$k$-次幂等矩阵线性组合群逆和超广义幂等矩阵线性组合Moore-Penrose广义逆的表

在 $T_{1}T_{2}T_{1}=T_{2}$, $T_{2}T_{1}^{k-1}=T_{1}T_{2}^{k-1}$ 和 $T_{1}T_{2}T_{1}=T_{2}T_{1}$的条件下, 得到k-次幂等矩阵线性组合群逆的表示. 另外, 在$T_{1}T_{2}T_{1}=T_{2}$ 和 $T_{1}^{2}T_{2}=T_{2}$ 的条件下, 计算超广义幂等矩阵线性组合Moore-Penrose 广义逆的表示     

一类四次Hamilton函数Abel积分零点个数的估计

证明了Abel积分I(h)=∮ΓhQ(x,y)dx-P(x,y)dy的零点个数的最小上界B(2n+2)=B(2n+1)≤3[n/2]+12[(n-1)/2]+4([p]表示P的整数部分),这里n是代数曲线H(x,Y)=x2士x4+Y4=h的连通闭分支,h∈E(Γh存在的最大开区间),P(x,y),Q(x,Y)是关于x,y 的次数不超过2n+2或2n+1的实多项式.     

奇数方幂和的通项公式

In this paper, by using superposition method, we aim to show that ∑^n i=1 （2/- 1）^2k-1 is the product of n2 and a rational polynomial in n2 with degree k- 1, and that ∑^ni=1 （2i - 1）^2k is the product of n（2n - 1）（2n ＋ 1） and a rational polynomial in （2n - 1）（2n ＋ 1） with degree k - 1. Moreover, recurrence formulas to compute the coefficients of the corresponding rational polynomials are also obtained.     

三类平方图的点边邻点可区别全色数

根据平方图的结构性质,用穷染,递推的方法,讨论了路,圈,扇的平方图的点边邻点可区别全染色,得到了相应的色数,即并给出了一种染色方案.     

一类高阶有理差分方程解的收敛性(英文)

本文考查下列高阶有理差分方程xn+1=(α+B1xn-1+B3xn-3+…+B2k+1xn-2k-1)/(A+B0xn+B2xn-2+…+B2kxn-2k,),n=0,1,…,其中k是非负整数,参数α,A,Bi,i=0,1,2,…,2k+1和初始值x-2k-1,x-2k,x-2k+1,…,x0是非负实数.给出充分条件,在此条件下当且仅当∑k+1i=1B2i-1=A时,方程的每个解收敛于方程的一个二周期解.     

Chromaticity of two-trees

The graphs called 2-trees are defined by recursion. The smallest 2-tree is the complete graph on 2 vertices. A 2-tree on n + 1 vertices (where n ≥ 2) is obtained by adding a new vertex adjacent to each of 2 arbitrarily selected adjacent vertices in a 2-tree on n vertices. A graph G is a 2-tree on n(≥2) vertices if and only if its chromatic polynomial is equal to γ(γ - 1)(γ - 2)^n—2.     

Estimates of the capacity of orthogonal arrays of large strength

D.G. Fon-Der-Flaass showed that Boolean correlation-immune n-variable functions of order m are resilient for $ m \geqslant \frac{{2n - 2}} {3} $ m \geqslant \frac{{2n - 2}} {3} . In this paper this theorem is generalized to orthogonal arrays. It is shown that orthogonal arrays of strength m not less than $ \frac{{2n - 2}} {3} $ \frac{{2n - 2}} {3} , where n is a number of factors having size at least 2 ⁿ⁻¹ and all arrays of size 2 ⁿ⁻¹, are simple.     

钢筋混凝土板的弯曲问题解法

本以含高阶项的试函数，用Galerkin法求得了周边固支的钢筋混凝土板在均布荷载作用下的挠度表达式，所得结果在特殊情况下与[1]的各向同性均质板在均布荷载下的结果相符合．     

On even cycle decompositions of line graphs of cubic graphs

An even cycle decomposition of a graph is a partition of its edges into cycles of even length. In 2012, Markström conjectured that the line graph of every 2-connected cubic graph has an even cycle decomposition and proved this conjecture for cubic graphs with oddness at most 2. However, for 2-connected cubic graphs with oddness 2, Markström only considered these graphs with a chordless 2-factor. (A chordless 2-factor of a graph is a 2-factor consisting of only induced cycles.) In this paper, we first construct an infinite family of 2-connected cubic graphs with oddness 2 and without chordless 2-factors. We then give a complete proof of Markström’s result and further prove this conjecture for cubic graphs with oddness 4.     

Exact asymptotic behavior of singular values of a class of integral operators

We find an exact asymptotic formula for the singular values of the integral operator of the form , a Jordan measurable set) where and L is slowly varying function with some additional properties. The formula is an explicit expression in terms of L and T.     

Entropy Numbers of Embeddings of Weighted Besov Spaces

We investigate the asymptotic behavior of the entropy numbers of the compact embedding $$ B^{s_1}_{p_1,q_1} \!\!(\mbox{\footnotesize\bf R}^d, \alpha) \hookrightarrow B^{s_2}_{p_2,q_2} \!\!({\xxR}). $$ Here $B^s_{p,q} \!({\mbox{\footnotesize\bf R}^d}, \alpha)$ denotes a weighted Besov space, where the weight is given by $w_\alpha (x) = (1+| x |^2)^{\alpha/2}$, and $B^{s_2}_{p_2,q_2} \!({\mbox{\footnotesize\bf R}^d})$ denotes the unweighted Besov space, respectively. We shall concentrate on the so-called limiting situation given by the following constellation of parameters: $s_2 < s_1$, $0 < p_1,p_2 \le \infty$, and $$ \alpha = s_1 - \frac{d}{p_1} - s_2 + \frac{d}{p_2} > d \, \max \Big(0, \frac{1}{p_2}-\frac{1}{p_1}\Big). $$ In almost all cases we give a sharp two-sided estimate.     

有穷正级亚纯函数的T方向和Borel方向

对任意正数λ,正整数q_1和q_2,记E_1={argz=θ_j|0∣θ_1＜θ_2<…＜θ_(q1)＜2π}及E_2={axgz=φ_j|0■1＜φ2＜…＜φq2＜2π},使得E_1∩E_2=■,则(1)存在复平面上的λ级亚纯函数f(z),恰以E_1∪E_2为其T方向且恰以E_2为其Borel方向,(2)存在复平面上的级与下级均为λ的亚纯函数g(z),恰以E_1∪E_2为其Borel方向且恰以E_2为其T方向．     

On the number of representations of integers by some quadratic forms in ten variables

A method of finding the so-called Liouville's type formulas for the number of representations of integers by $$a_1 (x_1^2 + x_2^2 ) + a_2 (x_3^2 + x_4^2 ) + a_3 (x_5^2 + x_6^2 ) + a_4 (x_7^2 + x_8^2 ) + a_5 (x_9^2 + x_{10}^2 )$$ quadratic forms is developed.     

奇异伪辛群作用下子空间轨道的长度

设F_q是q个元素的有限域,q是2的幂,F_q~(2ν+δ+l)是F_q上2ν+δ+l维行向量空间,Ps_(2ν+δ+l,2ν+δ)(F_q)是F_q上级数为2ν+δ+l而秩为2ν+δ的伪辛群.F_q~(2ν+δ+l)在Ps_(2ν+δ+l,2ν+δ)(F_q)的作用下划分成一些子空间轨道Μ(m,2s+τ,s,∈,k;2ν+δ,2ν+δ).采用矩阵初等行变换的方法,给出轨道Μ(m,2s+τ,s,∈,k;2ν+δ,2ν+ε)的长度.     

Perfect powers from the sums of terms of linear recurrences

Let Gi= {Gi n1 n=0 (i = 1;2 ;m; m 2) be linear recursive se- quences of order ki 2 andGn 2 Z. Further let K >1 be a fixed real number and S = s 2 Z : s = p e 11p ev v ; ei 2 N , wherepi"s are fixed primes. In this paper, under some restrictions, we prove that, if m P i=1 G (i) n i = sw q holds for positive in- tegers w 2; q; n1; n2; nm with n1 > K max (n2; nm), then q tegers w 2; q; n1; n2; nm with n1 > K max (n2; nm), then q...     

3个素数平方和的非线性型的整数部分

假设λ,μ,υ是不全为负的非零实数,λ是无理数,k是正整数,则存在无穷多素数p_1,p_2,p_,p,3使得[λp_1~2+μp_2~2+υp_3~2]=kp.特别地,[λp_1~2+μp_2~2+υp_3~2]表示无穷多素数.     

A Construction of Difference Sets

In this paper, we will give a construction of a family of -difference sets in thegroup , where q is any power of 2, K is any group with and G is an abelian 2-group of order which contains anelementary abelian subgroup of index 2.     

4个素数平方及若干2的次幂和的丢番图逼近}

证明了在一定条件下, 不等式 $|\lambda_1p_1^2+\lambda_2p_2^2+\lambda_3p_3^2+\lambda_4p_4^2+\mu_12^{m_1}+\cdots+\mu_s2^{m_s}+\varpi|<\eta$关 于素数$p_1, p_2, p_3, p_4$ 和正整数$m_1, \cdots, m_s$有无穷多解, 改进了之前的结果.     

两类积图的邻点可区别全染色

本文.证明了,当n≥2时,Xat(K_n×K′_n)=2n;当p,q≥2时,Xat(C_(2p)×K_(2q))=2q 3,其中K_n×K′_n是两个不同标号完全图的积图,C_(2p)×K_(2q)是偶圈和偶阶完全图的积图.     

关于虚二次域类数的可除性

设α＞１，ｂ＞１，（α，ｂ）＝１，ｈ（－αｂ）表虚二次域的类数。如果有正整数ｘ，ｙ，ｎ，ｋ满足（１）αｘ￣２＋ｂｙ￣２＝４ｋ￣ｎ，ｂ且；或（２）αｘ￣２＋ｂｙ￣２＝ｋ￣ｎ，ｘ｜α，ｙ｜ｂ且αｂ≡２（ｍｏｄ４），则本文证明了关于ｈ（－αｂ）的可除性的两个定理（见定理１，２），其中符号ｘ｜α表示ｘ的每一个素因子整除α。