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.

Search and seizure

Search and seizure is a procedure used in many civil law and common law legal systems whereby police or other authorities and their agents, who suspect that a crime has been committed, do a search of a person's property and confiscate any relevant evidence to the crime.

Some countries have provisions in their constitutions that provide the public with the right to be free from "unreasonable" search and seizure. This right is generally based on the premise that everyone is entitled to a reasonable right to privacy.

Though interpretation may vary, this right sometimes requires law enforcement to obtain a search warrant before engaging in any form of search and seizure. In cases where evidence is seized in a search, that evidence might be rejected by court procedures, such as with a motion to suppress the evidence under the exclusionary rule.

Italy

In Italy protection from search and seizure is enshrined in Article 14 of the Constitution, which states:

"The home is inviolable. Home inspections, searches, or seizures shall not be admissible save in the cases and manners complying with measures to safeguard personal liberty. Controls and inspections for reason of public health and safety, or for economic and fiscal purposes, shall be regulated by appropriate laws."

Search (TV series)

Search is an American science fiction series that aired on Wednesday nights on NBC at 10 pm ET, from September 1972 to August 1973. It ran for 23 episodes, not including the two-hour pilot film originally titled Probe. When picked up for series production, the title had to be changed because Probe was the name of an existing PBS series. In the UK the series aired on BBC 1 under the title Search Control.

The show was created by Leslie Stevens, and produced by Stevens, Robert Justman, John Strong and Anthony Spinner. The high concept was described as "science fiction in today's world" and the episodes featured many high-tech elements which are now considered common in current science fiction shows.

Plot

The series centers on World Securities Corporation, a high-tech international private investigation company that employs field operatives — the elite of whom are aided by implanted audio receivers and who carry Scanners, tiny video camera/telemetry units which can be attached to tie clips or other jewelry. The most common method is to wear the Scanner on a ring, enabling it to be discreetly aimed.