关于有限群的可解性

利用极大子群的几乎正规的概念得到了有限群为可解群的若干充要条件．     

具有反馈控制的Logistic扩散系统周期解的存在与稳定

利用上下解，Ｂｒｏｕｗｅｒ不动点原理及Ｌｙａｐｕｎｏｖ泛函方法，讨论了一类具有反馈控制的Ｌｏｇｉｓｔｉｃ扩散系统的周期解问题；获得了周期解存在且稳定的判别条件．     

连续时延神经网络的Hopf分岔现象研究

讨论了带连续时延神经网络的Hopf分岔现象。对于强核和弱核的情况,利用平均时延作为分岔参数,证明了模型经历了Hopf分岔过程。在带弱核的神经网络模型中,得到了分岔周期解稳定性准则。给出了一些数值例子,通过计算机仿真验证了所得结论的正确性。     

Complete moment convergence and Lr convergence for asymptotically almost negatively associated random variables

In this paper, we investigate the complete moment convergence and L_r convergence for maximal partial sums of asymptotically almost negatively associated random variables under some general conditions. The results obtained in the paper generalize some corresponding ones for negatively associated random variables.     

Uniform consistency rate of kNN regression estimation for functional time series data

In this paper, we investigate the k-nearest neighbours (kNN) estimation of nonparametric regression model for strong mixing functional time series data. More precisely, we establish the uniform almost complete convergence rate of the kNN estimator under some mild conditions. Furthermore, a simulation study and an empirical application to the real data analysis of sea surface temperature (SST) are carried out to illustrate the finite sample performances and the usefulness of the kNN approach.     

光子晶体带隙结构的数值计算

该文简述了光子晶体的基本概念及基于平面波方法的理论分析。光子晶体是周期性介质结构,其带隙结构计算复杂,难于进行解析分析,只能使用数值模拟,所以关于光子晶体带隙的计算成为其理论研究的一个重要分支。该文在推导出一维光子晶体的解析解后,使用平面波方法在MATLAB下编写了通用的二维光子晶体能带结构计算程序,找到了出现最大带隙的结构参数,为设计和制作二维光子晶体提供了理论依据。     

Efficiency of the generalized-difference-based weighted mixed almost unbiased two-parameter estimator in partially linear model

In this paper, a generalized difference-based estimator is introduced for the vector parameter β in partially linear model when the errors are correlated. A generalized-difference-based almost unbiased two-parameter estimator is defined for the vector parameter β. Under the linear stochastic constraint r = Rβ + e, we introduce a new generalized-difference-based weighted mixed almost unbiased two-parameter estimator. The performance of this new estimator over the generalized-difference-based estimator and generalized- difference-based almost unbiased two-parameter estimator in terms of the MSEM criterion is investigated. The efficiency properties of the new estimator is illustrated by a simulation study. Finally, the performance of the new estimator is evaluated for a real dataset.     

Varying kernel marginal density estimator for a positive time series

This paper analyses the large sample behaviour of a varying kernel density estimator of the marginal density of a non-negative stationary and ergodic time series that is also strongly mixing. In particular we obtain an approximation for bias, mean square error and establish asymptotic normality of this density estimator. We also derive an almost sure uniform consistency rate over bounded intervals of this estimator. A finite sample simulation shows some superiority of the proposed density estimator over the one based on a symmetric kernel.     

Asymptotic behaviour of proportions of observations in random regions determined by central order statistics from stationary processes

In this paper, we show that proportions of observations that fall into a random region determined by a given Borel set and a central order statistic converge almost surely, provided that the corresponding population quantile is unique. We also describe three types of possible asymptotic behaviour of these proportions in the case of non-unique population quantile. As an application of our findings we establish limiting properties of numbers of ties with a central order statistics in a discrete sample. Our results are derived not only for independent and identically distributed observations but more generally for strictly stationary and ergodic sequences of random variables.     

文献研究中语言学方法的限度

学术研究中,语言学方法常常用于文献的断代研究,但是,这一方法是具有一定限度的。若干失误往往表现在方法论的预设,凡是某一时代文献没有记载的语汇就不属于该时代;且在语汇的时间层次、语言使用的差异性、语法的时间层次上皆有一定的盲区。认识这一现象,有助于我们在使用上述方法进行学术研究时确定其存在的限度。