In this paper, we propose a new approach to solve the approximate implicitization problem based on RBF networks and MQ quasi-interpolation. This approach possesses the advantages of shape preserving, better smoothness...In this paper, we propose a new approach to solve the approximate implicitization problem based on RBF networks and MQ quasi-interpolation. This approach possesses the advantages of shape preserving, better smoothness, good approximation behavior and relatively less data etc. Several numerical examples are provided to demonstrate the effectiveness and flexibility of the proposed method.展开更多
In this paper, we use a univariate multiquadric quasi-interpolation scheme to solve the one-dimensional nonlinear sine-Gordon equation that is related to many physical phenomena. We obtain a numerical scheme by using ...In this paper, we use a univariate multiquadric quasi-interpolation scheme to solve the one-dimensional nonlinear sine-Gordon equation that is related to many physical phenomena. We obtain a numerical scheme by using the derivative of the quasi-interpolation to approximate the spatial derivative and a difference scheme to approximate the temporal derivative. The advantage of the obtained scheme is that the algorithm is very simple so that it is very easy to implement. The results of numerical experiments are presented and compared with analytical solutions to confirm the good accuracy of the presented scheme.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
Based on the multiquadric trigonometric B-spline quasi-interpolant, this paper proposes a meshless scheme for some partial differential equations whose solutions are periodic with respect to the spatial variable. This...Based on the multiquadric trigonometric B-spline quasi-interpolant, this paper proposes a meshless scheme for some partial differential equations whose solutions are periodic with respect to the spatial variable. This scheme takes into ac- count the periodicity of the analytic solution by using derivatives of a periodic quasi-interpolant （multiquadric trigonometric B-spline quasi-interpolant） to approximate the spatial derivatives of the equations. Thus, it overcomes the difficulties of the previous schemes based on quasi-interpolation （requiring some additional boundary conditions and yielding unwanted high-order discontinuous points at the boundaries in the spatial domain）. Moreover, the scheme also overcomes the dif- ficulty of the meshless collocation methods （i.e., yielding a notorious ill-conditioned linear system of equations for large collocation points）. The numerical examples that are presented at the end of the paper show that the scheme provides excellent approximations to the analytic solutions.展开更多
The aim of this survey paper is to propose a new concept ＂generator＂. In fact, generator is a single function that can generate the basis as well as the whole function space. It is a more fundamental concept than ba...The aim of this survey paper is to propose a new concept ＂generator＂. In fact, generator is a single function that can generate the basis as well as the whole function space. It is a more fundamental concept than basis. Various properties of generator are also discussed. Moreover, a special generator named multiquadric function is introduced. Based on the multiquadric generator, the multiquadric quasi-interpolation scheme is constructed, and furthermore, the properties of this kind of quasi-interpolation are discussed to show its better capacity and stability in approximating the high order derivatives.展开更多
Quasi-interpolation has been studied in many papers, e. g., [5]. Here we introduce nonseparable scaling function quasi-interpolation and show that its approximation can provide similar convergence properties as scalar...Quasi-interpolation has been studied in many papers, e. g., [5]. Here we introduce nonseparable scaling function quasi-interpolation and show that its approximation can provide similar convergence properties as scalar wavelet system. Several equivalent statements of accuracy of nonseparable scaling function are also given. In the numerical experiments, it appears that nonseparable scaling function interpolation has better convergence results than scalar wavelet systems in some cases.展开更多
Objective: To measure IQ and MQ of patients with cerebral vascular diseases (CVD) involving different cerebral lobes and basal ganglia areas. To provide useful data for clinical assessment of brain functions with resp...Objective: To measure IQ and MQ of patients with cerebral vascular diseases (CVD) involving different cerebral lobes and basal ganglia areas. To provide useful data for clinical assessment of brain functions with respect to degree and range of IQ and MQ impairments. Methods: 60 cases of localized CVD were confirmed by clinical diagnosis and CT scan. The patients were evaluated by the WAIS-RC and WMS-RC after convalescence. Results: There were reliable differences between patients and normal controls ( P <0.001), indicating significant intelligence and memory impairments. More pronounced impairments were found in cases with frontal, temporal, occipital and thalamus lesions, but less so with parietal and basal ganglia lesions. Conclusion: The frontal, temporal, occipital lobes and the thalamus play a key and interactive role in the various cognitive processes underlying IQ and MQ.展开更多
基金Project supported by the National Natural Science Fbundation of China(No.10271022,No.60373093 and No.60533060).
文摘In this paper, we propose a new approach to solve the approximate implicitization problem based on RBF networks and MQ quasi-interpolation. This approach possesses the advantages of shape preserving, better smoothness, good approximation behavior and relatively less data etc. Several numerical examples are provided to demonstrate the effectiveness and flexibility of the proposed method.
基金supported by the State Key Development Program for Basic Research of China (Grant No 2006CB303102)Science and Technology Commission of Shanghai Municipality,China (Grant No 09DZ2272900)
文摘In this paper, we use a univariate multiquadric quasi-interpolation scheme to solve the one-dimensional nonlinear sine-Gordon equation that is related to many physical phenomena. We obtain a numerical scheme by using the derivative of the quasi-interpolation to approximate the spatial derivative and a difference scheme to approximate the temporal derivative. The advantage of the obtained scheme is that the algorithm is very simple so that it is very easy to implement. The results of numerical experiments are presented and compared with analytical solutions to confirm the good accuracy of the presented scheme.
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 Shanghai Guidance of Science and Technology,China(Grant No.12DZ2272800)the Natural Science Foundation of Education Department of Anhui Province,China(Grant No.KJ2013B203)the Foundation of Introducing Leaders of Science and Technology of Anhui University,China(Grant No.J10117700057)
文摘Based on the multiquadric trigonometric B-spline quasi-interpolant, this paper proposes a meshless scheme for some partial differential equations whose solutions are periodic with respect to the spatial variable. This scheme takes into ac- count the periodicity of the analytic solution by using derivatives of a periodic quasi-interpolant （multiquadric trigonometric B-spline quasi-interpolant） to approximate the spatial derivatives of the equations. Thus, it overcomes the difficulties of the previous schemes based on quasi-interpolation （requiring some additional boundary conditions and yielding unwanted high-order discontinuous points at the boundaries in the spatial domain）. Moreover, the scheme also overcomes the dif- ficulty of the meshless collocation methods （i.e., yielding a notorious ill-conditioned linear system of equations for large collocation points）. The numerical examples that are presented at the end of the paper show that the scheme provides excellent approximations to the analytic solutions.
基金Supported by the 973program-2006CB303102SGST 09DZ 2272900NSFC No.11026089
文摘The aim of this survey paper is to propose a new concept ＂generator＂. In fact, generator is a single function that can generate the basis as well as the whole function space. It is a more fundamental concept than basis. Various properties of generator are also discussed. Moreover, a special generator named multiquadric function is introduced. Based on the multiquadric generator, the multiquadric quasi-interpolation scheme is constructed, and furthermore, the properties of this kind of quasi-interpolation are discussed to show its better capacity and stability in approximating the high order derivatives.
文摘Quasi-interpolation has been studied in many papers, e. g., [5]. Here we introduce nonseparable scaling function quasi-interpolation and show that its approximation can provide similar convergence properties as scalar wavelet system. Several equivalent statements of accuracy of nonseparable scaling function are also given. In the numerical experiments, it appears that nonseparable scaling function interpolation has better convergence results than scalar wavelet systems in some cases.
文摘Objective: To measure IQ and MQ of patients with cerebral vascular diseases (CVD) involving different cerebral lobes and basal ganglia areas. To provide useful data for clinical assessment of brain functions with respect to degree and range of IQ and MQ impairments. Methods: 60 cases of localized CVD were confirmed by clinical diagnosis and CT scan. The patients were evaluated by the WAIS-RC and WMS-RC after convalescence. Results: There were reliable differences between patients and normal controls ( P <0.001), indicating significant intelligence and memory impairments. More pronounced impairments were found in cases with frontal, temporal, occipital and thalamus lesions, but less so with parietal and basal ganglia lesions. Conclusion: The frontal, temporal, occipital lobes and the thalamus play a key and interactive role in the various cognitive processes underlying IQ and MQ.
