Generalized Weyl–Wigner–Moyal–Ville Formalism and Topological Groups

Discussed are some geometric aspects of the phase space formalism in quantum mechanics in the sense of Weyl, Wigner, Moyal, and Ville. We analyze the relationship between this formalism and geometry of the Galilei group, classical momentum mapping, theory of unitary projective representations of groups, and theory of groups algebras. Later on, we present some generalization to quantum mechanics on locally compact Abelian groups. It is based on Pontryagin duality. Indicated are certain physical aspects in quantum dynamics of crystal lattices, including the phenomenon of ‘Umklapp–Prozessen’. Copyright © 2011 John Wiley & Sons, Ltd.     

Viscosity of Bi–Zn liquid alloys

Viscosity of Bi_100?xZn_x (x = 0, 8, 16, 50, 80, 85, 89, 100) liquid alloys has been measured by means of the oscillating crucible method. Temperature dependences of the viscosity coefficient have revealed anomalous behavior in the vicinity of the demixing curve. The maximum on background of Arrhenius type dependence of viscosity is most resolved for melt of critical concentration. The viscosity measurements results are analyzed from the point of view of concentration fluctuations. It is concluded that concentration–concentration fluctuations are responsible for the anomalous behavior of viscosity.     

Uniform Expansions of Periodic Solutions for the Third Superharmonic Resonance

A new method of uniform expansions of periodic solutions to ordinary differential equations has recently been proposed to study quasi-harmonic processes in non-linear dynamical systems, in particular, when a small parameter of non-linearity is absent. The main idea of the method consists in using the ratio of the amplitudes of higher harmonics to the amplitude of the first harmonic of a periodic solution as a small formal parameter that appears due to descending the amplitudes of harmonics monotonically with increasing their number (this is the condition that the term quasi-harmonic implies). In this paper, the method is generalized for the third superharmonic resonance (when the first and the third harmonics become of the same magnitude) in a harmonically forced oscillator with arbitrary odd polynomial non-linearity.     

Pseudo-spherical Submanifolds with Degenerate Bianchi Transformation

We describe pseudo-spherical submanifolds with degenerate Bianchi transformation in constant curvature spaces.     

Structure parameters and structure sensitive properties of Sn0.739Pb0.261 melt

Structure, interdiffusion, and dynamic viscosity of eutectic Sn-Pb melt have been experimentally investigated in a wide temperature range. On the basis of the obtained data on the position and form of the first maximum of the structure factor in the framework of the hard sphere model, values of sphere packing index and sphere diameter have been determined for the melt at 470 and 570 K. Correlations resulting from the model of hard spheres served to calculate coefficients of dynamic viscosity and interdiffusion of liquid alloy. Besides, temperature dependence of dynamic viscosity has been calculated with the use of thermodynamic approximation of Kozlov — Romanov — Petrov. Calculated values of the properties have been compared with experimental data.     

Synthesis of 3‐Aryl/methoxycarbonyl‐3,4‐dihydroisocoumarin‐6‐carboxylic Acid Derivatives

3‐Substituted methyl 3,4‐dihydroisocoumarin‐6‐carboxylates were obtained by the intramolecular cyclization of 2,5‐dimethoxycarbonyl benzenediazonium bromides with methyl/ethyl acrylate and styrenes under Meerwein's arylation conditions.     

Highly enantioselective catalytic hydrogenation of a 5-amino-3,5-dioxopentanoic ester

The highly enantioselective hydrogenation of methyl 4-tert-butylcarbamoyl-3-oxo-butyrate to the corresponding secondary alcohol, representing an interesting chiral building block, for example, for the synthesis of statins, has been investigated in the presence of homogeneous chiral Rh(I) and Ru(II) complexes bearing phosphine ligands. The highest enantioselectivity (up to 96%) was achieved with a [Ru((R)-BINAP)(p-cymene)Cl]Cl complex (sub./cat. ratio 100:1, 5 bar H₂, rt, MeOH).     

Structure-energy relationships in unsaturated esters of carboxylic acids. Thermochemical measurements and ab initio calculations

Standard molar enthalpies of formation in the gaseous state of a series of alkyl 3-methylbut-2-enoates have been obtained from combustion calorimetry and results from the temperature dependence of the vapor pressure measured by the transpiration method. To verify the experimental data, we have performed ab initio calculations of all compounds. Enthalpies of formation derived from the G3MP2 method are in excellent agreement with the experimental results. Quantitative analysis of strain effects in alkyl 3-methylbut-2-enoates was discussed in terms of deviations of deltafH degrees m(g) from the group additivity rules. Energetics of the cis-trans isomerization of carboxylic acid derivatives was studied using G3MP2 and DFT methods. Values of strain and cis-trans corrections derived in this work provide further improvement on the group-contribution methodology for prediction of the thermodynamic properties of compounds relevant to biodiesel.     

Synthesis and crystal structures of Nd6Pt13In22, Sm6Pt12.30In22.70, and Gd6Pt12.48In22.52

The rare earth-platinum-indides Nd₆Pt₁₃In₂₂, Sm₆Pt_12.30In_22.70, and Gd₆Pt_12.48In_22.52 were synthesized from the elements by arc-melting of the components. Single crystals were grown using special annealing sequences. The three indides were investigated by X-ray powder and single crystal diffraction: Tb₆Pt₁₂In₂₃ type, C2/m, Z=2, a=2811.9(6), b=441.60(9), , β=112.10(3)°, wR₂=0.0629, 3645 F² values, 126 variables for Nd₆Pt₁₃In₂₂, a=2821.9(6), b=443.06(9), , β=112.39(3)°, wR₂=0.0543, 3679 F² values, 127 variables for Sm₆Pt_12.30In_22.70, and a=2818.5(6), b=439.90(9), , β=112.29(3)°, wR₂=0.0778, 3938 F² values, 127 variables for Gd₆Pt_12.48In_22.52. Most platinum atoms in these structures have a distorted trigonal prismatic coordination by rare earth metal and indium atoms. Together, the platinum and indium atoms build up a complex three-dimensional [Pt_12+xIn_23−x] polyanionic network in which the rare earth metal atoms fill distorted pentagonal and hexagonal channels. The 2c Wyckoff site in these structures plays a peculiar role. This site is occupied by indium in the prototype Tb₆Pt₁₂In₂₃, while platinum atoms fill the 2c site in Nd₆Pt₁₃In₂₂, leading to a linear Pt₃ chain with Pt-Pt distances of 275 pm. The crystals with samarium and gadolinium as rare earth metal component show mixed Pt/In occupancies.