盒维数的一个等价定义及其应用

给出了盒维数的一个等价定义．该定义与盒维数的现有定义相比,从理论上更容易验证,在应用中更适合于数值计算．据此给出了计算盒维数的一个数值算法．     

一类分形曲面的精细计盒维数公式

本文研究由一个二变元四阶差分方程边值问题生成的分形曲面的精细计盒维数问题,给出了一个自然的维数公式,若该边值问题的边界上的连续函数的图象的精细计盒维数为γ,则该解曲面的精细计盒维数为（1＋γ）。     

关于可数点集的盒维数的一些探讨

本文研究了一类可数点集的盒维数的计算问题.通过构造双Lipschitz映射,把原可数点集的盒维数的求解问题转化为求解一类相对简单的可数点集的盒维数.获得了两个单调的可数点集在具有同阶间隔时具有相同的上盒维数和下盒维数的结论.该结论为计算一类可数点集的盒维数提供了方便.     

一类随机Moran集的分形维数

本文研究了随机压缩向量满足一定条件下的随机Moran集的分形维数.利用计算上盒维数的上界和分形维数之间的性质,得到Moran集各种分形维数. 并在一般情形下,给出随机Moran集的上盒维数的上界.     

一类分形曲面的精细计盒维数

研究一类分形曲面的精细计盒维数,得到了星积分形曲面与其生成元的精细计盒维数的关系.     

乘积概率空间中的维数结果

在Ｒ＾ｄ１，Ｒ＾ｄ２中的分形测度和Ｒ＾ｄ１＋ｒ２中乘积测度之间的关系已经被许多作者发展。     

一类递归集Hausdorff维数及Bouligand维数

本语言给出了递归集的Ｈａｕｓｄｏｒｆｆ维数的下界估计，并由此确定了一类递归集的维数，所获结果包含并推广了Ｂｅｄｆｏｒｄ，Ｄｅｋｋｉｎｇ及文志英，钟红柳等人的有关结果。     

一类齐次Moran集的上盒维数

该文利用连通分支与其间隔构造了一类特殊的齐次Moran集:{m_k}-拟齐次完全集,并证明该集合在sup{m_k}有限的条件下其上盒维数与packing维数可以达到所有齐次Moran集的最小值,并得到该集合在一定条件下上盒维数取值范围,并找到了上盒维数取到精确表达式所需的一个充分条件.     

关于自相似集的一个维数定理

本文对严格自相似集，提出了一个比“开集”条件更弱的“可解”条件，并且证明：在可解条件下，自相似集的Ｈａｕｓｄｏｒｆｆ维数及Ｂｏｕｌｉｇａｎｄ维数与其相似维数一致．     

The Box counting Dimension of Invariant Sets for Iterated Function Systems

Ｕｎｄｅｒｔｈｅｏｐｅｎｓｅｔｃｏｎｄｉｔｉｏｎ,ａｎｉｎｅｑｕａｌｉｔｙｏｎｔｈｅｂｏｘ－ｃｏｕｎｔｉｎｇｄｉｍｅｎｓｉｏｎｏｆｉｎｖａｒｉ－ａｎｔｓｅｔｓｆｏｒｃｏｎｔｒａｃｔｉｏｎｉｔｅｒａｔｅｄｆｕｎｃｔｉｏｎｓｙｓｔｅｍｓｗｅｒｅｇｉｖｅｎ...     

Bouligand Dimension of Fractal Curve of Almost Periodic Series

in this paper, we obtain the calculating formulas for Bouligand dimension offractal curves represented by some almost periodic function series.     

Dimension of Slices Through Fractals with Initial Cubic Pattern

In this paper, the Hausdorff dimension of the intersection of self-similar fractals in Euclidean space R~n generated from an initial cube pattern with an(n-m)-dimensional hyperplane V in a fixed direction is discussed. The authors give a sufficient condition which ensures that the Hausdorff dimensions of the slices of the fractal sets generated by "multirules" take the value in Marstrand's theorem, i.e., the dimension of the self-similar sets minus one. For the self-similar fractals generated with initial cube pattern, this sufficient condition also ensures that the projection measure μVis absolutely continuous with respect to the Lebesgue measure L~m. When μV《 L~m, the connection of the local dimension ofμVand the box dimension of slices is given.     

A Note on Dimension Modules

In [2 Camillo , V. P. , Zelmanowitz , J. M. ( 1980 ). Dimension modules . Pacific J. Math. 91 : 249 – 261 .[Crossref], [Web of Science ®] , [Google Scholar]] Camillo and Zelmanowitz stated that rings all whose modules are dimension modules are semisimple Artinian. It seem however that the proof in [2 Camillo , V. P. , Zelmanowitz , J. M. ( 1980 ). Dimension modules . Pacific J. Math. 91 : 249 – 261 .[Crossref], [Web of Science ®] , [Google Scholar]] contains a gap and applies to rings with finite Goldie dimension only. In this paper we show that the result indeed holds for all rings with a basis as well as for all commutative rings with Goldie dimension attained.     

Box dimension and fractional integral of linear fractal interpolation functions

In this paper, we present a new method to calculate the box dimension of a graph of continuous functions. Using this method, we obtain the box dimension formula for linear fractal interpolation functions (FIFs). Furthermore we prove that the fractional integral of a linear FIF is also a linear FIF and in some cases, there exists a linear relationship between the order of fractional integral and box dimension of two linear FIFs.     

Dimension of the Fractal Curve in Plane and Its Derivative of the Fractional Order

Ｄｉｍｅｎｓｉｏｎ　ｏｆ　ｔｈｅ　Ｆｒａｃｔａｌ　Ｃｕｒｖｅ　ｉｎ　Ｐｌａｎｅ　ａｎｄ　Ｉｔｓ　Ｄｅｒｉｖａｔｉｖｅ　ｏｆ　ｔｈｅ　Ｆｒａｃｔｉｏｎａｌ　ＯｒｄｅｒＤｅｎｇＧｕａｎｔｉｅ（邓冠铁）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ｈｕ...     

A Half-Space Approach to Order Dimension

The aim of the present paper is to investigate the half-spaces in the convexity structure of all quasiorders on a given set and to use them in an alternative approach to classical order dimension. The main result states that linear orders can almost always be replaced by half-space quasiorders in the definition of the dimension of a partially ordered set. The work of the first named author was partially supported by the European Community’s Marie Curie Program (contract MTKD-CT-2004-003006). The second named author’s work was supported by OTKA of Hungary No. T043034.     

Finite Dimensional Behavior for Weakly Damped Generalized KdV-Burgers Equations

ＦｉｎｉｔｅＤｉｍｅｎｓｉｏｎａｌＢｅｈａｖｉｏｒｆｏｒＷｅａｋｌｙＤａｍｐｅｄＧｅｎｅｒａｌｉｚｅｄＫｄＶ－Ｂｕｒｇｅｒｓ　ＥｑｕａｔｉｏｎｓＧｕｏＢｏｌｉｎｇ（郭柏灵）（ＣｅｎｔｒｅｆｏｒＮｏｎｌｉｎｅａｒＳｔｕｄｉｅｓ，ＩｎｓｔｉｔｕｔｅｏｆＡ...     

Dimension of compact metric spaces

We give a survey of old and new results in dimension theory of compact metric spaces. Most of the relatively new results presented in the survey are based on the cohomological dimension approach. We complement the survey by stating the basics of cohomological dimension theory and listing some of its applications beyond the dimension theory.