Sentence examples for exists a pair of from inspiring English sources

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.

Let J∗T v) denote the set of all integers s such that there exists a pair of disjoint S 2,4,v s intersecting in s triangles.

It is proved in this paper that for any v≡9 (mod 18), v⩾45, there exists a pair of Kirkman triple systems of order v having exactly k triples in common if and only if k∈{0,1,…,tv−6,tv−4,tv}, with the possible exception k=tv−4.

The flower intersection problem for Steiner systems is the determination of all pairs (v,suchuch that there exists a pair of Steiner systems (X,B1) and (X,B2) of order v having a common flower F satisfying |(B1∖F)∩(B2∖F)|="s.

Let Adm v)="{ s,t):s+t≤bv,s∈J v),2s+t∈JT v)}∖{(bv−3,1 }, where J v) (or JT v)) denotes the set of positive integers s (or t) such that there exists a pair of (K4−e -designs of order v intersecting in s blocK4−e -designsngles), and bv="v(v−1)/10.

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

In general, a set A is finite and its cardinality is n if there exists a pairing of its elements with the set {1, 2, 3, …, n}.

(Because the empty set has no elements, its cardinality is defined as 0.) In general, a set A is finite and its cardinality is n if there exists a pairing of its elements with the set {1, 2, 3, …, n}.

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.