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Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
A Pair Of General Series-Transformation Formulas, Tian-Xiao He, Leetsch Hsu, Peter Shiue
A Pair Of General Series-Transformation Formulas, Tian-Xiao He, Leetsch Hsu, Peter Shiue
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.
A Symbolic Operator Approach To Several Summation Formulas For Power Series, Tian-Xiao He, Leetsch Hsu, Peter Shiue, D. Torney
A Symbolic Operator Approach To Several Summation Formulas For Power Series, Tian-Xiao He, Leetsch Hsu, Peter Shiue, D. Torney
Tian-Xiao He
This paper deals with the summation problem of power series of the form Sba (f; x) = ∑a ≤ k ≤ b f(k) xk, where 0≤ a < b ≤ ∞, and {f(k)} is a given sequence of numbers with k Є [a, b) or f(t) is a differentiable function defined on [a, b). We present a symbolic summation operator with its various expansions, and construct several summation formulas with estimable remainders for Sba (f; x), by the aid of some classical interpolation series due to Newton, Gauss and Everett, respectively.
On An Extension Of Abel-Gontscharoff's Expansion Formula, Tian-Xiao He, Leetsch C. Hsu, Peter J.-S. Shiue
On An Extension Of Abel-Gontscharoff's Expansion Formula, Tian-Xiao He, Leetsch C. Hsu, Peter J.-S. Shiue
Tian-Xiao He
We present a constructive generalization of Abel-Gontscharoff’s series expansion to higher dimensions. A constructive application to a problem of multivariate interpolation is also investigated. In addition, two algorithms for the constructing the basis functions of the interpolants are given.