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1.
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 constructing the basis functions of the interpolants are given.  相似文献   

2.
Based on the theory of semi-global classical solutions to quasilinear hyperbolic systems, the authors apply a unified constructive method to establish the local exact boundary(null) controllability and the local boundary(weak) observability for a coupled system of 1-D quasilinear wave equations with various types of boundary conditions.  相似文献   

3.
The mathematical problem of an infinite elastic plane consisting of three different media with an arbitrary number of cracks is considered. It is reduced to singular integral equations along the interfaces and the cracks by a constructive method. Those along the interfaces are further reduced to Fredholm ones.  相似文献   

4.
正Exact Boundary Observability for a Kind of Second-Order Quasilinear Hyperbolic Systems Ke WANG Based on the theory of semi-global classical solutions to quasilinear hyperbolic systems,the local exact boundary observability for a kind of second-order quasilinear hyperbolic systems is obtained by a constructive method.  相似文献   

5.
The inverse problem of determining two convection coefficients of an ellipticpartial differential equation by Dirichlet to Neumann map is discussed.It is well knownthat this is a severely ill-posed problem with high nonlinearity.By the inverse scatteringtechnique for first order elliptic system in the plane and the theory of generalized analyticfunctions,we give a constructive method for this inverse problem.  相似文献   

6.
The periodic multiresolution analysis (PMRA) and the periodic frame multiresolution analysis (PFMRA) provide a general recipe for the construction of periodic wavelets and periodic wavelet frames, respectively. This paper addresses PFMRAs by the introduction of the notion of spectrum sequence. In terms of spectrum sequences, the scaling function sequences generating a normalized PFMRA are characterized; a characterization of the spectrum sequences of PFMRAs is obtained, which provides a method to construct PFMRAs since its proof is constructive; a necessary and sufficient condition for a PFMRA to admit a single wavelet frame sequence is obtained; a necessary and sufficient condition for a PFMRA to be contained in a given PMRA is also obtained. What is more, it is proved that an arbitrary PFMRA must be contained in some PMRA. In the meanwhile, some examples are provided to illustrate the general theory.  相似文献   

7.
The exact boundary controllability and the exact boundary observability for the 1-D first order linear hyperbolic system were studied by the constructive method in the framework of weak solutions in the work [Lu, X. and Li, T. T., Exact boundary controllability of weak solutions for a kind of first order hyperbolic system — the constructive method, Chin. Ann. Math. Ser. B, 42(5), 2021, 643–676]. In this paper, in order to study these problems from the viewpoint of duality, the authors establish ...  相似文献   

8.
Standard tri-point transition function   总被引:1,自引:0,他引:1  
It is usually difficult to express a family of tri-point transition function (TTF) by a transition matrix as Markov processes with one parameter. In this paper, we define three kinds of connection matrixes on the states of standard tri-point transition function (STTF) and study their essential character, give a constructive method on the constant-value standard tri-point transition function and a general expression of the state-symmetric standard tri-point transition function by a sequence of the transition matrixes of special and simple Markov processes with one parameter.  相似文献   

9.
In this note, we give an elementary and constructive proof for that the additive character group of a locally compact field is isomorphic to itself as an additive topological group.  相似文献   

10.
We investigate the construction of two-direction tight wavelet frames First, a sufficient condition for a two-direction refinable function generating two-direction tight wavelet frames is derived. Second, a simple constructive method of two-direction tight wavelet frames is given. Third, based on the obtained two-direction tight wavelet frames, one can construct a symmetric multiwavelet frame easily. Finally, some examples are given to illustrate the results.  相似文献   

11.
朱平 《东北数学》2005,21(3):336-344
In this paper, we consider the Straight Line Type Node Configuration C (SLTNCC) in multivariate polynomial interpolation as the result of different kinds of transformations of lines (such as parallel translations, rotations). Corresponding to these transformations we define different kinds of interpolation problems for the SLTNCC. The expression of the confluent multivariate Vandermonde determinant of the coefficient matrix for each of these interpolation problems is obtained, and from this expression we conclude the related interpolation problem is unisolvent. Also, we give a kind of generalization of the SLTNCC in Section 5. As well, we obtain an expression of the interpolating polynomial for a kind of interpolation problem discussed in this paper.  相似文献   

12.
13.
One of the problems in bivariate polynomial interpolation is the choice of a space of polynomials suitable for interpolating a given set of data. Depending on the number of data, a usual space is that of polynomials in 2 variables of total degree not greater than k. However, these spaces are not enough to cover many interpolation problems. Here, we are interested in spaces of polynomials of total degree not greater than k whose degree diminishes along some prescribed directions. These spaces arise naturally in some interpolation problems and we describe them in terms of polynomials satisfying some asymptotic interpolation conditions. This provides a general frame to the interpolation problems studied in some of our recent papers.  相似文献   

14.
1 IntroductionIn this paper,we letPn,… ,nsn′s( or Psn) be the ( s-variate) polynomial space of all real ( s-variate) polynomials with the degreeof each variate atmostn and use the usual multivariate notationwj =wj11 … wjss,| j| =j1 +… + js( j1 ,… ,js∈ Z+) .[1 ] and [2 ] have discussed the Cross Type Node Configuration ( CRTNC) and thecorresponding bivariate interpolation in R2 .In this paper,we considerRs={ ( w1 ,… ,ws) :wi ∈ R,i =1 ,… ,s} .We say that s( s-1 ) -dimensional h…  相似文献   

15.
This is an extension and emendation of recent results on the use of Gauss elimination in multivariate polynomial interpolation and, in particular, ideal interpolation. Dedicated to Mariano Gasca on the occasion of his sixtieth birthday  相似文献   

16.
A lemma of Micchelli's, concerning radial polynomials and weighted sums of point evaluations, is shown to hold for arbitrary linear functionals, as is Schaback's more recent extension of this lemma and Schaback's result concerning interpolation by radial polynomials. Schaback's interpolant is explored. Happy 60th and beyond, Charlie! Mathematics subject classifications (2000) 41A05, 41A6.  相似文献   

17.
In this paper we construct certain continuous piecewise rational wavelets on arbitrary spherical triangulations, giving explicit expressions of these wavelets. Our wavelets have small support, a fact which is very important in working with large amounts of data, since the algorithms for decomposition, compression and reconstruction deal with sparse matrices. We also give a quasi-interpolant associated to a given triangulation and study the approximation error. Some numerical examples are given to illustrate the efficiency of our wavelets.

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18.
A kind of generalization of the Curve Type Node Configuration is given in this paper,and it is called the generalized node configuration CTNCB in RS(S>2).The related multivariate polynomial interpolation problem is discussed.It is proved that the CTNCB is an appropriate node configuration for the polynomial space PSn (S>2).And the expressions of the multivariate Vandermonde determinants that are related to the Odd Curve Type Node Configuration in R2 are also obtained.  相似文献   

19.
竖线型结点组上的插值及向高维情形的推广   总被引:1,自引:0,他引:1  
朱平 《数学杂志》1998,18(4):393-399
本文讨论了R^2中竖线型结点组插值的适定性,得到了相应的插值多项式,并将这些结果推广到R^s(s〉2)的情形。  相似文献   

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