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An axiomatic system is said to be categorical if there is only one essentially distinct representation for it. In particular, the names and types of objects within the system ...

A Gaussian quadrature-like formula for numerical estimation of integrals. It uses weighting function W(x)=1 in the interval [-1,1] and forces all the weights to be equal. The ...

A recursively enumerable set A is creative if its complement is productive. Creative sets are not recursive. The property of creativeness coincides with completeness. Namely, ...

Consider the distribution of distances l between a point picked at random in the interior of a unit cube and on a face of the cube. The probability function, illustrated ...

The Drazin inverse is a matrix inverse-like object derived from a given square matrix. In particular, let the index k of a square matrix be defined as the smallest ...

The Earth-Moon problem is a special case of the empire problem for countries with m=2 disjoint regions, with one region of each country lying on the Earth and one on the Moon ...

Let T_n(x) be an arbitrary trigonometric polynomial T_n(x)=1/2a_0+{sum_(k=1)^n[a_kcos(kx)+b_ksin(kx)]} (1) with real coefficients, let f be a function that is integrable over ...

The first Fermat point X (or F_1) (sometimes simply called "the Fermat point," Torricelli point, or first isogonic center) is the point X which minimizes the sum of distances ...

Nice approximations for the golden ratio phi are given by phi approx sqrt((5pi)/6) (1) approx (7pi)/(5e), (2) the last of which is due to W. van Doorn (pers. comm., Jul. 18, ...

An n-mark Golomb ruler is a set of n distinct nonnegative integers (a_1,a_2,...,a_n), called "marks," such that the positive differences |a_i-a_j|, computed over all possible ...