Automorphic equivalence of the representations of Lie algebras

We prove that if a field k is infinite, char(k)=0 and k has not nontrivial automorphisms then automorphic equivalence of representations of Lie algebras coincide with geometric equivalence. We achieve our result by consideration of 1-sorted objects. We suppose that our method can be perspective in the further researches.Comment: 28 page

Associative nil-algebras over finite fields

The nilpotency degree of a relatively free finitely generated associative algebra with the identity $x^n=0$ is studied over finite fields.Comment: 12 page

Indexing of the space data in the CSDB Microsoft SQL Server 2000

2 schemes of space indexing are realized in environment of CSDB Microsoft SQL Server 2000. The experimental research of the realized methods for window inquiries is carried out. Comparison of the realized methods with available in the standard means of indexing being in the given CSDB has been carried out. To find the quadrant splitting in methods Z-and XZ-indexing the heuristic algorithm which gives a smaller error of approximation in comparison with standard algorithm is proposed

Impurity-induced smearing of the spin resonance peak in Fe-based superconductors

The spin resonance peak in the iron-based superconductors is observed in inelastic neutron scattering experiments and agrees well with predicted results for the extended s-wave ($s_\pm$) gap symmetry. On the basis of four-band and three-orbital tight binding models we study the effect of nonmagnetic disorder on the resonance peak. Spin susceptibility is calculated in the random phase approximation with the renormalization of the quasiparticle self-energy due to the impurity scattering in the static Born approximation. We find that the spin resonance becomes broader with the increase of disorder and its energy shifts to higher frequencies. For the same amount of disorder the spin response in the $s_\pm$ state is still distinct from that of the $s_{++}$ state.Comment: 4 pages, 2 figure