T-norm

In mathematics, a t-norm (also T-norm or, unabbreviated, triangular norm) is a kind of binary operation used in the framework of probabilistic metric spaces and in multi-valued logic, specifically in fuzzy logic. A t-norm generalizes intersection in a lattice and conjunction in logic. The name triangular norm refers to the fact that in the framework of probabilistic metric spaces t-norms are used to generalize triangle inequality of ordinary metric spaces.

Definition

A t-norm is a function T: [0, 1] × [0, 1] → [0, 1] which satisfies the following properties:

Since a t-norm is a binary algebraic operation on the interval [0, 1], infix algebraic notation is also common, with the t-norm usually denoted by .

The defining conditions of the t-norm are exactly those of the partially ordered Abelian monoid on the real unit interval [0, 1]. (Cf. ordered group.) The monoidal operation of any partially ordered Abelian monoid L is therefore by some authors called a triangular norm on L.

Norm

Norm or NORM may refer to:

In academia

In mathematics

List of Crash Bandicoot series characters

Crash Bandicoot is a series of platform video games published by Activision. The series was formerly developed by Naughty Dog from 1996 to 1999, and by Traveller's Tales, Eurocom and Vicarious Visions from 2000 to 2004. The series features a large cast of distinctively quirky characters designed by numerous different artists, the most notable of which include Charles Zembillas and Joe Pearson. In addition, it features an all-star cast of veteran voice actors.

The series centers on the conflicts between a mutated bandicoot named Crash Bandicoot and his creator, Doctor Neo Cortex. Crash acts as the main playable character of the series, though other characters have had occasional player access, most notable Coco Bandicoot and Doctor Neo Cortex, as well as Crunch Bandicoot. Out of the numerous characters in the series (numbering over sixty), only a few have significantly contributed to the story of the series.

Protagonists

Crash Bandicoot

Aku Aku

Aku Aku, also known as Holiugd, is the guardian of the Wumpa Islands and the father figure of Crash Bandicoot and his friends. Aku Aku is the spirit of an ancient witch doctor encased in a floating, wooden mask. During Crash's missions to stop Doctor Cortex, he scattered copies of himself throughout the travels in an effort to aid him in his mission. Whenever Crash possesses an Aku Aku mask, he will be shielded from one enemy attack or contact. Collecting three Aku Aku masks gives Crash temporary invulnerability from all minor dangers, but does not protect from falling down holes. In his English speaking appearances, he is voiced by Mel Winkler up to Crash Twinsanity, and Greg Eagles in Crash of the Titans and Crash: Mind over Mutant. In the Japanese versions of his speaking appearances, he is voiced by Kenichi Ogata up to Crash Twinsanity.

Norm (abelian group)

In mathematics, specifically abstract algebra, if (G, +) is an abelian group then is said to be a norm on the abelian group (G, +) if:

,

,

.

The norm ν is discrete if there is some real number ρ > 0 such that ν(g) > ρ whenever g ≠ 0.

Free abelian groups

An abelian group is a free abelian group if and only if it has a discrete norm.

References