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.

     

Dispersion relations for normal waves in a cylinder made of orthorhombic monocrystal with pyro- and piezoelectric properties

By integrating the system of differential equations of coupled thermoelectroelastic vibrations of a pyroactive crystal medium of the orthorbombic system in special nonclassical vector-valued functions of ordinary and generalized complex variables we construct the dispersion equation for normal waves in a cylindrical waveguide of circular cross section. The dispersion function is obtained in the form of a determinant of infinite order subject to reduction in numerical investigations. Bibliography: 3 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 28, 1998, pp. 118–123.     

Propagation,Dispersion, and Localization of Elastic Waves in Low-Symmetric Anisotropic Waveguides

The results of a theoretical investigation into ultrasonic linear normal wavefields in anisotropic three-dimensional bodies with mechanical orthorhombic symmetry are presented. A detailed study is made of the dispersion dependencies for higher normal wave modes in a single-layered orthorhombic plate-type waveguide. Moreover, the distribution of complex branches corresponding to the edge standing wave modes is studied and their role in the transformation of the entire spectrum upon a change in the travel direction in the waveguide plane is analyzed. A new type of localization of the higher modes of high-frequency short-range normal waves in a crystal layer is described. An efficient method is developed for studying the spectrum of ultrasonic normal waves in a circular cylindrical waveguide made of an orthorhombic monocrystal     

A numerical-analytic method of studying the dispersion of elastic waves in a fixed orthotropic cylinder with a simply connected curvilinear section

We give a method of constructing the dispersion equations for waveguides made of recitilinearly orthotropic materials and having a section that is either elliptic or approximately that of a regular 2n-gon (n>-2) with rounded corners. The equations of motion for the waveguide can be integrated in series of basic particular solutions of exponential type. The dispersion functions are obtained in the form of reduced infinite determinants from homogeneous functional boundary conditions on the lateral surface of the waveguide after these conditions have been algebraized using orthogonal series expansions. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 25, 1995, pp. 97–102.     

Measurement of rate constants of vibrational-rotational relaxation by the probing field method

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 55, No. 2, pp. 304–309, August, 1991.     

Dispersion of normal waves in a linearly orthotropic circular cylinder with a clamped lateral surface

We propose a method of obtaining the dispersion equation for normal waves in an orthotropic cylinder from the boundary conditions on the rigidly clamped boundary using a system of exponential particular solutions of the three-dimensional equations of its stationary wave motions. We compute the real and imaginary branches of the dispersion spectrum for a waveguide made of monocrystalline strontium sulfate. On figure. Bibliography: 7 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 26, 1996, pp. 96–99.     

IR-Spectroscopic Study of the Binding Isomerism of Adsorbed Molecules

This paper discusses the use of IR spectroscopy in the studies of isomerism in the binding of adsorbed molecules with a surface when a molecule may form several different surface species at the same site. Species whose geometry does not provide minimal adsorption energy can be considered as adsorption complexes in an excited state. The spectral manifestations of such a steric excitation are compared with the electronic and vibrational excitations of surface species. The sterically excited isomeric states existing in thermodynamic equilibrium with ordinary adsorption species are found and studied in detail. Examples are CO molecules bound through C and O atoms with metal cations in zeolites or with surface hydroxyl groups, the thiophene molecule via hydrogen bonding with silanol groups, and HD molecules dissociatively adsorbed on ZnO. A possible role of sterically activated isomeric states in catalysis is discussed.     

Differaction of plane deformation waves on a cylindrical cavity in an anisotropic bulk composed of a monoclinic system

An analytic-numerical method based on perturbations in the elastic moduli is proposed for solving problems involving the diffraction of two-dimensional longitudinal-shear harmonic deformation waves on a cavity with a smooth curvilinear cross section in an elastic medium with an anisotropy corresponding to a monoclinic system in the dynamic deformation plane. Results from a numerical analysis of the distribution of the dynamic stresses in the near diffraction field are presented for the case of longitudinal waves scattered on a dome-shaped cavity as the direction of the incident wave and the degree of anisotropy of the medium are varied. Donetsk State University. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 30, pp. 137–147, 1999.