Sentence examples for most general assumptions from inspiring English sources

Necessary and sufficient conditions of optimality under the most general assumptions are deduced for the considered and for discrete approximation problems.

It is demonstrated that, even under these most general assumptions, the power-law left tail is preserved in the bundle and the tail exponent of the bundle is the sum of the exponents of the power-law tails of all the fibers.

The second issue, that is the center point of the present article, is the most general assumptions upon which these traditional estimation methods are based.

These results tell us that the joint distribution specified in Eq. (3) has the most general form under the assumption of exponential family node-conditional distributions.

In the most general case, a standard assumption for a GLMM with both random intercept and slope is that b i =(b0 i, b1 i ) Tfollows a bivariate normal distribution with mean zero and an unknown precision matrix Q= Q depending on parameters ϕ, i.e. b i | Q ∼ iid N 2 (0, Q − 1 ).

Moreover, the study is done in the most general case, without any additional assumptions concerning the flow or the cocycle.

Instead of using the common von Karman assumptions, the most general form of the strain tensor in curvilinear coordinates is used.

We introduce a new and natural admissibility concept and we show that the trichotomic behavior of skew-product flows can be studied in the most general case, without any additional assumptions.

The statistical average in Eq. (35) for the most general case, where no statistical assumption on the distribution of noise is required, is expressed as: mu = frac{1}{{NL}}sumlimits_{n = - N/2}^{N/2} {sumlimits_{i = 0}^{L - 1} {textbf{w}_{n}^{H} left(l right)textbf{R}_{upsilon} textbf{w}_{n}^ left(l right)}.

By an example we show that the stability result is the most general in the topic and that the assumptions on the underlying sequence spaces cannot be removed.

General assumptions that cropland is the most sensitive area to wind erosion and heavily and moderately grazed grasslands are both sensitive etc. can be refined by the modelling of CFD-WEM.