随机函数

From this,two algorithms to find low degree annihilators of a Boolean function are present:complete searching and stochastic searching.The complete one can not only get all the low degree annihilators of a Boolean function,but also get the algebraic immunity of the function.

利用完全搜索法可以得到布尔函数的所有低次零化子，同时还可以确定该布尔函数的代数免疫度；利用随机搜索法能快速得到布尔函数的任意一个低次零化子。

In this paper the method of combinational mathematics is used to deduce the probability generation function of the longest run in the Bernoulli trials,and get the probability generation function without using its probability function of kth order geometric distribution.

游程及其相关理论广泛地应用于随机检验、质量控制、DNA数据分析等许多领域，提出使用组合数学的方法推导出贝努利试验中最长游程的概率发生函数的计算公式，利用所得到的结果可以不用k阶几何分布的概率函数而很容易地得出它的概率发生函数。

Its mean function, variance function and correlation coefficient function can be gained by the method in time domain.

该方法首先在时域进行全程分析，得到相关系数平稳过程的均值函数、方差函数和相关系数函数，然后可以对其进行傅里叶变换、短时傅里叶变换或小波变换，给出相关系数平稳过程的谱密度，同时提出了随机项谱密度和趋势项谱密度的概念。

In this article the usual method of determining the distribution density of function of one-dimensional continuous random variable——distribution function method.

本文给出了求一维连续型随机变量函数分布密度的一般方法：分布函数法，并用分布函数法对现有文献中的计算公式进行了理论探讨，对现有的定理进行修正拓展，扩大了应用范围。

The monotone class theorem of multiple dimension functional format.This is the generalization from the one dimension monotone class theorem.

给出了多维函数形式的单调类定理，它是一维函数形式单调类定理的推广，也是处理多维可测函数、多维随机过程的有力工具。

In this paper,we propose a novel model named distribution-free data density estimation,which is based on distribution-free(i.e.,independent of data distributions) sampling on global cumulative distribution to achieve high estimation accuracy with low estimation cost regardless of distribution models of the underlying data.

分布无关密度估计算法首先将底层数据的任意分布转换成一中间分布——累计概率分布函数。由于累计概率分布函数的输出在[0，1]之间均匀分布，因此接着对累计概率分布函数的输出随机采样，可以准确估计当前网络中数据的密度分布。

Compared with deterministic systems, the infinitesimal generator for the system is a second-order differential operation. In this dissertation, we designed the quartic control Lyapunov function and systematically design the state-feedback and output feedback adaptive controller using integrator backstepping methodology. The closed-loop system is asymptotically stable in the large.

与确定性系统相比，随机系统的Lyapunov函数的微分运算包含二阶导，所以设计适当形式的控制Lyapunov函数十分关键，本文设计了四次型的控制Lyapunov函数，并应用积分反推技术，给出了状态反馈及输出反馈自适应控制器和鲁棒自适应控制器的设计方法，证明了闭环系统概率意义下的渐近稳定性和有界稳定性。

The interpolation formula can be compiled into standard computer code.

在此，我们首先论述了保单调性的插值方法，根据分布函数的逆函数具有单调性的特点，用保单调的插值曲线去逼近分布函数的逆函数，进而用得到的插值公式进行随机变量的抽样，这样做可以节省抽样的时间，并且在分布函数具有一定的光滑性条件时，插值公式具有比较好的收敛阶。

Secondly, the stationary responses of non-linear systems with unilateral constraints are studied by using the quasi-conservative averaging method.

基于非光滑线性系统研究的基础上，借助一种非光滑变换，引进狄拉克函数，把随机单边约束非线性系统转化为光滑随机非线性系统，进而运用拟保守平均方法得到转换的光滑随机系统的平稳响应。

An equal cross-section blade was investigated and a finite element model was built parametrically. Geometrical parameters (such as length, width and thickness), material parameters (such as young's modulus and density) and speed of blade were considered as input random variables while the static frequencies and dynamic frequencies were output random variables. Combining the finite element method, response surface method and Monte Carlo method, the statistical properties and cumulative distribution functions of static frequencies and dynamic frequencies were obtained. Probability sensitivities analysis, which combined the slope of the gradient and the width of the scatter range of the random input variables, was applied to quantitatively evaluate the sensitivities of static frequencies and dynamic frequencies with respect to the random variables. The Scatter plots of structural responses with respect to the random input variables were illustrated how to adjust the values of the static frequencies and dynamic frequencies by changing input random variables.

文中以某试验台用汽轮机等直叶片为研究对象，考虑几何参数、材料参数和转速的随机性，通过有限元参数化建模，将确定性有限元方法、响应面方法和Monte-Carlo模拟法相结合，从而获得了叶片静频、动频的统计特性和累积分布函数；同时考虑随机变量的梯度和离散范围对静、动频的影响，通过概率敏感性分析，定量地判断出叶片静、动频对随机输入变量的敏感性；通过绘制叶片静、动频与输入变量的散点图，定量地分析了如何改变随机变量以调整静、动频率的方法。

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。