For p = 2, we have a grid on the circle, for p = 1, a grid on the diamond(rhombus) and for p = 2/3, a uniform and refinable
grid on the astroid.
In the following, we will give a compactly supported real-valued refinable
function [phi] : R [right arrow] R with finite mask and real mask coefficients; that is, [phi] satisfies a two-scale relation:
Mo, "Multiwavelet frames from refinable
function vectors," Advances in Computational Mathematics, vol.
This polynomial approach reflects convolutions of refinable
functions and has been extensively studied in the univariate setting, cf.
Then there exists a framelet system X ([[PSI].sup.d.sub.0.]) associated with a refinable
function [[phi].sup.d] [member of] [R.sup.[beta]] and corresponding [[tau].sup.d] so that the pair (X ([[PSI].sub.0]), X ([[PSI].sup.d.sub.0])) is a bi-framelet.
In this paper, we will construct pairs of biorthogonal symmetric multiwavelets with high balanced orders from any orthogonal refinable
function vector, which simultaneously has symmetric and antisymmetric components.
Let the function [phi]: [R.sup.d] [right arrow] R be bounded, compactly supported, and refinable
, so that there is a sequence [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] of real numbers for which [phi] = [summation over (k[member of][Z.sup.d])][h.sub.k][phi](2 x -k).
 Wayne Lawton, Infinite convolution products and refinable
distributions on Lie groups, Trans.
PENA, Local decomposition of refinable
Coking units increase the amount of refinable
material obtained from a barrel of oil and convert residual crude into petroleum coke, which can be used as coal substitute.
A continuous refinable
function [psi] is interpolatory if
The flexicoker increases the amount of refinable
material from a barrel of crude oil and converts residual crude oil to petroleum coke, a coal substitute.
A coking unit increases the amount of refinable
material obtained from a barrel of oil and converts gunky residual crude into petroleum coke, a coal substitute.