Solution of the Problem of Convecitve Heat Exchange for A Two-Dimensional Body in A Low-Prandtl-Number Fluid Flow

It is shown that the exact solution of the problem of convective heat exchange in a low-Prandtl-number fluid flow (Pr ? 1) can be obtained for a two-dimensional body of arbitrary shape provided that the conformal mapping relating the body contour with a circle is known. By way of example, the Joukowsky airfoil is considered.     

On finite convolutions of singular distributions and a “singular analog” of the Jessen-Wintner theorem

We study the fractal properties of a convolution of two Cantor distributions. By using the method of characteristic functions, we establish sufficient conditions for the singularity of the convolution of an arbitrary finite number of distributions of random variables with independent s-adic digits. We disprove the hypothesis on the validity of a “singular analog” of the Jessen-Wintner theorem for anomalously fractal distributions. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 8, pp. 1082–1088, August, 1998. The present work was partially supported by the International Soros Program of Educational Support in Exact Sciences (grant No. APU 061086).     

Homogeneous Stäckel-type systems

A class of Hamiltonian dynamic systems integrated by the variable separation method is considered. The integration for this class is the inversion of an Abel mapping on hyperelliptic curves. We prove that the derivative of the Abel mapping is the Stäckel matrix, which determines a diagonal Riemannian metric and curvilinear orthogonal coordinate systems in a flat space. Lax representations with the spectral parameter are constructed. The corresponding classicalr-matrices are dynamic. It is shown how the class of pointwise canonical transformations can be naturally generalized using the Abel integral reduction theory.     

Constructing a model transport equation for a massless bose gas and its analytic solution

A model kinetic equation is constructed for the transport of a massless Bose gas. This equation is applied to solve the boundary value problem for the transport of radiation in the half-space occupied by a dispersive medium that is in local thermal equilibrium with the radiation. It is shown that the difference in temperature between the dispersive medium and the incident radiation substantially depends on the character of the scattering properties of the particles in the medium. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 111, No. 3, pp. 462–472, June, 1997.     

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.     

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.     

Application of synthetic reference materials in the medical radiological research centre

The contents of 21 chemical elements (Ag, Br, Ca, Cl, Co, Cr, Cs, Fe, Hg, K, Mg, Mn, Na, P, Rb, Sb, Sc, Se, Sr, Zn, Zr) in synthetic reference materials (SRMs) were compared with those in natural reference materials (NRMs) using short- and long-lived radionuclides. SRMs called synthetic standards (SSs) and synthetic standards, biological (SSBs) were prepared on the basis of phenol-formaldehyde resol resins in the Institute of Physics, Georgian Academy of Science. The NRMs included such IAEA reference materials as H-4 (animal muscle), A-13 (animal blood), H-5 (animal bone), SL-1 (lake sediment), SOIL-7 (soil), A-9 (mixed human diet), and IAEA-153 (milk powder). It was shown that SSB-SRMs possessed good representativity of the 30–50 mg tablets, high precision, operational convenience, and could be recommended for the INAA of a wide range of medico-biological and bioecological objects.     

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.