Sentence examples for generalized contours from inspiring English sources

In this paper, we will present an algebraic condition, see (20), which guarantees that a canal surface, given by its rational medial axis transform (MAT), possesses rational generalized contours (i.e., contour curves with respect to a given viewpoint).

Thus, this phase necessitates the historian withdrawing or 'zooming out' from the day-to-day lived experiences of historical actors to view the more generalized contours of historical change.

There is a generalized form as well.

To this end, we assume that a random vector X=(X 1,…,X d ) T follows an axes-aligned p-generalized elliptically contoured distribution having density generating function g and vector of scaling parameters a, (Xsim Phi _{g, B_{a,p}}).

Section 4 deals with testing equality of scaling parameters of principal components of general, i.e. arbitrarily rotated, p-generalized elliptically contoured p-power exponential distributions.

This class includes that of p-generalized elliptically contoured distributions.

Derivations are omitted in the sections on Gaussian and axes-aligned p-generalized elliptically contoured distributions.

In the present paper, geometric and stochastic representations are derived for the big class of p-generalized elliptically contoured distributions.

More specific distributions are l n,p -symmetric and p-generalized elliptically contoured distributions considered, e.g., in (Richter 2012, 2014), respectively.

A closely related but nevertheless rather different study in Richter (2016) compares scaling parameters of two-dimensional axes-aligned p-generalized elliptically contoured distributions.

We remark that the present statistic becomes the same as that in the axes-aligned p-generalized elliptically contoured case in Section 3 if (hat alpha =tilde alpha in left {0,frac {pi }{2}right }) and μ 1=μ 2=0.