THE STRUCTURE AND PRECISE MODERATE DEVIATIONS OF RANDOM VARIABLES WITH DOMINATEDLY VARYING TAILS

This paper shows the structure of the random variables with dominatedly varying tails and that of the associated random variables, and obtains some results on these r.v.s' precise moderate deviations with random centralizing constants, which extend the boundary γλ(t) of large deviations to γ(λ(t))1/s, where γ> 0, 1 < s < 2, λ(t) is the expectation of the random index N(t), t > 0.     

Robust stability for stochastic interval delayed Hopfield neural networks

A type of stochastic interval delayed Hopfield neural networks as du(t) = [-AIu(t) WIf(t,u(t)) WIτf7τ(uτ(t)] dt σ(t, u(t), uτ(t)) dw(t) on t≥0 with initiated value u(s) = ζ(s) on - τ≤s≤0 has been studied. By using the Razumikhin theorem and Lyapunov functions, some sufficient conditions of their globally asymptotic robust stability and global exponential stability on such systems have been given. All the results obtained are generalizations of some recent ones reported in the literature for uncertain neural networks with constant delays or their certain cases.     

THE DIRICHLET PROBLEM AND NEUMANN PROBLEM FOR NONLINEAR PARABOLIC SYSTEMS OF SECOND ORDER EQUATIONS WITH MEASURABLE COEFFICIENTS IN A HIGHER DIMENSIONAL DOMAIN

1 Formulation of Dirichlet Problem and Neumann Problem fOrParabolic SystemsLet O be a bounded domain in Rn and the boundary On E C2. Denote Q = g x I,I =0 < t 5 T, 0 < T < ool 0Q = Sl U S2 is the parabolic boundary where S1 = a x {t = 0} is thebottom and S2 = an x I is the lateral boundary. We consider the nonlinear parabolic systemof second order equationsFh(t, xl ut D.u, D:u) -- Hukt = 0 in Q, k = 1, 2,'',m. (l.l)Under certain conditions, system (1.1) can be reduced to the fOrmw…     

具有时滞的线性系统渐近稳定的时滞相关条件

确定了线性时滞系统 x(t) =Ax(t) Bx(t-τ)稳定的时滞界 ,以改进现有有关该系统研究结果的保守性 ,并降低稳定验算的计算复杂度。详细介绍了确定时滞界的数值算法 ,给出了释例并与现有有关结果进行了比较。     

单滞后区间动力系统的指数稳定性

用矩阵测度和不等式研究了单滞后时变区间动力系统 x=N[P ,Q]x(t) N[C ,D]x(t-τ) (τ≥0 )的指数稳定性 ,给出了其指数稳定的判别准则 ,而没有使用通常的指数变换 ,并给出了数值例子。推广和改进了文献 [1～ 3]的工作。     

Class of numerical methods for differential-algebraic systems with discontinuous right-hand sides

1.INTRODUCTION Differential algebraicsystemswithdiscontinuous right handsides My′=f(t,y),a≤t≤b,　y(t0)=y0(1) discontinuitiesoff(t,y)aredeterminedbythestate ofswitchingfunctionφ(t,y).Adiscontinuityissaid tooccuratt whenφ(t ,y(t ))=0.Theex pressionoff(t,y)is f(t,y)=f-(t,y)φ(t,y)<0f+(t,y)φ(t,y)≥0(2) tistheindependentvariableofsystem,y=( y1, y2, …, yn)Tisstatevariableofndimensions,f=(f1, f2,…,fn)T,somefiisdiscontinuousfunction,M= [m1,…,mn]n×nisann×ndiagonalmatrix,thedi …     

STRONG CONSISTENCY OF THE PERIODIC SMOOTHING SPLINES

Consider the regression model Y_i=u(x_i)+ε_i,i=1,2,…,n,where u(x)∈W_(2,per)~2[0,1],x_i=(i-1)/n,{ε_i}(?)are i.i.d,random variables.We use the periodic smoothing spline u_(λp)(x)toestimate u(x).Under certain conditions,strong consistency results of u_(λp)(x)are obtained,i.e.,forall 0相似文献   

A NOTE ON THE SPECTRUM OF NEUTRON TRANSPORT OPERATOR IN A SLAB WITH GENERALIZED BOUNDARY CONDITIONS

The spectrum of neutron transport operator A in an arbitrary non-homogeneous slab geometry is discussed in consideration of anisotropic scatteringand fission.Under the assumptions that the boundary reflection coefficient func-tion α(v,μ),γ(v,μ)and the scattering-fission kernel k(x,v,v′,μ,μ′)are boundedmeasurable,and the total collision frequency v∑(x,v)is square integrable,it isshown that A has at most finite spectrum points in any strip{λ=β+i(?)|β_1(?)β(?)β_2},where β_2>β_1>-λ~*,with λ~* the essential infimum of v∑(x,v).Fi-nally,the asymptotic expansion of the solution for the time-dependent equation(dN)/(dt)=AN,N(0)=N_0 is given as a corollary.     

模糊控制器是泛逼近器的若干充分条件

通过分析模糊控制器的一般算法,发现模糊控制器是否具有泛逼近性,关键取决于模糊蕴涵算子θ(ɑ,0)和θ(ɑ,1)时的表达式或取值.在此基础上给出了模糊控制器具有泛逼近性的若干充分条件.进而,由这些充分条件验证了当规则取并时有29个模糊蕴涵算子构成的模糊控制器具有函数的泛逼近性;当规则取交时有40个模糊蕴涵算子构成的模糊控制器具有函数的泛逼近性.     

滞时微分方程二级θ-方法的数值耗散性

主要研究求解具有常滞时微分方程的二级θ-方法的数值耗散性。证明了二级θ-方法是耗散的当且仅当θ∈[1/2，1]。数值试验表明该理论结论是正确的。     

关于褶积的几个基本概念

一 函数的时移 给定一个函数K(τ),当自变量τ变动时,有下列这些常见的情况函数(例) 定义域     

OPTIMAL RATE OF CONVERGENCE FOR ESTIMATORS IN THE NONPARAMETRIC MEDIAN MODEL

Let(Y,X)be a random vector with its value in R~1×R~d,d(?)1.Let(?)be the collection of real valued functions θ(x) on R~d which is p times differ-entiable at x=0 and p-1 times differentiable on an open neighborhood U ofthe origin of R~d.The conditional distribution of Y is assumed to be of the formof f(y|x,θ(x))dy where θ(x)∈(?)is called the parameter of the family.(Y,X)iscalled a nonparametric median model if furthermore the conditional median of Ygiven X=x is θ(x).In this paper,the optimal rate of convergence for estimatorsof T(θ)=θ(0)is discussed.Under certain conditions,it is proved that for thenonparametric median model the optimal rate of convergence is r=p/(2p+d).A sequence of estimators,which is asymptotically normal with the optimal rate ofcovergence,is constructed.     

系统可靠性决策规则发掘方法研究

为根据已有的经验提炼出对系统可靠性评判的决策准则,基于汪培庄的因素空间理论与笔者提出的空间事故树理论思想,构造了一套从决策经验中提取决策准则的方法.该方法适用于条件属性为域值的多因素影响系统.首先数据归一化构建基础信息决策表Ψ(T).计算x_i与x_j关于属性a_q的相似度S(x_i,x_j,a_q),形成相似性表Θ(U,C,S).根据相似性阈值f将Θ(U,C,S)化简得Θ′(U,C′,S).根据模糊度θ,将Θ′(U,C′,S)改造为模糊二项相似表Ω(Θ′,θ),从而构建区分矩阵Γ(Ω).对U进行决策组划分,形成决策项,组成决策归纳表L(T).利用L(T)和Ψ(T)得到了切合实际使用的决策语义表L(T).从方法处理实际问题的结果看,在只利用条件属性集合与对象集合的条件下,即可判断经验决策的合理性.经过一系列的数据处理最终得到的决策语义表L(T),它可以判断系统工作状态属于哪种系统可靠性的决策,并确定了这种决策的置信度.     

网络上具有一般直接免疫的SIRS传染病模型分析

考虑复杂网络上具有一般直接免疫率的SIRS传染病模型。由地方病平衡点的存在性,确定了传染病的流行阈值λc,并且通过构造合适的李雅普诺夫函数证明:当λ≤λ_c时,无病平衡点全局渐近稳定;当λλ_c时,地方病平衡点全局渐近稳定。根据免疫率的分布,提出了一致性直接免疫和目标性直接免疫。结果表明,在平均免疫率相等的条件下存在免疫丧失率的临界值δ_c,当δδ_c(δδ_c)时,目标性免疫的流行阈值小于(大于)一致性免疫的流行阈值。     

A class of twostep continuity Runge-Kutta methods for solving singular delay differential equations and its convergence

1.INTRODUCTION Considerthefollowingdelaydifferentialequations(DDEs)y′(x)=f(x,y(x),y(x-τ(x))),a≤x≤b y(x)=φ(x),xmin≤x≤a(1)wherey,f,φaren vectorfunctions,φ(x)isinitial valuefunction,τ(x)≥0isdelayfunction.Definition1DDEs(1)issingularatthepoint xαifthelagsatisfiesτ(xα)=0.Ifthereisnosuch pointxα∈[a,b],thentheDDEs(1)isnon singular.InthenumericalsolutionofDDEs(1)byacon tinuousexplicitRunge Kuttamethod,wesuppose thatwehaveanapproximationyntoy(x)atxnand wishtocomputeanapproxima…     

A Stock Pricing Model Based on Arithmetic Brown Motion

1　 IntroductionStock value is an old and new study field.Gordon presented a model to estimate stockvalue in1 962 and now the model is widely used in the world.In Gordon model company′sdividends per share increase in geometric Brown motion,that is,dividend at the end of tyear isDt=D0 eμt ( 1 )where D0 denotes dividend per share in last year;μ denotes the mean of the logarithmnormal distribution and is calculated byμ =1( n -1 )△ t∑n- 1t=1ln( Dt 1 /Dt) ( 2 )where△t is interval of sampl…     

方格网络上部分用户可控时流量分配效率

针对方格网络上部分用户可控的流量分配问题,给出了相应的分配策略,当路阻函数是线性函数时,分配效率是1;当路阻函数是非负、非递减的可微函数时,当1≤A≤2时,分配效率是1;当A>2时,分配效率是(A-1)2,其中A≥1为路阻函数的雅可比矩阵相似性系数。     

基于时变假设的修正负二项车险索赔频率精算模型

传统车险索赔频率模型都采用风险水平在保险期间保持不变的假设,采用风险水平时变假设,选择Weibull过程作为风险强度函数,引入传统的负二项索赔频率模型。新模型修改原有频域方法为时域参数方法进行参数估计,并使用极大似然估计结合贝叶斯估计的方法估计出Weibull过程的水平参数λ和形状参数β。在β=1时,新模型就等价于传统负二项模型;此外,新模型可为风险上升(β1)和风险下降(β1)的保单确定更准确的风险保费。     

A Concise Proof of the Relation between Poisson Process and Exponential Distribution

1　IntroductionWehaveknownthatthePoissonprocessisveryimportantinqueueingtheoryreseach,oneofthedefinitionsisgivenby[8]:Consideracountingprocess{N(t),t≥0},whereN(t)denotesthearrivalnumberin(0,t],if:(i)N(0)=0;(ii){N(t),t≥0}hasstationaryincrements,name...     

UNIQUENESS OF THE POSITIVE SOLUTION FOR SINGULAR NONLINEAR BOUNDARY VALUE PROBLEMS

This paper is concerned with the bounded value problems1/p(t)(p(t)u')'+f(u)=0, t>0, u'(0)=0, lim t→+∞ u(t)=0,where f(0)=0. Such problems arise in the study of semi-linear elliptic differential equa-tions in R~n. It is shown that the problem has at most one positive solution under appro-priate conditions on f and p. Our result can include the important case that p(t)=f~(n-1)and f(u)=u~P-u, where n>1, p>1 are some given constants.