Sentence examples for all orders of the from inspiring English sources

The numerical tests confirm that the proposed method achieves spectral accuracy and ensures infinite differentiability to all orders of the numerical solution, by construction.

One choice is methods based on standard Chebyshev polynomials; although these may be efficiently computed using fast transforms, differentiability to all orders of the obtained solution at the origin is not guaranteed.

In [1] the regularized traces of all orders of the operator generated by the expression l ( y ) ≡ ( - 1 ) n d 2 n y d x 2 n + x y. and the boundary conditions ∑ j = 0 k m a m j y ( k m - j ) ( 0 ) = 0, m = 1, n ¯, a m 0 = 1, k n < k n - 1 < ⋯ < k 1 < 2 n. are obtained.

Two conditions each sufficient to guarantee this behaviour are: (i) that the normalized once-through residence-time density functions become independent of the recycle rate for recycle rates in excess of some finite value; or (ii) that the moments of all orders of the normalized density functions are bounded.

For an objective operating under the sine-condition, an axial shift of the diffraction-limited focus corresponds to a defocus and to all orders of the spherical aberrations [ 34].

As an example, CGTC repeats have been identified in all orders of the alpha subdivision, but are missing in several alpha-Proteobacteria, among which bacteria belonging to the families of Acetobacteraceae, Bartonellaceae and Brucellaceae.

Assuming this tree representing relationships among all orders of angiosperms, the probability of observing 10 gains and 0 losses of parasitism is < 0.001.

The decree confirmed also that all three orders of the College of Cardinals (bishops, priests and deacons) are equal in the papal elections.

We identified orthologs of these genes in all three orders of the Melainabacteria, suggesting that these are uniquely ancestral features of the phylum.

We consider the family of all ordered partitions of the users into nonempty groups.

Its main idea is to express the probability distribution characteristics by the expansion series made up of all-order derivatives of the standard normal distribution.