Sentence examples for exist a pair of from inspiring English sources

We also provide an analytical proof of the D-optimality when there exist a pair of blocks of odd size and remaining blocks are of even size.

For example, it is shown that for ducted shear flows, there exist a pair of even and odd eigenfunctions, in the absence of critical levels.

For each case, there exist a pair of differential equations coupled in terms of the flexural displacement and the angle of rotation due to bending.

Similarly, since A 2 − 4 B > 0, F = 0, and there does not exist a pair of conjugate complex roots with modulus 1.

1. L K ( E ) has exponential growth if and only if there exist a pair of distinct cycles in E which are not disjoint.

L K ( E ) has exponential growth if and only if there exist a pair of distinct cycles in E which are not disjoint.

By introducing a definition for the coupled lower and upper solutions of BVP (1.1) and (1.2), we obtain the existence of solutions of the problem based on the assumption that there exists a pair of coupled lower and upper solutions.

Theorem 5 Assume that there exists a pair of lower and upper solutions of problem (1 - 2).

If there exists a pair of conjugate points on with respect to (1.12), then (1.14).

If the graph is not 3-connected, there exists a pair of vertices whose removal disconnects the graph.

It is wellknown that if there exists a pair of conjugate points in, then the classical Lyapunov inequality (1.11).