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.

Scuderia Milano

Scuderia Milano was an Italian motor racing team run by the Ruggeri (or Ruggieri) brothers that raced Maseratis in the early post-war period. They participated in a single Formula One Grand Prix as a constructor in 1950. The team scored two World Championship points, with a best finish (in its debut race) of fifth for Felice Bonetto at the 1950 Swiss Grand Prix.

Scuderia Milano modified two Maserati 4CLT single-seaters with a shorter wheelbase, De Dion suspensions, larger brakes and an engine redesigned by Mario Speluzzi, refitted with two-stage superchargers, racing them in the 1950 and 1951 F1 seasons. One Scuderia Milano 4CLT was redesigned as the Arzani-Volpini in 1955.

Complete World Championship results

(key) (results in bold indicate pole position)

* Constructor's Championship not awarded until 1958.

References

PizzaExpress

PizzaExpress is a restaurant group with over 400 restaurants across the United Kingdom and 40 overseas in Europe, Hong Kong, India and the Middle East. It was founded in 1965 by Peter Boizot. In July 2014 the group was sold to the China-based private equity firm Hony Capital in a deal worth £900 million ($1.54 billion).

History

Founded in 1965 by Peter Boizot, PizzaExpress opened its first restaurant in London's Wardour Street. Inspired by a trip to Italy, Boizot brought back to London a pizza oven from Naples and a chef from Sicily.

In 1969 jazz performances began at its Dean Street restaurant, London.

In 1995, PizzaExpress expanded into Ireland and currently operates 14 restaurants there under the brand name Milano. The company also owns the brand name Marzano. Originally Marzano was used in countries where the brand name Pizza Express was not available, as with the use of the name Milano in Ireland, but it also exists in some territories, such as Cyprus, to differentiate between the restaurants selling primarily pizza and those offering a wider range of non-pizza meals inspired by Italy. It is also used for a cafe-bar run as an adjunct to the branch of Pizza Express in The Forum in Norwich, "Cafe Bar Marzano".

Milano Due

Milano Due (Milan 2, also known as Milano 2) is a residential centre in the Italian town of Segrate (Province of Milan). It was built as a new town by Edilnord, a company associated with the Fininvest group of Silvio Berlusconi.

Overview

The main peculiarity of Milano Due is a system of walkways and bridges that connects the whole neighborhood, so that it is possible to walk around without ever intersecting traffic. It was marketed as a residential neighborhood for families of the upper middle class with children.

The works started in 1970, and were completed in 1979. Distinctive landmarks are the sporting facilities, a small artificial lake (il laghetto) and a children's playground.

Media

Milano Due also hosted the headquarters of the first Italian private television channel, TeleMilano, a small cable network who started broadcasting in the area in 1974. It later evolved into Canale 5, the first national private TV station.

External links