Stability of narrow beams in bulk Kerr-type nonlinear media

We consider (2+1)-dimensional beams, whose transverse size may be comparable to or smaller than the carrier wavelength, on the basis of an extended version of the nonlinear Schr\"{o}dinger equation derived from the Maxwell`s equations. As this equation is very cumbersome, we also study, in parallel to it, its simplified version which keeps the most essential term: the term which accounts for the {\it nonlinear diffraction}. The full equation additionally includes terms generated by a deviation from the paraxial approximation and by a longitudinal electric-field component in the beam. Solitary-wave stationary solutions to both the full and simplified equations are found, treating the terms which modify the nonlinear Schr\"{o}dinger equation as perturbations. Within the framework of the perturbative approach, a conserved power of the beam is obtained in an explicit form. It is found that the nonlinear diffraction affects stationary beams much stronger than nonparaxiality and longitudinal field. Stability of the beams is directly tested by simulating the simplified equation, with initial configurations taken as predicted by the perturbation theory. The numerically generated solitary beams are always stable and never start to collapse, although they display periodic internal vibrations, whose amplitude decreases with the increase of the beam power.Comment: 7 pages, 6 figures Accepted for publication in PR

TO THE ASSESSMENT OF SEISMIC RISK OF AREAS

The main components of seismic risk areas are: seismic hazard, seismic vulnerability of the elements of building area, social and economic losses in the earthquake. Each of them depends on a large number of parameters, both the earthquake and buildings. One of the main object is the lack of earthquake resistance of buildings on the basis of which. You can determine the possibleextent of his injuries. Calculate the probabilities of degrees of damage to buildings on the territory of seismic hazard and vulnerability of buildings, depending on the extent of damage, we can estimate the seismic risk areas. In the article, this approach is implemented by the example of building the city of Makhachkala

METHODOLOGY OF SYSTEM APPROACHE TO SEISMIC RISK ASSESSMENT AND REDUCTION

Abstract. Ensuring of urban areas seismic safety is a task which do not require delay. But it cannot be solved by separate parts. It is essential that all components of the seismic hazard must be grouped together in one problem based on the system approach. In the present paper is presented not only the main flowchart of systems approach to ensuring the territory seismic safety but also the flowcharts of components of each main unit. They cover the whole package of measures for a full assessment of territory seismic hazard, seismic risk and its reduction.The proposed methodology can be carried out for design and implementation of regional territory seismic safety programs

Comparative rating of regional universities as indicator of effectiveness in educational service

Анализируется рейтинг вузов, характеризующий соотношение мнений различных целевых ауди-торий о сложившейся ситуации в сфере высшего профессионального образования Республики Дагестан.In this paper the authors proposed a ranking of universities which characterizes the ratio of the views of the various target audiences, on the situation in the field of higher education of the Republic of Dagestan