一类微分-差分方程组的内禀对称和等价群变换

研究一类微分-差分方程组的对称和等价群变换.采取内禀的无穷小算子方法,给出了方程组的内禀对称和等价群变换.为结合抽象Lie代数结构,给方程完全分类提供了理论基础.     

椭圆方程的变换群与变分恒等式

讨论了椭圆方程的变换群与变分恒等式的关系,利用变分对称群的性质得到一类变分恒等式.通过计算变分对称群得到了寻找非星形区域方法并举例进行了说明.     

Heisenberg群上移动球面法的应用——一类半线性方程的Liouville型定理

作为Heisenberg群上移动球面法的基础,在Heisenberg群上引入了一类CR反演变换.作为应用,讨论了Heisenberg群上的次临界方程,证明任意非负柱对称解均为平凡解.     

带幂非线性项变系数非线性波动方程的李对称分类与等价性变换

从微分方程群理论分析角度,研究了一类含有3个任意函数和2个幂非线性项的变系数非线性波动方程.由于方程具有很强的任意性和非线性项,可通过等价性变换寻找方程的不变对称分类.首先给出了等价性变换的一般结果,其中包括一些包含任意元的非局部变换.然后对所研究的方程,利用广义扩展等价群和条件等价群给出了方程的完全对称分类.最后获得并分析了方程的特殊类相似解.     

Abel群在数论函数中的一个应用

<正> 数论函数是研究数论的极其重要的工具。用群的观点研究一类数论函数,能使一类数论函数的证明简易,能对一类数论函数的认识更加清晰,下面仅就一类数论函数形成Abel群作一介绍,并通过化简证明标准的 Mobius变换定理(下面简称标准定理),说明其应用.     

群代数作用遍历性的一点注记

证明了由自由群整数环上一类元素确定的代数作用的遍历性,计算了Heisenberg群因子中特定元素的Fuglede-Kadison行列式值.     

一类中心循环的有限p-群的自同构群的研究

本文研究了一类中心循环的有限p-群G的自同构群.利用在G的导群上作用平凡的自同构以及环上的辛群和正交群,确定了G的自同构群的结构,这推广了Bornand的相应结果.     

局部流代数和可微分变换群的表示

本文给出广义函数空间上关于可微分变换群拟不变测度的Radon-Nikodym导数一个基本解析表达式.并且给出用这个表达式来求一类局部流代数表示的方法.     

一类变系数非线性Schrodinger方程的对称群分类和容许变换

从对称群和容许变换的角度讨论一类变系数非线性Schrodinger方程,给出所考察方程的非平凡点对称群。     

一类变系数非线性Schrǒdinger方程的对称群分类和容许变换(英文)

从对称群和容许变换的角度讨论一类变系数非线性Ｓｃｈｒｏｄｉｎｇｅｒ方程,给出所考察方程的非平凡点对称群     

素数立方阶群局部传递的图

目的是研究局部传递图的性质和分类.运用置换群和陪集图的理论,获得了关于素数立方阶群局部传递图的完全分类,证明了这些图是一些互不相交的关于素数立方阶群边传递图的并.     

On the weak isometries of the Boolean cube

The p-weak isometries of the Boolean cube are considered, i.e., the mappings of the cube onto itself which preserve a fixed distance p. Some necessary and sufficient conditions are obtained for coincidence of the group of p-weak isometries with the group of standard isometries (automorphisms of the cube).     

L_1-norm packings from function fields

In this paper,we study some packings in a cube,namely,how to pack n points in a cube so as to maximize the minimal distance.The distance is induced by the L_1-norm which is analogous to the Hamming distance in coding theory.Two constructions with reasonable parameters are obtained,by using some results from a function field including divisor class group,narrow ray class group,and so on.We also present some asymptotic results of the two packings.     

A reduction of Keller's conjecture

A family of translates of a closedn-dimensional cube is called a cube tiling if the union of the cubes is the wholen-space and their interiors are disjoint. According to a famous unsolved conjecture of O. H. Keller, two of the cubes in ann-dimensional cube tiling must share a complete (n – 1)-dimensional face. In this paper we shall prove that to solve Keller's conjecture it is sufficient to examine certain factorizations of direct sum of finitely many cyclic group of order four.     

Rank Rigidity for Cat(0) Cube Complexes

We prove that any group acting essentially without a fixed point at infinity on an irreducible finite-dimensional CAT(0) cube complex contains a rankone isometry. This implies that the Rank Rigidity Conjecture holds for CAT(0) cube complexes. We derive a number of other consequences for CAT(0) cube complexes, including a purely geometric proof of the Tits alternative, an existence result for regular elements in (possibly non-uniform) lattices acting on cube complexes, and a characterization of products of trees in terms of bounded cohomology.     

<Emphasis Type="Italic">L</Emphasis><Subscript>1</Subscript>-norm packings from function fields

In this paper, we study some packings in a cube, namely, how to pack n points in a cube so as to maximize the minimal distance. The distance is induced by the L₁-norm which is analogous to the Hamming distance in coding theory. Two constructions with reasonable parameters are obtained, by using some results from a function field including divisor class group, narrow ray class group, and so on. We also present some asymptotic results of the two packings.     

A curiously cubulated group

Geometriae Dedicata - We construct a finitely generated 2-dimensional group that acts properly on a locally finite CAT(0) cube complex but does not act properly on a finite dimensional CAT(0) cube...     

Coxeter groups are virtually special

In this paper we prove that every finitely generated Coxeter group has a finite index subgroup that is the fundamental group of a special cube complex. Some consequences include: Every f.g. Coxeter group is virtually a subgroup of a right-angled Coxeter group. Every word-hyperbolic Coxeter group has separable quasiconvex subgroups.     

A Bo?ejko-Picardello type inequality for finite-dimensional CAT(0) cube complexes

We prove a Bo?ejko-Picardello type inequality for finite-dimensional CAT(0) cube complexes and as a consequence we obtain that a group acting properly on a finite-dimensional CAT(0) cube complex is weakly amenable with the Cowling-Haagerup constant 1.     

Stallings’ folds for cube complexes

We describe a higher dimensional analogue of Stallings’ folding sequences for group actions on CAT(0) cube complexes. We use it to give a characterization of quasiconvex subgroups of hyperbolic groups that act properly and cocompactly on CAT(0) cube complexes via finiteness properties of their hyperplane stabilizers.