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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 ...

A connective in logic known as the "exclusive or," or exclusive disjunction. It yields true if exactly one (but not both) of two conditions is true. The XOR operation does ...

Discrete Mathematics

The constant e with decimal expansion e=2.718281828459045235360287471352662497757... (OEIS A001113) can be computed to 10^9 digits of precision in 10 CPU-minutes on modern ...

The objective of global optimization is to find the globally best solution of (possibly nonlinear) models, in the (possible or known) presence of multiple local optima. ...

If F is an algebraic Galois extension field of K such that the Galois group of the extension is Abelian, then F is said to be an Abelian extension of K. For example, ...

The polynomials a_n^((beta))(x) given by the Sheffer sequence with g(t) = (1-t)^(-beta) (1) f(t) = ln(1-t), (2) giving generating function ...

The combining of two or more quantities using the plus operator. The individual numbers being combined are called addends, and the total is called the sum. The first of ...

The coordinates representing any point of an n-dimensional affine space A by an n-tuple of real numbers, thus establishing a one-to-one correspondence between A and R^n. If V ...

An algebraic equation in n variables is an polynomial equation of the form f(x_1,x_2,...,x_n)=sum_(e_1,...,e_n)c_(e_1,e_2,...,e_n)x_1^(e_1)x_2^(e_2)...x_n^(e_n)=0, where the ...