随机函数

Thirdly, we study the α-invariant Radon measures for random walks and Levy processes and give some nice ratio limit theorems that is relative to the α-invariant Radon measures.

同时我们研究了随机游动和Levy过程的α-过分函数和α-过分测度，并给出过程沿着矩母函数的次微分方向趋于α-不变Radon测度的一些比例极限定理。

Using the method of analysis to study strong limit theorem proposed by professor Liu Wen, and a plying Legbesuge theoremon differentiability of monotone function, a new proof of the theorem of strong law of large numbers for the sequence of random variables of the product distribution of Poisson is forwarded.

利用文献[1]刘文教授提出的研究强极限的纯分析方法，通过构造适当的辅助函数，然后利用单调函数异数存在定理，给出具有乘积泊松分布的随机变量序列的一个强大数定理的新证明。

By introducing the NCP function, the KKT conditions of POPF system are transformed equivalently. Based on the transformed nonsmooth nonlinear algebraic equations, the FOSMM is used to determine the POPF model expressed by the numerical characteristic of variables. The model includes nonsmooth functions, so it can be solved by a semismooth L-M method based on the subdifferential.

将概率最优潮流表述为随机非线性规划问题后，利用非线性互补函数将该问题的KKT条件进行转化，基于转化后的非线性代数方程组，利用一次二阶矩法确定了以待求量的数字特征表示的概率最优潮流模型，由于该模型包含不光滑函数，因此采用基于次微分的半光滑L-M方法求解。

A mathematical model including the suspension and tire parameters is developed for analyzing the automotive interior noises caused by road irregularity excitation in this paper.The interi-or noises at driver's ear position are calculated by means of admittance functions at suspension mounting points,noise transfer functions from suspension mounting points to driver's ear and suspen-sion and tire parameters.

本文建立了因路面不平度随机激励所产生的车内噪声的数学模型，借助于测得的车身悬置连接点的导纳函数、各连接点到车内耳旁位置的噪声传递函数以及悬置和轮胎参数，计算了由路面不平度所引起的车内耳旁噪声的大小。

About the theory of the model errors, there are many theoretical problems to be solved, and many disscusional fields to be expanded and perfected.

但是测量平差中的模型误差的理论还有许多问题有待完善、扩展、深入，如函数模型可扩展到附有条件模型、概括函数模型、非线性模型；随机模型可扩展到相关、秩亏等情况；误差理论可扩展到线性近似误差。

Applied widely in the data encryption, pseudorandom sequences can be generated not only by hardware but also by trace function, and it is found that the sequences generated by trace function are much better than those generated by hardware, especially in the aspects of correlation properties.

摘要伪随机序列被广泛应用于数据加密，它既能利用硬件产生，也可以利用有限域上的迹函数来生成，并且由后者生成的序列的密码特性远远优于前者，特别是在相关函数方面更是如此。

When processing the restrained conditions, we convert the restrained conditions into punish function and add it to fitness function which profits from the conventional method. We introduce the support vector machine to the selection operator, which increases the multiplicity of selection and increases the probability of the algorithm getting the overall optimal solution. Also, we use the adaptive probabilities of crossover and mutation in mixed GAs which enhances the efficiency of the algorithm. The result of tests about the system indicates that the improved genetic algorithm has more high convergence speed and better solution quality.

在生成初始种群时，不是简单的随机生成，而是用支持向量机对历史数据进行分类，用较优的一类历史数据作为初始种群；在约束条件的处理上，本文借鉴常规方法中的罚函数法，采用将约束条件作为罚函数包含到适应度评价中去的方法；在选择算子上，本文引入了支持向量机的方法，增加了选择的多样性，增加算法搜索到全局最优解的概率；同时针对交叉概率和变异概率在算法的前后期不同的情况，本文引入了Srinvivas等提出的动态自适应的方法，使得交叉概率和变异概率能够随着算法中个体的质量动态改变，提高算法的效率。

The main achievements of the project are as follows: 1 the hypothesis that a decrease in seed mass causes an increase in mean dispersal distance has been tested based on the experiments of weed dispersal by wind. The experimental results partly support the hypothesis. The results will help farmers to make an optimal strategy of weed control; 2 a statistic method for inferring probabilistic distribution function of a random variable has been developed, by which probabilistic distribution functions of weed species dispersal have been determined; 3 the reproduction structure of Bromus sterilis has been studied; 4 a more complex CA model with 25 neighborhood cells were built, which can simulate spread of a weed population. This work promotes developments in both theory and application of CA models; 5 the "mean law" in weed control has been proposed. Accordingly, the algorism of patch spring may be calibrated; 6 the "patch" and "true patch" have been mathematically defined so that herbicide can be efficiently applied; 7 simulation validates that initial configurations of weed will affect dispersal of its population and strategies of controlling it, or its distribution patterns affect its dispersal progresses.

主要完成的工作和取得的成果有：1）用实验证实了重量较轻的杂草种子并不一定飞得比较重的远，其结果有助于农民制订杂草的优化控制策略；2）发展了一种推断随机变量分布函数的统计方法并用它来获得了几个杂草种的扩散分布函数；3）对杂草Bromus sterilis的繁殖结构进行了研究；4）建立了一个具有25邻的较复杂的能模拟杂草扩散的CA模型，并在理论和应用方面促进了CA模型的发展；5）在杂草控制方面提出了&平均法则&，据此可对按块施药方法进行校正；6）精确地定义了&块&和&真块&以便在杂草控制中能更有效地使用除草剂；7）模拟证实杂草种群的初始配置影响其扩散和控制策略，或者格局影响过程。

The main factors effecting on exploration precision of surface wave are analyzed in the light of calculation of phase velocity of surface wave; the merits and demetits of common computing methods for phase velocity between stations and their applied range are discussed and calculation of interstation Green's function for correcting phase is put forward to get the precise phase difference between two stations.

分析了影响面波勘探精度的主要因素，针对计算面波相速度的精度问题，讨论了常用测量台间面波相速度方法的优缺点及其适用范围，并提出通过测量台间格林函数进行相位校正，以得到两台之间的精确相位。以合成的高频理论地震图作为记录信号，并在理论地震图上叠加了 2 0 %的随机噪声，利用这些方法分析理论信号，数字实验表明：在相干频率范围内，格林函数方法能够精确测量台间相速度，而互相关法和窄带通滤波互相关法所得结果较为离散。

With that the random noise is filtered out.The change of the wavelength may lead to the drift of the non-exchange phase drift, so influence the stability of the scale factor, also it is known the temperature is the key factor that affect the wavelength of the light-source.

论文在详细分析各种噪声的基础上围绕提高陀螺稳定性和精度做了以下工作：在深入分析陀螺物理特性的基础上，通过试验确定了陀螺系统的传递函数，通过分析将传递函数离散化并应用于自适应滤波，主要是滤除随机噪声。

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。