研究二元样条空间维数的Blossoming方法

本文综述了研究二元样条的Ｂｌｏｓｓｏｍｉｎｇ方法．成功地重建了平面上贯穿剖分的维数公式．而且利用这种方法，对定义在Ｍｏｒｇａｎ－Ｓｃｏｔ剖分上样条空间的维数取得了一些新的结果．     

广义自相似集的维数研究

广义自相似集的维数研究华苏（清华大学应用数学系，北京１０００８４）ＯＮＴＨＥＤＩＭＥＮＳＩＯＮＯＦＧＥＮＥＲＡＬＩＺＥＤＳＥＬＲ－ＳＩＭＩＬＡＲＳＥＴＳ￥ＨＵＡＳＵ（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ＴｓｉｎｇｈｕａＵｎｉ...     

Excellent扩张和弱维数

在这篇文章里，我们证明了，当环Ｓ是Ｒ的ｅｘｃｅｌｌｅｎｔ扩张，Ｍ是Ｓ－模时，Ｍ做为Ｓ－模的弱维数与Ｍ做为Ｒ－模的弱维数相等。     

具阻尼的KdV—KSV方程的整体吸引子

本文证明了有阻尼的、没有Ｍａｒａｎｇｏｎｉ效应的ＫｄＶ－ＫＳＶ方程的周期初值问题存在整体吸引子,并且给出了该吸引子的Ｈａｕｓｄｏｒｆ维数和分形维数的上界估计     

虫洞和时空的维数

本文在１０维的Ｅｉｎｓｔｅｉｎ—Ｍａｘｗｅｌｌ理论中，讨论了虫洞对时空维数的作用，发现时空拓朴结构为自发紧致的Ｓ４Ｓ４Ｓ２的几率最大，从而说明可观测宇宙为什么是４维的．     

G—半局部环及其同调维数

本文中讨论了一类比半局部环更广的环类，即Ｇ－半局部环，对Ｇ－半局部我们通过模去环的左Ｓｏｃｈｅ及Ｊａｃｏｂｓｏｎ根，研究了环的同调维数，并得到Ｇｄ（Ｒ／Ｓ）＝Ｇｄ（Ｒ／Ｓ∩Ｊ），式中的Ｇｄ表示环Ｒ的左整体维数或右整体维数，Ｓ＝Ｓｏｃ（Ｒ＾Ｒ）以及Ｊ是环Ｒ的Ｊａｃｏｂｓｏｎ根，当Ｒ还时半本原环时，即得Ｇｄ（Ｒ／Ｓ）＝Ｇｄ（Ｒ）。     

两参数Ornstein－Uhlenbeck过程的自相交局部时与k重时的维数

本文研究两参数ｄ维Ｏｒｎｓｔｅｉｎ－Ｕｈｌｅｎｂｅｃｋ过程的相交局部时的联合连续性，ｋ重点的存在性．当４ｋ＞（ｋ－１）ｄ时，得到了ＯＵＰ２．ｄ的ｋ重时集的Ｈａｕｓｄｏｒｆｆ维数与ｐａｃｋｉｎｇ维数．     

SG(2,2)上布朗运动的维数性质

本文研究分形集合ＳＧ（２,２）上布朗运动的维数性质,得到了ＳＧ（２,２）上布朗运动的样本图以及象集的Ｈａｕｓｄｏｒｆｆ维数与盒维数。     

分形几何从UCSMP教材内容引发的思考

分形几何从ＵＣＳＭＰ教材内容引发的思考钱玲（北京师范大学１００８７５）美国芝加哥大学数学课程设计（简称ＵＣＳＭＰ）第四册高中代数中，第１４章“维数和空间”最后一节的内容是“分形”（Ｆｒａｃｔａｌｓ），它用８页篇幅，介绍了分形的创始人曼德勃罗（Ｂｅ...     

R^d中Hausdorff维数和packing维数的确定

本文目的在于建立确定Ｒ＾ｄ中Ｈａｕｓｄｏｒｆｆ维数ｄｉｍ和ｐａｃｋｉｎｇ维数Ｄｉｍ的两个命题，进而寻求Ｒ＾ｄ中Ｈａｕｓｄｏｒｆｆ维数ｄｉｍ与ｐａｃｋｉｎｇ维数Ｄｉｍ相等的条件；这使得我们能够引入分形测度的测度论定义。     

Regular Steinhaus graphs of odd degree

A Steinhaus matrix is a binary square matrix of size n which is symmetric, with a diagonal of zeros, and whose upper-triangular coefficients satisfy a_i,j=a_i−1,j−1+a_i−1,j for all 2?i<j?n. Steinhaus matrices are determined by their first row. A Steinhaus graph is a simple graph whose adjacency matrix is a Steinhaus matrix. We give a short new proof of a theorem, due to Dymacek, which states that even Steinhaus graphs, i.e. those with all vertex degrees even, have doubly-symmetric Steinhaus matrices. In 1979 Dymacek conjectured that the complete graph on two vertices K₂ is the only regular Steinhaus graph of odd degree. Using Dymacek’s theorem, we prove that if (a_i,j)_1?i,j?n is a Steinhaus matrix associated with a regular Steinhaus graph of odd degree then its sub-matrix (a_i,j)_2?i,j?n−1 is a multi-symmetric matrix, that is a doubly-symmetric matrix where each row of its upper-triangular part is a symmetric sequence. We prove that the multi-symmetric Steinhaus matrices of size n whose Steinhaus graphs are regular modulo 4, i.e. where all vertex degrees are equal modulo 4, only depend on parameters for all even numbers n, and on parameters in the odd case. This result permits us to verify Dymacek’s conjecture up to 1500 vertices in the odd case.     

环的Extensions扩张与余纯维数(英文)

Let R be a noetherian ring and S an excellent extension of R.cid(M) denotes the copure injective dimension of M and cfd(M) denotes the copure flat dimension of M.We prove that if M S is a right S-module then cid(M S)=cid(M R) and if S M is a left S-module then cfd(S M)=cfd(R M).Moreover,cid-D(S)=cid-D(R) and cfd-D(S)=cfdD(R).     

关于FP-内射维数的一个注记

Let R and S be a left coherent ring and a right coherent ring respectively,RωS be a faithfully balanced self-orthogonal bimodule.We give a sufficient condition to show that l.FP-idR（ω） ∞ implies G-dimω（M） ∞,where M ∈ modR.This result generalizes the result by Huang and Tang about the relationship between the FP-injective dimension and the generalized Gorenstein dimension in 2001.In addition,we get that the left orthogonal dimension is equal to the generalized Gorenstein dimension when G-dimω（M） is finite.     

A dimensional result for random self-similar sets

A very important property of a deterministic self-similar set is that its Hausdorff dimension and upper box-counting dimension coincide. This paper considers the random case. We show that for a random self-similar set, its Hausdorff dimension and upper box-counting dimension are equal

     

Generalized steinhaus graphs

A generalized Steinhaus graph of order n and type s is a graph with n vertices whose adjacency matrix (a_i,j) satisfies the relation where 2 ≦i≦n?1, i + s(i ? 1 ≦ j ≦ n, c_r,i,j ? {0,1} for all 0 ≦ r ≦ s(i) ?1 and c_s(i)?1,i,j = 1. The values of s(i) and c_r,i,j are fixed but arbitrary. Generalized Steinhaus graphs in which each edge has probability ½ are considered. In an article by A. Blass and F. Harary [“Properties of Almost All Graphs and Complexes,” Journal of Graph Theory, Vol. 3 (1976), pp. 225–240], a collection of first-order axioms are given from which any first-order property in graph theory or its negation can be deduced. We show that almost all generalized Steinhaus graphs satisfy these axioms. Thus the first-order theory of random generalized Steinhaus graphs is identical with the theory of random graphs. Quasi-random properties of graphs are described by F. R. K. Chung, R. L. Graham, and R. M. Wilson, [“Quasi-Random Graphs,” Combinatorica, Vol. 9 (1989), pp. 345–362]. We conclude by demonstrating that almost all generalized Steinhaus graphs obey Property 2 and hence all equivalent quasi-random properties. © 1996 John Wiley & Sons, Inc.     

Dimension scales of bicompacta

We introduce the notion of a (stable) dimension scale d-sc(X) of a space X, where d is a dimension invariant. A bicompactum X is called dimensionally unified if dim F = dim_G F for every closed F ? X and for an arbitrary abelian group G. We prove that there exist dimensionally unified bicompacta with every given stable scale dim-sc.     

Gorenstein AC-projective dimension of unbounded complexes

Recently, the notion of Gorenstein AC-projective (resp., Gorenstein AC-injective) modules was introduced in [3 Bravo, D., Gillespie, J., Hovey, M. The stable module category of a general ring. http://arxiv.org/abs/1405.5768. [Google Scholar]] by which the so-called “Gorenstein AC-homological algebra” was established. Here, we define and study a notion of Gorenstein AC-projective dimension for complexes (not necessarily bounded) over associative rings, which is inspired by Veliche’s construction of defining Gorenstein projective dimension. In particular, we show that such a dimension can be closely related to the “proper” Gorenstein AC-projective resolutions of complexes induced by a complete and hereditary cotorsion pair in the category of complexes of modules. This enables us to interpret this dimension of a complex in terms of vanishing of the derived functor RHom_R(?,?). As applications, some characterizations of the Gorenstein AC-projective dimension of a module are also obtained.     

Parity-regular Steinhaus graphs

Steinhaus graphs on vertices are certain simple graphs in bijective correspondence with binary -sequences of length . A conjecture of Dymacek in 1979 states that the only nontrivial regular Steinhaus graphs are those corresponding to the periodic binary sequences of any length . By an exhaustive search the conjecture was known to hold up to 25 vertices. We report here that it remains true up to 117 vertices. This is achieved by considering the weaker notion of parity-regular Steinhaus graphs, where all vertex degrees have the same parity. We show that these graphs can be parametrized by an -vector space of dimension approximately and thus constitute an efficiently describable domain where true regular Steinhaus graphs can be searched by computer.

     

Dimensions of supercritical branching processes in varying environments

Let ∂Γ be the boundary of a family tree Γ associated with a supercritical branching process in varying environments. In this paper, the Hausdorff dimension, the upper box dimension and the packing dimension of ∂Γ are computed explicitly. In contrast to the (fixed environment) Galton–Watson case, the Hausdorff and upper box dimension may take different values.