on a topological space X. Choose an open cover of X. That is, is a set of open subsets of X which together cover X. Let denote the presheaf which takes an open set U to the qth cohomology of on U, that is, to . For any presheaf , let denote the pth Čech cohomology of with respect to the cover . Then the Čech-to-derived functor spectral sequence is: Properties If consists of only two open sets, then this spectral sequence degenerates to the Mayer–Vietoris sequence. See Spectral sequence#Long exact sequences. If for all finite intersections of a covering the cohomology vanishes, the E2-term degenerates and the edge morphisms yield an isomorphism of Čech cohomology for this covering to sheaf cohomology. This provides a method of computing sheaf cohomology using Čech cohomology. For instance, this happens if is a quasi-coherent sheaf on a scheme and each element of is an open affine subscheme such that all finite intersections are again affine (e.g. if the scheme is separated). This can be used to compute the cohomology of line bundles on projective space. See also Leray's theorem Notes References Spectral sequences
https://en.wikipedia.org/wiki/Pseudo-abelian%20category
In mathematics, specifically in category theory, a pseudo-abelian category is a category that is preadditive and is such that every idempotent has a kernel. Recall that an idempotent morphism is an endomorphism of an object with the property that . Elementary considerations show that every idempotent then has a cokernel. The pseudo-abelian condition is stronger than preadditivity, but it is weaker than the requirement that every morphism have a kernel and cokernel, as is true for abelian categories. Synonyms in the literature for pseudo-abelian include pseudoabelian and Karoubian. Examples Any abelian category, in particular the category Ab of abelian groups, is pseudo-abelian. Indeed, in an abelian category, every morphism has a kernel. The category of associative rngs (not rings!) together with multiplicative morphisms is pseudo-abelian. A more complicated example is the category of Chow motives. The construction of Chow motives uses the pseudo-abelian completion described below. Pseudo-abelian completion The Karoubi envelope construction associates to an arbitrary category a category together with a functor such that the image of every idempotent in splits in . When applied to a preadditive category , the Karoubi envelope construction yields a pseudo-abelian category called the pseudo-abelian completion of . Moreover, the functor is in fact an additive morphism. To be precise, given a preadditive category we construct a pseudo-abelian category in the following way. The objects of are pairs where is an object of and is an idempotent of . The morphisms in are those morphisms such that in . The functor is given by taking to . Citations References Category theory
https://en.wikipedia.org/wiki/Kazuhiro%20Kawata
is a former Japanese football player who last appeared for Blaublitz Akita. Kamata previously played for Oita Trinita in J. League Division 1. Club statistics Updated to 23 February 2017. References External links 1982 births Living people Fukuoka University alumni Association football people from Fukuoka Prefecture Japanese men's footballers J1 League players J3 League players Japan Football League players Oita Trinita players Gainare Tottori players Matsumoto Yamaga FC players Blaublitz Akita players Men's association football midfielders Akita FC Cambiare players
https://en.wikipedia.org/wiki/Fisher%E2%80%93Tippett%E2%80%93Gnedenko%20theorem
In statistics, the Fisher–Tippett–Gnedenko theorem (also the Fisher–Tippett theorem or the extreme value theorem) is a general result in extreme value theory regarding asymptotic distribution of extreme order statistics. The maximum of a sample of iid random variables after proper renormalization can only converge in distribution to one of 3 possible distributions: the Gumbel distribution, the Fréchet distribution, or the Weibull distribution. Credit for the extreme value theorem and its convergence details are given to Fréchet (1927), Fisher and Tippett (1928), Mises (1936) and Gnedenko (1943). The role of the extremal types theorem for maxima is similar to that of central limit theorem for averages, except that the central limit theorem applies to the average of a sample from any distribution with finite variance, while the Fisher–Tippet–Gnedenko theorem only states that if the distribution of a normalized maximum converges, then the limit has to be one of a particular class of distributions. It does not state that the distribution of the normalized maximum does converge. Statement Let be a sequence of independent and identically-distributed random variables with cumulative distribution function . Suppose that there exist two sequences of real numbers and such that the following limits converge to a non-degenerate distribution function: , or equivalently: . In such circumstances, the limit distribution belongs to either the Gumbel, the Fréchet or the Weibull family. In other words, if the limit above converges, then up to a linear change of coordinates will assume the form: or else for some parameter This is the cumulative distribution function of the generalized extreme value distribution (GEV) with extreme value index . The GEV distribution groups the Gumbel, Fréchet and Weibull distributions into a single one. Note that the second formula (the Gumbel distribution) is the limit of the first as goes to zero. Conditions of convergence The Fisher–Tippett–Gnedenko theorem is a statement about the convergence of the limiting distribution above. The study of conditions for convergence of to particular cases of the generalized extreme value distribution began with Mises (1936) and was further developed by Gnedenko (1943). Let be the distribution function of , and an i.i.d. sample thereof. Also let be the populational maximum, i.e. . The limiting distribution of the normalized sample maximum, given by above, will then be: A Fréchet distribution () if and only if and for all . This corresponds to what is called a heavy tail. In this case, possible sequences that will satisfy the theorem conditions are and . A Gumbel distribution (), with finite or infinite, if and only if for all with . Possible sequences here are and . A Weibull distribution () if and only if is finite and for all . Possible sequences here are and . Examples Fréchet distribution For the Cauchy distribution the cumulative distribution functio
https://en.wikipedia.org/wiki/Additive%20model
In statistics, an additive model (AM) is a nonparametric regression method. It was suggested by Jerome H. Friedman and Werner Stuetzle (1981) and is an essential part of the ACE algorithm. The AM uses a one-dimensional smoother to build a restricted class of nonparametric regression models. Because of this, it is less affected by the curse of dimensionality than e.g. a p-dimensional smoother. Furthermore, the AM is more flexible than a standard linear model, while being more interpretable than a general regression surface at the cost of approximation errors. Problems with AM, like many other machine learning methods, include model selection, overfitting, and multicollinearity. Description Given a data set of n statistical units, where represent predictors and is the outcome, the additive model takes the form or Where , and . The functions are unknown smooth functions fit from the data. Fitting the AM (i.e. the functions ) can be done using the backfitting algorithm proposed by Andreas Buja, Trevor Hastie and Robert Tibshirani (1989). See also Generalized additive model Backfitting algorithm Projection pursuit regression Generalized additive model for location, scale, and shape (GAMLSS) Median polish Projection Pursuit References Further reading Breiman, L. and Friedman, J.H. (1985). "Estimating Optimal Transformations for Multiple Regression and Correlation", Journal of the American Statistical Association 80:580–598. Nonparametric regression Regression models
https://en.wikipedia.org/wiki/Collage%20theorem
In mathematics, the collage theorem characterises an iterated function system whose attractor is close, relative to the Hausdorff metric, to a given set. The IFS described is composed of contractions whose images, as a collage or union when mapping the given set, are arbitrarily close to the given set. It is typically used in fractal compression. Statement Let be a complete metric space. Suppose is a nonempty, compact subset of and let be given. Choose an iterated function system (IFS) with contractivity factor where (the contractivity factor of the IFS is the maximum of the contractivity factors of the maps ). Suppose where is the Hausdorff metric. Then where A is the attractor of the IFS. Equivalently, , for all nonempty, compact subsets L of . Informally, If is close to being stabilized by the IFS, then is also close to being the attractor of the IFS. See also Michael Barnsley Barnsley fern References External links A description of the collage theorem and interactive Java applet at cut-the-knot. Notes on designing IFSs to approximate real images. Expository Paper on Fractals and Collage theorem Fractals Theorems in geometry
https://en.wikipedia.org/wiki/Performance%20Analysis%20of%20Telecommunication%20Systems
The Performance Analysis of Telecommunication Systems (PATS) research group is part of the Department of Mathematics and Computer Science of the University of Antwerp. The group was founded in 1995. PATS performs basic, applied, and contract research related to the performance analysis of telecommunication systems and the impact of performance on the architecture and the design of these systems. The PATS research group is one of the groups that are involved in the Interdisciplinary Institute for Broadband Technology (IBBT) which was founded by the Flemish government on 19 March 2004. References External links PATS homepage Scientific organisations based in Belgium University of Antwerp
https://en.wikipedia.org/wiki/ATS%20theorem
In mathematics, the ATS theorem is the theorem on the approximation of a trigonometric sum by a shorter one. The application of the ATS theorem in certain problems of mathematical and theoretical physics can be very helpful. History of the problem In some fields of mathematics and mathematical physics, sums of the form are under study. Here and are real valued functions of a real argument, and Such sums appear, for example, in number theory in the analysis of the Riemann zeta function, in the solution of problems connected with integer points in the domains on plane and in space, in the study of the Fourier series, and in the solution of such differential equations as the wave equation, the potential equation, the heat conductivity equation. The problem of approximation of the series (1) by a suitable function was studied already by Euler and Poisson. We shall define the length of the sum to be the number (for the integers and this is the number of the summands in ). Under certain conditions on and the sum can be substituted with good accuracy by another sum where the length is far less than First relations of the form where are the sums (1) and (2) respectively, is a remainder term, with concrete functions and were obtained by G. H. Hardy and J. E. Littlewood, when they deduced approximate functional equation for the Riemann zeta function and by I. M. Vinogradov, in the study of the amounts of integer points in the domains on plane. In general form the theorem was proved by J. Van der Corput, (on the recent results connected with the Van der Corput theorem one can read at ). In every one of the above-mentioned works, some restrictions on the functions and were imposed. With convenient (for applications) restrictions on and the theorem was proved by A. A. Karatsuba in (see also,). Certain notations [1]. For or the record means that there are the constants and such that [2]. For a real number the record means that where is the fractional part of ATS theorem Let the real functions ƒ(x) and satisfy on the segment [a, b] the following conditions: 1) and are continuous; 2) there exist numbers and such that and Then, if we define the numbers from the equation we have where The most simple variant of the formulated theorem is the statement, which is called in the literature the Van der Corput lemma. Van der Corput lemma Let be a real differentiable function in the interval moreover, inside of this interval, its derivative is a monotonic and a sign-preserving function, and for the constant such that satisfies the inequality Then where Remark If the parameters and are integers, then it is possible to substitute the last relation by the following ones: where On the applications of ATS to the problems of physics see,; see also,. Notes Theorems in analysis
https://en.wikipedia.org/wiki/TransMagic
TransMagic is a commercial computer program that converts computer-aided design (CAD) files from one native file format to another. During the translation process, TransMagic performs “geometry mapping”, mapping from one CAD kernel to another. During the conversion, TransMagic avoids what are known as “stitching errors” by repairing geometry via techniques such as correcting slightly overlapping or misaligned surfaces, removing duplicate control points, and duplicate vertices. Overview A large number of CAD programs are on the market, among them Autodesk Inventor, Cobalt, Form-Z, Pro/ENGINEER, and SolidWorks. With rare exceptions, each program saves data files (2D and 3D drawings and 3D solid models) in its own native file format. Since major CAD programs are expensive—several thousand dollars or more—and require great skill and time to master, it is common for individuals and companies to own just one type of program. The existence of many different file types presents no problems when engineers and designers share files within an organization that has standardized upon a common CAD program. However, file-transfer problems can arise when files must be shared with outside individuals who are using a different type of CAD program. The typical work-around when sharing files with an outside organization is to export the file using two open-file-type standards: IGES, which was released in 1980 by the National Institute of Standards and Technology (then known as the National Bureau of Standards), and STEP, released in 1984/85. The proprietary file format DXF is also a common file format for exchange. When a file is exported by one CAD program into an intermediate file format and opened in another CAD program, it is not unusual for translation errors to occur. This inability to reliably transfer files between disparate programs is especially problematic with 3D solid modeling software, because of behind-the-scenes technical complexities that arise whenever complex surfaces abut or blend into each other; surfaces no longer align or some features do not translate due to the way CAD programs employ different approaches to handling certain object classes. To minimize translation errors, TransMagic typically—but not always—translates directly from one native CAD kernel to another. Still, “stitching errors” (gaps and overlaps) can occur while trying to import the file and reinterpret geometry. TransMagic's “Auto Repair Wizard” corrects these flaws while translating the file. TransMagic is available as a stand-alone program. It is also available as a plug-in for many CAD programs so that the Open and Save dialog boxes are extended with TransMagic's functionality. Supported file types As of September 2010, TransMagic reads and writes to the following file types: See also List of file formats List of file formats (alphabetical) List of CAD programs Comparison of CAD editors for CAE Notes External links National Institute of Standards and Technolog
https://en.wikipedia.org/wiki/Canadian%20Society%20for%20Epidemiology%20and%20Biostatistics
The Canadian Society for Epidemiology and Biostatistics (CSEB), or Société Canadienne d'épidémiologie et de biostatistique (SCEB), was founded in 1990 to promote epidemiology and biostatistics research in Canada; encourage the use of epidemiologic data in formulating public health policy; increase the level of epidemiology and biostatistics funding available through federal, provincial, and private sources; facilitate communications among epidemiologists and biostatisticians; and assist faculty or schools of medicine and public health to improve training in epidemiology and biostatistics. President Mark Oremus, PhD, School of Public Health and Health Systems, University of Waterloo Past presidents 1991-1993 Nancy Kreiger 1993-1995 Jean Joly 1995-1997 Roy West 1997-1999 Nancy Mayo 1999-2001 Jack Siemiatycki 2001-2003 Rick Gallagher 2003-2007 Yang Mao 2007–2011 Colin Soskolne 2011–2013 Susan Jaglal 2013–2016 Thy Dinh 2016–Present Mark Oremus Collaborators and affiliates CSEB bridges both the research and practice aspects of epidemiology and biostatistics through close collaboration with other groups such as the Public Health Agency of Canada (PHAC), Health Canada, the Association of Public Health Epidemiologists in Ontario (APHEO), the Saskatchewan Epidemiology Association (SEA), the Statistical Society of Canada (SSC), and the International Joint Policy Committee of the Societies of Epidemiology (IJPC-SE). References Organizations established in 1990 Medical and health organizations based in Canada 1990 establishments in Canada Epidemiology organizations
https://en.wikipedia.org/wiki/Thiam
Thiam is a both a surname of West African origin and an element in Chinese given names. Surname Origins and statistics As a surname, Thiam is found among the Fula and Wolof people of Senegal and nearby countries, and originated from a family of goldsmiths. In the modern Fula language and Wolof language orthographies, it is spelled Caam. Thiam is one of a number of older spellings which originated during French colonial rule; others include Tyam, Chiam, and Cham. This surname is spelled Thiam in Senegal, and Cham in the Gambia. The surname originated from Toucouleur or Laobe people, and is found among Pulaar language speakers. It is not authentically Wolof, and only made its way to the Wolof through Wolof mixture. French government statistics show 508 people with the surname Thiam born in France from 1991 to 2000, 532 from 1981 to 1990, 196 from 1971 to 1980, and 143 in earlier time periods. The 2010 United States Census found 935 people with the surname Thiam, making it the 26,171st-most-common surname in the country. This represented an increase from 494 people (41,522nd-most-common) in the 2000 census. In both censuses, about nine-tenths of the bearers of the surname identified as Black, and roughly two to three percent as White or Asian. Government officials and politicians Awa Thiam (born 1936), Senegalese government official in the Ministry of Women and Children Amadou Thiam (born 1984), Malian politician Augustin Thiam (born 1952), Ivorian politician, governor of the Yamoussoukro Autonomous District Brenda Thiam (born 1969), American politician Doudou Thiam (1926–1999), Senegalese diplomat and politician Habib Thiam (1933–2017), Senegalese politician who twice served as prime minister Safiatou Thiam (), Senegalese public health official Samba Diouldé Thiam, Senegalese legislator and mathematician Tidjane Thiam (born 1962), Ivorian banker and economic advisor to the Ivorian government Athletes Abdou Mbacke Thiam (born 1992), Senegalese footballer in the United States Abdoul Thiam (born 1976), German footballer Abdoulaye Thiam (born 1984), Senegalese sabre fencer Abdoulkader Thiam (born 1998), Mauritanian footballer in France Amy Mbacké Thiam (born 1976), Senegalese sprinter Assane Thiam (born 1948), Senegalese basketball player Brahim Thiam (born 1974), French and Malian footballer Chiekh Thiam (born 2001), Italian footballer of Senegalese descent Demba Thiam (footballer, born 1989), French footballer of Senegalese descent Demba Thiam (footballer, born 1998) (born 1998), Senegalese footballer in Italy Djibril Thiam (born 1986), Senegalese basketball player Ibrahima Thiam (born 1981), Senegalese footballer in Belgium Khaly Thiam (born 1994), Senegalese footballer in Bulgaria Mame Baba Thiam (born 1992), Senegalese footballer in Turkey Mamadou Thiam (born 1995), Senegalese footballer in England Mamadou Touré Thiam (born 1992), Senegalese footballer in Israel Mbayang Thiam (born 1982), Senegalese footballer, member of the Senegalese women'
https://en.wikipedia.org/wiki/State%20of%20the%20Coast
The State of the Coast is a website launched by the National Oceanic and Atmospheric Administration (NOAA) in March 2010. The site contains quick facts and detailed statistics offered on communities, economy, ecology, and climate. The website aims to communicate and highlight the connections among a healthy coastal ecosystem, a robust U.S. economy, a safe population, and a sustainable quality of life for coastal residents. The Web site is periodic, and is updated on a monthly basis. Communities Topics The U.S. Population Living in Coastal Counties Swimming at Our Nation's Beaches Marine Protected Areas: Conserving our Nation's Marine Resources Economy Topics The Coast - Our Nation's Economic Engine Recreational Fishing - An American Pastime Commercial Fishing - A Cultural Tradition Ports - Crucial Coastal Infrastructure Response Topics The Overall Health of Our Nation's Coastal Waters Invasive Species Disrupt Coastal Ecosystems and Economies Coral Reef Ecosystems - Critical Coastal Habitat Nutrient Pollution and Hypoxia - Everything is Upstream of the Coast Climate Topics Vulnerability of Our Nation's Coasts to Sea Level Rise U.S. Population in the 100-year Coastal Flood Hazard Area Federally-Insured Assets along the Coast External links NOAA's State of the Coast Web Site Retired NOS State of the Coast Web Site National Oceanic and Atmospheric Administration NOAA National Oceanic and Atmospheric Administration
https://en.wikipedia.org/wiki/Bulging%20factor
Bulging factor is an engineering term describing the geometry of out-of plane deformations of the surface of a crack on a pressurized fuselage structure. It is used in evaluating the damage tolerance of airframe fuselages. The single curved geometry and pressure differential causes a longitudinal crack to bulge out or protrude from the original shape. This change in geometry, or “bulging effect”, significantly increases the stress intensity factor at the crack tips. The effects of this loading condition can trigger different types of failure mechanisms. For the case of unstiffened shell structures, the bulging factor can be defined as the ratio of stress-intensity (SIF) of a curved shell to the stress-intensity factor of a flat panel: The representation of this phenomenon becomes rather complex due to the biaxial and internal pressure load and structural configuration. References Lazghab Tarek, Fayza Ayari, Lotfi Chelbi. Crack growth in cylindrical aluminum shells with inner reinforcing foam layer. Springer, 2006. pp. 151. Pressure vessels Fracture mechanics
https://en.wikipedia.org/wiki/Horst%20Steffen
Horst Steffen (born 3 March 1969) is a German football coach and a former player. He manages SV Elversberg. Managerial statistics Honours Borussia Mönchengladbach DFB-Pokal runner-up: 1991–92 MSV Duisburg DFB-Pokal runner-up: 1997–98 References External links 1969 births Living people German men's footballers Footballers from Düsseldorf (region) Men's association football midfielders Germany men's under-21 international footballers German football managers Bundesliga players KFC Uerdingen 05 players Borussia Mönchengladbach players MSV Duisburg players 3. Liga managers Stuttgarter Kickers managers SC Preußen Münster managers Chemnitzer FC managers West German men's footballers People from Rhein-Kreis Neuss
https://en.wikipedia.org/wiki/Pettis%20integral
In mathematics, the Pettis integral or Gelfand–Pettis integral, named after Israel M. Gelfand and Billy James Pettis, extends the definition of the Lebesgue integral to vector-valued functions on a measure space, by exploiting duality. The integral was introduced by Gelfand for the case when the measure space is an interval with Lebesgue measure. The integral is also called the weak integral in contrast to the Bochner integral, which is the strong integral. Definition Let where is a measure space and is a topological vector space (TVS) with a continuous dual space that separates points (that is, if is nonzero then there is some such that ), for example, is a normed space or (more generally) is a Hausdorff locally convex TVS. Evaluation of a functional may be written as a duality pairing: The map is called if for all the scalar-valued map is a measurable map. A weakly measurable map is said to be if there exists some such that for all the scalar-valued map is Lebesgue integrable (that is, ) and The map is said to be if for all and also for every there exists a vector such that In this case, is called the of on Common notations for the Pettis integral include To understand the motivation behind the definition of "weakly integrable", consider the special case where is the underlying scalar field; that is, where or In this case, every linear functional on is of the form for some scalar (that is, is just scalar multiplication by a constant), the condition simplifies to In particular, in this special case, is weakly integrable on if and only if is Lebesgue integrable. Relation to Dunford integral The map is said to be if for all and also for every there exists a vector called the of on such that where Identify every vector with the map scalar-valued functional on defined by This assignment induces a map called the canonical evaluation map and through it, is identified as a vector subspace of the double dual The space is a semi-reflexive space if and only if this map is surjective. The is Pettis integrable if and only if for every Properties An immediate consequence of the definition is that Pettis integrals are compatible with continuous linear operators: If is linear and continuous and is Pettis integrable, then is Pettis integrable as well and The standard estimate for real- and complex-valued functions generalises to Pettis integrals in the following sense: For all continuous seminorms and all Pettis integrable , holds. The right-hand side is the lower Lebesgue integral of a -valued function, that is, Taking a lower Lebesgue integral is necessary because the integrand may not be measurable. This follows from the Hahn-Banach theorem because for every vector there must be a continuous functional such that and for all , . Applying this to gives the result. Mean value theorem An important property is that the Pettis integral with respect to a finite mea
https://en.wikipedia.org/wiki/Urysohn%20universal%20space
The Urysohn universal space is a certain metric space that contains all separable metric spaces in a particularly nice manner. This mathematics concept is due to Pavel Urysohn. Definition A metric space (U,d) is called Urysohn universal if it is separable and complete and has the following property: given any finite metric space X, any point x in X, and any isometric embedding f : X\{x} → U, there exists an isometric embedding F : X → U that extends f, i.e. such that F(y) = f(y) for all y in X\{x}. Properties If U is Urysohn universal and X is any separable metric space, then there exists an isometric embedding f:X → U. (Other spaces share this property: for instance, the space l∞ of all bounded real sequences with the supremum norm admits isometric embeddings of all separable metric spaces ("Fréchet embedding"), as does the space C[0,1] of all continuous functions [0,1]→R, again with the supremum norm, a result due to Stefan Banach.) Furthermore, every isometry between finite subsets of U extends to an isometry of U onto itself. This kind of "homogeneity" actually characterizes Urysohn universal spaces: A separable complete metric space that contains an isometric image of every separable metric space is Urysohn universal if and only if it is homogeneous in this sense. Existence and uniqueness Urysohn proved that a Urysohn universal space exists, and that any two Urysohn universal spaces are isometric. This can be seen as follows. Take , two Urysohn universal spaces. These are separable, so fix in the respective spaces countable dense subsets . These must be properly infinite, so by a back-and-forth argument, one can step-wise construct partial isometries whose domain (resp. range) contains (resp. ). The union of these maps defines a partial isometry whose domain resp. range are dense in the respective spaces. And such maps extend (uniquely) to isometries, since a Urysohn universal space is required to be complete. References Metric geometry
https://en.wikipedia.org/wiki/Fredholm%20module
In noncommutative geometry, a Fredholm module is a mathematical structure used to quantize the differential calculus. Such a module is, up to trivial changes, the same as the abstract elliptic operator introduced by . Definition If A is an involutive algebra over the complex numbers C, then a Fredholm module over A consists of an involutive representation of A on a Hilbert space H, together with a self-adjoint operator F, of square 1 and such that the commutator [F, a] is a compact operator, for all a in A. References The paper by Atiyah is reprinted in volume 3 of his collected works, External links Fredholm module, on PlanetMath Noncommutative geometry Mathematical quantization
https://en.wikipedia.org/wiki/Jordan%27s%20inequality
In mathematics, Jordan's inequality, named after Camille Jordan, states that It can be proven through the geometry of circles (see drawing). Notes Further reading Serge Colombo: Holomorphic Functions of One Variable. Taylor & Francis 1983, , p. 167-168 (online copy) Da-Wei Niu, Jian Cao, Feng Qi: Generealizations of Jordan's Inequality and Concerned Relations. U.P.B. Sci. Bull., Series A, Volume 72, Issue 3, 2010, Feng Qi: Jordan's Inequality: Refinements, Generealizations, Applications and related Problems . RGMIA Res Rep Coll (2006), Volume: 9, Issue: 3, Pages: 243–259 Meng-Kuang Kuo: Refinements of Jordan's inequality. Journal of Inequalities and Applications 2011, 2011:130, doi:10.1186/1029-242X-2011-130 External links Jordan's inequality at the Proof Wiki Jordan's and Kober's inequalities at cut-the-knot.org Inequalities
https://en.wikipedia.org/wiki/Computers%20and%20Mathematics%20with%20Applications
Computers and Mathematics with Applications () is a peer-reviewed scientific journal published by Elsevier, covering scholarly research and communications in the area relating to both mathematics and computer science. It includes the more specific subjects of mathematics for computer systems, computing science in mathematics research, and advanced mathematical and computing applications in contemporary scientific fields, such as ecological sciences, large-scale systems sciences and operations research. The current Editor-in-Chief is Ervin Y. Rodin, who founded the journal in the 1980s. The impact factor for 2020 was 3.476, ranking it 16th out of the 265 journals in the field of applied Mathematics in the Journal Citation Reports. References External links Journal home page Elsevier academic journals
https://en.wikipedia.org/wiki/Peter%20K%C3%B6zle
Peter Közle (born 18 November 1967 in Trostberg) is a retired German football player. Club career Club statistics References External links Peter Közle at skynet.be 1967 births Living people German men's footballers Cercle Brugge K.S.V. players BSC Young Boys players Grasshopper Club Zürich players MSV Duisburg players VfL Bochum players 1. FC Union Berlin players Bundesliga players 2. Bundesliga players Men's association football midfielders Men's association football forwards SV 19 Straelen players Old Xaverians SC players German expatriate men's footballers West German men's footballers West German expatriate men's footballers West German expatriate sportspeople in Belgium West German expatriate sportspeople in Switzerland German expatriate sportspeople in Switzerland German expatriate sportspeople in Australia Expatriate men's footballers in Belgium Expatriate men's footballers in Switzerland Expatriate men's soccer players in Australia People from Traunstein (district) Footballers from Upper Bavaria
https://en.wikipedia.org/wiki/Park%20Ju-sung
Park Ju-Sung (born 20 February 1984 in Jinhae, Gyeongsangnam-do) is a South Korean football player currently playing for Daejeon Citizen. Club statistics References External links National Team Player Record FIFA Player Statistics 1984 births Living people Men's association football defenders South Korean men's footballers South Korean expatriate men's footballers South Korea men's international footballers Suwon Samsung Bluewings players Gimcheon Sangmu FC players Vegalta Sendai players Gyeongnam FC players Beijing Chengfeng F.C. players Chinese Super League players K League 1 players J1 League players J2 League players Expatriate men's footballers in Japan South Korean expatriate sportspeople in Japan Expatriate men's footballers in China South Korean expatriate sportspeople in China Daejeon Hana Citizen players Footballers from South Gyeongsang Province
https://en.wikipedia.org/wiki/Yang%20Sang-min
Yang Sang-Min (; born February 24, 1984) is a South Korean football player. Club career statistics External links National Team Player Record 1984 births Living people Men's association football defenders South Korean men's footballers South Korea men's international footballers Jeonnam Dragons players Suwon Samsung Bluewings players Asan Mugunghwa FC players K League 1 players K League 2 players Footballers from Incheon
https://en.wikipedia.org/wiki/Park%20Ho-jin
Park Ho-Jin (Hangul: 박호진; Hanja: 朴虎珍; born 22 October 1976) is a South Korean football player and football coach who plays for Gwangju FC. Club career statistics External links 1976 births Living people Men's association football goalkeepers South Korean men's footballers Suwon Samsung Bluewings players Gimcheon Sangmu FC players Gwangju FC players Gangwon FC players K League 1 players Footballers from Gyeonggi Province Yonsei University alumni
https://en.wikipedia.org/wiki/Shin%20Young-chol
Shin Young-chol (; born 14 March 1986) is a South Korean footballer, who plays as midfielder. Club career statistics References External links 1986 births Living people Men's association football midfielders South Korean men's footballers South Korean expatriate men's footballers Seongnam FC players K League 1 players Expatriate men's footballers in Thailand South Korean expatriate sportspeople in Thailand Sportspeople from Seongnam Footballers from Gyeonggi Province
https://en.wikipedia.org/wiki/Quarterly%20Census%20of%20Employment%20and%20Wages
The Quarterly Census of Employment and Wages (fka ES-202) is the name of the QCEW program. QCEW is a program of the Bureau of Labor Statistics, U.S. Department of Labor. ES-202 is the old name and stood for Employment Security Report 202. Unemployment Insurance tax reports provide the samples for federal QCEW data, but gig workers (e.g. in the platform economy) are typically classified as independent contractors and therefore not included in those or other federal data. External links Employment and wage profile of the Louisiana and Texas counties affected by Hurricane Ike - Representative article using QCEW data References Reports of the Bureau of Labor Statistics
https://en.wikipedia.org/wiki/Park%20Woo-hyun
Park Woo-Hyun (born April 28, 1980) is a South Korean football player who last played for Gangwon FC. Career statistics References 1980 births Living people South Korean men's footballers People from Sokcho K League 1 players Seongnam FC players Busan IPark players Gangwon FC players Men's association football defenders Footballers from Gangwon Province, South Korea
https://en.wikipedia.org/wiki/Algebra%20Universalis
Algebra Universalis is an international scientific journal focused on universal algebra and lattice theory. The journal, founded in 1971 by George Grätzer, is currently published by Springer-Verlag. Honorary editors in chief of the journal included Alfred Tarski and Bjarni Jónsson. External links Algebra Universalis on Springer.com Algebra Universalis homepage, including instructions to authors Universal algebra Mathematics journals Academic journals established in 1971 Springer Science+Business Media academic journals
https://en.wikipedia.org/wiki/Seo%20Jung-jin
Seo Jung-jin (; born 6 September 1989) is a South Korean footballer who plays as a winger for Hwaseong FC. Club career statistics References External links 1989 births Living people Men's association football wingers South Korean men's footballers South Korea men's under-20 international footballers South Korea men's under-23 international footballers South Korea men's international footballers Jeonbuk Hyundai Motors players Suwon Samsung Bluewings players Ulsan Hyundai FC players Seoul E-Land FC players Asian Games medalists in football Footballers at the 2010 Asian Games K League 1 players K League 2 players Asian Games bronze medalists for South Korea Footballers from Daegu Medalists at the 2010 Asian Games Jung-jin
https://en.wikipedia.org/wiki/List%20of%20the%20busiest%20airports%20in%20Bulgaria
This is a list of the busiest airports in Bulgaria by number of passengers begins 2013. In graph Passenger statistics References Bulgaria Bulgaria, busy Airports, busiest Airports, busiest
https://en.wikipedia.org/wiki/S%C3%A9bastien%20Truchet
Jean Truchet (1657 – 5 February 1729), known as Father Sébastian, was a French Dominican priest born in Lyon, who lived under the reign of Louis XIV. He was active in areas such as mathematics, hydraulics, graphics, and typography. He is also known for many inventions. Biography Truchet was born in 1657, the son of a merchant father and a very pious mother. At age 16, he joined the Discalced Carmelites. He took the name Sébastien to honor his mother, who was named Sébastiane. In 1693, he was selected by Abbé Bignon to assist his commission investigating the feasibility of compiling a description of all France's artistic and industrial processes for the minister Colbert. For his assistance, he was named an of the French Royal Academy in 1699. Death Truchet died on 5 February 1729, with the Descriptions of the Arts and Trades still incomplete. Contributions Alongside the royal typographer Jacques Jaugeon, Truchet studied the proportions of typefaces using the French line ( French inch), a measurement derived from silversmithing. The commission then invented the first typographic point, using minute fractions of the line to create a bitmap that could be used to mathematically describe and italicize metal type. Their system had unnecessarily great precision relative to the accuracy with which fonts could actually be cut. Further, it did not match the sizes of the fonts then in use. Fournier subsequently corrected these failings, using a larger point with greater compatibility with existing forms of type. The commission also designed the ("King's Roman"), which influenced Philippe Grandjean and through him the popular Times New Roman fonts. Other typographic innovations in the work of the commission involved the use of both bitmap and vector representations of letter shapes, tabulations of font metrics, and oblique font faces. In 1699, at the second public meeting of the French Academy, Truchet spoke on the motion of falling bodies, and nearly 20 years later he was one of several scientists to confirm Newton's model of the separation of white light into colors. As a hydraulics expert, he designed most of the French canals. Inspired by decorations he had seen on the canals, Truchet studied decorative patterns on ceramic tiles. One particular pattern that he studied involved square tiles split by a diagonal line into two triangles, decorated in contrasting colors. By placing these tiles in different orientations with respect to each other, as part of a square tiling, Truchet observed that many different patterns could be formed. This model of pattern formation was later taken up by Fournier, and is now known to mathematicians and designers as Truchet tiling. He is also known for his expertise as a watchmaker, and for his inventions concerning sundials, weapons and tools for transplanting large trees within the Versailles gardens. See also Truchet point Notes External links Sébastien Truchet biography: http://jacques-andre.fr/faqtypo/truc
https://en.wikipedia.org/wiki/Alok%20Bhargava
Alok Bhargava (born 13 July 1954) is an Indian econometrician. He studied mathematics at Delhi University and economics and econometrics at the London School of Economics. He is currently a full professor at the University of Maryland School of Public Policy. Education In 1974 he received his B.A with honors in Mathematics at Delhi University. In 1977 he got his B.Sc in Economics at London School of Economics. In 1978 he received his M.Sc in Economometrics at London School of Economics. Bhargava received his Ph.D. in econometrics from the London School of Economics under the supervision of John Denis Sargan in 1982. His thesis (The Theory of the Durbin–Watson Statistic with special reference to the Specification of Models in Levels as against in Differences) led to many tests for unit roots that were used in co-integration analyses. Bhargava was also one of the pioneers in econometric methods for longitudinal ("panel") data. Career From 1983 till 1989 he served as an Assistant Professor of Economics at University of Pennsylvania. From 1989 till 1993 he was an Associate Professor of Economics at University of Houston and was a full professor from 1994 to around 2012. During the autumn of 1995 he was invited to teach at Harvard University as a Visiting Professor. In 1999 he was a Senior Global Health Leadership Fellow at World Health Organization. In 2005 he served as a Visiting Professor at University of Paris. Since 1991, Bhargava has been publishing on important aspects of nutrition, food policy, population health, child development, demography, epidemiology, AIDS, and finance in developing and developed countries. His academic publications demonstrate the usefulness of rigorous econometric and statistical methods in addressing issues of under-nutrition and poor child health in developing countries, as well as obesity in developed countries. Bhargava was an editor of the Journal of Econometrics (1997 and 2014) and is an associate editor of the multi-disciplinary journal Economics and Human Biology. He has held teaching positions at the University of Pennsylvania, Harvard University and University of Houston, and has published over 70 articles in academic journals. Books and reviews A collection of his works has been reprinted in a separate volume in 2006 entitled "Econometrics, statistics and computational approaches in food and health sciences". A monograph entitled "Food, economics, and health" was published in 2008 [4] and was reviewed in the Journal of the American Medical Association with the commendation that "Alok Bhargava is a pioneer in efforts to break down the existing firewalls between the biomedical and social sciences and between the health profession and the food systems (https://jamanetwork.com/journals/jama/article-abstract/186008). Selected publications References Econometricians Living people Indian emigrants to the United States Alumni of the London School of Economics Harvard University faculty University of Penn
https://en.wikipedia.org/wiki/Kuratowski%20embedding
In mathematics, the Kuratowski embedding allows one to view any metric space as a subset of some Banach space. It is named after Kazimierz Kuratowski. The statement obviously holds for the empty space. If (X,d) is a metric space, x0 is a point in X, and Cb(X) denotes the Banach space of all bounded continuous real-valued functions on X with the supremum norm, then the map defined by is an isometry. The above construction can be seen as embedding a pointed metric space into a Banach space. The Kuratowski–Wojdysławski theorem states that every bounded metric space X is isometric to a closed subset of a convex subset of some Banach space. (N.B. the image of this embedding is closed in the convex subset, not necessarily in the Banach space.) Here we use the isometry defined by The convex set mentioned above is the convex hull of Ψ(X). In both of these embedding theorems, we may replace Cb(X) by the Banach space ℓ ∞(X) of all bounded functions X → R, again with the supremum norm, since Cb(X) is a closed linear subspace of ℓ ∞(X). These embedding results are useful because Banach spaces have a number of useful properties not shared by all metric spaces: they are vector spaces which allows one to add points and do elementary geometry involving lines and planes etc.; and they are complete. Given a function with codomain X, it is frequently desirable to extend this function to a larger domain, and this often requires simultaneously enlarging the codomain to a Banach space containing X. History Formally speaking, this embedding was first introduced by Kuratowski, but a very close variation of this embedding appears already in the paper of Fréchet where he first introduces the notion of metric space. See also Tight span, an embedding of any metric space into an injective metric space defined similarly to the Kuratowski embedding References Functional analysis Metric geometry
https://en.wikipedia.org/wiki/Nodar%20Mammadov
Nodar Mammadov (; born 3 June 1988 in Kaspi, Georgia) is an Azerbaijani football defender who plays for Kapaz PFK. Career statistics References External links 1988 births Living people Azerbaijani men's footballers Azerbaijan men's international footballers Georgian Azerbaijanis Men's association football defenders Azerbaijani expatriate men's footballers Qarabağ FK players MOIK Baku players Gabala SC players Ravan Baku FK players Sumgayit FK players Khazar Lankaran FK players Khazar Baku FK players Turan Tovuz players Shuvalan FK players Azerbaijan Premier League players Expatriate men's footballers in Cyprus
https://en.wikipedia.org/wiki/FIFA%20Club%20World%20Cup%20records%20and%20statistics
The FIFA Club World Cup is an international association football competition organised by the Fédération Internationale de Football Association (FIFA). The championship was first contested as the FIFA Club World Championship in 2000. It was not held between 2001 and 2004 due to a combination of factors, most importantly the collapse of FIFA's marketing partner International Sport and Leisure. Following a change in format which saw the FIFA Club World Championship absorb the Intercontinental Cup, it was relaunched in 2005 and took its current name the season afterwards. The current format of the tournament involves seven teams competing for the title at venues within the host nation over a period of about two weeks; the winners of that year's edition of the Asian AFC Champions League, African CAF Champions League, North American CONCACAF Champions League, South American Copa Libertadores, Oceanian OFC Champions League and European UEFA Champions League, along with the host nation's national champion, participate in a straight knock-out tournament. This page details the records and statistics of the FIFA Club World Cup, a collection, organization, analysis, interpretation, and presentation of data pertaining to the tournament. As a general rule, statistics should ideally be added after the end of a FIFA Club World Cup edition. General performances By club By nation By confederation Final statistics Final success rate Three clubs have appeared in the final of the FIFA Club World Cup more than once, with a 100% success rate: Corinthians (2000, 2012) Real Madrid (2014, 2016, 2017, 2018, 2022) Bayern Munich (2013, 2020) Six clubs have appeared in the final once, being victorious on that occasion: São Paulo (2005) Internacional (2006) Milan (2007) Manchester United (2008) Internazionale (2010) One club has appeared in the final four times, losing only on one occasion: Barcelona (lost in 2006, won in 2009, 2011, and 2015) Two clubs have appeared in the final twice, won once and lost once: Liverpool (lost in 2005, won in 2019) Chelsea (lost in 2012, won in 2021) Final failure rate On the opposite end of the scale, sixteen clubs have played one final and lost: Vasco da Gama (2000) Boca Juniors (2007) LDU Quito (2008) Estudiantes (2009) TP Mazembe (2010) Santos (2011) Raja Casablanca (2013) San Lorenzo (2014) River Plate (2015) Kashima Antlers (2016) Grêmio (2017) Al-Ain (2018) Flamengo (2019) UANL (2020) Palmeiras (2021) Al-Hilal (2022) All-time club final appearances One club has participated in the FIFA Club World Cup final five times: Real Madrid (2014, 2016, 2017, 2018, 2022) All-time player final appearances Toni Kroos has participated in the FIFA Club World Cup final six times and won all of them; he appeared in 2013 as a member of Bayern Munich, and in 2014, 2016, 2017, 2018 and 2022 as a member of Real Madrid. All-time manager final appearance record Rafael Benítez, Pep Guardiola and Carlo Ancelotti h
https://en.wikipedia.org/wiki/Arthur%20Milgram
Arthur Norton Milgram (3 June 1912 – 30 January 1961) was an American mathematician. He made contributions in functional analysis, combinatorics, differential geometry, topology, partial differential equations, and Galois theory. Perhaps one of his more famous contributions is the Lax–Milgram theorem—a theorem in functional analysis that is particularly applicable in the study of partial differential equations. In the third chapter of Emil Artin's book Galois Theory, Milgram also discussed some applications of Galois theory. Milgram also contributed to graph theory, by co-authoring the article Verallgemeinerung eines graphentheoretischen Satzes von Rédei with Tibor Gallai in 1960. Milgram was born in Philadelphia, and received his Ph.D. from the University of Pennsylvania in 1937. He worked under the supervision of John Kline (a student of Robert Lee Moore). His dissertation was titled "Decompositions and Dimension of Closed Sets in ". Milgram advised 2 students at Syracuse University in the 1940s and 1950s (Robert M. Exner and Adnah Kostenbauder ). In the 1950s, Milgram moved to the University of Minnesota at Minneapolis and helped found Minnesota's well-known PDE group (). At Minnesota, Milgram was also the Ph.D. advisor for Robert Duke Adams . It is also worth noting that Milgram's son R. James (Richard) Milgram (Professor Emeritus at Stanford ) also studied mathematics and received his Ph.D. from Minnesota. Selected publications . . See also Babuška–Lax–Milgram theorem Fichera's existence principle Lions–Lax–Milgram theorem List of Jewish American mathematicians Notes References . . . External links 20th-century American mathematicians Combinatorialists Differential geometers Mathematical analysts Topologists Mathematicians from New York (state) Jewish American scientists University of Minnesota faculty Syracuse University faculty Institute for Advanced Study visiting scholars University of Notre Dame faculty University of Pennsylvania alumni 1912 births 1960 deaths
https://en.wikipedia.org/wiki/Disorder%20problem
In the study of stochastic processes in mathematics, a disorder problem or quickest detection problem (formulated by Kolmogorov) is the problem of using ongoing observations of a stochastic process to detect as soon as possible when the probabilistic properties of the process have changed. This is a type of change detection problem. An example case is to detect the change in the drift parameter of a Wiener process. See also Compound Poisson process Notes References Kolmogorov, A. N., Prokhorov, Yu. V. and Shiryaev, A. N. (1990). Methods of detecting spontaneously occurring effects. Proc. Steklov Inst. Math. 1, 1–21. Stochastic processes Optimal decisions
https://en.wikipedia.org/wiki/Kenji%20Suzuki%20%28footballer%29
is a Japanese football player. He plays for Tochigi Uva FC. References External links Player statistics 1986 births Living people Association football people from Akita Prefecture Japanese men's footballers J1 League players J3 League players Japan Football League players FC Tokyo players Gainare Tottori players Blaublitz Akita players Tochigi City FC players Singapore Premier League players Albirex Niigata Singapore FC players Akita FC Cambiare players Men's association football midfielders
https://en.wikipedia.org/wiki/2008%E2%80%9309%20Swansea%20City%20A.F.C.%20season
The 2008–09 season was Swansea City A.F.C.'s first time in the second tier of English football for 24 years. Swansea gained promotion as champions of League One by 10 points. Squad statistics Playing stats Last updated on 10 March 2009 |} No longer at the club |} Disciplinary record For games in the 2008–09 Championship. For games in the 2008–09 League Cup. For games in the 2008–09 FA Cup. Awards Manager of the Month January: Roberto Martínez Player of the Month February: Jason Scotland Championship Team of the Week The following Swansea players have been selected in the official Championship team of the week. 26 August 2008: Àngel Rangel 6 October 2008: Ashley Williams, Jason Scotland 27 October 2008: Artur Krysiak, Jordi Gómez 3 November 2008: Dimitrios Konstantopoulos, Jordi Gómez 1 December 2008: Leon Britton 30 December 2008: Darren Pratley 12 January 2009: Garry Monk, Jason Scotland 19 January 2009: Joe Allen 2 February 2009: Jordi Gómez 9 February 2009: Jordi Gómez, Jason Scotland 23 February 2009: Jordi Gómez 6 April 2009: Nathan Dyer 15 April 2009: Leon Britton, Ashley Williams, Jason Scotland 20 April 2009: Garry Monk Player transfers In Out Loans in Loans out Fixtures and results Pre-season friendlies Swansea City scores given first The Championship The season finished on 3 May when Swansea City played Blackpool at the Liberty Stadium. Results by round The FA Cup League Cup Swansea reached the fourth round of the League Cup before losing to Championship strugglers Watford. References 2008-09 2008–09 Football League Championship by team Welsh football clubs 2008–09 season
https://en.wikipedia.org/wiki/A-League%20Women%20records%20and%20statistics
This is a list of A-League Women records and statistics. Club honours Champions This is a list of the clubs that have won the finals series (play-offs), where the winning team is crowned as the A-League Women (previously W-League) champions. The numbers in brackets indicate the number of championships won by a team. Premiers This is a list of the teams that have won the premiership of the A-League Women (previously W-League). <small>The numbers in brackets indicate the number of premierships won by a team.</small> Summary Individual honours Julie Dolan Medal The medal is awarded annually to the player voted to be the best player in the W-League, the top women's football (soccer) league in Australia. The award is named after former Matildas Captain and football administrator Julie Dolan. The format was changed for the 2015–16 season, with a panel featuring former players, media, referees and technical staff, who voted on each regular-season match. The following table contains only the winners of the medal during the W-League era. The award was also presented for the best player in the previous Women's National Soccer League prior to the W-League. Young Footballer of the Year FMA Player of the Year Player's Player of the Year Goalkeeper of the Year (Golden Glove) Golden Boot Goal of the Year Coach of the Year Referee of the Year Fair Play Award Club records Biggest victories Highest aggregate scores W-League streaksupdated to end 2022–23 seasonPlayer recordsAs of 1 December 2021 (prior to commencement of 2021–22 A-League Women season).Players listed in bold are still actively playing in the A-League Women. Top scorersAs of 11 April 2021 (end of 2020–21 post-season).Most Goals In A Match Most hat-tricks Fastest hat-tricks All-time W-League ladders Regular season matchesAs of the end of the 2020–21 regular season, ranked by average points per game Finals matchesAs of the end of the 2020–21 post-season'' See also List of A-League Women hat-tricks Notes References A-League Women records and statistics Australia Women's association football records and statistics A-League Women lists
https://en.wikipedia.org/wiki/Port%20of%20Vienna
The Port of Vienna is the largest Austrian river port and one of the largest ports on the Danube River, with a total annual traffic capacity of around 12 million tonnes of cargo. Statistics In 2007 the Port of Vienna handled 12,000,000 tonnes of cargo and 323,000 TEUs making it the busiest cargo and container port in Austria and one of the largest in Central Europe. * figures in millions of tonnes Terminals Container terminal The terminal was opened in 2000 and has a storage area of . Automobile terminal The cars terminal is one of the largest in Central Europe used for imports of new cars and can accommodate 10,000 cars at once on a plot of land. General cargo The general cargo terminal has a storage area of . Passenger terminal The Port of Vienna has one of the largest passenger terminals on the Danube River; it handled 305,000 passengers in 2007. References Ports and harbours of Austria River ports
https://en.wikipedia.org/wiki/Ilomba%20%28Mbeya%20ward%29
Ilomba is an administrative ward in the Mbeya Urban district of the Mbeya Region in Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 37,495 people in the ward, from 34,021 in 2012. Ilomba is among the best developed wards in Mbeya Urban. Socially the ward has some education centres such as public primary schools of Hayanga, Ikulu, Ivumwe, Ruanda Nzovwe and Veta. For secondary education, Ilomba (public) and Ivumwe high school (parents) are found. In vocation education Ilomba-Veta Vocation centre provides variety of technical courses. Several health centres are also found. In infrastructure, the Tanzania-Zambia highway and Tanzania-Zambia railways pass through Ilomba ward making it among few wards in Mbeya to harbour both road and railway transportation ways. Internally, a wide distribution of aggregated and tarmac roads connects Ilomba bus station (being almost the centre of ward) with other areas such as Nane Nane Bus Terminal, Uyole and Mwanjelwa. Economically, several trading centers such as open markets of Ilomba, Ituha Ivumwe and Mwambene are used by small entrepreneurs and traders to conduct business plus various of supermarkets. Ilomba is rich and diverse in cultural practices due to having various tribes of Tanzania and people of different races though the typical indigenous tribes on the area are Nyakyusa and Safwa. People of different beliefs and religion inhabit the area. Among the places for worship include EAGT-Ilomba, KKKT-Sae, Moravian-Sinai Church, Pentecost Holiness Mission(PHM-Sae), Roman Catholic-Luanda and Sae Mosque. Upon travelling and for accommodation, several Hotels and motels of Green and Peter Safar are found in the area. Ilomba Police Post is situated on Tanzania-Zambia highway only 400 meters from Ilomba bus stop. Neighborhoods The ward has 7 neighborhoods. Hayanga Ihanga Ilomba Ituha Kagera Sae Tonya References Wards of Mbeya Region
https://en.wikipedia.org/wiki/Ghana%20%28Mbeya%20ward%29
Ghana is an administrative ward in the Mbeya Urban district of the Mbeya Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 5,384 people in the ward, from 4,885 in 2012. Neighborhoods The ward has 3 neighborhoods Ghana Magharibi, Ghana Mashariki, and Mbata. References Wards of Mbeya Region
https://en.wikipedia.org/wiki/Mapping%20torus
In mathematics, the mapping torus in topology of a homeomorphism f of some topological space X to itself is a particular geometric construction with f. Take the cartesian product of X with a closed interval I, and glue the boundary components together by the static homeomorphism: The result is a fiber bundle whose base is a circle and whose fiber is the original space X. If X is a manifold, Mf will be a manifold of dimension one higher, and it is said to "fiber over the circle". As a simple example, let be the circle, and be the inversion , then the mapping torus is the Klein bottle. Mapping tori of surface homeomorphisms play a key role in the theory of 3-manifolds and have been intensely studied. If S is a closed surface of genus g ≥ 2 and if f is a self-homeomorphism of S, the mapping torus Mf is a closed 3-manifold that fibers over the circle with fiber S. A deep result of Thurston states that in this case the 3-manifold Mf is hyperbolic if and only if f is a pseudo-Anosov homeomorphism of S. References General topology Geometric topology Homeomorphisms
https://en.wikipedia.org/wiki/Osmo%20Pekonen
Osmo Pekonen (2 April 1960 – 12 October 2022) was a Finnish mathematician, historian of science, and author. He was a docent of mathematics at the University of Helsinki and at the University of Jyväskylä, a docent of history of science at the University of Oulu, and a docent of history of civilization at the University of Lapland. He was the Book Reviews section editor of The Mathematical Intelligencer. Personal life and death Pekonen died suddenly in his sleep on 12 October 2022, at the age of 62, in Uzès, France during a bicycle tour. Honours and distinctions Osmo Pekonen was a corresponding member of four French academies; these are: Académie des sciences, arts et belles-lettres de Caen (founded in 1652), Académie des sciences, belles-lettres et arts de Besançon et de Franche-Comté (founded in 1752), Académie d'Orléans (founded in 1809) and Académie européenne des sciences, des arts et des lettres (founded in 1979). In 2012, he was awarded the Prix Chaix d'Est-Ange of the Académie des sciences morales et politiques in the field of history. Bibliography Doctoral theses Contributions to and a survey on moduli spaces of differential geometric structures with applications in physics, PhD thesis, University of Jyväskylä, 1988 La rencontre des religions autour du voyage de l'abbé Réginald Outhier en Suède en 1736-1737, D.Soc.Sci thesis, Rovaniemi: Lapland University Press, 2010 Monographies and edited volumes Topological and Geometrical Methods in Field Theory, Osmo Pekonen & Jouko Mickelsson (eds.), Singapore: World Scientific, 1992 Symbolien metsässä: Matemaattisia esseitä, Osmo Pekonen (ed.), Helsinki: Art House, 1992 Ranskan tiede: Kuuluisia kouluja ja instituutioita, Helsinki: Art House, 1995 Marian maa. Lasse Heikkilän elämä 1925–1961, Helsinki: SKS, 2002 Osmo Pekonen & Lea Pulkkinen: Sosiaalinen pääoma ja tieto- ja viestintätekniikan kehitys, Helsinki: The Parliament of Finland, Committee for the Future, 2002 Suomalaisen modernin lyriikan synty. Juhlakirja 75-vuotiaalle Lassi Nummelle, Osmo Pekonen (ed.), Kuopio: Snellman-instituutti, 2005 Porrassalmi. Etelä-Savon kulttuurin vuosikirja (ten volumes, I-X), Jorma Julkunen, Jutta Julkunen & Osmo Pekonen et alia (eds.) Mikkeli: Savon Sotilasperinneyhdistys Porrassalmi ry, 2008-2017 Lapin tuhat tarinaa. Anto Leikolan juhlakirja,Osmo Pekonen & Johan Stén (eds.), Ranua: Mäntykustannus, 2012 Salaperäinen Venus, Ranua: Mäntykustannus, 2012 Maupertuis en Laponie, with Anouchka Vasak, Paris: Hermann, 2014 Maan muoto, with Marja Itkonen-Kaila, Tornio: Väylä, 2019 Markkasen galaksit. Tapio Markkanen in memoriam, edited with Johan Stén, Helsinki: Ursa, 2019 Valon aika, with Johan Stén, Helsinki: Art House, 2019 Pohjan Tornio. Matkamiesten ääniä vuosisatain varrelta 1519-1919, Rovaniemi: Väylä, 2022 Essay collections Danse macabre: Eurooppalaisen matkakirja, Jyväskylä: Atena, 1994 Tuhat vuotta, Helsinki: WSOY, 1998 Minä ja Dolly: Kolumneja, esseitä, runoja, Jyväskylä: Atena, 1
https://en.wikipedia.org/wiki/Gaspare%20Mainardi
Gaspare Mainardi (June 1800 in Abbiategrasso, Milan – 9 March 1879 in Lecco) was an Italian mathematician active in differential geometry. He is remembered for the Gauss–Codazzi–Mainardi equations. References Tricomi: La Matematica Italiana 1800-1950 (entry on Mainardi) 19th-century Italian mathematicians 1800 births 1879 deaths
https://en.wikipedia.org/wiki/Johann%20II%20Bernoulli
Johann II Bernoulli (also known as Jean; 18 May 1710 in Basel – 17 July 1790 in Basel) was the youngest of the three sons of the Swiss mathematician Johann Bernoulli. He studied law and mathematics, and, after travelling in France, was for five years professor of eloquence in the university of his native city. In 1736 he was awarded the prize of the French Academy for his suggestive studies of aether. On the death of his father he succeeded him as professor of mathematics in the University of Basel. He was thrice a successful competitor for the prizes of the Academy of Sciences of Paris. His prize subjects were the capstan, the propagation of light, and the magnet. He enjoyed the friendship of P. L. M. de Maupertuis, who died under his roof while on his way to Berlin. He himself died in 1790. His two sons, Johann and Jakob, are the last noted mathematicians of the Bernoulli family. References External links 1710 births 1790 deaths Scientists from Basel-Stadt 18th-century Swiss mathematicians Members of the French Academy of Sciences Swiss Calvinist and Reformed Christians Johann II
https://en.wikipedia.org/wiki/Haefliger%20structure
In mathematics, a Haefliger structure on a topological space is a generalization of a foliation of a manifold, introduced by André Haefliger in 1970. Any foliation on a manifold induces a special kind of Haefliger structure, which uniquely determines the foliation. Definition A codimension- Haefliger structure on a topological space consists of the following data: a cover of by open sets ; a collection of continuous maps ; for every , a diffeomorphism between open neighbourhoods of and with ; such that the continuous maps from to the sheaf of germs of local diffeomorphisms of satisfy the 1-cocycle condition for The cocycle is also called a Haefliger cocycle. More generally, , piecewise linear, analytic, and continuous Haefliger structures are defined by replacing sheaves of germs of smooth diffeomorphisms by the appropriate sheaves. Examples and constructions Pullbacks An advantage of Haefliger structures over foliations is that they are closed under pullbacks. More precisely, given a Haefliger structure on , defined by a Haefliger cocycle , and a continuous map , the pullback Haefliger structure on is defined by the open cover and the cocycle . As particular cases we obtain the following constructions: Given a Haefliger structure on and a subspace , the restriction of the Haefliger structure to is the pullback Haefliger structure with respect to the inclusion Given a Haefliger structure on and another space , the product of the Haefliger structure with is the pullback Haefliger structure with respect to the projection Foliations Recall that a codimension- foliation on a smooth manifold can be specified by a covering of by open sets , together with a submersion from each open set to , such that for each there is a map from to local diffeomorphisms with whenever is close enough to . The Haefliger cocycle is defined by germ of at u. As anticipated, foliations are not closed in general under pullbacks but Haefliger structures are. Indeed, given a continuous map , one can take pullbacks of foliations on provided that is transverse to the foliation, but if is not transverse the pullback can be a Haefliger structure that is not a foliation. Classifying space Two Haefliger structures on are called concordant if they are the restrictions of Haefliger structures on to and . There is a classifying space for codimension- Haefliger structures which has a universal Haefliger structure on it in the following sense. For any topological space and continuous map from to the pullback of the universal Haefliger structure is a Haefliger structure on . For well-behaved topological spaces this induces a 1:1 correspondence between homotopy classes of maps from to and concordance classes of Haefliger structures. References Differential geometry Smooth manifolds Topological spaces Structures on manifolds Foliations
https://en.wikipedia.org/wiki/Principal%20indecomposable%20module
In mathematics, especially in the area of abstract algebra known as module theory, a principal indecomposable module has many important relations to the study of a ring's modules, especially its simple modules, projective modules, and indecomposable modules. Definition A (left) principal indecomposable module of a ring R is a (left) submodule of R that is a direct summand of R and is an indecomposable module. Alternatively, it is an indecomposable, projective, cyclic module. Principal indecomposable modules are also called PIMs for short. Relations The projective indecomposable modules over some rings have very close connections with those rings' simple, projective, and indecomposable modules. If the ring R is Artinian or even semiperfect, then R is a direct sum of principal indecomposable modules, and there is one isomorphism class of PIM per isomorphism class of simple module. To each PIM P is associated its head, P/JP, which is a simple module, being an indecomposable semi-simple module. To each simple module S is associated its projective cover P, which is a PIM, being an indecomposable, projective, cyclic module. Similarly over a semiperfect ring, every indecomposable projective module is a PIM, and every finitely generated projective module is a direct sum of PIMs. In the context of group algebras of finite groups over fields (which are semiperfect rings), the representation ring describes the indecomposable modules, and the modular characters of simple modules represent both a subring and a quotient ring. The representation ring over the complex field is usually better understood and since PIMs correspond to modules over the complexes using p-modular system, one can use PIMs to transfer information from the complex representation ring to the representation ring over a field of positive characteristic. Roughly speaking this is called block theory. Over a Dedekind domain that is not a PID, the ideal class group measures the difference between projective indecomposable modules and principal indecomposable modules: the projective indecomposable modules are exactly the (modules isomorphic to) nonzero ideals and the principal indecomposable modules are precisely the (modules isomorphic to) nonzero principal ideals. References Representation theory of finite groups Module theory
https://en.wikipedia.org/wiki/Greedy%20coloring
In the study of graph coloring problems in mathematics and computer science, a greedy coloring or sequential coloring is a coloring of the vertices of a graph formed by a greedy algorithm that considers the vertices of the graph in sequence and assigns each vertex its first available color. Greedy colorings can be found in linear time, but they do not, in general, use the minimum number of colors possible. Different choices of the sequence of vertices will typically produce different colorings of the given graph, so much of the study of greedy colorings has concerned how to find a good ordering. There always exists an ordering that produces an optimal coloring, but although such orderings can be found for many special classes of graphs, they are hard to find in general. Commonly used strategies for vertex ordering involve placing higher-degree vertices earlier than lower-degree vertices, or choosing vertices with fewer available colors in preference to vertices that are less constrained. Variations of greedy coloring choose the colors in an online manner, without any knowledge of the structure of the uncolored part of the graph, or choose other colors than the first available in order to reduce the total number of colors. Greedy coloring algorithms have been applied to scheduling and register allocation problems, the analysis of combinatorial games, and the proofs of other mathematical results including Brooks' theorem on the relation between coloring and degree. Other concepts in graph theory derived from greedy colorings include the Grundy number of a graph (the largest number of colors that can be found by a greedy coloring), and the well-colored graphs, graphs for which all greedy colorings use the same number of colors. Algorithm The greedy coloring for a given vertex ordering can be computed by an algorithm that runs in linear time. The algorithm processes the vertices in the given ordering, assigning a color to each one as it is processed. The colors may be represented by the numbers and each vertex is given the color with the smallest number that is not already used by one of its neighbors. To find the smallest available color, one may use an array to count the number of neighbors of each color (or alternatively, to represent the set of colors of neighbors), and then scan the array to find the index of its first zero. In Python, the algorithm can be expressed as: def first_available(color_list): """Return smallest non-negative integer not in the given list of colors.""" color_set = set(color_list) count = 0 while True: if count not in color_set: return count count += 1 def greedy_color(G, order): """Find the greedy coloring of G in the given order. The representation of G is assumed to be like https://www.python.org/doc/essays/graphs/ in allowing neighbors of a node/vertex to be iterated over by "for w in G[node]". The return value is a dictionary mapping vertices t
https://en.wikipedia.org/wiki/Sergio%20Bustos
Sergio Bustos (born December 20, 1972) is a retired Argentine football player. References External links Argentine Primera statistics 1972 births Living people Footballers from Buenos Aires Argentine men's footballers Racing Club de Avellaneda footballers 1. FC Nürnberg players Chacarita Juniors footballers Club Atlético Platense footballers Argentinos Juniors footballers Dresdner SC players Chemnitzer FC players Defensa y Justicia footballers Talleres de Córdoba footballers Bundesliga players 2. Bundesliga players Expatriate men's footballers in Germany Expatriate men's footballers in Ecuador Argentine expatriate sportspeople in Ecuador Men's association football midfielders Argentine expatriate sportspeople in Germany
https://en.wikipedia.org/wiki/Manifold%20%28magazine%29
Manifold was a mathematical magazine published at the University of Warwick. It was established in 1968. Its philosophy was "It is possible to be serious about mathematics, without being solemn." Its best known editor was the mathematician Ian Stewart who edited the magazine in the late 1960s. A 1969 edition of the magazine mentioned a game called "Finchley Central", which became the basis for the game of Mornington Crescent as popularised by the BBC Radio 4 panel game I'm Sorry I Haven't a Clue. In 1983 the magazine was reincarnated as 2-Manifold. References External links Manifold web site Science and technology magazines published in the United Kingdom Defunct magazines published in the United Kingdom Magazines established in 1968 Magazines disestablished in 1980 Mathematics magazines University of Warwick
https://en.wikipedia.org/wiki/Lajos%20Heged%C5%B1s
Lajos Hegedűs (born 19 December 1987) is a Hungarian former football goalkeeper. In 2020, he was called up in the Hungary national team without making any appearances. Club statistics Updated to games played as of 15 May 2021. References HLSZ database International career He was first called up to the senior side for November 2020 games. References 1987 births Living people Footballers from Budapest Hungarian men's footballers Men's association football goalkeepers MTK Budapest FC players BFC Siófok players Pécsi MFC players Puskás Akadémia FC players Paksi FC players Nyíregyháza Spartacus FC players Szolnoki MÁV FC footballers Dunaújváros PASE players Nemzeti Bajnokság I players Nemzeti Bajnokság II players
https://en.wikipedia.org/wiki/Crown%20graph
In graph theory, a branch of mathematics, a crown graph on vertices is an undirected graph with two sets of vertices and and with an edge from to whenever . The crown graph can be viewed as a complete bipartite graph from which the edges of a perfect matching have been removed, as the bipartite double cover of a complete graph, as the tensor product , as the complement of the Cartesian direct product of and , or as a bipartite Kneser graph representing the 1-item and -item subsets of an -item set, with an edge between two subsets whenever one is contained in the other. Examples The 6-vertex crown graph forms a cycle, and the 8-vertex crown graph is isomorphic to the graph of a cube. In the Schläfli double six, a configuration of 12 lines and 30 points in three-dimensional space, the twelve lines intersect each other in the pattern of a 12-vertex crown graph. Properties The number of edges in a crown graph is the pronic number . Its achromatic number is : one can find a complete coloring by choosing each pair as one of the color classes. Crown graphs are symmetric and distance-transitive. describe partitions of the edges of a crown graph into equal-length cycles. The -vertex crown graph may be embedded into four-dimensional Euclidean space in such a way that all of its edges have unit length. However, this embedding may also place some non-adjacent vertices a unit distance apart. An embedding in which edges are at unit distance and non-edges are not at unit distance requires at least dimensions. This example shows that a graph may require very different dimensions to be represented as a unit distance graphs and as a strict unit distance graph. The minimum number of complete bipartite subgraphs needed to cover the edges of a crown graph (its bipartite dimension, or the size of a minimum biclique cover) is the inverse function of the central binomial coefficient. The complement graph of a -vertex crown graph is the Cartesian product of complete graphs , or equivalently the rook's graph. Applications In etiquette, a traditional rule for arranging guests at a dinner table is that men and women should alternate positions, and that no married couple should sit next to each other. The arrangements satisfying this rule, for a party consisting of n married couples, can be described as the Hamiltonian cycles of a crown graph. For instance, the arrangements of vertices shown in the figure can be interpreted as seating charts of this type in which each husband and wife are seated as far apart as possible. The problem of counting the number of possible seating arrangements, or almost equivalently the number of Hamiltonian cycles in a crown graph, is known in combinatorics as the ménage problem; for crown graphs with 6, 8, 10, ... vertices the number of (oriented) Hamiltonian cycles is 2, 12, 312, 9600, 416880, 23879520, 1749363840, ... Crown graphs can be used to show that greedy coloring algorithms behave badly in the worst case: if th
https://en.wikipedia.org/wiki/Aleksandar%20Jevti%C4%87
Aleksandar Jevtić (, ; born 30 March 1985) is a Serbian retired football striker . Career statistics References External links Profile at Serbian Federation site. Profile at Srbijafudbal. Aleksandar Jevtić Stats at Utakmica.rs 1985 births Living people Footballers from Šabac Serbian men's footballers Men's association football forwards Serbia men's international footballers Serbian expatriate men's footballers Serbian expatriate sportspeople in Turkey Serbian expatriate sportspeople in China Serbian expatriate sportspeople in Belarus Serbian expatriate sportspeople in Thailand Expatriate men's footballers in Turkey Expatriate men's footballers in China Expatriate men's footballers in Belarus Expatriate men's footballers in Thailand Serbian SuperLiga players Süper Lig players Chinese Super League players FK Balkan Mirijevo players FK Smederevo 1924 players FK Mačva Šabac players FK Borac Čačak players Hacettepe S.K. footballers OFK Beograd players Red Star Belgrade footballers Jiangsu F.C. players Liaoning F.C. players FC BATE Borisov players FK Jagodina players FK Čukarički players Aleksandar Jevtic FK Voždovac players
https://en.wikipedia.org/wiki/Cartan%E2%80%93Eilenberg%20resolution
In homological algebra, the Cartan–Eilenberg resolution is in a sense, a resolution of a chain complex. It can be used to construct hyper-derived functors. It is named in honor of Henri Cartan and Samuel Eilenberg. Definition Let be an Abelian category with enough projectives, and let be a chain complex with objects in . Then a Cartan–Eilenberg resolution of is an upper half-plane double complex (i.e., for ) consisting of projective objects of and an "augmentation" chain map such that If then the p-th column is zero, i.e. for all q. For any fixed column , The complex of boundaries obtained by applying the horizontal differential to (the st column of ) forms a projective resolution of the boundaries of . The complex obtained by taking the homology of each row with respect to the horizontal differential forms a projective resolution of degree p homology of . It can be shown that for each p, the column is a projective resolution of . There is an analogous definition using injective resolutions and cochain complexes. The existence of Cartan–Eilenberg resolutions can be proved via the horseshoe lemma. Hyper-derived functors Given a right exact functor , one can define the left hyper-derived functors of on a chain complex by Constructing a Cartan–Eilenberg resolution , Applying the functor to , and Taking the homology of the resulting total complex. Similarly, one can also define right hyper-derived functors for left exact functors. See also Hyperhomology References Homological algebra
https://en.wikipedia.org/wiki/Volume%20of%20an%20n-ball
In geometry, a ball is a region in a space comprising all points within a fixed distance, called the radius, from a given point; that is, it is the region enclosed by a sphere or hypersphere. An -ball is a ball in an -dimensional Euclidean space. The volume of a -ball is the Lebesgue measure of this ball, which generalizes to any dimension the usual volume of a ball in 3-dimensional space. The volume of a -ball of radius is where is the volume of the unit -ball, the -ball of radius . The real number can be expressed via a two-dimension recurrence relation. Closed-form expressions involve the gamma, factorial, or double factorial function. The volume can also be expressed in terms of , the area of the unit -sphere. Formulas The first volumes are as follows: Closed form The -dimensional volume of a Euclidean ball of radius in -dimensional Euclidean space is: where is Euler's gamma function. The gamma function is offset from but otherwise extends the factorial function to non-integer arguments. It satisfies if is a positive integer and if is a non-negative integer. Two-dimension recurrence relation The volume can be computed without use of the Gamma function. As is proved below using a vector-calculus double integral in polar coordinates, the volume of an -ball of radius can be expressed recursively in terms of the volume of an -ball, via the interleaved recurrence relation: This allows computation of in approximately steps. Alternative forms The volume can also be expressed in terms of an -ball using the one-dimension recurrence relation: Inverting the above, the radius of an -ball of volume can be expressed recursively in terms of the radius of an - or -ball: Using explicit formulas for particular values of the gamma function at the integers and half-integers gives formulas for the volume of a Euclidean ball in terms of factorials. For non-negative integer , these are: The volume can also be expressed in terms of double factorials. For a positive odd integer , the double factorial is defined by The volume of an odd-dimensional ball is There are multiple conventions for double factorials of even integers. Under the convention in which the double factorial satisfies the volume of an -dimensional ball is, regardless of whether is even or odd, Instead of expressing the volume of the ball in terms of its radius , the formulas can be inverted to express the radius as a function of the volume: Approximation for high dimensions Stirling's approximation for the gamma function can be used to approximate the volume when the number of dimensions is high. In particular, for any fixed value of the volume tends to a limiting value of 0 as goes to infinity. Which value of maximizes depends upon the value of ; for example, the volume is increasing for , achieves its maximum when , and is decreasing for . Relation with surface area Let denote the hypervolume of the -sphere of radius . The -sphere is the -dimensi
https://en.wikipedia.org/wiki/M%C3%A9nage%20problem
In combinatorial mathematics, the ménage problem or problème des ménages asks for the number of different ways in which it is possible to seat a set of male-female couples at a round dining table so that men and women alternate and nobody sits next to his or her partner. (Ménage is the French word for "household", referring here to a male-female couple.) This problem was formulated in 1891 by Édouard Lucas and independently, a few years earlier, by Peter Guthrie Tait in connection with knot theory. For a number of couples equal to 3, 4, 5, ... the number of seating arrangements is 12, 96, 3120, 115200, 5836320, 382072320, 31488549120, ... . Mathematicians have developed formulas and recurrence equations for computing these numbers and related sequences of numbers. Along with their applications to etiquette and knot theory, these numbers also have a graph theoretic interpretation: they count the numbers of matchings and Hamiltonian cycles in certain families of graphs. Touchard's formula Let Mn denote the number of seating arrangements for n couples. derived the formula Much subsequent work has gone into alternative proofs for this formula and into various generalized versions of the problem. A different umbral formula for Mn involving Chebyshev polynomials of first kind was given by . Ménage numbers and ladies-first solutions There are 2×n! ways of seating the women: there are two sets of seats that can be arranged for the women, and there are n! ways of seating them at a particular set of seats. For each seating arrangement for the women, there are ways of seating the men; this formula simply omits the 2×n! factor from Touchard's formula. The resulting smaller numbers (again, starting from n = 3), 1, 2, 13, 80, 579, 4738, 43387, 439792, ... are called the ménage numbers. The factor is the number of ways of forming non-overlapping pairs of adjacent seats or, equivalently, the number of matchings of edges in a cycle graph of vertices. The expression for is the immediate result of applying the principle of inclusion–exclusion to arrangements in which the people seated at the endpoints of each edge of a matching are required to be a couple. Until the work of , solutions to the ménage problem took the form of first finding all seating arrangements for the women and then counting, for each of these partial seating arrangements, the number of ways of completing it by seating the men away from their partners. Bogart and Doyle argued that Touchard's formula may be derived directly by considering all seating arrangements at once rather than by factoring out the participation of the women. However, found the even more straightforward ladies-first solution described above by making use of a few of Bogart and Doyle's ideas (although they took care to recast the argument in non-gendered language). The ménage numbers satisfy the recurrence relation and the simpler four-term recurrence from which the ménage numbers themselves can easily be cal
https://en.wikipedia.org/wiki/Arik%20Gilrovich
Arik Gilrovich is a former Israeli footballer and manager. Managerial statistics References External links Official website 1960 births Living people Israeli Jews Israeli men's footballers Hapoel Ramat Gan Givatayim F.C. players Maccabi Sha'arayim F.C. players Maccabi HaShikma Ramat Hen F.C. players Hapoel Rishon LeZion F.C. managers Hapoel Ramat Gan Givatayim F.C. managers Footballers from Ashkelon Men's association football forwards Israeli football managers Men's association football defenders
https://en.wikipedia.org/wiki/Jekuthiel%20Ginsburg
Jekuthiel Ginsburg (1889–1957) was a professor of mathematics at Yeshiva University. He established the journal Scripta Mathematica. He also was honored as a fellow of the New York Academy of Sciences. References . . 1889 births 1957 deaths 20th-century American mathematicians American Jews