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A (presumably autobiographical) character in one of astrophysicist Fred Hoyle's novels opined the following. "I figure that if to be totally known and totally loved is worth ...

A point process N on R is said to be interval stationary if for every r=1,2,3,... and for all integers i_i,...,i_r, the joint distribution of {tau_(i_1+k),...,tau_(i_r+k)} ...

Kakutani's fixed point theorem is a result in functional analysis which establishes the existence of a common fixed point among a collection of maps defined on certain ...

The most general form of this theorem states that in a commutative unit ring R, the height of every proper ideal I generated by n elements is at most n. Equality is attained ...

In practice, the vertical offsets from a line (polynomial, surface, hyperplane, etc.) are almost always minimized instead of the perpendicular offsets. This provides a ...

The commutator series of a Lie algebra g, sometimes called the derived series, is the sequence of subalgebras recursively defined by g^(k+1)=[g^k,g^k], (1) with g^0=g. The ...

The lower central series of a Lie algebra g is the sequence of subalgebras recursively defined by g_(k+1)=[g,g_k], (1) with g_0=g. The sequence of subspaces is always ...

The set of left cosets of a subgroup H of a topological group G forms a topological space. Its topology is defined by the quotient topology from pi:G->G/H. Namely, the open ...

The study of number fields by embedding them in a local field is called local class field theory. Information about an equation in a local field may give information about ...

Let L be a lattice (or a bounded lattice or a complemented lattice, etc.), and let C_L be the covering relation of L: C_L={(x,y) in L^2|x covers y or y covers x}. Then C_L is ...