偏最小二乘回归的应用效果分析

本文介绍了偏最小二乘回归 (PLS)的建模方法 ,比较了PLS与普通最小二乘回归 (OLS)及主成分回归的应用效果 ,并总结了PLS回归的基本特点 .     

岭回归中确定K值方法的推广

给出了一种新的逐步改进岭参数 k的方法 .这种方法能够通过调整岭参数来进一步减少岭估计的均方误差 ,并改进了 Hoerl和 Kennard的结果 .     

Mie散射大气激光雷达回波信号消光系数边界值估算

报道了一种使用最小二乘法拟合大气激光雷达回波信号,计算消光系数边界值的算法。无云层天气条件下,利用最小二乘法对回波信号全程拟合获得大气消光系数边界值;有云层天气下,先将激光雷达信号在大气中的传输光路分段为云层区和非云层区,忽略回波信号中的云层信息,假设非云层区大气近似均匀,利用最小二乘法拟合获得大气消光系数边界值。     

R矩阵模型拟合中的协方差传递

对⁷Li,¹¹B和¹⁷O系统的R矩阵模型拟合进行了系统的协方差传递特性研究;揭示出部分协方差传递的规律性,发现系统误差的中程相关项在协方差传递中起到非常重要的作用     

用等效矩形波导近似研究双模椭圆芯光纤的特性

用等效矩形波导近似，结合一级微扰理论，研究了双模椭圆芯光纤的传播特性，得到了双模运行的Ｖ值范围和Ｅｘ２１模与Ｅｘ１１模之间的双折射、模间色散随归一化频率和椭圆比的变化关系曲线     

Abnormal behavior of the least squares estimate of multiple regression

An example is given to reveal the abnormal behavior of the least squares estimate of multiple regression. It is shown that the least squares estimate of the multiple linear regression may be “improved” in the sense of weak consistency when nuisance parameters are introduced into the model. A discussion on the implications of this finding is given.     

Least squares methods for Volterra equations and generalizations

In this article least squares approximations to Volterra integral equations are considered, both with exact integration and with quadrature. Optimal error estimates are derived, and it is shown that the same order of convergence is obtained in both cases with only modest requirements on the quadrature rule used in the latter. The most important practical setting for least squares is the case of convolution kernels, and these are also studied in this article. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 679–693, 1998     

Partition identities involving gaps and weights

We obtain interesting new identities connecting the famous partition functions of Euler, Gauss, Lebesgue, Rogers-Ramanujan and others by attaching weights to the gaps between parts. The weights are in general multiplicative. Some identities involve powers of 2 as weights and yield combinatorial information about some remarkable partition congruences modulo powers of 2.

     

Wave Properties of A Free Elliptical Helix Slow-Wave Structure with Arbitrary Eccentricity

This paper gives the investigations of the fundamental wave of a free elliptical helix slow-wave structure (SWS) with arbitrary eccentricity. The wave properties including the phase velocity characteristics, interaction impedance and the longitudinal electric field distribution of this mode has been fully studied. It is found that, when the eccentricity increases, the interaction impedance and the operating frequency of such SWS will be improved, which allows to have a higher gain and operating in a higher frequency band. Furthermore, the field configuration is different from that of a round helix; the azimuthal distribution of the E-field follows with the angular Mathieu function of the first kind, even with mode of zero. In radial, E-field is elliptical surface wave. When the eccentricity tends to zero, all the characteristics will be smoothly degenerates to the case of round helix correspondingly.     

求全局最优解的新算法

利用局部极大值点与动力系统的稳定奇点的对应性，计算代数方程的根、无约束极大值点、有约束极大值点、非线性规划解、及最小二乘解．我们采用了常微分方程数值解的Euler算法及网格初始点的循序迭代算法，并以具体的例子和程序说明创立的方法具有通用性，同时考虑了一些存在的问题以便在理论和算法上作进一步的改进。