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.     

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.     

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.     

Database reverse engineering: From requirements to CARE tools

This paper analyzes the requirements that CASE tools should meet for effective database reverse engineering (DBRE), and proposes a general architecture for data-centered applications reverse engineering CASE environments. First, the paper describes a generic DBMS-independent DBRE methodology, then it analyzes the main characteristics of DBRE activities in order to collect a set of desirable requirements. Finally, it describes DB-MAIN, an operational CASE tool developed according to these requirements. The main features of this tool that are described in this paper are its unique generic specification model, its repository, its transformation toolkit, its user interface, the text processors, the assistants, the methodological control and its functional extensibility. Finally, the paper describes five real-world projects in which the methodology and the CASE tool were applied. This is a heavily revised and extended version of “Requirements for Information System Reverse Engineering Support” by J.-L. Hainaut, V. Englebert, J. Henrard, J.-M. Hick, D. Roland, which first appeared in the Proceedings of the Second Working Conference on Reverse Engineering, IEEE Computer Society Press, pp. 136–145, July 1995. This paper presents some results of the DB-MAIN project. This project is partially supported by the Région Wallonne, the European Union, and by a consortium comprising ACEC-OSI (Be), ARIANE-II (Be), Banque UCL (Lux), BBL (Be), Centre de recherche public H. Tudor (Lux), CGER (Be), Cockerill-Sambre (Be), CONCIS (Fr), D'Ieteren (Be), DIGITAL, EDF (Fr), EPFL (CH), Groupe S (Be), IBM, OBLOG Software (Port), ORIGIN (Be), Ville de Namur (Be), Winterthur (Be), 3 Suisses (Be). The DB-Process subproject is supported by the Communauté Fran?aise de Belgique.     

Kinetics of benzonitrile nitration with mixed acid under homogeneous conditions

Chemical kinetics of benzonitrile nitration with mixed acid is investigated in the temperature range 283–299 K. Pseudo-first-order rate constants are evaluated by means of rate experiments on homogeneous reacting mixtures having large stoichiometric excesses of nitric acid. The second-order kinetic constants for nitronium ion attack to the aromatic substrate are derived on the basis of the assessed nitration mechanism. An activation energy of 604 ± 37 kJ mol^?1 is calculated for this reaction step. © 1993 John Wiley & Sons, Inc.