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The Radon-Nikodym theorem asserts that any absolutely continuous complex measure lambda with respect to some positive measure mu (which could be Lebesgue measure or Haar ...

If f:D->Y is a map (a.k.a. function, transformation, etc.) over a domain D, then the range of f, also called the image of D under f, is defined as the set of all values that ...

The distribution with probability density function and distribution function P(r) = (re^(-r^2/(2s^2)))/(s^2) (1) D(r) = 1-e^(-r^2/(2s^2)) (2) for r in [0,infty) and parameter ...

A number n is said to be refactorable, sometimes also called a tau number (Kennedy and Cooper 1990), if it is divisible by the number of its divisors sigma_0(n), where ...

Reversion to the mean, also called regression to the mean, is the statistical phenomenon stating that the greater the deviation of a random variate from its mean, the greater ...

A circle packing is called rigid (or "stable") if every circle is fixed by its neighbors, i.e., no circle can be translated without disturbing other circles of the packing ...

A sequence is an ordered set of mathematical objects. Sequences of object are most commonly denoted using braces. For example, the symbol {2n}_(n=1)^infty denotes the ...

The shah function is defined by m(x) = sum_(n=-infty)^(infty)delta(x-n) (1) = sum_(n=-infty)^(infty)delta(x+n), (2) where delta(x) is the delta function, so m(x)=0 for x not ...

A standard normal distribution is a normal distribution with zero mean (mu=0) and unit variance (sigma^2=1), given by the probability density function and distribution ...

Let a and b be nonzero integers such that a^mb^n!=1 (except when m=n=0). Also let T(a,b) be the set of primes p for which p|(a^k-b) for some nonnegative integer k. Then ...