Growth of graded noetherian rings

We show that every graded locally finite right noetherian algebra has sub-exponential growth. As a consequence, every noetherian algebra with exponential growth has no finite dimensional filtration which leads to a right (or left) noetherian associated graded algebra. We also prove that every connected graded right noetherian algebra with finite global dimension has finite GK-dimension. Using this, we can classify all connected graded noetherian algebras of global dimension two.

     

物理实验与量纲

本文提出在物理实验课中应该引入量纲的应用，并通过事例阐述了引入量纲的必要性与可行性     

截断半径变化对汽液界面参数和分维数的影响

本文在分形理论基础上,采用分子动力学模拟方法研究了在平衡状态下的汽液界面参数,得了界面区内的密度、 温度、压力张量、表面张力和分维数的分布。研究表明,利用分形理论可以较好的反映汽液界面的特性。势函数的截断半 径对汽液界面参数和分维数的模拟值存在影响。     

关于“关于自相似集的一个维数定理”一文的意见

本文指出了“关于自相似集的一个维数定理”一文中的一些问题。并给出反例说明该文的结论是不正确的。     

基于近距自相似模型的分形图像编码方法

为了克服分形图像编码方法速度低的弱点，提出了根据图像模型研究相应算法的思想。基于ρ｜ｒ｜图像模型，导出了与之相应的近距自相似模型，提供了一种适合于该模型的分形图像编码方法。实验结果表明，这种方法大大提高了编码速度，而且能有效地压缩图像数据     

十进制展示的误差和函数

研究了十进制误差和函数,利用分形几何的方法,得到了误差和函数的积分值,介值定理以及其图的Hausdorff维数.     

ZERO SET OF SOBOLEV FUNCTIONS WITH NEGATIVE POWER OF INTEGRABILITY

§1. Introduction Let ? ? Rn (n ≥1) be an open set, p ≥1. We consider functions u ∈W1 (?), such ,pthat, for some α> 0, |u|? < ∞. α (1.1) ?When p = 1, it is also natural to consider u ∈BV (?) which satis?es (1.1). For any u ∈W1 (?), p ≥1 or u ∈BV (?), we de?ne its zero set by …     

Eu(DBM)3超细微粒的分形聚集的TEM研究

本文利用透射电镜（ＴＥＭ）和Ｘ射线能谱（ＥＤＳ）对铕－二苯甲酰甲烷配合物（Ｅｕ（ＤＢＭ）３）在溶液中的分形聚集进行了研究，结果表明：Ｅｕ（ＤＢＭ）３超细微粒在表面活性剂形成的溶胶中，以及在溶胶中长时间静置后，其聚集体均具有分形特征，Ｈａｕｓｄｏｒｆｆ分形维数Ｄｆ分别为１．６６、１．６８。     

相对Hopf模的同调维数与半单性

Let H be a Hopf algebra over a field with bijective antipode, and A a commutative cleft right H-comodule algebra. In this paper, we investigate the ho-mological dimensions and the semisimplicity of the category of relative Hopf modulesAMH.     

Graded Witt ring and unramified cohomology

It is proved that for a smooth affine curveX over a local ring or global field, the graded Witt ring ofX is isomorphic to the graded unramified cohomology ring ofX. IfX is projective and has a rational point, the same result holds if and only if every quadratic space defined on the complement of a rational point extends toX. Such an extension is possible, for instance, if the canonical line bundle onX is a square in PicX.