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Let theta be the angle between two vectors. If 0<theta<pi, the vectors are positively oriented. If pi<theta<2pi, the vectors are negatively oriented. Two vectors in the plane ...

Given two intersecting lines, the two nonadjacent angles with the same vertex are said to be vertical angles. One can easily prove that vertical angles are congruent. Some ...

The connective in logic corresponding to the exclusive nor operation. A XNOR B is equivalent to (A ^ B) v (!A ^ !B), where ^ denotes AND, v denotes OR, and !A denotes NOT. ...

The connective in logic corresponding to the exclusive nor operation. A XNOR B is equivalent to (A ^ B) v (!A ^ !B), where ^ denotes AND, v denotes OR, and !A denotes NOT. ...

If W is a simply connected, compact manifold with a boundary that has two components, M_1 and M_2, such that inclusion of each is a homotopy equivalence, then W is ...

A quadrilateral, sometimes also known as a tetragon or quadrangle (Johnson 1929, p. 61) is a four-sided polygon. If not explicitly stated, all four polygon vertices are ...

The Brouwer-Haemers graph is the unique strongly regular graph on 81 vertices with parameters nu=81, k=20, lambda=1, mu=6 (Brouwer and Haemers 1992, Brouwer). It is also ...

An involution of a set S is a permutation of S which does not contain any permutation cycles of length >2 (i.e., it consists exclusively of fixed points and transpositions). ...

A quadratic form Q(z) is said to be positive definite if Q(z)>0 for z!=0. A real quadratic form in n variables is positive definite iff its canonical form is ...

The phrase Tomita-Takesaki theory refers to a specific collection of results proven within the field of functional analysis regarding the theory of modular Hilbert algebras ...