The rationality of the moduli spaces of Coble surfaces and of nodal Enriques surfaces

We prove the rationality of the coarse moduli spaces of Coble surfaces and of nodal Enriques surfaces over the field of complex numbers.Comment: 15 page

Surface-enhanced optical third-harmonic generation in Ag island films

Surface-enhanced optical third-harmonic generation (THG) is observed in silver island films. The THG intensity from Ag nanoparticles is enhanced by more than two orders of magnitude with respect to the THG intensity from a smooth and homogeneous silver surface. This enhancement is attributed to local plasmon excitation and resonance of the local field at the third-harmonic wavelength. The diffuse and depolarized component of the enhanced THG is associated with the third-order hyper-Rayleigh scattering in a 2-D random array of silver nanoparticles.Comment: 4 pages, 2 figure

Treatment of Industrial Effluents Using Evaporation Installations

The purpose of the paper is to present the structure of the needs of industrial enterprises in the treatment of industrial effluents using evaporation installations and to analyse parameters of these effluents using the example of Russia. These parameters are the volume flow of wastewater that is supposed to feed the plant, their composition, the origin of the runoff, the type of production, where the runoff was formed. The obtained results of the analysis of data on the effluents of enterprises will help to find out whether the technological schemes and the evaporation installations included in them will be the most popular and efficient from the point of view of environmental safety of production. In addition, based on this work, it becomes clear what conditions require increased attention when developing hardware design of industrial wastewater treatment processes. Main problems of thermal desalination of industrial effluents by evaporation were considered in this paper. © Published under licence by IOP. Publishing Ltd

The Kodaira dimension of the moduli of K3 surfaces

The moduli space of polarised K3 surfaces of degree 2d is a quasi-projective variety of dimension 19. For general d very little has been known about the Kodaira dimension of these varieties. In this paper we present an almost complete solution to this problem. Our main result says that this moduli space is of general type for d>61 and for d=46,50,54,58,60.Comment: 47 page

Academic educational provisions to motivate students for physical education practices

Objective of the study was to analyze benefits of special academic educational provisions to encourage students’ physical education interests and motivation

Lagrangian fibrations of holomorphic-symplectic varieties of K3^[n]-type

Let X be a compact Kahler holomorphic-symplectic manifold, which is deformation equivalent to the Hilbert scheme of length n subschemes of a K3 surface. Let L be a nef line-bundle on X, such that the 2n-th power of c_1(L) vanishes and c_1(L) is primitive. Assume that the two dimensional subspace H^{2,0}(X) + H^{0,2}(X), of the second cohomology of X with complex coefficients, intersects trivially the integral cohomology. We prove that the linear system of L is base point free and it induces a Lagrangian fibration on X. In particular, the line-bundle L is effective. A determination of the semi-group of effective divisor classes on X follows, when X is projective. For a generic such pair (X,L), not necessarily projective, we show that X is bimeromorphic to a Tate-Shafarevich twist of a moduli space of stable torsion sheaves, each with pure one dimensional support, on a projective K3 surface.Comment: 34 pages. v3: Reference [Mat5] and Remark 1.8 added. Incorporated improvement to the exposition and corrected typos according to the referees suggestions. To appear in the proceedings of the conference Algebraic and Complex Geometry, Hannover 201