Building (mathematics)

In mathematics, a building (also Tits building, Bruhat–Tits building, named after François Bruhat and Jacques Tits) is a combinatorial and geometric structure which simultaneously generalizes certain aspects of flag manifolds, finite projective planes, and Riemannian symmetric spaces. Initially introduced by Jacques Tits as a means to understand the structure of exceptional groups of Lie type, the theory has also been used to study the geometry and topology of homogeneous spaces of p-adic Lie groups and their discrete subgroups of symmetries, in the same way that trees have been used to study free groups.

Overview

The notion of a building was invented by Jacques Tits as a means of describing simple algebraic groups over an arbitrary field. Tits demonstrated how to every such group G one can associate a simplicial complex Δ = Δ(G) with an action of G, called the spherical building of G. The group G imposes very strong combinatorial regularity conditions on the complexes Δ that can arise in this fashion. By treating these conditions as axioms for a class of simplicial complexes, Tits arrived at his first definition of a building. A part of the data defining a building Δ is a Coxeter group W, which determines a highly symmetrical simplicial complex Σ = Σ(W,S), called the Coxeter complex. A building Δ is glued together from multiple copies of Σ, called its apartments, in a certain regular fashion. When W is a finite Coxeter group, the Coxeter complex is a topological sphere, and the corresponding buildings are said to be of spherical type. When W is an affine Weyl group, the Coxeter complex is a subdivision of the affine plane and one speaks of affine, or Euclidean, buildings. An affine building of type is the same as an infinite tree without terminal vertices.

Building (disambiguation)

A building is a constructed object intended for occupancy by humans or animals.

Building may also refer to:

See also

Online creation

Online creation, also referred to as OLC, online coding, online building, and online editing, is a software feature of MUDs that allows users to edit a virtual world from within the game itself. In the absence of online creation, content is created in a text editor or level editor, and the program generally requires a restart in order to implement the changes.

Online creation as original content

An aspect of online creation that separates it from "mere game play" is that online creation systems can generally be used to create new content — new objects, new locations, new creatures — rather than simply creating instances of predefined items in the game world. Some have observed that certain forms of online creation — notably those associated with creating new commands — can threaten the stability of the server.

History

Origins

The first publicly available MUD that featured in-game creation of the game world was Skrenta's 1988 Monster.

Arco (band)

Arco are a British band noted for unusually slow, quiet, poetic music: a gig review in national newspaper The Guardian suggested "an hour in arco's company is the aural equivalent of a day in a flotation tank". Similarly, a review in Q, a UK monthly music magazine, described first album Coming To Terms as "the aural equivalent of a human being pausing for thought as the world speeds on around".

Their track "Lullaby" was featured on the soundtrack album of Californication on the US Showtime network.

In Korea two tracks, "Alien" and "Perfect World", were featured on the soundtrack album of network drama series Coffee Prince, while "Lullaby" featured in an advertisement for Sky mobile phones, and "Babies Eyes" in an advert for "17" tea. "Alien" also appeared in the soundtrack of the film Turning Green, and in the soundtrack of One Tree Hill (series 1, episode 15).

In 2005 they played a tour of the US west coast, including gigs at Los Angeles, Santa Cruz, San Francisco, Portland and Seattle.

ARCO

Atlantic Richfield Company (ARCO) is an American oil company with operations in the United States, Indonesia, the North Sea, and the South China Sea. It has more than 1,300 gas stations in the western part of the United States. ARCO was formed by the merger of East Coast–based Atlantic Refining and California-based Richfield Oil Corporation in 1966. A merger in 1969 brought in Sinclair Oil Corporation. It became a subsidiary of UK-based BP plc in 2000 through its BP West Coast Products LLC (BPWCP) affiliate. On August 13, 2012, it was announced that Tesoro would purchase ARCO and its refinery for $2.5 billion. However, the deal came under fire due to increasing fuel prices. Many activists urged state and federal regulators to block the sale due to concerns that it would reduce competition and could lead to higher fuel prices at ARCO stations (ARCO stations make up more than half of all stations with the lowest fuel prices in California). On June 3, 2013, BP sold ARCO and the Carson Refinery to Tesoro for $2.5 billion. BP sold its Southern California terminals (Vinvale, Colton, San Diego, Hathaway, and Hynes) to Tesoro Logistics LP, including the Carson Storage Facility. BP will continue to own the ampm brand and sell it to Tesoro for Southern California, Arizona, and Nevada. BP exclusively licensed the ARCO rights from Tesoro for Northern California, Oregon, and Washington.