M_(π-)群的一个注记

设π是一个素数集合Isaacs建立了特征标π-理论,推广了Brauer模特征标理论.基于Isaacs的工作,定义了M_π-群,推广了M_p-群的概念,证明了若G是一个有限π-幂零群,则G是M-群当且仅当G是M-群.     

水热合成超分子网络化合物[Mn(phen)_2I_2] (phen=邻菲咯啉)及晶体结构

采用水热法设计并合成了一个新颖的超分子网络化合物[Mn(phen)_2I_2],并对其进行了元素分析,红外光谱分析和X-射线单晶衍射分析.结果表明:该化合物属三斜晶系, P_1~-空间群,晶胞参数为:a=0.92705(19) nm,b=1.0370(2) nm,c=1.2775(3) nm,α=77.32(3) °,β=81.26 (3) °,γ=70.30(3) °,V=1.1240(4) nm~3,Z= 2.该化合物通过四种C-H...I氢键相互作用与两种π-π堆积相互作用把各个独立的结构单元连接成了超分子网络化合物.     

Synthesis and Crystal Structure of catena-Poly[bis-(benzimidazole)cobalt(Ⅱ) μ- Phthalato]

The title polymeric complex [Co(C8H4O4)(C7H6N2)2]n has been prepared and its crystal structure was determined by X-ray diffraction method. The crystal belongs to monoclinic,space group C2/c with a = 7.7865(12), b = 20.4215(18), c = 13.4880(14) (A),β = 103.298(2)°, V = 2087.3(4) (A)3, Mr = 459.32, Z = 4, Dc= 1.462 g/cm3,μ = 0.859 mm-1, F(000) = 940, R = 0.0636 and wR = 0.1639 for 1278 observed reflections (I ＞ 2σ(Ⅰ)). The complex assumes a distorted tetrahedral coordination geometry, formed by two phthalate anions and two benzimidazoles (bzim). The phthalate anions bridge the neighboring Co(Ⅱ) atoms to form the polymeric chains. The centroid distance of 3.471(3) (A) between the parallel bzim rings of adjacent polymeric chains suggests the existence of π-π stacking.     

Adiabatic population transfer in effective three-level systems driven by laser beams

The population transfer in effective three-state systems driven by laser beams has been studied based on the theory of Lewis－Riesenfeld Hermitian invariants in the full- and partial-adiabatic approximations. A strict formulation of adiabatic conditions is given, and a new adiabatic condition for inducing a complete population transfer is found.     

Intermacrocyclic Interactions upon Stepwise Oxidations in a Monometallic Porphyrin Dimer: Ring versus Metal-Center Oxidations and Effect of Counter Anions

The effect of intermacrocyclic interactions was studied by controlled and stepwise oxidations of a monometallic silver(II) porphyrin dimer that contains a highly flexible ethane bridge. Monometallic dimers are unique systems and behave differently from their dimetallic analogues on the basis of their available sites for storing oxidizing equivalents. UV-visible spectrometry, ¹H NMR spectroscopy, XPS and single crystal X-ray diffraction studies clearly suggest the removal of the first electron from the metal center. The removal of the second electron occurred from the ring center to form a π-cation radical and, thereby, form a very unique mixed-valent species. However, unlike in all other ethane-bridged metalloporphyrin dimers reported earlier, the 2e-oxidized species showed quite unusual structures depending on the nature of counter ions. Ions, such as SbF₆, SbCl₆ and PF₆, are engaged in strong interactions with the porphyrin π-cation radical and causes substantial structural changes, including large deformation of the ring. The solid-state structure remains intact in solution as well. The observations are further supported by DFT calculations.      

具有素中心环的若干性质(英文)

给出了素中心环的若干新的性质 ,在具有素中心的条件下 ,我们证明了 :环的幂零元与强幂零元是一致的 ;环的素根与诣零根是相同的 ;环的满自同态是自同构 ;对于每个 a∈ R,序列 Ra Ra2 …是稳定的当且仅当对于每个 a∈ R,存在自然数 n使得 an是一个正则元 .研究了某些具有素中心的特殊环     

Using the Simplex Code to Construct Relative Difference Sets in 2-groups

Relative Difference Sets with the parameters (2a, 2b, 2a, 2a-b) have been constructed many ways (see davis, EB, jung, maschmidt, and pottsurvey for examples). This paper modifies an example found in arasusehgal to construct a family of relative difference sets in 2-groups that gives examples for b = 2 and b = 3 that have a lower rank than previous examples. The Simplex code is used in the construction.     

On maximal abelian subgroups in finite 2-groups

We determine here up to isomorphism the structure of any finite nonabelian 2-group G in which every two distinct maximal abelian subgroups have cyclic intersection. We obtain five infinite classes of such 2-groups (Theorem 1.1). This solves for p = 2 the problem Nr. 521 stated by Berkovich (in preparation). The more general problem Nr. 258 stated by Berkovich (in preparation) about the structure of finite nonabelian p-groups G such that A ∩ B = Z(G) for every two distinct maximal abelian subgroups A and B is treated in Theorems 3.1 and 3.2. In Corollary 3.3 we get a new result for an arbitrary finite 2-group. As an application of Theorems 3.1 and 3.2, we solve for p = 2 a problem of Heineken-Mann (Problem Nr. 169 stated in Berkovich, in preparation), classifying finite 2-groups G such that A/Z(G) is cyclic for each maximal abelian subgroup A (Theorem 4.1).      

有限可解群的若干充分条件

运用有限群的弱c-正规性,得到了有限可解群的若干充分条件,推广了相关文献的一些结果.