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https://en.wikipedia.org/wiki/Estermann%20measure
|
In plane geometry the Estermann measure is a number defined for any bounded convex set describing how close to being centrally symmetric it is. It is the ratio of areas between the given set and its smallest centrally symmetric convex superset. It is one for a set that is centrally symmetric, and less than one for sets whose closure is not centrally symmetric. It is invariant under affine transformations of the plane.
Properties
If is the center of symmetry of the smallest centrally-symmetric set containing a given convex body , then the centrally-symmetric set itself is the convex hull of the union of with its reflection across .
Minimizers
The shapes of minimum Estermann measure are the triangles, for which this measure is 1/2. The curve of constant width with the smallest possible Estermann measure is the Reuleaux triangle.
History
The Estermann measure is named after Theodor Estermann, who first proved in 1928 that this measure is always at least 1/2, and that a convex set with Estermann measure 1/2 must be a triangle. Subsequent proofs were given by Friedrich Wilhelm Levi, by István Fáry, and by Isaak Yaglom and Vladimir Boltyansky.
See also
Kovner–Besicovitch measure, a measure of central symmetry defined using subsets in place of supersets
References
Euclidean symmetries
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https://en.wikipedia.org/wiki/Kim%20Ju-hwan%20%28footballer%2C%20born%202001%29
|
Kim Ju-hwan (; born 17 February 2001) is a South Korean footballer currently playing as a right back for Pohang Steelers.
Career statistics
Club
References
2001 births
Living people
South Korean men's footballers
South Korea men's youth international footballers
Men's association football defenders
K League 1 players
Pohang Steelers players
|
https://en.wikipedia.org/wiki/Franck%20Chaumin
|
Franck Chaumin (born 2 November 1969) is a French former footballer.
Career statistics
Club
Notes
Honours
Individual
Toulon Tournament Best Goalkeeper: 1989
References
1969 births
Living people
French men's footballers
France men's youth international footballers
France men's under-21 international footballers
Men's association football goalkeepers
Championnat National players
Ligue 2 players
INF Clairefontaine players
Quimper Kerfeunteun F.C. players
Gazélec Ajaccio players
FC Sochaux-Montbéliard players
FC Mulhouse players
Amicale de Lucé players
French expatriate sportspeople in Mali
Sportspeople from Blois
Footballers from Centre-Val de Loire
|
https://en.wikipedia.org/wiki/Sergio%20Fortunato
|
Sergio Elio Ángel Fortunato (born 23 October 1956) is an Argentine former footballer. He was capped by the Argentina national team in 1979.
Career statistics
International
References
1956 births
Living people
Argentine men's footballers
Argentine expatriate men's footballers
Argentina men's youth international footballers
Argentina men's international footballers
Men's association football forwards
Kimberley de Mar del Plata footballers
Club Atlético Aldosivi footballers
Racing Club de Avellaneda footballers
Quilmes Atlético Club footballers
Estudiantes de La Plata footballers
AC Perugia Calcio players
UD Las Palmas players
Favoritner AC players
La Liga players
Serie A players
Austrian Football Bundesliga players
Argentine expatriate sportspeople in Italy
Expatriate men's footballers in Italy
Argentine expatriate sportspeople in Spain
Expatriate men's footballers in Spain
Argentine expatriate sportspeople in Austria
Expatriate men's footballers in Austria
Footballers from Mar del Plata
Pan American Games bronze medalists for Argentina
Pan American Games medalists in football
Medalists at the 1975 Pan American Games
Footballers at the 1975 Pan American Games
|
https://en.wikipedia.org/wiki/Adam%20Harper
|
Adam Harper is a mathematician specialising in number theory, particularly in analytic, combinatorial and probabilistic number theory, and serving as Professor with University of Warwick, England. Harper was awarded the SASTRA Ramanujan Prize in 2019 "for several outstanding contributions to analytic and probabilistic number theory." This annual prize is awarded for outstanding contributions by individuals not exceeding the age of 32 in areas of mathematics influenced by Srinivasa Ramanujan. The age limit has been set at 32 because Ramanujan died at the age of 32 years.
"Harper's research, both individually and in collaboration, covers the theory of the Riemann zeta function, random multiplicative functions, S-unit equations, smooth numbers, the large sieve, and the recent highly innovative "pretentious" approach to number theory. In establishing these results, he has shown mastery over probabilistic methods which he has used with remarkable effect in analytic number theory."
Academic career
Adam Harper was born in Lowestoft in the United Kingdom. He did a four year MMath Course at Exeter College, Oxford and won the Oxford Junior Mathematics Prize. He completed his PhD in 2012 at Cambridge University under the guidance of Professor Ben Green, and as a PhD student won the Smith Essay Prize. He was a Post-Doctoral Fellow with Professor Andrew Granville at CRM Montréal during 2012–13, following which he was a Research Fellow at Jesus College, Cambridge during 2013–16. He returned to Montréal in 2018 as Simons CRM Visiting Professor. He is currently a Professor at the University of Warwick.
Other awards
Adam Harper was awarded a Whitehead Prize in 2020 for "his deep and important contributions to analytic number theory, and in particular for his work on the value distribution of the Riemann zeta function and random multiplicative functions using sophisticated ideas and techniques from probability theory."
References
Number theorists
Recipients of the SASTRA Ramanujan Prize
Living people
Year of birth missing (living people)
|
https://en.wikipedia.org/wiki/Reilly%20formula
|
In the mathematical field of Riemannian geometry, the Reilly formula is an important identity, discovered by Robert Reilly in 1977. It says that, given a smooth Riemannian manifold-with-boundary and a smooth function on , one has
in which is the second fundamental form of the boundary of , is its mean curvature, and is its unit normal vector. This is often used in combination with the observation
with the consequence that
This is particularly useful since one can now make use of the solvability of the Dirichlet problem for the Laplacian to make useful choices for . Applications include eigenvalue estimates in spectral geometry and the study of submanifolds of constant mean curvature.
References
Bennett Chow, Peng Lu, and Lei Ni. Hamilton's Ricci flow. Graduate Studies in Mathematics, 77. American Mathematical Society, Providence, RI; Science Press Beijing, New York, 2006. xxxvi+608 pp.
Tobias Holck Colding and William P. Minicozzi II. A course in minimal surfaces. Graduate Studies in Mathematics, 121. American Mathematical Society, Providence, RI, 2011. xii+313 pp. .
Peter Li. Geometric analysis. Cambridge Studies in Advanced Mathematics, 134. Cambridge University Press, Cambridge, 2012. x+406 pp. .
R. Schoen and S.-T. Yau. Lectures on differential geometry. Lecture notes prepared by Wei Yue Ding, Kung Ching Chang, Jia Qing Zhong and Yi Chao Xu. Translated from the Chinese by Ding and S.Y. Cheng. With a preface translated from the Chinese by Kaising Tso. Conference Proceedings and Lecture Notes in Geometry and Topology, I. International Press, Cambridge, MA, 1994. v+235 pp.
External links
In Memoriam Robert Cunningham Reilly
Differential geometry
|
https://en.wikipedia.org/wiki/1960%E2%80%9361%20Rochdale%20A.F.C.%20season
|
The 1960–61 season saw Rochdale compete for their second season in the Football League Fourth Division.
Statistics
|}
Final League Table
Competitions
Football League Fourth Division
F.A. Cup
League Cup
Lancashire Cup
References
Rochdale A.F.C. seasons
Rochdale
|
https://en.wikipedia.org/wiki/Maximal%20surface
|
In the mathematical field of differential geometry, a maximal surface is a certain kind of submanifold of a Lorentzian manifold. Precisely, given a Lorentzian manifold , a maximal surface is a spacelike submanifold of whose mean curvature is zero. As such, maximal surfaces in Lorentzian geometry are directly analogous to minimal surfaces in Riemannian geometry. The difference in terminology between the two settings has to do with the fact that small regions in maximal surfaces are local maximizers of the area functional, while small regions in minimal surfaces are local minimizers of the area functional.
In 1976, Shiu-Yuen Cheng and Shing-Tung Yau resolved the "Bernstein problem" for maximal hypersurfaces of Minkowski space which are properly embedded, showing that any such hypersurface is a plane. This was part of the body of work for which Yau was awarded the Fields medal in 1982. The Bernstein problem was originally posed by Eugenio Calabi in 1970, who proved some special cases of the result. Simple examples show that there are a number of hypersurfaces of Minkowski space of zero mean curvature which fail to be spacelike.
By an extension of Cheng and Yau's methods, Kazuo Akutagawa considered the case of spacelike hypersurfaces of constant mean curvature in Lorentzian manifolds of positive constant curvature, such as de Sitter space. Luis Alías, Alfonso Romero, and Miguel Sánchez proved a version of Cheng and Yau's result, replacing Minkowski space by the warped product of a closed Riemannian manifold with an interval.
As a problem of partial differential equations, Robert Bartnik and Leon Simon studied the boundary-value problem for maximal surfaces in Minkowski space. The general existence of maximal hypersurfaces in asymptotically flat Lorentzian manifolds, due to Bartnik, is significant in Demetrios Christodoulou and Sergiu Klainerman's renowned proof of the nonlinear stability of Minkowski space under the Einstein field equations. They use a maximal slicing of a general spacetime; the same approach is common in numerical relativity.
References
Footnotes
Books
John K. Beem, Paul E. Ehrlich, and Kevin L. Easley. Global Lorentzian geometry. Second edition. Monographs and Textbooks in Pure and Applied Mathematics, 202. Marcel Dekker, Inc., New York, 1996. xiv+635 pp.
Yvonne Choquet-Bruhat. General relativity and the Einstein equations. Oxford Mathematical Monographs. Oxford University Press, Oxford, 2009. xxvi+785 pp.
Demetrios Christodoulou and Sergiu Klainerman. The global nonlinear stability of the Minkowski space. Princeton Mathematical Series, 41. Princeton University Press, Princeton, NJ, 1993. x+514 pp.
Éric Gourgoulhon. 3 + 1 formalism in general relativity. Bases of numerical relativity. Lecture Notes in Physics, 846. Springer, Heidelberg, 2012. xviii+294 pp.
Articles
Kazuo Akutagawa. On spacelike hypersurfaces with constant mean curvature in the de Sitter space. Math. Z. 196 (1987), no. 1, 13–19.
Luis J. Alías, A
|
https://en.wikipedia.org/wiki/Iga%20%C5%9Awi%C4%85tek%20career%20statistics
|
This is a list of the main career statistics of professional Polish tennis player Iga Świątek.
Performance timelines
Only main-draw results in WTA Tour, Grand Slam tournaments, Fed Cup/Billie Jean King Cup and Olympic Games are included in win–loss records.
Singles
Current through the 2023 China Open.
Doubles
Current through 2023 Italian Open
Mixed doubles
Grand Slam tournament finals
Świątek won her first Grand Slam singles title at the French Open in 2020, defeating Sofia Kenin in straight sets.
Singles: 4 (4 titles)
Doubles: 1 (runner-up)
WTA 1000 finals
Singles: 8 (6 titles, 2 runner-ups)
WTA career finals
Singles: 20 (16 titles, 4 runner-ups)
Doubles: 1 (1 runner-up)
ITF Circuit finals
Świątek made her debut at the ITF Women's Circuit in 2016 at the $10k event in Stockholm, where she also won her first ITF title in singles event. Since then, she reached seven singles finals in total, winning all of them. Her most significant titles are two $60k events, NEK Open and Montreux Open, both achieved in 2018 in singles. In doubles, she reached only one final, but failed to win the title at the $15k event in Sharm El Sheikh.
Singles: 7 (7 titles)
Doubles: 1 (1 runner-up)
Fed Cup/Billie Jean King Cup participation
Świątek made her debut at the Fed Cup playing for Poland in 2018. Since then, she has a singles record of 7–2, and a doubles record of 2–1.
Singles: 9 (7–2)
Doubles: 3 (2–1)
ITF Junior Circuit
Grand Slam tournament finals
Girls' singles: 1 (1 title)
Girls' doubles: 2 (1 title, 1 runner-up)
ITF Junior Circuit finals
Singles: 8 (6 titles, 2 runner-ups)
Doubles: 5 (3 titles, 2 runners-ups)
Team competition: 1 (1 title)
WTA Tour career earnings
Current through 16 October 2023
Career Grand Slam statistics
Career Grand Slam tournament seedings
The tournaments won by Świątek are in boldface, and advanced into finals by Świątek are in italics.
Best Grand Slam tournament results details
Grand Slam winners are in boldface, and runner-ups are in italics.
Record against other players
Top 10 win-loss
She has a record against players who were, at the time the match was played, ranked in the top 10.
Double-bagel matches
Longest winning streak
Świątek's 37-match win streak is the longest in the 21st century and is tied for the 12th longest in the Open Era.
37-match win streak (2022)
Notes
References
External links
career statistics
Swiatek, Iga
|
https://en.wikipedia.org/wiki/Ecuador%20national%20football%20team%20results%20%282020%E2%80%93present%29
|
This page details the match results and statistics of the Ecuador national football team from 2020 to present.
Key
Key to matches
Att.=Match attendance
(H)=Home ground
(A)=Away ground
(N)=Neutral ground
Key to record by opponent
Pld=Games played
W=Games won
D=Games drawn
L=Games lost
GF=Goals for
GA=Goals against
Results
Ecuador's score is shown first in each case.
Notes
Record by opponent
References
Ecuador national football team results
|
https://en.wikipedia.org/wiki/Royal%20Spanish%20Mathematical%20Society
|
The Royal Spanish Mathematical Society (Spanish: Real Sociedad Matemática Española, RSME) is the main professional society of Spanish mathematicians and represents Spanish mathematics within the European Mathematical Society (EMS) and the International Mathematical Union (IMU).
History
The RSME was founded in 1911 by a group of mathematicians, among whom were Luis Octavio de Toledo y Zulueta and Julio Rey Pastor, under the name of the Spanish Mathematical Society. The initiative arose at the first congress of the Spanish Association for the Progress of Science (AEPC), where the convenience of establishing a mathematics society was raised.
Throughout its more than 100 years it has gone through various stages of greater or lesser activity. Since 1996, it has been in one of its most active periods, counting in August 2005 about 1700 members, among which there are individual members, as well as institutional members such as, for example, university faculties and departments and high school institutes.
It has reciprocal agreements with a large number of mathematical societies around the world. It is one of the societies that forms part of the Spanish Mathematical Committee and is an institutional member of the European Mathematical Society (EMS) and of the Confederation of Spanish Scientific Societies (COSCE).
Presidents
José Echegaray y Eizaguirre: 1911-1916
Zoel García de Galdeano: 1916-1920
Leonardo Torres Quevedo: 1920-1924
Luis Octavio de Toledo y Zulueta: 1924-1934
Julio Rey Pastor: 1934-1934
Juan López Soler: 1935-1937
José Barinaga: 1937-1939
Juan López Soler: 1939-1954
Julio Rey Pastor: 1955-1961
Alberto Dou Mas de Xaxàs: 1961-1963
Francisco Botella: 1963-1970
Enrique Linés Escardó: 1970-1976
José Javier Etayo: 1976-1982
Pedro Luis García Pérez: 1982-1988
José Manuel Aroca: 1988-1996
Antonio Martínez Naveira: 1996-2000
Carlos Andradas: 2000-2006
Olga Gil Medrano: 2006-2009
Antonio Campillo López: 2009-2015
Francisco Marcellán Español: 2015-2022
Eva Gallardo: 2022-
Activities
The RSME actively collaborates with other scientific societies in Spain in various activities such as the celebration, in 2000, of the World Year of Mathematics, the preparation of the Spanish candidacy and the subsequent organization of the International Congress of Mathematicians (ICM) that was held in August 2006 in Madrid and the work of the Senate Report on the teaching of science in secondary education (2003-04 academic year).
The RSME prepares, through its various commissions, reports on topics such as the situation of mathematical research in Spain, the problems of teaching mathematics in high school, the situation of mathematics in relation to the European higher education area, professional opportunities and the participation of women in mathematical research.
In addition, it is involved in international cooperation projects: digitization of mathematical literature, support of mathematics in Latin America, among others. The society organized the fir
|
https://en.wikipedia.org/wiki/Kanta%20Tanaka
|
is a Japanese footballer who plays as a goalkeeper for Tochigi City FC.
Career statistics
Club
.
References
External links
1998 births
Living people
Association football people from Iwate Prefecture
Biwako Seikei Sport College alumni
Japanese men's footballers
Japan men's youth international footballers
Men's association football goalkeepers
J3 League players
Kataller Toyama players
Iwaki FC players
Tochigi City FC players
|
https://en.wikipedia.org/wiki/Zhang%20Shuai%20career%20statistics
|
This is a list of the main career statistics of professional Chinese tennis player Zhang Shuai.
Performance timelines
P = postponed
Only main-draw results in WTA Tour, Grand Slam tournaments, Fed Cup/Billie Jean King Cup and Olympic Games are included in win–loss records.
Singles
Current through the 2023 French Open.
Doubles
Current after the 2023 Australian Open.
Mixed doubles
Significant finals
Grand Slam tournaments
Doubles: 3 (2 titles, 1 runner-up)
WTA 1000 finals
Doubles: 2 (1 title, 1 runner-up)
WTA Elite Trophy
Doubles: 1 (runner-up)
WTA career finals
Singles: 6 (3 titles, 3 runner-ups)
Doubles: 26 (13 titles, 13 runner-ups)
WTA Challenger finals
Singles: 6 (2 titles, 4 runner-ups)
Doubles: 3 (2 titles, 1 runner-up)
ITF Circuit finals
Singles: 30 (21 titles, 9 runner–ups)
Doubles: 12 (8 titles, 4 runner–ups)
WTA Tour career earnings
Current after the 2022 Cincinnati.
{|cellpadding=3 cellspacing=0 border=1 style=border:#aaa;solid:1px;border-collapse:collapse;text-align:center;
|-style=background:#eee;font-weight:bold
|width="90"|Year
|width="100"|Grand Slam <br/ >titles|width="100"|WTA <br/ >titles
|width="100"|Total <br/ >titles
|width="120"|Earnings ($)
|width="100"|Money list rank
|-
|2011
|0
|1
|1
| align="right" |235,750
|82
|-
|2012
|0
|2
|2
| align="right" |304,426
|100+
|-
|2013
|0
|1
|1
| align="right" |304,426
|85
|-
|2014
|0
|1
|1
| align="right" |425,826
|70
|-
|2015
|0
|0
|0
| align="right" |173,407
|145
|-
|2016
|0
|0
|0
| align="right" |1,033,120
|32
|-
|2017
|0
|1
|1
| align="right" |843,444
|43
|-
|2018
|0
|3
|3
| align="right" |982,583
|39
|-
|2019
|1
|0
|1
| align="right" |1,661,425
|24
|-
|2020
|0
|0
|0
| align="right" |543,404
|37
|-
|2021
|1
|2
|3
| align="right" |1,020,886
|31
|-
|2022
|0
|2
|2
| align="right" |1,088,085
|24
|- style="font-weight:bold;"
|Career
|2
|13
|15
| align="right" |8,909,447
|66
|}
Career Grand Slam statistics
Seedings
The tournaments won by Zhang are in boldface', and advanced into finals by Zhang are in italics.
Singles
Doubles
Best Grand Slam results details
Head-to-head records
Record against top 10 playersZhang's record against players who have been ranked in the top 10. Active players are in boldface.''
No. 1 wins
Top 10 wins
Notes
References
Tennis career statistics
|
https://en.wikipedia.org/wiki/Laura%20Siegemund%20career%20statistics
|
This is a list of the main career statistics of professional German tennis player Laura Siegemund. She has won two singles titles on the WTA Tour. In doubles, she has won thirteen titles, including the 2020 US Open. She also won the 2016 US Open mixed doubles title.
Performance timelines
Only main-draw results in WTA Tour, Grand Slam tournaments, Billie Jean King Cup and Olympic Games are included in win–loss records.
Singles
Current through the 2023 Jiangxi Open.
Doubles
Current through the 2023 Jiangxi Open.
Mixed doubles
Grand Slam tournament finals
Doubles: 2 (1 title, 1 runner-up)
Mixed doubles: 1 (1 title)
WTA 1000 finals
Doubles: 2 (1 title, 1 runner-up)
WTA career finals
Singles: 4 (2 titles, 2 runner-ups)
Doubles: 19 (13 titles, 6 runner-ups)
ITF Circuit finals
Singles: 28 (14 titles, 14 runner-ups)
Doubles: 32 (20 titles, 12 runner-ups)
Head-to-head records
Record against top-10 players
Siegemund's record against players who have been ranked in the top 10, with those who are active in boldface.
Record against No. 11–20 players
Siegemund's record against players who have been ranked world No. 11–20, with those who are active in boldface.
Magda Linette
Jennifer Brady
Mirjana Lučić-Baroni
Alison Riske-Amritraj
Alizé Cornet
Klára Koukalová
Anastasia Pavlyuchenkova
Kirsten Flipkens
Petra Martić
María José Martínez Sánchez
Liudmila Samsonova
Anastasija Sevastova
Barbora Strýcová
Elena Vesnina
Mihaela Buzărnescu
Eleni Daniilidou
Ana Konjuh
Martina Trevisan
Ekaterina Alexandrova
Elise Mertens
Yanina Wickmayer
Varvara Lepchenko
* Statistics correct .
Wins over top-10 players
Siegemund has a record against players who were, at the time the match was played, ranked in the top 10.
National participation
Billie Jean King Cup (2–4)
United Cup (1–3)
References
Siegemund
|
https://en.wikipedia.org/wiki/Hsieh%20Su-wei%20career%20statistics
|
This is a list of the main career statistics of professional Taiwanese tennis player Hsieh Su-wei. To date, Hsieh has won three singles and 32 doubles career titles, including six Grand Slam doubles titles at the Wimbledon Championships in 2013, 2019, 2021 and 2023, as well as at the French Open in 2014 and 2023. She has also won one WTA Finals doubles title in 2013, 12 WTA 1000 doubles titles. Hsieh has also been a runner–up at the 2020 Australian Open, and a semifinalist at the 2012 US Open. She reached her career-high doubles ranking of world No. 1 on 12 May 2014 and has spent a combined total of 47 weeks with the top ranking.
Performance timelines
Only main-draw results in WTA Tour, Grand Slam tournaments, Fed Cup/Billie Jean King Cup and Olympic Games are included in win–loss records.
Singles
Current after the 2021 Courmayeur.
Doubles
Mixed doubles
Significant finals
Grand Slam tournaments
Doubles: 7 (6 titles, 1 runner-up)
Year-end championships
Doubles: 4 (1 title, 3 runner-ups)
WTA 1000 tournaments
Doubles: 13 (12 titles, 1 runner-up)
WTA career finals
Singles: 3 (3 titles)
Doubles: 47 (32 titles, 15 runner-ups)
WTA Challenger finals
Singles: 1 (runner–up)
Doubles: 1 (title)
ITF Circuit finals
Singles: 31 (27 titles, 4 runner–ups)
Doubles: 38 (23 titles, 15 runner–ups)
WTA Tour career earnings
Current after the 2022 Melbourne Summer Set 1.
* Hsieh won her first tour title in 2007, so relevant stats begin from there. Statistics for WTA Prize Money Leaders only includes the top 100 till 2013. By utilizing Career Prize Money information, prize money earned from 2001 to 2007, and from 2010 to 2011, is $604,427.
Head-to-head records
Record against top 10 players
Hsieh's record against players who have been ranked in the top 10. Active players are in boldface.
No. 1 wins
Top 10 wins
Notes
References
Tennis career statistics
|
https://en.wikipedia.org/wiki/Alan%20%28footballer%2C%20born%202000%29
|
Alan de Souza Guimarães (born 8 March 2000), simply known as Alan or Alanzinho, is a Brazilian footballer who plays as an attacking midfielder for Primeira Liga club Moreirense.
Career statistics
Club
Honours
Moreirense
Liga Portugal 2: 2022–23
References
2000 births
Living people
Footballers from São Paulo
Brazilian men's footballers
Brazil men's youth international footballers
Brazil men's under-20 international footballers
Men's association football midfielders
Sociedade Esportiva Palmeiras players
Guarani FC players
Operário Ferroviário Esporte Clube players
Sport Club do Recife players
Moreirense F.C. players
Campeonato Brasileiro Série B players
Campeonato Pernambucano players
Liga Portugal 2 players
Primeira Liga players
Brazilian expatriate men's footballers
Expatriate men's footballers in Portugal
Brazilian expatriate sportspeople in Portugal
|
https://en.wikipedia.org/wiki/Wielandt%20theorem
|
In mathematics, the Wielandt theorem characterizes the gamma function, defined for all complex numbers for which by
as the only function defined on the half-plane such that:
is holomorphic on ;
;
for all and
is bounded on the strip .
This theorem is named after the mathematician Helmut Wielandt.
See also
Bohr–Mollerup theorem
Hadamard's gamma function
References
.
Gamma and related functions
Theorems in complex analysis
|
https://en.wikipedia.org/wiki/Gauss%20curvature%20flow
|
In the mathematical fields of differential geometry and geometric analysis, the Gauss curvature flow is a geometric flow for oriented hypersurfaces of Riemannian manifolds. In the case of curves in a two-dimensional manifold, it is identical with the curve shortening flow. The mean curvature flow is a different geometric flow which also has the curve shortening flow as a special case.
Definition and well-posedness
Let be a smooth -dimensional manifold and let be a smooth Riemannian manifold of dimension . Given an immersion of into together with a unit normal vector field along , the second fundamental form of can be viewed as a symmetric 2-tensor field on . Via the first fundamental form, it can also be viewed as a (1,1)-tensor field on , where it is known as the shape operator. The Gaussian curvature or Gauss–Kronecker curvature of , denoted by , can then be defined as the point-by-point determinant of the shape operator, or equivalently (relative to local coordinates) as the determinant of the second fundamental form divided by the determinant of the first fundamental form.
The equation defining the Gauss curvature flow is
So a Gauss curvature flow consists of a smooth manifold , a smooth Riemannian manifold of dimension one larger, and a one-parameter family of immersions of into , together with a smooth unit normal vector field along each immersion, such that the above equation is satisfied.
The well-posedness of the Gauss curvature flow is settled if is closed. Then, if is greater than one, and if a given immersion, along which a smooth unit normal vector field has been chosen, has positive-definite second fundamental form, then there is a unique solution of the Gauss curvature flow with "initial data" . If is equal to one, so that one is in the setting of the curve shortening flow, the condition on the second fundamental form is unnecessary.
Convergence theorems
Due to the existence & uniqueness theorem above, the Gauss curvature flow has essentially only been studied in the cases of curve shortening flow, and in higher dimensions for closed convex hypersurfaces. Regardless of dimension, it has been most widely studied in the case that is the Euclidean space .
In the case of curve shortening flow, Michael Gage and Richard Hamilton showed that any convex embedding of the circle into the plane is deformed to a point in finite time, in such a way that rescalings of the curves in the flow smoothly approach a round circle. This was enhanced by a result of Matthew Grayson showing that any embedded circle in the plane is deformed into a convex embedding, at which point Gage and Hamilton's result applies. Proofs have since been found which do not treat the two cases of convexity and non-convexity separately. In the more general setting of a complete two-dimensional Riemannian manifold which has a certain convexity near infinity, Grayson proved the convergence to a closed geodesic or to a round point.
Kaising Tso applied the meth
|
https://en.wikipedia.org/wiki/Danzer%27s%20configuration
|
In mathematics, Danzer's configuration is a self-dual configuration of 35 lines and 35 points, having 4 points on each line and 4 lines through each point. It is named after the German geometer Ludwig Danzer and was popularised by Branko Grünbaum. The Levi graph of the configuration is the Kronecker cover of the odd graph O4, and is isomorphic to the middle layer graph of the seven-dimensional hypercube graph Q7. The middle layer graph of an odd-dimensional hypercube graph Q2n+1(n,n+1) is a subgraph whose vertex set consists of all binary strings of length 2n + 1 that have exactly n or n + 1 entries equal to 1, with an edge between any two vertices for which the corresponding binary strings differ in exactly one bit. Every middle layer graph is Hamiltonian.
Danzer's configuration DCD(4) is the fourth term of an infinite series of configurations DCD(n), where DCD(1) is the trivial configuration (11), DCD(2) is the trilateral (32) and DCD(3) is the Desargues configuration (103). In configurations DCD(n) were further generalized to the unbalanced configuration DCD(n,d) by introducing parameter d with connection DCD(n) = DCD(2n-1,n). DCD stands for Desargues-Cayley-Danzer. Each DCD(2n,d) configuration is a subconfiguration of
the Clifford configuration. While each DCD(n,d) admits a realisation as a geometric point-line configuration, the Clifford configuration can only be realised as a point-circle configuration
and depicts the Clifford's circle theorems.
Example
See also
Miquel configuration
Reye configuration
References
Bibliography
.
.
.
.
Configurations (geometry)
|
https://en.wikipedia.org/wiki/Adam%20Tren%C4%8Dan
|
Adam Trenčan (born July 10, 1990) is a Slovak professional ice hockey goaltender for the HKM Zvolen of the Slovak Extraliga.
Career statistics
Regular season and playoffs
References
External links
Living people
HC Slezan Opava players
HC 07 Detva players
HK 36 Skalica players
HC Oceláři Třinec players
HC Benátky nad Jizerou players
HK Spišská Nová Ves players
Lausitzer Füchse players
HK Nitra players
HK Dukla Michalovce players
HKM Zvolen players
1990 births
Slovak ice hockey goaltenders
Ice hockey people from Banská Bystrica
Slovak expatriate ice hockey players in Germany
Slovak expatriate ice hockey players in the Czech Republic
|
https://en.wikipedia.org/wiki/Al-Horjelah
|
Al-Horjelah (also spelled Al-Horgelah or Al-Harjalah; ), is a Syrian village located in Markaz Rif Dimashq, Rif Dimashq. According to the Syria Central Bureau of Statistics (CBS), Al-Horjelah had a population of 3,550 in the 2004 census. The village also hosts a military base for the 4th Armoured Division.
Sports
The town is known for its football team, Al-Horgelah SC.
References
Populated places in Rif Dimashq Governorate
|
https://en.wikipedia.org/wiki/Welington%20%28footballer%29
|
Welington Damascena Santos (born 19 February 2001), known as Welington, is a Brazilian professional footballer who plays as a left-back for São Paulo.
Career statistics
Honours
São Paulo
Copa São Paulo de Futebol Jr.: 2019
Campeonato Paulista: 2021
Copa do Brasil: 2023
References
2001 births
Living people
Brazilian men's footballers
Brazil men's youth international footballers
Men's association football defenders
Campeonato Brasileiro Série A players
São Paulo FC players
Footballers from São Paulo
|
https://en.wikipedia.org/wiki/Kaito%20Kasuya
|
born 23 May 1998.
He is a Japanese footballer currently playing as a defender for Toledo.
Career statistics
Club
.
Notes
References
1998 births
Living people
Japanese men's footballers
Japanese expatriate men's footballers
Men's association football defenders
Toledo Esporte Clube players
Japanese expatriate sportspeople in Brazil
Expatriate men's footballers in Brazil
|
https://en.wikipedia.org/wiki/Pilar%20Ribeiro
|
Pilar Ribeiro (5 October 191128 March 2011) was a mathematician who was a founder of the Portuguese Mathematical Society (SPM) and also of the Gazeta de Matemática (Mathematics Gazette).
Early life
Maria do Pilar Baptista Ribeiro was born in the Portuguese capital of Lisbon, on 5 October 1911, the daughter of Joaquim Rodrigues Carreira and Luísa Loureiro Peres. She graduated in Mathematics from the Faculty of Sciences of the University of Lisbon in 1933, at a time when it was still unusual for women to study such a subject. A year later, she married mathematician Hugo Baptista Ribeiro (1910–88), who she had met during the course. The couple shared an opposition to the established Estado Novo dictatorship and participated in activities of the Portuguese Communist Party. After graduating she taught mathematics in Lisbon as well as attending seminars given by the mathematician António Aniceto Monteiro. As a founding member of the Portuguese Mathematical Society, together with Bento de Jesus Caraça, she held the position of First Secretary for the 1941/1942 biennium. She returned to that same position in 1946/1947, when her husband was Secretary-General. The Mathematics Gazette, the Society’s publication, played an important role in the preservation and dissemination of the history of mathematics in Portugal and elsewhere in the 1940s.
Exile
Between 1942 and 1946, she accompanied her husband to Zurich, where he studied for his PhD. Pilar Ribeiro took the opportunity to attend several specialized courses in mathematics at the Federal Polytechnic School of Zurich. When her husband stopped receiving the Portuguese scholarship to which he was entitled, she started to work so that he could complete his doctorate. She also sent papers to Gazeta de Matemática, on teaching mathematics in Switzerland. Returning to Portugal, the couple faced opposition to science on the part of the Estado Novo, which condemned independent thinking. This forced some scientists into exile. They left the country for the United States where Pilar Ribeiro taught mathematics at Pennsylvania State University. She and her husband also spent some time in Brazil, where her husband taught in Recife. Together with José da Silva Paulo, she was responsible for the translation into Portuguese of David Hilbert's classic work, Grundlagen der Geometrie (Foundations of Geometry).
Return to Portugal
The couple did not return permanently to Portugal until after the Carnation Revolution on 25 April 1974, which overthrew the Estado Novo. From 1976 to 1980, at the invitation of Ruy Luís Gomes, Pilar Ribeiro was a professor at the University of Porto and at its Abel Salazar Biomedical Sciences Institute graduate school.
In January 2005, she donated her husband's estate to the National Library, consisting essentially of correspondence from national and foreign personalities, including a core of family letters and some drafts of letters sent. She died in Cascais, Portugal on 28 March 2011, a few mon
|
https://en.wikipedia.org/wiki/YanYan%20Li
|
YanYan Li (also stylized as Yanyan Li, Yan-yan Li, and Yan Yan Li) is a Professor of mathematics at Rutgers University, specializing in elliptic partial differential equations. He received his Ph.D. at New York University in 1988, under the direction of Louis Nirenberg. He joined Rutgers University in 1990.
Li was an invited lecturer at the International Congress of Mathematicians in 2002, and is a Fellow of the American Mathematical Society. He has been an ISI Highly Cited Researcher. He is a member of the editorial board of Advances in Mathematics, among several other academic journals.
Major publications
Yan Yan Li and Itai Shafrir. Blow-up analysis for solutions of in dimension two. Indiana Univ. Math. J. 43 (1994), no. 4, 1255–1270.
Yan Yan Li. Prescribing scalar curvature on and related problems. I. J. Differential Equations 120 (1995), no. 2, 319–410.
Yan Yan Li. Prescribing scalar curvature on and related problems. II. Existence and compactness. Comm. Pure Appl. Math. 49 (1996), no. 6, 541–597.
References
External links
YanYan Li's home page at Rutgers
Mathematics Genealogy page
Google Scholar page
Living people
Year of birth missing (living people)
Rutgers University faculty
20th-century American mathematicians
21st-century American mathematicians
New York University alumni
|
https://en.wikipedia.org/wiki/1984%20Costa%20Rican%20census
|
The Costa Rica 1984 census was elaborated by then , predecessor of current National Institute of Statistics and Census. The total population was at the moment .
Results by canton
References
Censuses in Costa Rica
1984 in Costa Rica
1984 censuses
|
https://en.wikipedia.org/wiki/1973%20Costa%20Rican%20census
|
The Costa Rica 1973 census was elaborated by then , predecessor of current National Institute of Statistics and Census. The total population was at the moment .
Results by canton
References
Censuses in Costa Rica
1973 in Costa Rica
1973 censuses
|
https://en.wikipedia.org/wiki/1963%20Costa%20Rican%20census
|
The Costa Rica 1963 census was elaborated by then , predecessor of current National Institute of Statistics and Census. The total population was at the moment .
Results by canton
References
Censuses in Costa Rica
1963 in Costa Rica
1963 censuses
|
https://en.wikipedia.org/wiki/1950%20Costa%20Rican%20census
|
The Costa Rica 1950 census was elaborated by then , predecessor of current National Institute of Statistics and Census. The total population was at the moment .
Results by canton
References
Censuses in Costa Rica
1950 in Costa Rica
1950 censuses
|
https://en.wikipedia.org/wiki/1927%20Costa%20Rican%20census
|
The Costa Rica 1927 census was elaborated by then , predecessor of current National Institute of Statistics and Census. The total population was at the moment .
Results by canton
References
Censuses in Costa Rica
1927 in Costa Rica
1927 censuses
|
https://en.wikipedia.org/wiki/1892%20Costa%20Rican%20census
|
The Costa Rica 1892 census was elaborated by then , predecessor of current National Institute of Statistics and Census. The total population was at the moment .
Results by canton
References
Censuses in Costa Rica
1892 in Costa Rica
1892 censuses
|
https://en.wikipedia.org/wiki/1883%20Costa%20Rican%20census
|
The Costa Rica 1883 census was elaborated by then , predecessor of current National Institute of Statistics and Census. The total population was at the moment .
Results by canton
References
Censuses in Costa Rica
1883 in Costa Rica
1883 censuses
|
https://en.wikipedia.org/wiki/1864%20Costa%20Rican%20census
|
The Costa Rica 1864 Census was the first official census elaborated in the country by the , predecessor of current National Institute of Statistics and Census. The total population was at the moment .
Results by canton
References
Censuses in Costa Rica
1864 in Costa Rica
1864 censuses
|
https://en.wikipedia.org/wiki/Cameron%20O%27Donnell
|
Cameron O'Donnell (born 29 September 2001) is a Scottish professional footballer who plays as a midfielder for Scottish Championship club Alloa Athletic.
Career statistics
References
Living people
2001 births
Scottish men's footballers
Men's association football midfielders
Place of birth missing (living people)
Alloa Athletic F.C. players
Scottish Professional Football League players
|
https://en.wikipedia.org/wiki/Douglas%20Quadling
|
Douglas Arthur Quadling (1926–2015) was an English mathematician, school master and educationalist who was one of the four drivers behind the School Mathematics Project (SMP) in the 1960s and 70s.
Life
Quadling was educated at the City of London School. In 1939 the school was moved out of London, at the start of World War II, with most of the pupils attending Marlborough College though not accommodated there. Quadling had use of the College library at weekends, was influenced by Gordon Nobbs, one of the masters, and decided on a teaching career. In 1943 he won a scholarship to Emmanuel College, Cambridge.
Graduating as a wrangler, with a two-year Part II in the Mathematical Tripos, Quadling worked briefly at the end of the war at Fort Halstead for the Ministry of Supply. At this period, based near Orpington, he met and influenced the young Michael Saward, who found him "a pleasant if somewhat owlish young man", while canvassing support for the Crusaders.
Quadling taught at Mill Hill School from 1946 to 1952. He was at Marlborough College from 1952 to 1967, becoming Head of Mathematics and a housemaster (C2). He was then a tutor at the Cambridge Institute of Education, from 1968 to 1985.
As a novice mathematics teacher in the late 1940s, Quadling joined the Mathematical Association, serving as its President in 1980–1. He spoke at a mathematics education conference in Ghana in 1968. He took over from Edwin A. Maxwell as editor of the Mathematical Gazette in 1971; his successor in 1980 was Victor Bryant. In 1983 he was awarded the OBE for services to mathematical education. He married Ruth Starte of the Cambridge Institute of Education.
Creation of School Mathematics Project
The School Mathematics Project, which changed the course of mathematics teaching in Britain, arose from a meeting between Quadling and three others, Martyn Cundy of Sherborne School, Tom Jones of Winchester College and Professor Bryan Thwaites of University of Southampton, in September 1961. Cundy, like Quadling, was involved with the Mathematical Association.
By 1963 the compilation of new SMP mathematics syllabuses had been given to Cundy, Jones, Quadling and T. D. Morris of Charterhouse School. From July 1964 three examination boards offered an SMP syllabus for the General Certificate of Education. When the A-level syllabus was constructed, Cundy and Quadling wrote with John Durran, Laurence Ellis, Colin Goldsmith, Tim Lewis and others.
Views
In public life, Quadling was known for lamenting the state of mathematics education, advocating the need for university courses which were more practical and scientific, in contrast to, say, the exacting Mathematical Tripos at the University of Cambridge. It was at school level, however, that he had greatest influence, through the SMP.
Selected publications
Quadling was head-hunted as a textbook writer at the Mathematical Association conference in 1955, by the authors C. V. Durell and Alan Robson (Marlborough College), and A. V.
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https://en.wikipedia.org/wiki/Argentina%20national%20football%20team%20results%20%282020%E2%80%93present%29
|
This page details the match results and statistics of the Argentina national football team from 2020 to present.
Key
Key to matches
Att.=Match attendance
(H)=Home ground
(A)=Away ground
(N)=Neutral ground
Key to record by opponent
Pld=Games played
W=Games won
D=Games drawn
L=Games lost
GF=Goals for
GA=Goals against
Results
Argentina's score is shown first in each case.
Notes
Record by opponent
References
Argentina national football team results
2020s in Argentine sport
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https://en.wikipedia.org/wiki/Bolivia%20national%20football%20team%20results%20%282020%E2%80%93present%29
|
This page details the match results and statistics of the Bolivia national football team from 2020 to present.
Key
Key to matches
Att.=Match attendance
(H)=Home ground
(A)=Away ground
(N)=Neutral ground
Key to record by opponent
Pld=Games played
W=Games won
D=Games drawn
L=Games lost
GF=Goals for
GA=Goals against
Results
Bolivia's score is shown first in each case.
Notes
Record by opponent
References
Bolivia national football team results
|
https://en.wikipedia.org/wiki/Barbora%20Krej%C4%8D%C3%ADkov%C3%A1%20career%20statistics
|
This is a list of the main career statistics of professional Czech tennis player Barbora Krejčíková. She is known for good results and titles in all three events: singles, doubles and mixed doubles. Until 2021, she been known mostly for her great results in doubles and mixed doubles. Her big progress in singles came during the season of 2021, when among many good results, she won her first Women's Tennis Association (WTA) singles title, first Grand Slam singles title and also being ranked as No. 3. The following year she had the chance to be world No. 1 after the Australian Open but she missed that opportunity. A month later, she climbed to place No. 2 as her career-highest. At the 2023 Dubai Championships, she won her first WTA 1000 title and in that way collected at least one title from all categories in either singles or doubles - only missing Year-end championships title in singles. There she also achieved wins against the three highest ranked players on the WTA Ranking, becoming one of the few players to do so.
Despite focusing more in singles, Krejčíková continued to make significant results in doubles as well. After winning French Open and Wimbledon in doubles events in 2018, she became No. 1 doubles player. At the 2020 Tokyo Summer Olympics, postponed in 2021 due to COVID-19, she has won Gold medal in doubles event. In 2021, she also won WTA Finals. All mentioned doubles achievements she made alongside countrymate Kateřina Siniaková.
Krejčíková has won titles of the all tiers. At the Grand Slams, she has total of 11 titles: 1 in singles, 7 in doubles and 3 in mixed doubles. She completed her "Career Grand Slam" in doubles by winning the 2022 US Open alongside Siniaková. By winning this title, she did not only collected all grand slams but also achieved "Career Golden Slam" and "Career Super Slam" at the same time. Achieving this alongside Siniaková, they became the second women's pair (and the third and fourth women overall, after Gigi Fernández and Pam Shriver) to complete this goal.
Performance timelines
Only main-draw results in WTA Tour, Grand Slam tournaments, Fed Cup/Billie Jean King Cup and Olympic Games are included in win–loss records.
Singles
Current after the 2023 WTA Elite Trophy.
Doubles
Current after the 2023 China Open.
Mixed doubles
Grand Slam finals
Singles: 1 (1 title)
Doubles: 8 (7 titles, 1 runner-ups)
Mixed doubles: 3 (3 titles)
Other significant finals
Olympic finals
Doubles: 1 (1 Gold Medal)
Year-end championships finals
Doubles: 3 (1 title, 2 runner-ups)
WTA 1000 finals
Singles: 2 (1 title, 1 runner-up)
Doubles: 5 (3 titles, 2 runner-ups)
WTA Tour finals
Singles: 12 (7 titles, 5 runner-ups)
Doubles: 28 (18 titles, 10 runner-ups)
Note: Tournaments sourced from official WTA archives
Team competition finals
Billie Jean King Cup: 1 (1 titles)
WTA Challenger finals
Doubles: 1 (1 title)
Note: Tournaments sourced from official WTA archives
ITF Circuit finals
Singles: 21 (14 titles, 7 runner–u
|
https://en.wikipedia.org/wiki/Frankel%20conjecture
|
In the mathematical fields of differential geometry and algebraic geometry, the Frankel conjecture was a problem posed by Theodore Frankel in 1961. It was resolved in 1979 by Shigefumi Mori, and by Yum-Tong Siu and Shing-Tung Yau.
In its differential-geometric formulation, as proved by both Mori and by Siu and Yau, the result states that if a closed Kähler manifold has positive bisectional curvature, then it must be biholomorphic to complex projective space. In this way, it can be viewed as an analogue of the sphere theorem in Riemannian geometry, which (in a weak form) states that if a closed and simply-connected Riemannian manifold has positive curvature operator, then it must be diffeomorphic to a sphere. This formulation was extended by Ngaiming Mok to the following statement:
In its algebro-geometric formulation, as proved by Mori but not by Siu and Yau, the result states that if is an irreducible and nonsingular projective variety, defined over an algebraically closed field , which has ample tangent bundle, then must be isomorphic to the projective space defined over . This version is known as the Hartshorne conjecture, after Robin Hartshorne.
References
Theodore Frankel. Manifolds with positive curvature. Pacific J. Math. 11 (1961), 165–174.
Robin Hartshorne. Ample subvarieties of algebraic varieties. Notes written in collaboration with C. Musili. Lecture Notes in Mathematics, Vol. 156 (1970). Springer-Verlag, Berlin-New York. xiv+256 pp.
Shoshichi Kobayashi and Takushiro Ochiai. Characterizations of complex projective spaces and hyperquadrics. J. Math. Kyoto Univ. 13 (1973), 31–47.
Ngaiming Mok. The uniformization theorem for compact Kähler manifolds of nonnegative holomorphic bisectional curvature. J. Differential Geom. 27 (1988), no. 2, 179–214.
Shigefumi Mori. Projective manifolds with ample tangent bundles. Ann. of Math. (2) 110 (1979), no. 3, 593–606.
Yum Tong Siu and Shing Tung Yau. Compact Kähler manifolds of positive bisectional curvature. Invent. Math. 59 (1980), no. 2, 189–204.
Differential geometry
Algebraic geometry
Conjectures
|
https://en.wikipedia.org/wiki/Konstantinos%20Chatzipirpiridis
|
Konstantinos Chatzipirpiridis (; born 1 May 2001) is a Greek professional footballer who plays as a right winger for Austrian club SK Bischofshofen.
Career statistics
References
2001 births
Living people
Greek men's footballers
Super League Greece players
Aris Thessaloniki F.C. players
Men's association football midfielders
Footballers from Thessaloniki
Expatriate men's footballers in Austria
Olympiacos Volos F.C. players
Greek expatriate sportspeople in Austria
Greek expatriate men's footballers
Iraklis F.C. (Thessaloniki) players
|
https://en.wikipedia.org/wiki/Aldridge%20Bousfield
|
Aldridge Knight Bousfield (April 5, 1941 – October 4, 2020), known as "Pete", was an American mathematician working in algebraic topology, known for the concept of Bousfield localization.
Work and life
Bousfield obtained both his undergraduate degree (1963) and his doctorate (1966) at the Massachusetts Institute of Technology. His doctoral thesis, entitled "Higher Order Suspension Maps for Non-Additive Functors", was written under the supervision of Daniel Kan. He was a lecturer and assistant professor at Brandeis University and moved to the University of Illinois at Chicago where he worked from 1972 to his retirement in 2000.
Bousfield married Marie Vastersavendts, a Belgian mathematician, in 1968. She worked as demographer for the city of Chicago and died in 2016.
Research
Within algebraic topology, he specialised in homotopy theory. The Bousfield-Kan spectral sequence, Bousfield localization of spectra and model categories, and the Bousfield-Friedlander model structure are named after Bousfield (and Kan and Friedlander, respectively).
Recognition
He was named to the 2018 class of fellows of the American Mathematical Society "for contributions to homotopy theory and for exposition".
Selected publications
References
20th-century American mathematicians
Massachusetts Institute of Technology School of Science alumni
1941 births
2020 deaths
Fellows of the American Mathematical Society
Writers from Boston
Brandeis University faculty
University of Illinois Chicago faculty
|
https://en.wikipedia.org/wiki/Alison%20Riske%20career%20statistics
|
This is a list of the main career statistics of professional American tennis player Alison Riske-Amritraj.
Performance timelines
Only main-draw results in WTA Tour, Grand Slam tournaments, Fed Cup/Billie Jean King Cup and Olympic Games are included in win–loss records.
Singles
Current through the 2023 French Open.
Doubles
Current after the 2023 Australian Open.
Significant finals
WTA 1000 finals
Singles: 1 (runner up)
WTA career finals
Singles: 13 (3 titles, 10 runner-ups)
ITF Circuit finals
Singles: 13 (9 titles, 4 runner–ups)
Doubles: 4 (1 title, 3 runner–ups)
WTA Tour career earnings
Current after the 2022 French Open
Career Grand Slam statistics
Grand Slam seedings
The tournaments won by Riske are in boldface, and advanced into finals by Riske are in italics.
Best Grand Slam results details
Record against other players
No. 1 wins
Record against top 10 players
Notes
References
Riske, Alison
|
https://en.wikipedia.org/wiki/Donna%20Veki%C4%87%20career%20statistics
|
Donna Vekić is a Croatian tennis player, accomplished in singles. Her breakthrough came in 2019 when she reached her first quarterfinal at a Grand Slam championship, at the US Open, which brought her into the top 20 of the WTA rankings. In her prize collection, she has three WTA Tour singles titles, as well as five singles titles and one doubles title on the ITF Circuit. In addition, she has played one Premier-level tournament, the 2019 St. Petersburg Ladies' Trophy, as the biggest final of her career. She also has played in national competitions for Croatia including Fed Cup and Olympic Games. At the 2020 Tokyo Olympics, she made her biggest win so far, defeating world No. 3, Aryna Sabalenka. She used to be Croatian number one a couple of times.
Performance timelines
Only main-draw results in WTA Tour, Grand Slam tournaments, Fed Cup/Billie Jean King Cup and Olympic Games are included in win–loss records.
Singles
Current through the 2023 US Open.
Doubles
Current through the 2023 Australian Open.
WTA Tour finals
Singles: 12 (4 titles, 8 runner-ups)
ITF Circuit finals
Singles: 13 (5 titles, 8 runner–ups)
Doubles: 1 (title)
National representation
Billie Jean King Cup
Current in 2022.
Singles (13–7)
Doubles (3–1)
United Cup participation
Singles (3–0)
Hopman Cup participation
Singles (2–1)
Mixed doubles (2–0)
WTA Tour career earnings
Current through the 2022 Tallinn Open.
{|cellpadding=3 cellspacing=0 border=1 style=border:#aaa;solid:1px;border-collapse:collapse;text-align:center;
|-style=background:#eee;font-weight:bold
|width="90"|Year
|width="100"|Grand Slam <br/ >singles titles|width="100"|WTA <br/ >singles titles
|width="100"|Total <br/ >singles titles
|width="120"|Earnings ($)
|width="100"|Money list rank
|-
|2014
|0
|1
|1
| align="right" |325,466
|95
|-
|2015
|0
|0
|0
| align="right" |240,387
|119
|-
|2016
|0
|0
|0
| align="right" |243,988
|120
|-
|2017
|0
|1
|1
| align="right" |574,399
|59
|-
|2018
|0
|0
|0
| align="right" |830,793
|46
|-
|2019
|0
|0
|0
| align="right" |1,534,830
|26
|-
|2020
|0
|0
|0
| align="right" |450,884
|47
|-
|2021
|0
|1
|1
| align="right" |571,182
|64
|-
|2022
|0
|0
|0
| align="right" |379,228
|123
|- style="font-weight:bold;"
|Career
|0
|3
|3
| align="right" |5,448,690
|119
|}
Grand Slam statistics
Seedings
The tournaments won by Vekić are in boldface', and advanced into finals by Vekić are in italics.''
Record against other players
Top-10 wins
Notes
References
Vekić, Donna
|
https://en.wikipedia.org/wiki/Ali%20Al-Balochi
|
Ali Saeed Al-Balochi (; born 27 November 2000), is an Emirati professional footballer who plays as a midfielder for Al Urooba.
Career statistics
Club
Notes
References
External links
2000 births
Living people
Emirati men's footballers
Emirati people of Baloch descent
Men's association football midfielders
UAE Pro League players
UAE First Division League players
Al Ain FC players
Al Bataeh Club players
Al Urooba Club players
|
https://en.wikipedia.org/wiki/Aliz%C3%A9%20Cornet%20career%20statistics
|
This is a list of the main career statistics of professional French tennis player Alizé Cornet.
Performance timelines
Only main-draw results in WTA Tour, Grand Slam tournaments, Fed Cup/Billie Jean King Cup, Hopman Cup, United Cup and Olympic Games are included in win–loss records.
Singles
Current through the 2023 US Open.
Doubles
Current after the 2023 French Open.
Significant finals
Tier I / Premier Mandatory & Premier 5 / WTA 1000 finals
Singles: 1 (1 runner-up)
WTA career finals
Singles: 15 (6 titles, 9 runner-ups)
Doubles: 7 (3 titles, 4 runner-ups)
Tournaments sourced from official WTA archives
ITF Circuit finals
Singles: 7 (3 titles, 4 runner–ups)
Doubles: 4 (3 titles, 1 runner–up)
Team competition: 1 (1 title, 1 runner-up)
Tournaments sourced from official ITF archives
WTA Tour career earnings
Current through the 2022 Australian Open.
{|cellpadding=3 cellspacing=0 border=1 style=border:#aaa;solid:1px;border-collapse:collapse;text-align:center;
|-style=background:#eee;font-weight:bold
|width="90"|Year
|width="100"|Grand Slam <br/ >titles|width="100"|WTA <br/ >titles
|width="100"|Total <br/ >titles
|width="120"|Earnings ($)
|width="100"|Money list rank
|-
|2007
|0
|0
|0
| align="right" |158,605
|95
|-
|2008
|0
|1
|1
| align="right" |506,891
| 34
|-
|2009
|0
|0
|0
| align="right" |349,192
| 62
|-
|2010
|0
|0
|0
| align="right" |208,586
|88
|-
|2011
|0
|0
|0
| align="right" |246,729
| 78
|-
|2012
|0
|1
|1
| align="right" |322,285
|69
|-
|2013
|0
|1
|1
| align="right" |684,893
|34
|-
|2014
|0
|1
|1
| align="right" |1,163,655
|23
|-
|2015
|0
|0
|0
| align="right" |682,321
|46
|-
|2016
|0
|1
|1
| align="right" |626,111
|53
|-
|2017
|0
|0
|0
| align="right" |842,144
|44
|-
|2018
|0
|1
|1
| align="right" |680,149
|55
|-
|2019
|0
|0
|0
| align="right" |622,345
|67
|-
|2020
|0
|0
|0
| align="right" |499,897
|41
|-
|2021
|0
|0
|0
| align="right" |551,017
|69
|-
|2022
|0
|0
|0
| align="right" |421,836
|bgcolor=eee8aa|7
|- style="font-weight:bold;"
|Career
|0
|6
|6
| align="right" |8,668,433
|66
|}
Career Grand Slam statistics
Career Grand Slam seedings
The tournaments won by Cornet are in boldface, and advanced into finals by Cornet 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 playersCornet's record against players who have been ranked in the top 10. Active players are in boldface.''
No. 1 wins
Top 10 wins
Exhibition Finals
Notes
References
Cornet, Alizé
|
https://en.wikipedia.org/wiki/Anastasija%20Sevastova%20career%20statistics
|
This is a list of the main career statistics of the professional Latvian tennis player Anastasija Sevastova.
Performance timelines
Only main-draw results in WTA Tour, Grand Slam tournaments, Fed Cup/Billie Jean King Cup and Olympic Games are included in win–loss records.
Singles
Current after the 2022 Australian Open.
Significant finals
Premier-Mandatory & Premier-5 tournaments
Singles: 1 (1 runner-up)
WTA career finals
Sevastova made her WTA Tour debut in 2007 and since then has won four singles titles. In singles, she also finished as runner-up at the Premier Mandatory China Open in 2018, where she lost to Caroline Wozniacki. In doubles, she reached one final, at the Mallorca Open in 2017, alongside Jelena Janković.
Singles: 8 (4 titles, 4 runner-ups)
Doubles: 1 (runner-up)
ITF Circuit finals
Sevastova made her debut on the ITF Women's Circuit in 2016.
Singles: 23 (13 titles, 10 runner–ups)
Doubles: 5 (4 titles, 1 runner–up)
WTA Tour career earnings
Current as of 15 November 2021
Career Grand Slam statistics
Grand Slam tournament seedings
The tournaments won by Sevastova are in boldface, and advanced into finals by Sevastova are in italics.
Best Grand Slam results details
Grand Slam winners are in boldface, and runner–ups are in italics.
Head-to-head record
Record against top 10 players
Sevastova's record against players who have been ranked in the top 10. Active players are in boldface.
Top 10 wins
Notes
References
Sevastova, Anastasija
|
https://en.wikipedia.org/wiki/Yulia%20Putintseva%20career%20statistics
|
This is a list of the main career statistics of the Kazakh professional tennis player Yulia Putintseva. Putintseva has won two WTA Tour singles titles, the 2019 Nuremberg Cup and the 2021 Budapest Grand Prix. She has reached three Grand Slam quarterfinals, two of them at the French Open (2016 and 2018) and one at the US Open (2020). She has also reached one Premier 5 quarterfinal, at the 2020 Italian Open. Putintseva achieved her highest singles ranking of world No. 27 on 6 February 2017.
Performance timelines
Only main-draw results in WTA Tour, Grand Slam tournaments, Fed Cup/Billie Jean King Cup, Hopman Cup, United Cup and Olympic Games are included in win–loss records.
Singles
Current through the 2023 US Open.
Doubles
WTA Tour finals
Putintseva debuted at the WTA Tour in October 2010 at the Luxembourg Open in singles. Since then, she reached two International and one Premier-level finals, all in singles, winning only one of them, International-level Nuremberg Cup in May 2019.
Singles: 5 (2 titles, 3 runner–ups)
Doubles: 1 (runner-up)
ITF Circuit finals
Putintseva debuted at the ITF Women's World Tennis Tour in 2010 at the $10k event in Amiens in singles. She has been in twelve finals and won half of them, while in doubles she has not reached any final. Her biggest title on the ITF Circuit came in May 2012, at the $100k Open de Cagnes-sur-Mer.
Singles: 12 (6 titles, 6 runner–ups)
WTA Tour career earnings
Current through the 2022 Indian Wells Open
Career Grand Slam statistics
Seedings
The tournaments won by Putintseva are in boldface, and advanced into finals by Putintseva are in italics.
Best Grand Slam results details
Record against other players
No. 1 wins
Record against other top 10 players
Putintseva has a record against players who were, at the time the match was played, ranked in the top 10.
Notes
References
Putintseva, Yulia
|
https://en.wikipedia.org/wiki/Adam%20Nagy%20%28ice%20hockey%29
|
Adam Nagy (born August 29, 1993) is a Slovak professional ice hockey goaltender. He is currently a free agent.
Career statistics
Regular season and playoffs
References
External links
Living people
HK Dukla Trenčín players
HK 91 Senica players
HK 95 Panthers Považská Bystrica players
HC '05 Banská Bystrica players
ŠHK 37 Piešťany players
HC 07 Detva players
MHk 32 Liptovský Mikuláš players
Peliitat Heinola players
HK Nitra players
1993 births
Slovak ice hockey goaltenders
People from Levice
Ice hockey people from the Nitra Region
Slovak expatriate ice hockey players in Finland
|
https://en.wikipedia.org/wiki/Paul%20Gauduchon
|
Paul Gauduchon (born March 22, 1945) is a French mathematician, known for his work in the field of differential geometry. He is particularly known for his introduction of Gauduchon metrics in hermitian geometry. His textbook on spectral geometry, written with Marcel Berger and Edmond Mazet, is a standard reference in the field.
from 1965, Gauduchon studied at the École polytechnique and carried out research for the CNRS from 1968. In 1975, he received his doctorate (Doctor d'Etat) with André Lichnerowicz at the University of Paris VII () and completed his habilitation in 1986. Since 1990 he has been research director of the CNRS at the Center de Mathématiques of the École Polytechnique in Palaiseau Paris. There he heads the geometry group and organizes the Arthur Besse seminar on Riemannian geometry. He also teaches at the Institut des Mathematiques de Jussieu.
Notable publications
Marcel Berger, Paul Gauduchon, and Edmond Mazet. Le spectre d'une variété riemannienne. Lecture Notes in Mathematics, Vol. 194 Springer-Verlag, Berlin-New York 1971 vii+251 pp.
Paul Gauduchon. La 1-forme de torsion d'une variété hermitienne compacte. Math. Ann. 267 (1984), no. 4, 495–518.
Paul Gauduchon. Hermitian connections and Dirac operators. Boll. Un. Mat. Ital. B (7) 11 (1997), no. 2, suppl., 257–288.
References
External links
Homepage
Conference for Gauduchon's 60th birthday (2005)
1945 births
Living people
French mathematicians
École Polytechnique alumni
French National Centre for Scientific Research scientists
Differential geometry
University of Paris alumni
Riemannian geometry
Spectral theory
Research directors of the French National Centre for Scientific Research
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https://en.wikipedia.org/wiki/Shiho%20Ogawa%20%28footballer%2C%20born%202003%29
|
is a Japanese footballer currently playing as a forward for Cerezo Osaka U-23.
Career statistics
Club
.
Notes
References
External links
2003 births
Living people
Japanese men's footballers
Men's association football forwards
J3 League players
Cerezo Osaka players
Cerezo Osaka U-23 players
|
https://en.wikipedia.org/wiki/Lee%20Yun-oh
|
Lee Yun-oh (; born 23 March 1999) is a South Korean footballer who currently plays as a goalkeeper for Gamba Osaka U-23, on loan from Vegalta Sendai.
Career statistics
Club
.
Notes
References
External links
1999 births
Living people
South Korean men's footballers
South Korean expatriate men's footballers
Men's association football goalkeepers
J3 League players
Ulsan Hyundai FC players
Vegalta Sendai players
Fukushima United FC players
Gamba Osaka players
Gamba Osaka U-23 players
Daegu FC players
South Korean expatriate sportspeople in Japan
Expatriate men's footballers in Japan
Footballers from Seoul
|
https://en.wikipedia.org/wiki/Michael%20Herzog%20%28neuroscientist%29
|
Michael Herzog (born 1964) is a German neuroscientist and psychophysicist. His interdisciplinary research draws on biology, neurosciences, mathematics, and philosophy with a focus on perception. Herzog is a professor for neuroscience at the School of Life Sciences at EPFL (École Polytechnique Fédérale de Lausanne) and head of the Laboratory of Psychophysics.
Career
Herzog studied mathematics, biology and philosophy at the University of Erlangen, at the University of Tübingen, and at the Massachusetts Institute of Technology (MIT). In 1992, he received a diploma in mathematics from the University of Tübingen for his thesis on "Automorphism groups of Hamming graphs" supervised by Christoph Hering. In 1993, Herzog earned a Master's degree in philosophy from the University of Tübingen for his research with Herbert Keuth about approaches to intentionality and representation. He then joined Manfred Fahle at the University of Tübingen and Tomaso Poggio at MIT, and earned a PhD in biology for his thesis on "mathematical models and psychophysical experiments of perceptual learning".
From 1998 to 1999, he joined the laboratory of Christof Koch at California Institute of Technology as a postdoctoral fellow to investigating the characteristics of temporal processing and feature integration. In 1999, he went to work as a senior researcher with Manfred Fahle at the section of Human Neurobiology at the University of Bremen where he was project leader at the Center of Excellence 517 on "Neurocognition" that was funded by German Research Council (DFG). In 2003 he became a professor for neurobiopsychology at the Osnabrück University for one year.
In 2004, Herzog was appointed as professor for neuroscience at the Brain Mind Institute of the School of Life Sciences at EPFL and head of the Laboratory of Psychophysics. In 2015, he was promoted as Full Professor at EPFL.
Research
Herzog's laboratory investigates visual information processing in humans applying psychophysical methods, TMS, EEG, and mathematical modelling. Their research focuses on feature integration, contextual modulation, time course of information processing, and perceptual learning. They also perform clinical studies in schizophrenic patients and healthy older people to study visual information processing deficits.
Selected works
Herzog is also the author of a text book:
References
External links
Publication listed on ORCID
Website of the Laboratory of Psychophysics
1964 births
Living people
University of Tübingen alumni
Massachusetts Institute of Technology alumni
Academic staff of the École Polytechnique Fédérale de Lausanne
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https://en.wikipedia.org/wiki/Troy%20Garner
|
Troy Garner (born February 15, 1978) is a former American soccer player who played for the Raleigh Express in the A-League.
Career statistics
Club
Notes
References
1978 births
Living people
Duke University alumni
American men's soccer players
United States men's youth international soccer players
Men's association football forwards
California Jaguars players
North Carolina Fusion U23 players
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https://en.wikipedia.org/wiki/Standard%20Occupational%20Classification%20%28United%20Kingdom%29
|
The Standard Occupational Classification, often abbreviated as the SOC, is the system used by the United Kingdom's Office for National Statistics (ONS) to classify people for statistical purposes according to their job. Under this system, a job is defined as "a set of tasks or duties to be carried out by one person". The SOC classifies jobs according to the level and specialisation of skill. The SOC was introduced in 1990. It has undergone several revisions; the latest, SOC 2020, includes nine major groups of occupations, each broken down into smaller units: there are 26 sub-major groups, 104 minor groups and 412 unit groups. The groups are designed to be as similar as possible to the International Standard Classification of Occupations 2008.
Major groups
Managers, directors and senior officials
These are defined by the ONS as "occupations whose tasks consist of planning, directing and coordinating resources to achieve the efficient functioning of organisations and businesses". Most of these jobs require a large amount of experience and knowledge about the way businesses function.
The 2010 version of the SOC codes these occupations under Major Group 1. This is divided into Sub-Major Group 11 (corporate managers) and Sub-Major Group 12 (other managers and proprietors). The former includes chief executives, senior officials (including elected officials), production, functional and financial managers, as well as managers in transport, logistics, health and social services and retail and wholesale services; it also includes senior officials in protective services (including the armed forces and emergency services). Sub-Major Group 12 includes managers and proprietors in agriculture, hospitality and leisure, health and care, and other services.
There are often no specific qualifications required for roles and most jobs are filled through appointment or promotion based on experience, though some may require academic or professional qualifications (such as jobs in financial or engineering management); some appointments are made through management trainee schemes which will have minimum academic requirements. On-the-job training is provided for some roles and professional qualifications are available for many of them. In the armed forces and emergency services, appointment to senior posts may require a medical examination and there are age-based restrictions for promotion.
Professional occupations
Coded as Major Group 2 in the 2010 SOC, professional occupations are those "whose main tasks require a high level of knowledge and experience in the natural sciences, engineering, life sciences, social sciences, humanities and related fields." Most of the work involves applying a large amount of theoretical knowledge to practical tasks, conducting research to widen that knowledge, or disseminating that knowledge (for instance, by teaching).
Under the 2010 version, the ONS breaks this group down into science, research, and engineering professionals (sub-
|
https://en.wikipedia.org/wiki/Tsvetana%20Pironkova%20career%20statistics
|
This is a list of the main career statistics of professional Bulgarian tennis player Tsvetana Pironkova. She has won one WTA singles title, a Premier-level Sydney International in 2014, while at the ITF Women's Circuit, she has won six singles titles. During the years, she progressed more in singles and made more significant results, reaching semifinal of the 2010 Wimbledon and quarterfinals of the 2011 Wimbledon, 2016 French Open and 2020 US Open. On the WTA rankings, she has place of 31 as her career-high singles ranking, achieved in September 2010, while in doubles she has place of 141, reached in March 2009. As of March 2021, she earned more than $5m prize money.
Career achievements
Pironkova made her WTA Tour debut in 2005, but got first recognized at the 2006 Australian Open, when she made her first top-ten win, defeating Venus Williams in the first round. Then, at the 2008 Italian Open, she reached her first significant quarterfinal, where she also defeated world No. 3, Ana Ivanovic, in the second round. At 2010 Wimbledon, she defeated top 10 Venus Williams in order to reach her first Grand Slam semifinal. The following year, she reached quarterfinal of Wimbledon, but also defeated another top 10 player in that moment, Russian player Vera Zvonareva. At the end of season 2012, Pironkova qualified for her first year-end championships, an elite-level WTA Tournament of Championships (now known as WTA Elite Trophy) and reached semifinal, after defeating Zheng Saisai and losing to Nadia Petrova and Maria Kirilenko in the round-robin group. In the semifinal match, she lost to Caroline Wozniacki in the straight sets.
She had strong start of the season of 2014, reaching and winning her first WTA final at the Premier-level Sydney International. On her way to the trophy, she defeated three top-ten players, Sara Errani and Petra Kvitová and then in the final, Angelique Kerber. At the 2016 French Open, she had another strong Grand Slam performance, reaching her another quarterfinal, after defeating top-ten Agnieszka Radwańska in the previous round. After comeback of three-years absence, Pironkova had strong performance on her comeback tournament, 2020 US Open, where she reached another Grand Slam quarterfinal. There, in the second round, she defeated former world No. 1, Garbiñe Muguruza, but later she lost to Serena Williams in the quarterfinal match.
Performance timeline
Only main-draw results in WTA Tour, Grand Slam tournaments, Fed Cup/Billie Jean King Cup and Olympic Games are included in win–loss records.
Singles
Current through the 2021 BNP Paribas Open.
Doubles
WTA career finals
Singles: 1 (1 title)
ITF Circuit finals
Singles: 13 (6 titles, 7 runner–ups)
WTA Tour career earnings
Correct as of 15 November 2021
Career Grand Slam statistics
Best results details
Grand Slam winners are in boldface, and runner–ups are in italics.
Top-10 wins
Notes
References
Pironkova, Tsvetana
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https://en.wikipedia.org/wiki/Deryk%20Shockley
|
Deryk Shockley (born August 6, 1976) is a former American soccer player who played for the Richmond Kickers in the A-League.
Career statistics
Club
Notes
References
1976 births
Living people
Spartanburg Methodist College alumni
American men's soccer players
United States men's youth international soccer players
Men's association football midfielders
Baltimore Bays (1993–1998) players
Richmond Kickers players
Wilmington Hammerheads FC players
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https://en.wikipedia.org/wiki/Igor%20%C5%A0o%C5%A1o
|
Igor Šošo (born 27 August 1976) is a former Serbian footballer and futsal player who played for the Milwaukee Rampage in the A-League.
Career statistics
Club
Notes
References
1976 births
Living people
Serbian men's footballers
Serbian men's futsal players
Serbian expatriate men's footballers
Milwaukee Rampage players
A-League (1995–2004) players
Serbian expatriate sportspeople in the United States
Expatriate men's soccer players in the United States
Men's association football players not categorized by position
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https://en.wikipedia.org/wiki/Tetsushi%20Yamakawa
|
is a Japanese footballer currently playing as a centre back for Vissel Kobe.
Career statistics
Club
.
Notes
References
External links
1997 births
Living people
Sportspeople from Amagasaki
Association football people from Hyōgo Prefecture
University of Tsukuba alumni
Japanese men's footballers
Japan men's youth international footballers
Men's association football defenders
Vissel Kobe players
J1 League players
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https://en.wikipedia.org/wiki/Takuya%20Hitomi
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is a Japanese footballer currently playing as a forward for FC Ryukyu.
Career statistics
Club
.
Notes
References
External links
1997 births
Living people
Association football people from Tochigi Prefecture
Japanese men's footballers
Rissho University alumni
Men's association football forwards
FC Ryukyu players
J2 League players
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https://en.wikipedia.org/wiki/Jo%C3%A3o%20Victor%20%28footballer%2C%20born%202002%29
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João Victor da Silva Oliveira (born 6 April 2002), commonly known as João Victor, is a Brazilian footballer who currently plays as a left back for Athletico Paranaense.
Career statistics
Club
References
External links
Athletico Paranaense profile
2002 births
Living people
Footballers from Campinas
Brazilian men's footballers
Men's association football defenders
Campeonato Brasileiro Série A players
Club Athletico Paranaense players
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https://en.wikipedia.org/wiki/Overcategory
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In mathematics, specifically category theory, an overcategory (and undercategory) is a distinguished class of categories used in multiple contexts, such as with covering spaces (espace etale). They were introduced as a mechanism for keeping track of data surrounding a fixed object in some category . There is a dual notion of undercategory, which is defined similarly.
Definition
Let be a category and a fixed object of pg 59. The overcategory (also called a slice category) is an associated category whose objects are pairs where is a morphism in . Then, a morphism between objects is given by a morphism in the category such that the following diagram commutesThere is a dual notion called the undercategory (also called a coslice category) whose objects are pairs where is a morphism in . Then, morphisms in are given by morphisms in such that the following diagram commutesThese two notions have generalizations in 2-category theory and higher category theorypg 43, with definitions either analogous or essentially the same.
Properties
Many categorical properties of are inherited by the associated over and undercategories for an object . For example, if has finite products and coproducts, it is immediate the categories and have these properties since the product and coproduct can be constructed in , and through universal properties, there exists a unique morphism either to or from . In addition, this applies to limits and colimits as well.
Examples
Overcategories on a site
Recall that a site is a categorical generalization of a topological space first introduced by Grothendieck. One of the canonical examples comes directly from topology, where the category whose objects are open subsets of some topological space , and the morphisms are given by inclusion maps. Then, for a fixed open subset , the overcategory is canonically equivalent to the category for the induced topology on . This is because every object in is an open subset contained in .
Category of algebras as an undercategory
The category of commutative -algebras is equivalent to the undercategory for the category of commutative rings. This is because the structure of an -algebra on a commutative ring is directly encoded by a ring morphism . If we consider the opposite category, it is an overcategory of affine schemes, , or just .
Overcategories of spaces
Another common overcategory considered in the literature are overcategories of spaces, such as schemes, smooth manifolds, or topological spaces. These categories encode objects relative to a fixed object, such as the category of schemes over , . Fiber products in these categories can be considered intersections, given the objects are subobjects of the fixed object.
See also
Comma category
References
Category theory
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https://en.wikipedia.org/wiki/The%20Secrets%20of%20Triangles
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The Secrets of Triangles: A Mathematical Journey is a popular mathematics book on the geometry of triangles. It was written by Alfred S. Posamentier and , and published in 2012 by Prometheus Books.
Topics
The book consists of ten chapters, with the first six concentrating on triangle centers while the final four cover more diverse topics including the area of triangles, inequalities involving triangles, straightedge and compass constructions, and fractals.
Beyond the classical triangle centers (the circumcenter, incenter, orthocenter, and centroid) the book covers other centers including the Brocard points, Fermat point, Gergonne point, and other geometric objects associated with triangle centers such as the Euler line, Simson line, and nine-point circle.
The chapter on areas includes both trigonometric formulas and Heron's formula for computing the area of a triangle from its side lengths, and the chapter on inequalities includes the Erdős–Mordell inequality on sums of distances from the sides of a triangle and Weitzenböck's inequality relating the area of a triangle to that of squares on its sides.
Under constructions, the book considers 95 different triples of elements from which a triangle's shape may be determined (taken from its side lengths, angles, medians, heights, or angle bisectors) and describes how to find a triangle with each combination for which this is possible. Triangle-related fractals in the final chapter include the Sierpiński triangle and Koch snowflake.
Audience and reception
Reviewer Alasdair McAndrew criticizes the book as being too "breathless" in its praise of the geometry it discusses and too superficial to be of interest to professional mathematicians, and Patricia Baggett writes that it little of its content would be of use in high school mathematics education. However, Baggett suggests that it may be usable as a reference work, and similarly Robert Dawson suggests using its chapter on inequalities in this way. The book is written at a level suitable for high school students and interested amateurs, and McAndrew recommends the book to them.
Both Baggett and Gerry Leversha find the chapter on fractals (written by Robert A. Chaffer) to be the weakest part of the book, and Joop van der Vaart calls this chapter interesting but not a good fit for the rest of the book. Leversha calls the chapter on area "a bit of a mish-mash". Otherwise, Baggett evaluates the book as "well written and well illustrated", although lacking a glossary. Robert Dawson calls the book "very readable", and recommends it to any mathematics library.
See also
Encyclopedia of Triangle Centers
99 Points of Intersection
References
Popular mathematics books
Triangle geometry
2012 non-fiction books
Prometheus Books books
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https://en.wikipedia.org/wiki/Carleson%20%28disambiguation%29
|
Carleson may refer to:
Mathematics
Carleson measure, a mathematical method applied to dimensional space
Carleson's inequality, a generalisation of Carleman's inequality
Carleson–Jacobs theorem, a function applied to the unit of a circle
People
Carleson, a Swedish surname
See also
Charleson
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https://en.wikipedia.org/wiki/National%20Organization%20for%20Civil%20Registration%20of%20Iran
|
National Organization for Civil Registration of Iran is one of the governmental organizations in Iran that is responsible for collecting information and population statistics of Iran. This organization with independent duties and functions is one of the subordinate institutions of the Ministry of Interior of Iran. The organization is responsible for providing basic registration information such as births, deaths and marriages, as well as issuing identity documents such as birth certificates and Identity certificate. The current head of the organization is Hashem Kargar. In Iran, the third day of Dey (month) (23 or 24 December) has been named as National Organization for Civil Registration Day.
It was successfuly hacked September 2023 vital records of l entire population stolen.
History
In the past, birth and marriage registration in Iran was traditionally done mostly by referring to clerics, neighborhood elders, or tribal elders. Gradually registration in the current European bye method became popular in Iran. According to the decision of the Cabinet of Ministers on 12 December 1918, the regulations for the establishment of the Civil Registry Office in the Ministry of Interior were prepared and the first Iranian Identity Booklet (Shenasnameh) for a girl named Fatemeh Irani was issued on 25 December (3 Dey (month) SH) of the same year. Because of that in many years later, the third day of Dey (month) (23 or 24 December) has been named as National Organization for Civil Registration Day. From March 1925, according to the law, obtaining identity booklet was required for all Iranian citizens in the areas where the Civil Registry Office was established. The General Office of Census and Civil Registration, in accordance with the decree of 10 June 1928, began its work with independent duties and as an institution affiliated to the Ministry of Interior. With the revision of the duties and regulations related to this institution, its name was changed to the General Directorate of Statistics and Civil Registration in 1940. The last time in 1976, with the definition of new duties and structure, this agency was renamed to its current name, the National Organization for Civil Registration. After the Iranian Revolution in 1979, some of the duties and bylaws of this organization were reviewed by the Islamic Consultative Assembly in 1984.
Structure
The National Organization for Civil Registration of Iran has a headquarter and thirty-one general offices in thirty-one provinces of Iran. The administrative structure of each general administration is almost similar to the structure of the headquarter. The headquarter area has three deputies and six general administrations. The head of the National Organization for Civil Registration of Iran is considered as one of the Deputy Ministers of Interior.
National population database
Created in 1997 National population database keeps national identity code and postal address code.
The Main Duties
The National Organiz
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https://en.wikipedia.org/wiki/1962%E2%80%9363%20Rochdale%20A.F.C.%20season
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The 1962–63 season saw Rochdale compete for their 4th season in the Football League Fourth Division.
Statistics
|}
Final League Table
Competitions
Football League Fourth Division
Final League Table
F.A. Cup
League Cup
Lancashire Cup
Rose Bowl
References
Rochdale A.F.C. seasons
Rochdale
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https://en.wikipedia.org/wiki/Lila%20Elveback
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Lillian Rose (Lila) Elveback (December 5, 1915 – April 30, 2004) was an American biostatistician, a professor of biostatistics at the Mayo Clinic Graduate School of Biomedical Sciences, a textbook author, a Fellow of the American Statistical Association, and a founder of the American College of Epidemiology.
Life
Elveback was born on December 5, 1915 in Sidney, Montana. She graduated from the University of Minnesota in 1941, earned a master's degree at Columbia University in 1948, and returned to the University of Minnesota for a doctorate, which she completed in 1955. Her dissertation was Some Aspects of Estimation Problems in Follow-Up Studies in Chronic Disease, and was supervised by Joseph Berkson.
She became a professor of biostatistics at Tulane University before moving in 1961 to the Public Health Research Institute in New York, where she became head of statistics in the division of epidemiology. She worked at the Mayo Clinic from 1965 until her retirement in 1980, and was one of the founding directors of the American College of Epidemiology at its incorporation in 1979.
She died on April 30, 2004, in Rochester, Minnesota.
Textbook
Elveback was the coauthor, with John P. Fox and Carrie E. Hall, of a textbook on epidemiology, Epidemiology: Man and Disease (Macmillan, 1970).
Recognition
In 1970, Elveback was elected as a Fellow of the American Statistical Association "for her outstanding role in advancing the statistical quality of research at the Mayo Clinic by consulting and teaching, and for significant publications in medical statistics".
References
1915 births
2004 deaths
People from Sidney, Montana
American statisticians
Women statisticians
University of Minnesota alumni
Columbia University alumni
Tulane University faculty
Mayo Clinic people
Biostatisticians
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https://en.wikipedia.org/wiki/N%C3%BCzhet%20G%C3%B6kdo%C4%9Fan
|
Hatice Nüzhet Gökdoğan (; 14 August 1910 – 24 April 2003) was a Turkish astronomer, mathematician and academic. After studying mathematics and astronomy in France as a young adult, Gökdoğan joined the faculty of Istanbul University in 1934 and completed her PhD. She was elected Dean of the university's Faculty of Science in 1954, becoming the first Turkish woman to serve as a university dean, and she was later made Chair of the astronomy department, significantly expanding her department's capacity and working to improve national and international collaboration between astronomers.
Gökdoğan co-founded the Turkish Mathematical Society, the Turkish Astronomy Association and the Turkish University Women's Association. She was Turkey's first national representative at the International Astronomical Union (IAU), and has been credited as Turkey's first female astronomer.
Early life and education
Nüzhet Gökdoğan was born on 14 August 1910 in Istanbul (then Constantinople). Her mother was named Nebihe Hanım, while her father was Mehmet Zihni Toydemir, a major general.
In her late teens, Gökdoğan received a scholarship to study in France; she enrolled in the University of Lyon and in 1932 she completed her undergraduate degree in mathematics. She had a strong interest in astronomy and subsequently studied physics at the University of Paris, where she received a Diplome d'Etudes Superieures. She then completed an internship at the Paris Observatory.
Career
Returning to Turkey in 1934, Gökdoğan applied to work at the Kandilli Observatory, but was turned down because the director did not want a woman working there. She instead joined Istanbul University as a faculty member in the Astronomy Department. She was the first woman member of the school's faculty of science. She completed her PhD three years later, submitting a dissertation entitled Contribution aux recherches sur l'existence d'une matière obscure interstellaire homogène autour du soleil (Contribution to research on the existence of homogeneous interstellar dark matter around the sun). Gökdoğan's dissertation was recorded as the first doctoral thesis completed at Istanbul University's faculty of science.
In 1948, Gökdoğan was made full professor at the university, and also co-founded the Turkish Mathematical Society. She served as president of the Turkish Union of Soroptimists in the early 1950s. Upon being elected Dean of Istanbul University's science faculty in 1954, Gökdoğan became the first Turkish woman to serve as a university dean. She was a founding member of the Turkish Astronomy Association that same year, and she served as president of the association for the next two decades. In 1958, she was appointed Chair of the Astronomy Department at Istanbul University, and she held the role for the rest of her time as a faculty member. Gökdoğan worked hard to expand her department, gradually increasing the number of staff from 5 to 18, and she developed a number of new collaborative program
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https://en.wikipedia.org/wiki/John%20A.%20Thorpe
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John Alden Thorpe (born February 29, 1936 in Lewiston, Maine - died January 18, 2021) was an American mathematician, known for contributions to the field of differential geometry.
Thorpe obtained his Bachelor's degree in 1958 from the Massachusetts Institute of Technology. His Ph.D. was done at Columbia University, under the direction of James Eells (Higher Order Sectional Curvature). From 1963 to 1965, he was Moore Instructor at MIT and Assistant Professor at Haverford College in 1965. In 1967 and 1968 he was a visitor at the Institute for Advanced Study. From 1968, he was Associate Professor and then Professor at the State University of New York at Stony Brook (SUNY). From 1987 he was Professor and Dean at the State University of New York in Buffalo, and from 1993 at Queens College of City University of New York, where he also served as Provost. From 1984 to 1987 he served on the Board of Governors of the Mathematical Association of America. From 1998 to 2001 he was Executive Director of the National Council of Teachers of Mathematics.
He and Nigel Hitchin independently found an inequality between topological invariants, which provides a necessary condition for the existence of Einstein metrics on four-dimensional smooth compact manifolds. It is now known as the Hitchin-Thorpe inequality.
Books
Elementary Topics in Differential Geometry, Springer Verlag, Undergraduate Texts in Mathematics, 1979
Lecture Notes on Elementary Topology and Geometry (with I.M. Singer), Springer Verlag, Undergraduate Texts in Mathematics, 1967
References
1936 births
Living people
People from Lewiston, Maine
20th-century American mathematicians
Massachusetts Institute of Technology alumni
Columbia University College of Pharmacy alumni
University at Buffalo faculty
Stony Brook University faculty
Queens College, City University of New York faculty
21st-century American mathematicians
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https://en.wikipedia.org/wiki/Kenmotsu%20manifold
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In the mathematical field of differential geometry, a Kenmotsu manifold is an almost-contact manifold endowed with a certain kind of Riemannian metric. They are named after the Japanese mathematician Katsuei Kenmotsu.
Definitions
Let be an almost-contact manifold. One says that a Riemannian metric on is adapted to the almost-contact structure if:
That is to say that, relative to the vector has length one and is orthogonal to furthermore the restriction of to is a Hermitian metric relative to the almost-complex structure One says that is an almost-contact metric manifold.
An almost-contact metric manifold is said to be a Kenmotsu manifold if
References
Sources
Differential geometry
Riemannian geometry
Riemannian manifolds
Smooth manifolds
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https://en.wikipedia.org/wiki/Almost-contact%20manifold
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In the mathematical field of differential geometry, an almost-contact structure is a certain kind of geometric structure on a smooth manifold. Such structures were introduced by Shigeo Sasaki in 1960.
Precisely, given a smooth manifold an almost-contact structure consists of a hyperplane distribution an almost-complex structure on and a vector field which is transverse to That is, for each point of one selects a codimension-one linear subspace of the tangent space a linear map such that and an element of which is not contained in
Given such data, one can define, for each in a linear map and a linear map by
This defines a one-form and (1,1)-tensor field on and one can check directly, by decomposing relative to the direct sum decomposition that
for any in Conversely, one may define an almost-contact structure as a triple which satisfies the two conditions
for any
Then one can define to be the kernel of the linear map and one can check that the restriction of to is valued in thereby defining
References
David E. Blair. Riemannian geometry of contact and symplectic manifolds. Second edition. Progress in Mathematics, 203. Birkhäuser Boston, Ltd., Boston, MA, 2010. xvi+343 pp. ,
Differential geometry
Smooth manifolds
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https://en.wikipedia.org/wiki/Simons%27%20formula
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In the mathematical field of differential geometry, the Simons formula (also known as the Simons identity, and in some variants as the Simons inequality) is a fundamental equation in the study of minimal submanifolds. It was discovered by James Simons in 1968. It can be viewed as a formula for the Laplacian of the second fundamental form of a Riemannian submanifold. It is often quoted and used in the less precise form of a formula or inequality for the Laplacian of the length of the second fundamental form.
In the case of a hypersurface of Euclidean space, the formula asserts that
where, relative to a local choice of unit normal vector field, is the second fundamental form, is the mean curvature, and is the symmetric 2-tensor on given by .
This has the consequence that
where is the shape operator. In this setting, the derivation is particularly simple:
the only tools involved are the Codazzi equation (equalities #2 and 4), the Gauss equation (equality #4), and the commutation identity for covariant differentiation (equality #3). The more general case of a hypersurface in a Riemannian manifold requires additional terms to do with the Riemann curvature tensor. In the even more general setting of arbitrary codimension, the formula involves a complicated polynomial in the second fundamental form.
References
Footnotes
Books
Articles
Differential geometry of surfaces
Riemannian manifolds
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https://en.wikipedia.org/wiki/Full%20Count%20Baseball
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Full Count Baseball is a 1984 video game published by Lance Haffner Games.
Gameplay
Full Count Baseball is a game in which players may run statistics-based baseball games as a simulations, or create teams for league play.
Reception
Lew Fisher and Eric Faust reviewed the game for Computer Gaming World, and stated that "FC is first rate, by far the best game in Haffner's line of sports games."
David M. Wilson and Johnny L. Wilson reviewed the game for Computer Gaming World, and stated that "this text-heavy statistics-based baseball simulation offers extremely accurate replays."
Duane E. Widner reviewed the game for Computer Gaming World, and stated that "One nice feature is the ability to input your own players and teams. This capability, combined with one's own baseball encyclopedia, allows a player to program virtually anyone that has ever picked up a bat (including his minor league seasons)."
References
External links
Review in Compute!
Review in Supercommodore 64/128
Review in Compute!'s Gazette
1984 video games
Apple II games
Baseball video games
Commodore 64 games
Simulation video games
Video games developed in the United States
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https://en.wikipedia.org/wiki/C.%20Robin%20Graham
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Charles Robin Graham is professor emeritus of mathematics at the University of Washington, known for a number of contributions to the field of conformal geometry and CR geometry; his collaboration with Charles Fefferman on the ambient construction has been particularly widely cited. The GJMS operators are, in part, named for him. He is a 2012 Fellow of the American Mathematical Society. Graham received his Ph.D. from Princeton University in 1981, under the direction of Elias Stein.
Major publications
Fefferman, Charles; Graham, C. Robin. Conformal invariants. The mathematical heritage of Élie Cartan (Lyon, 1984). Astérisque 1985, Numéro Hors Série, 95–116.
Graham, C. Robin; Jenne, Ralph; Mason, Lionel J.; Sparling, George A.J. Conformally invariant powers of the Laplacian. I. Existence. J. London Math. Soc. (2) 46 (1992), no. 3, 557–565.
Fefferman, Charles; Graham, C. Robin. The Ambient Metric. Annals of Mathematics Studies 178, Princeton University Press, 2012.
References
Year of birth missing (living people)
Living people
20th-century American mathematicians
21st-century American mathematicians
Princeton University alumni
University of Washington faculty
Fellows of the American Mathematical Society
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https://en.wikipedia.org/wiki/F.%20Reese%20Harvey
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Frank Reese Harvey is Professor Emeritus of mathematics at Rice University, known for contributions to the field of differential geometry. He obtained his Ph.D. from Stanford University in 1966, under the direction of Hikosaburo Komatsu. Over half of his work has been done in collaboration with Blaine Lawson. Their 1982 introduction of calibrated geometry, in particular, is among the most widely cited papers in differential geometry. It is instrumental in the formulation of the SYZ conjecture.
In 1983 he was an invited speaker at the International Congress of Mathematicians in Warsaw.
Major publications
References
Living people
Rice University faculty
20th-century American mathematicians
Year of birth missing (living people)
Stanford University alumni
21st-century American mathematicians
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https://en.wikipedia.org/wiki/Lenn%20Jastremski
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Lenn Jastremski (born 24 January 2001) is a German professional footballer who plays as a centre-forward or right winger for 3. Liga club SSV Ulm, on loan from Bayern Munich II.
Career statistics
References
Living people
2001 births
People from Salzgitter
German men's footballers
Footballers from Lower Saxony
Men's association football forwards
Men's association football wingers
Germany men's youth international footballers
Regionalliga players
3. Liga players
2. Liga (Austria) players
VfL Wolfsburg II players
FC Bayern Munich II players
FC Viktoria Köln players
FC Erzgebirge Aue players
Grazer AK players
German expatriate men's footballers
German expatriate sportspeople in Austria
Expatriate men's footballers in Austria
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https://en.wikipedia.org/wiki/Kenta%20Watanabe
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is a Japanese footballer currently playing as a goalkeeper for Azul Claro Numazu.
Career statistics
Club
.
Notes
References
External links
1998 births
Living people
Sportspeople from Wakayama (city)
Association football people from Wakayama Prefecture
Japanese men's footballers
Men's association football goalkeepers
J2 League players
J3 League players
Gamba Osaka players
FC Machida Zelvia players
Fukushima United FC players
Kamatamare Sanuki players
Azul Claro Numazu players
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https://en.wikipedia.org/wiki/Marko%20Nikoli%C4%87%20%28footballer%2C%20born%201998%29
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Marko Nikolić (born 16 June 1998) is a Serbian professional footballer who plays for Aksu in Kazakhstan Premier League.
Career statistics
.
References
1998 births
Footballers from Belgrade
Living people
Serbian men's footballers
Men's association football defenders
FK Zemun players
FK Inđija players
FC Arsenal Kyiv players
FK Rad players
Budafoki MTE footballers
Debreceni VSC players
FK Riteriai players
Serbian First League players
Ukrainian Premier League players
Serbian SuperLiga players
Nemzeti Bajnokság I players
A Lyga players
Serbian expatriate men's footballers
Expatriate men's footballers in Ukraine
Serbian expatriate sportspeople in Ukraine
Expatriate men's footballers in Hungary
Serbian expatriate sportspeople in Hungary
Expatriate men's footballers in Lithuania
Serbian expatriate sportspeople in Lithuania
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https://en.wikipedia.org/wiki/M%C3%A1t%C3%A9%20Fekete
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Máté Fekete (born 22 August 1995) is a Hungarian football forward who plays for Budafok.
Career statistics
References
External links
1995 births
Footballers from Budapest
Living people
Hungarian men's footballers
Men's association football midfielders
Budafoki MTE footballers
Erzsébeti Spartacus MTK LE footballers
Nemzeti Bajnokság I players
Nemzeti Bajnokság II players
Nemzeti Bajnokság III players
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https://en.wikipedia.org/wiki/Bhupati%20Mohan%20Sen
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Bhupati Mohan Sen () was an Indian physicist and mathematician. He made remarkable contributions in the fields of Quantum Mechanics and Fluid Mechanics. He taught at the Mathematics Department of Presidency College and Applied Mathematics Department of University of Calcutta. He was also a member of the Governing Body of Bose Institute. In 1974, he was awarded Padma Bhushan by Government of India.
Birth and family
Bhupathi Mohan Sen was born on 1 March 1888 in Rajshahi (now in Bangladesh). His father Raj Mohan Sen was Professor of Mathematics and Vice-Principal of Rajshahi Government College. His mother, Nishi Tara Devi, was a very devoted and pious lady.
He married Santa Sircar, daughter of Sir Nilratan Sircar, with whom he had one daughter and two sons - Monishi Mohan Sen and Subrata Kumar Sen.
Educational life
Bhupathi Mohan Sen had his early education in Rajshahi Collegiate School and Rajshahi College. After completing school education he took admission in Presidency College and passed his B.Sc. Examination in 1908, with triple Honours, first class in Mathematics, second class in Physics and second class in Chemistry. In 1910 he obtained the M.Sc. degree from Calcutta University occupying first position in the first class in Applied Mathematics. After completing his M.Sc. degree he went to Cambridge as a foundation scholar of King's College for the period 1911–1915. In 1912 he took up his M.A. degree of Cambridge University obtaining the distinction of being a Senior Wrangler with the mark of distinction in special subjects. In 1914 he won Smith's prize from Cambridge University for his very great academic distinction. He was the first Indian to win this prize.
Working life
After returning India In 1915, he entered into Indian Educational Service. He was Professor of Mathematics of Dacca Government College from 1915 to 1921 and was Professor of Mathematics of Dacca University from 1921 to 1923. In 1923 he returned Calcutta and joined Presidency College (Presidency University) as Professor of Mathematics and held this position from 1923 to 1930. In 1931 he officiated as Principal of Presidency College and was confirmed in the post in 1934. In 1934 he became principal of the Presidency College and held the post for the period 1934-42 and retired from Government Service in 1943. After retirement, he was appointed Part-time Professor of Pure Mathematics, Presidency College, Calcutta University and held the same post till 1954 when he retired from University Service.
Research Area
Sen's research work was concentrated in the following subjects:
Differential Geometry
Hydrodynamics
Modern Physics
He published a seminal paper in Nature in 1933. His paper titled Tidal Oscillation on a Spheroid was published in the Bulletin of Calcutta Mathematical Society. He was authored two books titled A New Classical Theory of the Photon and the Electron and Light and Matter: A New Classical Theory of Light and Matter based on the Maxwell Equations an
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https://en.wikipedia.org/wiki/Ruriko%20Yoshida
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Ruriko (Rudy) Yoshida is a Japanese-American mathematician and statistician whose research topics have ranged from abstract mathematical problems in algebraic combinatorics to optimized camera placement in sensor networks and the phylogenomics of fungi. She works at the Naval Postgraduate School in Monterey, California as a professor of operations research. She was promoted as a rank of professor on July 1st 2023.
Early life and education
Yoshida grew up in Japan. Despite a love of mathematics that began in middle school, she was discouraged from studying mathematics by her teachers, and in response dropped out of her Japanese high school and took the high school equivalency examination instead. In order to continue her study of mathematics, she moved to the US, and after studying at a junior college, transferred to the University of California, Berkeley. Her parents, who had been supporting her financially, stopped their support when they learned that she was studying mathematics instead of business, and she put herself through school working both as a grader in the mathematics department and in the university's police department. She graduated with a bachelor's degree in mathematics in 2000.
She went to the University of California, Davis for graduate study, under the supervision of Jesús A. De Loera. De Loera had been a student of Berkeley professor Bernd Sturmfels, and Yoshida also considers Sturmfels to be an academic mentor. Part of her work there involved implementing a method of Alexander Barvinok for counting integer points in convex polyhedra by decomposing the input into cones, and her 2004 dissertation was Barvinok's Rational Functions: Algorithms and Applications to Optimization, Statistics, and Algebra.
Career
After completing her doctorate, Yoshida returned to the University of California, Berkeley as a postdoctoral researcher, working with Lior Pachter in the Center for Pure and Applied Mathematics, and then went to Duke University for more postdoctoral research as an assistant research professor of mathematics, working with Mark L. Huber. She became an assistant professor of statistics at the University of Kentucky in 2006, and was promoted to a tenured associate professor in 2012. In 2016 she moved to her present position at the Naval Postgraduate School, moving there in part to be closer to her husband's family in Northern California. She has also returned to Japan as a visitor to the Institute of Statistical Mathematics. She is also known as a superb teacher of mathematics and statistics as is testified by the provost's announcement and the list of her students .
References
External links
Home page
Year of birth missing (living people)
Living people
Japanese emigrants to the United States
21st-century American mathematicians
American women mathematicians
American women statisticians
Japanese mathematicians
Japanese women mathematicians
Japanese statisticians
Operations researchers
University of California, Berkeley alu
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https://en.wikipedia.org/wiki/Basis%20of%20a%20matroid
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In mathematics, a basis of a matroid is a maximal independent set of the matroid—that is, an independent set that is not contained in any other independent set.
Examples
As an example, consider the matroid over the ground-set R2 (the vectors in the two-dimensional Euclidean plane), with the following independent sets: It has two bases, which are the sets {(0,1),(2,0)} , {(0,3),(2,0)}. These are the only independent sets that are maximal under inclusion.
The basis has a specialized name in several specialized kinds of matroids:
In a graphic matroid, where the independent sets are the forests, the bases are called the spanning forests of the graph.
In a transversal matroid, where the independent sets are endpoints of matchings in a given bipartite graph, the bases are called transversals.
In a linear matroid, where the independent sets are the linearly-independent sets of vectors in a given vector-space, the bases are just called bases of the vector space. Hence, the concept of basis of a matroid generalizes the concept of basis from linear algebra.
In a uniform matroid, where the independent sets are all sets with cardinality at most k (for some integer k), the bases are all sets with cardinality exactly k.
In a partition matroid, where elements are partitioned into categories and the independent sets are all sets containing at most kc elements from each category c, the bases are all sets which contain exactly kc elements from category c.
In a free matroid, where all subsets of the ground-set E are independent, the unique basis is E.
Properties
Exchange
All matroids satisfy the following properties, for any two distinct bases and :
Basis-exchange property: if , then there exists an element such that is a basis.
Symmetric basis-exchange property: if , then there exists an element such that both and are bases. Brualdi showed that it is in fact equivalent to the basis-exchange property.
Multiple symmetric basis-exchange property: if , then there exists a subset such that both and are bases. Brylawski, Greene, and Woodall, showed (independently) that it is in fact equivalent to the basis-exchange property.
Bijective basis-exchange property: There is a bijection from to , such that for every , is a basis. Brualdi showed that it is equivalent to the basis-exchange property.
Partition basis-exchange property: For each partition of into m parts, there exists a partition of into m parts, such that for every , is a basis.
However, a basis-exchange property that is both symmetric and bijective is not satisfied by all matroids: it is satisfied only by base-orderable matroids.
In general, in the symmetric basis-exchange property, the element need not be unique. Regular matroids have the unique exchange property, meaning that for some , the corresponding b is unique.
Cardinality
It follows from the basis exchange property that no member of can be a proper subset of another.
Moreover, all bases of a given
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https://en.wikipedia.org/wiki/Base-orderable%20matroid
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In mathematics, a base-orderable matroid is a matroid that has the following additional property, related to the bases of the matroid. For any two bases and there exists a feasible exchange bijection, defined as a bijection from to , such that for every , both and are bases.The property was introduced by Brualdi and Scrimger. A strongly-base-orderable matroid has the following stronger property:For any two bases and , there is a strong feasible exchange bijection, defined as a bijection from to , such that for every , both and are bases.
The property in context
Base-orderability imposes two requirements on the function :
It should be a bijection;
For every , both and should be bases.
Each of these properties alone is easy to satisfy:
All bases of a given matroid have the same cardinality, so there are n! bijections between them (where n is the common size of the bases). But it is not guaranteed that one of these bijections satisfies property 2.
All bases and of a matroid satisfy the symmetric basis exchange property, which is that for every , there exists some , such that both and are bases. However, it is not guaranteed that the resulting function f be a bijection - it is possible that several are matched to the same .
Matroids that are base-orderable
Every partition matroid is strongly base-orderable. Recall that a partition matroid is defined by a finite collection of categories, where each category has a capacity denoted by an integer with . A basis of this matroid is a set which contains exactly elements of each category . For any two bases and , every bijection mapping the elements of to the elements of is a strong feasible exchange bijection.
Every transversal matroid is strongly base-orderable.
Matroids that are not base-orderable
Some matroids are not base-orderable. A notable example is the graphic matroid on the graph K4, i.e., the matroid whose bases are the spanning trees of the clique on 4 vertices. Denote the vertices of K4 by 1,2,3,4, and its edges by 12,13,14,23,24,34. Note that the bases are:
{12,13,14}, {12,13,24}, {12,13,34}; {12,14,23}, {12,14,34}; {12,23,24}, {12,23,34}; {12,24,34};
{13,14,23}, {13,14,24}; {13,23,24}, {13,23,34}; {13,24,34};
{14,23,24}, {14,23,34}; {14,24,34}.
Consider the two bases A = {12,23,34} and B = {13,14,24}, and suppose that there is a function f satisfying the exchange property (property 2 above). Then:
f(12) must equal 14: it cannot be 24, since A \ {12} + {24} = {23,24,34} which is not a basis; it cannot be 13, since B \ {13} + {12} = {12,14,24} which is not a basis.
f(34) must equal 14: it cannot be 24, since B \ {24} + {34} = {13,14,34} which is not a basis; it cannot be 13, since A \ {34} + {13} = {12,13,23} which is not a basis.
Then f is not a bijection - it maps two elements of A to the same element of B.
There are matroids that are base-orderable but not strongly-base-orderable.
Properties
In base-orderable matroids, a fea
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https://en.wikipedia.org/wiki/1963%E2%80%9364%20Rochdale%20A.F.C.%20season
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The 1963–64 season saw Rochdale compete for their 5th consecutive season in the Football League Fourth Division.
Statistics
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Final League Table
Competitions
Football League Fourth Division
F.A. Cup
League Cup
Lancashire Cup
Rose Bowl
References
Rochdale A.F.C. seasons
Rochdale
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https://en.wikipedia.org/wiki/Daniel%20Afedzi%20Akyeampong
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Daniel Afedzi Akyeampong (24 November 1938 – 7 March 2015) was a Ghanaian academic. He was the first Ghanaian to attain full professorship status in mathematics at the University of Ghana, Legon. In 1966, Daniel Akyeampong and Francis Allotey became the first Ghanaians to obtain a doctorate in mathematical sciences. He was the Pro-Vice Chancellor of the University of Ghana from 1983 to 1985.
Early life and education
Akyeampong was born on 24 November 1938 at Senya Beraku in the Gold Coast colony (now Ghana). He was the youngest child of his father, Peter Napoleon Akyeampong, and his mother, Charity Afful. He was a pupil at the Senya Beraku Local Council School in 1945 when he was six years old and completed in 1953. In 1954, he entered Mfantsipim School, Cape Coast for his secondary education and was a member of Balmer-Acquah House. Upon matriculating at Mfantsipim, his intellect became apparent after only a few weeks - he skipped his first year entirely and was quickly promoted to the second year. Akyeampong received prizes in Mathematics and Physical Sciences upon his graduation in 1959. The following year, he gained admission to study at the University of Ghana, where he was a resident of the all-male Commonwealth Hall. He graduated in 1963 with a Bachelor of Science degree in Mathematics. After his undergraduate studies, Akyeampong proceeded to the United Kingdom and enrolled at the University of London for his postgraduate research. He was admitted to Imperial College London in 1963 to complete the foundational diploma course in Mathematical Physics prior to his doctoral work. He later recalled the unexpected turns in his academic journey: "Professor Abdus Salam taught the class in group theory. His lectures were very popular and one had to go early to find a seat. Following my successful completion of the coursework in the summer of 1964, he invited me to his office one day, and told me about a new international centre for theoretical physics to be established in Trieste, Italy, which he was going to direct in the autumn of the same year, and the reason why he expected me to join him there. That was how in October 1964, Jimmy Boyce, Ray Rivers and myself became the first postgraduate students of Salam in Trieste, and so had the honour of joining the post doctoral colleagues Bob Delbourgo and John Strathdee to become members of the group that was christened by Ms. Jean Bouckley and Ms Miriam Lewis as "the Salam Boys"."In 1965, Akyeampong became one of the first Fellows of the International Centre for Theoretical Physics, Trieste. About the vibrant scholarly culture at the Trieste institution, Akyeampong recounted:"Salam worked hard to get the Centre known world-wide and we were naturally infected by his ceaseless dedication. We had our lunches together at the Mensa dei Ferrovieri with him at the table head, John and Ray at one side of the table and Bob and Jimmy on the other, with me deciding when to sit next to Ray or to Jimmy. These bec
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https://en.wikipedia.org/wiki/Don%20Watson%20%28English%20footballer%29
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Don Watson (27 August 1932 – June 2018) was an English professional footballer who played for several clubs in the north of England.
Career statistics
References
1932 births
2018 deaths
English men's footballers
Men's association football forwards
Rochdale A.F.C. players
Sheffield Wednesday F.C. players
Lincoln City F.C. players
Bury F.C. players
Barnsley F.C. players
Barrow A.F.C. players
Buxton F.C. players
Worsbrough Bridge Athletic F.C. players
Footballers from Barnsley
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https://en.wikipedia.org/wiki/Right%20group
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In mathematics, a right group is an algebraic structure consisting of a set together with a binary operation that combines two elements into a third element while obeying the right group axioms. The right group axioms are similar to the group axioms, but while groups can have only one identity and any element can have only one inverse, right groups allow for multiple identity elements and multiple inverse elements.
It can be proven (theorem 1.27 in ) that a right group is isomorphic to the direct product of a right zero semigroup and a group, while a right abelian group is the direct product of a right zero semigroup and an abelian group. Left group and left abelian group are defined in analogous way, by substituting right for left in the definitions. The rest of this article will be mostly concerned about right groups, but everything applies to left groups by doing the appropriate right/left substitutions.
Definition
A right group, originally called multiple group, is a set with a binary operation ⋅, satisfying the following axioms:
Closure
For all and in , there is an element c in such that .
Associativity
For all in , .
Left identity element
There is at least one left identity in . That is, there exists an element such that for all in . Such an element does not need to be unique.
Right inverse elements
For every in and every identity element , also in , there is at least one element in , such that . Such element is said to be the right inverse of with respect to .
Examples
Direct product of finite sets
The following example is provided by. Take the group , the right zero semigroup and construct a right group as the direct product of and .
is simply the cyclic group of order 3, with as its identity, and and as the inverses of each other.
is the right zero semigroup of order 2. Notice the each element repeats along its column, since by definition , for any and in .
The direct product of these two structures is defined as follows:
The elements of are ordered pairs such that is in and is in .
The operation is defined element-wise:
Formula 1:
The elements of will look like and so on. For brevity, let's rename these as , and so on. The Cayley table of is as follows:
Here are some facts about :
has two left identities: and . Some examples:
Each element has two right inverses. For example, the right inverses of with regards to and are and , respectively.
Complex numbers in polar coordinates
Clifford gives a second example involving complex numbers. Given two non-zero complex numbers a and b, the following operation forms a right group:
All complex numbers with modulus equal to 1 are left identities, and all complex numbers will have a right inverse with respect to any left identity.
The inner structure of this right group becomes clear when we use polar coordinates: let and , where A and B are the magnitudes and and are the arguments (angles) of a and b, respectively. (this is
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https://en.wikipedia.org/wiki/Knockoffs%20%28statistics%29
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In statistics, the knockoff filter, or simply knockoffs, is a framework for variable selection. It was originally introduced for linear regression by Rina Barber and Emmanuel Candès, and later generalized to other regression models in the random design setting. Knockoffs has found application in many practical areas, notably in genome-wide association studies.
Fixed-X knockoffs
Consider a linear regression model with response vector and feature matrix , which is treated as deterministic. A matrix is said to be knockoffs of if it does not depend on and satisfies for . Barber and Candès showed that, equipped with a suitable feature importance statistic, fixed-X knockoffs can be used for variable selection while controlling the false discovery rate (FDR).
Model-X knockoffs
Consider a general regression model with response vector and random feature matrix . A matrix is said to be knockoffs of if it is conditionally independent of given and satisfies a subtle pairwise exchangeable condition: for any , the joint distribution of the random matrix does not change if its th and th columns are swapped, where is the number of features. While it is less clear how to create model-X knockoffs compared to their fixed-X counterpart, various algorithms have been proposed to construct knockoffs. Once constructed, model-X knockoffs can be used for variable selection following the same procedure as fixed-X knockoffs and control the FDR.
Properties
The knockoffs can be understood as negative controls. Informally speaking, knockoffs has the property that no method can statistically distinguish the original matrix from its knockoffs without looking at . Mathematically, the exchangeability conditions translate to symmetry that allows for an estimation of the type I error (e.g., if one wishes to choose the FDR as the type I error rate, the false discovery proportion is estimated), which then leads to exact type I error control.
Model-X knockoffs provides valid type I error control regardless of the unknown conditional distribution of given , and it can work with black-box variable importance statistics, including the ones derived from complicated machine learning methods. A most significant challenge of implementing model-X knockoffs is that it requires nontrivial knowledge on the distribution of , which is usually high-dimensional. This knowledge can be gained with the help of unlabeled data.
References
External links
Official website
Regression analysis
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https://en.wikipedia.org/wiki/Santiago%20Mu%C3%B1oz%20%28footballer%2C%20born%201999%29
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Santiago Muñoz Gómez (born 8 June 1999) is a Colombian footballer who currently plays as a forward for Envigado.
Career statistics
Club
Notes
References
1999 births
Living people
Colombian men's footballers
Men's association football forwards
Leones F.C. footballers
Envigado F.C. players
Categoría Primera A players
Categoría Primera B players
Footballers from Bogotá
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https://en.wikipedia.org/wiki/Karen%20Pence%20%28economist%29
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Karen M. Pence is an American economist who is Deputy Associate Director of the Research and Statistics Section of the Federal Reserve Board of Governors, responsible for the Survey of Consumer Finances, and former Chair of the Board of the Panel Study of Income Dynamics. She is a past president of the American Real Estate and Urban Economics Association.
Her research focuses on household housing finance, particularly mortgage lending and mortgage default.
Selected works
Mayer, Christopher, Karen Pence, and Shane M. Sherlund. "The rise in mortgage defaults." Journal of Economic perspectives 23, no. 1 (2009): 27–50.
Dynan, Karen, Atif Mian, and Karen M. Pence. "Is a household debt overhang holding back consumption?[with comments and discussion]." Brookings Papers on Economic Activity (2012): 299–362.
Pence, Karen M. "Foreclosing on opportunity: State laws and mortgage credit." Review of Economics and Statistics 88, no. 1 (2006): 177–182.
Campbell, Sean, Daniel Covitz, William Nelson, and Karen Pence. "Securitization markets and central banking: An evaluation of the term asset-backed securities loan facility." Journal of Monetary Economics 58, no. 5 (2011): 518–531.
Pence, Karen M. "The role of wealth transformations: An application to estimating the effect of tax incentives on saving." The BE Journal of Economic Analysis & Policy 5, no. 1 (2006).
References
21st-century American economists
21st-century American women
Federal Reserve economists
American women economists
Living people
University of Wisconsin–Madison alumni
Swarthmore College alumni
Financial economists
Year of birth missing (living people)
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https://en.wikipedia.org/wiki/Bianca%20Viray
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Bianca L. Viray (born 1983) is an American mathematician and professor at the University of Washington in Seattle. She works in arithmetic geometry, which is a blend of algebraic geometry and algebraic number theory.
Education
Viray received a B.S. in mathematics (cum laude) from the University of Maryland in 2005. She received a Ph.D. in mathematics from the University of California, Berkeley in 2010; her thesis advisor was Bjorn Poonen. After receiving her degree, Viray became a Tamarkin Assistant Professor and National Science Foundation (NSF) Postdoc at Brown University; she was at Brown from 2010 to 2014.
Career and recognition
Viray started at the University of Washington as an assistant professor in 2014 and was promoted to associate professor in 2017 and full professor in 2021. She serves on the Board of Girls' Angle, a math club and magazine for girls. She received an NSF CAREER Award in 2016. She was selected in fall 2017 to deliver the University of Oregon Distinguished Lecture for their Association for Women in Mathematics Student Chapter.
She was selected as a Simons Fellow in mathematics in 2020. She was elected a Fellow of the American Mathematical Society in the class of 2021. Her citation was "for contributions to arithmetic geometry, in particular to the subject of rational points on varieties, and for sustained efforts to support underrepresented groups in mathematics". She was named to the 2022 class of Fellows of the Association for Women in Mathematics, "for her leadership and support of women and girls in math through her work on Girl’s Angle, the Women In Numbers research network, the Noetherian Ring, the Western Algebraic Geometry Symposium, and for launching new and impactful mentoring programs".
Viray received the 2022-2023 American Mathematical Society Joan and Joseph Birman Fellowship, a fellowship "that gives exceptionally talented women extra research support during their mid-career years." She is a former American Mathematical Society Council member at large. She currently serves as the AMS Vice President.
References
External links
Bianca Viray on the ArXiV https://arxiv.org/a/viray_b_1.html
Bianca Viray's Profile on MathSciNet https://mathscinet.ams.org/mathscinet/search/author.html?mrauthid=890397
Living people
20th-century American mathematicians
21st-century American mathematicians
American women mathematicians
University of Washington faculty
Fellows of the American Mathematical Society
1983 births
UC Berkeley College of Letters and Science alumni
University System of Maryland alumni
20th-century American women
21st-century American women
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https://en.wikipedia.org/wiki/Statistica%20Sinica
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Statistica Sinica is an international journal publishing papers in all areas of statistics and data science, including theory, methods, and applications. First issued in 1991, this journal published semiannually in January and July from 1991 to 1995. From 1996 onward, it became quarterly in January, April, July, and October. It is co-sponsored by the Institute of Statistical Science, Academia Sinica, and International Chinese Statistical Association.
Abstracting and indexing
Statistica Sinica has been indexed and abstracted in Scopus, Science Citation Index Expanded, maintained by Institute for Scientific Information (ISI) and Current Contents (CC) from 1998. It is the first journal in statistics that is included in SCI in Asia. In 2000, it has been indexed in Current Index to Statistics (CIS). The journal is also included in JSTOR database.
Awards
In 1997 to 2004, Statistica Sinica has been awarded "Excellent Academic Research Journal" for 8 consecutive years by National Science Council, R.O.C.
External links
Official Website
International Chinese Statistical Association
References
Statistics journals
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https://en.wikipedia.org/wiki/Statistics%20of%20the%20COVID-19%20pandemic%20in%20Malaysia
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Charts
Tables and lists
Distribution of cases by administrative regions
List of death cases
Distribution of cases by districts
Early cases
Prior to the detection of higher volumes of cases in mid-March 2020, cases detected in the first month were well-publicised, incorporating extensive details of the patients' travel history, sources of transmission and dates of diagnosis and discharge. The following data covers positive cases detected until 10 March 2020.
See also
COVID-19 pandemic in Malaysia
COVID-19 pandemic in Sabah
COVID-19 pandemic in Sarawak
Timeline of the COVID-19 pandemic in Malaysia
Notes and references
COVID-19 pandemic in Malaysia
Malaysia
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https://en.wikipedia.org/wiki/Gianluca%20Muniz
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Gianluca Muniz Estevam (born 9 May 2001), sometimes known as Gian, is a Brazilian footballer who currently plays for Ajman on loan from Al Wahda.
Career statistics
Club
Notes
References
External links
2001 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Men's association football fullbacks
UAE Pro League players
Cruzeiro Esporte Clube players
F.C. Alverca players
Al Wahda FC players
Al Urooba Club players
Ajman Club players
Expatriate men's footballers in Portugal
Brazilian expatriate sportspeople in Portugal
Expatriate men's footballers in the United Arab Emirates
Brazilian expatriate sportspeople in the United Arab Emirates
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https://en.wikipedia.org/wiki/Brian%20Ram%C3%ADrez
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Brian Aramis Ramírez (born 29 August 2000) is an Argentine footballer who currently plays for Ittihad Kalba.
Career statistics
Club
Notes
References
External links
2000 births
Living people
Argentine men's footballers
Argentine expatriate men's footballers
Men's association football midfielders
UAE Pro League players
Club Atlético Banfield footballers
Hatta Club players
Ittihad Kalba FC players
Expatriate men's footballers in the United Arab Emirates
Argentine expatriate sportspeople in the United Arab Emirates
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https://en.wikipedia.org/wiki/Maria%20Cristina%20Villalobos
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Maria Cristina Villalobos is an American applied mathematician at the University of Texas Rio Grande Valley, where she is Myles and Sylvia Aaronson Endowed Professor of mathematics, associate dean of sciences, and director of the Center of Excellence in STEM Education. Her research interests include mathematical optimization, control theory, and their application to retinitis pigmentosa treatment and to antenna design.
Education and career
Villalobos is originally from McAllen, Texas and grew up in Donna, Texas, both in the Rio Grande Valley, the oldest of three children of two immigrants from Mexico, and the first in her family with a college education. After participating in engineering programs at the University of Texas–Pan American as a high school student, she did her undergraduate studies in mathematics at the University of Texas at Austin, also including summer research programs at Rice University, the University of California, Berkeley, and the Sandia National Laboratories.
She went to Rice University for graduate study in mathematics, and completed her doctorate there in 2000. Her dissertation, The Behavior of Newton's Method on Two Equivalent Systems from Linear and Nonlinear Programming, was supervised by Richard A. Tapia.
She became a faculty member in mathematics at the University of Texas–Pan American in 2001; the university merged with the University of Texas at Brownsville creating the present University of Texas Rio Grande Valley, where she continues to work. In 2019 she was named associate dean for strategic initiatives and institutional effectiveness.
Recognition
The University of Texas system gave Villalobos their 2013 Regents’ Outstanding Teaching Award. She was also the 2013 winner of the SACNAS Distinguished Undergraduate Institution Mentor Award of the Society for the Advancement of Chicanos/Hispanics and Native Americans in Science. She won the 2019 Richard A. Tapia Achievement Award for Scientific Scholarship, Civic Sciences, and Diversifying Computing. She was one of three 2020 recipients of the Presidential Award for Excellence in Science, Mathematics, and Engineering Mentoring.
She was named to the 2023 class of Fellows of the American Mathematical Society, "for contributions to modelling and optimization and for broadening the participation of underrepresented groups in mathematics".
References
Year of birth missing (living people)
Living people
American people of Mexican descent
21st-century American mathematicians
American women mathematicians
Applied mathematicians
Control theorists
University of Texas at Austin alumni
Rice University alumni
University of Texas–Pan American people
University of Texas Rio Grande Valley people
21st-century American women
Fellows of the American Mathematical Society
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https://en.wikipedia.org/wiki/Chris%20Danforth
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Chris Danforth is a computer scientist and a professor of applied mathematics at the University of Vermont. He is known for his work with the Hedonometer, a tool developed for measuring collective mood with sentiment analysis.
Danforth directs the Computational Story Lab at Vermont Complex Systems Center. His research job is focused on exploring human behavior through social media data.
In 2007, Danforth collaborated with Peter Sheridan Dodds to develop a tool to measure happiness that they called a "hedonometer." For creating it, a team directed by Danforth surveyed speakers of several languages to rate words on a scale of happiest to saddest.
In collaboration with social psychologist Andrew Reece, Danforth found that depressed people post photos on Instagram whose colors are cooler and darker than those of non-depressed people. In 2020, he found evidence that analyzing social media techniques might identify viral outbreaks.
References
University of Vermont faculty
Living people
American computer scientists
Year of birth missing (living people)
University of Maryland, College Park alumni
Bates College alumni
Complex systems scientists
21st-century American mathematicians
Graph drawing people
Information visualization experts
Network scientists
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https://en.wikipedia.org/wiki/Istv%C3%A1n%20Solt%C3%A9sz
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István Soltész (born 29 November 2000) is a Hungarian professional footballer who plays for Zalaegerszeg.
Career statistics
.
References
2000 births
Living people
Footballers from Budapest
Hungarian men's footballers
Men's association football midfielders
Budapest Honvéd FC II players
Budafoki MTE footballers
Zalaegerszegi TE players
Nemzeti Bajnokság I players
Nemzeti Bajnokság II players
|
https://en.wikipedia.org/wiki/Statistics%20of%20the%20COVID-19%20pandemic%20in%20Japan
|
Statistics
Statistics by prefecture
Number of cases and deaths
Cummulative
No. of total confirmed cases
No. of total deaths
No. of total cases by age groups
Daily
No. of new cases per day
No. of new deaths per day
No. of total active cases per day
Case fatality rate
The trend of case fatality rate for COVID-19 from 16 January, the day first case in the country was recorded.
References
COVID-19 pandemic in Japan
Japan
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https://en.wikipedia.org/wiki/1964%E2%80%9365%20Rochdale%20A.F.C.%20season
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The 1964–65 season saw Rochdale compete for their 6th consecutive season in the Football League Fourth Division.
Statistics
|}
Final League Table
Competitions
Football League Fourth Division
F.A. Cup
League Cup
Lancashire Cup
Rose Bowl
References
Rochdale A.F.C. seasons
Rochdale
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https://en.wikipedia.org/wiki/Almost%20open%20map
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In functional analysis and related areas of mathematics, an almost open map between topological spaces is a map that satisfies a condition similar to, but weaker than, the condition of being an open map.
As described below, for certain broad categories of topological vector spaces, surjective linear operators are necessarily almost open.
Definitions
Given a surjective map a point is called a for and is said to be (or ) if for every open neighborhood of is a neighborhood of in (note that the neighborhood is not required to be an neighborhood).
A surjective map is called an if it is open at every point of its domain, while it is called an each of its fibers has some point of openness.
Explicitly, a surjective map is said to be if for every there exists some such that is open at
Every almost open surjection is necessarily a (introduced by Alexander Arhangelskii in 1963), which by definition means that for every and every neighborhood of (that is, ), is necessarily a neighborhood of
Almost open linear map
A linear map between two topological vector spaces (TVSs) is called a or an if for any neighborhood of in the closure of in is a neighborhood of the origin.
Importantly, some authors use a different definition of "almost open map" in which they instead require that the linear map satisfy: for any neighborhood of in the closure of in (rather than in ) is a neighborhood of the origin;
this article will not use this definition.
If a linear map is almost open then because is a vector subspace of that contains a neighborhood of the origin in the map is necessarily surjective.
For this reason many authors require surjectivity as part of the definition of "almost open".
If is a bijective linear operator, then is almost open if and only if is almost continuous.
Relationship to open maps
Every surjective open map is an almost open map but in general, the converse is not necessarily true.
If a surjection is an almost open map then it will be an open map if it satisfies the following condition (a condition that does depend in any way on 's topology ):
whenever belong to the same fiber of (that is, ) then for every neighborhood of there exists some neighborhood of such that
If the map is continuous then the above condition is also necessary for the map to be open. That is, if is a continuous surjection then it is an open map if and only if it is almost open and it satisfies the above condition.
Open mapping theorems
Theorem: If is a surjective linear operator from a locally convex space onto a barrelled space then is almost open.
Theorem: If is a surjective linear operator from a TVS onto a Baire space then is almost open.
The two theorems above do require the surjective linear map to satisfy topological conditions.
Theorem: If is a complete pseudometrizable TVS, is a Hausdorff TVS, and is a closed and almost open linear surjection, then is an open map.
Theorem: Su
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