In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order ...In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.展开更多
Target tracking control for wheeled mobile robot (WMR) need resolve the problems of kinematics model and tracking algorithm.High-order sliding mode control is a valid method used in the nonlinear tracking control sy...Target tracking control for wheeled mobile robot (WMR) need resolve the problems of kinematics model and tracking algorithm.High-order sliding mode control is a valid method used in the nonlinear tracking control system,which can eliminate the chattering of sliding mode control.Currently there lacks the research of robustness and uncertain factors for high-order sliding mode control.To address the fast convergence and robustness problems of tracking target,the tracking mathematical model of WMR and the target is derived.Based on the finite-time convergence theory and second order sliding mode method,a nonlinear tracking algorithm is designed which guarantees that WMR can catch the target in finite time.At the same time an observer is applied to substitute the uncertain acceleration of the target,then a smooth nonlinear tracking algorithm is proposed.Based on Lyapunov stability theory and finite-time convergence,a finite time convergent smooth second order sliding mode controller and a target tracking algorithm are designed by using second order sliding mode method.The simulation results verified that WMR can catch up the target quickly and reduce the control discontinuity of the velocity of WMR.展开更多
Based on the newly-developed element energy projection (EEP) method with optimal super-convergence order for computation of super-convergent results, an improved self-adaptive strategy for one-dimensional finite ele...Based on the newly-developed element energy projection (EEP) method with optimal super-convergence order for computation of super-convergent results, an improved self-adaptive strategy for one-dimensional finite element method (FEM) is proposed. In the strategy, a posteriori errors are estimated by comparing FEM solutions to EEP super-convergent solutions with optimal order of super-convergence, meshes are refined by using the error-averaging method. Quasi-FEM solutions are used to replace the true FEM solutions in the adaptive process. This strategy has been found to be simple, clear, efficient and reliable. For most problems, only one adaptive step is needed to produce the required FEM solutions which pointwise satisfy the user specified error tolerances in the max-norm. Taking the elliptical ordinary differential equation of the second order as the model problem, this paper describes the fundamental idea, implementation strategy and computational algorithm and representative numerical examples are given to show the effectiveness and reliability of the proposed approach.展开更多
In the paper quasi_weak convergence is introduced in ordered Banach space and it is weaker than weak convergence. Besed on it, the fixed point existence theorem of increasing operator is proved without the suppose of ...In the paper quasi_weak convergence is introduced in ordered Banach space and it is weaker than weak convergence. Besed on it, the fixed point existence theorem of increasing operator is proved without the suppose of continuity and compactness in the sense of norm and weak compactness and is applied to the Hammerstein nonlinear intergal equation.展开更多
In this paper, we study the relationship between the convergence of the sinusoidal series and the infinity integrals (any real number α ∈[0,1], parameter p > 0). First of all, we study the convergence of the seri...In this paper, we study the relationship between the convergence of the sinusoidal series and the infinity integrals (any real number α ∈[0,1], parameter p > 0). First of all, we study the convergence of the series (any real number α ∈[0,1], parameter p > 0), mainly using the estimation property of the order to obtain that the series diverges when 0 p ≤1-α, the series converges conditionally when 1-α p ≤1, and the series converges absolutely when p >1. In the next part, we study the convergence state of the infinite integral (any real number α ∈[0,1], parameter p > 0), and get that when 0 p ≤1-α, the infinite integral diverges;when 1-α p ≤1, the infinite integral conditionally converges;when p >1, the infinite integral absolutely converges. Comparison of the conclusions of the above theorem, it is not difficult to derive the theorem: the level of and the infinity integral with the convergence of the state (any real number α ∈[0,1], the parameter p >0), thus promoting the textbook of the two with the convergence of the state requires the function of the general term or the product of the function must be monotonically decreasing conditions.展开更多
The sequences defined in Example 3 and Example 4 do not serve our purpose for any λ = (λn). Because this sequences are just the sequences x = (xk) = (k) and x = (xk) = (1) respectively and any term of thes...The sequences defined in Example 3 and Example 4 do not serve our purpose for any λ = (λn). Because this sequences are just the sequences x = (xk) = (k) and x = (xk) = (1) respectively and any term of these sequences can not be 0. In this short not we give Example 3* and Example 4* to show that the inclusions given in Theorem 2.4 and Theorem 2.9 are strict for some λ = (λn) , α and β such that 0 α β ≤ 1.展开更多
The sample estimates of higher-order statistics are studied. Under certain conditions, the almost sure convergence of the third- and fourth-order moment and cumulant estimates of stationary processes is established. T...The sample estimates of higher-order statistics are studied. Under certain conditions, the almost sure convergence of the third- and fourth-order moment and cumulant estimates of stationary processes is established. The rate of almost sure convergence is obtained for the sample estimates of third- and fourth-order moment and cumulant. Additionally, it is shown that the third- and fourth-order moment and cumulant estimates are asymptotic normal.展开更多
This paper presents a new family of twelfth-order methods for solving simple roots of nonlinear equations which greatly improves the order of convergence and the computational efficiency of the Newton’s method and so...This paper presents a new family of twelfth-order methods for solving simple roots of nonlinear equations which greatly improves the order of convergence and the computational efficiency of the Newton’s method and some other known methods.展开更多
In this paper, a new class of triangular summation operators based on the equidistant nodes was constructed. It is proved that this class of operators converges uniformly to arbitrary continuous fimctions with the per...In this paper, a new class of triangular summation operators based on the equidistant nodes was constructed. It is proved that this class of operators converges uniformly to arbitrary continuous fimctions with the period 2π on the whole axis, Fttrthermore, the best approximation order and the highest convergence order are obtained. In contrast to certain operators constructed by Bernstein and Kis in the previous works, the convergence properties of the new operator constructed in this paper are superior.展开更多
Convergence behaviors of solutions arising from certain system of third-order nonlinear differential equations are studied. Such convergence of solutions corresponding to extreme stability of solutions when relates a ...Convergence behaviors of solutions arising from certain system of third-order nonlinear differential equations are studied. Such convergence of solutions corresponding to extreme stability of solutions when relates a pair of solutions of the system considered. Using suitable Lyapunov functionals, we prove that the solutions of the nonlinear differential equation are convergent. Result obtained generalizes and improves some known results in the literature. Example is included to illustrate the result.展开更多
Independent component analysis (ICA) is the primary statistical method for solving the problems of blind source separation. The fast ICA is a famous and excellent algorithm and its contrast function is optimized by ...Independent component analysis (ICA) is the primary statistical method for solving the problems of blind source separation. The fast ICA is a famous and excellent algorithm and its contrast function is optimized by the quadratic convergence of Newton iteration method. In order to improve the convergence speed and the separation precision of the fast ICA, an improved fast ICA algorithm is presented. The algorithm introduces an efficient Newton's iterative method with fifth-order convergence for optimizing the contrast function and gives the detail derivation process and the corresponding condition. The experimental results demonstrate that the convergence speed and the separation precision of the improved algorithm are better than that of the fast ICA.展开更多
This article investigates the convergence and growth of multiple Dirichlet series. The Valiron formula of Dirichlet series is extended to n-tuple Dirichlet series and an equivalence relation between the order of n-tup...This article investigates the convergence and growth of multiple Dirichlet series. The Valiron formula of Dirichlet series is extended to n-tuple Dirichlet series and an equivalence relation between the order of n-tuple Dirichlet series and its coefficients and exponents is obtained.展开更多
An equivalent description of u-uniform convergence is presented first. Then the relations among the order convergence, u-uniform convergence and norm convergence of sequences are discussed in Riesz spaces. An equivale...An equivalent description of u-uniform convergence is presented first. Then the relations among the order convergence, u-uniform convergence and norm convergence of sequences are discussed in Riesz spaces. An equivalence of the three convergences is brought forward; namely, {fn} is a u-uniform Cauchy sequence. Finally the relations among the three convergences of sequences are also extended to the relations among the convergences of nets in Riesz spaces.展开更多
A three-stage method is proposed to study the convergence clubs for the dynamic total factor carbon productivity (DCP) and the initial conditions. The first stage is to measure the DCP that reflects the initial differ...A three-stage method is proposed to study the convergence clubs for the dynamic total factor carbon productivity (DCP) and the initial conditions. The first stage is to measure the DCP that reflects the initial difference. The second stage is to identify the convergence club of DCP. The last stage is to examine the initial factors that may affect the formation of the convergence club. Construction industry data from 30 provinces in China's Mainland from 2005 to 2016 were adopted to conduct an empirical study. The empirical results showed that (1) the arithmetic mean value of China’s provincial DCP showed an upward trend and the standard deviation showed an expanding trend.(2) There are five convergence clubs, but 13 provinces failed to converge to any club.(3) The higher the degree of construction industry marketization in 2005, the greater the probability that the provinces belong to a club with higher DCP. To improve the DCP, the effective diffusion of low-carbon construction technologies and the market-oriented reform of state-owned construction companies should be promoted. The three-stage method can also be applied to study different industries in different countries or regions.展开更多
The aim of this paper is to study the weak integral convergence of Kergin interpolation. The results of the weighted integral convergence and the weighted (partial) derivatives integral convergence of Kergin interpola...The aim of this paper is to study the weak integral convergence of Kergin interpolation. The results of the weighted integral convergence and the weighted (partial) derivatives integral convergence of Kergin interpolation polynomial for the smooth functions on the unit disk were obtained in the paper. Those generalized Liang's main results were acquired in 1998 to the more extensive situation. At the same time, the estimation of convergence rate of Kergin interpolation polynomial is given by means of introducing a new kind of smooth norm.展开更多
In this paper, based on the idea of El-Mistikawy and Werle[1] we construct a difference scheme for a singularly perturbed self-adjoint ordinary differential equation in conservation form. We prove that it is a uniform...In this paper, based on the idea of El-Mistikawy and Werle[1] we construct a difference scheme for a singularly perturbed self-adjoint ordinary differential equation in conservation form. We prove that it is a uniformly convergent second order scheme.展开更多
The purpose of this paper is that we give an extension of Halley’s method (Section 2), and the formulas to compare the convergences of the Halley’s method and extended one (Section 3). For extension of Halley’s met...The purpose of this paper is that we give an extension of Halley’s method (Section 2), and the formulas to compare the convergences of the Halley’s method and extended one (Section 3). For extension of Halley’s method we give definition of function by variable transformation in Section 1. In Section 4 we do the numerical calculations of Halley’s method and extended one for elementary functions, compare these convergences, and confirm the theory. Under certain conditions we can confirm that the extended Halley’s method has better convergence or better approximation than Halley’s method.展开更多
文摘In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.
基金supported by National Natural Science Foundation of China (Grant No. 61075081)State Key Laboratory of Robotics Technique and System Foundation,Harbin Institute of Technology,China(Grant No. SKIRS200802A02)
文摘Target tracking control for wheeled mobile robot (WMR) need resolve the problems of kinematics model and tracking algorithm.High-order sliding mode control is a valid method used in the nonlinear tracking control system,which can eliminate the chattering of sliding mode control.Currently there lacks the research of robustness and uncertain factors for high-order sliding mode control.To address the fast convergence and robustness problems of tracking target,the tracking mathematical model of WMR and the target is derived.Based on the finite-time convergence theory and second order sliding mode method,a nonlinear tracking algorithm is designed which guarantees that WMR can catch the target in finite time.At the same time an observer is applied to substitute the uncertain acceleration of the target,then a smooth nonlinear tracking algorithm is proposed.Based on Lyapunov stability theory and finite-time convergence,a finite time convergent smooth second order sliding mode controller and a target tracking algorithm are designed by using second order sliding mode method.The simulation results verified that WMR can catch up the target quickly and reduce the control discontinuity of the velocity of WMR.
基金the National Natural Science Foundation of China(No.50678093)Program for Changjiang Scholars and Innovative Research Team in University(No.IRT00736)
文摘Based on the newly-developed element energy projection (EEP) method with optimal super-convergence order for computation of super-convergent results, an improved self-adaptive strategy for one-dimensional finite element method (FEM) is proposed. In the strategy, a posteriori errors are estimated by comparing FEM solutions to EEP super-convergent solutions with optimal order of super-convergence, meshes are refined by using the error-averaging method. Quasi-FEM solutions are used to replace the true FEM solutions in the adaptive process. This strategy has been found to be simple, clear, efficient and reliable. For most problems, only one adaptive step is needed to produce the required FEM solutions which pointwise satisfy the user specified error tolerances in the max-norm. Taking the elliptical ordinary differential equation of the second order as the model problem, this paper describes the fundamental idea, implementation strategy and computational algorithm and representative numerical examples are given to show the effectiveness and reliability of the proposed approach.
文摘In the paper quasi_weak convergence is introduced in ordered Banach space and it is weaker than weak convergence. Besed on it, the fixed point existence theorem of increasing operator is proved without the suppose of continuity and compactness in the sense of norm and weak compactness and is applied to the Hammerstein nonlinear intergal equation.
文摘In this paper, we study the relationship between the convergence of the sinusoidal series and the infinity integrals (any real number α ∈[0,1], parameter p > 0). First of all, we study the convergence of the series (any real number α ∈[0,1], parameter p > 0), mainly using the estimation property of the order to obtain that the series diverges when 0 p ≤1-α, the series converges conditionally when 1-α p ≤1, and the series converges absolutely when p >1. In the next part, we study the convergence state of the infinite integral (any real number α ∈[0,1], parameter p > 0), and get that when 0 p ≤1-α, the infinite integral diverges;when 1-α p ≤1, the infinite integral conditionally converges;when p >1, the infinite integral absolutely converges. Comparison of the conclusions of the above theorem, it is not difficult to derive the theorem: the level of and the infinity integral with the convergence of the state (any real number α ∈[0,1], the parameter p >0), thus promoting the textbook of the two with the convergence of the state requires the function of the general term or the product of the function must be monotonically decreasing conditions.
文摘The sequences defined in Example 3 and Example 4 do not serve our purpose for any λ = (λn). Because this sequences are just the sequences x = (xk) = (k) and x = (xk) = (1) respectively and any term of these sequences can not be 0. In this short not we give Example 3* and Example 4* to show that the inclusions given in Theorem 2.4 and Theorem 2.9 are strict for some λ = (λn) , α and β such that 0 α β ≤ 1.
文摘The sample estimates of higher-order statistics are studied. Under certain conditions, the almost sure convergence of the third- and fourth-order moment and cumulant estimates of stationary processes is established. The rate of almost sure convergence is obtained for the sample estimates of third- and fourth-order moment and cumulant. Additionally, it is shown that the third- and fourth-order moment and cumulant estimates are asymptotic normal.
文摘This paper presents a new family of twelfth-order methods for solving simple roots of nonlinear equations which greatly improves the order of convergence and the computational efficiency of the Newton’s method and some other known methods.
文摘In this paper, a new class of triangular summation operators based on the equidistant nodes was constructed. It is proved that this class of operators converges uniformly to arbitrary continuous fimctions with the period 2π on the whole axis, Fttrthermore, the best approximation order and the highest convergence order are obtained. In contrast to certain operators constructed by Bernstein and Kis in the previous works, the convergence properties of the new operator constructed in this paper are superior.
文摘Convergence behaviors of solutions arising from certain system of third-order nonlinear differential equations are studied. Such convergence of solutions corresponding to extreme stability of solutions when relates a pair of solutions of the system considered. Using suitable Lyapunov functionals, we prove that the solutions of the nonlinear differential equation are convergent. Result obtained generalizes and improves some known results in the literature. Example is included to illustrate the result.
文摘Independent component analysis (ICA) is the primary statistical method for solving the problems of blind source separation. The fast ICA is a famous and excellent algorithm and its contrast function is optimized by the quadratic convergence of Newton iteration method. In order to improve the convergence speed and the separation precision of the fast ICA, an improved fast ICA algorithm is presented. The algorithm introduces an efficient Newton's iterative method with fifth-order convergence for optimizing the contrast function and gives the detail derivation process and the corresponding condition. The experimental results demonstrate that the convergence speed and the separation precision of the improved algorithm are better than that of the fast ICA.
基金Supported by the National Science Foundation of China(10771011)the National Key Basic Research Project of China(2005CB321902)
文摘This article investigates the convergence and growth of multiple Dirichlet series. The Valiron formula of Dirichlet series is extended to n-tuple Dirichlet series and an equivalence relation between the order of n-tuple Dirichlet series and its coefficients and exponents is obtained.
文摘An equivalent description of u-uniform convergence is presented first. Then the relations among the order convergence, u-uniform convergence and norm convergence of sequences are discussed in Riesz spaces. An equivalence of the three convergences is brought forward; namely, {fn} is a u-uniform Cauchy sequence. Finally the relations among the three convergences of sequences are also extended to the relations among the convergences of nets in Riesz spaces.
文摘A three-stage method is proposed to study the convergence clubs for the dynamic total factor carbon productivity (DCP) and the initial conditions. The first stage is to measure the DCP that reflects the initial difference. The second stage is to identify the convergence club of DCP. The last stage is to examine the initial factors that may affect the formation of the convergence club. Construction industry data from 30 provinces in China's Mainland from 2005 to 2016 were adopted to conduct an empirical study. The empirical results showed that (1) the arithmetic mean value of China’s provincial DCP showed an upward trend and the standard deviation showed an expanding trend.(2) There are five convergence clubs, but 13 provinces failed to converge to any club.(3) The higher the degree of construction industry marketization in 2005, the greater the probability that the provinces belong to a club with higher DCP. To improve the DCP, the effective diffusion of low-carbon construction technologies and the market-oriented reform of state-owned construction companies should be promoted. The three-stage method can also be applied to study different industries in different countries or regions.
文摘The aim of this paper is to study the weak integral convergence of Kergin interpolation. The results of the weighted integral convergence and the weighted (partial) derivatives integral convergence of Kergin interpolation polynomial for the smooth functions on the unit disk were obtained in the paper. Those generalized Liang's main results were acquired in 1998 to the more extensive situation. At the same time, the estimation of convergence rate of Kergin interpolation polynomial is given by means of introducing a new kind of smooth norm.
文摘In this paper, based on the idea of El-Mistikawy and Werle[1] we construct a difference scheme for a singularly perturbed self-adjoint ordinary differential equation in conservation form. We prove that it is a uniformly convergent second order scheme.
文摘The purpose of this paper is that we give an extension of Halley’s method (Section 2), and the formulas to compare the convergences of the Halley’s method and extended one (Section 3). For extension of Halley’s method we give definition of function by variable transformation in Section 1. In Section 4 we do the numerical calculations of Halley’s method and extended one for elementary functions, compare these convergences, and confirm the theory. Under certain conditions we can confirm that the extended Halley’s method has better convergence or better approximation than Halley’s method.