The Exterior Degree of a Pair of Finite Groups

The exterior degree of a pair of finite groups (G, N), which is a generalization of the exterior degree of finite groups, is the probability for two elements (g, n) in (G, N) such that g ? n = 1. In the present paper, we state some relations between this concept and the relative commutatively degree, capability and the Schur multiplier of a pair of groups.     

Protection of Alcohols and Phenols with Dihydropyran and Detetrahydropyranylation by ZrCl4

Alcohols and Phenols are protected efficiently with dihydropyran(DHP) in the presence of catalytic amounts of zirconium tetrachloride in dichloromethane. Deprotection of THP-ethers is also afforded in a methanolic solution at room temperature.     

Synthesis and properties of poly(ethylene oxide)‐grafted polyethylene copolymer and terpolymer

A series of graft copolymers were synthesized based on ethylene‐co‐m,p‐methylstyrene (EMS) (backbone copolymer), ethylene‐1‐hexene‐m,p‐methylstyrene (EHMS) (backbone terpolymer), and polyethylene glycol monomethyl ethers (PEGM) (grafts) in this study. The PEGMs with molecular weights of 750 and 2000 were used. The chemical composition of the graft copolymers was analyzed by NMR and DSC measurements. The graft copolymers exhibited a phase‐separated morphology with the backbone and the methoxy polyethylene glycol (MPEG) grafts forming separate crystalline phases. The MPEG phase had a melting temperature lower than the corresponding MPEG homopolymer, as determined by DSC. The melting point of the crystalline phase formed by the EMS and EHMS main chains was lower than that of pure polymer backbone. Copyright © 2009 John Wiley & Sons, Ltd.     

Rarefaction effects in thermally-driven microflows

Rarefied gas flow in a parallel-plate micro-channel is considered, where a streamwise constant temperature gradient is applied in the channel walls. An analytical approach to the problem is conducted based on linearized and semi-linearized forms of the regularized 13-moment equations (R13 equations), which are a set of macroscopic transport equations for rarefied gases at the super-Burnett order. Typical nonequilibrium effects at the boundary, i.e., velocity slip, temperature jump, and formation of Knudsen boundary layers are investigated. Nonlinear contributions lead to temperature, density, and normal stress profiles across the channel which are not reported elsewhere in literature.     

The converse of Schur’s theorem

Schur’s theorem states that for a group G finiteness of G/Z(G) implies the finiteness of G′. In this paper, we show the converse is true provided that G/Z(G) is finitely generated and in such case, we have |G/Z(G)| ≤ |G′| ^d(G/Z(G)). In the special case of G being nilpotent, we prove |G/Z(G)| divides |G′| ^d(G/Z(G)).     

A practical and versatile approach toward a one-pot synthesis of 2,3-disubstituted 4(3H)-quinazolinones

Abstract  

An effective one-pot three-component route to 4(3H)-quinazolinones from commercially available starting materials is reported. Thus, isatoic anhydride reacted with ammonium acetate or primary amines and aldehydes in the presence of iodine to produce the corresponding quinazolinone derivatives in moderate to good yields.     

Essential oil variation of Salvia officinalis aerial parts during its phenological cycle

In this paper the variation in the quantity and quality of the essential oil of Salvia officinalis during its life cycle stages is reported. The oils were obtained by hydrodistillation of air-dried samples. The yield of essential oil (w/w %) in different stages was in the order: floral budding (0.9%) > vegetative (0.7%) > flowering (0.5%) > immature fruit (0.4%) > ripen fruit (0.2%). The essential oils were analyzed by GC and GC-MS. In total, 36, 41, 40, 38, and 41 constituents were identified and quantified in the subsequent stages, respectively. Oxygenated monoterpenes were the main group of compounds in the fruiting set (56.9%), vegetative (48.5%), flowering (47.7%), and floral budding (45.3%) stage. 1,8-cineole as one of the major constituents of all samples was lower in the vegetative stage and gradually increased in subsequent harvesting times to reach a maximum in flowering and then decreased in the fruiting set. In contrast, the globulol content was higher in the first stage and decreased drastically during fruit maturation. Published in Khimiya Prirodnykh Soedinenii, No. 1, pp. 16–19, January–February, 2006.     

Efficient synthesis of mono- and disubstituted 2,3-dihydroquinazolin-4(1H)-ones using KAl(SO4)2·12H2O as a reusable catalyst in water and ethanol

KAl(SO₄)₂·12H₂O was found to catalyze efficiently a one-pot three-component cyclocondensation of isatoic anhydride and primary amines or ammonia sources such as (NH₄)₂CO₃, NH₄OAc and NH₄Cl with aromatic aldehydes under mild conditions to afford the corresponding mono- and disubstituted 2,3-dihydroquinazolin-4(1H)-ones in good yields.