Eigen-spectra in the Dirac-attractive radial problem plus a tensor interaction under pseudospin and spin symmetry with the SUSY approach

We approximately solve the Dirac equation for attractive radial potential including a Coulomb-like tensor interaction under pseudospin and the spin symmetry limit for any arbitrary spin-orbit quantum number, by employing the supersymmetric （SUSY） quantum mechanics and supersymmetric shape invariance technique. We obtain the energy eigenvalue equation under the pseudospin and spin conditions. Some numerical results are compared with those obtained by the Nikiforove-Uvarov （NU） method.     

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.     

Ultrasound promoted selective synthesis of 2-aryl-5,6-dihydro-4H-1,3-oxazines catalyzed by K-10 and KSF montmorillonite clays: A practical procedure under mild and solvent-free conditions

Montmorillonite K-10 and KSF were found to be highly efficient, environmentally friendly and recyclable heterogeneous catalysts for the selective synthesis of a variety of 2-aryl-5,6-dihydro-4H-1,3-oxazines from arylnitriles and 3-amino-1-propanol under ultrasound irradiation. This new methodology provides excellent yields in short reaction times (10–25 min). The reaction work-up is very simple and the catalysts can be easily separated from the reaction mixture and reused several times in subsequent reactions. This catalytic system also exhibits excellent chemoselectivity in the synthesis of mono-oxazines from dinitriles.     

Ab initio and DFT studies of hydrogen bond interactions in difluoroacetic acid dimer

Density functional theory (DFT) and ab initio calculations were performed for difluoroacetic acid (DFA). Eight theoretically possible conformers were considered and by using conformational analysis only three stable conformers were found. The hydrogen bonding interaction of DFA complex has been investigated using DFT and ab initio methods for cis conformers. Stabilization energies of dimers including basis set superposition error and ZPE were found in the range 8.89–13.08 kcal mol⁻¹. It was found that EFC dimer is slightly more stable. Red shift of O–H bond in the range −226.3 to 505.7 cm⁻¹ predicted for dimers. The natural bond orbital analysis was applied to characterize nature of the interaction.     

Sonochemical synthetic methods to produce functionalized conducting copolymers

Polyaniline (PANI) is one of the most investigated intrinsically conducting polymers. Copolymerization of aniline with aniline derivatives was considered one of the most effective and promising ways of improving the properties of PANI. In this work, firstly ethyl 3‐aminobenzoate and butyl 3‐aminobenzoate were synthesized from 3‐aminobenzoic acid by direct esterification. Then the copolymerization of 3‐amino benzoic acid, ethyl 3‐aminobenzoate, and butyl 3‐aminobenzoate with aniline was carried out by sonochemical polymerization in aqueous hydrochloric acid using ammonium persulfate (APS) as an initiator. The effects of variation in the molar ratio of the two monomers on chain structure, conductivity, and the redox properties of the copolymer are discussed. The prepared polymers are characterized by ¹H NMR spectroscopy, X‐ray diffraction (XRD) and Fourier transform infrared spectroscopy (FT‐IR). Thermal behavior of the prepared copolymers was studied by differential scanning calorimetry. The copolymers were doped with HCl and their conductivity was measured. 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.     

One‐pot three‐component synthesis of 2‐substituted 4‐aminoquinazolines

A facile and rapid synthesis of the title compounds via one‐pot reaction of 2‐aminobenzonitrile, orthoesters and ammonium acetate under solvent‐free and microwave condition is described.     

NMR investigation of methyl-2,4-dimethoxysalicylate: effect of solvent and temperature

(1)H NMR and (13)C NMR of methyl-2,4-dimethoxysalicylate 2 was measured in chloroform-d at the temperature range of 220-330 K, in dimethyl sulfoxide-d(6) at the temperature range of 300-400 K and in a polar protic solvent (CD(3)OD) at 300 K. The structure of 2 in liquid phase (solvent) is compared with those in solid phase (X-ray) and in the gas phase (quantum mechanical calculations). The relationship between molecular geometry, (1)H NMR chemical shift and W coupling of involved protons has a complex nature, but hydrogen bonds [C=O...H-O and C=O...H-CH(2)O] strength is the principle factor.     

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)).