Integration of the equations of planar and flexural vibrations of anisotropic plates in special functions of generalized complex variables

On the basis of the method of successive approximations in formal series we construct systems of particular solutions of the equations of planar and flexural harmonic vibrations of thin rectilinear anisotropic plates with a plane of symmetry of elastic properties parallel to the faces. The solutions constructed are classified as special sk-functions of generalized complex variables. Translated fromTeoreticheskaya i Prikladnaya Mekhanika No. 24, 1993, pp. 54–61.     

Symmetric normal wave spectrum in an orthotropic layer

A solution is constructed for an orthotropic layer with free plane faces, that corresponds to the plane elastic waves symmetric over the thickness. The dynamical reconstruction of the normal wave spectrum during rotation of the wave vector from one to another elastically equivalent direction is investigated on the basis of a numerical analysis of the dispersion equation.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 19, pp. 116–121, 1988.     

Numerical and experimental investigation of burner device for anode gas reburning

A complex numerical and experimental investigation of burner devices for a reburning of the anode gas of aluminum production was carried out. The chosen mathematical model of the processes of aerodynamics, heat exchange, and gas burning was identified and adapted on the basis of data of real-scale measurements. Basing on computational experiments the optimization of the design of elements of the system for anode gas detoxication and transport was carried out. A new system was proposed and tested for reburning the anode gases of electrolysis production, which consists of an improved burner device and a dust-sedimenting chamber with a possibility of regulating the amount of gas suction.     

Redox troponization of (η5-cyclopentadienyl)(η4-4-menthyl-4-exo-trichloromethylcyclohexa-2,5-dien-1-one)rhodium as a novel approach to the synthesis of metal-coordinated nonbenzenoid aromatics of the tropone seriesas a novel approach to the synthesis of metal-coordinated nonbenzenoid aromatics of the tropone series

The possibility of redox troponization of a gem-polyhalomethylated semiquinoid system, π-coordinated to a metal atom, was shown in relation to the reaction of (η⁵-cyclopentadienyl)(η⁴-4-menthyl-4-exo-trichloromethylcyclohexa-2,5-dien-1-one)rhodium with Pd(PPh₃)₄. The reaction occurs with retention of the metal coordination affording a sevenmembered organometallic derivative of the nonbenzoid aromatic series, namely, (η⁵-cyclopentadienyl)(η⁴-4-chloro-5-menthylcyclohepta-2,4,6-trien-1-one)rhodium, whose structure was established by means of elemental analysis, NMR, and mass-spectral data. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1255–1256, June, 1998.     

New aromatizational transformations of 4-methyl-4-trichloromethyl-substituted 2,5-cyclohexadiene triphenylphosphonium and pyridinium ylides: Abstraction or 1,6-migration of the CCl3 group

4-methyl-4-trichloromethylcyclohexadiene triphenylphosphonium ylide obtained by treatment of (1-methyl-1-tricholoromethylcyclohexa-2,4-dien-4-yl)-triphenylphosphonium bromide with BuⁿLi in THF is stabilized by the abstraction of the CCl₃ group to give (p-tolyl)triphenylphosphonium cation, which was isolated as the corresponding hydroxide. Conversely, an analogous pyridinium ylide, obtained by treatment ofZ/E stereoizomericN-(1-methyl-1-trichloromethylcyclohexa-2,5-dien-4-yl)pyridiunium bromide with a base (piperidine in CD₂Cl₂, BuⁿLi in THF), at temperatures above −40 °C, undergoes a novel high-yield aromatizational skeletal rearrangement with migration of the CCl₃ group to position 2 of the heterocycle. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 386–388, February, 1997.     

Numerical simulation of nanoparticle melting inside a matrix

A theoretical model is proposed for describing the melting of a metal nanoparticle embedded into a solid matrix. The model is based on a thermodynamic approach that takes into account matrix elasticity. The melting process is described for gold nanoparticles embedded in a solid matrix whose elastic modulus is varied in a wide range. Both spherical and ellipsoidal particles are considered. It is shown that particle melting temperature can be both higher and lower than the melting point of a bulk sample depending on the interaction intensity of the solid and liquid particle surfaces with the matrix. An increase in the shear modulus of the matrix causes a rise in the nanoparticle melting temperature, with the effect of the matrix elasticity becoming noticeable at some critical shear modulus. The conditions are revealed at which only a surface layer of a nanoparticle, the thickness of which depends on the particle radius and temperature, is melted.     

Bending normal waves in a crystal layer surrounded by a liquid

We obtain the dispersion relations that describe the spectrum of the “effluent” harmonic antisymmetric normal waves for an arbitrary direction in the plane of an orthotropic layer surrounded by a viscous or ideally compressible fluid. We present the results of computation of the lower branches of the dispersion spectrum for elastically equivalent directions of propagation in a layer of monocrystal Seignette salt in water. Four figures. Bibliography: 5 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 28, 1998, pp. 123–131.     

Electrostatic field and charge distribution in small charged dielectric droplets

The charge distribution in small dielectric droplets is calculated on the basis of continuum medium approximation. There are considered charged liquid spherical droplets of methanol in the range of nanometer sizes. The problem is solved by the following way. We find the free energy of some ion in dielectric droplet, which is a function of distribution of other ions in the droplet. The probability of location of the ion in some element of volume in the droplet is a function of its free energy in this element of volume. The same approach can be applied to other ions in the droplet. The obtained charge distribution differs considerably from the surface distribution. The curve of the charge distribution in the droplet as a function of radius has maximum near the surface. Relative concentration of charges in the vicinity of the center of the droplet does not equal to zero, and it is the higher, the less is the total charge of the droplet. According to the estimates the model is applicable if the droplet radius is larger than 10 nm.     

On identities in groups of fractions of cancellative semigroups

To solve two problems of Bergman stated in 1981, we construct a group such that contains a free noncyclic subgroup (hence, satisfies no group identity) and , as a group, is generated by its subsemigroup that satisfies a nontrivial semigroup identity.