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Let a graph G have graph vertices with vertex degrees d_1<=...<=d_m. If for every i<n/2 we have either d_i>=i+1 or d_(n-i)>=n-i, then the graph is Hamiltonian.

Inside a ball B in R^3, {rectifiable currents S in BL area S<=c, length partialS<=c} is compact under the flat norm.

Let sigma_1, ..., sigma_4 be four planes in general position through a point P and let P_(ij) be a point on the line sigma_i·sigma_j. Let sigma_(ijk) denote the plane ...

Let (X,B,mu) be a measure space and let E be a measurable set with mu(E)<infty. Let {f_n} be a sequence of measurable functions on E such that each f_n is finite almost ...

Relates evolutes to single paths in the calculus of variations. Proved in the general case by Darboux and Zermelo in 1894 and Kneser in 1898. It states: "When a single ...

Any nondegenerate closed space curve may be nondegenerately deformed into either of the two curves illustrated above. Neither of these can be nondegenerately transformed into ...

Let D be a planar Abelian difference set and t be any divisor of n. Then t is a numerical multiplier of D, where a multiplier is defined as an automorphism alpha of a group G ...

Pick any point P on a conic section, and draw a series of right angles having this point as their vertices. Then the line segments connecting the rays of the right angles ...

At least one power series solution will be obtained when applying the Frobenius method if the expansion point is an ordinary, or regular, singular point. The number of roots ...

Let t be an infinite word over a finite alphabet Sigma. Then there exists a uniformly recurrent infinite word r such that Sub(r) subset= Sub(t), where Sub(w) is the set of ...