On Normal Embedding of Subgroups

We survey conditions for a group to allow an embedding as a normal subgroup of another finite group, with an additional condition of containment in some given characteristic subgroup. The main objects will be finite p-groups.     

相对Hopf模和广义cleft扩张

本文研究了π-cleft扩张的余代数分解问题及对偶的η-cocleft扩张的代数分解问题.利用相对Hopf模结构定理,给出了一个条件,使得具有余代数结构的π-cleft扩张有较好的余代数分解形式.作为特例,可以重新得到Radford给出的具有投射的双代数的双积分解定理.     

Embeddings of minimal non-abelian p-groups

By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. For a given finite group G, let p(G) denote the minimal degree of a faithful representation of G by permutation matrices, and let c(G) denote the minimal degree of a faithful representation of G by quasi-permutation matrices. See [4]. It is easy to see that c(G) is a lower bound for p(G). Behravesh [H. Behravesh, The minimal degree of a faithful quasi-permutation representation of an abelian group, Glasg. Math. J. 39 (1) (1997) 51-57] determined c(G) for every finite abelian group G and also [H. Behravesh, Quasi-permutation representations of p-groups of class 2, J. Lond. Math. Soc. (2) 55 (2) (1997) 251-260] gave the algorithm of c(G) for each finite group G. In this paper, we first improve this algorithm and then determine c(G) and p(G) for an arbitrary minimal non-abelian p-group G.     

Theoretical evaluation to improve the performance of composite wax powder: cooperativity effects involving the strong Na+···π/σ and weak hydrogen-bonding interactions in the complex of graphene oxide with Na+ and CH4

ABSTRACT

To provide a reasonable design scheme to improve the performance of composite wax powder, the ternary complex Na⁺···graphene oxide (GO)···CH₄ was selected as a model system to evaluate the cooperativity effect between the Na⁺···σ/π and H-bonding interactions in the composite wax powder doped with GO at the M06-2X/6-311++G(2d,p) and MP2/6-311++G(2d,p) levels. The cooperativities in GO···(CH₄)_n (n?=?1～10) and thermodynamic cooperativity effects in Na⁺···GO···CH₄ were also investigated. Although the changes of the absolute values of H-bonding interactions were slight, from those of relative values, the influence of the Na⁺···π or Na⁺···O interaction on the C–H···π, O–H···C or C–H···O interaction was notable upon the formation of ternary systems. The anti-cooperativity effect was found in the cyclic structure, while the cooperativity effect appeared in the linear conformation. The Na⁺···σ/π and H-bonding interactions as well as cooperativities in Na⁺···GO···CH₄ were stronger than those in Na⁺···coronene···CH₄. The formation of Na⁺···GO···CH₄ is a thermodynamic cooperativity process driven by the enthalpy change. Therefore, it could be inferred that, when graphite powder or carbon black was replaced by GO, the compatibilities could be strengthened among various components, and thus the performance of casting moulds could be improved. Atoms-in-molecules (AIM) and reduced density gradient (RDG) analyses confirmed the cooperativity effect and revealed the nature of the improved performance of composite wax powder with GO. The GO···(CH₄)_n (n?=?1～3) are positively cooperative, while the negative cooperativity is shown when n?=?4～10.     

M2Al2(M=Au,Ag,Cu)混合小团簇的密度泛函研究

采用基于密度泛函理论的B3LYP方法,利用小核实赝势LANL2DZ,优化了含重金属二元混合团簇M2Al2(M=Au,Ag,Cu)的稳定结构,并得出具有C2v(1A1)对称性的蝴蝶结构比平面构型更加稳定,其中团簇Au2Al2最稳定.计算了稳定结构的结合能、电离势、电子亲和能、最高占据轨道能级和最低空轨道能级及二者间的能隙,得出参杂团簇M2Al2比非参杂团簇M4(M=Au,Ag,Cu)更稳定的结论.     

P型NFDE的(h_0,h,M_0)稳定性

本文将M0稳定性结合欢度量的概念推广到P型NFDE，并给出了稳定性的几个定理．     

Characteristic properties of large subgroups in primary abelian groups

SupposeG is an arbitrary additively written primary abelian group with a fixed large subgroupL. It is shown thatG is (a) summable; (b) σ-summable; (c) a Σ-group; (d) p^ω+1-projecrive only when so isL. These claims extend results of such a kind obtained by Benabdallah, Eisenstadt, Irwin and Poluianov,Acta Math. Acad. Sci. Hungaricae (1970) and Khan,Proc. Indian Acad. Sci. Sect. A (1978).     

Magnetic Interactions in Insulating BEDT-TTF Salts

Inter-dimer magnetic interactions J in BEDT-TTF (bis(ethylenedithio)tetrathiafulvalene) salts in the Mott insulator regime are estimated from the intermolecular overlap integrals. The estimated J values are compared with the experimental results, and the stable spin alignment and the dimensionality of the spin systems are discussed.     

The Chemistry of the Cyaphide Ion

We review the known chemistry of the cyaphide ion, (C≡P)⁻. This remarkable diatomic anion has been the subject of study since the late nineteenth century, however its isolation and characterization eluded chemists for almost a hundred years. In this mini-review, we explore the pioneering synthetic experiments that first allowed for its isolation, as well as more recent developments demonstrating that cyaphide transfer is viable in well-established salt-metathesis protocols. The physical properties of the cyaphide ion are also explored in depth, allowing us to compare and contrast the chemistry of this ion with that of its lighter congener cyanide (an archetypal strong field ligand and important organic functional group). Recent studies show that the cyaphide ion has the potential to be used as a versatile chemical regent for the synthesis of novel molecules and materials, hinting at many interesting future avenues of investigation.     

Recent Development of SnII,SbIII-based Birefringent Material: Crystal Chemistry and Investigation of Birefringence

The combination of Sn^II or Sb^III with π, non-π-conjugated units has produced birefringent crystals with birefringence ranging from 0.005 to 0.468@1064 nm. It is proven that introducing Sn^II or Sb^III into crystals is a feasible strategy to enlarge the birefringence, which not only promotes the miniaturization of fabricated devices, but also effectively modulates polarized light. Herein, recently discovered Sn^II, Sb^III-based birefringent crystals with birefringence investigated are summarized, including their crystal structure and optical properties, especially birefringence. This review also presents the influence of Sn^II, Sb^III with stereochemically active lone pair on the optical anisotropy. We hope that this work provides a clear perspective on the crystal chemistry of Sn^II, Sb^III-based optical functional crystals and promotes the development of new birefringent crystals with large optical anisotropy.