Sentence examples for be the refinable function from inspiring English sources

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

Let (phi_{m,l,alpha}) be the refinable functions from generalized Bernstein polynomials with the refinement mask (2).

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

We are interested in knowing whether the function ψ defined in (4.1) is a Riesz wavelet when the refinable function ϕ is chosen to be different refinable functions.

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

When the refinable function ϕ is chosen to be a pseudo spline, Dong in [3] gave the same results.

When the refinable function ϕ is a B-spline, Han showed in [19] that the wavelet defined in (4.1) is a Riesz wavelet.

If the refinable function ϕ is a smoothed pseudo spline, Zhuang obtained the following results.

[3] The refinable function vector (varPhi =left( phi _iright) _{i=1}^{n}) is symmetric if each component function (phi _i,1le ile n) is symmetric about some point (a_iin mathbb {R}).

If the refinable function ϕ satisfies the Strang-Fix (SF) condition of order (m_{0}) and the corresponding mask â satisfies (1- |hat{a} |^{2}= O (|cdot|^{m_{2}} )) at the origin, then (m_{1}=min{m_{0},m_{2}}).