本原半环的稠密性及Kaplansky定理

若半环S有忠实既约S－半模M，叫S为本原半环，证明了本原半环具有稠密性，然后在此基础上证明了名的Kaplansky定理，即PI－本原半环是单的，在其中民上是有限维的。     

基于密钥交换中离散对数生成元的研究

从离散对数的生成元的选择问题出发，根据欧拉定理和拉格朗日定理提出加快寻找生成元的简便算法，该算法的重要思想是：如果我们选择安全素P＝2＊Q＋1，则判断集合ZP中的元素是否是生成元的次数达到最少。该算法加快了生成元的寻找速度，节约了计算时间和计算空间。     

A paleontological perspective of vertebrate origin

The Early Cambrian Haikouichthys and Haikouella have been claimed to be related to contribute in an important way to our understanding of vertebrate origin,but there have been heated debates about how exactly they are to be interpreted. New discoveries of numerous specimens of Haikouichthys not only confirm the identity of previously described structures such as the dorsal and the ventral fins, and chevron-shaped myomeres, but also reveal many new important characteristics, including sensory organs of the head (e.g. large eyes), and a prominent notochord with differentiated vertebral elements. This “first fish” appears, however, to retain primitive reproductive features of acraniates, suggesting that it is a stem-group craniates. A new order (Myllokunmingiida) and a new family (Myllokunmingiidae) are erected, and a new species, Zhongjianichthys rostratus (gen. et sp. nov.), is described herein. Over 1400 newly-discovered specimens of Haikouella provide a wealth of anatomical information on this organism. It differs from chordates in many organs and organ systems, including the skin, muscles, respiratory, circulatory and nervous systems.In contrast, its body-design resembles that of vetulicolians,and the presence of a “transitional” nervous system with both dorsal and ventral nerve cords suggests an affinity with living hemichordates. On the basis of these and other recent findings of fossil deuterostomes, a five-step hypothesis for vertebrate origin is proposed, intended to bridge the long-standing gap between protostomes and vertebrates. Four of the five steps accord with established ideas current in modern evolutionary zoology. Evidence for the first step is obtainable only from fossils, and specifically from fossils found from South China, hence the crucial importance of S. China sites for our understanding of early vertebrate origins and evolution. Accordingly, South China is suggested as the oldest-known birthplace of the whole vertebrates.     

Distribution of 0 and 1 in the highest level of primitive sequences overZ/(2 e ) (II)

The distribution of 0 and 1 is studied in the highest level a_{r− 1} of primitive sequences over Z/(2^e). It is proved that the proportion of 0 (or 1) in one period of a_{e 1} is between 40% and 60% for e≥8.     

素AW—代数A的本原性的证明

讨论了不可分素Ｃ－代数与本原Ｃ－代数的关系问题,给出了素ＡＷ－代数的本原性的证明。     

求解一般粘性阻尼多自由度系统瞬态响应的原坐标分析法及程序设计

本文应用复模态理论和线性系统振型迭加原理,采用原坐标分析法,建立了一般粘性阻尼多自由度系统对任意激振力的瞬态响应的新的数学模型,并编制了相应的计算机程序。本文所建立的方法和程序,既可以用来求解系统的位移瞬态响应,又能用来直接求解系统的弹性力(或弹性力矩)的瞬态响应。该程序已用于工程实际计算,得到满意的结果。     

围长为2的n阶本原有向图的Lewin指数集

分析了围长为2的n阶本原有向图的l(G)的上界及相应的指数集,并讨论了极端情形.