在区间截断的情况下,两点分布估计及其收敛速度

假设总体$X$服从两点均匀分布, 即$\pr(X=x_1)=\pr(X=x_2)=1/2$, 但是随机变量$X$的取值$x_1$和$x_2$是未知的\bd 在区间截断的情况下, 利用样本获得了$x_1$和$x_2$估计量$\wh{x}_1$和$\wh{x}_2$, 并给出了估计量$\wh{x}_1$和$\wh{x}_2$的收敛速度$o(n^{-1/3+\xs})$.     

不同标准差估计方法下的过程能力指数的置信区间的比较研究

采用样本标准差$s$、$s/c_4$、$\ol{R}/d_2$以及MVA分析后的$\wh{\sigma}_{\text{TOTAL}}$分别估计总体标准差,介绍了相应的$\wh{C}_p$和$\wh{C}_{pk}$以及$C_p$的置信区间,分析了每种标准差估计方法的特点, 结合案例进行比较研究.     

应力为GBVE分布强度为指数分布下并联结构可靠度的估计

考虑应力服从GBVE分布,强度服从指数分布的应力—强度模型,分别在应力参数未知和强度参数未知情形下给出了该模型在并联系统下可靠度的估计并讨论了其性质.     

应力为MOBVE分布强度为指数分布下串联结构可靠度的估计

考虑了应力服从MOBVE分布,强度服从指数分布的应力——强度模型,分别在应力参数未知和强度参数未知情形下给出了该模型在串联系统下可靠度的估计并讨论了其性质.     

应力为GBVE分布强度为指数分布下结构可靠度的估计

本文考虑应力服从GBVE分布，强度服从指数分布的应力一强度模型，分别在应力参数未知和强度参数未知情形下给出了该模型可靠度的估计并讨论了其性质．     

有结构变化的半参数回归模型

结合半参数回归模型和含未知变点的结构变化模型提出 一个新的模型\,---\,有结构变化的半参数回归模型, 给出了新模型的有关参数$\beta,\beta^\ast,\gamma,k$的加权最小二乘估计和$f(t)$的核估计, 证明了参数\, $\beta,\beta^\ast,\gamma$的估计的$\sqrt{n}$\,-相合性, 强相合性, 讨论了模型的检验等问题, 并进一步通过随机模拟验证了新模型的优越性.     

应力为SGBVE分布强度为指数分布下结构可靠度的估计

考虑了应力服从SGBVE分布,强度服从指数分布的应力—强度模型,分别在应力参数未知和部分强度参数未知的情形下给出了该模型可靠度的估计,并讨论了其性质.     

多维广义线性模型拟极大似然估计的弱相合性

本文考虑多维广义线性模型的拟似然方程$\tsm^n_{i=1}X_i(y_i-\mu(X_i'\xb))=0$, 在一定条件下证明了此方程的解$\wh\xb_n$渐近存在, 并得到了其收敛速度, 即$\wh\xb_n-\xb_0=O_p({\underline{\xl}}_n^{-1/2})$, 其中$\xb_0$为参数$\xb$的真值, $\underline{\xl}_n$是方阵$S_n=\tsm^n_{i=1}X_iX_i'$的最小特征值。     

三角Banach代数的Lie弱顺从性

设$\mathcal {A,\ B}$ 是含单位元的Banach代数, $\mathcal M$ 是一个Banach $\mathcal {A,\ B}$-双模. $\mathcal {T}=\left ( \begin{array}{cc} \mathcal {A} & \mathcal M \\ & \mathcal {B} \\ \end{array} \right )$按照通常矩阵加法和乘法,范数定义为$\|\left( \begin{array}{cc} a & m \\ & b\\ \end{array} \right)\|=\|a\|_{\mathcal A}+\|m\|_{\mathcal M}+\|b\|_{\mathcal B}$,构成三角Banach 代数.如果从$\mathcal T$到其$n$次对偶空间$\mathcal T^{n}$上的Lie导子都是标准的,则称$\mathcal T$是Lie $n$弱顺从的.本文研究了三角Banach代数$\mathcal T$上的Lie $n$弱顺从性,证明了有限维套代数是Lie $n$弱顺从的.     

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考虑半参数回归模型$y_i=x_i\beta+g(t_i)+V_i$ $(1\le i\len)$, 其中$(x_i,t_i)$是已知的设计点, 斜率参数$\beta$是未知的,$g(\cdot)$是未知函数, 误差$V_i=\tsm^\infty_{j=-\infty}c_je_{i-j}$,$\tsm^\infty_{j=-\infty}|c_j|<\infty$并且$e_i$是负相关的随机变量.在适当的条件下, 我们研究了$\beta$与$g(\cdot)$小波估计量的强收敛速度.结果显示$g(\cdot)$的小波估计量达到最优收敛速度. 同时,对$\beta$小波估计量也作了模拟研究.     

子群的S-条件置换性对有限群结构的影响

Let G be a finite group. Fix a prime divisor p of IGI and a Sylow p-subgroup P of G, let d be the smallest generator number of P and Ma（P） denote a family of maximal subgroups P1, P2 , Pd of P satisfying ∩^di=1 Pi = Ф（P）, the Frattini subgroup of P. In this paper, we shall investigate the influence of s-conditional permutability of the members of some fixed .Md（P） on the structure of finite groups. Some new results are obtained and some known results are generalized.     

P2r,6图的优美性

Kathiresan KM证实$P_{2r,2m-1}$($r,m$皆为任意正整数)是优美的且猜想:除了$(a,b)=(2r-1,4m-2)$外,所有的$P_{a,b}$都是优美的.杨元生证实$P_{2r+1,2m+1}$是优美的,并且证实了当$r\leq7$, $r=9$时的$P_{2r,2m}$是优美的.严谦泰证实$r$为奇数时$P_{2r,2m}$是优美的.采用回溯和分支限界算法搜索到了一个适合于所有$P_{2r,b}$图($r,b$皆为任意正整数)的优美标号,用函数构造法提取其规律并从数学的严格性进行了证明,使得所有的$P_{2r,b}$图($r,b$ 皆为任意正整数)的优美性得到了证实.     

An Adaptive Mesh-Refining Algorithm Allowing for an <Emphasis Type="Italic">H</Emphasis><Superscript>1</Superscript> Stable <Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript> Projection onto Courant Finite Element Spaces

Suppose $\cal{S}^1({\cal T})\subset H^1(\Omega)$ is the $P_1$-finite element space of $\cal{T}$-piecewise affine functions based on a regular triangulation $\cal{T}$ of a two-dimensional surface $\Omega$ into triangles. The $L^2$ projection $\Pi$ onto $\cal{S}^1(\cal{T})$ is $H^1$ stable if $\norm{\Pi v}{H^1(\Omega)}\le C\norm{v}{H^1(\Omega)}$ for all $v$ in the Sobolev space $H^1(\Omega)$ and if the bound $C$ does not depend on the mesh-size in $\cal{T}$ or on the dimension of $\cal{S}^1(\cal{T})$. \hskip 1em A red–green–blue refining adaptive algorithm is designed which refines a coarse mesh $\cal{T}_0$ successively such that each triangle is divided into one, two, three, or four subtriangles. This is the newest vertex bisection supplemented with possible red refinements based on a careful initialization. The resulting finite element space allows for an $H^1$ stable $L^2$ projection. The stability bound $C$ depends only on the coarse mesh $\cal{T}_0$ through the number of unknowns, the shapes of the triangles in $\cal{T}_0$, and possible Dirichlet boundary conditions. Our arguments also provide a discrete version $\norm{h_\cal{T}^{-1}\,\Pi v}{L^2(\Omega)}\le C\norm{h_\cal{T}^{-1}\,v}{L^2(\Omega)}$ in $L^2$ norms weighted with the mesh-size $h_\T$.     

On a conjectured inequality of Gautschi and Leopardi for Jacobi polynomials

Motivated by work on positive cubature formulae over the spherical surface, Gautschi and Leopardi conjectured that the inequality holds for α,β > − 1 and n ≥ 1, θ ∈ (0, π), where are the Jacobi polynomials of degree n and parameters (α, β). We settle this conjecture in the special cases where .      

图P2r,2m的优美标号

设u,v是两个固定顶点,用b条内部互不相交且长度皆为a的道路连接u,v所得图用P_(a,b)表示．K．M．Kathiresan证明：P_(2r,2m-1)(r,m皆为任意正整数)是优美的,且猜想,除了(a,b)=(2r 1,4s 2)外,所有的P_(a,b)都是优美的．杨元生已证明P_(2r 1,2m-1)是优美的,并且证明了,当r=1,2,3,4,5,6,7时,P_(2r,2m)也是优美的．作者证明：r为任意奇数时,P_(2r,2m)也是优美的．     

Duality and perfect probability spaces

Given probability spaces let denote the set of all probabilities on the product space with marginals and and let be a measurable function on Continuous versions of linear programming stemming from the works of Monge (1781) and Kantorovich-Rubin\v{s}tein (1958) for the case of compact metric spaces are concerned with the validity of the duality

(where is the collection of all probability measures on with and as the marginals). A recently established general duality theorem asserts the validity of the above duality whenever at least one of the marginals is a perfect probability space. We pursue the converse direction to examine the interplay between the notions of duality and perfectness and obtain a new characterization of perfect probability spaces.

     

Finite Element Approximations of Symmetric Tensors on Simplicial Grids in $\mathbb{R}^n$: The Higher Order Case

The design of mixed finite element methods in linear elasticity with symmetric stress approximations has been a longstanding open problem until Arnold and Winther designed the first family of mixed finite elements where the discrete stress space is the space of $H(div, Ω\;\mathbb{S}) — P_{k+1}$ tensors whose divergence is a $P_{k-1}$ polynomial on each triangle for $k$ ≥ 2. Such a two dimensional family was extended, by Arnold, Awanou and Winther, to a three dimensional family of mixed elements where the discrete stress space is the space of $H(div, Ω\;\mathbb{S}) — P_{k+2}$ tensors, whose divergence is a $P_{k-1}$ polynomial on each tetrahedron for $k$ ≥ 2. In this paper, we are able to construct, in a unified fashion, mixed finite element methods with symmetric stress approximations on an arbitrary simplex in $\mathbb{R}^n$ for any space dimension. On the contrary, the discrete stress space here is the space of $H(div, Ω\;\mathbb{S}) — P_k$ tensors, and the discrete displacement space here is the space of $L²(Ω ; \mathbb{R}^n) — P_{k-1}$ vectors for $k ≥ n$+1. These finite element spaces are defined with respect to an arbitrary simplicial triangulation of the domain, and can be regarded as extensions to any dimension of those in two and three dimensions by Hu and Zhang.     

关于核型$C^{*}$代数单调积的注记

Given two nuclear C^＊-algebras A1 and A2 with states φ1 and φ2, we show that the monotone product C^＊-algebra A1 △→ A2 is still nuclear. Furthermore, if both the states φ1 and φ2 are faithful, then the monotone product ,A1 △→ A2 is nuclear if and only if the C^＊-algebras ,A1 and A2 both are nuclear.     

Conclaves of planes in PG (4,2) and certain planes external to the Grassmannian ${\cal G}_{1,4,2} \subset$ PG(9,2)

We show that in $\operatorname{PG}(4,2)$ there exist octets $\mathcal{P} _{8}=\{\pi_{1},\,\ldots\,,\pi_{8}\}$ of planes such that the 28 intersections $\pi_{i}\cap\pi_{j}$ are distinct points. Such conclaves (see [6]) $\mathcal{P}_{8}$ of planes in $\operatorname{PG}(4,2)$ are shown to be in bijective correspondence with those planes $P$ in $\operatorname{PG}(9,2)$ which are external to the Grassmannian $\mathcal{G}_{1,4,2}$ and which belong to the orbit $\operatorname{orb}(2\gamma)$ (see [4]). The fact that, under the action of $\operatorname{GL}(5,2),$ the stabilizer groups $\mathcal{G}_{\mathcal{P}_{8}}$ and $\mathcal{G}_{P}$ both have the structure $2^{3}:(7:3)$ is thus illuminated. Starting out from a regulus-free partial spread $\mathcal{S}_{8}$ in $\operatorname{PG}(4,2)$ we also give a construction of a conclave of planes $P\in\operatorname{orb}(2\gamma)\subset\operatorname{PG}(9,2).$     

Blockwise Perturbation Theory for 2x2 Block Markov Chains

Let P be a transition matrix of a Markov chain and be of the form $$P=\Bigg( \begin{matrix} P_{11} &P_{12} \\P_{21} &P_{22} \end{matrix} \Bigg).$$ The stationary distribution $π^T$ is partitioned conformally in the form $(π^T_1, π^T_2)$. This paper establish the relative error bound in $π^T_i (i=1,2)$ when each block $P_{ij}$ get a small relative perturbation.