Sentence examples for necessary estimates for from inspiring English sources

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

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

In this section, we collect some known results about the auxiliary function ρ ( x ) and some necessary estimates for the kernel of the Riesz transform in the paper (cf. [20] or [7]).

This was necessary because estimates for incidence and mortality were imprecise for less frequent conditions.

Of these, 151 (86.3%) provided an estimate of their weight, 109 (62.3%) an estimate of height, and 170 (97.1%) a Stunkard assessment for a total of 92 (52.3%) women with the necessary BMI estimates for validation (see Table  1 for participant demographics).> Participants were first asked to estimate their current height and weight.

So we just need to establish a necessary energy estimate for the classic solution ( u ε, v ε ) and then establish the existence of weak solution of the initial boundary value problem by letting ε → 0. For convenience, here and below, C denotes various positive constants independent of ε.

After verifying the compactness of the operator and some necessary a priori estimates for the solutions, we then obtain a fixed point of the operator in a suitable functional space with σ = 1, which is the desired solution of problem (1.1 - 1.3).

Rates of meningococcal disease were calculated using demographic data for Philadelphia County from the 1990 and 2000 US censuses, with linear interpolation and extrapolation used as necessary to generate estimates for age and sex strata in between-census years (22).

The noncancer effects were not considered because of difficulties in estimating the exposure response relationships and the other input parameters necessary for estimating DALYs; therefore, the estimates were calculated by first assuming all attributable cancer cases fatal during the first year after clinical detection and then using PAF from Equation 4 in method 2a.

Such models are necessary for estimating the potential for adaptation to reduce the projected negative consequences of climate change.

In studies that require lifelong exposures, it may be necessary to make informed estimates for previously occurring exposures.