Variation of the instability index on stationary curves of elliptic equations depending on a parameter

The set of solutions of the equation A(u, )=0 in the case of general position consists of smooth curves. Solutions of a quasilinear elliptic equation with large instability index are constructed and an estimate obtained for the number of turning points of the solution curves.Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 12, pp. 47–58, 1987.     

Spectrum of the algebra of pseudodifferential operators in a halfspace

One considers C*-algebras, generated by pseudodifferential operators in a halfspace. The operators act in functional spaces with weighted norms. One describes the set of all classes of equivalent irreducible representations of algebras and reveals the topology on the spectrum. One investigates, in particular, the dependence of the spectrum on the choice of the weighted functional space.Translated from Problemy Matematicheskogo Analiza, No. 10, pp. 160–180, 1986.     

Homogeneous spaces and invariant tensors

In the present survey a method is presented for the construction of invariant tensors (with respect to a given representation) called the inclusion principle and the possibility of applying the cited method to various problems of algebra, topology, geometry, and analysis.Translated from Itogi Nauki i Tekhniki, Seriya Problemy Geometrii, Vol. 18, pp. 105–142, 1986.     

Relative index theorems and supersymmetric scattering theory

We discuss supersymmetric scattering theory and employ Krein's theory of spectral shift functions to investigate supersymmetric scattering systems. This is the basis for the derivation of relative index theorems on some classes of open manifolds. As an example we discuss the de Rham complex for obstacles in ^N and asymptotically flat manifolds. It is shown that the absolute or relative Euler characteristic of an obstacle in ^N may be obtained from scattering data for the Laplace operator on forms with absolute or relative boundary conditions respectively. In the case of asymptotically flat manifolds we obtain the Chern-Gauss-Bonnet theorem for theL ²-Euler characteristic.On leave of absence from Institute of Physics, Leningrad State University, Leningrad     

Sensitivity of hydrodynamic system of the Obukhov type

The paper deals with the regime of advanced Bénard instabilities (described usually by the Lorenz system) in a more general system formulated firstly by Obukhov. It has been shown that triplet co-operation leads to characteristic courses where some new regularities occur.     

Computer-simulated diffraction patterns for metastable austenitic steels

The paper deals with the computer simulation of composite theoretical electron-diffraction patterns for metastable austenitic steels, containing deformation and martensite transformation structures. In many cases generated data can be used for interpretation of experimentally determined diffraction patterns. A few examples are presented which demonstrate that the application of the composite theoretical diffraction patterns may be complicated due to various diffraction effects which can modify the geometry of experimentally obtained diffraction patterns.     

Linear mode conversion of waves near the maxima or minima of the density in a warm magnetized plasma

Behaviour of the h. f. electrostatic waves near the plasma or upper hybrid resonances was studied in the case that these resonances are situated at the maxima or minima of the plasma density. Supposing the parabolic density profile in these regions we obtained the connection formulae for the WKB solutions. In a weakly inhomogeneous magnetoplasma the effect of the parabolic profile manifests itself only in narrow frequency band centred at the resonance frequency corresponding to the extreme value of the density. The whole process can be then described by only two coefficients, viz. the power conversion and power transmission coefficients.     

Structural and electrical properties of quasicrystalline Al-14 at% Mn alloy

Quasicrystalline Al-14 at. % Mn alloy was prepared by melt-spinning and its structural and electrical properties were studied. This alloy consists of icosahedral grains with sizes from 1 to 4 m and of crystalline aluminium phase. The electrical resistivity was almost temperature independent with a value of about 765 n gWm at 4·2 K.