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

Gaussian modeling and Schmidt modes of SPDS biphoton states

A double-Gaussian model and the Schmidt modes are found for the biphoton wave function characterizing spontaneous parametric down-conversion with the degenerate collinear phase-matching of the type I and with a pulsed pump. The obtained results are valid for all durations of the pump pulses, short, long and intermediately long

Structure and stability of chiral beta-tapes: a computational coarse-grained approach

We present two coarse-grained models of different levels of detail for the description of beta-sheet tapes obtained from equilibrium self-assembly of short rationally designed oligopeptides in solution. Here we only consider the case of the homopolymer oligopeptides with the identical sidegroups attached, in which the tapes have a helicoid surface with two equivalent sides. The influence of the chirality parameter on the geometrical characteristics, namely the diameter, inter-strand distance and pitch, of the tapes have been investigated. The two models are found to produceequivalent results suggesting a considerable degree of universality in conformations of the tapes.Comment: 24 pages, 5 PS figures. Accepted to J. Chem. Phy

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

Eu3+ multicenter formation and luminescent properties of Ca3Sc2Si3O12:Eu and Ca2YScMgSiO12:Eu single crystalline films

The work is dedicated to the investigation of Eu3+ multicenter formation and luminescent properties of Ca3Sc2Si3O12:Eu (CSSG:Eu) and Ca2YScMgSiO12:Eu (CYMSSG:Eu) single crystalline film (SCF) phosphors, grown by liquid phase epitaxy method onto Gd3Ga2.5Al2.5O12 (GAGG) and Y3Al5O12 (YAG) substrates, respectively. We have found notable differences in the luminescent properties of CSSG:Eu and CYMSSG:Eu SCFs caused by the Eu3+ multicenter formation in both garnets due to the different local surrounding of Eu3+ ions in the dodecahedral positions by the non-isovalent Sc3+/Mg2+ and Si4+ cations in the octahedral and tetrahedral positions of garnet hosts, respectively. A feature of the Eu3+ center creation in CYMSSG:Eu garnet in comparison with CSSG:Eu counterpart is the possibility of localization of Eu3+ ions in dodecahedral sites of both Ca2+ and Y3+ cations. However, based on the obtained results, we have presupposed preferable localization of the Eu3+ ions mainly in the Y3+ positions of this garnet