Polynomial factorization is indispensable in many fields and we are looking forward to having an efficient algorithm. The methods of Kronecker-Hermann and Van der Waerden-Tr?ger are too complicated to be put into prac...Polynomial factorization is indispensable in many fields and we are looking forward to having an efficient algorithm. The methods of Kronecker-Hermann and Van der Waerden-Tr?ger are too complicated to be put into practice in concrete cases. In recent years, there are many works about polynomial factorization, for example, [4 and 5], but the methods are not very efficient yet. In this paper,展开更多
Considering the polynomial f<sub>n</sub>（z）=a<sub>0</sub>z<sup>n</sup>+a<sub>1</sub>z<sup>n-1</sup>+...+a<sub>n-1</sub>z+a<sub>n</sub&...Considering the polynomial f<sub>n</sub>（z）=a<sub>0</sub>z<sup>n</sup>+a<sub>1</sub>z<sup>n-1</sup>+...+a<sub>n-1</sub>z+a<sub>n</sub>, （1） let P=（P<sub>0</sub>, P<sub>1</sub>,...,P<sub>n</sub>）, q=（q<sub>0</sub>, q<sub>1</sub>,...,q<sub>n</sub>）, a=（a<sub>0</sub>, a<sub>1</sub>,...,a<sub>n</sub>）, where p<sub>i</sub>, q<sub>i</sub>, a<sub>i</sub> are real numbers, satisfying the展开更多
This paper proposes a novel recursive partitioning method based on constrained learning neural networks to find an arbitrary number (less than the order of the polynomial) of (real or complex) roots of arbitrary polyn...This paper proposes a novel recursive partitioning method based on constrained learning neural networks to find an arbitrary number (less than the order of the polynomial) of (real or complex) roots of arbitrary polynomials. Moreover, this paper also gives a BP network constrained learning algorithm (CLA) used in root-finders based on the constrained relations between the roots and the coefficients of polynomials. At the same time, an adaptive selection method for the parameter d P with the CLA is also given. The experimental results demonstrate that this method can more rapidly and effectively obtain the roots of arbitrary high order polynomials with higher precision than traditional root-finding approaches.展开更多
Our general mechanization method of polynomial equations-solving is applied to the chemical equilibrium problem. A concrete case is analyzed and discussed in details.
An increase in crop intensity could improve crop yield but may also lead to a series of environmental problems, such as depletion of ground water and increased soil salinity. The generation of high resolution(30 m) cr...An increase in crop intensity could improve crop yield but may also lead to a series of environmental problems, such as depletion of ground water and increased soil salinity. The generation of high resolution(30 m) crop intensity maps is an important method used to monitor these changes, but this is challenging because the temporal resolution of the 30-m image time series is low due to the long satellite revisit period and high cloud coverage. The recently launched Sentinel-2 satellite could provide optical images at 10–60 m resolution and thus improve the temporal resolution of the 30-m image time series. This study used harmonized Landsat Sentinel-2(HLS) data to identify crop intensity. The sixth polynomial function was used to fit the normalized difference vegetation index(NDVI) and enhanced vegetation index(EVI) curves. Then, 15-day NDVI and EVI time series were then generated from the fitted curves and used to generate the extent of croplands. Lastly, the first derivative of the fitted VI curves were used to calculate the VI peaks;spurious peaks were removed using artificially defined thresholds and crop intensity was generated by counting the number of remaining VI peaks. The proposed methods were tested in four study regions, with results showing that 15-day time series generated from the fitted curves could accurately identify cropland extent. Overall accuracy of cropland identification was higher than 95%. In addition, both the harmonized NDVI and EVI time series identified crop intensity accurately as the overall accuracies, producer’s accuracies and user’s accuracies of non-cropland, single crop cycle and double crop cycle were higher than 85%. NDVI outperformed EVI as identifying double crop cycle fields more accurately.展开更多
针对群组移动节点定位算法普遍基于不切实际的假设,存在普适性欠佳和精度不高的问题,提出一种基于运动参数预测的群组移动节点定位算法。该算法根据群组移动节点具有相似运动的特点,运用Hermite插值多项式预测、过滤节点运动参数。为确...针对群组移动节点定位算法普遍基于不切实际的假设,存在普适性欠佳和精度不高的问题,提出一种基于运动参数预测的群组移动节点定位算法。该算法根据群组移动节点具有相似运动的特点,运用Hermite插值多项式预测、过滤节点运动参数。为确保定位精度,应对节点移动性带来的采样区域变化,运用预测节点运动参数构建粒子有效采样区域;为节省时间开销,基于采样粒子真实分布与其极大似然估计值之间的最大K-L(Kullback-Leibler)距离确定能够满足不同采样区域的最少粒子数目;为改善算法收敛性,运用预测运动参数创建滤波公式,并选取优质粒子参与节点位置估计。在与经典算法MCL(Monte Carlo localization)法和加权最小二乘法的MATLAB对比实验中,分析了节点移动速度、自由度、K-L距离阈值、采样方格边长对定位精度的影响。结果表明,较上述算法,本算法的定位误差和时间开销较小,无须锚节点辅助,普适性较好。展开更多
A new nonlinear force model based on experimental data is proposed to replace the classical Hertzian contact model to solve the fractional index nonlinearity in a ball bearing system. Firstly, the radial force and the...A new nonlinear force model based on experimental data is proposed to replace the classical Hertzian contact model to solve the fractional index nonlinearity in a ball bearing system. Firstly, the radial force and the radial deformation are measured by statics experiments, and the data are fitted respectively by using the Hertzian contact model and the cubic polynomial model. Then~ the two models are compared with the approximation formula appearing in Aeroengine Design Manual. In consequence, the two models are equivalent in an allowable deformation range. After that, the relationship of contact force and contact deformation for single rolling element between the races is cal- culated based on statics equilibrium to obtain the two kinds of nonlinear dynamic models in a rigid-rotor ball bearing system. Finally~ the displacement response and frequency spectrum for the two system models are compared quantitatively at different rotational speeds, and then the structures of frequency-amplitude curves over a wide speed range are compared qualitatively under different levels of radial clearance, amplitude of excitation, and mass of supporting rotor. The results demonstrate that the cubic polynomial model can take place of the Hertzian contact model in a range of deformation.展开更多
文摘Polynomial factorization is indispensable in many fields and we are looking forward to having an efficient algorithm. The methods of Kronecker-Hermann and Van der Waerden-Tr?ger are too complicated to be put into practice in concrete cases. In recent years, there are many works about polynomial factorization, for example, [4 and 5], but the methods are not very efficient yet. In this paper,
文摘Considering the polynomial f<sub>n</sub>（z）=a<sub>0</sub>z<sup>n</sup>+a<sub>1</sub>z<sup>n-1</sup>+...+a<sub>n-1</sub>z+a<sub>n</sub>, （1） let P=（P<sub>0</sub>, P<sub>1</sub>,...,P<sub>n</sub>）, q=（q<sub>0</sub>, q<sub>1</sub>,...,q<sub>n</sub>）, a=（a<sub>0</sub>, a<sub>1</sub>,...,a<sub>n</sub>）, where p<sub>i</sub>, q<sub>i</sub>, a<sub>i</sub> are real numbers, satisfying the
文摘This paper proposes a novel recursive partitioning method based on constrained learning neural networks to find an arbitrary number (less than the order of the polynomial) of (real or complex) roots of arbitrary polynomials. Moreover, this paper also gives a BP network constrained learning algorithm (CLA) used in root-finders based on the constrained relations between the roots and the coefficients of polynomials. At the same time, an adaptive selection method for the parameter d P with the CLA is also given. The experimental results demonstrate that this method can more rapidly and effectively obtain the roots of arbitrary high order polynomials with higher precision than traditional root-finding approaches.
文摘Our general mechanization method of polynomial equations-solving is applied to the chemical equilibrium problem. A concrete case is analyzed and discussed in details.
基金supported by the China Postdoctoral Science Foundation (2017M620075 and BX201700286)the National Natural Science Foundation of China (NSFC-61661136006)
文摘An increase in crop intensity could improve crop yield but may also lead to a series of environmental problems, such as depletion of ground water and increased soil salinity. The generation of high resolution(30 m) crop intensity maps is an important method used to monitor these changes, but this is challenging because the temporal resolution of the 30-m image time series is low due to the long satellite revisit period and high cloud coverage. The recently launched Sentinel-2 satellite could provide optical images at 10–60 m resolution and thus improve the temporal resolution of the 30-m image time series. This study used harmonized Landsat Sentinel-2(HLS) data to identify crop intensity. The sixth polynomial function was used to fit the normalized difference vegetation index(NDVI) and enhanced vegetation index(EVI) curves. Then, 15-day NDVI and EVI time series were then generated from the fitted curves and used to generate the extent of croplands. Lastly, the first derivative of the fitted VI curves were used to calculate the VI peaks;spurious peaks were removed using artificially defined thresholds and crop intensity was generated by counting the number of remaining VI peaks. The proposed methods were tested in four study regions, with results showing that 15-day time series generated from the fitted curves could accurately identify cropland extent. Overall accuracy of cropland identification was higher than 95%. In addition, both the harmonized NDVI and EVI time series identified crop intensity accurately as the overall accuracies, producer’s accuracies and user’s accuracies of non-cropland, single crop cycle and double crop cycle were higher than 85%. NDVI outperformed EVI as identifying double crop cycle fields more accurately.
文摘针对群组移动节点定位算法普遍基于不切实际的假设,存在普适性欠佳和精度不高的问题,提出一种基于运动参数预测的群组移动节点定位算法。该算法根据群组移动节点具有相似运动的特点,运用Hermite插值多项式预测、过滤节点运动参数。为确保定位精度,应对节点移动性带来的采样区域变化,运用预测节点运动参数构建粒子有效采样区域;为节省时间开销,基于采样粒子真实分布与其极大似然估计值之间的最大K-L(Kullback-Leibler)距离确定能够满足不同采样区域的最少粒子数目;为改善算法收敛性,运用预测运动参数创建滤波公式,并选取优质粒子参与节点位置估计。在与经典算法MCL(Monte Carlo localization)法和加权最小二乘法的MATLAB对比实验中,分析了节点移动速度、自由度、K-L距离阈值、采样方格边长对定位精度的影响。结果表明,较上述算法,本算法的定位误差和时间开销较小,无须锚节点辅助,普适性较好。
基金Project supported by the National Basic Research Program(973 Program)of China(No.2015CB057400)the National Natural Science Foundation of China(No.11602070)+1 种基金the China Postdoctoral Science Foundation(No.2016M590277)the Heilongjiang Postdoctoral Financial Assistance(No.LBH-Z16067)
文摘A new nonlinear force model based on experimental data is proposed to replace the classical Hertzian contact model to solve the fractional index nonlinearity in a ball bearing system. Firstly, the radial force and the radial deformation are measured by statics experiments, and the data are fitted respectively by using the Hertzian contact model and the cubic polynomial model. Then~ the two models are compared with the approximation formula appearing in Aeroengine Design Manual. In consequence, the two models are equivalent in an allowable deformation range. After that, the relationship of contact force and contact deformation for single rolling element between the races is cal- culated based on statics equilibrium to obtain the two kinds of nonlinear dynamic models in a rigid-rotor ball bearing system. Finally~ the displacement response and frequency spectrum for the two system models are compared quantitatively at different rotational speeds, and then the structures of frequency-amplitude curves over a wide speed range are compared qualitatively under different levels of radial clearance, amplitude of excitation, and mass of supporting rotor. The results demonstrate that the cubic polynomial model can take place of the Hertzian contact model in a range of deformation.
