Sentence examples for cases there exists from inspiring English sources

In all cases there exists an optimum value of ρ maximizing the Jain Index.

therefore, in both cases there exists a integer such that (3.30).

In all these cases there exists a wide variation of Knudsen number within the geometries, as well as substantial compressibility despite the Mach number being very low.

Hence in both cases there exists ( x n k ) k ∈ N such that lim k → ∞ x n k = x.

Then, to quantify a potential decrease in our coverage results when the semantics of Stack Overflow posts is taken into account, we manually analyzed a sample of threads to investigate in how many cases there exists content for documenting API elements in how-to-do-it and debug-corrective discussions.

While indeed general graph matching methods to solve (4) can be applied to solve (2), we show in the next section that in some cases there exists a simple polynomial time algorithm to solve (2) directly even for large non-sparse graphs.

In many cases there exist more than one crack on the shaft.

For several cases there exist analytical solutions for this ODE system, which have been reported elsewhere [ 3, 5].

In the classical case, there exists the canonical embedding of n-dimensional Toda lattice ↪n+1-dimensional Toda lattice.

In this case, there exists at least one true literal in each clause.

In the other case, there exists at least one arc and the leftmost one is k1 k1.