分布矩

Cauchy distribution is a particular one in probability and it has a lot of special properties.

柯西分布是概率统计学中的一个极具特色的连续型分布，其独有的性质历来备受重视，利用特征函数这一工具，讨论了柯西分布的结构、矩存在性、可加性、无穷可分性等概率性质。

The distribution function of the system response and state function is approximately determined by the standard normal distribution functions using Edgeworth series, and its reliability is obtained.

在结构系统响应和状态函数的前四阶矩的一般数学表达式的基础上，使用 Edgeworth级数把未知响应和状态函数的概率分布展开成标准的正态分布表达式，并放松了对随机参数的分布概型和激励类型的限制，从而确定了系统的可靠度

Using the characteristic found,the maximum likelihood estimators and the moment estimator s of parameters of the multivariate exponential distribution of Freund are obtained.

利用分布密度分拆的思想，导出了二元及多元Freund型指数分布的一个特征，利用该特征，获得了二元及多元Freund型指数分布参数的最大似然估计及矩估计，还给出了强度服从二元Fre-und型指数分布时并联结构系统的可靠度估计及模拟。

The wavelet energy moment can reflect the distribution of signal energy in frequency domain and that in time domain indirectly as well.

信号能量的时频分布可以反映不同信号的本质区别，小波能量矩既可以反映信号能量在频域上的分布，也可以间接体现能量在时域上的分布。

The distribution of signal energy in time domain and frequency domain can reveal essential differences among various signals in detail comparatively. The wavelet energy moment can reflect the distribution of signal energy in frequency domain and that in time domain indirectly as well.

信号能量的时频分布可以反映不同信号的本质区别，小波能量矩既可以反映信号能量在频域上的分布，也可以间接体现能量在时域上的分布。

We obtain the risk process involved in this model,the statistical properties of the surplus process,and statistical features of the claim numbers and the probability distribution of the total amount of compensation.The three types of business of the risk model is given when the number of claims obey Poisson distribution and negative binomial distribution.We make a comparison between the risk model built in the thesis and the classic risk models with independent claim numbers when the amount of claims obey Weillbull distribution and Exponential distribution.The results have a good practical significance.

其次，考虑不同险种间的相互关系，建立了一种含有主副理赔的风险分析模型；借助随机过程和经典风险理论，对该风险模型所涉及的风险过程、盈余过程的统计特性以及理赔总额的概率分布、数字特征和矩母函数进行解析研究，给出了主理赔次数服从泊松分布和负二项分布的这种风险模型的具体实例，并在理赔额变量服从Weillbul分布和Exponential分布的情况下，把文中所建风险模型和理赔次数相互独立的风险模型作了比较，所得结果有很好的现实意义。

The class of distribution of decreasing variance residual life an that of decreasing percentile residual life are investigated,some their characters are also given,and their characteristic result is given when the general moments of residual life function are taken as their basis.

阐述了递减方差剩余寿命分布与平衡分布的平均剩余寿命函数的密切联系；研究了递减方差剩余寿命分布类及递减百分位数剩余寿命分布类，并且给出了它们的一些特征；给出了以剩余寿命函数的一般矩为基础的特征结果。

The results indicate that in the synchronizing condition the MRF is unyielded, every point of MRF in the flow field has the same angular velocity. Under the slipping condition, with the increase of magnetic field or the decrease of slip speed, MRF may transfer from whole yield to partial yield. When the MRF wholly yields, the angular velocity of MRF increases nonlinearly with its radius, the non-linear distribution becomes more obvious as the magnetic intensity in the working gap increases. When the MRF partially yields, the yield region expands with the decrease of magnetic intensity or the increase of slip speed and the unyield region always reaches the driven rotor. The transfer torque of MRTD increases with the increase of the external magnetic field, but the transfer torque maintains a constant value approximately with the variation of slip speed at the same magnetic intensity.

研究结果表明，在同步工况下，传动装置流场中磁流变液未屈服，各点角速度相同；在滑差工况下，随外加磁场的增大和滑差转速的减小，磁流变液逐渐从完全屈服向部分屈服转变；磁流变液完全屈服时，磁流变液角速度随半径呈非线性增加，工作间隙中磁场越强，流场的非线性分布越明显；磁流变液部分屈服时屈服区域随外加磁场的增大而减小，随滑差转速的增大而增大，未屈服区与主动转子相连；稳态下磁流变传动装置传递的转矩随外加磁场的增加而近似呈线性增大，但在相同外加磁场下，传递转矩基本不随滑差转速改变而改变，表现出良好的恒转矩特性。

Based on density functional theory and electronegativity equalization principle,applying an atom-bond electronegativity equalization σπ model,using a separated program,we calculated the charge distributions and dipole moments of guanine tautomers.

以密度泛函和电负性均衡原理为基础发展的原子-键电负性均衡方法的σπ模型。并结合自编程序，计算了鸟嘌呤五种异构体的电荷分布和偶极矩，计算结果表明，所计算出的电荷分布可以和从头算结果很好地关联。所计算的偶极矩与其它从头计算方法和力场方法相比总体趋势相同，进一步说明了ABEEMσπ模型的合理性

The ideal quantum gases obey Bose-Einstein or Fermi-Dirac statistics and the flux can be derived from the known distribution function. In this sense, we develop the kinetic schemes that suitable for ideal quantum gas and investigate the influence of the quantum effect. In this thesis we discuss shock tube problems and shock diffraction by wedges and shock diffraction by cylinders for the ideal quantum gases.

理想量子气体之速度分布依循Bose-Einstein或Fermi-Dirac分布，在已知气体分布函数的情况下，对分布函数取矩可得宏观量及其通量，本文即利用此概念发展适用於理想量子气体之气体运动算则，并探讨量子效应造成之影响，本文探讨理想量子气体之震波管、楔形体和圆柱震波绕射问题。

I use an example quoted by Hu Jiaqi:"It is reported that America separates the DNA of a kind of virus by making use of genetic technology and combines it with another kind of DNA. Finally, they get a kind of virulent biological agent called a "pyrotoxin". Someone discloses in private that 20 grams of such a kind of biological agent could result in the global death of 6 billion people due to infection."

我在这里例举胡家奇所引用过的例子："据报道，美国利用转基因技术，将一种病毒的DNA分离出来，与另外一种DNA进行结合，拼结成一种剧毒的"热毒素"生物战剂，且私下有人透露，这种生物战剂只需20克，就可以导致全球60亿人全部感染死亡。"

Waiting, for the queers and the coons and the Reds and the Jews.

等待着疯子和黑人还有红色共产主义者还有犹太人