A covariant quasipotential operator for a composite system of two scaler particles

A quasipotential operator for a system of two scalar particles, and also an integral equation and a normalization condition for the wave function of the connected state, are obtained by the method of two-time Green's functions in an explicitly covariant form. The cases are considered of scalar and electromagnetic interactions of particles of the system.Frantsiska Skoriny Gomel' State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 112–118, June, 1993.     

Inhomogeneous Gevrey classes and ultradistributions

The inhomogeneous Gevrey classes, defined in terms of Fourier transform, are a natural extension of the standard Gevrey classes. We find equivalent characterizations and discuss algebraic and topological properties. We therefore introduce the dual spaces, the inhomogeneous ultradistributions, giving some equivalent definitions and corresponding algebraic and topological properties; in particular, a version of the Paley-Wiener-Schwartz theorem is proved in our framework. Finally, as an important example, the multianisotropic Gevrey classes and ultradistributions are considered.     

Triorganotin 4-isopropylbenzoates as model transesterification catalysts for triorganotin carboxylates grafted to cross-linked polystyrene

Starting from 4-isopropylbenzoic acid, three new triorganotin carboxylates bearing methyl, butyl and phenyl substituents at tin, respectively, were prepared and fully characterized by spectroscopic and thermal techniques, with particular regard to the coordination number of tin atom, in solution as well as in the solid state. The triorganotin compounds, tested as transesterification catalysts in the reaction between ethyl acetate and primary, secondary or tertiary alcohol, respectively, displayed, as expected, a strong decrease of activity on passing from the primary to the tertiary alcohol reactant. Different activities by the tin carboxylates were also observed in the reaction between primary alcohol and ethyl acetate. The reaction mechanism, as elucidated by Sn NMR, involves coordination of both ester substrate and alcohol reactant to the triorganotin compound, the reaction conversion appearing related not only to the Lewis acidity of the tin atom, but also to the nature of the reactants. Preliminary catalytic tests were also carried out in the reaction between glyceryl tridodecanoate (as a model of natural triglyceride) and ethanol, mimicking the preparation of biodiesel fuel. Although in this case lower conversions were obtained with respect to the reactions on ethyl acetate, the catalytic activity of organotin derivatives appears considerable.     

The thermal decomposition of NaHCO3 powders and single crystals

The thermal decomposition of four commercial powders and of differently stored single crystals of sodium hydrogen carbonate is studied by power compensation DSC and by optical and FT-IR microscopy. Independently of manufacturer, specified purity and price, the thermal curves of all the commercial powders show a more or less pronounced low temperature peak preceding the one due to the main decomposition. Such small peak is not observed when samples of laboratory recrystallized material are used. However the thermal behaviour of the latter preparation differs remarkably depending on storage conditions: the material kept in closed glass containers decomposes at temperatures higher than those of the material stored in a dessiccator in the presence of concentrated H₂SO₄. The observation by optical microscopy of the behaviour of the surfaces of single crystals coming from different storage conditions when the temperature is raised in a Kofler heater helps the interpretation of the data collected. The mechanism of the decomposition is discussed and the relevant kinetic parameters reported.     

Combined charge and spin density experimental study of the yttrium(III) semiquinonato complex Y(HBPz3)2(DTBSQ) and DFT calculations

High-resolution X-ray diffraction and polarized neutron diffraction experiments have been performed on the Y-semiquinonate complex, Y(HBPz3)2(DTBSQ), in order to determine the charge and spin densities in the paramagnetic ground state, S = (1/2). The aim of these combined studies is to bring new insights to the antiferromagnetic coupling mechanism between the semiquinonate radical and the rare earth ion in the isomorphous Gd(HBPz3)2(DTBSQ) complex. The experimental charge density at 106 K yields detailed information about the bonding between the Y3+ ion and the semiquinonate ligand; the topological charge of the yttrium atom indicates a transfer of about 1.5 electrons from the radical toward the Y3+ ion in the complex, in agreement with DFT calculations. The electron density deformation map reveals well-resolved oxygen lone pairs with one lobe polarized toward the yttrium atom. The determination of the induced spin density at 1.9 K under an applied magnetic field of 9.5 T permits the visualization of the delocalized magnetic orbital of the radical throughout the entire molecule. The spin is mainly distributed on the oxygen atoms [O1 (0.12(1) mu B), O2(0.11(1) mu B)] and the carbon atoms [C21 (0.24(1) mu B), C22(0.20(1) mu B), C24(0.16(1) mu B), C25(0.12(1) mu B)] of the carbonyl ring. A significant spin delocalization on the yttrium site of 0.08(2) mu B is observed, proving that a direct overlap with the radical magnetic orbital can occur at the rare earth site and lead to antiferromagnetic coupling. The DFT calculations are in good quantitative agreement with the experimental charge density results, but they underestimate the spin delocalization of the oxygen toward the yttrium and the carbon atoms of the carbonyl ring.     

Sugli insiemi di permutazioni strettamente k-transitivi (k ≥ 3)

Summary Let G be a sharply 3-transitive permutation set on a finite set E of even cardinality and let 1 be in G. The following theorems are proved. G is one of the known examples if and only if there exists a non-identity normal subgroup N of G and an element of E such that NG G.G is a group if and only if G for every G and for every G and for every G .By using the classification of finite single groups a result concerning sharply k-transitive permutation sets k>3 is also proved.

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Dedicato a Guido Zappa in occasione del suo 70° compleanno

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Lavoro eseguito nell'ambito dei progetti finanziati dal Ministero della Pubblica Istruzione.     

Nickel-Ruthenium Mixed-Metal Carbonyl Clusters Syntheses and Solid State Structures of the Two Tetrahedral Clusters [PPh4][NiRu3(μ3 H)(CO)9(μ-CO)3] and [NEt4]2[NiRu3(CO)8(μ-CO)4]

Redox condensation of [Ru₃H(CO)₁₁]- with Ni(CO)₄, in tetrahydrofuran solution, under a nitrogen atmosphere, yields the tetranuclear anion [NiRu_H(CO)₁₁)-. Subsequent deprotonation with Bu'OK in acetonitrile solution leads to the formation of the related dianion. Both anions have been characterized by spectroscopic techniques, elemental analysis and single crystal X-ray diffraction. [PPh₄][NiRu₃H(CO)₁₂] crystallizes in the triclinic space group PI with unit cell dimensionsof a = 11.842(2) Å,b = 12.335(3) Å, c = 13.3080) Å,a = 91.89(2)°, = 93.35(1)°,y = 96.41(2)°, Z = 2, V= 1926.9(7) Å'. The NiRu₃, metal core of the molecule defines a distorted tetrahedron with nine terminal and three edge bridging carbonyl groups. The hydrido ligand was located by difference Fourier techniques and was found to bridge the NiRu₂ basal triangle at a distance of 0.88(6) A from this plane. Selected average distances and angles are: Ru-Ru = 2.839 Å, Ru-Ni = 2.640 Å, Ru-C, = 1.910 A,Ru-C _b = 2.084 Å, Ni-C _b = 2.022 Å, Ru-H = 1.77 Å, C-0, = 1.135 Å, C-O _b = 1.159 Å, M-C-O, = 176.3°,M-C--O _b = 139.3°;other distances are: Ni-C₁ = l.758(7) Å, Ni-H= 1.85(7) Å. [NEt₄]₂[NiRu₃(CO)₁₂] crystallizes in the orthorhombic space group Pnma (no. 62) with unit cell dimensions ofa=20.247(5) Å,b = 15.038(4)Å,c = 12.079(3) Å, Z=4, V=3678(2) A'. The molecule contains a tetrahedral NiRu₃ core with eight terminal and four edge bridging carbon monoxide groups which bridge the three Ni-Ru and one Ru-Ru bond. Average distances and angles are: Ru -Ru =2.3050A Ru-Ni 2.648 Å, Ru-C _t = 1.878 Å, Ru-C _b 2.045 Å, Ni-C _b = 2.055 Å, C-O _t = 1.145 Å, C-01,=1.157 Å, M-C-O,= 176.9°, M-C-O _b = 138.6°; other distance is: Ni-C _t = 1.754(10) Å,t = terminal,b = bridging.