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Let r be the correlation coefficient. Then defining z^'=tanh^(-1)r (1) zeta=tanh^(-1)rho, (2) gives sigma_(z^') = (N-3)^(-1/2) (3) var(z^') = 1/n+(4-rho^2)/(2n^2)+... (4) ...

An action with G=R. Flows are generated by vector fields and vice versa.

Consider a symmetric triangle wave T(x) of period 2L. Since the function is odd, a_0 = 0 (1) a_n = 0, (2) and b_n = (3) = (32)/(pi^2n^2)cos(1/4npi)sin^3(1/4npi) (4) = ...

Let R(x) be the ramp function, then the Fourier transform of R(x) is given by F_x[R(x)](k) = int_(-infty)^inftye^(-2piikx)R(x)dx (1) = i/(4pi)delta^'(k)-1/(4pi^2k^2), (2) ...

If F is a group, then the extensions G of F of order o with G/phi(G)=F, where phi(G) is the Frattini subgroup, are called Frattini extensions.

A congruence of the form f(x)=g(x) (mod n), where f(x) and g(x) are both integer polynomials. Functional congruences are sometimes also called "identical congruences" (Nagell ...

The gabled rhombohedra are a family of elongated gyrobifastigium that are space-filling. The equilateral elongated gyrobifastigium, illustrated above, is one such example.

Let Pi be a permutation of n elements, and let alpha_i be the number of permutation cycles of length i in this permutation. Picking Pi at random, it turns out that ...

The dual of the great ditrigonal dodecicosidodecahedron U_(42) and Wenninger dual W_(81).

A partially ordered set is defined as an ordered pair P=(X,<=). Here, X is called the ground set of P and <= is the partial order of P.