GLn(k)和SLn(k)的阶

本文利用矩阵行的初等变换 ,采用递推的方法 ,求出了有限域 k上 n次一般线性群 GLn(k)和 n次特殊线性群 SLn(k)的阶 .     

Representations of Dq(k[x])

We prove that the meager idealMis Tukey reducible to the Mycielski ideal J(Si) which is the ideal associated with Silver forcing Si. This implies add (J(Si)) ? add (M) and answers a question of Laguzzi and others.     

On the series ∑ k=1 ∞ ( k 3k )−1 k −n x k

In this paper we investigate the series ∑ _k=1 ^∞ ( _k ^3k )⁻¹ k ⁻ⁿ x ^k . Obtaining some integral representations of them, we evaluated the sum of them explicitly forn = 0, 1, 2.     

The Asymptotic Stability of x(n + k) + ax(n) + bx(n-l) = 0

We established necessary and sufficient conditions for the asymptotic stability of the difference equation where the coefficients a and b are real numbers and k and l are nonnegative integers.     

On the central limit theorem for f (n k x)

By a classical observation in analysis, lacunary subsequences of the trigonometric system behave like independent random variables: they satisfy the central limit theorem, the law of the iterated logarithm and several related probability limit theorems. For subsequences of the system ( f (nx)) _n≥1 with 2π-periodic ${f\in L^2}$ this phenomenon is generally not valid and the asymptotic behavior of ( f (n _k x)) _k≥1 is determined by a complicated interplay between the analytic properties of f (e.g., the behavior of its Fourier coefficients) and the number theoretic properties of n _k . By the classical theory, the central limit theorem holds for f (n _k x) if n _k  = 2 ^k , or if n _k+1/n _k → α with a transcendental α, but it fails e.g., for n _k  = 2 ^k  ? 1. The purpose of our paper is to give a necessary and sufficient condition for f (n _k x) to satisfy the central limit theorem. We will also study the critical CLT behavior of f (n _k x), i.e., the question what happens when the arithmetic condition of the central limit theorem is weakened “infinitesimally”.     

On set {N k − (x)} n k=0

Suppose that C is the complex plane and k is a non-negative integer. Define functions N _k ⁻ (x) = |x|^kif k is even and K _k ⁻ (x) = x|x|^k−1 if k is odd. Some approximation properties of N _k ⁻ (x)’s is discussed and a new example of a Tchebycheff system is given out.     

A（x）－C（x）的渐近公式

设Ａ、Ｃ是一些自然数的集合。对于Ａ中任一自然数ｍ，每一ｍ阶群都是Ａｂｅｌ群；对于Ｃ中任一自然数ｎ，每一ｎ阶群都是循环群。本文的目的是证明下面的渐近公式：此处γ是Ｅｕｌｅｒ常数，ｌｏｇｒｘ＝ｌｏｇ（ｌｏｇ＿（ｒ－１）ｘ），ｌｏｇ＿１ｘ＝ｌｏｇｘ。     

关于热方程U_t—c(x)(k(x)U_x)_x=0确定未知系数k(x)的一个反问题

本文讨论了热方程U_1—c(x)k(x)U_x)_x=0在区域x>0,t>0上确定未知系数k(x)的反问题,文中给出了局部解的存在,唯一性。     

Q_k(x)与F_k(x)的渐近公式

设ｎ，ｋ为自然数，Ｇ（ｎ）阶群中的同构类数，Ｆｋ（ｘ）与Ｑｋ（ｘ）分别表示不超过ｘ的自然数中使Ｇ（ｎ）＝ｋ的自然数、无平方因子自然数的个数．本文的目的是用Ｂｒｕｎ筛法证明Ｑｋ（ｘ）的条件渐近公式并对Ｆｋ（ｘ）的渐近性质做出了推测．     

一类联图的符号边控制数

设G=(V,E)是一个简单图,一个函数f:E→{-1,1},若满足∑_(e′∈N[e])f(e)≥1对E(G)中的每个边e都成立,则称f是图G的一个符号边控制函数,图G的符号边控制数定义为γ′_s(G)=min{∑_(e∈E)f(e)|f是G的符号边控制函数}.给出了联图C_(2k)+C_(2k)的符号边控制数.