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The even part Ev(n) of a positive integer n is defined by Ev(n)=2^(b(n)), where b(n) is the exponent of the exact power of 2 dividing n. The values for n=1, 2, ..., are 1, 2, ...

A generalized Vandermonde matrix of two sequences a and b where a is an increasing sequence of positive integers and b is an increasing sequence of nonnegative integers of ...

An axiom proposed by Huntington (1933) as part of his definition of a Boolean algebra, H(x,y)=!(!x v y) v !(!x v !y)=x, (1) where !x denotes NOT and x v y denotes OR. Taken ...

The longest increasing (contiguous) subsequence of a given sequence is the subsequence of increasing terms containing the largest number of elements. For example, the longest ...

A type of cryptography in which the encoding key is revealed without compromising the encoded message. The two best-known methods are the knapsack problem and RSA encryption.

A random permutation is a permutation containing a fixed number n of a random selection from a given set of elements. There are two main algorithms for constructing random ...

A root-finding algorithm which assumes a function to be approximately linear in the region of interest. Each improvement is taken as the point where the approximating line ...

A square matrix U is a special unitary matrix if UU^*=I, (1) where I is the identity matrix and U^* is the conjugate transpose matrix, and the determinant is detU=1. (2) The ...

That part of a positive integer left after all square factors are divided out. For example, the squarefree part of 24=2^3·3 is 6, since 6·2^2=24. For n=1, 2, ..., the first ...

The multiplicative suborder of a number a (mod n) is the least exponent e>0 such that a^e=+/-1 (mod n), or zero if no such e exists. An e always exists if GCD(a,n)=1 and n>1. ...