COMPACTLY SUPPORTED NON-TENSOR PRODUCT FORM TWO-DIMENSION WAVELET FINITE ELEMENT

Some theorems of compactly supported non-tensor product form two-dimension Daubechies wavelet were analysed carefully. Compactly supported non-tensor product form two-dimension wavelet was constructed, then non-tensor product form two dimension wavelet finite element was used to solve the deflection problem of elastic thin plate. The error order was researched. A numerical example was given at last.

COMPACTLY SUPPORTED BOX-SPLINE WAVELETS

A general procedure for constructing multivariate non-tensor-product wavelets that gen- erate an orthogonal decomposition of L^2(R~),s≥ 1,is described and applied to yield explicit formulas for compactly supported spline-wavelets based on the multiresolution analysis of L^2(R^s),1≤s≤3,generated by any box spline whose direction set constitutes a unimodular matrix.In particular,when univariate cardinal B-splines are considered,the minimally sup- ported cardinal spline-wavelets of Chui and Wang are recovered.A refined computational scheme for the orthogonalization of spaces with compactly supported wavelets is given.A recursive approximation scheme for“truncated”decomposition sequences is developed and a sharp error bound is included.A condition on the symmetry or anti-symmetry of the wavelets is applied to yield symmetric box-spline wavelets.

The Parametrization of Orthonormal Compactly Supported Wavelets and Wave Digital Filter

In this paper, the close relationship among wavelet transform and quadrature mirror filter (QMF) banks and the scattering matrix of wave digital filter (WDF) is analyzed in detail. The parametrization of orthonormal compactly supported wavelet bases that have an arbitrary number of vanishing moment is obtained by building any QMF pair out of elementary factors of the scatteringmatrix. In addition, the optimization of parameter is also presented. As comparison, some examples about orthonormal compactly supported wavelet that has arbitrary number of vanishing moment and the most number of vanishing moment are given respectively. Then we give the efficient lattice structure to implement the transform.

Reconfiguration of face expressions based on the discrete capture data of radial basis function interpolation

Compactly supported radial basis function can enable the coefficient matrix of solving weigh linear system to have a sparse banded structure, thereby reducing the complexity of the algorithm. Firstly, based on the compactly supported radial basis function, the paper makes the complex quadratic function （Multiquadric, MQ for short） to be transformed and proposes a class of compactly supported MQ function. Secondly, the paper describes a method that interpolates discrete motion capture data to solve the motion vectors of the interpolation points and they are used in facial expression reconstruction. Finally, according to this characteris- tic of the uneven distribution of the face markers, the markers are numbered and grouped in accordance with the density level, and then be interpolated in line with each group. The approach not only ensures the accuracy of the deformation of face local area and smoothness, but also reduces the time complexity of computing.

BOUND STATES OF SCHRODINGER EQUATIONS WITH ELECTROMAGNETIC FIELDS AND VANISHING POTENTIALS

We study the bound states to nonlinear Schrodinger equations with electro magnetic fields ihδψ/δt=（h/i -A（x））^2ψ＋V（x）ψ-K（x）｜ψ｜^p-1ψ=0,on R＋ ×R^N. Let G（x）=[V（x）p＋1/p-1-N/2][K（x）]-2/p-1 and suppose that G（x） has k local minimum points. For h 〉 0 small, we find multi-bump bound states ~bh （x, t） ---- e-iE~/huh （X） with Uh concentrating at the local minimum points of G（x） simultaneously as h ~ O. The potentials V（x） and K（x） are allowed to be either compactly supported or unbounded at infinity.

Parameterization of Bivariate Nonseparable Orthogonal Symmetric Scaling Functions with Short Support

Let I be the 2 × 2 identity matrix, and M a 2 × 2 dilation matrix with M2 = 2I. First, we present the correlation of the scaling functions with dilation matrix M and 2I. Then by relating the properties of scaling functions with dilation matrix 2I to the properties of scaling functions with dilation matrix M, we give a parameterization of a class of bivariate nonseparable orthogonal symmetric compactly supported scaling functions with dilation matrix M. Finally, a construction example of nonseparable orthogonal symmetric and compactly supported scaling functions is given.

SIGNAL DETECTION OF GLOBAL CLIMATE CHANGE AND EXTERNAL FORCING FACTORS

In this paper,we displayed one-dimensional climate signals,such as global temperature variation,Southern Oscillation Index and variation of external forcing factors,on a two- dimensional time-scale plane using compactly supported wavelet decomposition.Using the lag- correlation analysis method,and interpretative variance analysis method,and phase comparison method to the wavelet analysis result,we not only gained the variation on different scales to the global temperature and El Nino signals,the location of the jump point and intrinsic scale of these series,but also indicated the magnitude,extent and time of the effect of external forcing factors on them.We also put forward reasonable explanation to the main variation of recent 140 years.