为实现利用水稻叶片光谱指数实时预测稻米蛋白质含量,该研究采集了不同年份中氮素、品种差异下寒地水稻主要生育期(T1拔节期、T2齐穗期、T3结实期)顶部3片叶(L1、L2、L3)的叶片光谱反射率,探究其变化规律以及光谱指数与稻米蛋白质含量...为实现利用水稻叶片光谱指数实时预测稻米蛋白质含量,该研究采集了不同年份中氮素、品种差异下寒地水稻主要生育期(T1拔节期、T2齐穗期、T3结实期)顶部3片叶(L1、L2、L3)的叶片光谱反射率,探究其变化规律以及光谱指数与稻米蛋白质含量的关系,并用P-k、均方根误差(Root Mean Square Error,RMSE)和对称平均绝对百分比误差(Symmetric Mean Absolute Percentage Error,SMAPE)对模型精度进行验证。结果显示:施氮量多则稻米蛋白质含量高,蛋白质含量高的稻米食味值评分低。提高氮肥投入量,叶片反射率在可见光区域内呈降低趋势,而在近红外平台叶片反射率上升。随着生育期的推进,可见光区域内的叶片反射率逐渐上升,叶片反射率在近红外平台表现出先增加后降低的趋势,其变化规律与蛋白质营养转运有着密切联系。对光谱指标和稻米蛋白质含量进行相关分析,T2时期的L2的光谱指数与蛋白质含量的相关性优于其他时期的叶片,其中T2时期L1叶ARI1指标((1/R_(550))-(1/R_(700)))、L2叶CTR1指标((R_(695)/R_(420)))以及T3时期L3叶Rg指标(绿光范围510~560 nm内的最大波段反射率)显示出与蛋白质含量良好的拟合关系,指标验证的P-k分别为0.01、0.01、0.03,RMSE分别为0.19、0.11、0.14,SMAPE分别为1.56%、1.24%、1.44%,其中以T2时期L2叶CTR1指标表现最优,蛋白质含量拟合方程R2为0.75。综上,借助CTR1指标能够实现快捷、无损和实时预测稻米蛋白质含量的目的,达到按质收获以及品质实时监测的要求,促进优质寒地水稻的可持续发展。展开更多
The authors investigate Petrov-Galerkin spectral element method. Some results on Legendre irrational quasi-orthogonal approximations are established, which play important roles in Petrov-Galerkin spectral element meth...The authors investigate Petrov-Galerkin spectral element method. Some results on Legendre irrational quasi-orthogonal approximations are established, which play important roles in Petrov-Galerkin spectral element method for mixed inhomogeneous boundary value problems of partial differential equations defined on polygons. As examples of applications, spectral element methods for two model problems, with the spectral accuracy in certain Jacobi weighted Sobolev spaces, are proposed. The techniques developed in this paper are also applicable to other higher order methods.展开更多
Time-spectral solution of ordinary and partial differential equations is often regarded as an inefficient approach. The associated extension of the time domain, as compared to finite difference methods, is believed to...Time-spectral solution of ordinary and partial differential equations is often regarded as an inefficient approach. The associated extension of the time domain, as compared to finite difference methods, is believed to result in uncomfortably many numerical operations and high memory requirements. It is shown in this work that performance is substantially enhanced by the introduction of algorithms for temporal and spatial subdomains in combination with sparse matrix methods. The accuracy and efficiency of the recently developed time spectral, generalized weighted residual method (GWRM) are compared to that of the explicit Lax-Wendroff and implicit Crank-Nicolson methods. Three initial-value PDEs are employed as model problems;the 1D Burger equation, a forced 1D wave equation and a coupled system of 14 linearized ideal magnetohydrodynamic (MHD) equations. It is found that the GWRM is more efficient than the time-stepping methods at high accuracies. The advantageous scalings Nt<sup style="margin-left:-6px;">1.0Ns<sup style="margin-left:-6px;">1.43 and Nt<sup style="margin-left:-6px;">0.0Ns<sup style="margin-left:-6px;">1.08 were obtained for CPU time and memory requirements, respectively, with Nt and Ns denoting the number of temporal and spatial subdomains. For time-averaged solution of the two-time-scales forced wave equation, GWRM performance exceeds that of the finite difference methods by an order of magnitude both in terms of CPU time and memory requirement. Favorable subdomain scaling is demonstrated for the MHD equations, indicating a potential for efficient solution of advanced initial-value problems in, for example, fluid mechanics and MHD.展开更多
A proof is given that any λ _polynome over real quaternionic sfield can be factorized into produce of some linear factors.By the way,some properties and applications of this factorization in matrix theory are given.
文摘为实现利用水稻叶片光谱指数实时预测稻米蛋白质含量,该研究采集了不同年份中氮素、品种差异下寒地水稻主要生育期(T1拔节期、T2齐穗期、T3结实期)顶部3片叶(L1、L2、L3)的叶片光谱反射率,探究其变化规律以及光谱指数与稻米蛋白质含量的关系,并用P-k、均方根误差(Root Mean Square Error,RMSE)和对称平均绝对百分比误差(Symmetric Mean Absolute Percentage Error,SMAPE)对模型精度进行验证。结果显示:施氮量多则稻米蛋白质含量高,蛋白质含量高的稻米食味值评分低。提高氮肥投入量,叶片反射率在可见光区域内呈降低趋势,而在近红外平台叶片反射率上升。随着生育期的推进,可见光区域内的叶片反射率逐渐上升,叶片反射率在近红外平台表现出先增加后降低的趋势,其变化规律与蛋白质营养转运有着密切联系。对光谱指标和稻米蛋白质含量进行相关分析,T2时期的L2的光谱指数与蛋白质含量的相关性优于其他时期的叶片,其中T2时期L1叶ARI1指标((1/R_(550))-(1/R_(700)))、L2叶CTR1指标((R_(695)/R_(420)))以及T3时期L3叶Rg指标(绿光范围510~560 nm内的最大波段反射率)显示出与蛋白质含量良好的拟合关系,指标验证的P-k分别为0.01、0.01、0.03,RMSE分别为0.19、0.11、0.14,SMAPE分别为1.56%、1.24%、1.44%,其中以T2时期L2叶CTR1指标表现最优,蛋白质含量拟合方程R2为0.75。综上,借助CTR1指标能够实现快捷、无损和实时预测稻米蛋白质含量的目的,达到按质收获以及品质实时监测的要求,促进优质寒地水稻的可持续发展。
基金supported by the National Natural Science Foundation of China (No. 10871131)the Fund for Doctoral Authority of China (No. 200802700001)+1 种基金the Shanghai Leading Academic Discipline Project(No. S30405)the Fund for E-institutes of Shanghai Universities (No. E03004)
文摘The authors investigate Petrov-Galerkin spectral element method. Some results on Legendre irrational quasi-orthogonal approximations are established, which play important roles in Petrov-Galerkin spectral element method for mixed inhomogeneous boundary value problems of partial differential equations defined on polygons. As examples of applications, spectral element methods for two model problems, with the spectral accuracy in certain Jacobi weighted Sobolev spaces, are proposed. The techniques developed in this paper are also applicable to other higher order methods.
文摘Time-spectral solution of ordinary and partial differential equations is often regarded as an inefficient approach. The associated extension of the time domain, as compared to finite difference methods, is believed to result in uncomfortably many numerical operations and high memory requirements. It is shown in this work that performance is substantially enhanced by the introduction of algorithms for temporal and spatial subdomains in combination with sparse matrix methods. The accuracy and efficiency of the recently developed time spectral, generalized weighted residual method (GWRM) are compared to that of the explicit Lax-Wendroff and implicit Crank-Nicolson methods. Three initial-value PDEs are employed as model problems;the 1D Burger equation, a forced 1D wave equation and a coupled system of 14 linearized ideal magnetohydrodynamic (MHD) equations. It is found that the GWRM is more efficient than the time-stepping methods at high accuracies. The advantageous scalings Nt<sup style="margin-left:-6px;">1.0Ns<sup style="margin-left:-6px;">1.43 and Nt<sup style="margin-left:-6px;">0.0Ns<sup style="margin-left:-6px;">1.08 were obtained for CPU time and memory requirements, respectively, with Nt and Ns denoting the number of temporal and spatial subdomains. For time-averaged solution of the two-time-scales forced wave equation, GWRM performance exceeds that of the finite difference methods by an order of magnitude both in terms of CPU time and memory requirement. Favorable subdomain scaling is demonstrated for the MHD equations, indicating a potential for efficient solution of advanced initial-value problems in, for example, fluid mechanics and MHD.
文摘A proof is given that any λ _polynome over real quaternionic sfield can be factorized into produce of some linear factors.By the way,some properties and applications of this factorization in matrix theory are given.
