指数分布抽样基本定理及在三参数一般指数分布参数估计中的应用

讨论三参数一般指数分布的参数估计,首先讨论了三参数一般指数分布参数的最大似然估计的求解问题,当其中参数α=1时,应用指数分布抽样基本定理,得到了三参数一般指数分布其它参数的一致最小方差无偏估计;并且由此给出求解三参数一般指数分布参数最大似然估计的迭代方法,得到了三参数一般指数分布参数最大似然估计的近似值,给出了模拟结果以说明迭代方法的收敛性;并以相关文献的观察数据作为样本,得到了三参数一般指数分布的参数估计,从而说明了迭代方法的有效性.     

解析几何中一类含参问题的基本解法

在解析几何中,有一类求参数取值范围的问题,解决这类问题往往通过“引进”新的参数,寻找待求参数与新参数之间的某种制约关系,然后“借用”新参数的取值范围,进而求出待求参数的取值范围．     

双参数 C-半群

引入单参数C-半群和双参数C0-半群,给出了更一般的双参数C-半群和无穷小生成元的定义,应用双参数半群与单参数半群的关系和双参数半群的性质,给出了双参数C-半群的阶全微分,偏微分,指数有界性,和双参数C-半群是由C、A1和A2唯一确定的闭稠定线性算子的一个充分条件.     

一类非光滑分布参数系统的可辨识性及最优性条件

变压器温度场参数辨识问题是一种分片光滑的分布参数辨识问题,以流速为辨识参数,针对传质传热的一类分布参数系统参数辨识问题,证明了系统最优参数的存在性和控制参数为最优的必要条件,为变压器温度场的数值模拟研究提供了理论基础.     

微极流体蠕动泵经由滑移边界管道输送的Stokes流动

计及管道边界条件滑移的影响,研究微极流体蠕动泵,经由圆柱形管道输运的Stokes流动.壁面运动的控制方程为正弦波方程.使用润滑理论,得到了轴向速度、微转动向量、流函数、压力梯度、摩擦力和机械效率的解析数值解.用图形表示出构成参数,如像耦合参数、微极参数和表征蠕流泵特性的滑移参数、摩擦力和俘获现象的影响.数值计算表明,当耦合参数较大时,需要蠕动泵的压力更大,而微极参数和滑移参数正相反.俘获团块的大小随耦合参数和微极参数的减小而缩小,而随滑移参数的增大而缩小.     

基于二阶滑移边界的MHD在可渗透延伸壁面上的驻点流研究

研究了多孔介质中带二阶滑移边界的不可压缩MHD粘性流体在可渗透指数延伸壁面上的驻点流问题.通过相似变换将描述驻点流的控制方程转换为非线性常微分方程,并利用MATLAB的bvp5c函数求解非线性问题.分析并讨论了一、二阶滑移参数,抽吸/喷注参数以及渗透参数对速度分布和壁面剪切力的影响.结果显示在多孔介质中当壁面延伸速度小于外界主流速度时,随着一阶滑移参数、二阶滑移参数绝对值、抽吸/喷注参数以及渗透参数的增大,速度增大,壁面剪切力减小且均为正数;而当壁面延伸速度大于外界主流速度时形成一个反边界层,速度减小,壁面剪切力绝对值也减小且均为负数;二阶滑移参数对速度剖面和壁面剪切力的影响略大于一阶滑移参数的影响,抽吸/喷注参数对速度剖面和壁面剪切力的影响明显大于渗透参数或磁场参数的影响.     

面向下一代光通信的VCSEL激光器仿真模型

根据L-I经验公式得到参数待定的L-I模型,并利用遗传算法搜索最优参数得到参数模型,对结果进行拟合优度检验,求出误差.在该模型基础上对环境温度进行修正并且考虑电流瞬时变化的影响,建立微分方程模型,采用Ode23求解,并利用遗传算法搜索最优参数得到参数,对结果进行拟合优度检验,得出了该激光器不同温度下的L-I特性曲线和激光器小信号幅频响应.同时根据速率方程推导出了带宽响应的数学模型,对参数归一化后,利用遗传算法搜索最优参数得到参数.     

基于云参数修正模型的空战威胁评估方法

针对定量属性参数对空战威胁评估结果会产生片面性的问题,提出将目标的定性参数与定量参数一起用于空战威胁评估中,并用云参数修正模型对目标参数进行修正来提高威胁评估结果的准确性.最后将基于云参数修正模型的方法与其它威胁评估方法进行了对比,仿真结果证明了方法的有效性.     

参数思想及参数方法在解析几何中的应用

当直接寻找变量x，y之间的关系显得很困难的时候，恰当地引入一个中间变量t（称之为参数）．分别建立起变量x,t与参数t的直接关系。从而间接地知道了x与y之间的关系，这种数学思想称为参数思想．通过引入参数、建立参数方程求解数学问题的方法称为参数方法．     

半参数ACD模型及其在中国股票市场中的应用研究

本文提出了半参数ACD模型并基于模拟样本与调整后的中国股票市场的价格时间间隔样本对模型进行实证分析.半参数ACD模型对条件期望的函数形式与随机误差项的分布形式要求都没有参数ACD模型强,因此不会像参数ACD模型那样因模型形式设定错误而得出错误结论.这一点在我们的实证分析中可以得到证实.与非参数ACD模型相比,半参数ACD模型能够估计出参数,这增加了模型的解释能力.半参数ACD模型估计出来的各个可加部分图形的形状对于正确设定参数ACD模型具有一定的指导作用.     

Global solutions of partitioning problems ∗

In this paper, a special kind of optimization problems is considered. The total cost function for a homogeneous group of participants– each with the same convex-concave cost function – is to be minimized. The particular structure of this problem makes it possible to find global minimizers in dependence on the linking parameter. The symmeric partition is a stationary solution and the optimal one for small parameter values. Beyond a critical parameter value one obtains certain non-symmetric solutions. Two geometrical applications are discussed. They are related to perimeter and volume partitions     

Biased Online Parameter Inference for State-Space Models

We consider Bayesian online static parameter estimation for state-space models. This is a very important problem, but is very computationally challenging as the state-of-the art methods that are exact, often have a computational cost that grows with the time parameter; perhaps the most successful algorithm is that of SM C² (Chopin et al., J R Stat Soc B 75: 397–426 2013). We present a version of the SM C² algorithm which has computational cost that does not grow with the time parameter. In addition, under assumptions, the algorithm is shown to provide consistent estimates of expectations w.r.t. the posterior. However, the cost to achieve this consistency can be exponential in the dimension of the parameter space; if this exponential cost is avoided, typically the algorithm is biased. The bias is investigated from a theoretical perspective and, under assumptions, we find that the bias does not accumulate as the time parameter grows. The algorithm is implemented on several Bayesian statistical models.     

极值分布参数检验的样本崩溃点

检验的样本崩溃点是样本中能逆转判决的离群值的最小比例.本文计算和分析了一类极值分布位置参数的似然比检验的样本崩溃点.并用截尾方法改进了这类检验的样本崩溃性质.     

How much do we “pay” for using default parameters?

This paper explores the potential benefit of using tuned parameter settings for integer programming instances. Three metrics are considered for selecting parameters: Time-to-Optimality, Proven-Gap and Best-Integer-Solution. Good parameter settings for each metric are found using the open-source software tool Selection Tool for Optimization Parameters. Computational tests are presented using CPLEX solver (version 9.0) on MIPLIB test instances, showing substantial improvements over the default parameter setting. Although the benefit of a tuned parameter setting on an individual instance is outweighed by the cost of identifying the tuned setting, these results indicate that substantial benefit may be achieved in cases where the cost of tuning parameter settings is justified.     

On ε-optimal continuous selectors and their application in discounted dynamic programming

A quadratic regulator problem for a class of nonlinear systems is considered in which the control cost is multiplied by a small parameter, which becomes a so-called cheap control problem. Conditions are found under which the minimum cost becomes zero (perfect regulation) and the linear part in the optimal control law becomes dominant as the small parameter goes to zero. Near optimality of control laws truncated from the optimal control law in series form is also found.     

ON THE STABILITY OF THE RESIDUAL-FREE BUBBLES FOR THE NAVIER-STOKES EQUATIONS

This paper considers the Calerkin finite element method for the incompressible Navier-Stokes equations in two dimensions, where the finite-dimensional spaces employed consist of piecewise polynomials enriched with residual-free bubble （RFB） functions. The stability features of the residual-free bubble functions for the linearized Navier-Stokes equations are analyzed in this work. It is shown that the enrichment of the velocity space by bubble functions stabilizes the numerical method for any value of the viscosity parameter for triangular elements and for values of the viscosity parameter in the vanishing limit case for quadrilateral elements.     

含交易费用的证券组合投资模型的满意解

在证券组合投资过程中,忽略交易费用会导致非有效的证券组合投资,本文提出了一个考虑交易费用的证券组合投资的区间数线性规划模型,通过引入区间数线性规划问题中的目标函数优化水平参数λ和约束条件满足水平参数η将目标函数和约束条件均为区间数的区间数线性规划模型转化为确定型的一般线性规划模型,进而求得相应于优化水平λ和满足水平η的满意解.     

A marginal cost analysis for prevetive replacement policies

Some well known preventive replacement policies are each characterized by a single parameter which governs the sequence of planned replacements. In this paper we define and compute for any one of these policies the marginal cost of a planned replacement in terms of the policy parameter. This function is used to obtain the equation of optimality, with respect to two common objective functions: the expected cost per unit time and the expected total discounted costs, and to investigate the existence of a unique finite solution. Moreover, the marginal cost notion provides reasoning to the mathematical results of the models and thereby clarifies the effect of the various components of the model on these results. This better insight into models is perhaps the most important benefit of a marginal cost analysis.     

A production–inventory model in an imperfect production process

The paper develops a model to determine the optimal product reliability and production rate that achieves the biggest total integrated profit for an imperfect manufacturing process. The basic assumption of the classical Economic Manufacturing Quantity (EMQ) model is that all manufacturing items are of perfect quality. The assumption is not true in practice. Most of the production system produces perfect and imperfect quality items. In some cases the imperfect quality (non conforming) items are reworked at a cost to restore its quality to the original one. Rework cost may be reduced by improvements in product reliability (i.e., decreasing in product reliability parameter). Lower value of product reliability parameter results in increase development cost of production and also smaller quantity of nonconforming products. The unit production cost is a function of product reliability parameter and production rate. As a result, higher development cost increases unit production cost. The problem of optimal planning work and rework processes belongs to the broad field of production–inventory model which deals with all kinds of reuse processes in supply chains. These processes aim to recover defective product items in such a way that they meet the quality level of ‘good item’. The benefits from imperfect quality items are: regaining the material and value added on defective items and improving the environment protection. In this point of view, a model is introduced here to guide a firm/industry in addressing variable product reliability factor, variable unit production cost and dynamic production rate for time-varying demand. The paper provides an optimal control formulation of the problem and develops necessary and sufficient conditions for optimality of the dynamic variables. In this purpose, the Euler–Lagrange method is used to obtain optimal solutions for product reliability parameter and dynamic production rate. Finally, numerical examples are given to illustrate the proposed model.     

分布参数与集中参数耦合系统的极点配置问题

设 H 是可分的 Hilbert 空间,A 是空间 H 中的线性算子,b∈H 是非零元.考察空间H 中的一阶发展方程描述的控制系统(dx)/(dt)=Ax+bu(t),x(0)=x_0,(1)这里 u(t) 是控制量,是一数值函数.考察反馈控制律u(t)=〈x(t),g〉,(2)这里 g∈H 是非零元,〈·,·〉是 H 上的内积.