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https://en.wikipedia.org/wiki/List%20of%20HFX%20Wanderers%20FC%20records%20and%20statistics | This is an almanac of seasons played by HFX Wanderers FC in the Canadian Premier League (CPL) and other soccer competitions, from HFX's inaugural CPL campaign in 2019 to the present day. It also includes club and individual honours and records for the team. It is updated once yearly near the end of the calendar year, and friendly matches and competitions are excluded.
Key
Key to competitions
Canadian Premier League (CPL) – The top-flight of soccer in Canada, established in 2019.
Canadian Championship (CC) – The premier knockout cup competition in Canadian soccer, first contested in 2008.
CONCACAF Champions Cup (CCC) – The premier competition in North American soccer since 1962. It went by the name of Champions' Cup until 2008 and the Champions League until 2024.
Key to colors and symbols
Key to league record
Season = The year and article of the season
Div = Level on pyramid
League = League name
Pld = Played
W = Games won
L = Games lost
D = Games drawn
GF = Goals scored
GA = Goals against
Pts = Points
PPG = Points per game
Pos. = League position
Key to cup record
DNE = Did not enter
DNQ = Did not qualify
NH = Competition not held or canceled
QR = Qualifying round
PR = Preliminary round
GS = Group stage
R1 = First round
R2 = Second round
R3 = Third round
R4 = Fourth round
R5 = Fifth round
QF = Quarterfinals
SF = Semifinals
RU = Runners-up
W = Winners
Overview
1. Average attendance include statistics from league matches only.
2. Top goalscorer(s) includes all goals scored in league season, league playoffs, Canadian Championship, CONCACAF League, and other competitive continental matches.
Year-by-year statistics
Club honours
None
Individual honours
Golden Boot: Akeem Garcia (2020)
Coach of the Year: Stephen Hart (2020)
U21 Player of the Year nomination: Chrisnovic N'sa (2020)
Goalkeeper of the Year nomination: Christian Oxner (2020)
Golden Boot: João Morelli (2021)
CPL Player of the Year: João Morelli (2021)
Coach of the Year nomination: Patrice Gheisar (2023)
Defender of the Year nomination: Daniel Nimick (2023)
CPL Player of the Year nomination: Lorenzo Callegari (2023)
Privateers 1882 awards
The Privateer 1882 Player of the Year award is selected by a general vote of all members of the Privateers 1882 Supporters Group.
Down The Pub awards (a.k.a. The Pubbies)
The Pubbies are awards given upon review of the season by the Down The Pub podcast and invited journalists.
Club records
Wins
Record win (all major competitions):
3-0 vs Pacific FC, 25 June 2022
3-0 vs Vancouver FC, 12 August 2023
3-0 vs Valour FC, 26 August 2023
Record Canadian Premier League (CPL) win:
3-0 vs Pacific FC, 25 June 2022
3-0 vs Vancouver FC, 12 August 2023
3-0 vs Valour FC, 26 August 2023
Record Canadian Championship win:
2-0 vs Valour FC, 12 June 2019
2-0 vs Guelph United F.C., 10 May 2022
Record home win (CPL):
3-0 vs Vancouver FC, 12 August 2023
3-0 vs Valour FC, 26 August 2023
Record home win (Canadian Champions |
https://en.wikipedia.org/wiki/Germany%20national%20football%20team%20goal%20records | This summarises various goal statistics of the Germany national football team.
Youngest goalscorers
19 youngest goalscorers were younger than 20 years, 38 still underage at their first goal. Lukas Podolski is the youngest player to score two goals in one match, but only in his eighth match. By contrast, Fritz Walter in his first international match as the youngest player yet three goals. Josef Gauchel is the youngest player to score his first goal in a competitive fixture, in the OG 1936 1st Round, all other of the 20 youngest goalscorers scored in friendly matches. The youngest competitive goal scorer is Mario Götze, who scored his second goal at the age of 19 years and 91 days on 2 September 2011 in the EC 2012 Qualification against Austria. The following table lists all national players who have not reached the age of 20 years.
Oldest goalscorers
17 players were over 33 in their last goal, including record goal scorer Miroslav Klose, who also scored the most goals after his 30th birthday. His precursor Gerd Müller scored his last of 68 international goals with 28 years and 246 days, making him the player with the most goals before the 30th Birthday. Klose was 35 years and 362 days old at his 69th international goal, with whom he replaced Müller as the record scorer. Müller was at his 44th international goal, with whom he substituted Uwe Seeler as a record holder 26 years and 205 days old. In turn, he was 29 years and 230 days old when he scored his 34th goal Fritz Walter, who had become 16 days after his 35th birthday record goalscorer, but was unable to play internationals for 8.5 years. The following table lists all national players who have reached the age of 33.
Scorers with at least three goals in a match
50 players score at least three goals in at least one match, 16 of them in at least two matches. Only six players scored in this in their first match. Otto Dumke was the only of them get no further goals. Two other players also scored only these goals, including Julius Hirsch after all four in one match. For four players it was the first goals, but they had previously played a match without scoring. Two players scored only three goals in their last match, for Paul Pömpner it was the only goal.
Most often, three goals of a player in matches against Finland (even two players) and against Switzerland (seven times). In seven matches two players could score at least three goals. In friendly match the most common (50 times) was to score at least three goals by one player. Gerd Müller is the only player who scored three goals in two consecutive matches: On 7 and 10 June 1970, he scored in the World Cup matches against Bulgaria and Peru three goals each. The two matches on 18 and 26 April 1926, in which initially Josef Pöttinger and then Otto Harder scored three goals, followed immediately after each other. Richard Hofmann is the only player who has succeeded in three consecutive years (1928-1932) in each match a "hat-trick". For Mirosla |
https://en.wikipedia.org/wiki/Polly%20Phipps | Polly A. Phipps is an American sociologist and social statistician. She is a Senior Survey Methodologist in the Office of Survey Methods Research of the US Bureau of Labor Statistics. She has also collaborated with several societies of mathematicians to survey the employment of recent doctorates in mathematics.
Education and career
Phipps is originally from Spokane, Washington. She has a bachelor's degree, master's degree, and Ph.D. in sociology, from the University of Washington, Vanderbilt University, and University of Michigan respectively. At the University of Michigan, Phipps' doctoral research included studying the inroads made by women into previously male-dominated careers in pharmacy and insurance; her 1989 dissertation was Sex segregation and the changing sex composition of insurance adjusters and examiners. She joined the Bureau of Labor Statistics in the late 1980s.
Recognition
In 2006–2007, the Washington Statistical Society gave Phipps their President's Award.
She was elected as a Fellow of the American Statistical Association in 2013.
References
Year of birth missing (living people)
Living people
American sociologists
American women sociologists
American statisticians
Women statisticians
University of Washington alumni
Vanderbilt University alumni
University of Michigan alumni |
https://en.wikipedia.org/wiki/Lukas%20Brambilla | Lukas Pivetta Brambilla (born 4 January 1995) is a Brazilian professional footballer who plays as a midfielder for Cypriot club Othellos Athienou.
Career statistics
Club
Notes
References
External links
1995 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Men's association football midfielders
Ykkönen players
Football League (Greece) players
Cypriot First Division players
Qatari Second Division players
Esporte Clube Juventude players
Clube Náutico Capibaribe players
Guarany Futebol Clube players
FC Krymteplytsia Molodizhne players
AC Kajaani players
Apollon Larissa F.C. players
Doxa Katokopias FC players
Mesaimeer SC players
POFC Botev Vratsa players
Brazilian expatriate sportspeople in Ukraine
Expatriate men's footballers in Ukraine
Brazilian expatriate sportspeople in Finland
Expatriate men's footballers in Finland
Brazilian expatriate sportspeople in Greece
Expatriate men's footballers in Greece
Brazilian expatriate sportspeople in Cyprus
Expatriate men's footballers in Cyprus
Brazilian expatriate sportspeople in Qatar
Expatriate men's footballers in Qatar
Brazilian expatriate sportspeople in Bulgaria
Expatriate men's footballers in Bulgaria |
https://en.wikipedia.org/wiki/Cal%20%28footballer%29 | Carlos Alberto Matos Rodrigues (born 14 March 1996), commonly known as Cal, is a Brazilian footballer who currently plays as a midfielder for Enosis.
Career statistics
Club
Notes
References
1996 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Men's association football midfielders
Campeonato Brasileiro Série B players
Cypriot First Division players
Clube Náutico Capibaribe players
Ferroviário Atlético Clube (CE) players
Enosis Neon Paralimni FC players
Brazilian expatriate sportspeople in Cyprus
Expatriate men's footballers in Cyprus
Footballers from Recife |
https://en.wikipedia.org/wiki/Till%20Schumacher | Till Sebastian Schumacher (born 10 December 1997) is a German professional footballer who plays as a defender for Austrian Bundesliga side Austria Klagenfurt.
Career statistics
Club
Notes
References
1997 births
Living people
German men's footballers
Germany men's youth international footballers
German expatriate men's footballers
Men's association football midfielders
Regionalliga players
Czech First League players
Czech National Football League players
Austrian Football Bundesliga players
Rot-Weiss Essen players
Borussia Dortmund players
Borussia Dortmund II players
FC Vysočina Jihlava players
Bohemians 1905 players
SK Austria Klagenfurt (2007) players
German expatriate sportspeople in the Czech Republic
Expatriate men's footballers in the Czech Republic
Footballers from Essen |
https://en.wikipedia.org/wiki/Artem%20Kovernikov | Artem Kovernikov (; born 1 July 2000) is a Ukrainian football defender who played for Dukla Prague.
Career statistics
Club
.
Notes
References
2000 births
Living people
Ukrainian men's footballers
Ukrainian expatriate men's footballers
Men's association football defenders
Czech National Football League players
FC Arsenal Kyiv players
FK Dukla Prague players
Ukrainian expatriate sportspeople in the Czech Republic
Expatriate men's footballers in the Czech Republic |
https://en.wikipedia.org/wiki/William%20Palacios%20%28footballer%2C%20born%202000%29 | William Mackleyther Palacios Vera (born 26 December 2000) is a Colombian footballer playing as a midfielder for Colombian club Deportes Quindío.
Career statistics
Club
.
Notes
References
2000 births
Living people
Colombian men's footballers
Men's association football midfielders
Boca Juniors de Cali footballers
Deportes Quindío footballers
FK Dukla Prague players
C.D. Feirense players
Czech First League players
Czech National Football League players
Liga Portugal 2 players
Colombian expatriate men's footballers
Colombian expatriate sportspeople in the Czech Republic
Expatriate men's footballers in the Czech Republic
Colombian expatriate sportspeople in Portugal
Expatriate men's footballers in Portugal |
https://en.wikipedia.org/wiki/Esteban%20Beltr%C3%A1n | Johan Esteban Beltrán Montano (born 18 October 1999) is a Colombian footballer playing as a midfielder for Once Caldas.
Career statistics
Club
.
Notes
References
1999 births
Living people
Colombian men's footballers
Colombian expatriate men's footballers
Men's association football midfielders
Czech National Football League players
Categoría Primera A players
Once Caldas footballers
FC Vysočina Jihlava players
Colombian expatriate sportspeople in the Czech Republic
Expatriate men's footballers in the Czech Republic |
https://en.wikipedia.org/wiki/Felipe%20Eg%C3%ADdio | Felipe de Oliveira Egídio (born 21 May 1998) is a Brazilian footballer playing as a forward.
Career statistics
Club
.
Notes
References
1998 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Men's association football forwards
Czech National Football League players
Ituano FC players
Mirassol Futebol Clube players
FK Viktoria Žižkov players
Brazilian expatriate sportspeople in the Czech Republic
Expatriate men's footballers in the Czech Republic |
https://en.wikipedia.org/wiki/Maximiliano%20Caba%C3%B1a | Maximiliano Ezequiel Cabaña (born 4 March 1999) is an Argentine footballer currently playing as a midfielder for OTP.
Career statistics
Club
.
Notes
References
1999 births
Living people
Argentine men's footballers
Argentine expatriate men's footballers
Men's association football midfielders
Ettan Fotboll players
Czech National Football League players
FK Viktoria Žižkov players
Argentine expatriate sportspeople in Sweden
Expatriate men's footballers in Sweden
Argentine expatriate sportspeople in the Czech Republic
Expatriate men's footballers in the Czech Republic
Kristianstad FC players
People from Ituzaingó, Corrientes
Footballers from Corrientes Province |
https://en.wikipedia.org/wiki/Maxime%20Vandelannoitte | Maxime Vandelannoitte (born 23 January 2002) is a Belgian footballer who currently plays as a defender for K.S.V. Roeselare.
Career statistics
Club
Notes
References
2002 births
Living people
Belgian men's footballers
Men's association football defenders
Challenger Pro League players
K.S.V. Roeselare players |
https://en.wikipedia.org/wiki/Central%20configuration | In celestial mechanics and the mathematics of the -body problem, a central configuration is a system of point masses with the property that each mass is pulled by the combined gravitational force of the system directly towards the center of mass, with acceleration proportional to its distance from the center. Central configurations may be studied in Euclidean spaces of any dimension, although only dimensions one, two, and three are directly relevant for celestial mechanics.
Examples
For equal masses, one possible central configuration places the masses at the vertices of a regular polygon (forming a Klemperer rosette), a Platonic solid, or a regular polytope in higher dimensions. The centrality of the configuration follows from its symmetry. It is also possible to place an additional point, of arbitrary mass, at the center of mass of the system without changing its centrality.
Placing three masses in an equilateral triangle, four at the vertices of a regular tetrahedron, or more generally masses at the vertices of a regular simplex produces a central configuration even when the masses are not equal. This is the only central configuration for these masses that does not lie in a lower-dimensional subspace.
Dynamics
Under Newton's law of universal gravitation, bodies placed at rest in a central configuration will maintain the configuration as they collapse to a collision at their center of mass. Systems of bodies in a two-dimensional central configuration can orbit stably around their center of mass, maintaining their relative positions, with circular orbits around the center of mass or in elliptical orbits with the center of mass at a focus of the ellipse. These are the only possible stable orbits in three-dimensional space in which the system of particles always remains similar to its initial configuration.
More generally, any system of particles moving under Newtonian gravitation that all collide at a single point in time and space will approximate a central configuration, in the limit as time tends to the collision time. Similarly, a system of particles that eventually all escape each other at exactly the escape velocity will approximate a central configuration in the limit as time tends to infinity. And any system of particles that move under Newtonian gravitation as if they are a rigid body must do so in a central configuration. Vortices in two-dimensional fluid dynamics, such as large storm systems on the earth's oceans, also tend to arrange themselves in central configurations.
Enumeration
Two central configurations are considered to be equivalent if they are similar, that is, they can be transformed into each other by some combination of rotation, translation, and scaling.
With this definition of equivalence, there is only one configuration of one or two points, and it is always central.
In the case of three bodies, there are three one-dimensional central configurations, found by Leonhard Euler. The finiteness of the set of three-po |
https://en.wikipedia.org/wiki/Tait%E2%80%93Kneser%20theorem | In differential geometry, the Tait–Kneser theorem states that, if a smooth plane curve has monotonic curvature, then the osculating circles of the curve are disjoint and nested within each other.
The logarithmic spiral or the pictured Archimedean spiral provide examples of curves whose curvature is monotonic for the entire curve. This monotonicity cannot happen for a simple closed curve (by the four-vertex theorem, there are at least four vertices where the curvature reaches an extreme point) but for such curves the theorem can be applied to the arcs of the curves between its vertices.
The theorem is named after Peter Tait, who published it in 1896, and Adolf Kneser, who rediscovered it and published it in 1912. Tait's proof follows simply from the properties of the evolute, the curve traced out by the centers of osculating circles.
For curves with monotone curvature, the arc length along the evolute between two centers equals the difference in radii of the corresponding circles.
This arc length must be greater than the straight-line distance between the same two centers, so the two circles have centers closer together than the difference of their radii, from which the theorem follows.
Analogous disjointness theorems can be proved for the family of Taylor polynomials of a given smooth function, and for the osculating conics to a given smooth curve.
References
Theorems in differential geometry |
https://en.wikipedia.org/wiki/Milislav%20Popovic | Milislav Popovic (born 6 March 1997) is an Australian footballer currently playing as a forward for Luxembourg National Division club Victoria Rosport.
Career statistics
Club
.
Notes
References
1997 births
Living people
Australian men's soccer players
Australia men's youth international soccer players
Australian expatriate men's soccer players
Australian expatriate sportspeople in Germany
Men's association football forwards
A-League Men players
Regionalliga players
2. Liga (Austria) players
Blacktown City FC players
Macarthur FC players
SS Lazio players
TSV Havelse players
1. FC Köln II players
Eintracht Braunschweig II players
SV Lafnitz players
Australian expatriate sportspeople in Italy
Expatriate men's footballers in Italy
Australian expatriate sportspeople in Austria
Expatriate men's footballers in Austria
Australian expatriate sportspeople in Bulgaria
Expatriate men's footballers in Bulgaria
Australian people of Serbian descent
Soccer players from Sydney |
https://en.wikipedia.org/wiki/Eetu%20Rissanen | Eetu Rissanen (born 15 October 2002) is a Finnish footballer who plays as a forward.
Career statistics
Club
Notes
References
2002 births
Living people
Finnish men's footballers
Finland men's youth international footballers
Men's association football forwards
Pallo-Kerho 37 players
Kuopion Palloseura players
SC Kuopio Futis-98 players
Vaasan Palloseura players
Kokkolan Palloveikot players
Veikkausliiga players
Kakkonen players
Ykkönen players |
https://en.wikipedia.org/wiki/Rotation%20distance | In discrete mathematics and theoretical computer science, the rotation distance between two binary trees with the same number of nodes is the minimum number of tree rotations needed to reconfigure one tree into another. Because of a combinatorial equivalence between binary trees and triangulations of convex polygons, rotation distance is equivalent to the flip distance for triangulations of convex polygons.
Rotation distance was first defined by Karel Čulík II and Derick Wood in 1982. Every two -node binary trees have rotation distance at most , and some pairs of trees have exactly this distance. The computational complexity of computing the rotation distance is unknown.
Definition
A binary tree is a structure consisting of a set of nodes, one of which is designated as the root node, in which each remaining node is either the left child or right child of some other node, its parent, and in which following the parent links from any node eventually leads to the root node.
(In some sources, the nodes described here are called "internal nodes", there exists another set of nodes called "external nodes", each internal node is required to have exactly two children, and each external node is required to have zero children. The version described here can be obtained by removing all the external nodes from such a tree.)
For any node in the tree, there is a subtree of the same form, rooted at and consisting of all the nodes that can reach by following parent links. Each binary tree has a left-to-right ordering of its nodes, its inorder traversal, obtained by recursively traversing the left subtree (the subtree at the left child of the root, if such a child exists), then listing the root itself, and then recursively traversing the right subtree.
In a binary search tree, each node is associated with a search key, and the left-to-right ordering is required to be consistent with the order of the keys.
A tree rotation is an operation that changes the structure of a binary tree without changing its left-to-right ordering. Several self-balancing binary search tree data structures use these rotations as a primitive operation in their rebalancing algorithms. A rotation operates on two nodes and , where is the parent of , and restructures the tree by making be the parent of and taking the place of in the tree. To free up one of the child links of and make room to link as a child of , this operation may also need to move one of the children of to become a child of .
There are two variations of this operation, a right rotation in which begins as the left child of and ends as the right child of , and a left rotation in which begins as the right child of and ends as the left child of .
Any two trees that have the same left-to-right sequence of nodes may be transformed into each other by a sequence of rotations. The rotation distance between the two trees is the number of rotations in the shortest possible sequence of rotations that performs this tr |
https://en.wikipedia.org/wiki/Incomplete%20Bessel%20functions | In mathematics, the incomplete Bessel functions are types of special functions which act as a type of extension from the complete-type of Bessel functions.
Definition
The incomplete Bessel functions are defined as the same delay differential equations of the complete-type Bessel functions:
And the following suitable extension forms of delay differential equations from that of the complete-type Bessel functions:
Where the new parameter defines the integral bound of the upper-incomplete form and lower-incomplete form of the modified Bessel function of the second kind:
Properties
for integer
for non-integer
for non-integer
for non-integer
Differential equations
satisfies the inhomogeneous Bessel's differential equation
Both , , and satisfy the partial differential equation
Both and satisfy the partial differential equation
Integral representations
Base on the preliminary definitions above, one would derive directly the following integral forms of , :
With the Mehler–Sonine integral expressions of and mentioned in Digital Library of Mathematical Functions,
we can further simplify to and , but the issue is not quite good since the convergence range will reduce greatly to .
References
External links
Special hypergeometric functions |
https://en.wikipedia.org/wiki/Lucas%20Esteves | Lucas Esteves Souza (born 24 June 2000) is a Brazilian footballer who plays as a left back for Atlético Goianiense, on loan from Palmeiras.
Career statistics
Club
Notes
Honours
Palmeiras
Campeonato Paulista: 2020
Copa do Brasil: 2020
Copa Libertadores: 2020
Fortaleza
Campeonato Cearense: 2023
References
External links
2000 births
Living people
Footballers from São Paulo
Brazilian men's footballers
Men's association football defenders
Sociedade Esportiva Palmeiras players
Fortaleza Esporte Clube players
Colorado Rapids players
Campeonato Brasileiro Série A players
Major League Soccer players
Brazilian expatriate men's footballers
Brazilian expatriate sportspeople in the United States
Expatriate men's soccer players in the United States |
https://en.wikipedia.org/wiki/Juan%20%28footballer%2C%20born%20March%202002%29 | Juan Santos da Silva (born 6 March 2002), commonly known as Juan, is a Brazilian professional footballer who plays for São Paulo as a forward.
Career statistics
Club
Notes
Honours
São Paulo
Copa do Brasil: 2023
References
External links
2002 births
Living people
Brazilian men's footballers
Brazil men's youth international footballers
Men's association football forwards
Campeonato Brasileiro Série A players
Associação Desportiva São Caetano players
União Agrícola Barbarense Futebol Clube players
São Paulo FC players
Footballers from São Paulo |
https://en.wikipedia.org/wiki/Lucas%20Perri | Lucas Estella Perri (born 10 December 1997) is a Brazilian professional footballer who plays as a goalkeeper for Botafogo.
Career statistics
Honours
São Paulo
Campeonato Paulista: 2021
Náutico
Campeonato Pernambucano: 2022
Botafogo
Taça Rio: 2023
References
1997 births
Living people
Footballers from Campinas
Brazilian men's footballers
Men's association football goalkeepers
Brazil men's youth international footballers
Brazil men's under-20 international footballers
Campeonato Brasileiro Série A players
Associação Atlética Ponte Preta players
São Paulo FC players
Clube Náutico Capibaribe players
Botafogo de Futebol e Regatas players
Crystal Palace F.C. players
Brazilian expatriate men's footballers
Brazilian expatriate sportspeople in England
Expatriate men's footballers in England |
https://en.wikipedia.org/wiki/Charles%20Rezk | Charles Waldo Rezk (born 26 January 1969) is an American mathematician, specializing in algebraic topology, category theory, and spectral algebraic geometry.
Education and career
Rezk matriculated at the University of Pennsylvania in 1987 and graduated there in 1991 with B.A. and M.A. in mathematics. In 1996 he received his PhD from MIT with thesis Spaces of Algebra Structures and Cohomology of Operads and advisor Michael J. Hopkins. At Northwestern University Rezk was a faculty member from 1996 to 2001. At the University of Illinois he was an assistant professor from 2001 to 2006 and an associate professor from 2006 to 2014 and is a full professor since 2014.
He was at the Institute for Advanced Study in the fall of 1999, the spring of 2000, and the spring of 2001. He held visiting positions at MIT in 2006 and at Berkeley's MSRI in 2014. Since 2015 he has been a member of the editorial board of Compositio Mathematica.
Rezk was an invited speaker at the International Congress of Mathematicians in Seoul in 2014. He was elected a Fellow of the American Mathematical Society in the class of 2015 (announced in late 2014).
Selected publications
References
External links
1969 births
Living people
20th-century American mathematicians
21st-century American mathematicians
University of Pennsylvania alumni
Massachusetts Institute of Technology School of Science alumni
Northwestern University alumni
University of Illinois Urbana-Champaign faculty
Fellows of the American Mathematical Society
Topologists
Category theorists |
https://en.wikipedia.org/wiki/Geometry%20Wars | Geometry Wars is a series of top-down multi-directional shooter video games developed by Bizarre Creations, and, later, Lucid Games. Originally published by Microsoft Games Studios, the first title was included as a minigame in Project Gotham Racing 2 for Xbox. An updated version was released in 2005 as a launch title for Xbox 360 and later ported to Microsoft Windows.
Other titles in the series was launched in follow years to other platforms by Bizarre Creations and publishers Vivendi Games and Activision. The latest entry in the series, Geometry Wars 3: Dimensions, was developed by Lucid Games and launched in 2014.
Games
Geometry Wars
Geometry Wars was released in the form of an easter egg minigame in the 2003 racing game Project Gotham Racing 2 on the original Xbox. The game was accessed from within Project Gotham Racing 2 by interacting with an arcade cabinet present in the player's virtual garage.
Geometry Wars: Retro Evolved
Geometry Wars: Retro Evolved was developed by Bizarre Creations and released for Xbox Live Arcade on Xbox 360. At one point, it held the record for the most downloaded Xbox Live Arcade Game.
Geometry Wars: Waves
Geometry Wars: Waves was developed by Stephen Cakebread of Bizarre Creations, released as a bonus mini-game as part of Project Gotham Racing 4 on Xbox 360 on October 2, 2007. The game is a variant of Geometry Wars: Retro Evolved where the player is given one life to survive continual waves of orange rockets that pace back and forth across the edges of the play-field for as long as possible.
Geometry Wars: Galaxies
Geometry Wars: Galaxies was developed by Bizarre Creations and Kuju Entertainment, and published by Vivendi Games for the Wii and Nintendo DS in November 2007, becoming the first Geometry Wars game available on non-Microsoft platforms and the only one available on Nintendo platforms. This updated version includes a single-player campaign mode, several multiplayer modes, Geometry Wars: Retro Evolved, and support for online leaderboards. The Wii version supports widescreen and 480p progressive scan display.
Geometry Wars: Retro Evolved 2
Geometry Wars: Retro Evolved 2 was developed by Bizarre Creations, and released on Xbox Live Arcade on Xbox 360 on July 30, 2008 as a sequel to Geometry Wars: Retro Evolved.
Geometry Wars: Touch
An iOS port of Geometry Wars: Retro Evolved 2 was released in 2010 entitled Geometry Wars: Touch. It added a seventh game mode, Titans, which had gameplay similar to Asteroids, but removed the multiplayer functionality entirely.
Geometry Wars 3: Dimensions
Geometry Wars 3: Dimensions was developed by Lucid Games and published by Activision under the Sierra Entertainment brand name. The game was released on November 25, 2014 for Microsoft Windows, OS X, Linux, PlayStation 3 and PlayStation 4, on November 26, 2014 for Xbox 360 and Xbox One and in the middle of 2015 for iOS, Android and PlayStation Vita. Geometry Wars 3: Dimensions is the first Sierra video ga |
https://en.wikipedia.org/wiki/Takasuke%20Goto | is a Japanese former footballer and beach soccer player.
Career statistics
Club
Notes
References
External links
Official website
1985 births
Living people
Association football people from Kanagawa Prefecture
Nippon Bunri University alumni
Okinawa International University alumni
Japanese men's footballers
Japanese beach soccer players
Japanese expatriate men's footballers
Men's association football midfielders
Singapore Premier League players
Albirex Niigata Singapore FC players
Japanese expatriate sportspeople in Singapore
Expatriate men's footballers in Singapore
Japanese expatriate sportspeople in Switzerland
Japanese expatriate sportspeople in Italy
Japanese expatriate sportspeople in Brazil
Japanese expatriate sportspeople in Germany
Japanese expatriate sportspeople in Israel
Japanese expatriate sportspeople in the United States
Japanese expatriate sportspeople in China
Japanese expatriate sportspeople in Portugal
Japanese expatriate sportspeople in Spain
Japanese expatriate sportspeople in Estonia
Japanese expatriate sportspeople in France |
https://en.wikipedia.org/wiki/Kunihiro%20Honda | is a Japanese former footballer.
Career statistics
Club
Notes
References
1987 births
Living people
Association football people from Tokyo
Shizuoka Sangyo University alumni
Japanese men's footballers
Japanese expatriate men's footballers
Men's association football midfielders
Singapore Premier League players
Albirex Niigata Singapore FC players
Japanese expatriate sportspeople in Singapore
Expatriate men's footballers in Singapore
Japanese expatriate sportspeople in Germany
Expatriate men's footballers in Germany |
https://en.wikipedia.org/wiki/Kazuki%20Yoshino | is a Japanese former footballer.
Career
After playing in Singapore and Thailand, Yoshino played in Myanmar, where he established a charity to help local children.
Career statistics
Club
Notes
References
1985 births
Living people
Sportspeople from Saitama Prefecture
Association football people from Saitama Prefecture
Seisa Dohto University alumni
Japanese men's footballers
Japanese expatriate men's footballers
Men's association football defenders
Albirex Niigata Singapore FC players
Woodlands Wellington FC players
Kazuki Yoshino
Blaublitz Akita players
Zweigen Kanazawa players
Yangon United F.C. players
Singapore Premier League players
Japan Football League players
Japanese expatriate sportspeople in Singapore
Expatriate men's footballers in Singapore
Japanese expatriate sportspeople in Myanmar
Expatriate men's footballers in Myanmar
Magwe F.C. players |
https://en.wikipedia.org/wiki/Ryuta%20Hayashi | is a Japanese former footballer.
Career statistics
Club
Notes
References
1990 births
Living people
Association football people from Gifu Prefecture
Japanese men's footballers
Japanese expatriate men's footballers
Men's association football defenders
Men's association football midfielders
Singapore Premier League players
Japan Soccer College players
Albirex Niigata Singapore FC players
FC Gifu players
Japanese expatriate sportspeople in Singapore
Expatriate men's footballers in Singapore
Japanese expatriate sportspeople in Germany
Expatriate men's footballers in Germany |
https://en.wikipedia.org/wiki/Malwina%20Luczak | Malwina J. Luczak is a mathematician specializing in probability theory and the theory of random graphs. She is Professor of Applied Probability and Leverhulme International Professor at the Department of Mathematics at the University of Manchester.
Education and research
Luczak grew up in Poland, and began her university studies at age 16 at the Nicolaus Copernicus University in Toruń, studying the philology of the English language. However, after a second year studying philology at Keele University in the UK, she decided to switch to mathematics, and enrolled at St Catherine's College, Oxford. After her first year's examinations, she was able to obtain scholarship support and continue her studies and remain at Oxford for doctoral work. She completed her D.Phil. in 2001 with a dissertation, Probability, algorithms and telecommunication systems, supervised by Colin McDiarmid and Dominic Welsh.
She became an assistant lecturer at the Statistical Laboratory at the University of Cambridge and then a reader in mathematics at the London School of Economics. However, in 2010, failing to receive an expected promotion to professor, she took instead a professorial chair at the University of Sheffield and a five-year Engineering and Physical Sciences Research Council Leadership Fellowship. She moved again to Queen Mary University of London before taking a Professorship in Melbourne in 2017. Most recently, in 2023 she joined the University of Manchester.
Research
Luczak's publications include research on the supermarket model in queueing theory,
cores of random graphs, the giant component in random graphs with specified degree distributions, and the Glauber dynamics of the Ising model.
They include:
References
External links
Department of Mathematics, University of Manchester
Year of birth missing (living people)
Living people
Polish women mathematicians
20th-century Polish mathematicians
21st-century Polish mathematicians
Australian mathematicians
Women mathematicians
Probability theorists
Graph theorists
Alumni of St Catherine's College, Oxford
Academics of the University of Cambridge
Academics of the London School of Economics
Academics of the University of Sheffield
Academics of Queen Mary University of London
Academic staff of the University of Melbourne
Academics of the University of Manchester |
https://en.wikipedia.org/wiki/Mark%20H.%20Holmes | Mark H. Holmes is an American applied mathematician and Professor of Mathematics at Rensselaer Polytechnic Institute, where he served as Chair of the Department of Mathematical Sciences, and was the founding Director of the Center for Modeling, Optimization and Computational Analysis (MOCA).
Personal life
Mark H. Holmes was born in Onawa, Iowa on November 7, 1950. He attended Colorado State University, where he earned his B.S. in 1973, and the University of California, Los Angeles, where he received his PhD in mathematics in 1978. His PhD thesis advisor was Julian Cole.
Research
He is known for his contributions in mathematical biology, including mechanoreception (hearing and touch), neurobiology (Parkinson's Disease and the sleep-wake cycle), and tissue mechanics (articular cartilage). His research articles are listed on his Google Scholar page.
Educational initiatives
He has been instrumental in numerous educational initiatives. This has included starting the Rensselaer laptop program (in 1995), co-directing Project Links for developing web-based learning modules (1995–2003), creating the Gateway Exam (1999–2007), organizing the Rensselaer Calculus Video Project (2000–2008), and heading the Rensselaer GAANN program (2009–2016) for recruiting, and retaining, under-represented groups in mathematics. Holmes has written several textbooks based on some of the applied math courses offered at Rensselaer. These are held in 950 libraries worldwide.
Honors and awards
Guggenheim Fellow
Y.C. Fung Young Investigator Award
Premier Award for Excellence in Engineering Education Courseware
American Society of Mechanical Engineers (ASME) Curriculum Innovation Award for 2001
Rensselaer Trustee's Outstanding Teacher Award for 2007
Books
Introduction to Differential Equations, XanEdu Publishing, 2020.
Introduction to Differential Equations, XanEdu Publishing, 2020.
Introduction to the Foundations of Applied Mathematics (2nd Ed), Springer International Publishing, 2019.
Introduction to the Foundations of Applied Mathematics (2nd Ed), Springer International Publishing, 2019.
Introduction to Scientific Computing and Data Analysis, Springer International Publishing, 2016.
Introduction to Scientific Computing and Data Analysis, Springer International Publishing, 2016.
Introduction to Perturbation Methods (2nd Ed), Springer-Verlag New York, 2013.
Introduction to Perturbation Methods (2nd Ed), Springer-Verlag New York, 2013.
Introduction to Numerical Methods in Differential Equations, Springer-Verlag New York, 2007.
Introduction to Numerical Methods in Differential Equations, Springer-Verlag New York, 2007.
References
External links
Holmes' home page at Rensselaer Polytechnic Institute
Mark Holmes at the Mathematics Genealogy Project
1950 births
Living people
20th-century American mathematicians
Applied mathematicians
Rensselaer Polytechnic Institute faculty
Colorado State University alumni
University of California, Los Angeles alumni
21st-century American ma |
https://en.wikipedia.org/wiki/Gian%20%28footballer%2C%20born%201974%29 | Giancarlo Dias Dantas (born 25 August 1974), commonly known as Gian, is a Brazilian former footballer.
Career statistics
Club
Notes
References
1974 births
Living people
Brazilian men's footballers
Brazil men's youth international footballers
Brazilian expatriate men's footballers
Men's association football midfielders
Men's association football forwards
Sociedade Esportiva Matsubara players
CR Vasco da Gama players
América Futebol Clube (RN) players
Sociedade Esportiva Matonense players
FC Luzern players
Associação Atlética Portuguesa (Santos) players
Clube do Remo players
Paysandu Sport Club players
Ceará Sporting Club players
Goiás Esporte Clube players
Campeonato Brasileiro Série A players
Swiss Super League players
Campeonato Brasileiro Série D players
Brazilian expatriate sportspeople in Switzerland
Expatriate men's footballers in Switzerland |
https://en.wikipedia.org/wiki/Mikal%20Kvinge | Mikael Berg Kvinge (born 24 June 2003) is a Norwegian footballer who plays as a forward for Brann.
Career statistics
Club
Notes
References
2003 births
Living people
Footballers from Bergen
Norwegian men's footballers
Norway men's youth international footballers
Men's association football forwards
SK Brann players
Eliteserien players |
https://en.wikipedia.org/wiki/Tomas%20Stabell | Tomas Stabell (born 30 January 2002) is a Norwegian footballer who plays as a midfielder.
Career statistics
Club
Notes
References
2002 births
Living people
Norwegian men's footballers
Men's association football midfielders
Tromsø IL players
IF Fløya (men) players
Eliteserien players |
https://en.wikipedia.org/wiki/Jennifer%20Schultens | Jennifer Carol Schultens (born 1965) is an American mathematician specializing in low-dimensional topology and knot theory. She is a professor of mathematics at the University of California, Davis.
Education
Schultens earned her Ph.D. in 1993 at the University of California, Santa Barbara. Her dissertation, Classification of Heegaard Splittings for Some Seifert Manifolds, was supervised by Martin Scharlemann.
Research
Schultens is the author of the book Introduction to 3-Manifolds (Graduate Studies in Mathematics, 2014). With Martin Scharlemann and Toshio Saito, she is a co-author of Lecture Notes On Generalized Heegaard Splittings (World Scientific, 2016).
Her dissertation research involved the classification of Heegaard splittings of three-dimensional manifolds into handlebodies, which she also published in the Proceedings of the London Mathematical Society.
Other topics in her research include the behavior of knot invariants like bridge number when knots are combined by the connected sum operation, and the Kakimizu complexes of knot complements and other spaces.
Personal
Schultens is married to mathematician Michael Kapovich.
References
External links
Home page
1965 births
Living people
20th-century American mathematicians
21st-century American mathematicians
American women mathematicians
Topologists
University of California, Santa Barbara alumni
University of California, Davis faculty
20th-century American women
21st-century American women |
https://en.wikipedia.org/wiki/Mia%20Hubert | Mia Hubert is a Belgian mathematical statistician known for her research on topics in robust statistics including medoid-based clustering, regression depth, the medcouple for robustly measuring skewness, box plots for skewed data, and robust principal component analysis, and for her implementations of robust statistical algorithms in the R statistical software system, MATLAB, and S-PLUS. She is a professor in the statistics and data science section of the department of mathematics at KU Leuven.
Education and career
Hubert earned a diploma in mathematics in 1992 from the University of Antwerp, and obtained her Ph.D. in 1997 at the same university. Her dissertation, Robust Regression for Data Analysis, was supervised by Peter Rousseeuw. She joined the KU Leuven faculty in 2001.
She was the original developer of the R package cluster along with Peter Rousseeuw and Anja Struyf.
Recognition
Hubert became an Elected Member of the International Statistical Institute in 2013.
Selected publications
References
External links
Cluster R package
Year of birth missing (living people)
Living people
Belgian statisticians
Women statisticians
University of Antwerp alumni
Academic staff of KU Leuven
Elected Members of the International Statistical Institute
R (programming language) people |
https://en.wikipedia.org/wiki/Reconfiguration | In discrete mathematics and theoretical computer science, reconfiguration problems are computational problems involving reachability or connectivity of state spaces.
Types of problems
Here, a state space is a discrete set of configurations of a system or solutions of a combinatorial problem, called states, together with a set of allowed moves linking one state to another. Reconfiguration problems may ask:
For a given class of problems, is the state space always connected? That is, can one transform every pair of states into each other with a sequence of moves? If not, what is the computational complexity of determining whether the state space for a particular problem is connected?
What is the diameter of the state space, the smallest number such that every two states can be transformed into each other with at most moves?
Given two states, what is the complexity of determining whether they can be transformed into each other, or of finding the shortest sequence of moves for transforming one into another?
If moves are chosen randomly with a carefully chosen probability distribution so that the resulting Markov chain converges to a discrete uniform distribution, how many moves are needed in a random walk in order to ensure that the state at the end up the walk is nearly uniformly distributed? That is, what is the Markov chain mixing time?
Examples
Examples of problems studied in reconfiguration include:
Games or puzzles such as the 15 puzzle or Rubik's cube. This type of puzzle can often be modeled mathematically using the theory of permutation groups, leading to fast algorithms for determining whether states are connected; however, finding the state space diameter or the shortest path between two states may be more difficult. For instance, for version's of the Rubik's cube, the state space diameter is , and the complexity of finding shortest solutions is unknown, but for a generalized version of the puzzle (in which some cube faces are unlabeled) it is NP-hard. Other reconfiguration puzzles such as Sokoban may be modeled as token reconfiguration but lack a group-theoretic structure. For such problems, the complexity can be higher; in particular, testing reachability for Sokoban is PSPACE-complete.
Rotation distance in binary trees and related problems of flip distance in flip graphs. A rotation is an operation that changes the structure of a binary tree without affecting the left-to-right ordering of its nodes, often used to rebalence binary search trees. Rotation distance is the minimum number of rotations needed to transform one tree into another. The same state space also models the triangulations of a convex polygon, and moves that "flip" one triangulation into another by removing one diagonal of the polygon and replacing it by another; similar problems have also been studied on other kinds of triangulation. The maximum possible rotation distance between two trees with a given number of nodes is known, but it remains an open problem whether |
https://en.wikipedia.org/wiki/J%C3%BCrgen%20Herzog | Jürgen Reinhard Gerhard Herzog (; born 21 December 1941) is an Emeritus Professor of Mathematics at University of Duisburg-Essen, in Essen, Germany. From 1969 to 1975, he was Lecturer at University of Regensburg and from 1975 to 2009 a professor of Mathematics at University of Duisburg-Essen.
Life
Herzog was born in Heidelberg and raised in Eberbach. After military service in the German Army, he enrolled at the University of Kiel from 1963 and began studying mathematics and physics. Herzog transferred to the University of Heidelberg in 1964, and completed his undergraduate studies there. He received his Ph.D. with a thesis titled, Generators and Relations of Abelian Semigroups and Semigroup Rings at Louisiana State University in 1969 under the supervision of . He completed his habilitation at the University of Regensburg in 1974. He is an expert in the field of commutative algebra and its interactions to other mathematical fields such as combinatorics.
Selected publications
Bruns, Winfred, Herzog, Jürgen, (1993). Cohen-Macaulay rings, Cambridge studies in advanced mathematics 39, Cambridge University Press.
Herzog, Jürgen, Hibi, Takayuki, (2011). Monomial Ideals, Graduate Text in Mathematics.
Ene, Viviana, Herzog, Jürgen] (2012). Gröbner Bases in Commutative Algebra, Graduate Studies in Mathematics, 130. American Mathematical Society, Providence, RI.
Herzog, Jürgen, Hibi, Takayuki, Ohsugi, Hidefumi, (2018). Binomial Ideals, Springer Graduate Texts in Mathematics.
References
20th-century German mathematicians
1941 births
Living people
Scientists from Heidelberg
Louisiana State University alumni
Purdue University alumni
University of Regensburg alumni
Academic staff of the University of Duisburg-Essen
Academic staff of the University of Regensburg
Heidelberg University alumni
People from Eberbach (Baden)
University of Kiel alumni |
https://en.wikipedia.org/wiki/Michael%20Vaughan-Lee | Michael Rogers Vaughan-Lee is a mathematician and retired academic. He was Professor of Mathematics at the University of Oxford from 1996 to 2010 and a tutor at Christ Church, Oxford, between 1971 and 2010.
Career
Vaughan-Lee completed his Doctor of Philosophy (DPhil) degree at the University of Oxford in 1968 and then taught at Vanderbilt University for two years as an assistant professor. In 1970, he was appointed to a lectureship at the University of Queensland, but resigned the following year and returned to the United Kingdom to become a tutor in mathematics at Christ Church, Oxford, where he remained until he retired in 2010. In 1996, he was awarded the title of Professor of Mathematics by the University of Oxford; since retirement in 2010, he has been an emeritus professor.
Research
Vaughan-Lee specialises in group theory, especially the restricted Burnside problem. He has also made contributions relating to Engel Lie algebras, computational algebra, and other areas.
Selected publications
"Lie rings of groups of prime exponent", Journal of the Australian Mathematical Society, vol. 49 (1990), pp. 386–398.
The Restricted Burnside Problem (Oxford University Press, 1st ed., 1990; 2nd ed., 1993).
(with E. I. Zel'manov) "Upper bounds in the restricted Burnside problem", Journal of Algebra, vol. 162 (1993), pp. 107–145.
"An algorithm for computing graded algebras", Journal of Symbolic Computation, vol. 16 (1993), pp. 345–354.
"The nilpotency class of finite groups of exponent p", Transactions of the American Mathematical Society, vol. 346 (1994), pp. 617–640.
(with E. I. Zel'manov) "Upper bounds in the restricted Burnside problem II", International Journal of Algebra and Computation, vol. 6 (1996), pp. 735–744.
"Engel-4 groups of exponent 5", Proceedings of the London Mathematical Society, vol. 74 (1997), pp. 306–334.
"Superalgebras and dimensions of algebras", International Journal of Algebra and Computation, vol. 8 (1998), pp. 97–125.
(with M. F. Newman) "Engel-4 groups of exponent 5. II. Orders", Proceedings of the London Mathematical Society, vol. 79 (1999), pp. 283–317.
(with E. I. Zel'manov) "Bounds in the restricted Burnside problem", Journal of the Australian Mathematical Society, vol. 67 (1999), pp. 261–271.
(with Daniel Groves) "Finite groups of bounded exponent", Bulletin of the London Mathematical Society, vol. 35 (2003), pp. 37–40.
"Simple Lie Algebras of Low Dimension Over GF (2)", LMS Journal of Computation and Mathematics, vol. 9 (2006), pp. pp. 174–192.
"On 4-Engel Groups", LMS Journal of Computation and Mathematics, vol. 10 (2007), pp. 341–353.
References
Living people
Group theorists
Alumni of the University of Oxford
Vanderbilt University faculty
Academic staff of the University of Queensland
Fellows of Christ Church, Oxford
Year of birth missing (living people)
British mathematicians |
https://en.wikipedia.org/wiki/Gy%C3%B6rgy%20Kom%C3%A1romi | György Komáromi (born 19 January 2002) is a Hungarian footballer who currently plays as a forward for Puskás Akadémia.
Career statistics
References
2002 births
Living people
Hungarian men's footballers
Hungary men's youth international footballers
Hungary men's under-21 international footballers
Men's association football forwards
Puskás Akadémia FC players
Aqvital FC Csákvár players
Nemzeti Bajnokság I players
Nemzeti Bajnokság II players |
https://en.wikipedia.org/wiki/Mih%C3%A1ly%20Kata | Mihály Kata (born 13 April 2002) is a Hungarian footballer who plays as a midfielder for MTK and the Hungary national team.
Career statistics
References
2002 births
Living people
Footballers from Budapest
Hungarian men's footballers
Men's association football midfielders
MTK Budapest FC players
Nemzeti Bajnokság I players
Hungary men's youth international footballers
Hungary men's under-21 international footballers
Hungary men's international footballers |
https://en.wikipedia.org/wiki/Mat%C3%ADas%20Segovia | Matías Emanuel Segovia Torales (born 4 January 2003), known as Segovinha, is a Paraguayan footballer who plays as a winger for Brazilian club Botafogo.
Career statistics
Club
Notes
References
2003 births
Living people
People from Caaguazú Department
Paraguayan men's footballers
Men's association football wingers
Paraguayan Primera División players
Club Guaraní players
Campeonato Brasileiro Série A players
Botafogo de Futebol e Regatas players
Paraguayan expatriate men's footballers
Paraguayan expatriate sportspeople in Brazil
Expatriate men's footballers in Brazil
Paraguay men's youth international footballers |
https://en.wikipedia.org/wiki/Diego%20Torres%20%28footballer%2C%20born%202002%29 | Diego Joel Torres Garcete (born 14 October 2002) is a Paraguayan footballer who plays as a midfielder for Celaya F.C.
Career statistics
Club
Notes
References
2002 births
Living people
Men's association football midfielders
Paraguayan men's footballers
Club Olimpia footballers
Paraguayan Primera División players
Paraguay men's youth international footballers |
https://en.wikipedia.org/wiki/Pierre%20Akono | Pierre Ramses Pe Akono (born 29 June 2000) is a Cameroonian footballer who plays as a midfielder for Emirati Club Dibba Al-Hisn.
Career statistics
International
References
External links
2000 births
Living people
Cameroonian men's footballers
Cameroon men's international footballers
Men's association football midfielders
Eding Sport FC players
K.A.S. Eupen players
CD Alcoyano footballers
Dibba Al-Hisn Sports Club players
Belgian Pro League players
Primera Federación players
UAE First Division League players
Cameroonian expatriate men's footballers
Cameroonian expatriate sportspeople in Belgium
Expatriate men's footballers in Belgium
Cameroonian expatriate sportspeople in Spain
Expatriate men's footballers in Spain
Cameroonian expatriate sportspeople in the United Arab Emirates
Expatriate men's footballers in the United Arab Emirates |
https://en.wikipedia.org/wiki/Guillermo%20Tegue | Guillermo Alejandro Tegue Caicedo (born 6 February 2000) is a Colombian footballer who currently plays as a defender for Independiente Medellín.
Career statistics
Club
Notes
References
2000 births
Living people
Colombian men's footballers
Colombia men's youth international footballers
Men's association football defenders
Independiente Medellín footballers
Categoría Primera A players
Footballers from Cauca Department |
https://en.wikipedia.org/wiki/Yadir%20Meneses | Yadir Meneses Betancur (born 1 April 2000) is a Colombian footballer who currently plays as a midfielder for Llaneros.
Career statistics
Club
Notes
References
2000 births
Living people
Colombian men's footballers
Colombia men's youth international footballers
Men's association football midfielders
Envigado F.C. players
Llaneros F.C. players
Categoría Primera A players
Footballers from Antioquia Department |
https://en.wikipedia.org/wiki/Etilson%20Mart%C3%ADnez | Etilson José Martínez Palacio (born 12 May 2000) is a Colombian footballer who currently plays as a midfielder for Real Cartagena.
Career statistics
Club
Notes
References
2000 births
Living people
Colombian men's footballers
Colombia men's youth international footballers
Men's association football midfielders
Bogotá F.C. footballers
Patriotas Boyacá footballers
Llaneros F.C. players
Real Cartagena footballers
Categoría Primera B players
Footballers from Barranquilla |
https://en.wikipedia.org/wiki/Deyman%20Cort%C3%A9s | Deyman Andrés Cortés Herrera (born 29 July 2000) is a Colombian footballer who plays as a forward.
Career statistics
Club
Notes
References
2000 births
Living people
Colombian men's footballers
Colombia men's youth international footballers
Men's association football forwards
Atlético Huila footballers
Categoría Primera A players
People from Rionegro
Footballers from Antioquia Department
21st-century Colombian people |
https://en.wikipedia.org/wiki/Helen%20MacGillivray | Helen Louise MacGillivray is an Australian statistician and statistics educator. She is the former president of the International Statistical Institute, the International Association for Statistical Education, and the Statistical Society of Australia, and chair of the United Nations Global Network of Institutions for Statistical Training.
Education and career
MacGillivray entered her studies at the University of Queensland planning to work in physics, but ended up earning a bachelor's degree with honours in mathematics, in the course of which she discovered her love for statistics. She remained at the University of Queensland for graduate study, and completed a Ph.D. in statistics there. Her dissertation was Moment inequalities with applications to particle size distributions.
She was a professor of statistics and director of the Maths Access Centre at Queensland University of Technology (QUT), until her retirement. She continues to hold an adjunct professorship at QUT.
Service
MacGillivray is the editor of the journal Teaching Statistics.
She was president of the International Statistical Institute for the 2017–2019 term. When she was elected president she became both the second woman and the second Australian to hold the position, after Denise Lievesley and Dennis Trewin.
She was the first female president of the Statistical Society of Australia. She was president of the International Association for Statistical Education for 2009–2011, and is the founding chair of the Global Network of Institutions for Statistical Training of the United Nations.
Books
With Peter Petocz, MacGillivray is the coauthor of the two-volume textbook Statistics and Probability in the Australian Curriculum (Years 7 and 8, and Years 9 and 10), and is the author of Utts & Heckard's Mind on Statistics (Nelson Australia, 2010, adapted from previous work by Jessica Utts and Robert Heckard).
Recognition
MacGillivray is a Fellow of the Royal Statistical Society,
an Australian Learning and Teaching Fellow,
an honorary life member of the Statistical Society of Australia,
and a Principal Fellow of the Higher Education Academy.
References
Year of birth missing (living people)
Living people
Australian statisticians
Women statisticians
Statistics educators
University of Queensland alumni
Academic staff of Queensland University of Technology
Presidents of the International Statistical Institute
Fellows of the Royal Statistical Society
Mathematical statisticians |
https://en.wikipedia.org/wiki/Ali%20Gholamzadeh | Ali Gholamzadeh (; born 13 February 2000) is an Iranian footballer who plays as a goalkeeper for Persian Gulf Pro League side Foolad.
Career statistics
Club
Notes
Honours
Foolad
Hazfi Cup: 2020–21
Iranian Super Cup: 2021
Iran U16
AFC U-16 Championship runner-up: 2016
References
2000 births
Living people
Iranian men's footballers
Persian Gulf Pro League players
Foolad F.C. players
Men's association football goalkeepers
Footballers from Khuzestan province |
https://en.wikipedia.org/wiki/Alireza%20Koushki | Ali Reza Kooshki (; born 16 February 2000) is an Iranian footballer who plays as a midfielder for Persian Gulf Pro League side Foolad.
Career statistics
Club
Notes
Honours
Foolad
Iranian Super Cup: 2021
References
External links
2000 births
Living people
Iranian men's footballers
Persian Gulf Pro League players
Naft va Gaz Gachsaran F.C. players
Sepidrood Rasht S.C. players
Paykan F.C. players
Men's association football midfielders
Foolad F.C. players
People from Kohgiluyeh and Boyer-Ahmad Province
Footballers at the 2022 Asian Games
Alireza Koushki at PersianLeague.com |
https://en.wikipedia.org/wiki/Mohammad%20Ghaderi | Mohammad Ghaderi (; born 27 February 2000) is an Iranian footballer who plays as a midfielder for Persian Gulf Pro League side Tractor.
Career statistics
Club
Notes
Honours
International
Iran U16
AFC U-16 Championship runner-up: 2016
References
External links
2000 births
Living people
Iranian men's footballers
Persian Gulf Pro League players
Machine Sazi F.C. players
Men's association football midfielders
People from Hormozgan Province |
https://en.wikipedia.org/wiki/Luis%20Gam%C3%ADz | Luis Javier Gamíz Ávila (born 4 April 2000) is a Mexican professional footballer who plays as a midfielder.
Career statistics
Club
Honours
Mexico U17
CONCACAF U-17 Championship: 2017
References
2000 births
Living people
Mexican men's footballers
Men's association football midfielders
Club Tijuana footballers
Liga MX players
Tercera División de México players
Footballers from Tijuana
Mexico men's youth international footballers |
https://en.wikipedia.org/wiki/Complex%20Lie%20algebra | In mathematics, a complex Lie algebra is a Lie algebra over the complex numbers.
Given a complex Lie algebra , its conjugate is a complex Lie algebra with the same underlying real vector space but with acting as instead. As a real Lie algebra, a complex Lie algebra is trivially isomorphic to its conjugate. A complex Lie algebra is isomorphic to its conjugate if and only if it admits a real form (and is said to be defined over the real numbers).
Real form
Given a complex Lie algebra , a real Lie algebra is said to be a real form of if the complexification is isomorphic to .
A real form is abelian (resp. nilpotent, solvable, semisimple) if and only if is abelian (resp. nilpotent, solvable, semisimple). On the other hand, a real form is simple if and only if either is simple or is of the form where are simple and are the conjugates of each other.
The existence of a real form in a complex Lie algebra implies that is isomorphic to its conjugate; indeed, if , then let denote the -linear isomorphism induced by complex conjugate and then
,
which is to say is in fact a -linear isomorphism.
Conversely, suppose there is a -linear isomorphism ; without loss of generality, we can assume it is the identity function on the underlying real vector space. Then define , which is clearly a real Lie algebra. Each element in can be written uniquely as . Here, and similarly fixes . Hence, ; i.e., is a real form.
Complex Lie algebra of a complex Lie group
Let be a semisimple complex Lie algebra that is the Lie algebra of a complex Lie group . Let be a Cartan subalgebra of and the Lie subgroup corresponding to ; the conjugates of are called Cartan subgroups.
Suppose there is the decomposition given by a choice of positive roots. Then the exponential map defines an isomorphism from to a closed subgroup . The Lie subgroup corresponding to the Borel subalgebra is closed and is the semidirect product of and ; the conjugates of are called Borel subgroups.
Notes
References
.
Algebra
Lie algebras |
https://en.wikipedia.org/wiki/Seo%20Jin-su | Seo Jin-su (; born 18 October 2000) is a South Korean footballer currently playing as a forward for Jeju United.
Career statistics
Club
Notes
References
2000 births
Living people
South Korean men's footballers
Men's association football forwards
K League 1 players
Jeju United FC players |
https://en.wikipedia.org/wiki/Lee%20Seung-yeop%20%28footballer%29 | Lee Seung-yeop (; born 20 July 2000) is a South Korean footballer currently playing as a forward for Gyeongnam.
Career statistics
Club
Notes
References
2000 births
Living people
South Korean men's footballers
Men's association football forwards
K League 1 players
Gyeongnam FC players |
https://en.wikipedia.org/wiki/Lee%20Dong-ryul | Lee Dong-ryul (; born 9 June 2000) is a South Korean footballer currently playing as a forward for Seoul E-Land.
Career statistics
Club
Notes
Honours
LJeju United
K League 2: 2020
Individual
K League Young Player of the Year (K League 2): 2020
References
External links
2000 births
Living people
South Korean men's footballers
South Korea men's youth international footballers
Men's association football forwards
K League 1 players
K League 2 players
Jeju United FC players
Seoul E-Land FC players |
https://en.wikipedia.org/wiki/List%20of%20South%20African%20provinces%20by%20life%20expectancy | This article lists the provinces of South Africa by their average life expectancy at birth according to data by Statistics South Africa.
Males
Females
See also
List of African countries by life expectancy
References
Health in South Africa
Life expectancy
South African provinces by life expectancy
South Africa |
https://en.wikipedia.org/wiki/Homam%20Ahmed | Homam Al-Amin Ahmed (; born 25 August 1999) is a Qatari professional footballer who plays as a left back for Qatar Stars League side Al-Gharafa and the Qatar national football team.
Career statistics
International goals
Scores and results list Qatar's goal tally first.
Honours
Club
Al-Gharafa
Qatari Stars Cup: 2017-18, 2018-19
References
External links
1999 births
Living people
Qatari men's footballers
Qatari expatriate men's footballers
Qatar men's international footballers
Men's association football defenders
Al-Gharafa SC players
K.A.S. Eupen players
Qatar Stars League players
Belgian Pro League players
Expatriate men's footballers in Belgium
Qatari expatriate sportspeople in Belgium
2021 CONCACAF Gold Cup players
Qatar men's under-20 international footballers
Qatar men's youth international footballers
2022 FIFA World Cup players
2023 CONCACAF Gold Cup players |
https://en.wikipedia.org/wiki/International%20Association%20for%20Statistical%20Education | The International Association for Statistical Education (IASE) is a section of the International Statistical Institute (ISI), a professional association of statisticians, devoted to statistics education. It was founded in 1991 as an outgrowth of the ISI Statistical Education Committee, which had operated since 1948.
Since 2002 the ISI and IASE have published the Statistics Education Research Journal. The IASE is also associated with the quadrennial International Conference on Teaching Statistics, with satellite conferences of the World Statistics Congress, and with smaller roundtable workshops.
The presidents of the IASE have included
David Vere-Jones (1991–1993),
David S. Moore (1993–1995),
Anne Hawkins (1995–1997),
Maria Gabriella Ottaviani (1997–1999),
Brian Phillips (1999–2001),
Carmen Batanero (2001–2003),
Chris Wild (2003–2005),
Gilberte Schuyten (2005–2007),
Allan Rossman (2007–2009),
Helen MacGillivray (2009–2011),
John Harraway (2011–2013),
Iddo Gal (2013–2015),
Andrej Blejec (2015–2017),
Gail F. Burrill (2017–2019),
and Joachim Engel (2019–2021).
References
External links
Home page
International Statistical Institute
Statistics education |
https://en.wikipedia.org/wiki/Kaplansky%27s%20theorem%20on%20projective%20modules | In abstract algebra, Kaplansky's theorem on projective modules, first proven by Irving Kaplansky, states that a projective module over a local ring is free; where a not-necessarily-commutative ring is called local if for each element x, either x or 1 − x is a unit element. The theorem can also be formulated so to characterize a local ring (#Characterization of a local ring).
For a finite projective module over a commutative local ring, the theorem is an easy consequence of Nakayama's lemma. For the general case, the proof (both the original as well as later one) consists of the following two steps:
Observe that a projective module over an arbitrary ring is a direct sum of countably generated projective modules.
Show that a countably generated projective module over a local ring is free (by a "[reminiscence] of the proof of Nakayama's lemma").
The idea of the proof of the theorem was also later used by Hyman Bass to show big projective modules (under some mild conditions) are free. According to , Kaplansky's theorem "is very likely the inspiration for a major portion of the results" in the theory of semiperfect rings.
Proof
The proof of the theorem is based on two lemmas, both of which concern decompositions of modules and are of independent general interest.
Proof: Let N be a direct summand; i.e., . Using the assumption, we write where each is a countably generated submodule. For each subset , we write the image of under the projection and the same way. Now, consider the set of all triples (, , ) consisting of a subset and subsets such that and are the direct sums of the modules in . We give this set a partial ordering such that if and only if , . By Zorn's lemma, the set contains a maximal element . We shall show that ; i.e., . Suppose otherwise. Then we can inductively construct a sequence of at most countable subsets such that and for each integer ,
.
Let and . We claim:
The inclusion is trivial. Conversely, is the image of and so . The same is also true for . Hence, the claim is valid.
Now, is a direct summand of (since it is a summand of , which is a summand of ); i.e., for some . Then, by modular law, . Set . Define in the same way. Then, using the early claim, we have:
which implies that
is countably generated as . This contradicts the maximality of .
Proof: Let denote the family of modules that are isomorphic to modules of the form for some finite subset . The assertion is then implied by the following claim:
Given an element , there exists an that contains x and is a direct summand of N.
Indeed, assume the claim is valid. Then choose a sequence in N that is a generating set. Then using the claim, write where . Then we write where . We then decompose with . Note . Repeating this argument, in the end, we have: ; i.e., . Hence, the proof reduces to proving the claim and the claim is a straightforward consequence of Azumaya's theorem (see the linked article for the argument).
Proof of the theorem: Le |
https://en.wikipedia.org/wiki/Leimkuhler%E2%80%93Matthews%20method | In mathematics, the Leimkuhler-Matthews method (or LM method in its original paper ) is an algorithm for finding discretized solutions to the Brownian dynamics
where is a constant, is an energy function and is a Wiener process. This stochastic differential equation has solutions (denoted at time ) distributed according to in the limit of large-time, making solving these dynamics relevant in sampling-focused applications such as classical molecular dynamics and machine learning.
Given a time step , the Leimkuhler-Matthews update scheme is compactly written as
with initial condition , and where . The vector is a vector of independent normal random numbers redrawn at each step so (where denotes expectation). Despite being of equal cost to the Euler-Maruyama scheme (in terms of the number of evaluations of the function per update), given some assumptions on and solutions have been shown to have a superconvergence property
for constants not depending on . This means that as gets large we obtain an effective second order with error in computed expectations. For small time step this can give significant improvements over the Euler-Maruyama scheme, at no extra cost.
Discussion
Comparison to other schemes
The obvious method for comparison is the Euler-Maruyama scheme as it has the same cost, requiring one evaluation of per step. Its update is of the form
with error (given some assumptions ) as with constant independent of . Compared to the above definition, the only difference between the schemes is the one-step averaged noise term, making it simple to implement.
For sufficiently small time step and large enough time it is clear that the LM scheme gives a smaller error than Euler-Maruyama. While there are many algorithms that can give reduced error compared to the Euler scheme (see e.g. Milstein, Runge-Kutta or Heun's method) these almost always come at an efficiency cost, requiring more computation in exchange for reducing the error. However the Leimkuhler-Matthews scheme can give significantly reduced error with minimal change to the standard Euler scheme. The trade-off comes from the (relatively) limited scope of the stochastic differential equation it solves: must be a scalar constant and the drift function must be of the form . The LM scheme also is not Markovian, as updates require more than just the state at time . However, we can recast the scheme as a Markov process by extending the space.
Markovian Form
We can rewrite the algorithm in a Markovian form by extending the state space with a momentum vector so that the overall state is at time . Initializing the momentum to be a vector of standard normal random numbers, we have
where the middle step completely redraws the momentum so that each component is an independent normal random number. This scheme is Markovian, and has the same properties as the original LM scheme.
Applications
The algorithm has application in any area where the weak (i.e. average) prop |
https://en.wikipedia.org/wiki/Mor%20Ndiaye | Mor Ndiaye (born 22 November 2000) is a Senegalese footballer who currently plays as a defensive midfielder for Estoril.
Career statistics
Club
Honours
Porto Youth
UEFA Youth League: 2018–19
References
2000 births
Living people
Senegalese men's footballers
Senegalese expatriate men's footballers
Men's association football midfielders
Liga Portugal 2 players
FC Porto B players
Primeira Liga players
G.D. Estoril Praia players
Expatriate men's footballers in Portugal
Senegalese expatriate sportspeople in Portugal |
https://en.wikipedia.org/wiki/Boris%20Enow | Boris Enow Takang (born 30 March 2000) is a Cameroonian footballer who currently plays as a midfielder for Maccabi Netanya.
Career statistics
Club
.
Notes
References
2000 births
Living people
Cameroonian men's footballers
Cameroon men's youth international footballers
Men's association football midfielders
FC Porto players
FC Porto B players
RC Lens players
Maccabi Netanya F.C. players
Liga Portugal 2 players
Championnat National 2 players
Israeli Premier League players
Cameroonian expatriate men's footballers
Expatriate men's footballers in Portugal
Expatriate men's footballers in France
Expatriate men's footballers in Israel
Cameroonian expatriate sportspeople in Portugal
Cameroonian expatriate sportspeople in France
Cameroonian expatriate sportspeople in Israel
Place of birth missing (living people) |
https://en.wikipedia.org/wiki/Taddeus%20Nkeng | Taddeus Nkeng Fomakwang (born 26 February 2000) is a Cameroonian footballer who plays as a forward.
Career statistics
Club
Notes
References
2000 births
Living people
Cameroonian men's footballers
Cameroonian expatriate men's footballers
Men's association football forwards
Liga Portugal 2 players
Ukrainian Premier League players
Veikkausliiga players
FC Porto players
FC Porto B players
FC Olimpik Donetsk players
Helsingin Jalkapalloklubi players
Expatriate men's footballers in Portugal
Cameroonian expatriate sportspeople in Portugal
Expatriate men's footballers in Ukraine
Cameroonian expatriate sportspeople in Ukraine
Expatriate men's footballers in Finland
Cameroonian expatriate sportspeople in Finland |
https://en.wikipedia.org/wiki/Lu%C3%ADs%20Pinheiro | Luís Carlos Ventura Pinheiro (born 8 January 2000) is a Portuguese professional footballer who plays as a right-back for Liga 3 club Pêro Pinheiro.
Career statistics
Club
References
2000 births
Living people
People from Vila Viçosa
Portuguese men's footballers
Portugal men's youth international footballers
Men's association football defenders
Men's association football fullbacks
Liga Portugal 2 players
Liga 3 (Portugal) players
S.L. Benfica B players
Varzim S.C. players
Sportspeople from Évora District |
https://en.wikipedia.org/wiki/Mary-Elizabeth%20Hamstrom | Mary-Elizabeth Hamstrom (May 24, 1927 – December 2, 2009) was an American mathematician known for her contributions to topology, and particularly to point-set topology and the theory of homeomorphism groups of manifolds. She was for many years a professor of mathematics at the University of Illinois at Urbana–Champaign.
Early life and education
Hamstrom was born in Pittsburgh, one of three sisters.
She frequently abbreviated her name as M-E, but never Mary.
She was a student at Germantown High School (Philadelphia),
where Anna Mullikin, a mathematician and doctoral student of Robert Lee Moore, had become a teacher. She did her undergraduate studies at the University of Pennsylvania, where Moore had taught many years previously, and completed her bachelor's degree there in mathematics in 1948, after having worked there as an assistant to John Robert Kline, who had been another of Moore's students at the University of Pennsylvania before becoming a faculty member there himself.
Given this background, "she seemed predestined to pursue graduate work with Robert Lee Moore at the University of Texas", as on Kline's recommendation she did. A letter from Moore to Hamstrom, while she was still a senior at the University of Pennsylvania, describes the Moore method of teaching mathematics and expresses Moore's regret that she had already begun study in her intended specialty; Moore preferred to begin with a clean slate. This letter has been described as being "of considerable importance in the history of mathematics education".
Hamstrom completed her Ph.D. at the University of Texas at Austin in 1952. Her dissertation, under Moore's supervision, was Concerning Webs in the Plane. F. Burton Jones, another Moore student on the Texas faculty, became another of her mentors.
Career and later life
On completing her doctorate, Hamstrom became a faculty member at Goucher College, then a women's college, and she earned tenure there in 1957 after a year at the Institute for Advanced Study. While visiting the institute, she was encouraged to move to the University of Illinois at Urbana–Champaign by Paul T. Bateman, who was a professor there and was also visiting the Institute at the same time. Hamstrom had known Bateman from the University of Pennsylvania, where he was a graduate student when she was an undergraduate.
Following Bateman's advice, she moved to the University of Illinois in 1961.
Five years later, when the university promoted her to full professor, she became only one of four women with that rank in the College of Liberal Arts and Sciences. She retired in 1999.
Hamstrom's "period of greatest creative activity" was from 1950 to 1980, during which she published 24 papers on point set topology, geometric topology, and the homeomorphisms of manifolds, and supervised eight doctoral students. (A ninth student completed a doctorate in 1999, the year of Hamstrom's retirement.)
References
External links
Mary-Elizabeth Hamstrom Papers, 1929–2004, University |
https://en.wikipedia.org/wiki/List%20of%20South%20African%20provinces%20by%20fertility%20rate | This article lists the provinces of South Africa by their average total fertility rate per woman according to data by Statistics South Africa.
References
Fertility rate
South African provinces by fertility rate
Fertility |
https://en.wikipedia.org/wiki/Hao%20Huang%20%28mathematician%29 | Hao Huang is a mathematician known for solving the sensitivity conjecture. Huang is currently an associate professor in the mathematics department at National University of Singapore.
Huang was an assistant professor from 2015 to 2021 in the Department of Mathematics at Emory University. He obtained his Ph.D in mathematics from UCLA in 2012 advised by Benny Sudakov. His postdoctoral research was done at the Institute for Advanced Study in Princeton and DIMACS at Rutgers University in 2012-2014, followed by a year at the Institute for Mathematics and its Applications at University of Minnesota.
In July 2019, Huang announced a breakthrough, which gave a proof of the sensitivity conjecture. At that point the conjecture had been open for nearly 30 years, having been posed by Noam Nisan and Mario Szegedy in 1992.
Theoretical computer scientist Scott Aaronson said of Huang's ingenious two-page proof, "I find it hard to imagine that even God knows how to prove the Sensitivity Conjecture in any simpler way than this."
Huang received an NSF Career Award in 2019 and a Sloan Research Fellowship in 2020.
References
External links
Year of birth missing (living people)
Living people
Academic staff of the National University of Singapore
Emory University faculty
Sloan Research Fellows
Peking University alumni
University of California, Los Angeles alumni
University of Minnesota alumni
21st-century Chinese mathematicians
Combinatorialists |
https://en.wikipedia.org/wiki/Ho%20Weang%20Kee | Ho Weang Kee is a Malaysian statistician whose research focuses on the application of statistical methods to genetic data analysis. She is an associate professor of statistics at the University of Nottingham Malaysia Campus in the Department of Applied Mathematics. In 2018, Ho received the L'Oréal-UNESCO International Rising Talent Award in recognition of her work toward developing a predictive model estimating the risk of breast cancer for Southeast Asian women.
Education
Ho attended Northumbria University from 2002 to 2005 and graduated with a Bachelor of Science with Honours (BSc(Hons)) degree in Mathematics. In 2005, she began her graduate studies in mathematics at Newcastle University. Ho's early interest in mathematics eventually inspired her to study statistics. Her doctoral advisor, biostatistician Robin Henderson, introduced her to the potential applications of mathematics and statistics in answering scientific questions. Ho conducted research on how to approach and account for incomplete data in longitudinal and survival studies. She completed her Doctor of Philosophy (PhD) degree in 2009.
Career and research
Ho's first postdoctoral research experience was at the National Institute for Health Research, where she applied advanced mathematic methodology to child speech and development studies and trained health professionals in the use of statistical methods. In 2010, Ho returned to Newcastle University to conduct postdoctoral research in its School of Mathematics and Statistics. From January 2011 to April 2013, Ho worked as a medical and genetic statistician at the University of Cambridge Department of Public Health and Primary Care.
Predicting breast cancer risk
In May 2013, Ho left the United Kingdom and returned to Malaysia. A month later, in June 2013, she joined the University of Nottingham Malaysia Campus as an assistant professor in the Department of Applied Mathematics and was promoted to associate professor in 2017. Rather than the rare mutations of BRCA1 and BRCA2, the relatively common and more subtle variations associated with breast cancer are of greater interest to Ho. While having only one of these variations typically results in little to no effect on an individual's health, inheriting a combination of these variations could be detrimental for breast cancer risk. Thus, the goal of Ho's current research is to determine which combination of variations associated with breast cancer risk will result in the greatest predicted breast cancer risk. Ho's research utilizes research led by her friend and colleague Teo Soo Hwang, the CEO of Cancer Research Malaysia, the largest breast cancer study in Malaysia. The motivation behind Ho's research is to improve the efficiency and effectiveness of breast cancer screening in Malaysia, where the number of breast cancer cases are expected to increase by 50% in the next decade. By identifying women with a greater risk of developing breast cancer, Ho hopes to establish a more personali |
https://en.wikipedia.org/wiki/Stephen%20A.%20Fulling | Stephen Albert Fulling (born 29 April 1945, Evansville, Indiana) is an American mathematician and mathematical physicist, specializing in the mathematics of quantum theory, general relativity, and the spectral and asymptotic theory of differential operators. He is known for preliminary work that led to the discovery of the hypothetical Unruh effect (also known as
the Fulling-Davies-Unruh effect).
Education and career
After secondary education at Missouri's Lindbergh High School, Fulling graduated in 1967 with A.B. in physics from Harvard University. At Princeton University he became a graduate student in physics and received M.S. in 1969 and Ph.D. in 1972. His thesis Scalar Quantum Field Theory in a Closed Universe of Constant Curvature was supervised by Arthur Wightman. Fulling was a postdoc from 1972 to 1974 at the University of Wisconsin-Milwaukee and from 1974 to 1976 at King’s College London. At Texas A&M University he joined the mathematics faculty in 1976 and was promoted to full professor in 1984. In addition to mathematics, he holds a joint appointment in physics and astronomy.
In 2018 Fulling was elected a fellow of the American Physical Society. He has also been elected a foreign member of the Royal Society of Sciences in Uppsala.
Selected publications
Books
Articles
See also
Differential operator
Fulling–Davies–Unruh effect
General relativity
Mathematical formulation of quantum mechanics
Quantum Field Theory
References
External links
Oral history interview transcript with Stephen Fulling on 8 July 2021, American Institute of Physics, Niels Bohr Library & Archives
1945 births
Living people
20th-century American mathematicians
21st-century American mathematicians
20th-century American physicists
21st-century American physicists
Mathematical physicists
Harvard College alumni
Princeton University alumni
Texas A&M University faculty
Fellows of the American Physical Society
People from Evansville, Indiana
Mathematicians from Missouri
Physicists from Missouri |
https://en.wikipedia.org/wiki/Convex%20hull%20of%20a%20simple%20polygon | In discrete geometry and computational geometry, the convex hull of a simple polygon is the polygon of minimum perimeter that contains a given simple polygon. It is a special case of the more general concept of a convex hull. It can be computed in linear time, faster than algorithms for convex hulls of point sets.
The convex hull of a simple polygon can be subdivided into the given polygon itself and into polygonal pockets bounded by a polygonal chain of the polygon together with a single convex hull edge. Repeatedly reflecting an arbitrarily chosen pocket across this convex hull edge produces a sequence of larger simple polygons; according to the Erdős–Nagy theorem, this process eventually terminates with a convex polygon.
Structure
The convex hull of a simple polygon is itself a convex polygon. Overlaying the original simple polygon onto its convex hull partitions this convex polygon into regions, one of which is the original polygon. The remaining regions are called pockets. Each pocket is itself a simple polygon, bounded by a polygonal chain on the boundary of the given simple polygon and by a single edge of the convex hull. A polygon that is already convex has no pockets.
One can form a hierarchical description of any given polygon by constructing its hull and its pockets in this way and then recursively forming a hierarchy of the same type for each pocket. This structure, called a convex differences tree, can be constructed efficiently.
Algorithms
Finding the convex hull of a simple polygon can be performed in linear time. Several early publications on this problem were discovered to be incorrect, often because they led to intermediate states with crossings that caused them to break. The first correct linear-time algorithm for this problem was given by . Even after its publication, other incorrect algorithms continued to be published. write that a majority of the published algorithms for the problem are incorrect, although a later history collected by Greg Aloupis lists only seven out of fifteen algorithms as being incorrect.
A particularly simple algorithm for this problem was published by and . Like the Graham scan algorithm for convex hulls of point sets, it is based on a stack data structure. The algorithm traverses the polygon in clockwise order, starting from a vertex known to be on the convex hull (for instance, its leftmost point). As it does, it stores a convex sequence of vertices on the stack, the ones that have not yet been identified as being within pockets. The points in this sequence are the vertices of a convex polygon (not necessarily the hull of all vertices seen so far) that may have pockets attached to some of its edges. At each step, the algorithm follows a path along the polygon from the stack top to the next vertex that is not in one of the two pockets adjacent to the stack top. Then, while the top two vertices on the stack together with this new vertex are not in convex position, it pops the stack, before fina |
https://en.wikipedia.org/wiki/G.%20Nanjundan | G. Nanjundan ( – December 2019) was an Indian academic and writer. He was conferred Sahitya Akademi Award for Tamil Translation in 2012. He was a professor of Bangalore University's statistics department.
Biography
Nanjundan was a professor of Bangalore University's statistics department. He was involved in teaching for over 32 years. He had more than 10 publications, too.
Nanjundan translated several Kannada books into Tamil. He translated more than 12 books from Kannada to Tamil. He was awarded Sahitya Akademi Award for Tamil Translation in 2012 for translation of Akka from Kannada into Tamil titled Akka. The original book was the short story collections of several women writers. He also translated Bhava and Avaste into Tamil which were written by U. R. Ananthamurthy.
Nanjundan was found dead on 21 December 2019 in his apartment.
References
1960s births
2019 deaths
Indian translators
Recipients of the Sahitya Akademi Award in Tamil
Academic staff of Bangalore University
Translators from Kannada
Translators to Tamil
20th-century translators
Recipients of the Sahitya Akademi Prize for Translation |
https://en.wikipedia.org/wiki/Dillon%20Forte | Dillon Forte (born February 1987 in Santa Monica, California) is an American tattoo artist and entrepreneur, based in Oakland and Venice, Los Angeles. Known for his use of sacred geometry-inspired patterns, Forte has been featured in Paramount Network's The Art of Ink (2018) and the Amazon Studios comedy Jean-Claude Van Johnson (2017).
Biography
Forte was born in Santa Monica, California. His mother is a romance novelist, and his father worked as a fashion photographer. He grew up in Berkeley and Oakland, and got his first tattoo at 16. After spending two years seeking an apprenticeship, at 19, Forte began working for tattoo artist Mark Freitas in Berkley, Forte saw a career in tattoo as a natural progression from his childhood interests of drawing, painting and skateboarding. Inspired by reading Drunvalo Melchizedek's The Ancient Secret of the Flower of Life (1999), Forte became interested in incorporating geometric patterns found in nature, as well as the geometric shapes found in traditional sacred geometry.
After six years, Forte opened his first tattoo studio in Oakland in 2012, and opened his second on Abbot Kinney Boulevard in Venice, Los Angeles in 2019. Forte developed a tetrahedral kite tattoo for artist Kat Von D, and tattooed actor Chris Hemsworth in Morocco, based on a design Hemsworth's daughter made while he was filming Men in Black: International in 2018. Forte additionally worked on tattoos with singer Kehlani and linebacker DeAndre Levy, and in 2018 was featured in an episode of Paramount Network's The Art of Ink, focusing on geometric designs.
In 2019, Forte worked with singer Usher on an elaborate head tattoo, and on a hand tattoo for Imagine Dragons' bassist Ben McKee. In 2020, Forte launched a range of naturally derived eco-friendly tattoo products.
Style
Forte's designs are inspired by sacred geometry and underlying mathematical principles found in nature, and additionally by ancient cosmology, tribal and spiritual art. Forte uses blackwork and dot work tattooing techniques.
Filmography
Television
References
External links
1987 births
Living people
American businesspeople
American tattoo artists
People from Berkeley, California
People from Oakland, California
People from Santa Monica, California |
https://en.wikipedia.org/wiki/Red%20August | Red August () is a term used to indicate a period of political violence and massacres in Beijing beginning in August 1966, during the Chinese Cultural Revolution. According to official statistics published in 1980, Red Guards in Beijing killed a total of 1,772 people during Red August, while 33,695 homes were ransacked and 85,196 families were forcibly displaced. However, according to official statistics published in November 1985, the number of deaths in Beijing during Red August was 10,275.
On August 18, 1966, Chairman Mao Zedong met with Song Binbin, a leader of the Red Guards, atop Tiananmen. This event instigated a wave of violence and mass killings in the city by the Red Guards, who also started a campaign to destroy the "Four Olds". The killings by the Red Guards also impacted several rural districts in Beijing, such as in the Daxing Massacre, in which 325 people were killed from August 27 to September 1 in the Daxing District of Beijing. Meanwhile, a number of people, including notable writer Lao She, committed suicide or attempted suicide after being persecuted. During the massacres, Mao Zedong publicly opposed any governmental intervention to the student movement, and Xie Fuzhi, the Minister of Ministry of Public Security, instructed police and public security organs to protect the Red Guards instead of arresting them. However, the situation went out of control at the end of August 1966, forcing the Central Committee of the Chinese Communist Party (CCP) and Chinese government to take multiple interventions which gradually brought the massacres to an end.
Red August is considered the origin of Red Terror in the Chinese Cultural Revolution. It has also been compared with Nazi Germany's Kristallnacht, as well as with the Nanjing Massacre conducted by the Japanese military during the Second Sino-Japanese War.
History
Historical Background
On May 16, 1966, Mao Zedong launched the Cultural Revolution in mainland, China. On August 5, Bian Zhongyun, the first vice principal of the Experimental High School Attached to Beijing Normal University, was beaten to death by a group of Red Guards—mostly her students—and became the first education worker in Beijing killed by the Red Guards.
Massacre in Beijing
On August 18, 1966, Mao Zedong met with Song Binbin, a leader of the Red Guards, atop Tiananmen of Beijing. Mao asked Song Binbin whether the "Bin" in her given name was the same Chinese character as that in Chinese Chengyu "Wen Zhi Bin Bin (文质彬彬)"; upon receiving confirmation, Mao commented that, “Yao Wu Ma (要武嘛)”, meaning "be valiant" or "(you'd) better fight". After this meeting, the morale of the Red Guards was significantly boosted, triggering their massive slaughter in Beijing. In particular, on August 25, 1966, thousands of Red Guards started a week-long massacre in Langan Market () of the Chongwen District. At the same time, Red Guards launched a nationwide campaign to destroy the "Four Olds". In Beijing alone, a total of 4,922 his |
https://en.wikipedia.org/wiki/Witold%20Abramowicz%20%28scientist%29 | Witold Abramowicz is a Polish scientist, professor of economics, postdoctoral degree in mathematics and engineer, chair of the Department of Information Systems at PUEB. He received the Knight's Cross of the Polonia Restituta Cross in 2019.
References
Living people
Knights of the Order of Polonia Restituta
Polish scientists
Academic staff of the Poznań University of Economics and Business
Year of birth missing (living people) |
https://en.wikipedia.org/wiki/Susan%20G.%20Bond | Susan Bond (born 1942), was a scientific officer and computer programmer for the Mathematics Division of the Royal Radar Establishment (RRE) in the United Kingdom. She worked extensively on the programming language ALGOL 68 and the Royal Radar Establishment Automatic Computer (RREAC), an early solid-state electronics, ICL 1907F computer.
Early life
Bond was born in 1942 and grew up in Dagenham, Essex, in the United Kingdom (UK). Both her parents were teachers, and she was an only child. She studied at Bristol University from 1962 to 1965, where she studied mathematics and science and received first-class honours.
Career and research
After graduating from Bristol, Bond was interested in working in applied mathematics, although she didn't have computer training before then. She applied to and joined the Mathematics Division of the RRE in 1965; she was hired by British mathematician and engineer Philip Woodward. Her work mostly consisted of writing operating systems and compilers, not "numerical" computing. At the start of her career, Bond was the only female scientific officer with a graduate education at RRE. Bond later learned that her supervisor Woodward had been, as historian Janet Abbate describes, "'actively recruiting women' as an affordable source of high-quality researchers".
One of her first projects was reimplementing Syntax Improving Device (SID), a compiler-compiler tool developed by fellow RRE employee Michael Foster, to generate compilers for high-level programming languages. Afterward, she worked with Ian Currie on CORAL 64, a high-level language for embedded system computers.
Implementing ALGOL 68
The RRE had originally used ALGOL 60 for the RREAC from its initial development in 1963. After the International Federation for Information Processing (IFIP) published the specifications for the more powerful ALGOL 68 in 1968, RRE attempted to adapt it for use on the RREAC. Bond worked with John Morison and Ian Currie on ALGOL 68-R, the first compiler implementation of ALGOL 68, and they announced its creation at the 20–24 July 1970 IFIP Working Conference on ALGOL 68 Implementation in Munich. Their ALGOL 68-R was an adaptation of the ALGOL 60 compiler they had built for RREAC. The team that worked on ALGOL 68-R intended for the language to become the RRE's primary programming language, which could be used for scientific programming as well as business administration tasks like payroll and taking inventory.
After the publication of the ALGOL 68-R specifications, Bond and Woodward published a narrative guide to ALGOL 68, titled "ALGOL 68-R User’s Guide" through HM Stationery Office. The initial 17,000 copy run sold out. Bond effectively provided ongoing support for the compiler: readers would contact her whenever they had trouble implementing it. Bond and Woodward continued to update and publish new versions of their guide for the RRE's later implementations of ALGOL, such as ALGOL 68RS. One reviewer, Richard Shreeve, contested th |
https://en.wikipedia.org/wiki/Ole%20Sigmund | Ole Sigmund (born 28 May 1966) is a Danish Professor in Mechanical Engineering who has made fundamental contributions to the field of topology optimization, including microstructure design, nano optics, photonic crystals, Matlab code, acoustics, and fluids. In 2003 he co-authored the highly cited book "Topology Optimization: Theory, Methods and Applications" with Martin P. Bendsøe. His research group was the first to achieve giga-resolution topology optimization, making it for the first time possible to optimize an entire Boeing 777 wing structure.
Education
Ole Sigmund attended Tornbjerg Gymnasium before enrolling at the Technical University of Denmark, where he earned his MSc in Mechanical Engineering (1991), his PhD in Mechanical Engineering (1995), and his Dr. Techn. (Danish Habilitation) in (2001).
Career
He is a professor (faculty since 1997) at the Technical University of Denmark. He has been a research assistant at Essen University (1991–1992) and Postdoc at Princeton Materials Institute, Princeton University (1995–1996). He has been on sabbatical leave at the University of Colorado Boulder (2012). He is currently a VILLUM Investigator supported by the VILLUM Foundation. 2004–2010 he served as the Chairman of the Danish Center for Applied Mathematics and Mechanics (DCAMM) and as the elected President of the International Society for Structural and Multidisciplinary Optimization (ISSMO) in the period 2011–2015 (and Executive Member 2015–2023). He was elected member of the Royal Danish Academy of Sciences and Letters in 2008 and the Danish Academy of Technical Sciences (ATV) in 2003.
References
1966 births
Living people
Academic staff of the Technical University of Denmark
Technical University of Denmark alumni |
https://en.wikipedia.org/wiki/Adela%20Ruiz%20de%20Royo | Adela María Ruiz González , customary married name Ruiz de Royo (December 15, 1943 – June 19, 2019) was a Spanish-born Panamanian mathematics academic and educator. She served as the First Lady of Panama from 1978 until 1982 during the presidency of her husband, Aristides Royo. She also served President of the Panamanian Academy of Language (Academia Panameña de la Lengua).
Biography
Ruiz was born Adela María Ruiz González in a home in the municipality of Grado, Asturias, Spain to parents, José María and Rosalina. She was raised in the nearby city of Oviedo alongside her three sisters, Marta, Mabel, and María José. Ruiz was nicknamed Deli.
By 1960, Ruiz had moved to Salamanca to study medicine. That same year, she met her future husband, a Panamanian national and fellow student at the University of Salamanca named Aristides Royo. The couple married in the early 1960s and eventually had three children - Marta Elena, Irma Natalia, and Aristides José. Ruiz, Royo and their oldest daughter, Marta, moved to Panama permanently on September 17, 1965.
In addition to her own career, Ruiz held the role of the wife of a government minister and politician. She became First Lady of Panama from 1978 to 1982. During her tenure as first lady, Ruiz created the Asociación Pro Obras de Beneficencia.
Ruiz was diagnosed with colon and liver cancer in 2017. She died from the disease on June 19, 2019, at the age of 75. Adela Ruiz was survived by her husband, Aristides Royo, and their three children, Marta Elena, Natalia, and Arístides José. Her funeral was held at the National Sanctuary in Bella Vista, Panama City on June 24, 2019. Ruiz's ashes were returned to her native Spain, where they were partially buried at the Praviano cemetery in Riberas, Asturias. A second funeral mass was held at the Carmelite Catholic Church of Oviedo on October 4, 2019. Shortly before the funeral, her remaining ashes were sprinkled into the Cantabrian Sea by her husband and children.
In December 2019, Ruiz's daughter, Natalia Royo de Hagerman, was appointed as Panama's ambassador to the United Kingdom.
References
2019 deaths
First ladies and gentlemen of Panama
Panamanian educators
Panamanian women educators
Panamanian academic administrators
Panamanian mathematicians
Women mathematicians
Mathematics educators
University of Salamanca alumni
Spanish emigrants to Panama
Panamanian people of Asturian descent
People from Oviedo
1943 births
Panamanian women scientists |
https://en.wikipedia.org/wiki/Eakin%E2%80%93Nagata%20theorem | In abstract algebra, the Eakin–Nagata theorem states: given commutative rings such that is finitely generated as a module over , if is a Noetherian ring, then is a Noetherian ring. (Note the converse is also true and is easier.)
The theorem is similar to the Artin–Tate lemma, which says that the same statement holds with "Noetherian" replaced by "finitely generated algebra" (assuming the base ring is a Noetherian ring).
The theorem was first proved in Paul M. Eakin's thesis and later independently by . The theorem can also be deduced from the characterization of a Noetherian ring in terms of injective modules, as done for example by David Eisenbud in ; this approach is useful for a generalization to non-commutative rings.
Proof
The following more general result is due to Edward W. Formanek and is proved by an argument rooted to the original proofs by Eakin and Nagata. According to , this formulation is likely the most transparent one.
Proof: It is enough to show that is a Noetherian module since, in general, a ring admitting a faithful Noetherian module over it is a Noetherian ring. Suppose otherwise. By assumption, the set of all , where is an ideal of such that is not Noetherian has a maximal element, . Replacing and by and , we can assume
for each nonzero ideal , the module is Noetherian.
Next, consider the set of submodules such that is faithful. Choose a set of generators of and then note that is faithful if and only if for each , the inclusion implies . Thus, it is clear that Zorn's lemma applies to the set , and so the set has a maximal element, . Now, if is Noetherian, then it is a faithful Noetherian module over A and, consequently, A is a Noetherian ring, a contradiction. Hence, is not Noetherian and replacing by , we can also assume
each nonzero submodule is such that is not faithful.
Let a submodule be given. Since is not faithful, there is a nonzero element such that . By assumption, is Noetherian and so is finitely generated. Since is also finitely generated, it follows that is finitely generated; i.e., is Noetherian, a contradiction.
References
Further reading
Math StackExchange - Exercise from Kaplansky's Commutative Rings and Eakin-Nagata Theorem
Theorems in ring theory
Commutative algebra |
https://en.wikipedia.org/wiki/Weakly%20simple%20polygon | In geometry, a weakly simple polygon is a generalization of a simple polygon, allowing the polygon sides to touch each other in limited ways. Different authors have defined weakly simple polygons in different ways:
One definition is that, when a simply connected open set in the plane is bounded by finitely many line segments, then its boundary forms a weakly simple polygon. In the image, ABCDEFGHJKLM is a weakly simple polygon according to this definition, with the color blue marking the region for which it is the boundary. This type of weakly simple polygon can arise in computer graphics and CAD as a computer representation of polygonal regions with holes: for each hole a "cut" is created to connect it to an external boundary. Referring to the image above, ABCM is an external boundary of a planar region with a hole FGHJ. The cut ED connects the hole with the exterior and is traversed twice in the resulting weakly simple polygonal representation.
In an alternative and more general definition of weakly simple polygons, they are the limits of sequences of simple polygons. The polygons in the sequence should all have the same combinatorial type as each other, with convergence under the Fréchet distance. This formalizes the notion that such a polygon allows segments to touch but not to cross. This generalizes the notion of the polygonal boundary of a topological disk: this boundary is the limit of a sequence of polygons, offset from it within the disk. However, this type of weakly simple polygon does not need to form the boundary of a region, as its "interior" can be empty. For example, referring to the same image, the polygonal chain ABCBA is a weakly simple polygon according to this definition: it may be viewed as the limit of "squeezing" of the polygon ABCFGHA.
References
Types of polygons |
https://en.wikipedia.org/wiki/Relative%20convex%20hull | In discrete geometry and computational geometry, the relative convex hull or geodesic convex hull is an analogue of the convex hull for the points inside a simple polygon or a rectifiable simple closed curve.
Definition
Let be a simple polygon or a rectifiable simple closed curve, and let be any set enclosed by .
A geodesic between two points in is a shortest path connecting those two points that stays entirely within .
A subset of the points inside is said to be relatively convex, geodesically convex, or -convex if, for every two points of , the geodesic between them in stays within . Then the relative convex hull of can be defined as the intersection of all relatively convex sets containing .
Equivalently, the relative convex hull is the minimum-perimeter weakly simple polygon in that encloses . This was the original formulation of relative convex hulls, by . However this definition is complicated by the need to use weakly simple polygons (intuitively, polygons in which the polygon boundary can touch or overlap itself but not cross itself) instead of simple polygons when is disconnected and its components are not all visible to each other.
Special cases
Finite sets of points
, who provided an efficient algorithm for the construction of the relative convex hull for finite sets of points inside a simple polygon. With subsequent improvements in the time bounds for two subroutines, finding shortest paths between query points in a polygon, and polygon triangulation, this algorithm takes time on an input with points in a polygon with vertices. It can also be maintained dynamically in sublinear time per update.
The relative convex hull of a finite set of points is always a weakly simple polygon, but it might not actually be a simple polygon, because parts of it can be connected to each other by line segments or polygonal paths rather than by regions of nonzero area.
Simple polygons
For relative convex hulls of simple polygons, an alternative but equivalent definition of convexity can be used. A simple polygon within another simple polygon is relatively convex or -convex if every line segment contained in that connects two points of lies within . The relative convex hull of a simple polygon within can be defined as the intersection of all -convex polygons that contain , as the smallest -convex polygon that contains , or as the minimum-perimeter simple polygon that contains and is contained by .
generalizes linear time algorithms for the convex hull of a simple polygon to the relative convex hull of one simple polygon within another. The resulting generalized algorithm is not linear time, however: its time complexity depends on the depth of nesting of certain features of one polygon within another. In this case, the relative convex hull is itself a simple polygon. Alternative linear time algorithms based on path planning are known.
A similar definition can also be given for the relative convex hull of two disjoint simple poly |
https://en.wikipedia.org/wiki/Kids%20Count%20Data%20Book | The Kids Count Data Book is an annual publication of the Annie E. Casey Foundation—at times in cooperation with the Center for the Study of Social Policy—reporting comparative statistics on child welfare in each of the 50 states of the United States of America.
Form and content
Annual editions are prefaced with the year of publication—hence the 2019 edition is commonly titled 2019 Kids Count Data Book. The book's first annual edition was published in 1990.
Separate editions, for each individual state—with detailed information on that state, plus comparisons to national data—are available.
An interactive, online edition is available, as well.
Topics covered, in past annual issues, have included U.S. children's economic status, health, education, family and community, child protection, foster care, juvenile justice and incarceration—with current and historical data, and comparative rankings of states.
Use
The book is widely quoted as a leading reference on the subject of child welfare in the United States. In 1992, it was reportedly featured in about 1,400 of America's 1,600 daily newspapers.
KIDS COUNT Network
In each of the 50 states, AECF originally selected a single local child-issues organization to partially fund with an AECF grant, and to partner with to develop a customized version of the Data Book for each state. However, AECF later modified its plan, treating the grantees as its "KIDS COUNT Network," and began to use them as outlets for its media and influence efforts—including distribution and promotion of the KIDS COUNT Data Book—although AECF accepts that the grantees' individual goals and priorities may differ somewhat from AECF's.
Criticism
Critics have suggested that the KIDS COUNT Data Book and other media efforts by AECF (and copycat efforts by other organizations) may be an attempt to promote government spending on social programs, generally—and particularly for the poor—using public sympathy for "kids" to generate public support for social programs that serve adults as well. Others have suggested that it sometimes paints a picture that is more gloomy than realistic.
References
External links
Interactive Kids Count Data Book
2019 KIDS COUNT Data Book, official free PDF download
Annie E. Casey Foundation
Child welfare in the United States |
https://en.wikipedia.org/wiki/Inverse%20Pythagorean%20theorem | In geometry, the inverse Pythagorean theorem (also known as the reciprocal Pythagorean theorem or the upside down Pythagorean theorem) is as follows:
Let , be the endpoints of the hypotenuse of a right triangle . Let be the foot of a perpendicular dropped from , the vertex of the right angle, to the hypotenuse. Then
This theorem should not be confused with proposition 48 in book 1 of Euclid's Elements, the converse of the Pythagorean theorem, which states that if the square on one side of a triangle is equal to the sum of the squares on the other two sides then the other two sides contain a right angle.
Proof
The area of triangle can be expressed in terms of either and , or and :
given , and .
Using the Pythagorean theorem,
as above.
Special case of the cruciform curve
The cruciform curve or cross curve is a quartic plane curve given by the equation
where the two parameters determining the shape of the curve, and are each .
Substituting with and with gives
Inverse-Pythagorean triples can be generated using integer parameters and as follows.
Application
If two identical lamps are placed at and , the theorem and the inverse-square law imply that the light intensity at is the same as when a single lamp is placed at .
See also
References
Geometry |
https://en.wikipedia.org/wiki/Antisemitism%20in%20the%20United%20States%20in%20the%2021st%20century | In 2018 and 2019, reports of antisemitism in the United States was reported to have increased compared to previous years according to statistics collected by both the Federal Bureau of Investigation and the Anti-Defamation League. These statistics include both violent antisemitic attacks on Jews and cases of harassment.
2013 knockout game
During the 2013 knockout game spate of violent assaults, all reported "knockout" assaults in New York City targeted Jews. ABC Nightline reported that New York City police believed that antisemitism was likely to be a motive in the attacks, as all eight victims were identified as Jewish.
Brooklyn assaults
2019 saw a spate of attacks in which pedestrians wearing identifiably Jewish clothing were assaulted, beaten and often knocked to the ground by an assailant or group of assailants, many of whom shouted antisemitic slurs. The assailants were black and Hispanic.
One assailant, Tiffany Harris, who was released without bail after attacking a Jewish woman, attacked three other Jewish women the very next day; all of the victims were dressed in distinctively Jewish clothing.
Although the Williamsburg and Crown Heights neighborhoods of Brooklyn where most of the assaults have taken place are experiencing gentrification, no similar assaults have been reported on the gentrifiers, although their clothing makes them easy to identify.
Writing in neoconservative magazine Commentary, Brookings Institution fellow Jamie Kirchick said in 2018 that antisemitism has been a particular problem in parts of America's black community since the split between the mainstream Civil rights movement led by Martin Luther King Jr. and the more radical Black Power movement of the late 1960s. Kirchick says that leaders on the political left continue to foment antisemitism.
A 2019 study found that 28% of African Americans believed that they were seeing more Black people that they personally knew express antisemitism than in the past. In the same study, 19% of African Americans believed that Jewish people were impeding Black progress in America. Four percent (4%) of African Americans self-identified as being Black Hebrew Israelites in 2019.
Maugham Elementary School Adolf Hitler assignment controversy
In Early April 2021, a fifth-grade teacher at Maugham Elementary School, a public grammar school in Tenafly, New Jersey, instructed a 5th grade student to dress up as Adolf Hitler and write a first-person essay from the perspective of the Nazi leader touting his "accomplishments" as a part of a class assignment. The student wrote a biography of Hitler that glorified the Nazi leader, stated that Hitler's "greatest accomplishment was uniting a great mass of German and Austrian people" in his support, framed the Holocaust in a positive light, and added that Hitler was "pretty great". The student's essay was displayed publicly within the school's hallway during the month of April. In May 2021, the details of the school assignment became known to |
https://en.wikipedia.org/wiki/James%20Vennings | James Frederick Vennings (born 20 November 2000) is an English professional footballer who plays as a midfielder for Bromley.
Career statistics
Honours
Bromley
FA Trophy: 2021–22
References
English men's footballers
2000 births
Living people
Men's association football midfielders
England men's semi-pro international footballers
Charlton Athletic F.C. players
Aldershot Town F.C. players
Bromley F.C. players
English Football League players
National League (English football) players
Place of birth missing (living people) |
https://en.wikipedia.org/wiki/Saket%20Elhami | Saket Elhami () is an Iranian football manager who currently manages Mes Rafsanjan in Persian Gulf Pro League.
He played as a player for Pas, Esteghlal Ahvaz, and Tractor.
Managerial statistics
Honours
Manager
Tractor
Hazfi Cup: 2019–20
Nassaji
Hazfi Cup: 2021–22
References
External links
Living people
Iranian football managers
1971 births
Tractor S.C. managers
Sportspeople from Ardabil
PAS Hamedan F.C. players
Bahman F.C. players
Esteghlal Ahvaz F.C. players
Keshavarz F.C. players
Tractor S.C. players
Iranian men's footballers
Men's association football players not categorized by position
F.C. Nassaji Mazandaran managers
Persian Gulf Pro League managers
Havadar S.C. managers |
https://en.wikipedia.org/wiki/Mark%C3%A9ta%20Vondrou%C5%A1ov%C3%A1%20career%20statistics | This is a list of the main career statistics of Czech tennis player Markéta Vondroušová. In July 2023, she won her biggest title up to date at the Wimbledon Championships. As a result, she made her top-ten debut, and two months later, her ranking rose to her career-high of world No. 6. Playing for her home nation, the Czech Republic, she won the silver medal at the 2020 Summer Olympics (postponed to 2021 due to COVID-19) in the singles event, and she also played two Billie Jean King Cup semifinals and finished runner-up at the 2019 French Open.
From the beginning Vondroušová showed competition talent: she won two girls' doubles titles at major tournaments, alongside Miriam Kolodziejová, at the Australian Open and French Open in 2015. She also finished runners-up in girls' doubles with CiCi Bellis, at the French Open in 2014.
Performance timelines
Only main-draw results in WTA Tour, Grand Slam tournaments, Billie Jean King Cup, Hopman Cup, United Cup and Olympic Games are included in win–loss records.
Singles
Current through the 2023 China Open.
Doubles
Current through the 2023 US Open.
Mixed doubles
Significant finals
Grand Slam finals
Singles: 2 (1 title, 1 runner-up)
Olympic Games medal matches
Singles: 1 (silver)
WTA 1000 finals
Doubles: 1 (runner-up)
WTA Tour finals
Singles: 6 (2 titles, 4 runner-ups)
Doubles: 3 (3 runner-ups)
WTA Challenger finals
Doubles: 1 (runner-up)
ITF Circuit finals
Singles: 11 (8 titles, 3 runner–ups)
Doubles: 8 (6 titles, 2 runner–ups)
Junior Grand Slam finals
Girls' doubles: 3 (2 titles, 1 runner–up)
WTA Tour career earnings
Current through the 2023 Canadian Open.
Career Grand Slam statistics
Seedings
The tournaments won by Vondroušová are in boldface, and advanced into finals by Vondroušová are in italics.
Best Grand Slam results details
Grand Slam winners are in boldface, and runner–ups are in italics.
Record against other players
Record against top 10 players
She has a 11–21 () record against players who were, at the time the match was played, ranked in the top 10.
Double bagel matches (6–0, 6–0)
Longest winning streaks
9-match winning streak in singles (2023)
Notes
References
External links
Tennis career statistics |
https://en.wikipedia.org/wiki/K-stability | In mathematics, and especially differential and algebraic geometry, K-stability is an algebro-geometric stability condition, for complex manifolds and complex algebraic varieties. The notion of K-stability was first introduced by Gang Tian and reformulated more algebraically later by Simon Donaldson. The definition was inspired by a comparison to geometric invariant theory (GIT) stability. In the special case of Fano varieties, K-stability precisely characterises the existence of Kähler–Einstein metrics. More generally, on any compact complex manifold, K-stability is conjectured to be equivalent to the existence of constant scalar curvature Kähler metrics (cscK metrics).
History
In 1954, Eugenio Calabi formulated a conjecture about the existence of Kähler metrics on compact Kähler manifolds, now known as the Calabi conjecture. One formulation of the conjecture is that a compact Kähler manifold admits a unique Kähler–Einstein metric in the class . In the particular case where , such a Kähler–Einstein metric would be Ricci flat, making the manifold a Calabi–Yau manifold. The Calabi conjecture was resolved in the case where by Thierry Aubin and Shing-Tung Yau, and when by Yau. In the case where , that is when is a Fano manifold, a Kähler–Einstein metric does not always exist. Namely, it was known by work of Yozo Matsushima and André Lichnerowicz that a Kähler manifold with can only admit a Kähler–Einstein metric if the Lie algebra is reductive. However, it can be easily shown that the blow up of the complex projective plane at one point, is Fano, but does not have reductive Lie algebra. Thus not all Fano manifolds can admit Kähler–Einstein metrics.
After the resolution of the Calabi conjecture for attention turned to the loosely related problem of finding canonical metrics on vector bundles over complex manifolds. In 1983, Donaldson produced a new proof of the Narasimhan–Seshadri theorem. As proved by Donaldson, the theorem states that a holomorphic vector bundle over a compact Riemann surface is stable if and only if it corresponds to an irreducible unitary Yang–Mills connection. That is, a unitary connection which is a critical point of the Yang–Mills functional
On a Riemann surface such a connection is projectively flat, and its holonomy gives rise to a projective unitary representation of the fundamental group of the Riemann surface, thus recovering the original statement of the theorem by M. S. Narasimhan and C. S. Seshadri. During the 1980s this theorem was generalised through the work of Donaldson, Karen Uhlenbeck and Yau, and Jun Li and Yau to the Kobayashi–Hitchin correspondence, which relates stable holomorphic vector bundles to Hermitian–Einstein connections over arbitrary compact complex manifolds. A key observation in the setting of holomorphic vector bundles is that once a holomorphic structure is fixed, any choice of Hermitian metric gives rise to a unitary connection, the Chern connection. Thus one can either search for |
https://en.wikipedia.org/wiki/Donald%20A.%20Danielson | Donald A. Danielson is Professor Emeritus in the Department of Applied Mathematics and the Space Systems Academic Group at the Naval Postgraduate School.
Early life and education
Danielson received a B.S. degree in mathematics from MIT in 1964 and a Ph.D. in applied mathematics from Harvard University in 1968.
Career
Danielson joined the faculty of the University of Virginia in 1968. He moved to the University of California, San Diego in 1979, and to the Naval Postgraduate School in 1985. Danielson is an applied mathematician with contributions to structural mechanics, biomechanics, and orbital dynamics. Publications include: "Dynamic Buckling Loads of Imperfection Sensitive Structures from Perturbation Procedures", AIAA Journal 1506-1510 (1969); "Nonlinear Shell Theory with Finite Rotation and Stress Function Vectors", Journal of Applied Mechanics 1085 - 1090 (1972); "Human Skin as an Elastic Membrane", Journal of Biomechanics 539-546 (1973); "Tension Field Theory and the Stress in Stretched Skin", Journal of Biomechanics 135-142 (1975); "Tension Field Theories for Soft Tissues", Bulletin of Mathematical Biology 161-182 (1978); "A Beam Theory for Large Global Rotation, Moderate Local Rotation, and Small Strain", Journal of Applied Mechanics 179-184 (1988); "Fiber-optic Ellipsoidal Flextensional Hydrophones"; Journal of Lightwave Technology 1995-2002 (1989); "Parallelization of the Naval Space Surveillance Satellite Motion Model", Journal of Astronautical Sciences 207-216 (1993); "Semianalytic Satellite Theory", Naval Postgraduate School Technical Report NPS-MA-95-002 (1995); "The Naval Space Command Automatic Differential Correction Process", Proceedings of the AAS Astrodynamics Conference 991-1008 (1999); "Buckling of Stiffened Plates with Bulb Flat Flanges", International Journal of Solids and Structures 6407-6427 (2004). He also wrote a graduate textbook on Vectors and Tensors.
References
Naval Postgraduate School faculty
University of Virginia faculty
University of California, San Diego faculty
Massachusetts Institute of Technology School of Science alumni
Harvard University alumni
American mechanical engineers
Living people
20th-century American engineers
Year of birth missing (living people) |
https://en.wikipedia.org/wiki/Abdulaziz%20Khalid | Abdulaziz Khalid Ahmed Khalifa Rajab (born 17 March 1997), commonly referred to as Abdulaziz Khalid, is a Bahraini international footballer who plays as a forward for Al-Najma.
Career statistics
International
References
External links
1997 births
Living people
Bahraini men's footballers
Bahrain men's international footballers
Men's association football forwards |
https://en.wikipedia.org/wiki/Kim%20Kum-chol | Kim Kum-chol (, born 7 April 1997) is a North Korean footballer who currently plays as a defender for Rimyongsu.
Career statistics
International
References
External links
Kim Kum-chol at DPRKFootball
1997 births
Living people
North Korean men's footballers
North Korea men's international footballers
North Korea men's youth international footballers
Men's association football defenders
Rimyongsu Sports Club players
Footballers at the 2018 Asian Games |
https://en.wikipedia.org/wiki/Kim%20Tae-hyeon | Kim Tae-hyeon (; Hanja:金太鉉; born 17 September 2000) is a South Korean footballer currently playing as a defender for Vegalta Sendai.
Career statistics
Club
Notes
Honours
South Korea U23
AFC U-23 Championship: 2020
Asian Games: 2022
Notes
References
External links
2000 births
Living people
South Korean men's footballers
South Korea men's youth international footballers
Men's association football defenders
K League 2 players
Ulsan Hyundai FC players
Daejeon Hana Citizen players
Seoul E-Land FC players
Vegalta Sendai players
Footballers at the 2022 Asian Games |
https://en.wikipedia.org/wiki/Kim%20Dong-hyun%20%28footballer%2C%20born%201997%29 | Kim Dong-hyun (; born 11 June 1997) is a South Korean footballer who plays as a defensive midfielder or a right back for Gimcheon Sangmu and the South Korea national team.
Career statistics
Club
Notes
Notes
References
1997 births
Living people
Footballers from Seoul
South Korean men's footballers
South Korea men's under-20 international footballers
South Korea men's under-23 international footballers
Men's association football midfielders
K League 2 players
K League 1 players
Pohang Steelers players
Gwangju FC players
Seongnam FC players
Gangwon FC players
Footballers at the 2020 Summer Olympics
Olympic footballers for South Korea |
https://en.wikipedia.org/wiki/Divisorial%20scheme | In algebraic geometry, a divisorial scheme is a scheme admitting an ample family of line bundles, as opposed to an ample line bundle. In particular, a quasi-projective variety is a divisorial scheme and the notion is a generalization of "quasi-projective". It was introduced in (in the case of a variety) as well as in (in the case of a scheme). The term "divisorial" refers to the fact that "the topology of these varieties is determined by their positive divisors." The class of divisorial schemes is quite large: it includes affine schemes, separated regular (noetherian) schemes and subschemes of a divisorial scheme (such as projective varieties).
Definition
Here is the definition in SGA 6, which is a more general version of the definition of Borelli. Given a quasi-compact quasi-separated scheme X, a family of invertible sheaves on it is said to be an ample family if the open subsets form a base of the (Zariski) topology on X; in other words, there is an open affine cover of X consisting of open sets of such form. A scheme is then said to be divisorial if there exists such an ample family of invertible sheaves.
Properties and counterexample
Since a subscheme of a divisorial scheme is divisorial, "divisorial" is a necessary condition for a scheme to be embedded into a smooth variety (or more generally a separated Noetherian regular scheme). To an extent, it is also a sufficient condition.
A divisorial scheme has the resolution property; i.e., a coherent sheaf is a quotient of a vector bundle. In particular, a scheme that does not have the resolution property is an example of a non-divisorial scheme.
See also
Jouanolou's trick
References
Algebraic geometry |
https://en.wikipedia.org/wiki/Appalachian%20Forest%20National%20Heritage%20Area | {
"type": "FeatureCollection",
"features": [
{
"type": "Feature",
"properties": {},
"geometry": {
"type": "Point",
"coordinates": [
-79.85112190246583,
38.923351020249946
]
}
}
]
}The Appalachian Forest National Heritage Area (abbreviated to AFNHA) is a National Heritage Area encompassing 16 counties in West Virginia and 2 counties in Western Maryland.
In Maryland, AFNHA encompasses Allegany and Garrett Counties. In West Virginia, AFNHA encompasses Barbour, Braxton, Grant, Greenbrier, Hampshire, Hardy, Mineral, Morgan, Nicholas, Pendleton, Pocahontas, Preston, Randolph, Tucker, Upshur and Webster Counties.
It was designated a National Heritage Area in part of the Natural Resources Management Act in 2019.
References
Appalachian forests
Forests of West Virginia
Western Maryland
National Heritage Areas of the United States |
https://en.wikipedia.org/wiki/List%20of%20Palestine%20national%20football%20team%20managers | The male Palestinian national (association) football team has been under the supervision of 19 different permanent managers since 1998.
Last updated: 20 June 2023. Statistics include FIFA-recognised matches only.
Notes
References
Palestine |
https://en.wikipedia.org/wiki/Journal%20of%20Functional%20Analysis | The Journal of Functional Analysis is a mathematics journal published by Elsevier. Founded by Paul Malliavin, Ralph S. Phillips, and Irving Segal, its editors-in-chief are Daniel W. Stroock, Stefaan Vaes, and Cedric Villani.
It is covered in databases including Scopus, the Science Citation Index, and the SCImago Journal Rank service.
References
Elsevier academic journals
Mathematics journals
Academic journals established in 1967
Semi-monthly journals |
https://en.wikipedia.org/wiki/Ross%20County%20F.C.%20records%20and%20statistics | Ross County Football Club are a Scottish professional association football club based in Dingwall. Ross County joined the Highland Football League in 1929, and then were one of two clubs voted into the Scottish Professional Football League System in 1994.
The club's record appearance maker is Michael Gardyne, who has made Over 400 appearances through four spells at the club. Gardyne is also the club's record goalscorer, scoring over 70 goals in major competitions during his time at Ross County.
This list encompasses the major honours won by Ross County, records set by the club, their managers and their players. The player records section includes details of the club's leading goalscorers and those who have made most appearances in first-team competitions. It also records notable achievements by Ross County players on the international stage, and the highest transfer fees paid and received by the club. Attendance records are also included in the list.
Honours
League
First Division/Championship (second tier)
Winners (2): 2011–12, 2018–19
Second Division (third tier)
Winners (1): 2007–08
Third Division (fourth tier)
Winners (1): 1998–99
Highland Football League
Winners (3): 1966–67, 1990–91, 1991–92
Runners-up (2): 1967–68, 1972–73
North Caledonian Football League
Winners (2): 1965–66, 1996–97
Cup
Scottish Cup
Runners-up (1): 2009–10
Scottish League Cup:
Winners (1): 2015–16
Challenge Cup
Winners (3): 2006–07, 2010–11, 2018–19
Runners-up (2): 2004–05, 2008–09
Qualifying Cup (North)
Winners (1): 1993–94
Runners-up (5): 1933–34, 1965–66, 1969–70, 1972–73, 1973–74
North of Scotland Cup
Winners (6): 1929–30, 1969–70, 1971–72, 1991–92, 2006–07, 2018–19
Highland League Cup
Winners (4): 1949–50, 1968–69, 1978–79, 1991–92
Youth
SPFL Development League (Under-20)
Winners (1): 2016–17
Player records
Individual Records
Most Appearance Holder: Michael Gardyne (444)
Record Goalscorer: Michael Gardyne (73)
Most Goals in a season (all competitions): Andrew Barrowman (29)
Most Goals in a season (league): Andrew Barrowman (24)
Most Clean Sheets: Nicky Walker (54)
Most Hat-Tricks: Liam Boyce (5)
Most appearances
As of 27 May 2021
Source:
Top goalscorers
As of 15 October 2023
Source:
Clean Sheets
As of 15 October 2023
Source:
Club captains
Team of the Decade
In January 2020 Ross County Twitter put out a poll to fans to decide on the team of the 2010s. The Results were as follows:
GK: Scott Fox
DF: Marcus Fraser
DF: Andrew Davies
DF: Scott Boyd
DF: Evangelos Ikonomou
MF: Richard Brittain
MF: Jackson Irvine
MF: Iain Vigurs
MF: Michael Gardyne
FW: Liam Boyce
FW: Alex Schalk
Source:
International players
This is a list of former and current players who have played at full international level while with the club and the year of their first International cap while at the club.
2001 Richard Hastings
2006 Sean Webb
2010 Michael McGovern
2010 Atli Gregersen
2013 André Hainault
2014 Yoann Arquin
2014 |
https://en.wikipedia.org/wiki/Ina%20Kersten | Ina Kersten (born 1946) is a German mathematician and former president of the German Mathematical Society. Her research concerns abstract algebra including the theory of field extensions and algebraic groups. She is a professor emerita at the University of Göttingen.
Kersten was born in Hamburg, and earned her Ph.D. at the University of Hamburg in 1977. Her dissertation, p-Algebren über semilokalen Ringen, was supervised by Ernst Witt.
She completed a habilitation at the University of Regensburg in 1983.
Kersten was president of the German Mathematical Society from 1995 to 1997, which meant she was the first woman to head the society. Under her leadership, the society founded the journal Documenta Mathematica.
References
External links
Home page
1946 births
Living people
20th-century German mathematicians
Women mathematicians
Algebraists
University of Hamburg alumni
Academic staff of the University of Göttingen
Presidents of the German Mathematical Society |
https://en.wikipedia.org/wiki/Monica%20Nevins | Monica A. Nevins (born 1973) is a Canadian mathematician, and a professor of mathematics and statistics at the University of Ottawa. Her research interests include abstract algebra, representation theory, algebraic groups, and mathematical cryptography.
Education and career
Nevins went to high school in Val-d'Or, Quebec. She graduated from the University of Ottawa in 1994, and completed a PhD in mathematics at the Massachusetts Institute of Technology in 1998. Her dissertation, Admissible Nilpotent Coadjoint Orbits of p-adic Reductive Lie Groups, was supervised by David Vogan.
After postdoctoral research at the University of Alberta, Nevins joined the faculty of the University of Ottawa, where she was promoted to full professor in 2014.
Recognition
Nevins was the 2010–2011 winner of the University of Ottawa Award for Excellence in Teaching.
She was elected as a fellow of the Canadian Mathematical Society in 2019.
Personal
Her husband, Ralph Nevins, is a computer scientist and mathematical artist.
References
External links
Home page
1973 births
Living people
Canadian women mathematicians
University of Ottawa alumni
Massachusetts Institute of Technology School of Science alumni
Academic staff of the University of Ottawa
Fellows of the Canadian Mathematical Society |
https://en.wikipedia.org/wiki/OneFootball | OneFootball is a global platform-based football media company who based in Germany who founded in early 2008. The OneFootball app features live-scores, statistics and news from more than 200 leagues in 12 different languages covered by a newsroom located in Berlin. In 2019, OneFootball partnered up with Eleven Sports to have the rights to stream directly on the app La Liga in UK, with Sky to transmit 2. Bundesliga and DFB-Pokal matches in Germany, and with Bushiroad to distribute J1 League for Southeast Asian countries starts 2024 season. In 2020, OneFootball bought club-founded video forum Dugout. Speaking of the deal to Bloomberg, OneFootball CEO Lucas von Cranach said that the move will " might benefit the whole football ecosystem with clubs, federations and leagues able to increase audience reach and harness our powerful data insights to gain a deeper understanding of their fans' engagement as the rise of advertising means they need to know as much as possible ".
History
The company was founded under the name Motain by Lucas Von Cranach in 2013. In 2009, Von Cranach launched iLiga (THE football app abroad). Following a move to the new HQ in Berlin, Motain and its products (iLiga and THE football app) were merged under the name of OneFootball. On 7 September 2016 OneFootball was featured in the Apple keynote in San Francisco for the release of watchOS 3. The management team, which included Silke Kuisle as CFO, expanded in 2018 with the arrival of the ex-Puma CEO, Franz Koch, as the new COO and the SPORT1MEDIA ex-CEO Patrick Fischer, as the new CBO. On 15 December 2020, the company took over Dugout, a multimedia forum founded by a host of Europe's biggest clubs, for reportedly more than $61 million. In May 2022 OneFootball raised €300 million in a series D financing round led by Liberty City Ventures and included participation from Animoca Brands, Dapper Labs, DAH Beteiligungs GmbH, Quiet Capital, RIT Capital Partners, Senator Investment Group and Alsara Investment Group.
Controversies
Seven months after raising more than $300 million in NFT funds, the company made three waves of layoffs.
The first wave, comes after the termination of the partnership with the application Spitch, a football fantasy app. The end of this partnership will result in the dismissal of 10 employees in November 2022.
A month later, the company repeats with 62 new employees laid off.
In early 2023, a new wave of dismissals arrived with 150 employees laid off.
Some rumours mention problems of management and discrimination affecting the mental health of employees.
In total, the company will have reduced its workforce by 40% in 4 months.
In August 2023, a new wave of redundancies - the 4th in less than a year took place at OneFootball. The company is reducing its workforce to 250 employees. This comes just 1 year after an astronomical fund-raising of over 300 million dollars.
Accusation of NFT Scams
The decision to terminate the AERA project in June 2023 related |
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