一类催化媒体中的超扩散

本文研究一类分形结构上超布朗运动的存在性.通过对特殊分形上布朗运动的转移密度的分析以及对一类微分方程解的存在性证明,得出了相应的超布朗运动的存在性.     

一类催化媒体中的超扩散

本文研究一类分形结构上超布朗运动的存在性．通过对特殊分形上布朗运动的转移密度的分析以及对一类微分方程解的存在性证明,得出了相应的超布朗运动的存在性．     

一类分形集及其刻划

本文中我们构造了R~d中一类较普遍的分形集,它包括瘦分形与胖分形,瘦分形为R~d中的Cantor尘集,分维D_f=ln2~d/ln(2/k~(1/d)),对胖分形集我们求得分形指数β=-lnk/ln2(0相似文献   

一类Moran测度的重分形谱

证明一类支撑在某些Moran分形上的Moran测度的重分形形式成立.     

一类非均匀分形插值函数的可微性

本文研究一类分形插值函数的可微性问题，通过构造一迭代函数系，利用迭代函数系的唯一吸引子。给出了一类分形插值函数。并获得了此类分形插值函数在[0，1]区间上几乎处处可微和在[0，1]区间上某一点不可微判定的充分条件，推广了文献[2]的结论。     

关于具分形边界连通区域上的谱渐近及弱Weyl-Berry猜想

本文研究了连通分形鼓上的谱渐近，对满足“切口”条件的连通分形鼓以及一类自然连通的分形鼓，分别证明了弱Weyl－Berry猜想是成立的.     

一类分形函数及其维数估计

本文作者首先借助于b进制分数及无穷级数构造了一类分形函数,然后研究了这些函数图象的分形维数及其Hoelder性质,得到了一些维数结果。     

自相似分形上的非线性抛物方程(英文)

本文研究了分形区域上的一类半线性抛物方程.对于分形上恰当定义的拉普拉斯算子,建立了抛物方程的比较原理.利用上下解方法,我们得到了在一定条件下半线性抛物方程正解的存在性和唯一性.     

分形曲面的构造算法研究

以分形理论为依据 ,根据分形几何描绘自然界景物的基本思想 ,结合解析几何中旋转曲面的构造 ,把已生成的二维平面分形曲线绕着同一平面上的直线旋转 ,获得一类三维旋转曲面的构造算法 ,给出了相应的三维迭代函数系统和三维仿射变换矩阵 ,并进行了深入的理论分析 .本文的研究为分形曲面的构造探求了一种简易算法 ,并为分形曲面的生成和实践应用提供了理论依据 .     

星积分形曲面及其维数

通过分形曲线定义了一类分形曲面(被称为星积分形曲面),讨论了这类分形曲面的分形维数,得出了分形曲线的维数与它们所构造出的分形曲面维数之间的关系。     

Weak Uncertainty Principles on Fractals

We use the analytic tools such as the energy, and the Laplacians defined by Kigami for a class of post-critically finite (pcf) fractals which includes the Sierpinski gasket (SG), to establish some uncertainty relations for functions defined on these fractals. Although the existence of localized eigenfunctions on some of these fractals precludes an uncertainty principle in the vein of Heisenberg’s inequality, we prove in this article that a function that is localized in space must have high energy, and hence have high frequency components. We also extend our result to functions defined on products of pcf fractals, thereby obtaining an uncertainty principle on a particular type of non-pcf fractal.     

一类Moran测度的Lq-谱

此文考虑了一类Moran分形，在其生成过程中每一阶的压缩比及压缩比的个数可以是不相同的，证明了支撑在此类Moran分形上的Moran测度的L^q-谱的存在性．     

Fractals and generalized inner products

The generation of fractals by a generalization of the matrix product is described. These matrix products allow visualization of additional structure of the fractals as well as producing fractals of new types.     

Wavelets on fractals and besov spaces

Wavelets on self-similar fractals are introduced. It is shown that for certain totally disconnected fractals, function spaces may be characterized by means of the magnitude of the wavelet coefficients of the functions.     

Existence of self-similar energies on finitely ramified fractals

A self-similar energy on finitely ramified fractals can be constructed starting from an eigenform, i.e., an eigenvector of a special operator defined on the fractal. In this paper, we prove two existence results for regular eigenforms that consequently are existence results for self-similar energies on finitely ramified fractals. The first result proves the existence of a regular eigenform for suitable weights on fractals, assuming only that the boundary cells are separated and the union of the interior cells is connected. This result improves previous results and applies to many finitely ramified fractals usually considered. The second result proves the existence of a regular eigenform in the general case of finitely ramified fractals in a setting similar to that of P.C.F. self-similar sets considered, for example, by R. Strichartz in [11]. In this general case, however, the eigenform is not necessarily on the given structure, but is rather on only a suitable power of it. Nevertheless, as the fractal generated is the same as the original fractal, the result provides a regular self-similar energy on the given fractal.     

随机自仿射集的Hausdorff维数估计

定义了一类广泛的随机自仿射集,得到了此类集合的Ｈａｕｓｄｏｒｆｆ维数估计．此前的随机自相似（包括Ｇｒａｆ,Ｍａｕｌｄｉｎ与Ｆａｌｃｏｎｅｒ等定义的随机自相似情形）和Ｆａｌｃｏｎｅｒ定义的（严格）自仿射以及作者定义的μ 统计自仿射情形均成为该文结果的特例．     

Homogenization of quadratic forms on fractals

We define a notion of homogenization for quadratic energies defined on fractals structures and present, without proofs, a result of homogenization for fractals having special symmetry properties.     

On the description of self-similarity for attractors by means of conditional entropy

There exist several sets having similar structure on arbitrarily small scales. Mandelbrot called such sets fractals, and defined a dimension that assigns non-integer numbers to fractals. On the other hand, a dynamical system yielding a fractal set referred to as a strange attractor is a chaotic map. In this paper, a characterization of self-similarity for attractors is attempted by means of conditional entropy.     

Calculus on fractals based upon local fields In memory of Founding Editor Professor M. T. Cheng with great respect and deep sorrow

The main contents in this note are: 1. introduction: 2. locally compact groups and local fields: 3. calculus on fractals based upon local fields: 4. fractional calculus and fractals: 5. fractal function spaces and PDE on fractals.     

Calculus on fractals based upon local fields

The main contents in this note are: 1. introduction: 2. locally compact groups and local fields: 3. calculus on fractals based upon local fields: 4. fractional calculus and fractals: 5. fractal function spaces and PDE on fractals.