ON THE DISTRIBUTION OF RANDOM LINES IN THE GENERAL CASE

$L$ is a line in a plane through the origin, with an angle $\[\alpha \]$ to the $x$-axis,$\[0 < \alpha < \pi \]$.$M$ is a point process on positive $x$-axis, Through the nth point of $M$ draw a line with a random angle $\[{\theta _n}\]$ to $x$-axis, $\[{\varphi ^ + }\]$ is the set of intersections of those lines with $\[{L^ + }\]$. Let $\[m = EM\]$. If, for every $\[c > 0\]$, then $\[{\varphi ^ + }\]$ is locally finite on $L$, and let $\[\tilde M\]$ be the point process constructed by $\[{\varphi ^ + }\]$ , then $\[E\tilde M\]$ exists. If, for all interval $\[L \subset {L^ + }\]$, $\[\int_0^\infty {r(I,x)M(dx)} = \infty \]$ then $\[{\varphi ^ + }\]$ is dense on $\[{L^ + }\]$. If $L$ is drawn parallel to $x$-axis,. the same results can be got，and this time $\[\tilde M\]$ is a cluster point process with cluster center $M$.     

广义Grotzsch环函数的几个精确不等式

对$a\in(0,1/2]$和$r\in(0,1)$, Ramanujan广义模方程中的广义Gr\"otzsch环函数$\mu_a(r)$定义如下:$\mu_a(r)=[\pi\K'_a(r)]/[2\sin(\pi a)\K_a(r)]$. 该文通过研究$\mu_a(r)$和$\mu(r)$的关系,以及$\mu_a(r)$和一些初等函数的组合的单调性和凹凸性,获得了$\mu_a(r)$的几个精确不等式,从而把$\mu(r)$的一些熟知的性质推广到$\mu_a(r)$上.     

有限群的$\Phi$-$\tau$-可补子群

假设$\tau$是一个子群算子, $H$是有限群$G$的一个$p$-子群. 令 $\bar{G}=G/H_{G}$且$\bar{H}=H/H_{G}$, 如果$\bar{G}$有一个次正规子群$\bar{T}$ 和一个包含于$\bar{H}$ 的$\tau$-子群$\bar{S}$满足$\bar{G}=\bar{H}\bar{T}$且$\bar{H}\cap\bar{T}\leq \bar{S}\Phi(\bar{H})$, 就称$H$是$G$的一个$\Phi$-$\tau$- 可补子群. 文章通过讨论群$G$的准素数子群的$\Phi$-$\tau$-可补性给出了超循环嵌入和$p$-幂零性的一些新的特征.     

环GR(4,2)上一类负循环码的Gray象

研究了$GR(4,2)$上长为$2^{s}$的负循环码的Gray象,证明了$GR(4,2)$上长为$2^{s}$的负循环码的Gray象是$F_{4}$上长为$2^{s+2}$指数为2的准循环码. 通过计算$GR(2^{a},m)$上长为$2^{s}$的负循环码的齐次距离, 确定了$GR(4,2)$上长为$2^{s}$的负循环码的Gray象的汉明距离.     

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$o(n^{-1/3+\xs})$.     

不同权Bloch型空间之间的加权Cesàro 算子

该文讨论了$\a$-Bloch空间$\ba$和对数Bloch空间$\bl$之间的加权Ces\'aro算子$\tg$的有界性和紧性,给出$\tg$是$\ba$到$\bl$的有界算子或紧算子的充要条件和$\tg$是$\bl$到$\ba$的有界算子或紧算子的充要条件.     

$\mathbb{C}^{n}$中$\mu$-Bergman空间的刻画和微分复合算子

设$p>0$, $\mu$和$\mu_{1}$是$[0,1)$上的正规函数. 本文首先给出了$\mathbb{C}^{n}$中单位球上$\mu$-Bergman空间$A^{p}(\mu)$的几种等价刻画; 然后 分别刻画了$A^{p}(\mu)$到$A^{p}(\mu_{1})$的 微分复合算子$D_{\varphi}$为有界算子以及紧算子的充要条件, 同时给出了当$p>1$时$D_{\varphi}$为 $A^{p}(\mu)$到$A^{p}(\mu_{1})$上紧算子的一种简捷充分条件和必要条件.     

$\alpha$阶星象亚纯函数

令$S(p)$表示单位圆盘$\mathbb{D}$上在$p\in(0,1)$处有一个简单极点的单叶亚纯函数全体.令$\alpha\in[0,1)$,我们用$\Sigma^{*}(p,\omega_{0},\alpha)$表示$f\in S(p)$使得$\hat{\mathbb{C}}\setminus f(\mathbb{D})$是关于不动点$\omega_{0}\neq0$, $\infty$星象的$\alphga$阶区域的函数全体.在本文中,$f\in\Sigma^{*}(p,\omega_{0},\alpha)$的一些解析刻画条件和系数估计被考虑.     

以PSL(2,q)作为本原自同构群的旗传递对称$(v,k,\lambda)$设计的分类

设$D$是一个非平凡的对称$(v,k,\lambda)$设计, $G$是$D$的一个自同构群.本文证明了如果$G$以二维典型群PSL$(2,q)$作为基柱且在$D$上的作用是旗传递和点本原的,那么设计$D$的参数只能为$(7, 3, 1)$, $(7, 4, 2)$, $(11, 5, 2)$, $(11, 6, 3)$或$(15, 8, 4)$.     

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.     

THE OPTIMAL RATE OF CONVERGENCE OF ERROR FOR kNN MEDIAN REGRESSION ESTIMATES

Let(X,Y),(X_1,Y_1),…,(X_n,Y_n)be iid.random vectors,where Y is one-dimensional.It is desired to estimate the conditional median(X)of Y,by use of Z_n={(X_i,Y_i),i=1,…,n}and X.Denote by(X,Z_n)the kNN estimate of(X),and putH_(nk)(Z_n)=E{|(X,Z_n)-(X)||Z_n},the conditional mean absolute error.This articalestablishes the optimal convergence rate of P(H_(nk_n)(Z_n)>ε),under fairly generalassumptions on(X,Y)and k_n,which tends to ∞ in some suitable way.     

BAHADUR ASYMPTOTIC EFFICIENCY IN A SEMIPARAMETRIC REGRESSION MODEL

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On the Number of Frequency Hypercubes F $ {}^{n}(4;2,2) $

Siberian Mathematical Journal - A&nbsp;frequency $ n $ -cube F $ {}^{n}(4;2,2) $ is an $ n $ -dimensional $ 4 $ -by-…-by- $ 4 $ array filled by&nbsp; $ 0 $ s and&nbsp; $ 1 $ s...     

On the Existence of $ G $ -Permutable Subgroups in Simple Sporadic Groups

Siberian Mathematical Journal - A subgroup $ A $ of a group $ G $ is $ G $ -permutable in&nbsp; $ G $ if for every subgroup $ B\leq G $ there is $ x\in G $ satisfying $ AB^{x}=B^{x}A $ ....     

有限域上幂剩余正规元的存在性

GF(q)是q个元的有限域,q是素数的方幂,n是正整数,GF(q~n)为GF(q)的n次扩张.用指数和估计的方法给出了3种情形下幂剩余正规元存在的充分条件,即(1)GF(q~n)中存在元ξ为GF(q)上的幂剩余正规元;(2)GF(q~n)中存在元ξ与ξ~(-1)同时为GF(q)上幂剩余正规元;(3)对GF(q~n)~*中任意给定的非零元a和b,GF(q~n)中存在元ξ与ξ~(-1)同时为GF(q)上d次幂剩余正规元,且满足Tr(ξ)=a,Tr(ξ~(-1))=b.     

On Poincaré-Friedrichs Type Inequalities for the Broken Sobolev Space ${\rm W}^{2,1}$

We are concerned with the derivation of Poincaré-Friedrichs type inequalities in the broken Sobolev space $W^{2,1}$($Ω$; $\mathcal{T}_h$) with respect to a geometrically conforming, simplicial triagulation $\mathcal{T}_h$ of a bounded Lipschitz domain $Ω$ in $\mathbb{R}^d$ , $d$ $∈$ $\mathbb{N}$. Such inequalities are of interest in the numerical analysis of nonconforming finite element discretizations such as ${\rm C}^0$ Discontinuous Galerkin (${\rm C}^0$${\rm DG}$) approximations of minimization problems in the Sobolev space $W^{2,1}$($Ω$), or more generally, in the Banach space $BV^2$($Ω$) of functions of bounded second order total variation. As an application, we consider a ${\rm C}^0$${\rm DG}$ approximation of a minimization problem in$BV^2$($Ω$) which is useful for texture analysis and management in image restoration.     

投影的约化极小模和空间的夹角

Let M and N be nonzero subspaces of a Hilbert space H, and PM and PN denote the orthogonal projections on M and N, respectively. In this note, an exact representation of the angle and the minimum gap of M and N is obtained. In addition, we study relations between the angle, the minimum gap of two subspaces M and N, and the reduced minimum modulus of （I - PN）PM,     

与$\zeta(2k 1)$函数有关的两类快速收敛级数

Values of new series sum（（（2n-1）!ζ（2n））/（2n ＋ 2k）!）α2n from n=1 to ∞,sum（（（2n-1）!ζ（2n））/（2n＋2k ＋1）!）β2n from n=1 to ∞ are given concerning ζ（2k ＋ 1）,where k is a positive integer,α can be taken as 1,1/2,1/3,2/3,1/4,3/4,1/6,5/6 and β can be taken as 1,1/2.Some previous results are included as special cases in the present paper and new series converges more rapidly than those exsiting results for α = 1/3,or α = 1/4,or α = 1/6.     

AUTOMORPHISMS OF SL (2, K) OVER SKEW FIELDS

In this paper, the author proves the following resu: It Let K be a skew field and A be an automorphism of SL(2, K). Then there exists A∈GL(2, K), an automorphism σ or an anti-automorphism τ of K, such that A is of theform AX=AX~σA~(-1) for all X∈SL(2, K)or AX=A(X~τ~2)~(-1)A~(-1) for all X∈SL(2, K),where X~σ, X~τ are the matrices obtained by applying σ, τ on X respee tively and X' is thetranspose of X.     

全矩阵代数的抛物子代数上具有可导性的非线性映射

Let F be a field of characteristic 0, Mn（F） the full matrix algebra over F, t the subalgebra of Mn（F） consisting of all upper triangular matrices. Any subalgebra of Mn（F） containing t is called a parabolic subalgebra of Mn（F）. Let P be a parabolic subalgebra of Mn（F）. A map φ on P is said to satisfy derivability if φ（x·y） = φ（x）·y＋x·φ（y） for all x,y ∈ P, where φ is not necessarily linear. Note that a map satisfying derivability on P is not necessarily a derivation on P. In this paper, we prove that a map φ on P satisfies derivability if and only if φ is a sum of an inner derivation and an additive quasi-derivation on P. In particular, any derivation of parabolic subalgebras of Mn（F） is an inner derivation.