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The set of octonions, also sometimes called Cayley numbers and denoted O, consists of the elements in a Cayley algebra. A typical octonion is of the form ...

The operator norm of a linear operator T:V->W is the largest value by which T stretches an element of V, ||T||=sup_(||v||=1)||T(v)||. (1) It is necessary for V and W to be ...

An integer-relation algorithm which is based on a partial sum of squares approach, from which the algorithm takes its name.

The parabiaugmented hexagonal prism is a convex equilateral solid that is Johnson solid J_(56). The parabiaugmented hexagonal prism has volume V=1/6(2sqrt(2)+9sqrt(3)) (1) ...

In three dimensions, a parallelepiped is a prism whose faces are all parallelograms. Let A, B, and C be the basis vectors defining a three-dimensional parallelepiped. Then ...

A pentagonal pyramid is pyramid having a pentagonal base. The edge length e and slant height s of a pentagonal pyramid with regular base of side length a are given by e = ...

The term perimeter refers either to the curve constituting the boundary of a lamina or else to the length of this boundary. The perimeter of a circle is called the ...

A graphical plot with abscissa given by the number p of consecutive numbers constituting a single period and ordinate given by the correlation ratio eta. The equation of the ...

Two lines, vectors, planes, etc., are said to be perpendicular if they meet at a right angle. In R^n, two vectors a and b are perpendicular if their dot product a·b=0. (1) In ...

Polynomials s_k(x;lambda,mu) which are a generalization of the Boole polynomials, form the Sheffer sequence for g(t) = (1+e^(lambdat))^mu (1) f(t) = e^t-1 (2) and have ...