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.     

One-loop divergences of linear gravity with torsion terms

We investigate the role of the torsion field at the quantum level. One-loop counterterms are calculated in the theory with terms quadratic in the torsion field. We have shown that the theory is finite at the one-loop level.     

Bases of free metabelian and transmetabelian groups

A definition of the basis of a group written in additive form is given based on P. Hall's collecting process. The bases of free rank 2 groups of the following three types are found: metabelian, transmetabelian of the first type (with an Abelian third term in the lower central series), and transmetabelian of the second type (the nilpotency class of whose derived group is equal to two).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademiya Nauk SSSR, Vol. 191, pp. 126–139, 1991.     

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.