The upper estimation of Hausdorff measure for Sierpinski gasket has beengreatly hoprovd in Refs. [1, 2]. As the basis of these two works, the codingteclmique of the upper estimation seardsng for regular fractal sets o...The upper estimation of Hausdorff measure for Sierpinski gasket has beengreatly hoprovd in Refs. [1, 2]. As the basis of these two works, the codingteclmique of the upper estimation seardsng for regular fractal sets on computerdiscusses thoroughly in this paper through a troical example of Sierpinski gasket.展开更多
Based on the concepts of fractal super fibers, the （3, 9＋2）-circle and （9＋2, 3）-circle binary fractal sets are abstracted form such prototypes as wool fibers and human hairs, with the （3）-circle and the （9＋2...Based on the concepts of fractal super fibers, the （3, 9＋2）-circle and （9＋2, 3）-circle binary fractal sets are abstracted form such prototypes as wool fibers and human hairs, with the （3）-circle and the （9＋2）-circle fractal sets as subsets. As far as the （9＋2） topological patterns are concerned, the following propositions are proved： The （9＋2） topological patterns accurately exist, but are not unique. Their total number is 9. Among them, only two are allotropes. In other words, among the nine topological patterns, only two are independent （or fundamental）. Besides, we demonstrate that the （3, 9＋2）-circle and （9＋2, 3）-circle fractal sets are golden ones with symmetry breaking.展开更多
In this paper we consider a class of equations for the flow and magnetic field within the earth, for initial-boundary value problem, we prove existence of inertial sets and it's fractal dimension has been given, t...In this paper we consider a class of equations for the flow and magnetic field within the earth, for initial-boundary value problem, we prove existence of inertial sets and it's fractal dimension has been given, the squeezing rate to inertial sets from trajectory of absorbing set has been estimated.展开更多
文摘The upper estimation of Hausdorff measure for Sierpinski gasket has beengreatly hoprovd in Refs. [1, 2]. As the basis of these two works, the codingteclmique of the upper estimation seardsng for regular fractal sets on computerdiscusses thoroughly in this paper through a troical example of Sierpinski gasket.
基金supported by the National Natural Science Foundation of China (Nos. 10572076 and10872114)the Natural Science Foundation of Jiangsu Province (No. BK2008370)
文摘Based on the concepts of fractal super fibers, the （3, 9＋2）-circle and （9＋2, 3）-circle binary fractal sets are abstracted form such prototypes as wool fibers and human hairs, with the （3）-circle and the （9＋2）-circle fractal sets as subsets. As far as the （9＋2） topological patterns are concerned, the following propositions are proved： The （9＋2） topological patterns accurately exist, but are not unique. Their total number is 9. Among them, only two are allotropes. In other words, among the nine topological patterns, only two are independent （or fundamental）. Besides, we demonstrate that the （3, 9＋2）-circle and （9＋2, 3）-circle fractal sets are golden ones with symmetry breaking.
文摘In this paper we consider a class of equations for the flow and magnetic field within the earth, for initial-boundary value problem, we prove existence of inertial sets and it's fractal dimension has been given, the squeezing rate to inertial sets from trajectory of absorbing set has been estimated.
