Reenable function vectors are usually given in the form of an innnite product of their reenement (matrix) masks in the frequency domain and approximated by a cascade algorithm in both time and frequency domains. We provide necessary and suu-cient conditions for the convergence of the cascade algorithm. We also give necessary and suucient conditions for the stability and orthonormality of reenab...

In this paper we use the lifting scheme to construct biorthogonal spline wavelet bases on regularly refined non-uniform grids. The wavelets have at least one vanishing moment and on each resolution level they form an L2 Riesz basis. Furthermore we are interested in determining the exact range of Sobolev exponents for which the complete multilevel system forms a Riesz basis. Hereto we need to ex...

We give a continuum limit value of the lowest moment of a twist-2 operator in pion states from non-perturbative lattice calculations. We find that the non-perturbatively obtained renormalization group invariant matrix element is 〈x〉RGI = 0.179(11), which corresponds to 〈x〉 MS(2 GeV) = 0.246(15). In obtaining the renormalization group invariant matrix element, we have controlled important system...

—The design of the nite impulse response (FIR) adaptive notch lter with controlled null width is expressed as a derivatively contrained quadratic optimization problem. The problem is then transformed into an unconstrained one by choosing a null matrix orthogonal to the derivative constraint matrix. In this paper, wavelet lters are employed to construct the null matrix. Taking advantage of the v...

Motivated by [B. Han and Q. Mo, Adv. Comp. Math. 18 (2003) 211-245] and [B. Han and Z. Shen, Constr. Approx. 29 (2009) 369-406], we propose dual two-direction frames in dual Sobolev spaces (H(R), H−s(R)), with s > 0. Based on the dual two-direction frames from a pair of two-direction refinable functions, dual multiwavelet frames with symmetry {Ψ(x) := (ψ 1(x), ψ 2(x)) T }`=1 and {Ψ̃(x) : = (ψ̃ 1(...

This paper studies how vanishing moment, or regularity, of a desired degree can be imposed onto the dyadic-based building blocks of a class of M channel (M ≥ 2) causal biorthogonal filter banks having anti-causal inverses, without necessarily constraining the phase responses of the filters. Structural conditions for regularity are derived in terms of the elements of the dyadic-based building bl...

We derive a general framework for describing semi-inclusive deep-inelastic lepton-nucleon scattering in terms of the unintegrated parton distributions and other higher twist parton correlations. Such a framework provides a consistent approach to the calculation of inclusive and semi-inclusive cross sections including higher twist effects. As an example, we calculate the azimuthal asymmetries to...

We calculate the two-loop diagrams that give a non-zero contribution to the electric dipole moment dl of a charged lepton l due to possible Majorana masses of neutrinos. Using the example with one generation of the Standard Model leptons and two heavy right-handed neutrinos, we demonstrate that the non-vanishing result for dl first appears in order O(mlm 2 νG 2 F ), where mν is the mass of the ...

This paper studies the vanishing of $Ext$ modules over group rings. Let $R$ be a commutative noetherian ring and $ga$ a group. We provide a criterion under which the vanishing of self extensions of a finitely generated $Rga$-module $M$ forces it to be projective. Using this result, it is shown that $Rga$ satisfies the Auslander-Reiten conjecture, whenever $R$ has finite global dimension and $ga...

Tour into the picture (TIP) proposed by Horry et al.13 is a method for generating a sequence of walk-through images from a single reference picture (or image). By navigating a 3D scene model constructed from the picture, TIP produces convincing 3D effects. Assuming that the picture has one vanishing point, they proposed the scene modeling scheme called spidery mesh. However, this scheme has to ...