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If two curves phi and psi of multiplicities r_i!=0 and s_i!=0 have only ordinary points or ordinary singular points and cusps in common, then every curve which has at least ...

A paracompact space is a T2-space such that every open cover has a locally finite open refinement. Paracompactness is a very common property that topological spaces satisfy. ...

Let p be an odd prime, k be an integer such that pk and 1<=k<=2(p+1), and N=2kp+1. Then the following are equivalent 1. N is prime. 2. There exists an a such that ...

Stochastic optimization refers to the minimization (or maximization) of a function in the presence of randomness in the optimization process. The randomness may be present as ...

An irregular icosagon, also called the gammadion or fylfot, which symbolized good luck in ancient Arabic and Indian cultures. The mirror image of the above, sometimes called ...

In the theory of special functions, a class of functions is said to be "of the third kind" if it is similar to but distinct from previously defined functions already defined ...

If S_1, S_2, and S_3 are three conics having the property that there is a point X, not on any of the conics, lying on a common chord of each pair of the three conics (with ...

A rational number expressed in the form a/b (in-line notation) or a/b (traditional "display" notation), where a is called the numerator and b is called the denominator. When ...

A set of four points, one of which is the orthocenter of the other three. In an orthocentric system, each point is the orthocenter of the triangle of the other three, as ...

The Higman-Sims graph is the unique strongly regular graph on 100 nodes (Higman and Sims 1968, Brouwer 1983, Brouwer and Haemers 1993). It was also constructed independently ...