Q-complements on log surfaces

In this paper the log surfaces without \QQ-complement are classified. In particular, they are non-rational always. This result takes off the restriction in the theory of complements and allows one to apply it in the most wide class of log surfaces.Comment: Latex2e, 3 page

Upper bounds for the number of orbital topological types of planar polynomial vector fields "modulo limit cycles"

The paper deals with planar polynomial vector fields. We aim to estimate the number of orbital topological equivalence classes for the fields of degree n. An evident obstacle for this is the second part of Hilbert's 16th problem. To circumvent this obstacle we introduce the notion of equivalence modulo limit cycles. This paper is the continuation of the author's paper in [Mosc. Math. J. 1 (2001), no. 4] where the lower bound of the form 2^{cn^2} has been obtained. Here we obtain the upper bound of the same form. We also associate an equipped planar graph to every planar polynomial vector field, this graph is a complete invariant for orbital topological classification of such fields.Comment: 23 pages, 5 figure

Modelling of free positron states in TiHx

Electron energy structure, positron spectrum and positron characteristics of a-Ti and a-TiH[0.125] were calculated. Self-consistent calculations of the band structure were performed by the linear muffin-tin orbital method in the atomic sphere approximation. Modelling has been made on low content of hydrogen into a-Ti with expanded close-packed hexagonal cell inclusive 8 titanium atoms. Variation of sphere radiuses permitted to consider anisotropy and spherical symmetry of potential. Positron potential and positron wave function were calculated on a base of self-consistent electron density. Then positron probability of existence into TiHx lattice and lifetime were founded. Theoretical calculation indicated a satisfactory agreement of positron characteristics absolute values with the experimental data is achieved but the tendency of values with hydrogen defects increasing is not. The reason of divergence is discussed. On the basis of experimental data and theoretical calculations it was shown that different hydrogen atom states demonstrate the different influence in the lifetime spectra

Pseudoscalar mesons and their radial excitations from the Effective Chiral Lagrangian

Effective Chiral Lagrangian is derived from QCD in the framework of Field Correlator Method. It contains the effects of both confinement and chiral symmetry breaking due to a special structure of the resulting quark mass operator. It is shown that this Lagrangian describes light pseudoscalar mesons, and Gell-Mann-Oakes-Renner relations for pions, eta and K mesons are reproduced. Spectrum of radial excitations of pions and K mesons is found and compared to experimentally known masses.Comment: 6 pages; v3: minor corrections, references adde

Polarization-dependent transformation of a paraxial beam upon reflection and refraction: a real-space approach

We analyze the paraxial beam transformation upon reflection and refraction at a plane boundary. In contrast to the usual approach dealing with the beam angular spectrum, we apply the continuity conditions to explicit spatial representations of the electric and magnetic fields on both sides of the boundary. It is shown that the polarization-dependent distortions of the beam trajectory (in particular, the "longitudinal" Goos-H\"anchen shift and the "lateral" Imbert-Fedorov shift of the beam center of gravity) are directly connected to the incident beam longitudinal component and appear due to its transformation at the boundary.Comment: 10 pages, 1 figure. Formulae (32), (33), footnote 2 and Ref. 27 are added, some sentences are correcte