Banach fixed-point theoremIn mathematics, the Banach fixed-point theorem (also known as the contraction mapping theorem or contractive mapping theorem or Banach-Caccioppoli theorem) is an important tool in the theory of metric spaces; it guarantees the existence and uniqueness of fixed points of certain self-maps of metric spaces, and provides a constructive method to find those fixed points. It can be understood as an abstract formulation of Picard's method of successive approximations. The theorem is named after Stefan Banach (1892–1945) who first stated it in 1922.
Small-world networkA small-world network is a mathematical graph in which most nodes are not neighbors of one another, but the neighbors of any given node are likely to be neighbors of each other. Due to this, most neighboring nodes can be reached from every other node by a small number of hops or steps. Specifically, a small-world network is defined to be a network where the typical distance L between two randomly chosen nodes (the number of steps required) grows proportionally to the logarithm of the number of nodes N in the network, that is: while the global clustering coefficient is not small.
Apollo Guidance ComputerThe Apollo Guidance Computer (AGC) was a digital computer produced for the Apollo program that was installed on board each Apollo command module (CM) and Apollo Lunar Module (LM). The AGC provided computation and electronic interfaces for guidance, navigation, and control of the spacecraft. The AGC was the first computer based on silicon integrated circuits. The computer's performance was comparable to the first generation of home computers from the late 1970s, such as the Apple II, TRS-80, and Commodore PET.
Regula falsiIn mathematics, the regula falsi, method of false position, or false position method is a very old method for solving an equation with one unknown; this method, in modified form, is still in use. In simple terms, the method is the trial and error technique of using test ("false") values for the variable and then adjusting the test value according to the outcome. This is sometimes also referred to as "guess and check". Versions of the method predate the advent of algebra and the use of equations.
Parking guidance and informationParking guidance and information (PGI) systems, or car park guidance systems, present drivers with dynamic information on parking within controlled areas. The systems combine traffic monitoring, communication, processing and variable message sign technologies to provide the service. Modern parking lots utilize a variety of technologies to help motorists find unoccupied parking spaces, car location when returning to the vehicle and improve their experience.
Analytical hierarchyIn mathematical logic and descriptive set theory, the analytical hierarchy is an extension of the arithmetical hierarchy. The analytical hierarchy of formulas includes formulas in the language of second-order arithmetic, which can have quantifiers over both the set of natural numbers, , and over functions from to . The analytical hierarchy of sets classifies sets by the formulas that can be used to define them; it is the lightface version of the projective hierarchy.
