Sentence examples for necessary for considering from inspiring English sources

First the basic principles necessary for considering mitigation measures related to hazard maps are defined.

It is a matter of judgement which hallmarks are deemed necessary for considering the dynamics truly chaotic; see [6] for examples and further discussion on this point.

We next prove that Green's function (G t,s)) in (2.8) satisfies a variety of properties that are necessary for considering the existence of a positive solution to problem (1.1).

Though this is not an article on the natural law, these points are necessary preliminaries for considering Grotius' natural law views.

This ensures that Dxy is always zero if x and y are identical, a necessary prerequisite for considering a formula a distance function (e.g., [ 60]: p. 274).

I've heard mixed views on whether or not a PhD is necessary for people considering industrial posts.

When limited resection has been performed for small-sized NSCLC presenting solid nodule on thin-slice CT images, long-term postoperative follow-up time will be necessary for monitoring, considering the possibility of cut-end recurrence.

In this paper, we first show that this condition is necessary for the considered mappings to have a fixed point.

The assumption (4.7) is also necessary for all considered boundary conditions simultaneously, but for a particular boundary condition it may be weakened.

The techniques of the proof of our theorems are more complex then in the corresponding previously published articles, since a new technique was necessary for the considered class of mappings.

Hence, the assessment of sodium concentration is necessary while considering the suitability for irrigation.