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A subset tau in S_n of a permutation {1,...,n} is said to contain alpha in S_k if there exist 1<=i_1<...<i_k<=n such that tau=(tau_i,...,tau_k) is order isomorphic to ...

The system of partial differential equations u_t = (u^2-u_x+2v)_x (1) v_y = (2uv+v_x)_x. (2)

A singular point a for which f(z)(z-a)^n is not differentiable for any integer n>0.

Let p_i denote the ith prime, and write m=product_(i)p_i^(v_i). Then the exponent vector is v(m)=(v_1,v_2,...).

A closed embedded smooth plane curve has at least four vertices, where a vertex is defined as an extremum of curvature.

In a noncommutative ring R, a left ideal is a subset I which is an additive subgroup of R and such that for all r in R and all a in I, ra in I. A left ideal of R can be ...

A function for which several distinct functional values correspond (as a result of different continuations) to one and the same point (Knopp 1996, p. 94).

For b>a>0, 1/b<(lnb-lna)/(b-a)<1/a.

Except for convex polygons, every simple polygon has at least one mouth.

A right or left ideal of a ring. The term is used especially in noncommutative rings to denote a right ideal that is not a left ideal, or conversely.