五族非平凡群具有复杂性和对称性的特例，也更加难于预测。其中复杂部分的细节问题已经困扰了人们近120年。
The five non-simple groups—dubbed“exceptional” in their complexity and symmetry—are harder to envisage and, for almost 120 years, the details of the mostintricate of these have lain beyond reach.
并且依据广义条件对称和所考虑方程的相容性求得了相应方程的群不变解。
Exact solutions to the resulting equations are constructed via the compatibility of the generalized conditional symmetry and the considered equation.
鞋帮处的泡沫群、不对称背线和阿基里斯凹槽用于增强缓冲、支撑，提供全天的舒适感。
Anatomically-placed foam pods, an asymmetrical topline and a pronounced Achilles notch for enhanced cushioning, support and all-day comfort.
再次，运用二维轴对称有限元法以及三维有限元法，系统分析了挤扩支盘桩单桩和群桩的承载变形性状。
Thirdly, the bearing and deformation characteristics of single and group piles are investigated by means of axisymmetric finite element analysis (FEA) and three-dimensional FEA.
分别讨论了时空对称性和内部对称性及其与数学中的群的关系。
The space-time symmetry, the internal symmetry and the relation between the symmetries and the groups are discussed.
通过研究特殊四阶幻方的变换，结合对称群中的置换元素相互作用生成的轮换关系，给出了192阶和384阶变换群。
We will manifest the existence of the transformation groups of order 192 and 384 by studying the transformations and rotation relations.
通过研究特殊四阶幻方的变换，结合对称群中的置换元素相互作用生成的轮换关系，给出了192阶和384阶变换群。
We will manifest the existence of the transformation groups of order 192 and 384 by studying the transformations and rotation relations.
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