ρ-混合序列部分和乘积的几乎处处极限定理

设{X_n,n≥1}是一严平稳的ρ-混合的正的随机变量序列,且EX_1=μ＞0, Var(X_1)=σ~2,记S_n=Σ_(i=1)~n X_i和γ=σ/μ,在较弱的条件下,证明了对任意的x,,其中σ_1~2=1+2/(σ~2)∑_(j=2)~∞Cov(X_1,X_j),F(·)是随机变量e~(2~(1/2)N)的分布函数,N是标准正态随机变量,我们的结果推广了i．i．d时的情形．     

方差未知的多总体均值检验的一种有效方法

本文对n 个相互独立、服从正态分布总体的均值统计假设H_0:μ_1=μ_2…=μ_n 的检验,进行了探讨。在方差σ_j~2(j=1,2,…,n)未知,且σ_1~2=σ_2~2=…=σ_n~2的条件下,利用正态分布及X~2分布的再生性,构造了T_n,T_n~′统计量,给假设H_0的检验提供了切实可行的有效方法。     

正态—正态模式下,结构串联系统可靠度的置信下界

设X_1,…,X_niid.～N(μ,σ~2),Y～N(0,1),Y与X_1,…,X_n独立,Z_1,…,Z_m为N(μ,σ~2)的iid.样本,σ~2已知,μ未知,本文证明R=P_r{X_1≥Y,…,X_n≥Y}的MVUE存在的充要条件是m≥nσ~2/n+σ~2,得到R的MVUE和UMA置信下界。     

一类微分方程組在一个临界情形中的解的稳定条件

<正> 其中γ及p_(sσ)(s,σ=1,…,n)为实常数,且γ>0,而q_(sσ)(t)(s,σ=1,…,n)为实变数t之实函数,当一切t≥T>0时定义、連續及有界;X_s~((1))(s=1,…,n)为x_1,…,x_n之正則函数,其展开式不含低于二次之項,并具实常数系数;至于X_s~((2))(s=1,…,n)为x_1,…,x_n之正則函数,其按x_1,…,x_n之冪的展开式为:     

具强迫项高阶非线性中立型差分方程的振动性与渐近性

讨论具强迫项高阶非线性中立型差分方程△m(xn ∑si=1pi(n)xγi(n)) ∑kj=1qj(n)hj(xσj(n))=fn,n=0,1,2,…及其相关联的差分方程△m(xn ∑si=1pi(n)xγi(n)) ∑kj=1qj(n)hj(xσj(n))=0,n=0,1,2,…的振动性与渐近性,得到了所有解振动或趋于零的充分性判据.     

n維向量間的一個問题

本文是討論4個n維向量問的一個問題,具體地來說,就是定理:設A=(a_1,a_2,…,a_n),B=(b_1,b_2,…,b_n),X=(x_1,x_2,…,x_n)和Y=(y_1,y_2,…,y_n)為4個非零的n維向量,其向量分適合 (1) a_ib_j+a_jb_i=x_iy_j+x_jy_i(i,j=1,2,…,n)之諸關係式:那麼A,B一定分别和X,Y或Y,X成比例,即必有二數λ≠0,μ≠0致A=λX,B=μY,或A=λY.B=μX。 證明:當n=1時,A=(a_1),B=(b_1),X=(x_1),Y=(y_1)。因題設A,B,X,Y均非零向量,故此時應為a_1b_1x_1y_1≠0,故A=λX,B=μY或A=σY,B=γX之4個異於零之數λ,μ,σ,γ之存在甚為顯明,此即示定理對於一維向量來講是成立的——實際上,由於(1)的原故,此時還顯然有λμ=1或σγ=1。今用數學歸納法假定定理對於n-1維向量而言是成立的,而來考察適合關係式(1)的4個n維向量A,B,X和Y。因A為非零向量,故它必至少有一個向量分     

随机截尾情形下正态分布参数的最大似然估计

设x1,…,xn,y1,…,yn是相互独立的随机变量,其中x1,…,xn服从相同的正态分布N(μ,σ2)或对数正态分布LN(μ,σ2),参数(μ,σ2)未知.我们的观测数据为(ti,δi), i=1,…,n,其中ti=min(xi,yi),δi=I(xi≤yi),这里I(·)为示性函数.基于上述数据,本文的主要结果是论证了(μ,σ2)的最大似然估计(MLE)存在的充要条件是下列条件至少一条满足:(1)有ti＜tj使δi=δj=1;(2)有ti＜tj使δi=1,δj=0.此外,我们还给出了MLE的计算方法和一些算例.     

牛顿公式的一个初等证明

设x_1,x_2,…,x_n是一元n次方程x~n-σ_1x~(n-1)+σ_2x~(n-2)-…+(-1)~nσ_n=0的n个根,并设S_k=x_1~k+x_2~k+…+x_n~k(k=1,2,…),那么 当k相似文献   

三维复Ginzburg-Landau方程的整体解的存在惟一性

在三维空间中研究带2σ次非线性项的复值Ginzburg—Landau方程(CGL) ut=ρu (1 iγ)△u-(1 iμ)|u|^2σu,通过先验估计的方法,在适当的σ的假设下,获得该方程周期边值问题整体解的存在性和惟一性．     

强相依非平稳高斯序列超过数点过程与部分和的联合渐近分布

设{Xi}∞i=1是标准化强相依非平稳高斯序列,记Sn=∑Xi,σn=√var(Sn),Mktn为X1,X2,…,Xtn的第k个最大值,Ntn为X1,X2,…,Xtn对水平μn(x)的超过数形成的点过程,tn是-列单调增加的正整数列,在一定条件下得到Ntn与Sn/σn,Mktn与Sn/σn的联合渐近分布.     

Estimation of the number of components of finite mixtures of multivariate distributions

An estimator of the number of components of a finite mixture ofk-dimensional distributions is given on the basis of a one-dimensional independent random sample obtained by a transformation of ak-dimensional independent random sample. A consistency of the estimator is shown. Some simulation results are given in a case of finite mixtures of two-dimensional normal distributions.     

Galois Structure of K-Groups of Rings of Integers

N/Kbe a Galois extension of number fields with finite Galois group G.We describe a new approach for constructing invariants of the G-module structure of the K groups of the ring of integers of N in the Grothendieck group of finitely generated projective Z[G]modules. In various cases we can relate these classes, and their function field counterparts, to the root number class of Fröhlich and Cassou-Noguès.     

Eigenvector p-Bases of Rings of Constants of Derivations

Let A be a UFD of characteristic p > 0, let 𝒵 be a set of some eigenvectors of a derivation of A. We prove, under some additional assumptions, a necessary and sufficient condition for 𝒵 to be a p-basis of the minimal ring of constants containing 𝒵. The main preparatory result is the unique decomposition theorem with respect to a factor from a given subalgebra containing A^p.     

有资格限制的指派问题的求解方法

在实际的指派工作中，常会遇到某个人有没有资格去承担某项工作的问题，因此，本建立了有资格限制的指派问题的数学模型。在此数学模型中，将效益矩阵转化为判定矩阵，由此给出了判定此种指派问题是否有解的方法；在有解的情况下，进一步将效益矩阵转化为求解矩阵，从而将有资格限制的指派问题化为传统的指派问题来求解。最后给出了一个数值例子来说明这样的处理方法是有效的。     

Extreme values of the sum of squares of degrees of bipartite graphs

In this paper we determine the minimum and maximum values of the sum of squares of degrees of bipartite graphs with a given number of vertices and edges.     

On Sums of Coefficients of Products of Polynomials

We study the nilpotency of the sums of all coefficients of some sorts of products of polynomials over reversible, IFP, and NI rings, and introduce an SCN ring as a generalization. We characterize SCN rings in relation with related ring properties, and also provide several useful properties and ring extensions of SCN rings.     

Convergence of sequences of sets of associated primes

It is a well-known result of M. Brodmann that if is an ideal of a commutative Noetherian ring , then the set of associated primes of the -th power of is constant for all large . This paper is concerned with the following question: given a prime ideal of which is known to be in for all large integers , can one identify a term of the sequence beyond which will subsequently be an ever-present? This paper presents some results about convergence of sequences of sets of associated primes of graded components of finitely generated graded modules over a standard positively graded commutative Noetherian ring; those results are then applied to the above question.

     

Number of connected components of groups of real points of adjoint groups

We present a unified approach to compute the number of connected components in the group of real points of adjoint almost simple real algebraic groups.     

Radius of convexity of certain classes of analytic functions

We consider the classes of analytic functions introduced recently by K.I. Noor which are defined by conditions joining ideas of close-to-convex and of bounded boundary rotation functions. We investigate coefficients estimates and radii of convexity.