Sentence examples for weak regularity from inspiring English sources

We show that these conclusions still hold under weak regularity hypotheses and without any gap condition.

It is known that, under some weak regularity assumptions, the MMSE estimator is given by θ ^ MMSE = E { θ | y }.

Moreover, we show that in some cases the weak regularity of boundary conditions is also necessary for the completeness.

Our results yield the existence of unstable solutions, localized by means of α and β, requiring weak regularity of the coefficients of the equation.

While those estimators have desirable asymptotic properties under weak regularity conditions, simulation studies have shown these estimators to exhibit a small sample bias in the opposite direction of the least squares bias for censored data.

It turns out that, provided that some very weak regularity conditions are met, the range of the effective diffusivity matrix can be read off the shape of the support of the invariant measure for the periodic diffusion.

The effects of light and humidity on quality traits showed weaker regularity compared to temperature.

Finally, all estimates in Proposition 27 hold under these weaker regularity assumptions.

Our approach allows us to prove the result directly for kth order differential inclusions, under weaker regularity assumptions on the involved multifunction.

In 1938 Morrey observed that a weaker regularity sufficed in order that the solutions in elliptic differential equations were smooth [1].

Then for (nu (varepsilon )= O varepsilon |log varepsilon |^{-1})),36 we can recover the remainder estimate (O(h^{1-d})); under even weaker regularity conditions by rescaling, we can recover weaker remainder estimates.