关于分子和晶体对称性的几个问题

Schenflies记号和国际记号描写对称性时,常常由于一号多义导致混乱。本文提出了克服这种混乱的建议,确立了对称元素Sn与n、点群n与Sn的关系。依据群论的观点将32个晶体点群划分为7个晶系,每个晶系以最大子群为代表并包括所属的其他子群     

论社会结构的对称与非对称

对作为自然界中一种普遍现象和联系的对称与非对称，自然科学已进行了较为深入持久的研究，并且取得了可喜的成绩。但对称与非对称是否也存在于人类社会，它们在自然界中所形成的规律，是否也适用于人类社会？本文试图通过对社会结构中的对称与非对称现象及其规律的考察，进一步揭示社会发展的内在原因和外在表现，以及对称、非对称与社会规律的关系。     

Testing a block exchangeable covariance matrix

Testing hypotheses about the structure of a covariance matrix for doubly multivariate data is often considered in the literature. In this paper the Rao's score test (RST) is derived to test the block exchangeable covariance matrix or block compound symmetry (BCS) covariance structure under the assumption of multivariate normality. It is shown that the empirical distribution of the RST statistic under the null hypothesis is independent of the true values of the mean and the matrix components of a BCS structure. A significant advantage of the RST is that it can be performed for small samples, even smaller than the dimension of the data, where the likelihood ratio test (LRT) cannot be used, and it outperforms the standard LRT in a number of contexts. Simulation studies are performed for the sample size consideration, and for the estimation of the empirical quantiles of the null distribution of the test statistic. The RST procedure is illustrated on a real data set from the medical studies.     

论分形艺术美的本质

分形艺术是基于分形几何理论所创建的一类奇特的新媒体艺术,是计算机技术在图形图像艺术领域的应用,富于视觉冲击力,具有非同寻常的美感。分形几何具有自相似和分数维两大重要特征,它们正是分形艺术美感的数学缘起。此外,分形艺术也是一门创造艺术,分形艺术家运用数学算法作为画笔来进行造型、色彩设计,这种艺术灵感的挥洒过程实现了美的创造。基于分形理论和数学方法创作的分形艺术,不仅象征了科学与艺术自然而完美的结合,更具有独特的美学意义。从美学角度来分析,分形艺术具有数学和谐、标度对称和奇异性等特点,在超越传统美学标准审美的同时形成其独特的审美感染力,而分形艺术这种活跃的生命力正是分形美的本质。     

试用导数法判断曲线的对称性

利用函数的奇偶性和导数的有关概念,推导了几个用导数的方法判断函数图象对称性的结论,并通过实例验证了这些结论对判断一般曲线的对称性是方便可行的.     

What’s in a face? Facial appearance associated with emergence but not success in entrepreneurship

Facial appearance has been associated with leader selection in domains where effective leadership is considered crucial, such as politics, business and the military. Few studies, however, have so far explored associations between facial appearance and entrepreneurship, despite the growing expectation that societies project on entrepreneurs for providing exemplary leadership in activities leading to the creation of disruptive start-ups. By using computer vision tools and a large-scale sample of entrepreneurs and non-entrepreneurs from Crunchbase, we investigate whether three geometrically based facial characteristics - facial width-to-height ratio (fWHR), cheekbone prominence, and facial symmetry - as well as advanced statistical models of whole facial appearance, are associated with a) the likelihood of an individual to emerge as an entrepreneur and b) the performance of the company founded by that individual. We find that cheekbone prominence, facial symmetry and two whole facial appearance statistical models are associated with the likelihood of an individual to emerge as an entrepreneur. In contrast to entrepreneurship emergence, none of the examined facial characteristics are associated with performance. Overall, our results suggest that facial appearance is associated with the emergence of leaders in the entrepreneurial endeavor, however, it is not informative about their subsequent performance.     

试论文本双层时空与主体对称

书面叙事文本的物质层面与话语意义层面分别表征不同的时空。真实文本“事”在“叙”前,双层时空可以导通;虚构文本“事”在“叙”后,文本虚拟时空孤立封闭。既定阅读程式并未严格分辨“事”与“叙”的两种逻辑关系。主体对称性分析则需引入“形式叙述者”和“形式受述者”概念