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For a power function f(x)=x^k with k>=0 on the interval [0,2L] and periodic with period 2L, the coefficients of the Fourier series are given by a_0 = (2^(k+1)L^k)/(k+1) (1) ...

Power formulas include sin^2x = 1/2[1-cos(2x)] (1) sin^3x = 1/4[3sinx-sin(3x)] (2) sin^4x = 1/8[3-4cos(2x)+cos(4x)] (3) and cos^2x = 1/2[1+cos(2x)] (4) cos^3x = ...

A power floor prime sequence is a sequence of prime numbers {|_theta^n_|}_n, where |_x_| is the floor function and theta>1 is real number. It is unknown if, though extremely ...

Informally, self-similar objects with parameters N and s are described by a power law such as N=s^d, where d=(lnN)/(lns) is the "dimension" of the scaling law, known as the ...

Let lambda be (possibly complex) eigenvalues of a set of random n×n real matrices with entries independent and taken from a standard normal distribution. Then as n->infty, ...

An object is said to be self-similar if it looks "roughly" the same on any scale. Fractals are a particularly interesting class of self-similar objects. Self-similar objects ...

A scale-free network is a connected graph or network with the property that the number of links k originating from a given node exhibits a power law distribution ...

No A is not-A.

If bc=bd (mod a) and (b,a)=1 (i.e., a and b are relatively prime), then c=d (mod a).

Gibrat's distribution is a continuous distribution in which the logarithm of a variable x has a normal distribution, P(x)=1/(xsqrt(2pi))e^(-(lnx)^2/2), (1) defined over the ...