多重线性

In conclusion, all our results further enrich, develop and perfect the theoretical system of the algebraic multigrid method.

代数多重网格方法是根据一般多重网格方法的原理建立起来的一种自动求解线性代数方程组的快速算法，它采用分层思想通过一种纯代数的多水平方法处理矩阵方程，特别是二维或三维大规模无结构方程组。

Combined the basic knowledge based on elliptic curve signature and proxy multi-signature system with the bilinear map, constructed a proxy multi-signature scheme.

3结合基于椭圆曲线的代理签名体制和代理多重签名的基本知识，使用双线性映射，构造了一种代理多重签名方案。

Lasso regression is one of the popular methods of dealing with Collinearity.

Lasso回归是目前处理多重共线性的主要方法之一，相对于其他方法，更容易产生稀疏解，在参数估计的同时实现变量选择，因而可以用来解决检验中的多重共线性问题，以提高检验的效率。

In many methods, PLS is a useful method for dealing with the collinearities.This paper discusses and researches the method of PLS, and mainly does following several aspects.First, the harm of the collinearity in the regression model is discussed, and several methods of dealing the collinearity are introduced.

本文对偏最小二乘法进行了探讨和研究，主要做了以下几方面的工作：第一，本文提出了多重共线性问题，讨论了共线性在回归建模中引起的危害，并介绍了处理多重共线性的几种常用方法。

The aim of this paper is to study the existence of solution and multiply results for quasilinear elliptic system in bounded domain and the whole space, semilinear elliptic equation in two dimension space, second order nonlinear difference equation by variational methods. The main results are listed in the following:1. An abstract compactness theorem is proved, and then, under weak Boccardo and De.

本文主要利用变分法，分别研究了有界区域和全空间上拟线性椭圆型方程组、二维空间上半线性椭圆型方程和二阶非线性差分方程问题的解与多重解的存在性，具体内容如下： 1。

Since the multiple scattering should be considered, the scattering problem of many-cylinders is more complicated than single cylinder. By using scattering matrix method to solve the scattering problem of many-cylinders, first we have to express the incident fieldand scattered field by special function（for example, Bessel function and Hankel function）under cylindrical coordinate, then use the addition theorem of special function to get a linear system of equations to relate the incident field coefficients and scattered field coefficients. The incident and scattered field coefficients for every cylinder can be solved from the linear equations by matching electromagnetic boundary condition pointwisely.

单颗圆柱散射体的散射场解析解很早就被解出，而多个圆柱阵列的散射场问题因为涉及到入射光在圆柱与圆柱间的多重散射，故散射行为较单颗圆柱的散射复杂，因此圆柱阵列的多重散射问题需要利用加法定理来处理；散射矩阵法的主要精神即是先用圆柱座标下的特殊函数对平面波和圆柱散射体的内外域电磁场做无穷级数展开，再藉由特殊函数的加法定理将所有圆柱散射体的展开中心移到同一个展开中心，最后可以得到一组连结整个散射系统的入射电磁场系数及散射电磁场系数的线性方程组，将该组线性方程配合电磁场在散射体边界的连续条件，便可分别求出圆柱阵列中各个圆柱体的内部电磁场与外部散射场，再利用线性叠加原理即可求得整个圆柱系统的全域电磁场分布。

This thesis is devoted to study the properties of the solutions of some specialrefinable equations,such as properties of multi-refinable,global linear independence,local linear independence and local polynomial property,etc,by using fractal theory,measure theory and theory of generalized functions.

本文的主要目的是通过用分形几何中的一些想法以及测度论和广义函数中的一些知识来研究一些特殊的细分方程的解的一些性质，如多重可细分性、整体线性无关性、局部线性无关性和局部多项式性质等。

And the author also gave us a example, the method is a new method to lower the dimensions of data.

该方法是不同于主成分分析法的一种新的降维方法，它能有效地减小多重共线性问题带来的影响，尤其在处理数据多重相关性突出的武器费用数据时，该方法有着良好的效果，最后，作者用一个实用算例证明了其有效性和可行性。

In the rest of this dissertation, we apply our above abstract results,"global Morse theory"and other critical point theorems to some semilinear resonant elliptic boundary value problems as well as some asymptotically"linear"or super"linear"p-Laplacian equations, and obtain the existence or multiplicity of solutions.

在后半部分，我们运用上面的抽象结果，以及大范围Morse理论和其他临界点理论，研究一些半线性椭圆共振问题的多重解的存在性，以及一些渐近线性或超线性p-Laplacian方程的解的存在性或多重性。

At last, the research test the logistic regression model with sample dada. The results are as the following:(1)Based on the time series dada, the financial early-warning model contains more crucial information reflecting the dada characters, so it can avoid the obvious logic problem in the other analysis such as single section dada and multi-section dada analysis. The test result indicate that the new model have a more accuracy than others.(2) the research adopt the global principal component analysis to settle the problem of multiple collinearity, so the model would be more normative and precise.(3)the early-warning model uses the backward method to regress, so it gets a terser model of only five variables, but it still has a precise forecasting ability.

通过本文研究说明：（1）建立以时序数据为基础的财务危机预警模型，提高了样本中重要财务趋势特征的信息含量，从而克服了国内外单截面及多重截面分析中普遍存在的明显逻辑问题，检验结果表明，利用时序数据建立的logistic财务危机判别模型较截面数据基础模型的判别准确率要高；（2）采用全局主成份分析方法解决了模型中因子间的多重共线性问题，这一处理使logistic回归方法应用的规范度和严谨度得到明显改善；（3）我们采用向后逐步回归的办法进行回归，使模型大大得到了简化，其中只包含五个自变量，但是它的整体预测准确性却仍然比较高，使模型更具有实用性。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。