Asymptotics of solutions of a linear singularity perturbed system with degeneracy

Asymptotic expansions with respect to a small parameter e are constructed for a fundamental system of solutions of a linear singularity perturbed system of equations of the form

Results on the Generic Kurepa Hypothesis

K.J. Devlin has extended Jensen's construction of a model ofZFC andCH without Souslin trees to a model without Kurepa trees either. We modify the construction again to obtain a model with these properties, but in addition, without Kurepa trees inccc-generic extensions. We use a partially defined -sequence, given by a fine structure lemma. We also show that the usual collapse of Mahlo to ₂ will give a model without Kurepa trees not only in the model itself, but also inccc-extensions.     

Instability of the boundary layer on a curved surface

The excitation of instability of the boundary layer on a curved surface in the limit R (R is the Reynolds number) is analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 176–179, January–February, 1990.I am grateful to O. S. Ryzhov for his interest in the work.     

Behavior on the real line of entire functions represented by Dirichlet series with complex exponents

It is shown, in particular, that if _{n k} when n k, Re _n > 0, and , then an entire function F that is bounded on the real line and represented by a Dirichlet series d_n exp (_nz) that is uniformly and absolutely convergent on each compactum in is identically zero.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 7, pp. 882–888, July, 1990.     

A certain functional algebra

We study the algebra of functions on the set of natural numbers with respect to the generalized convolution, generated by the generalized translation operator T_nf(k)=f(max (n, k)), n, k. With the help of the generalized Fourier transform, connected with this convolution, we establish numerous identities and recurrence relations, connecting, in particular, sums of powers of natural numbers.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 3, pp. 372–377, March, 1990.     

Ray Theory of the Diffraction of Sound by an Inhomogeneous Membrane

Present address: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, U.K. In this paper, a ray approach is developed for calculating theacoustic radiation into a fluid generated by a localized forcingon an elastic boundary. We consider here the case of fluid-loadedmembrane with a rigid line-mass distribution subject to infiniteplane-wave incidence from the fluid. It is demonstrated howray methods can be used to determine each of the constituentwaves of the scattered acoustic field, showing that non-uniformitiesarise whenever two such waves have tangential wavefronts. Transitionanalyses are presented to remove these non-uniformities, resultingin the prediction of beam-like structures in the scattered field.     

A numerical analysis of chaotic behaviour in Bianchi IX models

In this paper we investigate the chaotic behaviour of the Bianchi IX cosmological models using techniques developed in the study of dynamical systems and chaotic behaviour. We numerically calculate the Lyapunov exponent, , and show that instead of converging to a constant value, it decreases steadily. We study this effect further by studying the Lyapunov exponent using short-time averages. We show that the usual method of calculating is invalid in the case of a cosmological model.     

Random fields and quantum effects in proton glasses

The effects of quantum fluctuations on the proton glass phase in mixed hydrogen-bonded ferro-antiferroelectric systems are considered. The system is described in terms of the infinite-ranged Ising pseudospin glass model in a transverse tunneling field in the presence of random parallel fields. The stability limit of the high-temperature proton glass phase is determined within the thermofield dynamic approach, and the behavior or linear and nonlinear susceptibility is evaluated.     

The clinical status of low energy laser therapy in 1989

Low energy laser therapy has gained varying acceptance as a treatment for a broad range of soft tissue, musculoskeletal and neurological conditions. A controversial, but surprisingly large body of research with cell cultures suggests that laser irradiation can nondestructively alter cellular processes. Unfortunately, animal and human studies are often contradictory and difficult to evaluate due to differing study designs. As a result, the clinical effectiveness of low energy laser therapy remains debatable. Nevertheless, the findings are intriguing and deserve further investigation.     

Relativistically covariant chronological ordering of interaction lagrangians

A general form of chronological ordering is proposed, based on introduction of relativistically invariant multipoint step functions (x₁, ..., x_n). A system of recursive relations is established for these functions, which guarantees that the scattering matrix is unitary, covariant, and causal. The explicit form of the first four -functions is found. A comparative analysis of the known methods of chronological ordering is given.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 70–73, May, 1990.