Least square fitting of low resolution gamma ray spectra with cubic B-spline basis functions

In this paper, the least square fitting method with the cubic B-spline basis lunctions is derived to reduce the influence of statistical fluctuations in the gamma ray spectra. The derived procedure is simple and automatic. The results show that this method is better than the convolution method with a sufficient reduction of statistical fluctuation.     

二维无限深方势阱中粒子运动的路径积分解法

用路径积分的方法计算了二维无限深方势阱中粒子的传播子,并由传播函数推导出二维无限深方势阱中粒子的波函数和能量,进一步体现了路径积分与其他经典量子化方法的等价性,反映了路径积分应用于难以处理的量子力学问题的价值.     

牛奶中三聚氰胺的可见/近红外光谱快速判别分析方法的研究

为探讨基于可见一近红外光谱技术快速检测牛奶中是否含有三聚氰胺的可行性.文章通过往液态奶中添加不同含量的三聚氰胺,共制备样本160个.利用Handheld Field Spec光谱仪获取样本光谱,其后采用不同的预处理方法对光谱数据进行预处理,然后分别建立数学模型,比较模型的好坏,得到采用移动平均平滑作为数据的预处理方法较好.从160个样本中随机的取出120个样本建模,剩下的40个样本作为独立的验证集.采用偏最小二乘回归法(PLS)和最小二乘支持向苗机法(LS-SVM)方法分别建立判别分析模型,利用独立的验证集对判别模型进行了预测验证.预测结果的预测相关系数(R2)分别为0.917 4(PLS)和0.910 9(LS-SVM),预测标准误差(RMSEP)分别为0.030 4(PLS)和0.046 7(LS-SVM).研究结果表明近红外反射光谱可以作为一种快速检测牛奶中三聚氰胺的方法.     

A MESHLESS LOCAL PETROV-GALERKIN METHOD FOR GEOMETRICALLY NONLINEAR PROBLEMS

Nonlinear formulations of the meshless local Petrov-Galerkin （MLPG） method are presented for geometrically nonlinear problems. The method requires no mesh in computation and therefore avoids mesh distortion difficulties in the large deformation analysis. The essential boundary conditions in the present formulation axe imposed by a penalty method. An incremental and iterative solution procedure is used to solve geometrically nonlinear problems. Several examples are presented to demonstrate the effectiveness of the method in geometrically nonlinear problems analysis. Numerical results show that the MLPG method is an effective one and that the values of the unknown variable are quite accurate.     

修正样条小波最小二乘法用于分辨高噪声重叠峰

采用连续样条小波变换确定重叠信号的组分峰的数目和峰位置,将样条小波最小二乘法加以改进,使其成为既能滤出噪声又能分峰的新方法.对信噪比为1的重叠峰进行处理,得到满意结果.该方法只需对信号进行一次处理,处理速度快,且数据点无须为2n(n∈Z).应用于毛细管电泳电导信号的处理,得到满意结果.     

Carbon polyhedrons formed by squares and hexagons obeying isolated square rule

To gain insight into the structures and stability of F₄F₆ polyhedrons formed by squares and hexagons, a density functional theory study was performed on all isomers of F₄F₆ polyhedrons with sizes from 8 to 60. The calculated results demonstrate that the six squares tend to isolate from each other, i.e. these F₄F₆ polyhedrons obey the isolated square rule. Those isomers with fewer B₄₄ bonds (square-square adjacencies) are more stable than those with more B₄₄ bonds, i.e. they obey square adjacency penalty rule. Both of the two rules in F₄F₆ polyhedrons are in the same status as the isolated pentagon rule and pentagon adjacency penalty rule in F₅F₆ fullerenes and can be used to screen the lowest energy isomers of F₄F₆ polyhedrons as IPR and PAPR do in classic fullerenes. Structural analysis demonstrates that the pyramidalization of carbon atoms at the square-square adjacencies determines the stability of corresponding structures. Electronic Supplementary Material  Supplementary material is available for this article at and is accessible for authorized users. Supported from Southwest University, China (Grant No. SWNUB2005002) and Key Laboratory of the Three Gorges Reservoir Region’s Eco-Environment within Ministry of Education, Chongqing University (Grant No. KLVF-2007-5)     

半参数回归模型的几乎无偏岭估计

提出了半参数回归模型的几乎无偏岭估计,并与岭估计进行了比较,在均方误差意义下,几乎无偏岭估计优于岭估计. 然后讨论了有偏参数的选取问题. 最后,用模拟算例和实际应用说明了几乎无偏岭估计的有效性和可行性.     

二个四参数增长曲线模型参数初始值的确定方法与模型应用

对非线性回归模型进行非线性最小二乘估计一般需要确定参数初始值.在非线性回归模型中,General Logistic模型和Von Bertalanffy模型是二个含有四参数的增长曲线模型,对数据的拟合有较强的适应性,应用较为广泛.本文给出这两个模型参数初始值的确定方法,并应用于实际拟合,得到很好的效果.     

AHP判断矩阵权向量的改进最小二乘求解

提出了基于最小二乘法计算判断矩阵权向量的新方法.固定AHP判断矩阵权向量中的一个值为常量,利用判断矩阵的上三角部分元素,设计了一种计算判断矩阵权向量的新算法,算法简单,计算容易,与特征向量排序方法导出标度相同,并且能够证明存在唯一解.实验表明该算法具有有效性和可行性.