FLAT TIME-LIKE SUBMANIFOLDS IN ANTI-DE SITTER SPACE H1^2n-1 S1 （-1）

By using dressing actions of the Gn-1,n-1^1,1-system,the authors study geometric transformations for flat time-like n-submanifolds with flat,non-degenerate normal bundle in anti-de Sitter space H1^2n-1(-1),where Gn-1,n-1^1,1=0（2n-2,2/O(n-1,1)×O(n-1,1).     

半正的分数阶微分方程(n-1,1)-型积分边值问题的多个正解

采用Riemann-Liouville分数阶导数,研究了半正的分数阶微分方程(n-1,1)-型积分边值问题,获得了参数λ的一个区间,使得λ落在这个区间的时候,该半正的分数阶微分方程边值问题有多个正解.     

n-1／n（G）表决系统中的可靠性分析

本文通过补充变量法研究了n-1/n(G)表决系统中可靠度,可用度,以及故障频度等可靠性的一系列指标.     

An optimal rigidity theorem for complete submanifolds in a sphere

It is proved that if M^n is an n-dimensional complete submanifold with parallel mean curvature vector and flat normal bundle in S^n＋p（1）, and if supM S 〈 α（n, H）, where α（n,H）=n＋n^3/2（n-1）H^2-n（n-2）/n（n-1）√n^2H^4＋4（n-1）H^2,then M^n must be the totally urnbilical sphere S^n（1/√1＋H^2）.An example to show that the pinching constant α（n, H） appears optimal is given.     

连续可导函数类的最优拉格朗日插值

在构造拉格朗日插值算法时,插值结点的选择是十分重要的.给定一个足够光滑的函数,如果结点选择的不好,当插值结点个数趋于无穷时,插值函数不收敛于函数本身.例如龙格现象:对于龙格函数f(x)=1/1+25x^2,如果拉格朗日插值的结点取[-1,1]上的等距结点,那么逼近的误差会随着结点个数增多而趋于无穷大⑴,由此可知插值结点的选择尤为重要.     

TheT-ideal generated by the standard identitys 3[x 1,x 2,x 3]

LetK = T_o(s₃), {c_n} its codimensions, {l_n} its colengths and {Χ_n} its sequence of co-characters. For 9≦n, c_n =2n - 1 or c_n =n(n + l)/2- 1, 3≦l_n ≦4 and χ_n =[n] + 2[n-1,1] + α[n-2,2] + β[2²,1^n?4] where α + β≦l.     

一个Hessian商方程强解的光滑性

我们获得了一个Hessian商方程W2p强解当p＞n(n-1)/2时的C1,1局部估计,并证明了这些解是光滑的.有反例表明这个正则性结果在n=3时是最优的.     

围长为2的本原极小强连通有向图的1-指数集

本文研究了围长为2的本原极小强连通有向图的1-指数，证明了：当n为偶数时{4，5，7，8，9，11，…，2n-7，2n-5，2n-4}真包含 En（1）。     

关于数论函数方程φ(x_1…x_(n-1)x_n)=m(φ(x_1)+…+φ(x_(n-1))+φ(x_n))

运用Euler函数的性质证明了:当n>1时,方程φ(x_1…x_(n-1)x_n)=m(φ(x_1)+…+φ(x_(n-1))+φ(x_n))仅有有限多组正整数解(x_1,…,x_(n-1),x_n),得到了这些解都满足max{x_1,…,x_(n-1),x_n}≤2m⁴(n-1)4(n-1)²n2n².     

奇异(n-1,1)共轭边值问题的多重正解

利用锥映射不动点指数定理证明了非线性(n-1,1)共轭边值问题u(n)+a(t)[f(u)+m2u]=0,u(j)(0)=u(1)=0,0≤j≤n-2至少存在两个正解.本文允许a(t)在[0,1]两端点处具有奇性,并允许a(t)在[0,1]某些子区间上恒为零.     

形如2kp+1的数的素性检验

本文初步探讨了如何快速检验一个大数n是素数(这里n-1含有大的素因子)的算法问题以及如何生成一个大素数p使得p-1有大的素因子q的算法问题.我们给出了形如n=2kp+1的数的素性检验的多项式时间算法,这里p是一个给定的大素数,k是正整数满足22k＜2kp.该算法的计算量为O(log32n).然后我们给出了生成一个大素数p使得p-1有大的素因子q的算法,其中q满足q＞(p-1)/log2(p-1).特别地,我们给出了判定并生成一个安全素数p的算法.     

On the divisibility properties concerning sums of binomial coefficients

For any integer \(n> 1,\) we prove

$$\begin{aligned} 2n{2n\atopwithdelims ()n}&\bigg |\sum _{k=0}^{n-1}(3k+1){2k\atopwithdelims ()k}^3(-8)^{n-1-k},\\ 2n{2n\atopwithdelims ()n}&\bigg |\sum _{k=0}^{n-1}(6k+1){2k\atopwithdelims ()k}^3(-512)^{n-1-k},\\ 2n{2n\atopwithdelims ()n}&\bigg |\sum _{k=0}^{n-1}(42k+5){2k\atopwithdelims ()k}^3 4096^{n-1-k},\\ 2n{2n\atopwithdelims ()n}&\bigg |\sum _{k=0}^{n-1}(20k^2+8k+1){2k\atopwithdelims ()k}^5(-4096)^{n-1-k}. \end{aligned}$$

The first three results confirm three divisibility properties on sums of binomial coefficients conjectured by Z.-W. Sun.

     

Large time behavior of solutions for critical and subcritical complex Ginzburg-Landau equations in H~1

Considering the Cauchy problem for the critical complex Ginzburg-Landau equation in H1 (Kn), we shall show the asymptotic behavior for its solutions inAnalogous results also hold in the case that the nonlinearity has the subcritical power in H1(Rn), n≥1.     

完全对换网络的限制连通度

完全对换网络是基于 Cayley 图模型的一类重要互连网络. 一个图 G 的 k-限制点(边)连通度是使得 G-F 不连通且每个分支至少有 k 个顶点的最小点(边)子集 F 的基数, 记作 \kappa_{k}(\lambda_{k}). 它是衡量网络可靠性的重要参数之一, 也是图的容错性的一种精化了的度量. 一般地, 网络的 k-限制点(边)连通度越大, 它的连通性就越好. 证明了完全对换网络 CT_{n} 的 2-限制点(边)连通度和 3-限制点(边)连通度, 具体来说: 当 n\geq4 时, \kappa_{2}(CT_{n})=n(n-1)-2, \kappa_{3}(CT_{n})=\frac{3n(n-1)}{2}-6; 当 n\geq3 时, \lambda_{2}(CT_{n})=n(n-1)-2, \lambda_{3}(CT_{n})=\frac{3n(n-1)}{2}-4.     

The weak global dimension of commutative coherent rings

Let R be a commutative coherent ring and wD(R) denote the weak global dimension of R.We prove that for an integer n≥2 the following are equivalent:.

(a) wD(R)n;.

(b) FP-idM ?Gn-2 for all (FP-)injectives G and for all modules M;.

(c) fdHom(G,M)n-2 for all (FP-)injectives G and for all modules M;.

(d) fdHom(M,G)n-2 for all flat modules G and for all modules M.     

Further properties of several classes of Boolean functions with optimum algebraic immunity

Based on a method proposed by the first author, several classes of balanced Boolean functions with optimum algebraic immunity are constructed, and they have nonlinearities significantly larger than the previously best known nonlinearity of functions with optimal algebraic immunity. By choosing suitable parameters, the constructed n-variable functions have nonlinearity for even for odd n, where Δ(n) is a function increasing rapidly with n. The algebraic degrees of some constructed functions are also discussed.      

Hermite-Fejér插值算子的一个渐近估计式

设f(x)在[-1,1]上的二阶导数存在且有界,H_n[f(t);x]、R_n[f(t);x]分别为具有第一类、第二类零点的Hermite-Fejér插值多项式,则当n→∞时,有 H_n[f(t);x]-f(x)=O(1/n)(-1相似文献   

A degree condition for the existence of regular factors in K1, n-free graphs

A graph is called K_{1, n}-free if it contains no K_{1, n} as an induced subgraph. Let n(≥3), r be integers (if r is odd, r ≥ n − 1). We prove that every K_{1, n}-free connected graph G with r|V(G)| even has an r-factor if its minimum degree is at least. $ \left(n+{{n-1}\over{r}}\right) \left\lceil {n\over{2(n-1)}}r \right\rceil - {{n-1}\over{r}}\left(\left\lceil {n\over{2(n-1)}}r \right\rceil \right)^2+n-3. $ This degree condition is sharp. © 1996 John Wiley & Sons, Inc.     

Covering lattice points by subspaces

We find tight estimates for the minimum number of proper subspaces needed to cover all lattice points in an n-dimensional convex body C , symmetric about the origin 0. This enables us to prove the following statement, which settles a problem of G. Halász. The maximum number of n-wise linearly independent lattice points in the n-dimensional ball r B n of radius r around 0 is O(rn/(n-1)). This bound cannot be improved. We also show that the order of magnitude of the number of diferent (n - 1)-dimensional subspaces induced by the lattice points in r&Bgr;n is rn/(n-1).     

一类离散型奇异积分算子

设｛αｋ｝∞ｋ＝－∞为正数缺项序列，满足ｉｎｆｋαｋ＋１／ｄｋ＝α＞１，Ω（ｙ′）为Ｂｅｓｏｖ空间Ｂ０，１１（Ｓｎ－１）上的函数，其中Ｓｎ－１为Ｒｎ（ｎ２）上的单位球面．本文证明：若∫Ｓｎ－１Ω（ｙ′）ｄσ（ｙ′）＝０，则离散型奇异积分ＴΩ（ｆ）（ｘ）＝∑∞ｋ＝－∞∫Ｓｎ－１ｆ（ｘ－αｋｙ′）Ω（ｙ′）ｄσ（ｙ′）和相关的极大算子ＴΩ（ｆ）（ｘ）＝ｓｕｐＮ∑∞ｋ＝Ｎ∫Ｓｎ－１ｆ（ｘ－αｋｙ′）Ω（ｙ′）ｄσ（ｙ′）均在Ｌ２（Ｒｎ）上有界．上述结果推广了Ｄｕｏａｎｄｉｋｏｅｔｘｅａ和ＲｕｂｉｏｄｅＦｒａｎｃｉａ［１］在Ｌ２情形下的一个结果