随机函数

On the basis of some elementary theories about Galton-Watson branching process, the bisexual Galton-Watson branching process and the branching process with random environment are introduced in the paper.

本文在介绍GW分支过程一些基本理论的基础上，又介绍了两性分支过程模型及随机环境分支过程模型，并以两性分支过程为前提，研究了带配对函数L=x的两性分支过程{Z_n}。

Using parameters of states and coefficient, we simulated the branching process of young maize radicel and illustrated the simulation results by visualization method.

利用获取的状态分布函数与分支系数，以单位根段长(10mm)为模拟步长，采用随机模拟的方法，生成的玉米胚根的形态结构数据，最后将其可视化。

In Part two, it is proved that, the evolution strategy of uniform distribution for continuous functions, asymptotically converges to the global optimal solutions in probability, by using central limit theorem, under suitable conditions. Then a new kind of evolution strategies is proposed.

第二部分，针对连续函数优化问题，利用中心极限定理，在较弱的条件下，首先证明了基于均匀分布的进化策略是依概率收敛的，然后给出了采用一般连续型随机变量作为变异算子的进化策略依概率收敛的证明。

Aiming at the problems of over-fitting and generalization for neural networks, the locally most entropic colored Gaussian joint input-output probability density function estimate is studied, and a new method by means of Chebyshev inequality is proposed to self-revise respectively according to every cluster.

针对神经网络的过拟合和泛化能力差的问题，研究了样本数据的输入输出混合概率密度函数的局部最大熵密度估计，提出了运用Chebyshev不等式的样本参数按类分批自校正方法，以此估计拉伸样本集，得到新的随机扩充训练集。

The work is the preparation of the seismic ground motion coherency function analysis in the aspect of random vibration theory.

这一工作为地震动相干函数的计算分析奠定了随机理论方面的基础。

First, the backward Kolmogorov equation for the conditional reliability function and the Pontryagin equation for mean first-passage time and then- associated boundary and initial conditions are derived based on the stochastic averaging methods for quasi non-integrable, quasi integrable and quasi partially integ...

首先利用拟不可积、拟可积非共振及拟部分可积非共振Hamilton系统的随机平均法分别给出了研究该系统首次穿越问题的提法，包括计算条件可靠性函数的后向Kolmogorov方程及计算平均首次穿越时间的Pontryagin方程及其边值条件。

Eular -Bernonulli beam model and Tomosimko beam model were adapted to study the inherence vibration properties of the pipelines under dynamical loads, and the analytical answers of the chanmical results were brought out in the fifth chapter. And gave priority to the Eular -Bernonulli beam model, the simply and convenient analytical resolution for the response of the pipelines under dynamical traffic loads through the impulse function and the congruence method of the vibration form and so on.

本文采用Eular-Bernonulli梁模型和Tomosimko梁模型对动力下Kelvin粘弹性地基中管道固有振动性状进行了分析，提出了各力学结果描述的解析式；并以Eular-Bernonulli梁模型为主，基于脉冲函数、振型迭加法等对管道在动力交通荷载作用下的管道响应问题提出简单便捷的解析算法；在管道受力结果的分析中，考虑管道响应输出的随机性，将管道响应用随机过程来描述其概率特征，使得结果描述更加真实准确。

Mathematical model has been dealt with by punish function search method. Hooke-Jeeves modular vector search method and Powell conjugate direction search method have been adopted and modified.

利用"惩罚函数"法进行了数学模型的处理，采用并改进了Hooke-Jeeves的模矢搜索法及Powell的共轭方向法，还提出一种随机搜索法。

In view of continuous function problems, it is first proved that the-ES algorithm based on uniform distribution converges in probability in a weaker condition by means of the central limit theorem. Then it is proved that the-ES algorithm which adopts the general continuous random variables as its variable operators converges in probability.

针对连续函数优化问题，利用中心极限定理，在较弱的条件下，首先证明了基于均匀分布的-ES算法依概率收效，然后给出了采用一般连续性随机变量作为变异算子的-ES算法依概率收效的证明。

In view of continuous function problems,it is first proved that the-ES algorithm based on uniform distribution converges in probability in a weaker condition by means of the central limit theorem.Then it is proved that the-ES algorithm which adopts the general continuous random variables as its variable operators converges in probability.

针对连续函数优化问题，利用中心极限定理，在较弱的条件下，首先证明了基于均匀分布的-ES算法依概率收敛，然后给出了采用一般连续性随机变量作为变异算子的-ES算法依概率收敛的证明。

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。