With Newton＇s interpolating formula, we construct a kind of block based Newton-like blending osculatory interpolation.The interpolation provides us many flexible interpolation schemes for choices which include the ex...With Newton＇s interpolating formula, we construct a kind of block based Newton-like blending osculatory interpolation.The interpolation provides us many flexible interpolation schemes for choices which include the expansive Newton＇s polynomial inter- polation as its special case. A bivariate analogy is also discussed and numerical examples are given to show the effectiveness of the interpolation.展开更多
Global look-up table strategy proposed recently has been proven to be an efficient method to accelerate the interpolation, which is the most time-consuming part in the iterative sub-pixel digital image correlation （...Global look-up table strategy proposed recently has been proven to be an efficient method to accelerate the interpolation, which is the most time-consuming part in the iterative sub-pixel digital image correlation （DIC） algorithms. In this paper, a global look-up table strategy with cubic B-spline interpolation is developed for the DIC method based on the inverse compositional Gauss-Newton （IC-GN） algorithm. The performance of this strategy, including accuracy, precision, and computation efficiency, is evaluated through a theoretical and experimental study, using the one with widely employed bicubic interpolation as a benchmark. The global look-up table strategy with cubic B-spline interpolation improves significantly the accuracy of the IC-GN algorithm-based DIC method compared with the one using the bicubic interpolation, at a trivial price of computation efficiency.展开更多
Predicting the lifetime of polymeric insulators is one of the most important research topics in studying the life cycle of high voltage insulators in the power transmission and distribution networks. HTV （high temper...Predicting the lifetime of polymeric insulators is one of the most important research topics in studying the life cycle of high voltage insulators in the power transmission and distribution networks. HTV （high temperature vulcanized） silicone rubber is a high performance dielectric material used within electrical power equipment, in particular transmission and distribution insulators. In this paper, we proposed a new approach using the Newton＇s method and Lagrange method to predict the aging of HTV silicone rubber that are subjected to multiple stress conditions. Concentration of chemical elements such as carbon, oxygen, silicon and aluminum were obtained and evaluated using a SEM （scanning electron microscope） with EDS （energy dispersive X-ray spectroscopy）. Curve fitting using the Newton＇s and Lagrange interpolation methods yield useful linear interpolation equations that describe the aging characteristic of the specimens under study. This approach can be applied to predict the change in chemical concentration of polymeric insulators over the life cycle with good accuracy.展开更多
This paper presents a general formula for (2m + 2)-point n-ary interpolating subdivision scheme for curves for any?integer m ≥ 0 and n ≥ 2 by using Newton interpolating polynomial. As a consequence, the proposed wor...This paper presents a general formula for (2m + 2)-point n-ary interpolating subdivision scheme for curves for any?integer m ≥ 0 and n ≥ 2 by using Newton interpolating polynomial. As a consequence, the proposed work is extended for surface case, which is equivalent to the tensor product of above proposed curve case. These formulas merge several notorious curve/surface schemes. Furthermore, visual performance of the subdivision schemes is also presented.展开更多
In this paper, several usually used polynomial interpolation methods are explained in view of vector basis and dimension in linearalgebra theory. Using transition matrixes, general conversion formula between the basis...In this paper, several usually used polynomial interpolation methods are explained in view of vector basis and dimension in linearalgebra theory. Using transition matrixes, general conversion formula between the basis function sets of these polynomialinterpolation methods are given. An example also shows the effectiveness of the results.展开更多
Because of the features involved with their varied kernels,differential operators relying on convolution formulations have been acknowledged as effective mathematical resources for modeling real-world issues.In this p...Because of the features involved with their varied kernels,differential operators relying on convolution formulations have been acknowledged as effective mathematical resources for modeling real-world issues.In this paper,we constructed a stochastic fractional framework of measles spreading mechanisms with dual medication immunization considering the exponential decay and Mittag-Leffler kernels.In this approach,the overall population was separated into five cohorts.Furthermore,the descriptive behavior of the system was investigated,including prerequisites for the positivity of solutions,invariant domain of the solution,presence and stability of equilibrium points,and sensitivity analysis.We included a stochastic element in every cohort and employed linear growth and Lipschitz criteria to show the existence and uniqueness of solutions.Several numerical simulations for various fractional orders and randomization intensities are illustrated.展开更多
基金Supported by the Key Project Foundation of the Department of Education of Anhui Province(No.KJ2008A027)the Project Foundation of the Department of Education of Anhui Province(No.KJ2010B182)
文摘With Newton＇s interpolating formula, we construct a kind of block based Newton-like blending osculatory interpolation.The interpolation provides us many flexible interpolation schemes for choices which include the expansive Newton＇s polynomial inter- polation as its special case. A bivariate analogy is also discussed and numerical examples are given to show the effectiveness of the interpolation.
基金financially supported by the National Natural Science Foundation of China(11202081,11272124,and 11472109)the State Key Lab of Subtropical Building Science,South China University of Technology(2014ZC17)
文摘Global look-up table strategy proposed recently has been proven to be an efficient method to accelerate the interpolation, which is the most time-consuming part in the iterative sub-pixel digital image correlation （DIC） algorithms. In this paper, a global look-up table strategy with cubic B-spline interpolation is developed for the DIC method based on the inverse compositional Gauss-Newton （IC-GN） algorithm. The performance of this strategy, including accuracy, precision, and computation efficiency, is evaluated through a theoretical and experimental study, using the one with widely employed bicubic interpolation as a benchmark. The global look-up table strategy with cubic B-spline interpolation improves significantly the accuracy of the IC-GN algorithm-based DIC method compared with the one using the bicubic interpolation, at a trivial price of computation efficiency.
文摘Predicting the lifetime of polymeric insulators is one of the most important research topics in studying the life cycle of high voltage insulators in the power transmission and distribution networks. HTV （high temperature vulcanized） silicone rubber is a high performance dielectric material used within electrical power equipment, in particular transmission and distribution insulators. In this paper, we proposed a new approach using the Newton＇s method and Lagrange method to predict the aging of HTV silicone rubber that are subjected to multiple stress conditions. Concentration of chemical elements such as carbon, oxygen, silicon and aluminum were obtained and evaluated using a SEM （scanning electron microscope） with EDS （energy dispersive X-ray spectroscopy）. Curve fitting using the Newton＇s and Lagrange interpolation methods yield useful linear interpolation equations that describe the aging characteristic of the specimens under study. This approach can be applied to predict the change in chemical concentration of polymeric insulators over the life cycle with good accuracy.
文摘This paper presents a general formula for (2m + 2)-point n-ary interpolating subdivision scheme for curves for any?integer m ≥ 0 and n ≥ 2 by using Newton interpolating polynomial. As a consequence, the proposed work is extended for surface case, which is equivalent to the tensor product of above proposed curve case. These formulas merge several notorious curve/surface schemes. Furthermore, visual performance of the subdivision schemes is also presented.
文摘In this paper, several usually used polynomial interpolation methods are explained in view of vector basis and dimension in linearalgebra theory. Using transition matrixes, general conversion formula between the basis function sets of these polynomialinterpolation methods are given. An example also shows the effectiveness of the results.
文摘Because of the features involved with their varied kernels,differential operators relying on convolution formulations have been acknowledged as effective mathematical resources for modeling real-world issues.In this paper,we constructed a stochastic fractional framework of measles spreading mechanisms with dual medication immunization considering the exponential decay and Mittag-Leffler kernels.In this approach,the overall population was separated into five cohorts.Furthermore,the descriptive behavior of the system was investigated,including prerequisites for the positivity of solutions,invariant domain of the solution,presence and stability of equilibrium points,and sensitivity analysis.We included a stochastic element in every cohort and employed linear growth and Lipschitz criteria to show the existence and uniqueness of solutions.Several numerical simulations for various fractional orders and randomization intensities are illustrated.
