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https://en.wikipedia.org/wiki/Muxuyuan%20station | Muxuyuan (Ming Xiaoling Mausoleum) Station is a railway station on Line 2 of Nanjing Metro. It started operations on 28 May 2010 along with the rest of Line 2.
Statistics
It has a length of , a width of , a height of , and it covers an area of .
Decorations
Since Line 2 of the Nanjing Metro is centered on Chinese traditional festivals, the theme of this station's decorations is the Qixi Festival. At , It features the largest painting area of any Line 2 station, if not the entire Nanjing Metro system. Several traditional romance stories can be seen if one looks up at the ceiling, such as Niulang and Zhinü, Houyi and Chang'e and so on.
In April 2013, the station became the second in the Nanjing Metro system, after , to install a set of "musical stairs" leading up from the station platform. The stairs, christened "music stairs" (), were intended to play chords from the Butterfly Lovers' Violin Concerto whenever passengers would use the stairs. However, repeated wear and tear on the steps has caused loss of this unique functionality.
Gallery
Around the station
Ming Xiaoling Mausoleum
Nanjing Botanical Garden, Memorial Sun Yat-Sen
References
Nanjing Metro stations
Railway stations in China opened in 2010 |
https://en.wikipedia.org/wiki/Adl%C3%A8ne%20Boutnaf | Adlène Boutnaf (born 23 February 1984 in Hussein Dey, Algiers) is an Algerian professional footballer. He currently plays as a defender for the Algerian Ligue 2 club Olympique de Médéa.
Statistics
References
External links
1984 births
Living people
Algerian men's footballers
Olympique de Médéa players
CR Belouizdad players
NA Hussein Dey players
USM Bel Abbès players
OMR El Annasser players
AS Khroub players
MC Saïda players
Footballers from Algiers
Algerian Ligue Professionnelle 1 players
Algerian Ligue 2 players
Algeria men's under-23 international footballers
Men's association football defenders
21st-century Algerian people |
https://en.wikipedia.org/wiki/1936%E2%80%9337%20Swedish%20football%20Division%203 | Statistics of Swedish football Division 3 for the 1936–37 season.
League standings
Uppsvenska Östra 1936–37
Uppsvenska Västra 1936–37
Östsvenska 1936–37
Mellansvenska 1936–37
Nordvästra 1936–37
Södra Mellansvenska 1936–37
Sydöstra 1936–37
Västsvenska Norra 1936–37
Västsvenska Södra 1936–37
Sydsvenska 1936–37
Footnotes
References
Swedish Football Division 3 seasons
3
Sweden |
https://en.wikipedia.org/wiki/1937%E2%80%9338%20Swedish%20football%20Division%203 | Statistics of Swedish football Division 3 for the 1937–38 season.
League standings
Uppsvenska Östra 1937–38
Uppsvenska Västra 1937–38
Östsvenska 1937–38
Centralserien Norra 1937–38
Centralserien Södra 1937–38
Nordvästra 1937–38
Södra Mellansvenska 1937–38
Sydöstra 1937–38
Västsvenska Norra 1937–38
Västsvenska Södra 1937–38
Sydsvenska 1937–38
Footnotes
References
Swedish Football Division 3 seasons
3
Sweden |
https://en.wikipedia.org/wiki/Zahlbericht | In mathematics, the Zahlbericht (number report) was a report on algebraic number theory by .
History
In 1893 the German Mathematical Society invited Hilbert and Minkowski to write reports on the theory of numbers. They agreed that Minkowski would cover the more elementary parts of number theory while Hilbert would cover algebraic number theory. Minkowski eventually abandoned his report, while Hilbert's report was published in 1897. It was reprinted in volume 1 of his collected works, and republished in an English translation in 1998.
and and the English introduction to give detailed discussions of the history and influence of Hilbert's Zahlbericht.
Some earlier reports on number theory include the report by H. J. S. Smith in 6 parts between 1859 and 1865, reprinted in , and the report by . wrote an update of Hilbert's Zahlbericht that covered class field theory (republished in 1 volume as ).
Contents
Part 1 covers the theory of general number fields, including ideals, discriminants, differents, units, and ideal classes.
Part 2 covers Galois number fields, including in particular Hilbert's theorem 90.
Part 3 covers quadratic number fields, including the theory of genera, and class numbers of quadratic fields.
Part 4 covers cyclotomic fields, including the Kronecker–Weber theorem (theorem 131), the Hilbert–Speiser theorem (theorem 132), and the Eisenstein reciprocity law for lth power residues (theorem 140) .
Part 5 covers Kummer number fields, and ends with Kummer's proof of Fermat's last theorem for regular primes.
References
External links
Introduction to the English Edition of Hilbert's Zahlbericht
1897 in science
1897 non-fiction books
Algebraic number theory
History of mathematics
Mathematics books
Treatises |
https://en.wikipedia.org/wiki/1938%E2%80%9339%20Swedish%20football%20Division%203 | Statistics of Swedish football Division 3 for the 1938–39 season.
League standings
Uppsvenska Östra 1938–39
Uppsvenska Västra 1938–39
Östsvenska 1938–39
Centralserien Norra 1938–39
Centralserien Södra 1938–39
Nordvästra 1938–39
Mellansvenska 1938–39
Sydöstra 1938–39
Västsvenska Norra 1938–39
Västsvenska Södra 1938–39
Sydsvenska 1938–39
Footnotes
References
Swedish Football Division 3 seasons
3
Sweden |
https://en.wikipedia.org/wiki/Effective%20domain | In convex analysis, a branch of mathematics, the effective domain extends of the domain of a function defined for functions that take values in the extended real number line
In convex analysis and variational analysis, a point at which some given extended real-valued function is minimized is typically sought, where such a point is called a global minimum point. The effective domain of this function is defined to be the set of all points in this function's domain at which its value is not equal to It is defined this way because it is only these points that have even a remote chance of being a global minimum point. Indeed, it is common practice in these fields to set a function equal to at a point specifically to that point from even being considered as a potential solution (to the minimization problem). Points at which the function takes the value (if any) belong to the effective domain because such points are considered acceptable solutions to the minimization problem, with the reasoning being that if such a point was not acceptable as a solution then the function would have already been set to at that point instead.
When a minimum point (in ) of a function is to be found but 's domain is a proper subset of some vector space then it often technically useful to extend to all of by setting at every By definition, no point of belongs to the effective domain of which is consistent with the desire to find a minimum point of the original function rather than of the newly defined extension to all of
If the problem is instead a maximization problem (which would be clearly indicated) then the effective domain instead consists of all points in the function's domain at which it is not equal to
Definition
Suppose is a map valued in the extended real number line whose domain, which is denoted by is (where will be assumed to be a subset of some vector space whenever this assumption is necessary).
Then the of is denoted by and typically defined to be the set
unless is a concave function or the maximum (rather than the minimum) of is being sought, in which case the of is instead the set
In convex analysis and variational analysis, is usually assumed to be unless clearly indicated otherwise.
Characterizations
Let denote the canonical projection onto which is defined by
The effective domain of is equal to the image of 's epigraph under the canonical projection That is
For a maximization problem (such as if the is concave rather than convex), the effective domain is instead equal to the image under of 's hypograph.
Properties
If a function takes the value such as if the function is real-valued, then its domain and effective domain are equal.
A function is a proper convex function if and only if is convex, the effective domain of is nonempty, and for every
See also
References
Convex analysis
Functions and mappings |
https://en.wikipedia.org/wiki/Siegel%20domain | In mathematics, a Siegel domain or Piatetski-Shapiro domain is a special open subset of complex affine space generalizing the Siegel upper half plane studied by . They were introduced by in his study of bounded homogeneous domains.
Definitions
A Siegel domain of the first kind (or first type, or genus 1) is the open subset of Cm of elements z such that
where V is an open convex cone in Rm. These are special cases of tube domains. An example is the Siegel upper half plane, where V⊂Rk(k + 1)/2 is the cone of positive definite quadratic forms in Rk and m = k(k + 1)/2.
A Siegel domain of the second kind (or second type, or genus 2), also called a Piatetski-Shapiro domain, is the open subset of Cm×Cn of elements (z,w) such that
where V is an open convex cone in Rm and F is a V-valued Hermitian form on Cn.
If n = 0 this is a Siegel domain of the first kind.
A Siegel domain of the third kind (or third type, or genus 3) is the open subset of Cm×Cn×Ck of elements (z,w,t) such that
and t lies in some bounded region
where V is an open convex cone in Rm and Lt is a V-valued semi-Hermitian form on Cn.
Bounded homogeneous domains
A bounded domain is an open connected bounded subset of a complex affine space. It is called homogeneous if its group of automorphisms acts transitively, and is called symmetric if for every point there is an automorphism acting as –1 on the tangent space. Bounded symmetric domains are homogeneous.
Élie Cartan classified the homogeneous bounded domains in dimension at most 3 (up to isomorphism), showing that they are all Hermitian symmetric spaces. There is 1 in dimension 1 (the unit ball), two in dimension 2 (the product of two 1-dimensional complex balls or a 2-dimensional complex ball). He asked whether all bounded homogeneous domains are symmetric. answered Cartan's question by finding a Siegel domain of type 2 in 4 dimensions that is homogeneous and biholomorphic to a bounded domain but not symmetric. In dimensions at least 7 there are infinite families of homogeneous bounded domains that are not symmetric.
showed that every bounded homogeneous domain is biholomorphic to a Siegel domain of type 1 or 2.
described the isomorphisms of Siegel domains of types 1 and 2 and the Lie algebra of automorphisms of a Siegel domain. In particular two Siegel domains are isomorphic if and only if they are isomorphic by an affine transformation.
j-algebras
Suppose that G is the Lie algebra of a transitive connected group of analytic automorphisms of a bounded homogeneous domain X, and let K be the subalgebra fixing a point x. Then the almost complex structure j on X induces a vector space endomorphism j of G such that
j2=–1 on G/K
[x,y] + j[jx,y] + j[x,jy] – [jx,jy] = 0 in G/K; this follows from the fact that the almost complex structure of X is integrable
There is a linear form ω on G such that ω[jx,jy]=ω[x,y] and ω[jx,x]>0 if x∉K
if L is a compact subalgebra of G with jL⊆K+L then L⊆K
A j-algebra is a Lie algebra G |
https://en.wikipedia.org/wiki/Midpoint-stretching%20polygon | In geometry, the midpoint-stretching polygon of a cyclic polygon is another cyclic polygon inscribed in the same circle, the polygon whose vertices are the midpoints of the circular arcs between the vertices of . It may be derived from the midpoint polygon of (the polygon whose vertices are the edge midpoints) by placing the polygon in such a way that the circle's center coincides with the origin, and stretching or normalizing the vector representing each vertex of the midpoint polygon to make it have unit length.
Musical application
The midpoint-stretching polygon is also called the shadow of ; when the circle is used to describe a repetitive time sequence and the polygon vertices on it represent the onsets of a drum beat, the shadow represents the set of times when the drummer's hands are highest, and has greater rhythmic evenness than the original rhythm.
Convergence to regularity
The midpoint-stretching polygon of a regular polygon is itself regular, and iterating the midpoint-stretching operation on an arbitrary initial polygon results in a sequence of polygons whose shape converges to that of a regular polygon.
References
Polygons |
https://en.wikipedia.org/wiki/1939%E2%80%9340%20Swedish%20football%20Division%203 | Statistics of Swedish football Division 3 for the 1939–40 season.
League standings
Uppsvenska Östra 1939–40
Uppsvenska Västra 1939–40
Östsvenska 1939–40
Centralserien Norra 1939–40
Centralserien Södra 1939–40
Nordvästra 1939–40
Mellansvenska 1939–40
Sydöstra 1939–40
Västsvenska Norra 1939–40
Västsvenska Södra 1939–40
Sydsvenska 1939–40
Footnotes
References
Swedish Football Division 3 seasons
3
Sweden |
https://en.wikipedia.org/wiki/1940%E2%80%9341%20Swedish%20football%20Division%203 | Statistics of Swedish football Division 3 for the 1940–41 season.
League standings
Uppsvenska Sydöstra 1940–41
Uppsvenska Sydvästra 1940–41
Östsvenska Norra 1940–41
Östsvenska Södra 1940–41
Centralserien Norra 1940–41
Centralserien Södra 1940–41
Nordvästra Norra 1940–41
Nordvästra Södra 1940–41
Mellansvenska Norra 1940–41
Mellansvenska Södra 1940–41
Sydöstra Norra 1940–41
Sydöstra Södra 1940–41
Västsvenska Norra 1940–41
Västsvenska Södra 1940–41
Sydsvenska Norra 1940–41
Sydsvenska Södra 1940–41
Footnotes
References
Swedish Football Division 3 seasons
3
Swed |
https://en.wikipedia.org/wiki/Rep-tile | In the geometry of tessellations, a rep-tile or reptile is a shape that can be dissected into smaller copies of the same shape. The term was coined as a pun on animal reptiles by recreational mathematician Solomon W. Golomb and popularized by Martin Gardner in his "Mathematical Games" column in the May 1963 issue of Scientific American. In 2012 a generalization of rep-tiles called self-tiling tile sets was introduced by Lee Sallows in Mathematics Magazine.
Terminology
A rep-tile is labelled rep-n if the dissection uses n copies. Such a shape necessarily forms the prototile for a tiling of the plane, in many cases an aperiodic tiling.
A rep-tile dissection using different sizes of the original shape is called an irregular rep-tile or irreptile. If the dissection uses n copies, the shape is said to be irrep-n. If all these sub-tiles are of different sizes then the tiling is additionally described as perfect. A shape that is rep-n or irrep-n is trivially also irrep-(kn − k + n) for any k > 1, by replacing the smallest tile in the rep-n dissection by n even smaller tiles. The order of a shape, whether using rep-tiles or irrep-tiles is the smallest possible number of tiles which will suffice.
Examples
Every square, rectangle, parallelogram, rhombus, or triangle is rep-4. The sphinx hexiamond (illustrated above) is rep-4 and rep-9, and is one of few known self-replicating pentagons. The Gosper island is rep-7. The Koch snowflake is irrep-7: six small snowflakes of the same size, together with another snowflake with three times the area of the smaller ones, can combine to form a single larger snowflake.
A right triangle with side lengths in the ratio 1:2 is rep-5, and its rep-5 dissection forms the basis of the aperiodic pinwheel tiling. By Pythagoras' theorem, the hypotenuse, or sloping side of the rep-5 triangle, has a length of .
The international standard ISO 216 defines sizes of paper sheets using the , in which the long side of a rectangular sheet of paper is the square root of two times the short side of the paper. Rectangles in this shape are rep-2. A rectangle (or parallelogram) is rep-n if its aspect ratio is :1. An isosceles right triangle is also rep-2.
Rep-tiles and symmetry
Some rep-tiles, like the square and equilateral triangle, are symmetrical and remain identical when reflected in a mirror. Others, like the sphinx, are asymmetrical and exist in two distinct forms related by mirror-reflection. Dissection of the sphinx and some other asymmetric rep-tiles requires use of both the original shape and its mirror-image.
Rep-tiles and polyforms
Some rep-tiles are based on polyforms like polyiamonds and polyominoes, or shapes created by laying equilateral triangles and squares edge-to-edge.
Squares
If a polyomino is rectifiable, that is, able to tile a rectangle, then it will also be a rep-tile, because the rectangle will have an integer side length ratio and will thus tile a square. This can be seen in the octominoes, which are cr |
https://en.wikipedia.org/wiki/Florian%20Schnitzer | Florian Schnitzer (born January 28, 1981) is a former German professional ice hockey player. He last played for Bietigheim Steelers in the 2nd Bundesliga.
Career statistics
References
External links
1981 births
Living people
Augsburger Panther players
Hamburg Freezers players
Krefeld Pinguine players
SC Bietigheim-Bissingen players
SC Riessersee players
Straubing Tigers players
German ice hockey right wingers
Ice hockey people from Garmisch-Partenkirchen |
https://en.wikipedia.org/wiki/Aek%20Godang%20Airport | Aek Godang Airport is an airport in South Tapanuli Regency, North Sumatra, Indonesia.
Airlines and destinations
The following destinations are served from this airport:
Statistics
References
Airports in North Sumatra |
https://en.wikipedia.org/wiki/1941%E2%80%9342%20Swedish%20football%20Division%203 | Statistics of Swedish football Division 3 for the 1941–42 season.
League standings
Uppsvenska Sydöstra 1941–42
Uppsvenska Sydvästra 1941–42
Östsvenska Norra 1941–42
Östsvenska Södra 1941–42
Centralserien Norra 1941–42
Centralserien Södra 1941–42
Nordvästra Norra 1941–42
Nordvästra Södra, Dalsland 1941–42
Nordvästra Södra, Bohus 1941–42
Mellansvenska Norra 1941–42
Mellansvenska Södra 1941–42
Sydöstra Norra 1941–42
Sydöstra Södra 1941–42
Västsvenska Norra 1941–42
Västsvenska Södra 1941–42
Sydsvenska Norra 1941–42
Sydsvenska Södra 1941–42
Footnotes
References
Swedish Football Division 3 seasons
3
Swed |
https://en.wikipedia.org/wiki/1942%E2%80%9343%20Swedish%20football%20Division%203 | Statistics of Swedish football Division 3 for the 1942–43 season.
League standings
Uppsvenska Sydöstra 1942–43
Uppsvenska Sydvästra 1942–43
Östsvenska Norra 1942–43
Östsvenska Södra 1942–43
Centralserien Norra 1942–43
Centralserien Södra 1942–43
Nordvästra Norra 1942–43
Nordvästra Södra, Dalsland 1942–43
Nordvästra Södra, Bohus 1942–43
Mellansvenska Norra 1942–43
Mellansvenska Södra 1942–43
Sydöstra Norra 1942–43
Sydöstra Södra 1942–43
Västsvenska Norra 1942–43
Västsvenska Södra 1942–43
Sydsvenska Norra 1942–43
Sydsvenska Södra 1942–43
Footnotes
References
Swedish Football Division 3 seasons
3
Swed |
https://en.wikipedia.org/wiki/List%20of%20A.D.%20Isidro%20Metapan%20records%20and%20statistics | This page details Isidro Metapán records.
Honours
Domestic competitions
Primera División
Winner (10): Clausura 2007, Apertura 2008, Clausura 2009, Clausura 2010, Apertura 2010, Apertura 2011, Apertura 2012, Apertura 2013, Clausura 2014, Apertura 2014
Liga de Ascenso
Winner (1): 2000–01
Player records
Appearances
Youngest
Youngest first-team player – TBD, - years - days (v. TBD, TBD, TBD)
Youngest first-team player in the First Division – TBD, - years - days (v. TBD, Premier League, TBD)
Youngest first-team player in an Official Concacaf Competition – TBD, - years - days (v. TBD, TBD, TBD)
Oldest
Oldest first-team player – TBD, - years - days (v. TBD, TBD, TBD)
Oldest first-team player in the First Division - TBD, - years - days (v. TBD, TBD)
Oldest first-team player in an Official Concacaf competition – TBD, - years - days (v. TBD, TBD, TBD)
Oldest first-team debutant – TBD, - years - days (v. TBD, TBD, TBD)
Most Number of Appearances
Competitive, professional matches only including substitution, number of appearances as a substitute appears in brackets.
Last updated -
Current player with most appearances – Milton Molina, 366 (18), as of 2010
Most consecutive appearances – TBA, - (TBD – TBD)
Most separate spells with the club - TBD, - (TBA)
Concacaf appearances
As of 16 November 2015 (October2011)
Goalscorers
In a season
Most goals in a season – 14, Williams Reyes (-)
Most League goals in a season – ?, TBD, (TBD)
Most Primera Division goals in a season 14, Williams Reyes, (TBD)
In a single match
Most goals in a single match – ?, TBD (v. TBD, TBD, )
Most goals in a single match at home – ?, TBD (v. TBD, TBD, date unknown)
Most goals in a single First Division away match - 4 TBD (v. TBD, date Unknown)
Most goals in a Concacaf competition match – 3 Nicolás Muñoz (v. Puerto Rico Islanders, CONCACAF Champions League, August 2, 2012)
Fastest recorded goal – ? seconds, TBD (v. TBD, TBD, )
Fastest recorded goal in a First Division Match – 24 seconds, Spaniard Gregori Diaz (v. C.D. Platense Municipal Zacatecoluca, 3 April 2022)
Youngest and oldest
Youngest goalscorer – TBD, - years - days (v. TBD, TBD, )
Youngest goalscorer in the league – TBD, - years - days (v. TBD, TBD, )
Youngest goalscorer in a Concacaf Competition – Edwin Sanchez, 21 years 156 days (v. Puerto Rico Islanders, 2011–12 CONCACAF Champions League preliminary round, July 27, 2011 )
Youngest hat-trick scorer – TBD, - years - days (v. TBD, TBD, )
Oldest goalscorer – TBD, - years - days (v. TBD, TBD, TBD)
Oldest goalscorer in a Concacaf Competition – Elias Montes, 35 years 65 days (v. Houston Dynamo, 2009–10 CONCACAF Champions League Group Stage, October 21, 2009)
Leading Scorers
Last updated -
Competitive, professional matches only, appearances including substitutes appear in brackets.
Concacaf scorers
As of 21 October 2011
Club Records
Record Victory: 6-0 vs San Salvador F.C., October 27, 2007
Record Defeat: 1-7 vs Alianza F.C., 22 |
https://en.wikipedia.org/wiki/1943%E2%80%9344%20Swedish%20football%20Division%203 | Statistics of Swedish football Division 3 for the 1943–44 season.
League standings
Uppsvenska Sydöstra 1943–44
Uppsvenska Sydvästra 1943–44
Östsvenska Norra 1943–44
Östsvenska Södra 1943–44
Centralserien Norra, Uppland 1943–44
Centralserien Norra, Västmanland 1943–44
Centralserien Södra 1943–44
Nordvästra Norra 1943–44
Nordvästra Södra, Dalsland 1943–44
Nordvästra Södra, Bohus 1943–44
Mellansvenska Norra 1943–44
Mellansvenska Södra 1943–44
Sydöstra Norra 1943–44
Sydöstra Södra 1943–44
Västsvenska Norra 1943–44
Västsvenska Södra 1943–44
Sydsvenska Norra 1943–44
Sydsvenska Södra 1943–44
Footnotes
References
Swedish Football Division 3 seasons
3
Swed |
https://en.wikipedia.org/wiki/1944%E2%80%9345%20Swedish%20football%20Division%203 | Statistics of Swedish football Division 3 for the 1944–45 season.
League standings
Uppsvenska Sydöstra 1944–45
Uppsvenska Sydvästra 1944–45
Östsvenska Norra 1944–45
Östsvenska Södra 1944–45
Centralserien Norra, Uppland 1944–45
Centralserien Norra, Västmanland 1944–45
Centralserien Södra 1944–45
Nordvästra Norra 1944–45
Nordvästra Södra, Dalsland 1944–45
Nordvästra Södra, Bohus 1944–45
Mellansvenska Norra 1944–45
Mellansvenska Södra 1944–45
Sydöstra Norra 1944–45
Sydöstra Södra 1944–45
Västsvenska Norra 1944–45
Västsvenska Södra 1944–45
Sydsvenska Norra 1944–45
Sydsvenska Södra 1944–45
Footnotes
References
Swedish Football Division 3 seasons
3
Swed |
https://en.wikipedia.org/wiki/1945%E2%80%9346%20Swedish%20football%20Division%203 | Statistics of Swedish football Division 3 for the 1945–46 season.
League standings
Uppsvenska Sydöstra 1945–46
Uppsvenska Sydvästra 1945–46
Östsvenska Norra 1945–46
Östsvenska Södra 1945–46
Centralserien Norra, Uppland 1945–46
Centralserien Norra, Västmanland 1945–46
Centralserien Södra 1945–46
Nordvästra Norra 1945–46
Nordvästra Södra, Dalsland 1945–46
Nordvästra Södra, Bohus 1945–46
Mellansvenska Norra 1945–46
Mellansvenska Södra 1945–46
Sydöstra Norra 1945–46
Sydöstra Södra 1945–46
Västsvenska Norra 1945–46
Västsvenska Södra 1945–46
Sydsvenska Norra 1945–46
Sydsvenska Södra 1945–46
Footnotes
References
Swedish Football Division 3 seasons
3
Swed |
https://en.wikipedia.org/wiki/Dominika%20Cibulkov%C3%A1%20career%20statistics | This is a list of the main career statistics of the professional Slovak tennis player Dominika Cibulková.
Performance timelines
Only main-draw results in WTA Tour, Grand Slam tournaments, Fed Cup and Olympic Games are included in win–loss records.
Singles
Doubles
Significant finals
Grand Slam finals
Singles: 1 (1 runner-up)
WTA Tour Championships finals
Singles: 1 (1 title)
WTA Premier Mandatory & 5 finals
Singles: 3 (3 runner-ups)
WTA career finals
Singles: 21 (8 titles, 13 runner-ups)
Doubles: 3 (1 title, 2 runner-ups)
Team competitions: 1 (1 title)
ITF Circuit finals
Singles: 6 (2 titles, 4 runner-ups)
Doubles: 1 (1 runner–up)
WTA Tour career earnings
Cibulková earned more than 13 million dollars during her career.
Career Grand Slam statistics
Grand Slam tournament seedings
The tournaments won by Cibulková are in boldface, and advanced into finals by Cibulková are in italics.
Singles
Best Grand Slam results details
Fed Cup participation
This table shows Cibulková's participation for Slovakia Fed Cup team up to 17, April 2016.
Source: fedcup.com
Singles (20–11)
Doubles (1–8)
Record against other players
Record against top 10 players
Cibulková's record against players who have been ranked in the top 10 (correct to 15 September 2022):
No. 1 wins
Top 10 wins
Longest winning streaks
9–match singles winning streak (2016)
Notes
References
External links
Official website
Cibulkova, Dominika |
https://en.wikipedia.org/wiki/Mounir%20Benmeddour | Mounir Benmeddour (born 8 May 1988 in Algiers, Algeria) is an Algerian professional footballer. He currently plays as a goalkeeper of AS Khroub in the Algerian Ligue Professionnelle 2.
Statistics
References
External links
1988 births
Algerian men's footballers
Algerian Ligue Professionnelle 1 players
Algerian Ligue 2 players
Living people
AS Khroub players
Olympique de Médéa players
Paradou AC players
Footballers from Algiers
USM El Harrach players
USM Blida players
ESM Koléa players
RC Kouba players
Men's association football goalkeepers
21st-century Algerian people |
https://en.wikipedia.org/wiki/Ahmed%20Abdel-Sattar | Ahmed Abdel-Sattar Nawwas (; born 6 July 1984) is a Jordanian footballer who is a goalkeeper for Al-Wehdat and the Jordan national football team.
International career statistics
Honours
Jordan Premier League: 2005–06
Jordan FA Cup: 2006, 2007
Jordan FA Shield: 2007
Jordan Super Cup: 2007
AFC Cup: 2007
Best Goalkeeper in Jordan Premier League (2012-2013)
References
External links
1984 births
Living people
Jordanian Muslims
Jordanian men's footballers
Jordan men's international footballers
Jordanian Pro League players
Saudi Pro League players
Men's association football goalkeepers
Shabab Al-Ordon SC players
Al-Jazeera SC (Amman) players
Al-Wehdat SC players
Al-Ettifaq FC players
Jordanian expatriate men's footballers
Jordanian expatriate sportspeople in Saudi Arabia
Expatriate men's footballers in Saudi Arabia
2015 AFC Asian Cup players
Footballers from Amman
2019 AFC Asian Cup players |
https://en.wikipedia.org/wiki/Kappa%20calculus | In mathematical logic, category theory, and
computer science, kappa calculus is a
formal system for defining first-order
functions.
Unlike lambda calculus, kappa calculus has no
higher-order functions; its functions are
not first class objects. Kappa-calculus can be
regarded as "a reformulation of the first-order fragment of typed
lambda calculus".
Because its functions are not first-class objects, evaluation of kappa
calculus expressions does not require
closures.
Definition
The definition below has been adapted from the diagrams on pages 205 and 207 of Hasegawa.
Grammar
Kappa calculus consists of types and expressions, given by the
grammar below:
In other words,
1 is a type
If and are types then is a type.
Every variable is an expression
If is a type then is an expression
If is a type then is an expression
If is a type and e is an expression then is an expression
If and are expressions then is an expression
If x is a variable, is a type, and e is an expression, then is an expression
The and the subscripts of , , and are
sometimes omitted when they can be unambiguously determined from the
context.
Juxtaposition is often used as an abbreviation for a combination of
and composition:
Typing rules
The presentation here uses sequents () rather than hypothetical judgments in order to ease comparison with the simply typed lambda calculus. This requires the additional Var rule, which does not appear in Hasegawa
In kappa calculus an expression has two types: the type of its source and the type of its target. The notation is used to indicate that expression e has source type and target type .
Expressions in kappa calculus are assigned types according to the following rules:
{| cellpadding="9" style="text-align:center;"
| || (Var)
|-
| || (Id)
|-
| || (Bang)
|-
| || (Comp)
|-
|
| (Lift)
|-
|
|(Kappa)
|}
In other words,
Var: assuming lets you conclude that
Id: for any type ,
Bang: for any type ,
Comp: if the target type of matches the source type of they may be composed to form an expression with the source type of and target type of
Lift: if , then
Kappa: if we can conclude that under the assumption that , then we may conclude without that assumption that
Equalities
Kappa calculus obeys the following equalities:
Neutrality: If then and
Associativity: If , , and , then .
Terminality: If and then
Lift-Reduction:
Kappa-Reduction: if x is not free in h
The last two equalities are reduction rules for the calculus,
rewriting from left to right.
Properties
The type can be regarded as the unit type. Because of this, any two functions whose argument type is the same and whose result type is should be equal – since there is only a single value of type both functions must return that value for every argument (Terminality).
Expressions with type can be regarded as "constants" or values of "ground type"; this is because is the unit type, and so a function from this type is ne |
https://en.wikipedia.org/wiki/Conj | Conj may refer to:
Linguistics
Conjugation (grammar)
Conjunction (grammar)
a part of speech tag
Mathematics
Conjugacy class, a partition of group into elements that share properties of a group.
Conjugate (algebra), the image of an element in a quadratic extension field of a field K under the unique non-identity automorphism of the extended field that fixes K.
Complex conjugate, one half of a pair of complex numbers, both having the same real part, but with imaginary parts of equal magnitude and opposite signs.
conj, a function in programming languages such as C++ or MATLAB that computes the complex conjugate.
See also
Conjugation (disambiguation)
Conjunction (disambiguation) |
https://en.wikipedia.org/wiki/Stephan%20Retzer | Stephan Retzer (born October 11, 1976) is a German professional ice hockey defenceman. He is currently playing for ERC Ingolstadt in the Deutsche Eishockey Liga (DEL).
Career statistics
Regular season and playoffs
International
References
External links
1976 births
Living people
Adler Mannheim players
ERC Ingolstadt players
EV Landshut players
German ice hockey defencemen
Hamburg Freezers players
Kassel Huskies players |
https://en.wikipedia.org/wiki/Thomas%20Dolak | Thomas Dolak (born March 25, 1979) is a retired Czech-born German professional ice hockey player. He last played for Dusseldorfer EG in the Deutsche Eishockey Liga (DEL).
Career statistics
References
External links
1979 births
Living people
Ice hockey people from Zlín
Hamburg Freezers players
German ice hockey forwards
Kingston Frontenacs players
North Bay Centennials players
Kassel Huskies players
München Barons players
Hannover Scorpions players
Düsseldorfer EG players
EHC Freiburg players
Czechoslovak emigrants to Germany
German expatriate sportspeople in Canada
German expatriate ice hockey people |
https://en.wikipedia.org/wiki/Andrea%20Petkovic%20career%20statistics | This is a list of the main career statistics of professional German tennis player, Andrea Petkovic. To date, Petkovic has won seven WTA singles titles including one year-ending championship at the 2014 Tournament of Champions. Other highlights of Petkovic's career include a runner-up finish at the 2011 China Open, a semifinal appearance at the 2014 French Open and quarterfinal appearances at the 2011 Australian Open and 2011 US Open. Petkovic achieved a career-high singles ranking of world No. 9 on October 10, 2011.
Career achievements
In July 2009, Petkovic won the first WTA Tour singles title of her career at the International event in Bad Gastein, Austria after a straight sets win over Ioana Raluca Olaru in the final. At the 2011 Australian Open, she defeated the 2008 champion and former world No. 1, Maria Sharapova in the fourth round to reach her first Grand Slam quarterfinal where she lost in straight sets to the ninth seed and eventual runner-up, Li Na. In March 2011, she reached her first Premier Mandatory semifinal at the Sony Ericsson Open, upsetting world No. 1, Caroline Wozniacki, and sixth seed Jelena Janković en route before falling to Sharapova in three sets. Two months later, she won her second career singles title at the Internationaux de Strasbourg before reaching her second consecutive Grand Slam quarterfinal at the French Open where she lost to Sharapova in straight sets, winning just three games. After quarterfinal and semifinal appearances at the Rogers Cup and Western & Southern Open respectively, Petkovic reached her third Grand Slam quarterfinal of the year at the US Open, where she lost in straight sets to the top-seeded Wozniacki. In October, she reached the biggest final of her career to date at the China Open where she lost to the 11th seed Agnieszka Radwańska in three sets. Petkovic rose to a career high of World No. 9 as a result of this performance and eventually finished the year ranked World No. 10, marking her first finish in the year-end top ten.
In April 2014, Petkovic won her first WTA Premier singles title and first career title on green clay at the Family Circle Cup, defeating Jana Čepelová (who had upset world No. 1 and two-time defending champion, Serena Williams earlier in the tournament) in the final. It was Petkovic's first tour level singles title in three years and remains the biggest title of her career thus far. In June, Petkovic advanced to her first Grand Slam semifinal at the French Open, defeating tenth seed and 2012 finalist Sara Errani en route before losing to the eventual runner-up, Simona Halep, in straight sets. The following month, she won her second title in Bad Gastein, defeating first time finalist Shelby Rogers, in straight sets.
Performance timelines
Only main-draw results in WTA Tour, Grand Slam tournaments, Fed Cup/Billie Jean King Cup and Olympic Games are included in win–loss records.
Singles
Doubles
Significant finals
WTA Tournament of Champions
Singles: 1 (1 title)
|
https://en.wikipedia.org/wiki/Andreas%20Morczinietz | Andreas Morczinietz (born March 11, 1978) is a German professional ice hockey player. He is currently playing for Hannover Scorpions in the Deutsche Eishockey Liga (DEL).
Career statistics
Regular season and playoffs
International
References
External links
1978 births
Living people
German ice hockey right wingers
Hannover Scorpions players
Olympic ice hockey players for Germany
People from Wolfratshausen
Ice hockey people from Upper Bavaria |
https://en.wikipedia.org/wiki/PBLAS | Parallel Basic Linear Algebra Subprograms (PBLAS) is an implementation of Level 2 and 3 BLAS intended for distributed memory architectures.
It provides a computational backbone for ScaLAPACK, a parallel implementation of LAPACK. It depends on Level 1 sequential BLAS operations for local computation and BLACS for communication between nodes.
References
Distributed computing |
https://en.wikipedia.org/wiki/Cutting%20sequence | In digital geometry, a cutting sequence is a sequence of symbols whose elements correspond to the individual grid lines crossed ("cut") as a curve crosses a square grid.
Sturmian words are a special case of cutting sequences where the curves are straight lines of irrational slope.
References
Notes
Bibliography
Discrete mathematics
Digital geometry
Sequences and series |
https://en.wikipedia.org/wiki/Lasse%20Kopitz | Lasse Kopitz (born May 21, 1980) is a German former professional ice hockey defenceman. He most notably played for the Iserlohn Roosters in the Deutsche Eishockey Liga (DEL).
Career statistics
Regular season and playoffs
International
References
External links
1980 births
Living people
Frankfurt Lions players
Füchse Duisburg players
German ice hockey defencemen
Ice hockey players at the 2006 Winter Olympics
Olympic ice hockey players for Germany
Iserlohn Roosters players
Kölner Haie players
Krefeld Pinguine players
Revier Löwen players
Thomas Sabo Ice Tigers players |
https://en.wikipedia.org/wiki/Du%C5%A1an%20Milo | Dušan Milo (born March 5, 1973) is a Slovak professional ice hockey defenceman. He is currently playing for HK Nitra in the Slovak Extraliga (SVK).
Career statistics
Regular season and playoffs
International
He played 90 matches in the Slovak national team, scored 15 goals. He holds a gold medal from the 2002 World Championships and a bronze medal from the 2003 World Championships. He also represented at the 2006 World Championships and the 2002 Olympic Games in Salt Lake City.
WC 2002
His first world championships were the World Cup in Sweden, when he was a member of the team coach Ján Floc. He played in the third defensive pair with Martin Štrbák. [3] He scored the only goal of Slovakia in the match against Finland in the basic group (1: 2). He scored the winning goal in the superstructure against the home team Sweden (2: 1). He also scored in the group's match against Russia (6: 4). Slovakia won over Russia in the final 4: 3 and became the world champion.
WC 2006
Coach František Hossa nominated him for the Latvian Riga World Championship. In the match against Switzerland, he scored the second goal of Slovakia (2: 2). He also scored in the match against Ukraine in the last match of the superstructure part (9: 0). He scored his team's only goal in the quarterfinals against Canada (1: 4).
References
External links
1973 births
Living people
Krefeld Pinguine players
Slovak ice hockey defencemen
Ice hockey people from Nitra
Ice hockey players at the 2002 Winter Olympics
Olympic ice hockey players for Slovakia
Slovak expatriate ice hockey players in Germany
Slovak expatriate ice hockey players in Sweden
Slovak expatriate ice hockey players in Switzerland |
https://en.wikipedia.org/wiki/Roland%20Verwey | Roland Verwey (born December 27, 1981) is a German professional ice hockey player. He is currently playing for Krefeld Pinguine in the Deutsche Eishockey Liga (DEL).
Career statistics
References
External links
1981 births
Living people
Essen Mosquitoes players
Füchse Duisburg players
German ice hockey forwards
Iserlohn Roosters players
Krefeld Pinguine players
Sportspeople from Duisburg |
https://en.wikipedia.org/wiki/1946%E2%80%9347%20Swedish%20football%20Division%203 | Statistics of Swedish football Division 3 for the 1946–47 season. At the end of this season major re-structuring of the Swedish third tier took place with the number of divisions reduced from 16 sections to 4 sections. There were no promotions to Division 2 and most of the third tier teams were relegated to Division 4 for the 1947-48 season.
League standings
Uppsvenska Sydöstra 1946–47
The league table is not currently available but it is known that Ljusne AIK won the division and Strands IF qualified for the relegation playoffs.
Uppsvenska Östra 1946–47
Uppsvenska Västra 1946–47
Östsvenska 1946–47
Centralserien Norra 1946–47
NB: Riddarhytte SK withdrew.
Centralserien Södra 1946–47
Nordvästra Norra 1946–47
Nordvästra Södra 1946–47
Mellansvenska Norra 1946–47
Mellansvenska Södra 1946–47
Sydöstra Norra 1946–47
Sydöstra Södra 1946–47
Västsvenska Norra 1946–47
Västsvenska Södra 1946–47
Sydsvenska Norra 1946–47
Sydsvenska Södra 1946–47
Footnotes
References
Swedish Football Division 3 seasons
3
Swed |
https://en.wikipedia.org/wiki/Projections%20of%20population%20growth | Population projections are attempts to show how the human population statistics might change in the future. These projections are an important input to forecasts of the population's impact on this planet and humanity's future well-being. Models of population growth take trends in human development and apply projections into the future. These models use trend-based-assumptions about how populations will respond to economic, social and technological forces to understand how they will affect fertility and mortality, and thus population growth.
The 2022 projections from the United Nations Population Division (chart #1) show that annual world population growth peaked at 2.3% per year in 1963, has since dropped to 0.9% in 2023, equivalent to about 74 million people each year, and projected that it could drop even further to minus 0.1% by 2100. Based on this, the UN projected that the world population, 8 billion , would peak around the year 2086 at about 10.4 billion, and then start a slow decline, assuming a continuing decrease in the global average fertility rate from 2.5 births per woman during the 2015–2020 period to 1.8 by the year 2100, (the medium-variant projection).
However, estimates outside of the United Nations have put forward alternative models based on additional downward pressure on fertility (such as successful implementation of education and family planning goals in the UN's Sustainable Development Goals) which could result in peak population during the 2060–2070 period rather than later.
According to the UN, of the predicted growth in world population between 2020 and 2050, all of that change will come from less developed countries, and more than half will come from sub-Saharan Africa. Half of the growth will come from just eight countries, five of which are in Africa. It is predicted that the population of sub-Saharan Africa will double by 2050. The Pew Research Center observes that 50% of births in the year 2100 will be in Africa. Other organizations project lower levels of population growth in Africa, based particularly on improvement in women's education and successful implementation of family planning.During the remainder of this century some countries will see population growth, some will see population decline. For example the UN projects that Nigeria will gain about 340 million people, about the present population of the US, to become the 3rd most populous country, and China will lose almost half of its population.
Even though the global fertility rate continues to fall, chart #2 shows that because of population momentum the global population will continue to grow, although at a steadily slower rate, until the mid 2080s (the median line).
The main driver of long-term future population growth on this planet is projected to be the continuing evolution of fertility and mortality.
History of population projections
Projections of global human population are generally based on birth rates and death rates, and since thes |
https://en.wikipedia.org/wiki/Faculty%20of%20Informatics%20and%20Statistics%2C%20University%20of%20Economics%20in%20Prague | The Faculty of Informatics and Statistics (FIS VŠE) (, abbreviated FIS, F4), also known as the School of Informatics and Statistics, is the fourth of six faculties at Prague University of Economics and Business. The faculty was established in 1991, following the dissolution of the Faculty of Direction. Its academic focus is informatics, statistics, econometrics and other mathematical methods applied to business practice. The faculty has eight departments and several research laboratories, and hosts around 2,500 students across its programs.
Departments
Departments of the faculty include:
Department of Demography (; KDEM)
Department of Econometrics (; KEKO)
Department of Economic Statistics (; KEST)
Department of Information and Knowledge Engineering (; KIZI)
Department of Information Technologies (; KIT) Research activities of the department focus on methodologies for development, operation and management of information systems.
Department of Mathematics (; KMAT)
Department of Multimedia (; KME)
Department of Statistics and Probability (; KSTP)
Department of Systems Analysis (; KSA), focusing on the application of principles of systems methodology and systems thinking into the fields of information systems, and business and management. Its main areas of research interest include: implementation of information systems within an organization, information management, strategic planning and business reengineering.
Academics
The faculty offers Bachelor, Master and doctoral study programs.
Bachelor programs
Bachelor study programs are 3-3,5 years in length and conclude with a Bachelor State Examination and defence of a Bachelor thesis. Bachelor theses usually focus on practical topics.
Applied Informatics
Information Media and Services
Mathematical Methods in Economics, a program focusing on quantitative methods, and the inter-related fields of economics, business economics and mathematical methods.
Multimedia in Economic Practice
Socio-economic demography, a study program focused mainly on reproduction of human resources and human capital, covering topics from demography to social and economic policy.
Statistical Methods in Economics, a program focusing on applying statistical methods to real economics.
Statistics and Econometrics, a course focusing on statistics, various methods bordering economics and mathematics, econometric and mathematical modelling and informatics.
Master programs
Masters programs end with a Final State Examination and defence of a thesis. Available subjects are divided into Major and Minor:
Doctoral programs
Doctoral programs are usually at least three years long and conclude with the defence of a PhD thesis. Programs offered include Informatics, Econometrics and Operations Research, and Statistics.
Academic cooperation
The faculty cooperates with several academic and non-academic institutions, including Czech Technical University in Prague, Academy of Sciences of the Czech Republic, Czech Stati |
https://en.wikipedia.org/wiki/1947%E2%80%9348%20Swedish%20football%20Division%203 | Statistics of Swedish football Division 3 for the 1947–48 season.
League standings
Norra 1947–48
Östra 1947–48
Västra 1947–48
Södra 1947–48
Footnotes
References
Swedish Football Division 3 seasons
3
Swed |
https://en.wikipedia.org/wiki/1948%E2%80%9349%20Swedish%20football%20Division%203 | Statistics of Swedish football Division 3 for the 1948–49 season.
League standings
Norra 1948–49
Östra 1948–49
Västra 1948–49
Södra 1948–49
Footnotes
References
Swedish Football Division 3 seasons
3
Swed |
https://en.wikipedia.org/wiki/1949%E2%80%9350%20Swedish%20football%20Division%203 | Statistics of Swedish football Division 3 for the 1949–50 season.
League standings
Norra 1949–50
Östra 1949–50
Västra 1949–50
Södra 1949–50
Footnotes
References
Swedish Football Division 3 seasons
3
Swed |
https://en.wikipedia.org/wiki/1950%E2%80%9351%20Swedish%20football%20Division%203 | Statistics of Swedish football Division 3 for the 1950–51 season.
League standings
Norra 1950–51
Östra 1950–51
Västra 1950–51
Södra 1950–51
Footnotes
References
Swedish Football Division 3 seasons
3
Swed |
https://en.wikipedia.org/wiki/1951%E2%80%9352%20Swedish%20football%20Division%203 | Statistics of Swedish football Division 3 for the 1951–52 season.
League standings
Norra 1951–52
Östra 1951–52
Västra 1951–52
Södra 1951–52
Footnotes
References
Swedish Football Division 3 seasons
3
Swed |
https://en.wikipedia.org/wiki/1952%E2%80%9353%20Swedish%20football%20Division%203 | Statistics of Swedish football Division 3 for the 1952–53 season.
League standings
Norrländska Norra 1952–53
Norrländska Södra 1952–53
Norra 1952–53
Östra 1952–53
Västra 1952–53
Södra 1952–53
Footnotes
References
Swedish Football Division 3 seasons
3
Swed |
https://en.wikipedia.org/wiki/1953%E2%80%9354%20Swedish%20football%20Division%203 | Statistics of Swedish football Division 3 for the 1953–54 season.
League standings
Norra Norrland 1953–54
Mellersta Norrland 1953–54
Södra Norrland 1953–54
Norra Svealand 1953–54
Östra Svealand 1953–54
Västra Svealand 1953–54
Östra Götaland 1953–54
Västra Götaland 1953–54
Södra Götaland 1953–54
Footnotes
References
Swedish Football Division 3 seasons
3
Swed |
https://en.wikipedia.org/wiki/Louis%20Carr%C3%A9%20%28mathematician%29 | Louis Carré (26 July 1663 – 17 April 1711) was a French mathematician and member of the French Academy of Sciences. He was the author of one of the first books on integral calculus.
Early life
Due to his father's wish that he become a priest, Carré studied theology for several years but did not join the priesthood. He took a post as an amanuensis for philosopher Nicolas Malebranche, a mathematics professor at the Congregation of the Oratory, and tutored students as well.
On February 4, 1699, he became a student of Pierre Varignon at the Academy of Sciences. In 1700, his book Une méthode pour Ia mesure des surfaces, la dimension des solides, leurs centres de pesanteur, de percussion, et d'oscillation par l'application du calcul integral was published.
Publications
Between 1701 and 1705, Carré published over a dozen papers on a variety of mathematical and physical subjects:
Méthode pour la rectification des lignes courbes par les tangentes (1701)
Solution du problème proposé aux Géomètres dans les mémoires de Trévoux, des mois de Septembre et d'Octobre (1701)
Réflexions ajoutées par M Carré à la Table des Equations (1701)
Observation sur la cause de la réfraction de la lumière (1702)
Pourquoi les marées vont toujours en augmentant depuis Brest jusqu'à Saint-Malo, et en diminuant le long des côtes de Normandie (1702)
Nombre et noms des instruments de musique (1702)
Observations sur la vinaigre qui fait rouler de petites pierres sur un plan incline (1703)
Observation sur la rectification des caustiques par réflexions formées par le cercle, la cycloïde ordinaire, et la parabole, et de leurs développées, avec la mesure des espaces qu'elle renferment (1703)
Méthode pour la rectification des courbes (1704)
Observation sur ce qui produit le son (1704)
Examen d'une courbe formée par le moyen du cercle (1705)
Expériences physiques sur la réfraction des balles de mousquet dans l'eau, et sur la résistance de ce fluide (1705)
Problème d'hydrodynamique sur la proportion des tuyaux pour avoir une quantité d'eau déterminée (1705)
References
Members of the French Academy of Sciences
1663 births
1711 deaths
People from Seine-et-Marne
17th-century French mathematicians
18th-century French mathematicians |
https://en.wikipedia.org/wiki/1954%E2%80%9355%20Swedish%20football%20Division%203 | Statistics of Swedish football Division 3 for the 1954–55 season.
League standings
Norra Norrland 1954–55
Mellersta Norrland 1954–55
Södra Norrland 1954–55
Norra Svealand 1954–55
Östra Svealand 1954–55
Västra Svealand 1954–55
Östra Götaland 1954–55
Västra Götaland 1954–55
Södra Götaland 1954–55
Footnotes
References
Swedish Football Division 3 seasons
3
Swed |
https://en.wikipedia.org/wiki/1955%E2%80%9356%20Swedish%20football%20Division%203 | Statistics of Swedish football Division 3 for the 1955–56 season.
League standings
Norra Norrland 1955–56
Mellersta Norrland 1955–56
Södra Norrland 1955–56
Norra Svealand 1955–56
Östra Svealand 1955–56
Västra Svealand 1955–56
Nordöstra Götaland 1955–56
Nordvästra Götaland 1955–56
Mellersta Götaland 1955–56
Sydöstra Götaland 1955–56
Sydvästra Götaland 1955–56
Södra Götaland 1955–56
Footnotes
References
Swedish Football Division 3 seasons
3
Swed |
https://en.wikipedia.org/wiki/1956%E2%80%9357%20Swedish%20football%20Division%203 | Statistics of Swedish football Division 3 for the 1956–57 season.
League standings
Norra Norrland 1956–57
Mellersta Norrland 1956–57
Södra Norrland 1956–57
Norra Svealand 1956–57
Östra Svealand 1956–57
Västra Svealand 1956–57
Nordöstra Götaland 1956–57
Nordvästra Götaland 1956–57
Mellersta Götaland 1956–57
Sydöstra Götaland 1956–57
Sydvästra Götaland 1956–57
Södra Götaland 1956–57
Footnotes
References
Swedish Football Division 3 seasons
3
Swed |
https://en.wikipedia.org/wiki/1957%E2%80%9358%20Swedish%20football%20Division%203 | Statistics of Swedish football Division 3 for the 1957–58 season.
League standings
Norra Norrland 1957–58
Mellersta Norrland 1957–58
Södra Norrland 1957–58
Norra Svealand 1957–58
Östra Svealand 1957–58
Västra Svealand 1957–58
Nordöstra Götaland 1957–58
Nordvästra Götaland 1957–58
Mellersta Götaland 1957–58
Sydöstra Götaland 1957–58
Sydvästra Götaland 1957–58
Södra Götaland 1957–58
Footnotes
References
Swedish Football Division 3 seasons
3
Swed |
https://en.wikipedia.org/wiki/1959%20Swedish%20football%20Division%203 | Statistics of Swedish football Division 3 for the 1959 season.
League standings
Norra Norrland 1959
Mellersta Norrland 1959
Södra Norrland 1959
Norra Svealand 1959
Östra Svealand 1959
Västra Svealand 1959
Nordöstra Götaland 1959
Nordvästra Götaland 1959
Mellersta Götaland 1959
Sydöstra Götaland 1959
Sydvästra Götaland 1959
Södra Götaland 1959
Footnotes
References
Swedish Football Division 3 seasons
3
Swed
Swed |
https://en.wikipedia.org/wiki/1960%20Swedish%20football%20Division%203 | Statistics of Swedish football Division 3 for the 1960 season.
League standings
Norra Norrland 1960
Mellersta Norrland 1960
Södra Norrland 1960
Norra Svealand 1960
Östra Svealand 1960
Västra Svealand 1960
Nordöstra Götaland 1960
Nordvästra Götaland 1960
Mellersta Götaland 1960
Sydöstra Götaland 1960
Sydvästra Götaland 1960
Södra Götaland 1960
Footnotes
References
Swedish Football Division 3 seasons
3
Swed
Swed |
https://en.wikipedia.org/wiki/1961%20Swedish%20football%20Division%203 | Statistics of Swedish football Division 3 for the 1961 season.
League standings
Norra Norrland 1961
Mellersta Norrland 1961
Södra Norrland 1961
Norra Svealand 1961
Östra Svealand 1961
Västra Svealand 1961
Nordöstra Götaland 1961
Nordvästra Götaland 1961
Mellersta Götaland 1961
Sydöstra Götaland 1961
Sydvästra Götaland 1961
Södra Götaland 1961
Footnotes
References
Swedish Football Division 3 seasons
3
Swed
Swed |
https://en.wikipedia.org/wiki/1971%20Swedish%20football%20Division%203 | Statistics of Swedish football Division 3 for the 1971 season.
League standings
Norra Norrland, Övre 1971
Norra Norrland, Nedre 1971
Södra Norrland, Övre 1971
Södra Norrland, Nedre 1971
Norra Svealand 1971
Östra Svealand 1971
Västra Svealand 1971
Nordöstra Götaland 1971
Nordvästra Götaland 1971
Mellersta Götaland 1971
Sydöstra Götaland 1971
Sydvästra Götaland 1971
Skåne 1971
Footnotes
References
Swedish Football Division 3 seasons |
https://en.wikipedia.org/wiki/2011%20Swedish%20Football%20Division%203 | Statistics of Swedish football Division 3 for the 2011 season.
League standings
Norra Norrland 2011
Mellersta Norrland 2011
Södra Norrland 2011
Norra Svealand 2011
Västra Svealand 2011
Södra Svealand 2011
Nordöstra Götaland 2011
Nordvästra Götaland 2011
Mellersta Götaland 2011
Sydöstra Götaland 2011
Sydvästra Götaland 2011
Södra Götaland 2011
Footnotes
References
Swedish Football Division 3 seasons
5
Sweden
Sweden |
https://en.wikipedia.org/wiki/2011%20Swedish%20Football%20Division%202 | Statistics of Swedish football Division 2 for the 2011 season.
League standings
Norrland 2011
Norra Svealand 2011
Södra Svealand 2011
Norra Götaland 2011
Västra Götaland 2011
Södra Götaland 2011
Player of the year awards
Ever since 2003 the online bookmaker Unibet have given out awards at the end of the season to the best players in Division 2. The recipients are decided by a jury of sportsjournalists, coaches and football experts. The names highlighted in green won the overall national award.
References
Swedish Football Division 2 seasons
4
Sweden
Sweden |
https://en.wikipedia.org/wiki/Shioda%20modular%20surface | In mathematics, a Shioda modular surface is one of the elliptic surfaces studied by .
References
Complex surfaces
Algebraic surfaces |
https://en.wikipedia.org/wiki/2010%20Swedish%20Football%20Division%203 | Statistics of Swedish football Division 3 for the 2010 season.
League standings
Norra Norrland 2010
Mellersta Norrland 2010
Södra Norrland 2010
Norra Svealand 2010
Västra Svealand 2010
Södra Svealand 2010
Nordöstra Götaland 2010
Nordvästra Götaland 2010
Mellersta Götaland 2010
Sydöstra Götaland 2010
Sydvästra Götaland 2010
Södra Götaland 2010
Footnotes
References
Swedish Football Division 3 seasons
5
Sweden
Sweden |
https://en.wikipedia.org/wiki/Automedian%20triangle | In plane geometry, an automedian triangle is a triangle in which the lengths of the three medians (the line segments connecting each vertex to the midpoint of the opposite side) are proportional to the lengths of the three sides, in a different order. The three medians of an automedian triangle may be translated to form the sides of a second triangle that is similar to the first one.
Characterization
The side lengths of an automedian triangle satisfy the formula or a permutation thereof, analogous to the Pythagorean theorem characterizing right triangles as the triangles satisfying the formula .
Equivalently, in order for the three numbers , , and to be the sides of an automedian triangle, the sequence of three squared side lengths , , and should form an arithmetic progression.
Construction from right triangles
If , , and are the three sides of a right triangle, sorted in increasing order by size, and if , then , , and are the three sides of an automedian triangle. For instance, the right triangle with side lengths 5, 12, and 13 can be used to form in this way an automedian triangle with side lengths 13, 17, and 7.
The condition that is necessary: if it were not met, then the three numbers , , and would still satisfy the equation characterizing automedian triangles, but they would not satisfy the triangle inequality and could not be used to form the sides of a triangle.
Consequently, using Euler's formula that generates primitive Pythagorean triangles it is possible to generate primitive integer automedian triangles (i.e., with the sides sharing no common factor) as
with and coprime, odd, and to satisfy the triangle inequality (if the quantity inside the absolute value signs is negative) or (if that quantity is positive). Then this triangle's medians are found by using the above expressions for its sides in the general formula for medians:
where the second equation in each case reflects the automedian feature
From this can be seen the similarity relationships
There is a primitive integer-sided automedian triangle that is not generated from a right triangle: namely, the equilateral triangle with sides of unit length.
Examples
There are 18 primitive integer automedian triangles, shown here as triples of sides , with :
For example, (26, 34, 14) is not a primitive automedian triple, as it is a multiple of (13, 17, 7) and does not appear above.
Additional properties
If is the area of the automedian triangle, by Heron's formula
The Euler line of an automedian triangle is perpendicular to the median to side .
If the medians of an automedian triangle are extended to the circumcircle of the triangle, then the three points where the extended medians meet the circumcircle form an isosceles triangle. The triangles for which this second triangle is isosceles are exactly the triangles that are themselves either isosceles or automedian. This property of automedian triangles stands in contrast to the Steiner–Lehmus theorem, acco |
https://en.wikipedia.org/wiki/2011%20South%20African%20census | The South African National Census of 2011 is the 3rd comprehensive census performed by Statistics South Africa.
The 2011 census was the first census to include geo-referencing for every individual dwelling in South Africa.
How the count was done
Planning
The development of an overall strategy began in April 2003, initially for a planned national census in 2006 to meet the United Nations global directive for a census every five years. After an application to the government, it was postponed to 2011 to improve strategies to reduce undercounting in gated communities, farmlands and rural areas.
In February 2007 a large-scale Community Survey was conducted in all provinces. It was based on a random sample, enumerating households. The main objective was to provide data of geography at district and municipal levels, build a logistics capacity for 2011 and primary data for population projections. The results were released in October 2007 with the caution that figures must be read with a "certain interval of confidence".
With lessons from the National Census in 2001 and Community Survey in 2007, a "team cells" approach was developed. This strategy was adopted mainly because of a skills-shortage, using experts from the United States, Kenya and United Kingdom to conduct on-the-job training for temporary Census staff. The programme was divided into a three-level hierarchy of sub-projects as follows:
Head office with the main function of providing support to the lower levels.
Provincial offices were responsible for coordination of all activities at their associated district and satellite offices.
District/Satellite offices implemented the fieldwork operations throughout the country.
During October 2010 a "dress rehearsal" was held, it tested all processed and refined the process to ensure a successful enumeration. There were a large number of non-response cases that were investigated by fieldworkers. This suggested that non-responses may be a "challenge" during the census night.
Pre-enumeration
The pre-enumeration phase involved over 7000 temporary staff, who concurrently demarcated enumeration areas, evaluated questionnaires and developed satellite office logistics.
The demarcation process involved dividing the country into "small pockets" of land, called enumeration areas based on administrative boundaries, size, and population density. The data used included satellite images, address data, gated community blueprints, sectional titles and sub-place spatial boundaries; sourced from private service providers and the geo-referencing Dwelling Frame Project. The objective of the project was to identity, locate and describe approximately 50% of dwelling structures in South Africa that have no address, predominantly in the former bantustans. It piloted in 2002 and was utilised for the first time in the 2011 National Census.
The geography division produced a list of 103,576 enumeration areas, a 25.68% increase of the 80,000 areas used in the 2001 Cens |
https://en.wikipedia.org/wiki/1962%20Swedish%20football%20Division%203 | Statistics of Swedish football Division 3 for the 1962 season.
League standings
Norra Norrland 1962
Mellersta Norrland 1962
Södra Norrland 1962
Norra Svealand 1962
Östra Svealand 1962
Västra Svealand 1962
Nordöstra Götaland 1962
Nordvästra Götaland 1962
Mellersta Götaland 1962
Sydöstra Götaland 1962
Sydvästra Götaland 1962
Södra Götaland 1962
Footnotes
References
Swedish Football Division 3 seasons
3
Swed
Swed |
https://en.wikipedia.org/wiki/1963%20Swedish%20football%20Division%203 | Statistics of Swedish football Division 3 for the 1963 season.
League standings
Norra Norrland 1963
Mellersta Norrland 1963
Södra Norrland 1963
Norra Svealand 1963
Östra Svealand 1963
Västra Svealand 1963
Nordöstra Götaland 1963
Nordvästra Götaland 1963
Mellersta Götaland 1963
Sydöstra Götaland 1963
Sydvästra Götaland 1963
Södra Götaland 1963
Footnotes
References
Swedish Football Division 3 seasons
3
Swed
Swed |
https://en.wikipedia.org/wiki/1970%20Swedish%20football%20Division%203 | Statistics of Swedish football Division 3 for the 1970 season.
League standings
Norra Norrland, Övre 1970
Norra Norrland, Nedre 1970
Södra Norrland, Övre 1970
Södra Norrland, Nedre 1970
Norra Svealand 1970
Östra Svealand 1970
Västra Svealand 1970
Nordöstra Götaland 1970
Nordvästra Götaland 1970
Mellersta Götaland 1970
Sydöstra Götaland 1970
Sydvästra Götaland 1970
Skåne 1970
Footnotes
References
Swedish Football Division 3 seasons |
https://en.wikipedia.org/wiki/Outline%20of%20mathematics | Mathematics is a field of study that investigates topics such as number, space, structure, and change.
Philosophy
Nature
Definitions of mathematics – Mathematics has no generally accepted definition. Different schools of thought, particularly in philosophy, have put forth radically different definitions, all of which are controversial.
Language of mathematics is the system used by mathematicians to communicate mathematical ideas among themselves, and is distinct from natural languages in that it aims to communicate abstract, logical ideas with precision and unambiguity.
Philosophy of mathematics – its aim is to provide an account of the nature and methodology of mathematics and to understand the place of mathematics in people's lives.
Classical mathematics refers generally to the mainstream approach to mathematics, which is based on classical logic and ZFC set theory.
Constructive mathematics asserts that it is necessary to find (or "construct") a mathematical object to prove that it exists. In classical mathematics, one can prove the existence of a mathematical object without "finding" that object explicitly, by assuming its non-existence and then deriving a contradiction from that assumption.
Predicative mathematics
Mathematics is
An academic discipline – branch of knowledge that is taught at all levels of education and researched typically at the college or university level. Disciplines are defined (in part), and recognized by the academic journals in which research is published, and the learned societies and academic departments or faculties to which their practitioners belong.
A formal science – branch of knowledge concerned with the properties of formal systems based on definitions and rules of inference. Unlike other sciences, the formal sciences are not concerned with the validity of theories based on observations in the physical world.
Concepts
Mathematical object an abstract concept in mathematics; an object is anything that has been (or could be) formally defined, and with which one may do deductive reasoning and mathematical proofs. Each branch of mathematics has its own objects.
Mathematical structure a set endowed with some additional features on the set (e.g., operation, relation, metric, topology). A partial list of possible structures are measures, algebraic structures (groups, fields, etc.), topologies, metric structures (geometries), orders, events, equivalence relations, differential structures, and categories.
Equivalent definitions of mathematical structures
Abstraction the process of extracting the underlying structures, patterns or properties of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena.
Branches and subjects
Quantity
Number theory is a branch of pure mathematics devoted primarily to the study of the |
https://en.wikipedia.org/wiki/1969%20Swedish%20football%20Division%203 | Statistics of Swedish football Division 3 for the 1969 season.
League standings
Norra Norrland, Övre 1969
Norra Norrland, Nedre 1969
Södra Norrland, Övre 1969
Södra Norrland, Nedre 1969
Norra Svealand 1969
Östra Svealand 1969
Västra Svealand 1969
Nordöstra Götaland 1969
Nordvästra Götaland 1969
Mellersta Götaland 1969
Sydöstra Götaland 1969
Sydvästra Götaland 1969
Skåne 1969
Footnotes
References
Swedish Football Division 3 seasons
3
Swed
Swed |
https://en.wikipedia.org/wiki/1968%20Swedish%20football%20Division%203 | Statistics of Swedish football Division 3 for the 1968 season.
League standings
Norra Norrland, Övre 1968
Norra Norrland, Nedre 1968
Södra Norrland, Övre 1968
Södra Norrland, Nedre 1968
Norra Svealand 1968
Östra Svealand 1968
Västra Svealand 1968
Nordöstra Götaland 1968
Nordvästra Götaland 1968
Mellersta Götaland 1968
Sydöstra Götaland 1968
Sydvästra Götaland 1968
Skåne 1968
Footnotes
References
Swedish Football Division 3 seasons
3
Swed
Swed |
https://en.wikipedia.org/wiki/John%20Foxx%20and%20the%20Maths | John Foxx and the Maths is a musical project featuring electronic music pioneer John Foxx, Benge and more recently Hannah Peel. The group specialises in the use of analogue synthesizers and drum machines. It was initially a studio based project working from Benge's studio in Shoreditch, London but has also engaged in live work.
Band history
Although it had been mentioned on Foxx's official Myspace blog in March 2009 that he "had been doing some recording with Benge", it was not until December of that year that the official John Foxx website Metamatic officially announced Foxx's new musical project. Benge had also already broken the news on his own blog in November calling The Maths "a new album project".
An initial single "Destination"/"September Town" was released in December 2009 as download only from Townsend Recordsand later via iTunes.
The duo continued to work in Benge's studio in Shoreditch throughout 2010 and some new tracks were previewed at the Short Circuit electronic music festival held at The Roundhouse in London on 5 June 2010. The performances were later released on the Analogue Circuit live album in 2012.
Interplay
An album entitled Interplay was announced in January 2011 and released on 21 March. The album gained much critical acclaim, with The Quietus calling it "one of the finest electronic records you will hear in 2011." This album features Mira Aroyo of Ladytron on vocals and synthesizers.
Another live event featuring John Foxx and the Maths originally scheduled for December 2010 was held in April 2011. 'Back to the Phuture' was billed as a special electronic music event – featuring live sets from John Foxx, Gary Numan, Mirrors and Motor – plus a DJ set by Mute Records founder Daniel Miller.
A cover version of the Pink Floyd track "Have a Cigar" was recorded for a tribute CD issued by Mojo magazine with their October 2011 issue. It was announced shortly afterwards that the version on the CD was not the completed version and a free download of the finished version was offered via the Mojo website.
Interplay Tour
A nine date UK tour by John Foxx and the Maths was announced in July 2011, plus live performances in Poland and Belgium. The setlist comprised mostly tracks from Interplay as well as tracks from Foxx's career with Ultravox and from his seminal electronic solo album Metamatic.
The group was augmented by Serafina Steer on keyboards and bass and Hannah Peel on keyboards and violin.
On 28 October 2011, it was announced that the final UK date in Holmfirth and the performance at the Sinners Day Festival in Belgium had to be cancelled as Foxx had suffered a fall and minor accident.
The Shape of Things and Evidence
A second album The Shape of Things was also announced prior to the tour and was initially only on available for purchase at tour venues.
The Shape of Things was issued as a limited edition special package, and described as being "a lot rougher around the edges and more experimental than “Interplay” – with so |
https://en.wikipedia.org/wiki/Jonathan%20Lubin | Jonathan Darby Lubin (born August 10, 1936, in Staten Island, New York) is a professor emeritus of mathematics at Brown University. He received an A.B. from Columbia College in 1957 and a Ph.D. from Harvard University in 1963 under the direction of John Tate. He taught at Bowdoin College from 1962–1967 and at Brown University from 1967–2000.
He and Tate introduced Lubin–Tate formal group laws and used them to construct explicit local class field theory.
References
Home page of Jonathan Lubin
Another home page of Jonathan Lubin
20th-century American mathematicians
21st-century American mathematicians
1936 births
Living people
Harvard University alumni
Brown University faculty
Columbia College (New York) alumni |
https://en.wikipedia.org/wiki/Amy%20Ellis | Amy Burns Ellis is a Full Professor in the Department of Mathematics and Science Education at the University of Georgia. She was formerly an associate professor in mathematics education in the Department of Curriculum & Instruction at the University of Wisconsin–Madison.
Education
Ellis received her BA in mathematics (with a minor in Japanese) from Washington University in St. Louis in 1993, and her MA in mathematics from San Jose State University in 1998. She received her Ph.D. in mathematics and science education in May, 2004, from the University of California at San Diego and San Diego State University. Her dissertation was titled Relationships between Generalizing and Justifying: Students' Reasoning with Linear Functions
Publications
Ellis has published articles in the Journal for Research in Mathematics Education, Cognition and Instruction, The Journal of the Learning Sciences, Science, and various other journals. In addition, Ellis has co-authored three books for the Essential Understandings Project book series by the National Council of Teachers of Mathematics, one published in 2010 one in 2011, and one in 2012.
Research funding
Ellis is a principal investigator on a variety of research projects, and has received numerous grants from the National Science Foundation, as well as other funding agencies.
Honors received
Ellis was awarded the Early Career Publication Award from the Research in Mathematics Education special interest group of the American Educational Research Association in 2008.
References
University of Wisconsin–Madison faculty
Living people
Mathematics educators
Year of birth missing (living people)
Washington University in St. Louis mathematicians
Washington University in St. Louis alumni
University of Georgia faculty
San Jose State University alumni
University of California, San Diego alumni
San Diego State University alumni |
https://en.wikipedia.org/wiki/2009%20Swedish%20Football%20Division%203 | Statistics of Swedish football Division 3 for the 2009 season.
League standings
Norra Norrland 2009
Mellersta Norrland 2009
Södra Norrland 2009
Norra Svealand 2009
Västra Svealand 2009
Södra Svealand 2009
Nordöstra Götaland 2009
Nordvästra Götaland 2009
Mellersta Götaland 2009
Sydöstra Götaland 2009
Sydvästra Götaland 2009
Södra Götaland 2009
Footnotes
References
Swedish Football Division 3 seasons
5
Sweden
Sweden |
https://en.wikipedia.org/wiki/Carlos%20Alb%C3%A1n | Carlos Albán (March 9, 1844 – January 20, 1902) was a Colombian inventor who specialized in mathematics, chemistry, medicine, and surgery. Albán also practiced as a political philosopher, journalist, and lawyer.
Early life and education
Born in Popayán, Colombia, the capital of the department of Cauca. Albán studied at the University of Cauca. In 1869, he was awarded a Doctor of Medicine and Surgery degree, and two years later, in 1871, he earned a doctorate of Law and Political Science, for which he wrote a thesis on the "Constitution of 1863". The thesis declared that the Colombian people could no longer be governed by liberalism, including the Constitution and its laws.
Career
Journalism
After returning from battle in 1865, Albán set about reorganizing the Conservative Party which had virtually disappeared. To achieve this, he founded Los Principios, a newspaper in Cali, in 1870. The newspaper called for political activism and denounced the state of social disorder, which had resulted from the Rionegro and Cauca Constitutions. He believed that there existed a "carte blanche for violence," that the regime of individual liberty had degenerated in favor of the liberal mindset, and that many conservatives "had abandoned the main focus." In 1871, the paper had to be closed due to distribution problems.
Later that year, Albán founded the Principios Político-Religiosos (the Politico-Religious Principles) newspaper in Popayan, with assistance from Fernando Angulo and Sergio Arboleda, with whom he reorganized the Conservative Party. The newspaper was forced to close after the first term, because the liberals warned that conservative reorganization would lead to war. It reopened in 1873 under the management of Manuel Carvajal Valencia and with the collaboration of Albán, who was also writing in El Tradicionista (the Traditionist) and other conservative newspapers in Bogotá.
Political activism
Albán began participating in political activities as a youth. In 1865, while still a student, he fought in the Battle of Santa Barbara in defense of the liberal government of the Sovereign State of Cauca, which faced a conservative revolution. His most active years were 1875-76 when he took advantage of the division of the liberal camp among radicals and independents and began to work on creating a "Catholic Party". Persons who "support Catholicism with all its consequences, and without restrictions of any kind, regardless of what may happen and also the political party to which they belong" were invited to join.
His journalism expressed the importance of Catholicism as an element of political cohesion. He had noted that the clergy, especially Carlos Bermudez, Bishop of Popayan and Manuel Canuto Restrepo, Bishop of Pasto, were important agitators. A huge image of the Virgin of Lourdes in Cauca was used in processions for political purposes. They formed various Catholic Societies, such as the society of St. Vincent de Paul, Sacred Heart and others.
Despit |
https://en.wikipedia.org/wiki/2008%20Swedish%20Football%20Division%203 | Statistics of Swedish football Division 3 for the 2008 season.
League standings
Norra Norrland 2008
Mellersta Norrland 2008
Södra Norrland 2008
Gestrike/Hammarby IF Withdrew
Norra Svealand 2008
Västra Svealand 2008
Södra Svealand 2008
Nordöstra Götaland 2008
Nordvästra Götaland 2008
Mellersta Götaland 2008
Sydöstra Götaland 2008
Sydvästra Götaland 2008
Södra Götaland 2008
Footnotes
References
Swedish Football Division 3 seasons
5
Sweden
Sweden |
https://en.wikipedia.org/wiki/2012%20Western%20Bulldogs%20season |
2012 NAB Cup
2012 Australian Football League season
See also
2012 AFL season
External links
AFL official site
Statistics and Results
AlltheStats
AFL Tables
Final Siren with comprehensive AFL Statistics 1980–2008
AFL Statistics by FootyWire
Comprehensive & unique AFL Statistics by ProWess Sports
Footystats Diary: AFL records/results/analysis plus news digest
AFL on Austadiums
Major AFL news Sites
Aussie Rules Latest News Headlines
The Age Footy News
Fox Sports Australia AFL news
Herald Sun Footy News
History
Full Points Footy
Western Bulldogs seasons
Western Bulldogs |
https://en.wikipedia.org/wiki/Morris%20method | In applied statistics, the Morris method for global sensitivity analysis is a so-called one-step-at-a-time method, meaning that in each run only one input parameter is given a new value. It facilitates a global sensitivity analysis by making a number r of local changes at different points x(1 → r) of the possible range of input values.
Method's details
Elementary effects' distribution
The finite distribution of elementary effects associated with the ith input factor, is obtained by randomly sampling different x from Ω, and is denoted by Fi
Variations
In the original work of Morris the two sensitivity measures proposed were respectively the mean, μ,
and the standard deviation, σ, of Fi. However, choosing Morris has the drawback that, if the distribution, Fi, contains negative elements, which occurs when the model is non-monotonic, when computing the mean some effects may cancel each other out. Thus, the measure μ on its own is not reliable for ranking factors in order
of importance. It is necessary to consider at the same time the values of μ and σ, as a factor with elementary effects of different signs (that cancel each other out) would have a low value of μ but a
considerable value of σ that avoids underestimating the factors.
μ*
If the distribution, Fi, contains negative elements, which occurs when the model is non-monotonic, when
computing the mean some effects may cancel each other out. When the goal is to rank factors in order of importance by making use of a single sensitivity measure, scientific advice is to use μ∗,which by making use of the absolute value, avoids the occurrence of effects of opposite signs.
In Revised Morris method μ* is used to detect input factors with an important overall influence on the output. σ is used to detect factors involved in interaction with other factors or whose effect is non-linear.
Method's steps
The method starts by sampling a set of start values within the defined ranges of possible values for all input variables and calculating the subsequent model outcome. The second step changes the values for one variable (all other inputs remaining at their start values) and calculates the resulting change in model outcome compared to the first run. Next, the values for another variable are changed (the previous variable is kept at its changed value and all other ones kept at their start values) and the resulting change in model outcome compared to the second run is calculated. This goes on until all input variables are changed. This procedure is repeated r times (where r is usually taken between 5 and 15), each time with a different set of start values, which leads to a number of r(k + 1) runs, where k is the number of input variables. Such number is very efficient compared to more demanding methods for sensitivity analysis.
A sensitivity analysis method widely used to screen factors in models of large dimensionality is the design proposed by Morris. The Morris method deals efficiently with models contain |
https://en.wikipedia.org/wiki/Weber%20modular%20function | In mathematics, the Weber modular functions are a family of three functions f, f1, and f2, studied by Heinrich Martin Weber.
Definition
Let where τ is an element of the upper half-plane. Then the Weber functions are
These are also the definitions in Duke's paper "Continued Fractions and Modular Functions". The function is the Dedekind eta function and should be interpreted as . The descriptions as quotients immediately imply
The transformation τ → –1/τ fixes f and exchanges f1 and f2. So the 3-dimensional complex vector space with basis f, f1 and f2 is acted on by the group SL2(Z).
Alternative infinite product
Alternatively, let be the nome,
The form of the infinite product has slightly changed. But since the eta quotients remain the same, then as long as the second uses the nome . The utility of the second form is to show connections and consistent notation with the Ramanujan G- and g-functions and the Jacobi theta functions, both of which conventionally uses the nome.
Relation to the Ramanujan G and g functions
Still employing the nome , define the Ramanujan G- and g-functions as
The eta quotients make their connection to the first two Weber functions immediately apparent. In the nome, assume Then,
Ramanujan found many relations between and which implies similar relations between and . For example, his identity,
leads to
For many values of n, Ramanujan also tabulated for odd n, and for even n. This automatically gives many explicit evaluations of and . For example, using , which are some of the square-free discriminants with class number 2,
and one can easily get from these, as well as the more complicated examples found in Ramanujan's Notebooks.
Relation to Jacobi theta functions
The argument of the classical Jacobi theta functions is traditionally the nome
Dividing them by , and also noting that , then they are just squares of the Weber functions
with even-subscript theta functions purposely listed first. Using the well-known Jacobi identity with even subscripts on the LHS,
therefore,
Relation to j-function
The three roots of the cubic equation
where j(τ) is the j-function are given by . Also, since,
and using the definitions of the Weber functions in terms of the Jacobi theta functions, plus the fact that , then
since and have the same formulas in terms of the Dedekind eta function .
See also
Ramanujan–Sato series, level 4
References
Notes
Modular forms |
https://en.wikipedia.org/wiki/1985%E2%80%9386%20NCAA%20Division%20I%20men%27s%20basketball%20season |
Season headlines
Blocked shots and steals both became official statistics tracked by the NCAA. David Robinson of Navy became the first national blocked shot champion, averaging 5.91 per game for the season. The first steals champion was Darron Brittman of Chicago State, with 4.96 per game.
Major rule changes
Beginning in 1985–86, the following rules changes were implemented:
The 45 second shot clock was introduced.
With the shot clock's introduction, the so-called "lack of action" count (when the offense fails to attempt a shot in a five-second timeframe) was abolished.
If a shooter was fouled intentionally and the shot was missed, the penalty was two shots and possession of the ball out of bounds to the team who was fouled.
Conferences were permitted to experiment with a three-point field goal, provided the distance was set to at least 19 feet, 9 inches from the center of the basket.
Season outlook
Pre-season polls
The top 20 from the AP Poll during the pre-season.
Regular season
Conference winners and tournaments
Statistical leaders
Conference standings
Postseason tournaments
NCAA tournament
Final Four - Reunion Arena, Dallas, Texas
National Invitation tournament
NIT Semifinals and Final
Played at Madison Square Garden in New York City
Third Place - Louisiana Tech 67, Florida 62
Award winners
Consensus All-American teams
Major player of the year awards
Wooden Award: Walter Berry, St. John's
Naismith Award: Johnny Dawkins, Duke
Associated Press Player of the Year: Walter Berry, St. John's
UPI Player of the Year: Walter Berry, St. John's
NABC Player of the Year: Walter Berry, St. John's
Oscar Robertson Trophy (USBWA): Walter Berry, St. John's
Adolph Rupp Trophy: Walter Berry, St. John's
Sporting News Player of the Year: Walter Berry, St. John's
Major coach of the year awards
Associated Press Coach of the Year: Eddie Sutton, Kentucky
UPI Coach of the Year: Mike Krzyzewski, Duke
Henry Iba Award (USBWA): Dick Versace, Bradley
NABC Coach of the Year: Eddie Sutton, Kentucky
CBS/Chevrolet Coach of the Year: Mike Krzyzewski, Duke
Sporting News Coach of the Year: Denny Crum, Louisville
Other major awards
Frances Pomeroy Naismith Award (Best player under 6'0): Jim Les, Bradley
Robert V. Geasey Trophy (Top player in Philadelphia Big 5): Harold Pressley, Villanova
NIT/Haggerty Award (Top player in New York City metro area): Walter Berry, St. John's
Coaching changes
A number of teams changed coaches during the season and after it ended.
References |
https://en.wikipedia.org/wiki/2007%20Swedish%20Football%20Division%203 | Statistics of Swedish football Division 3 for the 2007 season.
League standings
Norra Norrland 2007
Mellersta Norrland 2007
Södra Norrland 2007
Norra Svealand 2007
Östra Svealand 2007
Västra Svealand 2007
Nordöstra Götaland 2007
Nordvästra Götaland 2007
Mellersta Götaland 2007
Sydöstra Götaland 2007
Sydvästra Götaland 2007
Södra Götaland 2007
Footnotes
References
Swedish Football Division 3 seasons
5
Sweden
Sweden |
https://en.wikipedia.org/wiki/2011%E2%80%9312%20Adelaide%20United%20FC%20%28W-League%29%20season | The Adelaide United W-League 2011–12 season was Adelaide United's fourth season in the W-League.
Technical staff
Players
Squad
Transfers
In
Out
Squad statistics
Fixtures
Standings
References
External links
Official club website
W-League Match Centre Round 1
W-League Match Centre Round 2
2011-12
2011–12 W-League (Australia) by team |
https://en.wikipedia.org/wiki/Montgomery%20Slatkin | Montgomery Wilson Slatkin is an American biologist, and professor at University of California, Berkeley.
Education
Slatkin received his undergraduate degree in mathematics from Massachusetts Institute of Technology and his PhD from Harvard University.
Research
Slatkin is faculty of the Slatkin Research Group, in the Center for Theoretical Evolutionary Genomics.
Publications
Slatkin is the author of several books and scientific papers in peer-reviewed scientific journals.
Awards
In 2000, Slatkin won the Sewall Wright Award and is on the Science Board of the Santa Fe Institute.
References
21st-century American biologists
University of California, Berkeley faculty
Living people
Harvard University alumni
Santa Fe Institute people
Massachusetts Institute of Technology School of Science alumni
Year of birth missing (living people) |
https://en.wikipedia.org/wiki/Parallelization%20%28mathematics%29 | In mathematics, a parallelization of a manifold of dimension n is a set of n global smooth linearly independent vector fields.
Formal definition
Given a manifold of dimension n, a parallelization of is a set of n smooth vector fields defined on all of such that for every the set is a basis of , where denotes the fiber over of the tangent vector bundle .
A manifold is called parallelizable whenever it admits a parallelization.
Examples
Every Lie group is a parallelizable manifold.
The product of parallelizable manifolds is parallelizable.
Every affine space, considered as manifold, is parallelizable.
Properties
Proposition. A manifold is parallelizable iff there is a diffeomorphism such that the first projection of is and for each the second factor—restricted to —is a linear map .
In other words, is parallelizable if and only if is a trivial bundle. For example, suppose that is an open subset of , i.e., an open submanifold of . Then is equal to , and is clearly parallelizable.
See also
Chart (topology)
Differentiable manifold
Frame bundle
Orthonormal frame bundle
Principal bundle
Connection (mathematics)
G-structure
Web (differential geometry)
Notes
References
Differential geometry
Fiber bundles
Vector bundles |
https://en.wikipedia.org/wiki/2006%20Swedish%20Football%20Division%203 | Statistics of Swedish football Division 3 for the 2006 season.
League standings
Norra Norrland 2006
Mellersta Norrland 2006
Södra Norrland 2006
Norra Svealand 2006
Östra Svealand 2006
Västra Svealand 2006
Nordöstra Götaland 2006
Nordvästra Götaland 2006
Mellersta Götaland 2006
Sydöstra Götaland 2006
Sydvästra Götaland 2006
Södra Götaland 2006
Footnotes
References
Swedish Football Division 3 seasons
5
Sweden
Sweden |
https://en.wikipedia.org/wiki/Ihumwa | Ihumwa is an administrative ward in the Dodoma Urban district of the Dodoma Region of Tanzania. In 2016 the Tanzania National Bureau of Statistics report there were 11,490 people in the ward.
References
Populated places in Dodoma Region |
https://en.wikipedia.org/wiki/2005%20Swedish%20Football%20Division%203 | Statistics of Swedish football Division 3 for the 2005 season.
League standings
Norra Norrland 2005
Mellersta Norrland 2005
Södra Norrland 2005
Norra Svealand 2005
Östra Svealand 2005
Västra Svealand 2005
Nordöstra Götaland 2005
Nordvästra Götaland 2005
Mellersta Götaland 2005
Sydöstra Götaland 2005
Sydvästra Götaland 2005
Södra Götaland 2005
Footnotes
References
Swedish Football Division 3 seasons
4
Sweden
Sweden |
https://en.wikipedia.org/wiki/Two-way%20analysis%20of%20variance | In statistics, the two-way analysis of variance (ANOVA) is an extension of the one-way ANOVA that examines the influence of two different categorical independent variables on one continuous dependent variable. The two-way ANOVA not only aims at assessing the main effect of each independent variable but also if there is any interaction between them.
History
In 1925, Ronald Fisher mentions the two-way ANOVA in his celebrated book, Statistical Methods for Research Workers (chapters 7 and 8). In 1934, Frank Yates published procedures for the unbalanced case. Since then, an extensive literature has been produced. The topic was reviewed in 1993 by Yasunori Fujikoshi. In 2005, Andrew Gelman proposed a different approach of ANOVA, viewed as a multilevel model.
Data set
Let us imagine a data set for which a dependent variable may be influenced by two factors which are potential sources of variation. The first factor has levels and the second has levels . Each combination defines a treatment, for a total of treatments. We represent the number of replicates for treatment by , and let be the index of the replicate in this treatment .
From these data, we can build a contingency table, where and , and the total number of replicates is equal to .
The experimental design is balanced if each treatment has the same number of replicates, . In such a case, the design is also said to be orthogonal, allowing to fully distinguish the effects of both factors. We hence can write , and .
Model
Upon observing variation among all data points, for instance via a histogram, "probability may be used to describe such variation". Let us hence denote by the random variable which observed value is the -th measure for treatment . The two-way ANOVA models all these variables as varying independently and normally around a mean, , with a constant variance, (homoscedasticity):
.
Specifically, the mean of the response variable is modeled as a linear combination of the explanatory variables:
,
where is the grand mean, is the additive main effect of level from the first factor (i-th row in the contingency table), is the additive main effect of level from the second factor (j-th column in the contingency table) and is the non-additive interaction effect of treatment for samples from both factors (cell at row i and column j in the contingency table).
Another equivalent way of describing the two-way ANOVA is by mentioning that, besides the variation explained by the factors, there remains some statistical noise. This amount of unexplained variation is handled via the introduction of one random variable per data point, , called error. These random variables are seen as deviations from the means, and are assumed to be independent and normally distributed:
.
Assumptions
Following Gelman and Hill, the assumptions of the ANOVA, and more generally the general linear model, are, in decreasing order of importance:
the data points are relevant with respect to the sc |
https://en.wikipedia.org/wiki/2004%20Swedish%20Football%20Division%203 | Statistics of Swedish football Division 3 for the 2004 season.
League standings
Norra Norrland 2004
Mellersta Norrland 2004
Södra Norrland 2004
Norra Svealand 2004
Östra Svealand 2004
Västra Svealand 2004
Nordöstra Götaland 2004
Nordvästra Götaland 2004
Mellersta Götaland 2004
Sydöstra Götaland 2004
Sydvästra Götaland 2004
Södra Götaland 2004
Footnotes
References
Swedish Football Division 3 seasons
4
Sweden
Sweden |
https://en.wikipedia.org/wiki/Matthias%20Kreck | Matthias Kreck (born 22 July 1947, in Dillenburg) is a German mathematician who works in the areas of Algebraic Topology and Differential topology. From 1994 to 2002 he was director of the Oberwolfach Research Institute for Mathematics and from October 2006 to September 2011 he was the director of the Hausdorff Center for Mathematics at the University of Bonn, where he is currently a professor.
Life and work
Kreck grew up as the son of the theologian in Herborn and studied mathematics and physics from 1966 to 1970, and business administration at the Universities of Bonn, Berlin and Regensburg. In 1970 he submitted his diploma in Mathematics in Bonn and in 1972 he received his doctorate there under the supervision of Friedrich Hirzebruch, with a thesis titled An invariant for stably parallelized manifolds. From 1972 to 1976 he studied Protestant theology in Bonn: in a similar period he was also assistant from 1970 to 1976 to professor Hirzebruch. In 1977 he completed his habilitation in Bonn in Mathematics, titled Bordism groups of diffeomorphisms. In 1976 he became professor at the University of Wuppertal and in 1978 he moved to the University of Mainz. From 1994 to 2002 he was director of the Oberwolfach Research Institute for Mathematics. In 1999 he became professor at the University of Heidelberg. From 2007 until October 2011 he was the founding director of the Hausdorff Research Institute for Mathematics at the University of Bonn. In 1981/82 and from 1989 to 1992 he was visiting professor at the Max Planck Institute for Mathematics in Bonn. He was also a guest researcher at places including Paris, Princeton, Berkeley, Chicago, Aarhus, St. Petersburg, Moscow and Beijing.
Kreck worked on the classification of manifolds in differential topology (e.g. bordism groups), 4-manifolds with exotic differentiable structure and the interaction of differential geometry and topology. In his habilitation in 1977 he managed the complete classification of closed smooth manifolds with diffeomorphisms up to bordism: a problem that had already been worked on by René Thom, William Browder and Dennis Sullivan. Building on this work he developed a modified theory of surgery which is applicable under weaker conditions than classical surgery and he applied this theory to solve outstanding questions in differential geometry. In the 2000s (decade), he considered examples of asymmetric topological manifolds, finding the first example of such a manifold with trivial fundamental group.
From 1990 to 1998 he was an editor of Mathematische Annalen and from 1998 to 2002 for Archiv der Mathematik. Since 2000 he has been a member of the Heidelberg Academy of Sciences. In 2003 he was made an honorary doctor of the University of Siegen. In 2010 he was awarded the Cantor Medal. In 2012 the German Mathematical Society awarded him a Gauss Lectureship. In 2023, he was elected as a corresponding member of the Göttingen Academy of Sciences and Humanities.
Among his PhD s |
https://en.wikipedia.org/wiki/2003%20Swedish%20Football%20Division%203 | Statistics of Swedish football Division 3 for the 2003 season.
League standings
Norra Norrland 2003
Mellersta Norrland 2003
Södra Norrland 2003
Norra Svealand 2003
Östra Svealand 2003
Västra Svealand 2003
Nordöstra Götaland 2003
Nordvästra Götaland 2003
Mellersta Götaland 2003
Sydöstra Götaland 2003
Sydvästra Götaland 2003
Södra Götaland 2003
Footnotes
References
Swedish Football Division 3 seasons
4
Sweden
Sweden |
https://en.wikipedia.org/wiki/Novikov%E2%80%93Veselov%20equation | In mathematics, the Novikov–Veselov equation (or Veselov–Novikov equation) is a natural (2+1)-dimensional analogue of the Korteweg–de Vries (KdV) equation. Unlike another (2+1)-dimensional analogue of KdV, the Kadomtsev–Petviashvili equation, it is integrable via the inverse scattering transform for the 2-dimensional stationary Schrödinger equation. Similarly, the Korteweg–de Vries equation is integrable via the inverse scattering transform for the 1-dimensional Schrödinger equation. The equation is named after S.P. Novikov and A.P. Veselov who published it in .
Definition
The Novikov–Veselov equation is most commonly written as
where and the following standard notation of complex analysis is used: is the real part,
The function is generally considered to be real-valued. The function is an auxiliary function defined via up to a holomorphic summand, is a real parameter corresponding to the energy level of the related 2-dimensional Schrödinger equation
Relation to other nonlinear integrable equations
When the functions and in the Novikov–Veselov equation depend only on one spatial variable, e.g. , , then the equation is reduced to the classical Korteweg–de Vries equation. If in the Novikov–Veselov equation , then the equation reduces to another (2+1)-dimensional analogue of the KdV equation, the Kadomtsev–Petviashvili equation (to KP-I and KP-II, respectively) .
History
The inverse scattering transform method for solving nonlinear partial differential equations (PDEs) begins with the discovery of C.S. Gardner, J.M. Greene, M.D. Kruskal, R.M. Miura , who demonstrated that the Korteweg–de Vries equation can be integrated via the inverse scattering problem for the 1-dimensional stationary Schrödinger equation. The algebraic nature of this discovery was revealed by Lax who showed that the Korteweg–de Vries equation can be written in the following operator form (the so-called Lax pair):
where , and is a commutator. Equation () is a compatibility condition for the equations
for all values of .
Afterwards, a representation of the form () was found for many other physically interesting nonlinear equations, like the Kadomtsev–Petviashvili equation, sine-Gordon equation, nonlinear Schrödinger equation and others. This led to an extensive development of the theory of inverse scattering transform for integrating nonlinear partial differential equations.
When trying to generalize representation () to two dimensions, one obtains that it holds only for trivial cases (operators , , have constant coefficients or operator is a differential operator of order not larger than 1 with respect to one of the variables). However, S.V. Manakov showed that in the two-dimensional case it is more correct to consider the following representation (further called the Manakov L-A-B triple):
or, equivalently, to search for the condition of compatibility of the equations
at one fixed value of parameter .
Representation () for the 2-dimensional Schrödinger op |
https://en.wikipedia.org/wiki/Jun-Ichi%20Igusa | was a Japanese mathematician who for over three decades was on the faculty at Johns Hopkins University. He is known for his contributions to algebraic geometry and number theory. The Igusa zeta-function, the Igusa quartic, Igusa subgroups, Igusa curves, and Igusa varieties are named after him.
He was an invited speaker for the 1962 International Congress of Mathematicians in Stockholm. He was awarded Japan's Order of the Sacred Treasure. In 2012 he became a fellow of the American Mathematical Society.
Life and career
Igusa was born in Kiyosato village, Gunma Prefecture, Japan, on 30 January 1924. He graduated from the University of Tokyo in 1945 and received his Ph.D. from Kyoto University in 1953, after which he became professor of mathematics at the University of Tsukuba. After a brief period spent at Harvard University, he took up a permanent position at Johns Hopkins University, in Baltimore. Igusa taught at Johns Hopkins from 1955 to 1993. He joined the staff of the American Journal of Mathematics as an associate editor in 1964, and served as chief editor between 1978 and 1993. Igusa died, aged 89, of a stroke at Holly Hill Nursing Home in Towson, Maryland, on 24 November 2013.
He had three sons, Kiyoshi, Takeru and Mitsuru. Takeru Igusa is a professor of civil engineering at Johns Hopkins University. Kiyoshi Igusa is a professor of mathematics at Brandeis University.
Publications
References
1924 births
2013 deaths
20th-century Japanese mathematicians
21st-century Japanese mathematicians
Kyoto University alumni
Johns Hopkins University faculty
Fellows of the American Mathematical Society
Japanese expatriates in the United States
Academic journal editors
Recipients of the Order of the Sacred Treasure, 3rd class
University of Tokyo alumni
People from Gunma Prefecture
Academic staff of the University of Tsukuba
Harvard University Department of Mathematics faculty
Harvard University faculty |
https://en.wikipedia.org/wiki/Ubiratan%20D%27Ambrosio | Ubiratan D'Ambrosio (December 8, 1932 – May 12, 2021) was a Brazilian mathematics educator and historian of mathematics.
Life
D'Ambrosio was born in São Paulo, and earned his doctorate from the University of São Paulo in 1963. He retired as a professor of mathematics from the State University of Campinas, São Paulo, Brazil in 1993.
He was a member of many societies, including Pugwash, and served the International Commission on the History of Mathematics (ICHM) for five years.
D'Ambrosio was also the founder of the Brazilian Society for Mathematics and History of the International Group of Ethnomathematicians.
In 2001, he and Lam Lay Yong were jointly awarded the Kenneth O. May Prize.
Writings
Books
1996, Educação Matemática: da teoria à prática.
Book chapters
1997, Ethno Mathematics. Challenging Eurocentrism, in Arthur B. Powell, Marilyn Frankenstein (eds.) Mathematics Education, State University of New York Press, Albany 1997, p. 13–24.
Historiographical Proposal for Non-Western Mathematics, in Helaine Selin (ed.), Mathematics Across Cultures. The History of Non-Western Mathematics, Kluwer Academic Publishers, Dordrecht, 2000, pp. 79–92.
Articles
A Busca da paz como responsabilidade dos matemáticos. Cuadernos de Investigación y Formación en Educación Matemática 7 (2011)
A Etnomatemática no processo de construção de uma escola indígena. Em aberto 63 (1994)
External links
Selected works
References
1932 births
2021 deaths
Historians of mathematics
20th-century Brazilian historians
University of São Paulo alumni
Academic staff of the State University of Campinas
People from São Paulo |
https://en.wikipedia.org/wiki/Mathematical%20finance | Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets.
In general, there exist two separate branches of finance that require advanced quantitative techniques: derivatives pricing on the one hand, and risk and portfolio management on the other.
Mathematical finance overlaps heavily with the fields of computational finance and financial engineering. The latter focuses on applications and modeling, often by help of stochastic asset models, while the former focuses, in addition to analysis, on building tools of implementation for the models.
Also related is quantitative investing, which relies on statistical and numerical models (and lately machine learning) as opposed to traditional fundamental analysis when managing portfolios.
French mathematician Louis Bachelier's doctoral thesis, defended in 1900, is considered the first scholarly work on mathematical finance. But mathematical finance emerged as a discipline in the 1970s, following the work of Fischer Black, Myron Scholes and Robert Merton on option pricing theory. Mathematical investing originated from the research of mathematician Edward Thorp who used statistical methods to first invent card counting in blackjack and then applied its principles to modern systematic investing.
The subject has a close relationship with the discipline of financial economics, which is concerned with much of the underlying theory that is involved in financial mathematics. While trained economists use complex economic models that are built on observed empirical relationships, in contrast, mathematical finance analysis will derive and extend the mathematical or numerical models without necessarily establishing a link to financial theory, taking observed market prices as input.
See: Valuation of options; Financial modeling; Asset pricing.
The fundamental theorem of arbitrage-free pricing is one of the key theorems in mathematical finance, while the Black–Scholes equation and formula are amongst the key results.
Today many universities offer degree and research programs in mathematical finance.
History: Q versus P
There are two separate branches of finance that require advanced quantitative techniques: derivatives pricing, and risk and portfolio management. One of the main differences is that they use different probabilities such as the risk-neutral probability (or arbitrage-pricing probability), denoted by "Q", and the actual (or actuarial) probability, denoted by "P".
Derivatives pricing: the Q world
The goal of derivatives pricing is to determine the fair price of a given security in terms of more liquid securities whose price is determined by the law of supply and demand. The meaning of "fair" depends, of course, on whether one considers buying or selling the security. Examples of securities being priced are plain vanilla and exotic options, convertible bonds, etc.
Once a fair pric |
https://en.wikipedia.org/wiki/Christoph%20Scriba | Christoph J. Scriba (6 October 1929 – 26 July 2013) was a German historian of mathematics.
Life and work
Scriba was born in Darmstadt and studied at Justus-Liebig-University Giessen. He read James Gregory's early writings on the calculus with Joseph Ehrenfried Hofmann, and was awarded his doctorate in 1957. Continuing with J.E. Hofmann, and with Bernard Sticker, he investigated the papers of John Wallis in Oxford in 1966, contributing to Studies on the Mathematics of John Wallis.
Scriba then taught at the University of Kentucky, the University of Massachusetts and at the University of Toronto from 1959 to 1962. He became chairman of Technical University of Berlin's department of History of Mathematics in 1969. Then in 1975 he became Professor of History of Natural Science and Mathematics at the University of Hamburg and Director of the Institute until he retired in 1995. His successor there was Karin Reich.
Scriba was on the Executive Committee of the International Commission on the History of Mathematics and its president from 1977 to 1985. He was a member of Jungius company in Hamburg, the Leopoldina, the International Academy of the History of Science, and since 1995 the Göttingen Academy of Sciences. In 1993 he was awarded the Kenneth O. May Prize of the ICHM. He was the doctorate advisor of Eberhard Knobloch. He died in July 2013 in Hamburg.
Writings
1966: Studies on the mathematics of John Wallis (1616–1703): Angular divisions, combining theory and number theory problems. Appendix: the books and manuscripts of Valais . Wiesbaden (habilitation)
1968: The Concept of Number: A chapter in the history of mathematics, with applications of interest to teachers, BI university paperback
2003: (editor with Philip Beeley) The Correspondence of John Wallis, volume 1 (1641 to 59), 2005: volume 2 (1660 to September 1668), 2012: volume 3 (October 1668 to 71) Oxford University Press
Literature
Joseph W. Dauben (and other editors) (1996) History of mathematics. State of the Art Flores quadrivii. Studies in Honor of Christoph J. Scriba, Academic Press, .
Joseph Dauben (2002) Writing the History of Mathematics—its historic development, Birkhauser
Peter Schreiber (2004) Geometry 5000 years – history, culture, people, Springer
Edward Seidler, Wieland Berg (Editors) (1995) The Elite of the Nation in the Third Reich – The ratio of scientific academies and their environment to Nazism, Leopoldina symposium, Hall
References
External links
Homepage
20th-century German mathematicians
German historians of mathematics
1929 births
2013 deaths
German historians of philosophy
21st-century German mathematicians
20th-century German historians
21st-century German historians
University of Giessen alumni
Academic staff of the University of Toronto
Academic staff of the University of Hamburg
Academic staff of the Technical University of Berlin |
https://en.wikipedia.org/wiki/Mathematics%20and%20science%20partnerships | Mathematics and Science Partnerships (MSP) is education policy from Title 2, Part B, Sections 2201-2203 of the No Child Left Behind Act of 2001. The purpose of MSP is to increase student achievement in science and mathematics by partnering IHE science, math, and engineering departments with elementary and secondary science and math teachers in high-need local educational agencies (LEAs) in order to develop teachers' content knowledge and instructional performance. SEAs may apply for competitive grants and then IHEs and LEAs may apply for a subgrant of the SEA.
Historical context
The United States began to place a greater focus on math and science education during the "Space Race" that began in the 1950s. The launch of Sputnik in 1957 by the Soviet Union created a scare that the United States was not a leader in math and science. In response to Sputnik, the National Defense Education Act initiated education policy that aimed to increase college enrollment and prepare a workforce qualified to compete with the Soviet Union in science and technical fields.
Math and science education continued to receive attention following the Cold War through various programs and policy in the STEM fields. The STEM Education Coalition currently works to promote awareness about the need for improved STEM education and supports legislature that advances teaching and learning in STEM fields.
The National Science Foundation also provides great support for STEM fields through various projects aimed at enhancing interest and performance in STEM through various means of support at the elementary, secondary, and post-secondary levels. Examples of such programs include summer research opportunities for undergraduates, fellowships for graduate students, and professional development for K-12 classroom teacher.
In 2001, President Bush signed the No Child Left Behind Act with the goal of having all students proficient in reading and math by 2014. Mathematics and Science Partnerships fall in the Title 2 section of NCLB, "Improving Teacher Quality Grant Program". Since then, science and math education has continued to be an area of concern in education policy due to the continued fear the United States is not producing innovative leaders in science and technology.
Design of partnerships
The Mathematics and Science Partnerships policy is implemented with the following framework:
Teachers partner with math, science, and engineering departments of IHEs (or with businesses or other organizations that have shown success with teacher education in math and science)
Partners provide professional development for math and science teachers
Student achievement increases as a result of improved teaching
The policy defines a "partnership" as a relationship between, at a minimum, a high-need LEA and a science, math, or engineering department of an IHE. Partnerships may also include an IHE teacher education program in science or math, other LEAs or public, private, and charter schools |
https://en.wikipedia.org/wiki/A%20Mathematician%27s%20Lament | A Mathematician's Lament, often referred to informally as Lockhart's Lament, is a short book on mathematics education by Paul Lockhart, originally a research mathematician at Brown University and U.C. Santa Cruz, and subsequently a math teacher at Saint Ann's School in Brooklyn, New York City for many years. This strongly worded opinion piece is organized into two parts. The first part, "Lamentation", criticizes the way mathematics is typically taught in American schools and argues for an aesthetic, intuitive, and problem-oriented approach to teaching. The second part, "Exultation", gives specific examples of how to teach mathematics as an art.
Background
This book was developed from a 25-page essay that was written in 2002, originally circulated in typewritten manuscript copies, and subsequently published by Keith Devlin on his online column for the Mathematical Association of America's webzine MAA Online.
Quotes
"The first thing to understand is that mathematics is an art. The difference between math and the other arts, such as music and painting, is that our culture does not recognize it as such."
"Other math courses may hide the beautiful bird, or put it in a cage, but in geometry class, it is openly and cruelly tortured."
References
Further reading
Paul Lockhart, Measurement (Cambridge: Belknap Press of Harvard University Press, 2012).
------. Arithmetic (Cambridge: Belknap Press of Harvard University Press, 2017).
External links
Lockhart's Lament, the essay which prefigured A Mathematician's Lament, by Paul Lockhart
Lockhart's Lament, about the earlier essay, by Keith Devlin
Books about mathematics education
Books about philosophy of mathematics
2009 non-fiction books
Bellevue Literary Press books |
https://en.wikipedia.org/wiki/Blakers%E2%80%93Massey%20theorem | In mathematics, the first Blakers–Massey theorem, named after Albert Blakers and William S. Massey, gave vanishing conditions for certain triad homotopy groups of spaces.
Description of the result
This connectivity result may be expressed more precisely, as follows. Suppose X is a topological space which is the pushout of the diagram
,
where f is an m-connected map and g is n-connected. Then the map of pairs
induces an isomorphism in relative homotopy groups in degrees and a surjection in the next degree.
However the third paper of Blakers and Massey in this area determines the critical, i.e., first non-zero, triad homotopy group as a tensor product, under a number of assumptions, including some simple connectivity. This condition and some dimension conditions were relaxed in work of Ronald Brown and Jean-Louis Loday. The algebraic result implies the connectivity result, since a tensor product is zero if one of the factors is zero. In the non simply connected case, one has to use the nonabelian tensor product of Brown and Loday.
The triad connectivity result can be expressed in a number of other ways, for example, it says that the pushout square above behaves like a homotopy pullback up to dimension .
Generalization to higher toposes
The generalization of the connectivity part of the theorem from traditional homotopy theory to any other infinity-topos with an infinity-site of definition was given by Charles Rezk in 2010.
Fully formal proof
In 2013 a fairly short, fully formal proof using homotopy type theory as a mathematical foundation and an Agda variant as a proof assistant was announced by Peter LeFanu Lumsdaine; this became Theorem 8.10.2 of Homotopy Type Theory – Univalent Foundations of Mathematics. This induces an internal proof for any infinity-topos (i.e. without reference to a site of definition); in particular, it gives a new proof of the original result.
References
External links
Theorem 6.4.1
Theorems in algebraic topology |
https://en.wikipedia.org/wiki/List%20of%20Major%20League%20Baseball%20teams%20by%20payroll%20in%202011 | This is a list of the 30 Major League Baseball teams from the 2011 season, ranked by total team salary.
References
Major League Baseball lists
Major League Baseball statistics
Major League Baseball, payroll, 2011 |
https://en.wikipedia.org/wiki/Graham%20Brightwell | Graham Brightwell is a British mathematician working in the field of discrete mathematics.
Currently a professor at the London School of Economics, he has published nearly 100 papers in pure mathematics, including over a dozen with Béla Bollobás. His research interests include random combinatorial structures; partially ordered sets; algorithms; random graphs; discrete mathematics and graph theory. (Bollobás supervised his PhD on "Linear Extensions of Partially Ordered Sets" at Cambridge, awarded 1988.)
Othello
Brightwell started playing Othello in 1985, after finding himself sharing an apartment with fellow mathematician and Othello player Imre Leader. He has finished three times as runner-up in the World Othello Championship and is a 5-time British Champion, and has served as chairman of the British Othello Federation and as editor of the British Othello Newsletter.
He created the Brightwell Quotient, often used in Othello tournaments, to resolve ties.
References
1962 births
Alumni of the University of Cambridge
20th-century British mathematicians
21st-century British mathematicians
Reversi players
Combinatorialists
Academics of the London School of Economics
Living people |
https://en.wikipedia.org/wiki/2008%20Myanmar%20Premier%20League | Statistics of the Myanmar Premier League in the 2008 season.
Overview
Kanbawza won the championship.
Teams
Finance and Revenue
Ministry of Commerce
Transport
Ministry of Energy
YC Development Committee
Kanbawza
Construction
Home Affairs
Forestry
Defence
Myanmar Railway
A&I
Royal Eleven
Army
See also
2000 Myanmar Premier League
2003 Myanmar Premier League
2004 Myanmar Premier League
2005 Myanmar Premier League
2006 Myanmar Premier League
2007 Myanmar Premier League
References
http://www.rsssf.com/tablesm/myan08.html
Myanmar Premier League seasons
Burma
Burma
1 |
https://en.wikipedia.org/wiki/2011%20Division%204%20%28Swedish%20football%29 | Statistics of Swedish football Division 4 for the 2011 season. There are also 5 divisions that form a lower tier of Division 4 that feed into the Halland and Småland Elit divisions in Division 4.
League standings
Blekinge 2011
Bohuslän/Dalsland 2011
Note: Dals-Långeds IK - withdrew before season
Dalarna 2011
Gotland 2011
Gästrikland 2011
Göteborg A 2011
Göteborg B 2011
Halland Elit 2011
Hälsingland 2011
Jämtland/Härjedalen 2011
Medelpad 2011
Norrbotten Norra 2011
Norrbotten Södra 2011
Skåne Nordvästra 2011
Skåne Sydvästra 2011
Skåne Östra 2011
Småland Elit Västra 2011
Småland Elit Östra 2011
Stockholm Mellersta 2011
Stockholm Norra 2011
Stockholm Södra 2011
Sörmland 2011
Uppland 2011
Värmland 2011
Västerbotten Norra 2011
Västerbotten Södra 2011
Västergötland Norra 2011
Västergötland Södra 2011
Västergötland Västra 2011
Västmanland 2011
Ångermanland 2011
Örebro 2011
Östergötland Västra 2011
Östergötland Östra 2011
Footnotes
References
Swedish Football Division 4 seasons
6 |
https://en.wikipedia.org/wiki/Borel%20isomorphism | In mathematics, a Borel isomorphism is a measurable bijective function between two standard Borel spaces. By Souslin's theorem in standard Borel spaces (which says that a set that is both analytic and coanalytic is necessarily Borel), the inverse of any such measurable bijective function is also measurable. Borel isomorphisms are closed under composition and under taking of inverses. The set of Borel isomorphisms from a space to itself clearly forms a group under composition. Borel isomorphisms on standard Borel spaces are analogous to homeomorphisms on topological spaces: both are bijective and closed under composition, and a homeomorphism and its inverse are both continuous, instead of both being only Borel measurable.
Borel space
A measurable space that is Borel isomorphic to a measurable subset of the real numbers is called a Borel space.
See also
Federer–Morse theorem
References
Alexander S. Kechris (1995) Classical Descriptive Set Theory, Springer-Verlag.
External links
S. K. Berberian (1988) Borel Spaces from University of Texas
Richard M. Dudley (2002) Real Analysis and Probability, 2nd edition, page 487.
Sashi Mohan Srivastava (1998) A Course on Borel Sets
Measure theory |
https://en.wikipedia.org/wiki/2012%20Halmstads%20BK%20season | In 2012 Halmstads BK will compete in Superettan and Svenska Cupen.
2012 season squad
Statistics prior to season start only
Transfers
In
Out
Appearances and goals
As of 18 December 2012
|-
|colspan="14"|Players who have departed the club after the start of the season:
|}
Matches
Pre-season/friendlies
Superettan
Promotion/relegation play-offs
Halmstads BK promoted 6-4 on aggregate.
Svenska Cupen
Competitions
Superettan
Standings
Results summary
Results by round
Season statistics
Superettan
Goals and caps in the promotion/relegation play-offs are shown in the () as they are not official league matches.
= Number of bookings
8px= Number of sending offs after a second yellow card
= Number of sending offs by a direct red card
Svenska cupen
= Number of bookings
8px= Number of sending offs after a second yellow card
= Number of sending offs by a direct red card
International players
Does only contain players that represent the senior squad during the 2012 season.
Senior
U21
Youth
References
Footnotes
References
External links
Halmstads BK homepage
SvFF homepage
Halmstads BK seasons
Halmstad |
Subsets and Splits
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