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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 |
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