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https://en.wikipedia.org/wiki/Dehn%20function
In the mathematical subject of geometric group theory, a Dehn function, named after Max Dehn, is an optimal function associated to a finite group presentation which bounds the area of a relation in that group (that is a freely reduced word in the generators representing the identity element of the group) in terms of the length of that relation (see pp. 79–80 in ). The growth type of the Dehn function is a quasi-isometry invariant of a finitely presented group. The Dehn function of a finitely presented group is also closely connected with non-deterministic algorithmic complexity of the word problem in groups. In particular, a finitely presented group has solvable word problem if and only if the Dehn function for a finite presentation of this group is recursive (see Theorem 2.1 in ). The notion of a Dehn function is motivated by isoperimetric problems in geometry, such as the classic isoperimetric inequality for the Euclidean plane and, more generally, the notion of a filling area function that estimates the area of a minimal surface in a Riemannian manifold in terms of the length of the boundary curve of that surface. History The idea of an isoperimetric function for a finitely presented group goes back to the work of Max Dehn in 1910s. Dehn proved that the word problem for the standard presentation of the fundamental group of a closed oriented surface of genus at least two is solvable by what is now called Dehn's algorithm. A direct consequence of this fact is that for this presentation the Dehn function satisfies Dehn(n) ≤ n. This result was extended in 1960s by Martin Greendlinger to finitely presented groups satisfying the C'(1/6) small cancellation condition. The formal notion of an isoperimetric function and a Dehn function as it is used today appeared in late 1980s – early 1990s together with the introduction and development of the theory of word-hyperbolic groups. In his 1987 monograph "Hyperbolic groups" Gromov proved that a finitely presented group is word-hyperbolic if and only if it satisfies a linear isoperimetric inequality, that is, if and only if the Dehn function of this group is equivalent to the function f(n) = n. Gromov's proof was in large part informed by analogy with filling area functions for compact Riemannian manifolds where the area of a minimal surface bounding a null-homotopic closed curve is bounded in terms of the length of that curve. The study of isoperimetric and Dehn functions quickly developed into a separate major theme in geometric group theory, especially since the growth types of these functions are natural quasi-isometry invariants of finitely presented groups. One of the major results in the subject was obtained by Sapir, Birget and Rips who showed that most "reasonable" time complexity functions of Turing machines can be realized, up to natural equivalence, as Dehn functions of finitely presented groups. Formal definition Let be a finite group presentation where the X is a finite alphabet and where
https://en.wikipedia.org/wiki/ACM%20Transactions%20on%20Mathematical%20Software
ACM Transactions on Mathematical Software (TOMS) is a quarterly scientific journal that aims to disseminate the latest findings of note in the field of numeric, symbolic, algebraic, and geometric computing applications. The journal publishes two kinds of articles: Regular research papers that advance the development of algorithms and software for mathematical computing, and "algorithms papers" that describe a specific implementation of an algorithm and that are accompanied by the source code for this algorithm. Algorithms described in the transactions are generally published in the Collected Algorithms of the ACM (CALGO). Algorithms published since 1975 (and some earlier ones) are all still available. Software that accompanies algorithm papers is accessible by anyone via the CALGO website. History ACM Transactions on Mathematical Software is one of the oldest scientific journals specifically dedicated to mathematical algorithms and their implementation in software, and has been published since March 1975 by the Association for Computing Machinery (ACM). The journal is described as follows on the TOMS Homepage of the ACM Digital Library page: The purpose of the journal was laid out by its founding editor, John Rice, in the inaugural issue. The decision to found the journal came out of the 1970 Mathematical Software Symposium at Purdue University, also organized by Rice, who then negotiated with both SIAM and the ACM regarding its publication. References External links Journal home page ACM Collected Algorithms Transactions on Mathematical Software Academic journals established in 1975
https://en.wikipedia.org/wiki/Bumbuta
Bumbuta is an administrative ward in the Kondoa district of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 9,349 people in the ward, from 8,602 in 2012. References Kondoa District Wards of Dodoma Region
https://en.wikipedia.org/wiki/Busi%20%28Tanzanian%20ward%29
Busi is an administrative ward in the Kondoa district of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 8,459 people in the ward, from 18,724 in 2012. References Kondoa District Wards of Dodoma Region
https://en.wikipedia.org/wiki/Mondo%20%28Chemba%29
Mondo is an administrative ward in the Chemba District of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 10,318 people in the ward, from 9,494 in 2012. References Wards of Dodoma Region
https://en.wikipedia.org/wiki/Dalai%20%28Tanzanian%20ward%29
Dalai is an administrative ward in the Chemba District of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 16,387 people in the ward, from 15,078 in 2012. References Wards of Dodoma Region
https://en.wikipedia.org/wiki/Chemba
Chemba is an administrative ward in the Chemba district of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 5,341 people in the district, from 16,047 in 2012. References Wards of Dodoma Region
https://en.wikipedia.org/wiki/Paranga%2C%20Tanzania
Paranga is an administrative ward in the Chemba District of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 13,365 people in the ward, from 12,297 in 2012. References Wards of Dodoma Region
https://en.wikipedia.org/wiki/Mpendo
Mpendo is an administrative ward in the Chemba District of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 7,605 people in the ward, from 6,997 in 2012. References Wards of Dodoma Region
https://en.wikipedia.org/wiki/Kingale
Kingale is an administrative ward in the Kondoa district of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 11,958 people in the ward, from 11,003 in 2012. References Kondoa District Wards of Dodoma Region
https://en.wikipedia.org/wiki/Changaa%20%28Tanzanian%20ward%29
Changaa is an administrative ward in the Kondoa district of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 10,471 people in the ward, from 9,634 in 2012. References Kondoa District Wards of Dodoma Region
https://en.wikipedia.org/wiki/Thawi
Thawi is an administrative ward in the Kondoa District of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 11,737 people in the ward, from 10,799 in 2012. References Kondoa District Wards of Dodoma Region
https://en.wikipedia.org/wiki/Mnenia
Mnenia is an administrative ward in the Kondoa District of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 12,529 people in the ward, from 11,528 in 2012. References Kondoa District Wards of Dodoma Region
https://en.wikipedia.org/wiki/Kikilo
Kikilo is an administrative ward in the Kondoa district of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 10,127 people in the ward, from 9,318 in 2012. References Kondoa District Wards of Dodoma Region
https://en.wikipedia.org/wiki/Charles%20Sims%20%28mathematician%29
Charles Coffin Sims (April 14, 1937 – October 23, 2017) was an American mathematician best known for his work in group theory. Together with Donald G. Higman he discovered the Higman–Sims group, one of the sporadic groups. The permutation group software developed by Sims also led to the proof of existence of the Lyons group (also known as the Lyons–Sims group) and the O'Nan group (also known as the O'Nan–Sims group). Sims was born and raised in Elkhart, Indiana, and received his B.S. from the University of Michigan. He did his graduate studies at Harvard University, where he was a student of John G. Thompson and received his Ph.D. degree in 1963. In his thesis, he enumerated p-groups, giving sharp asymptotic upper and lower bounds. Sims is one of the founders of computational group theory and is the eponym of the Schreier–Sims algorithm. He was a faculty member at the Department of Mathematics at Rutgers University from 1965 to 2007. During that period he served, in particular, as Department Chair (1982–84) and Associate Provost for Computer Planning (1984–87). Sims retired from Rutgers in 2007 and moved to St. Petersburg, Florida. In 2012, he became a fellow of the American Mathematical Society. See also Higman–Sims graph Prevalence of p-groups Sims conjecture References External links Personal webpage 1937 births 2017 deaths 20th-century American mathematicians 21st-century American mathematicians Group theorists Computational group theory Harvard University alumni Rutgers University faculty Fellows of the American Mathematical Society Mathematicians from Indiana University of Michigan alumni People from Elkhart, Indiana
https://en.wikipedia.org/wiki/Kengo%20Ishii
is a Japanese footballer who currently plays for Nankatsu SC. Club statistics Updated to 30 November 2017. References External links Profile at Hokkaido Consadole Sapporo 1986 births Living people Association football people from Hokkaido Japanese men's footballers J1 League players J2 League players Hokkaido Consadole Sapporo players Ehime FC players Men's association football midfielders
https://en.wikipedia.org/wiki/Tomoki%20Suzuki%20%28footballer%29
is a Japanese former professional footballer who played as a midfielder. Career statistics References External links Living people 1985 births People from Iwamizawa, Hokkaido Association football people from Hokkaido Men's association football midfielders Japanese men's footballers J1 League players J2 League players Hokkaido Consadole Sapporo players
https://en.wikipedia.org/wiki/Yasuaki%20Okamoto
is a former Japanese football player who featured for Roasso Kumamoto. Club statistics Updated to 2 February 2018. References External links Profile at Roasso Kumamoto Profile at Consadole Sapporo 1988 births Living people Japanese men's footballers J1 League players J2 League players Hokkaido Consadole Sapporo players Roasso Kumamoto players Men's association football midfielders Association football people from Kumamoto
https://en.wikipedia.org/wiki/Hironobu%20Haga
is a former Japanese football player. Club statistics References External links 1982 births Living people Sendai University alumni Association football people from Miyagi Prefecture Japanese men's footballers J1 League players J2 League players JEF United Chiba players Hokkaido Consadole Sapporo players Men's association football midfielders
https://en.wikipedia.org/wiki/Kazumasa%20Uesato
is a Japanese football player who plays for FC Ryukyu. Club statistics Updated to 23 February 2018. References External links Profile at Roasso Kumamoto 1986 births Living people Association football people from Okinawa Prefecture Japanese men's footballers J1 League players J2 League players Hokkaido Consadole Sapporo players FC Tokyo players Tokushima Vortis players Roasso Kumamoto players FC Ryukyu players Men's association football midfielders
https://en.wikipedia.org/wiki/Yasuhiro%20Hiraoka
is a Japanese footballer who plays for Ehime FC from 2023. Club career On 18 December 2022, Hiraoka joined to J3 club, Ehime FC for upcoming 2023 season. Career statistics Updated to the end 2022 season. References External links Profile at Vegalta Sendai 1986 births Living people People from Fujinomiya, Shizuoka Association football people from Shizuoka Prefecture Japanese men's footballers J1 League players J2 League players J3 League players Shimizu S-Pulse players Hokkaido Consadole Sapporo players Vegalta Sendai players Ehime FC players Men's association football defenders
https://en.wikipedia.org/wiki/Split-pi%20topology
In electronics, a split-pi topology is a pattern of component interconnections used in a kind of power converter that can theoretically produce an arbitrary output voltage, either higher or lower than the input voltage. In practice the upper voltage output is limited to the voltage rating of components used. It is essentially a boost (step-up) converter followed by a buck (step-down) converter. The topology and use of MOSFETs make it inherently bi-directional which lends itself to applications requiring regenerative braking. The split-pi converter is a type of DC-to-DC converter that has an output voltage magnitude either greater than or less than the input voltage magnitude. It is a switched-mode power supply with a similar circuit configuration to a boost converter followed by a buck converter. Split-pi gets its name from the pi circuit due to the use of two pi filters in series and split with the switching MOSFET bridges. Other DC–DC converter topologies that can produce output voltage magnitude either greater than or less than the input voltage magnitude include the boost-buck converter topologies (the split-pi, the Ćuk converter, the SEPIC, etc.) and the buck–boost converter topologies. Principle of operation In typical operation where a source voltage is located at the left-hand side input terminals, the left-hand bridge operates as a boost converter and the right-hand bridge operates as a buck converter. In regenerative mode, the reverse is true with the left-hand bridge operating as a buck converter and the right as the boost converter. Only one bridge switches at any time to provide voltage conversion, with the unswitched bridge's top switch always switched on. A straight through 1:1 voltage output is achieved with the top switch of each bridge switch on and the bottom switches off. The output voltage is adjustable based on the duty cycle of the switching MOSFET bridge. Applications Electric drivetrain Motor control Battery balancing Regenerative braking References British Patent GB2376357B - Power converter and method for power conversion DC-to-DC converters Voltage regulation
https://en.wikipedia.org/wiki/Hiroki%20Miyazawa
is a Japanese football player currently playing for Hokkaido Consadole Sapporo. Career statistics Club Updated to the start of 2023 season. National team career statistics Appearances in major competitions References External links Profile at Consadole Sapporo 1989 births Living people Association football people from Hokkaido Japanese men's footballers J1 League players J2 League players Hokkaido Consadole Sapporo players Men's association football midfielders People from Date, Hokkaido
https://en.wikipedia.org/wiki/Junki%20Yokono
is a Japanese football player. Club statistics Updated to 8 March 2018. References External links 1989 births Living people Association football people from Hokkaido Japanese men's footballers J1 League players J2 League players J3 League players Japan Football League players Hokkaido Consadole Sapporo players Zweigen Kanazawa players Fukushima United FC players ReinMeer Aomori players Nara Club players Expatriate men's footballers in Thailand Men's association football forwards
https://en.wikipedia.org/wiki/Toshiyasu%20Takahara
is a former Japanese football player. Club statistics Updated to 31 December 2018. 1Includes J2/J3 Playoffs. References External links Profile at FC Machida Zelvia 1980 births Living people Aichi Gakuin University alumni Association football people from Gifu Prefecture Japanese men's footballers J1 League players J2 League players J3 League players Júbilo Iwata players Hokkaido Consadole Sapporo players Shimizu S-Pulse players FC Machida Zelvia players Men's association football goalkeepers Sportspeople from Gifu
https://en.wikipedia.org/wiki/Shingo%20Shibata
is a former Japanese football player. Club statistics References External links 1985 births Living people Tokoha University alumni Association football people from Tokyo Japanese men's footballers J1 League players J2 League players Hokkaido Consadole Sapporo players Thespakusatsu Gunma players Men's association football defenders People from Ōme, Tokyo
https://en.wikipedia.org/wiki/Hiroyuki%20Omichi
is a former Japanese football player. Club statistics References External links 1987 births Living people Association football people from Ibaraki Prefecture Japanese men's footballers J1 League players J2 League players J3 League players Japan Football League players Kashima Antlers players Fagiano Okayama players AC Nagano Parceiro players Iwate Grulla Morioka players Men's association football midfielders
https://en.wikipedia.org/wiki/Kenta%20Kasai
is a former Japanese football player. Club statistics References 1985 births Living people Association football people from Shizuoka Prefecture Japanese men's footballers Japanese expatriate men's footballers J1 League players Paulista Futebol Clube players Kashima Antlers players Men's association football defenders
https://en.wikipedia.org/wiki/Stratified%20Morse%20theory
In mathematics, stratified Morse theory is an analogue to Morse theory for general stratified spaces, originally developed by Mark Goresky and Robert MacPherson. The main point of the theory is to consider functions and consider how the stratified space changes as the real number changes. Morse theory of stratified spaces has uses everywhere from pure mathematics topics such as braid groups and representations to robot motion planning and potential theory. A popular application in pure mathematics is Morse theory on manifolds with boundary, and manifolds with corners. See also Digital Morse theory Discrete Morse theory Level-set method References DJVU file on Goresky's page Generalized manifolds Morse theory Singularity theory Stratifications
https://en.wikipedia.org/wiki/The%20Story%20of%20Maths
The Story of Maths is a four-part British television series outlining aspects of the history of mathematics. It was a co-production between the Open University and the BBC and aired in October 2008 on BBC Four. The material was written and presented by University of Oxford professor Marcus du Sautoy. The consultants were the Open University academics Robin Wilson, professor Jeremy Gray and June Barrow-Green. Kim Duke is credited as series producer. The series comprised four programmes respectively titled: The Language of the Universe; The Genius of the East; The Frontiers of Space; and To Infinity and Beyond. Du Sautoy documents the development of mathematics covering subjects such as the invention of zero and the unproven Riemann hypothesis, a 150-year-old problem for whose solution the Clay Mathematics Institute has offered a $1,000,000 prize. He escorts viewers through the subject's history and geography. He examines the development of key mathematical ideas and shows how mathematical ideas underpin the world's science, technology, and culture. He starts his journey in ancient Egypt and finishes it by looking at current mathematics. Between he travels through Babylon, Greece, India, China, and the medieval Middle East. He also looks at mathematics in Europe and then in America and takes the viewers inside the lives of many of the greatest mathematicians. "The Language of the Universe" In this opening programme Marcus du Sautoy looks at how important and fundamental mathematics is to our lives before looking at the mathematics of ancient Egypt, Mesopotamia, and Greece. Du Sautoy commences in Egypt where recording the patterns of the seasons and in particular the flooding of the Nile was essential to their economy. There was a need to solve practical problems such as land area for taxation purposes. Du Sautoy discovers the use of a decimal system based on the fingers on the hands, the unusual method for multiplication and division. He examines the Rhind Papyrus, the Moscow Papyrus and explores their understanding of binary numbers, fractions and solid shapes. He then travels to Babylon and discovered that the way we tell the time today is based on the Babylonian 60 base number system. So because of the Babylonians we have 60 seconds in a minute, and 60 minutes in an hour. He then shows how the Babylonians used quadratic equations to measure their land. He deals briefly with Plimpton 322. In Greece, the home of ancient Greek mathematics, he looks at the contributions of some of its greatest and well known mathematicians including Pythagoras, Plato, Euclid, and Archimedes, who are some of the people who are credited with beginning the transformation of mathematics from a tool for counting into the analytical subject we know today. A controversial figure, Pythagoras' teachings were considered suspect and his followers seen as social outcasts and a little be strange and not in the norm. There is a legend going around that one of his followers,
https://en.wikipedia.org/wiki/Yasushi%20Endo
is a Japanese footballer who plays for Vegalta Sendai. Career statistics . International career On 7 May 2015, Japan's coach Vahid Halilhodžić called him for a two-days training camp. Honours Club Kashima Antlers J. League Division 1 (4) : 2007, 2008, 2009, 2016 Emperor's Cup (3) : 2007, 2010, 2016 J. League Cup (3) : 2011, 2012, 2015 Japanese Super Cup (3) : 2009, 2010, 2017 Suruga Bank Championship (2) : 2012, 2013 AFC Champions League (1): 2018 References External links official instagram Profile at Kashima Antlers 1988 births Living people Association football people from Miyagi Prefecture Japanese men's footballers J1 League players Kashima Antlers players J2 League players Vegalta Sendai players Men's association football midfielders
https://en.wikipedia.org/wiki/Naoya%20Ishigami
is a Japanese footballer who is currently playing for FC Tiamo Hirakata. Career statistics Updated to 23 February 2020. 1Includes Promotion Playoffs to J1. Team honors Kashima Antlers J1 League (2): 2007, 2008 References External links Profile at Giravanz Kitakyushu 1985 births Living people Kanagawa University alumni Association football people from Ibaraki Prefecture Japanese men's footballers J1 League players J2 League players Japan Football League players Kashima Antlers players Cerezo Osaka players Shonan Bellmare players Oita Trinita players Tokyo Verdy players V-Varen Nagasaki players Giravanz Kitakyushu players FC Maruyasu Okazaki players FC Tiamo Hirakata players Men's association football defenders
https://en.wikipedia.org/wiki/Masaki%20Chugo
is a former Japanese football player. Club statistics Team honors J1 League - 2007, 2008 Emperor's Cup - 2007 References External links 1982 births Living people Komazawa University alumni Japanese men's footballers J1 League players J2 League players Kashima Antlers players JEF United Chiba players Cerezo Osaka players Tokyo Verdy players FISU World University Games gold medalists for Japan Universiade medalists in football Men's association football midfielders Association football people from Chiba (city)
https://en.wikipedia.org/wiki/Taishi%20Tsukamoto
is a former Japanese football player. Club statistics Personal life On 28 February 2010 was announced that the 24-year-old Japanese is injured with the Osteosarcoma at the knee. Whether the defender can continue his career is still uncertain. References External links 1985 births Living people Komazawa University alumni Association football people from Saitama Prefecture Japanese men's footballers J1 League players Omiya Ardija players Men's association football defenders
https://en.wikipedia.org/wiki/Hayato%20Hashimoto
is a former Japanese football player. Club statistics References External links 1981 births Living people Komazawa University alumni Association football people from Fukui Prefecture Japanese men's footballers J1 League players J2 League players Omiya Ardija players Expatriate men's footballers in Thailand Men's association football midfielders
https://en.wikipedia.org/wiki/Masahiko%20Ichikawa
is a former Japanese football player. Club statistics References External links 1985 births Living people Hosei University alumni Association football people from Tokyo Japanese men's footballers J1 League players J2 League players Omiya Ardija players Tokyo Verdy players Men's association football forwards
https://en.wikipedia.org/wiki/Tatsuya%20Kawahara
is a former Japanese football player. Club statistics References External links 1985 births Living people Toyo University alumni Association football people from Ibaraki Prefecture Japanese men's footballers J1 League players J2 League players Omiya Ardija players Thespakusatsu Gunma players Men's association football defenders
https://en.wikipedia.org/wiki/Takuya%20Aoki
is a Japanese professional footballer who plays as a defensive midfielder for J1 League club FC Tokyo. Career statistics Club Updated to 19 July 2022. 1Includes Japanese Super Cup, J. League Championship, FIFA Club World Cup. Honours Club Urawa Red Diamonds AFC Champions League: 2017 J.League Cup: 2016 References External links Profile at FC Tokyo 1989 births Living people Association football people from Gunma Prefecture Japanese men's footballers J1 League players Omiya Ardija players Urawa Red Diamonds players FC Tokyo players Men's association football midfielders
https://en.wikipedia.org/wiki/Mitsuki%20Ichihara
is a former Japanese football player. Club statistics References External links 1986 births Living people Japanese men's footballers J1 League players Singapore Premier League players JEF United Chiba players Albirex Niigata Singapore FC players Briobecca Urayasu players Men's association football defenders Japanese expatriate men's footballers Association football people from Chiba (city)
https://en.wikipedia.org/wiki/Atsushi%20Ito%20%28footballer%29
is a former Japanese football player. Club statistics References External links 1983 births Living people Association football people from Yamaguchi Prefecture Japanese men's footballers J1 League players J2 League players JEF United Chiba players Tochigi SC players Men's association football midfielders
https://en.wikipedia.org/wiki/Geir%20Axelsen
Geir Axelsen (born 15 May 1965) is a Norwegian economist, civil servant and politician for the Norwegian Labour Party. From 2018 he was appointed director general of Statistics Norway. Early life Born in Oslo, he has a cand.oecon. degree from the University of Oslo in 1994 and a Master of Public Administration from John F. Kennedy School of Government in 2004. Career He started his political career in the Workers' Youth League, and chaired that organization's chapter in Oslo from 1987 to 1988. He worked as party secretary for the Labour Party in Oslo from 1994 to 1997, when he was hired in the Ministry of Finance. In 2005 he became counsellor of the Norwegian embassy in Brussels. When the second cabinet Stoltenberg assumed office following the 2005 election, he was appointed State Secretary in the Ministry of Finance. References Biography at Government.no 1965 births Living people Labour Party (Norway) politicians Norwegian state secretaries Politicians from Oslo University of Oslo alumni Harvard Kennedy School alumni Norwegian civil servants Norwegian expatriates in the United States
https://en.wikipedia.org/wiki/Jiro%20Kamata
is a Japanese footballer who currently plays for Kashiwa Reysol. Club career statistics Updated to 28 February 2019. References External links Profile at Kashiwa Reysol Twitter 1985 births Living people Ryutsu Keizai University alumni Association football people from Tokyo Japanese men's footballers J1 League players J2 League players J3 League players Kashiwa Reysol players Vegalta Sendai players SC Sagamihara players Men's association football defenders
https://en.wikipedia.org/wiki/Chunyu%20%28ward%29
Chunyu is an administrative ward in the Mpwapwa district of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 12,600 people in the ward, from 11,593 in 2012. References Wards of Dodoma Region
https://en.wikipedia.org/wiki/Godegode
Gode Gode is an administrative ward in the Mpwapwa district of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 8,569 people in the ward, from 7,884 in 2012. References Wards of Dodoma Region
https://en.wikipedia.org/wiki/Ipera
Ipera is an administrative ward in the Mpwapwa district of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 8,362 people in the ward, from 12,870 in 2012. References Wards of Dodoma Region
https://en.wikipedia.org/wiki/Kimagai
Kimagai is an administrative ward in the Mpwapwa district of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 7,977 people in the ward, from 7,340 in 2012. References Wards of Dodoma Region
https://en.wikipedia.org/wiki/Luhundwa
Luhundwa is an administrative ward in the Mpwapwa district of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 13,217 people in the ward, from 12,161 in 2012. References Wards of Dodoma Region
https://en.wikipedia.org/wiki/Slovan%20Bratislava%20statistics%20and%20records
Several players for the Slovak football team ŠK Slovan Bratislava have been outstanding, in terms of goalscoring or in terms of appearances for the Slovak or Czechoslovak national teams. Most goals Jozef Adamec 170 Emil Pažický 123 Anton Moravčík 109 Marián Masný 103 Ján Čapkovič 100 Best scorers Emil Pažický 19 (1954/55) Ján Čapkovič 19 (1971/72) Marián Masný 16 (1980/81) Peter Dubovský 22 (1991/92), 23 (1992/93) Pavol Masaryk 15 (2008/09) Most matches in national team Marián Masný 75 Róbert Vittek 74 Ján Popluhár 62 Szilárd Németh 59 Anton Ondruš 58 ŠK Slovan Bratislava
https://en.wikipedia.org/wiki/Mazae
Mazae is an administrative ward in the Mpwapwa district of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics reported 8,717 people in the ward, from 8,021 in 2012. References Wards of Dodoma Region
https://en.wikipedia.org/wiki/Mbuga
Mbuga is an administrative ward in the Mpwapwa district of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 6,318 people in the ward, from 5,813 in 2012. References Wards of Dodoma Region
https://en.wikipedia.org/wiki/Mpwapwa%20Mjini
Mpwapwa Mjini is an administrative ward in the Mpwapwa district of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 23,190 people in the ward, from 21,337 in 2012. References Wards of Dodoma Region
https://en.wikipedia.org/wiki/Ving%27hawe
Ving'hawe is an administrative ward in the Mpwapwa district of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 12,712 people in the ward, from 12,277 in 2012. References Wards of Dodoma Region
https://en.wikipedia.org/wiki/H%20square
In mathematics and control theory, H2, or H-square is a Hardy space with square norm. It is a subspace of L2 space, and is thus a Hilbert space. In particular, it is a reproducing kernel Hilbert space. On the unit circle In general, elements of L2 on the unit circle are given by whereas elements of H2 are given by The projection from L2 to H2 (by setting an = 0 when n < 0) is orthogonal. On the half-plane The Laplace transform given by can be understood as a linear operator where is the set of square-integrable functions on the positive real number line, and is the right half of the complex plane. It is more; it is an isomorphism, in that it is invertible, and it isometric, in that it satisfies The Laplace transform is "half" of a Fourier transform; from the decomposition one then obtains an orthogonal decomposition of into two Hardy spaces This is essentially the Paley-Wiener theorem. See also H∞ References Jonathan R. Partington, "Linear Operators and Linear Systems, An Analytical Approach to Control Theory", London Mathematical Society Student Texts 60, (2004) Cambridge University Press, . Control theory Mathematical analysis
https://en.wikipedia.org/wiki/Pawe%C5%82%20Wojciechowski%20%28economist%29
Paweł Wojciechowski (born 3 January 1960) is a Polish economist. Life He graduated from the Foreign Trade Faculty of the Main School of Planning and Statistics in 1983. In 1986 he graduated with a bachelor's degree in Economics from John Carroll University, Ohio in the United States. Paweł Wojciechowski has academic, corporate and government experiences. While staying in Cleveland between 1983 and 1991, he worked as an analyst at the Center for Regional Economic Issues and lectured in statistics at John Carroll University. After returning to Warsaw, from 1992 to 1995, he advised the Polish government on privatisation and capital market development, including work for UNDP, the Polish Ministry of Privatisation and KPMG/USAID. From 1995 to 2005, he worked as CEO of three financial institutions: Polish Fund Management Group Sp. z o.o. – Polish Development Bank S.A. division (1995–1996); PBK ATUT TFI S.A. – Investment Fund Company (1996–1999); and PTE Allianz Poland S.A. – Allianz Pension Fund (1999–2005). In June 2006 Paweł Wojciechowski was entrusted with the position of Minister of Finance of Poland, earlier serving as economic advisor to the Prime Minister Kazimierz Marcinkiewicz. After the change of government, he became Chief Economist of the Polish Institute of Directors, and then he headed the Polish Information and Foreign Investment Agency for two years. From March 2009, until his nomination as Permanent Representative of Poland to the OECD, Paweł Wojciechowski was Undersecretary of State at the Ministry of Foreign Affairs in Poland, responsible for economic cooperation and development. On 11 August 2010, Paweł Wojciechowski took up his duties as Ambassador, Permanent Representative of Poland to the Organisation for Economic Co-operation and Development. In 2014, after his tenure as an Ambassador, Paweł Wojciechowski became the Chief Economist of the Polish Social Insurance Institution (ZUS). He is also the European Coordinator for the TEN-T Rhine-Alpine Corridor, since May 2015. References 1960 births Living people Writers from Warsaw John Carroll University alumni John Carroll University faculty Finance Ministers of Poland Polish economists Ambassadors of Poland to the Organisation for Economic Co-operation and Development SGH Warsaw School of Economics alumni Politicians from Warsaw
https://en.wikipedia.org/wiki/Pharmaceutical%20Statistics%20%28journal%29
Pharmaceutical Statistics is a peer-reviewed scientific journal that publishes papers related to pharmaceutical statistics. It is the official journal of Statisticians in the Pharmaceutical Industry and is published by John Wiley & Sons. Abstracting and indexing Pharmaceutical Statistics is indexed in the following services: Current Index to Statistics MEDLINE Science Citation Index Science Citation Index Expanded Scopus External links http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1539-1612 Biostatistics journals
https://en.wikipedia.org/wiki/Regiomontanus%27%20angle%20maximization%20problem
In mathematics, the Regiomontanus's angle maximization problem, is a famous optimization problem posed by the 15th-century German mathematician Johannes Müller (also known as Regiomontanus). The problem is as follows: A painting hangs from a wall. Given the heights of the top and bottom of the painting above the viewer's eye level, how far from the wall should the viewer stand in order to maximize the angle subtended by the painting and whose vertex is at the viewer's eye? If the viewer stands too close to the wall or too far from the wall, the angle is small; somewhere in between it is as large as possible. The same approach applies to finding the optimal place from which to kick a ball in rugby. For that matter, it is not necessary that the alignment of the picture be at right angles: we might be looking at a window of the Leaning Tower of Pisa or a realtor showing off the advantages of a sky-light in a sloping attic roof. Solution by elementary geometry There is a unique circle passing through the top and bottom of the painting and tangent to the eye-level line. By elementary geometry, if the viewer's position were to move along the circle, the angle subtended by the painting would remain constant. All positions on the eye-level line except the point of tangency are outside of the circle, and therefore the angle subtended by the painting from those points is smaller. Let a = the height of the painting´s bottom above eye level; b = the height of the painting´s top above eye level; A right triangle is formed from the centre of the circle, the centre of the picture and the bottom of the picture. The hypotenuse has the length of the circle´s radius a+(b-a)/2, the length of the two legs are the distance from the wall to the point of tangency and (b-a)/2 respectively. According to the Pythagorean theorem, the distance from the wall to the point of tangency is therefore , i. e. the geometric mean of the heights of the top and bottom of the painting. Solution by calculus In the present day, this problem is widely known because it appears as an exercise in many first-year calculus textbooks (for example that of Stewart ). Let a = the height of the bottom of the painting above eye level; b = the height of the top of the painting above eye level; x = the viewer's distance from the wall; α = the angle of elevation of the bottom of the painting, seen from the viewer's position; β = the angle of elevation of the top of the painting, seen from the viewer's position. The angle we seek to maximize is β − α. The tangent of the angle increases as the angle increases; therefore it suffices to maximize Since b − a is a positive constant, we only need to maximize the fraction that follows it. Differentiating, we get Therefore the angle increases as x goes from 0 to and decreases as x increases from . The angle is therefore as large as possible precisely when x = , the geometric mean of a and b. Solution by algebra We have s
https://en.wikipedia.org/wiki/Shu%20Abe
is a former Japanese football player. He generally plays from a central position as a defensively minded midfielder. Club statistics References External links 1984 births Living people Ryutsu Keizai University alumni Association football people from Osaka Prefecture Japanese men's footballers J1 League players J2 League players Japan Football League players Kashiwa Reysol players Avispa Fukuoka players Zweigen Kanazawa players FC Machida Zelvia players Men's association football midfielders
https://en.wikipedia.org/wiki/Jun%20Yanagisawa
is a Japanese football player. He plays for MIO Biwako Shiga. Club statistics References External links 1987 births Living people Association football people from Ibaraki Prefecture Japanese men's footballers J1 League players J2 League players Japan Football League players Kashiwa Reysol players Sagan Tosu players Azul Claro Numazu players Reilac Shiga FC players Men's association football midfielders
https://en.wikipedia.org/wiki/Ryoichi%20Kurisawa
is a Japanese football manager and former player. He is currently assistant coach for J1 League club Kashiwa Reysol. Club statistics Updated to 23 February 2019. 1Includes Japanese Super Cup and FIFA Club World Cup. References External links Profile at Kashiwa Reysol 1982 births Living people Ryutsu Keizai University alumni Association football people from Chiba Prefecture Japanese men's footballers J1 League players J2 League players FC Tokyo players Kashiwa Reysol players Men's association football midfielders
https://en.wikipedia.org/wiki/Hitoshi%20Shiota
is a Japanese football player who plays for Tochigi SC. Club statistics Updated to 23 February 2018. 1Includes Japanese Super Cup. References External links 1981 births Living people Ryutsu Keizai University alumni Association football people from Ibaraki Prefecture Japanese men's footballers J1 League players J2 League players FC Tokyo players Omiya Ardija players Tochigi SC players Men's association football goalkeepers FISU World University Games gold medalists for Japan Universiade medalists in football
https://en.wikipedia.org/wiki/Kota%20Morimura
is a Japanese football player currently playing for FC Machida Zelvia. Career statistics Updated to end of 2018 season. National team career statistics Appearances in major competitions References External links Profile at Machida Zelvia 1988 births Living people Association football people from Tokyo Metropolis People from Kodaira, Tokyo Japanese men's footballers J1 League players J2 League players J3 League players FC Tokyo players Mito HollyHock players Giravanz Kitakyushu players Avispa Fukuoka players FC Machida Zelvia players Men's association football midfielders
https://en.wikipedia.org/wiki/M%C3%A1ria%20Bal%C3%A1%C5%BEov%C3%A1
Mária Balážová (born 31 August 1956) is a contemporary Slovak artist. Her practise as an artist is usually associated with new geometry, post-geometry and postmodern. Life and work Balážová studied at the Academy of Muse Arts, Bratislava and Magister of Arts degree received in 1984. Since 1997, Balážová is also known as a teacher at the University of Trnava. Her husband is Blažej Baláž, Slovak painter. Immediately at the beginning, Mária Balážová, created her own „personal mythology“, emphasizing a snake motif in the geometrically stylised form of a cobra. This animal, which occupies an important position in world mythologies and religions, became the main motif of cycles of paintings, to which the artist gave the name Serpent Geometry. Balážová distinguished herself from classic Neo-Constructivism, outlined on subjectless combinations of shapes and colours, put together into geometric structures. Art theorists appreciate the „new significance“ she achieved by creating radically reductive forms (Jiří Valoch, 2002). " In her latest works, fear of violence, power and hegemony are projected in the intimate family background, where the dominant men´s element is systematically planned in the painting area and it culminates in the series of drawings and paintings called Domestic Violence. A distinctly expressive handwriting used in some places refers very straightforwardly to Balážová´s personal story and moves the general criticism of an androcentric society to a more intimate position. Here, the key role is played by the figure of a despotic father who permanently and demonically comes back in acrylic canvases and large-format drawings – destructively and aggressively . In the latest works, Mária Balážová bet on a straightforward expression of her personal story associated with a therapeutic character. This approach in her works represents a new dimension not only for her herself, but also for geometric painting in general. (Roman Gajdoš) Her works are held in the collections of Slovak National Gallery, Bratislava, National Gallery, Prague (CZ), Wannieck Gallery Brno (CZ), Jan Koniarek Gallery , Trnava. The artist has been a member of the revived Club of Concrete Artists 2 and the artist's group East of Eden. She lives and works in Trnava. Awards 1990 Honorable Mention, Drawing 1990, Provo (USA) 1995 Prize of Masaryk's Academy, Prague (CZ) 2019 Honorary Mention Award, International Drawing Biennale India 2018-19, New Delhi (India) Selected solo exhibitions Maria Balazova, Jan Koniarek Gallery, Trnava, 26 June – 30 July 1991 (catalogue) Maria Balazova, Gallery Arpex, Bratislava, 28 January – 17 February 1993 Serpent Geometry, Cyprian Majernik Gallery, Bratislava, 19 April – 8 May 1995 Serpent Geometry 2, Jan Koniarek Gallery, Trnava, 23 May – 23 June 1996 (catalogue) Dozen 1988-2000, The Central Slovakian Gallery, Banská Bystrica, 5 May – 30 June 2000 Dozen 1988-2000, The East Slovak Gallery, Košice, 14 September – 15 October 200
https://en.wikipedia.org/wiki/SORT%20%28journal%29
SORT or Statistics and Operations Research Transactions is a peer-reviewed open access scientific journal that publishes papers related to statistics. It is published by the Institut d'Estadística de Catalunya, the statistical office of Catalonia, in English with a brief summary in Catalan. The journal was established in 2003, when it replaced the journal Qüestiió (Quaderns d'Estadística i Investigació Operativa, 1977–2002). It publishes two issues each year, and is available online as open access. Abstracting and indexing SORT is indexed in the Current Index to Statistics, Science Citation Index Expanded, and Journal Citation Reports. External links Academic journals established in 1977 Open access journals Statistics journals Biannual journals English-language journals
https://en.wikipedia.org/wiki/REVSTAT
REVSTAT is a peer-reviewed open access scientific journal that publishes papers related to statistics. It is published in English by the Instituto Nacional de Estatística, the national statistical office of Portugal. The journal was established in 2003, when it replaced the journal Revista de Estatística. It publishes two issues each year, both in print (subscription) and online as open access. Abstracting and indexing REVSTAT is abstracted and indexed in Current Index to Statistics, Science Citation Index Expanded, MathSciNet, Statistical Theory and Method Abstracts, and Zentralblatt MATH. External links Statistics journals Academic journals established in 2003 Open access journals English-language journals Biannual journals
https://en.wikipedia.org/wiki/Armadillo%20%28C%2B%2B%20library%29
Armadillo is a linear algebra software library for the C++ programming language. It aims to provide efficient and streamlined base calculations, while at the same time having a straightforward and easy-to-use interface. Its intended target users are scientists and engineers. It supports integer, floating point (single and double precision), complex numbers, and a subset of trigonometric and statistics functions. Dense and sparse matrices are supported. Various matrix decompositions are provided through optional integration with Linear Algebra PACKage (LAPACK), Automatically Tuned Linear Algebra Software (ATLAS), and ARPACK. High-performance BLAS/LAPACK replacement libraries such as OpenBLAS and Intel MKL can also be used. The library employs a delayed-evaluation approach (during compile time) to combine several operations into one and reduce (or eliminate) the need for temporaries. Where applicable, the order of operations is optimised. Delayed evaluation and optimisation are achieved through template metaprogramming. Armadillo is related to the Boost Basic Linear Algebra Subprograms (uBLAS) library, which also uses template metaprogramming. However, Armadillo builds upon ATLAS and LAPACK libraries, thereby providing machine-dependent optimisations and functions not present in uBLAS. It is open-source software distributed under the permissive Apache License, making it applicable for the development of both open source and proprietary software. The project is supported by the NICTA research centre in Australia. An interface to the Python language is available through the PyArmadillo package, which facilitates prototyping of algorithms in Python followed by relatively straightforward conversion to C++. Armadillo is a core dependency of the mlpack machine learning library and the ensmallen C++ library for numerical optimization. Example in C++ 11 Here is a trivial example demonstrating Armadillo functionality: // Compile with: // $ g++ -std=c++11 main.cpp -o file_name -O2 -larmadillo #include <iostream> #include <armadillo> #include <cmath> int main() { // ^ // Position of a particle // | arma::vec Pos = {{0}, // | (0,1) {1}}; // +---x--> // Rotation matrix double phi = -3.1416/2; arma::mat RotM = {{+cos(phi), -sin(phi)}, {+sin(phi), +cos(phi)}}; Pos.print("Current position of the particle:"); std::cout << "Rotating the point " << phi*180/3.1416 << " deg" << std::endl; Pos = RotM*Pos; Pos.print("New position of the particle:"); // ^ // x (1,0) // | // +------> return 0; } Example in C++ 98 Here is another trivial example in C++ 98: #include <iostream> #include <armadillo> int main() { ar
https://en.wikipedia.org/wiki/Yohei%20Otake
is a Japanese football player currently playing for V-Varen Nagasaki. Club statistics Updated to 1 March 2019. References External links 1989 births Living people Association football people from Saitama Prefecture Japanese men's footballers J1 League players J2 League players FC Tokyo players Cerezo Osaka players Shonan Bellmare players Fagiano Okayama players V-Varen Nagasaki players Men's association football midfielders
https://en.wikipedia.org/wiki/Kenta%20Mukuhara
is a Japanese former football player. Career After three seasons playing for Fagiano Okayama in J2 League, Mukuhara retired in December 2020. Career statistics Club Updated to end of 2018 season. 1Includes Emperor's Cup. 2Includes J. League Cup. 3Includes AFC Champions League. 4Includes Suruga Bank Championship and Japanese Super Cup. Honours Club F.C. Tokyo J. League Division 2 (1) : 2011 Emperor's Cup (1) : 2011 J. League Cup (1) : 2009 Suruga Bank Championship (1) : 2010 References External links Profile at Cerezo Osaka 1989 births Living people Association football people from Tokyo Japanese men's footballers J1 League players J2 League players J3 League players FC Tokyo players Cerezo Osaka players Cerezo Osaka U-23 players Sanfrecce Hiroshima players Fagiano Okayama players Men's association football defenders
https://en.wikipedia.org/wiki/Kohei%20Shimoda
is a former Japanese football player who last played for Blaublitz Akita. Club statistics Updated to 2 February 2018. Honours FC Tokyo J2 League (1): 2011 Emperor's Cup (1): 2011 Blaublitz Akita J3 League (1): 2017 References External links Profile at Blaublitz Akita 1989 births Living people Association football people from Akita Prefecture Japanese men's footballers J1 League players J2 League players J3 League players FC Tokyo players Mito HollyHock players FC Machida Zelvia players V-Varen Nagasaki players Blaublitz Akita players Men's association football defenders People from Akita (city)
https://en.wikipedia.org/wiki/Tatsuya%20Suzuki%20%28footballer%2C%20born%201982%29
is a former Japanese football player. Club statistics References External links 1982 births Living people University of Tsukuba alumni Association football people from Kanagawa Prefecture Japanese men's footballers J1 League players J2 League players Kashiwa Reysol players FC Tokyo players Tokushima Vortis players Men's association football forwards
https://en.wikipedia.org/wiki/Taira%20Inoue
is a Japanese footballer. Club career statistics References External links 1983 births Living people Hosei University alumni Association football people from Tokyo People from Hachiōji, Tokyo Japanese men's footballers J1 League players J2 League players J3 League players Tokyo Verdy players FC Gifu players SC Sagamihara players Men's association football forwards
https://en.wikipedia.org/wiki/Brazilian%20Journal%20of%20Probability%20and%20Statistics
The Brazilian Journal of Probability and Statistics () is a peer-reviewed scientific journal that publishes papers related to statistics. It is published four times a year by the Brazilian Statistical Association with the support of the Institute of Mathematical Statistics. The journal was established in 1987. Abstracting and indexing The Brazilian Journal of Probability and Statistics is indexed in the Current Index to Statistics and Zentralblatt MATH. Probability journals Statistics journals Academic journals established in 1987 English-language journals Quarterly journals Academic journals published by learned and professional societies
https://en.wikipedia.org/wiki/Z88%20FEM%20software
Z88 is a software package for the finite element method (FEM) and topology optimization. A team led by Frank Rieg at the University of Bayreuth started development in 1985 and now the software is used by several universities, as well as small and medium-sized enterprises. Z88 is capable of calculating two and three dimensional element types with a linear approach. The software package contains several solvers and two post-processors and is available for Microsoft Windows, Mac OS X and Unix/Linux computers in 32-bit and 64-bit versions. Benchmark tests conducted in 2007 showed a performance on par with commercial software. History and functionalities Overview The software was developed by Frank Rieg, a professor for engineering design and CAD at the University of Bayreuth. Originally written in FORTRAN 77, the program was ported to the programming language C in the early 1990s. There are two programs for finite element analysis: Z88OS (current version 15.0) is available as free software including the source code under the GNU General Public License. Due to the modular structure of the program and the open availability of the source code it is possible to develop customized extensions and add-ons and several special case 2D and 3D continuum elements (e.g. anisotropic shell element) were developed by users. Z88Aurora (current version 5.0) originally described the user interface of the Z88 finite element analysis program. After several additions and further development it now comprises a significantly larger range of functionalities than Z88OS. Z88Aurora is freeware, however the source code is not publicly available. Since 2014 two Android Apps are also available: Z88Tina is a freeware FEA program for Android smartphones and tablets. Using Z88Tina it is not only possible to compute trusses and beams, but also continuum elements like plane stress elements, plates and tori. Z88Mobile is free, like all Z88 products. This app offers two different modes (basic and advanced) and has a touch interface. The product family is supported by a software for topology optimization since 2016: Z88Arion is a free program for topology optimization and provides three separate algorithms for computation (OC: Optimality Criteria, SKO: Soft Kill Option, TOSS: Topology Optimization for Stiffness and Stress). Functionalities of Z88Aurora Z88Aurora's current version contains several computation modules: In the case of linear static analyses it is assumed that the result is proportional to the applied forces. Nonlinear analyses are used for nonlinear geometries and nonlinear materials. Using thermal and thermomechanical analyses it is possible to not only compute results about temperature or heat currents, but also thermomechanical displacements and stresses. By utilizing natural frequency simulation natural frequencies and the resulting oscillations can be determined. A contact module makes it possible to simulate interacting parts and assemblies. An integra
https://en.wikipedia.org/wiki/Moderation%20%28statistics%29
In statistics and regression analysis, moderation (also known as effect modification) occurs when the relationship between two variables depends on a third variable. The third variable is referred to as the moderator variable (or effect modifier) or simply the moderator (or modifier). The effect of a moderating variable is characterized statistically as an interaction; that is, a categorical (e.g., sex, ethnicity, class) or continuous (e.g., age, level of reward) variable that is associated with the direction and/or magnitude of the relation between dependent and independent variables. Specifically within a correlational analysis framework, a moderator is a third variable that affects the zero-order correlation between two other variables, or the value of the slope of the dependent variable on the independent variable. In analysis of variance (ANOVA) terms, a basic moderator effect can be represented as an interaction between a focal independent variable and a factor that specifies the appropriate conditions for its operation. Example Moderation analysis in the behavioral sciences involves the use of linear multiple regression analysis or causal modelling. To quantify the effect of a moderating variable in multiple regression analyses, regressing random variable Y on X, an additional term is added to the model. This term is the interaction between X and the proposed moderating variable. Thus, for a response Y and two variables x1 and moderating variable x2,: In this case, the role of x2 as a moderating variable is accomplished by evaluating b3, the parameter estimate for the interaction term. See linear regression for discussion of statistical evaluation of parameter estimates in regression analyses. Multicollinearity in moderated regression In moderated regression analysis, a new interaction predictor () is calculated. However, the new interaction term may be correlated with the two main effects terms used to calculate it. This is the problem of multicollinearity in moderated regression. Multicollinearity tends to cause coefficients to be estimated with higher standard errors and hence greater uncertainty. Mean-centering (subtracting raw scores from the mean) may reduce multicollinearity, resulting in more interpretable regression coefficients. However, it does not affect the overall model fit. Post-hoc probing of interactions Like simple main effect analysis in ANOVA, in post-hoc probing of interactions in regression, we are examining the simple slope of one independent variable at the specific values of the other independent variable. Below is an example of probing two-way interactions. In what follows the regression equation with two variables A and B and an interaction term A*B, will be considered. Two categorical independent variables If both of the independent variables are categorical variables, we can analyze the results of the regression for one independent variable at a specific level of the other independent varia
https://en.wikipedia.org/wiki/Pseudoreflection
In mathematics, a pseudoreflection is an invertible linear transformation of a finite-dimensional vector space such that it is not the identity transformation, has a finite (multiplicative) order, and fixes a hyperplane. The concept of pseudoreflection generalizes the concepts of reflection and complex reflection and is simply called reflection by some mathematicians. It plays an important role in Invariant theory of finite groups, including the Chevalley-Shephard-Todd theorem. Formal definition Suppose that V is vector space over a field K, whose dimension is a finite number n. A pseudoreflection is an invertible linear transformation such that the order of g is finite and the fixed subspace of all vectors in V fixed by g has dimension n-1. Eigenvalues A pseudoreflection g has an eigenvalue 1 of multiplicity n-1 and another eigenvalue r of multiplicity 1. Since g has finite order, the eigenvalue r must be a root of unity in the field K. It is possible that r = 1 (see Transvections). Diagonalizable pseudoreflections Let p be the characteristic of the field K. If the order of g is coprime to p then g is diagonalizable and represented by a diagonal matrix diag(1, ... , 1, r ) = where r is a root of unity not equal to 1. This includes the case when K is a field of characteristic zero, such as the field of real numbers and the field of complex numbers. A diagonalizable pseudoreflection is sometimes called a semisimple reflection. Real reflections When K is the field of real numbers, a pseudoreflection has matrix form diag(1, ... , 1, -1). A pseudoreflection with such matrix form is called a real reflection. If the space on which this transformation acts admits a symmetric bilinear form so that orthogonality of vectors can be defined, then the transformation is a true reflection. Complex reflections When K is the field of complex numbers, a pseudoreflection is called a complex reflection, which can be represented by a diagonal matrix diag(1, ... , 1, r) where r is a complex root of unity unequal to 1. Transvections If the pseudoreflection g is not diagonalizable then r = 1 and g has Jordan normal form In such case g is called a transvection. A pseudoreflection g is a transvection if and only if the characteristic p of the field K is positive and the order of g is p. Transvections are useful in the study of finite geometries and the classification of their groups of motions. References Functions and mappings
https://en.wikipedia.org/wiki/Nehemiah%20Strong
Rev. Nehemiah Strong (24 February 1729 (N.S.) – 13 August 1807) was an American astronomer and meteorologist who was the first Professor of Mathematics and Natural Philosophy at Yale College from 1770 and produced a series of annual ephemerides, the astronomical element in almanacs, which were printed in Hartford, Connecticut, and in New Haven. Strong was born in Northampton, Massachusetts, eldest of three children of Nehemiah and Hannah Strong and the grandson of Samuel and Esther (Clapp) Strong, of Northampton, Massachusetts. Nehemiah Strong graduated from Yale College in 1755. He entered on a tutorship at Yale in November 1757 and was soon licensed to preach and was settled Congregationalist minister at Turkey Hill, now part of East Granby, Connecticut, 1761-67. His marriage to Lydia Smith proved to be an embarrassment, when after she had been granted a divorce in February 1759 on grounds of abandonment, her husband, Andrew Burr Jr of New Haven, having gone to the West Indies in January 1755, Burr reappeared and her marriage to Nehemiah Strong was necessarily annulled, and as a result of entanglements he was dismissed from his pastorate at Turkey Hill, 23 June 1767. He married Mrs Mary Thomas, the widow of Dr Lemuel Thomas of Newtown, 15 June 1778. Thereafter he resided in Newtown, in New Milford, where he kept an academy for boys, and, from 1803 in Bridgeport, giving occasional sermons and teaching to the time of his death. He resigned his chair at Yale in 1781, in a dispute over his salary, exacerbated by the sense on the part of the Corporation that he was not a sufficiently ardent Patriot. He represented Newtown in the Connecticut General Assembly, May 1784. His portrait by Ralph Earl, painted in 1789-90, was presented to Yale by the artist and remains in the University's collection. His treatise on astronomy won him such a wide reputation that anonymous almanacs were attributed to him. His first essay at compiling an almanac was anonymous, for Watson's Register for 1775, printed at Hartford; his second essay was The Connecticut Almanack for 1778, which identified his Yale title only. From 1782 he published almanacs under his own name at Hartford and as "Hosea Stafford" in New Haven (1776–1804). In addition, finding that he was publicly assumed to be the "Isaac Bickerstaff", having disclaimed authorship in a letter to the Connecticut Journal, New Haven, 27 October 1784, he apparently decided to take up the slack and issue almanacs as "Bickerstaff" himself: they appeared at Hartford for several years after 1785. In a letter of 6 May 1803 to Elisha Babcock, Strong remarks that the calculations for the forthcoming year will be his last: He recommended his pupil David Sanford of Newtown, Connecticut. Notes American astronomers Almanac compilers 1729 births 1807 deaths People from Northampton, Massachusetts Yale College alumni
https://en.wikipedia.org/wiki/Bures%20metric
In mathematics, in the area of quantum information geometry, the Bures metric (named after Donald Bures) or Helstrom metric (named after Carl W. Helstrom) defines an infinitesimal distance between density matrix operators defining quantum states. It is a quantum generalization of the Fisher information metric, and is identical to the Fubini–Study metric when restricted to the pure states alone. Definition The Bures metric may be defined as where is Hermitian 1-form operator implicitly given by which is a special case of a continuous Lyapunov equation. Some of the applications of the Bures metric include that given a target error, it allows the calculation of the minimum number of measurements to distinguish two different states and the use of the volume element as a candidate for the Jeffreys prior probability density for mixed quantum states. Bures distance The Bures distance is the finite version of the infinitesimal square distance described above and is given by where the fidelity function is defined as Another associated function is the Bures arc also known as Bures angle, Bures length or quantum angle, defined as which is a measure of the statistical distance between quantum states. Wootters distance When both density operators are diagonal (so that they are just classical probability distributions), then let and similarly , then the fidelity iswith the Bures length becoming the Wootters distance . The Wootters distance is the geodesic distance between the probability distributions under the chi-squared metric . Perform a change of variables with , then the chi-squared metric becomes . Since , the points are restricted to move on the positive quadrant of a unit hypersphere. So, the geodesics are just the great circles on the hypersphere, and we also obtain the Wootters distance formula. If both density operators are pure states, , then the fidelity is , and we obtain the quantum version of Wootters distance . In particular, the Bures distance between any two orthogonal states is . Quantum Fisher information The Bures metric can be seen as the quantum equivalent of the Fisher information metric and can be rewritten in terms of the variation of coordinate parameters as which holds as long as and have the same rank. In cases where they do not have the same rank, there is an additional term on the right hand side. is the Symmetric logarithmic derivative operator (SLD) defined from In this way, one has where the quantum Fisher metric (tensor components) is identified as The definition of the SLD implies that the quantum Fisher metric is 4 times the Bures metric. In other words, given that are components of the Bures metric tensor, one has As it happens with the classical Fisher information metric, the quantum Fisher metric can be used to find the Cramér–Rao bound of the covariance. Explicit formulas The actual computation of the Bures metric is not evident from the definition, so, some formulas were developed f
https://en.wikipedia.org/wiki/Statistical%20Applications%20in%20Genetics%20and%20Molecular%20Biology
Statistical Applications in Genetics and Molecular Biology is a bimonthly peer-reviewed scientific journal covering the application of statistics to problems in computational biology. It was established in 2002 and is published by de Gruyter. The editor-in-chief is Guido Sanguinetti. According to the Journal Citation Reports, the journal has a 2012 impact factor of 1.717. Abstracting and indexing The journal is abstracted and indexed in: Current Index to Statistics MEDLINE Science Citation Index Expanded Zentralblatt MATH References External links Biostatistics journals Statistics journals Academic journals established in 2002 Delayed open access journals English-language journals Bioinformatics and computational biology journals De Gruyter academic journals
https://en.wikipedia.org/wiki/L%C3%A9vy%20family%20of%20graphs
In graph theory, a branch of mathematics, a Lévy family of graphs is a family of graphs Gn, n = 1, 2, 3, ..., which possess a certain type of "compactness" or "tangledness". Many naturally occurring families of graphs are Lévy families. Many mathematicians have noted this fact and have expressed surprise that it does not appear to have a ready explanation. Formally, a family of graphs Gn, n = 1, 2, 3, ..., is a Lévy family if, for any where Here D is the graph diameter of G, and A(n) is the n-graph neighborhood of A. Note that the maximization ranges over subsets A of G, subject to A being over half the size of G In words, this means that one can take a subset of size at least half of G, and blow it up by only of the graph diameter, and end up with nearly all the set. Long "stringy" (i.e. not "compact") families of graphs such as the cycle graph of order n clearly don't have such a property: one could consider a subset comprising the n/2 neighborhood of a point (midnight to six o'clock, say). The graph has graph diameter D of about n/2. So the -neighborhood of the subset is only of size about n/2. A Levy family would have this neighborhood covering almost all the set. It should be clear that a Levy family must have a very special type of compact structure. Hypercube graphs of order n are known to be a Lévy family. If Sn is the graph with points that are elements of the permutation group of n elements, with edges joining points that differ by a transposition, then the series Si, i=1,2,..., is a Lévy family. References Bollobás (editor). Probabilistic combinatorics and its applications. American Mathematical Society, 1991 (p63) Graph families
https://en.wikipedia.org/wiki/Journal%20of%20Statistical%20Computation%20and%20Simulation
The Journal of Statistical Computation and Simulation is a peer-reviewed scientific journal that covers computational statistics. It is published by Taylor & Francis and was established in 1972. The editors-in-chief are Richard Krutchkoff (Virginia Polytechnic Institute and State University, Blacksburg) and Andrei Volodin (University of Regina). Abstracting and indexing The journal is abstracted and indexed in: Current Index to Statistics Science Citation Index Expanded Zentralblatt MATH According to the Journal Citation Reports, the journal has a 2018 impact factor of 0.767. References External links Computational statistics journals Statistics journals Academic journals established in 1972
https://en.wikipedia.org/wiki/Gompertz%20distribution
In probability and statistics, the Gompertz distribution is a continuous probability distribution, named after Benjamin Gompertz. The Gompertz distribution is often applied to describe the distribution of adult lifespans by demographers and actuaries. Related fields of science such as biology and gerontology also considered the Gompertz distribution for the analysis of survival. More recently, computer scientists have also started to model the failure rates of computer code by the Gompertz distribution. In Marketing Science, it has been used as an individual-level simulation for customer lifetime value modeling. In network theory, particularly the Erdős–Rényi model, the walk length of a random self-avoiding walk (SAW) is distributed according to the Gompertz distribution. Specification Probability density function The probability density function of the Gompertz distribution is: where is the scale parameter and is the shape parameter of the Gompertz distribution. In the actuarial and biological sciences and in demography, the Gompertz distribution is parametrized slightly differently (Gompertz–Makeham law of mortality). Cumulative distribution function The cumulative distribution function of the Gompertz distribution is: where and Moment generating function The moment generating function is: where Properties The Gompertz distribution is a flexible distribution that can be skewed to the right and to the left. Its hazard function is a convex function of . The model can be fitted into the innovation-imitation paradigm with as the coefficient of innovation and as the coefficient of imitation. When becomes large, approaches . The model can also belong to the propensity-to-adopt paradigm with as the propensity to adopt and as the overall appeal of the new offering. Shapes The Gompertz density function can take on different shapes depending on the values of the shape parameter : When the probability density function has its mode at 0. When the probability density function has its mode at Kullback-Leibler divergence If and are the probability density functions of two Gompertz distributions, then their Kullback-Leibler divergence is given by where denotes the exponential integral and is the upper incomplete gamma function. Related distributions If X is defined to be the result of sampling from a Gumbel distribution until a negative value Y is produced, and setting X=−Y, then X has a Gompertz distribution. The gamma distribution is a natural conjugate prior to a Gompertz likelihood with known scale parameter When varies according to a gamma distribution with shape parameter and scale parameter (mean = ), the distribution of is Gamma/Gompertz. If , then , and hence . Applications In hydrology the Gompertz distribution is applied to extreme events such as annual maximum one-day rainfalls and river discharges. The blue picture illustrates an example of fitting the Gompertz distribution to ranked annually maximum
https://en.wikipedia.org/wiki/Ethernet%20Ring%20Protection%20Switching
Ethernet Ring Protection Switching, or ERPS, is an effort at ITU-T under G.8032 Recommendation to provide sub-50ms protection and recovery switching for Ethernet traffic in a ring topology and at the same time ensuring that there are no loops formed at the Ethernet layer. This ITU-T specification is directly based on and derived from the Ethernet Automatic Protection Switching technology developed and patented by Extreme Networks. G.8032v1 supported a single ring topology and G.8032v2 supports multiple rings/ladder topology. Overview ERPS specifies protection switching mechanisms and a protocol for Ethernet layer network (ETH) rings. Ethernet Rings can provide wide-area multipoint connectivity more economically due to their reduced number of links. The mechanisms and protocol defined in this Recommendation achieve highly reliable and stable protection; and never form loops, which would fatally affect network operation and service availability. Each Ethernet Ring Node is connected to adjacent Ethernet Ring Nodes participating in the same Ethernet Ring, using two independent links. A ring link is bounded by two adjacent Ethernet Ring Nodes, and a port for a ring link is called a ring port. The minimum number of Ethernet Ring Nodes in an Ethernet Ring is three. The fundamentals of this ring protection switching architecture are: a) The principle of loop avoidance. b) The utilization of learning, forwarding, and Filtering Database (FDB) mechanisms defined in the Ethernet flow forwarding function (ETH_FF). Loop avoidance in an Ethernet Ring is achieved by guaranteeing that, at any time, traffic may flow on all but one of the ring links. This particular link is called the Ring Protection Link (RPL), and under normal conditions this ring link is blocked, i.e. not used for service traffic. One designated Ethernet Ring Node, the RPL Owner Node, is responsible for blocking traffic at one end of the RPL. Under an Ethernet ring failure condition, the RPL Owner Node is responsible for unblocking its end of the RPL (unless the RPL has failed) allowing the RPL to be used for traffic. The other Ethernet Ring Node adjacent to the RPL, the RPL Neighbour Node, may also participate in blocking or unblocking its end of the RPL. The event of an Ethernet Ring failure results in protection switching of the traffic. This is achieved under the control of the ETH_FF functions on all Ethernet Ring Nodes. An APS protocol is used to coordinate the protection actions over the ring. G.8032v2 Version 2 of G.8032 introduced many additional features, such as: Multi-ring/ladder network support Revertive/ Non-revertive mode after the condition that is causing the switch has been cleared Administrative commands: Forced Switch (FS), Manual Switch (MS) for blocking a particular ring port Flush FDB (Filtering database) Logic, which significantly reduces amount of flush FDB operations in the ring Support of multiple ERP instances on a single ring Principle of operation G.
https://en.wikipedia.org/wiki/Koreans%20in%20Spain
Koreans in Spain form one of the country's smaller Asian populations. Demography and distribution 2006 statistics from Spain's Instituto Nacional de Estadística showed 2,873 registered residents of Spain born in South Korea, of whom 514 held Spanish nationality, while 2,359 held other nationalities. Among Spanish nationals, men outnumbered women by a ratio of 1.3:1, which was almost exactly reversed among non-Spanish nationals. Between 1980 and 2004, a total of 696 people originally holding South Korean nationality became Spanish citizens. South Korea's Ministry of Foreign Affairs and Trade, whose statistics are based largely on registrations with consulates and count locally born persons of Korean descent as well as South Korean-born individuals, recorded a somewhat higher count of 3,769 individuals in 2005; of those, 2,538 resided in, with another 1,231 in Las Palmas. This made Koreans in Spain the fifth-largest Korean diaspora population in Western Europe, behind Koreans in the United Kingdom, Koreans in Germany, Koreans in France, and Koreans in Italy. The most recent statistics of the South Korean government, issued in July 2011, show only slight growth compared to the 2005 statistics. Of the 4,080 Koreans recorded as living in Spain, 929 had Spanish citizenship, 2,108 had permanent residence, 216 were on student visas, and the remaining 727 had other kinds of visas. Las Palmas Koreans in Las Palmas form a community distinct from that on the Spanish mainland. Theirs is the only concentration of Koreans in Spain whose presence has resulted in a recognisable Koreatown. They trace their origins to South Korean migrant workers who worked on deep-ocean fishing boats based on the island starting in the 1960s. Fishing, along with construction, was one of the main sources of overseas employment for South Koreans for decades; by the 1970s, nearly 15,000 Koreans resided in Las Palmas, making them about 4% of the city's population of 350,000. Many brought their families over and became rooted in Spain, sending their children to local schools. However, with the decline of South Korea's ocean fisheries industries in the 1990s, their population shrank, from 2,283 individuals in 1997 to just 1,292 by 1999, a number which decreased at a slower rate over the following decade to reach 1,197 by 2011. Most of the remaining Korean population have shifted away from the fishing industry, and their children have largely entered professional fields, achieving relative affluence. Mainland Spain The Korean community on the Spanish mainland consists mainly of two groups: primarily male small business owners and executives of South Korean companies along with their spouses and children, and primarily female international students at Spanish universities. Korean martial artists, though a smaller group, are also well represented; they either run their own dojang, or work for private security companies. They do not trace their origins exclusively to South Korea; some m
https://en.wikipedia.org/wiki/Mark%20Ronan
Mark Andrew Ronan (born 1947) is Emeritus Professor of Mathematics at the University of Illinois at Chicago and Honorary Professor of Mathematics at University College London. He has lived and taught in: Germany (at the University of Braunschweig and the Free University of Berlin); in England, where from 1989 to 1992 he was Mason Professor of Mathematics at the University of Birmingham; and America at the University of Illinois at Chicago, where his teaching included courses on ancient literature from Mesopotamia, and on the history of the calendar, as well as mathematics. In addition to his research papers, Ronan's popular account of the quest to discover and classify all the finite building blocks for symmetry (the finite simple groups) was published in 2006. In 2008 it formed the basis for a series of BBC radio broadcasts. In his research work he is an expert on the theory of buildings, with a standard text on the subject, now being reissued in paperback. Apart from his professional work, he has acted in many operas at the Lyric Opera of Chicago, danced in the Nutcracker, and maintains a blog on opera, ballet and theatre reviews. Bibliography Lectures on Buildings, original edition, Academic Press 1989; paperback edition, updated and revised, University of Chicago Press 2009. Symmetry and the Monster, Oxford University Press 2006. References External links Mark Ronan's Homepage Mark Ronan's Theatre Reviews 20th-century British mathematicians 21st-century British mathematicians 20th-century American mathematicians 21st-century American mathematicians Group theorists Academics of University College London University of Illinois Chicago faculty Living people Academic staff of the Technical University of Braunschweig 1947 births
https://en.wikipedia.org/wiki/Hate%20My%20Life
"Hate My Life" is a song by Canadian rock group Theory of a Deadman. It was released in October 2008 as the fourth overall single (third American single and fifth Canadian single) from their third studio album Scars & Souvenirs. The track was selected as BBC Radio One's Track of the Week for the week ending March 20, 2009. Background and writing According to Tyler Connolly, the band's lead singer, this song enables people to feel that no matter how bad their own life is going, that there is always someone out there who feels just as bad. Music video According to Theory's site, the video was shot on November 15, 2008. It was asked on the site, as a contest, for forty fans to star in the music video. It was filmed at the Warner Brothers Studio in Burbank, California. It was released January 9, 2009, on Yahoo! Music. It was directed by Bill Fishman. At the beginning of the video, Tyler sees a hobo, and then he starts singing the song, the lyrics matching everything that is happening in the video. He complains about how he hates hobos ("So sick of the hobos always begging for change, I don't like how I gotta work and they just sit around and get paid"), he almost gets hit by a car ("I hate all of the people, who can't drive their cars...), we meet his wife, played by his real wife Christine Danielle Connolly ("I hate how my wife; is always up my ass...), a girl drops her bag of lingerie (Tyler looking at it interestingly), a construction worker's boss telling him off ("I still hate my job, my boss is a dick...), and when he sings the chorus, a sign comes down from a building reading "I Hate My Life." Then, Tyler jumps onto a parade float with the rest of the band, performing the rest of the song. Behind them travels a huge group of people, which include the hobo, the construction workers, and the others Tyler ran into. Charts Weekly charts Year-end charts Certifications References Theory of a Deadman songs 2008 singles 604 Records singles Songs written by Tyler Connolly Song recordings produced by Howard Benson 2008 songs
https://en.wikipedia.org/wiki/Not%20Meant%20to%20Be
"Not Meant to Be" is a song recorded by Canadian rock group Theory of a Deadman for their third studio album, Scars & Souvenirs (2008). Band members Tyler Connolly, Dave Brenner, and Dean Back composed the song, while Connolly co-wrote the lyrics with songwriter and producer Kara DioGuardi. The song was released November 18, 2008 as the album's fifth overall radio single. It was the first song from the album to impact mainstream radio in the United States, concurrent with the release of "Hate My Life" to rock formats. In 2009, "Not Meant to Me" was included on the soundtrack to the science fiction action film, Transformers: Revenge of the Fallen. "Not Meant to Be" became the group's highest-charting entry in the United States, peaking at number 55 on the Billboard Hot 100 as well as their first top ten hit on the Billboard Adult Top 40 airplay chart. The song has been certified Platinum by both Music Canada and the Recording Industry Association of America (RIAA). Content "Not Meant to Be" is a ballad with influences of pop and rock music composed in the key of A minor and set in common time to a "slow" tempo of 120 BPM. The vocals range over two octaves from D to G. The song is written from the point of view of a man who wants to be with his ex-girlfriend so much after their relationship ends, but she is never satisfied with him and keeps pushing him away, leaving him thinking that their relationship is "not meant to be." Lead vocalist Tyler Connolly co-wrote the lyrics with Kara DioGuardi at the latter's house. "We wrote 'Not Meant To Be' in 5 minutes," Connolly said in a 2009 interview with The Gauntlet. "Our writing styles fit together so perfectly it was almost like it was 'meant to be.'" In the same interview, DioGuardi stated that "the best part about my job is that you never know who you are going to meet, and who's going to inspire you. Although I'd never worked with Tyler, when he started singing the song, I knew we were onto something special." The song's mid-tempo composition has been compared to the work of labelmates Nickelback. Critical reception In a review of the album Scars & Souvenirs for AllMusic, Katherine Fulton identified "Not Meant to Be" as an example of the album's "derivative" sound, writing that its "melody and chorus bear more than a passing resemblance to" Nickelback's 2006 single "Rockstar". Music video The band filmed the music video with Tony Petrossian in February 2009. It features Kara DioGuardi (the song's co-writer) as the love interest. It was released on March 25, 2009. The video begins when Kara walks out on Tyler, breaks up with him and drives away. By the first chorus in the song, all of the non-singing scenes start running backwards: all the objects in the house (including a fish tank, a wine rack, a mirror, a table, two chairs and more) change from broken to unbroken and Kara's car is also shown travelling backwards, implying that the whole timeline of the main story is running in reverse. At the en
https://en.wikipedia.org/wiki/Foster%27s%20theorem
In probability theory, Foster's theorem, named after Gordon Foster, is used to draw conclusions about the positive recurrence of Markov chains with countable state spaces. It uses the fact that positive recurrent Markov chains exhibit a notion of "Lyapunov stability" in terms of returning to any state while starting from it within a finite time interval. Theorem Consider an irreducible discrete-time Markov chain on a countable state space having a transition probability matrix with elements for pairs , in . Foster's theorem states that the Markov chain is positive recurrent if and only if there exists a Lyapunov function , such that and for for all for some finite set and strictly positive . Related links Lyapunov optimization References Theorems regarding stochastic processes Markov processes
https://en.wikipedia.org/wiki/2008%E2%80%9309%20Guam%20Men%27s%20Soccer%20League
Statistics of Guam League for the 2008–09 season. Final standings References Guam 2008/09 (RSSSF) Guam Soccer League seasons Guam Mens
https://en.wikipedia.org/wiki/Edmund%20F.%20Robertson
Edmund Frederick Robertson (born 1 June 1943) is a professor emeritus of pure mathematics at the University of St Andrews. Work Robertson is one of the creators of the MacTutor History of Mathematics archive, along with John J. O'Connor. Robertson has written over 100 research articles, mainly on the theory of groups and semigroups. He is also the author or co-author of 17 textbooks. Robertson obtained a Bachelor of Science degree at the University of St Andrews in 1965. He then went to the University of Warwick, where he received a Master of Science degree in 1966 and a Doctor of Philosophy degree in 1968. In 1998, he was elected a Fellow of the Royal Society of Edinburgh. In 2015, he received together with his colleague O'Connor, the Hirst Prize of the London Mathematical Society for his work on the MacTutor History of Mathematics archive. His thesis on "Classes of Generalised Nilpotent Groups" was done with Stewart E. Stonehewer. Personal life He is with his wife, Helena, and his two sons. Bibliography Algebra Through Practice: A Collection of Problems in Algebra with Solutions: Books 4-6 - with T.S.Blyth, Rings, Fields and Modules - with T.S.Blyth, 1985, Sets and mappings - with T.S.Blyth, 1986, Linear Algebra - with T.S.Blyth, 1986, Essential Student Algebra: Groups - with T.S.Blyth, 1986, Basic Linear Algebra - with T.S.Blyth, 1998, Colin MacLaurin (1698-1746): Argyllshire's Mathematician, 2000, Further Linear Algebra - with T.S.Blyth, 2002, References External links Group theorists 20th-century Scottish mathematicians Fellows of the Royal Society of Edinburgh Academics of the University of St Andrews 1943 births Living people 21st-century Scottish mathematicians People from St Andrews
https://en.wikipedia.org/wiki/StatXact
StatXact is a statistical software package for analyzing data using exact statistics. It calculates exact p-values and confidence intervals for contingency tables and non-parametric procedures. It is marketed by Cytel Inc. References External links StatXact homepage at Cytel Inc. Statistical software Windows-only proprietary software
https://en.wikipedia.org/wiki/Georges%20Reeb
Georges Henri Reeb (12 November 1920 – 6 November 1993) was a French mathematician. He worked in differential topology, differential geometry, differential equations, topological dynamical systems theory and non-standard analysis. Biography Reeb was born in Saverne, Bas-Rhin, Alsace, to Theobald Reeb and Caroline Engel. He started studying mathematics at University of Strasbourg, but in 1939 the entire university was evacuated to Clermont-Ferrand due to the German occupation of France. After the war, he completed his studies and in 1948 he defended his PhD thesis, entitled Propriétés topologiques des variétés feuilletées [Topological properties of foliated manifolds] and supervised by Charles Ehresmann. In 1952 Reeb was appointed professor at Université Joseph Fourier in Grenoble and in 1954 he visited the Institute for Advanced Study. From 1963 he worked at Université Louis Pasteur in Strasbourg. There, in 1965 he created with Jean Leray and Pierre Lelong the series of meeting Rencontres entre Mathématiciens et Physiciens Théoriciens. in 1966 Reeb and Jean Frenkel founded the Institute de Recherche mathématique Avancée, the first university laboratory associated to the Centre National de la Recherche Scientifique, which he directed between 1967 and 1972. In 1967 he was President of the Société Mathématique de France and in 1971 he was awarded the . In 1991 Reeb received an honorary doctorate from Albert-Ludwigs-Universität Freiburg and from Université de Neuchâtel. He died in 1993 in Strasbourg when he was 72 years old. Research Reeb was the founder of the topological theory of foliations, a geometric structure on smooth manifolds which partition them in smaller pieces. In particular, he described what is now called the Reeb foliation, a foliation of the 3-sphere, whose leaves are all diffeomorphic to , except one, which is a 2-torus. One of its first significant result, Reeb stability theorem, describes the local structure foliations around a compact leaf with finite holonomy group. His works on foliations had also applications in Morse theory. In particular, the Reeb sphere theorem says that a compact manifold with a function with exactly two critical points is homeomorphic to the sphere. In turn, in 1956 this was used to prove that the Milnor spheres, although not diffeomorphic, are homeomorphic to the sphere . Other important geometric concepts named after him include the Reeb graph and the Reeb vector field associated to a contact form. Towards the end of his career, Reeb become a supporter of the theory of non-standard analysis by Abraham Robinson, coining the slogan "The naïve integers don't fill up " and working on its applications to dynamical systems. Selected works Books with Wu Wen-Tsün: Sur les espaces fibrés et les variétés feuilletées, 1952 with A. Fuchs: Statistiques commentées, 1967 with J. Klein: Formules commentées de mathématiques: Programme P.C., 1971 Feuilletages: résultats anciens et nouveaux (Painlevé, Hect
https://en.wikipedia.org/wiki/Avner%20Friedman
Avner Friedman (; born November 19, 1932) is Distinguished Professor of Mathematics and Physical Sciences at Ohio State University. His primary field of research is partial differential equations, with interests in stochastic processes, mathematical modeling, free boundary problems, and control theory. Friedman received his Ph.D. degree in 1956 from the Hebrew University. He was a professor of mathematics at Northwestern University (1962–1985), a Duncan Distinguished Professor of Mathematics at Purdue University (1985–1987), and a professor of mathematics (Regents' Professor from 1996) at the University of Minnesota (1987–2001). He was director of the Institute for Mathematics and its Applications from 1987 to 1997. He was the founding director of Minnesota Center for Industrial Mathematics (1994-2001). He was the founding Director of the Mathematical Biosciences Institute at Ohio State University, serving as its first director from 2002–2008. Friedman has been the Chair of the Board of Mathematical Sciences (1994–1997) and the President of the Society for Industrial and Applied Mathematics (1993–1994). He has been awarded the Sloan Fellowship (1962–65), the Guggenheim Fellowship (1966–7), the Stampacchia Prize (1982), the National Science Foundation Special Creativity Award (1983–85; 1991–93). He is a Fellow of the American Academy of Arts and Sciences (since 1987) and a member of the National Academy of Sciences (since 1993). In 2009 he became a Fellow of the Society for Industrial and Applied Mathematics. In 2012 he became a fellow of the American Mathematical Society. He has been adviser to 27 doctoral students and has published 25 books and over 500 papers. Works Generalized Functions and Partial Differential Equations. Prentice-Hall (1963). Dover Publications 2005 ; 2011 Dover reprint Partial Differential Equations of Parabolic Type. Prentice-Hall (1964). 2008 Dover Publications; 2013 Dover reprint Partial Differential Equations. Holt, Rinehart, and Winston, New York (1969). reprint Dover Books 2008 Foundations of Modern Analysis. Holt, Rinehart, and Winston, New York (1970). (hbk); 1982 Dover reprint; Dover Publications on Mathematics 2010. Advanced Calculus. Holt, Rinehart, and Winston, New York (1971). Dover Publications 2007 Differential Games. John Wiley, Interscience Publishers (1971). Dover Publications 2006 2013 Dover reprint Stochastic Differential Equations and Applications. Vol. 1, Academic Press (1975). Dover Books 2006. Stochastic Differential Equations and Applications. Vol. 2, Academic Press (1976). Variational Principles and Free Boundary Problems, Wiley & Sons (1983). Dover Publications on Mathematics 2010 ; 2012 pbk reprint, Springer Mathematics in Industrial Problems, IMA Volume 16, Springer-Verlag (1988). Mathematics in Industrial Problems, Part 2, IMA Volume 24, Springer-Verlag (1989); 2012 pbk reprint Mathematics in Industrial Problems, Part 3, IMA Volume 31, Springer-Verlag (1990). Ma
https://en.wikipedia.org/wiki/Quartic%20reciprocity
Quartic or biquadratic reciprocity is a collection of theorems in elementary and algebraic number theory that state conditions under which the congruence x4 ≡ p (mod q) is solvable; the word "reciprocity" comes from the form of some of these theorems, in that they relate the solvability of the congruence x4 ≡ p (mod q) to that of x4 ≡ q (mod p). History Euler made the first conjectures about biquadratic reciprocity. Gauss published two monographs on biquadratic reciprocity. In the first one (1828) he proved Euler's conjecture about the biquadratic character of 2. In the second one (1832) he stated the biquadratic reciprocity law for the Gaussian integers and proved the supplementary formulas. He said that a third monograph would be forthcoming with the proof of the general theorem, but it never appeared. Jacobi presented proofs in his Königsberg lectures of 1836–37. The first published proofs were by Eisenstein. Since then a number of other proofs of the classical (Gaussian) version have been found, as well as alternate statements. Lemmermeyer states that there has been an explosion of interest in the rational reciprocity laws since the 1970s. Integers A quartic or biquadratic residue (mod p) is any number congruent to the fourth power of an integer (mod p). If x4 ≡ a (mod p) does not have an integer solution, a is a quartic or biquadratic nonresidue (mod p). As is often the case in number theory, it is easiest to work modulo prime numbers, so in this section all moduli p, q, etc., are assumed to positive, odd primes. Gauss The first thing to notice when working within the ring Z of integers is that if the prime number q is ≡ 3 (mod 4) then a residue r is a quadratic residue (mod q) if and only if it is a biquadratic residue (mod q). Indeed, the first supplement of quadratic reciprocity states that −1 is a quadratic nonresidue (mod q), so that for any integer x, one of x and −x is a quadratic residue and the other one is a nonresidue. Thus, if r ≡ a2 (mod q) is a quadratic residue, then if a ≡ b2 is a residue, r ≡ a2 ≡ b4 (mod q) is a biquadratic residue, and if a is a nonresidue, −a is a residue, −a ≡ b2, and again, r ≡ (−a)2 ≡ b4 (mod q) is a biquadratic residue. Therefore, the only interesting case is when the modulus p ≡ 1 (mod 4). Gauss proved that if p ≡ 1 (mod 4) then the nonzero residue classes (mod p) can be divided into four sets, each containing (p−1)/4 numbers. Let e be a quadratic nonresidue. The first set is the quartic residues; the second one is e times the numbers in the first set, the third is e2 times the numbers in the first set, and the fourth one is e3 times the numbers in the first set. Another way to describe this division is to let g be a primitive root (mod p); then the first set is all the numbers whose indices with respect to this root are ≡ 0 (mod 4), the second set is all those whose indices are ≡ 1 (mod 4), etc. In the vocabulary of group theory, the first set is a subgroup of index 4 (of the multiplica
https://en.wikipedia.org/wiki/Sho%20Asuke
is a former Japanese football player. Club statistics References External links 1985 births Living people Kokushikan University alumni Association football people from Tokyo Japanese men's footballers J1 League players J2 League players Tokyo Verdy players Kataller Toyama players Men's association football defenders
https://en.wikipedia.org/wiki/Masaki%20Iida
is a Japanese football player for Nara Club. Club statistics Updated to 24 February 2019. References External links Profile at Matsumoto Yamaga 1985 births Living people Ryutsu Keizai University alumni Association football people from Ibaraki Prefecture Japanese men's footballers J1 League players J2 League players Japan Football League players Tokyo Verdy players Matsumoto Yamaga FC players FC Maruyasu Okazaki players Nara Club players Men's association football defenders
https://en.wikipedia.org/wiki/Kosuke%20Kikuchi
is a Japanese football player currently playing for Renofa Yamaguchi FC. Career statistics Updated to 19 July 2022. Notes References External links Profile at Omiya Ardija Profile at Kawasaki Frontale 1985 births Living people Komazawa University alumni Association football people from Saitama Prefecture Japanese men's footballers J1 League players J2 League players Kawasaki Frontale players Omiya Ardija players Renofa Yamaguchi FC players Men's association football defenders
https://en.wikipedia.org/wiki/Tomonobu%20Yokoyama
is a retired Japanese footballer. Career On 5 February 2020, FC Gifu confirmed that 34-year old Yokoyama had decided to retire. Club statistics Updated to 2 January 2020. References External links Profile at Kawasaki Frontale Profile at Omiya Ardija Profile at Hokkaido Consadole Sapporo 1985 births Living people Waseda University alumni Association football people from Tokyo Japanese men's footballers J1 League players J2 League players Kawasaki Frontale players Cerezo Osaka players Omiya Ardija players Hokkaido Consadole Sapporo players Roasso Kumamoto players FC Gifu players Men's association football midfielders
https://en.wikipedia.org/wiki/Yuji%20Yabu
is a Japanese former football player. Career Yabu retired at the end of the 2019 season. Club statistics Updated to 23 February 2020. References External links Profile at V-Varen Nagasaki Profile at Kawasaki Frontale 1984 births Living people Kokushikan University alumni People from Isehara, Kanagawa Association football people from Kanagawa Prefecture Japanese men's footballers J1 League players J2 League players J3 League players Kawasaki Frontale players Ventforet Kofu players Roasso Kumamoto players V-Varen Nagasaki players Fujieda MYFC players Men's association football midfielders
https://en.wikipedia.org/wiki/Quartic%20surface
In mathematics, especially in algebraic geometry, a quartic surface is a surface defined by an equation of degree 4. More specifically there are two closely related types of quartic surface: affine and projective. An affine quartic surface is the solution set of an equation of the form where is a polynomial of degree 4, such as . This is a surface in affine space . On the other hand, a projective quartic surface is a surface in projective space of the same form, but now is a homogeneous polynomial of 4 variables of degree 4, so for example . If the base field is or the surface is said to be real or complex respectively. One must be careful to distinguish between algebraic Riemann surfaces, which are in fact quartic curves over , and quartic surfaces over . For instance, the Klein quartic is a real surface given as a quartic curve over . If on the other hand the base field is finite, then it is said to be an arithmetic quartic surface. Special quartic surfaces Dupin cyclides The Fermat quartic, given by x4 + y4 + z4 + w4 =0 (an example of a K3 surface). More generally, certain K3 surfaces are examples of quartic surfaces. Kummer surface Plücker surface Weddle surface See also Quadric surface (The union of two quadric surfaces is a special case of a quartic surface) Cubic surface (The union of a cubic surface and a plane is another particular type of quartic surface) References Complex surfaces Algebraic surfaces
https://en.wikipedia.org/wiki/William%20Shaw%20%28mathematician%29
William Shaw (born 14 May 1958) is a British mathematician, and formerly professor of the mathematics and computation of risk at University College London. He is a consultant on financial derivatives, an author of a primary book on using Mathematica to model financial derivatives, formerly co-Editor-in-Chief of the journal Applied Mathematical Finance. Shaw studied at King's College, Cambridge, where he studied mathematics; he was Wrangler and earned a B.A. in 1980. In 1981 he won the Mayhew Prize for his performance on the Cambridge Mathematical Tripos. In 1984 he received a D.Phil. (PhD) in mathematical physics from Wolfson College, Oxford. From 1984 to 1987 he was a research fellow at Clare College, Cambridge and C.L.E. Moore Instructor at the Massachusetts Institute of Technology. From 1987 to 1990, he worked for Smith Associates in Guildford, and ECL in Henley-on Thames. From 1991 to 2002 he was a lecturer in mathematics at Balliol College, Oxford. In 2002 he moved to St Catherine's College, Oxford, where he was University Lecturer in financial mathematics. In 2006 he moved to a Professorship at King's College London and in 2011 to a Professorship at UCL. He returned to the financial industry in 2012 and remained a visiting professor at UCL until 2017. Books Applied Mathematica: Getting Started, Getting it Done by W.T. Shaw and J. Tigg. Addison-Wesley, 1993. Modelling Financial Derivatives with Mathematica by W.T. Shaw, Cambridge University Press, 1998. Complex Analysis with Mathematica by W.T. Shaw, Cambridge University Press, 2006. References External links William Shaw's former UCL web-page Entry in Mathematics Genealogy Project LinkedIn profile 1958 births Living people Alumni of King's College, Cambridge Academics of King's College London Academics of University College London English mathematicians Mathematical finance Massachusetts Institute of Technology School of Science faculty
https://en.wikipedia.org/wiki/Federico%20Laurito
Federico Raúl Laurito (born 18 May 1990) is an Argentine professional footballer. External links Gazzetta profile Primera División statistics Federico Laurito at Soccerway 1990 births Living people Argentine men's footballers Argentina men's youth international footballers Argentina men's under-20 international footballers Argentine expatriate men's footballers Argentine Primera División players Primera B de Chile players Serie B players Ecuadorian Serie A players Categoría Primera A players Newell's Old Boys footballers Udinese Calcio players US Livorno 1915 players Venezia FC players Club Atlético Huracán footballers C.D. Cuenca footballers Everton de Viña del Mar footballers Barcelona S.C. footballers Arsenal de Sarandí footballers Fuerza Amarilla S.C. footballers L.D.U. Portoviejo footballers Independiente Medellín footballers Men's association football forwards Footballers from Rosario, Santa Fe Expatriate men's footballers in Chile Expatriate men's footballers in Italy Expatriate men's footballers in Ecuador Expatriate men's footballers in Colombia Argentine expatriate sportspeople in Chile Argentine expatriate sportspeople in Italy Argentine expatriate sportspeople in Ecuador Argentine expatriate sportspeople in Colombia