多重线性的

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。

By fixed point index theory, multiplicity question of solutions to superlinear operator equations in ordered Banach space is discussed.

通过不动点指数理论，讨论了一类超线性算子方程的多重解问题。

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。

It uses t-Test and Granger Causality Test to solve the problems of multicollinearity and spurious regression, so the whole model is convictive.

3实证分析部分采用岭回归和Granger因果关系检验的计量方法，有效地克服了时间序列多元线性回归模型中经常出现的多重共线性和伪回归现象，模型整体具有较强的说服力。

The traditional query tree optimization methods,parallel database optimization methods based on left linear trees and right linear trees,bushy trees,and operation of the forest,have their own pros and cons,they have been more in-depth and maturity of the study.The query optimization method based on multiple weighted tree has studied its model of parallel query plan,its complexity model of parallel query plan and query optimization algorithms.The semantic query method transforms an inquiry into one or several semantic equivalence inquiries then has to find and implement a strategy to achieve a better query.Agent-based parallel database query optimization using Multi-Agent technology to automatically search the integrity constraint conditions which are related to the determined query,there for,the efficiency between several relations' joins has been greatly improved.The parallel optimization algorithm,based on genetic algorithm which is suitable for multi-joins of cluster environment,has deeply studied the relations storage options,multi-joins query optimization and query processing and other key technologies based on cluster parallel database.

传统的查询树优化方法，即基于左线性树、右线性树、浓密树、操作森林的并行数据库查询优化方法，各有优劣，对其的研究比较深入、成熟；基于多重加权树的查询优化方法，研究了其并行查询计划模型、并行查询计划的复杂性模型和查询优化算法；语义查询优化方法将一个查询变换成一个或数个语义等价的查询，进而寻找并执行这些等价查询中具有较好实现策略的一个；基于Agent的并行数据库查询优化采用Multi-Agent技术自动查找与给定查询有关的完整性约束条件，使得多个关系间连接操作的效率得到很大的提高；基于遗传算法的并行优化算法，深入研究了基于机群并行数据库中关系存储的选择、多连接查询优化和查询处理等关键技术。

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。

Furthermore, we find that for MIMO systems with constant number of scatterers, increasing number of antennas cannot linearly increase the capacity.

更进一步的说，我们发现了对於一个具有固定数目的散射体的多重天线系统，增加天线的数目并不能使得容量呈现线性的增加。

These algorithms can resolve efficiently the two difficult problems in aero\|engine fault diagnosis, e.i., reduce the number of fault factors in the fault equation, and improve its abnomal condition.

这两种算法可以有效地解决发动机故障诊断中的两个技术难点，即减少故障方程中故障因子的个数以及克服故障方程的多重共线性的不良影响。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。