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.

Act

Act or ACT may mean:

Acts may mean:

ACT

Act! (Italy)

Act! (Italian: Fare!, F!) is a centre-right political party in Italy, based in Veneto.

The party is led by Flavio Tosi, mayor of Verona and former leader of Liga Veneta–Lega Nord, who was ejected from it in the run-up of the 2015 Venetian regional election, due to his opposition to Matteo Salvini's political line.

Act! was immediately joined by three deputies (Matteo Bragantini, Roberto Caon, Emanuele Prataviera), three senators (Patrizia Bisinella, Raffaela Bellot, Emanuela Munerato) and four regional councilors in Veneto (three elected with the Tosi List for Veneto and one with Il Veneto del Fare). All of them were Tosi loyalists who followed him out of the League.

In July Michele Boldrin, leader of Act to Stop the Decline, sued Act! as the names of the two parties looked too similar.

In September a fourth deputy joined the party: Marco Marcolin, also from Liga Veneta–Lega Nord.

In October Act! became an occasional supporter of the centre-left government led by Matteo Renzi, whom Tosi held in high esteem, fueling rumors that the party might either enter in stable alliance with or join Renzi's Democratic Party.

Investment Company Act of 1940

The Investment Company Act of 1940 is an act of Congress. It was passed as a United States Public Law (Pub.L. 76–768) on August 22, 1940, and is codified at 15 U.S.C. §§ 80a-1–80a-64. Along with the Securities Exchange Act of 1934 and Investment Advisers Act of 1940, and extensive rules issued by the Securities and Exchange Commission, it forms the backbone of United States financial regulation. It has been updated by the Dodd-Frank Act of 2010. Often known as the Company Act, the 1940 Act or simply the '40 Act, it is the primary source of regulation for mutual funds and closed-end funds, an investment industry now in the many trillions of dollars. In addition, the '40 Act impacts the operations of hedge funds, private equity funds and even holding companies.

Background

Following the founding of the mutual fund in 1924, investors welcomed the innovation with open arms and invested in this new investment vehicle heavily. Five and a half years later, the Wall Street Crash of 1929 occurred in the stock market, followed shortly thereafter by the United States entry into the Great Depression. In response to this crisis, the United States Congress wrote into law the Securities Act of 1933 and the Securities Exchange Act of 1934 in order to regulate the securities industry in the interest of the public.