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Consider the sum (1) where the x_js are nonnegative and the denominators are positive. Shapiro (1954) asked if f_n(x_1,x_2,...,x_n)>=1/2n (2) for all n. It turns out ...

A permutation which shifts all elements of a set by a fixed offset, with the elements shifted off the end inserted back at the beginning. For a set with elements a_0, a_1, ...

A group given by G/phi(G), where phi(G) is the Frattini subgroup of a given group G.

The illusion in view by staring at the small black dot for a half minute or so, then switching to the white dot. The black squares appear stationary when staring at the white ...

A formal theory is said to be incomplete if it contains fewer theorems than would be possible while still retaining consistency.

A minimal edge cover is an edge cover of a graph that is not a proper subset of any other edge cover. Every minimum edge cover is a minimal edge cover, but the converse does ...

A minimum clique covering is a clique covering of minimum size, and the size of such a minimum clique covering is known as the clique covering number. Note that while a ...

The radical circle of the mixtilinear incircles has a center with trilinear center function alpha_(999)=cosA-2, (1) which is Kimberling center X_(999). It has radius (2) ...

A quadrature (numerical integration) algorithm which has a number of desirable properties.

The zonal polynomials are a class of orthogonal polynomials. They are a special case of the Jack polynomials corresponding to the case alpha=2.