极限分布

Central Limit Theorem -- States that distribution of sample means tends towards an approximate normal distribution.

中心极限定理--样本的均值近似服从正态分布。如果样本容量较大，那么其均值的分布越近似于正态分布。

By using the generalized central limit theorem, the heavy-tailed distributions (heavy-tailed Rayleigh distribution for amplitude image and heavy-tailed exponential distribution for intensity image) are obtained from the symmetric stable distributions of real and imaginary parts of echoes. Taking the heavy-tailed Rayleigh distribution as an example, the algebraic tails of heavy-tailed distributions are explained as well as the statistics of sharp peak and heavy tail.

本文使用广义中心极限定理，由雷达回波的实部和虚部的对称稳定分布，得到SAR图像的拖尾分布（幅值图像的拖尾Rayleigh分布以及强度图像的拖尾指数分布），并以拖尾Rayleigh分布为例，讨论了拖尾分布的代数拖尾特征以及尖峰厚尾的统计特性。

This project also obtained several limit theorems for some important dependent random variables and stochastic processes, such as the Strassen law of the iterated logarithm for negatively dependent random variables, strong limit theorems for mixing random vectors in Banach spaces, sample path properties for two-parameter fractional Wiener processes, and so on.

随机环境中的随机变量与随机过程的研究在国内外相当活跃，本项目主要研究它们的极限性质，着重研究了随机风景中随机变量与随机过程的极限性质，主要取得了以下几个结果：首先对简单对称的Kesten-Spitzer随机游动在低阶矩的条件下给出了强逼近，大大减弱了前人要求任意阶矩的条件，然后对独立风景中的一般随机变量给出了强逼近的一般性结果，由此导出在风景和随机变量都只具有低阶矩的条件下的独立但不同分布、混合相依变量的强逼近，在只有弱高于二阶矩的条件下得到了重相对数律和弱收敛；给出了连续时间参数的Brown风景中Brown运动和稳定风景中稳定过程的滞后增量和连续模等精确样本轨道性质；同时给出了一些重要的相依随机变量和过程的若干极限定理，如负相关随机变量的Strassen重对数律、抽象空间上混合相依变量的一些强极限定理成立的充分必要条件、两参数分数Wiener过程的样本轨道性质等。

By using the GUI program, the user can deal with practical problem conveniently: soil space distributing, soils parameter; having or no water and water distribution, loads distribution and values; earthquake condition; start element of KEM; pointing out the elements which displacement should be known and the displacement value.

编制的图形用户界面程序能使用户方便地在图形界面下，按照菜单和对话框的提示，人机交互输入KEM土体极限分析需要的所有资料：土体的空间分布情况，各土层的土体参数，有无地下水以及地下水的水位分布情况，外荷载的分布及大小，地震情况，划分初始的KEM土体单元，指定需要施加虚位移的土体单元及与其相应虚位移的大小。

In the elastic limit state as defined in this paper, the stress distribution and the limit temperature of the plate are obtained.

对陶瓷 /金属功能梯度多层组合板进行了稳态热传导分析及热弹性极限分析，导出了稳态温度分布场，极限状态热弹性应力分布的计算式，并在弹性极限状态下，得到了弹性极限温度。

In order to reduce calculation error, the frequency distribution of average values is used to compute the mixed distribution's digital features of each component distribution, thereinto, the number of the component distribution is determined by AIC, choose the number that meets the minimum value of AIC as the component number of mixed distribution, and the other parameters are estimated by EM algorithm; Secondly, because each component distribution is corresponding to a kind of major gene genotype, according to the values of the average and variance of the each component distribution, we can use the limit error of the normal distribution to plot each individual into the correspondent component distribution, namely into correspondent major gene genotype. Then we regard each major gene genotype as a treatment level of one-way analysis of variances, and the one-way multivariate analysis of variance is carried out to calculate the covariance matrix of major gene effect, covariance matrix of polygene effect, covariance matrix of environment effect and so on; At last, combining the weights of the each component distribution of mixed distribution, we can calculate the variance of major gene effect, the variance of polygene effect, environmental variance and the genetic gain of the quantitative trait.

为减小计算误差，本研究采用均值的频数分布来计算各成分分布的数字特征，其中成分分布个数根据AIC准则，选择使AIC值达到最小的成分分布个数作为混合分布的成分分布数，分布中其它参数的确定利用EM算法来估计；其次，每个成分分布对应一种主基因基因型，根据各个成分分布的均值和方差，利用正态分布的极限误差将每个个体划分到相应的成分分布中，即相应的主基因基因型中，将每种主基因型作为单因素方差分析的一个处理水平，对其进行单因素的多元方差分析，分别计算主基因效应协方差阵、多基因效应协方差阵、环境协方差阵等参数；最后结合混合分布中各成分分布的权重即各主基因基因型的分离比例，计算主基因效应方差，多基因效应方差和环境方差，以及遗传力等参数，进而计算该数量性状的遗传进展。

The Parabola Hypothesis corrected by the authors. The authors have used this method on computer to get the bending fatigue test data of carburized and quenched gears and the fatigue limiting stress distribution. Furthermore, the...

然后对渗碳淬火钢齿轮的弯曲疲劳试验数据用JFKC法进行计算，得到了它的疲劳极限应力分布，并对比其相应的成组试验法测定的疲劳极限应力分布进行了分析和讨论。

The expression of the complex equipment failure rate under the normal operating conditions were researched based on the renewal theory .

基于更新理论，研究了正常使用条件下复杂设备故障率λ的表达问题，结果表明：对任意的故障分布，复杂设备故障率λ的极限为一积分表达式，仅在指数分布时，该极限是一个常数。

The capacity of single pile will enhance when the length and diameter of pile increases, but effect of pile diameter is more obvious. While pile diameter increases 20、40 and 60 percents, the capacity of pile will enhance 20.4、53.7 and 78.1 percents. And with the effect of mud-cake, the capacity of single bored pile will fall down nearly 20 percents, and pile-side resistance will also reduce 15 — 35 percents. In the centrifuge tests, when the relative displacement between pile and soil was 45 —85mm, which is much more than the criterions, the pile-side resistance will become most. Meanwhile the intenerated value of utmost resistance is close to the resistance in situ. In the pile group tests, the capacity of pile group , which the space among piles increases from 2D to 3D、 4D and 5D , will enhance 6.1、9.6、18 percents .

当桩径增加20%、40%、60%时，桩承载力分别增长了20.4%、53.7%和78.1%；在考虑泥皮效应后单桩侧摩阻力减小15～35%，极限承载力减小18%～24%，且减小率随桩径的增加而变小；试验中桩身侧阻软化值与原型桩实测侧阻软化值接近，且极限侧阻所对应的桩土相对位移试验要比规范值大得多，约为45～85mm；同时群桩极限承载力随桩距的增大而增加，其中桩距为3D、4D、5D的群桩承载力分别比间距为2D的群桩高6.1%、9.6%和18%；其承载力效应系数η接近或大于1，并随着桩间距的增大而不断提高；群桩侧摩阻力沿深度的分布与单桩略有不同，即桩身上部由于承台的作用，侧阻削弱，但桩身中部侧阻具有增加的趋势。

The program can be used to track the limit load and flex point of space structure, can take structural imperfection into consideration, gets the buckling model and vibration model of three-dimension steel structure, analyzes the elastic-plastic status or stress distributing of any intersection and any point and draws the nephogram of stress distributing, the hysteretic line subjected to cyclic load and local buckling deformation.

本软件能够跟踪分析任意空间结构中各种反弯点和极限荷载、并能够考虑结构的缺陷分布影响、求解三维空间钢结构屈曲模态和振动模态。进而分析钢构件任意截面、任意点的应力分布及塑性屈服状态，绘制截面的应力分布云图及循环荷载下的滞回曲线，绘制钢构件的局部屈曲变形图。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。