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https://en.wikipedia.org/wiki/Yuta%20Hashimura | is a former Japanese football player.
Club statistics
References
External links
J. League (#27)
1991 births
Living people
Association football people from Tokyo
Japanese men's footballers
J2 League players
Yokohama FC players
Giravanz Kitakyushu players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Normal%20form%20for%20free%20groups%20and%20free%20product%20of%20groups | In mathematics, particularly in combinatorial group theory, a normal form for a free group over a set of generators or for a free product of groups is a representation of an element by a simpler element, the element being either in the free group or free products of group. In case of free group these simpler elements are reduced words and in the case of free product of groups these are reduced sequences. The precise definitions of these are given below. As it turns out, for a free group and for the free product of groups, there exists a unique normal form i.e each element is representable by a simpler element and this representation is unique. This is the Normal Form Theorem for the free groups and for the free product of groups. The proof here of the Normal Form Theorem follows the idea of Artin and van der Waerden.
Normal Form for Free Groups
Let be a free group with generating set . Each element in is represented by a word where
Definition. A word is called reduced if it contains no string of the form
Definition. A normal form for a free group with generating set is a choice of a reduced word in for each element of .
Normal Form Theorem for Free Groups. A free group has a unique normal form i.e. each element in is represented by a unique reduced word.
Proof. An elementary transformation of a word consists of inserting or deleting a part of the form with . Two words and are equivalent, , if there is a chain of elementary transformations leading from to . This is obviously an equivalence relation on . Let be the set of reduced words. We shall show that each equivalence class of words contains exactly one reduced word. It is clear that each equivalence class contains a reduced word, since successive deletion of parts from any word must lead to a reduced word. It will suffice then to show that distinct reduced words and are not equivalent. For each define a permutation of by setting if is reduced and if . Let be the group of permutations of generated by the . Let be the multiplicative extension of to a map . If then ; moreover is reduced with It follows that if with reduced, then .
Normal Form for Free Products
Let be the free product of groups and . Every element is represented by where for .
Definition. A reduced sequence is a sequence such that for we have and are not in the same factor or . The identity element is represented by the empty set.
Definition. A normal form for a free product of groups is a representation or choice of a reduced sequence for each element in the free product.
Normal Form Theorem for Free Product of Groups. Consider the free product of two groups and . Then the following two equivalent statements hold.
(1) If , where is a reduced sequence, then in
(2) Each element of can be written uniquely as where is a reduced sequence.
Proof
Equivalence
The fact that the second statement implies the first is easy. Now suppose the first statement holds and let:
This |
https://en.wikipedia.org/wiki/Goro%20Kawanami | is a Japanese professional footballer who plays as a goalkeeper for J1 League club Sanfrecce Hiroshima.
Club statistics
.
Honours
Club
Sanfrecce Hiroshima
J.League Cup: 2022
References
External links
Profile at Sanfrecce Hiroshima
1991 births
Living people
Association football people from Ibaraki Prefecture
Japanese men's footballers
J1 League players
J2 League players
Kashiwa Reysol players
FC Gifu players
Tokushima Vortis players
Albirex Niigata players
Vegalta Sendai players
Sanfrecce Hiroshima players
Men's association football goalkeepers |
https://en.wikipedia.org/wiki/Hofstadter%20points | In plane geometry, a Hofstadter point is a special point associated with every plane triangle. In fact there are several Hofstadter points associated with a triangle. All of them are triangle centers. Two of them, the Hofstadter zero-point and Hofstadter one-point, are particularly interesting. They are two transcendental triangle centers. Hofstadter zero-point is the center designated as X(360) and the Hofstafter one-point is the center denoted as X(359) in Clark Kimberling's Encyclopedia of Triangle Centers. The Hofstadter zero-point was discovered by Douglas Hofstadter in 1992.
Hofstadter triangles
Let be a given triangle. Let be a positive real constant.
Rotate the line segment about through an angle towards and let be the line containing this line segment. Next rotate the line segment about through an angle towards . Let be the line containing this line segment. Let the lines and intersect at . In a similar way the points and are constructed. The triangle whose vertices are is the Hofstadter -triangle (or, the -Hofstadter triangle) of .
Special case
The Hofstadter 1/3-triangle of triangle is the first Morley's triangle of . Morley's triangle is always an equilateral triangle.
The Hofstadter 1/2-triangle is simply the incentre of the triangle.
Trilinear coordinates of the vertices of Hofstadter triangles
The trilinear coordinates of the vertices of the Hofstadter -triangle are given below:
Hofstadter points
For a positive real constant , let be the Hofstadter -triangle of triangle . Then the lines are concurrent. The point of concurrence is the Hofstdter -point of .
Trilinear coordinates of Hofstadter -point
The trilinear coordinates of the Hofstadter -point are given below.
Hofstadter zero- and one-points
The trilinear coordinates of these points cannot be obtained by plugging in the values 0 and 1 for in the expressions for the trilinear coordinates for the Hofstdter -point.
The Hofstadter zero-point is the limit of the Hofstadter -point as approaches zero; thus, the trilinear coordinates of Hofstadter zero-point are derived as follows:
Since
The Hofstadter one-point is the limit of the Hofstadter -point as approaches one; thus, the trilinear coordinates of the Hofstadter one-point are derived as follows:
Since
References
Triangle centers |
https://en.wikipedia.org/wiki/Hall%20plane | In mathematics, a Hall plane is a non-Desarguesian projective plane constructed by Marshall Hall Jr. (1943). There are examples of order p2n for every prime p and every positive integer n provided p2n > 4.
Algebraic construction via Hall systems
The original construction of Hall planes was based on the Hall quasifield (also called a Hall system), H of order for p a prime. The creation of the plane from the quasifield follows the standard construction (see quasifield for details).
To build a Hall quasifield, start with a Galois field, for p a prime and a quadratic irreducible polynomial over F. Extend , a two-dimensional vector space over F, to a quasifield by defining a multiplication on the vectors by when and otherwise.
Writing the elements of H in terms of a basis <1, λ>, that is, identifying (x,y) with x + λy as x and y vary over F, we can identify the elements of F as the ordered pairs (x, 0), i.e. x + λ0. The properties of the defined multiplication which turn the right vector space H into a quasifield are:
every element α of H not in F satisfies the quadratic equation f(α) = 0;
F is in the kernel of H (meaning that (α + β)c = αc + βc, and (αβ)c = α(βc) for all α, β in H and all c in F); and
every element of F commutes (multiplicatively) with all the elements of H.
Derivation
Another construction that produces Hall planes is obtained by applying derivation to Desarguesian planes.
A process, due to T. G. Ostrom, which replaces certain sets of lines in a projective plane by alternate sets in such a way that the new structure is still a projective plane is called derivation. We give the details of this process. Start with a projective plane of order and designate one line as its line at infinity. Let A be the affine plane . A set D of points of is called a derivation set if for every pair of distinct points X and Y of A which determine a line meeting in a point of D, there is a Baer subplane containing X, Y and D (we say that such Baer subplanes belong to D.) Define a new affine plane as follows: The points of are the points of A. The lines of are the lines of which do not meet at a point of D (restricted to A) and the Baer subplanes that belong to D (restricted to A). The set is an affine plane of order and it, or its projective completion, is called a derived plane.
Properties
Hall planes are translation planes.
All finite Hall planes of the same order are isomorphic.
Hall planes are not self-dual.
All finite Hall planes contain subplanes of order 2 (Fano subplanes).
All finite Hall planes contain subplanes of order different from 2.
Hall planes are André planes.
The Hall plane of order 9
The Hall plane of order 9 is the smallest Hall plane, and one of the three smallest examples of a finite non-Desarguesian projective plane, along with its dual and the Hughes plane of order 9.
Construction
While usually constructed in the same way as other Hall planes, the Hall plane of order 9 was actually |
https://en.wikipedia.org/wiki/Power%20diagram | In computational geometry, a power diagram, also called a Laguerre–Voronoi diagram, Dirichlet cell complex, radical Voronoi tesselation or a sectional Dirichlet tesselation, is a partition of the Euclidean plane into polygonal cells defined from a set of circles. The cell for a given circle C consists of all the points for which the power distance to C is smaller than the power distance to the other circles. The power diagram is a form of generalized Voronoi diagram, and coincides with the Voronoi diagram of the circle centers in the case that all the circles have equal radii.
Definition
If C is a circle and P is a point outside C, then the power of P with respect to C is the square of the length of a line segment from P to a point T of tangency with C. Equivalently, if P has distance d from the center of the circle, and the circle has radius r, then (by the Pythagorean theorem) the power is d2 − r2. The same formula d2 − r2 may be extended to all points in the plane, regardless of whether they are inside or outside of C: points on C have zero power, and points inside C have negative power.
The power diagram of a set of n circles Ci is a partition of the plane into n regions Ri (called cells), such that a point P belongs to Ri whenever circle Ci is the circle minimizing the power of P.
In the case n = 2, the power diagram consists of two halfplanes, separated by a line called the radical axis or chordale of the two circles. Along the radical axis, both circles have equal power. More generally, in any power diagram, each cell Ri is a convex polygon, the intersection of the halfspaces bounded by the radical axes of circle Ci with each other circle. Triples of cells meet at vertices of the diagram, which are the radical centers of the three circles whose cells meet at the vertex.
Related constructions
The power diagram may be seen as a weighted form of the Voronoi diagram of a set of point sites, a partition of the plane into cells within which one of the sites is closer than all the other sites. Other forms of weighted Voronoi diagram include the additively weighted Voronoi diagram, in which each site has a weight that is added to its distance before comparing it to the distances to the other sites, and the multiplicatively weighted Voronoi diagram, in which the weight of a site is multiplied by its distance before comparing it to the distances to the other sites. In contrast, in the power diagram, we may view each circle center as a site, and each circle's squared radius as a weight that is subtracted from the squared Euclidean distance before comparing it to other squared distances. In the case that all the circle radii are equal, this subtraction makes no difference to the comparison, and the power diagram coincides with the Voronoi diagram.
A planar power diagram may also be interpreted as a planar cross-section of an unweighted three-dimensional Voronoi diagram. In this interpretation, the set of circle centers in the cross-section plane |
https://en.wikipedia.org/wiki/Coincidence%20%28disambiguation%29 | A coincidence is the occurrence of unrelated events in close proximity of space or time.
Coincidence may also refer to:
Coincidence, mathematics term for a point tow mappings' domains sharing an image point; see Coincidence point
Coincidence, scientific term for an instance of rays of light striking a surface at the same point and at the same time
Coincidence, term for physical road bearing more than one designation; see Concurrency
Films
Coincidence, alternate English title for Blind Chance, the 1987 Polish film Przypadek by Krzysztof Kieślowski
Coincidence, English title for the 1958 film Jogajog, based on the novel Jogajog
Coincidence, English title for the 1969 Bollywood film Ittefaq
Coincidence (1915 film), a short film distributed by General Film Company
Coincidence (1921 film), an American silent film directed by Chet Withey and starring Robert Harron
Coincidences (film), a 1947 French film directed by Serge Debecque
See also
Concurrency (disambiguation) |
https://en.wikipedia.org/wiki/Rosenfeld%2C%20Manitoba | Rosenfeld is a local urban district within the Rural Municipality of Rhineland in the Canadian province of Manitoba. It is recognized as a designated place by Statistics Canada.
History
Rosenfeld was founded as a train station in 1882. It achieved unincorporated village status in 1949 and then local urban district status in 1996.
Demographics
As a designated place in the 2021 Census of Population conducted by Statistics Canada, Rosenfeld had a population of 318 living in 97 of its 108 total private dwellings, a change of from its 2016 population of 338. With a land area of , it had a population density of in 2021.
See also
List of communities in Manitoba
List of designated places in Manitoba
List of local urban districts in Manitoba
References
Designated places in Manitoba
Local urban districts in Manitoba |
https://en.wikipedia.org/wiki/Swan%20Lake%2C%20Manitoba | Swan Lake is a local urban district within the Municipality of Lorne in the Canadian province of Manitoba. It is recognized as a designated place by Statistics Canada.
Demographics
As a designated place in the 2021 Census of Population conducted by Statistics Canada, Swan Lake had a population of 276 living in 132 of its 149 total private dwellings, a change of from its 2016 population of 255. With a land area of , it had a population density of in 2021.
See also
List of communities in Manitoba
List of designated places in Manitoba
List of local urban districts in Manitoba
References
Designated places in Manitoba
Local urban districts in Manitoba |
https://en.wikipedia.org/wiki/Mordellic%20variety | In mathematics, a Mordellic variety is an algebraic variety which has only finitely many points in any finitely generated field. The terminology was introduced by Serge Lang to enunciate a range of conjectures linking the geometry of varieties to their Diophantine properties.
Formal definition
Formally, let X be a variety defined over an algebraically closed field of characteristic zero: hence X is defined over a finitely generated field E. If the set of points X(F) is finite for any finitely generated field extension F of E, then X is Mordellic.
Lang's conjectures
The special set for a projective variety V is the Zariski closure of the union of the images of all non-trivial maps from algebraic groups into V. Lang conjectured that the complement of the special set is Mordellic.
A variety is algebraically hyperbolic if the special set is empty. Lang conjectured that a variety X is Mordellic if and only if X is algebraically hyperbolic and that this is in turn equivalent to X being pseudo-canonical.
For a complex algebraic variety X we similarly define the analytic special or exceptional set as the Zariski closure of the union of images of non-trivial holomorphic maps from C to X. Brody's definition of a hyperbolic variety is that there are no such maps. Again, Lang conjectured that a hyperbolic variety is Mordellic and more generally that the complement of the analytic special set is Mordellic.
References
Diophantine geometry
Algebraic varieties |
https://en.wikipedia.org/wiki/Tower%20Road%2C%20Nova%20Scotia | Tower Road is a designated place within the Cape Breton Regional Municipality in Nova Scotia, Canada.
Demographics
In the 2021 Census of Population conducted by Statistics Canada, Tower Road had a population of 295 living in 128 of its 135 total private dwellings, a change of from its 2016 population of 272. With a land area of , it had a population density of in 2021.
References
Communities in Cape Breton County
Designated places in Nova Scotia |
https://en.wikipedia.org/wiki/Tsukasa%20Ozawa | is a Japanese football player for FC Imabari.
Club statistics
Updated to 20 February 2017.
References
External links
Profile at FC Imabari
1988 births
Living people
University of Tsukuba alumni
People from Odawara
Association football people from Kanagawa Prefecture
Japanese men's footballers
J2 League players
Japan Football League players
Mito HollyHock players
FC Imabari players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Kenji%20Arabori | Kenji Arabori (荒堀 謙次, born July 31, 1988) is a former Japanese football player.
Club statistics
Updated to 23 February 2020.
References
External links
Profile at Kamatamare Sanuki
1988 births
Living people
Doshisha University alumni
Association football people from Shiga Prefecture
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Yokohama FC players
Tochigi SC players
Shonan Bellmare players
Montedio Yamagata players
Kamatamare Sanuki players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Tomoyuki%20Suzuki | Tomoyuki Suzuki (鈴木 智幸, born December 20, 1985) is a Japanese football player for Iwate Grulla Morioka.
Club statistics
Updated to end of 2018 season.
References
External links
Profile at Matsumoto Yamaga
1985 births
Living people
Kokushikan University alumni
Japanese men's footballers
J2 League players
J3 League players
Tokyo Verdy players
Tochigi SC players
Matsumoto Yamaga FC players
Iwate Grulla Morioka players
Men's association football goalkeepers
Association football people from Saitama (city) |
https://en.wikipedia.org/wiki/Satoru%20Hoshino | Satoru Hoshino (星野 悟, born February 4, 1989) is a Japanese football player.
Club statistics
Updated to 23 February 2017.
References
External links
1989 births
Living people
Chukyo University alumni
Association football people from Gunma Prefecture
Japanese men's footballers
J2 League players
J3 League players
Thespakusatsu Gunma players
FC Machida Zelvia players
Men's association football defenders |
https://en.wikipedia.org/wiki/Hiroto%20Yamamoto | is a former Japanese football player.
Club statistics
Updated to 23 February 2017.
References
External links
1988 births
Living people
Nihon University alumni
Association football people from Ibaraki Prefecture
Japanese men's footballers
J2 League players
J3 League players
Japan Football League players
Thespakusatsu Gunma players
Kagoshima United FC players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Ryota%20Kajikawa | Ryota Kajikawa (梶川 諒太, born April 17, 1989) is a Japanese football player for Tokyo Verdy.
Club statistics
Updated to end of 2018 season.
References
External links
Profile at Tokyo Verdy
Profile at V-Varen Nagasaki
1989 births
Living people
Kwansei Gakuin University alumni
Association football people from Hyōgo Prefecture
Japanese men's footballers
J1 League players
J2 League players
Tokyo Verdy players
Shonan Bellmare players
V-Varen Nagasaki players
Tokushima Vortis players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Ryuji%20Sugimoto | Ryuji Sugimoto (杉本 竜士, born 1 June 1993) is a Japanese football player for Thespakusatsu Gunma, on loan from Tokyo Verdy.
Career statistics
Club
.
References
External links
Profile at Nagoya Grampus
1993 births
Living people
Association football people from Tokyo Metropolis
People from Fuchū, Tokyo
Japanese men's footballers
J1 League players
J2 League players
Japan Football League players
Tokyo Verdy players
FC Machida Zelvia players
Nagoya Grampus players
Tokushima Vortis players
Yokohama F. Marinos players
Yokohama FC players
Men's association football forwards |
https://en.wikipedia.org/wiki/Kensuke%20Sato | is a Japanese football player for Yokohama FC.
Club statistics
Updated to 1 March 2019.
References
External links
Profile at Yokohama FC
1989 births
Living people
Chuo University alumni
Association football people from Saitama Prefecture
Japanese men's footballers
J1 League players
J2 League players
Yokohama FC players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Park%20Tae-hong | Park Tae-Hong (; born March 25, 1991) is a South Korean football player who currently plays for K3 League side Busan Transportation Corporation FC.
Club statistics
References
External links
1991 births
Living people
Men's association football defenders
South Korean men's footballers
South Korean expatriate men's footballers
J2 League players
K League 2 players
Yokohama FC players
Kataller Toyama players
Daegu FC players
Busan IPark players
Gyeongnam FC players
Expatriate men's footballers in Japan
South Korean expatriate sportspeople in Japan
Hong Kong First Division League players
Expatriate men's footballers in Hong Kong
South Korean expatriate sportspeople in Hong Kong
Metro Gallery FC players |
https://en.wikipedia.org/wiki/Ken%20Iwao | Ken Iwao (岩尾 憲, born April 18, 1988) is a Japanese professional footballer who plays as a defensive midfielder for J1 League club Urawa Red Diamonds, on loan from Tokushima Vortis.
Club statistics
Honours
Club
Urawa Red Diamonds
Japanese Super Cup: 2022
AFC Champions League: 2022
References
External links
Profile at Tokushima Vortis
Profile at Urawa Reds
1988 births
Living people
Nippon Sport Science University alumni
Association football people from Gunma Prefecture
Japanese men's footballers
J1 League players
J2 League players
Shonan Bellmare players
Mito HollyHock players
Tokushima Vortis players
Urawa Red Diamonds players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Yuzo%20Iwakami | Yuzo Iwakami (岩上 祐三, born July 28, 1989) is a Japanese football player for Thespakusatsu Gunma.
Club statistics
Updated to 24 February 2019.
References
External links
Profile at Omiya Ardija
Profile at Matsumoto Yamaga
1989 births
Living people
Tokai University alumni
Association football people from Ibaraki Prefecture
Japanese men's footballers
J1 League players
J2 League players
Shonan Bellmare players
Matsumoto Yamaga FC players
Omiya Ardija players
Thespakusatsu Gunma players
Men's association football defenders
Men's association football midfielders |
https://en.wikipedia.org/wiki/Kaoru%20Takayama | is a Japanese football player for SC Sagamihara.
Club statistics
Updated to 25 February 2019.
References
External links
Profile at Shonan Bellmare
1988 births
Living people
Senshu University alumni
Association football people from Kanagawa Prefecture
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Shonan Bellmare players
Kashiwa Reysol players
Oita Trinita players
SC Sagamihara players
Men's association football forwards |
https://en.wikipedia.org/wiki/Takuya%20Yoshikawa | is a Japanese football player.
Club statistics
Updated to 23 February 2016.
References
External links
1988 births
Living people
Kyoto Sangyo University alumni
Association football people from Shiga Prefecture
Japanese men's footballers
J2 League players
J3 League players
Japan Football League players
Kataller Toyama players
Zweigen Kanazawa players
Men's association football defenders |
https://en.wikipedia.org/wiki/Yuki%20Matsubara | is a Japanese football player.
Club statistics
Updated to 23 February 2020.
References
External links
Profile at Nagano Parceiro
1988 births
Living people
Kindai University alumni
Association football people from Wakayama Prefecture
Japanese men's footballers
J2 League players
J3 League players
Japan Football League players
Kataller Toyama players
AC Nagano Parceiro players
Men's association football defenders |
https://en.wikipedia.org/wiki/Akihiro%20Noda | is a Japanese football player.
Club statistics
Updated to 14 February 2017.
References
External links
Fukushima United FC
1988 births
Living people
Waseda University alumni
Association football people from Nagasaki Prefecture
Japanese men's footballers
J2 League players
J3 League players
Japan Football League players
FC Gifu players
Fukushima United FC players
Men's association football fullbacks |
https://en.wikipedia.org/wiki/Hidemi%20Jinushizono | is a Japanese former football player.
Career
On 4 January 2023, Jinushizono announcement officially retirement from football after 12 years career at professional.
Club statistics
Updated to 20 February 2015.
References
External links
Profile at FC Maruyasu Okazaki
1989 births
Living people
Tokai Gakuen University alumni
Association football people from Kagoshima Prefecture
Japanese men's footballers
J2 League players
Japan Football League players
FC Gifu players
FC Maruyasu Okazaki players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Bruno%20%28footballer%2C%20born%201989%29 | Bruno Moreira Silva (born November 12, 1989) is a Brazilian football player.
Club statistics
References
External links
1989 births
Living people
Brazilian men's footballers
J2 League players
FC Gifu players
Brazilian expatriate men's footballers
Expatriate men's footballers in Japan
Men's association football midfielders |
https://en.wikipedia.org/wiki/Takashi%20Uchino%20%28footballer%2C%20born%201988%29 | Takashi Uchino (内野 貴志, born February 15, 1988) is a Japanese football player.
Club statistics
Updated to 23 February 2020.
References
External links
Profile at Nagano Parceiro
1988 births
Living people
Biwako Seikei Sport College alumni
Association football people from Shiga Prefecture
Japanese men's footballers
J2 League players
J3 League players
Japan Football League players
Kyoto Sanga FC players
AC Nagano Parceiro players
Reilac Shiga FC 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/Yohei%20Naito | is a Japanese football player.
Club statistics
Updated to 23 February 2019.
References
External links
Profile at Giravanz Kitakyushu
1988 births
Living people
Ritsumeikan University alumni
Association football people from Kanagawa Prefecture
Japanese men's footballers
J2 League players
J3 League players
Kyoto Sanga FC players
Giravanz Kitakyushu players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Noriaki%20Sanenobu | is a former Japanese football player and is currently manager of FC Kagura Shimane
Club statistics
Updated to 22 February 2014.
References
External links
J. League (#10)
1980 births
Living people
Tokyo University of Agriculture alumni
Association football people from Hiroshima Prefecture
Japanese men's footballers
J2 League players
Japan Football League players
Gainare Tottori players
FC Kagura Shimane players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Kim%20Sun-min | Kim Sun-min (; born December 12, 1991) is a South Korean football player who plays for Suwon FC.
Club statistics
References
External links
1991 births
Living people
Sportspeople from Suwon
Footballers from Gyeonggi Province
Men's association football midfielders
South Korean men's footballers
South Korean expatriate men's footballers
J2 League players
Korea National League players
K League 1 players
K League 2 players
Gainare Tottori players
Ulsan Hyundai Mipo Dockyard FC players
Ulsan Hyundai FC players
FC Anyang players
Daejeon Hana Citizen players
Daegu FC players
Asan Mugunghwa FC players
Seoul E-Land FC players
Suwon FC players
Expatriate men's footballers in Japan
South Korean expatriate sportspeople in Japan |
https://en.wikipedia.org/wiki/Eijiro%20Mori | is a former Japanese football player.
Club statistics
Updated to 2 February 2018.
1Includes JFL/J2 Playoff.
References
External links
Profile at Grulla Morioka
Twitter account
1986 births
Living people
Juntendo University alumni
Association football people from Kanagawa Prefecture
Japanese men's footballers
J2 League players
J3 League players
Japan Football League players
Gainare Tottori players
Iwate Grulla Morioka players
Men's association football defenders |
https://en.wikipedia.org/wiki/Katsunari%20Mizumoto | Katsunari Mizumoto (水本勝成 | born February 19, 1990) is a Japanese football player for Kagoshima United FC.
Club statistics
Updated to 23 February 2018.
References
External links
Profile at Kagoshima United FC
1990 births
Living people
Association football people from Kumamoto Prefecture
Japanese men's footballers
J2 League players
J3 League players
Japan Football League players
Gainare Tottori players
Kagoshima United FC players
Men's association football defenders |
https://en.wikipedia.org/wiki/Akito%20Miura | is a former Japanese football player.
Club statistics
References
External links
1987 births
Living people
Juntendo University alumni
Association football people from Osaka Prefecture
Japanese men's footballers
J1 League players
J2 League players
Japan Football League players
Yokohama F. Marinos players
Gainare Tottori players
FC Ryukyu players
Renofa Yamaguchi FC players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Pseudo-canonical%20variety | In mathematics, a pseudo-canonical variety is an algebraic variety of "general type".
Formal definition
Formally, a variety X is pseudo-canonical if the canonical class is pseudo-ample.
Results
For a non-singular projective variety, a result of Kodaira states that this is equivalent to a divisor in the class being the sum of an ample divisor and an effective divisor.
See also
Bombieri–Lang conjecture
References
Algebraic varieties |
https://en.wikipedia.org/wiki/Kojiro%20Shinohara | Kojiro Shinohara (篠原 弘次郎, born July 20, 1991) is a Japanese football player for Matsumoto Yamaga FC.
Club statistics
Updated to end of 2018 season.
References
External links
Profile at Avispa Fukuoka
1991 births
Living people
Association football people from Saga Prefecture
Japanese men's footballers
J2 League players
J3 League players
Fagiano Okayama players
Roasso Kumamoto players
Avispa Fukuoka players
Matsumoto Yamaga FC players
Men's association football defenders |
https://en.wikipedia.org/wiki/Takanori%20Maeno | is a Japanese football player for Ehime FC.
Career statistics
Club
Updated to end of 2018 season.
1Includes Suruga Bank Championship.
Honours
Club
Kashima Antlers
Suruga Bank Championship (1) : 2013
References
External links
Profile at Albirex Niigata
Profile at Ehime FC
1988 births
Living people
Ritsumeikan University alumni
Association football people from Ehime Prefecture
Japanese men's footballers
J1 League players
J2 League players
Ehime FC players
Kashima Antlers players
Albirex Niigata players
Men's association football defenders
Sportspeople from Matsuyama, Ehime |
https://en.wikipedia.org/wiki/Hiroshi%20Azuma | is a Japanese football player who plays for AC Nagano Parceiro in J3 League.
Club statistics
Updated to January 1st, 2022.
References
External links
Profile at Nagano Parceiro
1987 births
Living people
Hannan University alumni
Association football people from Miyagi Prefecture
Japanese men's footballers
J2 League players
J3 League players
Ehime FC players
V-Varen Nagasaki players
AC Nagano Parceiro players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Yusei%20Ogasawara | is a Japanese football player. He plays for Nongbua Pitchaya in the Thai League 2.
Club statistics
References
External links
J. League (#23)
1988 births
Living people
Kyoto Sangyo University alumni
Association football people from Ehime Prefecture
Japanese men's footballers
J2 League players
Ehime FC players
V-Varen Nagasaki players
Yusei Ogasawara
Men's association football midfielders |
https://en.wikipedia.org/wiki/Kim%20Jong-pil%20%28footballer%2C%20born%201992%29 | Kim Jong-pil (; born March 9, 1992) is a South Korean football player who plays for Gyeongnam FC.
Club statistics
Updated to 23 February 2018.
References
External links
Profile at Tokushima Vortis
1992 births
Living people
Men's association football midfielders
South Korean men's footballers
South Korean expatriate men's footballers
J1 League players
J2 League players
Giravanz Kitakyushu players
Tokyo Verdy players
Shonan Bellmare players
Kim Jong-pil
Tokushima Vortis players
Gyeongnam FC players
Expatriate men's footballers in Japan
South Korean expatriate sportspeople in Japan
Expatriate men's footballers in Thailand
Footballers from Seoul |
https://en.wikipedia.org/wiki/Shunichi%20Tanaka | is a former Japanese football player.
Club statistics
References
External links
J. League (#26)
1987 births
Living people
Osaka Kyoiku University alumni
Association football people from Osaka Prefecture
Japanese men's footballers
J2 League players
Roasso Kumamoto players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Hayato%20Nakama | is a Japanese professional footballer who plays as an attacking midfielder for club Kashima Antlers.
Club statistics
References
External links
Profile at Kashima Antlers
1992 births
Living people
Association football people from Gunma Prefecture
Japanese men's footballers
J1 League players
J2 League players
Roasso Kumamoto players
Kamatamare Sanuki players
Fagiano Okayama players
Kashiwa Reysol players
Kashima Antlers players
Men's association football forwards |
https://en.wikipedia.org/wiki/Yu%20Yasukawa | is a Japanese footballer.
Club statistics
Updated to 23 February 2018.
1Includes Promotion and Relegation Playoffs.
References
External links
Profile at Matsumoto Yamaga
1988 births
Living people
Doshisha University alumni
Japanese men's footballers
J1 League players
J2 League players
Oita Trinita players
Matsumoto Yamaga FC players
Men's association football defenders
Association football people from Fukuoka (city) |
https://en.wikipedia.org/wiki/Martin%20Gardner%20bibliography | In a publishing career spanning 80 years (1930–2010), popular mathematics and science writer Martin Gardner (1914–2010) authored or edited over 100 books and countless articles, columns and reviews.
All Gardner's works were non-fiction except for two novels — The Flight of Peter Fromm (1973) and Visitors from Oz (1998) — and two collections of short pieces — The Magic Numbers of Dr. Matrix (1967, 1985) and The No-Sided Professor (1987).
Books
Original works
Match-ic (1936), Illus. by Nelson C. Hahne;Ireland Magic Company.
Here's New Magic: An Array of New and Original Magic Secrets (1937) "by Joe Berg" [actually ghostwritten by Gardner], Illus. by Nelson C. Hahne; Chicago: Privately printed.
12 Tricks with a Borrowed Deck (1940), Ireland Magic Company, illust. by Harlan Tarbell, intro. by Paul Rosini.
After the Dessert (1941), Max Holden, illust. by Nelson Hahne.
Cut the Cards (1942), Max Holden, illust. by Nelson Hahne.
Over the Coffee Cups (1949), Tulsa: Montandon Magic, illust. by the author (close-up magic, including "dinner-table tricks and gags")
In the Name of Science: An Entertaining Survey of the High Priests and Cultists of Science, Past and Present (1952), G. P. Putnam's Sons
Republished (revised & expanded) as Fads and Fallacies in the Name of Science (1957), Mineola, New York: Dover Publications; .
Mathematics, Magic, and Mystery (1956), Mineola, New York: Dover Publications, .
Logic Machines and Diagrams (1958), McGraw-Hill: New York
Republished (1968) as Logic Machines, Diagrams, and Boolean Algebra; Dover Publications, Inc.
2nd edition (1983) as Logic Machines and Diagrams with introduction by Donald Michie, University of Chicago Press.
Mathematical Puzzles (1961), New York: Thomas Y. Crowell (Illust. by Anthony Ravielli).
Reprinted w/corrections in 1986 as Entertaining Mathematical Puzzles, Dover; .
Relativity for the Million (1962); New York: MacMillan Company (Illust. by Anthony Ravielli).
Revised/updated 1976 as The Relativity Explosion New York: Vintage Books, .
Revised/enlarged 1997 as Relativity Simply Explained, New York: Dover; .
The Ambidextrous Universe: Mirror Asymmetry and Time-Reversed Worlds (1964)
2nd edition, 1969.
3rd edition, 1990 as The New Ambidextrous Universe: Symmetry and Asymmetry from Mirror Reflections to Superstrings; W.H. Freeman & Company.
3rd edition, Revised, 2005, Dover; .
Never Make Fun of a Turtle, My Son (1969), Simon & Schuster (poems; illust. by John Alcorn)
The Flight of Peter Fromm (1973), Los Altos, California: William Kaufmann, Inc. Prometheus Books (novel).
Confessions of a Psychic: The Secret Notebooks of Uriah Fuller (1975), Teaneck, New Jersey: Karl Fulves.
Aha! Insight (1978), W.H. Freeman & Company;
Further Confessions of a Psychic: The Secret Notebooks of Uriah Fuller (1980), Teaneck, New Jersey: Karl Fulves; 70 pp.
Aha! Gotcha: Paradoxes to Puzzle and Delight (1982), (Series: Tools for Transformation); W.H. Freeman & Company;
The Whys of a Philosophical Scrivener (1983; |
https://en.wikipedia.org/wiki/Nevanlinna%20invariant | In mathematics, the Nevanlinna invariant of an ample divisor D on a normal projective variety X is a real number connected with the rate of growth of the number of rational points on the variety with respect to the embedding defined by the divisor. The concept is named after Rolf Nevanlinna.
Formal definition
Formally, α(D) is the infimum of the rational numbers r such that is in the closed real cone of effective divisors in the Néron–Severi group of X. If α is negative, then X is pseudo-canonical. It is expected that α(D) is always a rational number.
Connection with height zeta function
The Nevanlinna invariant has similar formal properties to the abscissa of convergence of the height zeta function and it is conjectured that they are essentially the same. More precisely, Batyrev–Manin conjectured the following. Let X be a projective variety over a number field K with ample divisor D giving rise to an embedding and height function H, and let U denote a Xariski open subset of X. Let α = α(D) be the Nevanlinna invariant of D and β the abscissa of convergence of Z(U, H; s). Then for every ε > 0 there is a U such that β < α + ε: in the opposite direction, if α > 0 then α = β for all sufficiently large fields K and sufficiently small U.
References
Diophantine geometry
Geometry of divisors |
https://en.wikipedia.org/wiki/Inger%20Jalakas | Inger Marianne Elisabeth Jalakas (born 15 December 1951) is a Swedish author and journalist. She studied mathematics and Earth science at the University of Gothenburg 1975–76 and 1978–79 she studied at Journalisthögskolan i Göteborg.
Selected bibliography
Non-fiction books
1980 – Smockor och smek: hotande läsning: om ungdomstidningar
1995 – Bara barn: om sexturism och slaveri
1997 – Jävlar anamma, mamma!: handbok i överlevnad för ensamma mammor
2000 – Den nyttiga nosen
2003 – Från utbränd till nytänd
2005 – Agility: från start till mål
2007 – Nördsyndromet: allt du behöver veta om Aspergers syndrom
2010 – Sex, kärlek & Aspergers syndrom: med kärleksskola för aspergare
Novels/short stories
1999 – Lustmord (short stories, together with Ulla Trenter)
2000 – Krokodilens leende
2004 – Svarta diamanter: elva berättelser om liv och död (anthology, together with among Carina Burman)
Detective novels about Margareta Nordin
2001 – Borde vetat bättre
2005 – Sinne utan svek
2006 – Den ryske mannen
2007 – Ur min aska
2009 – Hat
Children's books
2003 – Min modiga mormor (illustrator: Helena Bergendahl)
2005 – Min modiga mormor och noshörningen Nofu (illustrator: Helena Bergendahl)
2006 – Min modiga mormor och den dansande elefanten (illustrator: Helena Bergendahl)
References
External links
Official website
bibliography
1951 births
Living people
People from Nässjö Municipality
Swedish women writers
Swedish crime fiction writers
Writers from Småland
Swedish-language writers
Swedish children's writers
Swedish journalists
Women crime fiction writers |
https://en.wikipedia.org/wiki/Height%20zeta%20function | In mathematics, the height zeta function of an algebraic variety or more generally a subset of a variety encodes the distribution of points of given height.
Definition
If S is a set with height function H, such that there are only finitely many elements of bounded height, define a counting function
and a zeta function
Properties
If Z has abscissa of convergence β and there is a constant c such that N has rate of growth
then a version of the Wiener–Ikehara theorem holds: Z has a t-fold pole at s = β with residue c.a.Γ(t).
The abscissa of convergence has similar formal properties to the Nevanlinna invariant and it is conjectured that they are essentially the same. More precisely, Batyrev–Manin conjectured the following. Let X be a projective variety over a number field K with ample divisor D giving rise to an embedding and height function H, and let U denote a Zariski-open subset of X. Let α = α(D) be the Nevanlinna invariant of D and β the abscissa of convergence of Z(U, H; s). Then for every ε > 0 there is a U such that β < α + ε: in the opposite direction, if α > 0 then α = β for all sufficiently large fields K and sufficiently small U.
References
Diophantine geometry
Geometry of divisors |
https://en.wikipedia.org/wiki/Variable%20geometry%20turbomachine | A variable geometry turbomachine uses movable vanes to optimize its efficiency at different operating conditions. This article refers to movable vanes as used in liquid pumps and turbocharger turbines. It does not cover the widespread use of movable vanes in gas turbine compressors.
Performance characteristics of turbomachines
If all fluid velocities at corresponding points within the turbomachine are in the same direction and proportional to the blade speed, then the operating condition of a turbomachine at two different rotational speeds will be dynamically similar.
If two points, each on dissimilar head-flow characteristics curve, represent similar dynamic operation of the turbo machine, then the non-dimensional variables (ignoring Reynolds number effects) will have same values.
Head coefficient
Efficiency
Power coefficient
Where,
is speed of rotation.
is flow rate.
is impeller diameter.
Thus non-dimensional representation is highly advantageous for converging to single performance curve that would otherwise result in multiple curves if plotted dimensionally.
Figure 1 shows head characteristics of centrifugal pump versus flow coefficient. Within the normal operating range of this pump, , the head characteristic curves approximately coincide for different values of speed rev/min) and little scatter appears may be due to the effect of Reynolds number. For smaller flow co-efficient, Q/(ND3) < 0.025, the flow became unsteady but dynamically similar conditions still appear i.e. head characteristic curves still coincides for different values of speed. But at high flow rates deviation from the single-curve are noticed for higher values of speed. This effect is due to cavitation, a high speed phenomenon of hydraulic machines caused by the release of vapour bubbles at low pressures.
Thus during off-design operating conditions, i.e. Q/(ND3) < 0.03 and Q/(ND3) > 0.06, the flow become unsteady and cavitations occurs . So to avoid cavitation increase efficiency at high flow rates we resort to Variable Geometry Turbomachine.
Fixed geometry turbomachine
Fixed geometry machines are designed to operate at maximum efficiency condition. The efficiency of a fixed geometry machine depends on the flow coefficient and Reynolds number. For a constant Reynolds number as flow coefficient increases, efficiency also increases, reaches a maximum value and then decreases. Thus off-design operation is completely inefficient and may result in cavitation at higher flow rates.
Variable geometry turbomachine
A variable geometry turbomachine uses movable vanes to regulate the flow. Vane angles are varied using cams driven by servo motor (actuator). In large installations involving many thousands of kilowatts and where operating conditions fluctuate, sophisticated systems of control are incorporated. Thus variable geometry turbomachine offer a better match of efficiency with changing flow conditions.
Figure 2 describes the envelope of optimum efficiency for a var |
https://en.wikipedia.org/wiki/Ken%20Riley%20%28physicist%29 | Ken Riley is a physicist.
Career
Ken Riley read mathematics at the University of Cambridge and proceeded to a Ph.D. there in theoretical and experimental nuclear physics.
He became a research associate in elementary particle physics in Brookhaven, and then, having taken up lectureship at the Cavendish Laboratory, Cambridge, continued this research at the Rutherford Laboratory and Stanford; in particular he was involved in the experimental discovery of a number of the early baryonic resonances.
As well as having been Senior Tutor at Clare College, where he has taught physics and mathematics for over 40 years, he has served on many committees concerned with the teaching and examining of these subjects at all levels of tertiary and undergraduate education.
He is also one of the authors of 200 Puzzling Physics Problems and Mathematical Methods for Physics and Engineering.
References
British physicists
Living people
Year of birth missing (living people) |
https://en.wikipedia.org/wiki/Superelliptic%20curve | In mathematics, a superelliptic curve is an algebraic curve defined by an equation of the form
where is an integer and f is a polynomial of degree with coefficients in a field ; more precisely, it is the smooth projective curve whose function field defined by this equation.
The case and is an elliptic curve, the case and is a hyperelliptic curve, and the case and is an example of a trigonal curve.
Some authors impose additional restrictions, for example, that the integer should not be divisible by the characteristic of , that the polynomial should be square free, that the integers m and d should be coprime, or some combination of these.
The Diophantine problem of finding integer points on a superelliptic curve can be solved by a method similar to one used for the resolution of hyperelliptic equations: a Siegel identity is used to reduce to a Thue equation.
Definition
More generally, a superelliptic curve is a cyclic branched covering
of the projective line of degree coprime to the characteristic of the field of definition. The degree of the covering map is also referred to as the degree of the curve. By cyclic covering we mean that the Galois group of the covering (i.e., the corresponding function field extension) is cyclic.
The fundamental theorem of Kummer theory implies that a superelliptic curve of degree defined over a field has an affine model given by an equation
for some polynomial of degree with each root having order , provided that has a point defined over , that is, if the set of -rational points of is not empty. For example, this is always the case when is algebraically closed. In particular, function field extension is a Kummer extension.
Ramification
Let be a superelliptic curve defined over an algebraically closed field , and denote the set of roots of in . Define set
Then is the set of branch points of the covering map given by .
For an affine branch point , let denote the order of as a root of . As before, we assume that . Then
is the ramification index at each of the ramification points of the curve lying over (that is actually true for any ).
For the point at infinity, define integer as follows. If
then . Note that . Then analogously to the other ramification points,
is the ramification index at the points that lie over . In particular, the curve is unramified over infinity if and only if its degree divides .
Curve defined as above is connected precisely when and are relatively prime (not necessarily pairwise), which is assumed to be the case.
Genus
By the Riemann-Hurwitz formula, the genus of a superelliptic curve is given by
See also
Hyperelliptic curve
Branched covering
Artin-Schreier curve
Kummer theory
Superellipse
References
Algebraic curves |
https://en.wikipedia.org/wiki/Journal%20of%20Mathematics%20and%20the%20Arts | The Journal of Mathematics and the Arts is a quarterly peer-reviewed academic journal that deals with relationship between mathematics and the arts.
The journal was established in 2007 and is published by Taylor & Francis. The editor-in-chief is Mara Alagic (Wichita State University, Kansas).
References
External links
Academic journals established in 2007
Mathematics journals
Arts journals
Multidisciplinary academic journals
Taylor & Francis academic journals
English-language journals
Quarterly journals
Mathematics and art |
https://en.wikipedia.org/wiki/Weak%20approximation | Weak approximation may refer to:
Weak approximation theorem, an extension of the Chinese remainder theorem to algebraic groups over global fields
Weak weak approximation, a form of weak approximation for varieties
Weak-field approximation, a solution in general relativity |
https://en.wikipedia.org/wiki/Tommy%20Rifka%20Putra | Tommy Rifka Putra (born June 26, 1984, in Padang Panjang, West Sumatra), is an Indonesian former footballer who plays as a defender.
Statistics
As of 14 May 2012.
References
1984 births
Indonesian men's footballers
Living people
Indonesian Premier League players
Liga 1 (Indonesia) players
Persela Lamongan players
Semen Padang F.C. players
People from Padang Panjang
Men's association football defenders
Sportspeople from West Sumatra |
https://en.wikipedia.org/wiki/7-simplex%20honeycomb | In seven-dimensional Euclidean geometry, the 7-simplex honeycomb is a space-filling tessellation (or honeycomb). The tessellation fills space by 7-simplex, rectified 7-simplex, birectified 7-simplex, and trirectified 7-simplex facets. These facet types occur in proportions of 2:2:2:1 respectively in the whole honeycomb.
A7 lattice
This vertex arrangement is called the A7 lattice or 7-simplex lattice. The 56 vertices of the expanded 7-simplex vertex figure represent the 56 roots of the Coxeter group. It is the 7-dimensional case of a simplectic honeycomb. Around each vertex figure are 254 facets: 8+8 7-simplex, 28+28 rectified 7-simplex, 56+56 birectified 7-simplex, 70 trirectified 7-simplex, with the count distribution from the 9th row of Pascal's triangle.
contains as a subgroup of index 144. Both and can be seen as affine extensions from from different nodes:
The A lattice can be constructed as the union of two A7 lattices, and is identical to the E7 lattice.
∪ = .
The A lattice is the union of four A7 lattices, which is identical to the E7* lattice (or E).
∪ ∪ ∪ = + = dual of .
The A lattice (also called A) is the union of eight A7 lattices, and has the vertex arrangement to the dual honeycomb of the omnitruncated 7-simplex honeycomb, and therefore the Voronoi cell of this lattice is an omnitruncated 7-simplex.
∪
∪
∪
∪
∪
∪
∪
= dual of .
Related polytopes and honeycombs
Projection by folding
The 7-simplex honeycomb can be projected into the 4-dimensional tesseractic honeycomb by a geometric folding operation that maps two pairs of mirrors into each other, sharing the same vertex arrangement:
See also
Regular and uniform honeycombs in 7-space:
7-cubic honeycomb
7-demicubic honeycomb
Truncated 7-simplex honeycomb
Omnitruncated 7-simplex honeycomb
E7 honeycomb
Notes
References
Norman Johnson Uniform Polytopes, Manuscript (1991)
Kaleidoscopes: Selected Writings of H. S. M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley–Interscience Publication, 1995,
(Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380–407, MR 2,10] (1.9 Uniform space-fillings)
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3–45]
Honeycombs (geometry)
8-polytopes |
https://en.wikipedia.org/wiki/Ferdinando%20Gandolfi | Ferdinando Gandolfi (born 5 January 1967) is an Italian former water polo player who competed in the 1992 Summer Olympics.
See also
Italy men's Olympic water polo team records and statistics
List of Olympic champions in men's water polo
List of Olympic medalists in water polo (men)
List of world champions in men's water polo
List of World Aquatics Championships medalists in water polo
References
External links
1967 births
Living people
Italian male water polo players
Olympic water polo players for Italy
Water polo players at the 1992 Summer Olympics
Olympic gold medalists for Italy
Olympic medalists in water polo
Medalists at the 1992 Summer Olympics
Water polo players from Genoa |
https://en.wikipedia.org/wiki/Gy%C3%B6rgy%20Ken%C3%A9z | György Kenéz (born 23 June 1956) is a Hungarian former water polo player who competed in the 1976 Summer Olympics.
See also
Hungary men's Olympic water polo team records and statistics
List of Olympic champions in men's water polo
List of Olympic medalists in water polo (men)
List of World Aquatics Championships medalists in water polo
References
External links
1956 births
Living people
Hungarian male water polo players
Olympic water polo players for Hungary
Water polo players at the 1976 Summer Olympics
Olympic gold medalists for Hungary
Olympic medalists in water polo
Medalists at the 1976 Summer Olympics
20th-century Hungarian people
21st-century Hungarian people
Friendship Games medalists in water polo
Water polo players from Budapest
Hungarian water polo coaches
Expatriate water polo players
Hungarian expatriate sportspeople in Italy
Hungarian expatriate sportspeople in Kuwait
Men's national water polo team coaches
Expatriate sports coaches
World Aquatics Championships medalists in water polo |
https://en.wikipedia.org/wiki/J%C3%A1nos%20Steinmetz | János Steinmetz (15 October 1947 – 9 May 2007) was a Hungarian water polo player who competed in the 1968 Summer Olympics.
See also
Hungary men's Olympic water polo team records and statistics
List of Olympic medalists in water polo (men)
List of men's Olympic water polo tournament goalkeepers
References
External links
1947 births
2007 deaths
Hungarian male water polo players
Water polo goalkeepers
Olympic water polo players for Hungary
Water polo players at the 1968 Summer Olympics
Olympic bronze medalists for Hungary
Olympic medalists in water polo
Medalists at the 1968 Summer Olympics
20th-century Hungarian people
21st-century Hungarian people |
https://en.wikipedia.org/wiki/Tuned%20exhaust | In an internal combustion engine, the geometry of the exhaust system can be optimised ("tuned") to maximise the power output of the engine. Tuned exhausts are designed so that reflected pressure waves arrive at the exhaust port at a particular time in the combustion cycle.
Two-stroke engines
Expansion chambers
In two-stroke engines where the exhaust port is opened by being uncovered by the piston (rather than by a separate valve), a tuned exhaust system usually consists of an expansion chamber. The expansion chamber is designed to produce a negative pressure wave to assist in filling the cylinder with the next intake charge, and then to produce a positive pressure wave which reduces the amount of fresh intake charge that escapes through the exhaust port (port blocking).
Uniflow scavenging
An alternate design of two-stroke engines is where the exhaust port is opened/closed using a poppet valve and the intake port is piston-controlled (opened by being uncovered by the piston). The timing of the exhaust valve closure is designed to assist in filling the cylinder with the next intake charge (as per four-stroke engines).
An opposed piston engine uses uniflow scavenging, however this design uses piston-controlled cylinder ports with one piston controlling the inlet port and the other the exhaust port. Similarly, split-single engines use uniflow scavenging, with the piston in one cylinder controlling the transfer port (where the intake mixture enters the cylinder) and the other piston controls the exhaust port.
Four-stroke engines
In a four-stroke engine, an exhaust manifold which is designed to maximise the power output of an engine is often called "extractors" or "headers". The pipe lengths and merging locations are designed to assist in filling the cylinder with the next intake charge using exhaust scavenging. Locations where exhaust pipes from individual cylinders merge are called "collectors". The diameters of the exhaust system are designed to minimise back-pressure by optimising the gas velocity.
Extractors/headers usually have equal length pipes for each cylinder, whereas a more basic exhaust manifold may have unequal length pipes.
4-2-1 exhausts
A 4-2-1 exhaust system is a type of exhaust manifold for an engine with four cylinders per bank, such as an inline-four engine or a V8 engine. The layout of a 4-2-1 system is as follows: four pipes (primary) come off the cylinder head, and merge into two pipes (secondary), which in turn finally link up to form one collector pipe.
Compared with a 4-1 exhaust system, a 4-2-1 often produces more power at mid-range engine speeds (RPM), while a 4-1 exhaust produces more power at high RPM.
Cylinder pairings
The purpose of a 4-2-1 exhaust system is to increase scavenging by merging the exhaust paths of specific pairs of cylinders. Therefore, the cylinder pairings are defined by the intervals between firing events, which is determined by the firing order and— for engines with an unevenly space |
https://en.wikipedia.org/wiki/2012%E2%80%9313%20Stevenage%20F.C.%20season | The 2012–13 season was Stevenage F.C.'s third season in the Football League, where the club competed in League One. This article shows statistics of the club's players in the season, and also lists all matches that the club played during the season. Their sixth-place finish and subsequent play-off semi-final defeat during the 2011–12 campaign means it was Stevenage's second season of playing in League One, having only spent two years as a Football League club. The season also marked the third season that the club played under its new name – Stevenage Football Club, dropping 'Borough' from its title as of 1 June 2010. It was manager Gary Smith's first start to a season as Stevenage manager, having been appointed in January 2012. However, Smith was sacked in March 2013 following a run of 14 defeats in 18 games. His successor was Graham Westley, returning for his third spell in-charge of Stevenage, having previously managed the club for three years from 2003 to 2006, and then four years during his second-spell from 2008 to 2012.
Ahead of the season, there were wholesale changes involving the playing squad. Eight players were released in May 2012, including Ronnie Henry, subsequently ending his seven-year association with the club. With a number of players out of contract, further departures were revealed as Chris Beardsley, Joel Byrom, Scott Laird and John Mousinho all rejected the offer of contract extensions at Stevenage, and all four ended up signing for Preston North End, who at the time were managed by Westley. Three more first-team players left Stevenage before the start of the new campaign, both Michael Bostwick and Lawrie Wilson made the step up to the Championship, signing for Peterborough United and Charlton Athletic for respective undisclosed fees; while Craig Reid signed for League Two side Aldershot Town for a five-figure fee. Smith's first three signings of the close season were announced at the end of May, with goalkeeper Steve Arnold joining from Wycombe Wanderers, as well as midfielders James Dunne and Greg Tansey signing from Exeter City and Inverness Caledonian Thistle respectively. Five more players joined the club before the start of pre-season, and Lee Hills and Matt Ball were further additions following successful trials. In terms of transfer activity during the season, both Don Cowan and Rob Sinclair left the club on free transfers. Strikers Patrick Agyemang and Dani López were signed before the close of the summer transfer window, while defenders Andy Iro and Ben Chorley were acquired mid-season.
Despite the squad overhaul, Stevenage began the season positively, going on an eleven-match unbeaten run, six of which victories, to open the new campaign. Following the club's 2–1 home victory over Portsmouth in late October 2012, Stevenage found themselves in second place, just a point behind the league leaders at the time. However, Stevenage were defeated heavily in three of their next four matches, conceding four goals in each |
https://en.wikipedia.org/wiki/8-simplex%20honeycomb | In eighth-dimensional Euclidean geometry, the 8-simplex honeycomb is a space-filling tessellation (or honeycomb). The tessellation fills space by 8-simplex, rectified 8-simplex, birectified 8-simplex, and trirectified 8-simplex facets. These facet types occur in proportions of 1:1:1:1 respectively in the whole honeycomb.
A8 lattice
This vertex arrangement is called the A8 lattice or 8-simplex lattice. The 72 vertices of the expanded 8-simplex vertex figure represent the 72 roots of the Coxeter group. It is the 8-dimensional case of a simplectic honeycomb. Around each vertex figure are 510 facets: 9+9 8-simplex, 36+36 rectified 8-simplex, 84+84 birectified 8-simplex, 126+126 trirectified 8-simplex, with the count distribution from the 10th row of Pascal's triangle.
contains as a subgroup of index 5760. Both and can be seen as affine extensions of from different nodes:
The A lattice is the union of three A8 lattices, and also identical to the E8 lattice.
∪ ∪ = .
The A lattice (also called A) is the union of nine A8 lattices, and has the vertex arrangement of the dual honeycomb to the omnitruncated 8-simplex honeycomb, and therefore the Voronoi cell of this lattice is an omnitruncated 8-simplex
∪
∪
∪
∪
∪
∪
∪
∪
= dual of .
Related polytopes and honeycombs
Projection by folding
The 8-simplex honeycomb can be projected into the 4-dimensional tesseractic honeycomb by a geometric folding operation that maps two pairs of mirrors into each other, sharing the same vertex arrangement:
See also
Regular and uniform honeycombs in 8-space:
8-cubic honeycomb
8-demicubic honeycomb
Truncated 8-simplex honeycomb
521 honeycomb
251 honeycomb
152 honeycomb
Notes
References
Norman Johnson Uniform Polytopes, Manuscript (1991)
Kaleidoscopes: Selected Writings of H. S. M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380–407, MR 2,10] (1.9 Uniform space-fillings)
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3–45]
Honeycombs (geometry)
9-polytopes |
https://en.wikipedia.org/wiki/2011%E2%80%9312%20Scottish%20Football%20League | Statistics of the Scottish Football League in season 2011–12.
After the season ended, Rangers were liquidated, and re-formed in the Third Division. This meant that three further promotion places were created: these went to Dundee, Airdrie United and Stranraer. Airdrie United and Stranraer earned promotion as the losers in the playoff finals.
Scottish First Division
Scottish Second Division
Scottish Third Division
See also
2011–12 in Scottish football
References
Scottish Football League seasons |
https://en.wikipedia.org/wiki/Statistics%20and%20Computing | Statistics and Computing is a peer-reviewed academic journal that deals with statistics and computing. It was established in 1991 and is published by Springer.
External links
Mathematics journals
Academic journals established in 1991
Statistics journals
Computer science journals
Springer Science+Business Media academic journals |
https://en.wikipedia.org/wiki/Apollonius%20point | In Euclidean geometry, the Apollonius point is a triangle center designated as X(181) in Clark Kimberling's Encyclopedia of Triangle Centers (ETC). It is defined as the point of concurrence of the three line segments joining each vertex of the triangle to the points of tangency formed by the opposing excircle and a larger circle that is tangent to all three excircles.
In the literature, the term "Apollonius points" has also been used to refer to the isodynamic points of a triangle. This usage could also be justified on the ground that the isodynamic points are related to the three Apollonian circles associated with a triangle.
The solution of the Apollonius problem has been known for centuries. But the Apollonius point was first noted in 1987.
Definition
The Apollonius point of a triangle is defined as follows.
Let be any given triangle. Let the excircles of opposite to the vertices be respectively. Let be the circle which touches the three excircles such that the three excircles are within . Let be the points of contact of the circle with the three excircles. The lines are concurrent. The point of concurrence is the Apollonius point of .
The Apollonius problem is the problem of constructing a circle tangent to three given circles in a plane. In general, there are eight circles touching three given circles. The circle referred to in the above definition is one of these eight circles touching the three excircles of triangle . In Encyclopedia of Triangle Centers the circle is the called the Apollonius circle of .
Trilinear coordinates
The trilinear coordinates of the Apollonius point are
References
See also
Apollonius' theorem
Apollonius of Perga (262–190 BC), geometer and astronomer
Apollonius problem
Apollonian circles
Isodynamic point of a triangle
Triangle centers |
https://en.wikipedia.org/wiki/Goudreau%20Museum%20of%20Mathematics%20in%20Art%20and%20Science | The Goudreau Museum of Mathematics in Art and Science was a museum of math that was open from 1980–2006 in Long Island, New York. The museum was named after mathematics teacher Bernhard Goudreau, who died in 1985, and featured many of the 3-dimensional solid models, oversized wooden math games, and puzzles built by Goudreau and his former students. After the museum closed, Glen Whitney, a former math professor, decided to open the Museum of Mathematics in Manhattan (New York City), which opened in December 2012.
References
Defunct museums in New York (state)
Museums established in 1980
Museums disestablished in 2006
Museums in Nassau County, New York
Mathematics museums |
https://en.wikipedia.org/wiki/April%20Sykes | April L. Sykes (born July 30, 1990) is an American professional basketball player most recently with the Los Angeles Sparks of the Women's National Basketball Association.
Rutgers statistics
Source
USA Basketball
Sykes was selected to represent the U.S. at the 2011 Pan American Games held in Guadalajara, Mexico. The USA team lost their first two games in close contests, losing to Argentina 58–55 and Puerto Rico 75–70. The team rebounded to win their games against Mexico and Jamaica, but the 2–2 overall record left them in seventh place. Sykes averaged 9.0 points per game.
References
1990 births
Living people
American women's basketball players
Basketball players at the 2011 Pan American Games
Basketball players from Mississippi
Los Angeles Sparks draft picks
Los Angeles Sparks players
McDonald's High School All-Americans
Pan American Games competitors for the United States
Parade High School All-Americans (girls' basketball)
Rutgers Scarlet Knights women's basketball players
Shooting guards
Small forwards
Sportspeople from Starkville, Mississippi |
https://en.wikipedia.org/wiki/Nearest%20neighbor%20value%20interpolation | In mathematics applied to computer graphics, nearest neighbor value interpolation is an advanced method of image interpolation. This method uses the pixel value corresponding to the smallest absolute difference when a set of four known value pixels has no mode. Proposed by Olivier Rukundo in 2012 in his PhD dissertation, the first work presented at the fourth International Workshop on Advanced Computational Intelligence, was based only on the pixel value corresponding to the smallest absolute difference to achieve high resolution and visually pleasant image. This approach was since upgraded to deal with a wider class of image interpolation artefacts which reduce the quality of image, and as a result, several future developments have emerged, drawing on various aspects of the pixel value corresponding to the smallest absolute difference.
References
Multivariate interpolation |
https://en.wikipedia.org/wiki/Noncommutative%20signal-flow%20graph | In automata theory and control theory, branches of mathematics, theoretical computer science and systems engineering, a noncommutative signal-flow graph is a tool for modeling interconnected systems and state machines by mapping the edges of a directed graph to a ring or semiring.
A single edge weight might represent an array of impulse responses of a complex system (see figure to the right), or a character from an alphabet picked off the input tape of a finite automaton, while the graph might represent the flow of information or state transitions.
As diverse as these applications are, they share much of the same underlying theory.
Definition
Consider n equations involving n+1 variables {x0, x1,...,xn}.
with aij elements in a ring or semiring R. The free variable x0 corresponds to a source vertex v0, thus having no defining equation. Each equation corresponds to a fragment of a directed graph G=(V,E) as show in the figure.
The edge weights define a function f from E to R. Finally fix an output vertex vm. A signal-flow graph is the collection of this data S = (G=(V,E), v0,vm V, f : E → R). The equations may not have a solution, but when they do,
with T an element of R called the gain.
Successive Elimination
Return Loop Method
There exist several noncommutative generalizations of Mason's rule. The most common is the return loop method (sometimes called the forward return loop method (FRL), having a dual backward return loop method (BRL)). The first rigorous proof is attributed to Riegle, so it is sometimes called Riegle's rule.
As with Mason's rule, these gain expressions combine terms in a graph-theoretic manner (loop-gains, path products, etc.). They are known to hold over an arbitrary noncommutative ring and over the semiring of regular expressions.
Formal Description
The method starts by enumerating all paths from input to output, indexed by j J. We use the following definitions:
The j-th path product is (by abuse of notation) a tuple of kj edge weights along it:
To split a vertex v is to replace it with a source and sink respecting the original incidence and weights (this is the inverse of the graph morphism taking source and sink to v).
The loop gain of a vertex v w.r.t. a subgraph H is the gain from source to sink of the signal-flow graph split at v after removing all vertices not in H.
Each path defines an ordering of vertices along it. The along path j, the i-th FRL (BRL) node factor is (1-Si(j))−1 where Si(j) is the loop gain of the i-th vertex along the j-th w.r.t. the subgraph obtained by removing v0 and all vertices ahead of (behind) it.
The contribution of the j-th path to the gain is the product along the path, alternating between the path product weights
and the node factors:
so the total gain is
An Example
Consider the signal-flow graph shown. From x to z, there are two path products: (d) and (e,a). Along (d), the FRL and BRL contributions coincide as both share same loop gain (whose split reappea |
https://en.wikipedia.org/wiki/2012%20Maldivian%20Second%20Division%20Football%20Tournament | Statistics of Second Division Football Tournament in the 2012 season. According to the FAM Calendar 2012, Second Division Football Tournament will start on 22 May.
Teams
10 teams are competing in the 2012 Second Division Football Tournament, and these teams were divided into 2 groups of 5.
Group stage round
From each group, the top two teams will be advanced for the league round.
Group 1
United Victory and BG Sports Club advanced to the league round as the top two teams of the group.
Group 2
Hurriyya SC and Sports Club Mecano advanced to the league round as the top two teams of the group.
League round
The top two teams from each group will be qualified to compete in this round. As a total of four teams will be playing in this round of the tournament, the top two teams from this round will be advanced to the Final. The top two teams of theis round will also play in the Playoff for 2013 Dhivehi League. United Victory and B.G. Sports Club claimed the first and second position to advance for the Final.
*Source:Haveeru Online
Final
Awards
References
External links
Huraa Beats JJ in first match at Haveeru Online (Dhivehi)
Maldivian Second Division Football Tournament seasons
Maldives
Maldives
2 |
https://en.wikipedia.org/wiki/P-stable%20group | In finite group theory, a p-stable group for an odd prime p is a finite group satisfying a technical condition introduced by in order to extend Thompson's uniqueness results in the odd order theorem to groups with dihedral Sylow 2-subgroups.
Definitions
There are several equivalent definitions of a p-stable group.
First definition.
We give definition of a p-stable group in two parts. The definition used here comes from .
1. Let p be an odd prime and G be a finite group with a nontrivial p-core . Then G is p-stable if it satisfies the following condition: Let P be an arbitrary p-subgroup of G such that is a normal subgroup of G. Suppose that and is the coset of containing x. If , then .
Now, define as the set of all p-subgroups of G maximal with respect to the property that .
2. Let G be a finite group and p an odd prime. Then G is called p-stable if every element of is p-stable by definition 1.
Second definition.
Let p be an odd prime and H a finite group. Then H is p-stable if and, whenever P is a normal p-subgroup of H and with , then .
Properties
If p is an odd prime and G is a finite group such that SL2(p) is not involved in G, then G is p-stable. If furthermore G contains a normal p-subgroup P such that , then is a characteristic subgroup of G, where is the subgroup introduced by John Thompson in .
See also
p-stability is used as one of the conditions in Glauberman's ZJ theorem.
Quadratic pair
p-constrained group
p-solvable group
References
Finite groups |
https://en.wikipedia.org/wiki/Trigonal%20prismatic%20molecular%20geometry | In chemistry, the trigonal prismatic molecular geometry describes the shape of compounds where six atoms, groups of atoms, or ligands are arranged around a central atom, defining the vertices of a triangular prism.
Examples
Hexamethyltungsten (W(CH3)6) was the first example of a molecular trigonal prismatic complex. The figure shows the six carbon atoms arranged at the vertices of a triangular prism with the tungsten at the centre. The hydrogen atoms are not shown.
Some other transition metals have trigonal prismatic hexamethyl complexes, including both neutral molecules such as Mo(CH3)6 and Re(CH3)6 and ions such as and .
The complex Mo(S−CH=CH−S)3 is also trigonal prismatic, with each S−CH=CH−S group acting as a bidentate ligand with two sulfur atoms binding the metal atom. Here the coordination geometry of the six sulfur atoms around the molybdenum is similar to that in the extended structure of molybdenum disulfide (MoS2).
References
Stereochemistry
Molecular geometry |
https://en.wikipedia.org/wiki/Tricapped%20trigonal%20prismatic%20molecular%20geometry | In chemistry, the tricapped trigonal prismatic molecular geometry describes the shape of compounds where nine atoms, groups of atoms, or ligands are arranged around a central atom, defining the vertices of a triaugmented triangular prism (a trigonal prism with an extra atom attached to each of its three rectangular faces).
It is very similar to the capped square antiprismatic molecular geometry, and there is some dispute over the specific geometry exhibited by certain molecules.
Examples
is usually considered to have a tricapped trigonal prismatic geometry, although its geometry is sometimes described as capped square antiprismatic instead.
(Ln = La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy)
Stereochemistry
Molecular geometry |
https://en.wikipedia.org/wiki/Hierarchical%20network%20model | Hierarchical network models are iterative algorithms for creating networks which are able to reproduce the unique properties of the scale-free topology and the high clustering of the nodes at the same time. These characteristics are widely observed in nature, from biology to language to some social networks.
Concept
The hierarchical network model is part of the scale-free model family sharing their main property of having proportionally more hubs among the nodes than by random generation; however, it significantly differs from the other similar models (Barabási–Albert, Watts–Strogatz) in the distribution of the nodes' clustering coefficients: as other models would predict a constant clustering coefficient as a function of the degree of the node, in hierarchical models nodes with more links are expected to have a lower clustering coefficient. Moreover, while the Barabási-Albert model predicts a decreasing average clustering coefficient as the number of nodes increases, in the case of the hierarchical models there is no relationship between the size of the network and its average clustering coefficient.
The development of hierarchical network models was mainly motivated by the failure of the other scale-free models in incorporating the scale-free topology and high clustering into one single model. Since several real-life networks (metabolic networks, the protein interaction network, the World Wide Web or some social networks) exhibit such properties, different hierarchical topologies were introduced in order to account for these various characteristics.
Algorithm
Hierarchical network models are usually derived in an iterative way by replicating the initial cluster of the network according to a certain rule. For instance, consider an initial network of five fully interconnected nodes (N=5). As a next step, create four replicas of this cluster and connect the peripheral nodes of each replica to the central node of the original cluster (N=25). This step can be repeated indefinitely, thereby for any k steps the number of nodes in the system can be derived by N=5k+1.
Of course there have been several different ways for creating hierarchical systems proposed in the literature. These systems generally differ in the structure of the initial cluster as well as in the degree of expansion which is often referred to as the replication factor of the model.
Properties
Degree distribution
Being part of the scale-free model family, the degree distribution of the hierarchical network model follows the power law meaning that a randomly selected node in the network has k edges with a probability
where c is a constant and γ is the degree exponent. In most real world networks exhibiting scale-free properties γ lies in the interval [2,3].
As a specific result for hierarchical models it has been shown that the degree exponent of the distribution function can be calculated as
where M represents the replication factor of the model.
Clustering coefficient |
https://en.wikipedia.org/wiki/Steiner%20point%20%28triangle%29 | In triangle geometry, the Steiner point is a particular point associated with a triangle. It is a triangle center and it is designated as the center X(99) in Clark Kimberling's Encyclopedia of Triangle Centers. Jakob Steiner (1796–1863), Swiss mathematician, described this point in 1826. The point was given Steiner's name by Joseph Neuberg in 1886.
Definition
The Steiner point is defined as follows. (This is not the way in which Steiner defined it.)
Let be any given triangle. Let be the circumcenter and be the symmedian point of triangle . The circle with as diameter is the Brocard circle of triangle . The line through perpendicular to the line intersects the Brocard circle at another point . The line through perpendicular to the line intersects the Brocard circle at another point . The line through perpendicular to the line intersects the Brocard circle at another point . (The triangle is the Brocard triangle of triangle .) Let be the line through parallel to the line , be the line through parallel to the line and be the line through parallel to the line . Then the three lines , and are concurrent. The point of concurrency is the Steiner point of triangle .
In the Encyclopedia of Triangle Centers the Steiner point is defined as follows;
Let be any given triangle. Let be the circumcenter and be the symmedian point of triangle . Let be the reflection of the line in the line , be the reflection of the line in the line and be the reflection of the line in the line . Let the lines and intersect at , the lines and intersect at and the lines and intersect at . Then the lines , and are concurrent. The point of concurrency is the Steiner point of triangle .
Trilinear coordinates
The trilinear coordinates of the Steiner point are given below.
Properties
The Steiner circumellipse of triangle , also called the Steiner ellipse, is the ellipse of least area that passes through the vertices , and . The Steiner point of triangle lies on the Steiner circumellipse of triangle .
Canadian mathematician Ross Honsberger stated the following as a property of Steiner point: The Steiner point of a triangle is the center of mass of the system obtained by suspending at each vertex a mass equal to the magnitude of the exterior angle at that vertex. The center of mass of such a system is in fact not the Steiner point, but the Steiner curvature centroid, which has the trilinear coordinates . It is the triangle center designated as X(1115) in Encyclopedia of Triangle Centers.
The Simson line of the Steiner point of a triangle is parallel to the line where is the circumcenter and is the symmmedian point of triangle .
Tarry point
The Tarry point of a triangle is closely related to the Steiner point of the triangle. Let be any given triangle. The point on the circumcircle of triangle diametrically opposite to the Steiner point of triangle is called the Tarry point of triangle . The Tarry point is a triangle center and i |
https://en.wikipedia.org/wiki/Protein%20topology | Protein topology is a property of protein molecule that does not change under deformation (without cutting or breaking a bond).
Frameworks
Two main topology frameworks have been developed and applied to protein molecules.
Knot Theory
Knot theory which categorises chain entanglements. The usage of knot theory is limited to a small percentage of proteins as most of them are unknot.
Circuit topology
Circuit topology categorises intra-chain contacts based on their arrangements. Circuit topology is a determinant of protein folding kinetics and stability.
Other Uses
In biology literature, the term topology is also used to refer to mutual orientation of regular secondary structures, such as alpha-helices and beta strands in protein structure . For example, two adjacent interacting alpha-helices or beta-strands can go in the same or in opposite directions. Topology diagrams of different proteins with known three-dimensional structure are provided by PDBsum (an example).
See also
Circuit topology
Membrane topology
Protein folding
References
External links
Pro-origami: Protein structure cartoons
TOPS services at Glasgow University
PTGL
TOPDRAW
Protein structure
Molecular topology |
https://en.wikipedia.org/wiki/Franz%20Aschenbrenner | Franz Aschenbrenner (born 24 May 1986) is a German motorcycle racer.
Career statistics
Grand Prix motorcycle racing
By season
Races by year
(key)
References
External links
Profile on MotoGP.com
Living people
1986 births
German motorcycle racers
250cc World Championship riders |
https://en.wikipedia.org/wiki/Charles-Fran%C3%A7ois-Maximilien%20Marie | Charles-François-Maximilien Marie (1819–1891) was a French mathematician, historian of mathematics. He was the author of History of the Mathematics and Theory of the variable imaginary functions (1874), relating to the imaginary unit.
Biography
Maximilien Marie was born in Paris on 1 January 1819. He was the son of Simon Marie (1775–1855) an infantry captain in Napoleon's Grande Armée from a modest background, and Henriette Josephine de Ficquelmont (1780–1843), poor, but from the nobility of Lorraine.
The financial situation of his father, retired Captain Marie, was dire for a household with a wife and three children: Clotilde (born in 1815), Maximilian (born in 1819) and Leon (born in 1820) therefore, his father was given an office of tax collector in Méru in Oise To help him.
Maximilian spent his childhood in Méru with his older sister Mary and his younger brother Leon.
He graduated from the École Polytechnique in 1838 and went on to attend the École d'application de l'artillerie et du génie in Metz as an officer student in artillery. While an officer in training in Metz, he discovered a key element of solid mechanics as he found out how solid matters are moving.
In 1841, he was made a lieutenant-major, but, more attracted by the field of mathematics, he chose to resign from the army and move back to Paris. Close to the positivist movements, Ficquelmont began to spend time with his former professor philosopher Auguste Comte, who soon became his mentor. In 1844, Maximilien Marie introduced him to his sister Clotilde de Vaux. Comte fell passionately in love with her, a feeling that she did not reciprocate, and the one-sided affair ended when Clotilde suddenly died of tuberculosis a year later. Following Clotilde's death in 1846, Maximilien Marie and Comte grow apart while Comte dedicated himself to reorganising his previous philosophical system into a new positivist secular religion inspired by Clotilde's moral values: the Positivist Church or Religion of Humanity.
In 1862, backed by the famous mathematicians Joseph Liouville and General Jean-Victor Poncelet, Maximilien Marie was appointed professor of Mechanics at the École Polytechnique. In 1875, he was appointed head of admissions . Besides his academic achievements at the Polytechnique, he wrote the book Théorie des fonctions de variables imaginaires relating to the Imaginary unit.
Growing old, he entered politics during the Third Republic and became mayor of Châtillon. In 1890, he retired from the Polytechnique and died a year later.
Honors
Maximilien Marie was made chevalier (1876) and officer (12 juillet 1880), of the Légion d’honneur.
Works
He published a 12-volume encyclopedia, History of the Mathematics, which was divided into two parts: Théorie des fonctions de variables imaginaires (tomes I à III, Gauthier-Villars, 1874–1876, 3 vol.) and Histoire des sciences mathématiques et physiques (tomes I à XII, Gauthier-Villars, 1883–1888, 12 vol.)
Family
He had one elder sister, |
https://en.wikipedia.org/wiki/Siegel%20identity | In mathematics, Siegel's identity refers to one of two formulae that are used in the resolution of Diophantine equations.
Statement
The first formula is
The second is
Application
The identities are used in translating Diophantine problems connected with integral points on hyperelliptic curves into S-unit equations.
See also
Siegel formula
References
Mathematical identities
Diophantine equations |
https://en.wikipedia.org/wiki/Peripheral%20subgroup | In algebraic topology, a peripheral subgroup for a space-subspace pair X ⊃ Y is a certain subgroup of the fundamental group of the complementary space, π1(X − Y). Its conjugacy class is an invariant of the pair (X,Y). That is, any homeomorphism (X, Y) → (X′, Y′) induces an isomorphism π1(X − Y) → π1(X′ − Y′) taking peripheral subgroups to peripheral subgroups.
A peripheral subgroup consists of loops in X − Y which are peripheral to Y, that is, which stay "close to" Y (except when passing to and from the basepoint). When an ordered set of generators for a peripheral subgroup is specified, the subgroup and generators are collectively called a peripheral system for the pair (X, Y).
Peripheral systems are used in knot theory as a complete algebraic invariant of knots. There is a systematic way to choose generators for a peripheral subgroup of a knot in 3-space, such that distinct knot types always have algebraically distinct peripheral systems. The generators in this situation are called a longitude and a meridian of the knot complement.
Full definition
Let Y be a subspace of the path-connected topological space X, whose complement X − Y is path-connected. Fix a basepoint x ∈ X − Y. For each path component Vi of X − Y∩Y, choose a path γi from x to a point in Vi. An element [α] ∈ π1(X − Y, x) is called peripheral with respect to this choice if it is represented by a loop in U ∪ ∪ iγi for every neighborhood U of Y. The set of all peripheral elements with respect to a given choice forms a subgroup of π1(X − Y, x), called a peripheral subgroup.
In the diagram, a peripheral loop would start at the basepoint x and travel down the path γ until it's inside the neighborhood U of the subspace Y. Then it would move around through U however it likes (avoiding Y). Finally it would return to the basepoint x via γ. Since U can be a very tight envelope around Y, the loop has to stay close to Y.
Any two peripheral subgroups of π1(X − Y, x), resulting from different choices of paths γi, are conjugate in π1(X − Y, x). Also, every conjugate of a peripheral subgroup is itself peripheral with respect to some choice of paths γi. Thus the peripheral subgroup's conjugacy class is an invariant of the pair (X, Y).
A peripheral subgroup, together with an ordered set of generators, is called a peripheral system for the pair (X, Y). If a systematic method is specified for selecting these generators, the peripheral system is, in general, a stronger invariant than the peripheral subgroup alone. In fact, it is a complete invariant for knots.
In knot theory
The peripheral subgroups for a tame knot K in R3 are isomorphic to Z ⊕ Z if the knot is nontrivial, Z if it is the unknot. They are generated by two elements, called a longitude [l] and a meridian [m]. (If K is the unknot, then [l] is a power of [m], and a peripheral subgroup is generated by [m] alone.) A longitude is a loop that runs from the basepoint x along a path γ to a point y on the boundary |
https://en.wikipedia.org/wiki/Bayesian%20interpretation%20of%20kernel%20regularization | Within bayesian statistics for machine learning, kernel methods arise from the assumption of an inner product space or similarity structure on inputs. For some such methods, such as support vector machines (SVMs), the original formulation and its regularization were not Bayesian in nature. It is helpful to understand them from a Bayesian perspective. Because the kernels are not necessarily positive semidefinite, the underlying structure may not be inner product spaces, but instead more general reproducing kernel Hilbert spaces. In Bayesian probability kernel methods are a key component of Gaussian processes, where the kernel function is known as the covariance function. Kernel methods have traditionally been used in supervised learning problems where the input space is usually a space of vectors while the output space is a space of scalars. More recently these methods have been extended to problems that deal with multiple outputs such as in multi-task learning.
A mathematical equivalence between the regularization and the Bayesian point of view is easily proved in cases where the reproducing kernel Hilbert space is finite-dimensional. The infinite-dimensional case raises subtle mathematical issues; we will consider here the finite-dimensional case. We start with a brief review of the main ideas underlying kernel methods for scalar learning, and briefly introduce the concepts of regularization and Gaussian processes. We then show how both points of view arrive at essentially equivalent estimators, and show the connection that ties them together.
The supervised learning problem
The classical supervised learning problem requires estimating the output for some new input point by learning a scalar-valued estimator on the basis of a training set consisting of input-output pairs, . Given a symmetric and positive bivariate function called a kernel, one of the most popular estimators in machine learning is given by
where is the kernel matrix with entries , , and . We will see how this estimator can be derived both from a regularization and a Bayesian perspective.
A regularization perspective
The main assumption in the regularization perspective is that the set of functions is assumed to belong to a reproducing kernel Hilbert space .
Reproducing kernel Hilbert space
A reproducing kernel Hilbert space (RKHS) is a Hilbert space of functions defined by a symmetric, positive-definite function called the reproducing kernel such that the function belongs to for all . There are three main properties make an RKHS appealing:
1. The reproducing property, which gives name to the space,
where is the inner product in .
2. Functions in an RKHS are in the closure of the linear combination of the kernel at given points,
.
This allows the construction in a unified framework of both linear and generalized linear models.
3. The squared norm in an RKHS can be written as
and could be viewed as measuring the complexity of the function.
The regul |
https://en.wikipedia.org/wiki/Order-2%20apeirogonal%20tiling | In geometry, an order-2 apeirogonal tiling, apeirogonal dihedron, or infinite dihedron is a tiling of the plane consisting of two apeirogons. It may be considered an improper regular tiling of the Euclidean plane, with Schläfli symbol Two apeirogons, joined along all their edges, can completely fill the entire plane as an apeirogon is infinite in size and has an interior angle of 180°, which is half of a full 360°.
Related tilings and polyhedra
The apeirogonal tiling is the arithmetic limit of the family of dihedra {p, 2}, as p tends to infinity, thereby turning the dihedron into a Euclidean tiling.
Similarly to the uniform polyhedra and the uniform tilings, eight uniform tilings may be based from the regular apeirogonal tiling. The rectified and cantellated forms are duplicated, and as two times infinity is also infinity, the truncated and omnitruncated forms are also duplicated, therefore reducing the number of unique forms to four: the apeirogonal tiling, the apeirogonal hosohedron, the apeirogonal prism, and the apeirogonal antiprism.
See also
Order-3 apeirogonal tiling - hyperbolic tiling
Order-4 apeirogonal tiling - hyperbolic tiling
Notes
References
The Symmetries of Things 2008, John H. Conway, Heidi Burgiel, Chaim Goodman-Strass,
External links
Jim McNeill: Tessellations of the Plane
Apeirogonal tilings
Euclidean tilings
Isogonal tilings
Isohedral tilings
Order-2 tilings
Regular tilings |
https://en.wikipedia.org/wiki/Eduard%20Uv%C3%ADra | Eduard Uvíra (born July 12, 1961) is an ice hockey defenceman who played for the Czechoslovak national team. He won a silver medal at the 1984 Winter Olympics.
Career statistics
Regular season and playoffs
International
References
External links
1961 births
Czech ice hockey defencemen
Czechoslovak ice hockey defencemen
HC Dukla Jihlava players
HC Litvínov players
HC Slovan Bratislava players
Ice hockey players at the 1984 Winter Olympics
Ice hockey players at the 1988 Winter Olympics
Living people
Medalists at the 1984 Winter Olympics
Olympic ice hockey players for Czechoslovakia
Olympic medalists in ice hockey
Olympic silver medalists for Czechoslovakia
Ice hockey people from Opava
Toronto Maple Leafs draft picks
Czechoslovak expatriate sportspeople in Germany
Czechoslovak expatriate ice hockey people
Czech expatriate ice hockey players in Germany
Naturalized citizens of Germany
German ice hockey coaches
Czech ice hockey coaches |
https://en.wikipedia.org/wiki/Thomas%20%C3%85hl%C3%A9n | Thomas Valter Åhlén (born March 8, 1959) is an ice hockey player who played for the Swedish national team. He won a bronze medal at the 1984 Winter Olympics.
Career statistics
Regular season and playoffs
International
References
1959 births
Living people
Ice hockey players at the 1984 Winter Olympics
Olympic ice hockey players for Sweden
Olympic medalists in ice hockey
Medalists at the 1984 Winter Olympics
Olympic bronze medalists for Sweden
Los Angeles Kings draft picks |
https://en.wikipedia.org/wiki/Tommy%20M%C3%B6rth | Tommy Jan Mörth (born July 16, 1959) is an ice hockey player who played for the Swedish national team. He won a bronze medal at the 1984 Winter Olympics.
Career statistics
Regular season and playoffs
International
References
1959 births
Living people
Ice hockey players at the 1984 Winter Olympics
Olympic bronze medalists for Sweden
Olympic ice hockey players for Sweden
Swedish ice hockey players
Olympic medalists in ice hockey
Medalists at the 1984 Winter Olympics
Djurgårdens IF Hockey players |
https://en.wikipedia.org/wiki/Egon%20Balas | Egon Balas (June 7, 1922 in Cluj, Romania – March 18, 2019) was an applied mathematician and a professor of industrial administration and applied mathematics at Carnegie Mellon University. He was the Thomas Lord Professor of Operations Research at Carnegie Mellon's Tepper School of Business and did fundamental work in developing integer and disjunctive programming.
Life and education
Balas was born in Cluj (Romania) in a Hungarian Jewish family. His original name was Blatt, which was first changed to the Hungarian Balázs and then later to the Romanian Balaş. He was married to art historian Edith Balas, a survivor of Auschwitz, with whom he had two daughters. He was imprisoned by the Communist authorities for several years after the war.
He left Romania in 1966 and accepted an appointment with Carnegie Mellon University in 1967. Balas obtained a "Diploma Licentiate" in economics (Bolyai University, 1949) and Ph.D.s in economics (University of Brussels, 1967) and mathematics (University of Paris, 1968).
His mathematics PhD thesis was titled Minimax et dualité en programmation discrète and was written under the direction of Robert Fortet.
Selected publications
E. Balas, A. Saxena: Optimizing Over the Split Closure, Mathematical Programming 113, 2 (2008), 219–240.
E. Balas, M. Perregaard: A Precise Correspondence Between Lift-and-Project Cuts, Simple Disjunctive Cuts, and Mixed Integer Gomory Cuts for 0-1 Programming, Mathematical Programming B (94), 2003; 221–245.
E. Balas, S. Ceria, G. Cornuéjols: Mixed 0-1 Programming by Lift-and-Project in a Branch-and-Cut Framework, Management Science 42, 1996; 1229–1246.
E. Balas: The Prize Collecting Traveling Salesman Problem: II Polyhedral Results, Networks 25, 1995; 199–216.
E. Balas, S. Ceria, G. Cornuéjols: A Lift-and-Project Cutting Plane Algorithm for Mixed 0-1 Programs, Mathematical Programming 58, 1993; 295–324.
E. Balas: The Prize Collecting Traveling Salesman Problem I, Networks 19, 1989; 621–636.
E. Balas, J. Adams, D. Zawack: The Shifting Bottleneck Procedure for Job Shop Scheduling, Management Science 34, 1988; 391–401.
E. Balas, V. Chvátal, J. Nesetril: On The Maximum-Weight Clique Problem, Mathematics of Operations Research 12, 1987; 522–536.
E. Balas: Disjunctive Programming, Annals of Discrete Mathematics 5, 1979; 3–51.
E. Balas: An Additive Algorithm for Linear Programming in Zero-One Variables, Operations Research 13 (4), 1965; 517–546.
Honors and awards
National Academy of Engineering, 2006
IFORS Hall of Fame, 2006
Honorary Doctorate in Mathematics, University of Waterloo, 2005
Hungarian Academy of Science, external member, 2004
INFORMS Fellow, 2002
Honorary Doctorate in Mathematics, Miguel Hernandez University, Elche, Spain, 2002
EURO Gold Medal, 2001
John von Neumann Theory Prize, INFORMS, 1995
Senior U.S. Scientist Award of the von Humboldt Foundation, 1980–1981
Notes
References
E. Balas: Will to Freedom: A Perilous Journey through Fascism and Communism (Syracuse U |
https://en.wikipedia.org/wiki/Anton%20Wassmuth | Anton Wassmuth (5 May 1844, Stift Tepl near Marienbad – 22 April 1927, Graz) was an Austrian physicist.
He studied mathematics, philosophy and natural sciences at the University of Prague, where he subsequently became an assistant to Ernst Mach (1838-1916). In 1871 he obtained his habilitation on electricity and magnetism from the University of Vienna. In 1876 became an associate professor at the recently established University of Czernowitz, where in 1882 he was appointed a full professor of theoretical physics. In 1890 he relocated to Innsbruck as a professor and director at the institute of mathematical physics. Here he served as dean to the faculty in 1891. From 1893 to 1914 he served as chair of theoretical physics at the University of Graz. Following retirement, his position at Graz was filled by Michael Radaković (1866-1934).
Wassmuth is best known for his research involving thermoelasticity, electromagnetism and statistical mechanics. Among his principal written works are: Die Elektrizität und ihre Anwendungen (Electricity and its applications, 1885) and Grundlagen und Anwendungen der statistischen Mechanik (Fundamentals and applications of statistical mechanics, 1915).
In 1885 he became a member of the "Deutsche Akademie der Naturforscher Leopoldina".
References
Geschichte des Instituts für Theoretische Physik der Universität innsbruck (1868-1988) (short biography)
Antiquariat Weinek, Ueber die Anwendung des Princips des kleinsten Zwanges auf die Electrodynamik (biographical information)
Academic staff of the University of Graz
Charles University alumni
Academic staff of the University of Innsbruck
Academic staff of Chernivtsi University
Austrian physicists
1927 deaths
1844 births |
https://en.wikipedia.org/wiki/Michael%20Radakovi%C4%87 | Michael Radaković (25 April 1866, in Graz – 16 August 1934) was an Austrian physicist.
From 1884, he studied physics and mathematics at the University of Graz, where he was influenced by the philosophical teachings of Alexius Meinong (1853–1920). Following his studies at Graz, he continued his education in Berlin, where his instructors included Hermann von Helmholtz and Gustav Kirchhoff. He received his habilitation at the University of Innsbruck, where in 1902 he became an associate professor.
In 1906 he replaced Ottokar Tumlirz (1856–1927) as chair of theoretical physics at the University of Czernowitz. In 1915 he returned to Graz, where he succeeded Anton Wassmuth (1844–1927) as professor of theoretical physics. In 1924–25 he served as dean to the faculty of sciences. After his death, his position at Graz was filled by Erwin Schrödinger (1887–1961).
Radaković is remembered for his studies in the field of ballistics, being acclaimed for his experiments involving the muzzle velocity of a projectile.
Published works
Über die Bedingungen für die Möglichkeit physikalischer Vorgänge. Popular lectures at the University of Czernowitz; (1913) - On the conditions for the possibility of physical processes.
References
Parts of this article are based on a translation of an article from the German Wikipedia, namely: Österreichisches Biographisches Lexikon 1815–1950 (ÖBL). Band 8, Verlag der Österreichischen Akademie der Wissenschaften, Wien 1983, .
Austrian physicists
Academic staff of the University of Graz
Academic staff of the University of Innsbruck
Academic staff of Chernivtsi University
1934 deaths
1866 births
Scientists from Graz
Physicists from Austria-Hungary |
https://en.wikipedia.org/wiki/List%20of%20the%20busiest%20airports%20in%20Iran |
2019 Statistics
2018 Statistics
Notes
1.The results had been converted from a report generated in Persian Solar Hijri calendar
2.The reports of the airports in Iranian islands had not been published since 2017; All the existing reports are estimates.
2017 Statistics
2016 Statistics
2015 Statistics
2014 Statistics
2013 Statistics
2012 Statistics
2011 Statistics
See also
List of airports in Iran
List of airlines of Iran
Iran Civil Aviation Organization
Transport in Iran
Iran
List of the busiest airports in the Middle East
References
(PDF) ماهنامه آمار عملکرد شرکت فرودگاههای کشور – شماره بیست و هشتم (in Persian). Iranian Airports Holding Company. September 2015
(PDF) پروازی \ آمار میلادی (in Persian). Iranian Airports Holding Company. February 2016
External links
Ministry of Road and Urban Development Of Iran Official Website
Civil Aviation Organization of Iran
Iran Airports Company
Iran
Airports, busiest |
https://en.wikipedia.org/wiki/MyMaths | MyMaths is a subscription-based mathematics website which can be used on interactive whiteboards or by students and teachers at home. It is owned and operated by Oxford University Press, who acquired the site in 2011. As of February 2021, MyMaths has over 4 million student users in over 70 countries worldwide.
Usage and Cost
MyMaths operates a subscription model, where schools must pay to access the service. There is a cost of £392 for primary schools or £695 for secondary schools, per annum and not including VAT. Limited resources are available as a free trial. Schools receive an institution username and password, allowing students to access content on the site, and can set up profiles for individual students, enabling teachers to track the progress and grades achieved on homework.
Content
MyMaths has a wide range of curriculum materials and resources aimed at students in primary and secondary schools, covering content from KS1 foundations to A-Level Further Mathematics. However, it does not cover all topics. Each topic consists of a 'Lesson' which teaches the methods and provides interactive examples, as well as an "Online homework" task which provides and automatically marks practice questions. "Booster packs" for revision purposes and simplistic games are also available.
Whilst MyMaths only provides content for UK examinations, the sister site MyiMaths provides content for international qualifications.
Flash
MyMaths was originally constructed in Flash, but most content has now been translated into HTML or other standards as of January 2021. 28 games and some other content was replaced or deleted after widespread support for Flash was ended at the end of 2020.
'Hacks'
Several websites claim to offer 'hacks' to easily access answers on the site, although these merely involve opening several tabs or checking client side source code. A popular excuse amongst students completing homework was that they had forgotten to click the 'Checkout' tab, which resulted in the results of supposedly completed work not being saved.
Impact
An impact study undertaken by Oxford University Press — the owners of the website — conducted 22 interviews with teachers, finding that using MyMaths saved teachers between 15 minutes and 5 hours a week, with an average of around 2 hours.
References
External links
Official website
British educational websites
Mathematics education in the United Kingdom |
https://en.wikipedia.org/wiki/2012%E2%80%9313%20FC%20O%C8%9Belul%20Gala%C8%9Bi%20season | The 2012–13 season will be Oțelul Galați's 21st consecutive season in the Liga I, and their 24th overall season in the top-flight of Romanian football.
Players
Transfers
In
Out
Player statistics
Squad statistics
Start formations
Disciplinary records
Suspensions
Competitions
Overall
{|class="wikitable" style="text-align: center;"
|-
!
!Total
! Home
! Away
|-
|align=left| Games played || 9 || 4 || 5
|-
|align=left| Games won || 1 || – || 1
|-
|align=left| Games drawn|| 4 || 3 || 1
|-
|align=left| Games lost || 4 || 1 || 3
|-
|align=left| Biggest win|| 2–1 vs CSMS Iaşi || – || 2–1 vs CSMS Iaşi
|-
|align=left| Biggest loss || 1–2 vs Petrolul || 1–2 vs CFR Cluj || 1–2 vs Petrolul
|-
|align=left| Clean sheets || 0 || 0 || 0
|-
|align=left| Goals scored || 11 || 4 || 7
|-
|align=left| Goals conceded|| 14 || 5 || 9
|-
|align=left| Goal difference || -3 || -1 || -2
|-
|align=left| Average per game || || ||
|-
|align=left| Average per game || || ||
|-
|align=left| Yellow cards || 26 || 9 || 17
|-
|align=left| Red cards || 2 || 1 || 1
|-
|align=left| Most appearances || colspan=3| Giurgiu, Râpă, Štromajer (9)
|-
|align=left| Most minutes played ||colspan=3| Giurgiu, Râpă (849)
|-
|align=left| Top scorer || colspan=3| Viglianti (4)
|-
|align=left| Top assister || colspan=3| Pena (3)
|-
|align=left| Points || 7/27(%) || 3/12(%) || 4/15(%)
|-
|align=left| Winning rate || % || % || %
|-
Liga I
League table
Results summary
Results by round
Points by opponent
Source: FCO
Matches
Kickoff times are in EET.
Cupa României
Friendlies
Netherlands training camp
Local friendlies
Spain training camp
Marbella Cup
Other friendlies
References
See also
FC Oțelul Galați
2012–13 Liga I
2012–13 Cupa României
2012-13
Otelul Galati season |
https://en.wikipedia.org/wiki/Gabriel%E2%80%93Popescu%20theorem | In mathematics, the Gabriel–Popescu theorem is an embedding theorem for certain abelian categories, introduced by . It characterizes certain abelian categories (the Grothendieck categories) as quotients of module categories.
There are several generalizations and variations of the Gabriel–Popescu theorem, given by (for an AB5 category with a set of generators), , (for triangulated categories).
Theorem
Let A be a Grothendieck category (an AB5 category with a generator), G a generator of A and R be the ring of endomorphisms of G; also, let S be the
functor from A to Mod-R (the category of right R-modules) defined by S(X) = Hom(G,X). Then the Gabriel–Popescu theorem states that S is full and faithful and has an exact left adjoint.
This implies that A is equivalent to the Serre quotient category of Mod-R by a certain localizing subcategory C. (A localizing subcategory of Mod-R is a full subcategory C of Mod-R, closed under arbitrary direct sums, such that for any short exact sequence of modules , we have M2 in C if and only if M1 and M3 are in C. The Serre quotient of Mod-R by any localizing subcategory is a Grothendieck category.) We may take C to be the kernel of the left adjoint of the functor S.
Note that the embedding S of A into Mod-R is left-exact but not necessarily right-exact: cokernels of morphisms in A do not in general correspond to the cokernels of the corresponding morphisms in Mod-R.
References
[Remark: "Popescu" is spelled "Popesco" in French.]
External links
Category theory
Functors
Theorems in abstract algebra |
https://en.wikipedia.org/wiki/Adriaan%20Gilles%20Camper | Adriaan Gilles Camper (March 31, 1759 – February 5, 1820) was a 19th-century Dutch mathematics and physics professor at the University of Franeker who took to politics and became a statesman in his later years. He was the son of Petrus Camper is known today primarily for his paleontological work in collaboration with his father, causing several fossil holotypes to be named after him, such as the Puppigerus P. Camperi. The engravings he commissioned on the basis of his father's work were published by Barthélemy Faujas de Saint-Fond. He himself wrote several books on paleontology, including a catalog of his collection of fossils and minerals.
His daughter Frederica married one of his pupils in Franeker, the Dutch geologist J.G.S. van Breda (who later became curator of the Teylers Museum in Haarlem). Van Breda wrote a biography of father-in-law, in which he describes him as the home-schooled wunderkind who entered the University of Franeker at age 14 already learned in natural history and modern languages from his close association with his father. Three years later, in 1776, his mother died, and his father was so struck by the loss that he undertook a leave of absence from the university to travel to Paris and the young Adriaan went with him. There due to the fame of his father, they were received with open arms by the various learned societies such as the French Academy of Sciences and consorted with Louis, Antoine Portal, Jacques-René Tenon, Julien-David Le Roy, the Count Jean-Charles de Borda, the Marquis de Condorcet, and Benjamin Franklin (the American liberator).
He became member of the Royal Institute of the Netherlands in 1808.
References
Dinosaurs and Other Extinct Saurians: A Historical Perspective, edited by Richard Moody, E. Buffetaut, D. Naish, D. M. Martill on Google books
Histoire naturelle de la montagne de Saint-Pierre de Maestricht, by Barthélemy Faujas de Saint-Fond on Google books
1759 births
1820 deaths
Scientists from Amsterdam
Dutch paleontologists
Academic staff of the University of Franeker
Members of the Royal Netherlands Academy of Arts and Sciences |
https://en.wikipedia.org/wiki/2012%E2%80%9313%20FK%20Partizan%20season | The 2012–13 season is FK Partizan's 7th season in Serbian SuperLiga. This article shows player statistics and all matches (official and friendly) that the club have and will play during the 2012–13 season.
Players
Squad information
Squad statistics
Starting 11
Top scorers
Includes all competitive matches. The list is sorted by shirt number when total goals are equal.
Transfers
In
Out
For recent transfers, see List of Serbian football transfers summer 2012 and List of Serbian football transfers winter 2012–13.
Competitions
Overview
Serbian SuperLiga
League table
Results and positions by round
Matches
Serbian Cup
UEFA Champions League
Qualifying phase
UEFA Europa League
Play-off round
Group
Friendlies
Sponsors
See also
List of FK Partizan seasons
References
External links
Official website
Partizanopedia 2012-13 (in Serbian)
FK Partizan seasons
Partizan
Partizan
Partizan
Serbian football championship-winning seasons |
https://en.wikipedia.org/wiki/Matteo%20Lucchesi | Matteo Lucchesi (1705–1776) was an Italian architect and Engineer, active mainly in his native Venice.
He learned mathematics and architecture from Tommaso Temanza. He was named by the Ducal Republic to be Magistrato delle Acque (Magistrate of Waterworks), an important post in the state. He designed the reconstruction of the church of San Giovanni Nuovo (San Zaninovo), built 1751–1762. He boasted that this church was the Redentore redento, meaning "redeemed redeemer" because it corrected the errors Lucchesi found in Palladio's church of Il Redentore. San Zaninovo's facade was never completed. Lucchesi also helped in reconstruction at the Ospedaletto. He also published works about artistic methods.
He also was an early mentor to his nephew, the famous engraver Giovanni Battista Piranesi.
References
Venetian engineers
Republic of Venice architects
18th-century Italian architects
1705 births
1776 deaths |
https://en.wikipedia.org/wiki/Transcendental%20law%20of%20homogeneity | In mathematics, the transcendental law of homogeneity (TLH) is a heuristic principle enunciated by Gottfried Wilhelm Leibniz most clearly in a 1710 text entitled Symbolismus memorabilis calculi algebraici et infinitesimalis in comparatione potentiarum et differentiarum, et de lege homogeneorum transcendentali. Henk J. M. Bos describes it as the principle to the effect that in a sum involving infinitesimals of different orders, only the lowest-order term must be retained, and the remainder discarded. Thus, if is finite and is infinitesimal, then one sets
Similarly,
where the higher-order term du dv is discarded in accordance with the TLH. A recent study argues that Leibniz's TLH was a precursor of the standard part function over the hyperreals.
See also
Law of continuity
Adequality
References
History of calculus
Gottfried Wilhelm Leibniz |
https://en.wikipedia.org/wiki/Codazzi%20tensor | In the mathematical field of differential geometry, a Codazzi tensor (named after Delfino Codazzi) is a symmetric 2-tensor whose covariant derivative is also symmetric. Such tensors arise naturally in the study of Riemannian manifolds with harmonic curvature or harmonic Weyl tensor. In fact, existence of Codazzi tensors impose strict conditions on the curvature tensor of the manifold. Also, the second fundamental form of an immersed hypersurface in a space form (relative to a local choice of normal field) is a Codazzi tensor.
Definition
Let be a n-dimensional Riemannian manifold for , let be a symmetric 2-tensor field, and let be the Levi-Civita connection. We say that the tensor is a Codazzi tensor if
for all
Examples
Any parallel -tensor field is, trivially, Codazzi.
Let be a space form, let be a smooth manifold with and let be an immersion. If there is a global choice of unit normal vector field, then relative to this choice, the second fundamental form is a Codazzi tensor on This is an immediate consequence of the Gauss-Codazzi equations.
Let be a space form with constant curvature Given any function on the tensor is Codazzi. This is a consequence of the commutation formula for covariant differentiation.
Let be a two-dimensional Riemannian manifold, and let be the Gaussian curvature. Then is a Codazzi tensor. This is a consequence of the commutation formula for covariant differentiation.
Let Rm denote the Riemann curvature tensor. Then (" has harmonic curvature tensor") if and only if the Ricci tensor is a Codazzi tensor. This is an immediate consequence of the contracted Bianchi identity.
Let denote the Weyl curvature tensor. Then (" has harmonic Weyl tensor") if and only if the "Schouten tensor"
is a Codazzi tensor. This is an immediate consequence of the definition of the Weyl tensor and the contracted Bianchi identity.
Rigidity of Codazzi tensors
Matsushima and Tanno showed that, on a Kähler manifold, any Codazzi tensor which is hermitian is parallel. Berger showed that, on a compact manifold of nonnegative sectional curvature, any Codazzi tensor with constant must be parallel. Furthermore, on a compact manifold of nonnegative sectional curvature, if the sectional curvature is strictly positive at least one point, then every symmetric parallel 2-tensor is a constant multiple of the metric.
See also
Weyl–Schouten theorem
References
Arthur Besse, Einstein Manifolds, Springer (1987).
Tensors |
https://en.wikipedia.org/wiki/Ettore%20Bortolotti | Ettore Bortolotti (6 March 1866 – 17 February 1947) was an Italian mathematician.
Biography
Bortolotti was born in Bologna. He studied mathematics under Salvatore Pincherle and Cesare Arzelà in Bologna. He graduated in mathematics in 1889 at the University of Bologna, under Pincherle. He was appointed as lecturer to the Lyceum of Modica in Sicily in 1891, then studied one year in Paris as a post-graduate, before lecturing at the University of Rome in 1893.
In 1900, he became professor for infinitesimal calculus at Modena. There, he became dean from 1913 to 1919, then moved back to the University of Bologna, where he retired in 1936.
He was an Invited Speaker of the ICM in 1924 in Toronto and in 1928 in Bologna.
Bortolotti must also be considered a differential geometer and a relativist too. In fact, in the year 1929, he commented on the geometric basis for Einstein’s absolute parallelism theory in a paper entitled "Stars of congruences and absolute parallelism: Geometric basis for a recent theory of Einstein".
His son Enea was a mathematician too. Bortolotti died in Bologna.
Selected works
On metric connections with absolute parallelism, Proc. Kon. Akad. Wet. Amsterdam 30 (1927), 216-218.
Reti di Cebiceff e sistemi coniugati nelle Vn riemanniane, Rend. Reale Acc. dei Lincei (6a) 5 (1927), 741-747.
Stelle di congruenze e parallelismo assoluto: basi geometriche di una recente teoria di Einstein, Rend. Reale Acc. dei Lincei 9 (1929), 530-538.
I primi algoritmi infiniti nelle opere dei matematici italiani del secolo XVII (1939)
L'Opera geometrica di Evangelista Torricelli (1939)
Le fonti della matematica moderna. Matematica sumerica e matematica babilonese (1940)
Influenza del campo numerico sullo sviluppo delle teorie algebriche (1941)
Il carteggio matematico di Giovanni Regiomontano con Giovanni Bianchini, Giacomo Speier e Cristiano Roder (1942)
La pubblicazione delle opere e del carteggio matematico di Paolo Ruffini (1943)
Il problema della tangente nell'opera geometrica di Evangelista Torricelli (1943)
Le serie divergenti nel carteggio matematico di Paolo Ruffini (1944)
Il carteggio matematico di Paolo Ruffini (1947)
Notes
External links
An Italian biographical note of Ettore Bortolotti in Archivio storico dell'Università di Bologna
An Italian short biography of Ettore Bortolotti in Edizione Nazionale Mathematica Italiana online.
1866 births
1947 deaths
Scientists from Bologna
Italian historians of mathematics
Differential geometers
Italian relativity theorists |
https://en.wikipedia.org/wiki/Zimmert%20set | In mathematics, a Zimmert set is a set of positive integers associated with the structure of quotients of hyperbolic three-space by a Bianchi group.
Definition
Fix an integer d and let D be the discriminant of the imaginary quadratic field Q(√-d). The Zimmert set Z(d) is the set of positive integers n such that 4n2 < -D-3 and n ≠ 2; D is a quadratic non-residue of all odd primes in d; n is odd if D is not congruent to 5 modulo 8. The cardinality of Z(d) may be denoted by z(d).
Property
For all but a finite number of d we have z(d) > 1: indeed this is true for all d > 10476.
Application
Let Γd denote the Bianchi group PSL(2,Od), where Od is the ring of integers of. As a subgroup of PSL(2,C), there is an action of Γd on hyperbolic 3-space H3, with a fundamental domain. It is a theorem that there are only finitely many values of d for which Γd can contain an arithmetic subgroup G for which the quotient H3/G is a link complement. Zimmert sets are used to obtain results in this direction: z(d) is a lower bound for the rank of the largest free quotient of Γd and so the result above implies that almost all Bianchi groups have non-cyclic free quotients.
References
Integer sequences
Hyperbolic geometry |
https://en.wikipedia.org/wiki/Arthur%20March | Arthur March (23 February 1891 – 17 April 1957) was an Austrian physicist.
From 1909 he studied mathematics and physics at the Universities of Innsbruck, Munich and Vienna, earning his doctorate in 1913. In 1917 he obtained his habilitation, and in 1928 became an associate professor at Innsbruck. From 1934 to 1936 he was a visiting professor at the University of Oxford, afterwards returning to Innsbruck as a full professor of theoretical physics.
March is known for his research in the field of quantum mechanics. One of his more intriguing projects involved finding the smallest space-time distance.
Written works
Theorie der Strahlung und der Quanten, 1919 - Theory of radiation and quantum.
Die Grundlagen der Quantenmechanik, 1931 - The foundation of quantum mechanics.
Einführung in die moderne Atomphysik, 1933 - Introduction to modern atomic physics.
Der Weg des Universums, Bern 1948.
Natur und Erkenntnis in der Konstruktion des heutigen Physikers, 1948.
"Quantum mechanics of particles and wave fields", 1951.
"The new world of physics", 1962 (with Ira M. Freeman); based on Das neue Denken der modernen Physik, 1957, (second edition- 1967).
References
working link
Further reading
External links
Austrian physicists
Academic staff of the University of Innsbruck
1891 births
1957 deaths
People from Brixen |
https://en.wikipedia.org/wiki/Steinberg%20symbol | In mathematics a Steinberg symbol is a pairing function which generalises the Hilbert symbol and plays a role in the algebraic K-theory of fields. It is named after mathematician Robert Steinberg.
For a field F we define a Steinberg symbol (or simply a symbol) to be a function
, where G is an abelian group, written multiplicatively, such that
is bimultiplicative;
if then .
The symbols on F derive from a "universal" symbol, which may be regarded as taking values in . By a theorem of Matsumoto, this group is and is part of the Milnor K-theory for a field.
Properties
If (⋅,⋅) is a symbol then (assuming all terms are defined)
;
;
is an element of order 1 or 2;
.
Examples
The trivial symbol which is identically 1.
The Hilbert symbol on F with values in {±1} defined by
The Contou-Carrère symbol is a symbol for the ring of Laurent power series over an Artinian ring.
Continuous symbols
If F is a topological field then a symbol c is weakly continuous if for each y in F∗ the set of x in F∗ such that c(x,y) = 1 is closed in F∗. This makes no reference to a topology on the codomain G. If G is a topological group, then one may speak of a continuous symbol, and when G is Hausdorff then a continuous symbol is weakly continuous.
The only weakly continuous symbols on R are the trivial symbol and the Hilbert symbol: the only weakly continuous symbol on C is the trivial symbol. The characterisation of weakly continuous symbols on a non-Archimedean local field F was obtained by Moore. The group K2(F) is the direct sum of a cyclic group of order m and a divisible group K2(F)m. A symbol on F lifts to a homomorphism on K2(F) and is weakly continuous precisely when it annihilates the divisible component K2(F)m. It follows that every weakly continuous symbol factors through the norm residue symbol.
See also
Steinberg group (K-theory)
References
External links
Steinberg symbol at the Encyclopaedia of Mathematics
K-theory |
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