p-可分解群的一个定理

极小子群在有限群的研究中占据着重要的地位．本文利用了极小子群的弱c-正规性刻画了极小子群对有限群构造的影响，得出了p-可分解群的一个结果．     

高等师范学生教师职业技能训练及培养模式新论

高等师范学生的教师职业技能训练,自国家1995年《教师资格条例》颁布以来,虽在全国有关高校一度出现好的势头,但很快被我国高校扩招的形势冲淡了,目前情况令人担忧。因此,在我国高等教育发展的新形势下,从宏观上构建高等师范学生教师职业技能培养模式应是当务之急。     

四元数射影n-空间HPn的最小CW-复形伦型与它的法线数量特征

利用Morse理论给出四元数射影n-空间HP^n的CW-复形伦型的另个证明，并给出它的最小性与法线的一个数量特征。     

Consequences of an algorithm for bridged graphs

Chepoi showed that every breadth first search of a bridged graph produces a cop-win ordering of the graph. We note here that Chepoi's proof gives a simple proof of the theorem that G is bridged if and only if G is cop-win and has no induced cycle of length four or five, and that this characterization together with Chepoi's proof reduces the time complexity of bridged graph recognition. Specifically, we show that bridged graph recognition is equivalent to (C₄,C₅)-free graph recognition, and reduce the best known time complexity from O(n⁴) to O(n^3.376).     

求解随机变量数字特征的两种有效方法

求解随机变量的数字特征是数理统计中的一个重要课题，本文利用泰勒级数和条件数学期望给出了正态分布数字特征的求解方法，并将所得结果做了适当的推广。     

Anomalies in the Absorption and Reflection of a High-Power Ultrashort Laser Pulse by a Plasma with a Solid-State Density

The patterns of absorption and reflection of an ultrashort laser pulse by a plasma with a solid-state density, which are realized in the mode of the normal skin effect, are studied. It is shown that a decrease in low-power pulse duration shorter than the period corresponding to the fundamental frequency of radiation leads to an increase in the absorption coefficient. If the pulse power is so high as to provide electron heating during a time shorter than the reciprocal fundamental frequency, nonlinear suppression of absorption takes place and the spectrum of the reflected radiation contains odd harmonics of the fundamental frequency.     

A class of multivariate skew-normal models

The existing model for multivariate skew normal data does not cohere with the joint distribution of a random sample from a univariate skew normal distribution. This incoherence causes awkward interpretation for data analysis in practice, especially in the development of the sampling distribution theory. In this paper, we propose a refined model that is coherent with the joint distribution of the univariate skew normal random sample, for multivariate skew normal data. The proposed model extends and strengthens the multivariate skew model described in Azzalini (1985,Scandinavian Journal of Statistics,12, 171–178). We present a stochastic representation for the newly proposed model, and discuss a bivariate setting, which confirms that the newly proposed model is more plausible than the one given by Azzalini and Dalla Valle (1996,Biometrika,83, 715–726).     

Graceful Signed Graphs

A (p, q)-sigraph S is an ordered pair (G, s) where G = (V, E) is a (p, q)-graph and s is a function which assigns to each edge of G a positive or a negative sign. Let the sets E ⁺ and E ^– consist of m positive and n negative edges of G, respectively, where m + n = q. Given positive integers k and d, S is said to be (k, d)-graceful if the vertices of G can be labeled with distinct integers from the set {0, 1, ..., k + (q – 1)d such that when each edge uv of G is assigned the product of its sign and the absolute difference of the integers assigned to u and v the edges in E ⁺ and E ^– are labeled k, k + d, k + 2d, ..., k + (m – 1)d and –k, – (k + d), – (k + 2d), ..., – (k + (n – 1)d), respectively.In this paper, we report results of our preliminary investigation on the above new notion, which indeed generalises the well-known concept of (k, d)-graceful graphs due to B. D. Acharya and S. M. Hegde.     

Tail probabilities of the limiting null distributions of the Anderson–Stephens statistics

For the purpose of testing the spherical uniformity based on i.i.d. directional data (unit vectors) z_i, i=1,…,n, Anderson and Stephens (Biometrika 59 (1972) 613–621) proposed testing procedures based on the statistics S_max=max_u S(u) and S_min=min_u S(u), where u is a unit vector and nS(u) is the sum of squares of u′z_i's. In this paper, we also consider another test statistic S_range=S_max−S_min. We provide formulas for the P-values of S_max, S_min, S_range by approximating tail probabilities of the limiting null distributions by means of the tube method, an integral-geometric approach for evaluating tail probability of the maximum of a Gaussian random field. Monte Carlo simulations for examining the accuracy of the approximation and for the power comparison of the statistics are given.     

Highly edge‐connected detachments of graphs and digraphs

Let G = (V,E) be a graph or digraph and r : V → Z₊. An r‐detachment of G is a graph H obtained by ‘splitting’ each vertex ν ∈ V into r(ν) vertices. The vertices ν₁,…,ν_r(ν) obtained by splitting ν are called the pieces of ν in H. Every edge uν ∈ E corresponds to an edge of H connecting some piece of u to some piece of ν. Crispin Nash‐Williams 9 gave necessary and sufficient conditions for a graph to have a k‐edge‐connected r‐detachment. He also solved the version where the degrees of all the pieces are specified. In this paper, we solve the same problems for directed graphs. We also give a simple and self‐contained new proof for the undirected result. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 67–77, 2003