Explicit construction of elements of the ring S(n,r) of invariants of n-ary forms of degree r

Translated from Matematicheskie Zametki, Vol. 51, No. 2, pp. 139–143, February, 1992.     

Kink propagation induced by multiplicative noise

The influence of spatio-temporal external multiplicative fluctuations on a single kink in a bistable distributed system is studied. For this purpose we derive a stochastic dynamic equation for the position of the shifted kink. An analytical estimate for spatio-temporally uncorrelated fluctuations is represented and discussed. We draw the conclusion that multiplicative noise induces a propagation of the most probable kink into the region of larger noise. This effect is demonstrated in numerical simulations.     

Principles and recent developments in ultrasound contrast agents

The behaviour of gas bubbles and gas encapsulated spheres as echographic contrast agents is reviewed. Compared with rigid spheres, gas bubbles are superior scattering agents and they offer a number of useful properties which can be exploited in a variety of ways. The analysis of their velocity of sound, back-scatter intensity, second harmonic emission and resonant frequency opens up new perspectives in the development of contrast agents for echocardiographic research with potential clinical applications.     

Nonlinear and bistable properties of doped PMMA lightguides

Polymer lightguides of PMMA doped with the azo dyes methyl-red and N, N-dihexyl-4-amino-4'-nitro-azobenzene (DHANA) are investigated with respect to their opto-optical properties. The trans-cis photoisomerisation of the dyes leads to reversible polarization-dependent optically induced refractive index changes. The index changes are anisotropic. Birefringence is measured using index matched lightguides. The changes with respect to each polarization are determined by leaky mode spectroscopy and by using a half-integrated interferometer. These changes are intensity dependent and, with a suitable geometry, bistability at low intensities (3 mW/mm³) can be obtained.     

Matrix representation of three-dimensional astigmatic resonators

Three-dimensional astigmatic resonators, typical examples of which are the resonators bounded by cylindrical-spherical mirrors and cylindrical-cylindrical mirrors oriented at an arbitrary crossed angle, are investigated in detail by using a complex curvature tensor concept and generalized tensor ABCD law. Computerized numerical calculations illustrate some interesting characteristics of these astigmatic resonators.     

Nonlinear oblique propagation of magnetohydrodynamic waves in the solar wind

Summary Oblique propagating magnetohydrodynamic waves with various wave forms and amplitudes are observed both at the Earth's foreshock and at comets. The possibility of interpreting some observational results in terms of nonlinear evolution of one- and two-dimensional hydromagnetic waves is investigated. For this purpose both analytical and numerical techniques are employed. It is found that an initial monochromatic wave changes its polarization giving origin to magnetosonic shocks and rotational discontinuities; the time evolution of density-magnetic-field correlation is studied, as a function of the plasma parameters and of the propagation angle. In the two-dimensional case both a transverse instability and a self-focusing effect may take place. Moreover, a two-dimensional magnetosonic solution is found, in which the density fluctuations are driven by the total pressure fluctuation as in a one-dimensional simple wave. These theoretical predictions compare well with the features observed in the solar-wind waves. Paper presented at the V Cosmic Physics National Conference, S. Miniato, November 27–30, 1990.     

Specific carbon-13 labelling of leucine residues in human growth hormone.

Biosynthetic human growth hormone specifically 13C-labelled in the carbonyl positions of all 26 leucine residues has been obtained by recombinant DNA techniques using 13C-labelled leucine and an E. coli strain that requires leucine. It is shown that, on the whole, the labelling is specific with no significant mislabelling as would have been the case had the 13C-labelled leucine been metabolized.     

Scaling up in isolation of medium-size uraemic toxins

Plasmatic accumulation of uraemic toxins in the middle molecular mass range has been reported to be associated with several pathologies observed in uraemic patients. The very low concentration of these toxins in uraemic body fluids makes classical chromatography techniques inadequate in isolating sufficient amounts of these endogenous substances, thus precluding their identification. A scaling up of gel permeation and ion-exchange chromatographies was therefore developed. This considerably increased the amount of uraemic toxins isolated, thus allowing the study of their chemical nature and facilitating understanding of their biological activities.