Sentence examples for refinement function from inspiring English sources

A function (phiin L_{2}(mathbb{R})) is refinable if it satisfies the following refinement equation: phi=2sum_{kinmathbb{Z}}a k phi 2cdot-k), (2.1) where a is a finitely supported sequence on (mathbb{Z}}a k phi 2cdot-kfinement mask of the refinement function ϕ.

Modeller produces slightly fewer bumps, thanks to its model refinement function.

Consequently, Assemble provides a geometric refinement function to optimize structural parameters like nucleotide stereochemistry, all the base base interactions, the sugar pucker and atoms distances.

Possible applications of MGcV include: annotation refinement, function prediction on basis of a (phylogenetic) tree and conserved gene context, the sequence-based reconstruction of gene regulatory networks, and microarray/RNA-seq data analysis.

Let a ˆ be a refinement mask of the refinable function ϕ of the form | a ˆ | = cos n ( ξ / 2 ) | L |, ξ ∈.

Let τ be the refinement mask of the refinable function ϕ of the form biglvert tau omega bigrvert =cos^{n}biggl( frac{omega}{2}biggr biglvert mathcal{L} omega bigrvert,quad omega in[-pi,pi].

Let a ˆ be a finitely supported refinement mask of a refinable function ϕ ∈ L 2 ( R ) with a ˆ ( 0 ) = 1 and a ˆ = 0, such that a ˆ can be factorized into the form | a ˆ | = cos n ( ξ / 2 ) | L |, ξ ∈ , where ℒ is the Fourier series of a finitely supported sequence with L ≠ 0. Suppose that | a ˆ | 2 + | a ˆ | 2 ≠ 0, ξ ∈.

Let ϕ be the refinable function corresponding to the refinement mask â.

[6] Let (phiin L_{2}(mathbb{R})) be a compactly supported refinable function with finitely supported refinement mask a.

Hence, the basis functions at quad/triangle vertices are shifts of the refinable function associated with a nonhomogeneous refinement equation.

Here, we present a very different approach that also achieves the goal of improving structure quality; in this case by incorporating terms responsive to hydropathic interactions into the X-ray refinement target function using the empirical HINT (Hydropathic INTeractions) forcefield [11].