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Duality (order theory) In the mathematical area of order theory, every partially ordered set P gives rise to a dual (or opposite) partially ordered set which is often denoted by Pop or Pd. This dual order Pop is defined to be the same set, but with the inverse order, i.e. x ≤ y holds in Pop if and only if y ≤ x holds in P.
Duality (mathematics) In mathematics, a duality translates concepts, theorems or mathematical structures into other concepts, theorems or structures in a one-to-one fashion, often (but not always) by means of an involution operation: if the dual of A is B, then the dual of B is A. Such involutions sometimes have fixed points, so that the dual ...
Dually chordal graph. In the mathematical area of graph theory, an undirected graph G is dually chordal if the hypergraph of its maximal cliques is a hypertree. The name comes from the fact that a graph is chordal if and only if the hypergraph of its maximal cliques is the dual of a hypertree. Originally, these graphs were defined by maximum ...
Dual ( abbreviated DU) is a grammatical number that some languages use in addition to singular and plural. When a noun or pronoun appears in dual form, it is interpreted as referring to precisely two of the entities (objects or persons) identified by the noun or pronoun acting as a single unit or in unison. Verbs can also have dual agreement ...
Dually may refer to: Dualla, County Tipperary, a village in Ireland; A pickup truck with dual wheels on the rear axle; DUALLy, s platform for architectural languages ...
Dual (category theory) In category theory, a branch of mathematics, duality is a correspondence between the properties of a category C and the dual properties of the opposite category Cop. Given a statement regarding the category C, by interchanging the source and target of each morphism as well as interchanging the order of composing two ...
The map defines a norm on (See Theorems 1 and 2 below.) The dual norm is a special case of the operator norm defined for each (bounded) linear map between normed vector spaces. Since the ground field of ( or ) is complete, is a Banach space. The topology on induced by turns out to be stronger than the weak-* topology on.
A problem with this view is that there are a few words in which [ŋ] is followed neither by a velar nor a morpheme boundary (such as gingham, dinghy, orangutan and Singapore for those speakers who pronounce them without [ɡ]), and some in which the [ɡ] is not deleted before a morpheme boundary (longer etc., as noted above).