source stringlengths 31 168 | text stringlengths 51 3k |
|---|---|
https://en.wikipedia.org/wiki/2003%20Gamba%20Osaka%20season | 2003 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/2003%20Cerezo%20Osaka%20season | 2003 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/2003%20Vissel%20Kobe%20season | 2003 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/2003%20Oita%20Trinita%20season | 2003 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/2003%20Consadole%20Sapporo%20season | 2003 Consadole Sapporo season
Competitions
Domestic results
J. League 2
Emperor's Cup
Player statistics
Other pages
J. League official site
Consadole Sapporo
Hokkaido Consadole Sapporo seasons |
https://en.wikipedia.org/wiki/2003%20Montedio%20Yamagata%20season | 2003 Montedio Yamagata season
Competitions
Domestic results
J. League 2
Emperor's Cup
Player statistics
Other pages
J. League official site
Montedio Yamagata
Montedio Yamagata seasons |
https://en.wikipedia.org/wiki/2003%20Mito%20HollyHock%20season | 2003 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/2003%20Omiya%20Ardija%20season | 2003 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/2003%20Kawasaki%20Frontale%20season | 2003 Kawasaki Frontale season
Competitions
Domestic results
J. League 2
Emperor's Cup
Player statistics
Other pages
J. League official site
Kawasaki Frontale
Kawasaki Frontale seasons |
https://en.wikipedia.org/wiki/2003%20Yokohama%20FC%20season | 2003 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/2003%20Shonan%20Bellmare%20season | 2003 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/2003%20Ventforet%20Kofu%20season | 2003 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/2003%20Albirex%20Niigata%20season | This page lists statistics from the 2003 season of the Albirex Niigata football team.
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/2003%20Sanfrecce%20Hiroshima%20season | 2003 Sanfrecce Hiroshima season
Competitions
Domestic results
J. League 2
Emperor's Cup
Player statistics
Other pages
J. League official site
Sanfrecce Hiroshima
Sanfrecce Hiroshima seasons |
https://en.wikipedia.org/wiki/2003%20Avispa%20Fukuoka%20season | 2003 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/2003%20Sagan%20Tosu%20season | 2003 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/Algebraic%20geometry%20of%20projective%20spaces | The concept of a Projective space plays a central role in algebraic geometry. This article aims to define the notion in terms of abstract algebraic geometry and to describe some basic uses of projective spaces.
Homogeneous polynomial ideals
Let k be an algebraically closed field, and V be a finite-dimensional vector space over k. The symmetric algebra of the dual vector space V* is called the polynomial ring on V and denoted by k[V]. It is a naturally graded algebra by the degree of polynomials.
The projective Nullstellensatz states that, for any homogeneous ideal I that does not contain all polynomials of a certain degree (referred to as an irrelevant ideal), the common zero locus of all polynomials in I (or Nullstelle) is non-trivial (i.e. the common zero locus contains more than the single element {0}), and, more precisely, the ideal of polynomials that vanish on that locus coincides with the radical of the ideal I.
This last assertion is best summarized by the formula : for any relevant ideal I,
In particular, maximal homogeneous relevant ideals of k[V] are one-to-one with lines through the origin of V.
Construction of projectivized schemes
Let V be a finite-dimensional vector space over a field k. The scheme over k defined by Proj(k[V]) is called projectivization of V. The projective n-space on k is the projectivization of the vector space .
The definition of the sheaf is done on the base of open sets of principal open sets D(P), where P varies over the set of homogeneous polynomials, by setting the sections
to be the ring , the zero degree component of the ring obtained by localization at P. Its elements are therefore the rational functions with homogeneous numerator and some power of P as the denominator, with same degree as the numerator.
The situation is most clear at a non-vanishing linear form φ. The restriction of the structure sheaf to the open set D(φ) is then canonically identified with the affine scheme spec(k[ker φ]). Since the D(φ) form an open cover of X the projective schemes can be thought of as being obtained by the gluing via projectivization of isomorphic affine schemes.
It can be noted that the ring of global sections of this scheme is a field, which implies that the scheme is not affine. Any two open sets intersect non-trivially: ie the scheme is irreducible. When the field k is algebraically closed, is in fact an abstract variety, that furthermore is complete. cf. Glossary of scheme theory
Divisors and twisting sheaves
The Proj functor in fact gives more than a mere scheme: a sheaf in graded modules over the structure sheaf is defined in the process. The homogeneous components of this graded sheaf are denoted , the Serre twisting sheaves. All of these sheaves are in fact line bundles. By the correspondence between Cartier divisors and line bundles, the first twisting sheaf is equivalent to hyperplane divisors.
Since the ring of polynomials is a unique factorization domain, any prime ideal of height 1 |
https://en.wikipedia.org/wiki/Lubin%E2%80%93Tate%20formal%20group%20law | In mathematics, the Lubin–Tate formal group law is a formal group law introduced by to isolate the local field part of the classical theory of complex multiplication of elliptic functions. In particular it can be used to construct the totally ramified abelian extensions of a local field. It does this by considering the (formal) endomorphisms of the formal group, emulating the way in which elliptic curves with extra endomorphisms are used to give abelian extensions of global fields.
Definition of formal groups
Let Zp be the ring of p-adic integers. The Lubin–Tate formal group law is the unique (1-dimensional) formal group law F such that e(x) = px + xp is an endomorphism of F, in other words
More generally, the choice for e may be any power series such that
e(x) = px + higher-degree terms and
e(x) = xp mod p.
All such group laws, for different choices of e satisfying these conditions, are strictly isomorphic. We choose these conditions so as to ensure that they reduce modulo the maximal ideal to Frobenius and the derivative at the origin is the prime element.
For each element a in Zp there is a unique endomorphism f of the Lubin–Tate formal group law such that f(x) = ax + higher-degree terms. This gives an action of the ring Zp on the Lubin–Tate formal group law.
There is a similar construction with Zp replaced by any complete discrete valuation ring with finite residue class field, where p is replaced by a choice of uniformizer.
Example
We outline here a formal group equivalent of the Frobenius element, which is of great importance in class field theory, generating the maximal unramified extension as the image of the reciprocity map.
For this example we need the notion of an endomorphism of formal groups, which is a formal group homomorphism f where the domain is the codomain. A formal group homomorphism from a formal group F to a formal group G is a power series over the same ring as the formal groups which has zero constant term and is such that:
Consider a formal group F(X,Y) with coefficients in the ring of integers in a local field (for example Zp). Taking X and Y to be in the unique maximal ideal gives us a convergent power series and in this case we define F(X,Y) = X +F Y and we have a genuine group law. For example if F(X,Y)=X+Y, then this is the usual addition. This is isomorphic to the case of F(X,Y)=X+Y+XY, where we have multiplication on the set of elements which can be written as 1 added to an element of the prime ideal. In the latter case f(S) = (1 + S)p-1 is an endomorphism of F and the isomorphism identifies f with the Frobenius element.
Generating ramified extensions
Lubin–Tate theory is important in explicit local class field theory. The unramified part of any abelian extension is easily constructed, Lubin–Tate finds its value in producing the ramified part. This works by defining a family of modules (indexed by the natural numbers) over the ring of integers consisting of what can be considered as roots of the pow |
https://en.wikipedia.org/wiki/Abortion%20statistics%20in%20the%20United%20States | Both the Guttmacher Institute and the Centers for Disease Control and Prevention (CDC) regularly report abortion statistics in the United States. They use different methodologies, so they report somewhat different abortion rates, but they show similar trends. The Guttmacher Institute attempts to contact every abortion provider. The CDC relies on voluntary reporting of abortion data from the states and the District of Columbia. As of July 2022, the Guttmacher Institute had reported abortion data for the years 1973 through 2020 and the CDC had reported abortion data for the years 1970 through 2019.
Abortion statistics are commonly presented as the number of abortions, the abortion rate (the number of abortions per 1,000 women ages 15 to 44), and the abortion ratio. The Guttmacher Institute defines the abortion ratio as the number of abortions per 100 pregnancies ending in an abortion or a live birth, excluding miscarriages, and the CDC defines it as the number of abortions per 1,000 live births.
The figures reported by both organizations include only the legal induced abortions conducted by clinics, hospitals or physicians’ offices, or that make use of abortion pills dispensed from certified facilities such as clinics or physicians’ offices. They do not account for the use of abortion pills that were obtained outside of clinical settings.
Trends in abortion statistics
In 1973, the Roe v. Wade Supreme Court decision legalized abortion in all 50 states. From 1973 to 1980, the abortion rate rose almost 80%, peaking at 29.3 abortions per 1,000 women of childbearing age in 1980 and 1981.
From 1981 through 2017, the abortion rate fell by more than half, always falling faster in Democratic administrations than Republican ones. The abortion rate fell below the 1973 rate in 2012 and continued to fall through 2017, when it stood at 13.5 abortions per 1,000 women of childbearing age. The abortion rate then rose from 2018 through 2020.
During the 1980s, the population of women of childbearing age grew faster than the abortion rate fell, so the annual number of abortions performed did not peak until 1990, at about 1.6 million abortions. The number of abortions generally fell from 1991 through 2017, and rose thereafter. The largest percentage decrease in the number of abortions occurred in 2013, the year the contraceptive mandate of the Affordable Care Act took effect for most health insurance plans. Approximately 860,000 abortions were performed in 2017, rising to about 930,000 in 2020.
From 1973 to 1983, the abortion ratio reported by the Guttmacher Institute rose about 60%, peaking at 30.4 in 1983. From 1984 through 2016, the abortion ratio fell about 40%. It hit a low of 18.3 in 2016 and rose to 20.6 in 2020. The abortion ratio was slightly lower in 2016 and 2017 than in 1973 because a 40% decrease more than offsets a 60% increase.
This summary is largely based on data collected by the Guttmacher Institute. Data collected by the CDC shows similar |
https://en.wikipedia.org/wiki/Nambooripad%20order | In mathematics, Nambooripad order (also called Nambooripad's partial order) is a certain natural partial order on a regular semigroup discovered by K S S Nambooripad in late seventies. Since the same partial order was also independently discovered by Robert E Hartwig, some authors refer to it as Hartwig–Nambooripad order. "Natural" here means that the order is defined in terms of the operation on the semigroup.
In general Nambooripad's order in a regular semigroup is not compatible with multiplication. It is compatible with multiplication only if the semigroup is pseudo-inverse (locally inverse).
Precursors
Nambooripad's partial order is a generalisation of an earlier known partial order on the set of idempotents in any semigroup. The partial order on the set E of idempotents in a semigroup S is defined as follows: For any e and f in E, e ≤ f if and
only if e = ef = fe.
Vagner in 1952 had extended this to inverse semigroups as follows: For any a and b in an inverse semigroup S, a ≤ b if and only if a = eb for some idempotent e in S. In the symmetric inverse semigroup, this order actually coincides with the inclusion of partial transformations considered as sets. This partial order is compatible with multiplication on both sides, that is, if a ≤ b then ac ≤ bc and ca ≤ cb for all c in S.
Nambooripad extended these definitions to regular semigroups.
Definitions (regular semigroup)
The partial order in a regular semigroup discovered by Nambooripad can be defined in several equivalent ways. Three of these definitions are given below. The equivalence of these definitions and other definitions have been established by Mitsch.
Definition (Nambooripad)
Let S be any regular semigroup and S1 be the semigroup obtained by adjoining the identity 1 to S. For any x in S let Rx be the Green R-class of S containing x.
The relation Rx ≤ Ry defined by xS1 ⊆ yS1 is a partial order in the collection of Green R-classes in S. For a and b in S the relation ≤ defined by
a ≤ b if and only if Ra ≤ Rb and a = fb for some idempotent f in Ra
is a partial order in S. This is a natural partial order in S.
Definition (Hartwig)
For any element a in a regular semigroup S, let V(a) be the set of inverses of a, that is, the set of all x in S such that axa = a and xax = x.
For a and b in S the relation ≤ defined by
a ≤ b if and only if a'a = a'b and aa' = ba' for some a' in V(a)
is a partial order in S. This is a natural partial order in S.
Definition (Mitsch)
For a and b in a regular semigroup S the relation ≤ defined by
a ≤ b if and only if a = xa = xb = by for some element x and y in S
is a partial order in S. This is a natural partial order in S.
Extension to arbitrary semigroups (P.R. Jones)
For a and b in an arbitrary semigroup S, a ≤J b iff there exist e, f idempotents in S1 such that a = be = fb.
This is a reflexive relation on any semigroup, and if S is regular it coincides with the Nambooripad order.
Natural partial order of Mitsch
M |
https://en.wikipedia.org/wiki/DE-9IM | The Dimensionally Extended 9-Intersection Model (DE-9IM) is a topological model and a standard used to describe the spatial relations of two regions (two geometries in two-dimensions, R2), in geometry, point-set topology, geospatial topology, and fields related to computer spatial analysis. The spatial relations expressed by the model are invariant to rotation, translation and scaling transformations.
The matrix provides an approach for classifying geometry relations. Roughly speaking, with a true/false matrix domain, there are 512 possible 2D topologic relations, that can be grouped into binary classification schemes. The English language contains about 10 schemes (relations), such as "intersects", "touches" and "equals". When testing two geometries against a scheme, the result is a spatial predicate named by the scheme.
The model was developed by Clementini and others based on the seminal works of Egenhofer and others. It has been used as a basis for standards of queries and assertions in geographic information systems (GIS) and spatial databases.
Matrix model
The DE-9IM model is based on a 3×3 intersection matrix with the form:
where is the dimension of the intersection (∩) of the interior (I), boundary (B), and exterior (E) of geometries a and b.
The terms interior and boundary in this article are used in the sense used in algebraic topology and manifold theory, not in the sense used in general topology: for example, the interior of a line segment is the line segment without its endpoints, and its boundary is just the two endpoints (in general topology, the interior of a line segment in the plane is empty and the line segment is its own boundary).
In the notation of topological space operators, the matrix elements can be expressed also as
The dimension of empty sets (∅) are denoted as −1 or (false). The dimension of non-empty sets (¬∅) are denoted with the maximum number of dimensions of the intersection, specifically for points, for lines, for areas. Then, the domain of the model is .
A simplified version of values are obtained mapping the values to (true), so using the boolean domain . The matrix, denoted with operators, can be expressed as
The elements of the matrix can be named as shown below:
Both matrix forms, with dimensional and boolean domains, can be serialized as "DE-9IM string codes", which represent them in a single-line string pattern. Since 1999 the string codes have a standard format.
For output checking or pattern analysis, a matrix value (or a string code) can be checked by a "mask": a desired output value with optional asterisk symbols as wildcards — that is, "" indicating output positions that the designer does not care about (free values or "don't-care positions").
The domain of the mask elements is , or for the boolean form.
The simpler models 4-Intersection and 9-Intersection were proposed before DE-9IM for expressing spatial relations (and originated the terms 4IM and 9IM). They can be used ins |
https://en.wikipedia.org/wiki/Ta%27Shia%20Phillips | Ta'Shia Phillips (born January 24, 1989) is a professional basketball player who most recently played for the New York Liberty of the Women's National Basketball Association.
Xavier statistics
Source
USA Basketball
Phillips was named a member of the team representing the US at the 2009 World University Games held in Belgrade, Serbia. The team won all seven games to earn the gold medal. Phillips averaged 4.9 points per game.
WNBA
Phillips was selected the first round of the 2011 WNBA draft (8th overall) by the Atlanta Dream.
References
1989 births
Living people
All-American college women's basketball players
American women's basketball players
Atlanta Dream draft picks
Basketball players from Indianapolis
Centers (basketball)
New York Liberty players
Parade High School All-Americans (girls' basketball)
FISU World University Games gold medalists for the United States
Universiade medalists in basketball
Xavier Musketeers women's basketball players
Washington Mystics players
Medalists at the 2009 Summer Universiade |
https://en.wikipedia.org/wiki/Runcic%205-cubes | In six-dimensional geometry, a runcic 5-cube or (runcic 5-demicube, runcihalf 5-cube) is a convex uniform 5-polytope. There are 2 runcic forms for the 5-cube. Runcic 5-cubes have half the vertices of runcinated 5-cubes.
Runcic 5-cube
Alternate names
Cantellated 5-demicube/demipenteract
Small rhombated hemipenteract (sirhin) (Jonathan Bowers)
Cartesian coordinates
The Cartesian coordinates for the 960 vertices of a runcic 5-cubes centered at the origin are coordinate permutations:
(±1,±1,±1,±3,±3)
with an odd number of plus signs.
Images
Related polytopes
It has half the vertices of the runcinated 5-cube, as compared here in the B5 Coxeter plane projections:
Runcicantic 5-cube
Alternate names
Cantitruncated 5-demicube/demipenteract
Great rhombated hemipenteract (girhin) (Jonathan Bowers)
Cartesian coordinates
The Cartesian coordinates for the 480 vertices of a runcicantic 5-cube centered at the origin are coordinate permutations:
(±1,±1,±3,±5,±5)
with an odd number of plus signs.
Images
Related polytopes
It has half the vertices of the runcicantellated 5-cube, as compared here in the B5 Coxeter plane projections:
Related polytopes
This polytope is based on the 5-demicube, a part of a dimensional family of uniform polytopes called demihypercubes for being alternation of the hypercube family.
There are 23 uniform 5-polytopes that can be constructed from the D5 symmetry of the 5-demicube, of which are unique to this family, and 15 are shared within the 5-cube family.
Notes
References
H.S.M. Coxeter:
H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
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]
(Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
Norman Johnson Uniform Polytopes, Manuscript (1991)
N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D.
x3o3o *b3x3o - sirhin, x3x3o *b3x3o - girhin
External links
Polytopes of Various Dimensions
Multi-dimensional Glossary
5-polytopes |
https://en.wikipedia.org/wiki/Gavi%C3%A3o%20%28footballer%29 | Carlos Alberto Rodrigues Gavião (born February 2, 1980), known as just Gavião, is a Brazilian football player.
Club statistics
References
External links
1980 births
Living people
Brazilian men's footballers
J1 League players
Santos FC players
Criciúma Esporte Clube players
Júbilo Iwata players
Vila Nova Futebol Clube players
Duque de Caxias Futebol Clube players
Brazilian expatriate men's footballers
Expatriate men's footballers in Japan
Men's association football midfielders
People from Itaqui
Footballers from Rio Grande do Sul |
https://en.wikipedia.org/wiki/L%C3%AA%20%28footballer%2C%20born%201979%29 | Leandro Cesar de Sousa (born 6 July 1979) is a Brazilian football player.
Club statistics
References
External links
1979 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
Expatriate men's footballers in Japan
J2 League players
Santa Cruz Futebol Clube players
Ventforet Kofu players
Araguaína Futebol e Regatas players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Variable%20splitting | In applied mathematics and computer science, variable splitting is a decomposition method that relaxes a set of constraints.
Details
When the variable x appears in two sets of constraints, it is possible to substitute the new variables x1 in the first constraints and x2 in the second, and then join the two variables with a new "linking" constraint, which requires that
x1=x2.
This new linking constraint can be relaxed with a Lagrange multiplier; in many applications, a Lagrange multiplier can be interpreted as the price of equality between x1 and x2 in the new constraint.
For many problems, when the equality of the split variables is relaxed, then the system is decomposed, and each subsystem can be solved independently, at substantial reduction of computing time and memory storage. A solution to the relaxed problem (with variable splitting) provides an approximate solution to the original problem: further, the approximate solution to the relaxed problem provides a "warm start", a good initialization of an iterative method for solving the original problem (having only the x variable).
This was first introduced by Kurt O. Jörnsten, Mikael Näsberg, Per A. Smeds in 1985. At the same time, M. Guignard and S. Kim introduced the same idea under the name Lagrangean Decomposition (their papers appeared in 1987). The original references are
(1) Variable Splitting: A New Lagrangean Relaxation Approach to Some Mathematical Programming Models
Authors Kurt O. Jörnsten, Mikael Näsberg, Per A. Smeds Volumes 84-85 of LiTH MAT R.: Matematiska Institutionen Publisher - University of Linköping, Department of Mathematics, 1985 Length - 52 pages; and (2) Lagrangean Decomposition: A Model Yielding Stronger Bounds, Authors Monique Guignard and Siwhan Kim, Mathematical Programming, 39(2), 1987, pp. 215-228.
References
Bibliography
Decomposition methods |
https://en.wikipedia.org/wiki/Kazutaka%20Murase | is a former Japanese football player.
Club statistics
References
External links
1985 births
Living people
Association football people from Shiga Prefecture
Japanese men's footballers
J1 League players
J2 League players
Japan Football League players
Vissel Kobe players
Reilac Shiga FC players
Fukushima United FC players
Men's association football forwards |
https://en.wikipedia.org/wiki/Noriaki%20Ishizawa | is a former Japanese football player.
Club statistics
References
External links
1985 births
Living people
Association football people from Hyōgo Prefecture
Japanese men's footballers
J1 League players
J2 League players
Japan Football League players
Vissel Kobe players
Reilac Shiga FC players
Men's association football defenders
Sportspeople from Nishinomiya |
https://en.wikipedia.org/wiki/Hikaru%20Hironiwa | is a former Japanese football player.
Club statistics
References
External links
1985 births
Living people
Association football people from Tokyo
Japanese men's footballers
J1 League players
J2 League players
Japan Football League players
Kashiwa Reysol players
Ehime FC players
Zweigen Kanazawa players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Bruno%20Bertacchini | Bruno Bertacchini (1916-2003) was a Grand Prix motorcycle racer from Italy.
Career statistics
By season
References
External links
Profile on motogp.com
https://www.guzzipedia.it/persone/bruno-bertacchini/
Italian motorcycle racers
500cc World Championship riders
1916 births
2003 deaths |
https://en.wikipedia.org/wiki/Kazuya%20Iwakura | is a former Japanese football player.
Club statistics
References
External links
1985 births
Living people
Association football people from Toyama Prefecture
Japanese men's footballers
J1 League players
J2 League players
Japan Football League players
Yokohama FC players
Giravanz Kitakyushu players
Tokyo Verdy players
Men's association football defenders |
https://en.wikipedia.org/wiki/Ken%20Armstrong%20%28motorcyclist%29 | Ken Armstrong is a Grand Prix motorcycle racer from Great Britain.
Career statistics
By season
References
External links
Profile on motogp.com
British motorcycle racers
500cc World Championship riders |
https://en.wikipedia.org/wiki/Keith%20Stroyan | Keith D. Stroyan is Professor of Mathematics at the University of Iowa. His main research interests are in analysis and visual depth perception.
Publications
Stroyan, K. D.; Luxemburg, W. A. J. Introduction to the theory of infinitesimals. Pure and Applied Mathematics, No. 72. Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1976.
Reviewer Frank Wattenberg for Math Reviews wrote that "mathematicians whose principal interest is in functional analysis, complex analysis, or topology will find here some very valuable contributions to our understanding of these subjects" here.
The book was cited over 365 times at Google Scholar in 2011.
Stroyan, K. D.; Bayod, José Manuel: Foundations of infinitesimal stochastic analysis. Studies in Logic and the Foundations of Mathematics, 119. North-Holland Publishing Co., Amsterdam, 1986.
Reviewer Tom L. Lindström for Math Reviews wrote that "the authors have written a very comprehensive and readable monograph which will be a great help to experts and beginners alike" here.
Stroyan, K. D. Uniform continuity and rates of growth of meromorphic functions. Contributions to non-standard analysis (Sympos., Oberwolfach, 1970), pp. 47–64. Studies in Logic and Foundations of Math., Vol. 69, North-Holland, Amsterdam, 1972.
See also
Influence of non-standard analysis
References
Web page at the University of Iowa
Living people
20th-century American mathematicians
21st-century American mathematicians
Mathematical logicians
Year of birth missing (living people) |
https://en.wikipedia.org/wiki/Fotis%20Papadopoulos%20%28footballer%2C%20born%201954%29 | Fotis Papadopoulos (; born 1 July 1954) is a retired Greek footballer.
Career
Statistics
References
External links
1954 births
Living people
Footballers from Kilkis
Greek men's footballers
Greek expatriate men's footballers
Bundesliga players
VfL Bochum II players
VfL Bochum players
Kalamata F.C. players
Place of birth missing (living people)
Men's association football defenders
Men's association football midfielders |
https://en.wikipedia.org/wiki/Nilpotence%20theorem | In algebraic topology, the nilpotence theorem gives a condition for an element in the homotopy groups of a ring spectrum to be nilpotent, in terms of the complex cobordism spectrum . More precisely, it states that for any ring spectrum , the kernel of the map consists of nilpotent elements. It was conjectured by and proved by .
Nishida's theorem
showed that elements of positive degree of the homotopy groups of spheres are nilpotent. This is a special case of the nilpotence theorem.
See also
Ravenel's conjectures
References
.
Open online version.
Further reading
Connection of X(n) spectra to formal group laws
Homotopy theory
Theorems in algebraic topology |
https://en.wikipedia.org/wiki/Transverse%20knot | In mathematics, a transverse knot is a smooth embedding of a circle into a three-dimensional contact manifold such that the tangent vector at every point of the knot is transverse to the contact plane at that point.
Any Legendrian knot can be C0-perturbed in a direction transverse to the contact planes to obtain a transverse knot. This yields a bijection between the set of isomorphism classes of transverse knots and the set of isomorphism classes of Legendrian knots modulo negative Legendrian stabilization.
References
J. Epstein, D. Fuchs, and M. Meyer, Chekanov–Eliashberg invariants and transverse approximations of Legendrian knots, Pacific J. Math. 201 (2001), no. 1, 89–106.
Knots and links |
https://en.wikipedia.org/wiki/Li%20Na%20career%20statistics | This is a list of the main career statistics of Chinese professional tennis player, Li Na. Over the course of her career, Li won nine WTA singles titles, including two Grand Slam singles titles at the 2011 French Open and 2014 Australian Open and one Premier 5 singles title at the 2012 Western & Southern Open. She also finished in fourth place at the 2008 Beijing Olympics and was the runner-up at the 2011 and 2013 Australian Open and 2013 WTA Tour Championships. Li achieved a career-high singles ranking of world No. 2 on February 17, 2014.
Career achievements
On October 3, 2004, Li defeated Martina Suchá in the final of the Guangzhou International Women's Open to become the first Chinese woman to win a singles title on the WTA Tour. At the 2006 Wimbledon Championships, Li became the first Chinese player to be seeded in a Grand Slam event. She went on to reach the quarterfinals, becoming the first Chinese player in history (male or female) to achieve this feat but lost to second seed Kim Clijsters.
In January 2010, Li and her compatriot Zheng Jie reached the semifinals of the 2010 Australian Open in singles. This marked the first time in history where two Chinese players had reached the semifinals of a Grand Slam tournament simultaneously. Following this event, Li became the first Chinese player in history to achieve a top ten ranking in singles. Later that year, Li reached the quarterfinals of Wimbledon, losing to the eventual champion Serena Williams (this being the fourth Grand Slam tournament in a row in which Li had lost to the eventual champion).
At the 2011 Australian Open, Li defeated world No. 1 Caroline Wozniacki in the semifinals in three sets, saving a match point in the second set to become the first Chinese player in history to reach a Grand Slam final in singles. However, she lost to Kim Clijsters in three sets. At the 2011 French Open, Li defeated Petra Kvitová in the fourth round to become the first Chinese player in history to reach the quarterfinals or better at all four Grand Slam events in singles. She then defeated Victoria Azarenka and Maria Sharapova in the quarterfinals and semifinals respectively en route to her second consecutive Grand Slam final, where she defeated the defending champion, Francesca Schiavone, in straight sets to win her first Grand Slam singles title and thus became the first player from Asia to achieve such a feat. She achieved a new career high singles ranking of world No. 4 following the event. Following her strong performances throughout the year, Li qualified for the year-ending WTA Tour Championships, becoming the first Chinese player in history to do so. She finished the year ranked world No. 5, becoming the first Chinese player to finish a year ranked in the top ten.
In January 2013, Li won the first edition of the Shenzhen Open with a three set victory over Klára Zakopalová in the final. At the 2013 Australian Open, Li reached her third Grand Slam singles final without dropping a set but l |
https://en.wikipedia.org/wiki/2004%20Kashima%20Antlers%20season | 2004 Kashima Antlers season
Competitions
Domestic results
J. League 1
League table
Matches
Emperor's Cup
J. League Cup
Player statistics
Other pages
J. League official site
Kashima Antlers
Kashima Antlers seasons |
https://en.wikipedia.org/wiki/2004%20Urawa%20Red%20Diamonds%20season | 2004 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/2004%20JEF%20United%20Ichihara%20season | 2004 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/2004%20Kashiwa%20Reysol%20season | 2004 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/2004%20FC%20Tokyo%20season | 2004 FC Tokyo season
Competitions
Domestic results
J.League 1
Emperor's Cup
J.League Cup
Player statistics
Other pages
J. League official site
Tokyo
2004 |
https://en.wikipedia.org/wiki/2004%20Tokyo%20Verdy%201969%20season | 2004 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/2004%20Yokohama%20F.%20Marinos%20season | 2004 Yokohama F. Marinos season
Competitions
Domestic results
J.League 1
Emperor's Cup
J.League Cup
Player statistics
Kits
Other pages
J.League official site
Yokohama F. Marinos
Yokohama F. Marinos seasons |
https://en.wikipedia.org/wiki/2004%20Albirex%20Niigata%20season | 2004 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/2004%20J%C3%BAbilo%20Iwata%20season | 2004 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/2004%20Nagoya%20Grampus%20Eight%20season | 2004 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/2004%20Gamba%20Osaka%20season | 2004 Gamba Osaka season
Competitions
Domestic results
J. League 1
League table
Matches
Emperor's Cup
J. League Cup
Player statistics
Other pages
J. League official site
Gamba Osaka
Gamba Osaka seasons |
https://en.wikipedia.org/wiki/2004%20Cerezo%20Osaka%20season | 2004 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/2004%20Vissel%20Kobe%20season | 2004 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/2004%20Sanfrecce%20Hiroshima%20season | 2004 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/2004%20Oita%20Trinita%20season | 2004 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/2004%20Vegalta%20Sendai%20season | 2004 Vegalta Sendai season.
Competitions
Domestic results
J. League 2
Emperor's Cup
Player statistics
Other pages
J. League official site
Vegalta Sendai
Vegalta Sendai seasons |
https://en.wikipedia.org/wiki/2004%20Montedio%20Yamagata%20season | 2004 Montedio Yamagata season
Competitions
Domestic results
J. League 2
Emperor's Cup
Player statistics
Other pages
J. League official site
Montedio Yamagata
Montedio Yamagata seasons |
https://en.wikipedia.org/wiki/2004%20Mito%20HollyHock%20season | 2004 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/2004%20Omiya%20Ardija%20season | 2004 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/2004%20Kawasaki%20Frontale%20season | 2004 Kawasaki Frontale season
Competitions
Domestic results
J. League 2
Emperor's Cup
Player statistics
Other pages
J. League official site
Kawasaki Frontale
Kawasaki Frontale seasons |
https://en.wikipedia.org/wiki/2004%20Yokohama%20FC%20season | 2004 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/2004%20Shonan%20Bellmare%20season | 2004 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/2004%20Ventforet%20Kofu%20season | 2004 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/2004%20Kyoto%20Purple%20Sanga%20season | 2004 Kyoto Purple Sanga season
Competitions
Domestic results
J. League 2
Emperor's Cup
Player statistics
Other pages
J. League official site
Kyoto Purple Sanga
Kyoto Sanga FC seasons |
https://en.wikipedia.org/wiki/2004%20Avispa%20Fukuoka%20season | 2004 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/2004%20Sagan%20Tosu%20season | 2004 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/Takeo%20Wada | was a Japanese mathematician at Kyoto University working in analysis and topology. He suggested the Lakes of Wada to Kunizo Yoneyama, who wrote about them and named them after Wada.
Publications
References
1882 births
1944 deaths
20th-century Japanese mathematicians |
https://en.wikipedia.org/wiki/Siegfried%20B%C3%B6nighausen | Siegfried Bönighausen (born 20 March 1955) is a retired German football midfielder.
Career
Statistics
References
External links
1955 births
Living people
People from Gladbeck
Footballers from Münster (region)
German men's footballers
Bundesliga players
2. Bundesliga players
Rot-Weiss Essen players
Borussia Dortmund players
VfL Bochum players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Hall%27s%20identity | In mathematics, Hall's identity may be:
The Hall–Witt identity
The Hall identity [ [x,y]2,z] = 0 for 2 by 2 matrices, showing that this is a polynomial identity ring
The Hall–Petresco identity for groups expressing xmym in terms of powers of elements of the descending central series.
Group theory |
https://en.wikipedia.org/wiki/Norm%20%28abelian%20group%29 | In mathematics, specifically abstract algebra, if is an (abelian) group with identity element then is said to be a norm on if:
Positive definiteness: ,
Subadditivity: ,
Inversion (Symmetry): .
An alternative, stronger definition of a norm on requires
,
,
.
The norm is discrete if there is some real number such that whenever .
Free abelian groups
An abelian group is a free abelian group if and only if it has a discrete norm.
References
Abelian group theory |
https://en.wikipedia.org/wiki/Cellular%20algebra | In abstract algebra, a cellular algebra is a finite-dimensional associative algebra A with a distinguished cellular basis which is particularly well-adapted to studying the representation theory of A.
History
The cellular algebras discussed in this article were introduced in a 1996 paper of Graham and Lehrer. However, the terminology had previously been used by Weisfeiler and Lehman in the Soviet Union in the 1960s, to describe what are also known as coherent algebras.
Definitions
Let be a fixed commutative ring with unit. In most applications this is a field, but this is not needed for the definitions. Let also be an -algebra.
The concrete definition
A cell datum for is a tuple consisting of
A finite partially ordered set .
A -linear anti-automorphism with .
For every a non-empty finite set of indices.
An injective map
The images under this map are notated with an upper index and two lower indices so that the typical element of the image is written as .
and satisfying the following conditions:
The image of is a -basis of .
for all elements of the basis.
For every , and every the equation
with coefficients depending only on , and but not on . Here denotes the -span of all basis elements with upper index strictly smaller than .
This definition was originally given by Graham and Lehrer who invented cellular algebras.
The more abstract definition
Let be an anti-automorphism of -algebras with (just called "involution" from now on).
A cell ideal of w.r.t. is a two-sided ideal such that the following conditions hold:
.
There is a left ideal that is free as a -module and an isomorphism
of --bimodules such that and are compatible in the sense that
A cell chain for w.r.t. is defined as a direct decomposition
into free -submodules such that
is a two-sided ideal of
is a cell ideal of w.r.t. to the induced involution.
Now is called a cellular algebra if it has a cell chain. One can show that the two definitions are equivalent. Every basis gives rise to cell chains (one for each topological ordering of ) and choosing a basis of every left ideal one can construct a corresponding cell basis for .
Examples
Polynomial examples
is cellular. A cell datum is given by and
with the reverse of the natural ordering.
A cell-chain in the sense of the second, abstract definition is given by
Matrix examples
is cellular. A cell datum is given by and
For the basis one chooses the standard matrix units, i.e. is the matrix with all entries equal to zero except the (s,t)-th entry which is equal to 1.
A cell-chain (and in fact the only cell chain) is given by
In some sense all cellular algebras "interpolate" between these two extremes by arranging matrix-algebra-like pieces according to the poset .
Further examples
Modulo minor technicalities all Iwahori–Hecke algebras of finite type are cellular w.r.t. to the involution that maps the standard basis as . This includes for example th |
https://en.wikipedia.org/wiki/Marcus%20Ekenberg | Ulf Marcus Daniel Ekenberg (born 16 June 1980) is a Swedish footballer who plays as a forward for Sölvesborgs GoIF.
Career statistics
References
External links
(archive)
1980 births
Mjällby AIF players
Helsingborgs IF players
Allsvenskan players
Superettan players
Ettan Fotboll players
Division 2 (Swedish football) players
Swedish men's footballers
Living people
Men's association football forwards |
https://en.wikipedia.org/wiki/Living%20Costs%20and%20Food%20Survey | The Living Costs and Food Survey (LCF) is a survey carried out in the United Kingdom by the Office for National Statistics (ONS). It is carried out on a calendar year basis and collects information on expenditure of goods and services for private households. The survey is primarily designed to collect expenditure information, however it also gathers information about the income of household members.
The results of the survey are multi purpose, however it is primarily used to provide information for the Retail Prices Index and the National Accounts estimates of household expenditure, as well as analysis of the effect of taxes and benefits.
The Living Costs and Food Survey also collects specialist food data, which is used and sponsored by the Department for Environment, Food and Rural Affairs (DEFRA). While the ONS Social Surveys Division report the income and expenditure data, the DEFRA publish the detailed food and nutritional data.
History
In 2008 The Expenditure and Food Survey (EFS) became a module of the Integrated Household Survey (IHS) and was renamed as the Living Costs and Food Survey (LCF).
The EFS was the result of the amalgamation of the Family Expenditure Survey (FES) and the National Food Survey (NFS) in 2001.
Methodology
The LCF is a continuous survey, with interviews being spread evenly over the year to ensure that seasonal effects are covered.
The LCF has a sample size of approximately 6,000 responding households per year. The households are visited by an interviewer, and information is collected about income and regular expenditure, such as household bills and mortgage payments. Retrospective information on certain large, infrequent expenditures such as those on vehicles is also collected. Answers for children aged 15 years and younger are given by proxy by another household member.
Every individual aged 16 and over in the household visited is also asked to keep a diary that records daily expenditure for two weeks. The diary is where the specialist food data used by the DEFRA is collected. Since 1998–99 the results have also included information from simplified diaries kept by children aged between 7 and 15.
Survey results and data
ONS produce an annual 'Family Spending' publication, which gives a broad overview of the results of the survey. It also provides detailed information about some aspects of expenditure.
The Family Spending 2009 Edition, released in November 2010, found that the average household spend fell from £471 per week in 2008 to £455 in 2009. This was the first fall in average household spend since 2001-02, when the current system of measuring was introduced to allow better international comparisons.
Anonymised microdata from the Living Costs and Food Survey (LCF), the Expenditure and Food Survey (EFS) and the Family Expenditure Survey (FES) are available from the Economic and Social Data Service (ESDS), a service of the UK Data Archive. Details on how to access these datasets can be found at t |
https://en.wikipedia.org/wiki/Ole%20M%C3%B8ller%20Nielsen | Ole Møller Nielsen (born 26 November 1965) is a retired Danish footballer.
Statistics
References
External links
1965 births
Living people
Danish men's footballers
Denmark men's under-21 international footballers
Danish expatriate men's footballers
Bundesliga players
Vejle Boldklub players
VfL Bochum players
Randers FC players
Sportspeople from Horsens
Footballers from the Central Denmark Region
Men's association football midfielders
Men's association football forwards
Boldklubben 1913 players
Boldklubben 1909 players |
https://en.wikipedia.org/wiki/Johnson%E2%80%93Wilson%20theory | In algebraic topology, Johnson–Wilson theory E(n) is a generalized cohomology theory introduced by . Real Johnson–Wilson theory ER(n) was introduced by .
References
Homotopy theory |
https://en.wikipedia.org/wiki/FC%20Dinamo%20Bucure%C8%99ti%20in%20European%20football | Fotbal Club Dinamo București is a Romanian professional football club based in Bucharest.
Total statistics
As of August 3, 2017.
Statistics by country
As of 3 August 2017.
Statistics by competition
UEFA Champions League / European Cup
UEFA Cup Winners' Cup / European Cup Winners' Cup
UEFA Europa League / UEFA Cup
Including away match with Athletic Bilbao.
Inter-Cities Fairs Cup
UEFA Intertoto Cup
External links
Official website
Euro
Romanian football clubs in international competitions |
https://en.wikipedia.org/wiki/Branch%20and%20price | In applied mathematics, branch and price is a method of combinatorial optimization for solving integer linear programming (ILP) and mixed integer linear programming (MILP) problems with many variables. The method is a hybrid of branch and bound and column generation methods.
Description of the algorithm
Branch and price is a branch and bound method in which at each node of the search tree, columns may be added to the linear programming relaxation (LP relaxation). At the start of the algorithm, sets of columns are excluded from the LP relaxation in order to reduce the computational and memory requirements and then columns are added back to the LP relaxation as needed. The approach is based on the observation that for large problems most columns will be nonbasic and have their corresponding variable equal to zero in any optimal solution. Thus, the large majority of the columns are irrelevant for solving the problem.
The algorithm typically begins by using a reformulation, such as Dantzig–Wolfe decomposition, to form what is known as the Master Problem. The decomposition is performed to obtain a problem formulation that gives better bounds when the relaxation is solved than when the relaxation of the original formulation is solved. But, the decomposition usually contains many variables and so a modified version, called the Restricted Master Problem, that only considers a subset of the columns is solved. Then, to check for optimality, a subproblem called the pricing problem is solved to find columns that can enter the basis and reduce the objective function (for a minimization problem). This involves finding a column that has a negative reduced cost. Note that the pricing problem itself may be difficult to solve but since it is not necessary to find the column with the most negative reduced cost, heuristic and local search methods can be used. The subproblem must only be solved to completion in order to prove that an optimal solution to the Restricted Master Problem is also an optimal solution to the Master Problem. Each time a column is found with negative reduced cost, it is added to the Restricted Master Problem and the relaxation is reoptimized. If no columns can enter the basis and the solution to the relaxation is not integer, then branching occurs.
Most branch and price algorithms are problem specific since the problem must be formulated in such a way so that effective branching rules can be formulated and so that the pricing problem is relatively easy to solve.
If cutting planes are used to tighten LP relaxations within a branch and price algorithm, the method is known as branch price and cut.
Applications of branch and price
The branch and price method can be used to solve problems in a variety of application areas, including:
Graph multi-coloring. This is a generalization of the graph coloring problem in which each node in a graph must be assigned a preset number of colors and any nodes that share an edge cannot have a |
https://en.wikipedia.org/wiki/Fubini%27s%20theorem%20on%20differentiation | In mathematics, Fubini's theorem on differentiation, named after Guido Fubini, is a result in real analysis concerning the differentiation of series of monotonic functions. It can be proven by using Fatou's lemma and the properties of null sets.
Statement
Assume is an interval and that for every natural number k, is an increasing function. If,
exists for all then for almost any the derivatives exist and are related as:
In general, if we don't suppose fk is increasing for every k, in order to get the same conclusion, we need a stricter condition like uniform convergence of on I for every n.
References
Theorems in real analysis
Theorems in measure theory |
https://en.wikipedia.org/wiki/National%20Statistics%20Council | The National Statistics Council is a Canadian government agency which advises the Chief Statistician of Canada on Statistics Canada’s activities, primarily on program priorities.
The NSC drew media attention as a result of its objection to the removal of the long-form census deployed in the 2011 Census.
References
Statistics Canada |
https://en.wikipedia.org/wiki/Neto%20Potiguar | Antonio Carlos da Silva Neto (born October 29, 1985), known as Neto Potiguar, is a Brazilian football player who currently plays for Club Celaya.
Club statistics
References
External links
J. League
1985 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
J1 League players
Albirex Niigata players
Esporte Clube Bahia players
Atlético Clube Goianiense players
ABC Futebol Clube players
Paysandu Sport Club players
Vila Nova Futebol Clube players
Marília Atlético Clube players
Itumbiara Esporte Clube players
Sociedade Esportiva do Gama players
Sociedade Esportiva e Recreativa Caxias do Sul players
Lobos BUAP footballers
Expatriate men's footballers in Japan
Expatriate men's footballers in Mexico
Men's association football forwards
Footballers from Natal, Rio Grande do Norte |
https://en.wikipedia.org/wiki/Takuya%20Sugiyama | is a former Japanese football player.
Club statistics
References
External links
J. League
1983 births
Living people
Heisei International University alumni
Association football people from Fukushima Prefecture
Japanese men's footballers
J2 League players
J3 League players
Japan Football League players
Thespakusatsu Gunma players
FC Gifu players
Arte Takasaki players
V-Varen Nagasaki players
Fukushima United FC players
Men's association football defenders |
https://en.wikipedia.org/wiki/Alex%20Oliveira%20%28footballer%29 | Alexsandro Marques de Oliveira (born June 17, 1978) is a Brazilian former footballer.
Club statistics
References
jsgoal.jp
External links
1978 births
Living people
Brazilian men's footballers
Brazilian expatriate men's footballers
J2 League players
Ventforet Kofu players
Associação Atlética Ponte Preta players
Esporte Clube Santo André players
CR Vasco da Gama players
Associação Portuguesa de Desportos players
Villa Rio Esporte Clube players
Sport Club Barueri players
Jeju United FC players
K League 1 players
Expatriate men's footballers in Japan
Expatriate men's footballers in South Korea
Men's association football defenders
Footballers from Campinas |
https://en.wikipedia.org/wiki/Taiten%20Sato | is a former Japanese football player.
Club statistics
References
External links
J. League
1983 births
Living people
Shobi University alumni
Association football people from Tokyo
Japanese men's footballers
J2 League players
Japan Football League players
Thespakusatsu Gunma players
AC Nagano Parceiro players
Men's association football forwards |
https://en.wikipedia.org/wiki/Li%20Muhao | Li Muhao ( born June 2, 1992) is a Chinese basketball player who plays for Shenzhen Leopards in the Chinese Basketball Association.
Career statistics
CBA
References
1992 births
Living people
Basketball players at the 2016 Summer Olympics
Basketball players from Guizhou
Centers (basketball)
Chinese men's basketball players
Olympic basketball players for China
People from Guiyang
Shenzhen Leopards players |
https://en.wikipedia.org/wiki/Thorsten%20Bolzek | Thorsten Bolzek (born 7 July 1968) is a retired German football forward.
Career
Statistics
References
External links
1968 births
Living people
Footballers from Berlin
German men's footballers
Bundesliga players
2. Bundesliga players
VfL Bochum players
SC Fortuna Köln players
Füchse Berlin Reinickendorf players
Men's association football forwards |
https://en.wikipedia.org/wiki/Rufus%20Flint | Rufus Flint (born ) was a professor of English and mathematics at the National Autonomous University of Nicaragua, conducting early Central American biodiversity studies while enrolled at Cornell University. He took his degree in mechanical engineering from Cornell’s Sibley College of Engineering in 1887.
The Nicaraguan Study
In August 1887, Professor Robert Henry Thurston, director of the Sibley College of Engineering at Cornell University, presented Rufus Flint’s three-year study of Nicaragua hardwoods to the American Association for the Advancement of Science. The impetus behind the Cornell research conducted by Flint was to assess the viability of exploiting Central American timber stands when the Northwest American forest resources were exhausted. As Appleton’s Cyclopedia record, the study, “. . . proved that in that country there exist most valuable varieties of wood. The present impending wood famine may, the speaker said, be averted by the use of tropical timber.”
Family
Flint was the son of an American physician, Earl Flint. His mother was native to the Nicaraos nation. Dr. Flint arrived in Nicaragua from New England about 1850. He lived mainly in the cities of Granada and Rivas, Nicaragua, until his death in the late 1890s. In the 1870s, Earl Flint became an antiquities collector for the Smithsonian Institution. About 1878, he began working for the Peabody Museum of Archaeology and Ethnology at Harvard University about 1878, sending collections and letters to the museum until 1899. Rufus Flint donated land to build the sanctuary for the “Christo Negro”, or Black Christ, of La Conquista, Carazo, Nicaragua. La Conquista was named for the Spanish colonial response to an indigenous rebellion against imperial authority. His son, also named Rufus Flint, was the inaugural coach of the Nicaraguan soccer team, Railroad Star, in 1924. And in 1927, Rufus Flint, Jr. served as head of Nicaragua’s National Football League.
Member
While at Cornell, he was tapped into the Phi Kappa Psi fraternity in 1885.
References
Cornell University College of Engineering alumni
American mechanical engineers
1860s births
Year of death missing
Academic staff of the National Autonomous University of Nicaragua |
https://en.wikipedia.org/wiki/Triply%20periodic%20minimal%20surface | In differential geometry, a triply periodic minimal surface (TPMS) is a minimal surface in ℝ3 that is invariant under a rank-3 lattice of translations.
These surfaces have the symmetries of a crystallographic group. Numerous examples are known with cubic, tetragonal, rhombohedral, and orthorhombic symmetries. Monoclinic and triclinic examples are certain to exist, but have proven hard to parametrise.
TPMS are of relevance in natural science. TPMS have been observed as biological membranes, as block copolymers, equipotential surfaces in crystals etc. They have also been of interest in architecture, design and art.
Properties
Nearly all studied TPMS are free of self-intersections (i.e. embedded in ℝ3): from a mathematical standpoint they are the most interesting (since self-intersecting surfaces are trivially abundant).
All connected TPMS have genus ≥ 3, and in every lattice there exist orientable embedded TPMS of every genus ≥3.
Embedded TPMS are orientable and divide space into two disjoint sub-volumes (labyrinths). If they are congruent the surface is said to be a balance surface.
History
The first examples of TPMS were the surfaces described by Schwarz in 1865, followed by a surface described by his student E. R. Neovius in 1883.
In 1970 Alan Schoen came up with 12 new TPMS based on skeleton graphs spanning crystallographic cells.
While Schoen's surfaces became popular in natural science the construction did not lend itself to a mathematical existence proof and remained largely unknown in mathematics, until H. Karcher proved their existence in 1989.
Using conjugate surfaces many more surfaces were found. While Weierstrass representations are known for the simpler examples, they are not known for many surfaces. Instead methods from Discrete differential geometry are often used.
Families
The classification of TPMS is an open problem.
TPMS often come in families that can be continuously deformed into each other. Meeks found an explicit 5-parameter family for genus 3 TPMS that contained all then known examples of genus 3 surfaces except the gyroid. Members of this family can be continuously deformed into each other, remaining embedded in the process (although the lattice may change). The gyroid and lidinoid are each inside a separate 1-parameter family.
Another approach to classifying TPMS is to examine their space groups. For surfaces containing lines the possible boundary polygons can be enumerated, providing a classification.
Generalisations
Periodic minimal surfaces can be constructed in S3 and H3.
It is possible to generalise the division of space into labyrinths to find triply periodic (but possibly branched) minimal surfaces that divide space into more than two sub-volumes.
Quasiperiodic minimal surfaces have been constructed in ℝ2×S1. It has been suggested but not been proven that minimal surfaces with a quasicrystalline order in ℝ3 exist.
External galleries of images
TPMS at the Minimal Surface Archive
Periodi |
https://en.wikipedia.org/wiki/Orthoptic%20%28geometry%29 | In the geometry of curves, an orthoptic is the set of points for which two tangents of a given curve meet at a right angle.
Examples:
The orthoptic of a parabola is its directrix (proof: see below),
The orthoptic of an ellipse is the director circle (see below),
The orthoptic of a hyperbola is the director circle (in case of there are no orthogonal tangents, see below),
The orthoptic of an astroid is a quadrifolium with the polar equation (see below).
Generalizations:
An isoptic is the set of points for which two tangents of a given curve meet at a fixed angle (see below).
An isoptic of two plane curves is the set of points for which two tangents meet at a fixed angle.
Thales' theorem on a chord can be considered as the orthoptic of two circles which are degenerated to the two points and .
Orthoptic of a parabola
Any parabola can be transformed by a rigid motion (angles are not changed) into a parabola with equation . The slope at a point of the parabola is . Replacing gives the parametric representation of the parabola with the tangent slope as parameter: The tangent has the equation with the still unknown , which can be determined by inserting the coordinates of the parabola point. One gets
If a tangent contains the point , off the parabola, then the equation
holds, which has two solutions and corresponding to the two tangents passing . The free term of a reduced quadratic equation is always the product of its solutions. Hence, if the tangents meet at orthogonally, the following equations hold:
The last equation is equivalent to
which is the equation of the directrix.
Orthoptic of an ellipse and hyperbola
Ellipse
Let be the ellipse of consideration.
The tangents to the ellipse at the vertices and co-vertices intersect at the 4 points , which lie on the desired orthoptic curve (the circle ).
The tangent at a point of the ellipse has the equation (see tangent to an ellipse). If the point is not a vertex this equation can be solved for :
Using the abbreviations
and the equation one gets:
Hence
and the equation of a non vertical tangent is
Solving relations for and respecting leads to the slope depending parametric representation of the ellipse:
(For another proof: see .)
If a tangent contains the point , off the ellipse, then the equation
holds. Eliminating the square root leads to
which has two solutions corresponding to the two tangents passing through . The constant term of a monic quadratic equation is always the product of its solutions. Hence, if the tangents meet at orthogonally, the following equations hold:
The last equation is equivalent to
From (1) and (2) one gets:
Hyperbola
The ellipse case can be adopted nearly exactly to the hyperbola case. The only changes to be made are to replace with and to restrict to . Therefore:
Orthoptic of an astroid
An astroid can be described by the parametric representation
From the condition
one recognizes the distance in pa |
https://en.wikipedia.org/wiki/Jorge%20Sebasti%C3%A1n%20N%C3%BA%C3%B1ez | Jorge Sebastián Núñez (born December 10, 1986) is a former Argentine football player.
Club statistics
References
External links
1986 births
Living people
Argentine men's footballers
Argentine expatriate men's footballers
J1 League players
J2 League players
Nagoya Grampus players
Hokkaido Consadole Sapporo players
Expatriate men's footballers in Japan
Men's association football midfielders
Footballers from Rosario, Santa Fe |
https://en.wikipedia.org/wiki/Masateru%20Akita | is a former Japanese football player.
Club statistics
References
External links
Masateru Akita at footballjapan
1982 births
Living people
University of Tsukuba alumni
Association football people from Chiba Prefecture
Japanese men's footballers
J2 League players
Mito HollyHock players
Zweigen Kanazawa players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Yoji%20Sakai | is a former Japanese football player and current manager of Tochigi Uva FC.
Club statistics
References
External links
1977 births
Living people
Takushoku University alumni
Association football people from Saitama Prefecture
Japanese men's footballers
J2 League players
Japan Football League players
Thespakusatsu Gunma players
Men's association football forwards |
https://en.wikipedia.org/wiki/Masahiro%20Ikeda | is a former Japanese football player.
Club statistics
References
External links
J. League
1981 births
Living people
Ryutsu Keizai University alumni
Association football people from Mie Prefecture
Japanese men's footballers
J2 League players
Japan Football League players
Sagawa Shiga FC players
Shonan Bellmare players
Blaublitz Akita players
Nara Club players
Men's association football midfielders |
https://en.wikipedia.org/wiki/1527%20in%20science | The year 1527 in science and technology included a number of events, some of which are listed here.
Mathematics
Petrus Apianus publishes a handbook of commercial arithmetic, Ein newe und wolgegründete underweisung aller Kauffmanns Rechnung in dreyen Büchern, mit schönen Regeln und fragstücken begriffen, at Ingolstadt.
Military science
Albrecht Dürer publishes a treatise on fortifications, , in Nuremberg.
Births
c. May 1 – Jan Van Ostaeyen (Johannes Stadius), Flemish mathematician and astronomer (died 1579)
July 13 – John Dee, English alchemist, astrologer and mathematician (died 1609)
Deaths
January 21 – Juan de Grijalva, Spanish explorer (born c. 1489)
July 28 – Rodrigo de Bastidas, Spanish explorer (born c. 1460)
References
16th century in science
1520s in science |
https://en.wikipedia.org/wiki/Manabu%20Watanabe | is a former Japanese football player.
Club statistics
References
External links
1986 births
Living people
Association football people from Osaka Prefecture
Japanese men's footballers
J2 League players
Japan Football League players
Mito HollyHock players
Fukushima United FC players
YSCC Yokohama players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Kota%20Yanagisawa | is a former Japanese football player.
Club statistics
References
External links
1982 births
Living people
Tokai University alumni
Association football people from Gunma Prefecture
Japanese men's footballers
J2 League players
Japan Football League players
Thespakusatsu Gunma players
Kataller Toyama players
Men's association football defenders |
https://en.wikipedia.org/wiki/1545%20in%20science | The year 1545 in science and technology involved some significant events.
Botany
Orto botanico di Padova and di Firenze botanical gardens established.
Mathematics
Gerolamo Cardano publishes his algebra text Ars Magna, including the first published solutions to cubic and quartic equations.
Navigation
Pedro de Medina's Arte de navegar is published in Valladolid, the first treatise on the art of navigation to be published in Europe.
Physiology and medicine
Charles Estienne publishes De dissectione partium corporis humani, libri tres, including a description of the venous valves of the liver.
Ambroise Paré publishes his first book, a treatise on battlefield medicine, , in Paris.
Thomas Phaer publishes The Boke of Chyldren, the first book on paediatrics written in English.
Zoology
The giant squid (Architeuthis) is first seen.
Births
January 11 – Guidobaldo del Monte, Italian mathematician (died 1607)
March – Gaspare Tagliacozzi, Italian anatomist (died 1599)
John Gerard, English botanist (died 1612)
Deaths
Christoph Rudolff, Silesian mathematician (born 1499)
References
16th century in science
1540s in science |
https://en.wikipedia.org/wiki/Hopf%20algebroid | In mathematics, in the theory of Hopf algebras, a Hopf algebroid is a generalisation of weak Hopf algebras, certain skew Hopf algebras and commutative Hopf k-algebroids. If k is a field, a commutative k-algebroid is a cogroupoid object in the category of k-algebras; the category of such is hence dual to the category of groupoid k-schemes. This commutative version has been used in 1970-s in algebraic geometry and stable homotopy theory. The generalization of Hopf algebroids and its main part of the structure, associative bialgebroids, to the noncommutative base algebra was introduced by J.-H. Lu in 1996 as a result on work on groupoids in Poisson geometry (later shown equivalent in nontrivial way to a construction of Takeuchi from the 1970s and another by Xu around the year 2000). They may be loosely thought of as Hopf algebras over a noncommutative base ring, where weak Hopf algebras become Hopf algebras over a separable algebra. It is a theorem that a Hopf algebroid satisfying a finite projectivity condition over a separable algebra is a weak Hopf algebra, and conversely a weak Hopf algebra H is a Hopf algebroid over its separable subalgebra HL. The antipode axioms have been changed by G. Böhm and K. Szlachányi (J. Algebra) in 2004 for tensor categorical reasons and to accommodate examples associated to depth two Frobenius algebra extensions.
Definition
The main motivation behind of the definition of a Hopf algebroidpg301-302 is its a commutative algebraic representation of an algebraic stack which can be presented as affine schemes. More generally, Hopf algebroids encode the data of presheaves of groupoids on the category of affine schemes. That is, if we have a groupoid object of affine schemeswith an identity map giving an embedding of objects into the arrows, we can take as our definition of a Hopf algebroid as the dual objects in commutative rings which encodes this structure. Note that this process is essentially an application of the Yoneda lemma to the definition of the groupoid schemes in the category of affine schemes. Since we may want to fix a base ring, we will instead consider the category of commutative -algebras.
Scheme-theoretic definition
Algebraic objects in the definition
A Hopf algebroid over a commutative ring is a pair of -algebras in such that their functor of points encodes a groupoid in . If we fix as some object in , then is the set of objects in the groupoid and is the set of arrows. This translates to having mapswhere the text on the left hand side of the slash is the traditional word used for the map of algebras giving the Hopf algebroid structure and the text on the right hand side of the slash is what corresponding structure on the groupoid these maps correspond to, meaning their dual maps from the Yoneda embedding gives the structure of a groupoid. For example,corresponds to the source map .
Axioms these maps must satisfy
In addition to these maps, they satisfy a host of axioms dual to the axio |
https://en.wikipedia.org/wiki/Yohei%20Sakai | is a former Japanese football player.
Club statistics
References
External links
1986 births
Living people
Association football people from Kanagawa Prefecture
Japanese men's footballers
J1 League players
J2 League players
J3 League players
Yokohama F. Marinos players
Yokohama FC players
SC Sagamihara players
Mito HollyHock players
Thespakusatsu Gunma players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Yusuke%20Nakamura%20%28footballer%29 | is a former Japanese football player.
Club statistics
References
External links
web.archive.org
1986 births
Living people
Association football people from Shizuoka Prefecture
Japanese men's footballers
J1 League players
J2 League players
Japan Football League players
Vissel Kobe players
FC Ryukyu players
Men's association football midfielders |
https://en.wikipedia.org/wiki/1571%20in%20science | The year 1571 in science and technology included a number of events, some of which are listed here.
Mathematics
François Viète begins publication of Francisci Vietaei Universalium inspectionum ad Canonem mathematicum liber singularis containing many trigonometric tables and formulas on the sine and cosine, and novel in using a decimal notation; publication continued until 1579.
Medicine
Peder Sørensen publishes Idea medicinæ philosophicæ in Basel, asserting the superiority of the ideas of Paracelsus to those of Galen.
Technology
1571 or 1572 – Jacques Besson publishes his popular comprehensive treatise on machines, Theatrum Instrumentorum.
The first occurrence of the word theodolite is found in the surveying textbook A geometric practice named Pantometria by Leonard Digges, published posthumously by his son, Thomas.
Births
December 9 – Metius, Dutch mathematician (died 1635)
December 27 – Johannes Kepler, German astronomer (died 1630)
Willem Blaeu, Dutch cartographer (died 1638)
Frederick de Houtman, Dutch explorer (died 1627)
Deaths
Bartolomeo Maranta, Italian physician and botanist (born c. 1500)
References
16th century in science
1570s in science |
https://en.wikipedia.org/wiki/Kim%20Ki-su | Kim Ki-su (born August 5, 1982) is a North Korean former football player.
Club statistics
References
External links
1982 births
Living people
Association football people from Tokyo
North Korean men's footballers
J2 League players
Japan Football League players
Mito HollyHock players
Fukushima United FC players
Men's association football midfielders |
https://en.wikipedia.org/wiki/Keisuke%20Moriya | is a former Japanese football player.
Club statistics
References
External links
1986 births
Living people
Association football people from Kanagawa Prefecture
Japanese men's footballers
J2 League players
Japan Football League players
Shonan Bellmare players
SC Sagamihara players
Men's association football forwards |
https://en.wikipedia.org/wiki/National%20Records%20of%20Scotland | National Records of Scotland () is a non-ministerial department of the Scottish Government. It is responsible for civil registration, the census in Scotland, demography and statistics, family history, as well as the national archives and historical records.
National Records of Scotland was formed from the merger of the General Register Office for Scotland and the National Archives of Scotland in 2011; it combines all the functions of the two former organisations. The offices of Registrar General for Scotland and Keeper of the Records of Scotland remain separate, but since 2011 both have been vested ex officio in the Chief Executive of National Records of Scotland, currently Paul Lowe.
Location
National Records of Scotland is based in HM General Register House on Princes Street in the New Town in Edinburgh. The building was designed by Robert Adam for the Register House Trustees; it was opened to the public in 1788.
History
The first official tasked with the care and administration of the public records was first recorded in the role of Clericus Rotulorum (Clerk of the Rolls) in the Kingdom of Scotland in 1286. Registers, rolls and records were kept in Edinburgh Castle from about the 13th century. The role of the Clerk of the Rolls eventually became known as the Lord Clerk Register, the oldest surviving great offices of state in Scotland. However, records held by the Scottish Crown did not typically include personal data such as birth, death and marriage records. Instead, the clergy and other officials of the Church of Scotland kept parish records, which recorded personal data such as baptisms and marriages, but only for their own church members so parish records were limited in scope. In 1551, a council of Scottish clergy enacted that all parish ministers should keep a record of baptisms, burials and marriages. However, in 1801, the first national Census found that, out of the 850 parishes in Scotland, not more than 99 had regular registers. This was in part due to sporadic recording keeping and accidental destruction of registers.
In 1806, a Royal Warrant established the office of Deputy Clerk Register, effectively reducing the record keeping duties of the Lord Clerk Register to an honorary title with no day-to-day management of the Registers and Records of Scotland. However, personal data continued to be managed by the clergy, now largely ministers of the Church of Scotland. The Industrial revolution radically changed the population demographics of Scotland, with central belt parishes being swamped by migrants from the Highlands and Lowlands which also contributed to the poor record keeping in registers. A bill came before the United Kingdom Parliament in 1829 and several others in subsequent years to introduce a system of state registration, following the similar introduction of public registration in England & Wales in 1837, but the bills were unsuccessful. One of the main reasons they were unsuccessful was the opposition, including t |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.