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A morphism f:Y->X in a category is an epimorphism if, for any two morphisms u,v:X->Z, uf=vf implies u=v. In the categories of sets, groups, modules, etc., an epimorphism is ...

The inverse curve of the epispiral r=asec(ntheta) with inversion center at the origin and inversion radius k is the rose curve r=(kcos(ntheta))/a.

An equilateral polyhedron is a polyhedron whose edges are all of equal length. Platonic solids, Archimedean solids, canonical antiprisms, and canonical prisms, Johnson ...

Let A and B be two classes of positive integers. Let A(n) be the number of integers in A which are less than or equal to n, and let B(n) be the number of integers in B which ...

There exists an absolute constant C such that for any positive integer m, the discrepancy of any sequence {alpha_n} satisfies ...

For any integers a_i with 1<=a_1<a_2<...<a_k<=n, the proportion of permutations in the symmetric group S_n whose cyclic decompositions contain no cycles of lengths a_1, a_2, ...

The series sumf(n) for a monotonic nonincreasing f(x) is convergent if lim_(x->infty)^_(e^xf(e^x))/(f(x))<1 and divergent if lim_(x->infty)__(e^xf(e^x))/(f(x))>1.

A bounded operator U on a Hilbert space H is called essentially unitary if U^*U-I and UU^*-I are compact operators.

A weighted graph in which the weights are equal to the Euclidean lengths of the edges in a specified embedding (Skiena 1990, pp. 201 and 252).

A Euclidean motion of R^n is an affine transformation whose linear part is an orthogonal transformation.