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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. ...

In the process of attaching a k-handle to a manifold M, the boundary of M is modified by a process called (k-1)-surgery. Surgery consists of the removal of a tubular ...

Plotting l_x from a life expectancy table on a logarithmic scale versus x gives a curve known as a survivorship curve. There are three general classes of survivorship curves, ...

The triangular distribution is a continuous distribution defined on the range x in [a,b] with probability density function P(x)={(2(x-a))/((b-a)(c-a)) for a<=x<=c; ...

A module having only one element: the singleton set {*}. It is a module over any ring R with respect to the multiplication defined by a*=* (1) for every a in R, and the ...

An unhappy number is a number that is not happy, i.e., a number n such that iterating this sum-of-squared-digits map starting with n never reaches the number 1. The first few ...

A unit is an element in a ring that has a multiplicative inverse. If a is an algebraic integer which divides every algebraic integer in the field, a is called a unit in that ...

A vector Laplacian can be defined for a vector A by del ^2A=del (del ·A)-del x(del xA), (1) where the notation ✡ is sometimes used to distinguish the vector Laplacian from ...

The vertex cover number is the size of a minimum vertex cover in a graph G is known as the vertex cover number of G, denoted tau(G). The König-Egeváry theorem states that the ...

The matrix product of a square set of data d and a matrix of basis vectors consisting of Walsh functions. By taking advantage of the nested structure of the natural ordering ...