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Continuum percolation can be thought of as a continuous, uncountable version of percolation theory-a theory which, in its most studied form, takes place on a discrete, ...

There are a number of attractive polyhedron compounds of two cubes. The first (left figures) is obtained by allowing two cubes to share opposite polyhedron vertices then ...

A differential k-form is a tensor of tensor rank k that is antisymmetric under exchange of any pair of indices. The number of algebraically independent components in n ...

The Euler-Mascheroni constant gamma, sometimes also called 'Euler's constant' or 'the Euler constant' (but not to be confused with the constant e=2.718281...) is defined as ...

A root-finding method which was among the most popular methods for finding roots of univariate polynomials in the 19th and 20th centuries. It was invented independently by ...

Kobon Fujimura asked for the largest number N(n) of nonoverlapping triangles that can be constructed using n lines (Gardner 1983, p. 170). A Kobon triangle is therefore ...

A labeled graph G=(V,E) is a finite series of graph vertices V with a set of graph edges E of 2-subsets of V. Given a graph vertex set V_n={1,2,...,n}, the number of ...

For 2<=n<=32, it is possible to select 2n lattice points with x,y in [1,n] such that no three are in a straight line (where "straight line" means any line in the plane--not ...

Quicksort is the fastest known comparison-based sorting algorithm (on average, and for a large number of elements), requiring O(nlgn) steps. Quicksort is a recursive ...

The Remez algorithm (Remez 1934), also called the Remez exchange algorithm, is an application of the Chebyshev alternation theorem that constructs the polynomial of best ...