CMM中SQA评审改进模型及在ERP实施中的应用

CMM中SQA评审项只有通过和不通过两种选择,且不同子项权重相同,很难服务于标杆管理.因此,提出了基于模糊评价集的SQA评审改进模型,通过专家打分和综合评判,让评审结果更加客观.通过将改进模型应用于ERP实施过程,说明其可操作性,且能有效地提高ERP实施的质量.     

带有标准发生率和信息干预的时滞SIRS传染病模型的稳定性分析

本文考虑一类具有标准发生率和信息干预的时滞SIRS传染病模型.通过分析模型的特征方程,讨论无病平衡点和地方病平衡点局部渐近稳定性.应用Halanay不等式对无病平衡点的全局渐近稳定性进行证明.通过构造适当的Lyapunov函数讨论地方病平衡点全局渐近稳定性.最后通过数值模拟分析一些重要参数对疾病传播的影响.     

具有时滞的比率型三种群捕食模型的分支分析

本文研究了一类具有时滞的比率型三种群捕食模型.通过分析该模型的特征方程,证明了该模型在正平衡点的稳定性.通过选择时滞τ为分支参数,得到了当时滞τ通过一系列的临界值时,Hopf分支产生.应用中心流形和规范型理论,得到了关于确定Hopf分支特性的计算公式.最后进行数值模拟验证了我们所得结果的正确性.所得结果是对前人工作的补充.     

分数阶复杂网络的自适应同步

运用自适应控制方法,研究了分数阶复杂网络的同步.通过构造一种简单的Lyapuno函数,得到同步准则.最后通过数值例子表明所提出方法的有效性.     

空间半参数变系数部分线性回归中的分位数估计

本文研究了空间数据变系数部分线性回归中的分位数估计. 模型中的参数估计量通过未知系数函数的分段多项式逼近得到, 而未知系数函数的估计量通过将参数估计量代入模型中并通过局部线性逼近得到. 文中推导了未知参数向量估计量的渐近分布, 并建立了未知系数函数估计量在内点及边界点的渐近分布. 通过Monte Carlo 模拟研究了估计量的有限样本性质.     

三维非线性抛物型积分-微分方程的A.D.I.Galerkin方法及其分析

研究三维非线性抛物型积分-微分方程的A.D.I.Galerkin方法.通过交替方向,化三维为一维,简化计算;通过Galerkin法,保持高精度.成功处理了Volterra项的影响;对所提Galerkin及A.D.I.Galerkin格式给出稳定性和收敛性分析,得到最佳H1和L2模估计.     

交叉概率对遗传算法运算速度影响的测试与分析

在现有文献基础上,通过理论分析,提出了交叉概率应取1.通过4个测试函数的测试结果,表明交叉概率越大,运算速度越快,平均运行代数越少,验证了通过理论分析提出的交叉概率应取1的科学性和可行性.同时克服了交叉概率难以确定以及确定交叉概率时缺少理论依据的不足.     

一类不确定非线性时滞系统的模糊自适应控制

针对一类不确定上界未知的非线性时滞系统,基于松散稳定性条件,讨论了系统的模糊自适应控制问题 .通过在Lyapunov泛函中引入参数,得到带调节因子的时滞相关稳定性条件.设计出基于观测器的自适应模糊控制器,观测增益矩阵和反馈增益矩阵可以通过求解线性矩阵不等式得到 .当调节因子取不同值时,观测增益矩阵和反馈增益矩阵也是不同的,因此,闭环系统的动态性能可以通过选取合适的调节因子来优化.最后通过一个实例验证了所给结论的有效性.     

具有时延和乱序网络化系统的动态矩阵控制北大核心CSCD

研究了具有时延和数据包乱序的网络化系统的动态矩阵控制问题.首先,通过时序分析,给出了控制器端和执行器端处理乱序的方法,建立了包含时延和乱序的网络化系统模型.然后,针对所建立的模型,提出了改进的动态矩阵控制算法,给出了控制器的设计方法.进一步,通过对系统的稳定性分析,导出了保证闭环系统稳定的充分条件.最后,通过仿真验证了所提方法的有效性.     

交叉概率对改进遗传算法运算速度影响的测试与分析

在现有文献基础上,通过理论分析,提出了交叉概率应取1.通过四个测试函数的测试结果,表明交叉概率越大,运算速度越快,平均运行代数越少,验证了通过理论分析提出的交叉概率应取1的科学性和可行性.同时克服了交叉概率难以确定以及确定交叉概率时缺少理论依据的不足.     

On a Mathematical Comparison between Hierarchy and Network with a Classification of Coordination Structures

This paper proposes a mathematical model to compare a network organization with a hierarchical organization. In order to formulate the model, we define a three-dimensional framework of the coordination structure of a network and of other typical coordination structures. In the framework, we can define a network structure by contrasting it with a hierarchy, in terms of the distribution of decision making, which is one of the main features of information processing. Based on this definition, we have developed a mathematical model for evaluating coordination structures. Using this model, we can derive two boundary conditions among the coordination structures with respect to the optimal coordination structure. The boundary conditions help us to understand why an organization changes its coordination structure from a hierarchy to a network and what factors cause this change. They enable us, for example, to find points of structural change where the optimal coordination structure shifts from a hierarchy to a hierarchy with delegation or from a hierarchy with delegation to a network, when the nature of the task changes from routine to non-routine. In conclusion, our framework and model may provide a basis for discussing the processes that occur when coordination structures change between a hierarchy and a network.     

Improving the computational efficiency of metric-based spares algorithms

We propose a new heuristic algorithm to improve the computational efficiency of the general class of Multi-Echelon Technique for Recoverable Item Control (METRIC) problems. The objective of a METRIC-based decision problem is to systematically determine the location and quantity of spares that either maximizes the operational availability of a system subject to a budget constraint or minimizes its cost subject to an operational availability target. This type of sparing analysis has proven essential when analyzing the sustainment policies of large-scale, complex repairable systems such as those prevalent in the defense and aerospace industries. Additionally, the frequency of these sparing studies has recently increased as the adoption of performance-based logistics (PBL) has increased. PBL represents a class of business strategies that converts the recurring cost associated with maintenance, repair, and overhaul (MRO) into cost avoidance streams. Central to a PBL contract is a requirement to perform a business case analysis (BCA) and central to a BCA is the frequent need to use METRIC-based approaches to evaluate how a supplier and customer will engage in a performance based logistics arrangement where spares decisions are critical. Due to the size and frequency of the problem there exists a need to improve the efficiency of the computationally intensive METRIC-based solutions. We develop and validate a practical algorithm for improving the computational efficiency of a METRIC-based approach. The accuracy and effectiveness of the proposed algorithm are analyzed through a numerical study. The algorithm shows a 94% improvement in computational efficiency while maintaining 99.9% accuracy.     

Persistence Terrace for Topological Inference of Point Cloud Data

Topological data analysis (TDA) is a rapidly developing collection of methods for studying the shape of point cloud and other data types. One popular approach, designed to be robust to noise and outliers, is to first use a smoothing function to convert the point cloud into a manifold and then apply persistent homology to a Morse filtration. A significant challenge is that this smoothing process involves the choice of a parameter and persistent homology is highly sensitive to that choice; moreover, important scale information is lost. We propose a novel topological summary plot, called a persistence terrace, that incorporates a wide range of smoothing parameters and is robust, multi-scale, and parameter-free. This plot allows one to isolate distinct topological signals that may have merged for any fixed value of the smoothing parameter, and it also allows one to infer the size and point density of the topological features. We illustrate our method in some simple settings where noise is a serious issue for existing frameworks and then we apply it to a real dataset by counting muscle fibers in a cross-sectional image. Supplementary material for this article is available online.     

年龄点t0之后的NBU性的非参数检验方法

NBU＊t0寿命分布中新元件的寿命随机地大于旧的年龄不小于t0的元件的剩余寿命,这为更广泛地模拟元件的老化和劣化现象提供了丰富的内容。本文首先对那些t0年龄点之后剩余寿命随机等于新元件寿命的元件的结构加以刻画,然后建立了一个非参数检验方法以区分这种随机等价性和t0年龄点后的严格的NBU性,并给出了针对一个NBU＊t0但非NBU的寿命分布的例子的数值模拟结果。     

A multidimensional tropical optimization problem with a non-linear objective function and linear constraints

We examine a multidimensional optimization problem in the tropical mathematics setting. The problem involves the minimization of a non-linear function defined on a finite-dimensional semimodule over an idempotent semifield subject to linear inequality constraints. We start with an overview of known tropical optimization problems with linear and non-linear objective functions. A short introduction to tropical algebra is provided to offer a formal framework for solving the problem under study. As a preliminary result, a solution to a linear inequality with an arbitrary matrix is presented. We describe an example optimization problem drawn from project scheduling and then offer a general representation of the problem. To solve the problem, we introduce an additional variable and reduce the problem to the solving of a linear inequality, in which the variable plays the role of a parameter. A necessary and sufficient condition for the inequality to hold is used to evaluate the parameter, whereas the solution to the inequality is considered a solution to the problem. Based on this approach, a complete direct solution in a compact vector form is derived for the optimization problem under fairly general conditions. Numerical and graphical examples for two-dimensional problems are given to illustrate the obtained results.     

Evacuation and a geometric construction for Fibonacci tableaux

Tableaux have long been used to study combinatorial properties of permutations and multiset permutations. Discovered independently by Robinson and Schensted and generalized by Knuth, the Robinson–Schensted correspondence has provided a fundamental tool for relating permutations to tableaux. In 1963, Schützenberger defined a process called evacuation on standard tableaux which gives a relationship between the pairs of tableaux (P,Q) resulting from the Schensted correspondence for a permutation and both the reverse and the complement of that permutation. Viennot gave a geometric construction for the Schensted correspondence and Fomin described a generalization of the correspondence which provides a bijection between permutations and pairs of chains in Young's lattice.In 1975, Stanley defined a Fibonacci lattice and in 1988 he introduced the idea of a differential poset. Roby gave an insertion algorithm, analogous to the Schensted correspondence, for mapping a permutation to a pair of Fibonacci tableaux. The main results of this paper are to give an evacuation algorithm for the Fibonacci tableaux that is analogous to the evacuation algorithm on Young tableaux and to describe a geometric construction for the Fibonacci tableaux that is similar to Viennot's geometric construction for Young tableaux.     

Transverse curves and chain curvature in the Heisenberg group

A chain is the intersection of a complex totally geodesic subspace in complex hyperbolic 2-space with the boundary. The boundary admits a canonical contact structure, and chains are distiguished curves transverse to this structure. The space of chains is analyzed both as a quotient of the contact bundle, and as a subset of ℂP². The space of chains admits a canonical, indefinite Hermitian metric, and curves in the space of chains with null tangent vectors are shown to correspond to a path of chains tangent to a curve in the boundary transverse to the contact structure. A family of local differential chain curvature operators are introduced which exactly characterize when a transverse curve is a chain. In particular, operators that are invariant under the stabilizer of a point in the interior of complex hyperbolic space, or a point on the boundary, are developed in detail. Finally, these chain curvature operators are used to prove a generalization of Louiville's theorem: a sufficiently smooth mapping from the boundary of complex hyperbolic 2-space to itself which preserves chains must be the restriction of a global automorphism.     

Approximating connected facility location with buy-at-bulk edge costs via random sampling

In the connected facility location problem with buy-at-bulk edge costs we are given a set of clients with positive demands and a set of potential facilities with opening costs in an undirected graph with edge lengths obeying the triangle inequality. Moreover, we are given a set of access cable types, each with a cost per unit length and a capacity such that the cost per capacity decreases from small to large cables, and a core cable type of infinite capacity. The task is to open some facilities and to connect them by a Steiner tree using core cables, and to build a forest network using access cables such that the edge capacities suffice to simultaneously route all client demands unsplit to the open facilities. The objective is to minimize the total cost of opening facilities, building the core Steiner tree, and installing the access cables. In this paper, we devise a constant-factor approximation algorithm for this problem based on a random sampling technique.     

Minimizing Labor Requirements in a Periodic Vehicle Loading Problem

In this paper, we address a logistics problem that a manufacturer of auto parts in the north of Spain described to the authors. The manufacturer stores products in its warehouse until customers retrieve them. The customers and the manufacturer agree upon an order pickup frequency. The problem is to find the best pickup schedule, which consists of the days and times during the day that each customer is expected to retrieve his/her order. For a given planning horizon, the optimization problem is to minimize the labor requirements to load the vehicles that the customers use to pick up their orders. Heuristically, we approach this situation as a decision problem in two levels. At the first level, customers are assigned to a calendar, consisting of a set of days with the required frequency during the planning horizon. Then, for each day, the decision at the second level is to assign each customer to a time slot. The busiest time slot determines the labor requirement for a given day. Therefore, once customers have been assigned to particular days in the planning horizon, the second-level decision is a multiprocessor scheduling problem, where each time slot is the equivalent of a processor, and where the objective is to minimize the makespan. A metaheuristic procedure is developed for the problem of minimizing labor requirements in this periodic vehicle-loading problem and artificial as well as real data are used to assess its performance.     

Method of successive projections for finding a common point of sets in metric spaces

Many problems in applied mathematics can be abstracted into finding a common point of a finite collection of sets. If all the sets are closed and convex in a Hilbert space, the method of successive projections (MOSP) has been shown to converge to a solution point, i.e., a point in the intersection of the sets. These assumptions are however not suitable for a broad class of problems. In this paper, we generalize the MOSP to collections of approximately compact sets in metric spaces. We first define a sequence of successive projections (SOSP) in such a context and then proceed to establish conditions for the convergence of a SOSP to a solution point. Finally, we demonstrate an application of the method to digital signal restoration.