任意离散值随机变量序列泛函的一类强极限定理

当 {Xn,n≥ 0 }是离散值随机变量序列时 ,建立了关于泛函 { fn(X0 ,X1,… ,Xn) ,n≥ 1}的强极限定理 ,作为推论 ,得出了关于任意随机变量序列及m重非齐次马氏链的随机选择的强极限定理 ,它是关于 (单重 )非齐次马氏链的随机选择的强极限定理的推广 .     

概率空间上一类集合的分形维数

设｛Xn,n≥1｝是定义在概率空间（Ω,F,μ）上具有有限状态空间的随机过程,B→∪Ω,本利用马氏链的有关性质及强大数定律讨论了B的Hausdorff维数和填充维数的有关性质,并得到了一类与马氏链有关的子集的维数结果。     

任意随机变量序列的大数定律

设｛Xn,n≥0｝是任意实值随机变量序列,并且尾概率是一致有界于随机变量X0,通过构造适当的鞅,利用鞅收敛定理讨论随机变量序列｛X,n≥0｝的强极限定理和强弱大数定律,得到了大数定律成立的充分条件,推广了费勒在1946年给出的平均值无限时的大数定律。     

非齐次马氏链泛函变换的若干极限定理

设 { Xn,n≥ 0 }是一列非齐次马氏链 ,{ f (.,.) ,n≥ 1}是一列二元可测函数 ,{ Vn,n≥ 1}是一列可预报随机序列 .引入非齐次马氏链二元泛函停时变换的概念 ,即Γn =∑nk=1Vkfk(Xk-1,Xk) .利用鞅方法讨论了变换的强极限定理 ,得到 limn a-1n ∑nk=1Vk{ fk(Xk-1,Xk) - E[fk(Xk-1,Xk) | Xk-1]} =0 .作为特殊情形 ,将随机选择的概念拓展到非齐次马氏链中 ,得到了关于有限非齐次马氏链随机选择的若干极限定理     

Functional limit theorem for moving average processes generated by dependent random variables

Let ｛Xt,t≥1｝ be a moving average process defined by Xt=∑∞j=0bjξt-j, where ｛bj,j≥0｝ is a sequence of real numbers and ｛ξt,-∞＜t＜∞｝ is a doubly infinite sequence of strictly stationary ?-mixing random variables. Under conditions on ｛bj,j≥0｝ which entail that ｛Xt,t≥1｝ is either a long memory process or a linear process, we study asymptotics of Sn(s)=∑［ns］t=1Xt (properly normalized). When ｛Xt,t≥1｝ is a long memory process, we establish a functional limit theorem. When ｛Xt,t≥1｝ is a linear process, we not only obtain the multi-dimensional weak convergence for ｛Xt,t≥1｝, but also weaken the moment condition on ｛ξt,-∞＜t＜∞｝ and the restriction on ｛bj,j≥0｝. Finally, we give some applications of our results.     

随机阵列部分和高阶矩的上界

给出了中心化的独立随机变量阵列X={Xnj,1≤j≤kn,n≥1}的部分和(^kn∑j=1)Xnj的r阶矩的上界,这一上界的表达式为C(^r-2∑i=0)Kn^(r/r-i)||Xn1||r-i^r。     

逐步回归方法及其计算程序

(一)计算方法概述1.给出n一1个自变量X:,X:,…Xn一1和因变量Xn的m组观察值:xit(i二1,2,…n,t二1,2,一m)求线性回归方程Xn二bo bxX一 … bn一IXn一l(1)使与m组观察值在最小二乘意义下最佳拟合。由数理统计知识知道,求bi的正规方程为:n.1 艺101{m艺(Xit一又i)(Xj,一又j m_一、,一、=艺(Xjt一Xj)(Xnt一xn) t,l (j=1,n,!)‘2) .O、.,了」、.了t.l其中X 1一Mm艺Xit.1(Xit一又i)(Xjt一又j)=1,n) S‘石a‘j=百落了则(2)式可化为标准正规方程:n一l 乏aij ai== anj(j=l,n一l)(8)i一1在求得ai以后,则回归系数(盛) _n一1-bo=Xn一艺biX(5)解方…     

φ混合序列自正则加权和的中心极限定理

设｛X_n, n≥1｝为一严平稳φ混合随机变量序列, EX=0,V²_n为一实数阵列, 利用随机变量阵列的弱收敛定理, 在较一般的条件下, 证明了自正则加权和｛S_n/V_n, n≥1｝的中心极限定理, 改进并推广了已有混合序列自正则化中心极限定理的相关结果.     

惯量任意的符号模式

矩阵A的特征值的集合(含重数)记为σ(A),A的惯量是指三元有序数组i(A)=(i (A),i-(A),i0(A)),其中i (A),i-(A)和i0(A)分别表示具有正,负,零实部特征值的个数.n阶符号模式矩阵S=(sij)是指元素取自{1,-1,0}或者{ ,-,0}的矩阵,S的定性矩阵类是指集合Q(S)={A=(aij)∈Mn(R):对所有的i和j,sign(aij)=sij}.S的惯量是指集合i(S)={i(A):A∈Q(S)}.若对任意满足n1 n2 n3=n的非负三元数组(n1,n2,n3),都有(n1,n2,n3)∈i(S),则称符号模式S为惯量任意模式.考虑n阶符号模式Kn=(kij)n×n:当1≤j-i≤n-2或i=j=n时,kij=1;当1≤i-j≤n-2或i=j=1时,kij=-1;当|i-j|=n-1时,kij可以取任意固定值;其余情形时,kij=0.本文证明了Kn(n≥3)是惯量任意模式.     

由三级数定理导出的一类强极限定理

设 {an,n≥ 1 }是一正数列 ,{Xn,n≥ 1 }是一独立随机变量序列 ,{gn,n≥ 1 }是定义在 (-∞ , ∞ )上的一列非降的正值偶函数 ,对于每个gn,存在pn >0 ,当｜x｜增加时有gn(x)｜x｜pn ↓ .若∑∞n =1Egn(Xn)gn(an)1qn < ∞ ,其中qn ≥ 1 ;0 1 ,则∑∞n =1Xnana .s.收敛     

Markedness and its Interpretation in Language Use

Language markedness is a common phenomenon in languages, and is reflected from hearing, vision and sense, i.e. the variation in the three aspects such as phonology, morphology and semantics. This paper focuses on the interpretation of markedness in language use following the three perspectives, i.e. pragmatic interpretation, psychological interpretation and cognitive interpretation, with an aim to define the function of markedness.     

低渗透非均质砂岩油藏启动压力梯度研究

理论推导与室内实验相结合,建立了低渗透非均质砂岩油藏启动压力梯度确定方法。首先借助油藏流场与电场相似的原理,推导了非均质砂岩油藏启动压力梯度计算公式。其次基于稳定流实验方法,建立了非均质砂岩油藏启动压力梯度测试方法。结果表明:低渗透非均质砂岩油藏的启动压力梯度确定遵循两个等效原则。平面非均质油藏的启动压力梯度等于各级渗透率段的启动压力梯度关于长度的加权平均;纵向非均质油藏的启动压力梯度等于各渗透率层的启动压力梯度关于渗透率与渗流面积乘积的加权平均。研究成果可用于有效指导低渗透非均质砂岩油藏的合理井距确定,促进该类油藏的高效开发。     

On Tragic Consciousness In The Works By Ernest Hemingway

As an American modern novelist who were famous in the literary world, Hemingway was not a person who always followed the trend but a sharp observer. At the same time, he was a tragedy maestro, he paid great attention on existence, fate and end-result. The dramatis personae's tragedy of his works was an extreme limit by all means tragedy on the meaning of fearless challenge that failed. The beauty of tragedy was not produced on the destruction of life, but now this kind of value was in the impact activity. They performed for the reader about the tragedy on challenging for the limit and the death.     

Achieving Unusual States of Matter Under High Pressure

正The periodicity of the elements and the non-reactivity of the inner-shell electrons are two related principles of chemistry,rooted in the atomic shell structure.Within compounds,Group I elements,for example,invariably assume the+1 oxidation state,and their chemical properties differ completely from those of the p-block elements.These general rules govern our understanding of chemical structures and reactions.Using first principles calcula-     

Exchange-Correlation and Electronic Excitation Energies from Pairing Matrix Fluctuations

We have developed an adiabatic connection to formulate the ground-state exchange-correlation energy in terms of pairing matrix linear fluctuations.This formulation of the exchange-correlation energy opens a new channel for density functional approximations based on the many-body perturbation theory.We illustrate the potential of such approaches with an approximation based on the particle-particle Random Phase Approximation(pp-RPA).This re-     

Density Functional Theory for the Response of Periodic Systems to Electric Fields Based on the Vector Potential Approach

正The electronic and nuclear(structural/vibrational)response of 1D-3D nanoscale systems to electric fields gives rise to a host of optical,mechanical,spectral,etc.properties that are of high theoretical and applied interest.Due to the computational difficulty of treating such large systems it is convenient to model them as infinite and periodic(at least,in first approximation).The fundamental theoretical/computational problem in doing so is that     

On the Thermodynamic Limit for Responses to Static Electromagnetic Fields

For molecular systems,the quantum-mechanical treatment of their responses to static electromagnetic fields usually employs a scalar-potential treatment of the electric field and a vector-potential treatment of the magnetic field.Although the potential for each field separately is associated with the choice of an(unphysical)origin,the precise choice of the origin for the electrostatic field has little consequences for the results.This is different for the     

An affordable accurate evaluation of the binding conformations predicted by molecular docking studies in bio-system

Franck-Condon factors bridge the gap between theoretical modeling and experimental observations for molecular electronic spectroscopy and electron transfer.Under the displaced harmonic oscillator approximation,multidimensional Franck-Condon factors are decomposed into a product of many one-dimensional(1D)Franck-Condon(FC)factors,and each 1D-FC factor is associated with one Huang-Rhys factor that determines the leading contribution of     

Call for Papers

<正>"The Journal of Shanghai Normal University:Mathematics"is published by Shanghai Normal University as regular issues of The Journal of Shanghai Normal University each year from 2014 in English.The editors-in-chief of the issues are professors Yuhao Cong and Maoan Han.The Journal of Shanghai Normal University was started in 1958 with     

Journal of Donghua University ( English Edition) Contents of Volume 31

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