Search Results for ""

A piecewise linear, one-dimensional map on the interval [0,1] exhibiting chaotic dynamics and given by x_(n+1)=mu(1-2|x_n-1/2|). (1) The first few iterations of (1) give x_1 ...

The triakis truncated tetrahedron is a convex space-filling polyhedron which is the shape of the Voronoi cell of carbon atoms in diamond. It can be constructed from the ...

Over a small neighborhood U of a manifold, a vector bundle is spanned by the local sections defined on U. For example, in a coordinate chart U with coordinates (x_1,...,x_n), ...

A web diagram, also called a cobweb plot, is a graph that can be used to visualize successive iterations of a function y=f(x). In particular, the segments of the diagram ...

Two points P,Q on a compact Riemann surface such that P lies on every geodesic passing through Q, and conversely. An oriented surface where every point belongs to a ...

A confidence interval is an interval in which a measurement or trial falls corresponding to a given probability. Usually, the confidence interval of interest is symmetrically ...

An irrational number x can be called GK-regular (defined here for the first time) if the distribution of its continued fraction coefficients is the Gauss-Kuzmin distribution. ...

Let S_n be the sum of n random variates X_i with a Bernoulli distribution with P(X_i=1)=p_i. Then sum_(k=0)^infty|P(S_n=k)-(e^(-lambda)lambda^k)/(k!)|<2sum_(i=1)^np_i^2, ...

The Mills ratio is defined as m(x) = 1/(h(x)) (1) = (S(x))/(P(x)) (2) = (1-D(x))/(P(x)), (3) where h(x) is the hazard function, S(x) is the survival function, P(x) is the ...

The mean of a distribution with probability density function P(x) is the first raw moment mu_1^', defined by mu=<x>, (1) where <f> is the expectation value. For a continuous ...