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A graph G is said to be flexible if the vertices of G can be moved continuously so that (1) the distances between adjacent vertices are unchanged, and (2) at least two ...

If a proposition P is true for all B, this is written P forall B. forall is one of the two so-called quantifiers, and translates the universal quantifier forall . The Wolfram ...

An expression occurring in existential sentences. "For some x" is the same as " exists x." Unlike in everyday language, it is does not necessarily refer to a plurality of ...

Let four lines in a plane represent four roads in general position, and let one traveler T_i be walking along each road at a constant (but not necessarily equal to any other ...

A one-dimensional map whose increments are distributed according to a normal distribution. Let y(t-Deltat) and y(t+Deltat) be values, then their correlation is given by the ...

A fractional clique of a graph G is a nonnegative real function on the vertices of G such that sum of the values on the vertices of any independent set is at most one. The ...

Consider a finite collection of points p=(p_1,...,p_n), p_i in R^d Euclidean space (known as a configuration) and a graph G whose graph vertices correspond to pairs of points ...

The free product G*H of groups G and H is the set of elements of the form g_1h_1g_2h_2...g_rh_r, where g_i in G and h_i in H, with g_1 and h_r possibly equal to e, the ...

An occurrence of a variable in a logic formula which is not inside the scope of a quantifier.

Frequency representation is the notation (1^(a_1)2^(a_2)...) used to abbreviate a partition {1,...,1_()_(a_1),2,...,2_()_(a_2),...} (Andrews 1998, p. 1).