Sentence examples for following refinement from inspiring English sources
Let a refinable function (phiin L_{2}(mathbb{R}) ) be a compactly supported orthonormal refinable function satisfying the following refinement equation: phi=2sum_{kinmathbb{Z}}a_{k}phi(2 cdot-k), one can easily obtain a wavelet function ψ by psi=2sum_{kinmathbb{Z}} -1)^{k-1} -1erline{a(1-k)}phi (2cdot-k).
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.
Refine in PHENIX with the following refinement strategies: 'XYZ coordinates', 'TLS parameters' and 'Individual B-factors'.
The following refinement of (1.4) is also valid [5].
The following refinement of (1.1) is also well-known.
By employing the same direction of Ha, we can derive the following refinement result.
If we apply inequality (4.10) for, we get the following refinement of the previous inequality.
which is used to derive the following refinement of (1.10) (38).
A similar analysis shows us that only the following refinements of inequality (20) are possible.
Our model is similar to the current model of Van Buren et al [9] with the following refinements.
The R code provided in Additional file 2 implements the nested sampling algorithm and the following refinements: The stepping-out procedure of slice sampling [ 28] is an effective way to explore a uniform prior for a new sample while respecting the constraint L > L*, as the step-size can be tuned to increase computational efficiency.
