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https://en.wikipedia.org/wiki/2010%20Ventforet%20Kofu%20season	2010 Ventforet Kofu season Competitions Player statistics Other pages J. League official site Ventforet Kofu Ventforet Kofu seasons
https://en.wikipedia.org/wiki/2010%20FC%20Gifu%20season	2010 F.C. Gifu season Competitions Player statistics Other pages J. League official site Gifu 2010
https://en.wikipedia.org/wiki/2010%20Tokushima%20Vortis%20season	The following is information on Tokushima Vortis during the 2010 football season. Competitions Player statistics Other pages J. League official site Tokushima Vortis Tokushima Vortis seasons
https://en.wikipedia.org/wiki/2010%20Ehime%20FC%20season	2010 Ehime F.C. season Competitions Player statistics Other pages J. League official site Ehime F.C. Ehime FC seasons
https://en.wikipedia.org/wiki/2010%20Avispa%20Fukuoka%20season	2010 Avispa Fukuoka season Competitions Player statistics Other pages J. League official site Avispa Fukuoka Avispa Fukuoka seasons
https://en.wikipedia.org/wiki/2010%20Giravanz%20Kitakyushu%20season	2010 Giravanz Kitakyushu season Competitions Player statistics Other pages J. League official site Giravanz Kitakyushu Giravanz Kitakyushu seasons
https://en.wikipedia.org/wiki/2010%20Sagan%20Tosu%20season	2010 Sagan Tosu season Competitions Player statistics Other pages J. League official site Sagan Tosu Sagan Tosu seasons
https://en.wikipedia.org/wiki/2010%20Roasso%20Kumamoto%20season	2010 Roasso Kumamoto season Competitions Player statistics Other pages J. League official site Roasso Kumamoto Roasso Kumamoto seasons
https://en.wikipedia.org/wiki/2010%20Oita%20Trinita%20season	2010 Oita Trinita season Competitions Player statistics Other pages J. League official site Oita Trinita Oita Trinita seasons
https://en.wikipedia.org/wiki/Tsuneyuki%20Ueda	is a Japanese football player. He plays for Honda Lock. Club statistics References External links 1985 births Living people Association football people from Miyazaki Prefecture Japanese men's footballers J2 League players Japan Football League players Hokkaido Consadole Sapporo players Zweigen Kanazawa players Minebea Mitsumi FC players Men's association football defenders People from Miyazaki (city)
https://en.wikipedia.org/wiki/Tetsu%20Sugiyama	is a Japanese football player. Club statistics Updated to 23 February 2016. References External links 1981 births Living people Fukuoka University alumni Association football people from Kumamoto Prefecture Japanese men's footballers J1 League players J2 League players Kashima Antlers players Hokkaido Consadole Sapporo players Men's association football goalkeepers Universiade medalists in football FISU World University Games gold medalists for Japan
https://en.wikipedia.org/wiki/Takuya%20Yamamoto	is a former Japanese football player. His brother Hiroto Yamamoto is also a footballer. Club statistics References External links 1986 births Living people Association football people from Ibaraki Prefecture Japanese men's footballers J1 League players J2 League players Japan Football League players Kashima Antlers players Thespakusatsu Gunma players Gainare Tottori players Men's association football defenders
https://en.wikipedia.org/wiki/Kenji%20Koyano	Kenji Koyano (小谷野顕治, born June 22, 1988) is a Japanese football player. He plays for Mito HollyHock. Club career statistics Updated to 23 February 2016. References External links Albirex Niigata 1988 births Living people Association football people from Ibaraki Prefecture Japanese men's footballers J1 League players J2 League players J3 League players Kashima Antlers players Albirex Niigata players Mito HollyHock players Gainare Tottori players Men's association football midfielders
https://en.wikipedia.org/wiki/Seiko%20Yamanaka	is a former Japanese football player. Club statistics References External links Fagiano Okayama 1989 births Living people Association football people from Kōchi Prefecture Japanese men's footballers J1 League players J2 League players JEF United Chiba players Fagiano Okayama players Men's association football defenders
https://en.wikipedia.org/wiki/Yasuhiro%20Okuyama	is a Japanese footballer who plays in the Tohoku Soccer League for Cobaltore Onagawa. Career statistics Club Updated to the start of the 2023 season. References External links Profile at ReinMeer Aomori Profile at Cobaltore Onagawa j-league 1985 births Living people Tohoku Gakuin University alumni Association football people from Miyagi Prefecture Japanese men's footballers J1 League players J2 League players J3 League players Japan Football League players JEF United Chiba players Gainare Tottori players ReinMeer Aomori players Cobaltore Onagawa players Men's association football midfielders
https://en.wikipedia.org/wiki/Nobuhisa%20Urata	is a Japanese football player who currently plays for ReinMeer Aomori. Club statistics Updated to 24 February 2019. References External links Profile at Matsumoto Yamaga 1989 births Living people Association football people from Tokyo Japanese men's footballers J1 League players J2 League players Yokohama F. Marinos players Sagan Tosu players Ehime FC players Matsumoto Yamaga FC players Men's association football defenders
https://en.wikipedia.org/wiki/Yuki%20Nagahata	is a Japanese retired football player. Career After being a key-player for Kagoshima United FC, Nagahata retired in December 2019. Club statistics Updated to 5 April 2020. References External links Profile at Kagoshima United FC 1989 births Living people Association football people from Kagoshima Prefecture Japanese men's footballers J1 League players J2 League players J3 League players Japan Football League players Shimizu S-Pulse players Giravanz Kitakyushu players Kagoshima United FC players Men's association football midfielders
https://en.wikipedia.org/wiki/Tatsuya%20Okamoto	is a Japanese footballer who plays as a forward for Criacao Shinjuku in Japan Football League. Club statistics References External links j-league 1986 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 Júbilo Iwata players Mito HollyHock players Gainare Tottori players Men's association football forwards
https://en.wikipedia.org/wiki/Masafumi%20Yoshida	is a former Japanese football player. Club statistics References External links 1985 births Living people Association football people from Hyōgo Prefecture Japanese men's footballers J1 League players J2 League players Vissel Kobe players Men's association football midfielders
https://en.wikipedia.org/wiki/Takahide%20Kishi	is a former Japanese football player. Club statistics References External links Vissel Kobe 1987 births Living people Association football people from Hyōgo Prefecture Japanese men's footballers J1 League players J2 League players Japan Football League players Vissel Kobe players Gainare Tottori players FC Osaka players Men's association football goalkeepers
https://en.wikipedia.org/wiki/Chilean%20Journal%20of%20Statistics	The Chilean Journal of Statistics is a biannual peer-reviewed scientific journal of statistics. It is published by the Chilean Statistical Society. The journal was established in 1984 as La Revista de la Sociedad Chilena de Estadística and obtained its current title in 2010. Abstracting and indexing The Chilean Journal of Statistics is indexed in MathSciNet, Zentralblatt MATH, and Latindex. External links Chilean Statistical Society (Sociedad Chilena de Estadística) Statistics journals Academic journals established in 1984 English-language journals Biannual journals Academic journals of Chile
https://en.wikipedia.org/wiki/Energy%20in%20Slovenia	Total primary energy supply (TPES) in Slovenia was 6.80 Mtoe in 2019. In the same year, electricity production was 16.1 TWh, consumption was 14.9 TWh. Statistics General The transportation and industrial sectors were the largest consumers of energy in Slovenia in 2019. Slovenia is a net energy importer, importing all its petroleum products (mainly for the transport sector) and natural gas, as well as some coal. Energy plan Slovenia has a target of reducing greenhouse gasses by 18% in 2030 when compared to 2015. Fuel sources Fossil fuels Coal and lignite Lignite deposits are found in the north central and northeastern regions of Slovenia; the country does not have any identified hard coal reserves. There is one active lignite mine in Slovenia, near Velenje in the north central region of the country. The mine produced 3.2 million tonnes of lignite in 2018 for combustion in the neighboring Šoštanj Power Plant. The mine is Slovenia's only producing fossil fuel facility. The power plant has an expected closure date of 2033 nonetheless the government hopes to close the plant between 2024 and 2029. Some coal is imported for district heating and electrical power generation use at the Ljubljana Power Station. Petroleum and natural gas Slovenia has essentially no natural gas or petroleum reserves or production. The possibility of a gas pipeline with Hungary has been proposed for years, a pipeline exists to the border with Hungary, but as of 2023 it has not been connected to Hungary. Slovenia has a gas interconnector project with Croatia and will be increasing the capacity by 5 bcm/y by 2027. Renewable energy Renewable energy includes wind, solar, biomass and geothermal energy sources. Solar energy Per analysis published by the World Bank which considers natural features of a location such as altitude, humidity, cloud cover, and topography, Slovenia's solar PV potential is relatively low compared to global resources, but is comparable to that of other central and eastern European countries which lie north of the Alps. The sunny coastal strip along the Adriatic Sea has better potential than the inland areas, similar to that of northern Italy and southern France. A solar power plant with a capacity of 6MW opened in 2023 at Brežice, linked to the hydro power plant. Wind energy Slovenia had just 2 wind turbines in 2022. Onshore wind energy potential for Slovenia is typical of central and eastern Europe. A northwest to southeast band of higher potential wind energy is found across far southwest Slovenia, roughly between Gorizia, Italy and Rijeka, Croatia. Unlike the Atlantic Ocean and North Sea offshore areas of western and northern Europe, the offshore wind resources for Slovenia in the Adriatic Sea are not that much greater than onshore. There is a plan for a wind power plant at Dolenja Vas of up to 66 MW. Biomass Biomass provides very little electricity capacity Hydroelectricity With abundant precipitation and numerous mountains, inc
https://en.wikipedia.org/wiki/1994%20Swedish%20Football%20Division%203	Statistics of Swedish football Division 3 for the 1994 season. League standings Norra Norrland 1994 Mellersta Norrland 1994 Södra Norrland 1994 Norra Svealand 1994 Östra Svealand 1994 Västra Svealand 1994 Nordöstra Götaland 1994 Nordvästra Götaland 1994 Mellersta Götaland 1994 Sydöstra Götaland 1994 Sydvästra Götaland 1994 Södra Götaland 1994 Footnotes References Swedish Football Division 3 seasons 4 Sweden Sweden
https://en.wikipedia.org/wiki/1993%20Swedish%20Football%20Division%203	Statistics of Swedish football Division 3 for the 1993 season. League standings Norra Norrland 1993 Mellersta Norrland 1993 Södra Norrland 1993 Norra Svealand 1993 Östra Svealand 1993 Västra Svealand 1993 Nordöstra Götaland 1993 Nordvästra Götaland 1993 Mellersta Götaland 1993 Sydöstra Götaland 1993 Sydvästra Götaland 1993 Södra Götaland 1993 Footnotes References Swedish Football Division 3 seasons 4 Sweden Sweden
https://en.wikipedia.org/wiki/Absorbing%20Markov%20chain	In the mathematical theory of probability, an absorbing Markov chain is a Markov chain in which every state can reach an absorbing state. An absorbing state is a state that, once entered, cannot be left. Like general Markov chains, there can be continuous-time absorbing Markov chains with an infinite state space. However, this article concentrates on the discrete-time discrete-state-space case. Formal definition A Markov chain is an absorbing chain if there is at least one absorbing state and it is possible to go from any state to at least one absorbing state in a finite number of steps. In an absorbing Markov chain, a state that is not absorbing is called transient. Canonical form Let an absorbing Markov chain with transition matrix P have t transient states and r absorbing states. Unlike a typical transition matrix, the rows of P represent sources, while columns represent destinations. Then where Q is a t-by-t matrix, R is a nonzero t-by-r matrix, 0 is an r-by-t zero matrix, and Ir is the r-by-r identity matrix. Thus, Q describes the probability of transitioning from some transient state to another while R describes the probability of transitioning from some transient state to some absorbing state. The probability of transitioning from i to j in exactly k steps is the (i,j)-entry of Pk, further computed below. When considering only transient states, the probability found in the upper left of Pk, the (i,j)-entry of Qk. Fundamental matrix Expected number of visits to a transient state A basic property about an absorbing Markov chain is the expected number of visits to a transient state j starting from a transient state i (before being absorbed). This can be established to be given by the (i, j) entry of so-called fundamental matrix N, obtained by summing Qk for all k (from 0 to ∞). It can be proven that where It is the t-by-t identity matrix. The computation of this formula is the matrix equivalent of the geometric series of scalars, . With the matrix N in hand, also other properties of the Markov chain are easy to obtain. Expected number of steps before being absorbed The expected number of steps before being absorbed in any absorbing state, when starting in transient state i can be computed via a sum over transient states. The value is given by the ith entry of the vector where 1 is a length-t column vector whose entries are all 1. Absorbing probabilities By induction, The probability of eventually being absorbed in the absorbing state j when starting from transient state i is given by the (i,j)-entry of the matrix . The number of columns of this matrix equals the number of absorbing states r. An approximation of those probabilities can also be obtained directly from the (i,j)-entry of for a large enough value of k, when i is the index of a transient, and j the index of an absorbing state. This is because . Transient visiting probabilities The probability of visiting transient state j when starting at a transient state i i
https://en.wikipedia.org/wiki/1967%20Swedish%20football%20Division%203	Statistics of Swedish football Division 3 for the 1967 season. League standings Norra Norrland, Övre 1967 Norra Norrland, Nedre 1967 Södra Norrland, Övre 1967 Södra Norrland, Nedre 1967 Norra Svealand 1967 Östra Svealand 1967 Västra Svealand 1967 Nordöstra Götaland 1967 Nordvästra Götaland 1967 Mellersta Götaland 1967 Sydöstra Götaland 1967 Sydvästra Götaland 1967 Skåne 1967 Footnotes References Swedish Football Division 3 seasons 3 Swed Swed
https://en.wikipedia.org/wiki/1966%20Swedish%20football%20Division%203	Statistics of Swedish football Division 3 for the 1966 season. League standings Norra Norrland, Övre 1966 Norra Norrland, Nedre 1966 Södra Norrland, Övre 1966 Södra Norrland, Nedre 1966 Norra Svealand 1966 Östra Svealand 1966 Västra Svealand 1966 Nordöstra Götaland 1966 Nordvästra Götaland 1966 Mellersta Götaland 1966 Sydöstra Götaland 1966 Sydvästra Götaland 1966 Skåne 1966 Footnotes References Swedish Football Division 3 seasons 3 Swed Swed
https://en.wikipedia.org/wiki/J%C3%BCrgen%20Duah	Jürgen Duah (born 19 December 1985) is a German football defender who played in the 3. Liga for SC Preußen Münster. Career statistics References External links 1985 births Living people Men's association football defenders SG Wattenscheid 09 players VfL Bochum II players SC Preußen Münster players 3. Liga players German men's footballers Footballers from Dortmund
https://en.wikipedia.org/wiki/Kentaro%20Seki	is a Japanese football player for Renofa Yamaguchi. Club statistics Updated to 18 February 2019. References External links Profile at Vegalta Sendai 1986 births Living people Meiji University alumni Association football people from Gunma Prefecture Japanese men's footballers J1 League players J2 League players Vegalta Sendai players Yokohama FC players Men's association football goalkeepers
https://en.wikipedia.org/wiki/Standard%20L-function	In mathematics, the term standard L-function refers to a particular type of automorphic L-function described by Robert P. Langlands. Here, standard refers to the finite-dimensional representation r being the standard representation of the L-group as a matrix group. Relations to other L-functions Standard L-functions are thought to be the most general type of L-function. Conjecturally, they include all examples of L-functions, and in particular are expected to coincide with the Selberg class. Furthermore, all L-functions over arbitrary number fields are widely thought to be instances of standard L-functions for the general linear group GL(n) over the rational numbers Q. This makes them a useful testing ground for statements about L-functions, since it sometimes affords structure from the theory of automorphic forms. Analytic properties These L-functions were proven to always be entire by Roger Godement and Hervé Jacquet, with the sole exception of Riemann ζ-function, which arises for n = 1. Another proof was later given by Freydoon Shahidi using the Langlands–Shahidi method. For a broader discussion, see . See also Zeta function References Zeta and L-functions
https://en.wikipedia.org/wiki/Fluid%20queue	In queueing theory, a discipline within the mathematical theory of probability, a fluid queue (fluid model, fluid flow model or stochastic fluid model) is a mathematical model used to describe the fluid level in a reservoir subject to randomly determined periods of filling and emptying. The term dam theory was used in earlier literature for these models. The model has been used to approximate discrete models, model the spread of wildfires, in ruin theory and to model high speed data networks. The model applies the leaky bucket algorithm to a stochastic source. The model was first introduced by Pat Moran in 1954 where a discrete-time model was considered. Fluid queues allow arrivals to be continuous rather than discrete, as in models like the M/M/1 and M/G/1 queues. Fluid queues have been used to model the performance of a network switch, a router, the IEEE 802.11 protocol, Asynchronous Transfer Mode (the intended technology for B-ISDN), peer-to-peer file sharing, optical burst switching, and has applications in civil engineering when designing dams. The process is closely connected to quasi-birth–death processes, for which efficient solution methods are known. Model description A fluid queue can be viewed as a large tank, typically assumed to be of infinite capacity, connected to a series of pipes that pour fluid in to the tank and a series of pumps which remove fluid from the tank. An operator controls the pipes and pumps controlling the rate at which fluid pours in to the buffer and the rate at which fluid leaves. When the operator puts the system in to state i we write ri for the net fluid arrival rate in this state (input less output). When the buffer contains fluid, if we write X(t) for the fluid level at time t, The operator is a continuous time Markov chain and is usually called the environment process, background process or driving process. As the process X represents the level of fluid in the buffer it can only take non-negative values. The model is a particular type of piecewise deterministic Markov process and can also be viewed as a Markov reward model with boundary conditions. Stationary distribution The stationary distribution is a phase-type distribution as first shown by Asmussen and can be computed using matrix-analytic methods. The additive decomposition method is numerically stable and separates the eigenvalues necessary for computation using Schur decomposition. On/off model For a simple system where service has a constant rate μ and arrival fluctuate between rates λ and 0 (in states 1 and 2 respectively) according to a continuous time Markov chain with generator matrix the stationary distribution can be computed explicitly and is given by and average fluid level Busy period The busy period is the period of time measured from the instant that fluid first arrives in the buffer (X(t) becomes non-zero) until the buffer is again empty (X(t) returns to zero). In earlier literature it is sometimes referred to as the w
https://en.wikipedia.org/wiki/Alessio%20Corti	Alessio Corti (born 1965) is a Professor of Mathematics at Imperial College London working in Algebraic Geometry. Corti studied at the University of Pisa and Scuola Normale Superiore in Pisa, where he gained a diploma (Laurea) in 1987. He obtained his PhD in 1992 at the University of Utah under the supervision of János Kollár. As a post-doctoral researcher, he was at the Scuola Normale Superiore in Pisa and at the Mathematical Sciences Research Institute in Berkeley, California. From 1993 to 1996 he was the Dickson Instructor at the University of Chicago and in 1996 became lecturer, later reader, of mathematics at the University of Cambridge. From 2005 he is a professor at Imperial College London. In 2002, he was awarded the London Mathematical Society's Whitehead Prize. He is the originator of a project to create a periodic table of shapes. He is married and has a daughter, Beatrice (born 17 September 1992). References External links Imperial website 1965 births Academics of Imperial College London Italian mathematicians Living people 20th-century British mathematicians 21st-century British mathematicians Winners of the Geneva International Music Competition University of Pisa alumni University of Utah alumni Cambridge mathematicians University of Chicago fellows Scientists from Milan
https://en.wikipedia.org/wiki/Steerable%20filter	In applied mathematics, a steerable filter is an orientation-selective convolution kernel used for image enhancement and feature extraction that can be expressed via a linear combination of a small set of rotated versions of itself. As an example, the oriented first derivative of a 2D Gaussian is a steerable filter. The oriented first order derivative can be obtained by taking the dot product of a unit vector oriented in a specific direction with the gradient. The basis filters are the partial derivatives of a 2D Gaussian with respect to and . The process by which the oriented filter is synthesized at any given angle is known as steering, which is used in similar sense as in beam steering for antenna arrays. Applications of steerable filters include edge detection, oriented texture analysis and shape from shading. Steerable filters may be designed as approximations of a given filter shape up to a desired error or computational complexity. References Image processing Feature detection (computer vision)
https://en.wikipedia.org/wiki/Shogo%20Tokihisa	is a former Japanese football player. Club statistics References External links j-league FC Gifu Official website - Profile 1984 births Living people Waseda University alumni Association football people from Fukuoka Prefecture Japanese men's footballers J1 League players J2 League players Ventforet Kofu players Giravanz Kitakyushu players FC Gifu players Men's association football goalkeepers
https://en.wikipedia.org/wiki/Shoji%20Yamada	is a former Japanese football player. Club statistics References External links J.League 1984 births Living people Association football people from Osaka Prefecture Japanese men's footballers J2 League players Japan Football League players Albirex Niigata players Men's association football forwards
https://en.wikipedia.org/wiki/Yasuhiro%20Tanaka%20%28footballer%29	is a former Japanese football player. Club statistics References External links J.League 1984 births Living people Association football people from Niigata Prefecture Japanese men's footballers J2 League players Albirex Niigata players Cobaltore Onagawa players Men's association football forwards
https://en.wikipedia.org/wiki/Kinoto%20Saito	is a former Japanese football player. Club statistics References External links j-league 1976 births Living people Rissho University alumni Association football people from Iwate Prefecture Japanese men's footballers J2 League players Mito HollyHock players Iwate Grulla Morioka players Men's association football midfielders
https://en.wikipedia.org/wiki/Shun%20Nogaito	is a Japanese football player who plays as a defender for Veertien Mie. Club statistics Updated to 20 February 2020. References External links Profile at FC Gifu 1986 births Living people Yokkaichi University alumni Association football people from Mie Prefecture Japanese men's footballers J2 League players Japan Football League players FC Gifu players Vanraure Hachinohe players Veertien Mie players Men's association football defenders
https://en.wikipedia.org/wiki/Daichi%20Kawashima	is a Japanese football player. Club statistics Updated to 23 February 2018. References External links Profile at Giravanz Kitakyushu 1986 births Living people Tokai University alumni Association football people from Ibaraki Prefecture Japanese men's footballers J1 League players J2 League players J3 League players Kashima Antlers players Montedio Yamagata players Giravanz Kitakyushu players Men's association football midfielders
https://en.wikipedia.org/wiki/Wataru%20Hashimoto	is a Japanese football player who plays for FC Gifu. Club statistics Updated to 23 February 2018. 1Includes FIFA Club World Cup, J. League Championship, Suruga Bank Championship and Japanese Super Cup. References External links Profile at Vissel Kobe 1986 births Living people Osaka University of Health and Sport Sciences alumni Association football people from Shiga Prefecture Japanese men's footballers J1 League players J2 League players J3 League players Kashiwa Reysol players Urawa Red Diamonds players Vissel Kobe players FC Gifu players Men's association football defenders
https://en.wikipedia.org/wiki/Kohei%20Higa	is a Japanese football player. Club statistics References External links 1990 births Living people Association football people from Saitama Prefecture Japanese men's footballers J1 League players J2 League players Japan Football League players Kashiwa Reysol players Blaublitz Akita players Montedio Yamagata players Men's association football midfielders
https://en.wikipedia.org/wiki/Kosuke%20Taketomi	Kosuke Taketomi (武富孝介, born September 23, 1990) is a Japanese footballer who plays as a midfielder for club Ventforet Kofu. Club statistics Honours J. League Division 2 (2) : 2010, 2014 References External links Profile at Urawa Red Diamonds Profile at Kashiwa Reysol 1990 births Living people Japanese men's footballers J1 League players J2 League players Kashiwa Reysol players Roasso Kumamoto players Shonan Bellmare players Urawa Red Diamonds players Kyoto Sanga FC players Ventforet Kofu players Men's association football midfielders Association football people from Saitama (city)
https://en.wikipedia.org/wiki/Ren%20Sengoku	is a Japanese football player. Club statistics Updated to 23 February 2018. References External links Profile at Tochigi SC 1990 births Living people Association football people from Saitama Prefecture Japanese men's footballers J1 League players J2 League players J3 League players Kashiwa Reysol players Fagiano Okayama players AC Nagano Parceiro players Tochigi SC players Gainare Tottori players Men's association football midfielders
https://en.wikipedia.org/wiki/Jin%20Hanato	is a Japanese football player for Tokyo Verdy. National team career In August 2007, Hanato was elected Japan U-17 national team for 2007 U-17 World Cup. He played all 3 matches. Club statistics Updated to 19 July 2022. Awards and honours Shonan Bellmare J2 League: 2017 Yokohama F. Marinos Emperor's Cup: 2013 Japan AFC U-17 Championship: 2006 References External links Profile at Shonan Bellmare 1990 births Living people Association football people from Kanagawa Prefecture Japanese men's footballers Japan men's youth international footballers J1 League players J2 League players Yokohama F. Marinos players Giravanz Kitakyushu players Shonan Bellmare players Tokyo Verdy players Men's association football forwards
https://en.wikipedia.org/wiki/Kazuya%20Myodo	is a former Japanese football player. Club statistics References External links j-league 1986 births Living people Association football people from Toyama Prefecture Japanese men's footballers J1 League players J2 League players Japan Soccer College players Albirex Niigata players Kataller Toyama players Japanese expatriate men's footballers Japanese expatriate sportspeople in Singapore Expatriate men's footballers in Singapore Japanese expatriate sportspeople in Thailand Expatriate men's footballers in Thailand Men's association football midfielders
https://en.wikipedia.org/wiki/Yu%20Kijima	is a Japanese footballer who plays as a forward for J-Lease FC. Club statistics Updated to 9 April 2023. References External links 1986 births Living people University of Tsukuba alumni Association football people from Hyōgo Prefecture Japanese men's footballers J1 League players J2 League players Japan Football League players Shimizu S-Pulse players Oita Trinita players Verspah Oita players Men's association football forwards
https://en.wikipedia.org/wiki/Ryo%20Takeuchi	Ryo Takeuchi (竹内涼, born March 8, 1991) is a Japanese football player currently playing for Shimizu S-Pulse. Club statistics Updated to 24 July 2022. References External links Profile at Shimizu S-Pulse 1991 births Living people Association football people from Shizuoka Prefecture Japanese men's footballers J1 League players J2 League players Shimizu S-Pulse players Giravanz Kitakyushu players Men's association football midfielders
https://en.wikipedia.org/wiki/Genta%20Matsuo	is a former Japanese football player. Club statistics References External links j-league 1986 births Living people Osaka University of Health and Sport Sciences alumni Association football people from Shiga Prefecture Japanese men's footballers J1 League players J2 League players Nagoya Grampus players Kyoto Sanga FC players Men's association football defenders
https://en.wikipedia.org/wiki/Hikaru%20Kuba	is a former Japanese football player. Club statistics References External links j-league 1990 births Living people Association football people from Okinawa Prefecture Japanese men's footballers J1 League players J2 League players Japan Football League players Nagoya Grampus players Ehime FC players FC Ryukyu players Men's association football forwards
https://en.wikipedia.org/wiki/Ryota%20Isomura	is a Japanese football player for Tochigi SC. Career statistics Club Updated to 28 February 2019. 1Includes Emperor's Cup. 2Includes J. League Cup. 3Includes AFC Champions League. References External links Profile at Albirex Niigata Profile at Nagoya Grampus 1991 births Living people People from Seto, Aichi Association football people from Aichi Prefecture Japanese men's footballers J1 League players J2 League players Nagoya Grampus players Albirex Niigata players V-Varen Nagasaki players Tochigi SC players Men's association football midfielders
https://en.wikipedia.org/wiki/Hilbert%E2%80%93Burch%20theorem	In mathematics, the Hilbert–Burch theorem describes the structure of some free resolutions of a quotient of a local or graded ring in the case that the quotient has projective dimension 2. proved a version of this theorem for polynomial rings, and proved a more general version. Several other authors later rediscovered and published variations of this theorem. gives a statement and proof. Statement If R is a local ring with an ideal I and is a free resolution of the R-module R/I, then m = n – 1 and the ideal I is aJ where a is a regular element of R and J, a depth-2 ideal, is the first Fitting ideal of I, i.e., the ideal generated by the determinants of the minors of size m of the matrix of f. References Commutative algebra Theorems in algebra
https://en.wikipedia.org/wiki/2006%E2%80%9307%20PFC%20CSKA%20Sofia%20season	The 2006–07 season was PFC CSKA Sofia's 59th consecutive season in A Group. This article shows player statistics and all matches (official and friendly) that the club have and will play during the 2006–07 season. Club Coaching staff Team kits The team kits for the 2006–07 season are produced by Uhlsport and sponsored by Vivatel. Squad As of 31 December 2006 Competitions A Group Table Results summary Results by round Fixtures and results Bulgarian Cup Bulgarian Super Cup UEFA Cup First qualifying round Second qualifying round First round UEFA Club Rankings This is the current UEFA Club Rankings, including season 2005-06. References External links CSKA Official Site CSKA Fan Page with up-to-date information Bulgarian A Professional Football Group Site PFC CSKA Sofia seasons Cska Sofia
https://en.wikipedia.org/wiki/Duffin%E2%80%93Kemmer%E2%80%93Petiau%20algebra	In mathematical physics, the Duffin–Kemmer–Petiau algebra (DKP algebra), introduced by R.J. Duffin, Nicholas Kemmer and G. Petiau, is the algebra which is generated by the Duffin–Kemmer–Petiau matrices. These matrices form part of the Duffin–Kemmer–Petiau equation that provides a relativistic description of spin-0 and spin-1 particles. The DKP algebra is also referred to as the meson algebra. Defining relations The Duffin–Kemmer–Petiau matrices have the defining relation where stand for a constant diagonal matrix. The Duffin–Kemmer–Petiau matrices for which consists in diagonal elements (+1,-1,...,-1) form part of the Duffin–Kemmer–Petiau equation. Five-dimensional DKP matrices can be represented as: , , , These five-dimensional DKP matrices represent spin-0 particles. The DKP matrices for spin-1 particles are 10-dimensional. The DKP-algebra can be reduced to a direct sum of irreducible subalgebras for spin‐0 and spin‐1 bosons, the subalgebras being defined by multiplication rules for the linearly independent basis elements. Duffin–Kemmer–Petiau equation The Duffin–Kemmer–Petiau equation (DKP equation, also: Kemmer equation) is a relativistic wave equation which describes spin-0 and spin-1 particles in the description of the standard model. For particles with nonzero mass, the DKP equation is where are Duffin–Kemmer–Petiau matrices, is the particle's mass, its wavefunction, the reduced Planck constant, the speed of light. For massless particles, the term is replaced by a singular matrix that obeys the relations and . The DKP equation for spin-0 is closely linked to the Klein–Gordon equation and the equation for spin-1 to the Proca equations. It suffers the same drawback as the Klein–Gordon equation in that it calls for negative probabilities. Also the De Donder–Weyl covariant Hamiltonian field equations can be formulated in terms of DKP matrices. History The Duffin–Kemmer–Petiau algebra was introduced in the 1930s by R.J. Duffin, N. Kemmer and G. Petiau. Further reading Kruglov, S. I. (2011). "Field theory of massive and massless vector particles in the Duffin-Kemmer-Petiau formalism". Int.J.Mod.Phys.A 26, 2487-2501 [arXiv:1009.4895]. Kruglov, S. I. (2010) "Kalb-Ramond fields in the Petiau-Duffin-Kemmer formalism and scale invariance " Mod.Phys.Lett.A 25, 2745-2751 [arXiv:1002.3574]. References Algebras
https://en.wikipedia.org/wiki/Compound%20of%20three%20octahedra	In mathematics, the compound of three octahedra or octahedron 3-compound is a polyhedral compound formed from three regular octahedra, all sharing a common center but rotated with respect to each other. Although appearing earlier in the mathematical literature, it was rediscovered and popularized by M. C. Escher, who used it in the central image of his 1948 woodcut Stars. Construction A regular octahedron can be circumscribed around a cube in such a way that the eight edges of two opposite squares of the cube lie on the eight faces of the octahedron. The three octahedra formed in this way from the three pairs of opposite cube squares form the compound of three octahedra. The eight cube vertices are the same as the eight points in the compound where three edges cross each other. Each of the octahedron edges that participates in these triple crossings is divided by the crossing point in the ratio 1:. The remaining octahedron edges cross each other in pairs, within the interior of the compound; their crossings are at their midpoints and form right angles. The compound of three octahedra can also be formed from three copies of a single octahedron by rotating each copy by an angle of /4 around one of the three symmetry axes that pass through two opposite vertices of the starting octahedron. A third construction for the same compound of three octahedra is as the dual polyhedron of the compound of three cubes, one of the uniform polyhedron compounds. The six vertices of one of the three octahedra may be given by the coordinates and . The other two octahedra have coordinates that may be obtained from these coordinates by exchanging the z coordinate for the x or y coordinate. Symmetries The compound of three octahedra has the same symmetry group as a single octahedron. It is an isohedral deltahedron, meaning that its faces are equilateral triangles and that it has a symmetry taking every face to every other face. There is one known infinite family of isohedral deltahedra, and 36 more that do not fall into this family; the compound of three octahedra is one of the 36 sporadic examples. However, its symmetry group does not take every vertex to every other vertex, so it is not itself a uniform polyhedron compound. The intersection of the three octahedra is a convex polyhedron with 14 vertices and 24 faces, a tetrakis hexahedron, formed by attaching a low square pyramid to each face of the central cube. Thus, the compound can be seen as a stellation of the tetrakis hexahedron. A different form of the tetrakis hexahedron, formed by using taller pyramids on each face of the cube, is non-convex but has equilateral triangle faces that again lie on the same planes as the faces of the three octahedra; it is another of the known isohedral deltahedra. A third isohedral deltahedron sharing the same face planes, the compound of six tetrahedra, may be formed by stellating each face of the compound of three octahedra to form three stellae octangulae. A fourth isoh
https://en.wikipedia.org/wiki/Marcelo%20Soares	Marcelo Gomes Soares (born March 9, 1982) is a Brazilian football player who currently plays for São Caetano. Club statistics References External links 1982 births Living people Brazilian men's footballers Brazilian expatriate men's footballers Associação Atlética Ponte Preta players Guaratinguetá Futebol players Sampaio Corrêa Futebol Clube players Associação Desportiva São Caetano players Esporte Clube XV de Novembro (Piracicaba) players J2 League players Vegalta Sendai players Expatriate men's footballers in Japan Men's association football forwards Footballers from Maceió
https://en.wikipedia.org/wiki/Kohei%20Yamamoto%20%28footballer%29	is a former Japanese football player. Club statistics References External links j-league 1986 births Living people Hosei University alumni Association football people from Kanagawa Prefecture Japanese men's footballers J2 League players Shonan Bellmare players Mito HollyHock players Men's association football forwards
https://en.wikipedia.org/wiki/Ryosuke%20Takayasu	is a former Japanese football midfielder. He played in the J2 League for Tochigi SC in 2009. Club statistics References External links j-league 1984 births Living people International Budo University alumni Association football people from Chiba Prefecture Japanese men's footballers J2 League players Japan Football League players Tochigi SC players Tochigi City FC players Men's association football midfielders
https://en.wikipedia.org/wiki/Hisahito%20Inaba	is a former Japanese football player. Club statistics References External links J League 2009 Tochigi S.C. player list 1985 births Living people Hosei University alumni Association football people from Tochigi Prefecture Japanese men's footballers J2 League players Japan Football League players Tochigi SC players Tochigi City FC players Men's association football forwards
https://en.wikipedia.org/wiki/Masaya%20Saito	is a former Japanese football player. Club statistics External links j-league 1985 births Living people Meiji University alumni Association football people from Tokyo Japanese men's footballers J2 League players Japan Football League players Tochigi SC players Sony Sendai FC players Men's association football defenders
https://en.wikipedia.org/wiki/Shinichi%20Mukai	is a Japanese football player. He plays for Nara Club. Club statistics Updated to 2 January 2020. References External links Profile at Nara Club j-league 1985 births Living people Hosei University alumni Association football people from Kanagawa Prefecture Japanese men's footballers J2 League players J3 League players Japan Football League players Tochigi SC players Tokyo Verdy players AC Nagano Parceiro players FC Machida Zelvia players Nara Club players Men's association football midfielders
https://en.wikipedia.org/wiki/Yusei%20Kudo	is a Japanese football player. Club statistics Updated to 23 February 2019. References External links 1986 births Living people Tokyo University of Agriculture alumni Association football people from Kanagawa Prefecture Japanese men's footballers J2 League players J3 League players Japan Football League players Tochigi SC players SC Sagamihara players Men's association football defenders Sportspeople from Sagamihara
https://en.wikipedia.org/wiki/Ryohei%20Hayashi	is a Japanese retired football player. Club statistics Updated to 1 March 2021. References External links Profile at Tokyo Verdy Profile at Mito HollyHock 1986 births Living people Meiji University alumni People from Hachiōji, Tokyo Association football people from Tokyo Japanese men's footballers J1 League players J2 League players Tokyo Verdy players Kashiwa Reysol players Montedio Yamagata players Mito HollyHock players FC Machida Zelvia players Thespakusatsu Gunma players Men's association football forwards
https://en.wikipedia.org/wiki/Takuya%20Wada	Takuya Wada (和田拓也, born 28 July 1990) is a Japanese football player. He plays for Yokohama FC. Club statistics Updated to 23 October 2022. Honours Club Yokohama F. Marinos J1 League: 2019 References External links Profile at Sanfrecce Hiroshima 1990 births Living people Association football people from Kanagawa Prefecture Japanese men's footballers J1 League players J2 League players Tokyo Verdy players Vegalta Sendai players Omiya Ardija players Sanfrecce Hiroshima players Yokohama F. Marinos players Yokohama FC players Men's association football defenders
https://en.wikipedia.org/wiki/Yu%20Tomidokoro	Yu Tomidokoro (富所悠, born April 21, 1990) is a Japanese football player for FC Ryūkyū. Club statistics Updated to end of 2018 season. References External links Profile at FC Ryukyu "登録選手一覧表" . J.League. February 24, 2016. 1990 births Living people Association football people from Saitama Prefecture Japanese men's footballers J2 League players J3 League players Japan Football League players Tokyo Verdy players AC Nagano Parceiro players FC Ryukyu players Men's association football midfielders
https://en.wikipedia.org/wiki/Yu%20Hyo-jin	Yu Hyo-jin (born April 5, 1981) is a South Korean football player. Club statistics References External links America Got Talent Short Stories jsgoal 1981 births Living people South Korean men's footballers South Korean expatriate men's footballers J2 League players Yokohama FC players Expatriate men's footballers in Japan South Korean expatriate sportspeople in Japan Men's association football midfielders
https://en.wikipedia.org/wiki/Go%20Nishida	is a Japanese football player for Ehime FC. Club statistics Updated to 23 February 2018. References External links Profile at Ehime FC 1986 births Living people Hannan University alumni Association football people from Kagoshima Prefecture Japanese men's footballers J2 League players Yokohama FC players Avispa Fukuoka players Ehime FC players Men's association football forwards
https://en.wikipedia.org/wiki/Eder%20%28footballer%2C%20born%201989%29	Ederson Bruno Domingos (born August 21, 1989), known as Eder, is a Brazilian football player who plays as a winger Hamrun Spartans. Club statistics References External links Eder at playmakerstats.com (English version of zerozero.pt) 1989 births Living people Brazilian men's footballers Brazilian expatriate men's footballers J2 League players Campeonato Brasileiro Série B players Campeonato Brasileiro Série C players Campeonato Brasileiro Série D players Sport Club Internacional players Yokohama FC players Ypiranga Futebol Clube players Canoas Sport Club players Ferroviário Atlético Clube (CE) players Veranópolis Esporte Clube Recreativo e Cultural players Esporte Clube Novo Hamburgo players Grêmio Esportivo Brasil players Clube Esportivo Lajeadense players Grêmio Esportivo Glória players Esporte Clube São José players Luverdense Esporte Clube players Esporte Clube São Luiz players Clube Esportivo Bento Gonçalves players Sociedade Esportiva e Recreativa Caxias do Sul players ABC Futebol Clube players Clube Esportivo Aimoré players Brazilian expatriate sportspeople in Japan Expatriate men's footballers in Japan Men's association football forwards
https://en.wikipedia.org/wiki/Tatsumi%20Iida	Tatsumi Iida (飯田健巳, born July 22, 1985) is a former Japanese football player who last played for Kataller Toyama. Club statistics Updated to 2 February 2018. References External links Profile at Kataller Toyama 1985 births Living people Jobu University alumni People from Zama, Kanagawa Association football people from Kanagawa Prefecture Japanese men's footballers J2 League players J3 League players Japan Football League players Tochigi SC players Yokohama FC players Kataller Toyama players Men's association football goalkeepers
https://en.wikipedia.org/wiki/Hermite%20ring	In algebra, the term Hermite ring (after Charles Hermite) has been applied to three different objects. According to (p. 465), a ring is right Hermite if, for every two elements a and b of the ring, there is an element d of the ring and an invertible 2×2 matrix M over the ring such that (a b)M = (d 0), and the term left Hermite is defined similarly. Matrices over such a ring can be put in Hermite normal form by right multiplication by a square invertible matrix (, p. 468.) (appendix to §I.4) calls this property K-Hermite, using Hermite instead in the sense given below. According to (§I.4, p. 26), a ring is right Hermite if any finitely generated stably free right module over the ring is free. This is equivalent to requiring that any row vector (b1,...,bn) of elements of the ring which generate it as a right module (i.e., b1R + ... + bnR = R) can be completed to a (not necessarily square) invertible matrix by adding some number of rows. The criterion of being left Hermite can be defined similarly. (p. 528) earlier called a commutative ring with this property an H-ring. According to (§0.4), a ring is Hermite if, in addition to every stably free (left) module being free, it has invariant basis number. All commutative rings which are Hermite in the sense of Kaplansky are also Hermite in the sense of Lam, but the converse is not necessarily true. All Bézout domains are Hermite in the sense of Kaplansky, and a commutative ring which is Hermite in the sense of Kaplansky is also a Bézout ring (, pp. 39-40.) The Hermite ring conjecture, introduced by (p. xi), states that if R is a commutative Hermite ring, then the polynomial ring R[x] is also a Hermite ring. References Ring theory
https://en.wikipedia.org/wiki/Alexandre%20Borovik	Alexandre V. Borovik (born 1956) is a Professor of Pure Mathematics at the University of Manchester, United Kingdom. He was born in Russia and graduated from Novosibirsk State University in 1978. His principal research lies in algebra, model theory, and combinatorics—topics on which he published several monographs and a number of papers. He also has an interest in mathematical practice: his book Mathematics under the Microscope: Notes on Cognitive Aspects of Mathematical Practice examines a mathematician's outlook on psychophysiological and cognitive issues in mathematics. Selected books and articles . Borovik, Alexandre; Nesin, Ali: Groups of finite Morley rank. Oxford Logic Guides, 26. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1994 Borovik, Alexandre V.; Gelfand, I. M.; White, Neil: Coxeter matroids. Progress in Mathematics, 216. Birkhäuser Boston, Inc., Boston, MA, 2003. . Notes External links Personal page Mathematics under the Microscope Living people 20th-century British mathematicians 21st-century British mathematicians British logicians Model theorists 1956 births
https://en.wikipedia.org/wiki/Sylvester%20domain	In mathematics, a Sylvester domain, named after James Joseph Sylvester by , is a ring in which Sylvester's law of nullity holds. This means that if A is an m by n matrix, and B is an n by s matrix over R, then ρ(AB) ≥ ρ(A) + ρ(B) – n where ρ is the inner rank of a matrix. The inner rank of an m by n matrix is the smallest integer r such that the matrix is a product of an m by r matrix and an r by n matrix. showed that fields satisfy Sylvester's law of nullity and are, therefore, Sylvester domains. References Ring theory
https://en.wikipedia.org/wiki/Jennifer%20Quinn	Jennifer J. Quinn is an American mathematician specializing in combinatorics, and professor of mathematics at the University of Washington Tacoma. She sits on the board of governors of the Mathematical Association of America, and is serving as its president for the years 2021 and 2022. From 2004 to 2008 she was co-editor of Math Horizons. Education and career Quinn went to Williams College as an undergraduate, graduating in 1985. She earned a master's degree from the University of Illinois at Chicago in 1987, and completed her doctorate at the University of Wisconsin–Madison in 1993. Her dissertation, Colorings and Cycle Packings in Graphs and Digraphs, was supervised by Richard A. Brualdi. She taught at Occidental College until 2005, when she gave up her position as full professor and department chair to move with her husband, biologist Mark Martin, to Washington. She became a part-time lecturer, and executive director of the Association for Women in Mathematics, until earning a faculty position at Tacoma in 2007. Recognition Quinn won a Distinguished Teaching Award from the Mathematical Association of America in 2001, and the Deborah and Franklin Tepper Haimo Award for Distinguished College or University Teaching of Mathematics of the association in 2007. Quinn's book with Arthur T. Benjamin, Proofs that Really Count: The Art of Combinatorial Proof (2003) won the CHOICE Award for Outstanding Academic Title of the American Library Association and the Beckenbach Book Prize of the Mathematical Association of America. In 2018, Quinn was elected an officer-at-large member of the board of directors of the Mathematical Association of America (MAA). In 2020, Quinn joined the board of directors of the MAA as president-elect. Her term as president began in 2021. In 2022 she will become a fellow of the Association for Women in Mathematics, "For her outstanding achievements as a teacher, mentor, leader, expositor, and editor; for her pioneering service as AWM executive director; and for continued service as AWM volunteer and supporter." References External links Year of birth missing (living people) Living people 20th-century American mathematicians 21st-century American mathematicians American women mathematicians Combinatorialists Williams College alumni University of Illinois Chicago alumni University of Wisconsin–Madison alumni Occidental College faculty University of Washington faculty 20th-century women mathematicians 21st-century women mathematicians 20th-century American women 21st-century American women
https://en.wikipedia.org/wiki/Yuki%20Toma	is a former Japanese football player. Club statistics References External links j-league 1987 births Living people Tokoha University alumni Association football people from Shizuoka Prefecture Japanese men's footballers J2 League players Japan Football League players Ventforet Kofu players FC Kariya players Azul Claro Numazu players Men's association football defenders
https://en.wikipedia.org/wiki/Yuki%20Koike%20%28footballer%29	is a former Japanese football player. Club statistics References External links j-league 1986 births Living people Chuo University alumni Association football people from Yamanashi Prefecture Japanese men's footballers J1 League players J2 League players Ventforet Kofu players Men's association football forwards
https://en.wikipedia.org/wiki/Naoki%20Hatada	is a Japanese former football player who last played for Blaublitz Akita. Club statistics Updated to 23 February 2016. References External links Profile at Blaublitz Akita 1990 births Living people Association football people from Chiba Prefecture Japanese men's footballers J2 League players J3 League players Japan Football League players Ventforet Kofu players Blaublitz Akita players AC Nagano Parceiro players Gainare Tottori players Men's association football midfielders
https://en.wikipedia.org/wiki/Weberton	Weberton Correia dos Santos (born July 26, 1990) is a Brazilian football player. Club statistics References j-league 1990 births Living people Brazilian men's footballers Brazilian expatriate men's footballers J2 League players Ventforet Kofu players Expatriate men's footballers in Japan Men's association football defenders
https://en.wikipedia.org/wiki/Kengo%20Tsutsumi	is a former Japanese football player. Club statistics References External links 1978 births Living people Kokushikan University alumni Association football people from Ōita Prefecture Japanese men's footballers J2 League players Japan Football League players Kataller Toyama players Men's association football defenders
https://en.wikipedia.org/wiki/Kazuya%20Nagayama	is a former Japanese football player. Club statistics References External links j-league 1982 births Living people Hosei University alumni Association football people from Kagoshima Prefecture Japanese men's footballers J2 League players Japan Football League players Kataller Toyama players Men's association football midfielders
https://en.wikipedia.org/wiki/Kazuma%20Matsushita	is a former Japanese football player. Club statistics References External links jsgoal 1982 births Living people Shizuoka Sangyo University alumni Association football people from Osaka Prefecture Japanese men's footballers J2 League players Japan Football League players Kataller Toyama players Men's association football forwards
https://en.wikipedia.org/wiki/Mitsuru%20Hasegawa	is a former Japanese football player. Club statistics References External links j-league 1979 births Living people Meiji University alumni Association football people from Fukui Prefecture Japanese men's footballers J2 League players Japan Football League players Kataller Toyama players Men's association football forwards
https://en.wikipedia.org/wiki/Hideyuki%20Ishida	is a former Japanese football player. Club statistics References External links j-league 1982 births Living people Ritsumeikan University alumni Association football people from Kyoto Prefecture Japanese men's footballers J2 League players Japan Football League players SP Kyoto FC players Kataller Toyama players Kamatamare Sanuki players Men's association football forwards
https://en.wikipedia.org/wiki/Kenji%20Kageyama	is a former Japanese football player. Club statistics References External links j-league 1980 births Living people Kokushikan University alumni Association football people from Nagano Prefecture Japanese men's footballers J2 League players Japan Football League players Kataller Toyama players Men's association football midfielders
https://en.wikipedia.org/wiki/Daigo%20Imai	is a former Japanese football player. Club statistics References External links 1984 births Living people Fukuyama University alumni Association football people from Okayama Prefecture Japanese men's footballers J2 League players Japan Football League players Sagawa Shiga FC players Kataller Toyama players Blaublitz Akita players Men's association football midfielders
https://en.wikipedia.org/wiki/Tomohisa%20Ishiguro	is a former Japanese football player. Club statistics References External links jsgoal.jp 1981 births Living people Aichi Gakuin University alumni Association football people from Toyama Prefecture Japanese men's footballers J2 League players Japan Football League players Kataller Toyama players Men's association football forwards
https://en.wikipedia.org/wiki/Hirotaku%20Hagiwara	is a former Japanese football player. Club statistics References External links j-league 1986 births Living people Association football people from Shizuoka Prefecture Japanese men's footballers J2 League players Japan Football League players Kataller Toyama players Men's association football midfielders
https://en.wikipedia.org/wiki/Ryo%20Nojima	is a former Japanese football player. Club statistics References External links j-league 1979 births Living people Shizuoka Sangyo University alumni Association football people from Toyama Prefecture Japanese men's footballers J2 League players Japan Football League players Kataller Toyama players Men's association football midfielders
https://en.wikipedia.org/wiki/Yohei%20Nakada	is a former Japanese football player. Club statistics References External links 1983 births Living people Kochi University alumni Association football people from Hyōgo Prefecture Japanese men's footballers J2 League players Japan Football League players Kataller Toyama players Men's association football defenders
https://en.wikipedia.org/wiki/Kazuhito%20Esaki	is a former Japanese football player. Club statistics References External links j-league Profile at Akita 1986 births Living people Hosei University alumni Association football people from Ibaraki Prefecture Japanese men's footballers J2 League players J3 League players Japan Football League players Kataller Toyama players Blaublitz Akita players Men's association football defenders
https://en.wikipedia.org/wiki/Shota%20Kanno	is a former Japanese football player. Club statistics References External links j-league 1984 births Living people Ryutsu Keizai University alumni Association football people from Kanagawa Prefecture Japanese men's footballers J2 League players Japan Football League players Kataller Toyama players Men's association football midfielders
https://en.wikipedia.org/wiki/Masato%20Sakurai	is a former Japanese football player. Club statistics References j-league External links 1986 births Living people Tokoha University alumni Association football people from Ibaraki Prefecture Japanese men's footballers J2 League players Japan Football League players Kataller Toyama players SP Kyoto FC players Men's association football forwards
https://en.wikipedia.org/wiki/Yasutaka%20Nomoto	is a Japanese football player. He plays for Nara Club. Club statistics References External links Profile at Nara Club j-league 1986 births Living people University of Tsukuba alumni Association football people from Ibaraki Prefecture Japanese men's footballers J2 League players Japan Football League players FC Gifu players Nara Club players Men's association football defenders
https://en.wikipedia.org/wiki/Shuto%20Tanaka	is a Japanese retired football player. Club statistics Updated to 2 January 2020. References External links Profile at Kagoshima United FC 1985 births Living people University of Tsukuba alumni Association football people from Tokyo Japanese men's footballers J2 League players J3 League players Japan Football League players FC Gifu players Kagoshima United FC players Men's association football defenders
https://en.wikipedia.org/wiki/Takuma%20Nagayoshi	is a Japanese football player for J-Lease FC Club statistics Updated to 23 February 2016. References External links 1986 births Living people University of Tsukuba alumni Association football people from Okayama Prefecture Japanese men's footballers J1 League players J2 League players J3 League players FC Gifu players Oita Trinita players Tochigi SC players SC Sagamihara players Men's association football defenders
https://en.wikipedia.org/wiki/Weak%20Hopf%20algebra	In mathematics, weak bialgebras are a generalization of bialgebras that are both algebras and coalgebras but for which the compatibility conditions between the two structures have been "weakened". In the same spirit, weak Hopf algebras are weak bialgebras together with a linear map S satisfying specific conditions; they are generalizations of Hopf algebras. These objects were introduced by Böhm, Nill and Szlachányi. The first motivations for studying them came from quantum field theory and operator algebras. Weak Hopf algebras have quite interesting representation theory; in particular modules over a semisimple finite weak Hopf algebra is a fusion category (which is a monoidal category with extra properties). It was also shown by Etingof, Nikshych and Ostrik that any fusion category is equivalent to a category of modules over a weak Hopf algebra. Definition A weak bialgebra over a field is a vector space such that forms an associative algebra with multiplication and unit , forms a coassociative coalgebra with comultiplication and counit , for which the following compatibility conditions hold : Multiplicativity of the Comultiplication : , Weak Multiplicativity of the Counit : , Weak Comultiplicativity of the Unit : , where flips the two tensor factors. Moreover is the opposite multiplication and is the opposite comultiplication. Note that we also implicitly use Mac Lane's coherence theorem for the monoidal category of vector spaces, identifying as well as . The definition weakens the compatibility between the algebra and coalgebra structures of a bialgebra. More specifically, the unit and counit are weakened. This remains true in the axioms of a weak Hopf algebra. A weak Hopf algebra is a weak bialgebra with a linear map , called the antipode, that satisfies: , , . Examples Hopf algebra. Of course any Hopf algebra is a weak Hopf algebra. Groupoid algebra. Suppose is a groupoid and let be the groupoid algebra, in other words, the algebra generated by the morphisms . This becomes a weak Hopf algebra if we define . Note that this second example is a weak Hopf algebra but not a Hopf algebra. Representation theory Let H be a semisimple finite weak Hopf algebra, then modules over H form a semisimple rigid monoidal category with finitely many simple objects. Moreover the homomorphisms spaces are finite-dimensional vector spaces and the endomorphisms space of simple objects are one-dimensional. Finally, the monoidal unit is a simple object. Such a category is called a fusion category. It can be shown that some monoidal category are not modules over a Hopf algebra. In the case of fusion categories (which are just monoidal categories with extra conditions), it was proved by Etingof, Nikshych and Ostrik that any fusion category is equivalent to a category of modules over a weak Hopf algebra. Notes References Hopf algebras
https://en.wikipedia.org/wiki/Richard%20Thomas%20%28mathematician%29	Richard Paul Winsley Thomas is a British mathematician working in several areas of geometry. He is a professor at Imperial College London. He studies moduli problems in algebraic geometry, and ‘mirror symmetry’—a phenomenon in pure mathematics predicted by string theory in theoretical physics. Education Thomas obtained his PhD on gauge theory on Calabi–Yau manifolds in 1997 under the supervision of Simon Donaldson at the University of Oxford. Together with Donaldson, he defined the Donaldson–Thomas invariants of Calabi–Yau 3-folds, now a major topic in geometry and the mathematics of string theory. Career and research Before joining Imperial College, he was member of the Institute for Advanced Study in Princeton, New Jersey, and affiliated with Harvard University and the University of Oxford. He was made professor of pure mathematics in 2005. Thomas has made contributions to algebraic geometry, differential Geometry, and symplectic geometry. His doctoral thesis, which introduced the invariants that later became known as Donaldson–Thomas invariants, was published in the Journal of Differential Geometry as `A holomorphic Casson invariant for Calabi-Yau 3-folds, and bundles on K3 fibrations'. Motivated by homological mirror symmetry, he produced braid group actions on derived categories of coherent sheaves in joint work with Paul Seidel. With Shing-Tung Yau he formulated a conjecture (now known as the Thomas–Yau conjecture) concerning the existence of a special Lagrangian in the Hamiltonian deformation class of a fixed Lagrangian submanifold of a Calabi–Yau manifold. Together with Rahul Pandharipande he formulated a refinement of the Donaldson–Thomas invariants for the special case of curve counting, the Pandharipande–Thomas (PT) stable pair invariants. With Martijn Kool and Vivek Shende, he used the PT invariants to prove the Göttsche conjecture—a classical algebro-geometric problem going back more than a century. With Davesh Maulik and Pandharipande he proved the Katz–Klemm–Vafa (KKV) conjecture, establishing links between the Gromov–Witten theory of K3 surfaces and modular forms. His collaboration with Daniel Huybrechts led to contributions to the deformation theory of complexes. With Nick Addington he established a compatibility result for two rationality conjectures on cubic fourfolds. He coauthored a book on mirror symmetry. Thomas also wrote expository notes on derived categories, curve counting, and homological projective duality. He appeared in the documentary film 'Thinking space' by Heidi Morstang. Thomas has played an important part in promoting geometry in the UK, encouraging younger mathematicians, and in bringing more geometry to Imperial college: "[...] There was little geometry in Imperial then, but now, thanks largely to the drive of my colleague Richard Thomas, we have one of the main centres for research in this area." - Simon Donaldson Awards and honours In 2004, Thomas was awarded the London Mathematical Society's Whiteh
https://en.wikipedia.org/wiki/Mark%20H.%20A.%20Davis	Mark Herbert Ainsworth Davis (25 April 1945 – 18 March 2020) was Professor of Mathematics at Imperial College London. He made fundamental contributions to the theory of stochastic processes, stochastic control and mathematical finance. Education and career After completing his BA degree in Electrical Engineering at the University of Cambridge, Davis pursued his PhD degree at UC Berkeley under the supervision of Pravin Varaiya. His PhD thesis, obtained in 1971, initiated the martingale theory of stochastic control. Returning to the UK in 1972, Davis joined the Control Group at Imperial College London. From 1995 to 1999 he was Head of Research and Product Development at Tokyo-Mitsubishi International, leading a quantitative research team providing pricing models and risk analysis for fixed income, equity and credit-related products. He returned to Imperial College London in August 2000 to build Imperial’s Mathematical Finance group within the Department of Mathematics. Research Davis made several contributions to the theory of stochastic processes, stochastic control and mathematical finance. His doctoral thesis initiated the martingale approach for the study of conditions for the optimal control of stochastic systems given by Ito equations. The approach permitted arbitrary non-anticipative feedback controls and remains the standard way of formulating stochastic control to this day. One of his key contributions is the martingale optimality principle in stochastic control, which characterizes optimal strategies through the martingale property of the value process. In a 1984 paper he introduced the concept of Piecewise deterministic Markov process, a class of Markov models which have been used in many applications in engineering and science. In the early 1990s, Davis introduced the deterministic approach to stochastic control by means of appropriate Lagrange multipliers. He was awarded the Naylor Prize by the London Mathematical Society in 2002 for his "contributions to stochastic analysis, stochastic control theory and mathematical finance" and delivered a lecture titled Optimal investment with randomly terminating income. Davis was one of the founding editors of the journal Mathematical Finance. He authored three books on stochastic analysis and optimization. Bibliography References 1945 births 2020 deaths English mathematicians Fellows of the Royal Statistical Society
https://en.wikipedia.org/wiki/Frequency%20format%20hypothesis	The frequency format hypothesis is the idea that the brain understands and processes information better when presented in frequency formats rather than a numerical or probability format. Thus according to the hypothesis, presenting information as 1 in 5 people rather than 20% leads to better comprehension. The idea was proposed by German scientist Gerd Gigerenzer, after compilation and comparison of data collected between 1976 and 1997. Origin Automatic encoding Certain information about one's experience is often stored in the memory using an implicit encoding process. Where did you sit last time in class? Do you say the word hello or charisma more? People are very good at answering such questions without actively thinking about it or not knowing how they got that information in the first place. This was the observation that lead to Hasher and Zacks' 1979 study on frequency. Through their research work, Hasher and Zacks found out that information about frequency is stored without the intention of the person. Also, training and feedback does not increase ability to encode frequency. Frequency information was also found to be continually registered in the memory, regardless of age, ability or motivation. The ability to encode frequency also does not decrease with old age, depression or multiple task requirements. They called this characteristic of the frequency encoding as automatic encoding. Infant study Another important evidence for the hypothesis came through the study of infants. In one study, 40 newborn infants were tested for their ability to discriminate between 2 dots versus 3 dots and 4 dots versus 6 dots. Even though infants were able to make the discrimination between 2 versus 3 dots, they were not able to distinguish between 4 versus 6 dots. The tested new born infants were only 21 hours to 144 hours old. Similarly in another study, to test whether infants could recognize numerical correspondences, Starkey et al. designed a series of experiments in which 6 to 8 month old infants were shown pairs of either a display of two objects or a display of three objects. While the displays were still visible, infants heard either two or three drumbeats. Measurement of looking time revealed that the infants looked significantly longer toward the display that matched the number of sounds. The contingency rule Later on, Barbara A. Spellmen from University of Texas describes the performance of humans in determining cause and effects as the contingency rule ΔP, defined as P = P(E\|C) - P(E\|~C) where P(E\|C) is the probability of the effect given the presence of the proposed cause and P(E\|~C) is the probability of the effect given the absence of the proposed cause. Suppose we wish to evaluate the performance of a fertilizer. If the plants bloomed 15 out of 20 times when the fertilizer was used, and only 5 out of 20 plants bloomed in the absence of the fertilizer. In this case P(E\|C) = 15/20 = 0.75 P(E\|~C)= 5/20 = 0.25 ΔP = P
https://en.wikipedia.org/wiki/Phil%20Haralson	Philip H. Haralson (November 3, 1851, Macon, Georgia - March 1934, Atlanta) was an American lawyer. At one time he headed up the Committee on Manufactures and Statistics. and at another went into real estate investment in Cuba. He married Mary E. Morris in 1881. Haralson had his mansion in the Inman Park neighborhood of Atlanta. He was buried in Oakland Cemetery. References Lawyers from Atlanta Lawyers from Macon, Georgia 1851 births 1934 deaths Burials at Oakland Cemetery (Atlanta)
https://en.wikipedia.org/wiki/2011%E2%80%9312%20Saudi%20First%20Division	Teams League table External links Saudi Arabia Football Federation Saudi League Statistics goalzz Saudi First Division League seasons Saudi 2011–12 in Saudi Arabian football
https://en.wikipedia.org/wiki/Immoral%20Mathematics	"Immoral Mathematics" is the second episode of the first season of the American television drama series Hell on Wheels; it aired November 13, 2011 on AMC, and was co-written by series co-creators Tony Gayton and Joe Gayton, and directed by David Von Ancken. Producers of this episode include: Tony Gayton, Joe Gayton, Jeremy Gold, John Shiban, and David Von Ancken. The episode centers on Cullen Bohannon (Anson Mount) fighting for his life as he answers for Johnson's death. Meanwhile, Lily Bell (Dominique McElligott) struggles to survive in the wilderness, Thomas Durant (Colm Meaney) attempts to spin tragedy for political gain, and Joseph Black Moon (Eddie Spears) tracks down the Cheyenne braves responsible for a massacre only to find one of them is his own brother (Gerald Auger). Plot Durant (Colm Meaney) arrives at Robert Bell's camp after the massacre and discovers Bell's body and that of his attacker, in the woods, along with a pocket watch containing a picture of Lily (Dominique McElligott) inside. The survey maps are nowhere to be found. Cullen Bohannon (Anson Mount) gets introduced to a man known as "The Swede", Durant's head of security at Hell on Wheels. The Swede (Christopher Heyerdahl) questions Bohannon about Johnson's murder. Bohannon declines to implicate anyone on his crew, thus taking the fall for the crime. The Swede has Bohannon chained up inside a freight car, where Bohannon sees a loose floorboard nail and tries to pry it out. While doing so, Bohannon thinks back to Meridian and his wife Mary (Kassia Warshawski) stitching needlepoint. Joseph Black Moon (Eddie Spears) finds the Cheyenne braves responsible for the massacre - one of which is his brother, Pawnee Killer (Gerald Auger). Joseph warns Pawnee Killer that his band will be hunted if they capture the white woman (Lily). Pawnee Killer doesn't care and reminds Joseph that he, too, once enjoyed killing and scalping whites. Joseph later finds an ailing Lily cowering from the nearby braves and helps her evade his brother's group. The next morning, The Swede tauntingly eats breakfast in front of Bohannon while describing his past experiences. He was a former bookkeeper, then an Army quartermaster, when taken by Confederates as a prisoner of war. Starving, and set upon by another starving POW who sought to cannibalize him, The Swede began using "immoral mathematics" to control people. Bohannon kicks The Swede's meal to the floor, and The Swede leaves without recovering his utensils. Bohannon uses the spoon to pry up nails in the car's floorboard, and escapes through the hole. Reverend Cole (Tom Noonan) aids Bohannon in eluding The Swede, then instructs Bohannon to beg God's forgiveness before he is caught. Bohannon refuses, stating he does not deserve forgiveness, and leaves. Elam (Common) later hammers the chain free from Bohannon's wrists. Out on the prairie, The Swede finds Durant's caravan. Durant asks him to offer a $100 reward for Lily's return, adding his orders t

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