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The phrase dependent percolation is used in two-dimensional discrete percolation to describe any general model in which the states of the various graph edges (in the case of ...

A weakened version of pointwise convergence hypothesis which states that, for X a measure space, f_n(x)->f(x) for all x in Y, where Y is a measurable subset of X such that ...

In probability, an event with Lebesgue measure 1.

An ansatz is an assumed form for a mathematical statement that is not based on any underlying theory or principle. An example from physics is the Bethe Ansatz (Müller).

A complex map is a map f:C->C. The following table lists several common types of complex maps. map formula domain complex magnification f(z)=az a in R, a>0 complex rotation ...

A robust nonparametric test which is an alternative to the paired t-test. This test makes the basic assumption that there is information only in the signs of the differences ...

A method for predicting the onset of widespread chaos. It is based on the hypothesis that the dissolution of an invariant torus can be associated with the sudden change from ...

Let f(s) defined and analytic in a half-strip D={s:sigma_1<=R[s]<=sigma_2,I[s]>=t_0 0}. If |f|<=M on the boundary partialD of D and there is a constant A such that ...

A proposition is a mathematical statement such as "3 is greater than 4," "an infinite set exists," or "7 is prime." An axiom is a proposition that is assumed to be true. With ...

A set of methods that are generally superior to ANOVA for small data sets or where sample distributions are non-normal.