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Any ideal of a ring which is strictly smaller than the whole ring. For example, 2Z is a proper ideal of the ring of integers Z, since 1 not in 2Z. The ideal <X> of the ...

A subfield which is strictly smaller than the field in which it is contained. The field of rationals Q is a proper subfield of the field of real numbers R which, in turn, is ...

An encoding which provides a bijection between the n^(n-2) labeled trees on n nodes and strings of n-2 integers chosen from an alphabet of the numbers 1 to n. A labeled tree ...

A simple closed curve on a sphere that is not necessarily a great circle but merely intersects as a great circle would (Billera et al. 1999).

Given a subset S subset R^n and a real function f which is Gâteaux differentiable at a point x in S, f is said to be pseudoconvex at x if del f(x)·(y-x)>=0,y in ...

A pseudoforest is an undirected graph in which every connected component contains at most one graph cycle. A pseudotree is therefore a connected pseudoforest and a forest ...

A pseudograph is a non-simple graph in which both graph loops and multiple edges are permitted (Zwillinger 2003, p. 220).

A pseudoinverse is a matrix inverse-like object that may be defined for a complex matrix, even if it is not necessarily square. For any given complex matrix, it is possible ...

The case of the Weierstrass elliptic function with invariants g_2=-1 and g_3=0. The half-periods for this case are L(1+i)/4 and L(-1+i)/4, where L is the lemniscate constant ...

A typical vector (i.e., a vector such as the radius vector r) is transformed to its negative under inversion of its coordinate axes. Such "proper" vectors are known as polar ...