代数表示论简介与综述

代数表示论是本世纪七十年代初兴起的代数学的一个新的分支。它的基本内容是研究一个Ａｒｔｉｎ代数上的模范畴。由于各国代数学家的共同努力，这一理论于最近二十年代有了异常迅猛的发展并逐步趋于完善。本文介绍了代数表示论的理论基础；几乎可裂序列；箭图和赋值箭图的表示；Ｃｏｘｅｔｅｒ函子；ＡＲ－箭图的覆盖及代数的Ｇａｌｏｉｓ覆盖。并简单介绍了在代数表示论中普遍应用的工具：Ｔｉｌｔ理论，以及著名的Ｄｐｏｚｇ定理证     

通用电学实验设备最大效益的探索与实践

为充分发挥通用电学实验设备的最大效益，我们从实验设备性能测试及原理图绘制与认识、实验教材的编写、实验室规章制度制定和完善、办成开放实验室等方面进行了探索与实践，并取得较好的效果。     

Local Polynomial Regression: Optimal Kernels and Asymptotic Minimax Efficiency

We consider local polynomial fitting for estimating a regression function and its derivatives nonparametrically. This method possesses many nice features, among which automatic adaptation to the boundary and adaptation to various designs. A first contribution of this paper is the derivation of an optimal kernel for local polynomial regression, revealing that there is a universal optimal weighting scheme. Fan (1993, Ann. Statist., 21, 196-216) showed that the univariate local linear regression estimator is the best linear smoother, meaning that it attains the asymptotic linear minimax risk. Moreover, this smoother has high minimax risk. We show that this property also holds for the multivariate local linear regression estimator. In the univariate case we investigate minimax efficiency of local polynomial regression estimators, and find that the asymptotic minimax efficiency for commonly-used orders of fit is 100% among the class of all linear smoothers. Further, we quantify the loss in efficiency when going beyond this class.     

画法几何在多功能机用虎钳装夹过程中的应用

该文运用画法几何中旋转法的理论，讨论利用多功能机用虎钳加工各种特殊位置的斜孔、斜面以及刃磨车床刀具的可行性，并分析在３种情况下，其装夹过程中工艺角度的图解计算方法。文中还运用解析法对３种情况下得出的工艺角度计算公式进行了精确验证，并在加工过程中作了具体应用，达到了加工精度的要求     

普通车床主轴组件设计中几个问题的探讨

本文就普通车床主轴组件设计时所涉及到的有关主轴组件最高转速与最低转速的确定、主轴组件支承的确定、滚动轴承类型的选定、各种滚动轴承搭配及每一种搭配方案的工作指标等问题,进行了研究,并提出一些看法。     

泛代数的商代数及其应用

对泛代数的合同关系和商代数作些讨论，主要涉及诱导的合同关系，关于合同关系的几个结果、商代数和同态定理、积代数的商代数等，分别得到了一些结果，并给出它们的一些应用。     

Emergence of life—how and where?—An update based on recent ideas

Panspermic origins notwithstanding, life, assuming that it started on Earth, may have taken root as soon as it became geologically permissible. There are multiple possibilities for early biogenesis from complex inorganic/organic geochemistry at diverse geological niches. Recent theoretical calculations have revived the possibility of Earth having a rather reduced early atmosphere, and had refueled arguments for a surface origin of life. Laboratory modeling of possible prebiotic RNA polymerization has seen interesting experimental advances, although a plausible replicator-like molecule has not yet been produced. The hydrothermal origin school of thought has also seen an interesting postulation for life’s early emergence and evolution—within contiguous, porous hydrothermal iron-sulfide (FeS) compartments, leading to a non-free living last universal common ancestor (LUCA). A confined LUCA evolving later into free-living archaebacteria and eubacteria could potentially reconcile some problems of molecular divergence between these two kingdoms. There are, however, many unresolved problems, and experimental evidence for such a scheme is lacking. Here, recent updates and refinements to the mainstay hypotheses for the emergence of life on Earth are reviewed and discussed.     

First-principles calculation of transport property in nano-devices under an external magnetic field

The mesoscopic quantum interference phenomenon （QIP） can be observed and behaves as the oscillation of conductance in nano-devices when the external magnetic field changes. Excluding the factor of impurities or defects, specific QIP is determined by the sample geometry. We have improved a first-principles method based on the matrix Green＇s function and the density functional theory to simulate the transport behaviour of such systems under a magnetic field. We have studied two kinds of QIP： universal conductance fluctuation （UCF） and Aharonov Bohm effect （A-B effect）. We find that the amplitude of UCF is much smaller than the previous theoretical prediction. We have discussed the origin of difference and concluded that due to the failure of ergodic hypothesis, the ensemble statistics is not applicable, and the conductance fluctuation is determined by the flux-dependent density of states （DOSs）. We have also studied the relation between the UCF and the structure of sample. For a specific structure, an atomic circle, the A-B effect is observed and the origin of the oscillation is also discussed.     

Properties of the Absolute That Affect Smoothness of Flows on Closed Surfaces

Let be a closed orientable surface of genus , endowed with the structure of a Riemann manifold of constant negative curvature. For the universal covering , there is the notion of absolute, each of whose points determines an asymptotic direction of a bundle of parallel equidirected geodesics. In the paper it is proved that there is a set on the absolute having the cardinality of the continuum and such that if an arbitrary flow on has a semitrajectory whose covering has asymptotic direction defined by a point from , then this flow is not analytical and has infinitely many stationary points.