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Ramsey's theorem is a generalization of Dilworth's lemma which states for each pair of positive integers k and l there exists an integer R(k,l) (known as the Ramsey number) ...

When computing the sample variance s numerically, the mean must be computed before s^2 can be determined. This requires storing the set of sample values. However, it is ...

The second, or diamond, group isomorphism theorem, states that if G is a group with A,B subset= G, and A subset= N_G(B), then (A intersection B)⊴A and AB/B=A/A intersection ...

Special functions which arise as solutions to second order ordinary differential equations are commonly said to be "of the first kind" if they are nonsingular at the origin, ...

Consider a second-order differential operator L^~u(x)=p_0(d^2u)/(dx^2)+p_1(du)/(dx)+p_2u, (1) where u=u(x) and p_i=p_i(x) are real functions of x on the region of interest ...

A number of four-tetrahedron compounds can be constructed by rotating about the center-centroid lines of each face. Three such compounds are shown above for rotations by ...

A tetraview is a visualization technique for bivariate complex functions. In the simplest case, the graph of a complex-valued function w=w(z) can be considered as a ...

A geometric implement discovered in a 19th century book, and whose inventor is unknown. It essentially consists of a semicircle, a segment SR which prolongs its diameter and ...

The total power of a triangle is defined by P=1/2(a_1^2+a_2^2+a_3^2), (1) where a_i are the side lengths, and the "partial power" is defined by p_1=1/2(a_2^2+a_3^2-a_1^2). ...

Given a triangle center X=l:m:n, the line mnalpha+nlbeta+lmgamma=0, where alpha:beta:gamma are trilinear coordinates, is called the trilinear polar (Kimberling 1998, p. 38). ...