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Approximations to Khinchin's constant include K = -(ln85181832)/(tan8) (1) = 1/(29)sqrt(6065) (2) = 6-sqrt(ln59055) (3) = 18^(27/79), (4) which are correct to 9, 7, 6, and 5 ...

A robust estimation based on linear combinations of order statistics. Examples include the statistical median and the trimean.

Let f(x) be a finite and measurable function in (-infty,infty), and let epsilon be freely chosen. Then there is a function g(x) such that 1. g(x) is continuous in ...

The maximal independence polynomial I_G(x) for the graph G may be defined as the polynomial I_G(x)=sum_(k=i(G))^(alpha(G))s_kx^k, where i(G) is the lower independence number, ...

The mean square displacement (MSD) of a set of N displacements x_n is given by <|x|^2>=sum_(k=1)^N|x_k|^2. It arises particularly in Brownian motion and random walk problems. ...

Two objects form a mirror pair if one can be translated and rotated in such a way that the two objects together possess mirror symmetry, i.e., one is the mirror image of the ...

The second-order ordinary differential equation y^('')+[alpha/(cosh^2(ax))+betatanh(ax)+gamma]y=0.

A continuous homomorphism of a group into the nonzero complex numbers. A multiplicative character omega gives a group representation on the one-dimensional space C of complex ...

The "natural exponential function" is the name sometimes given in elementary contexts to the function f(x)=e^x, where e =2.718... is the base of the natural logarithm. While ...

Every irrational number x can be expanded in a unique continued fraction expansion x=b_0+(e_1)/(b_1+(e_2)/(b_2+(e_3)/(b_3+...)))=[b_0;e_1b_1,e_2b_2,e_3b_3,...] such that b_0 ...