初等收敛群和拟初等收敛群

作为－／R^n上的离散收敛群中的初等群的推广,本文定义了－／R^n上一般收敛群中的初等群和拟初等群,并得到了初等收敛群、拟初等收敛群和非拟初等敛群各自的一些性质和特征。     

整数环上正交群的初等表示与换位子表示

令 R 为有1的结合环,G 表 R 上某类典型群(SL_nR,SP_(2n)R,O_ ~(2n)R 等),EG 表 G的由初等阵生成的子群,G′表 G 的换位子群.令 e(G),c_n(G)分别表示最小的正整数e_n,c_n,使得 EG,G′中每一元素可至多由 e_n 个初等阵,c_n 个换位子表出。若不存在这样的有限正整数 e_n,c_n,我们说 G 对于初等阵或换位子无界.     

椭圆曲线有理点扭子群的明显分类

本文给出了有理数域Q上椭圆曲线E按其偶数阶循环扭子群Etors(Q)的分 类,并给出了Etors(Q)的生成元.这些结果,连同新近Ono在Etors(Q)非循环情形 的结果,完全解决了E含2阶有理点时的分类和参数化问题.     

初等Abel群的加法定理

本文中用Kneser's定理得到下列结论一个新的简单证法.设G为初等Abel p-群(运算用加法),S={a1,a2,…,an)为G的一个n项不含有零然的元素列(元素可允许重复),∣s∣=n=pm-1 p-2,,其中p为素数,若对G的任意子群H,S最多含有∣H∣-1项,则:(1)当m=2时,∑0(S)=G;(2)当m 3时,∑(S)=G.特别有(1)Olson'猜想r(ZpZp)=2p-2;(2)r(mZp)=c(mZp)=pm-1 p-2,m 3.     

椭圆内接三角形最大面积的初等求法探究

探究性教学是教师创设一定的问题情境，让学生自主参与的学习过程．本文以椭圆内接三角形最大面积的初等求法为“探究主题”，以问题序列为“探索主线”展开研究，在探究过程中综合运用了函数的导数、不等式、坐标变换等数学工具和手段，     

实数加群子群的分类及其应用

由实数加群的常见子群启发,给出了实数加群的子群或者是离散的或者是稠密的完全分类,并给出了该分类的一个简单应用.     

线性群的自同构群的一类子群

设E为任意域,F为E的子域,分别以T=GL（n,E),S=GL(n,F)表示域E、F上的n阶一般线性群（n≥2）,则S为T的子群。本确定T的自同构群AutT中保持S中每个元不动的自同构全体形成的群Gal(T/S)。     

欧氏环上特殊正交群的一类极大子群

定出欧氏环上特殊正交群的一类极大子群,得到如下结果:设R是带有欧氏映射σ的特征不为2的欧氏环且不是域,SO(2m,R)为R上的特殊正交群,R*=R\{0},l=min{σ(x)|x∈R*\U(R)},任取a∈R*\U(R)使σ(a)=l,记a在R中生成的主理想为M.那么当m≥3时,AB CD∈SO(2m,R)|B∈Mm×m是SO(2m,R)的一个极大子群.     

正多边形对称群的子群

利用Lagrange定理和正多边形对称群的性质,首先对正多边形对称群的子群的性质进行了研究,其次讨论了正多边形对称群的子群的结构,由此完全确定了正多边形对称群的子群,最后应用所得结论求出了正六边形对称群的所有子群.     

Elliptic K3 Surfaces with Abelian and Dihedral Groups of Symplectic Automorphisms

We analyze K3 surfaces admitting an elliptic fibration ? and a finite group G of symplectic automorphisms preserving this elliptic fibration. We construct the quotient elliptic fibration ?/G comparing its properties to the ones of ?.

We show that if ? admits an n-torsion section, its quotient by the group of automorphisms induced by this section admits again an n-torsion section, and we describe the coarse moduli space of K3 surfaces with a given finite group contained in the Mordell–Weil group.

Considering automorphisms coming from the base of the fibration, we find the Mordell–Weil lattice of a fibration described by Kloosterman, and we find K3 surfaces with dihedral groups as group of symplectic automorphisms. We prove the isometries between lattices described by the author and Sarti and lattices described by Shioda and by Greiss and Lam.     

一类非线性椭圆型方程的一个Liouville定理

设 (Mn,g)是一个 n维的完备黎曼流形 ,其 Ricci曲率满足 Ric M(x)≥ - A(1 r2 (x) ln2 (2 r(x) ) ) ,其中 A是非负常数 ,r(x)表示点 x∈ M到某固定点 x0 ∈ M的测地距离 .则 M上方程 Δu Su Kuα=0在下述条件“ (i)在 M上 S≤ 0 ;(ii)在 M上 K<0且有常数 a>0使在一个紧集之外 K≤ - a2 ;(iii)常数 α>1”下的 C2 -非负解只有零解 .     

A Class of Singularly Perturbed Semilinear Elliptic Equations

The singularly perturbed problem for the semilinear elliptic equations is considered. Under appropriate conditions, by using the comparison theorem, the existence and asymptotic behavior of solution for the boundary value problems are studied.     

Morita Equivalent 3-Blocks of the 3-Dimensional Projective Special Linear Groups

If G is a projective special linear group PSL(3,q) with q 4or 7 (mod 9), then a Sylow 3-subgroup of G is elementary abelianof order 9. We show that the principal 3-blocks of any two suchgroups are Morita equivalent. This result and Okuyama's theoremfor PSL(3,4) prove the Broué conjecture for these blocks.1991 Mathematics Subject Classification: 20C05, 20C20.     

Tame Automorphisms of Elementary Free Groups

We prove that the automorphism group of a finitely generated fully residually free group is tame.     

Isometry Groups of Unimodular Simply Connected 3-Dimensional Lie Groups

We characterize the left-invariant Riemannian metrics on each of the six unimodular simply connected 3-dimensional Lie groups which give rise to 3-, 4-, or 6-dimensional isometry groups. It turns out that this classification is independent of curvature properties.     

Existence Results for a Class of Semilinear Elliptic Systems

In this paper, we study the existence of nontrivial solutions for the problem
{-△u=f（x,u,v）＋h1（x）in Ω
-△v=g（x,u,v）＋h2（x）inΩ
u=v=0 onδΩ
where Ω is bounded domain in R^N and h1,h2 ∈ L^2 （Ω）. The existence result is obtained by using the Leray-Schauder degree under the following condition on the nonlinearities f and g：
{lim s,｜t｜→＋∞f（x,s,t）/s=lim ｜s｜,t→＋∞g（x,s,t）/t=λ＋1 uniformly on Ω,
lim -s,｜t｜→＋∞f（x,s,t）/s=lim ｜s｜,-t→＋∞g（x,s,t）/t=λ-,uniformly on Ω,
where λ＋,λ-∈（0）∪σ（-△）,σ（-△）denote the spectrum of -△. The cases （i） where λ＋ = λ_ and （ii） where λ＋≠λ_ such that the closed interval with endpoints λ＋,λ_ contains at most one simple eigenvatue of -△ are considered.     

The Selmer Groups of Elliptic Curves

Let E/K be an elliptic curve with K-rational p-torsion points.The p-Selmer group of E is described by the image of a map λk and hence an upper bound of its order is given in terms of the class numbers of the S-ideal class group of K and the p-division field of E.