The intuitionistic propositional calculus with quantifiers

Let L be the language of the intuitionistic propositional calculus J completed by the quantifiers and , and let calculus 2J in language L contain, besides the axioms of J, the axioms xB (x) B(y) and B(y) xB (x). A Kripke semantics is constructed for 2J and a completeness theorem is proven. A result of D. Gabbay is generalized concerning the undecidability of C2J⁺-extension of 2J by schemes x (x B) and x(A B(x))A xB (x) specificially: the undecidability is proven of each T theory in language L such that [2J]T [C2J+] ([2J] ([2J] denotes the set of all theorems of calculus 2J).Translated from Matematicheskie Zametki, Vol. 22, No. 1, pp. 69–76, July, 1977.     

Anionic high-temperature conduction in single crystals of nonstoichiometric phases R1 ? y M y F3 ? y (R = La-Lu, M = Ca, Sr, Ba) with the tysonite (LaF3) structure

Electrophysical properties of single crystals of nonstoichiometric phases R_{1 − y} M _y F_{3 − y} , where R = La-Lu, M = Ca, Sr, or Ba, with the tysonite (LaF₃) structure, which are present in a metastable state after being grown and cooled, are measured in the temperature interval extending from 300 to 1073 K. It is discovered that, during a sufficiently long high-temperature investigation, solid solutions R_{1 − y} Ca _y F_{3 − y} , where R = Tb, Dy, or Ho, undergo irreversible variations in the phase composition in the temperature region 723 to 823 K. This level of temperatures, which correspond to partial decomposition of phases R_{1 − y} Ca _y F_{3 − y} with the rare-earth elements of the end of the period, lies above the temperatures to which the fluoride solid electrolytes are usually heated when used in solid-state electrochemical devices. The temperature and concentration dependences of the phases’ electroconduction are explained in the framework of the vacancy mechanism of anionic transport. Original Russian Text ? N.I. Sorokin, B.P. Sobolev, 2007, published in Elektrokhimiya, 2007, Vol. 43, No. 4, pp. 420–431. The paper is dedicated to the memory of Prof. M.W. Breiter, formerly of the Vienna Technical University, Austria.     

Phase diagrams of MgF2-(Y,Ln)F3 systems

By means of thermal and X-ray analyses with oxygen control, 14 phase diagrams of the systems MgF₂-(Y, Ln)F₃ have been obtained, where Ln are all lanthanides except Pm and Eu. All the systems are eutectic. Solid solutions up to 12 mole% MgF₂, which decompose by the eutectoid scheme, were detected based on high-temperature modifications of trifluorides of Y, Er, Tm, Yb and Lu, with a structure of the-YF₃ type.

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Zusammenfassung Durch Einsatz der Thermo- und Röntgenanalyse mit Sauerstoffkontrolle wurden 14 Phasendiagramme der Systeme MgF₂-(Y, Ln)F₃ erhalten, wobei Ln sämtliche Lanthanoide mit Ausnahme von Pm und Eu sind. Alle Systeme zeigten sich eutektisch. Feste, sich nach dem eutektoiden Schema zersetzende Lösungen bis zu 12 Mol% MgF₂ wurden an Hand der Hochtemperatur-Änderungen der Trifluoride von Y, Er, Tm, Yb, Lu mit-YF₃-Struktur nachgewiesen.

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Résumé 14 diagrammes de phases des systèmes MgF₂ — (Y, Ln) F₃, où Ln représente tous les lanthanoïdes à l'exception de Pm et Eu ont été établis par études aux rayons X et analyse thermique, avec contrôle de l'oxygène. Tous ces systèmes présentent un eutectique. Des solutions solides jusqu'à 12 moles % de MgF₂ à décomposition eutectoïde ont été décelées à l'aide des transitions à haute température des trifluorures d'Y, Er, Tm, Yb et Lu du type-YF₃.

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- , 14 MgF₂ — (Y, Ln)F₃, Ln- , u. -. 12 .% MgF₂, , Y, r, Tm, Yb, Lu, -YF₃.

     

Electronic state of Fe used as Mössbauer probe in the perovskites LaMO3 (M=Ni and Cu)

For the first time a comparative study of rhombohedral LaNiO₃ and LaCuO₃ oxides, using ⁵⁷Fe Mössbauer probe spectroscopy (1% atomic rate), has been carried out. In spite of the fact that both oxides are characterized by similar crystal structure and metallic properties, the behavior of ⁵⁷Fe probe atoms in such lattices appears essentially different. In the case of LaNi_0.99Fe_0.01O₃, the observed isomer shift (δ) value corresponds to Fe³⁺ (3d⁵) cations in high-spin state located in an oxygen octahedral surrounding. In contrast, for the LaCu_0.99Fe_0.01O₃, the obtained δ value is comparable to that characterizing the formally tetravalent high-spin Fe⁴⁺(3d⁴) cations in octahedral coordination within Fe(IV) perovskite-like ferrates. To explain such a difference, an approach based on the qualitative energy diagrams analysis and the calculations within the cluster configuration interaction method have been developed. It was shown that in the case of LaNi_0.99Fe_0.01O₃, electronic state of nickel is dominated by the d⁷ configuration corresponding to the formal ionic “Ni³⁺-O²⁻” state. On the other hand, in the case of LaCu_0.99Fe_0.01O₃ a large amount of charge is transferred via Cu-O bonds from the O:2p bands to the Cu:3d orbitals and the ground state is dominated by the d⁹L configuration (“Cu²⁺−O” state). The dominant d⁹L ground state for the (CuO₆) sublattice induces in the environment of the ⁵⁷Fe probe cations a charge transfer Fe³⁺+O⁻(L)→Fe⁴⁺+O²⁻, which transforms “Fe³⁺” into “Fe⁴⁺” state. The analysis of the isomer shift value for the formally “Fe⁴⁺” ions in perovskite-like oxides clearly proved a drastic influence of the 4s iron orbitals population on the Fe−O bonds character.     

Anion Transport in BaR2F8 Crystals at Elevated Temperatures

Electroconduction of BaR₂F₈ crystals (R = Y_0.9Er_0.1, Y_0.5Yb_0.5, Er_0.945Tm_0.05Ho_0.005) with the structure -BaTm₂F₈ (monoclinic syngony, spatial group C2/m) is studied at 323–1073 K. Effect of partial pyrohydrolysis on the conduction of Ba(Y, Er)₂F₈ single crystals is investigated. Anion conductivity of crystals of Ba(Y, Yb)₂F₈ and Ba(Er, Tm, Ho)₂F₈ is measured at high temperatures. To a first approximation, there is no change in the ion transport mechanism in these crystals at elevated temperatures. Charge carriers in BaR₂F₈ crystals are, most probably, fluorine vacancies, and the anion conductivity reaches 1–2 mS cm^–1 at 1073 K.     

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...