Lyapunov’s direct method in estimates of topological entropy

An upper estimate for the topological entropy of a dynamical system defined by a system of ODE is obtained. The estimate involves the Lyapunov functions and Losinskii’s logarithmic norm. The proof uses the known fact that the topological entropy of a mapping acting in a compact space K can be estimated via the fractal dimension of K. Bibliography: 28 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 231, 1995, pp. 62–75. Translated by V. A. Boichenko and G. A. Leonov.     

Stimulating effect of graphite admixture on hydrogen sorption-desorption properties of mechanically activated titanium powder

The effect of graphite admixture on hydrogen sorption-desorption properties of mechanically activated electron microscopy, temperature-programmed reaction, and temperature-programmed desorption techniques. The major effect of graphite addition was found to be the formation of microporous carbon matrix particles containing randomly distributed titanium particles only several nanometers in diameter. This powder architecture enhances hydrogen transport to the titanium surface without hindrances and promotes titanium-hydrogen interaction by modifying the titanium surface and subsurface layers with interstitial carbon atoms.     

Stability and Oscillations of Solutions of Integro-Differential Equations of Pendulum—like Systems

A system of nonlinear differential equations of the type on a domain of ?ⁿ is studied. Functional relations between the f_j's, j = 1, …, n, and other necessary conditions are deduced when at each point of the domain the system has a manifold of local solutions. A structure theorem, that makes possible to reduce the problems of the system, e.g. the global solvability of it, to the corresponding questions for a connection of the type ?_z?w = g(z, w) in a fibre bundle over a Riemann surface is proved, and through this reduction we obtain theorems of identity, extension, global factorization, and so on, for the solutions of the system. As an example, a system of nonlinear differential equations of the type is studied and its global solutions are constructed.     

Synthesis and structure of neutral π-arene complex (η6-C6H5Me)U(AlCl4)3

A new neutral -arene complex of trivalent uranium, (⁶-C₆H₅Me)U(AlCl₄)₃ (1), was obtained by the reductive Freidel-Crafts reaction. The crystal structure of 1 was determined by single crystal X-ray diffraction analysis. The U atom in 1 is bound to the C₆H₅Me group by the ⁶ mechanism and is linked to the three AICl₄ groups through two g-CI bridges. The coordination of the U atom is a distorted pentagonal bipyramid in which the center of the arene ring is in one apical position, and the bridging Cl atoms occupy the other vertices.Translated from Izvestiva Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 469–472, February, 1996.     

Workspaces of the Stewart platform in the 6D space of generalized coordinates

The kinematics and dynamics of the classical Stewart platform is studied. The platform is a rigid body supported by six rods of variable length. Well-known differential equations describing the motion of the platform are presented. The main attention is paid to an analysis of workspaces in the 6D space of generalized coordinates. The projections of these workspaces on spaces of lower dimension are found.     

Using localized surface plasmons to modify the optical properties and conformational rearrangements of organic dye molecules

Optical properties of the molecular layers of cyanine dyes and their modification in a nearby field of silver nanoparticles on a sapphire substrate are investigated experimentally. Enhancement of the fluorescence and absorption intensity of organic molecules in the presence of silver nanoparticles is observed. The results from photomodifications of the molecular layers’ absorption properties with and without the presence of silver nanoparticles are described.     

Aircraft control with anti-windup compensation

We consider an anti-windup compensation method ensuring the convergence of the closed-loop system for a class of reference signals. An application of the method to an aircraft flight control problem is shown.     

The Tricomi problem on the existence of homoclinic orbits in dissipative systems

The principles of the proof of the existence of homoclinic orbits in dissipative dynamical systems are described. The application of these principles in the case of a Lorenz system enables new criteria for the existence of homoclinic orbits to be formulated.