Sentence examples for includes the case that from inspiring English sources

We also observe the condition (C4) that lim sup n → ∞ α n < 1 <span class="lh">includes the case that α n = 0 as a special case.

Theorem 3.4 includes the case that for λ close to λ k + 1 A from the right-hand side, the linking with respect to E k + 1 ⊕ E k + 1 ⊥ is constructed provided the negative values of F are small.

This includes the case that even if the same message is being transmitted multiple times, the adversary still cannot link them together without knowing all the private keys of the intermediate nodes.

Unlike (P_{ii}(r,theta,phi )), (L_i r,theta,phi )) can be utilized to examine the continuous connectivity of the insulation phase for a specific direction because the function only includes the case that a whole line is positioned in the insulation phase Lu and Torquato (1992); therefore, (L_i r,theta,phi )) can be utilized as a complementary function of (P_{ii}(r,theta,phi )).

This definition of Z I also includes the case that i and j are base paired in the recursion (1).

The latter includes the cases that, besides the description of the food system, arrive to a selection of proper indicators with a varying level of in-depth examination.

In this section, we will study the existence of the traveling wave fronts to this equation (1.1) with general types of kernel functions, which includes the cases that have been studied before.

Finally, with 18 genes, class IV includes the cases that were re-annotated in this work with levels of information lower than those available in KEGG.

These include the case that resulted in the damning court ruling on Wednesday that Leeds unfairly dismissed and sexually discriminated against their former academy welfare officer Lucy Ward.

CDKN2A FISH was negative for deletion in 4 WDPMs tested (including the case that developed MM) and all 8 adenomatoid tumors.

He ran some of the United States' biggest doping investigations in recent history, including the case that helped bring down Lance Armstrong, the seven-time Tour de France winner who was found to have doped for most of his career.