随机

Many investigations show that randomicity of structures'parameter will bring large value of stochastic dynamic response of structures. Randomicity of structures'mechanics parameter may be dominant factors. Therefore, introduction of randomicity into system model of structure and using random system model are more reasonable than that of determinate system model.

众多的研究工作表明，结构参数的随机变异性可以引起结构随机动力响应的大幅度涨落，结构力学参数的随机性还可能成为主导因素，在结构系统模型中引入随机性的概念，采用随机结构系统模型是较确定性结构系统模型更为合理的一种选择。

E. , only are random variables, pointed that every objective important degree commonly is different, built the equivalent deterministic weighted programming model based on fuzzy set theory for multi - objective fuzzy stochastic linear programming.

研究了资源量b为随机变量的多目标随机线性规划问题，指出了多目标规划问题的目标一般不是同等重要的，针对多目标模糊线性规划问题，利用模糊集合理论建立了相应等价的确定性加权模糊随机规划模型。

The analysis in theory proves that cellular automaton is equal with a stochastic process that described by stochastic difference equations. The primary differential equation is expectation of this stochastic process. And its variance function is controllable. These results show that cellular automata are in agreement with primary differential equation in the statistical sense.

理论分析证明：该方法设计的细胞自动机等价于一个可用随机差分方程描述的随机过程，该随机过程以原微分方程为期望函数，并且，其方差函数是可控的，表明细胞自动机和原微分方程在统计意义上是一致的。

Content: In this paper, we investgated the type of two kinds of random Dirichlet series and the order and the type of two kinds of B-valued random Dirichlet series by use the methods of complex analysis, probability and random series.

本文运用复分析、概率论及随机级数的知识与研究方法，研究了两类随机Dirichlet级数的型和两类B-值随机Dirichlet级数的级和型，全文共分三个部分：第一章：简单介绍本研究方向的发展历史，研究现状以及一些必要的预备知识及其记号。

According to the Logistic Equation and the impact of stochastic factors, a stochastic nonlinear dynamical model had been presenred. The max Lyapunov exponent was calculated by Oseledec multiplicative ergodic theory, the local stability conditions had been obtained; the global stability conditions had also been obtained by judging the modality of the singular boundary; the stochastic Hopf bifurcation was analyzed using the invariant measure of stable probability density, and the condition of stochastic Hopf bifurcation had been discussed. The key parameter impacting the urban domestic water consumption had been found by numerical emulation.

根据Logistic阻滞增长模型原理，考虑到诸多随机因素的影响，本文建立了一个城市生活用水量的随机非线性模型，运用Oseledec乘性遍历定理计算了模型的最大Lyapunov指数，得到了局部稳定性的条件；通过对扩散边界性态的分析，得到了全局稳定性的条件；通过分析系统平稳状态概率密度的不变测度，得到了模型随机Hopf分岔的条件，结合实际进行了数值仿真，得到了影响用水量的关键参数。

Every existence theorem of them is proved, respectively.

本文所获的一些结果不仅是非线性泛函分析领域中一系列重要定理的推广，而且它们为随机微分方程、随机积分方程及随机算子方程的研究提供重要的工具。

Moreover,using Ito differential formul a to the constructed Lyapunov function along solutions of lto stochastic differential systems,Lyapunov method is adopted to set up the fundamental theory of dissipativity in the module corresponding to the theory on the dissipativity of deterministic ordinary dif- fere.

提出了有关Ito型随机微分系统耗散性理论的新概念：按模耗散、按模等度耗散和按模一致耗散，并利用Lyapunov方法，借助于Ito 微分公式沿着Ito型随机微分系统的解对所构造的Lyapunov函数求导数，给出了Ito型随机微分系统有关按模耗散理论的一些代数判据，获得了与确定性常微分系统耗散性理论相对应的结论，最后的算例证明了该方法的有效性和可行性。

The mechanical parameters in the model are treated as random variables and it is then resolved with Taylor extension stochastic finite element method, The distribution characteristics of the pore pressure, the effective stress and the displacement are researched by treating the mechanical parameters of the rock as random variables. The sensitivities of the pore pressure, the effective stress and the displacement to the random mechanical parameters are also analyzed.

视模型中的参数为随机变量，采用Taylor展开随机有限元法对该模型进行数值模拟，研究参数具有随机性情况下耦合场中孔隙压力、有效应力，位移等场变量的随机分布特征及孔隙压力、位移等场变量对参数的灵敏度。

Then we extend a lemma of Paley-Zygmund to-Zygmund to the cases of non-equally distributed and study the value distribution of more general random Dirichlet series with this lemma.

通常随机级数研究的是同分布随机变量序列，这里通过推广Paley-Zygmund引理，把随机级数的研究引向一般得多的不要求同分布的情况。

In ordinary regression analysis with random effects, the homoscedasticity of random effects is a basic assumption.

在随机效应回归模型中，随机效应存在时随机效应方差齐性是一个基本假定，在这些假定下，方可进行常规的统计推断。

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。