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Let u_1<=u_2<=... be harmonic functions on a connected open set U subset= C. Then either u_j->infty uniformly on compact sets or there is a finite-values harmonic function u ...

100=10^2. Madachy (1979) gives a number of algebraic equations using the digits 1 to 9 which evaluate to 100, such as (7-5)^2+96+8-4-3-1 = 100 (1) 3^2+91+7+8-6-5-4 = 100 (2) ...

Taking the pole as the inversion center, the hyperbolic spiral inverts to Archimedes' spiral r=atheta.

A game in which the possible moves are the same for each player in any position. All positions in all impartial games form an additive Abelian group. For impartial games in ...

Let A be a unital C^*-algebra, then an element u in A is called an isometry if u^*u=1.

A special ideal in a commutative ring R. The Jacobson radical is the intersection of the maximal ideals in R. It could be the zero ideal, as in the case of the integers.

The Krohn-Rhodes complexity, also called the group complexity or simply "the complexity," of a finite semigroup S is the smallest number of groups in a wreath product of ...

A family of subsets of a topological space such that every point has a neighborhood which intersects only a finite number of them.

A method for testing nested hypotheses. To apply the procedure, given a specific model, calculate the likelihood of observing the actual data. Then compare this likelihood to ...

A type I move (conjugation) takes AB->BA for A, B in B_n where B_n is a braid group. A type II move (stabilization) takes A->Ab_n or A->Ab_n^(-1) for A in B_n, and b_n, Ab_n, ...