为研究带电粒子(H_3O^+,OH^-,NO_2^+ and NO^+)对1,1-二氨基-2,2-二硝基乙烯(FOX-7)裂解通道的影响,采用密度泛函理论的B3LYP、B3PW91和PBE0泛函理论在6-31++G(d,p)基组下优化出了H_3O^+,OH^-,NO_2^+ 和 NO^+分别与FOX-7的复合体,从成...为研究带电粒子(H_3O^+,OH^-,NO_2^+ and NO^+)对1,1-二氨基-2,2-二硝基乙烯(FOX-7)裂解通道的影响,采用密度泛函理论的B3LYP、B3PW91和PBE0泛函理论在6-31++G(d,p)基组下优化出了H_3O^+,OH^-,NO_2^+ 和 NO^+分别与FOX-7的复合体,从成键方式和静电势变化的角度分析了复合方式。在相同水平下,计算了各复合体不同裂解通道的活化能,并基于键长、键级、成键方式等电子结构参数的变化分析了活化能变化的本质。结果表明,在B3LYP/6-31++G(d,p)水平上,OH^-使两种构型C—NH_2键的离解能分别下降了260.7 k J·mol-1和74.3 k J·mol-1,H_3O^+,NO_2^+ 和 NO^+使C—NO_2键的离解能下降44~260 k J·mol-1,带电粒子使大部分复合体C—C键的离解能提高,但对硝基异构的活化能影响甚微,由过渡态分析可知,这源于硝基异构的过渡态具有的极其相似的几何构型。四种带电粒子都扰乱了单分子FOX-7相对稳定的结构,降低了FOX-7后续裂解的能垒,影响了FOX-7裂解中后期自加速反应的进程。展开更多
为提高月径流时间序列预测精度,改进最小二乘孪生支持向量回归机(Least Squares Twin Support Vector Regression,LSTSVR)性能,首次基于高斯核函数、多项式核函数、线性核函数构建混合核函数,提出4种季节趋势分解(Seasonal and Trend de...为提高月径流时间序列预测精度,改进最小二乘孪生支持向量回归机(Least Squares Twin Support Vector Regression,LSTSVR)性能,首次基于高斯核函数、多项式核函数、线性核函数构建混合核函数,提出4种季节趋势分解(Seasonal and Trend decomposition using Loess,STL)-小波包变换(Wavelet Packet Transform,WPT)-裂狐优化(Rüppell's Fox Optimizer,RFO)算法-混合核最小二乘孪生支持向量回归机(Hybrid Kernel Least Squares Twin Support Vector Regression,HLSTSVR)模型,并构建STL-WPT-RFO-LSTSVR、STL-WPT-RFO-混合核最小二乘支持向量回归机(Hybrid Kerllel Least Squares Twin Suppart Vector Regression,HLSSVR)、STL-WPT-RFO-最小二乘支持向量回归机(Least Squares Support Vector Regression,LSSVR)等17种对比分析模型,通过云南省高桥、凤屯水文站月径流时间序列预测实例对21种模型进行验证。首先利用STL-WPT二次分解技术对月径流序列进行分解处理,合理划分训练集和验证集;然后基于高斯核函数、多项式核函数、线性核函数,采用“三三”线性组合和“两两”线性组合的方式构建4种混合核函数对月径流分解分量进行空间映射;最后利用RFO寻优HLSTSVR/LSTSVR/HLSSVR/LSSVR最佳超参数,利用最佳超参数建立21种模型对实例月径流序列各分解分量进行训练、预测和重构。结果表明:①4种STL-WPT-RFO-HLSTSVR模型能适应不同尺度的月径流数据分布,具有较好的模型性能和较小的预测误差,其中STL-WPT-RFO-HLSTSVR(高斯+多项式+线性)模型对高桥、凤屯站月径流预测的平均绝对百分比误差MAPE分别为2.85%、2.19%,决定系数R2均为0.9994,预测精度最高、效果最好;②混合核函数兼顾了不同核函数优势,能在模型复杂度与泛化能力之间取得平衡,显著提升模型性能和预测精度;③STL-WPT二次分解技术能有效解决复杂时间序列的非平稳性、非线性和多尺度特征,较STL更具分解优势;④组合模型融合了STL-WPT、RFO和HLSTSVR优点,具有较好的普适性和参考价值。展开更多
Let s and z be complex variables, Γ(s) be the Gamma function, and for any complex v be the generalized Pochhammer symbol. Wright Type Hypergeometric Function is defined (Virchenko et al. [1]), as: where which is a di...Let s and z be complex variables, Γ(s) be the Gamma function, and for any complex v be the generalized Pochhammer symbol. Wright Type Hypergeometric Function is defined (Virchenko et al. [1]), as: where which is a direct generalization of classical Gauss Hypergeometric Function 2F1(a,b;c;z). The principal aim of this paper is to study the various properties of this Wright type hypergeometric function 2R1(a,b;c;τ;z);which includes differentiation and integration, representation in terms of pFq and in terms of Mellin-Barnes type integral. Euler (Beta) transforms, Laplace transform, Mellin transform, Whittaker transform have also been obtained;along with its relationship with Fox H-function and Wright hypergeometric function.展开更多
The Fox function expression and the analytic expression for the concentration distribution of fractional anomalous diffusion caused by an instantaneous point source in n-dimensional space (n= 1, 2 or 3) are derived by...The Fox function expression and the analytic expression for the concentration distribution of fractional anomalous diffusion caused by an instantaneous point source in n-dimensional space (n= 1, 2 or 3) are derived by means of the condition of mass conservation , the time-space similarity of the solution , Mellin transform and the properties of the Fox function . And the asymptotic behaviors for the solutions are also given .展开更多
文摘为研究带电粒子(H_3O^+,OH^-,NO_2^+ and NO^+)对1,1-二氨基-2,2-二硝基乙烯(FOX-7)裂解通道的影响,采用密度泛函理论的B3LYP、B3PW91和PBE0泛函理论在6-31++G(d,p)基组下优化出了H_3O^+,OH^-,NO_2^+ 和 NO^+分别与FOX-7的复合体,从成键方式和静电势变化的角度分析了复合方式。在相同水平下,计算了各复合体不同裂解通道的活化能,并基于键长、键级、成键方式等电子结构参数的变化分析了活化能变化的本质。结果表明,在B3LYP/6-31++G(d,p)水平上,OH^-使两种构型C—NH_2键的离解能分别下降了260.7 k J·mol-1和74.3 k J·mol-1,H_3O^+,NO_2^+ 和 NO^+使C—NO_2键的离解能下降44~260 k J·mol-1,带电粒子使大部分复合体C—C键的离解能提高,但对硝基异构的活化能影响甚微,由过渡态分析可知,这源于硝基异构的过渡态具有的极其相似的几何构型。四种带电粒子都扰乱了单分子FOX-7相对稳定的结构,降低了FOX-7后续裂解的能垒,影响了FOX-7裂解中后期自加速反应的进程。
文摘为提高月径流时间序列预测精度,改进最小二乘孪生支持向量回归机(Least Squares Twin Support Vector Regression,LSTSVR)性能,首次基于高斯核函数、多项式核函数、线性核函数构建混合核函数,提出4种季节趋势分解(Seasonal and Trend decomposition using Loess,STL)-小波包变换(Wavelet Packet Transform,WPT)-裂狐优化(Rüppell's Fox Optimizer,RFO)算法-混合核最小二乘孪生支持向量回归机(Hybrid Kernel Least Squares Twin Support Vector Regression,HLSTSVR)模型,并构建STL-WPT-RFO-LSTSVR、STL-WPT-RFO-混合核最小二乘支持向量回归机(Hybrid Kerllel Least Squares Twin Suppart Vector Regression,HLSSVR)、STL-WPT-RFO-最小二乘支持向量回归机(Least Squares Support Vector Regression,LSSVR)等17种对比分析模型,通过云南省高桥、凤屯水文站月径流时间序列预测实例对21种模型进行验证。首先利用STL-WPT二次分解技术对月径流序列进行分解处理,合理划分训练集和验证集;然后基于高斯核函数、多项式核函数、线性核函数,采用“三三”线性组合和“两两”线性组合的方式构建4种混合核函数对月径流分解分量进行空间映射;最后利用RFO寻优HLSTSVR/LSTSVR/HLSSVR/LSSVR最佳超参数,利用最佳超参数建立21种模型对实例月径流序列各分解分量进行训练、预测和重构。结果表明:①4种STL-WPT-RFO-HLSTSVR模型能适应不同尺度的月径流数据分布,具有较好的模型性能和较小的预测误差,其中STL-WPT-RFO-HLSTSVR(高斯+多项式+线性)模型对高桥、凤屯站月径流预测的平均绝对百分比误差MAPE分别为2.85%、2.19%,决定系数R2均为0.9994,预测精度最高、效果最好;②混合核函数兼顾了不同核函数优势,能在模型复杂度与泛化能力之间取得平衡,显著提升模型性能和预测精度;③STL-WPT二次分解技术能有效解决复杂时间序列的非平稳性、非线性和多尺度特征,较STL更具分解优势;④组合模型融合了STL-WPT、RFO和HLSTSVR优点,具有较好的普适性和参考价值。
文摘Let s and z be complex variables, Γ(s) be the Gamma function, and for any complex v be the generalized Pochhammer symbol. Wright Type Hypergeometric Function is defined (Virchenko et al. [1]), as: where which is a direct generalization of classical Gauss Hypergeometric Function 2F1(a,b;c;z). The principal aim of this paper is to study the various properties of this Wright type hypergeometric function 2R1(a,b;c;τ;z);which includes differentiation and integration, representation in terms of pFq and in terms of Mellin-Barnes type integral. Euler (Beta) transforms, Laplace transform, Mellin transform, Whittaker transform have also been obtained;along with its relationship with Fox H-function and Wright hypergeometric function.
基金the National Natural Science Foundation of China (10272067) the Doctoral Foundation of Education Ministry of China (1999042211)
文摘The Fox function expression and the analytic expression for the concentration distribution of fractional anomalous diffusion caused by an instantaneous point source in n-dimensional space (n= 1, 2 or 3) are derived by means of the condition of mass conservation , the time-space similarity of the solution , Mellin transform and the properties of the Fox function . And the asymptotic behaviors for the solutions are also given .
