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Let suma_k and sumb_k be two series with positive terms and suppose lim_(k->infty)(a_k)/(b_k)=rho. If rho is finite and rho>0, then the two series both converge or diverge.

For two lines in the plane with endpoints (x_1,x_2) and (x_3,x_4), the angle between them is given by costheta=((x_2-x_1)·(x_4-x_3))/(|x_2-x_1||x_4-x_3|). (1) The angle theta ...

Two curves phi and psi satisfying phi+psi=0 are said to be linearly dependent. Similarly, n curves phi_i, i=1, ..., n are said to be linearly dependent if sum_(i=1)^nphi_i=0.

Loess local regression is a nonparametric technique for describing bivariate relationships where the functional form is not known in advance.

If all the eigenvalues of a real matrix A have real parts, then to an arbitrary negative definite quadratic form (x,Wx) with x=x(t) there corresponds a positive definite ...

A compact manifold admits a Lorentzian structure iff its Euler characteristic vanishes. Therefore, every noncompact manifold admits a Lorentzian structure.

A maximum likelihood estimator is a value of the parameter a such that the likelihood function is a maximum (Harris and Stocket 1998, p. 824).

The mean tetrahedron volume V^_ is the average volume of a tetrahedron in tetrahedron picking within some given shape. As summarized in the following table, it is possible to ...

The boundaries of the cells of a Voronoi diagram.

One million (10^6) bytes. Unfortunately, the term is sometimes also used to mean 2^(20)=1024^2=1048576 bytes. Furthermore, a third meaning of the term refers to 1024000 bytes ...