Sentence examples for necessary estimates from inspiring English sources

First, we give some necessary estimates for P k, R k and T τ.

The following lemma from [1] contains necessary estimates of the solution to (1.1).

Here, the necessary estimates are split into several parts which are separately considered in the following.

In this paper, we prove the necessary estimates for the proof of an existence theorem of asymptotically almost periodic solutions for (1.1).

The necessary estimates of the expected variance in species richness across areas were derived from a prior project on biodiversity patterns in Austrian agricultural landscapes [36].

In order to prove the solvability of the linear case with we establish necessary estimates applying the result of Di Blasio et al. [9] to (1.1)–(1.5) considered as an equation in as well as.

If necessary, estimate the number of sources, K.   4.

The empirical results state that knowing, or if necessary estimating from past occupations, two spouses' current occupations, helps predict whether their marriage will dissolve.

Together with your real estate agent, perform a preliminary feasibility analysis, in which you identify the repairs necessary, estimate the cost of these repairs, and estimate the market value of the home after the repairs.

This will be based on some more-pessimistic-than-necessary estimates of data that are not yet available.

A local center stable manifold theorem is given after deriving some necessary integral estimates involving well-known Mittag-Leffler functions.