二倍无平方因子阶的3度1-正则图

一个图叫做1-正则的, 如果它的自同构群在它的弧集上作用正则. 设n是一个无平方因子的正整数. 证明了存在2n阶3度1-正则图当且仅当n=3^tp₁p₂… p_s≥13, 其中t≤1, s≥1, p_i (1≤ i≤s)为互不相同的素数且满足3|(p_i-1). 进一步, 对每个满足上述条件的整数n, 共有2^s−1个互不同构的2n阶3度1-正则图, 并且这些图均为2n阶二面体群上的Cayley图. 由此可知, 不存在4m阶3度1-正则图, 其中m为无平方因子的奇数.     

应用exp-函数法求(n+1)维sine-Gordon方程的孤立波解

应用exp—函数法求得(n+1)维sine-Gordon方程的单孤子解、双孤子解、三孤子解,通过选取适当的参数,分别做出了单孤子解、双孤子解、三孤子解的函数图像,刻画了解的结构和性质.实践证明,应用exp-函数法研究非线性偏微分方程具有十分重要的作用和意义.     

Smarandache函数在两数列上的下界估计

设S(n)是Smarandache函数,其中n是一正整数.讨论Smarandache函数S(n)在数列F((2k),1)=F(n,1)=n2n+1(n=2k)与数列G(2n,1)=(2n)2n+1上的下界估计.基于初等方法证明了:当偶数n≥6时,有S(F((2k),1))=S(F(n,1))≥6×2n+1;当n≥4时,有S(G(2n,1))≥6×2n+1.     

具有高逼近阶和正则性的双向加细函数和双向小波

引入了双向加细函数和双向小波的概念,并研究双向加细方程 的分布解(或L²稳定解)的存在性, 其中整数m≥2. 基于正向面具{p_k⁺} 和 负向面具{p_k^-} , 建立了确保双向加细方程具有紧支撑分布解或L²稳定解所需要的条件. 更进一步地, 给出了双向加细方程的L²稳定解能产生一个MRA所需要的条件. 充分讨论了φ(x) 的支撑区间. 给出正交双向加细函数和双向小波的定义, 建立了双向加细函数的正交准则. 给出一类正交双向加细函数和正交双向小波 的构造算法. 另外,也给出了具有非负面具的、高逼近阶和正则性的双向加细函数的构造算法. 最后,构造了两个算例.     

广义(m,n)超环

本文研究了广义(m,n)超环,n元正则关系以及n元强正则关系等的一些性质.利用广义(m,n)超环间的同态关系以及正则和强正则关系,得到了(m,n)子超环和(m,n)超理想的不变性,广义(m,n)超环的商结构,以及构成商超环和商环的充分必要条件,推广了文献[5]的一些结果.     

共振点附近半线性Liénard方程的拟周期解

研究了方程 x″+ Fx(x, t)x′+ ω²x + φ(x, t) = 0的拟周期解的存在性, 其中F和φ是光滑函数, 且关于t是2π-周期的, ω > 0是一个常数. 在假设F和φ满足一定的奇偶性条件下, 证明了Dancer函数在研究方程的拟周期解存在性和Lagrange稳定性(即所有解的有界性)中起到关键作用. 以往这个函数通常用来研究周期解的存在性.     

切于已知球的单形宽度

Let w(△_n) denote the width of a non-degenerate simplex △_n in Eⁿ and r(△_n) denote the inradius of the simplex.Then, in this paper, we prove the ine-qunlity as below: Theorem:w(△_n)≤β_nr(△_n) where β_n =(n^1/2(n+1))/([(n+1)/2]^1/2(n+1-[(n+1)/2])^1/2) The equality holds if and only if the simplex is regular.     

二阶超线性差分方程周期解与次调和解的存在性

应用临界点理论, 为研究差分方程周期解与次调和解的存在性和多重性提供了一种新方法. 对二阶差分方程 D²x_n-1+f (n, x_n)=0, 当f(t, z)在0点及无穷远点为超线性增长时, 上述问题得到某些新结果.     

对于轮和完全图的 Ramsey 数的渐近上界

该文给出:对于偶数m≥4当n→ ∞时 r(W_m,K_n)≤l(1+o(1))C₁(m) (n/logn ) ^(2m-2)/(m-2)对于奇数m≥5当n→∞时r(W_m,K_n)≤(1+o(1))C₂(m) (n^2m/_m+1/^{_{log n)}(m+1)/(m-1)} .特别地,C₂(5)=12. 以及 c(ⁿ/_logn)^5/2≤r(K₄,K_n)≤ (1+o(1)) ^n3_/(logn)².此外,该文还讨论了轮和完全图的 Ramsey 数的一些推广.     

有界正则函数的导数估计

在这篇文章中,主要讨论了n阶导数的估计式,即对有界正则函数φ（z)=c0 c1z … cnz^n …(在│z│1内正则）,从已知的三阶、四阶导数估计式,利用归纳法原理及有界正则函数的性质推出n阶导数的一般估计式,并推出在│z│＜1内正则的正实部函数的n阶导数的一般估计式。     

非线性抛物椭圆方程组的正则解和奇异解

该文用单模方法在Lorentz空间研究了抛物椭圆方程组奇异解和正则解的存在性, 其中初值属于Lorentz空间L^{n/2,∞ ₍}Rⁿ), n≥ 3. 利用时间加权的Lorentz空间, 还得到了其正则解. 此外, 如果初值满足自相似结构, 也得到了自相似解的存在性.     

∑e1型Banach空间上C0半群稳定性的谱特征

讨论一类不可分解的∑_e¹型Banach空间上有界线性算子的谱的特殊性质;给出了∑_e¹型Banach空间上一致有界C₀半群稳定性的一个谱特征,并给出稳定性定理的一个应用.     

Uniform l1 behaviour for time discretization of a Volterra equation with completely monotonic kernel: I. stability

This paper is the first of two papers on the time discretizationof the equation u_t + ^t ₀ ß (t — s) Au (s) ds= 0, t > 0, u (0) = u₀, where A is a self-adjoint denselydefined linear operator on a Hilbert space H with a completeeigensystem {_m, _m}_{m = 1}, and ß (t) is completely monotonicand locally integrable, but not constant. The equation is discretizedin time using first-order differences in combination with order-oneconvolution quadrature. The stability properties of the timediscretization are derived in the l¹_t (0, ; H) norm.     

A hierarchical basis preconditioner for the biharmonic equation on the sphere

^** Email: jan.maes{at}cs.kuleuven.be In this paper, we propose a natural way to extend a bivariatePowell–Sabin (PS) B-spline basis on a planar polygonaldomain to a PS B-spline basis defined on a subset of the unitsphere in [graphic: see PDF] . The spherical basis inherits many properties of the bivariatebasis such as local support, the partition of unity propertyand stability. This allows us to construct a C¹ continuous hierarchicalbasis on the sphere that is suitable for preconditioning fourth-orderelliptic problems on the sphere. We show that the stiffnessmatrix relative to this hierarchical basis has a logarithmicallygrowing condition number, which is a suboptimal result comparedto standard multigrid methods. Nevertheless, this is a hugeimprovement over solving the discretized system without preconditioning,and its extreme simplicity contributes to its attractiveness.Furthermore, we briefly describe a way to stabilize the hierarchicalbasis with the aid of the lifting scheme. This yields a waveletbasis on the sphere for which we find a uniformly well-conditionedand (quasi-) sparse stiffness matrix.     

两两NQD随机序列的 Lr 收敛性

该文讨论了两两NQD随机变量列在满足$r(1\leq r<2)$阶Ces\`aro一致可积条件下的 L^r 收敛性,获得了与独立情形一致的结果.     

A posteriori H1 error estimation for a singularly perturbed reaction diffusion problem on anisotropic meshes

The paper deals with a singularly perturbed reaction diffusionmodel problem. The focus is on reliable a posteriori error estimatorsfor the H¹ seminorm that can be applied to anisotropic finiteelement meshes. A residual error estimator and a local problemerror estimator are proposed and rigorously analysed. They arelocally equivalent, and both bound the error reliably. Threemodifications of these estimators are introduced and discussed. Much attention is given to the performance of the error estimatorin numerical experiments. This helps to identify those estimatorsthat are suitable for practical applications.     

cut* 空间的拓扑性质

该文引入了 cut^*空间的概念,所谓的 cut^*空间是指去掉任意一点连通,去掉任意两点不连通的连通空间.通过对其性质的讨论,得到如下主要结论: 首先得到cut^*空间中每个点非开即闭,并且cut^*空间中有无限多个闭点;其次讨论了一类特殊的 cut^*空间,即去掉一点是COTS的 cut^* 空间.指出``$X$是 cut^*空间,任意 $x\inX,X\setminus\{x\}$是不可约cut空间'这样的空间类是不存在的.在文章的最后,讨论了去掉一点是LOTS的 cut^*空间的覆盖性质,得到这样的空间是紧空间或Lindel\"of空间的结论.     

The largest prime factor of X3+2

The largest prime factor of X³+2 was investigated in 1978 byHooley, who gave a conditional proo that it is infinitely oftenat least as large as X¹+, with a certain positive constant .It is trivial to obtain such a result with =0. One may thinkof Hooley's result as an approximation to the conjecture thatX³+2 is infinitely often prime. The condition required by Hooley,his R^* conjecture, gives a non-trivial bound for short Ramanujan–Kloostermansums. The present paper gives an unconditional proof that thelargest prime factor of X³+2 is infinitely often at least aslarge as X¹⁺, though with a much smaller constant than thatobtained by Hooley. In order to do this we prove a non-trivialbound for short Ramanujan–Kloosterman sums with smoothmodulus. It is also necessary to modify the Chebychev method,as used by Hooley, so as to ensure that the sums that occurdo indeed have a sufficiently smooth modulus. 2000 MathematicsSubject Classification: 11N32.     

C1,1半定规划的二阶最优性条件

该文研究了一类非光滑半定规划问题,其中目标函数是C^1,1函数,约束是半定的. 借助于Peano广义梯度,给出了其二阶最优性必要条件和二阶最优性充分条件     

Hilbert空间上线性算子广义逆A(2)T,S的存在性及其表示式

设H₁和H₂是两个Hilbert空间, B(H₁,H₂)表示从H₁到H₂的所有有界线性算子的集合, T和S分别是H₁和H₂的两个闭子空间. 如果存在线性算子X ∈ B(H₂,H₁)满足XAX=X, R(X)=T, N(X)=S,则称X为线性算子$A$的具有指定像空间T和零空间S的外逆,记为A⁽²⁾_T,S. 该文进一步研究了线性算子广义逆A⁽²⁾_T,S存在的若干等价条件及其性质,建立了算子广义逆A⁽²⁾_T,S的表示形式.