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https://en.wikipedia.org/wiki/Kazuki%20Sorimachi | is a former Japanese football player.
Club statistics
References
External links
1987 births
Living people
Waseda University alumni
Association football people from Gunma Prefecture
Japanese men's footballers
J2 League players
Thespakusatsu Gunma players
Men's association football forwards |
https://en.wikipedia.org/wiki/NUTS%20statistical%20regions%20of%20Montenegro | As a candidate country of the European Union, Montenegro (ME) is included in the Nomenclature of Territorial Units for Statistics'''''' (NUTS). The three NUTS levels are:
NUTS-1: ME0 Montenegro
NUTS-2: ME00 Montenegro
NUTS-3: ME000 Montenegro
Below the NUTS levels, there are two LAU levels (LAU-1: municipalities; LAU-2: settlements).
See also
Subdivisions of Montenegro
ISO 3166-2 codes of Montenegro
Sources
Hierarchical list of the Nomenclature of territorial units for statistics - NUTS and the Statistical regions of Europe
Montenegro
Subdivisions of Montenegro |
https://en.wikipedia.org/wiki/Lady%20Windermere%27s%20Fan%20%28mathematics%29 | In mathematics, Lady Windermere's Fan is a telescopic identity employed to relate global and local error of a numerical algorithm. The name is derived from Oscar Wilde's 1892 play Lady Windermere's Fan, A Play About a Good Woman.
Lady Windermere's Fan for a function of one variable
Let be the exact solution operator so that:
with denoting the initial time and the function to be approximated with a given .
Further let , be the numerical approximation at time , . can be attained by means of the approximation operator so that:
with
The approximation operator represents the numerical scheme used. For a simple explicit forward Euler method with step width this would be:
The local error is then given by:
In abbreviation we write:
Then Lady Windermere's Fan for a function of a single variable writes as:
with a global error of
Explanation
See also
Baker–Campbell–Hausdorff formula
Numerical error
Numerical analysis |
https://en.wikipedia.org/wiki/Ali%20Lashgari | Ali Lashgari () was an Iranian football player who played for Persepolis in Iran Pro League.
Club career
Club career statistics
References
Living people
Iranian men's footballers
Persepolis F.C. players
Men's association football forwards
Year of birth missing (living people)
Place of birth missing (living people) |
https://en.wikipedia.org/wiki/Mohammad%20Barzegar | Mohammad Barzegar (; born July 24, 1976, in Tehran) is an Iranian footballer. He won the 2001–02 Iran Pro League with Persepolis.
Club Career Statistics
References
External links
Profile at teammelli.com
1976 births
Living people
Iranian men's footballers
Iran men's international footballers
Persepolis F.C. players
Fajr Sepasi Shiraz F.C. players
Sanat Naft Abadan F.C. players
Shahid Ghandi Yazd F.C. players
F.C. Shahrdari Bandar Abbas players
Men's association football wingers
Sportspeople from Tehran
Persepolis F.C. non-playing staff |
https://en.wikipedia.org/wiki/Truncated%20cubic%20prism | In geometry, a truncated cubic prism is a convex uniform polychoron (four-dimensional polytope).
It is one of 18 convex uniform polyhedral prisms created by using uniform prisms to connect pairs of Platonic solids or Archimedean solids in parallel hyperplanes.
Net
Alternative names
Truncated-cubic hyperprism
Truncated-cubic dyadic prism (Norman W. Johnson)
Ticcup (Jonathan Bowers: for truncated-cube prism)
See also
Truncated tesseract,
External links
4-polytopes
Truncated tilings |
https://en.wikipedia.org/wiki/Truncated%20cuboctahedral%20prism | In geometry, a truncated cuboctahedral prism or great rhombicuboctahedral prism is a convex uniform polychoron (four-dimensional polytope).
It is one of 18 convex uniform polyhedral prisms created by using uniform prisms to connect pairs of Platonic solids or Archimedean solids in parallel hyperplanes.
Net
Alternative names
Truncated-cuboctahedral dyadic prism (Norman W. Johnson)
Gircope (Jonathan Bowers: for great rhombicuboctahedral prism/hyperprism)
Great rhombicuboctahedral prism/hyperprism
Related polytopes
A full snub cubic antiprism or omnisnub cubic antiprism can be defined as an alternation of an truncated cuboctahedral prism, represented by ht0,1,2,3{4,3,2}, or , although it cannot be constructed as a uniform polychoron. It has 76 cells: 2 snub cubes connected by 12 tetrahedrons, 6 square antiprisms, and 8 octahedrons, with 48 tetrahedrons in the alternated gaps. There are 48 vertices, 192 edges, and 220 faces (12 squares, and 16+192 triangles). It has [4,3,2]+ symmetry, order 48.
A construction exists with two uniform snub cubes in snub positions with two edge lengths in a ratio of around 1 : 1.138.
Vertex figure for the omnisnub cubic antiprism
Also related is the bialternatosnub octahedral hosochoron, constructed by removing alternating long rectangles from the octagons, but is also not uniform. It has 40 cells: 2 rhombicuboctahedra (with Th symmetry), 6 rectangular trapezoprisms (topologically equivalent to a cube but with D2d symmetry), 8 octahedra (as triangular antiprisms), 24 triangular prisms (as Cs-symmetry wedges) filling the gaps, and 48 vertices. It has [4,(3,2)+] symmetry, order 48. Its vertex figure is a chiral hexahedron topologically identical to the tetragonal antiwedge.
Vertex figure for the bialternatosnub octahedral hosochoron
External links
4-polytopes |
https://en.wikipedia.org/wiki/Snub%20cubic%20prism | In geometry, a snub cubic prism or snub cuboctahedral prism is a convex uniform polychoron (four-dimensional polytope).
It is one of 18 convex uniform polyhedral prisms created by using uniform prisms to connect pairs of Platonic solids or Archimedean solids in parallel hyperplanes.
See also
Snub cubic antiprism s{4,3,2} - A related nonuniform polychoron
Alternative names
Snub-cuboctahedral dyadic prism (Norman W. Johnson)
Sniccup (Jonathan Bowers: for snub-cubic prism)
Snub-cuboctahedral hyperprism
Snub-cubic hyperprism
External links
4-polytopes |
https://en.wikipedia.org/wiki/Truncated%20icosahedral%20prism | In geometry, a truncated icosahedral prism is a convex uniform polychoron (four-dimensional polytope).
It is one of 18 convex uniform polyhedral prisms created by using uniform prisms to connect pairs of Platonic solids or Archimedean solids in parallel hyperplanes.
Alternative names
Truncated-icosahedral dyadic prism (Norman W. Johnson)
Tipe (Jonathan Bowers: for truncated-icosahedral prism)
Truncated-icosahedral hyperprism
See also
Truncated 600-cell,
External links
4-polytopes |
https://en.wikipedia.org/wiki/Truncated%20icosidodecahedral%20prism | In geometry, a truncated icosidodecahedral prism or great rhombicosidodecahedral prism is a convex uniform 4-polytope (four-dimensional polytope).
It is one of 18 convex uniform polyhedral prisms created by using uniform prisms to connect pairs of Platonic solids or Archimedean solids in parallel hyperplanes.
Alternative names
Truncated icosidodecahedral dyadic prism (Norman W. Johnson)
Griddip (Jonathan Bowers: for great rhombicosidodecahedral prism/hyperprism)
Great rhombicosidodecahedral prism/hyperprism
Related polytopes
A full snub dodecahedral antiprism or omnisnub dodecahedral antiprism can be defined as an alternation of an truncated icosidodecahedral prism, represented by ht0,1,2,3{5,3,2}, or , although it cannot be constructed as a uniform 4-polytope. It has 184 cells: 2 snub dodecahedrons connected by 30 tetrahedrons, 12 pentagonal antiprisms, and 20 octahedrons, with 120 tetrahedrons in the alternated gaps. It has 120 vertices, 480 edges, and 544 faces (24 pentagons and 40+480 triangles). It has [5,3,2]+ symmetry, order 120.
Vertex figure for the omnisnub dodecahedral antiprism
External links
4-polytopes |
https://en.wikipedia.org/wiki/Snub%20dodecahedral%20prism | In geometry, a snub dodecahedral prism or snub icosidodecahedral prism is a convex uniform polychoron (four-dimensional polytope).
It is one of 18 convex uniform polyhedral prisms created by using uniform prisms to connect pairs of Platonic solids or Archimedean solids in parallel hyperplanes, in this case a pair of snub dodecahedra.
Alternative names
Snub-icosidodecahedral dyadic prism (Norman W. Johnson)
Sniddip (Jonathan Bowers: for snub-dodecahedral prism)
Snub-icosidodecahedral hyperprism
Snub-dodecahedral prism
Snub-dodecahedral hyperprism
See also
Snub dodecahedral antiprism ht0,1,2,3{5,3,2}, or - A related nonuniform polychoron
External links
4-polytopes |
https://en.wikipedia.org/wiki/Relative%20scalar | In mathematics, a relative scalar (of weight w) is a scalar-valued function whose transform under a coordinate transform,
on an n-dimensional manifold obeys the following equation
where
that is, the determinant of the Jacobian of the transformation. A scalar density refers to the case.
Relative scalars are an important special case of the more general concept of a relative tensor.
Ordinary scalar
An ordinary scalar or absolute scalar refers to the case.
If and refer to the same point on the manifold, then we desire . This equation can be interpreted two ways when are viewed as the "new coordinates" and are viewed as the "original coordinates". The first is as , which "converts the function to the new coordinates". The second is as , which "converts back to the original coordinates. Of course, "new" or "original" is a relative concept.
There are many physical quantities that are represented by ordinary scalars, such as temperature and pressure.
Weight 0 example
Suppose the temperature in a room is given in terms of the function in Cartesian coordinates and the function in cylindrical coordinates is desired. The two coordinate systems are related by the following sets of equations:
and
Using allows one to derive as the transformed function.
Consider the point whose Cartesian coordinates are and whose corresponding value in the cylindrical system is . A quick calculation shows that and also. This equality would have held for any chosen point . Thus, is the "temperature function in the Cartesian coordinate system" and is the "temperature function in the cylindrical coordinate system".
One way to view these functions is as representations of the "parent" function that takes a point of the manifold as an argument and gives the temperature.
The problem could have been reversed. One could have been given and wished to have derived the Cartesian temperature function . This just flips the notion of "new" vs the "original" coordinate system.
Suppose that one wishes to integrate these functions over "the room", which will be denoted by . (Yes, integrating temperature is strange but that's partly what's to be shown.) Suppose the region is given in cylindrical coordinates as from , from and from (that is, the "room" is a quarter slice of a cylinder of radius and height 2).
The integral of over the region is
The value of the integral of over the same region is
They are not equal. The integral of temperature is not independent of the coordinate system used. It is non-physical in that sense, hence "strange". Note that if the integral of included a factor of the Jacobian (which is just ), we get
which is equal to the original integral but it is not however the integral of temperature because temperature is a relative scalar of weight 0, not a relative scalar of weight 1.
Weight 1 example
If we had said was representing mass density, however, then its transformed value
should include the Jacobian factor that takes int |
https://en.wikipedia.org/wiki/Livability.com | Livability.com is a website that ranks the most livable small and mid-sized cities in the United States. The website includes demographic information, statistics, articles, photography and video that summarize the quality of life in cities, including information about schools, neighborhoods, local restaurants, and cultural events. The website's content is anchored by original photography shot by Journal Communications Inc. staff photographers. The site also provides moving tools and tips, do-it-yourself project help and home and garden advice.
Principals
Livability.com is owned and operated by Journal Communications, based in Franklin, Tennessee, a publisher over 100 custom magazines for chambers of commerce, economic development agencies and corporations, (such as the Tennessee Farm Bureau Federation).
Services
Livability.com publishes lists of small- to medium-sized US cities, such as "Best Affordable Places to Live," "Top 10 Best Places to Retire," and "10 Best Cities for Families."
References
Further reading
American review websites
American blogs |
https://en.wikipedia.org/wiki/2000%E2%80%9301%20V-League | Statistics of the V-League in the 2000–01 season.
Standings
References
2000–01 V-League at RSSSF
Vietnamese Super League seasons
Vietnam
1
1 |
https://en.wikipedia.org/wiki/1999%E2%80%932000%20V-League | Statistics of the V-League in the 1999-00 season.
Standings
NOTE: Vinh Long's matches annulled.
References
1999–2000 V-League at RSSSF
Vietnamese Super League seasons
Viet
1999 in Vietnamese football
2000 in Vietnamese football |
https://en.wikipedia.org/wiki/1998%20V-League | Statistics of the V-League in the 1998 season.
Standings
Champions: The Cong (18th)
Runners-Up: Song Lam Nghe An
Third: Cong An
Fifth: Cang Saigon
Other teams in first division include: Cong An (Hanoi) and Cong An (Haiphong).
Relegated: Hai Quan, (Ho Chi Minh City)
References
1998 V-League at RSSSF
Vietnamese Super League seasons
Viet
Viet
1 |
https://en.wikipedia.org/wiki/1997%20V-League | Statistics of the V-League in the 1997 season.
Standings
References
1997 V-League at RSSSF
Vietnamese Super League seasons
Viet
Viet
1 |
https://en.wikipedia.org/wiki/1996%20V-League | Statistics of the V-League in the 1996 season.
Standings
Championship final
Dong Thap 3-1 HCMC Police
References
1996 V-League at RSSSF
Vietnamese Super League seasons
Viet
Viet
1 |
https://en.wikipedia.org/wiki/1995%20V-League | Statistics of the V-League in the 1995 season.
Standings
Hồ Chí Minh City Police F.C.
Thừa Thiên Huế
Saigon Port
An Giang
Khanh Hoa
Dong Thap
Lam Dong
Song Lam Nghe An
Thể Công
HCMC Custom (Hải Quan)
Sông Bé
Long An
Binh Dinh
Quang Nam Danang
Final
HCMC Police 3-1 Thua Thien Hue
References
1995 V-League at RSSSF
Vietnamese Super League seasons
Viet
Viet
1 |
https://en.wikipedia.org/wiki/1993%E2%80%9394%20V-League | Statistics of the V-League in the 1993-94 season.
First stage
16 participants divided into 2 groups playing single round robin;
top-4 of both to second stage.
Group A
An Giang
Hai Quan (Q)
Dong Thap (Q)
Long An (Q)
CLB Quan Doi (Q)
CA Hai Phong
CA Thanh Hoa
Group B
Cang Saigon (Q)
CA TP.HCM (Q)
Quang Nam-Danang (Q)
Song Lam Nghe An
Binh Dinh (Q)
Song Be
Tien Giang
Duong Sat VN
Second stage
8 participants divided into 2 groups playing single round robin;
no draws; top-2 of both to semifinals
Group 1
Long An (Q)
CLB Quan Doi (Q)
Binh Dinh
Quang Nam-Danang
Group 2
Cang Saigon (Q)
CA Tp.HCM (Q)
Hai Quan
Dong Thap
Semifinals
Long An 1-3 CA Tp.HCM
Cang Saigon 1-0 CLB Quan Doi
Final
Cang Saigon 2-0 CA Tp.HCM
References
1993–94 V-League at RSSSF
Vietnamese Super League seasons
Viet
1993 in Vietnamese football
1994 in Vietnamese football |
https://en.wikipedia.org/wiki/1992%20V-League | Statistics of the V-League in the 1992 season.
First stage
18 participants divided into 2 groups playing single round robin;
top-4 of both to second stage
Known result:
Saigon Port 3-0 Hanoi Police
Note: Saigon Port did not reach second stage
Second stage
8 participants playing double round robin; top-4 to semifinals
Winners: Quang Nam-Da Nang FC
References
1992 V-League at RSSSF
Vietnamese Super League seasons
1
Viet
Viet |
https://en.wikipedia.org/wiki/1991%20V-League | Statistics of the V-League in the 1991 season.
First stage
19 participants divided into 3 groups playing double round robin;
8 clubs qualified for quarterfinals, while 6 clubs entered relegation
playoffs, 3 clubs going down
Semifinal (June 5, 1991)
Quang Nam 2-1 Saigon Port
Saigon Port finished 3rd
Final
Hai Quan (TP Ho Chi Minh) 2-0 Cong an (Hai Phong)
Second stage
8 participants playing double round robin; top-4 to semifinals
Winners: Quang Nam (Da Nang)
References
Vietnamese Super League seasons
1
Viet
Viet |
https://en.wikipedia.org/wiki/1990%20V-League | Statistics of the V-League in the 1990 season.
First round
18 participants (chosen from 32 entrants of National A1 Football Cup 1989):
Saigon Port
Hanoi Police
Nam Dinh Textile
Angiang
Tiengiang
Haiphong Police
Dongthap
Longan
Thanhhoa Police
HCM City Customs
Vietnamese Railway
Constructional Workers
Army Club (The Cong)
Haiphong Electricity
Nghiabinh Workers
Lamdong
Quangnam-Danang
Lam River-Nghetinh
Teams were divided into 3 groups playing double round robin;
no points for more than 3 draws;
bottom clubs of each group relegated:
top-2 of each and two best 3rd placed clubs to second phase
Second round
played in 2 groups of 4, single round robin; top-2 of each to semifinals
Saigon Port finished 5th overall
Final
Cau Lac Bo Quan doi (Ha Noi) 4-0 Quang Nam (Da Nang)
References
Vietnamese Super League seasons
1
Viet
Viet |
https://en.wikipedia.org/wiki/1989%20V-League | Statistics of the V-League in the 1989 season.
Group 1
Group 2
Group 3
Semifinals
Cau Lac Bo Quan Doi 1-0 Cong An Hanoi
Dong Thap 0-0 Dien Haiphong [4-3 on pens]
Third place match
Cong An Hanoi 2-1 Dien Haiphong
Final
Dong Thap 1-0 Cau Lac Bo Quan Doi
References
Vietnamese Super League seasons
1
Viet
Viet |
https://en.wikipedia.org/wiki/1987%E2%80%9388%20V-League | Statistics of the V-League in the 1987-88 season.
1987
First round
27 participants divided over 3 groups playing double round robin;
top-4 of each to second phase
Second round
12 participants divided over 3 groups playing single round robin;
top-2 of each and 2 best 3rd place teams to quarterfinals
Quarterfinals
An Giang 1-1 Saigon Port [4-2 pen]
Final
Cau Lac Bo Quan doi (Ha Noi) 1-0 Quang Nam (Da Nang)
1988
Overview
Season was cancelled, instead, regional friendship tournaments were held.
References
Vietnamese Super League seasons
1987 in Vietnamese football
1988 in Vietnamese football
Viet |
https://en.wikipedia.org/wiki/1986%20V-League | Statistics of the V-League in the 1986 season.
First phase
20 participants divided over 3 groups playing double round robin;
top-2 of each to second phase.
Similar to some Soviet Top League seasons, a draw limit was used. In this case, from the 4th draw on points would not be counted.
Second phase
6 participants playing single round robin; no draws
Results Saigon Port
Saigon Port 2–0 Army Club
Saigon Port drw Ha Nam Ninh Industry [4–1 pen]
Saigon Port 2–1 HCM City Industrial Department
Saigon Port 4–1 HCM City Custom
Saigon Port 1–0 HCM City Police
Champions: Saigon Port
References
Vietnamese Super League seasons
1
Viet
Viet |
https://en.wikipedia.org/wiki/1985%20V-League | Statistics of the V-League in the 1985 season.
First stage
Though not mentioned in any records, the draw limit was used similar to some Soviet Top League seasons. From the 4th draw on, points would not be counted.
Group A
Group B
Group C
Second stage
Group 1
Group 2
Semifinals
Two teams from Group B were disqualified, so there was no semifinals
Final
CN Ha Nam Ninh 3-1 So CN TP.HCM
Relegation
References
Vietnamese Super League seasons
1
Viet
Viet |
https://en.wikipedia.org/wiki/Limiting%20parallel | In neutral or absolute geometry, and in hyperbolic geometry, there may be many lines parallel to a given line through a point not on line ; however, in the plane, two parallels may be closer to than all others (one in each direction of ).
Thus it is useful to make a new definition concerning parallels in neutral geometry. If there are closest parallels to a given line they are known as the limiting parallel, asymptotic parallel or horoparallel (horo from — border).
For rays, the relation of limiting parallel is an equivalence relation, which includes the equivalence relation of being coterminal.
If, in a hyperbolic triangle, the pairs of sides are limiting parallel, then the triangle is an ideal triangle.
Definition
A ray is a limiting parallel to a ray if they are coterminal or if they lie on distinct lines not equal to the line , they do not meet, and every ray in the interior of the angle meets the ray .
Properties
Distinct lines carrying limiting parallel rays do not meet.
Proof
Suppose that the lines carrying distinct parallel rays met. By definition they cannot meet on the side of which either is on. Then they must meet on the side of opposite to , call this point . Thus . Contradiction.
See also
horocycle, In Hyperbolic geometry a curve whose normals are limiting parallels
angle of parallelism
References
Non-Euclidean geometry
Hyperbolic geometry |
https://en.wikipedia.org/wiki/Ravenel%27s%20conjectures | In mathematics, the Ravenel conjectures are a set of mathematical conjectures in the field of stable homotopy theory posed by Douglas Ravenel at the end of a paper published in 1984. It was earlier circulated in preprint. The problems involved have largely been resolved, with all but the "telescope conjecture" being proved in later papers by others. The telescope conjecture is now generally believed not to be true, though there are some conflicting claims concerning it in the published literature, and is taken to be an open problem. Ravenel's conjectures exerted influence on the field through the founding of the approach of chromatic homotopy theory.
The first of the seven conjectures, then the nilpotence conjecture, was proved in 1988 and is now known as the nilpotence theorem.
The telescope conjecture, which was #4 on the original list, remains of substantial interest because of its connection with the convergence of an Adams–Novikov spectral sequence. While opinion has been generally against the truth of the original statement, investigations of associated phenomena (for a triangulated category in general) have become a research area in its own right.
On June 6, 2023, Robert Burklund, Jeremy Hahn, Ishan Levy, and Tomer Schlank announced a disproof of the telescope conjecture. Their preprint is submitted on October 26, 2023.
See also
Homotopy groups of spheres
References
Homotopy theory
Conjectures |
https://en.wikipedia.org/wiki/2007%20Myanmar%20Premier%20League | Statistics of the Myanmar Premier League in the 2007 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
Ministry of Electric Power (relegated)
Ministry of Communications, Post and Telephone (relegated)
See also
2000 Myanmar Premier League
2003 Myanmar Premier League
2004 Myanmar Premier League
2005 Myanmar Premier League
2006 Myanmar Premier League
2008 Myanmar Premier League
References
http://www.rsssf.com/tablesm/myan07.html
Myanmar Premier League seasons
Burma
Burma
1 |
https://en.wikipedia.org/wiki/Paulo%20da%20Palma | Paulo da Palma (born 18 March 1965) is a German-born Portuguese former professional footballer who played as a midfielder.
Career statistics
References
External links
1965 births
Living people
Portuguese men's footballers
Men's association football midfielders
Bundesliga players
2. Bundesliga players
Eintracht Nordhorn players
VfB Oldenburg players
VfL Osnabrück players
VfL Bochum players
1. FC Saarbrücken players
FC 08 Homburg players
People from Nordhorn
Sportspeople from Lower Saxony |
https://en.wikipedia.org/wiki/Schreder%20HP-21 | The Schreder HP-21 was an American high-wing, variable geometry, V tailed, single seat motor glider project that was designed by Richard Schreder. None was ever completed or flown.
Design and development
The HP-21 project was publicly announced in August 1982 in Soaring Magazine. Schreder said at that time: "the HP-21 will out-perform any other factory-built 15-Meter racer now in production."
In April 1984 the design was revealed as a high performance V-tailed single seater, with a retractable KFM 107e powerplant of for self-launching, mounted behind the cockpit and retracting rearward to lie in a bay. The propeller remained exposed when the engine was retracted. The non-tapered wing had a carbon fiber spar with a span of and a chord of only , with winglets fitted. The wing incorporated a hand-crank operated retractable Dacron sailcloth flap that was intended to be extended for thermalling and retracted for glides. The flap was of triangular shape and when deployed would extend from the wing root to a point just inboard of the ailerons. The flap retracted by winding around a chrome-moly steel tube located inside the wing.
Schreder went on to start work on the HP-22 before the HP-21 was finished and, even though the prototype HP-21 carried the registration of N38100, it was never registered and there is no indication that it was ever completed or flown.
Specifications (HP-21)
See also
References
1980s United States sailplanes
Schreder aircraft
V-tail aircraft
Motor gliders
High-wing aircraft |
https://en.wikipedia.org/wiki/Sin%20Jin-ho | Sin Jin-ho (; Hanja: 申塡灝; born 7 September 1988) is a South Korean footballer who plays for Pohang Steelers as midfielder.
Career statistics
Club
Honours
Pohang Steelers
K League 1: 2013
Korean FA Cup: 2012, 2013
Ulsan Hyundai
AFC Champions League: 2020
External links
1988 births
Living people
Men's association football goalkeepers
South Korean men's footballers
South Korean expatriate men's footballers
Pohang Steelers players
Qatar SC players
Al-Sailiya SC players
Emirates Club players
FC Seoul players
Gimcheon Sangmu FC players
Ulsan Hyundai FC players
K League 1 players
Qatar Stars League players
Expatriate men's footballers in Qatar
Expatriate men's footballers in the United Arab Emirates
South Korean expatriate sportspeople in Qatar
South Korean expatriate sportspeople in the United Arab Emirates
UAE Pro League players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Hwang%20Kyo-chung | Hwang Kyo-Chung (; born 9 April 1985) is a South Korean footballer who plays as goalkeeper for Ulsan Hyundai Mipo in the Korea National League.
Club career statistics
External links
1985 births
Living people
Men's association football goalkeepers
South Korean men's footballers
Pohang Steelers players
Gangwon FC players
Ulsan Hyundai Mipo Dockyard FC players
K League 1 players
K League 2 players
Korea National League players |
https://en.wikipedia.org/wiki/Ko%20Moo-yeol | Ko Moo-yeol (; born 5 September 1990) is a South Korean footballer who plays as forward for Chungnam Asan in the K League 2.
Club career statistics
Honours
Club
Pohang Steelers
K League Classic (1): 2013
Korean FA Cup (2): 2012, 2013
Jeonbuk Hyundai Motors
K League Classic (1) : 2017
AFC Champions League (1): 2016
External links
1990 births
Living people
Men's association football forwards
South Korean men's footballers
Pohang Steelers players
Jeonbuk Hyundai Motors players
Asan Mugunghwa FC players
Chungnam Asan FC players
Gangwon FC players
K League 1 players
K League 2 players
Footballers from Busan
South Korean Buddhists |
https://en.wikipedia.org/wiki/Uniform%20module | In abstract algebra, a module is called a uniform module if the intersection of any two nonzero submodules is nonzero. This is equivalent to saying that every nonzero submodule of M is an essential submodule. A ring may be called a right (left) uniform ring if it is uniform as a right (left) module over itself.
Alfred Goldie used the notion of uniform modules to construct a measure of dimension for modules, now known as the uniform dimension (or Goldie dimension) of a module. Uniform dimension generalizes some, but not all, aspects of the notion of the dimension of a vector space. Finite uniform dimension was a key assumption for several theorems by Goldie, including Goldie's theorem, which characterizes which rings are right orders in a semisimple ring. Modules of finite uniform dimension generalize both Artinian modules and Noetherian modules.
In the literature, uniform dimension is also referred to as simply the dimension of a module or the rank of a module. Uniform dimension should not be confused with the related notion, also due to Goldie, of the reduced rank of a module.
Properties and examples of uniform modules
Being a uniform module is not usually preserved by direct products or quotient modules. The direct sum of two nonzero uniform modules always contains two submodules with intersection zero, namely the two original summand modules. If N1 and N2 are proper submodules of a uniform module M and neither submodule contains the other, then fails to be uniform, as
Uniserial modules are uniform, and uniform modules are necessarily directly indecomposable. Any commutative domain is a uniform ring, since if a and b are nonzero elements of two ideals, then the product ab is a nonzero element in the intersection of the ideals.
Uniform dimension of a module
The following theorem makes it possible to define a dimension on modules using uniform submodules. It is a module version of a vector space theorem:
Theorem: If Ui and Vj are members of a finite collection of uniform submodules of a module M such that and are both essential submodules of M, then n = m.
The uniform dimension of a module M, denoted u.dim(M), is defined to be n if there exists a finite set of uniform submodules Ui such that is an essential submodule of M. The preceding theorem ensures that this n is well defined. If no such finite set of submodules exists, then u.dim(M) is defined to be ∞. When speaking of the uniform dimension of a ring, it is necessary to specify whether u.dim(RR) or rather u.dim(RR) is being measured. It is possible to have two different uniform dimensions on the opposite sides of a ring.
If N is a submodule of M, then u.dim(N) ≤ u.dim(M) with equality exactly when N is an essential submodule of M. In particular, M and its injective hull E(M) always have the same uniform dimension. It is also true that u.dim(M) = n if and only if E(M) is a direct sum of n indecomposable injective modules.
It can be shown that u.dim(M) = ∞ if and |
https://en.wikipedia.org/wiki/Quasi-Frobenius%20ring | In mathematics, especially ring theory, the class of Frobenius rings and their generalizations are the extension of work done on Frobenius algebras. Perhaps the most important generalization is that of quasi-Frobenius rings (QF rings), which are in turn generalized by right pseudo-Frobenius rings (PF rings) and right finitely pseudo-Frobenius rings (FPF rings). Other diverse generalizations of quasi-Frobenius rings include QF-1, QF-2 and QF-3 rings.
These types of rings can be viewed as descendants of algebras examined by Georg Frobenius. A partial list of pioneers in quasi-Frobenius rings includes R. Brauer, K. Morita, T. Nakayama, C. J. Nesbitt, and R. M. Thrall.
Definitions
A ring R is quasi-Frobenius if and only if R satisfies any of the following equivalent conditions:
R is Noetherian on one side and self-injective on one side.
R is Artinian on a side and self-injective on a side.
All right (or all left) R modules which are projective are also injective.
All right (or all left) R modules which are injective are also projective.
A Frobenius ring R is one satisfying any of the following equivalent conditions. Let J=J(R) be the Jacobson radical of R.
R is quasi-Frobenius and the socle as right R modules.
R is quasi-Frobenius and as left R modules.
As right R modules , and as left R modules .
For a commutative ring R, the following are equivalent:
R is Frobenius
R is quasi-Frobenius
R is a finite direct sum of local artinian rings which have unique minimal ideals. (Such rings are examples of "zero-dimensional Gorenstein local rings".)
A ring R is right pseudo-Frobenius if any of the following equivalent conditions are met:
Every faithful right R module is a generator for the category of right R modules.
R is right self-injective and is a cogenerator of Mod-R.
R is right self-injective and is finitely cogenerated as a right R module.
R is right self-injective and a right Kasch ring.
R is right self-injective, semilocal and the socle soc(RR) is an essential submodule of R.
R is a cogenerator of Mod-R and is a left Kasch ring.
A ring R is right finitely pseudo-Frobenius if and only if every finitely generated faithful right R module is a generator of Mod-R.
Thrall's QF-1,2,3 generalizations
In the seminal article , R. M. Thrall focused on three specific properties of (finite-dimensional) QF algebras and studied them in isolation. With additional assumptions, these definitions can also be used to generalize QF rings. A few other mathematicians pioneering these generalizations included K. Morita and H. Tachikawa.
Following , let R be a left or right Artinian ring:
R is QF-1 if all faithful left modules and faithful right modules are balanced modules.
R is QF-2 if each indecomposable projective right module and each indecomposable projective left module has a unique minimal submodule. (I.e. they have simple socles.)
R is QF-3 if the injective hulls E(RR) and E(RR) are both projective modules.
The numbering scheme doe |
https://en.wikipedia.org/wiki/2005%20Kashima%20Antlers%20season | 2005 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/2005%20Omiya%20Ardija%20season | 2005 Omiya Ardija season
Competitions
Domestic results
J.League 1
Emperor's Cup
J.League Cup
Player statistics
Other pages
J. League official site
Omiya Ardija
Omiya Ardija seasons |
https://en.wikipedia.org/wiki/2005%20JEF%20United%20Chiba%20season | 2005 JEF United Ichihara Chiba season.
Competitions
Domestic results
J. League 1
Emperor's Cup
J. League Cup
Player statistics
Other pages
J. League official site
JEF United Ichihara Chiba
JEF United Chiba seasons |
https://en.wikipedia.org/wiki/2005%20Kashiwa%20Reysol%20season | 2005 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/2005%20FC%20Tokyo%20season | 2005 FC Tokyo season
Competitions
Domestic results
J.League 1
Emperor's Cup
J.League Cup
Player statistics
Other pages
J. League official site
Tokyo
2005 |
https://en.wikipedia.org/wiki/2005%20Kawasaki%20Frontale%20season | 2005 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/2005%20Albirex%20Niigata%20season | 2005 Albirex Niigata season
Competitions
Domestic results
J. League 1
Emperor's Cup
J. League Cup
Player statistics
Other pages
J. League official site
Albirex Niigata
Albirex Niigata seasons |
https://en.wikipedia.org/wiki/2005%20Gamba%20Osaka%20season | 2005 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/2005%20Cerezo%20Osaka%20season | 2005 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/Keith%20Hall%20%28economist%29 | Keith Hall served as the Director of the U.S. Congressional Budget Office from 2015 to 2019. He was the Commissioner of the U.S. Bureau of Labor Statistics from January 2008 until January 2012. He previously worked at the Department of Commerce, Department of Treasury, the U.S. International Trade Commission, and the White House Council of Economic Advisers.
Career
Hall was nominated by President George W. Bush to the position of Commissioner of the BLS in September 2007 and confirmed by the Senate in December. He was sworn into office in January 2008 and served a four-year term ending in 2012. Previously, he was Chief Economist for the White House Council of Economic Advisers. He also held the positions of Chief Economist for the Department of Commerce and Senior International Economist for the International Trade Commission's Research Division. He has also served on the faculties of the University of Arkansas and University of Missouri.
On April 1, 2011, Hall testified on Capitol Hill to the United States Congress Joint Economic Committee that the nation's unemployment rate had fallen to 8.8 percent, a two-year low. Statistics released by the BLS showed that non-farm payroll employment rose by 1.5 million from February 2010 and private sector employment increased by 1.8 million during the same period.
Hall was the ninth Director of the Congressional Budget Office from April 1, 2015 to May 31, 2019.
Education
Hall received his B.A. from the University of Virginia and his Ph.D. from Purdue University.
References
External links
Politico profile
American civil servants
Bureau of Labor Statistics
Directors of the Congressional Budget Office
Living people
Purdue University alumni
University of Virginia alumni
Year of birth missing (living people)
George W. Bush administration personnel
Obama administration personnel |
https://en.wikipedia.org/wiki/List%20of%20Rosenborg%20BK%20records%20and%20statistics | Rosenborg Ballklub is an association football club based in Trondheim, Norway. It is Norway's most successful club, having won the Norwegian Premier League 26 times and the Norwegian Football Cup 12 times. Although founded in 1917, it was not permitted to play Football Association of Norway-sanctioned matches until 1928. The club entered the cup for the first time in 1932, claiming its first title in 1960. Rosenborg joined the top league in 1967 and won the league in the club's inaugural top tier season. It has only spent one season outside the top tier since, which was in 1978. Rosenborg has played 186 matches and 27 seasons in Union of European Football Associations (UEFA) tournaments, starting with the 1965–66 European Cup Winners' Cup. Their only European trophy is the 2008 UEFA Intertoto Cup, with the second-best performance being the quarter-finals of the 1996–97 UEFA Champions League.
The club's record win is 17–0 in a cup match against Buvik in 2003; the league record is 10–0 against Brann in 1996 and the Champions League record is 6–0 against Helsingborg in 2000. In the league, the team had a record 87–20 goal difference in 1997, claimed a record 69 points in 2009 and went undefeated in 2010. Rosenborg was relegated after the 1977 season having won just a single match. The record home attendance is 28,569 spectators at Lerkendal Stadion against Lillestrøm in 1985.
Roar Strand, who played 21 seasons between 1989 and 2010, has played 416 league matches, more than any other Rosenborg player. He has also won the most titles with the club, having won the league 16 times and the cup 5 times. With 151 league goals, Harald Martin Brattbakk is the club's all-time top scorer and was the league's top scorer during six seasons. Sigurd Rushfeldt is the league's all-time top scorer, although he scored a majority of these for Tromsø. Odd Iversen holds the record for most goals in a single match and season, with 6 and 30 respectively. The club received it highest transfer fee for John Carew; they received 75 million Norwegian krone when he was sold to Valencia in 2000.
Honors
Major
1. divisjon / Norwegian Premier League:
Winners (26): 1967, 1969, 1971, 1985, 1988, 1990, 1992, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2006, 2009, 2010, 2015, 2016, 2017, 2018
Runners-up (7): 1968, 1970, 1973, 1989, 1991, 2013, 2014
Norwegian Football Cup:
Winners (12): 1960, 1964, 1971, 1988, 1990, 1992, 1995, 1999, 2003, 2015, 2016, 2018
Runners-up (6): 1967, 1972, 1973, 1991, 1998, 2013
Superfinalen:
Winners (1): 2010
Mesterfinalen:
Winners (2): 2017, 2018
Intertoto Cup:
Co-winner (1): 2008
Minor
Minor honors include lower-division league titles and pre-season friendly tournaments.
The double:
Winners (9): 1971, 1988, 1990, 1992, 1995, 1999, 2003, 2015, 2016, 2018
League of Norway District VIII:
Winners (1): 1938–39
Trøndelag Class A:
Winners (1): 1945
Runners-up (1): 1935, 1936
Third Division:
Winners (4): 1948–49, 1 |
https://en.wikipedia.org/wiki/Meisam%20Aghababaei | Meisam Aghababaei is an Iranian footballer who most recently plays for Naft Tehran in the IPL.
Club career
Aghababaei has played with Naft Tehran since 2009.
Club Career Statistics
References
Living people
Naft Tehran F.C. players
Iranian men's footballers
Men's association football defenders
Year of birth missing (living people)
Place of birth missing (living people) |
https://en.wikipedia.org/wiki/Branching%20random%20walk | In probability theory, a branching random walk is a stochastic process that generalizes both the concept of a random walk and of a branching process. At every generation (a point of discrete time), a branching random walk's value is a set of elements that are located in some linear space, such as the real line. Each element of a given generation can have several descendants in the next generation. The location of any descendant is the sum of its parent's location and a random variable.
This process is a spatial expansion of the Galton–Watson process. Its continuous equivalent is called branching Brownian motion.
Example
An example of branching random walk can be constructed where the branching process generates exactly two descendants for each element, a binary branching random walk. Given the initial condition that Xϵ = 0, we suppose that X1 and X2 are the two children of Xϵ. Further, we suppose that they are independent (0, 1) random variables. Consequently, in generation 2, the random variables X1,1 and X1,2 are each the sum of X1 and a (0, 1) random variable. In the next generation, the random variables X1,2,1 and X1,2,2 are each the sum of X1,2 and a (0, 1) random variable. The same construction produces the values at successive times.
Each lineage in the infinite "genealogical tree" produced by this process, such as the sequence Xϵ, X1, X1,2, X1,2,2, ..., forms a conventional random walk.
See also
Discrete-time dynamical system
References
Variants of random walks |
https://en.wikipedia.org/wiki/Symposium%20on%20Geometry%20Processing | Symposium on Geometry Processing (SGP) is an annual symposium hosted by the European Association For Computer Graphics (Eurographics). The goal of the symposium is to present and discuss new research ideas and results in geometry processing. The conference is geared toward the discussion of mathematical foundations and practical algorithms for the processing of complex geometric data sets, ranging from acquisition and editing all the way to animation, transmission and display. As such, it draws on many disciplines spanning pure and applied mathematics, computer science, and engineering. The proceedings of SGP appear as a special issue of the Computer Graphics Forum, the International Journal of the Eurographics Association. Since 2011, SGP has held a two-day "graduate school" preceding the conference, typically composed of workshop-style courses from subfield experts.
Venues
Best Paper Awards
Each year up to three papers are recognized with a Best Paper Award.
SGP Software Award
Each year, since 2011, SGP also awards a prize for the best freely available software related to or useful for geometry processing.
SGP Dataset Award
Each year, since 2016, SGP also awards a prize for the best freely available dataset related to or useful for geometry processing.
References
geometry processing course webpage, Alla Sheffer
EG digital library for SGP 2012
Computer graphics organizations |
https://en.wikipedia.org/wiki/Cohomology%20of%20algebras | In mathematics, the homology or cohomology of an algebra may refer to
Banach algebra cohomology of a bimodule over a Banach algebra
Cyclic homology of an associative algebra
Group cohomology of a module over a group ring or a representation of a group
Hochschild homology of a bimodule over an associative algebra
Lie algebra cohomology of a module over a Lie algebra
Supplemented algebra cohomology of a module over a supplemented associative algebra
See also
Cohomology
Ext functor
Tor functor
Homological algebra |
https://en.wikipedia.org/wiki/Haynsworth%20inertia%20additivity%20formula | In mathematics, the Haynsworth inertia additivity formula, discovered by Emilie Virginia Haynsworth (1916–1985), concerns the number of positive, negative, and zero eigenvalues of a Hermitian matrix and of block matrices into which it is partitioned.
The inertia of a Hermitian matrix H is defined as the ordered triple
whose components are respectively the numbers of positive, negative, and zero eigenvalues of H. Haynsworth considered a partitioned Hermitian matrix
where H11 is nonsingular and H12* is the conjugate transpose of H12. The formula states:
where H/H11 is the Schur complement of H11 in H:
Generalization
If H11 is singular, we can still define the generalized Schur complement, using the Moore–Penrose inverse instead of .
The formula does not hold if H11 is singular. However, a generalization has been proven in 1974 by Carlson, Haynsworth and Markham, to the effect that and .
Carlson, Haynsworth and Markham also gave sufficient and necessary conditions for equality to hold.
See also
Block matrix pseudoinverse
Sylvester's law of inertia
Notes and references
Linear algebra
Matrix theory
Theorems in algebra |
https://en.wikipedia.org/wiki/List%20of%20missionary%20schools%20in%20Malaysia | Missionary schools in Malaysia have their origins derived from British colonialism.
Background
Under the Aziz report, many missionary schools opted to be nationalised in 1971.
Statistics
Nearly half of such schools are located in the Christian-majority Sarawak state.
Primary schools
Methodist schools
Sekolah Kebangsaan Methodist, Nibong Tebal
Sekolah Kebangsaan Pykett Methodist
Sekolah Kebangsaan Perempuan Methodist, Pulau Pinang
Sekolah Kebangsaan Ho Seng Ong Methodist
Sekolah Kebangsaan Horley Methodist
Sekolah Kebangsaan Methodist, Ayer Tawar
Sekolah Kebangsaan Methodist, Ipoh
Sekolah Kebangsaan Perempuan Methodist, Ipoh
Sekolah Kebangsaan Methodist, Parit Buntar
Sekolah Kebangsaan Methodist, Sitiawan
Sekolah Kebangsaan Methodist, Sungai Siput
Sekolah Kebangsaan Methodist, Taiping
Sekolah Kebangsaan Methodist (Acs), Lumut
Sekolah Kebangsaan (P) Treacher Methodist
Sekolah Kebangsaan Methodist, Tanjong Malim
Sekolah Kebangsaan Methodist, Tanjong Rambutan
Sekolah Kebangsaan Perempuan Methodist, Teluk Intan
Sekolah Kebangsaan Methodist (1)
Sekolah Kebangsaan Methodist, Lumut
Sekolah Kebangsaan Methodist, Malim Nawar
Anglo Chinese School, Klang
Sekolah Kebangsaan Methodist (Integ) (M)
Sekolah Kebangsaan Methodist (M)
Sekolah Kebangsaan Methodist Acs, Selangor
Sekolah Kebangsaan Methodist, Petaling Jaya
Methodist Girls' School, Klang
Sekolah Kebangsaan Methodist Jalan Stadium
Sekolah Kebangsaan Methodist (L) Jalan Hang Jebat (M)
Sekolah Kebangsaan (P) Methodist (2), Kuala Lumpur
Sekolah Kebangsaan Methodist Acs, Melaka
Sekolah Kebangsaan (P) Methodist (1), Melaka
Sekolah Kebangsaan (P) Methodist (2), Melaka
Sekolah Kebangsaan Perempuan Methodist, Kuantan
Sekolah Kebangsaan Perempuan Methodist, Pahang
Sekolah Kebangsaan Methodist, Kapit
Sekolah Kebangsaan Methodist Anglo-Chinese
Convent schools
Sekolah Kebangsaan Convent, Kedah
Sekolah Kebangsaan Convent Father Barre
Sekolah Kebangsaan Convent 1, Butterworth
Sekolah Kebangsaan St Anne's Convent, Jalan Kulim
Sekolah Kebangsaan Convent, Green Lane
Sekolah Kebangsaan Convent, Lebuh Light
Sekolah Kebangsaan Convent, Pulau Tikus
Sekolah Jenis Kebangsaan (C) Convent Datuk Keramat
Sekolah Kebangsaan Convent, Sitiawan
Sekolah Kebangsaan Convent, Ipoh
Sekolah Jenis Kebangsaan (C) Ave Maria Convent
Sekolah Kebangsaan Tarcisian Convent
Sekolah Kebangsaan Marian Convent
Sekolah Jenis Kebangsaan (T) St. Philomena Convent
Sekolah Kebangsaan Convent, Teluk Intan
Sekolah Kebangsaan St. Bernadette'S Convent
Sekolah Kebangsaan Convent, Taiping
Sekolah Kebangsaan Convent Aulong, Taiping - One of only three coeducational Convent schools in Malaysia
Sekolah Jenis Kebangsaan (T) St. Teresa Convent - One of only three coeducational Convent schools in Malaysia
Sekolah Kebangsaan Convent, Selangor
Sekolah Kebangsaan Convent (1) (M)
Sekolah Kebangsaan Convent (2) (M)
Sekolah Kebangsaan St Anne's Convent, Selangor
Sekolah Kebangsaan Convent (1) Bukit Nanas (M)
S |
https://en.wikipedia.org/wiki/1945%20Mongolian%20independence%20referendum | An independence referendum was held in the Mongolian People's Republic on 20 October 1945. It was approved by 100% of voters, with no votes against, according to official statistics. Voter turnout was 98.5%.
Mongolia had gained de facto independence from the Republic of China in the Mongolian Revolution of 1921. In that year the last Chinese troops in Mongolia had been expelled by the White Russian general Roman von Ungern-Sternberg, prompting Soviet intervention. The Mongolian People's Republic was effectively an unrecognized satellite state of the Soviet Union (USSR). Towards the end of World War II, the USSR pushed China for formal recognition of the status quo, threatening to stir up Mongolian nationalism within China. In the Sino-Soviet Treaty of Friendship and Alliance signed on 14 August 1945, China agreed to recognize Mongolian independence after a successful referendum.
Results
Reactions
In January 1946, the Nationalist Government of the Republic of China officially recognized the "independence of Outer Mongolia" based on referendum results.
Analysis
At the scientific conference dedicated to the 70th anniversary of the referendum, Zandaakhüügiin Enkhbold, speaker of the State Great Khural, said that the referendum in 1945 was the first democratic vote in Mongolia, and was of great historical significance to the independence of the country.
Sergey Radchenko, a professor of East China Normal University noted that the "referendum was regarded by both sides as political theatre, due to the peculiarity of a supposed unanimous 100% vote in favour."
See also
Modern Mongolian history
Outer Mongolia
References
Mongolia
Mongolia
Independence
Referendums in Mongolia
Mongolia |
https://en.wikipedia.org/wiki/Banach%20algebra%20cohomology | In mathematics, Banach algebra cohomology of a Banach algebra with coefficients in a bimodule is a cohomology theory defined in a similar way to Hochschild cohomology of an abstract algebra, except that one takes the topology into account so that all cochains and so on are continuous.
References
Homological algebra
Banach algebras |
https://en.wikipedia.org/wiki/Geometric%20networks | A geometric network is an object commonly used in geographic information systems to model a series of interconnected features. A geometric network is similar to a graph in mathematics and computer science, and can be described and analyzed using theories and concepts similar to graph theory. Geometric networks are often used to model road networks and public utility networks (such as electric, gas, and water utilities). Geometric networks are called in recent years very often spatial networks.
Composition of a Geometric Network
A geometric network is composed of edges that are connected. Connectivity rules for the network specify which edges are connected and at what points they are connected, commonly referred to as junction or intersection points. These edges can have weights or flow direction assigned to them, which dictate certain properties of these edges that affect analysis results
. In the case of certain types of networks, source points (points where flow originates) and sink points (points where flow terminates) may also exist. In the case of utility networks, a source point may correlate with an electric substation or a water pumping station, and a sink point may correlate with a service connection at a residential household.
Functions
Networks define the interconnectedness of features. Through analyzing this connectivity, paths from one point to another on the network can be traced and calculated. Through optimization algorithms and utilizing network weights and flow, these paths can also be optimized to show specialized paths, such as the shortest path between two points on the network, as is commonly done in the calculation of driving directions. Networks can also be used to perform spatial analysis to determine points or edges that are encompassed in a certain area or within a certain distance of a specified point. This has applications in hydrology and urban planning, among other fields.
Applications
Routing: for calculating driving directions, paths from one point of interest to another, locating nearby points of interest
Urban Planning: for site suitability studies, and traffic and congestion studies.
Electric Utility Industry: for modeling an electrical grid in GIS, tracing from a generation source
Other Public Utilities: for modeling water distribution flow and natural gas distribution
See also
Graphs
Graph theory
Geographic Information Systems
References
Geographic information systems |
https://en.wikipedia.org/wiki/Information%20projection | In information theory, the information projection or I-projection of a probability distribution q onto a set of distributions P is
.
where is the Kullback–Leibler divergence from q to p. Viewing the Kullback–Leibler divergence as a measure of distance, the I-projection is the "closest" distribution to q of all the distributions in P.
The I-projection is useful in setting up information geometry, notably because of the following inequality, valid when P is convex:
.
This inequality can be interpreted as an information-geometric version of Pythagoras' triangle-inequality theorem, where KL divergence is viewed as squared distance in a Euclidean space.
It is worthwhile to note that since and continuous in p,
if P is closed and non-empty, then there exists at least one minimizer to the optimization problem framed above. Furthermore, if P is convex, then the optimum distribution is unique.
The reverse I-projection also known as moment projection or M-projection is
.
Since the KL divergence is not symmetric in its arguments, the I-projection and the M-projection will exhibit different behavior. For I-projection, will typically
under-estimate the support of and will lock onto one of its modes. This is due to , whenever to make sure KL divergence stays finite. For M-projection, will typically over-estimate the support of . This is due to whenever to make sure KL divergence stays finite.
The concept of information projection can be extended to arbitrary f-divergences and other divergences.
See also
Sanov's theorem
References
K. Murphy, "Machine Learning: a Probabilistic Perspective", The MIT Press, 2012.
Information theory |
https://en.wikipedia.org/wiki/Sanov%27s%20theorem | In mathematics and information theory, Sanov's theorem gives a bound on the probability of observing an atypical sequence of samples from a given probability distribution. In the language of large deviations theory, Sanov's theorem identifies the rate function for large deviations of the empirical measure of a sequence of i.i.d. random variables.
Let A be a set of probability distributions over an alphabet X, and let q be an arbitrary distribution over X (where q may or may not be in A). Suppose we draw n i.i.d. samples from q, represented by the vector . Then, we have the following bound on the probability that the empirical measure of the samples falls within the set A:
,
where
is the joint probability distribution on , and
is the information projection of q onto A.
In words, the probability of drawing an atypical distribution is bounded by a function of the KL divergence from the true distribution to the atypical one; in the case that we consider a set of possible atypical distributions, there is a dominant atypical distribution, given by the information projection.
Furthermore, if A is the closure of its interior,
References
Sanov, I. N. (1957) "On the probability of large deviations of random variables". Mat. Sbornik 42(84), No. 1, 11–44.
Санов, И. Н. (1957) "О вероятности больших отклонений случайных величин". ''МАТЕМАТИЧЕСКИЙ СБОРНИК' 42(84), No. 1, 11–44.
Information theory
Probabilistic inequalities |
https://en.wikipedia.org/wiki/Formally%20smooth%20map | In algebraic geometry and commutative algebra, a ring homomorphism is called formally smooth (from French: Formellement lisse) if it satisfies the following infinitesimal lifting property:
Suppose B is given the structure of an A-algebra via the map f. Given a commutative A-algebra, C, and a nilpotent ideal , any A-algebra homomorphism may be lifted to an A-algebra map . If moreover any such lifting is unique, then f is said to be formally étale.
Formally smooth maps were defined by Alexander Grothendieck in Éléments de géométrie algébrique IV.
For finitely presented morphisms, formal smoothness is equivalent to usual notion of smoothness.
Examples
Smooth morphisms
All smooth morphisms are equivalent to morphisms locally of finite presentation which are formally smooth. Hence formal smoothness is a slight generalization of smooth morphisms.
Non-example
One method for detecting formal smoothness of a scheme is using infinitesimal lifting criterion. For example, using the truncation morphism the infinitesimal lifting criterion can be described using the commutative squarewhere . For example, if and then consider the tangent vector at the origin given by the ring morphismsendingNote because , this is a valid morphism of commutative rings. Then, since a lifting of this morphism tois of the formand , there cannot be an infinitesimal lift since this is non-zero, hence is not formally smooth. This also proves this morphism is not smooth from the equivalence between formally smooth morphisms locally of finite presentation and smooth morphisms.
See also
Dual number
Smooth morphism
Deformation theory
References
External links
Formally smooth with smooth fibers, but not smooth https://mathoverflow.net/q/333596
Formally smooth but not smooth https://mathoverflow.net/q/195
Commutative algebra
Algebraic geometry |
https://en.wikipedia.org/wiki/Standard%20complex | In mathematics, the standard complex, also called standard resolution, bar resolution, bar complex, bar construction, is a way of constructing resolutions in homological algebra. It was first introduced for the special case of algebras over a commutative ring by and and has since been generalized in many ways.
The name "bar complex" comes from the fact that used a vertical bar | as a shortened form of the tensor product in their notation for the complex.
Definition
If A is an associative algebra over a field K, the standard complex is
with the differential given by
If A is a unital K-algebra, the standard complex is exact. Moreover, is a free A-bimodule resolution of the A-bimodule A.
Normalized standard complex
The normalized (or reduced) standard complex replaces with .
Monads
See also
Koszul complex
References
Homological algebra |
https://en.wikipedia.org/wiki/Yuya%20Onoe | is a former Japanese football player.
Club statistics
References
External links
J. League
1985 births
Living people
Association football people from Tokushima Prefecture
Japanese men's footballers
J2 League players
Japan Football League players
Ehime FC players
Tokushima Vortis players
Kamatamare Sanuki players
Mitsubishi Mizushima FC players
Reilac Shiga FC players
Men's association football defenders |
https://en.wikipedia.org/wiki/Yuki%20Okamoto | is a former Japanese football player.
Club statistics
References
External links
J. League
1983 births
Living people
Ryutsu Keizai University alumni
Association football people from Gunma Prefecture
Japanese men's footballers
J2 League players
Japanese expatriate men's footballers
Mito HollyHock players
Fukushima United FC players
Men's association football forwards |
https://en.wikipedia.org/wiki/Fl%C3%A1vio%20%28footballer%2C%20born%20April%201975%29 | Flávio Elias Cordeiro (born April 23, 1975), known as just Flávio, is a Brazilian football player.
Club statistics
References
External links
1975 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
J2 League players
Shonan Bellmare players
Paraná Clube players
Avaí FC players
Moreirense F.C. players
Expatriate men's footballers in Portugal
Expatriate men's footballers in Japan
Men's association football forwards |
https://en.wikipedia.org/wiki/Amarildo%20%28footballer%2C%20born%201986%29 | Amarildo de Jesus Santos (born July 6, 1986), known as just Amarildo, is a Brazilian football player.
Club statistics
References
External links
1986 births
Living people
Brazilian men's footballers
J2 League players
Shonan Bellmare players
Brazilian expatriate men's footballers
Expatriate men's footballers in Japan
Men's association football defenders |
https://en.wikipedia.org/wiki/Izaias%20%28footballer%29 | Izaias Maia Carneiro (born June 5, 1975), known as Izaias, is a former Brazilian football player.
Club statistics
References
External links
1975 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
J2 League players
Yokohama FC players
Expatriate men's footballers in Japan
Men's association football forwards |
https://en.wikipedia.org/wiki/Yutaka%20Kaneko%20%28footballer%29 | is a former Japanese football player.
Club statistics
References
External links
1979 births
Living people
Asia University (Japan) alumni
Association football people from Saitama Prefecture
Japanese men's footballers
J2 League players
Japan Football League players
Ehime FC players
Reilac Shiga FC players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Ryota%20Doi | Ryota Doi (土井 良太, born August 27, 1987) is a Japanese football player for Fujieda MYFC.
Club career statistics
Updated to 23 February 2017.
References
External links
Profile at Vissel Kobe
Profile at Fujieda MYFC
1987 births
Living people
Association football people from Hyōgo Prefecture
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Japan Football League players
Vissel Kobe players
Japan Soccer College players
Arte Takasaki players
Thespakusatsu Gunma players
Iwate Grulla Morioka players
AC Nagano Parceiro players
Fujieda MYFC players
Men's association football forwards |
https://en.wikipedia.org/wiki/Fukaya%20category | In symplectic topology, a Fukaya category of a symplectic manifold is a category whose objects are Lagrangian submanifolds of , and morphisms are Lagrangian Floer chain groups: . Its finer structure can be described as an A∞-category.
They are named after Kenji Fukaya who introduced the language first in the context of Morse homology, and exist in a number of variants. As Fukaya categories are A∞-categories, they have associated derived categories, which are the subject of the celebrated homological mirror symmetry conjecture of Maxim Kontsevich. This conjecture has now been computationally verified for a number of examples.
Formal definition
Let be a symplectic manifold. For each pair of Lagrangian submanifolds that intersect transversely, one defines the Floer cochain complex which is a module generated by intersection points . The Floer cochain complex is viewed as the set of morphisms from to . The Fukaya category is an category, meaning that besides ordinary compositions, there are higher composition maps
It is defined as follows. Choose a compatible almost complex structure on the symplectic manifold . For generators and of the cochain complexes, the moduli space of -holomorphic polygons with faces with each face mapped into has a count
in the coefficient ring. Then define
and extend in a multilinear way.
The sequence of higher compositions satisfy the relations because the boundaries of various moduli spaces of holomorphic polygons correspond to configurations of degenerate polygons.
This definition of Fukaya category for a general (compact) symplectic manifold has never been rigorously given. The main challenge is the transversality issue, which is essential in defining the counting of holomorphic disks.
See also
Homotopy associative algebra
References
Bibliography
Denis Auroux, A beginner's introduction to Fukaya categories.
Paul Seidel, Fukaya categories and Picard-Lefschetz theory. Zurich lectures in Advanced Mathematics
External links
The thread on MathOverflow 'Is the Fukaya category "defined"?'
Symplectic geometry
Categories in category theory |
https://en.wikipedia.org/wiki/Hitoyoshi%20Satomi | is a former Japanese football player.
Club statistics
References
External links
1983 births
Living people
Association football people from Gunma Prefecture
Japanese men's footballers
J2 League players
Japan Football League players
Honda FC players
Thespakusatsu Gunma players
Arte Takasaki players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Takuro%20Okuyama | is a former Japanese football player.
Club statistics
References
External links
J. League
1983 births
Living people
Asia University (Japan) alumni
Association football people from Saitama Prefecture
Japanese men's footballers
J2 League players
Japan Football League players
Thespakusatsu Gunma players
Mitsubishi Mizushima FC players
Men's association football forwards |
https://en.wikipedia.org/wiki/Kim%20Dong-chan%20%28footballer%2C%20born%201981%29 | Kim Dong-Chan (born December 19, 1981) is a South Korean footballer who plays as a forward. In 2013, he played for Persita Tangerang.
Club statistics
References
External links
Kim Dong-Chan profile at jsgoal.jp
Kim Dong-Chan profile at liga-indonesia.co.id
1981 births
Living people
South Korean men's footballers
J2 League players
Kim Dong-chan
Kim Dong-chan
Liga 1 (Indonesia) players
Malaysia Super League players
Mito HollyHock players
Kim Dong-chan
Kim Dong-chan
Putra Samarinda F.C. players
Persita Tangerang players
Selangor F.C. II players
South Korean expatriate men's footballers
Expatriate men's footballers in Japan
Expatriate men's footballers in Thailand
Expatriate men's footballers in Indonesia
Expatriate men's footballers in Malaysia
South Korean expatriate sportspeople in Japan
South Korean expatriate sportspeople in Thailand
South Korean expatriate sportspeople in Indonesia
South Korean expatriate sportspeople in Malaysia
Men's association football forwards |
https://en.wikipedia.org/wiki/Ryuichi%20Dogaki | is a former Japanese football player.
Club statistics
References
External links
1988 births
Living people
Kwansei Gakuin University alumni
Association football people from Osaka Prefecture
Japanese men's footballers
J1 League players
J2 League players
Cerezo Osaka players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Gustav%20Elfving | Erik Gustav Elfving (25 June 1908 – 25 March 1984) was a Finnish mathematician and statistician. He wrote pioneering works in mathematical statistics, especially on the design of experiments.
Early life
Erik Gustav Elfving was son of Fredrik Elfving (1854–1942), a professor of botany at the University of Helsinki, and Thyra Elfving (née Ingman). He was the youngest of four children. Gustav Elfving earned excellent grades at the Svenska normallyceum i Helsingfors, a Helsinki gymnasium for Swedish-speaking boys, from which he graduated in 1926. In the same year he enrolled at the University of Helsinki, planning to major in astronomy. He switched to mathematics, graduating in 1930 in mathematics, with astronomy and physics as minor subjects. From 1927 to 1929, he worked as a computational assistant at the astronomical observatory of
the University of Helsinki. He studied probability theory under J. W. Lindeberg, who is now known for Lindeberg's condition for the central limit theorem. He wrote his (1934) dissertation under the supervision of Rolf Nevanlinna; his thesis studied Riemann surfaces and their uniformization. In the Nevanlinna theory of the values of meromorphic functions, Elfving's results were praised by Drasin.
Fiancée's death and his 1935 expedition to Greenland
Elfving was engaged to a young woman, who died in 1935, probably from tuberculosis. The grieving parents of his fiancée helped Elfving contact the Danish Geodetic Institute, which hired him as the mathematician for a cartographic expedition
to Western Greenland in the summer of 1935. Elfving was photographed while he made theodolite measurements and peered from a tent. Heavy rains forced the expedition to remain sheltered in their tents for three days, during which Elfving started to think about the best locations to take measurements for least squares estimation.
Statistical research
In statistics, Elfving did research in the design of experiments, probability theory, and statistical inference, as well as applications.
Optimal design of experiments
In statistics, Elfving is known as one of the founders of the modern theory of the optimal design of experiments. While accompanying a surveying expedition to western Greenland, extended and intense rains left Elving with three days in his tent, during which time he considered the best locations of observations to estimate parameters of linear models. Elfving's ideas appeared in his paper on the optimal design of experiments for estimating linear models. This paper also introduced concepts from convex geometry, including "Elfving sets" and Elfving's theorem. Being symmetric, Elfving sets are formed by the union of a set and its reflection through the origin, −S ∪ S. According to , Elfving was generous in crediting others' results: His paper in the Cramér-festschrift acknowledged unpublished notes of L. J. Savage; Elfving was a referee for the fundamental paper on optimal designs by Kiefer and Wolfowitz.
Other statistical |
https://en.wikipedia.org/wiki/Quantum%20dilogarithm | In mathematics, the quantum dilogarithm is a special function defined by the formula
It is the same as the q-exponential function .
Let be "q-commuting variables", that is elements of a suitable noncommutative algebra satisfying Weyl's relation . Then, the quantum dilogarithm satisfies Schützenberger's identity
Faddeev-Volkov's identity
and Faddeev-Kashaev's identity
The latter is known to be a quantum generalization of Rogers' five term dilogarithm identity.
Faddeev's quantum dilogarithm is defined by the following formula:
where the contour of integration goes along the real axis outside a small neighborhood of the origin and deviates into the upper half-plane near the origin. The same function can be described by the integral formula of Woronowicz:
Ludvig Faddeev discovered the quantum pentagon identity:
where and are self-adjoint (normalized) quantum mechanical momentum and position operators satisfying Heisenberg's commutation relation
and the inversion relation
The quantum dilogarithm finds applications in mathematical physics, quantum topology, cluster algebra theory.
The precise relationship between the q-exponential and is expressed by the equality
valid for .
References
External links
Special functions
Q-analogs |
https://en.wikipedia.org/wiki/Arash%20Talebinejad | Arash Talebinejad (, born 1981) is a retired football player. Talebinejad has represented the Swedish national youth football team.
Career statistics
References
External links
Brommapojkarna har värvat Arash Talebinejad från norska Tromsö
1981 births
Living people
Iranian emigrants to Sweden
Iranian men's footballers
Swedish men's footballers
Sweden men's under-21 international footballers
Sweden men's youth international footballers
Allsvenskan players
Superettan players
Ettan Fotboll players
Eliteserien players
Västra Frölunda IF players
AIK Fotboll players
Tromsø IL players
IF Brommapojkarna players
Swedish expatriate men's footballers
Iranian expatriate men's footballers
Swedish expatriate sportspeople in Norway
Expatriate men's footballers in Norway
Gröndals IK players
Sportspeople of Iranian descent
Men's association football midfielders
People from Hormozgan Province |
https://en.wikipedia.org/wiki/Spectral%20network | In mathematics and supersymmetric gauge theory, spectral networks are "networks of trajectories on Riemann surfaces obeying certain local rules. Spectral networks arise naturally in four-dimensional N = 2 theories coupled to surface defects, particularly the theories of class S."
References
Riemann surfaces |
https://en.wikipedia.org/wiki/John%20Grundy%20Sr. | John Grundy, Sr. (c.1696 – 1748) was a teacher of mathematics, a land surveyor, and later a civil engineer. Grundy lived in Congerstone, Leicestershire, England for the first forty years of his life; he later moved to Spalding in Lincolnshire. He was one of the first engineers to apply mathematical principles to the problems of land drainage. His son, John Grundy Jr., was also a civil engineer.
Life history
John Grundy was the son of Benjamin and Mary Grundy. He was born in the village of Bilstone, probably in 1696, but resided in the nearby village of Congerstone for most of his early life. He married Elizabeth Dalton some time before 1719, for their first son, John Grundy Jr., was baptised in the church at Congerstone on 1 July of that year. He became well known as a land surveyor, and taught mathematics to private pupils, advertising his skills in Market Bosworth, Derby and Leicester. He visited Spalding in 1731, to do some surveying for the Duke of Buccleuch, where he noticed the work being undertaken by John Perry on the River Welland. He became convinced that "mathematical and philosophical principles" could be applied to the proper drainage of low-lying ground. He joined the Gentlemen's Society at Spalding in 1731, and presented them with a map of Spalding in 1732.
Over the next six years, he made several trips to the Spalding area and Deeping Fen to work on drainage projects; he moved his family to Spalding in 1738. He had trained his son well, for he undertook his first project at Pinchbeck sluice in 1739, and the two of them worked jointly on a survey of the River Witham from Lincoln to Boston, and plans for drainage of the fens bordering the river. He died at the age of 52, on 30 December 1748 at Spalding, but was buried in Congerstone. His son, who went on to become one of the leading English civil engineers of the eighteenth century, erected a memorial in the church building.
In memory of John Grundy, late of Spalding, in Lincolnshire, who without the advantage of a liberal education had gained by his industry a competent knowledge in several of the learned sciences and lived by all ingenious honest men deservedly beloved and died by all such truly regretted.
Surveying
Grundy used a number of devices to enable him to carry out surveys, including a theodolite, a circumferentor, Beighton's improved plane table, and a Gunter's chain. When he undertook work for the Duke of Baccleugh in 1731, surveying his south Lincolnshire estates, he used the opportunity to study banks, drains, sluices and outfalls. The contract lasted for six months, and it was during this time that his ideas about applying mathematical principles developed. In 1733, he worked for the Commissioners of Sewers, surveying the parish of Moulton, near Spalding, and suggesting ways in which its drainage could be improved. To assist him, he obtained a spirit level with telescopic sights from Jonathan Sisson, who was the best instrument maker at the time. With it, he was a |
https://en.wikipedia.org/wiki/CH-quasigroup | In mathematics, a CH-quasigroup, introduced by , is a symmetric quasigroup in which any three elements generate an abelian quasigroup. "CH" stands for cubic hypersurface.
References
Non-associative algebra |
https://en.wikipedia.org/wiki/Dickson%27s%20conjecture | In number theory, a branch of mathematics, Dickson's conjecture is the conjecture stated by that for a finite set of linear forms , , ..., with , there are infinitely many positive integers for which they are all prime, unless there is a congruence condition preventing this . The case k = 1 is Dirichlet's theorem.
Two other special cases are well-known conjectures: there are infinitely many twin primes (n and 2 + n are primes), and there are infinitely many Sophie Germain primes (n and 1 + 2n are primes).
Dickson's conjecture is further extended by Schinzel's hypothesis H.
Generalized Dickson's conjecture
Given n polynomials with positive degrees and integer coefficients (n can be any natural number) that each satisfy all three conditions in the Bunyakovsky conjecture, and for any prime p there is an integer x such that the values of all n polynomials at x are not divisible by p, then there are infinitely many positive integers x such that all values of these n polynomials at x are prime. For example, if the conjecture is true then there are infinitely many positive integers x such that , , and are all prime. When all the polynomials have degree 1, this is the original Dickson's conjecture.
This more general conjecture is the same as the Generalized Bunyakovsky conjecture.
See also
Prime triplet
Green–Tao theorem
First Hardy–Littlewood conjecture
Prime constellation
Primes in arithmetic progression
References
Conjectures about prime numbers
Unsolved problems in number theory |
https://en.wikipedia.org/wiki/Spencer%20cohomology | In mathematics, Spencer cohomology is cohomology of a manifold with coefficients in the sheaf of solutions of a linear partial differential operator. It was introduced by Donald C. Spencer in 1969.
References
Sheaf theory
Cohomology theories |
https://en.wikipedia.org/wiki/Deligne%20cohomology | In mathematics, Deligne cohomology is the hypercohomology of the Deligne complex of a complex manifold. It was introduced by Pierre Deligne in unpublished work in about 1972 as a cohomology theory for algebraic varieties that includes both ordinary cohomology and intermediate Jacobians.
For introductory accounts of Deligne cohomology see , , and .
Definition
The analytic Deligne complex Z(p)D, an on a complex analytic manifold X iswhere Z(p) = (2π i)pZ. Depending on the context, is either the complex of smooth (i.e., C∞) differential forms or of holomorphic forms, respectively.
The Deligne cohomology is the q-th hypercohomology of the Deligne complex. An alternative definition of this complex is given as the homotopy limit of the diagram
Properties
Deligne cohomology groups can be described geometrically, especially in low degrees. For p = 0, it agrees with the q-th singular cohomology group (with Z-coefficients), by definition. For q = 2 and p = 1, it is isomorphic to the group of isomorphism classes of smooth (or holomorphic, depending on the context) principal C×-bundles over X. For p = q = 2, it is the group of isomorphism classes of C×-bundles with connection. For q = 3 and p = 2 or 3, descriptions in terms of gerbes are available (). This has been generalized to a description in higher degrees in terms of iterated classifying spaces and connections on them ().
Relation with Hodge classes
Recall there is a subgroup of integral cohomology classes in called the group of Hodge classes. There is an exact sequence relating Deligne-cohomology, their intermediate Jacobians, and this group of Hodge classes as a short exact sequence
Applications
Deligne cohomology is used to formulate Beilinson conjectures on special values of L-functions.
Extensions
There is an extension of Deligne-cohomology defined for any symmetric spectrum where for odd which can be compared with ordinary Deligne cohomology on complex analytic varieties.
See also
Bundle gerbe
Motivic cohomology
Hodge structure
Intermediate Jacobian
References
Deligne-Beilinson cohomology
Geometry of Deligne cohomology
Notes on differential cohomology and gerbes
Twisted smooth Deligne cohomology
Bloch's Conjecture, Deligne Cohomology and Higher Chow Groups
Sheaf theory
Homological algebra
Cohomology theories |
https://en.wikipedia.org/wiki/2006%20Kashima%20Antlers%20season | 2006 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/2006%20Urawa%20Red%20Diamonds%20season | 2006 Urawa Red Diamonds season
Competitions
Domestic results
J.League 1
Emperor's Cup
J.League Cup
Japanese Super Cup
Player statistics
Other pages
J.League official site
Urawa Red Diamonds
Urawa Red Diamonds seasons |
https://en.wikipedia.org/wiki/2006%20Omiya%20Ardija%20season | 2006 Omiya Ardija season
Competitions
Domestic results
J.League 1
Emperor's Cup
J.League Cup
Player statistics
Other pages
J. League official site
Omiya Ardija
Omiya Ardija seasons |
https://en.wikipedia.org/wiki/2006%20JEF%20United%20Chiba%20season | 2006 JEF United Ichihara Chiba season
Competitions
Domestic results
J. League 1
Emperor's Cup
J. League Cup
Player statistics
Other pages
J. League official site
JEF United Ichihara Chiba
JEF United Chiba seasons |
https://en.wikipedia.org/wiki/2006%20FC%20Tokyo%20season | 2006 FC Tokyo season
Competitions
Domestic results
J.League 1
Emperor's Cup
J.League Cup
Player statistics
Other pages
J. League official site
Tokyo
2006 |
https://en.wikipedia.org/wiki/2006%20Kawasaki%20Frontale%20season | 2006 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/2006%20Yokohama%20F.%20Marinos%20season | 2006 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/2006%20Ventforet%20Kofu%20season | 2006 Ventforet Kofu season
Competitions
Domestic results
J. League 1
Emperor's Cup
J. League Cup
Player statistics
Other pages
J. League official site
Ventforet Kofu
Ventforet Kofu seasons |
https://en.wikipedia.org/wiki/2006%20Albirex%20Niigata%20season | 2006 Albirex Niigata season
Competitions
Domestic results
J. League 1
Emperor's Cup
J. League Cup
Player statistics
Other pages
J. League official site
Albirex Niigata
Albirex Niigata seasons |
https://en.wikipedia.org/wiki/2006%20J%C3%BAbilo%20Iwata%20season | 2006 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/2006%20Nagoya%20Grampus%20Eight%20season | 2006 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/2006%20Kyoto%20Purple%20Sanga%20season | 2006 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/2006%20Gamba%20Osaka%20season | 2006 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/2006%20Cerezo%20Osaka%20season | 2006 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/2006%20Sanfrecce%20Hiroshima%20season | 2006 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/2006%20Avispa%20Fukuoka%20season | 2006 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/2006%20Oita%20Trinita%20season | 2006 Oita Trinita season
Competitions
Domestic results
J. League 1
Emperor's Cup
J. League Cup
Player statistics
Other pages
J. League official site
Oita Trinita
Oita Trinita seasons |
https://en.wikipedia.org/wiki/2006%20Yokohama%20FC%20season | 2006 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 |
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