Finite p-Groups in Which the Number of Subgroups of Possible Order is Less Than or Equal to $p^3 $

In this paper, groups of order pn in which the number of subgroups of possible order is less than or equal to p3 are classified. It turns out that if p 2, n ≥ 5, then the classification of groups of order pn in which the number of subgroups of possible order is less than or equal to p3 and the classification of groups of order pn with a cyclic subgroup of index p2 are the same.     

基本超几何级数的变换公式及Rogers-Amanujan恒等式

本文通过组合反演技巧和级数重组的方法,得到了两个基本超几何级数的变换公式,其中一个的特殊情况包含了著名的Rogers-amanujan恒等式.     

有限表示型代数的一些刻画

Let A be a finite dimensional, connected, basic algebra over an algebraically closed field. We prove that A is of finite representation type if and only if there is a natural number m such that rad^m（End（M）） = 0, for any indecomposable A-modules M. This gives a partial answer to one of problems posed by Skowrofiski.     

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.     

Mirror objectives with variable focal length

We consider some issues involved in constructing a mirror system with a discrete variable focal length. We propose a procedure for designing two-mirror pancratic (zoom) systems with fixed image plane. In constructing the optimal layouts, we studied a basic two-mirror system to achieve minimum spherical aberration. We present the calculated design characteristics of an objective consisting of two spherical mirrors and providing a three-fold variation in focal length. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 76, No. 3, pp. 453–459, May–June, 2009.     

关于刚体的基本运动

文中介绍了恰斯尔定理和位移定理及两个定理的证明,最后得出刚体的一般运动都可看成是平动和定轴转动的合成运动的结论．这对于理解和处理刚体的运动是有益的．     

Some intersections and identifications in integral group rings

LetZG be the integral group ring of a groupG and I(G) its augmentation ideal. For a free groupF andR a normal subgroup ofF, the intersectionI ⁿ⁺¹ (F) ∩I ⁿ⁺¹ (R) is determined for alln≥ 1. The subgroupsF ∩ (1+ZFI (R) I (F) I (S)) ANDF ∩ (1 + I (R)I ³ (F)) of F are identified whenR and S are arbitrary subgroups ofF.     

Mulliken集居数的基本关系

Mulliken的集居数分析就是将MO的正交归一化关系向AO、AO重迭区或原子进行分解。本文即基于这一认识,对它作了统一详细的讨论,并以甲烷为例,对EHMO程序,FORTICON的主要输出结果给予了计算说明。     

有限交换环上线性群的Carter子群

令Ｒ为有限交换局部环，Ｋ为其剩余类域．本文研究了Ｒ上一般线性群ＧＬｎＲ的Ｃａｒｔｅｒ子群的存在性及结构．得到的结果是：若ｃｈａｒＫ为奇数或Ｋ＝Ｆ２，ＧＬｎＲ中存在唯一的Ｃａｒｔｅｒ子群的共轭类，即Ｓｙｌｏｗ－２子群的正规化子；若ｃｈａｒＫ＝２且｜Ｋ｜＞２，ＧＬｎＲ中不含Ｃａｒｔｅｒ子群．