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A set of positive integers is called weakly triple-free if, for any integer x, the set {x,2x,3x} !subset= S. For example, all subsets of {1,2,3,4,5} are weakly triple-free ...

The cross number of a zero-system sigma={g_1,g_2,...,g_n} of G is defined as K(sigma)=sum_(i=1)^n1/(|g_i|) The cross number of a group G has two different definitions. 1. ...

Consider the process of taking a number, taking its digit sum, then adding the digits of numbers derived from it, etc., until the remaining number has only one digit. The ...

The disjoint union of two sets A and B is a binary operator that combines all distinct elements of a pair of given sets, while retaining the original set membership as a ...

Householder (1953) first considered the matrix that now bears his name in the first couple of pages of his book. A Householder matrix for a real vector v can be implemented ...

Kelvin defined the Kelvin functions bei and ber according to ber_nu(x)+ibei_nu(x) = J_nu(xe^(3pii/4)) (1) = e^(nupii)J_nu(xe^(-pii/4)), (2) = e^(nupii/2)I_nu(xe^(pii/4)) (3) ...

For every ring containing p spheres, there exists a ring of q spheres, each touching each of the p spheres, where 1/p+1/q=1/2, (1) which can also be written (p-2)(q-2)=4. (2) ...

A piecewise linear function is a function composed of some number of linear segments defined over an equal number of intervals, usually of equal size. For example, consider ...

A mathematical object defined for a set and a binary operator in which the multiplication operation is associative. No other restrictions are placed on a semigroup; thus a ...

A separating family is a set of subsets in which each pair of adjacent elements are found separated, each in one of two disjoint subsets. The 26 letters of the alphabet can ...