Transfer theorems and the algebra of modal operators

A set theory ZFI′ which does not employ the Law of the Excluded Middle φ ∀ ⊥ φ, for all φ, retians the stock of expressive capacities of the classical set theory ZF, on the one hand, and has many of the features of an effective theory on the other. In the article, a broad class of formulas σ is constructed for which ZF ⊥ σ implies ZFI′ ⊥ σ. This result provides a generalization of Friedman's theorem on AE-arithmetic formulas. Besides, we prove transfer theorems of classical logic for the case of rings; in particular, Hilbert's theorem on zeros and Artin's theorem on ordered fields are extended to the case of regular f-rings, and we bring in appropriate upper bounds for them. Supported by RFFR grant No. 93-012-1027. Translated fromAlgebra i Logika, Vol. 36, No. 3, pp. 282–303, May–June, 1997.     

On finite-dimensional approximation of solutions of ill-posed problems

We show that the modified method for finite-dimensional approximation of solutions of Fredholm integral equations of the first kind presented in this paper is more economical than traditional methods for finite-dimensional approximation. Institute of Mathematies, Ukrainian Academy of Science, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 2, pp. 289–295, February, 1997.     

Superradiance of polaritons in finite one-dimensional crystals of increasing length: Passage from a dimer to an infinite crystal

Solutions of the dispersion equations for polariton states in finite one-dimensional crystals of arbitrary length are obtained. The appearance and evolution of the radiative and nonradiative polariton branches are traced as the length varies from two monomers to limiting values, above which the spectrum no longer undergoes significant changes. The dependences of the frequencies and radiative widths on the polariton wave vector are found for various orientations of the dipole moment of the quantum transition. The evolution of superradiance as the length of the crystal increases is traced. Some previously unknown significant features of the polariton spectrum are noted particularly the damping of the branch traditionally termed nonradiative as a consequence of emission from the end faces. Fiz. Tverd. Tela (St. Petersburg) 40, 2136–2140 (November 1998)     

Time-resolved synchrotron X-ray study of crystalline phase transition in poly(aryl ether ketone ketone) containing alternated terephthalic/isophthalic moieties

Unique crystallization and melting behavior in poly(aryl ether ketone ketone) containing alternated terephthalic and isophthalic moieties were studied by time-resolved synchrotron x-ray methods. Recently, this material has been shown to exhibit three polymorphs (forms I, II, and III). In this work, we further investigated their distinctive thermal properties and found that form I is the dominating and the most thermally stable phase while form II is favored by fast nucleation conditions and is the least stable phase. On the other hand, form III represents a minor intermediate phase that usually coexists with form I and can be transferred from form II and to form I. Structural and morphological changes in form I have been followed by simultaneous wide-angle x-ray diffraction (WAXD)/small-angle x-ray scattering (SAXS) measurements during cold- or melt-crystallization and subsequent melting. In all cases, a larger dimensional change was found in the crystallographic a-axis than the b-axis during heating and cooling. This may be due to the greater lateral stress variation with respect to temperature along the a direction of the primary lamellae which is induced by either the formation of secondary lamellae or the preferential chain-folding direction in poly(aryl ether ketone ketone)s. During the phase transitions of form II ← III in the cold-crystallized specimen and form III ← I in the melt-crystallized samples, lamellar variables (long period, lamellar thickness, and invariant) obtained from SAXS remain almost constant. This indicates that the density distribution in the long spacing is independent of the melting in form II or III. For melt-crystallization, the corresponding changes in unit-cell dimensions and lamellar morphology during the annealing-induced low endotherm are most consistent with the argument that these changes are due to the melting of thin lamellar population. © 1995 John Wiley & Sons, Inc.     

Thickness and temperature dependence of subsidiary absorption thresholds in yttrium-iron-garnet thin films

The microwave subsidiary absorption threshold in tangentially magnetized yttrium-iron-garnet (YIG) films was measured as a function of the static magnetic field, film thickness and decrease in the 0.3–3 μm range is observed. The effect is explained quantitatively by using modified Damon-Eshbach dispersion relations which take into account exchange interactions.

The effect of temperature on h_crit, the smallest threshold field amplitude, in the 250<T< 450 K temperature range can be expressed by an empirical relationship h_crit M_s(T)^-1.6 where M_s is the saturation magnetization. This h_crit vs M_s relationship is similar to that obtained for the magnetization dependence of parallel pump thresholds in Li-Ti ferrite compounds.     

EPMA of interfaces applied to the solid oxide fuel cell

Chemical interactions at the phase boundaries of materials applied for the solid oxide fuel cell (SOFC) have been studied by EPMA. The chemical reactivity at the interface of La_y-xSr_xMnO₃/ZrO₂-Y₂O₃ is dependent on the stoichiometry (y) and the Sr content (x) of the perovskite. Typical reaction products (zirconates) and a diffusion zone in the ZrO₂–Y₂O₃ have been observed. The extension of cation release (Mn) is related to the increasing chemical activity of Mn oxide in the perovskite by the Sr substitution for La. The wettability of the metal/oxide interface in the anode cermet (Ni/ZrO₂–Y₂O₃) has been found to be influenced by chemical reactions resulting from the applied reducing atmosphere with high carbon activity. The disintegration of ZrO₂–Y₂O₃ in contact with molten Ni or Ni-Ti and Ni-Cr alloys leads to the redeposition of Y₂O₃-enriched oxides and also to Zr-rich intermetallic compounds and eutectics.     

Vibrational control of crystal growth from liquid phase

Modeling and numerical simulations of the convective flows induced by the vibration of the monocrystal during crystal growth have been performed for two configurations simulating the Cz and FZ methods. This permitted to emphasize the role of different vibrational mechanisms in the formation of the average flows. It is shown that an appropriate combination of these mechanisms can be used to counteract the usual convective flows (buoyancy- and/or thermocapillary-driven) inherent to crystal growth processes from the liquid phase. While vibrational convection is rather complex due to these identified mechanisms, the new modeling used in the present paper opens up very promising perspectives to efficiently control heat and mass transfer during real industrial applications of crystal growth from the liquid phase.     

Pseudo-Strong Regularity Around a Set

A generalization of strong regularity around a vertex subset C of a graph Γ, which makes sense even if Γis non-regular, is studied. Such a structure appears, together with a kind of distance-regularity around C , when an spectral bound concerning the so-called predistance polynomial of C is attained. As a main consequence of these results, it is shown that a regular (connected) graph Γwith d + 1 distinct eigenvalues is distance-regular, and its distance- d graph Γ d is strongly regular with parameters a = c , if and only if the number of vertices at distance d from each vertex satisfies an expression which depends only on the order of Γand the different eigenvalues of Γ.