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https://en.wikipedia.org/wiki/Jesus%20and%20Mary%20College
Jesus and Mary College (JMC) is a women-only college of the University of Delhi located in New Delhi, India. The college offers bachelor's degrees in Commerce, Arts, and Mathematics. The college offers honors degrees in Elementary Education, History, Sociology, Political Science, Vocational Studies, Hindi, English, Economics, Psychology, Mathematics, and Commerce. The college is located in the Chanakyapuri diplomatic enclave in New Delhi, adjacent to Maitreyi College. Due to the construction of Pink Line, Jesus and Mary College is quite accessible via Delhi Metro. The nearest metro station is Durgabai Deshmukh South Campus metro station which is around 1 km from the college. History The college was founded by Religious of Jesus and Mary, a Roman Catholic congregation founded by St. Claudine Thevenet or known as Mary of St. Ignatius (1774–1837) in Lyon, France, in 1818. The Convent of Jesus and Mary, Delhi was established in 1919, and thereafter a college for women in Delhi and the college was founded in July 1968. At the time of opening, the college offered only two degrees: English (Hons.) and BA (Pass), but quickly expanded to offer degrees in other subjects. Jesus and Mary College is one of the few colleges in the University of Delhi whose student body is not affiliated with Delhi University Students Union (DUSU). Academics Rankings It is ranked 37th among colleges in India by National Institutional Ranking Framework in 2020. Admission The admission to the college is based on a competitive cut-off percentage in senior secondary exams. The college also reserves a certain number of seats for Scheduled Caste and Scheduled Tribe (SC/ST) candidates. As a minority institution, the college also has a 50% reservation for Catholic or other Christian students. Courses Undergraduate courses: Bachelor of Arts (Hons.) in Economics, English, Hindi, History, Political Science, Psychology, Sociology B.A. Programme: Discipline Subject Combination Bachelor of Commerce (Hons.) Bachelor of Commerce Bachelor of Science (Hons.) Mathematics Bachelor of Elementary Education (4 Years Course) Bachelor of Vocational Studies (B.Voc:-Health care Management & B.Voc:-Retail Management & IT) (Note: All undergraduate degree courses except B.El.Ed shall be taught in three years, semester mode) Postgraduate courses: Master of Arts—English Master of Arts—Hindi Projects Student involvement in projects as part of curriculum is given below: Departments like B.El.Ed. (IIIrd year) and Psychology have 100% student involvement in in-house projects over the past four years. The Department of Economics has 83% of its students work as interns in institutions and companies like DMRC, Ernst and Young, German National Tourists Services, HUDCO, King's College London, Lucid Solutions, the Planning Commission, Reliance Securities, Smilyo, Toxics Link, United Nations Projects. The department has also worked with NGOs like Kalpavriksha and Samavesh. The Department of
https://en.wikipedia.org/wiki/Yudai%20Nishikawa
is a Japanese former footballer. Club statistics References External links Profile at Kataller Toyama 1986 births Living people University of Tsukuba alumni Association football people from Saitama Prefecture Japanese men's footballers J2 League players J3 League players FC Gifu players Kataller Toyama players Tochigi SC players Men's association football forwards
https://en.wikipedia.org/wiki/Shinji%20Tominari
is a Japanese retired football player. Club statistics Updated to 23 February 2020. References External links Profile at Kagoshima United FC 1987 births Living people Fukuoka University alumni Association football people from Gifu Prefecture Japanese men's footballers J2 League players J3 League players Japan Football League players FC Gifu players Fujieda MYFC players Kagoshima United FC players Men's association football defenders Sportspeople from Gifu
https://en.wikipedia.org/wiki/Kazuki%20Someya
is a Japanese football player who plays as a midfielder for Azul Claro Numazu. Club statistics Updated to 23 February 2018. References External links Profile at Azul Claro Numazu 1986 births Living people Nara Gakuen University alumni Association football people from Osaka Japanese men's footballers J2 League players J3 League players Japan Football League players FC Gifu players Fagiano Okayama players Oita Trinita players Azul Claro Numazu players Men's association football midfielders
https://en.wikipedia.org/wiki/Cha%20Dong-hoon
Cha Dong-Hoon (born November 7, 1989) is a South Korean football player. Club statistics References External links 1989 births Living people South Korean men's footballers J2 League players Japan Football League players FC Gifu players FC Kariya players Men's association football forwards
https://en.wikipedia.org/wiki/Tomohiro%20Yamauchi
is a Japanese football player. Club statistics References External links j-league 1987 births Living people Tokai Gakuen University alumni Association football people from Kagoshima Prefecture Japanese men's footballers J2 League players FC Gifu players Kochi United SC players Men's association football defenders
https://en.wikipedia.org/wiki/Yuji%20Ozaki
is a former Japanese football player. Club statistics References External links j-league 1985 births Living people Momoyama Gakuin University alumni Association football people from Nagasaki Prefecture Japanese men's footballers J2 League players Japan Football League players Fagiano Okayama players Men's association football defenders
https://en.wikipedia.org/wiki/Mutsumi%20Tamabayashi
is a Japanese football player for Artista Asama. Club statistics Updated to end of 2018 season. References External links Profile at Ehime FC 1984 births Living people Kibi International University alumni People from Uwajima, Ehime Association football people from Ehime Prefecture Japanese men's footballers J2 League players Japan Football League players Fagiano Okayama players Matsumoto Yamaga FC players Ehime FC players Artista Asama players Men's association football defenders
https://en.wikipedia.org/wiki/Masahiko%20Sawaguchi
Masahiko Sawaguchi (澤口 雅彦, born July 22, 1985) is a Japanese football player who plays for Ococias Kyoto AC. Career On 8 February 2019, Sawaguchi joined Ococias Kyoto AC. Club statistics Updated to 23 February 2018. References External links 1985 births Living people Ryutsu Keizai University alumni Association football people from Ibaraki Prefecture Japanese men's footballers J2 League players Japan Football League players FC Ryukyu players Fagiano Okayama players Ococias Kyoto AC players Men's association football midfielders
https://en.wikipedia.org/wiki/Shugo%20Kawahara
is a former Japanese football player. Club statistics References External links j-league 1980 births Living people Fukuoka University alumni Association football people from Okayama Prefecture Japanese men's footballers J2 League players Japan Football League players Mitsubishi Mizushima FC players Fagiano Okayama players Men's association football midfielders
https://en.wikipedia.org/wiki/Yusuke%20Kobayashi%20%28footballer%2C%20born%201983%29
is a former Japanese football player. Club statistics References External links j-league 1983 births Living people Chuo University alumni Association football people from Hiroshima Prefecture Japanese men's footballers J2 League players Japan Football League players Fagiano Okayama players Men's association football midfielders
https://en.wikipedia.org/wiki/Keisuke%20Sekiguchi
is a former Japanese football player. Club statistics References External links Fagiano Okayama 1986 births Living people Association football people from Okayama Prefecture Japanese men's footballers J2 League players Japan Football League players Fagiano Okayama players Men's association football forwards
https://en.wikipedia.org/wiki/Ryusuke%20Senoo
is a former Japanese football player. Club statistics References External links j-league 1986 births Living people Osaka Gakuin University alumni Association football people from Okayama Prefecture Sportspeople from Okayama Prefecture Japanese men's footballers J2 League players Japan Football League players Fagiano Okayama players Men's association football midfielders
https://en.wikipedia.org/wiki/Shotaro%20Dei
is a former Japanese football player. Club statistics References External links j-league 1986 births Living people Kochi University alumni Association football people from Ehime Prefecture Japanese men's footballers J2 League players Fagiano Okayama players Men's association football forwards
https://en.wikipedia.org/wiki/Hidenori%20Mago
is a former Japanese football player. Club statistics References External links j-league 1982 births Living people University of Teacher Education Fukuoka alumni Association football people from Fukuoka Prefecture Japanese men's footballers J2 League players Japan Football League players Sagawa Shiga FC players Fagiano Okayama players Men's association football goalkeepers
https://en.wikipedia.org/wiki/Hitoshi%20Usui
is a former Japanese football player. Club statistics References External links j-league 1988 births Living people Association football people from Hyōgo Prefecture Japanese men's footballers J2 League players Japan Football League players Fagiano Okayama players Men's association football midfielders
https://en.wikipedia.org/wiki/Tsuyoshi%20Shinchu
Tsuyoshi Shinchu (新中 剛史, born November 28, 1986) is a Japanese football player. Club statistics Updated to 23 February 2016. References External links Profile at KUFC 1986 births Living people Biwako Seikei Sport College alumni Association football people from Kagoshima Prefecture Japanese men's footballers J2 League players J3 League players Japan Football League players Fagiano Okayama players Matsumoto Yamaga FC players Kagoshima United FC players Men's association football midfielders
https://en.wikipedia.org/wiki/Ryo%20Tadokoro
Ryo Tadokoro (田所 諒, born April 8, 1986) is a Japanese retired football player. Club statistics Updated to 23 February 2018. References External links Profile at Yokohama FC 1986 births Living people Osaka University of Health and Sport Sciences alumni Association football people from Osaka Prefecture People from Neyagawa, Osaka Japanese men's footballers J2 League players Fagiano Okayama players Yokohama FC players Men's association football midfielders
https://en.wikipedia.org/wiki/Yuki%20Kotera
is a former Japanese football player. Club statistics References External links 1986 births Living people Hannan University alumni Association football people from Wakayama Prefecture Japanese men's footballers J2 League players Fagiano Okayama players Men's association football midfielders
https://en.wikipedia.org/wiki/Yutaka%20Baba%20%28footballer%29
is a Japanese football player. He plays for MIO Biwako Shiga. Club statistics References External links 1986 births Living people Osaka Gakuin University alumni Association football people from Nara Prefecture Japanese men's footballers J2 League players Japan Football League players Fagiano Okayama players Zweigen Kanazawa players Renofa Yamaguchi FC players Nara Club players Reilac Shiga FC players Men's association football defenders
https://en.wikipedia.org/wiki/Takashi%20Nishihara
is a former Japanese football player. Club statistics References External links jsgoal 1986 births Living people Ehime University alumni Association football people from Ehime Prefecture Japanese men's footballers J2 League players Fagiano Okayama players Men's association football defenders
https://en.wikipedia.org/wiki/Verlinde%20algebra
In mathematics, a Verlinde algebra is a finite-dimensional associative algebra introduced by , with a basis of elements φλ corresponding to primary fields of a rational two-dimensional conformal field theory, whose structure constants N describe fusion of primary fields. Verlinde formula In terms of the modular S-matrix, the fusion coefficients are given by where is the component-wise complex conjugate of . Twisted equivariant K-theory If G is a compact Lie group, there is a rational conformal field theory whose primary fields correspond to the representations λ of some fixed level of loop group of G. For this special case showed that the Verlinde algebra can be identified with twisted equivariant K-theory of G. See also Fusion rules Notes References MathOverflow discussion with a number of references. Representation theory Conformal field theory
https://en.wikipedia.org/wiki/Myers%E2%80%93Steenrod%20theorem
Two theorems in the mathematical field of Riemannian geometry bear the name Myers–Steenrod theorem, both from a 1939 paper by Myers and Steenrod. The first states that every distance-preserving map (that is, an isometry of metric spaces) between two connected Riemannian manifolds is a smooth isometry of Riemannian manifolds. A simpler proof was subsequently given by Richard Palais in 1957. The main difficulty lies in showing that a distance-preserving map, which is a priori only continuous, is actually differentiable. The second theorem, which is much more difficult to prove, states that the isometry group of a Riemannian manifold is a Lie group. For instance, the group of isometries of the two-dimensional unit sphere is the orthogonal group O(3). References Differential geometry Theorems in Riemannian geometry
https://en.wikipedia.org/wiki/Preissmann%27s%20theorem
In Riemannian geometry, a field of mathematics, Preissmann's theorem is a statement that restricts the possible topology of a negatively curved compact Riemannian manifold. It is named for Alexandre Preissmann, who published a proof in 1943. Preissmann's theorem Consider a closed manifold with a Riemannian metric of negative sectional curvature. Preissmann's theorem states that every non-trivial abelian subgroup of the fundamental group must be isomorphic to the additive group of integers, . This can loosely be interpreted as saying that the fundamental group of such a manifold must be highly nonabelian. Moreover, the fundamental group itself cannot be abelian. As an example, Preissmann's theorem implies that the -dimensional torus admits no Riemannian metric of strictly negative sectional curvature (unless is two). More generally, the product of two closed manifolds of positive dimensions does not admit a Riemannian metric of strictly negative sectional curvature. The standard proof of Preissmann's theorem deals with the constraints that negative curvature makes on the lengths and angles of geodesics. However, it may also be proved by techniques of partial differential equations, as a direct corollary of James Eells and Joseph Sampson's foundational theorem on harmonic maps. Flat torus theorem The Preissmann theorem may be viewed as a special case of the more powerful flat torus theorem obtained by Detlef Gromoll and Joseph Wolf, and independently by Blaine Lawson and Shing-Tung Yau. This establishes that, under nonpositivity of the sectional curvature, abelian subgroups of the fundamental group are represented by geometrically special submanifolds: totally geodesic isometric immersions of a flat torus. There is a well-developed theory of Alexandrov spaces which extends the theory of upper bounds on sectional curvature to the context of metric spaces. The flat torus theorem, along with the special case of the Preissmann theorem, can be put into this broader context. References Books. Theorems in Riemannian geometry
https://en.wikipedia.org/wiki/Akihiro%20Sato%20%28footballer%2C%20born%20October%201986%29
Akihiro Sato (佐藤 晃大, born 22 October 1986) is a Japanese football player for Tokushima Vortis. Career statistics Club Updated to end of 2018 season. References External links Profile at Tokushima Vortis 1986 births Living people Tokai University alumni People from Zama, Kanagawa Association football people from Kanagawa Prefecture Japanese men's footballers J1 League players J2 League players Tokushima Vortis players Gamba Osaka players Men's association football forwards
https://en.wikipedia.org/wiki/Thiago%20%28footballer%2C%20born%20February%201983%29
Thiago dos Santos Costa (born February 28, 1983) is a Brazilian footballer who plays for São Luiz. Club statistics References j-league jsgoal Furacao.com 1983 births Living people Brazilian men's footballers J2 League players Ehime FC players Esporte Clube São Luiz players Brazilian expatriate men's footballers Expatriate men's footballers in Japan Men's association football defenders
https://en.wikipedia.org/wiki/Ryosuke%20Ochi
Ryosuke Ochi (越智 亮介, born April 7, 1990) is a Japanese football player who plays for FC Imabari. Club statistics Updated to 23 February 2018. References External links Profile at Fujieda MYFC 1990 births Living people People from Imabari, Ehime Association football people from Ehime Prefecture Japanese men's footballers J2 League players J3 League players Japan Football League players Ehime FC players Zweigen Kanazawa players Fujieda MYFC players FC Ryukyu players FC Imabari players Men's association football midfielders
https://en.wikipedia.org/wiki/Takeshi%20Okamoto
is a former Japanese football player. Club statistics References External links j-league 1991 births Living people Association football people from Ehime Prefecture Japanese men's footballers J2 League players Ehime FC players Men's association football forwards
https://en.wikipedia.org/wiki/Kazuhito%20Watanabe
Kazuhito Watanabe (渡邊 一仁, born September 1, 1986) is a Japanese football player for Ehime FC. Club statistics Updated to 14 April 2020. References External links Profile at Yokohama FC 1986 births Living people Tokyo Gakugei University alumni Association football people from Ehime Prefecture Japanese men's footballers J2 League players Ehime FC players Fagiano Okayama players Yokohama FC players Men's association football midfielders Sportspeople from Matsuyama, Ehime
https://en.wikipedia.org/wiki/Alex%20Henrique
Alex Henrique José (born March 20, 1985) is a Brazilian football player who currently plays as a midfielder for Aparecidense. Club statistics References External links 1985 births Living people Brazilian men's footballers Campeonato Brasileiro Série B players Campeonato Brasileiro Série C players Campeonato Brasileiro Série D players J2 League players Alex Henrique Avispa Fukuoka players Thespakusatsu Gunma players Tokyo Verdy players Agremiação Sportiva Arapiraquense players Alex Henrique Comercial Futebol Clube (Ribeirão Preto) players Centro Sportivo Alagoano players América Futebol Clube (RN) players Moto Club de São Luís players Associação Atlética Aparecidense players Vila Nova Futebol Clube players Sampaio Corrêa Futebol Clube players Esporte Clube Pelotas players Associação Desportiva Confiança players Brazilian expatriate men's footballers Expatriate men's footballers in Japan Expatriate men's footballers in Thailand Brazilian expatriate sportspeople in Japan Brazilian expatriate sportspeople in Thailand Men's association football midfielders Footballers from São Paulo
https://en.wikipedia.org/wiki/Yuto%20Takeoka
is a Japanese football player. Club statistics Updated to 23 February 2019. References External links Profile at Kawasaki Frontale 1986 births Living people Kokushikan University alumni Japanese men's footballers J1 League players J2 League players Sagan Tosu players Yokohama FC players Kawasaki Frontale players Ventforet Kofu players Renofa Yamaguchi FC players Men's association football midfielders Men's association football fullbacks Association football people from Kyoto
https://en.wikipedia.org/wiki/Samuel%20%28footballer%2C%20born%20July%201989%29
Samuel Henrique Silva Guimaraes (born July 23, 1989) is a Brazilian football player. Club statistics References j-league 1989 births Living people Brazilian men's footballers Brazilian expatriate men's footballers Expatriate men's footballers in Japan J2 League players Sagan Tosu players Men's association football midfielders
https://en.wikipedia.org/wiki/Kei%20Nakano
is a Japanese football player. He plays for FC Imabari. is a guitarist and Associate professor of Osaka University Of Arts. Club statistics References External links j-league 1988 births Living people Kochi University alumni Association football people from Ehime Prefecture Japanese men's footballers J1 League players J2 League players Japan Football League players Montedio Yamagata players SP Kyoto FC players FC Imabari players Men's association football defenders
https://en.wikipedia.org/wiki/Jun%20Kanakubo
Jun Kanakubo (金久保 順, born July 26, 1987) is a Japanese football player who currently plays for Mito HollyHock. Club statistics Updated to 9 August 2022. References External links Profile at Vegalta Sendai 1987 births Living people Ryutsu Keizai University alumni Association football people from Ibaraki Prefecture Japanese men's footballers J1 League players J2 League players Omiya Ardija players Avispa Fukuoka players Kawasaki Frontale players Vegalta Sendai players Kyoto Sanga FC players Men's association football midfielders
https://en.wikipedia.org/wiki/Masakazu%20Kihara
is a Japanese football player. Club statistics References External links 1987 births Living people Hannan University alumni Association football people from Yamaguchi Prefecture Japanese men's footballers J1 League players J2 League players Omiya Ardija players Avispa Fukuoka players Expatriate men's footballers in Cambodia Men's association football midfielders Angkor Tiger FC players Angkor Tiger FC managers Universiade bronze medalists for Japan Universiade medalists in football Japanese football managers Medalists at the 2009 Summer Universiade Japanese expatriate sportspeople in Cambodia
https://en.wikipedia.org/wiki/Taisuke%20Miyazaki
Taisuke Miyazaki (宮崎 泰右, born May 5, 1992) is a Japanese football player who plays for Shibuya City FC. Club statistics Updated to 23 February 2018. References External links Profile at Tochigi SC 1992 births Living people Association football people from Saitama Prefecture Japanese men's footballers J1 League players J2 League players J3 League players Omiya Ardija players Shonan Bellmare players Thespakusatsu Gunma players FC Machida Zelvia players Tochigi SC players Vanraure Hachinohe players Men's association football defenders
https://en.wikipedia.org/wiki/Hideto%20Takahashi
is a Japanese footballer who plays for Auckland United FC. Club statistics Updated to 24 February 2019. 1Includes Emperor's Cup. 2Includes J. League Cup. 3Includes AFC Champions League. National team statistics Honours Club FC Tokyo J2 League (1) : 2011 Emperor's Cup (1) : 2011 Japan EAFF East Asian Cup (1) : 2013 References External links Japan National Football Team Database Profile at Sagan Tosu 1987 births Living people Tokyo Gakugei University alumni Association football people from Gunma Prefecture Japanese men's footballers Japan men's international footballers J1 League players J2 League players J3 League players FC Tokyo players FC Tokyo U-23 players Vissel Kobe players Sagan Tosu players 2013 FIFA Confederations Cup players Men's association football midfielders Universiade bronze medalists for Japan Universiade medalists in football Medalists at the 2009 Summer Universiade
https://en.wikipedia.org/wiki/Ryo%20Hiraide
is a Japanese football player. Club statistics Updated to end of 2018 season. References External links Profile at Kagoshima United FC 1991 births Living people Association football people from Yamanashi Prefecture Japanese men's footballers J1 League players J2 League players J3 League players FC Tokyo players Kataller Toyama players Kagoshima United FC players Suzuka Point Getters players Men's association football defenders
https://en.wikipedia.org/wiki/Takumi%20Abe
Takumi Abe (阿部 巧, born May 26, 1991) is a Japanese football player for Thespakusatsu Gunma. Club statistics Updated to 23 February 2018. References External links Profile at Thespakusatsu Gunma 1991 births Living people Association football people from Tokyo Japanese men's footballers J1 League players J2 League players J3 League players FC Tokyo players Yokohama FC players Matsumoto Yamaga FC players Avispa Fukuoka players Thespakusatsu Gunma players SC Sagamihara players Tochigi City FC players Men's association football defenders
https://en.wikipedia.org/wiki/Hidenobu%20Takasu
is a former Japanese football player. He was a forward in the J1 League for Kawasaki Frontale in the 2010 season, but he did not appear in any league games. Club statistics References External links j-league 1991 births Living people Association football people from Aichi Prefecture Japanese men's footballers J1 League players Kawasaki Frontale players Men's association football forwards
https://en.wikipedia.org/wiki/Choi%20Seung-in
Choi Seung-in (born March 5, 1991) is a South Korean football player who plays for German club LSK Hansa. Club statistics As of 21 December 2019 References External links 1991 births Living people South Korean men's footballers Men's association football forwards Shonan Bellmare players Zweigen Kanazawa players Gangwon FC players Busan IPark players Lüneburger SK Hansa players K League 1 players J1 League players Japan Football League players K League 2 players Oberliga (football) players South Korean expatriate men's footballers South Korean expatriate sportspeople in Japan Expatriate men's footballers in Japan South Korean expatriate sportspeople in Germany Expatriate men's footballers in Germany
https://en.wikipedia.org/wiki/Takuya%20Matsumoto
Takuya Matsumoto (松本 拓也, born February 6, 1989) is a Japanese football player who currently plays for FC Gifu. Club statistics Updated to 25 December 2021. Honours Blaublitz Akita J3 League (1): 2017 References External links Profile at Blaublitz Akita Profile at Kawasaki Frontale 1989 births Living people Juntendo University alumni Association football people from Shizuoka Prefecture Japanese men's footballers J1 League players J2 League players J3 League players Shonan Bellmare players Kawasaki Frontale players Giravanz Kitakyushu players Blaublitz Akita players FC Gifu players Men's association football goalkeepers
https://en.wikipedia.org/wiki/Eijiro%20Takeda
Eijiro Takeda (武田 英二郎, born July 11, 1988) is a Japanese football player for Shonan Bellmare. Club statistics Updated to 1 March 2019. 1Includes J2's Relegation Playoffs. References External links Profile at Yokohama FC Profile at Shonan Bellmare 1988 births Living people Aoyama Gakuin University alumni Japanese men's footballers J1 League players J2 League players Shonan Bellmare players Yokohama F. Marinos players JEF United Chiba players Gainare Tottori players Avispa Fukuoka players Yokohama FC players Men's association football midfielders Association football people from Kawasaki, Kanagawa
https://en.wikipedia.org/wiki/Tatsuya%20Arai
is a former Japanese football player. Club statistics References External links j-league 1988 births Living people Chuo University alumni Association football people from Tokyo Japanese men's footballers J1 League players J2 League players Nagoya Grampus players FC Gifu players Men's association football defenders
https://en.wikipedia.org/wiki/Koki%20Arita
Koki Arita (有田 光希, born 23 September 1991) is a Japanese football player. Career statistics Club Updated to end of 2018 season. References External links Profile at Ehime FC 1991 births Living people Association football people from Niigata Prefecture Japanese men's footballers J1 League players J2 League players Vissel Kobe players Ehime FC players Kyoto Sanga FC players Men's association football forwards Sportspeople from Niigata (city)
https://en.wikipedia.org/wiki/Yutaro%20Takahashi
is a former Japanese football player. His elder brother Daisuke is also a former Japanese footballer. Club statistics References External links j-league 1987 births Living people Fukuoka University alumni Association football people from Fukuoka Prefecture Japanese men's footballers J1 League players J2 League players Vissel Kobe players Cerezo Osaka players Roasso Kumamoto players V-Varen Nagasaki players Men's association football forwards
https://en.wikipedia.org/wiki/Park%20Jin-soo
Park Jin-soo (born March 1, 1987) is a South Korean football player who currently plays for Chungju Hummel. His younger brother, Park Hyung-jin, is also a football player. Club statistics References External links jsgoal 1987 births Living people South Korean men's footballers South Korean expatriate men's footballers Hokkaido Consadole Sapporo players Gyeongnam FC players Chungju Hummel FC players J2 League players K League 1 players K League 2 players South Korean expatriate sportspeople in Japan Expatriate men's footballers in Japan Korea University alumni Men's association football midfielders
https://en.wikipedia.org/wiki/Yuichi%20Kubo
Yuichi Kubo (久保 裕一, born September 26, 1988) is a Japanese footballer who plays for Fagiano Okayama, as a striker for SC Sagamihara. Club statistics Updated to 23 February 2018. References External links Profile at SC Sagamihara 1988 births Living people Meiji University alumni Association football people from Wakayama Prefecture Japanese men's footballers J2 League players J3 League players JEF United Chiba players Gainare Tottori players Fagiano Okayama players Mito HollyHock players SC Sagamihara players Men's association football forwards
https://en.wikipedia.org/wiki/Akimi%20Barada
Akimi Barada (茨田 陽生, born 30 May 1991) is a Japanese football player. He currently plays for Shonan Bellmare. Career statistics Club Updated to end of 2018 season 1Includes FIFA Club World Cup and Japanese Super Cup. International Honours Club Kashiwa Reysol J. League Division 1 : 2011 J. League Division 2 : 2010 Emperor's Cup : 2012 Japanese Super Cup : 2012 J. League Cup : 2013 Suruga Bank Championship : 2014 References External links Profile at Omiya Ardija 1991 births Living people Association football people from Chiba Prefecture Japanese men's footballers J1 League players J2 League players Kashiwa Reysol players Omiya Ardija players Shonan Bellmare players Men's association football midfielders
https://en.wikipedia.org/wiki/Ryoji%20Fukui
Ryoji Fukui (福井 諒司, born August 7, 1987) is a Japanese football player. Club statistics Updated to end of 2018 season. References External links Profile at Mito HollyHock 1987 births Living people Fukuoka University alumni Association football people from Hyōgo Prefecture Japanese men's footballers J1 League players J2 League players Tokyo Verdy players Giravanz Kitakyushu players Kashiwa Reysol players Renofa Yamaguchi FC players Mito HollyHock players FC Ryukyu players Men's association football defenders
https://en.wikipedia.org/wiki/Shuto%20Minami
Shuto Minami (南 秀仁, born 5 May 1993) is a Japanese footballer who plays as a forward for Montedio Yamagata. Career statistics Club Updated to 26 July 2022. References External links Profile at Montedio Yamagata 1993 births Living people Association football people from Kanagawa Prefecture Japanese men's footballers J2 League players Japan Football League players Tokyo Verdy players FC Machida Zelvia players Montedio Yamagata players Men's association football midfielders Sportspeople from Sagamihara
https://en.wikipedia.org/wiki/Folium
Folium (, "leaf"), plural folia, may refer to a leaf of a book: see recto and verso Folium of Descartes, an algebraic curve Folium (spider), a marking on the abdomen of a spider Brain anatomy Folium (brain) Folium vermis Botany Turnsole or folium, a dyestuff Folium Phyllostachydis, processed leaves of bamboo Hydrangeae Dulcis Folium, processed leaves of hydrangea
https://en.wikipedia.org/wiki/Eastern%20Orthodoxy%20in%20Azerbaijan
Eastern Orthodoxy in Azerbaijan is the main Christian and the second largest religious group in the Republic of Azerbaijan (after Islam). According to statistics, the Eastern Orthodox, or Byzantine tradition in Azerbaijan is 2.3% (209.7 thousand people). The territory of Azerbaijan is in the jurisdiction of the Baku-Azerbaijan Diocese of the Russian Orthodox Church. History of Eastern Orthodoxy in Azerbaijan Serious changes in the Caucasian Albanian church occurred under the Arab rule, when the Catholicos Nerses I Bakur (688-704) attempted to convert to Chalcedonism, thus recognizing the spiritual authority of Constantinople. He was deposed by the Grand Duke of Albania Shero and other feudal lords who remained faithful to the Albanian church, and cursed at the national church cathedral. In the second half of the 10th century, the population of the left-bank Albania (Hereti) was included in the sphere of influence of the decision of the Chalcedon Council of the Georgian Church, adopted in the 7th century and got a great impact of Georgia. When the territories of Transcaucasia entered the Russian Empire, jurisdiction of Georgian Exarchate was expanded, encompassing territories of modern-day Georgia, Armenia and Azerbaijan. In 1905, Eparchy of Baku, nowadays Baku and Caspian Eparchy, was established. The Albanian Catholicos of the church in 1813 by the decree of Tsar Nicholas I passed into the status of the metropolite of the Albanian church. Eastern Orthodoxy became wide spread in Azerbaijan at the beginning of the 19th century. Eastern Orthodoxy in Azerbaijan nowadays In 1815, the first Russian Orthodox church appeared in Baku. Later such churches were built in Ganja, Goranboy (Borisi-Russian village, 1842), Shemakha (Alty-Aghadj village, 1834), Lankaran (Vel village, 1838), and Gedabek (Slavyanka village, 1844). There were 21 sectarian villages in Baku during 1868. In 1905, the Baku Diocese of the Russian Orthodox Church was established. During the Soviet era, the authorities repressed the priests of the Baku diocese, but in 1944 two churches were opened. In 1998, the Baku-Caspian Diocese of the Russian Orthodox Church was established. On March 22, 2011, the decision of the Holy Synod of the Russian Orthodox Church was changed to the Baku-Caspian diocese in Baku-Azerbaijan. In 2011 there were six Eastern Orthodox churches in the country. Five of them belong to the Russian Orthodox church (ROC): three of them are located in Baku one in Ganja and one in Khachmaz. Another temple belongs to the jurisdiction of the Georgian Orthodox Church - the Church of St. George in the village of Gakh-Inguila in the Qakh district, where the Ingiloy Georgians live compactly (about 7,500 people). In 2013, November, President Ilham Aliyev participated in the opening ceremony of Orthodox Religious and Cultural Center of Baku and Azerbaijan Eparchy. Firstly, The President visited the Holy Myrrhbearers Cathedral. There is also the Michael Archangel's Templ
https://en.wikipedia.org/wiki/Takahiro%20Nakazato
is a Japanese football player who plays for YSCC Yokohama in the J3 League. Club statistics Updated to 23 February 2018. References External links Profile at Yokohama FC 1990 births Living people Ryutsu Keizai University alumni Association football people from Tokyo Japanese men's footballers Japanese expatriate men's footballers J2 League players J3 League players K League 1 players Yokohama FC players Gangwon FC players Mito HollyHock players Suzuka Point Getters players YSCC Yokohama players Men's association football midfielders FISU World University Games gold medalists for Japan Universiade medalists in football Japanese expatriate sportspeople in South Korea Expatriate men's footballers in South Korea Medalists at the 2011 Summer Universiade
https://en.wikipedia.org/wiki/Yoshifumi%20Kashiwa
Yoshifumi Kashiwa (柏好文, Kashiwa Yoshifumi, born July 28, 1987) is a Japanese football player who plays for Sanfrecce Hiroshima. Club statistics 1Includes Japanese Super Cup, FIFA Club World Cup and J. League Championship. Honours Club Sanfrecce Hiroshima J.League Cup: 2022 References External links Profile at Sanfrecce Hiroshima 1987 births Living people Kokushikan University alumni Association football people from Yamanashi Prefecture Japanese men's footballers J1 League players J2 League players Ventforet Kofu players Sanfrecce Hiroshima players Men's association football midfielders
https://en.wikipedia.org/wiki/Tatsuya%20Murao
is a former Japanese football player. Club statistics References External links j-league 1988 births Living people Miyazaki Sangyo-keiei University alumni Association football people from Kagoshima Prefecture Japanese men's footballers J2 League players Japan Football League players FC Gifu players Fujieda MYFC players Tegevajaro Miyazaki players Men's association football goalkeepers
https://en.wikipedia.org/wiki/Kazuki%20Murakami%20%28footballer%29
is a Japanese football player for Ayutthaya United in Thai League 2. Club statistics References External links j-league Players Profile - Thai League 1987 births Living people Hiroshima University alumni Association football people from Ehime Prefecture Japanese men's footballers J2 League players Kazuki Murakami FC Gifu players Kazuki Murakami Japanese expatriate men's footballers Expatriate men's footballers in Thailand Japanese expatriate sportspeople in Thailand Men's association football central defenders Men's association football fullbacks
https://en.wikipedia.org/wiki/Kazuto%20Sakamoto
is a former Japanese football player. Shoichiro Sakamoto is his brother. Club statistics References External links j-league 1991 births Living people Association football people from Nara Prefecture Japanese men's footballers J2 League players FC Gifu players FC Kariya players FC Osaka players Men's association football defenders
https://en.wikipedia.org/wiki/Takanori%20Chiaki
Takanori Chiaki (千明 聖典, born July 19, 1987) is a Japanese football player for SC Sagamihara. Club statistics Updated to 23 February 2018. References External links Profile at SC Sagamihara 1987 births Living people Ryutsu Keizai University alumni Association football people from Tokyo Japanese men's footballers J2 League players J3 League players Fagiano Okayama players Oita Trinita players SC Sagamihara players Men's association football midfielders Universiade bronze medalists for Japan Universiade medalists in football People from Ōme, Tokyo Medalists at the 2009 Summer Universiade 21st-century Japanese people
https://en.wikipedia.org/wiki/Naoyoshi%20Fukumoto
is a former Japanese football player. Club statistics References External links j-league 1987 births Living people Ritsumeikan University alumni Association football people from Okayama Prefecture Japanese men's footballers J2 League players Fagiano Okayama players Men's association football midfielders
https://en.wikipedia.org/wiki/Naoki%20Miyata
is a former Japanese football player who last played for Tegevajaro Miyazaki. Club statistics Updated to 20 February 2020. References External links Profile at Azul Claro Numazu j-league 1987 births Living people Rissho University alumni Association football people from Nagano Prefecture Japanese men's footballers J2 League players Japan Football League players Fagiano Okayama players Matsumoto Yamaga FC players Azul Claro Numazu players Tegevajaro Miyazaki players Men's association football midfielders People from Matsumoto, Nagano
https://en.wikipedia.org/wiki/Oh%20Seung-hoon
Oh Seung-hoon (; born June 30, 1988) is a South Korean football player who plays for Daegu FC. Club statistics Updated to 22 October 2022. References External links j-league 1988 births Living people Men's association football goalkeepers South Korean men's footballers South Korean expatriate men's footballers J2 League players Tokushima Vortis players Kyoto Sanga FC players Daejeon Hana Citizen players Gimcheon Sangmu FC players Ulsan Hyundai FC players Jeju United FC players Daegu FC players K League 1 players Expatriate men's footballers in Japan South Korean expatriate sportspeople in Japan
https://en.wikipedia.org/wiki/Tatico
Wilson Deodato da Silva (born January 10, 1981) is a Brazilian football player. Club statistics References External links J.League 1981 births Living people Brazilian men's footballers J2 League players Japan Football League players FC Ryukyu players Giravanz Kitakyushu players ReinMeer Aomori players FC Osaka players Brazilian expatriate men's footballers Expatriate men's footballers in Japan Men's association football defenders
https://en.wikipedia.org/wiki/Takayuki%20Tada
Takayuki Tada (多田 高行, born April 7, 1988) is a Japanese football player. Club statistics Updated to 23 February 2016. References External links 1988 births Living people National Institute of Fitness and Sports in Kanoya alumni Association football people from Kagawa Prefecture Japanese men's footballers J2 League players Giravanz Kitakyushu players Men's association football midfielders
https://en.wikipedia.org/wiki/So%20Morita
So Morita (守田創, born May 14, 1992) is a Japanese football player. Club statistics Updated to 23 February 2018. References External links Profile at J. League 1992 births Living people Association football people from Kumamoto Prefecture Japanese men's footballers J1 League players J2 League players J3 League players Sagan Tosu players Iwate Grulla Morioka players Tochigi City FC players Men's association football defenders
https://en.wikipedia.org/wiki/Kohei%20Kuroki
is a Japanese football player for Roasso Kumamoto. He is the twin brother of Kyohei Kuroki. Club statistics Updated to 23 February 2018. References External links Profile at Roasso Kumamoto 1989 births Living people Saga University alumni Association football people from Kumamoto Prefecture Japanese men's footballers J1 League players J2 League players J3 League players Sagan Tosu players Roasso Kumamoto players Men's association football midfielders Japanese twins
https://en.wikipedia.org/wiki/Tsukasa%20Morimoto
is a Japanese football player. He plays for Nara Club. Club statistics Updated to 20 February 2017. References External links Profile at Nara Club j-league 1988 births Living people Chukyo University alumni Association football people from Aichi Prefecture Japanese men's footballers J2 League players J3 League players Japan Football League players Sagan Tosu players Yokohama FC players SC Sagamihara players Nara Club players Men's association football defenders Universiade bronze medalists for Japan Universiade medalists in football Medalists at the 2009 Summer Universiade
https://en.wikipedia.org/wiki/Ryunosuke%20Noda
is a Japanese football player who plays for FC Ryukyu. Career statistics Updated to 21 December 2019. References External links Profile at Shonan Bellmare Profile at Nagoya Grampus 1988 births Living people Japan University of Economics alumni Association football people from Fukuoka Prefecture Japanese men's footballers J1 League players J2 League players Sagan Tosu players Nagoya Grampus players Shonan Bellmare players Kyoto Sanga FC players FC Ryukyu players Men's association football forwards
https://en.wikipedia.org/wiki/Kim%20Ho-nam
Kim Ho-nam (; born June 14, 1989) is a South Korean football player who plays for Bucheon FC. Club statistics Honours Pohang Steelers AFC Champions League: 2021 (runners-up) References External links 1989 births Living people South Korean men's footballers South Korean expatriate men's footballers Men's association football forwards Sagan Tosu players Gwangju FC players Jeju United FC players Gimcheon Sangmu FC players J2 League players K League 1 players K League 2 players Expatriate men's footballers in Japan South Korean expatriate sportspeople in Japan Sportspeople from Jeonju
https://en.wikipedia.org/wiki/Kenta%20Kato
is a former Japanese football player. Club statistics References External links j-league 1987 births Living people Osaka Gakuin University alumni Association football people from Miyagi Prefecture Japanese men's footballers J2 League players Roasso Kumamoto players Men's association football midfielders
https://en.wikipedia.org/wiki/Geospatial%20topology
Geospatial topology is the study and application of qualitative spatial relationships between geographic features, or between representations of such features in geographic information, such as in geographic information systems (GIS). For example, the fact that two regions overlap or that one contains the other are examples of topological relationships. It is thus the application of the mathematics of topology to GIS, and is distinct from, but complementary to the many aspects of geographic information that are based on quantitative spatial measurements through coordinate geometry. Topology appears in many aspects of geographic information science and GIS practice, including the discovery of inherent relationships through spatial query, vector overlay and map algebra; the enforcement of expected relationships as validation rules stored in geospatial data; and the use of stored topological relationships in applications such as network analysis. Spatial topology is the generalization of geospatial topology for non-geographic domains, e.g., CAD software. Topological relationships In keeping with the definition of topology, a topological relationship between two geographic phenomena is any spatial relation that is not sensitive to measurable aspects of space, including transformations of space (e.g. map projection). Thus, it includes most qualitative spatial relations, such as two features being "adjacent," "overlapping," "disjoint," or one being "within" another; conversely, one feature being "5km from" another, or one feature being "due north of" another are metric relations. One of the first developments of Geographic Information Science in the early 1990s was the work of Max Egenhofer, Eliseo Clementini, Peter di Felice, and others to develop a concise theory of such relations commonly called the 9-Intersection Model, which characterizes the range of topological relationships based on the relationships between the interiors, exteriors, and boundaries of features. These relationships can also be classified semantically: Inherent relationships are those that are important to the existence or identity of one or both of the related phenomena, such as one expressed in a boundary definition or being a manifestation of a mereological relationship. For example, Nebraska lies within the United States simply because the former was created by the latter as a partition of the territory of the latter. The Missouri River is adjacent to the state of Nebraska because the definition of the boundary of the state says so. These relationships are often stored and enforced in topologically-savvy data. Coincidental relationships are those that are not crucial to the existence of either, although they can be very important. For example, the fact that the Platte River passes through Nebraska is coincidental because both would still exist unproblematically if the relationship did not exist. These relationships are rarely stored as such, but are usually discovered an
https://en.wikipedia.org/wiki/Veblen%27s%20theorem
In mathematics, Veblen's theorem, introduced by , states that the set of edges of a finite graph can be written as a union of disjoint simple cycles if and only if every vertex has even degree. Thus, it is closely related to the theorem of that a finite graph has an Euler tour (a single non-simple cycle that covers the edges of the graph) if and only if it is connected and every vertex has even degree. Indeed, a representation of a graph as a union of simple cycles may be obtained from an Euler tour by repeatedly splitting the tour into smaller cycles whenever there is a repeated vertex. However, Veblen's theorem applies also to disconnected graphs, and can be generalized to infinite graphs in which every vertex has finite degree . If a countably infinite graph G has no odd-degree vertices, then it may be written as a union of disjoint (finite) simple cycles if and only if every finite subgraph of G can be extended (by including more edges and vertices from G) to a finite Eulerian graph. In particular, every countably infinite graph with only one end and with no odd vertices can be written as a union of disjoint cycles . See also Cycle basis Cycle double cover conjecture Eulerian matroid References . Reprinted and translated in . . Theorems in graph theory
https://en.wikipedia.org/wiki/1980%20S%C3%A3o%20Paulo%20FC%20season
The 1980 season was São Paulo's 51st season since club's existence. Statistics Scorers Managers performance Overall {|class="wikitable" |- |Games played || 71 (44 Campeonato Paulista, 18 Campeonato Brasileiro, 9 Friendly match) |- |Games won || 34 (22 Campeonato Paulista, 8 Campeonato Brasileiro, 4 Friendly match) |- |Games drawn || 24 (13 Campeonato Paulista, 8 Campeonato Brasileiro, 3 Friendly match) |- |Games lost || 13 (9 Campeonato Paulista, 2 Campeonato Brasileiro, 2 Friendly match) |- |Goals scored || 106 |- |Goals conceded || 63 |- |Goal difference || +43 |- |Best result || 4–0 (A) v Palmeiras - Friendly match - 1980.08.054–0 (H) v Corinthians - Campeonato Paulista - 1980.08.10 |- |Worst result || 1–3 (H) v Internacional - Friendly match - 1980.02.131–3 (H) v Guarani - Campeonato Paulista - 1980.10.08 |- |Top scorer || Serginho Chulapa (26) |- Friendlies Official competitions Campeonato Brasileiro Record Campeonato Paulista Record External links official website Association football clubs 1980 season 1980 1980 in Brazilian football
https://en.wikipedia.org/wiki/P-adic%20gamma%20function
In mathematics, the p-adic gamma function Γp is a function of a p-adic variable analogous to the gamma function. It was first explicitly defined by , though pointed out that implicitly used the same function. defined a p-adic analog Gp of log Γ. had previously given a definition of a different p-adic analogue of the gamma function, but his function does not have satisfactory properties and is not used much. Definition The p-adic gamma function is the unique continuous function of a p-adic integer x (with values in ) such that for positive integers x, where the product is restricted to integers i not divisible by p. As the positive integers are dense with respect to the p-adic topology in , can be extended uniquely to the whole of . Here is the ring of p-adic integers. It follows from the definition that the values of are invertible in ; this is because these values are products of integers not divisible by p, and this property holds after the continuous extension to . Thus . Here is the set of invertible p-adic integers. Basic properties of the p-adic gamma function The classical gamma function satisfies the functional equation for any . This has an analogue with respect to the Morita gamma function: The Euler's reflection formula has its following simple counterpart in the p-adic case: where is the first digit in the p-adic expansion of x, unless , in which case rather than 0. Special values and, in general, At the Morita gamma function is related to the Legendre symbol : It can also be seen, that hence as . Other interesting special values come from the Gross–Koblitz formula, which was first proved by cohomological tools, and later was proved using more elementary methods. For example, where denotes the square root with first digit 3, and denotes the square root with first digit 2. (Such specifications must always be done if we talk about roots.) Another example is where is the square root of in congruent to 1 modulo 3. p-adic Raabe formula The Raabe-formula for the classical Gamma function says that This has an analogue for the Iwasawa logarithm of the Morita gamma function: The ceiling function to be understood as the p-adic limit such that through rational integers. Mahler expansion The Mahler expansion is similarly important for p-adic functions as the Taylor expansion in classical analysis. The Mahler expansion of the p-adic gamma function is the following: where the sequence is defined by the following identity: See also Gross–Koblitz formula References Number theory P-adic numbers
https://en.wikipedia.org/wiki/De%20Donder%E2%80%93Weyl%20theory
In mathematical physics, the De Donder–Weyl theory is a generalization of the Hamiltonian formalism in the calculus of variations and classical field theory over spacetime which treats the space and time coordinates on equal footing. In this framework, the Hamiltonian formalism in mechanics is generalized to field theory in the way that a field is represented as a system that varies both in space and in time. This generalization is different from the canonical Hamiltonian formalism in field theory which treats space and time variables differently and describes classical fields as infinite-dimensional systems evolving in time. De Donder–Weyl formulation of field theory The De Donder–Weyl theory is based on a change of variables known as Legendre transformation. Let xi be spacetime coordinates, for i = 1 to n (with n = 4 representing 3 + 1 dimensions of space and time), and ya field variables, for a = 1 to m, and L the Lagrangian density With the polymomenta pia defined as and the De Donder–Weyl Hamiltonian function H defined as the De Donder–Weyl equations are: This De Donder-Weyl Hamiltonian form of field equations is covariant and it is equivalent to the Euler-Lagrange equations when the Legendre transformation to the variables pia and H is not singular. The theory is a formulation of a covariant Hamiltonian field theory which is different from the canonical Hamiltonian formalism and for n = 1 it reduces to Hamiltonian mechanics (see also action principle in the calculus of variations). Hermann Weyl in 1935 has developed the Hamilton-Jacobi theory for the De Donder–Weyl theory. Similarly to the Hamiltonian formalism in mechanics formulated using the symplectic geometry of phase space the De Donder-Weyl theory can be formulated using the multisymplectic geometry or polysymplectic geometry and the geometry of jet bundles. A generalization of the Poisson brackets to the De Donder–Weyl theory and the representation of De Donder–Weyl equations in terms of generalized Poisson brackets satisfying the Gerstenhaber algebra was found by Kanatchikov in 1993. History The formalism, now known as De Donder–Weyl (DW) theory, was developed by Théophile De Donder and Hermann Weyl. Hermann Weyl made his proposal in 1934 being inspired by the work of Constantin Carathéodory, which in turn was founded on the work of Vito Volterra. The work of De Donder on the other hand started from the theory of integral invariants of Élie Cartan. The De Donder–Weyl theory has been a part of the calculus of variations since the 1930s and initially it found very few applications in physics. Recently it was applied in theoretical physics in the context of quantum field theory and quantum gravity. In 1970, Jedrzej Śniatycki, the author of Geometric quantization and quantum mechanics, developed an invariant geometrical formulation of jet bundles, building on the work of De Donder and Weyl. In 1999 Igor Kanatchikov has shown that the De Donder–Weyl covariant Hamilt
https://en.wikipedia.org/wiki/1998%203%20Nations%20Cup
The 1998 3 Nations Cup was a women's ice hockey tournament held in Finland from December 10–16, 1998. It was the third edition of the 3 Nations Cup. Rosters Results Round robin Statistics Final standings Scoring leaders Only the top ten skaters, sorted by points, then goals, are included in this list. Source: Hockey Canada Goaltending leaders The four goaltenders, based on save percentage, who played at least 40% of their team's minutes, are included in this list. Source: Hockey Canada External links Tournament on hockeyarchives.info 1998 1998–99 in American women's ice hockey 1998–99 in Canadian women's ice hockey 1998–99 in Finnish ice hockey 1998–99 in women's ice hockey 1998-99 December 1998 sports events in Europe
https://en.wikipedia.org/wiki/Gross%E2%80%93Koblitz%20formula
In mathematics, the Gross–Koblitz formula, introduced by expresses a Gauss sum using a product of values of the p-adic gamma function. It is an analog of the Chowla–Selberg formula for the usual gamma function. It implies the Hasse–Davenport relation and generalizes the Stickelberger theorem. gave another proof of the Gross–Koblitz formula (Boyarski being a pseudonym of Bernard Dwork), and gave an elementary proof. Statement The Gross–Koblitz formula states that the Gauss sum τ can be given in terms of the p-adic gamma function Γp by where q is a power pf of a prime p r is an integer with 0 ≤ r < q–1 r(i) is the integer whose base p expansion is a cyclic permutation of the f digits of r by i positions sp(r) is the sum of the digits of r in base p , where the sum is over roots of 1 in the extension Qp(π) π satisfies πp – 1 = –p ζπ is the pth root of 1 congruent to 1+π mod π2 References Theorems in algebraic number theory
https://en.wikipedia.org/wiki/1979%20S%C3%A3o%20Paulo%20FC%20season
The 1979 season was São Paulo's 50th season since club's existence. Statistics Scorers Overall {|class="wikitable" |- |Games played || 45 (43 Campeonato Paulista, 2 Friendly match) |- |Games won || 17 (16 Campeonato Paulista) |- |Games drawn || 18 (15 Campeonato Paulista, 2 Friendly match) |- |Games lost || 13 (12 Campeonato Paulista) |- |Goals scored || 51 |- |Goals conceded || 42 |- |Goal difference || +9 |- |Best result || 3–0 (H) v Portuguesa - Campeonato Paulista - 1979.07.223–0 (H) v Velo Clube - Campeonato Paulista - 1979.09.26 |- |Worst result || 0–3 (H) v Santos - Campeonato Paulista - 1979.10.28 |- |Top scorer || Serginho (14) |- Friendlies Official competitions Campeonato Paulista Record External links official website Association football clubs 1979 season 1979 1979 in Brazilian football
https://en.wikipedia.org/wiki/Natural%20Science%20Building%20%28University%20of%20Bergen%29
The Natural Science Building (Norwegian: Realfagbygget) is located in Allégaten 41 at Nygårdshøyden in Bergen, right next to Nygårdsparken. The building is a part of the Faculty of Mathematics and Natural Sciences at the University of Bergen. The building was drawn by architect Harald Ramm Østgård, and built between 1963 and 1977. The Sciences Building is one of Norway's largest buildings with 47000 square meters usable area. The building is considered one of the best examples of brutalistic architecture in Bergen. External links Docomomo - Realfagbygget (Norwegian) Landsverneplan for Kunnskapsdepartementet (Norwegian) University of Bergen
https://en.wikipedia.org/wiki/List%20of%20Hindustan%20Aeronautics%20S.C.%20managers
This is a list of Hindustan Aeronautics S.C.'s managers and their records, from 2010, when the first full-time manager was appointed, to the present day. Statistics Information correct as of 21 November 2011. Only competitive matches are counted. Wins, losses and draws are results at the final whistle; the results of penalty shoot-outs are not counted. Hindustan Aeronautics S.C. Managers
https://en.wikipedia.org/wiki/Crisis%20%28dynamical%20systems%29
In applied mathematics and astrodynamics, in the theory of dynamical systems, a crisis is the sudden appearance or disappearance of a strange attractor as the parameters of a dynamical system are varied. This global bifurcation occurs when a chaotic attractor comes into contact with an unstable periodic orbit or its stable manifold. As the orbit approaches the unstable orbit it will diverge away from the previous attractor, leading to a qualitatively different behaviour. Crises can produce intermittent behaviour. Grebogi, Ott, Romeiras, and Yorke distinguished between three types of crises: The first type, a boundary or an exterior crisis, the attractor is suddenly destroyed as the parameters are varied. In the postbifurcation state the motion is transiently chaotic, moving chaotically along the former attractor before being attracted to a fixed point, periodic orbit, quasiperiodic orbit, another strange attractor, or diverging to infinity. In the second type of crisis, an interior crisis, the size of the chaotic attractor suddenly increases. The attractor encounters an unstable fixed point or periodic solution that is inside the basin of attraction. In the third type, an attractor merging crisis, two or more chaotic attractors merge to form a single attractor as the critical parameter value is passed. Note that the reverse case (sudden appearance, shrinking or splitting of attractors) can also occur. The latter two crises are sometimes called explosive bifurcations. While crises are "sudden" as a parameter is varied, the dynamics of the system over time can show long transients before orbits leave the neighbourhood of the old attractor. Typically there is a time constant τ for the length of the transient that diverges as a power law (τ ≈ |p − pc|γ) near the critical parameter value pc. The exponent γ is called the critical crisis exponent. There also exist systems where the divergence is stronger than a power law, so-called super-persistent chaotic transients. See also Intermittency Bifurcation diagram Phase portrait References External links Scholarpedia: Crises Dynamical systems Nonlinear systems Bifurcation theory
https://en.wikipedia.org/wiki/1978%20S%C3%A3o%20Paulo%20FC%20season
The 1978 season was São Paulo's 49th season since club's existence. Statistics Scorers Overall {|class="wikitable" |- |Games played || 87 (6 Copa Libertadores, 26 Campeonato Brasileiro, 52 Campeonato Paulista, 3 Friendly match) |- |Games won || 36 (1 Copa Libertadores, 10 Campeonato Brasileiro, 24 Campeonato Paulista, 1 Friendly match) |- |Games drawn || 28 (3 Copa Libertadores, 8 Campeonato Brasileiro, 15 Campeonato Paulista, 2 Friendly match) |- |Games lost || 23 (2 Copa Libertadores, 8 Campeonato Brasileiro, 13 Campeonato Paulista, 0 Friendly match) |- |Goals scored || 126 |- |Goals conceded || 80 |- |Goal difference || +46 |- |Best result || 6–1 (H) v Ríver - Campeonato Brasileiro - 1978.04.06 |- |Worst result || 1–4 (A) v Santos - Campeonato Paulista - 1979.01.28 |- |Most appearances || |- |Top scorer || Milton (22) |- Friendlies Copa dos Campeões da Copa Brasil Official competitions Copa Libertadores Record Campeonato Brasileiro Record Campeonato Paulista Record External links official website Association football clubs 1978 season 1978 1978 in Brazilian football
https://en.wikipedia.org/wiki/Leave-one-out%20error
For mathematical analysis and statistics, Leave-one-out error can refer to the following: Leave-one-out cross-validation Stability (CVloo, for stability of Cross Validation with leave one out): An algorithm f has CVloo stability β with respect to the loss function V if the following holds: Expected-to-leave-one-out error Stability (, for Expected error from leaving one out): An algorithm f has stability if for each n there exists a and a such that: , with and going to zero for Preliminary notations With X and Y being a subset of the real numbers R, or X and Y ⊂ R, being respectively an input space X and an output space Y, we consider a training set: of size m in drawn independently and identically distributed (i.i.d.) from an unknown distribution, here called "D". Then a learning algorithm is a function from into which maps a learning set S onto a function from the input space X to the output space Y. To avoid complex notation, we consider only deterministic algorithms. It is also assumed that the algorithm is symmetric with respect to S, i.e. it does not depend on the order of the elements in the training set. Furthermore, we assume that all functions are measurable and all sets are countable which does not limit the interest of the results presented here. The loss of an hypothesis f with respect to an example is then defined as . The empirical error of f can then be written as . The true error of f is Given a training set S of size m, we will build, for all i = 1....,m, modified training sets as follows: By removing the i-th element and/or by replacing the i-th element See also Constructive analysis History of calculus Hypercomplex analysis Jackknife resampling Statistical classification Timeline of calculus and mathematical analysis References S. Mukherjee, P. Niyogi, T. Poggio, and R. M. Rifkin. Learning theory: stability is sufficient for generalization and necessary and sufficient for consistency of empirical risk minimization. Adv. Comput. Math., 25(1-3):161–193, 2006 Machine learning
https://en.wikipedia.org/wiki/Esscher%20transform
In actuarial science, the Esscher transform is a transform that takes a probability density f(x) and transforms it to a new probability density f(x; h) with a parameter h. It was introduced by F. Esscher in 1932 . Definition Let f(x) be a probability density. Its Esscher transform is defined as More generally, if μ is a probability measure, the Esscher transform of μ is a new probability measure Eh(μ) which has density with respect to μ. Basic properties Combination The Esscher transform of an Esscher transform is again an Esscher transform: Eh1 Eh2 = Eh1 + h2. Inverse The inverse of the Esscher transform is the Esscher transform with negative parameter: E = E−h Mean move The effect of the Esscher transform on the normal distribution is moving the mean: Examples See also Esscher principle Exponential tilting References Actuarial science Transforms
https://en.wikipedia.org/wiki/Ledyard%20Tucker
Ledyard R. Tucker (19 September 1910 – 16 August 2004) was an American mathematician who specialized in statistics and psychometrics. His Ph.D. advisor at the University of Chicago was Louis Leon Thurstone. He was a lecturer in psychology at Princeton University from 1948 to 1960, while simultaneously working at ETS. In 1960, he moved to working full-time in academia when he joined the University of Illinois. The rest of his career was spent as professor of quantitative psychology and educational psychology at UIUC until he retired in 1979. Tucker is best known for his Tucker decomposition and Tucker–Koopman–Linn model. He is credited with the invention of Angoff method. In 1957 he was elected as a Fellow of the American Statistical Association. He died at his home in Savoy, Illinois, on August 16, 2004, aged 93. Selected publications References A Conversation with Ledyard R Tucker by Neil J. Dorans Remembering Ledyard R Tucker by Tom Stewart 1910 births 2004 deaths University of Colorado alumni University of Chicago alumni Intelligence researchers 20th-century American mathematicians 21st-century American mathematicians American statisticians People from Glenwood Springs, Colorado Fellows of the American Statistical Association People from Savoy, Illinois Mathematicians from Colorado Mathematicians from Illinois
https://en.wikipedia.org/wiki/Artin%E2%80%93Verdier%20duality
In mathematics, Artin–Verdier duality is a duality theorem for constructible abelian sheaves over the spectrum of a ring of algebraic numbers, introduced by , that generalizes Tate duality. It shows that, as far as etale (or flat) cohomology is concerned, the ring of integers in a number field behaves like a 3-dimensional mathematical object. Statement Let X be the spectrum of the ring of integers in a totally imaginary number field K, and F a constructible étale abelian sheaf on X. Then the Yoneda pairing is a non-degenerate pairing of finite abelian groups, for every integer r. Here, Hr(X,F) is the r-th étale cohomology group of the scheme X with values in F, and Extr(F,G) is the group of r-extensions of the étale sheaf G by the étale sheaf F in the category of étale abelian sheaves on X. Moreover, Gm denotes the étale sheaf of units in the structure sheaf of X. proved Artin–Verdier duality for constructible, but not necessarily torsion sheaves. For such a sheaf F, the above pairing induces isomorphisms where Finite flat group schemes Let U be an open subscheme of the spectrum of the ring of integers in a number field K, and F a finite flat commutative group scheme over U. Then the cup product defines a non-degenerate pairing of finite abelian groups, for all integers r. Here FD denotes the Cartier dual of F, which is another finite flat commutative group scheme over U. Moreover, is the r-th flat cohomology group of the scheme U with values in the flat abelian sheaf F, and is the r-th flat cohomology with compact supports of U with values in the flat abelian sheaf F. The flat cohomology with compact supports is defined to give rise to a long exact sequence The sum is taken over all places of K, which are not in U, including the archimedean ones. The local contribution Hr(Kv, F) is the Galois cohomology of the Henselization Kv of K at the place v, modified a la Tate: Here is a separable closure of References Theorems in number theory Duality theories
https://en.wikipedia.org/wiki/Tate%20duality
In mathematics, Tate duality or Poitou–Tate duality is a duality theorem for Galois cohomology groups of modules over the Galois group of an algebraic number field or local field, introduced by and . Local Tate duality For a p-adic local field , local Tate duality says there is a perfect pairing of the finite groups arising from Galois cohomology: where is a finite group scheme, its dual , and is the multiplicative group. For a local field of characteristic , the statement is similar, except that the pairing takes values in . The statement also holds when is an Archimedean field, though the definition of the cohomology groups looks somewhat different in this case. Global Tate duality Given a finite group scheme over a global field , global Tate duality relates the cohomology of with that of using the local pairings constructed above. This is done via the localization maps where varies over all places of , and where denotes a restricted product with respect to the unramified cohomology groups. Summing the local pairings gives a canonical perfect pairing One part of Poitou-Tate duality states that, under this pairing, the image of has annihilator equal to the image of for . The map has a finite kernel for all , and Tate also constructs a canonical perfect pairing These dualities are often presented in the form of a nine-term exact sequence Here, the asterisk denotes the Pontryagin dual of a given locally compact abelian group. All of these statements were presented by Tate in a more general form depending on a set of places of , with the above statements being the form of his theorems for the case where contains all places of . For the more general result, see e.g. . Poitou–Tate duality Among other statements, Poitou–Tate duality establishes a perfect pairing between certain Shafarevich groups. Given a global field , a set S of primes, and the maximal extension which is unramified outside S, the Shafarevich groups capture, broadly speaking, those elements in the cohomology of which vanish in the Galois cohomology of the local fields pertaining to the primes in S. An extension to the case where the ring of S-integers is replaced by a regular scheme of finite type over was shown by . See also Artin–Verdier duality Tate pairing References Algebraic number theory Galois theory Duality theories
https://en.wikipedia.org/wiki/List%20of%20formulas%20in%20elementary%20geometry
This is a short list of some common mathematical shapes and figures and the formulas that describe them. Two-dimensional shapes Sources: Three-dimensional shapes This is a list of volume formulas of basic shapes: Cone – , where is the base's radius Cube – , where is the side's length; Cuboid – , where , , and are the sides' length; Cylinder – , where is the base's radius and is the cone's height; Ellipsoid – , where , , and are the semi-major and semi-minor axes' length; Sphere – , where is the radius; Parallelepiped – , where , , and are the sides' length,, and , , and are angles between the two sides; Prism – , where is the base's area and is the prism's height; Pyramid – , where is the base's area and is the pyramid's height; Tetrahedron – , where is the side's length. Sphere The basic quantities describing a sphere (meaning a 2-sphere, a 2-dimensional surface inside 3-dimensional space) will be denoted by the following variables is the radius, is the circumference (the length of any one of its great circles), is the surface area, is the volume. Surface area: Volume: Radius: Circumference: See also References Mathematics-related lists
https://en.wikipedia.org/wiki/Yuli%20Rudyak
Yuli B. Rudyak is a professor of mathematics at the University of Florida in Gainesville, Florida. He obtained his doctorate from Moscow State University under the supervision of M. M. Postnikov. His main research interests are geometry and topology and symplectic topology. Books Reviewer Donald M. Davis (mathematician) for MathSciNet wrote: "This book provides an excellent and thorough treatment of various topics related to cobordism. It should become an indispensable tool for advanced graduate students and workers in algebraic topology." The book listed 118 cites at Google Scholar in 2011. Personal life Rudyak is the father of Marina Rudyak, who is an Assistant Professor of Chinese Studies at the University of Heidelberg. Notes External links Webpage at UFL Topologists 20th-century American mathematicians University of Florida faculty Moscow State University alumni Living people Year of birth missing (living people) 21st-century American mathematicians
https://en.wikipedia.org/wiki/Cardinal%20characteristic%20of%20the%20continuum
In the mathematical discipline of set theory, a cardinal characteristic of the continuum is an infinite cardinal number that may consistently lie strictly between (the cardinality of the set of natural numbers), and the cardinality of the continuum, that is, the cardinality of the set of all real numbers. The latter cardinal is denoted or . A variety of such cardinal characteristics arise naturally, and much work has been done in determining what relations between them are provable, and constructing models of set theory for various consistent configurations of them. Background Cantor's diagonal argument shows that is strictly greater than , but it does not specify whether it is the least cardinal greater than (that is, ). Indeed the assumption that is the well-known Continuum Hypothesis, which was shown to be consistent with the standard ZFC axioms for set theory by Kurt Godel and to be independent of it by Paul Cohen. If the Continuum Hypothesis fails and so is at least , natural questions arise about the cardinals strictly between and , for example regarding Lebesgue measurability. By considering the least cardinal with some property, one may get a definition for an uncountable cardinal that is consistently less than . Generally one only considers definitions for cardinals that are provably greater than and at most as cardinal characteristics of the continuum, so if the Continuum Hypothesis holds they are all equal to . Examples As is standard in set theory, we denote by the least infinite ordinal, which has cardinality ; it may be identified with the set of all natural numbers. A number of cardinal characteristics naturally arise as cardinal invariants for ideals which are closely connected with the structure of the reals, such as the ideal of Lebesgue null sets and the ideal of meagre sets. non(N) The cardinal characteristic non() is the least cardinality of a non-measurable set; equivalently, it is the least cardinality of a set that is not a Lebesgue null set. Bounding number and dominating number We denote by the set of functions from to . For any two functions and we denote by the statement that for all but finitely many . The bounding number is the least cardinality of an unbounded set in this relation, that is, The dominating number is the least cardinality of a set of functions from to such that every such function is dominated by (that is, ) a member of that set, that is, Clearly any such dominating set is unbounded, so is at most , and a diagonalisation argument shows that . Of course if this implies that , but Hechler has shown that it is also consistent to have strictly less than . Splitting number and reaping number We denote by the set of all infinite subsets of . For any , we say that splits if both and are infinite. The splitting number is the least cardinality of a subset of such that for all , there is some such that splits . That is, The reaping number is the leas
https://en.wikipedia.org/wiki/Russians%20in%20Taiwan
Russians in Taiwan form a small community. As of August 2021, statistics of Taiwan's National Immigration Agency (NIA) showed 593 Russians holding valid Alien Resident Certificates. Informal estimates claim that their population may be as large as one thousand people. History Some Russians from Shanghai and Xinjiang fled the establishment of the People's Republic of China and resettled in Taiwan in 1949. One cultural institution among the Russian community in Taiwan that survives from those days is the Astoria Confectionery and Cafe near Taipei Railway Station, the first Russian-style eatery on the whole island. Founded in 1949 by five Russian émigrés from Shanghai, it continues operating today with an early local business partner as the sole owner. In recent years, the Representative Office for the Moscow-Taipei Coordination Commission on Economic and Cultural Cooperation has been active in promoting academic and professional exchanges between the two countries. According to NIA statistics, 174 Russian students studied at institutions in Taiwan, and 20 were employed as instructors; 21 were housewives, 28 were children under 15 years of age, and the remaining 120 engaged in other types of work. Unlike in other European communities, men are relatively scarce, with a sex ratio of 1.36 women for every man. See also Republic of China–Russia relations References Russian Russian diaspora in China Taiwan
https://en.wikipedia.org/wiki/Kernel%20Fisher%20discriminant%20analysis
In statistics, kernel Fisher discriminant analysis (KFD), also known as generalized discriminant analysis and kernel discriminant analysis, is a kernelized version of linear discriminant analysis (LDA). It is named after Ronald Fisher. Linear discriminant analysis Intuitively, the idea of LDA is to find a projection where class separation is maximized. Given two sets of labeled data, and , we can calculate the mean value of each class, and , as where is the number of examples of class . The goal of linear discriminant analysis is to give a large separation of the class means while also keeping the in-class variance small. This is formulated as maximizing, with respect to , the following ratio: where is the between-class covariance matrix and is the total within-class covariance matrix: The maximum of the above ratio is attained at as can be shown by the Lagrange multiplier method (sketch of proof): Maximizing is equivalent to maximizing subject to This, in turn, is equivalent to maximizing , where is the Lagrange multiplier. At the maximum, the derivatives of with respect to and must be zero. Taking yields which is trivially satisfied by and Extending LDA To extend LDA to non-linear mappings, the data, given as the points can be mapped to a new feature space, via some function In this new feature space, the function that needs to be maximized is where and Further, note that . Explicitly computing the mappings and then performing LDA can be computationally expensive, and in many cases intractable. For example, may be infinitely dimensional. Thus, rather than explicitly mapping the data to , the data can be implicitly embedded by rewriting the algorithm in terms of dot products and using kernel functions in which the dot product in the new feature space is replaced by a kernel function,. LDA can be reformulated in terms of dot products by first noting that will have an expansion of the form Then note that where The numerator of can then be written as: Similarly, the denominator can be written as with the component of defined as is the identity matrix, and the matrix with all entries equal to . This identity can be derived by starting out with the expression for and using the expansion of and the definitions of and With these equations for the numerator and denominator of , the equation for can be rewritten as Then, differentiating and setting equal to zero gives Since only the direction of , and hence the direction of matters, the above can be solved for as Note that in practice, is usually singular and so a multiple of the identity is added to it Given the solution for , the projection of a new data point is given by Multi-class KFD The extension to cases where there are more than two classes is relatively straightforward. Let be the number of classes. Then multi-class KFD involves projecting the data into a -d
https://en.wikipedia.org/wiki/Edward%20C.%20Waymire
Edward C. Waymire is an American mathematician, and professor of mathematics at Oregon State University. He was the chief editor of the Annals of Applied Probability between 2006 and 2008. From 2011 to 2013, he was president of the Bernoulli Society for Mathematical Statistics and Probability. He is the recipient of the 2014 Carver Medal from the Institute of Mathematical Statistics. Books Bhattacharya, R., E. Waymire (2007): A Basic Course in Probability Theory, Universitext, Springer, NY. Bhattacharya, R., E. Waymire (2009): Stochastic Processes with Applications, SIAM Classics in Applied Mathematics Series. References External links Edward C Waymire's homepage. Oregon State University faculty 21st-century American mathematicians Living people Year of birth missing (living people) Place of birth missing (living people)
https://en.wikipedia.org/wiki/Masahiko%20Kimura%20%28footballer%29
is a former Japanese football player. Club statistics References External links j-league 1984 births Living people Momoyama Gakuin University alumni Association football people from Hiroshima Prefecture Japanese men's footballers J2 League players Japan Football League players FC Gifu players Fagiano Okayama players Men's association football defenders
https://en.wikipedia.org/wiki/Generalized%20integer%20gamma%20distribution
In probability and statistics, the generalized integer gamma distribution (GIG) is the distribution of the sum of independent gamma distributed random variables, all with integer shape parameters and different rate parameters. This is a special case of the generalized chi-squared distribution. A related concept is the generalized near-integer gamma distribution (GNIG). Definition The random variable has a gamma distribution with shape parameter and rate parameter if its probability density function is and this fact is denoted by Let , where be independent random variables, with all being positive integers and all different. In other words, each variable has the Erlang distribution with different shape parameters. The uniqueness of each shape parameter comes without loss of generality, because any case where some of the are equal would be treated by first adding the corresponding variables: this sum would have a gamma distribution with the same rate parameter and a shape parameter which is equal to the sum of the shape parameters in the original distributions. Then the random variable Y defined by has a GIG (generalized integer gamma) distribution of depth with shape parameters and rate parameters . This fact is denoted by It is also a special case of the generalized chi-squared distribution. Properties The probability density function and the cumulative distribution function of Y are respectively given by and where and with and where Alternative expressions are available in the literature on generalized chi-squared distribution, which is a field wherecomputer algorithms have been available for some years. Generalization The GNIG (generalized near-integer gamma) distribution of depth is the distribution of the random variable where and are two independent random variables, where is a positive non-integer real and where . Properties The probability density function of is given by and the cumulative distribution function is given by where with given by ()-() above. In the above expressions is the Kummer confluent hypergeometric function. This function has usually very good convergence properties and is nowadays easily handled by a number of software packages. Applications The GIG and GNIG distributions are the basis for the exact and near-exact distributions of a large number of likelihood ratio test statistics and related statistics used in multivariate analysis. More precisely, this application is usually for the exact and near-exact distributions of the negative logarithm of such statistics. If necessary, it is then easy, through a simple transformation, to obtain the corresponding exact or near-exact distributions for the corresponding likelihood ratio test statistics themselves. The GIG distribution is also the basis for a number of wrapped distributions in the wrapped gamma family. As being a special case of the generalized chi-squared distribution, there are many other applications; fo
https://en.wikipedia.org/wiki/Volker%20Halbach
Volker Halbach (born 21 October 1965 in Ingolstadt, Germany) is a German logician and philosopher. His main research interests are in philosophical logic, philosophy of mathematics, philosophy of language, and epistemology, with a focus on formal theories of truth. He is Professor of Philosophy at the University of Oxford, Tutorial Fellow of New College, Oxford. Education and career Volker Halbach's philosophical studies began at Ludwig-Maximilians-Universität München. He graduated in 1991 with an M.A. (Master of Arts) and in 1994 with a doctorate in philosophy (D.Phil., summa cum laude) with a dissertation titled "Tarski-Hierarchien". In 2001 he earned his habilitation with a thesis on "Semantics and Deflationism". Halbach was an assistant professor at Universität Konstanz (1997-2004). In 2004, he took up at role at New College, University of Oxford, where he teaches logic-related courses including Introduction to Logic and Elements of Deductive Logic in the first year, Philosophical Logic, Formal Logic, Philosophy of Logic & Language, and Philosophy of Mathematics. Philosophical work Halbach is author of several articles and books including The Logic Manual, a textbook on undergraduate logic, and Axiomatic Theories of Truth. References External links Interview at 3AM Magazine German logicians 21st-century German philosophers Philosophers of mathematics German male writers 1965 births Living people Fellows of New College, Oxford Ludwig Maximilian University of Munich alumni University of Florence alumni Academic staff of the University of Konstanz
https://en.wikipedia.org/wiki/Michael%20Cates
Michael Elmhirst Cates (born 5 May 1961) is a British physicist. He is the 19th Lucasian Professor of Mathematics at the University of Cambridge and has held this position since 1 July 2015. He was previously Professor of Natural Philosophy at the University of Edinburgh, and has held a Royal Society Research Professorship since 2007. His work focuses on the theory of soft matter, such as polymers, colloids, gels, liquid crystals, and granular material. A recurring goal of his research is to create a mathematical model that predicts the stress in a flowing material as a functional of the flow history of that material. Such a mathematical model is called a constitutive equation. He has worked on theories of active matter, particularly dense suspensions of self-propelled particles which can include motile bacteria. His interests also include fundamental field theories of active systems in which time-reversal symmetry (T-symmetry, and more generally, CPT symmetry) is absent. Such theories are characterised by non-zero steady-state entropy production. At Edinburgh, Cates was the Principal Investigator of an EPSRC Programme Grant, awarded in 2011, entitled Design Principles for New Soft Materials. On his departure for Cambridge, Cait MacPhee took over as Principal Investigator. Cates remains an Honorary Professor at Edinburgh. Early life Cates was born on 5 May 1961. He read Natural Sciences and earned a PhD at Trinity College, Cambridge, in 1985, where he studied with Sam Edwards. Academic career Cates was a research fellow and lecturer at the Cavendish Laboratory, University of Cambridge before moving to Edinburgh in 1995. Honours Cates won the Bingham Medal of the US Society of Rheology in 2016. He had previously won the 2013 Weissenberg Award of the European Society of Rheology and the 2009 Gold Medal of the British Society of Rheology. He was awarded the 2009 Dirac Prize by the Institute of Physics. He won the 1991 Maxwell Medal and Prize. He has served as an elected member of the Council of the Royal Society, and chairs the International Scientific Committee of ESPCI ParisTech. He was an honorary fellow of Trinity College, Cambridge from 2013 until 2016, when he became instead a senior research fellow. He was also elected a member of the National Academy of Engineering in 2019 for research on the rheology, dynamics, and thermodynamics of complex fluids, and for scientific leadership in the European Community. Works Michael Cates has over 350 refereed scientific publications, attracting over 45 000 citations. His h-index is 112. Highly cited publications include: References External links 1961 births Living people British physicists Fellows of the Royal Society of Edinburgh Fellows of the Royal Society Academics of the University of Edinburgh Alumni of Trinity College, Cambridge Fellows of Trinity College, Cambridge Maxwell Medal and Prize recipients Lucasian Professors of Mathematics Foreign associates of the National Academy of Scie
https://en.wikipedia.org/wiki/Otto%20Keller%20%28footballer%29
Otto Keller (23 February 1939 - 6 August 2014) was a German football midfielder. Career Statistics References External links 1939 births 2014 deaths German men's footballers VfL Bochum players Rot-Weiß Oberhausen players Men's association football midfielders
https://en.wikipedia.org/wiki/Niven%27s%20theorem
In mathematics, Niven's theorem, named after Ivan Niven, states that the only rational values of θ in the interval 0° ≤ θ ≤ 90° for which the sine of θ degrees is also a rational number are: In radians, one would require that 0 ≤ x ≤ /2, that x/ be rational, and that sinx be rational. The conclusion is then that the only such values are sin 0 = 0, sin /6 = 1/2, and sin /2 = 1. The theorem appears as Corollary 3.12 in Niven's book on irrational numbers. The theorem extends to the other trigonometric functions as well. For rational values of θ, the only rational values of the sine or cosine are 0, ±1/2, and ±1; the only rational values of the secant or cosecant are ±1 and ±2; and the only rational values of the tangent or cotangent are 0 and ±1. History Niven's proof of his theorem appears in his book Irrational Numbers. Earlier, the theorem had been proven by D. H. Lehmer and J. M. H. Olmstead. In his 1933 paper, Lehmer proved the theorem for cosine by proving a more general result. Namely, Lehmer showed that for relatively prime integers and with , the number is an algebraic number of degree , where denotes Euler's totient function. Because rational numbers have degree 1, we must have and therefore the only possibilities are 1, 2, 3, 4, or 6. Next, he proved a corresponding result for sine using the trigonometric identity . In 1956, Niven extended Lehmer's result to the other trigonometric functions. Other mathematicians have given new proofs in subsequent years. See also Pythagorean triples form right triangles where the trigonometric functions will always take rational values, though the acute angles are not rational Trigonometric functions Trigonometric number References Further reading External links Rational numbers Trigonometry Theorems in geometry Theorems in algebra
https://en.wikipedia.org/wiki/Daniela%20L%C3%B6wenberg
Daniela Löwenberg (born 11 January 1988) is a German football midfielder, who plays for BV Cloppenburg. Club career Club statistics International career Löwenberg was a member of the German U-19 national team that won the 2006 and 2007 Under-19 European Championships. References External links 1988 births Living people Footballers from Dortmund German women's footballers SG Wattenscheid 09 (women) players SGS Essen players 1. FFC Turbine Potsdam players Frauen-Bundesliga players 2. Frauen-Bundesliga players Women's association football midfielders BV Cloppenburg (women) players