This research aims to understand the fractional order dynamics of the deadly Nipah virus(NiV)disease.We focus on using piecewise derivatives in the context of classical and singular kernels of power operators in the C...This research aims to understand the fractional order dynamics of the deadly Nipah virus(NiV)disease.We focus on using piecewise derivatives in the context of classical and singular kernels of power operators in the Caputo sense to investigate the crossover behavior of the considered dynamical system.We establish some qualitative results about the existence and uniqueness of the solution to the proposed problem.By utilizing the Newtonian polynomials interpolation technique,we recall a powerful algorithm to interpret the numerical findings for the aforesaid model.Here,we remark that the said viral infection is caused by an RNA type virus which can transmit from animals and also from an infected person to person.Fruits bats which are also known as flying foxes are one of the sources of transmission of NiV disease.Here in this work,we investigate its transmission mechanism through some new concepts of fractional calculus for further analysis and prediction.We present the approximate results for different compartments using different fractional orders.By using the piecewise derivative concept,we detect the crossover ormulti-steps behavior in the transmission dynamics of the mentioned disease.Therefore,the considered form of the derivative is used to deal with problems exhibiting crossover behaviors.展开更多
针对局部特征尺度分解(Local Characteristic-scale Decomposition,LCD)方法中两极值点连线在极值点处一阶微分不连续,引起分解精度降低问题,提出新非平稳信号分析方法 -基于分段多项式的局部特征尺度分解(Piecewise Polynomial based L...针对局部特征尺度分解(Local Characteristic-scale Decomposition,LCD)方法中两极值点连线在极值点处一阶微分不连续,引起分解精度降低问题,提出新非平稳信号分析方法 -基于分段多项式的局部特征尺度分解(Piecewise Polynomial based Local Characteristic-scale Decomposition,PPLCD)。用分段多项式取代LCD中直线连接,且均值曲线插值点由相邻3个同类极值点构成的多项式计算产生。通过仿真信号将PPLCD与LCD对比,结果表明,PPLCD在提高分量正交性、精确性等具有一定优越性;由转子碰摩故障诊断表明该方法的有效性。展开更多
The use of Bernstein-Bézier net in the study of bivariate splines was initiated by, G. Farin. In [1], Farin used Bèzier coordinates to express C^r continuity condition for bivariate splines. In [2], de Boor ...The use of Bernstein-Bézier net in the study of bivariate splines was initiated by, G. Farin. In [1], Farin used Bèzier coordinates to express C^r continuity condition for bivariate splines. In [2], de Boor and H(?)llig applied B-net method to obtain the approximation order of the space of C^1-cubic bivariate splines on a three-directionmesh. In this note, we study the B-net representation of multivariate splines. In展开更多
Homogeneous matrices are widely used to represent geometric transformations in computer graphics, with interpo- lation between those matrices being of high interest for computer animation. Many approaches have been pr...Homogeneous matrices are widely used to represent geometric transformations in computer graphics, with interpo- lation between those matrices being of high interest for computer animation. Many approaches have been proposed to address this problem, including computing matrix curves from curves in Euclidean space by registration, representing one-parameter curves on manifold by rational representations, changing subdivisional methods generating curves in Euclidean space to corresponding methods working for matrix curve generation, and variational methods. In this paper, we propose a scheme to generate rational one-parameter matrix curves based on exponential map for interpolation, and demonstrate how to obtain higher smoothness from existing curves. We also give an iterative technique for rapid computing of these curves. We take the computation as solving an ordinary differential equation on manifold numerically by a generalized Euler method. Furthermore, we give this algorithm’s bound of the error and prove that the bound is proportional to the shift length when the shift length is sufficiently small. Compared to direct computation of the matrix functions, our Euler solution is faster.展开更多
文摘This research aims to understand the fractional order dynamics of the deadly Nipah virus(NiV)disease.We focus on using piecewise derivatives in the context of classical and singular kernels of power operators in the Caputo sense to investigate the crossover behavior of the considered dynamical system.We establish some qualitative results about the existence and uniqueness of the solution to the proposed problem.By utilizing the Newtonian polynomials interpolation technique,we recall a powerful algorithm to interpret the numerical findings for the aforesaid model.Here,we remark that the said viral infection is caused by an RNA type virus which can transmit from animals and also from an infected person to person.Fruits bats which are also known as flying foxes are one of the sources of transmission of NiV disease.Here in this work,we investigate its transmission mechanism through some new concepts of fractional calculus for further analysis and prediction.We present the approximate results for different compartments using different fractional orders.By using the piecewise derivative concept,we detect the crossover ormulti-steps behavior in the transmission dynamics of the mentioned disease.Therefore,the considered form of the derivative is used to deal with problems exhibiting crossover behaviors.
文摘针对局部特征尺度分解(Local Characteristic-scale Decomposition,LCD)方法中两极值点连线在极值点处一阶微分不连续,引起分解精度降低问题,提出新非平稳信号分析方法 -基于分段多项式的局部特征尺度分解(Piecewise Polynomial based Local Characteristic-scale Decomposition,PPLCD)。用分段多项式取代LCD中直线连接,且均值曲线插值点由相邻3个同类极值点构成的多项式计算产生。通过仿真信号将PPLCD与LCD对比,结果表明,PPLCD在提高分量正交性、精确性等具有一定优越性;由转子碰摩故障诊断表明该方法的有效性。
文摘The use of Bernstein-Bézier net in the study of bivariate splines was initiated by, G. Farin. In [1], Farin used Bèzier coordinates to express C^r continuity condition for bivariate splines. In [2], de Boor and H(?)llig applied B-net method to obtain the approximation order of the space of C^1-cubic bivariate splines on a three-directionmesh. In this note, we study the B-net representation of multivariate splines. In
基金Project (No. 200038) partially supported by FANEDD, China
文摘Homogeneous matrices are widely used to represent geometric transformations in computer graphics, with interpo- lation between those matrices being of high interest for computer animation. Many approaches have been proposed to address this problem, including computing matrix curves from curves in Euclidean space by registration, representing one-parameter curves on manifold by rational representations, changing subdivisional methods generating curves in Euclidean space to corresponding methods working for matrix curve generation, and variational methods. In this paper, we propose a scheme to generate rational one-parameter matrix curves based on exponential map for interpolation, and demonstrate how to obtain higher smoothness from existing curves. We also give an iterative technique for rapid computing of these curves. We take the computation as solving an ordinary differential equation on manifold numerically by a generalized Euler method. Furthermore, we give this algorithm’s bound of the error and prove that the bound is proportional to the shift length when the shift length is sufficiently small. Compared to direct computation of the matrix functions, our Euler solution is faster.
