Non-uniform algebraic-trigonometric B-splines shares most of the properties as those of the usual polynomial B-splines. But they are not orthogonai. We construct an orthogonal basis for the n-order（n ≥ 3） algebraic...Non-uniform algebraic-trigonometric B-splines shares most of the properties as those of the usual polynomial B-splines. But they are not orthogonai. We construct an orthogonal basis for the n-order（n ≥ 3） algebraic-trigonometric spline space in order to resolve the theo- retical problem that there is not an explicit orthogonai basis in the space by now. Motivated by the Legendre polynomials, we present a novel approach to define a set of auxiliary functions, which have simple and explicit expressions. Then the proposed orthogonal splines are given as the derivatives of these auxiliary functions.展开更多
For a subdivision △ of a region in d-dimensional Euclidean space. we consider computation of dimension and of basis function in spline space S(△)consisting of all C(?)piecewise Polynomial func- tions over△of degree...For a subdivision △ of a region in d-dimensional Euclidean space. we consider computation of dimension and of basis function in spline space S(△)consisting of all C(?)piecewise Polynomial func- tions over△of degree at most k. A computational scheme is presented for computing the dimension and bases of spline space S(?)(△).This scheme based On the Grobner basis algorithm and the smooth co-factor method for computing multivariate spline. For bivariate splines, explicit basis functions of S(△)age obtained for any integer k and r when△is a cross-cut partition.展开更多
The explicit expression of the G3 basis function is presented in this paper. It is derived by constructing the conversion matrix between G3 basis function and Brzier representation. After the matrix decomposition, equ...The explicit expression of the G3 basis function is presented in this paper. It is derived by constructing the conversion matrix between G3 basis function and Brzier representation. After the matrix decomposition, equations for constructing G3 splines can be presented independently of geometric shape parameters＇ values. It makes the equation＇s solving easier. It is also known that the general form of the G3spline basis function is given in the first time. Its geometric construction method is presented.展开更多
A new geometric method to prove the total positivity of UE spline basis was proposed. UE spline basis is a kind of basis defined over algebraic-trigonometric unified space. UE spline basis shares most properties of th...A new geometric method to prove the total positivity of UE spline basis was proposed. UE spline basis is a kind of basis defined over algebraic-trigonometric unified space. UE spline basis shares most properties of the usual polynomial B-Splines. Total positivity is an important property for spline basis, it is highly related with shape preserving and variation diminishing properties. Knot inserted algorithm is the most useful algorithm for spline curves since many other useful properties are based on it. It is necessary to prove the total positivity of UE spline basis using knot inserted algorithm intuitively, not only enrich the UE spline basis theory, but also can be treated as supplement to the total positivity in algebraic sense. This approach also can be extended to other analogical bases.展开更多
The following article has been retracted due to the investigation of complaints received against it. The Editorial Board found that substantial portions of the text came from other published papers. The scientific com...The following article has been retracted due to the investigation of complaints received against it. The Editorial Board found that substantial portions of the text came from other published papers. The scientific community takes a very strong view on this matter, and the Health treats all unethical behavior such as plagiarism seriously. This paper published in Vol.3 No. 4, 334-339, 2012, has been removed from this site.展开更多
By using the blossom approach, we construct four new cubic rational Bernsteinlike basis functions with two shape parameters, which form a normalized B-basis and include the cubic Bernstein basis and the cubic Said-Bal...By using the blossom approach, we construct four new cubic rational Bernsteinlike basis functions with two shape parameters, which form a normalized B-basis and include the cubic Bernstein basis and the cubic Said-Ball basis as special cases. Based on the new basis, we propose a class of C2 continuous cubic rational B-spline-like basis functions with two local shape parameters, which includes the cubic non-uniform B-spline basis as a special case.Their totally positive property is proved. In addition, we extend the cubic rational Bernsteinlike basis to a triangular domain which has three shape parameters and includes the cubic triangular Bernstein-B′ezier basis and the cubic triangular Said-Ball basis as special cases. The G1 continuous conditions are deduced for the joining of two patches. The shape parameters in the bases serve as tension parameters and play a foreseeable adjusting role on generating curves and patches.展开更多
In this paper,a new quasi-interpolation with radial basis functions which satis- fies quadratic polynomial reproduction is constructed on the infinite set of equally spaced data.A new basis function is constructed by ...In this paper,a new quasi-interpolation with radial basis functions which satis- fies quadratic polynomial reproduction is constructed on the infinite set of equally spaced data.A new basis function is constructed by making convolution integral with a constructed spline and a given radial basis function.In particular,for twicely differ- entiable function the proposed method provides better approximation and also takes care of derivatives approximation.展开更多
We present the best bounds on the distance between 3-direction quartic box spline surface patch and its control net by means of analysis and computing for the basis functions of 3-direction quartic box spline surface....We present the best bounds on the distance between 3-direction quartic box spline surface patch and its control net by means of analysis and computing for the basis functions of 3-direction quartic box spline surface.Both the local bounds and the global bounds are given by the maximum norm of the first differences or second differences or mixed differences of the control points of the surface patch.展开更多
Based on the definition of MQ-B-Splines,this article constructs five types of univariate quasi-interpolants to non-uniformly distributed data. The error estimates and the shape-preserving properties are shown in detai...Based on the definition of MQ-B-Splines,this article constructs five types of univariate quasi-interpolants to non-uniformly distributed data. The error estimates and the shape-preserving properties are shown in details.And examples are shown to demonstrate the capacity of the quasi-interpolants for curve representation.展开更多
Isopaxametric quadrilateral elements are widely used in the finite element method. However, they have a disadvantage of accuracy loss when elements are distorted. Spline functions have properties of simpleness and con...Isopaxametric quadrilateral elements are widely used in the finite element method. However, they have a disadvantage of accuracy loss when elements are distorted. Spline functions have properties of simpleness and conformality. A 17onode quadrilateral element has been developed using the bivaxiate quaxtic spline interpolation basis and the triangular area coordinates, which can exactly model the quartic displacement fields. Some appropriate examples are employed to illustrate that the element possesses high precision and is insensitive to mesh distortions.展开更多
A supported framework of a gyroscope＇s rotor is designed and the B-Spline wavelet finite element model of nonlinear supported magnetic field is worked out. A new finite element space is studied in which the scaling f...A supported framework of a gyroscope＇s rotor is designed and the B-Spline wavelet finite element model of nonlinear supported magnetic field is worked out. A new finite element space is studied in which the scaling function of the B-spline wavelet is considered as the shape function of a tetrahedton. The magnetic field is spited by an artificial absorbing body which used the condition of field radiating, so the solution is unique. The resolution is improved via the varying gradient of the B-spline function under the condition of unchanging gridding. So there are some advantages in dealing with the focus flux and a high varying gradient result from a nonlinear magnetic field. The result is more practical. Plots of flux and in the space is studied via simulating the supported system model. The results of the study are useful in the research of the supported magnetic system for the gyroscope rotor.展开更多
The Marcinkiewicz-Zygmund inequality and the Bernstein inequality are established on ?2m (T, ?) ∩ L2 (?) which is the space of polynomial splines with irregularly distributed nodesT = {t j } j ∈?, where {t j }j∈? i...The Marcinkiewicz-Zygmund inequality and the Bernstein inequality are established on ?2m (T, ?) ∩ L2 (?) which is the space of polynomial splines with irregularly distributed nodesT = {t j } j ∈?, where {t j }j∈? is a real sequence such that {e it ξ} j }j ∈? constitutes a Riesz basis for L2([ ?π,π]). From these results, the asymptotic relation is proved, where B π,2 denotes the set of all functions from L2( R) which can be continued to entire functions of exponential type ? ?, i.e. the classical Paley-Wiener class.展开更多
This paper is concerned with stable solutions of time domain integral equation （TDIE） methods for transient scattering problems with 3D conducting objects. We use the quadratic B-spline function as temporal basis fu...This paper is concerned with stable solutions of time domain integral equation （TDIE） methods for transient scattering problems with 3D conducting objects. We use the quadratic B-spline function as temporal basis functions, which permits both the induced currents and induced charges to be properly approximated in terms of completeness. Because the B-spline function has the least support width among all polynomial basis functions of the same order, the resulting system matrices seem to be the sparsest. The TDIE formula-tions using induced electric polarizations as unknown function are adopted and justified. Numerical results demonstrate that the proposed approach is accurate and efficient, and no late-time instability is observed.展开更多
In this paper, the least square fitting method with the cubic B-spline basis lunctions is derived to reduce the influence of statistical fluctuations in the gamma ray spectra. The derived procedure is simple and autom...In this paper, the least square fitting method with the cubic B-spline basis lunctions is derived to reduce the influence of statistical fluctuations in the gamma ray spectra. The derived procedure is simple and automatic. The results show that this method is better than the convolution method with a sufficient reduction of statistical fluctuation.展开更多
基金Supported by the National Natural Science Foundation of China(60933008,61272300 and 11226327)the Science&Technology Program of Shanghai Maritime University(20120099)
文摘Non-uniform algebraic-trigonometric B-splines shares most of the properties as those of the usual polynomial B-splines. But they are not orthogonai. We construct an orthogonal basis for the n-order（n ≥ 3） algebraic-trigonometric spline space in order to resolve the theo- retical problem that there is not an explicit orthogonai basis in the space by now. Motivated by the Legendre polynomials, we present a novel approach to define a set of auxiliary functions, which have simple and explicit expressions. Then the proposed orthogonal splines are given as the derivatives of these auxiliary functions.
基金The Project is partly supported by the Science Technology New Star Plan of Beijing Education Committee of Beijing
文摘For a subdivision △ of a region in d-dimensional Euclidean space. we consider computation of dimension and of basis function in spline space S(△)consisting of all C(?)piecewise Polynomial func- tions over△of degree at most k. A computational scheme is presented for computing the dimension and bases of spline space S(?)(△).This scheme based On the Grobner basis algorithm and the smooth co-factor method for computing multivariate spline. For bivariate splines, explicit basis functions of S(△)age obtained for any integer k and r when△is a cross-cut partition.
基金Supported by National Natural Science Foundation of China(Grants 61100129)Open Program of Key Laboratory of Intelligent Information Processing,Institute of Computing Technology,Chinese Academy of Sciences(IIP2014-7)
文摘The explicit expression of the G3 basis function is presented in this paper. It is derived by constructing the conversion matrix between G3 basis function and Brzier representation. After the matrix decomposition, equations for constructing G3 splines can be presented independently of geometric shape parameters＇ values. It makes the equation＇s solving easier. It is also known that the general form of the G3spline basis function is given in the first time. Its geometric construction method is presented.
基金Supported by the National Science Foundation of China (60970079 and 60933008)
文摘A new geometric method to prove the total positivity of UE spline basis was proposed. UE spline basis is a kind of basis defined over algebraic-trigonometric unified space. UE spline basis shares most properties of the usual polynomial B-Splines. Total positivity is an important property for spline basis, it is highly related with shape preserving and variation diminishing properties. Knot inserted algorithm is the most useful algorithm for spline curves since many other useful properties are based on it. It is necessary to prove the total positivity of UE spline basis using knot inserted algorithm intuitively, not only enrich the UE spline basis theory, but also can be treated as supplement to the total positivity in algebraic sense. This approach also can be extended to other analogical bases.
文摘The following article has been retracted due to the investigation of complaints received against it. The Editorial Board found that substantial portions of the text came from other published papers. The scientific community takes a very strong view on this matter, and the Health treats all unethical behavior such as plagiarism seriously. This paper published in Vol.3 No. 4, 334-339, 2012, has been removed from this site.
基金Supported by the National Natural Science Foundation of China(60970097 and 11271376)Postdoctoral Science Foundation of China(2015M571931)Graduate Students Scientific Research Innovation Project of Hunan Province(CX2012B111)
文摘By using the blossom approach, we construct four new cubic rational Bernsteinlike basis functions with two shape parameters, which form a normalized B-basis and include the cubic Bernstein basis and the cubic Said-Ball basis as special cases. Based on the new basis, we propose a class of C2 continuous cubic rational B-spline-like basis functions with two local shape parameters, which includes the cubic non-uniform B-spline basis as a special case.Their totally positive property is proved. In addition, we extend the cubic rational Bernsteinlike basis to a triangular domain which has three shape parameters and includes the cubic triangular Bernstein-B′ezier basis and the cubic triangular Said-Ball basis as special cases. The G1 continuous conditions are deduced for the joining of two patches. The shape parameters in the bases serve as tension parameters and play a foreseeable adjusting role on generating curves and patches.
文摘In this paper,a new quasi-interpolation with radial basis functions which satis- fies quadratic polynomial reproduction is constructed on the infinite set of equally spaced data.A new basis function is constructed by making convolution integral with a constructed spline and a given radial basis function.In particular,for twicely differ- entiable function the proposed method provides better approximation and also takes care of derivatives approximation.
基金Supported by the National Natural Science Foundation of China (61170324 and 61100105)
文摘We present the best bounds on the distance between 3-direction quartic box spline surface patch and its control net by means of analysis and computing for the basis functions of 3-direction quartic box spline surface.Both the local bounds and the global bounds are given by the maximum norm of the first differences or second differences or mixed differences of the control points of the surface patch.
基金Supported by the National Natural Science Foundation of China( 1 9971 0 1 7,1 0 1 2 5 1 0 2 )
文摘Based on the definition of MQ-B-Splines,this article constructs five types of univariate quasi-interpolants to non-uniformly distributed data. The error estimates and the shape-preserving properties are shown in details.And examples are shown to demonstrate the capacity of the quasi-interpolants for curve representation.
基金supported by the Natural Science Foundation of China China (Nos. 60533060, 10672032, and 10726067)the Science Foundation of Dalian University of Technology (No. SFDUT07001)
文摘Isopaxametric quadrilateral elements are widely used in the finite element method. However, they have a disadvantage of accuracy loss when elements are distorted. Spline functions have properties of simpleness and conformality. A 17onode quadrilateral element has been developed using the bivaxiate quaxtic spline interpolation basis and the triangular area coordinates, which can exactly model the quartic displacement fields. Some appropriate examples are employed to illustrate that the element possesses high precision and is insensitive to mesh distortions.
文摘A supported framework of a gyroscope＇s rotor is designed and the B-Spline wavelet finite element model of nonlinear supported magnetic field is worked out. A new finite element space is studied in which the scaling function of the B-spline wavelet is considered as the shape function of a tetrahedton. The magnetic field is spited by an artificial absorbing body which used the condition of field radiating, so the solution is unique. The resolution is improved via the varying gradient of the B-spline function under the condition of unchanging gridding. So there are some advantages in dealing with the focus flux and a high varying gradient result from a nonlinear magnetic field. The result is more practical. Plots of flux and in the space is studied via simulating the supported system model. The results of the study are useful in the research of the supported magnetic system for the gyroscope rotor.
文摘The Marcinkiewicz-Zygmund inequality and the Bernstein inequality are established on ?2m (T, ?) ∩ L2 (?) which is the space of polynomial splines with irregularly distributed nodesT = {t j } j ∈?, where {t j }j∈? is a real sequence such that {e it ξ} j }j ∈? constitutes a Riesz basis for L2([ ?π,π]). From these results, the asymptotic relation is proved, where B π,2 denotes the set of all functions from L2( R) which can be continued to entire functions of exponential type ? ?, i.e. the classical Paley-Wiener class.
文摘This paper is concerned with stable solutions of time domain integral equation （TDIE） methods for transient scattering problems with 3D conducting objects. We use the quadratic B-spline function as temporal basis functions, which permits both the induced currents and induced charges to be properly approximated in terms of completeness. Because the B-spline function has the least support width among all polynomial basis functions of the same order, the resulting system matrices seem to be the sparsest. The TDIE formula-tions using induced electric polarizations as unknown function are adopted and justified. Numerical results demonstrate that the proposed approach is accurate and efficient, and no late-time instability is observed.
基金Supported by Science and Technology of Development Fund of Macao (042/2007/A3)
文摘In this paper, the least square fitting method with the cubic B-spline basis lunctions is derived to reduce the influence of statistical fluctuations in the gamma ray spectra. The derived procedure is simple and automatic. The results show that this method is better than the convolution method with a sufficient reduction of statistical fluctuation.
