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We study moduli spaces of O'Grady's ten-dimensional irreducible symplectic manifolds. These moduli spaces are covers of modular varieties of dimension 21, namely quotients of hermitian symmetric domains by a suitable arithmetic group. The interesting and new aspect of this case is that the group in question is strictly bigger than the stable orthogonal group. This makes it different from both the K3 and the K3^[n] case, which are of dimension 19 and 20 respectively.

The electronic structure of an oxygen vacancy in α-Al 2O3 and γ-Al2O3 is calculated. The calculation predicts an absorption peak at an energy of 6.4 and 6.3 eV in α-Al2O3 and γ-Al2O3, respectively. The luminescence and luminescence excitation spectra of amorphous Al2O3 are measured using synchrotron radiation. The presence of a luminescence band at 2.9 eV and a peak at 6.2 eV in the luminescence excitation spectrum indicates the presence of oxygen vacancies in amorphous Al2O3. © 2010 Pleiades Publishing, Ltd. ACKNOWLEDGMENTS This work was supported by the Siberian Branch, Russian Academy of Sciences (integration project no. 70).

This work gives the estimation of the influence of surface roughness, уІ and уІІ stresses, coherent regions size, dislocations density on the article structural strength after ion bombardment. It is found that the nanostructure formation and surface defects healing are of first importance for structural strength increase.

A failure of chips in a huge amount of modern electronic devices is connected as a rule with the undesirable capturing of charge (electrons and holes) by traps in a thin insulating film of silicon oxide in transistors. It leads to a breakdown of transistors or to a destructive change of their characteristics. It is suggested that silicon oxide will be replaced in the next generation of nanoscale devices by silicon oxynitride. Therefore, it is very important to understand the nature of traps in this material. We discuss this nature using the quantum-chemical simulation., Comment: 4 pages, LaTex, 1 gif file with 2 figures

The dominant dielectric used currently in silicon devices is silicon oxide. Its application for future devices will be impeded by several fundamental limitations which lead to low reliability of semiconductor devices and to the necessity of alternative dielectrics. Amorphous silicon nitride and oxynitride are considered now as alternative to silicon oxide in future devices. One of the unique property of amorphous silicon nitride is the electron and hole capture by the deep traps with extremely long life time (10 years) in the captured state (the memory effect). This property is employed in memory devices and microprocessors in computers. Despite numerous efforts the nature of traps responsible for the memory effect in this material is so far unclear. In this paper we discuss the nature of such traps using the quantum-chemical simulation. The calculations show that the defects responsible for the electron and hole capture in amorphous silicon nitride can be the Si-Si defects created by excess silicon atoms., Comment: 4 pages, LaTex

The elliptic genus (EG) of a compact complex manifold was introduced as a holomorphic Euler characteristic of some formal power series with vector bundle coefficients. EG is an automorphic form in two variables only if the manifold is a Calabi--Yau manifold. In physics such a function appears as the partition function of N=2 superconformal field theories. In these notes we define the modified Witten genus or the automorphic correction of elliptic genus. It is an automorphic function in two variables for an arbitrary holomorphic vector bundle over a compact complex manifold. This paper is an exposition of the talks given by the author at Symposium "Automorphic forms and L-functions" at RIMS, Kyoto (January, 27, 1999) and at Arbeitstagung in Bonn (June, 20, 1999)., Comment: AMS-TeX, 21 pages

In the paper we study two types of relations: a one is between the elliptic genus of Calabi-Yau manifolds and Jacobi modular forms, another one is between the second quantized elliptic genus, Siegel modular forms and Lorentzian Kac-Moody Lie algebras. We also determine the structure of the graded ring of the weak Jacobi forms with integral Fourier coefficients. It gives us a number of applications to the theory of elliptic genus and of the second quantized elliptic genus., Comment: To appear in Algebra i Analiz (St. Petersburg Math. Journal) 11:5 (1999); AMS-TeX, 25 pages