部分线性模型中估计的强相合性

考虑回归模型：ｙｉ＝ｘｉβ＋ｇ（ｔｉ）＋σｉｅｉ，１ｉｎ，其中σ２ｉ＝ｆ（ｕｉ），（ｘｉ，ｔｉ，ｕｉ）是固定非随机设计点列，ｆ（·）和ｇ（·）是未知函数，β是待估参数，ｅｉ是随机误差．对文［１］给出的基于ｇ（·）及ｆ（·）的一类非参数估计的β的最小二乘估计＾βｎ和加权最小二乘估计βｎ，我们在适当条件下证明了它们的强相合性．     

On Variation of Single Birth Processes

Suppose {X（t）; t≥ 0} is a single birth process with birth rate qii＋l （i 〉 0） and death rate qij （i 〉 j ≥ 0）. It is proved in this paper that （i） if there exists aconstant c≥ 0 such that b（i）-a（i）＋ci is nondecreasing with respect to i and a（i） ＋ u（i） - ci ≥ 0 （i≥ 0）, then VarX（t）-EX（t）≥-X（0）e^-2ct,t≥0, or （ii） if there exists a constant u（i） - c≥ 0 such that b（i）-a（i）＋ci is non-increasing with respect to i and a（i）＋u（i）-ci≤0（i≥0）,then VarX（t） - EX（t） ≤ -X（0）e^-2c,t ≥ 0 Hereb（i） = qii＋1, a（0） = 0, a（i） = ∑j=^ijqii-j （i≥ 1）, u（0） = u（1） =0 and u（i） = 1/2∑j=^ij（j - 1）qii-j （i ≥ 2） . This result covers the results for birth-death processes obtained in [7].     

关于正定厄米特矩阵的一个不等式的推广

本文推广了正定厄米特矩阵的一个不等式 ,得到以下结果 :设 A( i) ,B( i) ,… ,C( i) ( i=1 ,2 ,… ,m)都是 n阶正定厄米特矩阵 ,A( i)11,B( i)11,… ,C( i)11为其相应矩阵的 k阶顺序主子阵 ,1≤ k≤ n-1 ,α,β,… ,γ都是正实数 ,且 α+β+… +γ=p≥ 1 ,则有∑mi=1|A( i) |α|A( i)11|α,|B( i) |β|B( i)11|β… |C( i) |γ|C( i)11|γ) <∑mi=1A( i) α∑mi=1A( i)11α.∑mi=1B( i) β∑mi=1B( i)11β…∑mi=1C( i) γ∑mi=1C( i)11γ     

一类上三角矩阵环$W_{n}(p, q)$的斜Armendariz性质

设α是环R的一个自同态,称环R是α-斜Armendariz环,如果在R[x;α]中,(∑_(i=0)~ma_ix~i)(∑_(j=0)~nb_jx~j)=0,那么a_ia~i(b_j)=0,其中0≤i≤m,0≤j≤n.设R是α-rigid环,则R上的上三角矩阵环的子环W_n(p,q)是α~—-斜Armendariz环.     

污染数据半参数回归模型估计的渐近正态性

考虑半参数回归模型：ｙｉ＝ ｘｉβ＋ ｇ（ｔｉ）＋ ｅｉ,ｉ＝ １,２,…,ｎ．其中 Ｅｅｉ＝ ０, Ｅｅ２ｉ＝ σ２１ ＞ ０．假定ｙ１,ｙ２,…,ｙｎ 受到另一独立同分布随机变量序列 μ１,μ２,…,μｎ 的污染,｛μｉ｝与｛ｙｉ｝独立,且仅能观察到污染数据．文［１］对由污染数据作出的参数 β的估计 βｎ,证明了它的强相合性,而本文则证明了它的渐近正态性     

二元分布函数的密度收敛

设 { ( Xi,Yi) ,i≥ 1 }是独立同分布二维随机向量列 ,其共同分布函数为 F.设 F属于 G的吸引场 ,本文假定边缘分布满足 Von-Mises条件 ,主要考虑二维极大值向量 Mn 密度收敛局部一致成立的问题 .本文将 Resnick[3 ]的结果推广到了二维情形     

附加广义函数的几个导数

作者证明了广义函数（ｘ±ｉ０）^λｌｎ^k（ｘ±ｉ０）的表示定理,给出了附加广义函数的导数：（ｌｎ^kｘ_±）＇,（ｘ^λ_±ｌｎ^kｘ_±）＇,（ｘ^-n_±ｌｎ^k＇ｘ_±）＇,（ｄ／ｄｘ）｛（ｘ±ｉ０）^λｌｎ^k（ｘ±ｉ０     

一维$P$-Laplace二阶差分系统奇异边值问题正解的存在性

应用锥压缩锥拉伸不动点定理和Leray-Schauder 抉择定理研究了一类具有P-Laplace算子的奇异离散边值问题$$\left\{\begin{array}{l}\Delta[\phi (\Delta x(i-1))]+ q_{1}(i)f_{1}(i,x(i),y(i))=0, ~~~i\in \{1,2,...,T\}\\\Delta[\phi (\Delta y(i-1))]+ q_{2}(i)f_{2}(i,x(i),y(i))=0,\\x(0)=x(T+1)=y(0)=y(T+1)=0,\end{array}\right.$$的单一和多重正解的存在性,其中$\phi(s) = |s|^{p-2}s, ~p>1$,非线性项$f_{k}(i,x,y)(k=1,2)$在$(x,y)=(0,0)$具有奇性.     

Positive Periodic Solution of a Periodic Cooperative Model with State Dependent Delays

By using the continuation theorem of coincidence degree theory, sufficient conditions are obtained for the existence of positive periodic solution for the periodic cooperative system with state dependent delays where r i , a i , c i , i = 1, 2 are positive continuous y -periodic functions, b i , i = 1, 2 are nonnegative continuous y -periodic functions, and ij , i = 1, 2; j = 1, 2, 3 are nonnegative continuous functions and y -periodic with respect to their first argument.     

关于多项式系数的整除性

设 n是正整数 ,k1 ,k2 ,… ,ks 是适合 k1 +k2 +… +ks=n的非负整数 ,正整数 nk1 k2 … ks=n!k1 !k2 !… ks!称为多项式系数 .本文讨论了当n=a0 +a1 p+a2 p2 +… +arpr ,其中 p为素数且 p≤ n,0≤ ai相似文献   

Asymptotic Distribution of the Jump Change-Point Estimator

The asymptotic distribution of the change-point estimator in a jump changepoint model is considered.For the jump change-point model Xi =a + θI{[nTo] ＜ i ≤n} + εi,where εi (i =1,…,n) are independent ide...     

Principal Submatrices of a Hermitian Matrix

Suppose k 1 ,<, k m and n are positive integers such that k 1 + … + k m h n . We characterize those k i × k i Hermitian matrices A i , i = 1, < , m that can appear as diagonal blocks of an n × n Hermitian matrix C with prescribed eigenvalues. The characterization will be given in terms of the eigenvalues of C and A i , i = 1, <, m . Our results extend those of Thompson and Freede, Horn, Fan and Pall.     

无失效数据的Bayes和多层Bayes估计

对无失效数据的研究 ,是近些年来遇到的一个新问题 ,在实际问题中迫切需要解决 ,这项工作具有理论和实际应用价值 .本文对无失效数据 (ti,ni) ,在时刻ti 的失效概率pi=p{T 相似文献   

循环群$Z_{2}$的模向量不变式

Let G be the finite cyclic group Z_2 and V be a vector space of dimension 2n with basis x_1,...,x_n,y_1,...,y_n over the field F with characteristic 2.If σ denotes a generator of G,we may assume that σ（x_i）= ayi,σ（y_i）= a～-1x_i,where a ∈ F.In this paper,we describe the explicit generator of the ring of modular vector invariants of F[V]～G.We prove that F[V]～G = F[l_i = x_i ＋ ay_i,q_i = x_iy_i,1 ≤ i ≤ n,M_I = X_I ＋ a～-I-Y_I],where I∈An = {1,2,...,n},2 ≤-I-≤ n.     

一类离散系统的全局渐近稳定性

本文对一类离散系统xi 1=T(xi) ,i=0 ,1 ,2…给出全局渐近稳定的判据 ,这些判据推广了文 [1 3]中的结论 ,使得应用更为广泛 .     

Reduction of finite exhausters

In this paper we introduce the notation of shadowing sets which is a generalization of the notion of separating sets to the family of more than two sets. We prove that \({\bigcap_{i\in I}A_{i}}\) is a shadowing set of the family \({\{A_{i}\}_{i\in I}}\) if and only if \({\sum_{i\in I}A_{i}=\bigvee_{i\in I}\sum_{k\in I\setminus \{i\}}A_{i} + \bigcap_{i\in I}A_{i}}\). It generalizes the theorem stating that \({A\cap B}\) is separating set for A and B if and only if \({A+B=A\cap B+A\vee B}\). In terms of shadowing sets, we give a criterion for an arbitrary upper exhauster to be an exhauster of sublinear function and a criterion for the minimality of finite upper exhausters. Finally we give an example of two different minimal upper exhausters of the same function, which answers a question posed by Vera Roshchina (J Convex Anal, to appear).     

一类带p-Laplacian的Sturm-Liouville型2m点边值问题三个正解的存在性

该文考虑了下面的具一维$p$\,-Laplacian算子的多点边值问题 $ \left\{ \begin{array}{rl} &;\disp (\phi_{p}(x'(t)))'+h(t)f(t,x(t),x'(t))=0,\hspace{3mm}01,~\alpha_{i}>0,~\beta_{i}>0,~0<\sum\limits_{i=1}^{m-1}\alpha_{i}\xi_{i}\leq1,~ 0<\sum\limits_{i=1}^{m-1}\beta_{i}(1-\eta_{i})\leq1,~0=\xi_{0} <\xi_{1}<\xi_{2}<\cdots<\xi_{m-1}<\eta_{1}<\eta_{2}<\cdots<\eta_{m-1}<\eta_{m}=1,~i=1,2,\cdots,m-1.$ 通过运用锥上的不动点定理, 该文得到了至少三个正解的存在性. 有趣的是文中的边界条件是一个新型的Sturm-Liouville型边界条件, 这类边值问题到目前为止还很少被研究.     

Independence results for weak systems of intuitionistic arithmetic

This paper proves some independence results for weak fragments of Heyting arithmetic by using Kripke models. We present a necessary condition for linear Kripke models of arithmetical theories which are closed under the negative translation and use it to show that the union of the worlds in any linear Kripke model of HA satisfies PA. We construct a two‐node PA‐normal Kripke structure which does not force iΣ₂. We prove i?₁ ? i?₁, i?₁ ? i?₁, iΠ₂ ? iΣ₂ and iΣ₂ ? iΠ₂. We use Smorynski's operation Σ′ to show HA ? lΠ₁.     

Mathematical aspects of concept analysis

Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 18, Vychislitel'naya Matematika i Kibernetika, 1994     

误差为NA序列的半参数回归模型估计的r阶矩相合性

对于半参数回归模型 yi=xiβ+g( ti) +ei,i=1 ,2 ,… ,n,本文综合最小二乘法和一般加权方法 ,定义了 β,g( t)的估计量 βn,gn( t) .在误差为 NA序列时 ,得到了 βn,gn( t)的 r ( r≥ 2 )阶矩相合性 .