Sentence examples for the bound provides from inspiring English sources

Nevertheless, the bound provides a benchmark for evaluating the performance of the proposed estimator.

This outer bound is similar to the bound provided in [16] obtained using a different approach.

They report that their upper bound based on submodular maximization which is comparable to our objective cuts performs not as good as the bound provided by concave relaxation.

However, the bound provided here allows us to prove the complete convergence, and in the unconditional case, under assumptions different from those of Theorem 3.3 of Shen et al. [3].

In this way, a bound on the maximum number of equilibria can be provided independently of the exact channel realizations and only relying on the parameters K and S. Indeed, this is one of the main properties of the bound provided by Proposition 1 since, a calculation of the exact number of NE becomes cumbersome when the number of transmitters K and channels S grows to infinity.

The tests also allow an analysis of the gap of the bounds provided by linear relaxation.

Obviously, the bounds provided by Theorem 4.2 also hold for the deterministic equation (3) which justifies our claim in the introduction.

However, the bounds provided by the available inequalities in analyzing the dependence of solutions on the initial data for fractional differential equations involving Fredholm integral operators are not adequate.

But in the analysis of some certain difference equations, the bounds provided by the earlier inequalities are inadequate and it is necessary to seek some new discrete inequalities in order to obtain a diversity of desired results.

If in inequality (15) we set (k=K=1), that is, (r_{ij}= 1) for all ((i,j) in E), we get frac{m m-n+1)}{n-1} le CW(G) lefrac{m m-n+1)}{2} i.e. the bounds provided by Yang in [18], Theorem 3.13 and Corollary 3.14 for the global cyclicity index.

We apply our static model with those approaches and compare the performance to the upper bound provided by the dynamic model (which assumes perfect knowledge of the future).