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.     

Critical behavior of the wave functions of icosahedral quasicrystals

The character of the localization of the wave functions of an icosahedral quasicrystal is investigated in the tight-binding approximation. It is found that the wave functions exhibit “critical behavior”: they are neither localized, as in the case of Anderson localization, nor delocalized, as in the case of Bloch states. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 8, 559–563 (25 October 1996)     

Comparative kinetics of phospholipase A2 action on liposomes and monolayers of phosphatidylcholine spread at the air-water interface

A detailed kinetic model describing the surface transformation of spread liposomes along with their enzymatic hydrolysis was developed. The model was applied to the hydrolysis of the long-chain phosphatidylcholine generating reaction products which remain at the interface and to medium-chain substrates from which the products desorb rapidly into the bulk phase. The overall kinetic constants of the hydrolysis in liposomal systems were compared with those obtained with monolayers under barostatic conditions. The values of the interfacial Michaelis-Menten constant were estimated.     

Formation of ultrashort microwave pulses in coaxial cavities

We describe shaper cavities for the production of ultrashort microwave pulses with a minimum duration of one period of the high-frequency field and a power of several tens of megawatts. Experimental results are presented.Scientific and Research Insititute for Nuclear Physics at S. M. Kirov Polytechnical Institute, Tomsk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, No. 12, pp. 1250–1256, December, 1995.     

The stationary problem of thermoelasticity for a plate with a heated slit

We consider the stationary heat conduction and thermoelasticity problem for a plate that whose lateral surfaces are thermally insulated and which has a slit on whose edges a constant temperature is maintained. The heat conduction problem is solved using a modified logarithmic single-layer potential by reducing it to integral equations.Translated fromMatematicheskie Melody i Fiziko-Mekhanicheskie Polya, Issue 31, 1990, pp. 50–54.     

Numerical solution of the electron distribution function for ECRheating in magnetic mirror

The Fokker-Planck equation is solved with electron cyclotron resonance heating in a magnetic mirror with a fixed electrostatic potential on a loss-cone boundary and ECR heating. A self-consistent calculation of the plasma concentration justifies the fact that the degree of ionization of the ECR plasma is about 10%. The high values of the total electron energy (15-30 eV) are achieved. The electron concentration and the EVDF anisotropy degree are the nonmonotonic functions of the applied MW electric field. The basis for such dependencies is discussed. A linear perturbation analysis of the Vlasov equation together with with Maxwell's equations is briefly reviewed. The criteria for the start of unstable whistler oscillation growth are proposed. Using the simulated distribution function, the regimes where the unstable oscillations should to be taken into account are considered