Sentence examples for conditions of case from inspiring English sources

(ii) Similarly, under the conditions of Case (ii), we can discuss the existence of nonnegative solutions.  .

Similarly, under the conditions of Case (ii), we can discuss the existence of nonnegative solutions.

Let U, V be a pair of unitary matrices satisfying the conditions of case (ii).

To see that, we consider the subsequence of all viable admissible discontinuity curves in the conditions of Case 3, which we can denote without loss of generality by ({gamma_{n}}_{n in{scriptsize mathbb {N}}}).

In particular, the optimal control model (28) reduces to model (2) under the conditions of case 4. We include four simulations which compare the structure of solutions for the rumor spreading problems in Figure 4 a-d).

Let us consider the subsequence of all viable admissible discontinuity curves in the conditions of Case 3, which we denote again by { γ n } n ∈ N to avoid overloading notation.

Moreover, the conditions of cases (1) and (3) are weaker than those of Theorem 3.1 and Theorem 3.2 in [12].

Since maximizing propylene is the main aim of this work, and cases 1 and 2 could achieve the same value of 8.93 wt%, any of the operating conditions of cases 1 or 2 can be used for optimal operation of the riser to produce optimum value of propylene, however, case 2 is preferable because of the difference of C/O ratio of 0.05.

In this step the researcher obtained a summary of observed conditions of cases for the outcomes of interest i.e. a summary of the combinations of variables defining individual cases.

However, one possible source of bias that could explain case control differences in the levels of insulin as well as IGFBP-1 would be the differences in fasting vs nonfasting conditions of cases and controls at the time of blood sampling as (IGFBP-1 levels drop acutely as insulin rises, after food consumption).

Fig. 3 Presurgical condition of case 2 patient before Le Fort I osteotomy (a, d), immediate after the Le Fort I osteotomy (b).