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A Lie algebra over an algebraically closed field is called exceptional if it is constructed from one of the root systems E_6, E_7, E_8, F_4, and G_2 by the Chevalley ...

A shuffle of a deck of cards obtained by successively exchanging the cards in position 1, 2, ..., n with cards in randomly chosen positions. For 4<=n<=17, the most frequent ...

Define A^' to be the point (other than the polygon vertex A) where the triangle median through A meets the circumcircle of ABC, and define B^' and C^' similarly. Then the ...

A theorem stating the existence of an object, such as the solution to a problem or equation. Strictly speaking, it need not tell how many such objects there are, nor give ...

In predicate calculus, an existential formula is a prenex normal form formula (i.e., a formula written as a string of quantifiers and bound variables followed by a ...

An existential sentence is a statement claiming the existence of an object with given properties. In the language of set theory it can be formulated as follows, exists x in U ...

Draw a triangle DeltaA_1A_2A_3, and let A_1^' be the intersection of the parallel to A_3A_1 through A_2 (the A_2-exmedian) and the parallel to A_1A_2 through A_3 (the ...

The expectation value of a function f(x) in a variable x is denoted <f(x)> or E{f(x)}. For a single discrete variable, it is defined by <f(x)>=sum_(x)f(x)P(x), (1) where P(x) ...

The exponential factorial is defined by the recurrence relation a_n=n^(a_(n-1)), (1) where a_0=1. The first few terms are therefore a_1 = 1 (2) a_2 = 2^1=2 (3) a_3 = ...

The exponential transform is the transformation of a sequence a_1, a_2, ... into a sequence b_1, b_2, ... according to the equation ...