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封面上画面的主题是"雪花与对称"。天蓝色的背景下,针状植物的绿色枝条上坐落着洁白的残雪。画面的右下角、中部和左侧,分别点缀着经过彩色处理的雪花显微照片;画面的上侧和左上角,分别飘落着我们构造的超级分形雪花和彩色分形雪花;左下角的图案则取自画家埃舍尔的画作。 相似文献
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Based on fractal super fibers and binary fractal fibers, the following objectives are approached in this paper: First, the concept of multiple-cell elements is induced and abstracted. Second, through multiple-cell elements, the constructability of regular multifractals with strict self-similarities is confirmed, and the universality of the con- struction mode for regular multifractals is proved. Third, through the construction mode and multiple-cell elements, regular multifractals are demonstrated to be equivalent to generalized regular single fractals with multilayer fine structures. On the basis of such equivalence, the dimension formula of the regular single fractal is extended to that of the regular multifractal, and the geometry of regular single fractals is extended to that of regular multifractals. Fourth, through regular multifractals, a few golden fractals are constructed. 相似文献
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曲面物理和力学中有两个独立的基本微分算子(即"基本微分算子对"). 本文综述如下主题:在所有的基本微分算子对中,经典梯度▽(···) 和形状梯度▽ (···) 的配对[[▽,▽]] 是最佳的. 具体内容包括:(1)基本微分算子对的形式并不唯一;(2) 内积的可交换性确立了[[▽,▽]] 优于其他基本微分算子对的"最佳" 地位;(3) 基于[[▽,▽]] 可以最佳地构造曲面物理和力学的高阶标量微分算子,因而[[▽,▽]] 是构造曲面物理和力学微分方程的最佳"基本砖块";(4) [[▽,▽]] 在软物质曲面物理和力学中普遍存在. 相似文献
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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. 相似文献
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?????????????е??? 总被引:2,自引:0,他引:2
简要综述了生物膜力学与几何的新进展. 在生物膜力学中,着重介绍了基于微分算子的平衡
理论和几何约束理论;在生物膜几何中,重点评述了源于生物膜力学的新梯度算子及其积分
性质. 指出:新梯度算子可能在生物膜曲面上诱发新的驱动力;生物膜力学与几何是一个有
机整体,其背后存在着一个对称的几何体系,包括对称的微分算子以及对称的积分定理系统. 相似文献