In this paper,we construct a new sixth order iterative method for solving nonlinear equations.The local convergence and order of convergence of the new iterative method is demonstrated.In order to check the validity o...In this paper,we construct a new sixth order iterative method for solving nonlinear equations.The local convergence and order of convergence of the new iterative method is demonstrated.In order to check the validity of the new iterative method,we employ several chemical engineering applications and academic test problems.Numerical results show the good numerical performance of the new iterative method.Moreover,the dynamical study of the new method also supports the theoretical results.展开更多
Consider a branching random walk, where the underlying branching mechanism is governed by a Galton-Watson process and the moving law of particles by a discrete random variable on the integer lattice Z. Denote by Zn（z...Consider a branching random walk, where the underlying branching mechanism is governed by a Galton-Watson process and the moving law of particles by a discrete random variable on the integer lattice Z. Denote by Zn（z） the number of particles in the n-th generation in the model for each z ∈ Z. We derive the exact convergence rate in the local limit theorem for Zn（z） assuming a condition like ＂EN（logN）1＋λ 〈 ∞＂ for the offspring distribution and a finite moment condition on the motion law. This complements the known results for the strongly non-lattice branching random walk on the real line and for the simple symmetric branching random walk on the integer lattice.展开更多
A noninterior continuation method is proposed for semidefinite complementarity problem （SDCP）. This method improves the noninterior continuation methods recently developed for SDCP by Chen and Tseng. The main proper...A noninterior continuation method is proposed for semidefinite complementarity problem （SDCP）. This method improves the noninterior continuation methods recently developed for SDCP by Chen and Tseng. The main properties of our method are： （i） it is well d.efined for the monotones SDCP; （ii） it has to solve just one linear system of equations at each step; （iii） it is shown to be both globally linearly convergent and locally quadratically convergent under suitable assumptions.展开更多
A local energy conservation law is proposed for the Klein--Gordon-Schrrdinger equations, which is held in any local time-space region. The local property is independent of the boundary condition and more essential tha...A local energy conservation law is proposed for the Klein--Gordon-Schrrdinger equations, which is held in any local time-space region. The local property is independent of the boundary condition and more essential than the global energy conservation law. To develop a numerical method preserving the intrinsic properties as much as possible, we propose a local energy-preserving （LEP） scheme for the equations. The merit of the proposed scheme is that the local energy conservation law can hold exactly in any time-space region. With the periodic boundary conditions, the scheme also possesses the discrete change and global energy conservation laws. A nonlinear analysis shows that the LEP scheme converges to the exact solutions with order O（τ2 ＋ h2）. The theoretical properties are verified by numerical experiments.展开更多
This paper considers local median estimation in fixed design regression problems. The proposed method is employed to estimate the median function and the variance function of a heteroscedastic regression model. Strong...This paper considers local median estimation in fixed design regression problems. The proposed method is employed to estimate the median function and the variance function of a heteroscedastic regression model. Strong convergence rates of the proposed estimators are obtained. Simulation results are given to show the performance of the proposed methods.展开更多
In this paper,a local discontinuous Galerkin(LDG)scheme for the time-fractional diffusion equation is proposed and analyzed.The Caputo time-fractional derivative(of orderα,with 0<α<1)is approximated by a finit...In this paper,a local discontinuous Galerkin(LDG)scheme for the time-fractional diffusion equation is proposed and analyzed.The Caputo time-fractional derivative(of orderα,with 0<α<1)is approximated by a finite difference method with an accuracy of order3-α,and the space discretization is based on the LDG method.For the finite difference method,we summarize and supplement some previous work by others,and apply it to the analysis of the convergence and stability of the proposed scheme.The optimal error estimate is obtained in the L2norm,indicating that the scheme has temporal(3-α)th-order accuracy and spatial(k+1)th-order accuracy,where k denotes the highest degree of a piecewise polynomial in discontinuous finite element space.The numerical results are also provided to verify the accuracy and efficiency of the considered scheme.展开更多
利用全身定位体架及基部剂量计划补偿(BDPC)技术研究一种全脑全脊髓放疗方法。对本院11例中枢神经系统恶性肿瘤患者进行研究。采用全身定位体架配合头颈肩模和体膜进行患者体位固定并利用基部剂量计划补偿(Base Dose Plan Compensation,...利用全身定位体架及基部剂量计划补偿(BDPC)技术研究一种全脑全脊髓放疗方法。对本院11例中枢神经系统恶性肿瘤患者进行研究。采用全身定位体架配合头颈肩模和体膜进行患者体位固定并利用基部剂量计划补偿(Base Dose Plan Compensation,BDPC)模块进行调强优化。评价靶区适形度指数(CI)、均匀性指数(HI)和危及器官(OAR)受量及射野衔接处剂量。此种方法提高了靶区适形度和均匀性,简化了计划设计过程,提高了摆位精度并保证了重复性。射野衔接处未出现剂量冷热点,与计算值基本一致。通过本研究证明全身定位技术联合BDPC优化方法在全脑全脊髓放疗中能满足临床剂量学要求,操作简便,提高计划设计效率。展开更多
基金supported by the National Natural Science Foundation of China (No.12271518)the Key Program of the National Natural Science Foundation of China (No.62333016)。
文摘In this paper,we construct a new sixth order iterative method for solving nonlinear equations.The local convergence and order of convergence of the new iterative method is demonstrated.In order to check the validity of the new iterative method,we employ several chemical engineering applications and academic test problems.Numerical results show the good numerical performance of the new iterative method.Moreover,the dynamical study of the new method also supports the theoretical results.
文摘Consider a branching random walk, where the underlying branching mechanism is governed by a Galton-Watson process and the moving law of particles by a discrete random variable on the integer lattice Z. Denote by Zn（z） the number of particles in the n-th generation in the model for each z ∈ Z. We derive the exact convergence rate in the local limit theorem for Zn（z） assuming a condition like ＂EN（logN）1＋λ 〈 ∞＂ for the offspring distribution and a finite moment condition on the motion law. This complements the known results for the strongly non-lattice branching random walk on the real line and for the simple symmetric branching random walk on the integer lattice.
基金This work was supported by the National Natural Science Foundation of China (10201001, 70471008)
文摘A noninterior continuation method is proposed for semidefinite complementarity problem （SDCP）. This method improves the noninterior continuation methods recently developed for SDCP by Chen and Tseng. The main properties of our method are： （i） it is well d.efined for the monotones SDCP; （ii） it has to solve just one linear system of equations at each step; （iii） it is shown to be both globally linearly convergent and locally quadratically convergent under suitable assumptions.
基金supported by the National Natural Science Foundation of China(Grant Nos.11201169,11271195,and 41231173)the Project of Graduate Education Innovation of Jiangsu Province,China(Grant No.CXLX13 366)
文摘A local energy conservation law is proposed for the Klein--Gordon-Schrrdinger equations, which is held in any local time-space region. The local property is independent of the boundary condition and more essential than the global energy conservation law. To develop a numerical method preserving the intrinsic properties as much as possible, we propose a local energy-preserving （LEP） scheme for the equations. The merit of the proposed scheme is that the local energy conservation law can hold exactly in any time-space region. With the periodic boundary conditions, the scheme also possesses the discrete change and global energy conservation laws. A nonlinear analysis shows that the LEP scheme converges to the exact solutions with order O（τ2 ＋ h2）. The theoretical properties are verified by numerical experiments.
基金The first author’s research was supported by the National Natural Science Foundation of China(Grant No.198310110 and Grant No.19871003)the partly support of the Doctoral Foundation of China and the last three authors’research was supported by a gra
文摘This paper considers local median estimation in fixed design regression problems. The proposed method is employed to estimate the median function and the variance function of a heteroscedastic regression model. Strong convergence rates of the proposed estimators are obtained. Simulation results are given to show the performance of the proposed methods.
基金supported by the State Key Program of National Natural Science Foundation of China(11931003)the National Natural Science Foundation of China(41974133)。
文摘In this paper,a local discontinuous Galerkin(LDG)scheme for the time-fractional diffusion equation is proposed and analyzed.The Caputo time-fractional derivative(of orderα,with 0<α<1)is approximated by a finite difference method with an accuracy of order3-α,and the space discretization is based on the LDG method.For the finite difference method,we summarize and supplement some previous work by others,and apply it to the analysis of the convergence and stability of the proposed scheme.The optimal error estimate is obtained in the L2norm,indicating that the scheme has temporal(3-α)th-order accuracy and spatial(k+1)th-order accuracy,where k denotes the highest degree of a piecewise polynomial in discontinuous finite element space.The numerical results are also provided to verify the accuracy and efficiency of the considered scheme.
文摘利用全身定位体架及基部剂量计划补偿(BDPC)技术研究一种全脑全脊髓放疗方法。对本院11例中枢神经系统恶性肿瘤患者进行研究。采用全身定位体架配合头颈肩模和体膜进行患者体位固定并利用基部剂量计划补偿(Base Dose Plan Compensation,BDPC)模块进行调强优化。评价靶区适形度指数(CI)、均匀性指数(HI)和危及器官(OAR)受量及射野衔接处剂量。此种方法提高了靶区适形度和均匀性,简化了计划设计过程,提高了摆位精度并保证了重复性。射野衔接处未出现剂量冷热点,与计算值基本一致。通过本研究证明全身定位技术联合BDPC优化方法在全脑全脊髓放疗中能满足临床剂量学要求,操作简便,提高计划设计效率。
