Integrability of Solutions of Nonlinear Elliptic Equations with Right-Hand Sides from Logarithmic Classes

We establish the existence of a weak solution to the Dirichlet problem belonging to a Sobolev space for nonlinear elliptic equations of second order with right-hand sides from a wide class of functions defined in terms of the logarithmic function.     

The effect of side substituents on rotation hindrance in polyheteroarylenes

Hindered rotation was considered in calculations of the conformational parameters of a series of polyheteroarylenes with bulky side substituents by the Monte-Carlo method. Within the range of experimental errors, the results of calculations for several polyarylates coincide with the values of conformational rigidity, determined from hydrodynamic experimental data. The proposed procedure was used to estimate the rigidities of a number of polymers with bulky side substuents for which experimental determination is difficult. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1287–1296, July, 1998.     

An integral representation of solutions and the problem of coupling factors for a linear differential equation

The equation ²–(³+a ₂²+a ₁+a ₀)=0, which is encountered in problems of mechanics, is considered in the work. It has two singular points: a regular singular point at zero and an irregular singular point at infinity. A fundamental family of solutions (f.f.s.) can be constructed in the form of integrals of Mellin-Barns type where the integrand satisfies a linear difference equation with polynomial coefficients. On the basis of this representation a f.f.s. is constructed in a neighborhood of zero, and its asymptotics at infinity is found. The coefficients of this asymptotics (the coupling factors) can be represented in the form of analytic expressions containing certain solutions of the difference equation adjoint to the difference equation previously mentioned. In contrast to previous works of the author, the general case of the initial equation is investigated.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 140, pp. 88–104, 1984.     

The pyrylation of aromatic and heterocyclic compounds

Pyrylium salts having no substituents in position 4 react with aromatic and heteroaromatic compounds forming 4-aryl- and 4-heterylpyrylium derivatives. The reaction takes place through the stage of the formation of a pyran which, with an excess of the initial pyrylium salt, splits out a hydride ion, aromatizing into a trisubstituted pyrylium cation.Translated from Khimiya Geterotsiklicheskikh Soedinenii, Vol. 6, No. 6, pp. 733–738, June, 1970.     

Formation of semiconductor titanium disilicide

Nanostructured titanium disilicide powders with semiconductor properties are synthesized and studied. The optical and electrophysical properties of TiSi₂ are found to be controlled by its crystallite size.     

The properties of the surface of molten mixtures of the LiCl-KCl eutectic with praseodymium,samarium, erbium,and ytterbium chlorides

The temperature dependence of surface tension was studied and the excess Gibbs energy of the surface of a sphere with a molar volume of molten quasi-binary mixtures of the LiCl-KCl eutectics with LnCl₃ (Ln = Pr, Sm, Er, and Yb) was calculated. The influence of rare-earth and alkali metal cations on the surface properties of the systems studied was considered. Deviations from ideal surface tension isotherms and excess Gibbs energy of the surface of a sphere with a molar volume are explained by the complex structure of melts.     

Local modification of thin oxide films on a titanium surface

It is shown that a controllable structural rearrangement of a thin titanium oxide film, accompanied by a change in the bandgap width, can be accomplished under the probe tip of a scanning tunneling microscope (STM). The mechanism of the rearrangement is considered to be the migration of cations and oxygen vacancies in the electric field of the STM.