Viscoelastic state of a three-layer cylindrical shell during impulsive thermomechanical loading

Belorussian Institute of Railroad Transportation Engineers, Gomel'. Translated from Prikladnaya Mekhanika, Vol. 27, No. 3, pp. 46–52, March, 1991.     

Upper bounds for the moduli of zeros of Hermite–Padé approximations for a set of exponential functions

In this paper, we establish upper bounds for the moduli of zeros of Hermite–Padé approximations of type I for a system of exponential functions \(\left\{ {{e^{{\lambda _{{p^z}}}}}} \right\}_{p = 0}^k\), where \(\left\{ {{\lambda _p}} \right\}_{p = 0}^k\) are various arbitrary complex numbers. The proved statements supplement and generalize well-known results due to Saff and Varga, as well as those due to Stahl and Wielonsky, on the behavior of zeros of Hermite–Padé approximations for a set of exponential functions \(\left\{ {{e^{pz}}} \right\}_{p = 0}^k\).     

The Influence of the Molecular Structure of Cyanine Dye on the Component Composition of Molecular Layers

The formation of the component composition of symmetric cationic cyanine dyes on glass is studied. The absorption spectra of layers of three homologous series of dyes with end heterocyclic groups of different spatial and chemical compositions are measured, and the absorption spectra of monomer components and aggregates are separated. The component compositions of layers of different thicknesses are compared. It is shown that the widening of the absorption spectra of molecular layers against the spectra of ethanol solutions of these compounds is caused mainly by the formation of various monomer stereoisomers and molecular aggregates and their interaction with the substrate surface and the neighborhood. The number of isomer forms and their relative concentrations depend on the layer thickness, the electron donor ability and spatial structure of end groups, and the cation conjugation chain length. The influence of the anion manifests itself only in the concentration ratio of the formed monomers and a small shift of the maxima of their absorption bands. The increase in the number of monomer forms produced in the layer corresponds to the increase in the conjugation chain length. Spatial obstacles created by heterocyclic groups inhibit the formation of definite stereoisomers, which reduces the number of components of the layer.     

Optimal control of a cylinder rotating in a viscous fluid

Under consideration is the axisymmetric problem of optimal boundary control of a mechanical system consisting of two coaxial cylinders and an incompressible viscous fluid filling the region between them. The control parameter is the angular velocity of the outer cylinder. The goal is to stop the interior cylinder at a prescribed time with minimal energy expense. We prove that the problem is uniquely solvable and obtain the optimality system.     

Ion-implanted deuterium accumulation in a deposited tungsten coating

The effects of trapping of ion-implanted deuterium and its thermal desorption on the structure and stressed state of a tungsten coating deposited on a composite substrate is studied. The amount of accumulated deuterium, macrostresses of the coating, and the shape of thermal desorption spectra are shown to depend on the D⁺ ion fluence and the irradiation temperature. Possible mechanisms of these processes are proposed.     

Vibrations of a Sandwich Rod under Local and Impulsive Forces

The forced vibrations of a sandwich rod under local impulsive surface loads and concentrated forces and moments are studied. The hypothesis of broken normal is used to describe the kinematics of the rod, which is asymmetric in thickness. The core is assumed to be rigid and compressible. An analytic solution is obtained and analyzed numerically __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 7, pp. 122–129, July 2005.     

Thermoplastic strain of circular sandwich plates on an elastic base

We consider thermomechanical bending of an elastoplastic circular (solid or annular) light-filler sandwich plate resting on an elastic base. The hypotheses of broken normal are used to describe the kinematics of the plate stack nonsymmetric along the thickness. The base reaction is described by the Winkler model. We obtain the system of equilibrium equations and its exact solution in terms of displacements. We also present numerical results for a sandwich annular metal-polymer plate.     

Rational Approximations of Riemann--Liouville and Weyl Fractional Integrals

We obtain exact rational approximation orders for functions expressible as Riemann--Liouville and Weyl fractional integrals. New results and the strengthening and generalization of theorems due to Popov, Petrusheva, Pekarskii, Rusak, and the author, which are well known in the theory of rational approximation of differentiable functions, are obtained as consequences of theorems due to Pekarskii related to rational approximation of functions from the Hardy--Sobolev classes in the unit disk.