随机函数

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

According to Oseledec multiplicative ergodic theory and singular boundary theory, the conditions of local and global stability were acquired.

为了研究随机因素对经济系统稳定性的影响，建立了系统可靠性函数和首次穿越时间概率密度函数，并结合初始条件和边界条件得到了数值结果。

In order to set up the synthesis model of a function generating mechanism, the influence of controllable factors and noise factors on the movement precision of the mechanism was analyzed.

针对函数发生机构，分析了可控因素和不可控因素的随机变化对机构运动质量的影响，建立了考虑运动副间隙影响的机构稳健优化设计的数学模型，给出一曲柄滑块函数发生机构的稳健优化设计示例

The main procedures are as following: to generate small increment of parameters automatically and to calculate the FE several times and obtain the sensitivity of objective function to the parameters, and then form a Hermite polynomial approximation, the calculation of FE solutions are substitute by the calculation of polynomial approximation, so time cost decreases dramatically.

用n维埃尔米特插值技术建立设计变量在可行域上的目标函数的逼近函数；将局部寻优的梯度算法和全局寻优的随机算法结合起来，大幅度地降低寻优过程中电磁场的计算次数。

Because the weights are determined by the correlation of code sequence and estimation error of channels, which can be nearly determined by system load factor, we determine the sub-optimum weights by system load factor through simulations, and substitute the hard-decision symbol function by soft-decision hyperbolic tangent function to decrease the risk of error decision.

由于加权因子取决于前级符号估计的可靠性。也就是取决于扩频码互相关系数与信道估计精度，在随机扩频系统中，估计精度可近似由系统负荷决定，因此可根据系统负荷决定加权因子，以很小的性能降低代价换取计算量的极大降低。同时，为进一步降低误判风险，使用带有斜率控制因子的双曲正切函数代替常规的符号函数。

probability and density of power load ; kernel density estimation ; window width ; indexes of load probability characteristics ; Kolmogorov test

实际的电力负荷P是连续性随机变量，设我们要了解的负荷范围P∈a，b，F(p为电力负荷的分布函数，f为对应概率函数即分布

The paper provides a new dimension-reduced method of sensitivity analysis for stochastic user equilibrium assignment model based on the relation between its Lagrange function and logarithmic barrier function combined with a Courant quadratic penalty term. The advantage of this method is of smaller dimension than general sensitivity analysis and reducing the complexity.

基于随机用户平衡分配扰动模型的Lagrange函数及带柯朗二次惩罚项的对数边际函数之间的关系给出了一种的新的降维灵敏度分析方法，与通常所说的灵敏度分析相比它的优点是大大减小了计算的维数，降低了复杂性。

Supposeis two-dimension random variable, is unity density function and marginal density function leave each other, then sufficient and necessary condition for independence of and is: for all real values ,there are .

Theorem 3.3 设是二维连续型随机变量，分别是联合密度函数与边缘密度函数，则相互独立的充要条件是：对任意的实数，都有。

Copulas are functions that join multivariate distribution functions to their one-dimensional marginal distribution functions.

Copula函数是将多维随机变量的联合分布和其边缘分布连接起来的一种函数。

It obtained analytic expression or arithmetic solution of the mean value, the mean square value, the related function and the spectral density function of heat conduction system of 0-D, 1-D, 2-D and 3-D, by applying stochastically theory of linear system and the results of the first part.

该部分利用线性系统的随机理论和第一部分的成果，获得了0维、1维、2维和3维导热系统均值、均方值、相关函数、谱密度函数的解析表达式或数值解。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。