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For a set of n numbers or values of a discrete distribution x_i, ..., x_n, the root-mean-square (abbreviated "RMS" and sometimes called the quadratic mean), is the square ...

Probability and Statistics

"Chaos" is a tricky thing to define. In fact, it is much easier to list properties that a system described as "chaotic" has rather than to give a precise definition of chaos. ...

Let u^_ denote the mean of a set of quantities u_i, then the absolute deviation is defined by Deltau_i=|u_i-u^_|.

Also known as the Leibniz criterion. An alternating series converges if a_1>=a_2>=... and lim_(k->infty)a_k=0.

The azimuthal angle is an angle measured from the x-axis in the xy-plane in spherical coordinates, denoted theta in this work.

The word basis can arise in several different contexts. Speaking in general terms, an object is "generated" by a basis in whatever manner is appropriate. For example, a ...

A second-order ordinary differential equation of the form

The function Pi_(a,b)(x)=H(x-a)-H(x-b) which is equal to 1 for a<=x<=b and 0 otherwise. Here H(x) is the Heaviside step function. The special case Pi_(-1/2,1/2)(x) gives the ...

The Casoratian of sequences x_n^((1)), x_n^((2)), ..., x_n^((k)) is defined by the k×k determinant C(x_n^((1)),x_n^((2)),...,x_n^((k))) =|x_n^((1)) x_n^((2)) ... x_n^((k)); ...