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

The effect of geographical position and employment fluctuations on rural settlement trends

Structural changes in the economy and spatial and inter-settlement differences in living standards and quality of life lead to fundamental alterations in the national settlement system. Settlement polarisation is gathering momentum, along with the movement of rural population from Russia’s east and north to its southern and metropolitan regions. These processes benefit urban agglomerations. Typological differences between regional settlement systems, still poorly understood but essential for strategic and spatial planning, are growing. This article draws on the concept of the geographical demographic situation; it uses official statistics on Russian regions and Kaliningrad municipalities and settlements to explore the connection between rural settlement trends and employment fluctuations caused by structural shifts in Russian regional economies. It is shown how settlement polarisation affects differences in settlement trends of meso- and microdistrict levels. Regions are identified that have a capacity for rural-urban migration and corresponding rural employment structure and trends

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

The influence of the sea on the economic development and settlement structure in the Baltic Sea region

Earliest studies into the influence of the sea on the economy and settlement structure date back to the mid-19th century. They became common in the 20th century. Researchers have come to a general understanding that a coastal position has a beneficial effect on the development of regions. Such areas have a denser population and develop more rapidly than inland regions. At the same time, the effect of environmental, socioeconomic, demographic, and political factors is often stronger than the influence of the sea. Thus, an inland position can be more beneficial than a coastal one. Both trends are observed in the Baltic Sea macroregion. However, the ‘gravitational force’ of the sea varies from place to place. This article focuses on the most significant differences between territories and countries. These differences reflect the uneven influence of the proximity of the Baltic Sea on the development of population and national economies. Qualitative differences between mesoregions are measured using a combination of theoretical and empirical typologies. An economic, statistical, and cartographic analysis helps to identify a special type of mesoregions — coastal development corridors, which make an important contribution to the economic development and consolidation of the Baltic macroregion. In transnational macroregions, such typological differences must be taken into account in strategic and spatial planning at the intergovernmental level

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