关于有限群子群的弱S-可补性

设G是一个有限群,H是G的一个子群.称H为G的一个s-置换子群,若对于G的任意Sylow子群P,成立HP=PH.称H为G的一个弱s-可补的子群.若存在G的一个子群T,使得G=HT且H∩T≤H_s G,其中H_s G是包含在H中的G的最大的s-置换子群.本文在假设G的某些子群是弱s-可补的前提下,得到了G的一个结构定理,并推广了许多近期的结果.     

有限群的$p$-覆盖远离子群及$S$-拟正规嵌入子群

Let G be a finite group, p the smallest prime dividing the order of G and P a Sylow p-subgroup of G. If d is the smallest generator number of P, then there exist maximal subgroups P1, P2,..., Pd of P, denoted by Md(P) = {P1,...,Pd}, such that di=1 Pi = Φ(P), the Frattini subgroup of P. In this paper, we will show that if each member of some fixed Md(P) is either p-cover-avoid or S-quasinormally embedded in G, then G is p-nilpotent. As applications, some further results are obtained.     

本质子系满足链条件

Let S be a semigroup with zero and an S-act be a centered left S-act. This paper is devoted to the study of chain conditions on PS-acts. We prove that a PS-act having finite decomposition has ACC (DCC) on all subacts if it has ACC (DCC) on essential subacts. Moreover, a PS-act with ACC (DCC) on essential subacts has ACC (DCC) on all subacts if and only if it has finite decomposition. We characterize the structure of a PS-act and generalize some results of the Goldie dimension and semisimple S-acts.     

正则轨道的存在性与有限群的幂零长

本文给出了一些正则轨道存在性的条件，结合Ａ．Ｔｕｒｕｌｌ的近期定理，得到了关于有限可解群的幂零长的一些结论．     

关于允许一个无不动点自同构群的有限群的可解性

关于允许一个无不动点自同构(群)的有限群的可解性的猜想是有限群研究中的一个重要问题。结果比较丰富的是限制该自同构群为一个p-群的情形。Thompson于1959年证明了p阶群的情形。Martineail于1971年证明了初等Abel p-群的情形。Rickman于1979年证明了p²阶群的情形。本文借助Glauberman的一个定理,对p=2或3的一般情形给出了肯定的回答。实际上是用较初等的方法证明了更为广泛一些的结论。     

p-幂零群的一个判定准则（英文）

设G是一个有限群,P是G的一个Sylow p-子群.在N_G(P)为p-幂零的假设下,通过假定P的一个特殊的子群在G中满足覆盖远离性,本文给出了G为p-幂零群的一个判定准则.     

A COMPARISON OF FORECASTING MODELS OF THE VOLATILITY IN SHENZHEN STOCK MARKET

Based on the weekly closing price of Shenzhen Integrated Index, this article studies the volatility of Shenzhen Stock Market using three different models: Logistic, AR(1) and AR(2). The time-variable parameters of Logistic regression model is estimated by using both the index smoothing method and the time-variable parameter estimation method. And both the AR(1) model and the AR(2) model of zero-mean series of the weekly closing price and its zero-mean series of volatility rate are established based on the analysis results of zero-mean series of the weekly closing price. Six common statistical methods for error prediction are used to test the predicting results. These methods are: mean error (ME), mean absolute error (MAE), root mean squared error (RMSE), mean absolute percentage error (MAPE), Akaike's information criterion (AIC), and Bayesian information criterion (BIC). The investigation shows that AR(1) model exhibits the best predicting result, whereas AR(2) model exhibits predicting results that is intermediate between AR(1) model and the Logistic regression model.