Solving a special system of differential equations

An explicit solution is obtained for a special system of ordinary differential equations of a high order. Such systems arise in problems associated with reliability of evolving engineering networks. The proposed solution is easily implemented on a computer.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 64, pp. 107–111, 1988.     

Marchenko-Ostrovski mappings for periodic Jacobi matrices

We consider 1D periodic Jacobi matrices. The spectrum of this operator is purely absolutely continuous and consists of intervals separated by gaps. We solve the inverse problem (including a characterization) in terms of vertical slits on the quasimomentum domain. Furthermore, we obtain a priori two-sided estimates for vertical slits in terms of Jacobi matrices. Dedicated to the memory of Vladimir Geyler     

Properties of solutions and films of blends of ethyl cellulose with polyvinylpyrrolidone and Poviargol

Viscosity properties of dilute and concentrated ethanol solutions of blends of ethyl cellulose with polyvinylpyrrolidone and Poviargol bactericidal formulation (silver metal nanoparticles stabilized with polyvinylpyrrolidone) were studied. The physicomechanical and thermomechanical properties of films prepared from solutions of the polymer blends were determined. Experiments on solvent vapor sorption showed that ethyl cellulose is incompatible with polyvinylpyrrolidone and Poviargol in the solid state in the entire composition range examined.     

Fluorescence Study of Lipid Bilayer Interactions of Eu(III) Coordination Complexes

The interaction between Eu(III) tris-β-diketonato coordination complexes (EC), displaying antitumor activity, and lipid vesicles composed of zwitterionic lipid phosphatidylcholine has been studied using fluorescence spectroscopy techniques. To characterize EC-membrane binding, several fluorescent probes, including pyrene, Prodan and 1,6-diphenyl-1,3,5-hexatriene, have been employed. It has been found that EC display effective partitioning into lipid phase, giving rise to structural modifications of both polar and nonpolar lipid bilayer regions, viz. enhancement of membrane hydration and increase in tightness of lipid chain packing. The fact that EC accumulating in lipid bilayer are incapable of inducing significant disruption of membrane structural integrity creates strong prerequisites for development of liposomal nanocarriers of these potential antitumor drugs. Such a possibility is also corroborated by the observation that EC membrane incorporation does not prevent lipid bilayer partitioning of long-wavelength squaraine dyes which represent promising candidates for visualization of liposome biodistribution.     

The matrix sign function for solving surface wave problems in homogeneous and laterally periodic elastic half-spaces

The matrix sign function is shown to provide a simple and direct method to derive some fundamental results in the theory of surface waves in anisotropic materials. It is used to establish a shortcut to the basic formulas of the Barnett–Lothe integral formalism and to obtain an explicit solution of the algebraic matrix Riccati equation for the surface impedance. The matrix sign function allows the Barnett–Lothe formalism to be readily generalized for the problem of finding the surface wave speed in a periodically inhomogeneous half-space with material properties that are independent of depth. No partial wave solutions need to be found; the surface wave dispersion equation is formulated instead in terms of blocks of the matrix sign function of i$i$ times the Stroh matrix.