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A function f(n) has the normal order F(n) if f(n) is approximately F(n) for almost all values of n. More precisely, if (1-epsilon)F(n)<f(n)<(1+epsilon)F(n) for every positive ...

For a curve with radius vector r(t), the unit tangent vector T^^(t) is defined by T^^(t) = (r^.)/(|r^.|) (1) = (r^.)/(s^.) (2) = (dr)/(ds), (3) where t is a parameterization ...

Vector subtraction is the process of taking a vector difference, and is the inverse operation to vector addition.

The word "normal form" is used in a variety of different ways in mathematics. In general, it refers to a way of representing objects so that, although each may have many ...

Let H be a subgroup of a group G. The similarity transformation of H by a fixed element x in G not in H always gives a subgroup. If xHx^(-1)=H for every element x in G, then ...

A vector whose elements are complex numbers.

A real number that is b-normal for every base 2, 3, 4, ... is said to be absolutely normal. As proved by Borel (1922, p. 198), almost all real numbers in [0,1) are absolutely ...

A unit vector is a vector of length 1, sometimes also called a direction vector (Jeffreys and Jeffreys 1988). The unit vector v^^ having the same direction as a given ...

A vector whose elements are real numbers.

A normal extension is the splitting field for a collection of polynomials. In the case of a finite algebraic extension, only one polynomial is necessary.