Spectrum of relaxation times for ising spin clusters in random fields

Summary Exact results on the single-spin-flip Glauber dynamics of six-coupled random field Ising spins with the coordination number of four are presented. Two distributions of random fields (RF), binary (BD) and Gaussian (GD) ones, are investigated. The effects of the static magnetic field are discussed. In the zero-magnetic-field case, the number of diverging relaxation times is equal to the number of energy minima minus one. This rule breaks in the presence of a magnetic field. The longest relaxation times in the absence of the field verify the Arrhenius law with the energy barrier determined by the energy needed to invert the ground-state spin configuration. At low temperature, according to the Arrhenius law, the spectrum of relaxation times shows a two-peaked distribution on a logarithmic scale. In the GD case of RF, the energy barrier distribution is continuous, while it is quasi-discrete in the BD case.     

Hermitean Matrix Ensembles and Orthogonal Polynomials

In this article, we investigate orthogonal polynomials associated with complex Hermitean matrix ensembles using the combination of the methods of Coulomb fluid (or potential theory), chain sequences, and Birkhoff–Trjitzinsky theory. We give a general formula for the largest eigenvalue of the N×N Jacobi matrices (which is equivalent to estimating the largest zero of a sequence of orthogonal polynomials) and the two-level correlation function for the α ensembles (α>0) introduced previously for α>1. In the case of 0<α<1, we give a natural representation for the weight function that is a special case of the general Nevanlinna parametrization. We also discuss Hermitean matrix ensembles associated with general indeterminate moment problems.     

Nuclear shapes and interaction potentials of two colliding208Pb nuclei at finite temperature

The effect of nuclear and Coulomb interactions on the shapes of two colliding²⁰⁸Pb nuclei at finite temperature is investigated. The complex potential energy density derived by Faessler and collaborators and the kinetic energy density and entropy density for two Fermi spheres at finite temperature are used to calculate the free energy of the²⁰⁸Pb +²⁰⁸Pb system in the energy density formalism. Shell corrections are added to the free energy in the framework of the Strutinsky method. The total free energy is minimized with respect to the quadrupole deformation and the diffuseness to determine the density distribution of²⁰⁸Pb nucleus at certain distanceR and temperatureT assuming the deformed Woods-Saxon shape for each nucleus. It is found that the nucleus acquires larger deformation and diffuseness as the temperature increases. The interaction potential between two²⁰⁸Pb nuclei is calculated from the minimized free energy. The total (nuclear + Coulomb) potential is found to decrease with increasing temperature, whereas the real part of the nuclear potential becomes more repulsive as the temperature increases.     

Ramanujan continued fractions via orthogonal polynomials

Some Ramanujan continued fractions are evaluated using asymptotics of polynomials orthogonal with respect to measures with absolutely continuous components.     

Induced and Coinduced Representations of Hopf Group Coalgebras

The induction theory for a Hopf group coalgebra is outlined. Given a Hopf group coalgebra H, the notions of a quotient Hopf group coalgebra and group coisotropic quantum subgroup of H are introduced. The properties of (co)induced representations are studied and the geometric interpretation and simplicity theory of such representations are given.      

Some physico-chemical properties of pure and doped nickel oxide. Thermal analyses and X-ray diffraction studies

In this investigation pure and doped NiO with different concentrations of Al, Ga or In are thermally analysed. The results indicate the presence of two endothermic peaks at about 120 and 250°C which were attributed to the loss of adsorbed water and phase change, respectively. X-Ray data indicated that all samples belong to the cubic system. In the case of samples doped with high concentrations of Ga or In, a new line is observed which may be due to the formation of a spinel form. There is no systematic change between the calculated values of lattice parameters, α, of doped samples and the type or concentration of dopant. This change has been related to the difference in the values of the ionic radii of Ni²⁺ and those of dopant elements.     

Catalytic transfer reduction of conjugated alkenes and an imine using polymer-supported formates

An efficient and mild method for catalytic transfer hydrogenation of CC and CN double bonds with the aid of resin-supported formate (PSF) as the hydrogen donor and palladium acetate as the catalyst is reported.     

The effect of nuclear and Coulomb interactions on the nuclear shapes of two colliding208Pb nuclei

Using a complex energy density functional derived from the Reid soft-core potential, the changes in nuclear shapes of two colliding²⁰⁸Pb are investigated. At each separation distanceR, the total binding energy of the Pb + Pb system is minimized w.r.t. the quadrupole deformation and diffuseness parameters of nuclear densities. It is found that the nuclear shapes are strongly affected by the nuclear and Coulomb interactions. A sudden transition occurs from oblate to prolate shapes around R16.8fm and a smooth one from prolate to oblate shapes aroundR?11.76 fm.     

Experimental and theoretical studies on the functionalization reactions of 4-benzoyl-1,5-diphenyl-1H-pyrazole-3-carboxylic acid and acid chloride with 2,3-diaminopyridine

The 1H-pyrazole-3-carboxylic acid 2 was converted in good yield (69%) into the corresponding 1H-pyrazole-3-carboxamide 5 via reaction of the acid chloride 3 with 2,3- diaminopyridine (4). A different product, the 3H-imidazo[4,5-b] pyridine derivative 6, was formed from the reaction of 3 with 4 and base in benzene for 5 hours. The structures of the synthesized compounds were determined spectroscopically. The mechanism of the reaction between 3 and 4 was examined theoretically.