Sentence examples for there exist unique from inspiring English sources

for all By the proof of Theorem 2.5, there exist unique additive mappings satisfying (3.7) and (3.9).

Since there exist unique geometric properties for linear pushbroom images, we argue that the conventional DEM generation schemes developed for perspective images are not suitable for satellite images.

Theorem 1 For a given function γ ∈ H, there exist unique functions h ∈ S and μ ∈ H such that A g = γ + h + i μ (17).

For any realization of channel matrix, there exist unique values of the Lagrange dual variables and for any Nash equilibrium of the game.

Since for any non-negative integer n and a positive integer b, there exist unique non-negative integers r and i such that n = b r + i with 0 ≤ i ≤ b − 1.

The Hungarian mathematician Csiszar, winner of Shannon prize, had also proved that for a group of information which is not contradictory, there exist unique entropy maximization models and their mathematical forms are exponential functions.

Since is continuous, there exists unique such that.

Then has a unique coupled fixed point in ; that is, there exists unique such that and.

Since is increasing for, we get that there exists unique constant such that (2.17) holds.

That is, there exists unique ( x, y ) ∈ X × X such that F ( x, y ) = x and F ( y, x ) = y.

There exists unique such that.