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.

Token Racing

Token Racing was a short-lived Formula One team and constructor from the United Kingdom, participating in four Grands Prix of the 1974 Formula One season.

Token's history began in late 1973 when Rondel Racing, the successful Formula Two team founded by Ron Dennis and Neil Trundle, decided to enter F1. Dennis asked Ray Jessop to design the car, while backing was to come from the French oil company Motul, which had sponsored the team for the previous two years. But when the 1973 oil crisis hit, Motul withdrew, and Dennis was forced to close down the team. The F1 project was subsequently sold to shipbroker Tony Vlassopulo and Lloyd's underwriter Ken Grob, from whose first names the "Token" name was derived, while the car was called the RJ02 in honour of Jessop.

The team made its F1 debut in April 1974 at the non-Championship International Trophy race at Silverstone, with Welshman Tom Pryce at the wheel. Its first Championship race came the following month, at the Belgian Grand Prix, where Pryce qualified 20th but retired at three-quarter distance following a collision with Jody Scheckter's Tyrrell. The team entered the next race at Monaco but was forbidden from taking part on the basis of Pryce's supposed inexperience, prompting the Welshman to move to the Shadow team.

Access token

In computer systems, an access token contains the security credentials for a login session and identifies the user, the user's groups, the user's privileges, and, in some cases, a particular application.

Overview

An access token is an object encapsulating the security identity of a process or thread. A token is used to make security decisions and to store tamper-proof information about some system entity. While a token is generally used to represent only security information, it is capable of holding additional free-form data that can be attached while the token is being created. Tokens can be duplicated without special privilege, for example to create a new token with lower levels of access rights to restrict the access of a launched application. An access token is used by Windows when a process or thread tries to interact with objects that have security descriptors (securable objects). An access token is represented by the system object of type Token.

An access token is generated by the logon service when a user logs on to the system and the credentials provided by the user are authenticated against the authentication database. The authentication database contains credential information required to construct the initial token for the logon session, including its user id, primary group id, all other groups it is part of, and other information. The token is attached to the initial process created in the user session and inherited by subsequent processes created by the initial process. Whenever such a process opens a handle to any resource which has access control enabled, Windows reconciles the data in the target object's security descriptor with the contents of the current effective access token. The result of this access check evaluation is an indication of whether any access is allowed and, if so, what operations (read, write/modify, etc.) the calling application is allowed to perform.

Token coin

In the study of numismatics, tokens are coin-like objects used instead of coins. The field of tokens is part of exonumia. Tokens are used in place of coins and either have a denomination shown or implied by size, color or shape. "Tokens" are often made of cheaper metals: copper, pewter, aluminium, brass and tin were commonly used, while bakelite, leather, porcelain, and other less durable materials are also known.

The key point of difference between a token and a coin is that a coin is issued by a governmental local or national authority and is freely exchangeable for goods or other coins, whereas a token has a much more limited use and is often (but not always) issued by a private company, group, association or individual.

In the case of "currency tokens" issued by a company but also recognized by the State there is a convergence between tokens and currency.

Currency tokens

In their purest form, currency tokens issued by a company crossed the boundary of merely being "trade" tokens when they were sanctioned by the local government authority. This was sometimes a measure resulting from a severe shortage of money or the government's inability to issue its own coinage. In effect, the organization behind the tokens became the regional bank.