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https://en.wikipedia.org/wiki/Polarization%20%28Lie%20algebra%29
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In representation theory, polarization is the maximal totally isotropic subspace of a certain skew-symmetric bilinear form on a Lie algebra. The notion of polarization plays an important role in construction of irreducible unitary representations of some classes of Lie groups by means of the orbit method as well as in harmonic analysis on Lie groups and mathematical physics.
Definition
Let be a Lie group, the corresponding Lie algebra and its dual. Let denote the value of the linear form (covector) on a vector . The subalgebra of the algebra is called subordinate of if the condition
,
or, alternatively,
is satisfied. Further, let the group act on the space via coadjoint representation . Let be the orbit of such action which passes through the point and be the Lie algebra of the stabilizer of the point . A subalgebra subordinate of is called a polarization of the algebra with respect to , or, more concisely, polarization of the covector , if it has maximal possible dimensionality, namely
.
Pukanszky condition
The following condition was obtained by L. Pukanszky:
Let be the polarization of algebra with respect to covector and be its annihilator: . The polarization is said to satisfy the Pukanszky condition if
L. Pukanszky has shown that this condition guaranties applicability of the Kirillov's orbit method initially constructed for nilpotent groups to more general case of solvable groups as well.
Properties
Polarization is the maximal totally isotropic subspace of the bilinear form on the Lie algebra .
For some pairs polarization may not exist.
If the polarization does exist for the covector , then it exists for every point of the orbit as well, and if is the polarization for , then is the polarization for . Thus, the existence of the polarization is the property of the orbit as a whole.
If the Lie algebra is completely solvable, it admits the polarization for any point .
If is the orbit of general position (i. e. has maximal dimensionality), for every point there exists solvable polarization.
References
Bilinear forms
Representation theory of Lie algebras
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https://en.wikipedia.org/wiki/Tom%C3%A1%C5%A1%20T%C3%B6r%C3%B6k
|
Tomáš Török (born 18 June 1995) is a Slovak professional ice hockey winger playing for HC Slovan Bratislava of the Slovak Extraliga.
Career statistics
Regular season and playoffs
References
External links
1995 births
Living people
Slovak ice hockey left wingers
HKM Zvolen players
Sherbrooke Phoenix players
Drummondville Voltigeurs players
Sioux City Musketeers players
MHC Martin players
HK Poprad players
HC Prešov players
HC Nové Zámky players
HC 07 Detva players
HC '05 Banská Bystrica players
HK Dukla Michalovce players
HC Slovan Bratislava players
Ice hockey people from Martin, Slovakia
Slovak expatriate ice hockey players in the United States
Slovak expatriate ice hockey players in Canada
Slovak expatriate ice hockey players in the Czech Republic
|
https://en.wikipedia.org/wiki/Adeleke%20Adekunle
|
Adeleke Adekunle (born 27 July 2002) is a Nigerian professional footballer who currently plays as a defender for Enyimba
.
Career statistics
Club
Notes
International
References
2002 births
Living people
Nigerian men's footballers
Nigeria men's international footballers
Men's association football defenders
Abia Warriors F.C. players
Enyimba F.C. players
People from Maiduguri
|
https://en.wikipedia.org/wiki/Kseniya%20Garaschuk
|
Kseniya Garaschuk (born 1982) is a Soviet-born Canadian mathematician and mathematics educator. She is an associate professor of mathematics and statistics at the University of the Fraser Valley, and the editor-in-chief of the mathematics journal Crux Mathematicorum.
Education and career
Garaschuk was born to a family of mathematicians in Minsk, Belarus, at a time when it was part of the Soviet Union. She began studying mathematics and computer science at the Belarusian State University but after a year, when she was 18, moved with her parents to Canada. She took a gap year to improve her English and then completed her undergraduate studies at Simon Fraser University, staying at Simon Fraser for an additional year to earn a master's degree for work in exponential sums in 2008.
Next, she went to the University of Victoria for doctoral research in mathematics, in combinatorial design theory. She completed her PhD in 2014; her dissertation, Linear methods for rational triangle decompositions, was supervised by Peter Dukes. Finding herself isolated in her research work and more energized by teaching, Garaschuk took a postdoctoral fellowship in science education at the University of British Columbia, under the university's Carl Weiman Science Education Initiative, before joining the faculty at the University of the Fraser Valley, in 2016. Her current research interests include examining effectiveness of various classroom and assessment practices in undergraduate mathematics.
As well as her editorial work with Crux Mathematicorum, Garaschuk has been active in service to the Canadian Mathematical Society (CMS) since 2008, as student committee chair, a member of the board of directors, in running mathematics camps and community mathematics events. She is a member of the CMS Education Committee and is a contributing editor of the CMS Education Notes.
Book
With Andy Liu, Garaschuk is coauthor of the book Grade Five Competition from the Leningrad Mathematical Olympiad, 1979–1992 (Springer, 2020).
Recognition
In 2021, the Canadian Mathematical Society gave Garaschuk their Graham Wright Award for Distinguished Service, and named her as a fellow of the society.
In 2018, Garaschuk won University of the Fraser Valley Faculty of Science Teaching Award. In 2020, she was awarded University of the Fraser Valley Faculty of Science Achievement Award for overall excellence in academic endeavours.
References
1982 births
Living people
Belarusian emigrants to Canada
Scientists from Minsk
Canadian mathematicians
Canadian women mathematicians
Mathematics educators
Simon Fraser University alumni
University of Victoria alumni
Academic staff of the University of the Fraser Valley
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https://en.wikipedia.org/wiki/Imperial%20College%20Computing%20Engine
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ICCE I and ICCE II were digital computers built at the Imperial College Department of Mathematics in the post-war period.
Computing engines
ICCE I
The first Imperial College Computing Engine, ICCE I, was constructed by Sidney Michaelson, Tony Brooker and Keith Tocher in the Department of Mathematics at Imperial College London in the late 1940s and early 1950s. It was a relay based machine which gave relatively slow but highly reliable service. Its current whereabouts is unknown.
ICCE II
ICCE II was constructed by Sidney Michaelson, Keith Tocher and Manny Lehman in the early 1950s. This valve based machine was never completed. ICCE II was taken by Keith Tocher to British Steel. Its current whereabouts is unknown.
Influence on other machines
ICCE I and II influenced the design of SABRAC, the second computer constructed in Israel by The Israeli MoD Scientific Department.
Project termination
In 1956/7, the project was forcibly terminated. Staff dispersed. In 1951 Tony Brooker had left to join the Computing Machine Laboratory at the University of Manchester. Keith Tocher took ICCE II and went to work at British Steel, Sidney Michaelson went to the University of Edinburgh and founded the Computer Unit which subsequently became the Department of Computer Science, now the school of informatics. Manny Lehman ultimately joined the Israeli MoD Scientific Department which subsequently became Rafael.
See also
Wilks MV and Stringer LJB, Micro-Programming and the Design of the Control Circuits in an Electronic Computer, Proc. Camb. Phil. Soc., vol 49, no. 2, 1953
Tocher KD, Classification and Design of Operation Codes for Automatic Computers, Proc. IEE, 103B, Supplement 1, Apr. 1956
Tocher KD and Lehman MM, A Fast Parallel Arithmetic Unit, Proc. IEE 103B, Supplement 3, Apr. 1956, pp. 520 - 527
Lehman MM, Parallel Arithmetic Units and Their Control, PhD Thesis, University of London, Feb. 1957, 160pps.+
Lehman MM, Short-Cut Multiplication and Division in Automatic Binary Digital Computers with Special Reference to a New Multiplication Process, Proc. IEE, vol 105, Part B, No 23, Sept 1958, pps. 496 - 504
Tocher KD, Techniques of Multiplication and Division for Automatic Binary Computers, Quart. J. of Mechanics and Appl. Maths., v. 11, p. 3, 1958, pps. 364 - 384
http://www.macs.hw.ac.uk/~greg/icce/
References
British
Computers designed in the United Kingdom
History of computing in the United Kingdom
|
https://en.wikipedia.org/wiki/Redheffer%20star%20product
|
In mathematics, the Redheffer star product is a binary operation on linear operators that arises in connection to solving coupled systems of linear equations. It was introduced by Raymond Redheffer in 1959, and has subsequently been widely adopted in computational methods for scattering matrices. Given two scattering matrices from different linear scatterers, the Redheffer star product yields the combined scattering matrix produced when some or all of the output channels of one scatterer are connected to inputs of another scatterer.
Definition
Suppose are the block matrices
and
,
whose blocks have the same shape when
.
The Redheffer star product is then defined by:
,
assuming that are invertible,
where is an identity matrix conformable
to or , respectively.
This can be rewritten several ways making use of the so-called
push-through identity
.
Redheffer's definition extends beyond matrices to
linear operators on a Hilbert space .
.
By definition, are linear endomorphisms of ,
making linear endomorphisms of ,
where is the direct sum.
However, the star product still makes sense as long as the transformations are compatible,
which is possible when
and
so that .
Properties
Existence
exists if and only if
exists.
Thus when either exists, so does the Redheffer star product.
Identity
The star identity is the identity on ,
or .
Associativity
The star product is associative, provided all of the relevant matrices are defined.
Thus .
Adjoint
Provided either side exists, the adjoint of a Redheffer
star product is .
Inverse
If is the left matrix inverse of such that
, has a right inverse, and
exists, then .
Similarly, if is the left matrix inverse of such
that , has a right inverse, and
exists, then .
Also, if and has a left inverse
then .
The star inverse equals the matrix inverse and both can be computed with
block inversion as
.
Derivation from a linear system
The star product arises from solving multiple linear systems of equations that share
variables in common.
Often, each linear system models the behavior of one subsystem in a physical process
and by connecting the multiple subsystems into a whole, one can eliminate variables
shared across subsystems in order to obtain the overall linear system.
For instance, let be elements of a Hilbert space
such that
and
giving the following equations in variables:
.
By substituting the first equation into the last we find:
.
By substituting the last equation into the first we find:
.
Eliminating by substituting the two preceding equations
into those for results in the Redheffer star product
being the matrix such that:
.
Connection to scattering matrices
Many scattering processes take on a form that motivates a different
convention for the block structure of the linear system of a scattering matrix.
Typically a physical device that performs a linear transformation on inputs, such as
linear dielectric media on electromagnetic waves or in quantum mec
|
https://en.wikipedia.org/wiki/Tomohiro%20Tachi
|
Tomohiro Tachi (, born 1982) is a Japanese academic who studies origami from an interdisciplinary perspective, combining approaches from the mathematics of paper folding, structural rigidity, computational geometry, architecture, and materials science. His work was profiled in "The Origami Revolution" (2017), part of the Nova series of US science documentaries. He is a professor at the University of Tokyo.
Education and career
Tachi studied engineering and architecture at the University of Tokyo, earning bachelor's and master's degrees in 2005 and 2007 respectively, and completing his Ph.D. in 2010. He became an assistant professor in the Department of General Systems Studies at the University of Tokyo in 2010, and became an associate professor in 2018, adding at the same time affiliations with the Department of Information and Graphic Sciences and Department of Architecture.
Contributions
Tachi has been called a "renowned origami artist", and "one of the world experts on rigid origami. His artworks include a "calculated and precise" nudibranch, folded from mirror-finished metal, and an origami version of the Utah teapot, exhibited at the Tikotin Museum of Japanese Art in Israel.
With Erik Demaine, he has developed software that can automatically transform any three-dimensional object, represented as a polygon mesh, into an origami model of the object. His research also includes generalized versions of the Miura fold that can be used to model any smooth surface, and bistable hyperbolic paraboloid structures formed from nested square origami folds.
With Hiroya Tanaka, he is the author of the 2020 Japanese-language book コンピュテーショナル・ファブリケーション [Computational Fabrication: Design and Science of Origami and Tessellation].
Recognition
In 2009, Tachi won the Hangai Prize of the International Association for Shell and Spatial Structures (IASS), for his work on quadrilateral mesh origami. His work with Kōryō Miura on flexible polyhedra derived from the Miura fold won the 2013 Tsuboi Award award of the IASS.
He was the recipient of the 2016 A. T. Yang Memorial Award in Theoretical Kinematics of the American Society of Mechanical Engineers, with Tom Hull, for their joint work on predicting the motion of rigid origami patterns when forces are applied to them in their flat state. Together with his coauthors Evgueni T. Filipov and Glaucio H. Paulino, Tachi won the 2020 Cozzarelli Prize in Engineering and Applied Sciences for their work using the Miura fold to generate stiff but reconfigurable tubular structures.
References
External links
Home page
Origami models by Dr. Tomohiro Tachi, Google Arts & Culture
What I am thinking: origami artist and mathematician Tomohiro Tachi, interview with Tachi originally published in the proceedings of IASS 2018
1982 births
Living people
Origami artists
Japanese mechanical engineers
21st-century Japanese architects
21st-century Japanese mathematicians
Researchers in geometric algorithms
University of Tokyo alumni
Acade
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https://en.wikipedia.org/wiki/The%20Equidistribution%20of%20Lattice%20Shapes%20of%20Rings%20of%20Integers%20of%20Cubic%2C%20Quartic%2C%20and%20Quintic%20Number%20Fields
|
The Equidistribution of Lattice Shapes of Rings of Integers of Cubic, Quartic, and Quintic Number Fields: An Artist's Rendering is a mathematics book by Piper Harron (also known as Piper H), based on her Princeton University doctoral thesis of the same title. It has been described as "feminist", "unique", "honest", "generous", and "refreshing".
Thesis and reception
Harron was advised by Fields Medalist Manjul Bhargava, and her thesis deals with the properties of number fields, specifically the shape of their rings of integers. Harron and Bhargava showed that, viewed as a lattice in real vector space, the ring of integers of a random number field does not have any special symmetries. Rather than simply presenting the proof, Harron intended for the thesis and book to explain both the mathematics and the process (and struggle) that was required to reach this result.
The writing is accessible and informal, and the book features sections targeting three different audiences: laypeople, people with general mathematical knowledge, and experts in number theory. Harron intentionally departs from the typical academic format as she is writing for a community of mathematicians who "do not feel that they are encouraged to be themselves". Unusually for a mathematics thesis, Harron intersperses her rigorous analysis and proofs with cartoons, poetry, pop-culture references, and humorous diagrams. Science writer Evelyn Lamb, in Scientific American, expresses admiration for Harron for explaining the process behind the mathematics in a way that is accessible to non-mathematicians, especially "because as a woman of color, she could pay a higher price for doing it." Mathematician Philp Ording calls her approach to communicating mathematical abstractions "generous".
Her thesis went viral in late 2015, especially within the mathematical community, in part because of the prologue which begins by stating that "respected research math is dominated by men of a certain attitude". Harron had left academia for several years, later saying that she found the atmosphere oppressive and herself miserable and verging on failure. She returned determined that, even if she did not do math the "right way", she "could still contribute to the community". Her prologue states that the community lacks diversity and discourages diversity of thought. "It is not my place to make the system comfortable with itself", she concludes.
A concise proof was published in Compositio Mathematica in 2016.
Author
Harron earned her doctorate from Princeton in 2016. As of 2021, Harron, who also goes by the name of Piper H., is a teacher at Philips Exeter Academy.
References
External links
The Equidistribution of Lattice Shapes of Rings of Integers of Cubic, Quartic, and Quintic Number Fields (Harron's PhD thesis)
The Liberated Mathematician
2021 non-fiction books
Birkhäuser books
Feminist books
Literature by African-American women
Mathematical proofs
Mathematics books
Theses
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https://en.wikipedia.org/wiki/Zden%C4%9Bk%20Hedrl%C3%ADn
|
Zdeněk Hedrlín (1933 – April 22, 2018) was a Czech mathematician, specializing in universal algebra and combinatorial theory, both in pure and applied mathematics.
Zdeněk Hedrlín received his PhD from Prague's Charles University in 1963. His thesis on commutative semigroups was supervised by Miroslav Katětov. Hedrlín held the title of Docent (associated professor) at Charles University. There he worked at the Faculty of Mathematics and Physics for over 60 years until he died at age 85. He was among the first Czech mathematicians to do research on category theory.
In 1970 Hedrlín was an Invited Speaker at the International Congress of Mathematicians in Nice. In the later part of his career, he focused on applications of relational structures and led very successful special and interdisciplinary seminars. Applications to biological cell behavior earned him and his students a European grant. (He and his students worked on computational cell models of cancer.)
Hedrlín was a member of the editorial board of the Journal of Pure and Applied Algebra. His Erdős number is 1. His doctoral students include Vojtěch Rödl.
Selected publication
(over 160 citations)
References
20th-century Czech mathematicians
21st-century Czech mathematicians
Czech mathematicians
Category theorists
Combinatorialists
Charles University alumni
Academic staff of Charles University
1933 births
2018 deaths
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https://en.wikipedia.org/wiki/Ather%20El%20Tahir
|
Ather El Tahir Babikir Mohamed (; born 24 October 1996) is a Sudanese footballer who plays as a right-back for Sudanese club Al-Hilal Club and the Sudan national team.
Career statistics
International
Scores and results list Sudan's goal tally first, score column indicates score after each El Tahir goal.
References
External links
1996 births
Living people
Sportspeople from Khartoum
Sudanese men's footballers
Men's association football fullbacks
Al-Hilal Club (Omdurman) players
Smouha SC players
Sudan Premier League players
Egyptian Premier League players
Sudanese expatriate men's footballers
Sudanese expatriate sportspeople in Egypt
Expatriate men's footballers in Egypt
Sudan men's A' international footballers
2018 African Nations Championship players
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https://en.wikipedia.org/wiki/Sweden%20national%20football%20team%20records%20and%20statistics
|
The following is a list of the Sweden national football team's competitive records and statistics.
Honours
Major titles
FIFA World Cup
Runner-up (1): 1958
Third place (2): 1950, 1994
Fourth place (1): 1938
UEFA European Championship
Semi-final (1): 1992
Olympic football tournament
Gold Medal (1): 1948
Bronze Medal (2): 1924, 1952
Minor titles
Nordic Football Championship
Winners (9): 1933–36, 1937–47, 1948–51, 1952–55, 1956–59, 1960–63, 1964–67, 1968–71, 1972–77
Individual records
Player records
Players in bold are still active with Sweden.
Most capped players
Top goalscorers
Age-related records
Age-related records of the Swedish national football team.
Oldest player 40 years, 5 months and 26 days – Zlatan Ibrahimović (0–2 against Poland on 29 March 2022)
Youngest debutante 17 years, 2 months and 11 days – Gunnar Pleijel (5–2 against Finland on 22 October 1911)
Oldest debutante 34 years, 9 months and 1 day – Stendy Appeltoft (3–0 against Finland on 28 August 1955)
Longest national career 21 years, 1 month and 29 days – Zlatan Ibrahimović (from 31 January 2001 until 29 March 2022)
Oldest goalscorer 37 years, 11 months and 26 days – Gunnar Gren (two goals in a 4–4 draw against Denmark on 26 October 1958)
Youngest goalscorer 17 years, 3 months and 22 days – Alexander Isak (one goal in a 6–0 win against Slovakia on 12 January 2017)
Manager records
Team records
Competition records
Champions Runners-up Third place Fourth place Tournament held on home soil
FIFA World Cup
UEFA European Championship
UEFA Nations League
Olympic Games
Football at the Summer Olympics was first played officially in 1908. The Olympiads between 1896 and 1980 were only open for amateur players. The 1984 and 1988 tournaments were open to players with no appearances in the FIFA World Cup. After the 1988 Olympics, the football event was changed into a tournament for U23 teams with a maximum of three older players. See Sweden Olympic football team for competition record from 1984 until present day.
Nordic Football Championship
Minor tournaments
Head-to-head records
The following table shows Sweden's all-time international record. The abandoned match against Denmark on 2 June 2007 here counts as a draw.Statistics updated as of 18 June 2021.''
Matches not counted as international matches by FIFA
This is a list of matches that the Swedish FA counts as official international matches, but not FIFA. All these matches are included in the table above.
Sweden 1–6 England Amateurs (Gothenburg, Sweden; 8 September 1908)
England Amateurs 7–0 Sweden (Kingston upon Hull, England; 6 November 1909)
Sweden 1–5 England Amateurs (Solna, Sweden; 10 June 1914)
Sweden 4–1 Norway (Tampere, Finland; 21 July 1952)
Sweden 3–1 Austria (Helsinki, Finland; 23 July 1952)
Hungary 6–0 Sweden (Helsinki, Finland; 28 July 1952)
Sweden 2–0 Germany (Helsinki, Finland; 1 August 1952)
Hungary 4–0 Sweden (Budapest, Hungary; 4 May 1963)
Sweden 2–2 Hungary (
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https://en.wikipedia.org/wiki/Blooming%20%28geometry%29
|
In the geometry of convex polyhedra, blooming or continuous blooming is a continuous three-dimensional motion of the surface of the polyhedron, cut to form a polyhedral net, from the polyhedron into a flat and non-self-overlapping placement of the net in a plane. As in rigid origami, the polygons of the net must remain individually flat throughout the motion, and are not allowed to intersect or cross through each other. A blooming, reversed to go from the flat net to a polyhedron, can be thought of intuitively as a way to fold the polyhedron from a paper net without bending the paper except at its designated creases.
An early work on blooming by Biedl, Lubiw, and Sun from 1999 showed that some nets for non-convex but topologically spherical polyhedra have no blooming.
The question of whether every convex polyhedron admits a net with a blooming was posed by Robert Connelly, and came to be known as Connelly’s blooming conjecture. More specifically, Miller and Pak suggested in 2003 that the source unfolding, a net that cuts the polyhedral surface at points with more than one shortest geodesic to a designated source point (including cuts across faces of the polyhedron), always has a blooming. This was proven in 2009 by Demaine et al., who showed in addition that every convex polyhedral net whose polygons are connected in a single path has a blooming, and that every net can be refined to a path-connected net. It is unknown whether every net of a convex polyhedron has a blooming, and Miller and Pak were unwilling to make a conjecture in either direction on this question.
Because it is unknown whether every convex polyhedron has a net that cuts only edges of the polyhedron, and not across its faces ("Dürer's conjecture"), it is also unknown whether every convex polyhedron has a blooming that cuts only edges. In an unpublished manuscript from 2009, Igor Pak and Rom Pinchasi have claimed that this is indeed possible for every Archimedean solid.
The problem of finding a blooming for a polyhedral net has also been approached computationally, as a problem in motion planning.
References
Polyhedra
Paper folding
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https://en.wikipedia.org/wiki/Yuri%20Mikhailovich%20Smirnov
|
Yuri Mikhailovich Smirnov (Юрий Михайлович Смирнов, September 19, 1921, Kaluga – September 3, 2007, Moscow) was a Soviet and Russian mathematician, specializing in topology.
Biography
Yuri M. Smirnov was born in a family of clerical employees. His mother was imprisoned in 1937 for anti-Soviet activity and, as later revealed, was executed by gun shot. While studying at school, Yuri M. Smirnov was interested in mathematics and astronomy and after completing undergraduate study in 1939 entered the astronomy department of the Faculty of Mechanics and Mathematics of Moscow State University. However, soon under the influence of A. N. Kolmogorov, he transferred to the mathematical department of the same Faculty.
After his second year of undergraduate study, Smirnov went in autumn 1941 to the front and served as a radio operator in the Northern Fleet until the end of WW II. After demobilization in 1945, he continued his studies at the Faculty of Mechanics and Mathematics of Moscow State University and began to participate in the seminars of the famous topologist P. S. Alexandrov. In 1948 Smirnov graduated from the Faculty of Mechanics and Mathematics and entered the graduate school of the same faculty, at the same time starting to work as a junior researcher at the Steklov Institute of Mathematics. In 1951 he defended his Ph.D. (Russian Candidate of Sciences) thesis О топологических пространствах, компактных в данном отрезке мощностей (On topological spaces, compact in a given interval of cardinalities), which was supervised by P. S. Alexandrov. In 1957 Smirnov received his Russian Doctor of Sciences degree with thesis Исследование по общей и равномерной топологии методом покрытий (Investigation of general and uniform topology by the covering method).
From 1945 until the end of his life he worked at the Department of Higher Geometry and Topology of the Faculty of Mechanics and Mathematics of Moscow State University, from 1953 as an associate professor, and from 1958 as a full professor. He taught courses on analytical geometry, linear algebra and topology, linear algebra and geometry, differential geometry and topology, and the theories of retracts, shapes, and equivariant compactifications.
Smirnov published over a hundred scientific papers, most of which are related to general topology. He is the author of fundamental results on the problem of metrization of topological spaces and in equivariant topology, as well as in dimension theory and in the theories of shapes, retracts, and proximity spaces. His name is associated with the famous Nagata-Smirnov metrization theorem (proved independently by the Japanese mathematician Jun-iti Nagata). The theorem gives necessary and sufficient conditions for the existence of a metric generating the original topology.
Smirnov gave lectures not only in Russia, but also in Germany, Poland, Bulgaria, Georgia, Armenia, Uzbekistan, and Tajikistan. He supervised 12 Russian Doctor of Sciences (habilitation) degrees and
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https://en.wikipedia.org/wiki/Uruguay%20national%20football%20team%20records%20and%20statistics
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This article contains the list of Uruguay national football team's all records and statistics.
Management record
Competitive matches only as of 14 June 2016
Player records
, after the match against Canada.
Players in bold are still active with Uruguay.
Most caps
Top scorers
All-time head-to-head record
Below is a list of all matches Uruguay have played against FIFA recognised teams. Updated as of 18 June 2021.
World Cup records
Bolded names indicate that the player is active.
Most participations in the World Cup
Most goals scored in the World Cup
Most matches played in the World Cup
World Cup winning captains
Record against teams in the World Cup
after the match against Portugal.
Minor tournament records
†played consecutively with Taça do Atlantica in 1976
References
External links
Uruguay FIFA profile
RSSSF archive of results 1902–
National association football team records and statistics
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https://en.wikipedia.org/wiki/Yuki%20Kunii
|
is a Japanese motorcycle racer.
Career statistics
Asia Talent Cup
Races by year
(key) (Races in bold indicate pole position; races in italics indicate fastest lap)
Red Bull MotoGP Rookies Cup
Races by year
(key) (Races in bold indicate pole position; races in italics indicate fastest lap)
FIM CEV Moto3 Junior World Championship
Races by year
(key) (Races in bold indicate pole position, races in italics indicate fastest lap)
Grand Prix motorcycle racing
By season
By class
Races by year
(key) (Races in bold indicate pole position, races in italics indicate fastest lap)
References
External links
Japanese motorcycle racers
2003 births
Living people
Moto3 World Championship riders
People from Setagaya
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https://en.wikipedia.org/wiki/Condensed%20mathematics
|
Condensed mathematics is a theory developed by and Peter Scholze which aims to unify various mathematical subfields, including topology, complex geometry, and algebraic geometry.
Idea
The fundamental idea in the development of the theory is given by replacing topological spaces by condensed sets, defined below. The category of condensed sets, as well as related categories such as that of condensed abelian groups, are much better behaved than the category of topological spaces. In particular, unlike the category of topological abelian groups, the category of condensed abelian groups is an abelian category, which allows for the use of tools from homological algebra in the study of those structures.
The framework of condensed mathematics turns out to be general enough that considering various “spaces" with sheaves valued in condensed algebras, one is able to incorporate both algebraic geometry, p-adic analytic geometry and complex analytic geometry.
Definition
A condensed set is a sheaf of sets on the site of profinite sets, with the Grothendieck topology given by finite, jointly surjective collections of maps. Similarly, a condensed group, condensed ring, etc. is defined as a sheaf of groups, rings etc. on this site.
To any topological space one can associate a condensed set, customarily denoted , which to any profinite set associates the set of continuous maps . If is a topological group or ring, then is a condensed group or ring.
History
In 2013, Bhargav Bhatt and Peter Scholze introduced a general notion of pro-étale site associated to an arbitrary scheme. In 2018, together with Dustin Clausen they arrived at the conclusion that already the pro-étale site of a single point, which is isomorphic to the site of profinite sets introduced above, has rich enough structure to realize large classes of topological spaces as sheaves on it. Further developments have led to a theory of condensed sets and solid abelian groups, through which one is able to incorporate non-Archimedean geometry into the theory.
In 2020 Scholze completed a proof of a result which would enable the incorporation of functional analysis as well as complex geometry into the condensed mathematics framework, using the notion of liquid vector spaces. The argument has turned out to be quite subtle, and to get rid of any doubts about the validity of the result, he asked other mathematicians to provide a formalized and verified proof. Over a 6-month period a group led by Johan Commelin verified the central part of the proof using the proof assistant Lean. As of 14 July 2022, the proof has been completed.
Coincidentally, in 2019 Barwick and Haine introduced a very similar theory of pyknotic objects. This theory is very closely related to that of condensed sets, with the main differences being set-theoretic in nature: pyknotic theory depends on a choice of Grothendieck universes, whereas condensed mathematics can be developed strictly within ZFC.
References
External link
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https://en.wikipedia.org/wiki/Source%20unfolding
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In computational geometry, the source unfolding of a convex polyhedron is a net obtained by cutting the polyhedron along the cut locus of a point on the surface of the polyhedron. The cut locus of a point consists of all points on the surface that have two or more shortest geodesics to . For every convex polyhedron, and every choice of the point on its surface, cutting the polyhedron on the cut locus will produce a result that can be unfolded into a flat plane, producing the source unfolding. The resulting net may, however, cut across some of the faces of the polyhedron rather than only cutting along its edges.
The source unfolding can also be continuously transformed from the polyhedron to its flat net, keeping flat the parts of the net that do not lie along edges of the polyhedron, as a blooming of the polyhedron. The unfolded shape of the source unfolding is always a star-shaped polygon, with all of its points visible by straight line segments from the image of ; this is in contrast to the star unfolding, a different method for producing nets that does not always produce star-shaped polygons.
An analogous unfolding method can be applied to any higher-dimensional convex polytope, cutting the surface of the polytope into a net that can be unfolded into a flat hyperplane.
References
Polygons
Polyhedra
Computational geometry
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https://en.wikipedia.org/wiki/Foguinho%20%28footballer%2C%20born%201992%29
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Guilherme Seefeldt Krolow (born 15 June 1992), commonly known as Foguinho, is a Brazilian footballer who plays as a midfielder for Vegalta Sendai.
Career statistics
Club
Notes
References
External links
1992 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Men's association football midfielders
Campeonato Brasileiro Série B players
Campeonato Brasileiro Série D players
Campeonato Brasileiro Série C players
J1 League players
J2 League players
Esporte Clube Pelotas players
Grêmio Foot-Ball Porto Alegrense players
Ferroviário Atlético Clube (CE) players
Ceará Sporting Club players
Mirassol Futebol Clube players
Associação Desportiva Recreativa e Cultural Icasa players
Oeste Futebol Clube players
Associação Atlética Aparecidense players
G.D. Chaves players
Esporte Clube Cruzeiro players
Sociedade Esportiva e Recreativa Caxias do Sul players
Criciúma Esporte Clube players
Avaí FC players
Vegalta Sendai players
Brazilian expatriate sportspeople in Portugal
Expatriate men's footballers in Portugal
Brazilian expatriate sportspeople in Japan
Expatriate men's footballers in Japan
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https://en.wikipedia.org/wiki/Lucy%20Mensing
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Lucy Mensing (also Lucie), later Mensing-Schütz or Schütz, (11 March 1901 - 28 April 1995) was a German physicist and a pioneer of quantum mechanics.
Scientific career
Mensing studied mathematics, physics and chemistry at the University of Hamburg. During her studies she specialized in theoretical physics. In 1923/24 she wrote a thesis in which she applied the older quantum hypothesis based on Bohr-Sommerfeld's theory, which assumes electron trajectories, to diatomic molecules. This work was published in the Zeitschrift für Physik in 1925. In 1925 she received her doctorate under Wilhelm Lenz with a thesis on the influence of electric fields on the width of spectral lines.
After her doctorate, she got the opportunity to come to Göttingen and take part in the development of quantum mechanics, where she was advised by Pascual Jordan. She studied the rotational spectrum of diatomic molecules using the methods of matrix mechanics.
After Wolfgang Pauli's treatment of the hydrogen atom, this was one of the first applications of the new quantum mechanics to physical systems. In the course of this work she was the first to find the permissible values for the quantum mechanical orbital angular momentum. The results were published in the Zeitschrift für Physik in 1926.
In Hamburg she worked together with Wolfgang Pauli on the calculation of the electrical polarizability of gases from diatomic molecules with the help of matrix mechanics. The result was also published in 1926 in the Physikalische Zeitschrift. This work was another milestone in the application of quantum mechanics.
She then published in 1926 on the matrix mechanics applied to the partial Paschen-Back effect in continuation of the work of Werner Heisenberg and Pascual Jordan.
In 1926, Alfred Landé offered her a position in Tübingen, which she accepted. There she considered the scattering of slow electrons on atoms, about which she wrote a publication in 1927.
She published her last journal article in 1930 on the broadening of spectral lines.
Private life
Lucy Mensing was born in Hamburg. Her parents were the merchant Hermann Mensing and his wife Martha.
In Tübingen she met the physicist Wilhelm Schütz (1900–1972). He had received his doctorate from Walther Gerlach, and dealt experimentally with spectroscopy. Later he was a professor in Jena. At the time they met, he was assistant to Walther Gerlach. The two married in 1928. After the birth of her first son in 1930, she ended her scientific career and mainly took care of her family. She had a second son and two daughters. Lucy Mensing continued to follow what was happening in physics, maintained contacts with colleagues, and supported her husband in his work, for example by preparing scripts for his lectures. As a contribution to her husband's 1936 Handbuch der Experimentalphysik, she wrote a section on the quantum mechanical theory of the Faraday effect. She had a lifelong friendship with Ernst Ising.
The family moved to Munich in
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https://en.wikipedia.org/wiki/Aleksei%20Chernavskii
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Aleksei Viktorovich Chernavskii (or Chernavsky or Černavskii) (Алексей Викторович Чернавский, born January 17, 1938, in Moscow) is a Russian mathematician, specializing in differential geometry and topology.
Biography
Chernavskii completed undergraduate study at the Faculty of Mechanics and Mathematics of Moscow State University in 1959. He enrolled in graduate school at the Steklov Institute of Mathematics. In 1964 he defended his Candidate of Sciences (PhD) thesis, written under the under the guidance of Lyudmila Keldysh, on the topic Конечнократные отображения многообразий (Finite-fold mappings of manifolds). In 1970 he defended his Russian Doctor of Sciences (habilitation) thesis Гомеоморфизмы и топологические вложения многообразий (Homeomorphisms and topological embeddings of manifolds). In 1970 he was an Invited Speaker at the International Congress of Mathematicians in Nice.
Chernavskii worked as a senior researcher at the Steklov Institute until 1973 and from 1973 to 1980 at Yaroslavl State University. From 1980 to 1985 he was a senior researcher at the Moscow Institute of Physics and Technology.
Since 1985 he is employed the Kharkevich Institute for Information Transmission Problems of the Russian Academy of Sciences. Since 1993 he has been working part-time as a professor at the Department of Higher Geometry and Topology, Faculty of Mechanics and Mathematics, Moscow State University. He wrote a textbook on differential differential geometry for advanced students.
Chernavskii's theorem
Chernavskii's theorem (1964): If and are n-manifolds and is a discrete, open, continuous mapping of into then the branch set = { x: x is an element of and fails to be a local homeomorphism at x} satisfies dimension () ≤ n – 2.
Selected publications
References
External links
1938 births
Living people
Moscow State University alumni
20th-century Russian mathematicians
21st-century Russian mathematicians
Differential geometers
Topologists
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https://en.wikipedia.org/wiki/Alexandr%20Mishchenko
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Alexandr Sergeevich Mishchenko (; born August 18, 1941, in Rostov-on-Don) is a Russian mathematician, specializing in differential geometry and topology and their applications to mathematical modeling in the biosciences.
Education and career
After completing undergraduate study in 1965 in the Faculty of Mechanics and Mathematics of Moscow State University, Mishchenko became a graduate student in the Department of Higher Geometry and Topology of the same Faculty and graduated there in 1968 with Candidate of Sciences degree (PhD). His PhD thesis K-теория на категории бесконечных комплексов (K-theory on the category of infinite complexes) was supervised by Sergei Novikov. In 1973 Mishchenko received his Russian Doctor of Sciences degree (habilitation) with thesis Гомотопические инварианты неодносвязных многообразий (Homotopy invariants of non-simply connected varieties).
Mishchenko is since 1979 a full professor in the Department of Higher Geometry and Topology, Faculty of Mechanics and Mathematics, Moscow State University. He also works at the Steklov Institute of Mathematics. His research deals with geometry and topology, application of algebraic and functional methods in the theory of smooth varieties with non-commutative geometry and topology, and applications of geometry and topology to mathematical modeling in ecology, molecular biology, bioinformatics. He has done some research on the history of mathematics, mathematical education, and the history of teaching mathematics. He is the author or coauthor of over 100 research articles.
In 1970 he was an Invited Speaker at the International Congress of Mathematicians in Nice. In 1971 he was awarded, jointly with Victor Buchstaber, the Moscow Mathematical Society Prize for research on the K-theory of infinite-dimensional CW-complexes. In 1996 Mischenko, jointly with Anatoly Fomenko, was awarded the State Prize of the Russian Federation in the field of science and technology for a series of works involving investigation of invariants of smooth manifolds and Hamiltonian dynamical systems. In 2006 Mishchenko was awarded the title of Honored Professor of Moscow State University.
Selected publications
Articles
Izv. Akad. Nauk SSSR Ser. Mat. 38, 81–106 (1974)
Books
with coauthors:
with coauthors:
with coauthors:
with coauthors:
with coauthors:
References
1941 births
Living people
Moscow State University alumni
Academic staff of Moscow State University
20th-century Russian mathematicians
21st-century Russian mathematicians
Differential geometers
Topologists
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https://en.wikipedia.org/wiki/Irene%20Sabadini
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Irene Maria Sabadini is an Italian mathematician specializing in complex analysis, hypercomplex analysis and the analysis of superoscillations. She is a professor of mathematics at the Polytechnic University of Milan.
Education
Sabadini earned her PhD at the University of Milan in 1996. Her dissertation, Toward a Theory of Quaternionic Hyperfunctions, was supervised by Daniele C. Struppa.
Books
Sabadini is the author of multiple books in mathematics including:
Analysis of Dirac systems and computational algebra (with Colombo, Sommen, and Struppa, Birkhäuser 2004)
Noncommutative functional calculus: Theory and applications of slice hyperholomorphic functions (with Colombo and Struppa, Birkhäuser/Springer, 2011)
Entire slice regular functions (with Colombo and Struppa, Springer, 2016)
Slice hyperholomorphic Schur analysis (with Alpay and Colombo, Birkhäuser/Springer, 2016)
The mathematics of superoscillations (with Aharonov, Colombo, Struppa, and Tollaksen, American Mathematical Society, 2017)
Quaternionic approximation: With application to slice regular functions (with Gal, Birkhäuser/Springer, 2019)
Quaternionic de Branges spaces and characteristic operator function (Springer, 2020)
Michele Sce's works in hypercomplex analysis: A translation with commentaries (with Colombo and Struppa, Birkhäuser/Springer, 2020)
She is also the editor or coeditor of multiple edited volumes.
References
External links
Living people
Italian mathematicians
Italian women mathematicians
Functional analysts
University of Milan alumni
Academic staff of the Polytechnic University of Milan
Year of birth missing (living people)
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https://en.wikipedia.org/wiki/Charlie%20Mary%20Noble
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Charlie Mary Noble (October 31, 1877 – November 30, 1959) was a teacher in astronomy and mathematics education in Fort Worth, Texas. She founded many clubs, notably the Fort Worth Astronomical Society, which was one of the first amateur astronomy clubs in the United States. She contributed several generations of planetarium systems for the Fort Worth Children's Museum, which later became the Fort Worth Museum of Science and History. The planetarium at the museum was named after Noble, the first woman in the United States to be so honored.
Early life
Charlie Mary Noble was born in Giddings, Texas on October 31, 1877 to Sallie Mellette Noble and Stephen W. Noble. In 1888, she and her family moved to Fort Worth from Hearne, Texas.
Education
She graduated from Old Fort Worth High School. She attended Warren Institute in Fort Worth and Sam Houston State College in Huntsville, Texas. She received a B.S. from the University of Texas, and a B.S. and M.S. from Texas Christian University (TCU).
Teaching career
Fort Worth Public Schools
Starting in 1897, Noble taught mathematics at Paschal High School, in the Fort Worth public school system. In 1918, she was promoted to the head of the mathematics department, where she served for twenty-five more years. In 1926, she started the Penta Club, an honors mathematics society, which was one of the first science clubs for students in Fort Worth. In 1943, she retired after 46 years of teaching at Paschal High School but continued to teach.
Texas Christian University
Charlie Noble used astronomy in her mathematics instruction at Paschal High School and was asked to teach mathematics, astronomy, and celestial navigation at Texas Christian University (TCU) as part of the US Navy's V-12 officer training program during the World War II. After the war, she continued to teach astronomy at TCU.
Career after teaching
Fort Worth Children's Museum and the Fort Worth Museum of Science and History
Noble created the first planetarium in Fort Worth in the mid-1940s in a tent 18-foot in diameter, providing the first planetarium experience in north Texas. In 1947 Noble founded the Junior Astronomy Club of the Fort Worth Children's Museum and purchased one of the first mechanical planetariums available, a Spitz star-ball Model A, which had just been developed a year earlier by Armand Spitz. The Spitz star ball was presented to the Fort Worth Children's Museum, which at that time had just relocated from the De Zavala Elementary School to its location in the R.E. Harding House at 1306 Summit, south of downtown Fort Worth.
Two years later, Noble constructed of a more permanent tent as a planetarium, still on Summit Street. In 1954, the museum moved into a new building on Montgomery Avenue and the in 1955 a new Spitz A-1 was purchased and installed into a planetarium attached to the new building. The planetarium was installed in a structure that included a 30-foot plaster dome, rather than a tent. The Fort Worth Children's
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https://en.wikipedia.org/wiki/Daoud%20Wais
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Wais Daoud Wais (born 6 December 1986) is a Djiboutian professional footballer who plays as a defender for Djibouti Premier League club Arta/Solar7.
Career statistics
International
Scores and results list Djibouti's goal tally first, score column indicates score after each Wais goal.
Honours
ASAS Djibouti Télécom
Djibouti Premier League: 2012–13, 2013–14, 2014–15, 2015–16, 2016–17, 2017–18
Arta/Solar7
Djibouti Premier League: 2020–2021, 2021–2022
Djibouti Cup: 2020–2021, 2021–2022
Djibouti Super Cup: 2020, 2022
References
External links
1986 births
Living people
People from Djibouti (city)
Djiboutian men's footballers
Men's association football defenders
AS Ali Sabieh/Djibouti Télécom players
AS Arta/Solar7 players
Djibouti Premier League players
Djibouti men's international footballers
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https://en.wikipedia.org/wiki/Nikola%20Stankovi%C4%87%20%28footballer%2C%20born%202003%29
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Nikola Stanković (, born 24 April 2003) is a Serbian footballer who currently plays as a midfielder for Serbian club Čukarički.
Career statistics
Club
Honours
Club
Red Star Belgrade
Serbian SuperLiga: 2021–22
Serbian Cup: 2021–22
References
2003 births
Living people
Serbian men's footballers
Serbia men's youth international footballers
Men's association football midfielders
Serbian First League players
Red Star Belgrade footballers
RFK Grafičar Beograd players
Serbian SuperLiga players
Serbia men's under-21 international footballers
People from Vrnjačka Banja
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https://en.wikipedia.org/wiki/Ivan%20Gute%C5%A1a
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Ivan Guteša (, born 4 April 2002) is a Serbian footballer who currently plays as a goalkeeper for Grafičar Beograd.
Career statistics
Club
Notes
References
2002 births
Living people
Serbian men's footballers
Men's association football goalkeepers
Serbian First League players
RFK Grafičar Beograd players
People from Vršac
Footballers from South Banat District
Serbia men's under-21 international footballers
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https://en.wikipedia.org/wiki/Zhang%20Zhihao%20%28footballer%29
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Zhang Zhihao (; born 2 January 2001) is a Chinese footballer currently playing as a defender for Jiangxi Dark Horse Junior, on loan from Guangzhou.
Career statistics
Club
.
Notes
References
2001 births
Living people
Chinese men's footballers
Men's association football defenders
China League One players
China League Two players
Villarreal CF players
Guangzhou F.C. players
Beijing Sport University F.C. players
Chinese expatriate men's footballers
Chinese expatriate sportspeople in Spain
Expatriate men's footballers in Spain
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https://en.wikipedia.org/wiki/Chen%20Zhengfeng
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Chen Zhengfeng (; born 26 January 2001) is a Chinese footballer currently playing as a midfielder for Guangzhou.
Career statistics
Club
.
References
2001 births
Living people
Chinese men's footballers
Men's association football midfielders
China League Two players
Guangzhou F.C. players
21st-century Chinese people
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https://en.wikipedia.org/wiki/Wu%20Junhao
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Wu Junhao (; born 11 December 2004) is a Chinese footballer currently playing as a midfielder for Guangzhou.
Career statistics
Club
.
References
2004 births
Living people
Chinese men's footballers
Men's association football midfielders
Guangzhou F.C. players
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https://en.wikipedia.org/wiki/Ning%20Haoxu
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Ning Haoxu (; born 8 January 2001) is a Chinese footballer currently playing as a forward for Guangzhou.
Career statistics
Club
.
References
2001 births
Living people
Chinese men's footballers
Men's association football forwards
Guangzhou F.C. players
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https://en.wikipedia.org/wiki/Ruan%20Sai
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Ruan Sai (; born 15 February 2001) is a Chinese footballer currently playing as a midfielder for Guangzhou.
Career statistics
Club
.
References
2001 births
Living people
Chinese men's footballers
Men's association football midfielders
Guangzhou F.C. players
Chinese Super League players
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https://en.wikipedia.org/wiki/Chen%20Quanjiang
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Chen Quanjiang (; born 10 July 2000) is a Chinese footballer currently playing as a defender for Guangzhou.
Career statistics
Club
.
References
2000 births
Living people
Chinese men's footballers
Men's association football defenders
China League One players
Chinese Super League players
Guangzhou F.C. players
Inner Mongolia Zhongyou F.C. players
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https://en.wikipedia.org/wiki/Zhang%20Jianzhi%20%28footballer%29
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Zhang Jianzhi (; born 28 January 2000) is a Chinese footballer currently playing as a goalkeeper for Guangzhou.
Career statistics
Club
.
References
2000 births
Living people
Chinese men's footballers
Men's association football goalkeepers
Guangzhou F.C. players
Chinese Super League players
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https://en.wikipedia.org/wiki/Huang%20Guangliang
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Huang Guangliang (; born 18 February 1999) is a Chinese footballer currently playing as a midfielder for Guangzhou.
Career statistics
Club
.
References
1999 births
Living people
Chinese men's footballers
Men's association football midfielders
Guangzhou F.C. players
Chinese Super League players
21st-century Chinese people
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https://en.wikipedia.org/wiki/Fan%20Hengbo
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Fan Hengbo (; born 14 July 1999) is a Chinese footballer currently playing as a forward for Guangzhou.
Career statistics
Club
.
References
1999 births
Living people
Chinese men's footballers
China men's youth international footballers
Men's association football forwards
China League One players
Chinese Super League players
Guangzhou F.C. players
Inner Mongolia Zhongyou F.C. players
21st-century Chinese people
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https://en.wikipedia.org/wiki/Wang%20Tianqing
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Wang Tianqing (; born 1 April 2001) is a Chinese footballer currently playing as a defender for Guangzhou.
Career statistics
Club
.
References
2001 births
Living people
Chinese men's footballers
Men's association football defenders
Guangzhou F.C. players
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https://en.wikipedia.org/wiki/Zhang%20Zili
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Zhang Zili (; born 23 January 2002) is a Chinese footballer currently playing as a midfielder for Guangzhou.
Career statistics
Club
.
References
2002 births
Living people
Chinese men's footballers
Men's association football midfielders
Guangzhou F.C. players
Chinese Super League players
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https://en.wikipedia.org/wiki/Rao%20Chen
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Rao Chen (; born 10 February 2001) is a Chinese footballer currently playing as a defender for Guangzhou.
Career statistics
Club
.
References
2001 births
Living people
Chinese men's footballers
Men's association football defenders
Guangzhou F.C. players
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https://en.wikipedia.org/wiki/Huang%20Kaizhou
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Huang Kaizhou (; born 13 May 2002) is a Chinese footballer currently playing as a forward for Guangzhou.
Career statistics
Club
.
References
2002 births
Living people
Chinese men's footballers
Men's association football forwards
Guangzhou F.C. players
21st-century Chinese people
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https://en.wikipedia.org/wiki/Chen%20Rijin
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Chen Rijin (; born 17 January 1999) is a Chinese footballer currently playing as a defender for Guangzhou.
Career statistics
Club
.
References
1999 births
Living people
Chinese men's footballers
Men's association football defenders
Guangzhou F.C. players
Chinese Super League players
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https://en.wikipedia.org/wiki/Wang%20Wenxuan
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Wang Wenxuan (; born 26 December 1999) is a Chinese footballer currently playing as a defender for Guangzhou.
Career statistics
Club
.
References
1999 births
Living people
Chinese men's footballers
Men's association football defenders
China League One players
Chinese Super League players
Villarreal CF players
Guangzhou F.C. players
Inner Mongolia Zhongyou F.C. players
Chinese expatriate sportspeople in Spain
Expatriate men's footballers in Spain
21st-century Chinese people
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https://en.wikipedia.org/wiki/Oldrich%20Kotvan
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Oldrich Kotvan (born 20 July 1990) is a Slovak professional ice hockey defenseman playing playing for HK Poprad of the Slovak Extraliga.
Career statistics
Regular season and playoffs
Awards and honors
References
External links
1990 births
Living people
Ice hockey people from Skalica
Slovak ice hockey defencemen
HK Trnava players
Fargo Force players
Fairbanks Ice Dogs players
HC Olomouc players
PSG Berani Zlín players
HC Dukla Jihlava players
BK Mladá Boleslav players
HC Bílí Tygři Liberec players
HC Karlovy Vary players
HKM Zvolen players
HK Poprad players
Slovak expatriate ice hockey players in Canada
Slovak expatriate ice hockey players in the United States
Slovak expatriate ice hockey players in the Czech Republic
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https://en.wikipedia.org/wiki/Cobham%27s%20theorem
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Cobham's theorem is a theorem in combinatorics on words that has important connections with number theory, notably transcendental numbers, and automata theory. Informally, the theorem gives the condition for the members of a set S of natural numbers written in bases b1 and base b2 to be recognised by finite automata. Specifically, consider bases b1 and b2 such that they are not powers of the same integer. Cobham's theorem states that S written in bases b1 and b2 is recognised by finite automata if and only if S is a finite union of arithmetic progressions. The theorem was proved by Alan Cobham in 1969 and has since given rise to many extensions and generalisations.
Definitions
Let be an integer. The representation of a natural number in base is the sequence of digits such that
where and . The word is often denoted , or more simply, .
A set of natural numbers S is recognisable in base or more simply -recognisable or -automatic if the set of the representations of its elements in base is a language recognisable by a finite automaton on the alphabet .
Two positive integers and are multiplicatively independent if there are no non-negative integers and such that . For example, 2 and 3 are multiplicatively independent, but 8 and 16 are not since . Two integers are multiplicatively dependent if and only if they are powers of a same third integer.
Problem statements
Original problem statement
More equivalent statements of the theorem have been given. The original version by Cobham is the following: Another way to state the theorem is by using automatic sequences. Cobham himself calls them "uniform tag sequences.". The following form is found in Allouche and Shallit's book:We can show that the characteristic sequence of a set of natural numbers S recognisable by finite automata in base k is a k-automatic sequence and that conversely, for all k-automatic sequences and all integers , the set of natural numbers such that is recognisable in base .
Formulation in logic
Cobham's theorem can be formulated in first-order logic using a theorem proven by Büchi in 1960. This formulation in logic allows for extensions and generalisations. The logical expression uses the theory
of natural integers equipped with addition and the function defined by and for any positive integer , if is the largest power of that divides . For example, , and .
A set of integers is definable in first-order logic in if it can be described by a first-order formula with equality, addition, and .
Examples:
The set of odd numbers is definable (without ) by the formula
The set of the powers of 2 is definable by the simple formula .
We can push the analogy with logic further by noting that S is first-order definable in Presburger arithmetic if and only if it is ultimately periodic. So, a set S is definable in the logics and if and only if it is definable in Presburger arithmetic.
Generalisations
Approach by morphisms
An automatic sequence is a
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https://en.wikipedia.org/wiki/1993%E2%80%9394%20Rochdale%20A.F.C.%20season
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The 1993–94 season saw Rochdale compete in their 20th consecutive season in the fourth tier of the English football league, named at the time as the Football League Third Division.
Statistics
|}
Final League Table
Competitions
Football League Third Division
F.A. Cup
Football League Cup (Coca-Cola Cup)
Football League Trophy (Autoglass Trophy)
Lancashire Cup
References
Rochdale A.F.C. seasons
Rochdale
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https://en.wikipedia.org/wiki/Joyce%20E.%20Penner
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Joyce Penner is an atmospheric scientist known for her research on climate change, especially on the impact of aerosols and clouds.
Education and career
Penner has a B.A. in mathematics from the University of California Santa Barbara (1970), and an M.S. and a Ph.D. in applied mathematics from Harvard University (1972 and 1977, respectively). Penner moved to Lawrence Livermore National Laboratory in 1977 and remained there until 1996, serving as a group leader from 1987 until her departure for University of Michigan in 1996. At the University of Michigan, Penner was named the Ralph J. Cicerone Distinguished University Professor of Atmospheric Science in 2007.
Penner has contributed to multiple reports from the Intergovernmental Panel on Climate Change (IPCC), which was awarded the 2007 Nobel Peace Prize for its series of assessment reports. Penner was the coordinating lead author for chapter 5 on "Aerosols, their Direct and Indirect Effects" within the 2001 Assessment Report 3, Working Group 1 (AR3 WG1), and one of 18 lead authors for the technical summary of that same report. In 2007, she was one of 7 lead authors for chapter 9 on "Understanding and attributing climate change" (). In 2013, she served as a review editor for chapter 7 (Clouds and aerosols, ) and for the technical summary (). She was also one of the contributing authors for the 1995 IPCC report.
Penner was the president of the Atmospheric Sciences Section of the American Geophysical Union from 2017 to 2018. Since 2019 she has been the president of the International Association of Meteorology and Atmospheric Sciences.
Research
Penner's research interests focus on climate modeling, specifically the representation of aerosols in global climate models. Through her research, Penner has shown that the composition of aerosols impacts whether particles will increase or decrease global temperatures. For example, her investigation into how biomass burning produces aerosols concluded that smoke from burning tropical forests may cause cooling by an indirect effect because of the formation of droplets that reflect sunlight away from Earth's surface. Within her climate models, Penner has examined the role of nitrogen compounds and her research revealed that the nitric acid produced by supersonic aircraft (e.g., the Concorde) can lead to decreases in atmospheric ozone concentrations. She has also defined the uncertainties associated with modeling indirect aerosol forcing, including a consideration of differences across a suite of models. This indirect aerosol effect impacts the amount of radiation received at Earth's surface which is a function of how aerosol particles are formed.
Selected publications
Awards and honors
Fellow, American Geophysical Union (1999)
Fellow, American Association for the Advancement of Science (2009)
Haagen-Smit Clean Air Award, California Air Resources Board (2016)
References
External links
Fellows of the American Association for the Advancement of Sc
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https://en.wikipedia.org/wiki/Alan%20Grafite
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Alan Sebastião Alexandre (born 8 February 1998), simply known as Alan Grafite, is a Brazilian footballer who plays as a striker for V.League 1 club Binh Dinh.
Career statistics
Honours
Chapecoense
Campeonato Catarinense: 2020
Campeonato Brasileiro Série B: 2020
References
External links
1998 births
Living people
People from Criciúma
Brazilian men's footballers
Men's association football forwards
Campeonato Brasileiro Série A players
Campeonato Brasileiro Série B players
V.League 1 players
Criciúma Esporte Clube players
Associação Chapecoense de Futebol players
Toledo Esporte Clube players
Concórdia Atlético Clube players
Vila Nova Futebol Clube players
Quy Nhon Binh Dinh FC players
Footballers from Santa Catarina (state)
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https://en.wikipedia.org/wiki/Li%20Boxi
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Li Boxi (; born 30 October 2000) is a Chinese footballer currently playing as a forward for Shijiazhuang Gongfu on loan from Beijing Guoan.
Career statistics
Club
.
References
2000 births
Living people
Chinese men's footballers
Men's association football forwards
Beijing Guoan F.C. players
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https://en.wikipedia.org/wiki/Gao%20Jian%20%28footballer%2C%20born%202002%29
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Gao Jian (; born 29 January 2002) is a Chinese footballer currently playing as a forward for Beijing Guoan.
Career statistics
Club
.
References
2002 births
Living people
Chinese men's footballers
Men's association football forwards
Beijing Guoan F.C. players
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https://en.wikipedia.org/wiki/Tomoki%20Kondo
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is a Japanese footballer currently playing as a midfielder for Yokohama FC as a designated special player.
Career statistics
Club
.
Notes
References
External links
2001 births
Living people
Association football people from Aichi Prefecture
Nihon University alumni
Japanese men's footballers
Men's association football midfielders
Yokohama FC players
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https://en.wikipedia.org/wiki/Zhao%20Wenzhe
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Zhao Wenzhe (; born 10 January 2001) is a Chinese footballer currently playing as a defender for Guangzhou.
Career statistics
Club
.
References
2001 births
Living people
Footballers from Henan
Chinese men's footballers
Men's association football defenders
Chinese Super League players
Henan F.C. players
Villarreal CF players
Guangzhou F.C. players
Chinese expatriate men's footballers
Chinese expatriate sportspeople in Spain
Expatriate men's footballers in Spain
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https://en.wikipedia.org/wiki/Riku%20Nozawa
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is a Japanese footballer currently playing as a defender for Ventforet Kofu.
Career statistics
Club
.
Notes
Honours
Club
Ventforet Kofu
Emperor's Cup: 2022
References
External links
1998 births
Living people
Association football people from Tochigi Prefecture
Sanno Institute of Management alumni
Japanese men's footballers
Men's association football defenders
J2 League players
Tokyo Verdy players
Ventforet Kofu players
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https://en.wikipedia.org/wiki/Yamen%20Zelfani
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Yamen Zelfani (born 4 September 1979) is a Tunisian professional football manager.
Managerial statistics
Honours
Nouadhibou
Ligue 1 Mauritania runner-up: 2015–16
Al-Merrikh
Sudan Cup: 2018
Dhofar
Oman Super Cup: 2019
Individual
Tunisian Ligue Professionnelle 1 Manager of the Month: April 2021, May 2021
References
External links
Living people
Tunisian football managers
Al-Merrikh SC managers
Dhofar Club managers
JS Kabylie managers
Tunisian expatriate football managers
Expatriate football managers in Sudan
Tunisian expatriate sportspeople in Sudan
Expatriate football managers in Oman
Tunisian expatriate sportspeople in Oman
Expatriate football managers in Algeria
Tunisian expatriate sportspeople in Algeria
Expatriate football managers in Saudi Arabia
Tunisian expatriate sportspeople in Saudi Arabia
Algerian Ligue Professionnelle 1 managers
Saudi First Division League managers
1979 births
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https://en.wikipedia.org/wiki/Satoshi%20Osugi
|
is a Japanese footballer currently playing as a goalkeeper for Fukushima United.
Career statistics
Club
.
Notes
References
1996 births
Living people
Association football people from Shizuoka (city)
Nippon Sport Science University alumni
Japanese men's footballers
Japanese expatriate men's footballers
Men's association football goalkeepers
J3 League players
Kingston City FC players
Fujieda MYFC players
Japanese expatriate sportspeople in Australia
Expatriate men's soccer players in Australia
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https://en.wikipedia.org/wiki/Li%20Jingrun
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Li Jingrun (; born 7 May 2000) is a Chinese footballer most recently as a defender for Xinjiang Tianshan Leopard.
Career statistics
Club
.
References
2000 births
Living people
Chinese men's footballers
Men's association football defenders
China League One players
Beijing Guoan F.C. players
Xinjiang Tianshan Leopard F.C. players
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https://en.wikipedia.org/wiki/Bai%20Yunfei
|
Bai Yunfei (; born 8 April 2002) is a Chinese footballer currently playing as a forward for Beijing Guoan.
Career statistics
Club
.
References
2002 births
Living people
Chinese men's footballers
Men's association football forwards
Beijing Guoan F.C. players
21st-century Chinese people
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https://en.wikipedia.org/wiki/Shao%20Tianfa
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Shao Tianfa (; born 4 May 2001) is a Chinese footballer currently playing as a midfielder for Beijing Guoan.
Career statistics
Club
.
References
2001 births
Living people
Chinese men's footballers
Men's association football midfielders
Beijing Guoan F.C. players
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https://en.wikipedia.org/wiki/Kim%20Min-jun%20%28footballer%2C%20born%20February%202000%29
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Kim Min-jun (; born 12 February 2000) is a South Korean footballer currently playing as a forward for Gimcheon Sangmu.
Career statistics
Club
Notes
References
2000 births
Living people
University of Ulsan alumni
South Korean men's footballers
South Korea men's youth international footballers
Men's association football forwards
K League 1 players
Ulsan Hyundai FC players
Competitors at the 2019 Summer Universiade
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https://en.wikipedia.org/wiki/Kim%20Min-june%20%28footballer%2C%20born%20January%201994%29
|
Kim Min-june (; born 27 January 1994) is a South Korean footballer currently playing as a defender for Gimhae FC.
Career statistics
Club
Notes
References
1994 births
Living people
Hannam University alumni
South Korean men's footballers
Men's association football forwards
K League 1 players
Korea National League players
K3 League players
Gangwon FC players
Busan Transportation Corporation FC players
Gimhae FC players
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https://en.wikipedia.org/wiki/Kim%20Min-jun%20%28footballer%2C%20born%201996%29
|
Kim Min-jun (; born 12 January 1996) is a South Korean former footballer.
Career statistics
Club
Notes
References
1996 births
Living people
South Korean men's footballers
Men's association football forwards
K League 2 players
FC Seoul players
Gyeongnam FC players
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https://en.wikipedia.org/wiki/Kwon%20Gi-pyo
|
Kwon Gi-pyo (; born 26 June 1997) is a South Korean footballer currently playing as a right-back for Pohang Steelers.
Career statistics
Club
Notes
References
1997 births
Living people
Konkuk University alumni
South Korean men's footballers
South Korea men's youth international footballers
Men's association football defenders
K League 1 players
K League 2 players
Pohang Steelers players
Seoul E-Land FC players
FC Anyang players
Footballers from Daegu
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https://en.wikipedia.org/wiki/List%20of%20Swedish%20counties%20by%20fertility%20rate
|
This is a list of Swedish counties by fertility rate as of 2020 according to the Statistics Sweden.
References
Sweden, Fertility rate
Fertility
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https://en.wikipedia.org/wiki/Angelo%20Chaves
|
Angelo Samuel Chaves (born 10 February 2001) is a Brazilian professional footballer who plays as a left back for Brusque.
Career statistics
References
2001 births
Living people
Footballers from Curitiba
Brazilian men's footballers
Men's association football defenders
Campeonato Brasileiro Série A players
Campeonato Brasileiro Série B players
Coritiba Foot Ball Club players
Brusque Futebol Clube players
Associação Portuguesa de Desportos players
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https://en.wikipedia.org/wiki/Probability-proportional-to-size%20sampling
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In survey methodology, probability-proportional-to-size (pps) sampling is a sampling process where each element of the population (of size N) has some (independent) chance to be selected to the sample when performing one draw. This is proportional to some known quantity so that .
One of the cases this occurs in, as developed by Hanson and Hurwitz in 1943, is when we have several clusters of units, each with a different (known upfront) number of units, then each cluster can be selected with a probability that is proportional to the number of units inside it. So, for example, if we have 3 clusters with 10, 20 and 30 units each, then the chance of selecting the first cluster will be 1/6, the second would be 1/3, and the third cluster will be 1/2.
The pps sampling results in a fixed sample size n (as opposed to Poisson sampling which is similar but results in a random sample size with expectancy of n). When selecting items with replacement the selection procedure is to just draw one item at a time (like getting n draws from a multinomial distribution with N elements, each with their own selection probability). If doing a without-replacement sampling, the schema can become more complex.
See also
Bernoulli sampling
Poisson distribution
Poisson process
Sampling design
References
Sampling techniques
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https://en.wikipedia.org/wiki/Chen%20Kun%20%28footballer%29
|
Chen Kun (; born 3 October 2001) is a Chinese footballer currently playing as a defender for Guangzhou.
Career statistics
Club
.
References
2001 births
Living people
Chinese men's footballers
Men's association football defenders
Guangzhou F.C. players
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https://en.wikipedia.org/wiki/Bochner%27s%20tube%20theorem
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In mathematics, Bochner's tube theorem (named for Salomon Bochner) shows that every function holomorphic on a tube domain in can be extended to the convex hull of this domain.
Theorem Let be a connected open set. Then every function holomorphic on the tube domain can be extended to a function holomorphic on the convex hull .
A classic reference is (Theorem 9). See also for other proofs.
Generalizations
The generalized version of this theorem was first proved by Kazlow (1979), also proved by Boivin and Dwilewicz (1998) under more less complicated hypothese.
Theorem Let be a connected submanifold of of class-. Then every continuous CR function on the tube domain can be continuously extended to a CR function on . By "Int ch(S)" we will mean the interior taken in the smallest dimensional space which contains "ch(S)".
References
Several complex variables
Theorems in complex analysis
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https://en.wikipedia.org/wiki/1991%20Canadian%20census
|
The 1991 Canadian census was a detailed enumeration of the Canadian population. Census day was June 4, 1991. On that day, Statistics Canada attempted to count every person in Canada. The total population count of Canada was 27,296,859. This was a 7.9% increase over the 1986 census of 25,309,331.
The previous census was the 1986 census and the following census was in 1996 census.
Canada by the numbers
A summary of information about Canada.
Population by province
References
Censuses in Canada
Canadian
Census
Census
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https://en.wikipedia.org/wiki/2021%E2%80%9322%20PFC%20Levski%20Sofia%20season
|
The 2021–22 season was Levski Sofia's 101st season in the First League. This article shows player statistics and all matches (official and friendly) that the club has played during the season.
This season marked the end of a 13-year trophy drought with Levski winning the 2021–22 Bulgarian Cup.
Transfers
In
Out
Loans out
Squad
Updated on 7 April 2022.
Performance overview
Fixtures
Friendlies
Summer
Mid-season
Winter
First League
Preliminary stage
League table
Results summary
Results by round
Matches
Championship round
League table
Results summary
Results by round
Matches
Bulgarian Cup
Squad statistics
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|colspan="14"|Players away from the club on loan:
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|colspan="14"|Players who left the club during the season:
|}
Disciplinary record
Includes all competitive matches.
References
General
Official club website
Specific
Notes
PFC Levski Sofia seasons
Levski Sofia
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https://en.wikipedia.org/wiki/Malgrange%E2%80%93Zerner%20theorem
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In mathematics, Malgrange–Zerner theorem (named for Bernard Malgrange and Martin Zerner) shows that a function on allowing holomorphic extension in each variable separately can be extended, under certain conditions, to a function holomorphic in all variables jointly. This theorem can be seen as a generalization of Bochner's tube theorem to functions defined on tube-like domains whose base is not an open set.
Theorem Let
and let convex hull of . Let be a locally bounded function such that and that for any fixed point the function is holomorphic in in the interior of for each . Then the function can be uniquely extended to a function holomorphic in the interior of .
History
According to Henry Epstein, this theorem was proved first by Malgrange in 1961 (unpublished), then by Zerner (as cited in ), and commmunicated to him privately. Epstein's lectures contain the first published proof (attributed there to Broz, Epstein and Glaser). The assumption was later relaxed to (see Ref.[1] in ) and finally to .
References
Several complex variables
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https://en.wikipedia.org/wiki/Aristotelian%20realist%20philosophy%20of%20mathematics
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In the philosophy of mathematics, Aristotelian realism holds that mathematics studies properties such as symmetry, continuity and order that can be immanently realized in the physical world (or in any other world there might be). It contrasts with Platonism in holding that the objects of mathematics, such as numbers, do not exist in an "abstract" world but can be physically realized. It contrasts with nominalism, fictionalism, and logicism in holding that mathematics is not about mere names or methods of inference or calculation but about certain real aspects of the world.
Aristotelian realists emphasize applied mathematics, especially mathematical modeling, rather than pure mathematics as philosophically most important. Marc Lange argues that "Aristotelian realism allows mathematical facts to be explainers in distinctively mathematical explanations" in science as mathematical facts are themselves about the physical world. Paul Thagard describes Aristotelian realism as "the current philosophy of mathematics that fits best with what is known about minds and science."
History
Although Aristotle did not write extensively on the philosophy of mathematics, his various remarks on the topic exhibit a coherent view of the subject as being both about abstractions and applicable to the real world of space and counting.
Until the eighteenth century, the most common philosophy of mathematics was the Aristotelian view that it is the "science of quantity", with quantity divided into the continuous (studied by geometry) and the discrete (studied by arithmetic).
Aristotelian approaches to the philosophy of mathematics were rare in the twentieth century but were revived by Penelope Maddy in Realism in Mathematics (1990) and by a number of authors since 2000 such as James Franklin, Anne Newstead, Donald Gillies, and others.
Numbers and sets
Aristotelian views of (cardinal or counting) numbers begin with Aristotle's observation that the number of a heap or collection is relative to the unit or measure chosen: "'number' means a measured plurality and a plurality of measures ... the measure must always be some identical thing predicable of all the things it measures, e.g. if the things are horses, the measure is 'horse'." Glenn Kessler develops this into the view that a number is a relation between a heap and a universal that divides it into units; for example, the number 4 is realized in the relation between a heap of parrots and the universal "being a parrot" that divides the heap into so many parrots.
On an Aristotelian view, ratios are not closely connected to cardinal numbers. They are relations between quantities such as heights. A ratio of two heights may be the same as the relation between two masses or two time intervals.
Aristotelians regard sets as well as numbers as instantiated in the physical world (rather than being Platonist entities). Maddy argued that when an egg carton is opened, a set of three eggs is perceived (that is, a mathematical en
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https://en.wikipedia.org/wiki/Ana%20Justel
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Ana María Justel Eusebio is a Spanish statistician and Antarctic scientist specializing in nonparametric statistics, including work on multivariate versions of the Kolmogorov–Smirnov test and on mixture models, and applications to the limnology and meteorology of Antarctica. She is a professor of statistics at the Autonomous University of Madrid.
Education and career
Justel earned a licenciate in mathematics from the Complutense University of Madrid in 1990, and earned a doctorate in statistics and econometrics from Charles III University of Madrid in 1995, with the dissertation Algoritmos adaptativos de Gibbs Sampling para la identificación de heterogeneidad en regresión y series temporales.
After postdoctoral research at the Université catholique de Louvain, she joined the staff at the Autonomous University of Madrid in 1996; her position there was made permanent in 2000.
Recognition
Justel won the inaugural Margarita Salas Prize of the Talent Woman initiative, in 2019.
References
External links
Home page
Year of birth missing (living people)
Living people
Spanish statisticians
Women statisticians
Complutense University of Madrid alumni
Charles III University of Madrid alumni
Academic staff of the Autonomous University of Madrid
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https://en.wikipedia.org/wiki/Modified%20half-normal%20distribution
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In probability theory and statistics, the family of modified half-normal distributions (MHN)
is a three-parameter family of continuous probability distributions supported on the positive part of the real line. The truncated normal distribution, half-normal distribution, and square root of the gamma distribution are special cases of the modified half-normal distribution. The name of the distribution is motivated by the similarities of its density function with that of the half-normal distribution.
The MHN distribution can not only be used a probability model but it appears in a number of Markov chain Monte Carlo (MCMC) based Bayesian procedures including the Bayesian modeling of the directional data, Bayesian binary regression, Bayesian graphical model.
In Bayesian analysis new distributions often appear as a conditional posterior distribution; usage for many such probability distributions are too contextual, and they may not carry significance in a broader perspective. Additionally, many such distributions lack tractable representation of its distributional aspects, such as the known functional form of the normalizing constant. However, the MHN distribution occurs in the diverse areas of research signifying its relevance to the contemporary Bayesian statistical modeling and associated computation. Additionally, the moments and its other moment-based statistics (including variance and skewness) can be represented via the Fox–Wright Psi functions. There exists a recursive relation between the three consecutive moments of the distribution. It is not only be helpful in developing a efficient approximation for the mean of the distribution but also beneficial to construct moment-based estimation of its parameters. Note that the family of MHN distributions can be viewed as a generalizations of multiple families including half normal, truncated normal, square root of a gamma, and gamma distributions. Therefore, it is a flexible probability model to analyzing real valued positive data.
Definitions
The probability density function of the distribution is
where
denotes the Fox–Wright Psi function.
The connection between the normalizing constant of the distribution and the Fox–Wright function in provided in Sun, Kong, Pal.
The cumulative distribution function (CDF) is
where , denotes the lower incomplete gamma function.
Properties
The modified half normal distribution is an exponential family of distributions. Therefore, the properties of the exponential family of distributions are automatically applicable to the MHN distribution.
Moments
Let then for , then assuming to be a positive real number,
If , then
The variance of the distribution is
Moment generating function
The moment generating function of the distribution is given as
Modal characterization of MHN
Consider the MHN with , and .
The probability density function of the distribution is log-concave if .
The mode of the distribution is located at .
If
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https://en.wikipedia.org/wiki/1994%E2%80%9395%20Rochdale%20A.F.C.%20season
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The 1994–95 season saw Rochdale compete in their 21st consecutive season in the fourth tier of the English football league, named at the time as the Football League Third Division.
Statistics
|}
Final League Table
Competitions
Football League Third Division
F.A. Cup
Football League Cup (Coca Cola Cup)
Football League Trophy (Auto Windscreens Shield)
Lancashire Cup
Rose Bowl
References
Rochdale A.F.C. seasons
Rochdale
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https://en.wikipedia.org/wiki/Daiki%20Sato%20%28footballer%2C%20born%201999%29
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is a Japanese footballer currently playing as a forward for Machida Zelvia as a designated special player.
Career statistics
Club
.
Notes
References
External links
1999 births
Living people
People from Ebetsu, Hokkaido
Association football people from Hokkaido
Hosei University alumni
Japanese men's footballers
Men's association football forwards
J2 League players
FC Machida Zelvia players
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https://en.wikipedia.org/wiki/Koki%20Inoue%20%28footballer%29
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is a Japanese footballer currently playing as a defender for Azul Claro Numazu.
Career statistics
Club
.
Notes
References
External links
2001 births
Living people
Association football people from Kyoto Prefecture
Japanese men's footballers
Men's association football defenders
J3 League players
Japan Football League players
Kyoto Sanga FC players
Azul Claro Numazu players
Suzuka Point Getters players
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https://en.wikipedia.org/wiki/Li%20Xingxian
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Li Xingxian (; born 24 March 2005) is a Chinese footballer currently playing as a forward for Guangzhou.
Career statistics
Club
.
References
2005 births
Living people
Chinese men's footballers
Men's association football forwards
Guangzhou F.C. players
Chinese Super League players
21st-century Chinese people
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https://en.wikipedia.org/wiki/Chen%20Guanxuan
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Chen Guanxuan (; born 26 February 2005) is a Chinese footballer currently playing as a defender for Guangzhou.
Career statistics
Club
.
References
2005 births
Living people
Chinese men's footballers
Men's association football defenders
Guangzhou F.C. players
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https://en.wikipedia.org/wiki/Zhou%20Pinxi
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Zhou Pinxi (; born 23 April 2001) is a Chinese footballer currently playing as a midfielder for Jiangxi Dark Horse Junior, on loan from Guangzhou.
Career statistics
Club
.
References
2001 births
Living people
Chinese men's footballers
Men's association football midfielders
China League One players
Guangzhou F.C. players
Inner Mongolia Zhongyou F.C. players
21st-century Chinese people
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https://en.wikipedia.org/wiki/Kenneth%20L.%20Cooke
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Kenneth L. Cooke (August 13, 1925August 25, 2007) was an American mathematical biologist known for his contributions to the study of epidemics. He was the W. M. Keck Professor of Mathematics at Pomona College in Claremont, California.
Early life and education
Cooke was born in Kansas City, Missouri, in 1925. He enrolled at Pomona College, graduating in 1947 after serving in the Navy as a radar and radio technician during World War II. He subsequently earned a doctorate in mathematics from Stanford University.
Career
Cooke taught at Washington State University for seven years. He then joined the Pomona faculty in 1957 and remained at the college for the rest of his career. He was promoted to a named professorship in 1985.
His work on epidemics involved modeling parameters under which a disease will spread or die out. He studied HIV/AIDS and other contagious diseases. His work also involved delay differential equations.
References
20th-century American mathematicians
1925 births
2007 deaths
Pomona College alumni
Stanford University alumni
Washington State University faculty
Pomona College faculty
Mathematical and theoretical biology
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https://en.wikipedia.org/wiki/Kathi%20Irvine
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Kathryn Mary (Kathi) Irvine is an American research statistician for the United States Geological Survey (USGS), affiliated with the Bozeman Environmental and Ecological Statistics Research Group, at the USGS Northern Rocky Mountain Science Center in Bozeman, Montana. Her research involves environmental statistics including both the fundamentals of spatial statistics and its application to wildlife populations including bats, pikas, elk, pine trees, and sagebrush steppes.
Education and career
Irvine majored in biology at the University of North Carolina at Chapel Hill. She has a master's degree in ecology and environmental sciences from the University of Maine, and a second master's degree and PhD in statistics from Oregon State University, completed in 2007. Her dissertation, Graphical models for multivariate spatial data, was supervised by Alix Gitelman.
She became an assistant professor at Montana State University in 2008 before moving to the USGS in 2011. Beyond the USGS, she is a member of the core planning team of the North American Bat Monitoring Program, and maintains an affiliate faculty position in statistics at Montana State University.
Service and recognition
Irvine was the 2018 chair of the American Statistical Association (ASA) Section on Statistics and the Environment, has been president of the Montana Chapter of the ASA several times, and has been publications chair for the ASA Section on Government Statistics. She was named a Fellow of the American Statistical Association in 2021.
References
External links
Year of birth missing (living people)
Living people
American statisticians
American women statisticians
University of North Carolina at Chapel Hill alumni
University of Maine alumni
Oregon State University alumni
Montana State University faculty
United States Geological Survey personnel
Fellows of the American Statistical Association
21st-century American women
Spatial statisticians
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https://en.wikipedia.org/wiki/Damla%20%C5%9Eent%C3%BCrk
|
Damla Şentürk is a Turkish-American biostatistician and professor of biostatistics in the University of California, Los Angeles Fielding School of Public Health whose interests include longitudinal studies, functional data analysis, and applications of biostatistics in the study of autism and of dialysis outcomes.
Education and career
Şentürk studied mathematics at Boğaziçi University, graduating in 1999. She came to the University of California, Davis for graduate study in statistics, earned a master's degree in 2001, and completed her PhD at Davis in 2004. Her dissertation, Covariate Adjusted Regression and Correlation, was supervised by Hans-Georg Müller.
She became an assistant professor of statistics at Pennsylvania State University in 2004, and moved to the UCLA Department of Biostatistics in 2011, adding a joint appointment with the UCLA Department of Statistics in 2014.
Recognition
Şentürk became an Elected Member of the International Statistical Institute in 2006. She was named a Fellow of the American Statistical Association in 2020.
References
External links
Year of birth missing (living people)
Living people
American statisticians
American women statisticians
Turkish statisticians
Turkish women scientists
Biostatisticians
Boğaziçi University alumni
University of California, Davis alumni
UCLA School of Public Health faculty
Elected Members of the International Statistical Institute
Fellows of the American Statistical Association
21st-century American women
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https://en.wikipedia.org/wiki/Wilberd%20van%20der%20Kallen
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Wilberd Leo Johan van der Kallen (born 15 January 1947 in Nieuwer-Amstel) is a Dutch mathematician.
W. L. J. van der Kallen completed his undergraduate study of mathematics and physics at Utrecht University. There he received his PhD in 1973 with thesis advisor T. A. Springer and thesis Infinitesimally central extensions of Chevalley groups. In 1969 van der Kallen became a teaching assistant in Utrecht University's Mathematics Department and has spent his career there, eventually becoming a tenured professor. His research deals with algebraic K-theory and the representation theory of algebraic groups, among other topics. He has frequently been a visiting professor at Northwestern University in Evanston, Illinois and at the Tata Institute of Fundamental Research in Mumbai.
He is the author or coauthor of over 60 research articles. In 1977 he published an analogue of a 1977 theorem of Andrei Suslin and a generalization of a 1969 theorem of Hideya Matsumoto. In 1978 van der Kallen was an invited speaker at the International Congress of Mathematicians in Helsinki. His 1980 paper Homology stability for linear groups has over 200 citations. His 1977 paper Rational and generic cohomology, written with 3 other mathematicians, has over 240 citations.
Books
References
External links
20th-century Dutch mathematicians
21st-century Dutch mathematicians
Utrecht University alumni
Academic staff of Utrecht University
1947 births
Living people
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https://en.wikipedia.org/wiki/Alexander%20A.%20Voronov
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Alexander A. Voronov () (born November 25, 1962) is a Russian-American mathematician specializing in mathematical physics, algebraic topology, and algebraic geometry. He is currently a Professor of Mathematics at the University of Minnesota and a Visiting Senior Scientist at the Kavli Institute for the Physics and Mathematics of the Universe.
Biography
Voronov graduated from Moscow State School 57 in 1980. He received an M.S. in Mathematics in 1985 and a Ph.D. in Mathematics at Moscow State University in 1988 under Yuri I. Manin. Alexander Voronov is known for his work on the super Mumford isomorphism (see Mumford measure), semi-infinite cohomology, operads in quantum field theory (see Swiss-cheese operad), Deligne's and Kontsevich's conjectures on Hochschild cohomology, cohomology of vertex operator algebras, and string topology (see cactus operad). He is a Fellow of the American Mathematical Society, an AMS Centennial Fellow,, a Simons Fellow, and a 2010 Japan Society for the Promotion of Science (JSPS) Research Fellow.
Selected publications
References
External links
Alexander Voronov's University of Minnesota web page
Living people
University of Minnesota faculty
Michigan State University faculty
Mathematicians from Moscow
21st-century American mathematicians
20th-century American mathematicians
Russian emigrants to the United States
Moscow State University alumni
Fellows of the American Mathematical Society
1962 births
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https://en.wikipedia.org/wiki/%C3%9Clo%20Lumiste
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Ülo Lumiste (30 June 1929 Vändra – 20 November 2017) was an Estonian mathematician.
In 1952 he graduated from the University of Tartu in mathematics. In 1968 he defended his doctoral thesis at Kazan University. Since 1959 he taught at the University of Tartu.
Since 1993 he was a member of Estonian Academy of Sciences.
His main field of research was differential geometry. In 1960s he established the school of Estonian differential geometry.
Awards
1999 and 2012: Estonian State Science Prize
1999: Order of the White Star, III class.
References
1929 births
2017 deaths
Estonian mathematicians
University of Tartu alumni
Academic staff of the University of Tartu
Recipients of the Order of the White Star, 3rd Class
People from Vändra
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https://en.wikipedia.org/wiki/Yosei%20Sato
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is a Japanese footballer who plays as a forward.
Club career
Sato made his professional debut in a 1–2 Emperor's Cup loss against V-Varen Nagasaki.
Career statistics
Club
.
Notes
References
External links
2003 births
Living people
Association football people from Hokkaido
Japanese men's footballers
Men's association football forwards
Hokkaido Consadole Sapporo players
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https://en.wikipedia.org/wiki/2020%20Philippine%20census
|
The 2020 Census of Population and Housing (CPH) is the fifteenth census in the Philippines and is the second census conducted by the Philippine Statistics Authority.
Pilot run
The Philippine Statistics Authority (PSA) conducted a pilot run of the census from May 20 to June 17, 2019 covering eight areas. A new computer-aided system was tested, with PSA personnel to use an electronic questionnaire through digital tablets.
Postponement
The census was originally scheduled to start on May 4, 2020. The conduct of the census was postponed due to the COVID-19 pandemic. The census was planned to be held sometime after the lifting of the enhanced community quarantine in Luzon which was imposed as a response to the health crisis. The start of census was then rescheduled for September 2020.
Collection
Methods
The PSA used various methods for the conduct of the 2020 census namely:
Online census – with participants to be contacted through email and given access numbers
Face-to-face interview by enumerators – with the dissemination of the survey either through pen and paper or computer tablets
Scheduled phone interviews
Self-filling of questionnaire to be collected by an enumerator
The conduct of the census through online means was limited due to many households in the country's rural areas has no access to internet infrastructure. The online census covered 2,000 households – mostly with members affiliated with the PSA and other government agencies.
All persons to be enumerated as members of a household or as residents of an institutional living quarter were those alive as of 12:01 a.m. of May 1, 2020
The 2020 census coincided with the rollout of the PhilSys national ID program but the PSA could not legally collect data from the national ID system for the census.
Enumerators and supervisors
The PSA hired 140,000 people to serve as data enumerators and census supervisors for the 2020 census. Due to the COVID-19 pandemic, they were required to wear face masks and shields and observe social distancing when conducting the census as precaution against COVID-19. Prior to the postponement of the census due to the COVID-19 pandemic, the PSA planned to employ public school teachers for the conduct of the census. Such plans were abandoned after the opening of classes in public schools was postponed to October due to the pandemic.
Results
President Rodrigo Duterte through Proclamation No. 1179 stated that the population of the Philippines as of May 1, 2020 was 109,035,343. Pursuant to Batas Pambansa No. 72, the population count gathered from the 2020 census was made official upon proclamation of the results by the president. From 2015 to 2020, the Philippines' population increased by 1.63% which is lower than the 1.72% growth rate recorded in the 2010 to 2015 period.
Calabarzon was determined to be the most populated region as of 2020 with 16.20 million people. The most populated province was found to be Cavite (4.34 million) and the least populated being Ba
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https://en.wikipedia.org/wiki/Taiyo%20Nishino
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is a Japanese footballer currently playing as a forward for Tokushima Vortis.
Career statistics
Club
.
Notes
References
External links
2002 births
Living people
People from Tokushima (city)
Association football people from Tokushima Prefecture
Japanese men's footballers
Men's association football forwards
J1 League players
Tokushima Vortis players
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https://en.wikipedia.org/wiki/Douglas%20Clements
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Douglas H. Clements is an American scholar in the field of early mathematics education. Previously a preschool and kindergarten teacher, his research centers on the learning and teaching of early mathematics, computer applications for mathematics teaching, and scaling up successful educational interventions. Clements has contributed to the writing of educational standards including the Common Core State Standards, the NCTM's Principles and Standards for School Mathematics and the NCTM's 2006 Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics.
As of 2021, he is Distinguished University Professor and the Kennedy Endowed Chair in Early Childhood Learning at the University of Denver and the co-director of the Marsico Institute for Early Learning. He was previously a SUNY Distinguished Professor at the University at Buffalo.
Subitizing
Clements is notable for reviving interest in the importance of perceptual and conceptual subitizing in early childhood mathematics education. Perceptual subitizing is the ability to instantly recognise the number of objects in a small group, without counting. Conceptual subitising is the ability to see a whole quantity as groups of smaller quantities (for example, seeing eight as two groups of four). When learning to count, young children use subitizing to develop their understanding of cardinality. They also use their conceptual subitizing and pattern recognition skills to develop their understanding of arithmetic and number sense.
Building Blocks and Learning Trajectories
Together with Julie Sarama, Clements developed the Building Blocks curriculum and the Learning Trajectories approach to early mathematics education. Learning trajectories consist of a learning goal, a developmental path along which children develop to reach that goal, and a set of activities matched to each level in that learning path. Clements has evaluated this approach in randomized controlled trials and shown it to have a positive impact on children's learning. This research has influenced evidence reviews and teaching guidance produced by the Education Endowment Foundation in the UK and the What Works Clearinghouse in the USA.
Personal life
Clements is married to fellow early mathematics researcher and collaborator Professor Julie Sarama. He has four children: Luke Clements, Abby Clements, Leah Meredith, and Ryan Clements.
External links
Learning Trajectories website
Douglas Clements on Twitter
Portfolio on University of Denver website
References
1950 births
Educators from New York (state)
Education writers
University of Denver faculty
Mathematical cognition researchers
Living people
Early childhood education
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https://en.wikipedia.org/wiki/Izreen%20Izwandy
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Muhammad Izreen bin Izwandy (born 16 July 2000) is a Malaysian footballer who plays as a midfielder for Kuala Lumpur City.
Career statistics
Club
Honour
Club
KL City FC
Malaysia Cup: 2021
References
External links
2000 births
Living people
Footballers from Penang
Kuala Lumpur City F.C. players
Malaysian men's footballers
Men's association football midfielders
Malaysia Super League players
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https://en.wikipedia.org/wiki/Park%20Jin-seong
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Park Jin-seong (; born 15 May 2001) is a South Korean footballer currently playing as a left-back for Jeonbuk Hyundai Motors.
Career statistics
Club
Notes
References
2001 births
Living people
Yonsei University alumni
South Korean men's footballers
South Korea men's youth international footballers
Men's association football defenders
K League 1 players
Jeonbuk Hyundai Motors players
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https://en.wikipedia.org/wiki/Spherical%20conic
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In mathematics, a spherical conic or sphero-conic is a curve on the sphere, the intersection of the sphere with a concentric elliptic cone. It is the spherical analog of a conic section (ellipse, parabola, or hyperbola) in the plane, and as in the planar case, a spherical conic can be defined as the locus of points the sum or difference of whose great-circle distances to two foci is constant. By taking the antipodal point to one focus, every spherical ellipse is also a spherical hyperbola, and vice versa. As a space curve, a spherical conic is a quartic, though its orthogonal projections in three principal axes are planar conics. Like planar conics, spherical conics also satisfy a "reflection property": the great-circle arcs from the two foci to any point on the conic have the tangent and normal to the conic at that point as their angle bisectors.
Many theorems about conics in the plane extend to spherical conics. For example, Graves's theorem and Ivory's theorem about confocal conics can also be proven on the sphere; see confocal conic sections about the planar versions.
Just as the arc length of an ellipse is given by an incomplete elliptic integral of the second kind, the arc length of a spherical conic is given by an incomplete elliptic integral of the third kind.
An orthogonal coordinate system in Euclidean space based on concentric spheres and quadratic cones is called a conical or sphero-conical coordinate system. When restricted to the surface of a sphere, the remaining coordinates are confocal spherical conics. Sometimes this is called an elliptic coordinate system on the sphere, by analogy to a planar elliptic coordinate system. Such coordinates can be used in the computation of conformal maps from the sphere to the plane.
Applications
The solution of the Kepler problem in a space of uniform positive curvature is a spherical conic, with a potential proportional to the cotangent of geodesic distance.
Because it preserves distances to a pair of specified points, the two-point equidistant projection maps the family of confocal conics on the sphere onto two families of confocal ellipses and hyperbolae in the plane.
If a portion of the Earth is modeled as spherical, e.g. using the osculating sphere at a point on an ellipsoid of revolution, the hyperbolae used in hyperbolic navigation (which determines position based on the difference in received signal timing from fixed radio transmitters) are spherical conics.
Notes
References
English edition:
Republished in Journal de mathématiques pures et appliquées. Ser. 2. 5: 425-454. PDF from mathdoc.fr.
Conic sections
Spherical curves
Spherical geometry
Euclidean solid geometry
Algebraic curves
Analytic geometry
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https://en.wikipedia.org/wiki/Zheng%20Zelong
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Zheng Zelong (; born 13 November 1997) is a Chinese footballer currently playing as a midfielder for Shanghai Port.
Career statistics
Club
.
References
1997 births
Living people
Chinese men's footballers
Men's association football midfielders
China League Two players
Shanghai Port F.C. players
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https://en.wikipedia.org/wiki/Zhu%20Jiayi
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Zhu Jiayi (; born 31 January 1999) is a Chinese footballer currently playing as a defender for Chongqing Liangjiang.
Career statistics
Club
.
References
1999 births
Living people
Chinese men's footballers
Men's association football defenders
China League One players
Shanghai Port F.C. players
Inner Mongolia Zhongyou F.C. players
21st-century Chinese people
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https://en.wikipedia.org/wiki/Nie%20Meng
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Nie Meng (; born 7 February 1998) is a Chinese footballer currently playing as a left-back for Dandong Tengyue.
Career statistics
Club
.
References
1998 births
Living people
Chinese men's footballers
China men's youth international footballers
Men's association football defenders
Shanghai Port F.C. players
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https://en.wikipedia.org/wiki/Guo%20Tong
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Guo Tong (; born 19 February 2002) is a Chinese footballer currently playing as a goalkeeper for Ji'nan Xingzhou, on loan from Shanghai Port.
Career statistics
Club
.
References
2002 births
Living people
Chinese men's footballers
China men's youth international footballers
Men's association football goalkeepers
Shanghai Port F.C. players
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https://en.wikipedia.org/wiki/Mengmao
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Mengmao (; ) is a subdistrict in Ruili, Yunnan, China. As of the 2016 statistics it had a population of 104,681 and an area of . It is the political, economic and cultural center of Ruili.
Etymology
"Mengmao" means "foggy place" in Dai language.
Administrative division
As of 2016, the town is divided into seven villages and eight communities:
Youyi Community ()
Luchuan Community ()
Xing'an Community ()
Munao Community ()
Ruifeng Community ()
Menglongsha Community ()
Maoxiang Community ()
Guomen Community ()
Tuanjie ()
Mengmao ()
Jiegang ()
Jiele ()
Jiedong ()
Mangling ()
Mengli ()
History
Mengmao was designated as a town in 1934 by Ruili Shezhi Bureau (). After the establishment of the Communist State in 1949, it came under the jurisdiction of the 1st District of Ruili County. In 1969, during the Cultural Revolution, it was renamed "Mengmao People's Commune" and then "Hongcheng People's Commune" (). After smashing the Gang of Four, the town reverted to its former name of "Mengmao". The Jiele Township (), Yinhe Subdistrict () and Ruihong Subdistrict () were merged into Mengmao in January 2005. In October 2006, Tuanjie Village () and Maoxiang Community () of Ruili Border Economic Cooperation Zone were merged into Mengmao. Yunnan provincial government approve revoking Mengmao Town and establish Mengmao Subdistrict on 11 August 2021.
Geography
The highest point in the town is Huyong Mountain () which stands above sea level. The lowest point is Bingwu Village (), which, at above sea level. The local forest coverage is 50.48%.
The Shweli River flows through the town.
The Nongmo Lake is an oxbow lake is located in the town.
Economy
The local economy is primarily based upon agriculture and local industry. The main crops are rice, sugarcane, vegetables, medicinal materials, rubber, coffee and grapefruit.
Demographics
In 2016, the local population was 104,681, including 68,357 Han (65.3%), 28,055 Dai (26.8%) and 3,769 Jingpo (3.6%).
Tourist attractions
There are many natural and cultural landscapes in the town, the most famous of which are the Jiele Gold Pagoda, Nong'an Pagoda, Hansha Temple, Pinglu Townsite, Zhaduo Waterfall, and Nongmo Lake.
Transportation
Mengmao is the end of Longling–Ruili Expressway, China National Highway 320, and China National Highway 556.
References
Divisions of Ruili
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https://en.wikipedia.org/wiki/Matrix%20sign%20function
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In mathematics, the matrix sign function is a matrix function on square matrices analogous to the complex sign function.
It was introduced by J.D. Roberts in 1971 as a tool for model reduction and for solving Lyapunov and Algebraic Riccati equation in a technical report of Cambridge University, which was later published in a journal in 1980.
Definition
The matrix sign function is a generalization of the complex signum function
to the matrix valued analogue . Although the sign function is not analytic, the matrix function is well defined for all matrices that have no eigenvalue on the imaginary axis, see for example the Jordan-form-based definition (where the derivatives are all zero).
Properties
Theorem: Let , then .
Theorem: Let , then is diagonalizable and has eigenvalues that are .
Theorem: Let , then is a projector onto the invariant subspace associated with the eigenvalues in the right-half plane, and analogously for and the left-half plane.
Theorem: Let , and be a Jordan decomposition such that corresponds to eigenvalues with positive real part and to eigenvalue with negative real part. Then , where and are identity matrices of sizes corresponding to and , respectively.
Computational methods
The function can be computed with generic methods for matrix functions, but there are also specialized methods.
Newton iteration
The Newton iteration can be derived by observing that , which in terms of matrices can be written as , where we use the matrix square root. If we apply the Babylonian method to compute the square root of the matrix , that is, the iteration , and define the new iterate , we arrive at the iteration
,
where typically . Convergence is global, and locally it is quadratic.
The Newton iteration uses the explicit inverse of the iterates .
Newton–Schulz iteration
To avoid the need of an explicit inverse used in the Newton iteration, the inverse can be approximated with one step of the Newton iteration for the inverse, , derived by Schulz(de) in 1933. Substituting this approximation into the previous method, the new method becomes
.
Convergence is (still) quadratic, but only local (guaranteed for ).
Applications
Solutions of Sylvester equations
Theorem: Let and assume that and are stable, then the unique solution to the Sylvester equation, , is given by such that
Proof sketch: The result follows from the similarity transform
since
due to the stability of and .
The theorem is, naturally, also applicable to the Lyapunov equation. However, due to the structure the Newton iteration simplifies to only involving inverses of and .
Solutions of algebraic Riccati equations
There is a similar result applicable to the algebraic Riccati equation, . Define as
Under the assumption that are Hermitian and there exists a unique stabilizing solution, in the sense that is stable, that solution is given by the over-determined, but consistent, linear system
Proof sketch: The similarity transform
and the stab
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https://en.wikipedia.org/wiki/Nongdao
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Nongdao (; ) is a town in Ruili, Yunnan, China. As of the 2016 statistics it had a population of 14,146 and an area of .
Etymology
The name of "Nongdao" means moss pond in Dai language.
Administrative division
As of 2016, the town is divided into four villages:
Nongdao ()
Dengxiu ()
Leiyun (), also called Lowing
Dengga ()
History
In 1932, the Yunnan government set up the Ruili Administrative Bureau (), the government office was in the town. Two years later, Nongdao was designated as a town. At the end of 1948, the Ruili Incident broke out, the Jingpo people burned down the government office. After the establishment of the Communist State in 1949, it came under the jurisdiction of the 3rd District of Ruili County. During the Cultural Revolution, it was renamed "Weidong People's Commune" () and then "Nongdao People's Commune" (). Nongdao became a district in 1984 and a township in 1986. In February 1993, the Nongdao Economic Development Zone was founded in the town. In May 2000, it was upgraded to a town. In 2005, the economic development zone merged into the town. In 2013, Ruili government moved the Ruili Border Economic Cooperation Zone to Nongdao.
Geography
Nongdao is located at the confluence of Namwan River and Shweli River.
The town is located in the southwestern Ruili and borders Myanmar in the northwest, southwest and southeast, with a border of .
The highest point in the town is Sanda Mountain () which stands above sea level. The lowest point is Rongbangwang (), which, at above sea level.
Economy
The town's economy is based on nearby border trade and agricultural resources. The main crops are rice, sugarcane and tobacco.
The Ruili Border Economic Cooperation Zone is located in the town.
The Sino-Myanmar pipelines enters China from the town.
Demographics
In 2016, the local population was 14,146, including 2,167 Han (15.3%), 10,920 Dai (77.2%) and 1,018 Jingpo (7.2%).
Tourist attractions
The Site of Central Aircraft Manufacturing Company (Lowing Factory) and Mang'ai Temple are popular attractions in the town.
Transportation
The Longling–Ruili Expressway passes across the town.
References
Bibliography
Divisions of Ruili
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https://en.wikipedia.org/wiki/Patricia%20Wiberg
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Patricia Wiberg is a professor at University of Virginia known for her research on the transport of sediments in aquatic environments.
Education and career
Wiberg has a B.A. in mathematics from Brown University (1976), and an M.S. (1983) and a Ph.D. (1987) from the University of Washington. Wiberg is a fellow of the American Geophysical Union, and a fellow of the American Association for the Advancement of Science who cited her "for distinguished contributions to understanding the causes and consequences of sediment movements in aquatic systems."
Research
Wiberg studies coastal environments with a focus on how disturbances such as storms, sea-level rise, and temperature change coastal areas Through her integration of data and models, she examines changes in salt marshes in the context of environmental changes. While in graduate school, Wiberg and colleagues found evidence in the Brazos River beds in Texas for a tsunami that was at least 1000 feet high which would have occurred at the Cretaceous-Tertiary boundary. She has also examined the impact of the shape of sediments on eddy correlation flux measurements. Since 2006, Wiberg has been a co-principal investigator at the National Science Foundation-funded Virginia Coast Reserve Long-Term Ecological Research where she has been working on water and sediment dynamics.
Selected publications
Awards and honors
Fellow, American Geophysical Union (2017)
Fellow, American Association for the Advancement of Science (2020)
References
External links
Fellows of the American Geophysical Union
Brown University alumni
University of Washington alumni
University of Virginia faculty
Women hydrologists
Living people
Year of birth missing (living people)
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https://en.wikipedia.org/wiki/Asnan%20Ahmad
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Asnan bin Ahmad (born 3 May 1993) is a Malaysian professional footballer who plays as a defensive midfielder for Penang.
Career statistics
Club
References
1993 births
Living people
Malaysian men's footballers
Malaysia Super League players
UKM F.C. players
Terengganu FC players
Kedah Darul Aman F.C. players
Penang F.C. players
Footballers from Kedah
Malaysian people of Malay descent
Men's association football midfielders
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https://en.wikipedia.org/wiki/Fairuz%20Zakaria
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Mohammad Fairuz bin Zakaria (born 25 May 1997) is a Malaysian professional footballer who plays as a left-back for Penang.
Career statistics
Club
References
External links
1997 births
Living people
Footballers from Kedah
Malaysian men's footballers
Men's association football fullbacks
Men's association football defenders
Malaysia Super League players
Perlis F.A. players
Penang F.C. players
Kedah Darul Aman F.C. players
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