Sentence examples for regularity of the data from inspiring English sources

Various error estimates are derived, depending on the regularity of the data and on the choice of the finite elements.

The approximate entropy is an entropy metric that takes into consideration the ordering of the points of the discrete time sequence at hand, and hence, it is a good measure for the regularity of the data sequence.

In 1963, Meyers' counterexample in [29] demonstrates that the gradient of weak solutions to elliptic equations corresponding to highly oscillatory coefficients cannot be expected to have higher integrability irrespective of the regularity of the data (f(x)).

The contents of malic, citric, and total acid were determined to indicate fruit acidity and the regularity of the data were confirmed.

However, the precision and regularity of the data, and the collection of serial samples from each ST mother, argue that the results give accurate estimates of monthly percentage declines.

For quasi-optimal rates of the discretization error in the sense of   Theorem  4.5, additional regularity of the data has to be imposed for higher-order elements p ≥ 1, cf.   Consequence  5.2.

As a result, the underlying regularities of the data can be captured, leading to better performance, e.g., in recognition [23].

Measures of amplitude and signal regularity of the acceleration data were performed.

It allows us to circumvent difficulties stemming from the fact that the evolution does not improve the qualitative regularity of the initial data.

124 (2006 (2006) 747 779] implies the strong convergence in Sobolev norms and in the L1 norm towards it depending on the regularity of the initial data.

In the spatially homogeneous case, we first prove that the analytical solution preserves the regularity of the initial data in the random space, and then use it to establish the spectral accuracy of the proposed stochastic Galerkin method.