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The rth sample central moment m_r of a sample with sample size n is defined as m_r=1/nsum_(k=1)^n(x_k-m)^r, (1) where m=m_1^' is the sample mean. The first few sample central ...

The concurrence S of the Euler lines E_n of the triangles DeltaXBC, DeltaXCA, DeltaXAB, and DeltaABC where X is the incenter. It has equivalent triangle center functions ...

To pick a random point on the surface of a unit sphere, it is incorrect to select spherical coordinates theta and phi from uniform distributions theta in [0,2pi) and phi in ...

Abstract Algebra

Let V be an n-dimensional linear space over a field K, and let Q be a quadratic form on V. A Clifford algebra is then defined over T(V)/I(Q), where T(V) is the tensor algebra ...

A differential-algebraic equation (DAE) is a type of differential equation in which the derivatives are not (in general) expressed explicitly, and typically derivatives of ...

There are at least two definitions of hypercomplex numbers. Clifford algebraists call their higher dimensional numbers hypercomplex, even though they do not share all the ...

The Pauli matrices, also called the Pauli spin matrices, are complex matrices that arise in Pauli's treatment of spin in quantum mechanics. They are defined by sigma_1 = ...

A formula which transforms a given coordinate system by rotating it through a counterclockwise angle Phi about an axis n^^. Referring to the above figure (Goldstein 1980), ...

An untraceable graph is a graph that does not possess a Hamiltonian path, i.e., one that is not traceable. All disconnected graphs are therefore untraceable. Untraceable ...