椭圆型方程广义解Liouville型定理的一个注

在Ｅⁿ考虑椭圆方程(?)其中Ａ，Ｂ满足如下的结构条件：(?)本文证明如果广义整解ｕ∈W_p,loc¹(Eⁿ)∩ L_α(Eⁿ)，其中(?)那么ｕ≡０．     

偶错位图的张量幂的最大独立集和自同构群

若A_n 是X := {1, 2,..., n} 上的偶置换构成的交错群, E_n 是X 上的偶错位集, 则Cayley 图AΓ_n := Γ(A_n, E_n) 称为偶错位图. 令AΓ_n^q 为q 个AΓ_n 的张量幂. 在本文中, 我们研究了AΓ_n^q 的连通性、直径、独立数、团数、色数和最大独立集等性质. 利用AΓ_n^q 最大独立集的结果, 我们完全确定了AΓ_n^q 的自同构群的结构.     

En空间中张角定理及其应用

本文利用单形的体积公式,得到了n维欧氏空间En中的张角定理,由此又证得了单形中的一组恒等式,利用这组恒等式给出了Safta猜想在En空间中的加强形式.     

右半平面内解析函数的准确零(R)级

Let f(s)=(?)a_ne^-λ_m3(s=σ+it),0<λ_n↑+∞), where (?)(n/logU(λ_n))=E<+∞,(?)(log|α_n|/λ_n)=0.     

Morse引理的一个推广

设E_n是在0∈Rⁿ的C^∞函数芽环,M是En中唯一的极大理想.如果f∈M²且其二阶Hessain是非退化的,则f同构于它的二阶Hessain,这就是著名的Morse引理.本文将讨论两个变元的C^∞函数芽,得到:(1)若f∈M³?E_xy,且其三阶Hessain是非退化的,则f同构于它的三阶Hessain.(2)若f∈M⁴?E_xy     

Oppenheim不等式推广的简单证明

设Ｅｕｃｌｉｄ空间ｎ＋１元点集Ａ，Ｂ及其度量和Ｃ所构成的单形的体积、外接球半径分别为Ｖ_１，Ｖ₂，Ｖ和Ｒ_１，Ｒ₂，Ｒ．本文给出不等式V^2/n≥V₁^2/n+V₂^2/n,R²≤R₁²+R₂²一种简单的证法．该     

球面上等收敛算子的有界性

设Rⁿ 是n-维欧氏空间n≥3.用Ω_n表示Rⁿ 上的单位球面,对于函数f∈L（Ω_n）,E_N^δ（f）表示其Fourier-Laplace级数的δ阶Cesaro平均所决定的等收敛算子,其中,λ:=（n-2）/2,δ是熟知的临界指标.对于0<δ≤λ,令p₀:=(2λ)/（λ+δ）,本文主要证明了如下结果:     

伪对称集的一个充分必要条件

本文得到了共球诸点为Eⁿ—伪对称集的一个充分条要条件.     

关于P.Turán问题24,Ⅱ

在本文中我们得到了一个比[1]中更好的P.Turán问题24的答案:若Hermite—Fejér插值过程对于任何f∈C[-1,1]都一致收敛,则定义于同一组节点上的Lagrange插值过程对于每个f∈{f:E_n(f)=o(n^-(23)/(18)}都一致收敛,这里E_n(f)为f∈C[-1,1]的用次数≤n的代数多项式逼近的偏差.     

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.     

关于高维单形的两个性质

应用度量几何理论与解析方法,研究了n维欧氏空间En中n维单形的性质,将三角形内心与中线两个性质推广到n维单形,获得n维单形内心与中位面的两个性质.     

有关单形旁切球半径的几何不等式（英文）

In this paper, we study the problems of geometric inequality for the radii of escribed hyperspheres of an n-dimensional simplex in Euclidean space En. Some new geometric inequalities for the radii of escribed hyperspheres of a simplex are established.     

多元Bernstein—Sikkema算子的逼近性质

本文对定义在单形上的Ｂｅｒｎｓｔｅｉｎ－Ｓｉｋｋｅｍａ算子讨论其导数的收敛性质，同时出给出了高阶渐近展开式及Ｂｅｓｏｖ空间中的几个等价关系。     

关于单形的几个含参几何不等式

本给出了ｎ维欧氏空间中ｎ维单形的三个几何含参不等式,它们比目前出现的不等式更具一般性。     

一类涉及两个单形的三角不等式及其应用

应用解析方法和几何不等式理论研究了n维欧氏空间En中涉及两个n维单形的几何不等式问题,建立了涉及两个单形的一类三角不等式.作为其应用,获得了涉及两个单形及其内点的几何不等式,特别,获得了n维单形与其垂足单形的体积的一类关系式,改进了关于垂足单形体积的几类几何不等式.     

关于Veljan-Korchmaros不等式的改进

利用距离几何理论和数学归纳法相结合的方法,证明和改进了著名的Veljan-Korchmaros不等式,得到了三个更强的结果.并应用它推广了n维Euler不等式.     

E~n空间中k-n型Neuberg-Pedoe不等式

本文首先利用基本求导法则,证明了涉及单形的n-1维与n维体积的一个几何不等式,由此便得到En空间中k-n型Neuberg-Pedoe不等式.     

A simplicial approximation of a solution for the nonlinear complementarity problem

For a given map f from the n-dimensional Euclidean space En into itself, we consider the complementary problem of finding a nonnegative vector x in En whose imagef(x) is also nonnegative and such that the two vectors are orthogonal. It is the unifying mathematical form for several problems arising in different fields such as mathematical programming, game theory and economics.In this paper a new algorithm is developed based on the adjacent simplex technique , which was used by Garcia, Lemke and Lüthi for approximating an equilibrium point of a noncooperative n-person game. An almost-complementary path leads to a complementary simplex, which approximates a stationary point. Because most of the existence proofs for the nonlinear complementarity use the relationship between stationary points and complementarity, the algorithm gives constructive proofs for many existence theorems. If a better approximation is desired, the algorithm may be restarted from any point. The dimension of the simplices on the path is varying, which computationally should result in some savings.     

ILLUMINATION AND EXPOSITION OF A CONVEX n-DIMENSIONAL BODY DEPENDING ON ITS SHARPNESS

IInttodllCt1ODLet C be a(comp。t)con。x。－dimensional body in E”,n＞2,and d be a direction,l·e·a nonzero vector·A Point P EaC Is said to be illuminated by d ifthe line throughphavingthe dlrectlondco尬ams apomt qE nit Cwhi山followsp．ThebodyCis ssidtobeillttthillat6d by 8 S6t Of diY6CtiollS dl,dZ,…If gch Of佃加llldaty pollltS IS lllttthillst6d by tleast one of these directions．The Illumination Problem is to establish the minunum integer Ii(called llumination number…     

New series of odd non-congruent numbers Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

We determine all square-free odd positive integers n such that the 2-Selmer groups Sn and Sn of the elliptic curve En: y2 = x(x -n)(x - 2n) and its dual curve En: y2 = x3 6nx2 n2x have the smallest size: Sn = {1}, Sn = {1,2,n,2n}. It is well known that for such integer n, the rank of group En(Q) of the rational points on En is zero so that n is a non-congruent number. In this way we obtain many new series of elliptic curves En with rank zero and such series of integers n are non-congruent numbers.