Sentence examples for extend known from inspiring English sources

The results extend known results for Banach modulation spaces.

When coupled with uniform estimates, this method provides a strategy to extend known Riemannian results to the subRiemannian setting.

For typical examples, such as spatially one-dimensional stochastic heat equations with additive or multiplicative perturbations of fractional Brownian type, we recover and extend known results.

We show how to extend known interior point methods devised for linear programming to piecewise linear programming without resorting to equivalent linear programs.

We extend known reformulation approaches to reformulate the general 0 1 fractional programming problem such that it can be solved by standard MILP software.

Here we characterize the transcriptional landscape of the four human HOX loci at five base pair resolution in 11 anatomic sites and identify 231 HOX ncRNAs that extend known transcribed regions by more than 30 kilobases.

This extends known results for sublinear operators and improves some results for bilinear operators.

Our generator naturally extends known pseudorandom generators against advised regular languages.

Signal extrapolation is an important task in digital signal processing for extending known signals into unknown areas.

We prove that these spaces are additionally norm-equivalent, thus extending known results for and the polydisk.

Note in Theorem 4.1 Thus our Theorem 4.1 extends known description of diagonal of classical Bergman classes (see [1, 7]).