Sentence examples for normed distance from inspiring English sources

If split into two parts of equal Minkowskian lengths, then the normed distance of these points is called halving distance of     in direction  .

Strongly related to isoperimetric problems, in [36] the lower bound for the geometric dilation of a rectifiable simple closed curve in Minkowski planes is obtained; note that the geometric dilation is the supremum of the quotient between the Minkowski length of the shorter part of between two different points and of it, and the normed distance between these points.

The computation time of the EM algorithm increased as the normed distance between ϕ0 and the alternative starting value increased.

In general, the normed distance from ϕ ^ to the final estimate obtained by an alternative starting value was small and the corresponding log likelihood values were close.

This distance was generalized to the p-angular distance in normed space in [4].

In this section, let be a normed space supplied with a distance, and let be a subset of.

Suppose that is a positive integer, is a normed space supplied with a distance and is a subset of.

Let E ⊂ X be a nonempty convex set and G : E → 2 Z be a set-valued map with G ( x ) ≠ ∅, for all x ∈ E. G is said to be D-convex on E, if for any x 1, x 2 ∈ E and λ ∈ ( 0, 1 ), λ G ( x 1 ) + ( 1 − λ ) G ( x 2 ) ⊆ G ( λ x 1 + ( 1 − λ ) x 2 ) + D. Let X be a normed space supplied with a distance d and K be a subset of X.

Define p : X × X → R + by p ( x, y ) = ( 1 4 ) x 2. Then p is a u-distance on X but not a τ-distance on X. Example 1.3 Let X be a normed space with norm ∥ ⋅ ∥.

As a consequence of Theorem 2.4 we present the next result which is an extension of the corresponding results of [6] and [7], respectively, from metric space and normed space to the τ-distance.

Let be a normed space with norm.