Sentence examples for exists a case from inspiring English sources

In general, R o and R i r do not necessarily contain one another; however, there exists a case in which R o ( Z ) ⊆ R i r ( Z ).

For each region, there exists a case for which no rate splitting determines the overall region, i.e., each achievable rate region is obtained at λ = 0 or λ = 1.

Show that there exists a case in which R i r contains R o. Analyze the effect of rate splitting in a Gaussian setup where a necessary and sufficient condition is determined so that the union of the above regions is obtained without rate splitting.

Moreover, we have shown that there exists a case for which allowing the secondary receiver to decode a primary signal results in an achievable rate region that includes the achievable rate region obtained when the secondary receiver does not decode the primary signal.

Although there exists a case in which the CR model outperforms the IR model [34], a number of authors have recently begun to notice that the IR model is superior to the CR model in approximating the evolution of evolutionary rates in several cases [17], [35] [37].

However, there also exists a case report of limb amputation secondary to a tibial artery catheterization [ 67].

However, there exists a real case dealing with cotton spinning in which the three quality characteristics are Fiber Length, Fiber Strength, and Skein Strength.

If there exists a such that Case holds, then exists, and we claim that Otherwise, We can choose some positive integer such that for Thus, we obtain (2.23).

If there exists a such that case (2) holds, then exists, and We claim that Otherwise, We can choose some positive integer such that for Thus, we obtain.

If there exists a such that case (ii) holds, then exists, and ; we claim that Otherwise, We can choose some positive integer such that for and we obtain (2.13).

However, there exists an interesting border case, in which a model can be further reduced without affecting the input/output behavior.