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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.
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 ...
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 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 ...
In fact, as noted below, the pass was 100 metres wide, probably wider than the Greeks could have held against the Persian masses. Herodotus reports that the Phocians had improved the defences of the pass by channelling the stream from the hot springs to create a marsh, and it was a causeway across this marsh which was only wide enough for a ...
The Journal of Mental Science noted the arguments raised against adopting proxy voting for the Association. These included that possibility that it would diminish attendance at meetings. The rejoinder was that people did not go there to vote; they attending the meetings for the sake of the meeting, the discussion, and the good fellowship.
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.
Some of the most common causes of a constant, clear runny nose include allergies, infections, and nasal polyps. It can also be triggered by food, medications, and changes in hormones.