Integration of mappings of semiordered rings

Lebesgue type integrals of mappings f: E X, where X is a semiordered ring and E R, over a measure with values lying in X are studied. Usual properties of the integral are proved, including theorems on limits under the integral as well as those on absolute continuity and complete additivity of the (u, v)-integral. A theorem on the existence of a solution of a differential equation with (u, v)-derivatives is proved.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 4, pp. 547–555, July–August, 1992.     

Nanostructured Crystals of Fluorite Phases Sr1 – xRxF2 + x (R Are Rare-Earth Elements) and Their Ordering. 14: Concentration Dependence of the Defect Structure of Nonstoichiometric Phases Sr1 – xNdxF2 + x As Grown (x = 0.10, 0.25, 0.40, 0.50)

Crystallography Reports - The defect structure of as grown Sr1 – xNdxF2 + x (x = 0.10–0.50) crystals grown from a melt by...     

Anisotropy of Ionic Conductivity of TbF3 Crystals

Crystallography Reports - Temperature measurements (in the range of 375–830 K) of the ionic conductivity of terbium trifluoride single crystals (structure type β-YF3) along three...     

Spatial structure of molecular complexes of zinc(II)tetraphenylporphyrin with pyridine and aniline derivatives

Structure of molecular complexes of zinc(II)tetraphenylporphyrin with 4-dimethylaminopyridine and 4-methoxyaniline has been studied by X-ray diffraction analysis. 4-Dimethylaminopyridine is coordinated almost perpendicular to the porphyrin cycle plane, whereas 4-methoxyaniline is coordinated at lower dihedral angle. The hybridization of aniline nitrogen atom in the crystal depends on donor-acceptor properties and the volume of the substituents in the aromatic ring.     

Ordering of tysonite structure in an as-grown Er0.715Ca0.285F2.715 crystal and in a component of annealed two-phase crystal of the Er0.67Ca0.33F2.67 composition

The structures of the as-grown tysonite phase (TP) Er_0.715Ca_0.285F_2.715 as grown and the tysonite component in a crystal of the Er0.67Ca0.33F2.67 composition annealed at 760°C have been determined by X-ray diffraction methods from the main reflections in the sp. gr. P6₃/mmc, Z = 2. Ca²⁺ cations in the Er_0.715Ca_0.285F_2.715 structure occupy the 2c site on the 6₃ axis, thus confirming the conclusion about the symmetrizing effect of alkaline earth cation, which was made previously for the Y_0.715Ca_0.285F_2.715 compound. Er³⁺ cations are disordered over 6h sites around this axis. The Er_0.67Ca_0.33F_2.67 composition contains Er_0.67+δCa_0.33?δF_2.67+δ TP and inclusions of distorted fluorite phase rhβ-Ca₈Er₅F₃₁. The tysonite and two fluorite lattices have no “correct” relationship. Ca²⁺ cations and a half of TP Er³⁺ cations are fixed in the 2c sites, while the other Er³⁺ cations are disordered over the 6h sites. Superstructural ordering occurs in Er_0.715Ca_0.285F_2.715 crystals; however, the process is not completed, as follows from the character of the diffraction pattern. Weak satellite reflections in the diffraction pattern of the Er_0.67Ca_0.33F_2.67 composition are indicative of the development of TP ordering processes but remain unfit for structural calculations.     

Turbulent structure in supersonic jets with a high Reynolds number

The turbulent properties of a supersonic jet were studied related to a high level of pressure pulsation found in model jets of a reentry flight vehicle approaching the landing ground. This study comprised measurements of total pressure at a small-size target using a dynamic pressure probe placed in a free jet. The most comprehensive data about jet turbulence can be obtained by direct transformation of the pressure reading at the stagnation point near the target into the normalized velocity. The oscillogram of normalized velocity produces the velocity average value, root-mean-square value as well as turbulence intensity and turbulence spectrum. It was demonstrated that a high level of turbulence for a high-head jet retains along the supersonic core length and at the beginning of subsonic interval.     

Effect of the Solvent on the Coordination of Pyridine Derivatives with Zn Tetraphenylporphine

The coordination of zinc(II) tetraphenylporphine with pyridines was studied by electronic spectroscopy. Linear correlations were found between the thermodynamic and kinetic parameters of coordination in different solvents. The effect of the solvent on the stability constants of the complexes and the thermodynamics of complex formation are discussed.     

The Intrinsic Fluorine-Ion Conductivity of Crystalline Matrices of Fluoride Superionics: BaF2 (Fluorite Type) and LaF3 (Tysonite Type)

Physics of the Solid State - The intrinsic fluorine-ion conductivity σlat of BaF2 (CaF2 fluorite type) and LaF3 (tysonite type) crystals is studied by the impedance spectroscopy method. These...