有限CN-p-群

每个子群都C-正规的有限群称为CN-群.本文首先给出二元生成的CN-p-群的完全分类.在此基础上得到CN-p-群的结构:当p为奇素数时,有限群G为CNp-群当且仅当G的每个元都平凡地作用在Φ(G)上;有限群G为CN-2-群当且仅当对任意给定的a∈G,都有对任意g∈Φ(G),g~a=g或者对任意g∈Φ(G),g~a=g~(-1).最后给出两个CN-p-群的直积是CN-p-群的判定条件.     

Steady-state and Hopf bifurcations in the Langford ODE and PDE systems

This paper is concerned with the Langford ODE and PDE systems. For the Langford ODE system, the existence of steady-state solutions is firstly obtained by Lyapunov–Schmidt method, and the stability and bifurcation direction of periodic solutions are established. Then for the Langford PDE system, the steady-state bifurcations from simple and double eigenvalues are intensively studied. The techniques of space decomposition and implicit function theorem are adopted to deal with the case of double eigenvalue. Finally, by the center manifold theory and the normal form method, the direction of Hopf bifurcation and the stability of spatially homogeneous and inhomogeneous periodic solutions for the PDE system are investigated.     

Two-electron entanglement in elliptically deformed quantum dots

Entropic entanglement measures of a two-dimensional system of two Coulombically interacting particles confined in an anisotropic harmonic potential are discussed in dependence on the anisotropy and the interaction strength. The harmonic approximation appears exact in the strong interaction limit, allowing determination of the asymptotic expression for the linear entropy. Entanglement properties are dramatically influenced by the anisotropy of the confining potential in the strong-correlation regime.     

Atom-Efficient,Solvent-Free,Green Synthesis of Chalcones by Grinding

An improved Claisen–Schmidt condensation reaction of methyl ketones and aromatic aldehydes can be achieved by grinding at room temperature in the absence of solvents. This process is simple, efficient, economical, and environmentally benign compared to classical reactions.     

Facile Denitrosation of Cyclic N-Nitrosamines with Hydrazoic Acid

Abstract

A simple and facile method for the denitrosation of cyclic N-nitrosamines using HN₃ (concentrated H₂SO₄ + NaN₃) is reported. In this method, limited usage of this reagent does not affect the carbonyl group.     

Synthesis of New Iminocoumarins Bearing Parabanic Moieties

The synthesis of novel substituted 3-p-nitro-phenyliminocoumarins and corresponding N-ureaiminocoumarins is described. The condensation of these materials with oxalyl chloride leads to the corresponding N-parabanic iminocoumarins, which have not previously been described, in moderate or good yields and high selectivity. The structures were characterized by Fourier transform infrared, ¹H and ¹³C NMR, and elemental analysis.

Synthesis and Characterization of New Chalcone Derivatives from cis-Bicyclo[3.2.0]hept-2-en-6-one

A series of chalcone derivatives (3a–k) were prepared via the reaction of cis-bicyclo[3.2.0]hept-2-en-6-one (1) with the respective arylaldehydes (2a–k) and were then characterized by Fourier transform infrared (FT-IR), ¹H NMR, ¹³C NMR, and elemental analyses.     

Synthesis of Betulin-3-yl-β-D-Glucopyranoside

Two concise routes toward betulin-3-yl-β-D-glucopyranoside, being different in the protection of primary alcohol of betulin, were developed. The synthesis adopted a stepwise glycosidation method employing glycosyl trichloroacetimidate as donor.     

Ugi three-component coupling reaction for the synthesis of 2-(6-oxo-11-phenyl-7,8-dihydrobenzo[b]pyrrolo[1,2-d][1,4]diazocin-5(6H)-yl)-2-phenylacetamide derivatives

A three-component, four center Ugi reaction of 3-(1-(2-aminophenyl)-5-phenyl-1H-pyrrol-2-yl)propanoic acid with aromatic aldehyde and t-butyl isocyanide has been achieved to produce a novel class of N-tert-butyl-2-(6-oxo-11-phenyl-7,8-dihydrobenzo[b]pyrrolo[1,2-d][1,4]diazacine-5(6H)-yl)-2-phenylacetamides in moderate to good yields.