Sentence examples for the above defined from inspiring English sources

with the above defined matrices,.

Now, substituting the above defined expressions in the problems (WHP) and (WHD), we get.

Let us consider the transition from state to state in the above defined Markov chain.

The above defined function is a metric (see [19, Lemma  3.1]).

Let us give an example which will illustrate the role of the above defined notions.

In the case of correct reception, the above defined condition for QEF reception is satisfied.

Table 8 lists the above-defined optimal set of predictor variables model by model and Table 9 shows the corresponding model performance.

Thus the above-defined mappings are decreasing, and hence their limits exist in as.

Varying the above-defined ratio resulted in a commensurate change of the density of the NPs on the surface.

Further, we can impose some suitable conditions on the above-defined functions to verify the assumptions on Theorem 3.1.

With Patch Analyst 5.0.1.60 (Rempel et al. 2012), we analyzed different characteristics of the above-defined landscape elements.