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Full-Text Articles in Applied Mathematics
An Euler-Type Formula For Zeta (2k+1), Tian-Xiao He
An Euler-Type Formula For Zeta (2k+1), Tian-Xiao He
Tian-Xiao He
No abstract provided.
If F(X) =∫X2x F(T) Dt Is Constant, Must F(T) = C/T ?, Tian-Xiao He
If F(X) =∫X2x F(T) Dt Is Constant, Must F(T) = C/T ?, Tian-Xiao He
Tian-Xiao He
No abstract provided.
Mra Frame Wavelets With Certain Regularities Associated With The Refinable Generators Of Shift Invariant Spaces, Tian-Xiao He
Mra Frame Wavelets With Certain Regularities Associated With The Refinable Generators Of Shift Invariant Spaces, Tian-Xiao He
Tian-Xiao He
In this paper, we will start the discussion with the refinable generators of the shift invariant (SI) spaces in L2 (R) that possess the largest possible regularities and required vanishing moments. For the pseudo-scaling generators, the corresponding MRA frame wavelets with certain regularities are constructed. In addition, the stability of the refinable SI spaces and the corresponding complementary spaces, biorthogonality of the SI spaces, and the approximation property of the spaces are also discussed.
Biorthogonal Spline Type Wavelets, Tian-Xiao He
Biorthogonal Spline Type Wavelets, Tian-Xiao He
Tian-Xiao He
Let ¢ be an orthonormal scaling function with approximation degree p - 1, and let Bn be the B-spline of order n. Then, spline type scaling functions defined by fn = f * Bn (n = 1, 2, ... ) possess higher approximation order, p+n-1, and compact support. The corresponding biorthogonal wavelet functions are also constructed. This technique is extended to the case of biorthogonal scaling function system. As an application of the method supplied in this paper, one can easily construct a sequence of pairs of biorthogonal spline type scaling functions from one pair of biorthogonal scaling functions or …
Boundary-Type Quadrature And Boundary Element Method, Tian-Xiao He
Boundary-Type Quadrature And Boundary Element Method, Tian-Xiao He
Tian-Xiao He
In this paper, we apply a boundary-type quadrature technique to derive a type of boundary element scheme, which is used to solve the boundary-value problems of partial differential equations.Numerical examples for solving the exterior boundary-value problem of Helmholtz equation by using the spline approximation and the spline wavelet approximation are given.
Stable Refinable Generators Of Shift Invariant Spaces With Certain Regularities And Vanishing Moments, Tian-Xiao He
Stable Refinable Generators Of Shift Invariant Spaces With Certain Regularities And Vanishing Moments, Tian-Xiao He
Tian-Xiao He
In this paper, we discuss the stable refinable functions that generate shift in variant (SI) spaces and possess the largest possible regularities and required vanishing moments. The stability of the corresponding complementary spaces is also discussed.
Biorthogonal Wavelets With Certain Regularities, Tian-Xiao He
Biorthogonal Wavelets With Certain Regularities, Tian-Xiao He
Tian-Xiao He
In this paper, we will discuss the construction of biorthogonal wavelets that possess the largest possible regularities and required vanishing moments. For the sake of applications, we also give a general Daubechies’ iteration method of constructing biorthogonal wavelets by using biorthogonal splines.
Biorthogonal Wavelets With Certain Regularities, Tian-Xiao He
Biorthogonal Wavelets With Certain Regularities, Tian-Xiao He
Tian-Xiao He
No abstract provided.
Biorthogonal Wavelets With Certain Regularities, Tian-Xiao He
Biorthogonal Wavelets With Certain Regularities, Tian-Xiao He
Tian-Xiao He
No abstract provided.
Boundary Quadrature Formulas And Their Applications, Tian-Xiao He
Boundary Quadrature Formulas And Their Applications, Tian-Xiao He
Tian-Xiao He
This chapter surveys the analytical approach for constructing multivariate numerical integration formulas that use only boundary points as evaluation points. The applications of boundary quadrature formulas to boundary value problems of partial differential equations are also discussed.
C1 Quadratic Macroelements And C1 Orthogonal Multiresolution Analyses In 2d, Tian-Xiao He
C1 Quadratic Macroelements And C1 Orthogonal Multiresolution Analyses In 2d, Tian-Xiao He
Tian-Xiao He
Each triangle of an arbitrary regular triangulation Δ of a polygonal region in R2 is subdivided into twelve subtriangles by using three connecting lines joining three arbitrarily chosen points on its edges, three connecting lines from an arbitrarily chosen interior point in the triangle to its three vertices, and three connecting lines joining the points on the edges and the interior point. In this refinement, C1 quadratic finite elements can be constructed. In this paper, we will give explicit Bezier coefficients of elements in terms of the parameters that describe function and first partial derivative values at vertices …
Short Time Fourier Transform, Integral Wavelet Transform, And Wavelet Functions Associated With Splines, Tian-Xiao He
Short Time Fourier Transform, Integral Wavelet Transform, And Wavelet Functions Associated With Splines, Tian-Xiao He
Tian-Xiao He
In this article, we discuss short time Fourier transforms, integral wavelet transforms, and wavelet series expansions associated with spline functions in shift-invariant spaces of B-splines. A recurrence relation formula and the corresponding algorithm about the B-wavelets are also given.
Shape Criteria Of Bernstein-Bezier Polynomials Over Simplexes, Tian-Xiao He
Shape Criteria Of Bernstein-Bezier Polynomials Over Simplexes, Tian-Xiao He
Tian-Xiao He
This paper discusses the criteria of convexity, monotonicity, and positivity of Bernstein- Bezier polynomials over simplexes.
On A General Class Of Multivariate Linear Smoothing Operators, Tian-Xiao He
On A General Class Of Multivariate Linear Smoothing Operators, Tian-Xiao He
Tian-Xiao He
No abstract provided.
Asymptotic Properties Of Positive Summation-Integral Operators, Tian-Xiao He
Asymptotic Properties Of Positive Summation-Integral Operators, Tian-Xiao He
Tian-Xiao He
No abstract provided.
On Minimal And Quasi-Minimal Supported Bivariate Splines, Tian-Xiao He
On Minimal And Quasi-Minimal Supported Bivariate Splines, Tian-Xiao He
Tian-Xiao He
No abstract provided.