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P_y(nu)=lim_(T->infty)2/T|int_(-T/2)^(T/2)[y(t)-y^_]e^(-2piinut)dt|^2, (1) so int_0^inftyP_y(nu)dnu = lim_(T->infty)1/Tint_(-T/2)^(T/2)[y(t)-y^_]^2dt (2) = <(y-y^_)^2> (3) = ...

The mean square deviation of the best local fit straight line to a staircase cumulative spectral density over a normalized energy scale.

A spectrum sequence is a sequence formed by successive multiples of a real number a rounded down to the nearest integer s_n=|_na_|. If a is irrational, the spectrum is called ...

A moving average using 15 points having weights -3, -6, -5, 3, 21, 46, 67, 74, 67, 46, 21, 3, -5, -6, and -3. It is sometimes used by actuaries.

F(x) = -Li_2(-x) (1) = int_0^x(ln(1+t))/tdt, (2) where Li_2(x) is the dilogarithm.

F(x) = Li_2(1-x) (1) = int_(1-x)^0(ln(1-t))/tdt, (2) where Li_2(x) is the dilogarithm.

Johnson solid J_(86).

Johnson solid J_(88).

Find the tunnel between two points A and B on a gravitating sphere which gives the shortest transit time under the force of gravity. Assume the sphere to be nonrotating, of ...

A curve on the surface of a sphere. Examples include the baseball cover, Seiffert's spherical spiral, spherical helix, and spherical spiral.