On some near to nilpotent groups

Locally (soluble-by-finite) groups each of whose subgroups is either pronormal or subnormal are studied. It is proven that such torsion-free groups are nilpotent, and a sketch of the structure of locally finite groups of this type is obtained.     

Investigation of the crystallization features,atomic structure,and microstructure of chromium-doped monticellite

A series of Cr⁴⁺:CaMgSiO₄ single crystals is grown using floating zone melting, and their microstructure, composition, and crystal structure are investigated. It is shown that regions with inclusions of second phases, such as forsterite, akermanite, MgO, and Ca₄Mg₂Si₃O₁₂, can form over the length of the sample. The composition of the single-phase regions of the single crystals varies from the stoichiometric monticellite CaMgSiO₄ to the solid solution Ca_{(1 ? x)}Mg_{(1 + x)}SiO₄(x = 0.22). The Cr:(Ca_0.88Mg_0.12)MgSiO₄ crystal is studied using X-ray diffraction. It is revealed that, in this case, the olivine-like orthorhombic crystal lattice is distorted to the monoclinic lattice with the parameters a = 6.3574(5) Å, b = 4.8164(4) Å, c = 11.0387(8) Å, β = 90.30(1)^o, Z = 4, V = 337.98 ų, and space group P2₁/c. In the monoclinic lattice, the M(1) position of the initial olivine structure is split into two nonequivalent positions with the center of symmetry, which are occupied only by Mg²⁺ cations with the average length of the Mg-O bond R _av = 2.128 Å. The overstoichiometric Mg²⁺ cations partially replace Ca²⁺ cations (in the M(2) position of the orthorhombic prastructure) with the average bond length of 2.347 Å in the [(Ca,Mg)-O₆] octahedron. The average distance in SiO₄ distorted tetrahedra is 1.541 Å.     

Metal-free and transition-metal tetraferrocenylporphyrins part 1: synthesis, characterization, electronic structure, and conformational flexibility of neutral compounds

H(2)TFcP [TFcP = 5,10,15,20-tetraferrocenyl porphyrin(2-)] was prepared by a direct tetramerization reaction between pyrrole and ferrocene carbaldehyde in the presence of a BF(3) catalyst, while the series of MTFcP (M = Zn, Ni, Co and Cu) were prepared by a metallation reaction between H(2)TFcP and respective metal acetates. All compounds were characterized by UV-vis and MCD spectroscopy, APCI MS and MS/MS methods, high-resolution ESI MS and XPS spectroscopy. Diamagnetic compounds were additionally characterized using (1)H and (13)C NMR methods, while the presence of low-spin iron(ii) centers in the neutral compounds was confirmed by M?ssbauer spectroscopy and by analysis of the XPS Fe 2p peaks, revealing equivalent Fe sites. XPS additionally showed the influence on Fe 2p binding energies exerted by the distinct central metal ions. The conformational flexibility of ferrocene substituents in H(2)TFcP and MTFcP, was confirmed using variable-temperature NMR and computational methods. Density functional theory predicts that alpha,beta,alpha,beta atropisomers with ruffled porphyrin cores represent minima on the potential energy surfaces of both H(2)TFcP and MTFcP. The degree of non-planarity is central-metal dependent and follows the trend: ZnTFcP < H(2)TFcP approximately CuTFcP < CoTFcP < NiTFcP. In all cases, a set of occupied, predominantly ferrocene-based molecular orbitals were found between the highest occupied and the lowest unoccupied, predominantly porphyrin-based molecular orbitals. The vertical excitation energies of H(2)TFcP were calculated at the TDDFT level and confirm the presence of numerous predominantly metal-to-ligand charge-transfer bands coupled via configurational interaction with expected intra-ligand pi-pi* transitions.     

Mixed-valence states formation in conformationally flexible metal-free 5,10,15,20-tetraferrocenylporphyrin and 5,10-bisferrocenyl-15,20-bisphenylporphyrin

Metal-free 5,10,15,20-tetraferrocenylporphyrin and 5,10-bisferrocenyl-15,20-bisphenylporphyrin have been prepared and characterized by UV-Vis, MCD, (1)H, (13)C, and variable-temperature NMR, APCI- and ESI-MS, and M?ssbauer spectroscopy, while their redox properties were investigated using electrochemical (cyclic voltammetry and differential pulse voltammetry), spectroelectrochemical, and chemical oxidation approaches. The electronic structure calculations at Density Functional Theory level reveal that both compounds adopt saddle conformations and the HOMOs in both complexes are predominantly metal-centered, while the LUMOs predominantly consist of porphyrin pi* orbitals. In spite of the rotational freedom of ferrocenyl substituents at room temperature, both metal-free 5,10,15,20-tetraferrocenylporphyrin and 5,10-bisferrocenyl-15,20-bisphenylporphyrin are able to form mixed-valence states upon the successive ferrocene-based two- and one-electron oxidations, respectively, as confirmed by UV-Vis, MCD, M?ssbauer, electro-, and spectroelectrochemical methods, and thus, the earlier suggested (Boyd et al. Chem. Commun., 1999, 637) requirements for the formation of mixed-valence states in ferrocene-containing porphyrins should be revised.     

Evolution of the fractal surface of amorphous lead zirconate-titanate films during crystallization

The recrystallization kinetics of amorphous lead zirconate-titanate films prepared by sol-gel technology are investigated experimentally using elastic scattering of light. Sequences of elastic dependences of the scattered light intensity are recorded directly during thermal annealing. The evolution of the morphology of the film surface during annealing is described in terms of the variation of their fractal dimensionalities D _s. The experimental dependences D _s(t) are compared with the results of a computer simulation of the phase transition kinetics in a thin plate (film). Fiz. Tverd. Tela (St. Petersburg) 41, 306–309 (February 1999)     

A monopole mass filter with a hyperbolic V-shaped electrode

In this article we compare the classical monopole mass filter of von Zahn and the monopole mass filter with a hyperbolic V-shaped electrode. The experimental results and those of computer simulation for both mass spectrometers are presented. We show that the replacement of a conventional 90 degrees V-shaped electrode by an electrode with a hyperbolic profile substantially improves the peak shape of any given mass, and increases the mass resolution by a factor of 3-4 and the abundance sensitivity by a factor of 100. The potential of high analytical performance combined with electroforming techniques for electrode manufacture indicate future practical uses of such instruments. Copyright 1999 John Wiley & Sons, Ltd.     

On the phenomena of temperature hysteresis in hydrogenation reactions over heterogeneous catalysts

For the first time the phenomenon of a temperature hysteresis in the exothermic heterogeneous catalytic reactions of CO hydrogenation (methanation) and propene is discussed; the assumption is made, that the reason of hysteresis is the local overheating of the active centers caused by the complicated dissipation of the released energy through the dispersed particles of the catalyst. Dedicated to Professor Pál Tétényi on the occasion of his 70^th birthday     

Dimer Self-Organization of Impurity Erbium Ions in a Synthetic Forsterite

Physics of the Solid State - The electron paramagnetic resonance spectra of impurity trivalent erbium ions in synthetic forsterite single crystals (Mg2SiO4) have been studied by the electron...     

On the equality of Kolmogorov and relative widths of classes of differentiable functions

We obtain sharper estimates of the remainders in the expression for the least value of the multiplier M for which the Kolmogorov widths d _n (W _C ^r , C) and the relative widths K _n (W _C ^r ,MW _C ^j ,C) of the class W _C ^r with respect to the class MW _C ^j , j < r, where r ? j is odd, are equal.