Associator

In abstract algebra, the term associator is used in different ways as a measure of the nonassociativity of an algebraic structure.

Ring theory

For a nonassociative ring or algebra , the associator is the multilinear map given by

Just as the commutator measures the degree of noncommutativity, the associator measures the degree of nonassociativity of . It is identically zero for an associative ring or algebra.

The associator in any ring obeys the identity

The associator is alternating precisely when is an alternative ring.

The associator is symmetric in its two rightmost arguments when is a pre-Lie algebra.

The nucleus is the set of elements that associate with all others: that is, the n in R such that

It turns out that any two of being implies that the third is also the zero set.

Quasigroup theory

A quasigroup Q is a set with a binary operation such that for each a,b in Q, the equations and have unique solutions x,y in Q. In a quasigroup Q, the associator is the map defined by the equation

Nucleus (advocacy group)

Nucleus was a British-European advocacy group, the forerunner to British Influence (sometimes The Centre for British Influence). Nucleus was based in London, with additional operations in Brussels.

Founded in 2010, Nucleus promoted a 'euro-realist' British approach to European political and business affairs. As well as regular bulletins, Nucleus produced commentaries, and hosted briefings, seminars, and networking events both in London and Brussels. Nucleus was unaffiliated with any political party, and was a partner in both the British Brussels Network, along with Business for New Europe, the British Chamber of Commerce in Belgium, and the Institute of Chartered Accountants in England and Wales, and the pan-European EuropAssociation.

In 2013 Nucleus relaunched as British Influence, with a heavier campaigning focus, in response to the call by Prime Minister David Cameron for an in/out referendum on the UK's European Union membership

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Nucleus (order theory)

In mathematics, and especially in order theory, a nucleus is a function on a meet-semilattice such that (for every in ):

Every nucleus is evidently a monotone function.

Frames and locales

Usually, the term nucleus is used in frames and locales theory (when the semilattice is a frame).

Proposition: If is a nucleus on a frame , then the poset of fixed points of , with order inherited from , is also a frame.

References

Washington, Tyne and Wear

Coordinates: 54°54′N 1°31′W / 54.90°N 1.52°W / 54.90; -1.52

Washington is a town in the City of Sunderland, in Tyne and Wear, England, and part of historic County Durham. Washington is located geographically at an equal distance from the centres of Newcastle, Durham and Sunderland, hence it has close ties to all three cities.

Washington was designated a new town in 1964; it expanded dramatically, by the creation of new villages and the absorption of areas of Chester-le-Street, to house overspill population from surrounding cities.

At the 2011 census, its urban subdivision (which contains the neighboring settlement of New Herrington) had a population of 67,085.

Name

Early references appear around 1096 in Old English as Wasindone. The etymological origin is disputed and there are several proposed theories for how the name "Washington" came about. Early interpretations included Wasindone (people of the hill by the stream, 1096), or Wassyngtona (settlement of Wassa's people, 1183).

Washington (footballer)

Washington Stecanela Cerqueira, or simply Washington (born April 1, 1975 in Brasília), is a retired association footballer who played striker.

Career

In Turkish league 2002–2003 season he scored 10 goals in 17 games and then he was released by Fenerbahçe because of his health problems.

Washington was submitted to a coronary catheterization. Once recovered, physicians told him that playing football would not represent a risk to his condition. Then he signed with Atlético Paranaense where he was 2004 Série A top-scorer with 34 goals and broke the league's record. For his recovery, he was dubbed Coração Valente, the title of the movie Braveheart in Brazil.

In 2005 he moved to Japan to play for Tokyo Verdy in the J. League Division 1. He had a successful season there with 22 goals in 33 games but could not save his club from relegation. In 2006 he transferred to Urawa Red Diamonds and helped the Reds win their first ever J. League Division 1 title, becoming the top scorer in the league with 26 goals in 26 games. In 2007, he became 2007 FIFA Club World Cup top scorer and his team finished in third place.

Washington Railroad Station

Washington Railroad Station, was located in Washington, New Jersey. The station was built in 1900 and added to the National Register of Historic Places on July 3, 1979. The station was demolished in 1982.

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