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.
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.
A building is a constructed object intended for occupancy by humans or animals.
Building may also refer to:
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.
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.
The first publicly available MUD that featured in-game creation of the game world was Skrenta's 1988 Monster.
A drone is a male honey bee that is the product of an unfertilized egg. Unlike the female worker bee, drones do not have stingers and do not participate in nectar and pollen gathering. A drone's primary role is to mate with a fertile queen.
Drones carry only one type of allele at each chromosomal position, because they are haploid (containing only one set of chromosomes from the mother). During the development of eggs within a queen, a diploid cell with 32 chromosomes divides to generate haploid cells called gametes with 16 chromosomes. The result is a haploid egg, with chromosomes having a new combination of alleles at the various loci. This process is also called arrhenotokous parthenogenesis or simply arrhenotoky.
Because the male bee technically has only a mother, and no father, its genealogical tree is rather interesting. In the first generation there is one member (the male). One generation back there is also one member (the mother). Two generations back there are two members (the mother and father of the mother). Three generations back there are three members. Four back there are five members. That is, the numbers in each generation going back are 1, 1, 2, 3, 5, 8, ... —
Surveying or land surveying is the technique, profession, and science of determining the terrestrial or three-dimensional position of points and the distances and angles between them. A land surveying professional is called a land surveyor. These points are usually on the surface of the Earth, and they are often used to establish land maps and boundaries for ownership, locations like building corners or the surface location of subsurface features, or other purposes required by government or civil law, such as property sales.
Surveyors work with elements of geometry, trigonometry, regression analysis, physics, engineering, metrology, programming languages and the law. They use equipment like total stations, robotic total stations, GPS receivers, retroreflectors, 3D scanners, radios, handheld tablets, digital levels, drones, GIS and surveying software.
Surveying has been an element in the development of the human environment since the beginning of recorded history. The planning and execution of most forms of construction require it. It is also used in transport, communications, mapping, and the definition of legal boundaries for land ownership. It is an important tool for research in many other scientific disciplines.