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https://en.wikipedia.org/wiki/2000%20JEF%20United%20Ichihara%20season | 2000 JEF United Ichihara season
Competitions
Domestic results
J.League 1
Emperor's Cup
J.League Cup
Player statistics
Other pages
J.League official site
JEF United Ichihara
JEF United Chiba seasons |
https://en.wikipedia.org/wiki/2000%20Kashiwa%20Reysol%20season | 2000 Kashiwa Reysol season
Competitions
Domestic results
J.League 1
Emperor's Cup
J.League Cup
Player statistics
Other pages
J. League official site
Kashiwa Reysol
Kashiwa Reysol seasons |
https://en.wikipedia.org/wiki/2000%20FC%20Tokyo%20season | 2000 F.C. Tokyo season
Competitions
Domestic results
J.League 1
Emperor's Cup
J.League Cup
Player statistics
Other pages
J.League official site
Tokyo
2000 |
https://en.wikipedia.org/wiki/2000%20Verdy%20Kawasaki%20season | 2000 Verdy Kawasaki season
Competitions
Domestic results
J.League 1
Emperor's Cup
J.League Cup
Player statistics
Other pages
J. League official site
Verdy Kawasaki
Tokyo Verdy seasons |
https://en.wikipedia.org/wiki/2000%20Kawasaki%20Frontale%20season | 2000 Kawasaki Frontale season
Competitions
Domestic results
J.League 1
Emperor's Cup
J.League Cup
Player statistics
Other pages
J.League official site
Kawasaki Frontale
Kawasaki Frontale seasons |
https://en.wikipedia.org/wiki/2000%20Yokohama%20F.%20Marinos%20season | 2000 Yokohama F. Marinos season
Competitions
Domestic results
J.League 1
Emperor's Cup
J.League Cup
Player statistics
Other pages
J.League official site
References
Yokohama F. Marinos
Yokohama F. Marinos seasons |
https://en.wikipedia.org/wiki/2000%20J%C3%BAbilo%20Iwata%20season | 2000 Júbilo Iwata season
Competitions
Domestic results
J.League 1
Emperor's Cup
J.League Cup
Player statistics
Other pages
J.League official site
Jubilo Iwata
Júbilo Iwata seasons |
https://en.wikipedia.org/wiki/2000%20Nagoya%20Grampus%20Eight%20season | 2000 Nagoya Grampus Eight season
Competitions
Domestic results
J.League 1
Emperor's Cup
J.League Cup
Player statistics
Other pages
J.League official site
Nagoya Grampus Eight
Nagoya Grampus seasons |
https://en.wikipedia.org/wiki/2000%20Kyoto%20Purple%20Sanga%20season | 2000 Kyoto Purple Sanga season
Competitions
Domestic results
J.League 1
Emperor's Cup
J.League Cup
Player statistics
Other pages
J.League official site
Kyoto Purple Sanga
Kyoto Sanga FC seasons |
https://en.wikipedia.org/wiki/2000%20Gamba%20Osaka%20season | 2000 Gamba Osaka season
Competitions
Domestic results
J.League 1
Emperor's Cup
J.League Cup
Player statistics
Other pages
J.League official site
Gamba Osaka
Gamba Osaka seasons |
https://en.wikipedia.org/wiki/2000%20Cerezo%20Osaka%20season | 2000 Cerezo Osaka season
Competitions
Domestic results
J.League 1
Emperor's Cup
J.League Cup
Player statistics
Other pages
J. League official site
Cerezo Osaka
Cerezo Osaka seasons |
https://en.wikipedia.org/wiki/2000%20Vissel%20Kobe%20season | 2000 Vissel Kobe season
Competitions
Domestic results
J.League 1
Emperor's Cup
J.League Cup
Player statistics
Other pages
J. League official site
Vissel Kobe
Vissel Kobe seasons |
https://en.wikipedia.org/wiki/2000%20Sanfrecce%20Hiroshima%20season | 2000 Sanfrecce Hiroshima season
Competitions
Domestic results
J.League 1
Emperor's Cup
J.League Cup
Player statistics
Other pages
J. League official site
Sanfrecce Hiroshima
Sanfrecce Hiroshima seasons |
https://en.wikipedia.org/wiki/2000%20Avispa%20Fukuoka%20season | 2000 Avispa Fukuoka season
Competitions
Domestic results
J.League 1
Emperor's Cup
J.League Cup
Player statistics
Other pages
J.League official site
Avispa Fukuoka
Avispa Fukuoka seasons |
https://en.wikipedia.org/wiki/2000%20Consadole%20Sapporo%20season | This is the page for the 2000 Consadole Sapporo season.
Competitions
Domestic results
J.League 2
Emperor's Cup
J.League Cup
Player statistics
Other pages
J. League official site
Consadole Sapporo
Hokkaido Consadole Sapporo seasons |
https://en.wikipedia.org/wiki/2000%20Vegalta%20Sendai%20season | 2000 Vegalta Sendai season
Competitions
Domestic results
J.League 2
Emperor's Cup
J.League Cup
Player statistics
Other pages
J. League official site
Vegalta Sendai
Vegalta Sendai seasons |
https://en.wikipedia.org/wiki/2000%20Montedio%20Yamagata%20season | 2000 Montedio Yamagata season
Competitions
Domestic results
J.League 2
Emperor's Cup
J.League Cup
Player statistics
Other pages
J. League official site
Montedio Yamagata
Montedio Yamagata seasons |
https://en.wikipedia.org/wiki/2000%20Mito%20HollyHock%20season | 2000 Mito HollyHock season
Competitions
Domestic results
J.League 2
Emperor's Cup
J.League Cup
Player statistics
Other pages
J. League official site
Mito HollyHock
Mito HollyHock seasons |
https://en.wikipedia.org/wiki/2000%20Urawa%20Red%20Diamonds%20season | 2000 Urawa Red Diamonds season
Competitions
Domestic results
J.League 2
Emperor's Cup
J.League Cup
Player statistics
Other pages
J. League official site
Urawa Red Diamonds
Urawa Red Diamonds seasons |
https://en.wikipedia.org/wiki/2000%20Omiya%20Ardija%20season | 2000 Omiya Ardija season
Competitions
Domestic results
J.League 2
Emperor's Cup
J.League Cup
Player statistics
Other pages
J. League official site
Omiya Ardija
Omiya Ardija seasons |
https://en.wikipedia.org/wiki/2000%20Shonan%20Bellmare%20season | 2000 Shonan Bellmare season
Competitions
Domestic results
J.League 2
Emperor's Cup
J.League Cup
Player statistics
Other pages
J. League official site
Shonan Bellmare
Shonan Bellmare seasons |
https://en.wikipedia.org/wiki/2000%20Ventforet%20Kofu%20season | 2000 Ventforet Kofu season
Competitions
Domestic results
J.League 2
Emperor's Cup
J.League Cup
Player statistics
Other pages
J. League official site
Ventforet Kofu
Ventforet Kofu seasons |
https://en.wikipedia.org/wiki/2000%20Albirex%20Niigata%20season | 2000 Albirex Niigata season
Competitions
Domestic results
J.League 2
Emperor's Cup
J.League Cup
Player statistics
Other pages
J. League official site
Albirex Niigata
Albirex Niigata seasons |
https://en.wikipedia.org/wiki/2000%20Sagan%20Tosu%20season | 2000 Sagan Tosu season
Competitions
Domestic results
J.League 2
Emperor's Cup
J.League Cup
Player statistics
Other pages
J. League official site
Sagan Tosu
Sagan Tosu seasons |
https://en.wikipedia.org/wiki/2000%20Oita%20Trinita%20season | 2000 Oita Trinita season
Competitions
Domestic results
J.League 2
Emperor's Cup
J.League Cup
Player statistics
Other pages
J. League official site
Oita Trinita
Oita Trinita seasons |
https://en.wikipedia.org/wiki/2001%20Consadole%20Sapporo%20season | Consadole Sapporo is a Japanese football club. Its 2001 season results are set out below.
Competitions
Domestic results
J.League 1
Emperor's Cup
J.League Cup
Player statistics
Other pages
J.League official site
Consadole Sapporo
Hokkaido Consadole Sapporo seasons |
https://en.wikipedia.org/wiki/2001%20Kashima%20Antlers%20season | 2001 Kashima Antlers season
Competitions
Domestic results
J.League 1
Emperor's Cup
J.League Cup
Player statistics
Other pages
J.League official site
Kashima Antlers
Kashima Antlers seasons |
https://en.wikipedia.org/wiki/2001%20Urawa%20Red%20Diamonds%20season | 2001 Urawa Red Diamonds season
Competitions
Domestic results
J.League 1
Emperor's Cup
J.League Cup
Player statistics
Other pages
J.League official site
Urawa Red Diamonds
Urawa Red Diamonds seasons |
https://en.wikipedia.org/wiki/2001%20JEF%20United%20Ichihara%20season | 2001 JEF United Ichihara season
Competitions
Domestic results
J.League 1
Emperor's Cup
J.League Cup
Player statistics
Other pages
J.League official site
JEF United Ichihara
JEF United Chiba seasons |
https://en.wikipedia.org/wiki/2001%20Kashiwa%20Reysol%20season | 2001 Kashiwa Reysol season
Competitions
Domestic results
J.League 1
Emperor's Cup
J.League Cup
Player statistics
Other pages
J.League official site
Kashiwa Reysol
Kashiwa Reysol seasons |
https://en.wikipedia.org/wiki/2001%20FC%20Tokyo%20season | 2001 FC Tokyo season
Competitions
Domestic results
J.League 1
Emperor's Cup
J.League Cup
Player statistics
Other pages
J.League official site
Tokyo
2001 |
https://en.wikipedia.org/wiki/2001%20Tokyo%20Verdy%201969%20season | 2001 Tokyo Verdy 1969 season
Competitions
Domestic results
J.League 1
Emperor's Cup
J.League Cup
Player statistics
Other pages
J. League official site
Tokyo Verdy 1969
Tokyo Verdy seasons |
https://en.wikipedia.org/wiki/2001%20Yokohama%20F.%20Marinos%20season | 2001 Yokohama F. Marinos season
Competitions
Domestic results
J.League 1
Emperor's Cup
J.League Cup
Player statistics
Other pages
J.League official site
Yokohama F. Marinos
Yokohama F. Marinos seasons |
https://en.wikipedia.org/wiki/2001%20Gamba%20Osaka%20season | 2001 Gamba Osaka season
Competitions
Domestic results
J.League 1
Emperor's Cup
J.League Cup
Player statistics
Other pages
J. League official site
Gamba Osaka
Gamba Osaka seasons |
https://en.wikipedia.org/wiki/2001%20Cerezo%20Osaka%20season | 2001 Cerezo Osaka season
Competitions
Domestic results
J.League 1
Emperor's Cup
J.League Cup
Player statistics
Other pages
J.League official site
Cerezo Osaka
Cerezo Osaka seasons |
https://en.wikipedia.org/wiki/2001%20Vissel%20Kobe%20season | 2001 Vissel Kobe season
Competitions
Domestic results
J.League 1
Emperor's Cup
J.League Cup
Player statistics
Other pages
J.League official site
Vissel Kobe
Vissel Kobe seasons |
https://en.wikipedia.org/wiki/2001%20Sanfrecce%20Hiroshima%20season | 2001 Sanfrecce Hiroshima season
Competitions
Domestic results
J.League 1
Emperor's Cup
J.League Cup
Player statistics
Other pages
J.League official site
Sanfrecce Hiroshima
Sanfrecce Hiroshima seasons |
https://en.wikipedia.org/wiki/2001%20Avispa%20Fukuoka%20season | 2001 Avispa Fukuoka season
Competitions
Domestic results
J.League 1
Emperor's Cup
J.League Cup
Player statistics
Other pages
J.League official site
Avispa Fukuoka
Avispa Fukuoka seasons |
https://en.wikipedia.org/wiki/2001%20Vegalta%20Sendai%20season | 2001 Vegalta Sendai season
Competitions
Domestic results
J.League 2
Emperor's Cup
J.League Cup
Player statistics
Other pages
J. League official site
Vegalta Sendai
Vegalta Sendai seasons |
https://en.wikipedia.org/wiki/2001%20Montedio%20Yamagata%20season | 2001 Montedio Yamagata season
Competitions
Domestic results
J.League 2
Emperor's Cup
J.League Cup
Player statistics
Other pages
J. League official site
Montedio Yamagata
Montedio Yamagata seasons |
https://en.wikipedia.org/wiki/2001%20Mito%20HollyHock%20season | 2001 Mito HollyHock season
Competitions
Domestic results
J.League 2
Emperor's Cup
J.League Cup
Player statistics
Other pages
J. League official site
Mito HollyHock
Mito HollyHock seasons |
https://en.wikipedia.org/wiki/2001%20Omiya%20Ardija%20season | 2001 Omiya Ardija season
Competitions
Domestic results
J.League 2
Emperor's Cup
J.League Cup
Player statistics
Other pages
J. League official site
Omiya Ardija
Omiya Ardija seasons |
https://en.wikipedia.org/wiki/2001%20Kawasaki%20Frontale%20season | 2001 Kawasaki Frontale season
Competitions
Domestic results
J.League 2
Emperor's Cup
J.League Cup
Player statistics
Other pages
J.League official site
Kawasaki Frontale
Kawasaki Frontale seasons |
https://en.wikipedia.org/wiki/2001%20Yokohama%20FC%20season | 2001 Yokohama FC season
Competitions
Domestic results
J.League 2
Emperor's Cup
J.League Cup
Player statistics
Other pages
J.League official site
Yokohama FC
Yokohama FC seasons |
https://en.wikipedia.org/wiki/2001%20Shonan%20Bellmare%20season | 2001 Shonan Bellmare season
Competitions
Domestic results
J.League 2
Emperor's Cup
J.League Cup
Player statistics
Other pages
J. League official site
Shonan Bellmare
Shonan Bellmare seasons |
https://en.wikipedia.org/wiki/2001%20Ventforet%20Kofu%20season | 2001 Ventforet Kofu season
Competitions
Domestic results
J.League 2
Emperor's Cup
J.League Cup
Player statistics
Other pages
J. League official site
Ventforet Kofu
Ventforet Kofu seasons |
https://en.wikipedia.org/wiki/2001%20Albirex%20Niigata%20season | This article chronicles the 2001 season for the Japanese association football club Albirex Niigata.
Competitions
Domestic results
J.League 2
Emperor's Cup
J.League Cup
Player statistics
Other pages
J. League official site
Albirex Niigata
Albirex Niigata seasons |
https://en.wikipedia.org/wiki/2001%20Kyoto%20Purple%20Sanga%20season | 2001 Kyoto Purple Sanga season
Competitions
Domestic results
J.League 2
Emperor's Cup
J.League Cup
Player statistics
Other pages
J. League official site
Kyoto Purple Sanga
Kyoto Sanga FC seasons |
https://en.wikipedia.org/wiki/2001%20Sagan%20Tosu%20season | 2001 Sagan Tosu season
Competitions
Domestic results
J.League 2
Emperor's Cup
J.League Cup
Player statistics
Other pages
J. League official site
Sagan Tosu
Sagan Tosu seasons |
https://en.wikipedia.org/wiki/2001%20Oita%20Trinita%20season | 2001 Oita Trinita season
Competitions
Domestic results
J.League 2
Emperor's Cup
J.League Cup
Player statistics
Other pages
J. League official site
Oita Trinita
Oita Trinita seasons |
https://en.wikipedia.org/wiki/Andy%20Cowie | Andy Cowie (11 March 1913 – 19 January 1972) was a professional footballer who played for Dundee, Aberdeen and Swindon Town. Cowie retired from football in 1951 and died in 1972.
Career statistics
Club
Appearances and goals by club, season and competition
References
1913 births
1972 deaths
Footballers from Motherwell
Scottish men's footballers
Scottish Football League players
English Football League players
Dundee F.C. players
Aberdeen F.C. players
Swindon Town F.C. players
Men's association football wing halves
Scottish Football League representative players |
https://en.wikipedia.org/wiki/Density%20theorem | In mathematics, density theorem may refer to
Density conjecture for Kleinian groups
Chebotarev's density theorem in algebraic number theory
Jacobson density theorem in algebra
Kaplansky density theorem in algebra
Lebesgue's density theorem in measure theory
Density theorem (category theory) in category theory |
https://en.wikipedia.org/wiki/Affine%20sphere | In mathematics, and especially differential geometry, an affine sphere is a hypersurface for which the affine normals all intersect in a single point. The term affine sphere is used because they play an analogous role in affine differential geometry to that of ordinary spheres in Euclidean differential geometry.
An affine sphere is called improper if all of the affine normals are constant. In that case, the intersection point mentioned above lies on the hyperplane at infinity.
Affine spheres have been the subject of much investigation, with many hundreds of research articles devoted to their study.
Examples
All quadrics are affine spheres; the quadrics that are also improper affine spheres are the paraboloids.
If ƒ is a smooth function on the plane and the determinant of the Hessian matrix is ±1 then the graph of ƒ in three-space is an improper affine sphere.
References
Differential geometry |
https://en.wikipedia.org/wiki/5-simplex%20honeycomb | In five-dimensional Euclidean geometry, the 5-simplex honeycomb or hexateric honeycomb is a space-filling tessellation (or honeycomb or pentacomb). Each vertex is shared by 12 5-simplexes, 30 rectified 5-simplexes, and 20 birectified 5-simplexes. These facet types occur in proportions of 2:2:1 respectively in the whole honeycomb.
A5 lattice
This vertex arrangement is called the A5 lattice or 5-simplex lattice. The 30 vertices of the stericated 5-simplex vertex figure represent the 30 roots of the Coxeter group. It is the 5-dimensional case of a simplectic honeycomb.
The A lattice is the union of two A5 lattices:
∪
The A is the union of three A5 lattices:
∪ ∪ .
The A lattice (also called A) is the union of six A5 lattices, and is the dual vertex arrangement to the omnitruncated 5-simplex honeycomb, and therefore the Voronoi cell of this lattice is an omnitruncated 5-simplex.
∪
∪
∪
∪
∪
= dual of
Related polytopes and honeycombs
Projection by folding
The 5-simplex honeycomb can be projected into the 3-dimensional cubic honeycomb by a geometric folding operation that maps two pairs of mirrors into each other, sharing the same vertex arrangement:
See also
Regular and uniform honeycombs in 5-space:
5-cubic honeycomb
5-demicube honeycomb
Truncated 5-simplex honeycomb
Omnitruncated 5-simplex honeycomb
Notes
References
Norman Johnson Uniform Polytopes, Manuscript (1991)
Kaleidoscopes: Selected Writings of H. S. M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, Wiley-Interscience Publication, 1995,
(Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380–407, MR 2,10] (1.9 Uniform space-fillings)
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
Honeycombs (geometry)
6-polytopes |
https://en.wikipedia.org/wiki/2002%20Consadole%20Sapporo%20season | 2002 Consadole Sapporo season
Competitions
Domestic results
J.League 1
Emperor's Cup
J.League Cup
Player statistics
Other pages
J. League official site
Consadole Sapporo
Hokkaido Consadole Sapporo seasons |
https://en.wikipedia.org/wiki/2002%20Vegalta%20Sendai%20season | 2002 Vegalta Sendai season
Competitions
Domestic results
J.League 1
Emperor's Cup
J.League Cup
Player statistics
Other pages
J. League official site
Vegalta Sendai
Vegalta Sendai seasons |
https://en.wikipedia.org/wiki/2002%20Urawa%20Red%20Diamonds%20season | 2002 Urawa Red Diamonds season.
Competitions
Domestic results
J.League 1
Emperor's Cup
J.League Cup
International results
Player statistics
Other pages
J. League official site
Urawa Red Diamonds
Urawa Red Diamonds seasons |
https://en.wikipedia.org/wiki/2002%20JEF%20United%20Ichihara%20season | 2002 JEF United Ichihara season
Competitions
Domestic results
J.League 1
Emperor's Cup
J.League Cup
Player statistics
Other pages
J. League official site
JEF United Ichihara
JEF United Chiba seasons |
https://en.wikipedia.org/wiki/2002%20Kashiwa%20Reysol%20season | 2002 Kashiwa Reysol season
Competitions
Domestic results
J.League 1
Emperor's Cup
J.League Cup
Player statistics
Other pages
J. League official site
Kashiwa Reysol
Kashiwa Reysol seasons |
https://en.wikipedia.org/wiki/2002%20FC%20Tokyo%20season | 2002 F.C. Tokyo season
Competitions
Domestic results
J. League 1
Emperor's Cup
J. League Cup
Player statistics
Other pages
J. League official site
List of F.C.Tokyo players 2002 - J.League Official site
Tokyo
2002 |
https://en.wikipedia.org/wiki/2002%20Tokyo%20Verdy%201969%20season | 2002 Tokyo Verdy 1969 season
Competitions
Domestic results
J. League 1
Emperor's Cup
J. League Cup
International results
Player statistics
Other pages
J. League official site
Tokyo Verdy 1969
Tokyo Verdy seasons |
https://en.wikipedia.org/wiki/2002%20Yokohama%20F.%20Marinos%20season | 2002 Yokohama F. Marinos season
Competitions
Domestic results
J.League 1
Emperor's Cup
J.League Cup
Player statistics
Other pages
J.League official site
Yokohama F. Marinos
Yokohama F. Marinos seasons |
https://en.wikipedia.org/wiki/2002%20J%C3%BAbilo%20Iwata%20season | 2002 Júbilo Iwata season
Competitions
Domestic results
J. League 1
Emperor's Cup
J. League Cup
Player statistics
Other pages
J. League official site
Jubilo Iwata
Júbilo Iwata seasons |
https://en.wikipedia.org/wiki/2002%20Nagoya%20Grampus%20Eight%20season | The 2002 Nagoya Grampus Eight football season was as follows.
Competitions
Domestic results
J. League 1
Emperor's Cup
J. League Cup
Player statistics
Other pages
J. League official site
Nagoya Grampus Eight
Nagoya Grampus seasons |
https://en.wikipedia.org/wiki/2002%20Kyoto%20Purple%20Sanga%20season | 2002 Kyoto Purple Sanga season
Competitions
Domestic results
J. League 1
Emperor's Cup
J. League Cup
International results
Player statistics
Other pages
J. League official site
Kyoto Purple Sanga
Kyoto Sanga FC seasons |
https://en.wikipedia.org/wiki/2002%20Gamba%20Osaka%20season | 2002 Gamba Osaka season
Competitions
Domestic results
J. League 1
Emperor's Cup
J. League Cup
Player statistics
Other pages
J. League official site
Gamba Osaka
Gamba Osaka seasons |
https://en.wikipedia.org/wiki/2002%20Vissel%20Kobe%20season | 2002 Vissel Kobe season
Competitions
Domestic results
J. League 1
Emperor's Cup
J. League Cup
International results
Player statistics
Other pages
J. League official site
Vissel Kobe
Vissel Kobe seasons |
https://en.wikipedia.org/wiki/2002%20Sanfrecce%20Hiroshima%20season | 2002 Sanfrecce Hiroshima season
Competitions
Domestic results
J. League 1
First stage
Second stage
Overall table
Emperor's Cup
J. League Cup
International results
Player statistics
Other pages
J. League official site
Sanfrecce Hiroshima
Sanfrecce Hiroshima seasons |
https://en.wikipedia.org/wiki/2002%20Mito%20HollyHock%20season | 2002 Mito HollyHock season.
Competitions
Domestic results
J. League 2
Emperor's Cup
Player statistics
Other pages
J. League official site
Mito HollyHock
Mito HollyHock seasons |
https://en.wikipedia.org/wiki/2002%20Omiya%20Ardija%20season | 2002 Omiya Ardija season
Competitions
Domestic results
J.League 2
Emperor's Cup
Player statistics
Other pages
J. League official site
Omiya Ardija
Omiya Ardija seasons |
https://en.wikipedia.org/wiki/2002%20Yokohama%20FC%20season | 2002 Yokohama FC season
Competitions
Domestic results
J.League 2
Emperor's Cup
Player statistics
Other pages
J. League official site
Yokohama FC
Yokohama FC seasons |
https://en.wikipedia.org/wiki/2002%20Shonan%20Bellmare%20season | 2002 Shonan Bellmare season
Competitions
Domestic results
J. League 2
Emperor's Cup
Player statistics
Other pages
J. League official site
Shonan Bellmare
Shonan Bellmare seasons |
https://en.wikipedia.org/wiki/2002%20Ventforet%20Kofu%20season | 2002 Ventforet Kofu season
Competitions
League table
Domestic results
J. League 2
Emperor's Cup
Player statistics
Other pages
J. League official site
Ventforet Kofu
Ventforet Kofu seasons |
https://en.wikipedia.org/wiki/2002%20Albirex%20Niigata%20season | 2002 Albirex Niigata season
Competitions
Domestic results
J. League 2
Emperor's Cup
Player statistics
Other pages
J. League official site
Albirex Niigata
Albirex Niigata seasons |
https://en.wikipedia.org/wiki/2002%20Cerezo%20Osaka%20season | 2002 Cerezo Osaka season
Competitions
Domestic results
J. League 2
Emperor's Cup
Player statistics
Other pages
J. League official site
Cerezo Osaka
Cerezo Osaka seasons |
https://en.wikipedia.org/wiki/2002%20Avispa%20Fukuoka%20season | 2002 Avispa Fukuoka season
Competitions
Domestic results
J. League 2
Emperor's Cup
Player statistics
Other pages
J. League official site
Avispa Fukuoka
Avispa Fukuoka seasons |
https://en.wikipedia.org/wiki/2002%20Sagan%20Tosu%20season | 2002 Sagan Tosu season
Competitions
Domestic results
J. League 2
Emperor's Cup
Player statistics
Other pages
J. League official site
Sagan Tosu
Sagan Tosu seasons |
https://en.wikipedia.org/wiki/2002%20Oita%20Trinita%20season | 2002 Oita Trinita season
Competitions
Domestic results
J. League 2
Emperor's Cup
Player statistics
Other pages
J. League official site
Oita Trinita
Oita Trinita seasons |
https://en.wikipedia.org/wiki/Chintakani | Chintakani or Chinthakani is a mandal in Khammam district of Telangana, India.
Demographics
As per 2011 Census, the statistics of the mandal are:
Total Population: 47,962 in 11,898 Households.
Male Population: 24,271 and Female Population: 23,691
Children Under 6-years of age: 6,028 (Boys - 3,010 and Girls - 3,018)
Total Literates: 21,483
References
Mandals in Khammam district |
https://en.wikipedia.org/wiki/Jo%20Niemeyer | Jo Niemeyer (born in 1946 in Alf, Germany) is a concrete artist and designer. Niemeyer's work is based on the observation of nature through the use of mathematics and, especially, the "Golden Section". He has experimented with various media such as photography and film video, and today, he principally uses painting to compose his graphic works. Niemeyer also realized sculptural objects and big scale projects such as the land art "20 steps around the world".
Biography
Jo Niemeyer was born in 1946 in the German village Alf. He comes from a long-time artist family. His mother was a textile designer and worked in Saabrücken at the former State School for Art and Crafts, where she was in charge of a handloom weaving factory. His father began to paint at a relatively young age, in abstract and concrete art. Unfortunately, his paintings were considered to be degenerate and most of his works were destroyed or lost during WWII.
After three years of studying photography and graphic art, Niemeyer executed his first geometrical painting in 1966. He travelled in several countries, including the United States and Canada, and in Scandinavia where he was particularly fascinated by nature. In 1967, he pursued his training in industrial design at the Finnish Institute for Art "Atheneum". He decided in 1970 to quit his job as professional photographer to become a full-time independent artist.
In Finland, he met artist colleagues Lars-Gunnar Nordstrom and Matti Kujasalo, the former director of the Finnish Academy of Art in Helsinki. In the 80s, Kujasalo asked Niemeyer to lecture about different print techniques in the graphic art department. During this time, Niemeyer built up his knowledge of Finnish architecture. It was also in Helsinki in the late 60s that Niemeyer met his wife, Tuula Partanen. in 1972 she founded Edition Partanen which specialised in silkscreen prints and publication of graphic and art portfolios. The studio was established in South Germany with a showroom in Zurich, Switzerland. Edition Partanen collaborated with artists such as Rupprecht Geiger, Matti Kujasalo, Ilya Bolotowsky and Niemeyer himself.
Niemeyer began to elaborate his big scale project "20 steps around the world" which would be installed in 1997 in the City of Ropinsalmi in Finland. In this project, he explained, the Earth replaced the canvas. According to him, Earth is the carrier of his artistic work being integrated into the creative process only by minimal changes. In the context of this work, an arbitrarily defined route around the Earth is divided systematically and exactly into 20 segments which develop to a dynamic, logarithmic progression according to the 'Golden Section'. The 20 steps are visualized by using an installation of 20 stainless-steel elements around the globe, precisely located on continents. The location of the points is achieved by using a computer and satellite navigation.
Over the years, Niemeyer has held successful one-man and group shows in Scandi |
https://en.wikipedia.org/wiki/Geometric%20finiteness | In geometry, a group of isometries of hyperbolic space is called geometrically finite if it has a well-behaved fundamental domain. A hyperbolic manifold is called geometrically finite if it can be described in terms of geometrically finite groups.
Geometrically finite polyhedra
A convex polyhedron C in hyperbolic space is called geometrically finite if its closure in the conformal compactification of hyperbolic space has the following property:
For each point x in , there is a neighborhood U of x such that all faces of meeting U also pass through x .
For example, every polyhedron with a finite number of faces is geometrically finite. In hyperbolic space of dimension at most 2, every geometrically finite polyhedron has a finite number of sides, but there are geometrically finite polyhedra in dimensions 3 and above with infinitely many sides. For example, in Euclidean space Rn of dimension n≥2 there is a polyhedron P with an infinite number of sides. The upper half plane model of n+1 dimensional hyperbolic space in Rn+1 projects to Rn, and the inverse image of P under this projection is a geometrically finite polyhedron with an infinite number of sides.
A geometrically finite polyhedron has only a finite number of cusps, and all but finitely many sides meet one of the cusps.
Geometrically finite groups
A discrete group G of isometries of hyperbolic space is called geometrically finite if it has a fundamental domain C that is convex, geometrically finite, and exact (every face is the intersection of C and gC for some g ∈ G) .
In hyperbolic spaces of dimension at most 3, every exact, convex, fundamental polyhedron for a geometrically finite group has only a finite number of sides, but in dimensions 4 and above there are examples with an infinite number of sides .
In hyperbolic spaces of dimension at most 2, finitely generated discrete groups are geometrically finite, but showed that there are examples of finitely generated discrete groups in dimension 3 that are not geometrically finite.
Geometrically finite manifolds
A hyperbolic manifold is called geometrically finite if it has a finite number of components, each of which is the quotient of hyperbolic space by a geometrically finite discrete group of isometries .
See also
Density theorem for Kleinian groups
References
Hyperbolic geometry
Kleinian groups |
https://en.wikipedia.org/wiki/Lee%20Stiff | Lee Vernon Stiff (February 4, 1949 - March 19, 2021) was an American mathematics education researcher; a professor in the Department of Science, Technology, Engineering, and Mathematics Education and the Associate Dean for Faculty and Academic Affairs in the College of Education at North Carolina State University (NCSU); and the author of several mathematics textbooks. In his 72 years of living he wrote many books.
Stiff's father was "a factory worker with only a third-grade education". Stiff studied mathematics at the University of North Carolina at Chapel Hill, graduating in 1971, and went on to earn a master's degree from Duke University in 1974 and a doctorate in mathematics education from North Carolina State University in 1978. After teaching mathematics at the middle school and high school levels, and then holding a faculty position at the University of North Carolina at Charlotte beginning in 1978, he returned to NCSU in 1983.
From 2000 to 2002 Stiff was president of the National Council of Teachers of Mathematics (NCTM). Under his leadership, the NCTM pushed for a greater emphasis on basic computational skills in elementary and secondary school mathematics education, and for an appropriate emphasis on conceptual understanding. Stiff rejected simple solutions to complex issues, saying that "Back to basics is moving backward. Number-crunching alone is no longer enough." Instead, Stiff has recommended better training and incentives for mathematics teachers, a teaching style that incorporates a variety of ways of looking at the same material, and an attitude that all students can learn mathematics regardless of their background.
In 1995 he was a Fulbright scholar in Ghana. In 2010 the NC State College of Education gave him their Distinguished Alumni Award. In 2015 he received the Benjamin Banneker Lifetime Achievement Award, in 2017 he was given the TODOS Iris M. Carl Leadership and Equity Award, and in 2019 he was honored with the NCTM Lifetime Achievement Award.
In 2019, with Drs. Valerie Faulkner and Patricia Marshall, he wrote the critically important work, The Stories We Tell: Math, Race, Bias, and Opportunity, which "...sits the "gap problem" on the doorsteps of schools and districts and off the backs of children and parents."
References
External links
Faculty web site at NCSU
Personal web site
1941 births
Living people
African-American mathematicians
20th-century American mathematicians
21st-century American mathematicians
Mathematics educators
Duke University alumni
University of North Carolina at Chapel Hill alumni
North Carolina State University alumni
University of North Carolina at Charlotte faculty
North Carolina State University faculty
20th-century African-American people
21st-century African-American people |
https://en.wikipedia.org/wiki/Cavity%20perturbation%20theory | In mathematics and electronics, Cavity perturbation theory describes methods for derivation of perturbation formulae for performance changes of a cavity resonator.
These performance changes are assumed to be caused by either introduction of a small foreign object into the cavity, or a small deformation of its boundary. Various mathematical methods can be used to study the characteristics of cavities, which are important in the field of microwave systems, and more generally in the field of electro magnetism.
There are many industrial applications for cavity resonators, including microwave ovens, microwave communication systems, and remote imaging systems using electro magnetic waves. How a resonant cavity performs can affect the amount of energy that is required to make it resonate, or the relative stability or instability of the system.
Introduction
When a resonant cavity is perturbed, e.g. by introducing a foreign object with distinct material properties into the cavity or when the shape of the cavity is changed slightly, electromagnetic fields inside the cavity change accordingly. This means that all the resonant modes (i.e. the quasinormal mode) of the unperturbed cavity slightly change.
Analytically predicting how the perturbation changes the optical response is a classical problem in electromagnetics, with important implications spanning from the radio-frequency domain to present-day nano-optics. The underlying assumption of cavity perturbation theory is that electromagnetic fields inside the cavity after the change differ by a very small amount from the fields before the change. Then Maxwell's equations for original and perturbed cavities can be used to derive analytical expressions for the resulting resonant frequency shift and linewidth change (or Q factor change) by referring only to the original unperturbed mode (not the perturbed one).
General theory
It is convenient to denote cavity frequencies with a complex number , where is the angular resonant frequency and is the inverse of the mode lifetime. Cavity perturbation theory has been initially proposed by Bethe-Schwinger in optics
, and Waldron in the radio frequency domain. These initial approaches rely on formulae that consider stored energy
where and are the complex frequencies of the perturbed and unperturbed cavity modes, and and are the electromagnetic fields of the unperturbed mode (permeability change is not considered for simplicity). Expression () relies on stored energy considerations. The latter are intuitive since common sense dictates that the maximum change in resonant frequency occurs when the perturbation is placed at the intensity maximum of the cavity mode. However energy consideration in electromagnetism is only valid for Hermitian systems for which energy is conserved. For cavities, energy is conserved only in the limit of very small leakage (infinite Q’s), so that Expression () is only valid in this limit. For instance, it is apparent that Expre |
https://en.wikipedia.org/wiki/0N | 0N (zero N) or 0-N may refer to:
0N or 0°N, an expression of the latitude of the equator
0n, an abbreviation for Zero norm in mathematics
HP 0N, ISO/IEC 8859-1 character set on printers by Hewlett-Packard0ñ
See also
N0 (disambiguation) |
https://en.wikipedia.org/wiki/0Z | 0Z (zero Z) or 0-Z may refer to:
0Z, or zero protons; see Atomic number
0z, notation for no degree of redshift
0Z, a data set in statistics where the Standard score is zero
0Z, a Compressibility factor or zero
See also
Z0 (disambiguation) |
https://en.wikipedia.org/wiki/Tame%20manifold | In geometry, a tame manifold is a manifold with a well-behaved compactification. More precisely, a manifold is called tame if it is homeomorphic to a compact manifold with a closed subset of the boundary removed.
The Whitehead manifold is an example of a contractible manifold that is not tame.
See also
References
Differential geometry
Hyperbolic geometry
Manifolds |
https://en.wikipedia.org/wiki/Phillip%20Kott | Phillip S. Kott (born 1952) is an American statistician. He has worked in the field of survey statistics since 1984, and is regarded as a leader in this field. His areas of expertise include survey sampling design, analysis of survey data, and calibration weighting, among other areas. He revolutionized sampling design and estimation strategies with the Agricultural Resource Management Survey, which uses survey information more efficiently. He has taught at George Mason University, and USDA Graduate School. He is currently an Associate Editor for the Journal of Official Statistics and the scientific journal Survey Methodology.
Early professional years
Phillip Kott earned his BS in Mathematics from the State University of New York at Stony Brook in 1974. In 1975, Kott received his MA in Economics from Brown University. In 1978, Kott received his PhD in Mathematical Economics from Brown University at age 26. He was recruited as an economist by the Bureau of Labor Statistics in November 1978 and worked there until 1984 when he was hired by U.S. Energy Information Administration (EIA). In 1987, Kott began working for the National Agricultural Statistics Service of USDA, where he remained until 2008; he briefly worked at the Census Bureau in 1990.
Current professional activities
At the time of his retirement in 2008, Kott was the chief research statistician at NASS. He continued to work part-time at NASS through December 2010. Since January 2009, Kott has been a senior research statistician at Research Triangle Institute (RTI).
Notable achievements
In 1996, Dr. Kott was elected a Fellow of ASA. Kott has been an organizer of numerous conferences and sessions at national and international statistical organizations. He has also served as a representative to the Council of Chapters of ASA. He served as the president of the Washington Statistical Society from June 1996 to June 1997. In 1997, Kott was awarded the Distinguished Achievement Medal by American Statistical Association's Section on Statistics and the Environment. More recently, Kott received the Presidential Rank Award in 2007.
In 2017, Kott earned the NISS Distinguished Service Award for his "extraordinary service that advances NISS and its mission".
Select bibliography
Books edited
Kott was a co-editor of Business Survey Methods (1995), a collection of papers from diverse researchers regarding the process of conducting statistical surveys.
Papers published
Kott has written or collaborated on hundreds of papers advancing the science of survey methodology. The following are five of Kott's most influential and important published papers:
Kott, P., & Chang, T. (2010). Using calibration weighting to adjust for nonignorable unit nonresponse. Journal of the American Statistical Association, 105, 1265-1275.
Kott, P., & Liu, Y. (2009). One-sided coverage intervals for a proportion estimated from a stratified simple random sample. International Statistical Review, 77, 251–265.
Kott, P. (200 |
https://en.wikipedia.org/wiki/Robin%20S%C3%B6derling%20career%20statistics | This is a list of the main career statistics of Swedish professional tennis player, Robin Söderling. To date, Söderling has won ten ATP singles titles including one ATP Masters 1000 title at the 2010 BNP Paribas Masters. He was also the runner-up at the French Open in 2009 and 2010 and a semi-finalist at the year-ending ATP World Tour Finals in 2009. Söderling achieved a career high singles ranking of World No. 4 on November 15, 2010.
Söderling remained inactive from July 2011 until his retirement in December 2015. He initially sustained a wrist injury and was later diagnosed with mononucleosis.
Career achievements
In 2009, Söderling made history by becoming the first of two players (the other being Novak Djokovic in 2015) to defeat Rafael Nadal at the French Open. He prevailed in four sets and eventually reached his first grand slam singles final at the event where he lost to then World No. 2 Roger Federer in straight sets, allowing the Swiss to complete a Career Grand Slam in the process. Söderling reached the top ten of the ATP Singles Rankings for the first time in his career later that year and qualified for the year-ending ATP World Tour Finals where he lost in the semi-finals to eventual runner-up, Juan Martín del Potro in three sets. Nonetheless, Söderling finished the year at a then career high of World No. 8.
His good form carried over into 2010 as he reached the semifinals of an ATP Masters 1000 event for the first time at the 2010 BNP Paribas Open where he lost to seventh seed and eventual runner-up Andy Roddick in three sets. In June, Söderling reached his second consecutive final at the French Open, defeating World No. 2 and defending champion Roger Federer for the first time in his career at an ATP level match en route. This win also ended Federer's streak of 23 consecutive semifinal appearances at the grand slams. However, Söderling was not able to cause the same upset he had the previous year, losing to Nadal in straight sets in the final. At the remaining grand slams, Söderling reached the quarterfinals of Wimbledon for the first time in his career where he lost to Nadal in four sets and the quarterfinals of the US Open for the second year in a row where he lost once again to Federer. In November of the same year, Söderling won his first major singles title at the BNP Paribas Masters, defeating Frenchman Gaël Monfils in the final. The win also earned Söderling a new career high singles ranking of World No. 4.
In January 2011, Söderling reached the fourth round of the Australian Open for the first time in his career, but lost to unseeded Ukrainian, Alexandr Dolgopolov in five sets. In February of the same year, Söderling completed a successful title defense for the first time in his career by winning his second consecutive title at the ABN AMRO World Tennis Tournament.
Major Finals
Grand Slam Finals
Singles: 2 (2 runners-up)
ATP Masters 1000 Finals
Singles: 1 (1 title)
ATP career finals
Singles: 20 (10 titles, 10 runn |
https://en.wikipedia.org/wiki/Determinantal%20point%20process | In mathematics, a determinantal point process is a stochastic point process, the probability distribution of which is characterized as a determinant of some function. Such processes arise as important tools in random matrix theory, combinatorics, physics, and wireless network modeling.
Definition
Let be a locally compact Polish space and be a Radon measure on . Also, consider a measurable function .
We say that is a determinantal point process on with kernel if it is a simple point process on with a joint intensity or correlation function (which is the density of its factorial moment measure) given by
for every n ≥ 1 and x1, ..., xn ∈ Λ.
Properties
Existence
The following two conditions are necessary and sufficient for the existence of a determinantal random point process with intensities ρk.
Symmetry: ρk is invariant under action of the symmetric group Sk. Thus:
Positivity: For any N, and any collection of measurable, bounded functions k = 1, ..., N with compact support: If Then
Uniqueness
A sufficient condition for the uniqueness of a determinantal random process with joint intensities ρk is
for every bounded Borel
Examples
Gaussian unitary ensemble
The eigenvalues of a random m × m Hermitian matrix drawn from the Gaussian unitary ensemble (GUE) form a determinantal point process on with kernel
where is the th oscillator wave function defined by
and is the th Hermite polynomial.
Poissonized Plancherel measure
The poissonized Plancherel measure on partitions of integers (and therefore on Young diagrams) plays an important role in the study of the longest increasing subsequence of a random permutation. The point process corresponding to a random Young diagram, expressed in modified Frobenius coordinates, is a determinantal point process on + with the discrete Bessel kernel, given by:
where
For J the Bessel function of the first kind, and θ the mean used in poissonization.
This serves as an example of a well-defined determinantal point process with non-Hermitian kernel (although its restriction to the positive and negative semi-axis is Hermitian).
Uniform spanning trees
Let G be a finite, undirected, connected graph, with edge set E. Define Ie:E → ℓ2(E) as follows: first choose some arbitrary set of orientations for the edges E, and for each resulting, oriented edge e, define Ie to be the projection of a unit flow along e onto the subspace of ℓ2(E) spanned by star flows. Then the uniformly random spanning tree of G is a determinantal point process on E, with kernel
.
References
Point processes |
https://en.wikipedia.org/wiki/Tornadoes%20of%201983 | This page documents the tornadoes and tornado outbreaks of 1983, in the United States. Most tornadoes form in the U.S., although some events may take place internationally. Tornado statistics for older years like this often appear significantly lower than modern years due to fewer reports or confirmed tornadoes.
Synopsis
The 1983 season saw a relatively average number of tornadoes in the United States, but just four "violent" tornadoes (all F4) and the number killed by tornadoes, listed in official records was lower than average at just 34, and no tornado killed more than three people. However, local news media state that the Los Angeles tornado of March 1 killed nine people, even though none are listed in official records. Two notable outbreaks took place in May, but it was generally a much less destructive tornado season, particularly in the main tornado alley, which saw no tornadoes stronger than F3.
Events
Confirmed tornado total for the entire year 1983 in the United States.
January
There were 13 tornadoes confirmed in the US in January.
January 31 – February 2
A large upper-level trough that developed over New Mexico and produced a large storm complex that produced a blizzard in the north and severe weather in the south. Two people were killed in Louisiana in separate F3 tornadoes on January 31 and one person was killed by an F2 tornado in Florida, on February 2. A total of 33 tornadoes were confirmed in the outbreak.
February
There were 41 tornadoes confirmed in the US in February.
March
There were 71 tornadoes confirmed in the US in March.
March 1
An F2 tornado in Los Angeles, California hit just south of downtown, destroying property and causing 30 injuries, While official records for this tornado list no fatalities, local news media have stated that nine people were killed.
March 17
A severe weather event struck South Florida. Although only two tornadoes were confirmed, there may have been at least five in the region and as many as 17 were reported. Two injuries were reported from the F2 tornado.
April
There were 65 tornadoes confirmed in the US in April.
April 1
Two were killed and 20 others were injured by an F4 tornado in Collinston, Louisiana. It was part of an outbreak that spawned 13 tornadoes.
April 9
Three people were killed by an F3 tornado in Inverness, Florida.
April 23
An F3 tornado tracked through Barnwell County, South Carolina without causing any fatalities.
April 29
One person was killed by an F3 tornado in Springfield, Missouri.
May
There were 249 tornadoes confirmed in the US in May, resulting in 14 fatalities.
May 1–2 (U.S. and Canada)
Two were killed by an F0 tornado in Illinois on May 1 and an F3 tornado in Linn, Missouri caused no fatalities. On May 2, five were killed by tornadoes in Ohio and New York, while outside the US, an F4 tornado in Reece's Corners, Ontario caused no fatalities.
May 12–23
At least four tornadoes were confirmed every day between May 12 and May 23, with 157 tornadoes |
https://en.wikipedia.org/wiki/Universal%20law%20of%20generalization | The universal law of generalization is a theory of cognition stating that the probability of a response to one stimulus being generalized to another is a function of the “distance” between the two stimuli in a psychological space. It was introduced in 1987 by Roger N. Shepard, who began researching mechanisms of generalization while he was still a graduate student at Yale: "I was now convinced that the problem of generalization was the most fundamental problem confronting learning theory. Because we never encounter exactly the same total situation twice, no theory of learning can be complete without a law governing how what is learned in one situation generalizes to another"
Shepard’s 1987 paper gives a "generalization" example of a bird that has eaten one earthworm, and is presented with a slightly different-looking earthworm. Explaining the concept of "psychological space" in the abstract of his 1987 paper, Shepard wrote:"A psychological space is established for any set of stimuli by determining metric distances between the stimuli such that the probability that a response learned to any stimulus will generalize to any other is an invariant [monotonic function] of the distance between them"
Using experimental evidence from both human and non-human subjects, Shepard hypothesized, more specifically, that the probability of generalization will fall off exponentially with the distance measured by one of two particular metrics. His analysis goes on to argue for the universality of this rule for all sentient organisms, due to evolutionary internalization.
Additional Research and Commentary
In 1988, Shepard received a response to his research from Daniel M. Ennis from the Philip Morris Research Center. Ennis called into question whether Shepard’s theory was relevant as it echoed research already accomplished by Nosofsky, whose research presented “several exceptions” to Shepard’s theory. Shepard responded to him by asserting that Nosofsky’s experiments focused on “ the precise locations of individual stimuli in ‘psychological space’” whereas his experiments focused on the “location, size, and shape of the region of psychological space corresponding to the set of stimuli having the same important consequence as a given training stimulus”.
Other researchers have followed up Shepard’s research with their own looks into the law of generalization. In 2000, Ken Cheng from Macquarie University experimented on the special generalization of honeybees, comparing his findings with earlier research on humans and pigeons. Cheng explained his understanding of Shepard’s law of generalization in this study as such: “Suppose that an animal finds food in a container at one location (S+). When the animal returns, the container is at a noticeably different location. Will the animal still ‘bet’ on finding food in the container? Underlying this question is the assumption that the animal can discriminate the two locations. Shepard’s law does not apply when the a |
https://en.wikipedia.org/wiki/GKM | GKM may refer to:
General Kumaramangalam Colony or "GKM Colony" in Chennai
GKM College of Engineering and Technology in Chennai
Generalized Kac–Moody algebra
Grupo Kalise Menorquina, Spanish ice cream company
Gebauer Kényszermeghajtású Motorgéppuska, machine gun designed by Franz Gebauer
Gerard Klauer Mattison, company acquired by BMO Capital Markets in 2003
Grenzkommando Mitte (Border Command Center), part of the Border Troops of the German Democratic Republic |
https://en.wikipedia.org/wiki/Juan%20Mart%C3%ADn%20del%20Potro%20career%20statistics | This is a list of the main career statistics of Argentine professional tennis player, Juan Martín del Potro. To date, Del Potro has won 22 Association of Tennis Professionals (ATP) singles titles, including one Grand Slam singles title at the 2009 US Open and one Masters 1000 singles title at the 2018 BNP Paribas Open. He was also the runner-up at the 2009 ATP World Tour Finals, a semifinalist at the 2009 and 2018 French Opens and 2013 Wimbledon Championships, a quarterfinalist at the Australian Open in 2009 and 2012, a bronze medalist at the 2012 London Olympics, and a silver medalist at the 2016 Rio Olympics. On 13 August 2018, Del Potro achieved a career-high singles ranking of world No. 3 for the first time.
Career achievements
In 2008, Del Potro became the first player in ATP history to win his first four career titles in as many tournaments. This achievement is also the second-longest winning streak by a teenager in the Open Era, behind Rafael Nadal. Later that year, del Potro reached his first Grand Slam singles quarterfinal at the US Open, losing to Andy Murray in four sets. On October 6, 2008, Del Potro entered the top 10 of the ATP singles rankings for the first time in his career. His strong results throughout the year allowed him to qualify for the year-ending ATP World Tour Finals for the first time in his career. However, he failed to progress beyond the preliminary round-robin stage, losing two of the three matches he played. Nonetheless, Del Potro finished the year as world No. 9, the first time he had finished a year in the top 10.
Del Potro's good form carried over into the new year as he reached his second successive Grand Slam singles quarterfinal at the Australian Open, losing to world No. 2 and eventual runner-up Roger Federer. In June of the same year, del Potro reached his first Grand Slam singles semi-final at the French Open, where he once again lost to the world No. 2 and eventual champion, Roger Federer, this time in five sets. This marked the first time that del Potro had taken a set from Federer. In August, del Potro reached his first ATP Masters Series singles final at the Rogers Cup in Canada, losing to Andy Murray in three sets. Later that year, del Potro reached his first US Open final by defeating then-world No. 3, Rafael Nadal, in the semifinals in straight sets. Del Potro went on to win his first Grand Slam singles title by defeating world no. 1 and five-time defending champion Federer for the first time in his career, prevailing in five sets. In November, del Potro lost to Nikolay Davydenko in the final of the ATP World Tour Finals, in straight sets.
In January 2010, del Potro achieved a career-high singles ranking of world No. 4, but a wrist injury prevented him from competing for most of the year. In February 2011, del Potro won his first singles title since returning to the tour from injury, defeating Janko Tipsarević in the final of the Delray Beach International Tennis Championships. Later that year, |
https://en.wikipedia.org/wiki/Semitopological%20group | In mathematics, a semitopological group is a topological space with a group action that is continuous with respect to each variable considered separately. It is a weakening of the concept of a topological group; all topological groups are semitopological groups but the converse does not hold.
Formal definition
A semitopological group is a topological space that is also a group such that
is continuous with respect to both and . (Note that a topological group is continuous with reference to both variables simultaneously, and is also required to be continuous. Here is viewed as a topological space with the product topology.)
Clearly, every topological group is a semitopological group. To see that the converse does not hold, consider the real line with its usual structure as an additive abelian group. Apply the lower limit topology to with topological basis the family . Then is continuous, but is not continuous at 0: is an open neighbourhood of 0 but there is no neighbourhood of 0 continued in .
It is known that any locally compact Hausdorff semitopological group is a topological group. Other similar results are also known.
See also
Lie group
Algebraic group
Compact group
Topological ring
References
Topological groups |
https://en.wikipedia.org/wiki/Geometrization%20theorem | In geometry, geometrization theorem may refer to
Thurstons's hyperbolization theorem for Haken 3-manifolds
Thurston's geometrization conjecture proved by Perelman, a generalization of the hyperbolization theorem to all compact 3-manifolds. |
https://en.wikipedia.org/wiki/Sean%20Eddy | Sean Roberts Eddy is Professor of Molecular & Cellular Biology and of Applied Mathematics at Harvard University. Previously he was based at the Janelia Research Campus from 2006 to 2015 in Virginia. His research interests are in bioinformatics, computational biology and biological sequence analysis. projects include the use of Hidden Markov models in HMMER, Infernal Pfam and Rfam.
Education
Eddy graduated June, 1982 from Marion Center Area High School, Marion Center, Pennsylvania. He then completed a Bachelor of Science in Biology at California Institute of Technology in 1986, followed by a Doctor of Philosophy in molecular biology at the University of Colorado under the supervision of Larry Gold in 1991 studying the T4 phage.
Career
From 1992 to 1995 he was a postdoctoral research fellow at the Medical Research Council (MRC) Laboratory of Molecular Biology (LMB) in Cambridge UK working with John Sulston and Richard Durbin. From 1995 to 2007 he worked at Washington University School of Medicine and has been working for the Howard Hughes Medical Institute since 2000.
Awards and honours
In 2007, Sean was the winner of the Benjamin Franklin Award in Bioinformatics for contributions to Open Access in the Life Sciences.
In 2022, Eddy was elected as a Fellow of the International Society for Computational Biology.
References
Living people
American bioinformaticians
Human Genome Project scientists
Howard Hughes Medical Investigators
Washington University in St. Louis mathematicians
21st-century American biologists
Year of birth missing (living people)
Harvard University faculty
Washington University School of Medicine faculty
California Institute of Technology alumni |
https://en.wikipedia.org/wiki/1996%20Emperor%27s%20Cup | Statistics of Emperor's Cup in the 1996 season.
Overview
It was contested by 80 teams, and Verdy Kawasaki won the championship.
Results
1st Round
Denso 3–1 Juntendo University
Blaze Kumamoto 2–1 Kwansei Gakuin University
World Blitz Koyama 0–7 Vissel Kobe
Nippon Bunri University 1–3 Mitsubishi Motors Mizushima
Kaiho Bank SC 0–4 Montedio Yamagata
Renaiss Gakuen Koga SC 1–1 (PK 5–3) Hokkaido University
Morioka Zebra 0–5 Fujitsu
Fukuoka University 2–2 (PK 5–4) Albireo Niigata
Kawasoe Club 2–5 Ventforet Kofu
FC Matsue 0–9 Kokushikan University
Matsuyama University 0–11 Brummell Sendai
Tokai University 1–0 Osaka University of Commerce
Wakayama University 0–3 Consadole Sapporo
Gonohe City Hall 2–1 Sanyo FC
Fukushima 2–1 Hitachi Shimizu SC
Teihens FC 0–4 Tsukuba University
NTT Kanto 2–0 Doshisha University
YKK AP SC 0–5 Waseda University
Mind House Yokkaichi 1–5 Tokyo Gas
FC Ueda Gentian 1–2 Kunimi High School
Central Chugoku 0–3 Tosu Futures
Sony Sendai 2–1 Hiroshima Teachers
Tenri University 0–1 Cosmo Oil Yokkaichi FC
Prima Ham Tsuchiura 2–3 Komazawa University
Tokushima Shogyo High School 1–5 Oita Trinity
Volca Kagoshima 3–1 TDK
Yamagata FC 1–7 Otsuka Pharmaceutical
Kochi University 8–1 Miyazaki Teachers
Aoyama Gakuin University 0–4 Honda
Toa University 3–4 Kagawa Shiun Club
Maruoka High School 0–4 Seino Transportation SC
Yonago Higashi High School 0–4 Kansai University
2nd Round
Denso 3–1 Blaze Kumamoto
Vissel Kobe 4–2 Mitsubishi Motors Mizushima
Montedio Yamagata 6–0 Renaiss Gakuen Koga SC
Fujitsu 3–0 Fukuoka University
Ventforet Kofu 1–2 Kokushikan University
Brummell Sendai 4–1 Tokai University
Consadole Sapporo 4–0 Gonohe City Hall
Fukushima 3–0 Tsukuba University
NTT Kanto 1–0 Waseda University
Tokyo Gas 8–0 Kunimi High School
Tosu Futures 5–2 Sony Sendai
Cosmo Oil Yokkaichi FC 3–0 Komazawa University
Oita Trinity 6–1 Volca Kagoshima
Otsuka Pharmaceutical 2–1 Kochi University
Honda 3–2 Kagawa Shiun Club
Seino Transportation SC 1–2 Kansai University
3rd Round
Yokohama Flügels 4–0 Denso
Kyoto Purple Sanga 4–3 Vissel Kobe
Gamba Osaka 4–1 Montedio Yamagata
JEF United Ichihara 0–0 (PK 4–5) Fujitsu
Kashiwa Reysol 1–0 Kokushikan University
Sanfrecce Hiroshima 2–0 Brummell Sendai
Shimizu S-Pulse 1–0 Consadole Sapporo
Júbilo Iwata 1–2 Fukushima
Urawa Red Diamonds 3–0 NTT Kanto
Cerezo Osaka 3–1 Tokyo Gas
Bellmare Hiratsuka 1–0 Tosu Futures
Nagoya Grampus Eight 0–1 Cosmo Oil Yokkaichi FC
Verdy Kawasaki 4–0 Oita Trinity
Yokohama Marinos 1–2 Otsuka Pharmaceutical
Avispa Fukuoka 3–1 Honda
Kashima Antlers 2–0 Kansai University
4th Round
Yokohama Flügels 0–1 Kyoto Purple Sanga
Gamba Osaka 3–1 Fujitsu
Kashiwa Reysol 1–2 Sanfrecce Hiroshima
Shimizu S-Pulse 2–1 Fukushima
Urawa Red Diamonds 4–0 Cerezo Osaka
Bellmare Hiratsuka 3–1 Cosmo Oil Yokkaichi FC
Verdy Kawasaki 4–0 Otsuka Pharmaceutical
Avispa Fukuoka 0–2 Kashima Antlers
Quarterfinals
Kyoto Purple Sanga 2–3 Gamba Osaka
Sanfrecce Hiroshima 3–0 Shimizu S-Pulse
Urawa Red Diamonds 3–0 Bellmare Hirats |
https://en.wikipedia.org/wiki/1997%20Emperor%27s%20Cup | Statistics of Emperor's Cup in the 1997 season.
Overview
It was contested by 81 teams, and Kashima Antlers won the championship.
Results
1st round
Brummell Sendai 7–0 Yamaga Club
Iwami FC 0–7 Juntendo University
Mitsubishi Nagasaki SC 2–1 Hatsushiba Hashimoto High School
Mito HollyHock 3–0 Hokkaido Electric Power
Nirasaki Astros 0–2 NTT Kanto
Mitsubishi Motors Mizushima 0–0 (PK 6–7) Yamagata FC
Kusatsu Higashi High School 0–3 Sagan Tosu
Nara Sangyo University 3–1 Nippon Steel Corporation Oita FC
Saga Commercial High School 1–5 Oita Trinity
Mind House Yokkaichi 0–3 Momoyama Gakuin University
Kansai University 0–9 Tokyo Gas
Ehime Youth 2–1 Alo's Hokuriku
Blaze Kumamoto 0–2 Honda
Kwansei Gakuin University 2–6 Albirex Niigata
Jatco 1–0 Okinawa International University
Kagawa Shiun Club 1–0 Waseda University
Seino Transportation 5–0 Kochi University
Moka High School 1–5 Kokushikan University
Tottori 0–7 Kawasaki Frontale
Honda Luminoso Sayama 4–1 Nippon Steel Corporation Kamaishi FC
Kanagawa University 1–3 Ventforet Kofu
Fukuoka University 5–1 Akita City Hall
Aoyama Gakuin University 1–0 Denso
FC Primeiro 0–1 Hannan University
Maebashi Commercial High School 0–6 Fukushima
Nagoya Bank 3–4 Fukui Teachers
Kyoiku Kenkyusha 0–5 Montedio Yamagata
Hosho High School 3–2 Takagawa Gakuen High School
Kagoshima Commercial High School 1–2 Consadole Sapporo
Hiroshima University 2–3 Aster Aomori
Otsuka Pharmaceuticals 8–1 Teihens FC
Funabashi Municipal High School 0–2 Komazawa University
2nd round
Brummell Sendai 0–1 Juntendo University
Verdy Kawasaki 2–0 Mitsubishi Nagasaki SC
Mito HollyHock 1–2 Avispa Fukuoka
NTT Kanto 1–0 Yamagata FC
Sagan Tosu 4–0 Nara Sangyo University
Oita Trinity 1–1 (PK 3–5) Momoyama Gakuin University
Tokyo Gas 2–1 Ehime Youth
Honda 3–1 Albirex Niigata
Jatco 6–0 Kagawa Shiun Club
Seino Transportation 1–2 Kokushikan University
Kawasaki Frontale 3–0 Honda Luminoso Sayama
Ventforet Kofu 2–1 Fukuoka University
Aoyama Gakuin University 0–1 Hannan University
Fukushima 1–0 Fukui Teachers
Montedio Yamagata 8–0 Hosho High School
Consadole Sapporo 4–1 Aster Aomori
Otsuka Pharmaceuticals 1–3 Komazawa University
3rd round
Kashima Antlers 4–1 Juntendo University
Verdy Kawasaki 0–2 Avispa Fukuoka
Urawa Red Diamonds 2–1 NTT Kanto
Gamba Osaka 3–2 Sagan Tosu
Yokohama Marinos 5–0 Momoyama Gakuin University
Nagoya Grampus Eight 1–3 Tokyo Gas
Kyoto Purple Sanga 3–2 Honda
Bellmare Hiratsuka 7–0 Jatco
Kashiwa Reysol 4–1 Kokushikan University
Vissel Kobe 2–0 Kawasaki Frontale
Cerezo Osaka 5–1 Ventforet Kofu
Júbilo Iwata 3–0 Hannan University
Shimizu S-Pulse 3–0 Fukushima
Sanfrecce Hiroshima 3–1 Montedio Yamagata
JEF United Ichihara 1–0 Consadole Sapporo
Yokohama Flügels 4–3 Komazawa University
4th round
Kashima Antlers 6–0 Avispa Fukuoka
Urawa Red Diamonds 1–2 Gamba Osaka
Yokohama Marinos 1–2 Tokyo Gas
Kyoto Purple Sanga 1–5 Bellmare Hiratsuka
Kashiwa Reysol 2–1 Vissel Kobe
Cerezo Osaka 2–3 Júbilo Iwata
Shimizu S-Pulse 3–1 Sanfrecce Hiroshima
JEF United Ichi |
https://en.wikipedia.org/wiki/1998%20Emperor%27s%20Cup | Statistics of Emperor's Cup in the 1998 season.
Overview
It was contested by 82 teams, and Yokohama Flügels won the championship.
Results
1st round
Omiya Ardija 1–0 TDK
Mitsubishi Nagasaki SC 0–4 Chuo University
FC Primeiro 1–0 Nihon University Yamagata High School
Gifu Technical High School 1–2 Kagoshima Vocational High School
Kawasoe Club 0–6 Ventforet Kofu
Nippon Steel Corporation Oita FC 1–3 Doto University
Juntendo University 0–1 Otsuka Pharmaceuticals
Sanwa Club 1–4 Tokushima Municipal High School
Matsushita Electric Works FC 0–5 Denso
Maebashi Ikuei High School 0–7 Tsukuba University
Chukyo University 1–4 Tokyo Gas
Tokai University 0–0 (PK 3–0) Teihens FC
Kagawa Shiun Club 1–9 Kawasaki Frontale
Niigata Shukyu-Kai 0–2 YKK AP SC
Nirasaki Astros 2–3 Brummell Sendai
Tokuyama University 2–4 Kansai University
Kwansei Gakuin University 3–2 Shizuoka Sangyo University
Teijin SC 0–6 Kokushikan University
Iwami FC 1–9 Montedio Yamagata
Meiji University 5–0 Nippon Steel Corporation Kamaishi FC
Tenri University 2–3 Honda
Hosho High School 4–1 Ueda Gentian
Koga Club 0–9 Oita Trinita
Kyushu Sangyo University 1–2 Ritsumeikan University
Kyoiku Kenkyusha 0–4 Albirex Niigata
Hannan University 3–2 Hatsushiba Hashimoto High School
Gainare Tottori 0–3 Sagan Tosu
Tochigi SC 3–2 Ozu High School
Fukuyama University 2–2 (PK 4–3) Fukui Teachers
Sony Sendai 2–1 Aster Aomori
Mito HollyHock 4–2 Mitsubishi Motors Mizushima
Himawari Milk Nangoku SC 2–7 Komazawa University
2nd round
Omiya Ardija 2–0 Chuo University
Consadole Sapporo 1–0 FC Primeiro
Kagoshima Jitsugyo High School 0–7 Vissel Kobe
Ventforet Kofu 6–1 Doto University
Otsuka Pharmaceuticals 4–2 Tokushima Municipal High School
Denso 1–3 Tsukuba University
Tokyo Gas 2–0 Tokai University
Kawasaki Frontale 1–0 YKK AP SC
Brummell Sendai 2–1 Kansai University
Kwansei Gakuin University 3–1 Kokushikan University
Montedio Yamagata 1–0 Meiji University
Honda FC 4–0 Hosho High School
Oita Trinita 2–1 Ritsumeikan University
Albirex Niigata 3–1 Hannan University
Sagan Tosu 4–0 Tochigi SC
Kyoto Purple Sanga 9–0 Fukuyama University
Sony Sendai 0–5 Avispa Fukuoka
Mito HollyHock 4–3 Komazawa University
3rd round
Júbilo Iwata 2–0 Omiya Ardija
Consadole Sapporo 2–1 Vissel Kobe
Cerezo Osaka 4–6 Ventforet Kofu
Yokohama Flügels 4–2 Otsuka Pharmaceuticals
Kashima Antlers 3–1 Tsukuba University
Bellmare Hiratsuka 2–1 Tokyo Gas
Sanfrecce Hiroshima 2–1 Kawasaki Frontale
Yokohama Marinos 0–1 Brummell Sendai
Nagoya Grampus Eight 3–1 Kwansei Gakuin University
Gamba Osaka 1–2 Montedio Yamagata
JEF United Ichihara 0–2 Honda FC
Verdy Kawasaki 1–0 Oita Trinita
Urawa Red Diamonds 4–1 Albirex Niigata
Kashiwa Reysol 3–1 Sagan Tosu
Kyoto Purple Sanga 2–3 Avispa Fukuoka
Shimizu S-Pulse 5–0 Mito HollyHock
4th round
Júbilo Iwata 3–2 Consadole Sapporo
Ventforet Kofu 0–3 Yokohama Flügels
Kashima Antlers 3–0 Bellmare Hiratsuka
Sanfrecce Hiroshima 3–0 Brummell Sendai
Nagoya Grampus Eight 3–2 Montedio Yamagata
Honda FC 1–3 Verdy Kawasaki
Urawa Red D |
https://en.wikipedia.org/wiki/1999%20Emperor%27s%20Cup | Statistics of Emperor's Cup in the 1999 season.
Overview
It was contested by 80 teams, and Nagoya Grampus Eight won the championship.
Results
1st round
Juntendo University 2–0 Aichi Gakuin University
Tochigi SC 0–2 Júbilo Iwata Youth
Kusatsu Higashi High School 0–2 Tokyo
Hatsushiba Hashimoto High School 2–1 Hachinohe University
Nippon Bunri University 1–2 Sagan Tosu
Nagoya SC 3–4 Jatco SC
Maebashi Comercial High School 1–2 Ventforet Kofu
Sony Sendai 2–1 Iwate University
Maruoka High School 1–11 Otsuka Pharmaceuticals
Yamaguchi Teachers 2–3 Fukuoka University
Blaze Kumamoto 0–8 Montedio Yamagata
Okinawa International University 0–2 Teihens FC
FC Primeiro 0–2 Albirex Niigata
National Institute of Fitness and Sports in Kanoya 1–0 Konan University
Nara Sangyo University 2–7 Denso
Iwami FC 7–3 Tokushima Commercial High School
Kunimi High School 0–4 Kokushikan University
Senshu University 1–0 Yamagata FC
Hiroshima University 0–6 Oita Trinita
Kakamihara High School 2–8 ALO's Hokuriku
Hannan University 1–2 Consadole Sapporo
Mind House Yokkaichi 2–1 Mitsubishi Motors Mizushima
Nankoku Kochi FC 3–7 Honda
Kagawa Shiun Club 4–3 Nissei Industries FC
Honda Lock 0–5 Vegalta Sendai
Mito HollyHock 5–1 TDK
Ibaraki Sakai High School 0–6 Omiya Ardija
Nirasaki Astros 4–4 (PK 2–4) Doto University
Ehime FC 0–3 Kawasaki Frontale
Josai University 4–1 Kyushu INAX
Ritsumeikan University 2–1 Tsukuba University
Yokohama FC 8–0 Niigata University
2nd round
Juntendo University 3–0 Júbilo Iwata Youth
FC Tokyo 6–0 Hatsushiba Hashimoto High School
Sagan Tosu 2–1 Jatco SC
Ventforet Kofu 0–0 (PK 3–4) Sony Sendai
Otsuka Pharmaceuticals 0–2 Fukuoka University
Montedio Yamagata 3–0 Teihens FC
Albirex Niigata 1–0 NIFS Kanoya
Denso 7–0 Iwami FC
Kokushikan University 1–2 Senshu University
Oita Trinita 10–0 ALO's Hokuriku
Consadole Sapporo 3–0 Mind House Yokkaichi
Honda FC 6–0 Kagawa Shiun Club
Vegalta Sendai 1–2 Mito HollyHock
Omiya Ardija 3–0 Doto University
Kawasaki Frontale 5–1 Josai University
Ritsumeikan University 1–4 Yokohama FC
3rd round
Bellmare Hiratsuka 3–4 FC Tokyo (aet)
Kashima Antlers 1–0 Sagan Tosu
Nagoya Grampus Eight 4–0 Sony Sendai
Cerezo Osaka 4–1 Fukuoka University
Vissel Kobe 0–0 Montedio Yamagata (aet, 3-4 pen)
Urawa Red Diamonds 3–1 Albirex Niigata
Kashiwa Reysol 4–2 Denso
Kyoto Purple Sanga 1–0 Oita Trinita
Avispa Fukuoka 1–0 Consadole Sapporo
Sanfrecce Hiroshima 3–2 Honda FC
Yokohama F. Marinos 2–1 Mito HollyHock
Gamba Osaka 1–0 Omiya Ardija
JEF United Ichihara 2–3 Kawasaki Frontale
Verdy Kawasaki 3–2 Yokohama FC (aet)
Jubilo Iwata |
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