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Actually, such a generalized Cauchy distribution was the Pearson VII probability distribution. In this dissertation, the Lorentz distribution was regarded as a generalized Cauchy distribution with only one scale parameter; while the Pearson VII distribution was regarded as a generalized Cauchy distribution with a scale and a shape parameter both.

因此，本文提出应在Lorentz分布的密度函数中再增加一个能够反映分布函数尾部特征的形状参数，希望通过该参数的可调节性进一步改善稀疏编码算法的自适应性。

In Chapter 4, on the basis of introducing the theory of linear operator semigroup and the Cauchy problem in Hilbert space, this dissertation has researched the method on solving solution of distributed parameter system, and the model estimation and optimal control of the nonlinear distributed parameter system.

本文第四章在介绍线性算子半群理论及希尔伯特空间中的柯西问题的基础上，研究了分布参数系统的近似解求解方法，一类非线性分布参数系统的模型辩识和最优控制等问题。

The characteristic exponent based on a probabilistic dynamical system is calculated, which provides some useful information on unstable periodic orbits of the chaotic economic dynamical system. An effective controlling parameter is chosen by discussing the sign of the characteristic exponent. Furthermore, the control regions of the parameter variable are proposed. Therefore the controllable domain of chaos in the chaotic economic model can be obtained.

提出一种等价关系，计算基于概率的动力系统的特征指数，给出混沌经济动力系统的不稳定周期轨道的有用信息，通过讨论特征指数的符号，选择有效的控制参数，得到相应的控制参数取值范围，从而得到混沌经济模型中的参数变量的混沌控制域。

The core of this paper is to analyze and probe into ridge regression from different ideas, such as the existence of ridge parameter K, the choiceness of ridge estimation K , the choice of ridge parameter K and the methods of regression coefficients.

本文简单介绍了主成分回归，阐述了主成分估计方法的原理和优缺点；重点是从不同的角度不同的思想出发，对最常见的岭回归估计法进行了深入的探讨：岭参数K 的存在性，岭估计的优良性，岭参数K 的选择方法等。

The results indicate that as the value of fractal dimension is increased, the interfacial static friction coefficient first increases and then decreases; the interfacial static friction coefficient decreases as the fractal roughness parameter increases; while the inter-facial static friction coefficient increases as the material property or total normal load increases; the curve of static friction coefficient versus dimensionless total normal load is convex when the fractal dimension becomes smaller or fractal roughness parameter is larger or material property becomes smaller.

研究结果表明：界面的静摩擦因数首先随分形维数的增加而增加，然后随分形维数的增加而减小；界面的静摩擦因数随分形粗糙度参数的增加而减小，但随材料特性的增加而增加，也随总法向载荷的增加而增加；当分形维数较小或分形粗糙度参数较大或材料特性较小时，静摩擦因数－量纲一的总法向载荷曲线为凸弧。

According to these two joint density functions, various joint probability density functions between the ambiguity solution and the position parameter solution are obtained, and various conditional probability density functions of baseline position parameter vectors are also obtained.

根据这两个联合概率密度公式得到了各种类型的模糊度和基线位置参数向量的联合概率密度函数，还得到了各种类型基线位置参数向量的条件概率密度函数。

However, via intensive numerical computation, the author finds that actually some characteristic of this confidence intervals, for example, confidence coefficient, expectation width and coverage efficiency fluctuate intensely when the sample size varies given the parameter, or when the parameter varies given the sample size.

但是我们通过精细的数值计算发现，由于总体分布的离散性，这些置信区间的特性(置信系数、期望长度、覆盖效率)实际表现为当参数固定随着观测次数变化或当观测次数固定随着参数变化而发生强烈震动。

The confidence interval of unknown parameter represents the range of the value and the reliability about estimation of parameter.

未知参数的置信区间表示该参数的取值范围及其可信程度，置信区间的长度表示区间估计的精度。

A knowledge-based correction term in the objective function is proposed. The relationship between state estimatin and parameter estimation is analyzed. A strategy of projecting the objective function from the augmented solution space to the parameter space is proposed and proved.

该文提出基于经验知识的参数估计目标函数修正项，导出状态估计与参数估计目标函数极值的关系，由此提出将目标函数从增广解空间垂直投影到参数空间的估计策略，并指出参数估计偏差的成因。

The annual variation of each meteorological parameter likes cosmic ray flux. There is obvious correlation existing between cosmic ray and each meteorological parameter. After the meteorological effect of cosmic ray being corrected by using multianalysis, there is no annual variation of cosmic ray.

论文还对1994-2004年间的气象数据进行了整理分析，气压、室内温度、室外温度与宇宙线触发率有着相似的年变化，存在较强关联；之后对宇宙线触发率进行了多元气象参量修正，修正后的宇宙线触发率不再有明显的年变化。

Chinese traditional virtue is humility and wariness,the compliment and praise to the others should be declination

中国人的传统美德是谦虚谨慎，对别人的恭维和夸奖应是推辞。如

We bought this house on the never-never.

我们以分期付款的方式买下这座房子。