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There exists an absolute constant C such that for any positive integer m, the discrepancy of any sequence {alpha_n} satisfies ...

The series sumf(n) for a monotonic nonincreasing f(x) is convergent if lim_(x->infty)^_(e^xf(e^x))/(f(x))<1 and divergent if lim_(x->infty)__(e^xf(e^x))/(f(x))>1.

A Euclidean motion of R^n is an affine transformation whose linear part is an orthogonal transformation.

A special case of the Artin L-function for the polynomial x^2+1. It is given by L(s)=product_(p odd prime)1/(1-chi^-(p)p^(-s)), (1) where chi^-(p) = {1 for p=1 (mod 4); -1 ...

Expansion is an affine transformation (sometimes called an enlargement or dilation) in which the scale is increased. It is the opposite of a geometric contraction, and is ...

Factor analysis allows the determination of common axes influencing sets of independent measured sets. It is "the granddaddy of multivariate techniques (Gould 1996, pp. ...

Let f(theta) be Lebesgue integrable and let f(r,theta)=1/(2pi)int_(-pi)^pif(t)(1-r^2)/(1-2rcos(t-theta)+r^2)dt (1) be the corresponding Poisson integral. Then almost ...

The inverse curve of Fermat's spiral with the origin taken as the inversion center is the lituus.

The Fibonacci chain map is defined as x_(n+1) = -1/(x_n+epsilon+alphasgn[frac(n(phi-1))-(phi-1)]) (1) phi_(n+1) = frac(phi_n+phi-1), (2) where frac(x) is the fractional part, ...

The statistical index P_B=sqrt(P_LP_P), where P_L is Laspeyres' index and P_P is Paasche's index.