Sentence examples for which we explicitly from inspiring English sources

Toward this end, a simplified version of the problem is considered for which we explicitly characterize the optimal solution.

Assuming that λ→∞, we demonstrate that the minimizers of Eλ converge in H1(A) to an S1-valued harmonic map which we explicitly identify.

Next, we describe recent investigations conducted in our laboratory in which we explicitly adopt a neural-system perspective in examining the relations among these networks in MDD.

We are very clear that are not offering exact numbers, as that would likely involved insider information (in the case of private companies, of course), which we explicitly forbid in our terms of use and code of conduct.

Lastly, even if this type of measure can be criticized because of interpersonal comparison issues, authors prove that some econometric models tackle these problems [22] (see "Robustness checks" subsection for some robustness checks in which we explicitly consider this issue).

We use two avenues to obtain our results: a direct approach in which we explicitly construct a faithful, algebraically irreducible representation of the algebra on a separable Hilbert space, as well as an indirect, algebraic approach which utilizes the prime ideal structure of the algebra.

In fact, we are interested only in the associated Riemannian distance, which we describe explicitly.

We will use the following, which will be proved in the next section: ((VC1′) is a variant of (VC1) which we prove explicitly in the next section).

Note that there are many cases in which the three species coexist at the end of the simulations, which we discuss explicitly in the following section.

For a comparative evaluation, we selected five tools for which we could explicitly choose the used reference genomes to provide a strict separation between training and test data.

This is due to the addition of the upper fluid layer region which was not present in Pearson et al. (2013), and in which we can explicitly solve for the reduced water pressure.