Sentence examples for integral cases from inspiring English sources

In both discrete and integral cases, the point c belongs to the convex hull of the set (mathcal{S}), as the smallest convex set containing (mathcal{S}).

First of all, we consider the time-independent first integral case, that is, (I_{t}=0).

The correlation between barycenters, Jensen's inequality and convexity is studied in the integral case.

The following theorem can be regarded as a majorization theorem in integral case [1, page 325].

The integral case of the above theorem can be given as follows.

Seven interruptions of fin are explored and compared with the integral case.

The proofs are similar to those in the integral case given in the previous section, so we will state these results without the proofs.

The proofs are similar to those in the integral case given in the previous section, so we give these results with the proofs omitted.

The intention of this paper is still more to connect the quoted implication (in the extended form) with convex functions, in the discrete and integral case.

Obviously, the result obtained in this paper can be analogously given for the Riemann-Stieltjes integral case after some minor modifications.

The percentage variation in heat transfer coefficient for the interrupted fins as compared with the integral case is in the range of –9.3%to+43.6%6% while the percentage variation in the pressure drop is in the range of –43.5% to –92.7%.