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正四面体群
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  tetrahedral group
     Assuming that neutrinos have Majorana masses and imposing the discretesymmetry——tetrahedral group T upon the three-lepton SU(2)L×U(1)B-Lmodel, we find that various conserved additive lepton numbers can beunified by the discrete symmetry T, and that the corresponding neutrinomass matrices are given by the vaccum breaking of Higgs fields introduced.
     本文假定了中微子具有Majorana质量,并把分立对称性——正四面体群T引入3代轻子的SU(2)_L×U(1)_(B-L)模型中。 在此框架下,各种可能的相加轻子数可以统一在3代中微子间的分立对称性T之下,相应的中微子质量矩阵由引入的Higgs场的真空破缺所确定。
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  相似匹配句对
     Group B contains T.
     B由T .
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     HOMOMORPH-GROUP
     态
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     ENUMERATION AND DISTRIBUTION OF A TETRAHEDRAL LATICE AND ITS APPLICATIONS
     正四面体晶格的计数、分布及其应用
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     Hausdorff measure of Sierpinski block generated by normal tetrahedron
     正四面体生成的Sierpinski块的Hausdorff测度
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     Hausdorff Dimension of Sierpinski Block Generated by Normal Tetrahedron
     关于正四面体生成的Sierpinski块的Hausdorff维数
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  tetrahedral group
Comparison with the tetrahedral group IV solids affords some clues to the nature of the doped materials.
      
Comparison with the tetrahedral group IV solids affords some clues to the nature of the doped materials.
      
It is proved that among the finite groups of order 24 only the binary tetrahedral group is not determined by its endomorphism semigroup in the class of all groups.
      
The tetrahedral group, or straight tetrahedron group, is the set of points of a tetrahedron with 24 symmetry operators.
      


Assuming that neutrinos have Majorana masses and imposing the discretesymmetry——tetrahedral group T upon the three-lepton SU(2)L×U(1)B-Lmodel, we find that various conserved additive lepton numbers can beunified by the discrete symmetry T, and that the corresponding neutrinomass matrices are given by the vaccum breaking of Higgs fields introduced.The mass relation among three generations of neutrinos is: mv_τ= mv_μ+ mv_e.

本文假定了中微子具有Majorana质量,并把分立对称性——正四面体群T引入3代轻子的SU(2)_L×U(1)_(B-L)模型中。在此框架下,各种可能的相加轻子数可以统一在3代中微子间的分立对称性T之下,相应的中微子质量矩阵由引入的Higgs场的真空破缺所确定。文中也给出了3代中微子质量间的质量关系:m_(v_τ)=m_(v_μ)+m_(v_e)。

A new approach for the representation of 3D general Julia sets is put forward on the basis of tri-dimensional polynomial maps. The condition for a 3D polynomial map to be equivariant is theoretically analyzed and proved. The equations of two classes of 3D polynomial maps that are equivariant with respect to the rotational symmetries of either a regular tetrahedron group or a regular octahedron group are strictly given, on the basis of which the properties of the general Julia sets created by these 3D polynomial...

A new approach for the representation of 3D general Julia sets is put forward on the basis of tri-dimensional polynomial maps. The condition for a 3D polynomial map to be equivariant is theoretically analyzed and proved. The equations of two classes of 3D polynomial maps that are equivariant with respect to the rotational symmetries of either a regular tetrahedron group or a regular octahedron group are strictly given, on the basis of which the properties of the general Julia sets created by these 3D polynomial maps are discussed and proved. A ray-tracing volume rendering algorithm, which defines the color and opacity of every discrete point within a Julia set according to its escaping distance, is proposed in order to acquire high quality 3D fractal images. Experimental results demonstrate that the approach of generating 3D Julia sets from 3D polynomial maps not only enables us to predict the characteristics of Julia sets according to the properties of the maps, but also makes it possible for us to obtain various kinds of Julia sets with different rotational symmetries by altering the parameters of the maps. Consequently, drawbacks such as monotone structure of the resulting fractals and inability to predict fractal shape in the existing methods for generating 3D fractal sets can be effectually avoided. Furthermore, the method of generating 3D Julia sets by 3D polynomial maps can be applied to the construction of other 3D fractals, and hence would result in a different perspective for the generation of 3D fractals.

研究了基于三维多项式映射的三维广义Julia集表示方法.从理论上分析并证明了三维多项式映射满足等变的条件,精确地给出了关于正四面体群和正八面体群具有旋转不变对称性的两类三维等变映射的具体公式,在此基础上讨论并证明了三维多项式映射的广义Julia集所具有的性质.提出了基于逃逸距离色彩调配的光线跟踪体绘制算法,对给定三维空间中属于Julia集的离散点根据其逃逸距离赋予颜色和不透明度,并采用光线跟踪法进行体绘制.实验结果表明,利用三维多项式映射来构造三维Julia集,不仅可以根据映射的性质预知Julia集的总体结构特征,并且能够通过调控映射的参数来获得多种具有不同旋转对称结构的Julia集,因而有效地克服了现有三维分形集生成方法所构造的分形集包含信息量少、形状结构单一和分形形状无法预测等缺陷.进一步地,三维多项式映射可以应用于其他三维分形的构造,从而为三维分形的生成提供一个新的有效途径.

 
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