单函数(A,Γ)小波的存在性问题

小波分析是除了Fourier分析和Gabor分析以外一种新的时频分析工具．它被应用在信号处理、图像处理以及许多其他领域．小波分析的—个基本问题是什么样的(A,Γ)对,使得存在单函数(A,Γ)小波.本文填补了Ionascu,Yang Wang关于单函数小波存在性问题在二维情形论证中的漏洞.     

l_p(Γ,X)的λ性质(英文)

本文讨论lp（Γ．X）和（ΓXt）lp的λ性质和λ-函数，从而回答了[1]的一个公开问题．     

关于伽玛函数和不完全伽玛函数单调性的注记

利用含有两参数拓广加权平均值的单调性和不等式,我们证明了三类比的伽玛函数在条件r＞0,s＞0和x＞0下是递增的,Γ(s),Γ(s,x)和γ(s,x)分别表示伽玛函数和不完全伽玛函数.据此关于伽玛函数和不完全伽玛函数的单调性结果和不等式被推广了,同时给出了伽玛函数一些结果的证明.     

连续统与集函数T(Ⅱ)

集函数Γ是David P. Bellamy引入的。本文导出与集函数Γ的连续性有关的一些结果,也给出了一个蕴含集函数Γ连续性的条件。     

矩阵Г分布的一致渐近正态性

相对于两个密度函数之间的Kullback-Leibler距离,本文获得了矩阵Γ分布一致渐近正态分布的条件,由于矩阵Γ分布包含了Wishart分布,因此我们也指出了 Wishart分布一致渐近正态分布的条件．     

调和方程第一边值问题高效概率算法

１．调和方程边值问题和概率转移矩阵考虑调和方程Ｄｒｉｃｈｌｅｔ问题：或Ｄｒｉｃｈｌｅｔ外问题：其中　Г是Ω的周界,它是一条分段光猾封闭曲线,Ω是Г的外部区域．为简单起见,我们仅考虑问题（１．１）;外问题可以类似解决．问题（１．１）相应的变分问题是其中显然,在时,问题（１．１）或（１．３）的解存在唯一．设为有限多个固定的点,假定Γ的弧长为１,将Γ依弧参进行剖分得分点相应的Γ上的点记　以及对每个ｊ,在Γ上构作基函数于是得到边界　上的有限元空间对于每一个基函数　边值问题的解（唯一）是ｕｊ,依定义有时简…     

若干矩阵Γ分布的相关分布

本文研究了与矩阵Γ分布相关的若干分布的密度函数,利用矩阵Γ分布的特征函数和它的Bartlett分解等方法,获得了与矩阵Γ分布相关的几个分布的密度函数解析表达式,它们包括Γ分布随机矩阵的子矩阵、行列式、迹和特征根的分布密度,进一步还得到了相关系数矩阵的分布密度函数形式.     

Γ函数乘积公式的一个新证明

Γ函数的乘积公式的证明方法有多种.例如,依据Γ函数对数微商的表达式     

一个著名特殊函数恒等式的多元推广及其概率证明

将贝塔函数和伽玛函数推广到多元情形,利用随机变量的独立性和概率密度变换公式,得到广义贝塔函数和广义伽玛函数之间的一个重要关系式,它是贝塔函数与伽玛函数关系式:B(a,b)=(Γ(a)Γ(b))/(Γ(a+b))(a0,b0)的推广,还得到一些更加一般的积分恒等式.     

连续统与集函数Г

本文对集函数Γ的某些性质作了研究。我们给出Γ关于连续映射、单调映射、开映射的映射性质,也给出了集函数Γ可加性、对称性的一些结果。     

符号圈拼接图的零度

令$\eta(\Gamma)$和$c(\Gamma)$是符号图$\Gamma$的零度和基本圈数. 一个符号圈拼接图是指每个块都是圈的连通符号图. 本文证明了对任意符号拼接图$\eta(\Gamma)\le c(\Gamma)+1$成立, 并且刻画了等号成立的极图, 推广了王登银等人(2022)在简单圈拼接图上的结果. 此外, 我们证明了任意的符号拼接图$\eta(\Gamma)\neq c(\Gamma)$, 给出了满足$\eta(\Gamma)=c(\Gamma)-1$的符号拼接图的一些性质并刻画处$\eta(\Gamma)=c(\Gamma)-1$的二部符号拼接图.     

零度为$n-7$的双圈符号图

Let Γ be a signed graph and A(Γ) be the adjacency matrix of Γ. The nullity ofΓ is the multiplicity of eigenvalue zero in the spectrum of A(Γ). In this paper, the connected bicyclic signed graphs(including simple bicyclic graphs) of order n with nullity n-7 are completely characterized.     

关于余倾斜双模的k-挠自由模

Let A and F be left and right Noetherian rings and ∧ωr a cotilting bimodule. A necessary and sufficient condition for a finitely generated A-module to be ω-k-torsionfree is given and the extension closure of Tω^i is discussed. As applications, we give some results of ∧ωr related to l.id（ω） ≤ k.     

森田六元组的几乎分裂序列

令ΛA_1,Λ_2为两个环,M是(A_2-Λ_1)-双模,且N是(Λ_1-Λ_2)-双模.六元组Γ=(Λ_1,Λ_2,N,M,ψ,φ)是一个森田六元组.对于Γ的表示,确定其几乎分裂序列(也称AR-序列)是非常重要的.通过modΛ_1和modΛ_2的右(左)几乎分裂同态、既约同态构造Γ上的相应同态,并进一步确定它的几乎分裂序列.     

Extrapolation of Nyström Solutions of Boundary Integral Equations on Non-Smooth Domains

The interior Dirichlet problem for Laplace's equation on a plane polygonal region $\Omega$ with boundary $\Gamma$ may be reformulated as a second kind integral equation on $\Gamma$. This equation may be solved by the Nyström method using the composite trapezoidal rule. It is known that if the mesh has $O(n)$ points and is graded appropriately, then $O(1/n^2)$ convergence is obtained for the solution of the integral equation and the associated solution to the Dirichlet problem at any $x\in \Omega$. We present a simple extrapolation scheme which increases these rates of convergence to $O(1/n^4)$ .     

E1 ο Ed型距离正则图及 Q -多项式的性质

设$\Gamma$ 是一个直径$d\geq 3$的非二部距离正则图，其特征值 $\theta_{0}>\theta_{1}>\cdots>\theta_{d}.$ 设$\theta_{1'}\in\{ \theta_{1},\theta_{d}\}, $\theta_{d'}$ 是$\theta_{1'}$ 在 $\{\theta_{1},\theta_{d}\}$中的余. 又设 $\Gamma$ 是具有性质$E_{1}\circ E_{d}=|X|^{-1}(q^{d-1}_{1d}E_{d-1}+q^{d}_{1d}E_{d})$的$E_{1}\circ E_{d}$型距离正则图,$\sigma_{0},\sigma_{1},\cdots,\sigma_{d}$,$\rho_{0},\rho_{1},\cdots,\rho_{d}$和$\beta_{0},\beta_{1},\cdots,\beta_{d}$ 分别是关于$\theta_{1'}$,$\theta_{d'}$ 和 $\theta_{d-1}$的余弦序列.利用上述余弦序列,给出了 $\Gamma$关于 $\theta_{1}$ 或$\theta_{d}$是$Q$ -多项式的充要条件.     

GAMMA-MINIMAX ESTIMATORS FOR THE MEAN VECTOR OF A MULTIVARIATE NORMAL DISTRIBUTION

Γ-minimax estimators are determined for the mean vector of a multivariate normaldistribution under arbitrary squared error loss.Thereby the set Γ consists of all priorswhose vector of first moments and matrix of second moments satisfy some given restric-tions.Necessary and sufficient conditions are derived which ensure a prior being leastfavourable in Γ and the unique Bayes estimator with respect to this prior being Γ-minimax.By applying these results the Γ-minimax estimator is explicitly found in some special casesor can be computed by solving a system of non-linear equations or by minimizing a quad-ratic form on a compact and convex set.     

An estimate on the distortion of the logarithmic capacity

Let be a Fuchsian group. We show that the existence of a set on with no -equivalent points and positive logarithmic capacity does not imply that is of convergence type.

     

On Proximal Relations in Transformation Semigroups Arising from Generalized Shifts

For a finite discrete topological space $X$ with at least two elements, a nonempty set $\Gamma$, and a map $\varphi:\Gamma \to \Gamma$, $\sigma_{\varphi}:X^{\Gamma} \to X^{\Gamma}$with $\sigma_{\varphi}((x_{\alpha})_{\alpha \in \Gamma})=(x_{\varphi(\alpha)})_{\alpha \in \Gamma}$ (for $(x_{\alpha})_{\alpha \in \Gamma} \in X^{\Gamma}$) is a generalized shift. In this text for $\mathcal{S} = \{\sigma_{\varphi}:\varphi \in \Gamma^{\Gamma}\}$ and $\mathcal{H}=\{\sigma_{\varphi}:\Gamma \xrightarrow{\varphi} \Gamma$ is bijective$\}$ we study proximal relations of transformation semigroups $(\mathcal{S}, X^{\Gamma})$ and $(\mathcal{H}, X^{\Gamma})$. Regarding proximal relation we prove: $$P(\mathcal{S}, X^{\Gamma}) = \{((x_{\alpha})_{\alpha \in \Gamma},(y_{\alpha})_{\alpha \in \Gamma}) \in X^{\Gamma} \times X^{\Gamma} : \exists \beta \in \Gamma (x_{\beta} = y_{\beta})\}$$and $P(\mathcal{H}, X^{\Gamma} ) \subseteq \{((x_{\alpha})_{\alpha \in \Gamma},(y_{\alpha})_{\alpha \in \Gamma}) \in X^{\Gamma} \times X^{\Gamma} : \{\beta \in \Gamma : x_{\beta} = y_{\beta}\}$ is infinite$\}$ $\cup\{($ $x,x) : x \in \mathcal{X}\}$. Moreover, for infinite $\Gamma$, both transformation semigroups $(\mathcal{S}, X^{\Gamma})$ and $(\mathcal{H}, X^{\Gamma})$ are regionally proximal, i.e., $Q(\mathcal{S}, X^{\Gamma}) = Q(\mathcal{H}, X^{\Gamma} ) = X^{\Gamma} \times X^{\Gamma}$, also for sydetically proximal relation we have $L(\mathcal{H}, X^{\Gamma}) = \{((x_{\alpha})_{\alpha \in \Gamma},(y_{\alpha})_{\alpha \in \Gamma}) \in X^{\Gamma} \times X^{\Gamma} : \{\gamma ∈ \Gamma :$ $x_{\gamma} \neq y_{\gamma}\}$ is finite$\}$.     

Shift Generated Haar Spaces on Compact Domains in the Complex Plane

Haar spaces are certain finite-dimensional subspaces of $\cc(K)$, where $K$ is a compact set and $\cc(K)$ is the Banach space of continuous functions defined on $K$ having values in $\C$. We characterize those Haar spaces which are generated by shifts applied to a single, analytic function for $K\subset\C$. This means that an arbitrary finite number of shifts generates Haar spaces by forming linear hulls. We have to distinguish two cases: (a) $K\not=\overline{K^\circ}$; (b) $K=\overline{K^\circ}$. It turns out that, in case (a), an analytic Haar space generator for dimensions one and two is already a universal Haar space generator for all dimensions. The geometrically simplest case that, in case (b), $K$ is convex with smooth boundary turns out to be the most difficult case. There is one numerical example in which the entire function $f:=1/\Gamma$ is interpolated in a shift generated Haar space of dimension four.