Asymptotic analysis of acoustic black hole effect in cylindrical shells.

The acoustic black hole (ABH) effect is investigated within the framework of thin shell theory. Asymptotic solutions to the dispersion equation for the thin cylindrical shell are obtained, and the ABH effect is examined using analytical formulas for group velocities and anti-derivatives of the asymptotic expansions of wave numbers. It is shown that the ABH effect is achievable in thin cylindrical shells with variable thickness, in a similar manner as for beams and plates. However, it should not be expected to exist in the low-frequency range where the flexural wave motion in the wall of a shell is strongly coupled with uniform longitudinal wave motion.

A Poisson scaling approach to backward wave propagation in a tube.

A mathematical analysis of wave propagation along an elastic cylindrical tube is presented, with the aim of determining the range of Poisson's ratio for which backward wave propagation (i.e. at negative group velocity) can occur near the ring frequency. This range includes zero Poisson's ratio and a surrounding interval of positive and negative values, whose width depends on the thickness of the tube. The whole range of Poisson's ratio is considered, so that the work applies to modern materials, e.g. composites. All results are presented in simple analytic form by means of a dominant balance in parameter space. The identification of this balance, which is unique, is a main new result in the paper, which makes possible a new type of shell theory based on 'Poisson scaling'. The mathematical approach is deductive from the equations of motion, rather than being based on kinematic hypotheses. A key finding, accessible via the Poisson scaling, is that the regime of negative group velocities extends to high wavenumbers, while being confined to a narrow band of frequencies. Thus responses localized in space are possible for near-monochromatic forcing, an important fact for nonlinear theories of tube dynamics near the ring frequency. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 1)'.

(Bi)-orthogonality relation for eigenfunctions of self-adjoint operators.

The bi-orthogonality relation for eigenfunctions of self-adjoint operators is derived. Its composition is explained in view of the structure of a characteristic equation and of the energy flow components. Application of the bi-orthogonality relation for solving forcing problems is generalized and the connection between the bi-orthogonality relation and the virtual wave method is highlighted. Technicalities are illustrated in a non-trivial example of propagation of free/forced cylindrical waves in a thin elastic plate under heavy fluid loading. This article is part of the theme issue 'Modelling of dynamic phenomena and localization in structured media (part 1)'.

A class of reduced-order models in the theory of waves and stability.

This paper presents a class of approximations to a type of wave field for which the dispersion relation is transcendental. The approximations have two defining characteristics: (i) they give the field shape exactly when the frequency and wavenumber lie on a grid of points in the (frequency, wavenumber) plane and (ii) the approximate dispersion relations are polynomials that pass exactly through points on this grid. Thus, the method is interpolatory in nature, but the interpolation takes place in (frequency, wavenumber) space, rather than in physical space. Full details are presented for a non-trivial example, that of antisymmetric elastic waves in a layer. The method is related to partial fraction expansions and barycentric representations of functions. An asymptotic analysis is presented, involving Stirling's approximation to the psi function, and a logarithmic correction to the polynomial dispersion relation.

[Use of recombinant alpha2-interferon and a complex immunoglobulin preparation for the treatment of chlamydiosis in pregnancy women]. / Primenenie rekombinantnogo alpha2-interferona i kompleksnogo immunoglobulinovogo preparata pri lechenii khlamidioza u beremennykh.

The comparative study of the efficiency of using erythromycin and the combination of recombinant alpha 2-interferon with complex immunoglobulin preparation (CTP) for the treatment of chlamydiosis in pregnant women was made. 31 patients (group 1) received erythromycin orally in doses of 500 mg twice a day for 15-14 days. 30 other pregnant women were prescribed vaginal suppositories containing 300 mg. Of CTP, 2.0 x 10(6) I.U. of recombinant alpha 2-interferon and the intravaginal application of 15(2)-30 ml of solution containing the analogous amount of CTP and recombinant alpha 2-interferon. Immediately after treatment 7 patients with clinical signs of chlamydiosis were found in group 1 and 3 such patients, in group 2. In the pregnant women of group 1 the laboratory confirmation of chlamydial infection after treatment occurred 5.8 times more frequently than in the patients of group 2. In 7 women of group 1 vaginal candidiasis was diagnosed after treatment. In no case any side effects resulting from the proposed treatment were observed. Pathology caused by chlamydiae was shown to be absent in newborns and in parturient women who had received complex treatment for chlamydiosis.

Myelopeptides effect on longevity and immunological parameters in mice with congenital immunodeficiency.

Myelopeptides (MP) are regulatory molecules produced by animal and human bone marrow cells. A highly purified MP fraction has been isolated from supernatant of the porcine bone marrow cell culture by gel chromatography on Sephadex G-25 and HPLC. MP correct defective antibody response to SRBC in MRL/lpr mice with spontaneous autoimmune disease and increase hemoglobin level in Wv/Wv mice with congenital anemia. Hemoglobin enhancement in Wv/Wv mice is connected with MP influence of differentiation and proliferation of hemopoietic stem cells. MP correction of immunological parameters in MRL/lpr mice resulted in 2-fold prolongation of their life span.

[Effects of immune lymph node factors on formation of immunological memory]. / Vliianie faktorov immunykh limfaticheskikh uzlov na formirovanie immunologicheskoi pamiati.

Two various fractions have been formed on the sephadex G-200 from culture supernatants of the lymph nodes cells isolated in 6h after immunization of animals by various antigens. The first fraction possessed the main biological properties peculiar to the earlier described factor of the immune lymph nodes (FILN), intensified proliferation of cells of the popliteal lymph nodes and increased the killer activity of peritoneal lymphocytes. Introduction of FILN simultaneously with ram erythrocytes led to more than a five-fold increase of humoral immune response.