正十二面体

A mathematical model of the semibatch foam fractionation of surfactants was developed. Foam bed is assumed to consist of equal dodecahedral bubbles at any cross section.

本文建立了间歇式泡沫分离水中表面活性剂的模型，假设所有气泡均为正十二面体，在塔的每一截面上，泡沫半径均一。

It was also found that the film of smaller grains corresponded to a smaller lattice constant of the garnet structure, which implied that fewer Bi〓 ions substituted into the dodecahedral sites in the garnet, due to the fact that the smaller grains resulted in more grain boundaries, thus leading to more serious Bi segregation in the grain boundaries.

分析表明，细小的晶粒意味着薄膜中含有更多的晶界，这样将导致Bi组分在晶界上的偏析较显著，而进入石榴石结构中氧十二面体间隙的Bi〓较少，对于Bi，Al∶DyIG来说，石榴石相晶格常数与{Bi〓}〓呈正相关关系，由此可以解释具有细小晶粒的薄膜对应较小的石榴石相晶格常数。

A dodecahedron with twelve regular pentagons as faces.

有十二个正五角形面的十二面体。

A mathematic model of foam fractionation was set up based on the following assumptions: adsorption equilibrium,same bubble size and regular dodecahedron model of real bubbles.

假设吸附过程始终处于平衡态、气泡大小均一以及每一个气泡均为正十二面体，构建了泡沫分离过程的数学模型。

The shock wave has made a nearly standard dodecahedron pattern on the surface of centre sphere. This pattern is the result of shock waves interaction from two adjacent detonating spots, and its position shows how the detonating of two adjacent spots acts, synchronized or not. The nice dodecahedron stroke patterns on the surface of recovered centre sphere indicate that this detonating method has good synchronization and spherical converging shock-wave.

通过试验，由十二个起爆点发出的爆轰波通过相互作用在回收球体的表面留下了近乎标准的正十二面体刻痕图案，球体表面的每一道刻痕都是相邻两个起爆点所发出的爆轰波相互作用的结果，每一道刻痕与相邻两个起爆点的位置关系反映了该两个起爆点的起爆同步性情况。

Goldberg got a class of polyhedra which are icosahedral symmetry by appending hexagons on regular dodecahedron by rule in 1937. They are called Goldberg polyhedra which provides a new approach for polyhedral molecule design.

1937年，数学家Goldberg通过在正十二面体上有规律地添加六边形面得到一类具有二十面体对称性的多面体，即Goldberg多面体。

Regular icosahedron ; regular dodecahedron ; quasicrystal ; conjugate fractal structural model ; conjugate fractal structural model of quasicrystal ; Penrose pattern ; high resolution structural image by electron microscopy.

正十二面体；正二十面体；准晶体；共轭分数维模型；准晶共轭结构模型； Penrose拼图；高分辨电子显微结构图

We obtain three classes of polyhedra which have high symmetry. they are regular tetrahedral class belonging to tetrahedral group , regular hexahedral class and regular octahedral class belonging to octahedral group.

本文将Goldberg在正十二面体上构筑多面体的方法推广到其它柏拉图多面体上，分别得到了三类具有较高对称性的多面体：属于四面体群的正四面体类和属于八面体群的正六面体类、正八面体类。

The continuing of the process produces icosahedra of even higher orders (a2, a3,…,an).

实质上，这一模型可以看成正二十面体与正十二面体共轭生成的结果。

We obtain three classes of polyhedra which have high symmetry.

本文将Goldberg在正十二面体上构筑多面体的方法推广到其它柏拉图多面体上，分别得到了三类具有较高对称性的多面体：属于四面体群的正四面体类和属于八面体群的正六面体类、正八面体类。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。