A generalization of the method of Hermitian forms and an application of it in the theory of separation of spectra of operator bundles

We establish a connection between the methods of Hermite, Schur, and Lyapunov in the theory of stability of polynomials. We state generalizations of the criterion for stability and the concept of the resultant and the Bezoutiant to polynomial operator bundles. We consider some questions in the factorization of operator bundles. We study certain classes of generalized spectral problems (linear with respect to the spectral parameter and multiparameter problems).Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 35, 1992, pp. 185–189.     

Neutron diffraction study of magnetic properties of TmCo2

The present neutron diffraction studies have confirmed that TmCo₂ represents an exception within the RCo₂ series. It was found that, in contrast with other heavy RCo₂ compounds, the Co sublattice in TmCo₂ does not order magnetically below the Curie temperature (T_c = 3.9 K). This is assumed to be due the fact that in TmCo₂ the intersublattice (f-d) molecular field is smaller than the critical field necessary to induce magnetic order within the Co sublattice, as is the case in other RCo₂ compounds. Furthermore, we show that the magnetic structure and the onset of long-range order in TmCo₂ depend sensitively on the sample preparation, which partly explains the differing results published earlier.     

Rapid multielemental analysis of Chinese reference soils by laser ablation inductively coupled plasma-source mass spectrometry

Summary Laser ablation inductively coupled plasma-source mass spectrometry has been used to determine thirty elements (Na, Mg, Al, K, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, As, Rb, Sb, Cs, Ba, La, Ce, Nd, Sm, Eu, Dy, Ho, Yb, Hf, Ta, W, Th, U) in seven Chinese reference soils. The Surrey prototype spectrometer was employed with sample ablation by a free-running ruby laser. Concentrations in the soils (GSS-2 to GSS-8) were calculated from elemental responses and sensitivities derived from another soil in the series, namely GSS-1. Comparisons with previous neutron activation analyses are made. Rapid semiquantitative analyses are proved feasible. About eighty percent of the LA-ICP-MS determined concentrations were within a factor of two of the concentrations measured by INAA, and many were considerably closer than this. Precisions were typically in the range 2–10% RSD, but some were considerably poorer for elements present at trace levels.     

Study of perfection of layers of AlGaSb(AS) solid solution

Studies have been carried out on the perfection of then-Al_xGa_1–xSb_1–yAs_y (0.12x0.26) layer grown on GaSb substrates under different conditions of lattice matching. During the relaxation of the mechanical stresses at first a system of tilt dislocations with a density of up to 5 · 10⁵ cm^–2 is formed while in thick layers (h 20 m) a network of misfit dislocations parallel to the heteroboundary is formed. The time required to dissolve a weighed amount of GaAs in the melt is shown to be of major importance for obtaining layers of a solid solution that are isoperiodic with the substrate. The entry of arsenic only in the initial portion of the epitaxial layer can reduce the dislocation density in the layer without decreasing the measured value of Aa. Dissolution of a weighed amount of GaAs in a Ga + Sb melt for two hours at T=730–750°C is sufficient to obtain layers of Al_xGa_1–xSb_1–yAs_y solid solution that are isoperiodic with the substrate.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 84–89, January, 1988.In conclusion, we thank L. V. Druzhinina for useful discussions as well as Z. V. Korotchenko, L. S. Khludkova, and F. S. Kim for assistance in the performance of the experiments.     

Qualitative analysis of finite-gap solutions of the KgΦ equation by the automorphic approach

By the automorphic approach and the use of computer graphics, we carry out a qualitative analysis of finite-gap periodic solutions of the Kg equation. Graphs are constructed for multiphase solutions.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 165, pp. 31–41, 1987.     

A finiteness criterion for the number of rational points for twisted weil elliptic curves

We consider the Weil elliptic curve E/ℚ and let be its canonical L-series. Admitting the Birch-Swinnerton-Dyer conjecture and fixing the curve E, a criterion is given for the finiteness of the group E_D(ℚ) for twisted elliptic curves E_D, defined by the condition

Addendum to the paper “on a theorem of Miranda”

An existence theorem is proved for closed convex surfaces whose principal radii of curvature regarded as functions of the unit normal vectorn satisfy the equation

On the reductibility of the general existence problem for closed convex surfaces to Miranda's equation

It is proved that the solution of the general existence problem for closed convex surfaces with prescribed local propertiesf(R ₁ R ₂,R ₁+R ₂,n)=(n) can be obtained as the solution of Miranda's equationR ₁ R ₂+(f)+cn=((n),(n)) with right-hand side depending on the unknown surface under the hypothesis that the latter satisfies the closure condition , where is the unit sphere andd is its element of area.Translated from Ukrainskií Geometricheskií Sbornik, Issue 29, 1986, pp. 103–112.     

Comparative analysis of (p,d), (d,t) and (3He, α) reactions on13C nucleus

The angular distributions of the (p, d), (d, t) and(³He, ) reactions on¹³C have been analysed within the framework of DWBA in which additional information on nuclear vertex constants was introduced. Although all these reactions seem to be similar single nucleon transfer, their mechanism is shown to be quite different and so is the information extracted thereof. While from the (p, d) reactions spectroscopic factors may be extracted unambiguously, from the (d, t) reactions it is possible to obtain directly the values of vertex constants only, which in turn are consistent with those determined by extrapolation of the experimental cross sections of the (p, d) reactions to the pole.In the case of (³He, ) reactions, however, the analysis indicates inadequacy of the DWBA concerning the calculations of central partial amplitudes. For a more reliable extraction of structural information, besides the correct normalization of peripheral amplitudes, a contribution of more complex mechanisms must be taken into account.