ASYMPTOTIC NORMALITY OF SOME ESTIMATORS IN A FIXED-DESIGN SEMIPARAMETRIC REGRESSION MODEL WITH LINEAR TIME SERIES ERRORS

Consider a semiparametric regression model with linear time series errors Yk = x'kβ g(tk) εk, 1 < k < n, where Yk's are responses, xk = (xk1,xk2,..... ,xkp)' and tk ∈T ∪R are fixed design points, β= (β1, β2, ....., βp)' is an unknown parameter vector, g(.) is an unknown bounded real-valued function defined on a compact subset T of the real line R, and εk is a linear process given by εk = ∑j=0∞j(?)ek-j,(?)= 1, where , are i.i.d. random variables. In this paper we establish the asymptotic normality of the least squares estimator of β, a smooth estimator of g(.), and estimators of the autocovariance and autocorrelation functions of the linear process εk.     

自聚集、吸引核与聚集量

研究复杂系统的自聚集演化过程和聚集量.文中给出两个类似生长网络的模型.第一个模型比较简单,每一时间步长只有一条新边进入网中,但概括面较广,例如可描写选举、科学论文引用、食物源对蚁群蜂群的吸引、某种商品或股票、堤坝渗漏处,等等.第二个模型比较一般,每次可有m条新边进入网络.文中引用BA网络模型给出的“优先连接”的概念,研究上面两个网络中各点的聚集量.结果表明：对于这两个模型,各点可能的聚集量均可用一个数学期望的简单公式描述,即Et^s=ks/t0t .其中,s表示网中某点,t0是初始时间,ks是t0时点s的顶点度,t是任何时间,t也是此时网的总度数,或总聚集量.ks/t0表征点s的初始优势或初始吸引能力,点可称为吸引核,ks/t0可称为吸引系数.文中解释了对于不同情况下 Et^s=k/t0t的意义.     

停机位分配问题的顶点着色模型及算法

给出了停机位分配问题顶点着色模型及其分解算法.通过改良一种时间冲突算法,构建了航班使用停机位的时间冲突集合.以"先到先服务"原则为基础,把停机位分配问题转化为顶点着色问题,并建立了相应模型.利用笔者独创的分解算法,停机位的作业能力可得到改善.算法的计算复杂度为O(n2).该算法的特点在于:1)将顶点、颜色划分为若干个不同等级的集合;2)将顶点按照所属集合的等级、度进行分解,得到顶点的分解序列.在用一种颜色ck(1≤k≤K;K是可用颜色数)给顶点着色时,优先给这样一个顶点着色:该顶点能被着ck色,且其分解序列号最大.最后将该算法应用于一个算例,得到了最优解.     

成对需求的局内k-服务器问题及其工作函数策略

提出了多需求的k 服务器问题,建立了数学模型.研究了问题空间为k+2时的一个特例:即在任一时刻点都同时有两个服务需求提出.给出了此特例的工作函数策略,进行了相应的策略分析并给出了竞争比的证明.关于成对及多需求k 服务器问题的一般情形的策略设计及理论证明仍然是公开问题.     

A Note on the Tu-Deng Conjecture

Abstract Let k be a positive integer.For any positive integer x=∑∞i=0x i2i,where x i=0,1,we define the weight w(x)of x by w(x):=∑∞i=0x i.For any integer t with 0t2k-1,let S t:={(a,b)∈Z2|a+b≡t(mod 2k-1),w(a)+w(b)k,0≤a,b≤2k-2}.This paper gives explicit formulas for cardinality of S t in the cases of w(t)≤3 and an upper bound for cardinality of S t when w(t)=4.From this one then concludes that a conjecture proposed by Tu and Deng in 2011 is true if w(t)≤4.     

两级维修保障下k/N系统使用可用度模型

为满足一定的可靠性或精度要求,通常将装备系统设计成k/N结构的冗余系统,该类系统维修一般要等到失效部件达到一定数量时才进行.使用可用度是装备战备完好性的重要指标,能很好地反映装备系统的可靠性及维修保障系统的保障水平.因此以k/N系统为研究对象,结合装备两级维修保障模式,建立了m维修策略下两级维修保障的装备系统使用可用度模型.通过模型实例分析了两级备件储备对系统使用可用度的影响,验证了模型的有效性.     

局内军车调度的时间优化及其竞争策略

提出时间目标函数下的局内k－军车调度问题，应用复位策略给出该问题的几种竞争算法：给出了对应的局内k－服务器问题的竞争比的c时的该问题的竞争比为c 1 1/θ的竞争算法；分别给出了当k=n和k=n-1时该问题的竞争比为1和1＋1／θ的竞争算法。     

c个修理工同步多重休假的k/n(G)表决可修系统

本文首次将"多个修理工同步多重休假"规则引入到c个修理工的k/n(G)表决可修系统中,在假设部件的工作寿命、故障后的修理时间和修理工的休假时间 分别服从参数λ(>0)、μ(>0)和θ(>0)的负指数分布下,利用拟生灭过程 和矩阵几何解方法,讨论了在稳态下系统处于各状态的概率分布,以及一些刻画系统性能的可靠性指标 和排队指标,如系统的稳态可用度、稳态故障频度和故障部件的等待修理时间等,并且讨论了四种特殊情况: 1) c=1,θ→+∞; 2) c=1,k=1,θ→+∞; 3) c=1,k=n,θ→+∞; 4) c=1,k=n-1,θ→+∞.最后给出了在c=2,n=6,k=3,λ=1/10,μ=1/5,θ=1/2的数值计算例子.     

半导体制造两集束型装备调度模型和算法研究

针对单臂机器人的两集束型装备调度问题,利用分解方法将两集束型装备分解为两个单集束型装备.证明了分解后单集束型装备的缓冲模块加工时间必定在一个允许的时间范围内,并建立单集束型装备调度问题的线性规划(Linear Programming,LP)模型,提出了基于LP模型和机器人元碰撞约束条件的搜索算法.以半导体制造化学机械抛光设备为例,验证了模型和算法的有效性.     

On the Solutions of the Matrix Equations in Optimal Stochastic Control

1.INTRoDUCTIoNoFTHEPRoBLEMConsiderthetime-invariantlinearIt6stochasticsystemwherexER,uCRm,FER""",BER""m,a=const.(i=1,2,'',k)arenaturalnumbers;W(t)=[W(t),W2(t),Wk(t)]"(tSo)isak-dimensionalstandardWienerprocesswithindependentcomponentsdefinedonthecompleteprobabilityspace(fl,FP),(A,B)iscontrollable.SupposethatRERm"m,QERmxmaregivenpositivedefiniteweightingmatrices,Ereferstothemathematicalexpectation.ConsidertheoptimalstochasticcontrolDroblemItiswell-knownthatifthereisapositive…     

视情维修条件下k/N(G) 系统备件供需联合优化

针对传统m视情维修策略下k/N(G)系统维修决策模型对备件可获取性考虑不足的问题,提出了(m,Q)维修策略及备件订购与生产的联合决策优化方法,建立了两种视情维修条件下k/N(G)系统备件供需联合优化模型。证明了在满足约束条件的同时,(m,Q)维修策略下的联合模型((m,Q, n) 策略模型)具有使目标函数最小的订购阈值m、订货量Q和订货次数n,m维修策略下的联合模型((m,n)策略模型)存在最优订货量m和订货次数n使目标值最小。此外,比较分析了不同模型参数对两种模型决策的影响,结果表明, (m,Q,n)策略模型得到的成本始终小于(m,n) 策略模型,而系统使用可用度始终高于(m,n)策略模型。     

灰色GM(1,1)派生模型病态性的差异分析

本文主要研究GM(1,1)六种不同派生模型的病态性.首先利用特征分析法和参数估计矩阵B~TB的条件数探讨了辨识参数系数矩阵的病态性情况,根据病态性程度对派生模型进行归类,进而分析了各类模型产生病态性的原因,并对具有病态性的派生模型采用向量变换法进行改进.在此基础上,比较了定义型与派生模型在建模机理、计算繁简程度等方面的差异.研究结果表明:1)派生模型b型、派生模型内涵型属于第一类即不存在病态性的模型;定义型、派生模型x~(1)型、离散型属于第二类即存在一般程度病态性的模型;派生模型x~(0)型、派生模型指数型属于第三类即具有严重病态的模型;2)与各类派生模型相比,定义型在建模机理、计算量的大小等方面有明显优势.最后,通过数值实例验证了分析结果的合理性.     

New statistical model for radar HRRP target recognition

The mixture of factor analyzers (MFA) can accurately describe high resolution range profile (HRRP) statistical characteristics.But how to determine the proper number of the models is a problem.This paper develops a variational Bayesian mixture of factor analyzers (VBMFA) model.This procedure can obtain a lower bound on the Bayesian integral using the Jensen's inequality. An analytical solution of the Bayesian integral could be obtained by a hypothesis that latent variables in the model are independent.During computing the parameters of the model,birth-death moves are utilized to determine the optimal number of model automatically.Experimental results for measured data show that the VBMFA method has better recognition performance than FA and MFA method.     

TREE DECOMPOSITIONS OF MULTIGRAPHS

1.IntroductionInthispaperweconsideronlyfiniteundirectedlooplessgraphs.ForasubgraphHofG,E(H)andP(H)denotethenumberofedgesandthenUmberofcyclesinHrespectively.GiventwodisjointsubsetsXandYofV(G),wewriteEG(X,Y)={acEE(G)IxEX,y6Y}.IfTisatreeinGande=acEG--E(T)with{u,v}CV(T),thenT econtainsauniquecycle.WedenotethiscyclebyC(T,e).Aforestiscalledak-tree-forestifitconsistsofexactlykpairwisedisjointtrees.ForagraphG,ifE(G)canbepartitionedilltoseveralpairwisedisjointsetsas{EI,EZ,...,EI}such…     

APPLICATIONS OF INTEGRATED SEMIGROUPS TO HIGHER ORDER ABSTRACT CAUCHY PROBLEMS

This paper is concerned with applications of integrated semigroups tothe following Cauchy problem:(ACP_n) x~(n)(t)=sum from i=0 to n-1 B_ix~(i)(t),x~(i)(0)=x_i,0(?)i(?)n-1where B_i (0(?)i(?)n-1) are closed linear operators on a Banach space X.Auniqueness theorem,a condition of the solvability,a condition of the exponentialwell-posedness,and some results for the special case that B_(n-1) is bounded andD(B_(n-2))(?)D(B_i)(0(?)i(?)n-3) are obtained.     

A HEURISTIC FOR F3/bi= b/C_(max) AND ITSWORST-CASE ANALYSIS

1.IntroductionTheF3Cm..canbestatedasfOllows.Eachofthenjobs1,2,'')nistobeprocessedonthreemachinesA,B,Cinthesameorder.Giventheprocessingtimesal?hiandciofjobionmachinesA,BandC,findtheorderinwhicheachmachineshouldprocessethejobssoastominimizingthetotaltimesp…     

任意分布的冷备表决系统可靠度求解

k/n: M(G)冷备表决系统包含n个工作部件, M个冷储备件, 至少有k个部件工作时系统工作。然而, 现有对于k/n: M(G)冷备表决系统的研究集中在同型指数分布的情况, 缺乏针对其工作部件非同型且服从任意分布的情况的研究。本文研究了k/n: M(G)冷备表决系统的可靠度, 系统部件服从任意分布, 冷备件服从同一分布。对k=n的情况, 给出了M取任意值时部件同型和非同型情况下的系统可靠度解析式。对于k＜n的情况, 考虑了两种不同的冷备件替换策略, 给出了部件同型情况和非同型M取特定值情况下的系统可靠度解析式。蒙特卡罗仿真实验证明了所提方法的准确性。     

SCHEDULING TWO GROUPS OF JOBS WITH INCOMPLETE INFORMATION

In real world situations, most scheduling problems occur neither as complete off-line nor ascomplete on-line models. Most likely a problem arises as an on-line model with some partialinformation. In this article, we consider such a model. We study the scheduling problem P(n_1,n_2),where two groups of jobs are to be scheduled. The first job group is available beforehand. As soon asall jobs in the first group are assigned, the second job group appears. The objective is to minimize thelongest job completion time(makespan). We show a lower bound of 3/2 even for very special cases.Best possible algorithms are presented for a number of cases. Furthermore, a heuristic is proposed forthe general case. The main contribution of this paper is to discuss the impact of the quantity ofavailable information in designing an on-line algorithm. It is interesting to note that the absence ofeven a little bit information may significantly affect the performance of an algorithm.