Sentence examples for with respect to the mapping from inspiring English sources

where the second -inequality in (3.63) follows from the definitions of and, that contain all nonascending with respect to the mapping greater than,, respectively.

The so-called hierarchical variational inequality problem for a finite family of mappings { S i } with respect to the mapping T is to find an x ∗ ∈ F such that 〈 x ∗ − T x ∗, x ∗ − x 〉 ≤ 0, ∀ x ∈ F. (4.1).

An element is said to be nondescending (nonascending) with respect to the mapping if (3.58).

Then, the set of upper (lower) absorbing point with respect to the mapping is not empty.

It implies that is an upper (lower) absorbing point with respect to the mapping.

Since, the -inequality (3.67) implies that is nonascending with respect to the mapping, and, therefore, (3.68).

In this case, it is necessary to compute the camera pose with respect to the map again.

Denote by (V_infty ) the direct limit of the G-modules (V_n) with respect to the maps (iota _n).

Every convex function is preinvex with respect to the map η ( x, y ) = x − y, but not conversely.

In the tracking, the reconstructed map is tracked in the image to estimate the camera pose of the image with respect to the map.

Every convex function is a preinvex with respect to the map η ( x, y ) = x − y but the converse does not holds.