Sentence examples for with respect to ordering from inspiring English sources

If is comparable to with respect to ordering in, then (3.1).

Also in the sequel, we will consider that and are comparable with respect to ordering in if and.

If for every there exists that is comparable to and with respect to ordering in, then there exists a unique coupled point of coincidence of and.

The resulting Landau plots (free energy versus order parameter) have pointed out the temperatures below which instabilities with respect to ordering develops.

Definition 2.11 (see [10]). is called a superefficient point of a subset of with respect to ordering cone, written as, if, for each neighborhood of, there is neighborhood of such that (2.16).

( S, d X ) and ( T, d Y ) be ordered metric spaces, with respect to ordered vector spaces ( X, ≽ X ) and ( Y, ≽ Y ), respectively.

How specific is it, for example, with respect to orders given, and personnel involved in the attacks of 21 August?

"In Truth I found myself incorrigible with respect to Order; and now I am grown old, and my Memory bad," he wrote in 1784; "I feel very sensibly the want of it".

That is, each block appears in the same number of booklets, each time paired with a different block and balanced overall with respect to order.

Recently, Alam et al. [10] adopted the notions of completeness and continuity with respect to order-theoretic metrical structure, which run as follows.

Then we can explore some fixed point theorems similar to Theorem 3.4 with respect to order-decreasing upward (downward) set-valued mappings with values of reversed universally inductive posets.