Sentence examples for suppose there exist from inspiring English sources

Assume det B ≠ 0 and ||A -1 B|| ≤ 1. Suppose there exist constants R > 0, α ≥ 0 such that.

Assume det B ≠ 0 and ||B -1 A|| ≤ 1. Suppose there exist constants R > 0, α ≥ 0 such that (3.1).

Let be a completely continuous map and be a nonnegative continuous concave functional on such that Suppose there exist with such that (i) and   (ii)   (iii) with  .

Suppose there exist N measurements (similarity) in a field then there are N values for the corresponding porosity data and we are trying to determine the values of three model parameters ((a,b,c)).

Let F : X × X → X be a mapping such that F has the mixed monotone property on X. Suppose there exist non-negative real numbers α, β, γ and L with β + γ < 1 such that (2.16).

Suppose there exist n nodes in graph G V,E,S), to find r paths by using MIDMRA to maximize their communication efficiency C, the time complexity would be polynomial.

Suppose there exists, with.

Suppose there exists constants such that.

Case 1. Suppose there exists such that for some.

Suppose there exists d > 0 such that μ < f 0 d ≤ ∞. (3.3).

Suppose there exists another optimal feedback operator ( widetilde Theta (cdot)).