母函数

A model of an additive mixture of Gaussian and non-Gaussian impulsive noise is adopted, and the asymptotical solution of the closed-form expression for the average symbol error rate of orthogonal space-time block coding over Rayleigh flat fading channel is derived by means of the Moment Generating Function with the approximate equivalent Multiple-Input Single-Output model of mixture noise.

采用脉冲和高斯加性混合噪声模型，利用矩母函数分析方法，通过建立多发单收近似等效模型，推导出Rayleigh衰落信道下MISO空时分组码误符号率闭式表达式的渐近解。

We obtain the risk process involved in this model,the statistical properties of the surplus process,and statistical features of the claim numbers and the probability distribution of the total amount of compensation.The three types of business of the risk model is given when the number of claims obey Poisson distribution and negative binomial distribution.We make a comparison between the risk model built in the thesis and the classic risk models with independent claim numbers when the amount of claims obey Weillbull distribution and Exponential distribution.The results have a good practical significance.

其次，考虑不同险种间的相互关系，建立了一种含有主副理赔的风险分析模型；借助随机过程和经典风险理论，对该风险模型所涉及的风险过程、盈余过程的统计特性以及理赔总额的概率分布、数字特征和矩母函数进行解析研究，给出了主理赔次数服从泊松分布和负二项分布的这种风险模型的具体实例，并在理赔额变量服从Weillbul分布和Exponential分布的情况下，把文中所建风险模型和理赔次数相互独立的风险模型作了比较，所得结果有很好的现实意义。

The paper introduces a differential equation derived from Markov theory and probability generating function.

文章介绍用Markov理论与母函数方法建立相关微分方程，并导出近似解析解，着重对常数源在系统中的涨落作了数学描述，给出了数值例子。

After studying the MAC protocol of Ad hoc network and by modifying the Wireless Token Ring Protocol, a new uncontested Distributed Parallel Wireless Polling Access Protocol that can provide MAC QoS guarantees for Ad hoc network is presented, and the mathematical model is established by the embedded Markov chain theory and the probability generating function method. Based on it, the mean value of queue length and message waiting time are explicitly obtained.

摘要该文对Ad hoc网络的MAC层协议进行了研究，通过对无线令牌环协议进行改进，提出了一种新的具有QoS保障的无竞争的分布式并行无线轮询访问协议，并采用嵌入Markov链和概率母函数的分析方法，用限定服务规则进行了系统建模，在系统模型的基础上得到了系统的平均排队队长以及平均等待时间的解析结果。

Under the service rule that customers who first come would first get the service, we use the structure analysis method to get the stochastic decomposition of the queue length with the generating function of probability and the steady waiting time with Laplace-stieitjes transforms.

重点分析了带启动期的一般减量服务的单重休假$M/G/1$排队系统的一般结构，利用结构分析的方法，在先来先服务规则下求得稳态队长的随机分解的概率母函数和稳态等待时间的随机分解的$LST$，同时，讨论了系统处于平衡的条件及其概率含义的直观解释，进一步讨论了系统处于休假期、忙期、忙循环等状态时的各项性能指标及系统状态分布。

Secondly, by establishing a discrete time Markov model with spatial reuse for a MANET, we analyze the performance of the network under the AODV routing protocol. The average route length and the probability to communicate within a limited hop distance are obtained. Several performance parameters of the route discovery and route maintain process are analytically studied, such as the probability generating function and the expectation of the flooding distabce. the probability that a route is discovered by a query packet with a "hop limit", the probability that a request packet finds a valid route, the average time needed to discover a valid route and the cost to successfully route a data packet to its destination. Furthermore, we present a concrete example based on the transmitter characteristic of directional antennas and obtain the corresponding results.

建立了移动自组网络空间可重用的离散时间马氏链模型，得到了AODV路由协议下网络任意两节点间的平均路由长度、在指定"跳限"要求下通信的概率；对随选型路由协议下路由发现和路由维护过程中若干网络性能参数进行了解析分析，如网络中任意两节点问的泛洪距离的概率母函数及其期望、限定泛洪步数时成功寻路的概率、发现一条有效路由的平均时间、成功路由的代价等；并基于定向天线的发射特征给出了一个具体实例，分析计算了相应的网络性能参数。

The dissertation includes the work as follows: Firstly, we present a random graph model with spatial reuse for a dense MANET which using directional antennas. The analytic formula of several important performance parameters for the MANET are obtained under the DSR routing protocol, such as the average flooding distance, the probability generating function of the flooding distance, the probability of a flooding route to be symmetrically valid, the average time to find a symmetrically valid route and the cost to successfully route a data packet to its destination. We compare the two models with spatial reuse and without spatial reuse by evaluating these parameters. It is shown that the spatial reuse model is much more effcctive in terms of the performance of the dense network with directional antenna, because the bigger is the degree of spatial reuse, the smaller is the average flooding distance.

在定向天线技术的支持下，建立了移动自组网络空间可重用的贝努利随机图模型，获得了DSR路由协议下平均泛洪距离的解析公式和泛洪距离的概率母函数：给出了有效对称路由概率、发现有效路由平均时间、成功路由代价等关键性能参数的解析分析；在网络性能参数定量分析的基础上，对空间可重用和无重用的网络进行了比较分析，结果显示空间重用度增大，则平均泛洪距离、路由发现时延、网络代价减少。

Then the joint moment generating functions of a linear compound and a quadratic form, and two quadratic forms, and conditions for their independence are given.

其次我们推导出一个线性组合与一个二次形式，及两个二次形式的联合动差母函数，并且给出一些它们相互独立的条件。

In this paper, the theories of generation function and recursive relation in combinatorics is used to analyze the time complexity of some special recursive algorithm, with three conclusions reached simultaneously, which is of valuable reference to the analysis and research on algorithm.

提出了用组合数学中的母函数与递推关系理论来分析一些特殊的递归算法的时间复杂度，并同时得出三个推论，在算法的分析与研究方面具有一定的参考价值。

The numerical solutions of neutral atoms with attractive interaction in a harmonic trap and a spherically symmetric well potential of depth infinite are calculated.

根据最近的BEC的动力学模型和主方程，用母函数方法求得玻色凝聚体主方程的解，并计算了凝聚体形成的增率与起伏，增率曲线存在一平台，而平台的粒子数起伏则是超泊松分布的。

Do you know, i need you to come back

你知道吗，我需要你回来

Yang yinshu、Wang xiangsheng、Li decang,The first discovery of haemaphysalis conicinna.

1〕 杨银书，王祥生，李德昌。安徽省首次发现嗜群血蜱。