Spectral problems for pencils of polynomial matrices. Methods and algorithms. V

Methods and algorithms for the solution of spectral problems of singular and regular pencils D(λ, μ)=A(μ)-λB(μ) of polynomial matrices A(μ) and B(μ) are suggested (the separation of continuous and discrete spectra, the computation of points of a discrete spectrum with the corresponding, Jordan chains, the computation of minimal indices and a minimal basis of polynomial solutions, the computation of the determinant of a regular pencil). Bibliography: 13 titles. Translated by V. N. Kublanovskaya Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 202, 1992, pp. 26–70     

Asymptotic expansions of solutions to singularly perturbed systems

Under the condition that a degenerate system has an exponentially stable integral manifold, an asymptotic expansion of the Cauchy problem that generalizes the well known Vasil'eva expansion is constructed for a perturbed system.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 4, pp. 552–560, April, 1993.     

On the magnetic and crystallization behaviour of iron based amorphous alloys determined by nuclei quenched in

The tendency of boron-containing, iron-based glasses to show non monotonic changes of Curie Temperature (T _c ) and room temperature saturation magnetization (SM) was examined by magnetic measurements and Mossbauer spectroscopy. Depending on B/Fe ratio theT _c and SM first increased up to a maximum value and then steadily decreased, probably because of a shortrange ordering, due to the strong chemical interaction between iron and boron atoms, leading iron atoms in vicinity with Fe-atoms rather than another TM-atom. Finally, the phenomenon becomes analogous to the order-disorder phenomenon in crystalline alloys. An observed unusual crystallization behaviour, consisting of heterogeneous nucleation, was also ascribed to this ordering, which leads to the formation of associations, acting as the first nuclei of crystallization.     

Advances in the chemical synthesis of brassinosteroids

This review generalizes the latest advances in the chemical synthesis of the plant growth regulators brassinosteroids in 1990–1994.Institute of Bioorganic Chemistry, Belarus Academy of Sciences, 220141, Minsk, ul. Zhodinskaya, 5/2. Translated from Khimiya Prirodnykh Soedinenii, No. 4, pp. 507–544, July–August, 1997.