Inverse medium problem for a singular contrast

We consider an inverse medium problem in two- and three-dimensional cases. Namely, we investigate the problem of reconstruction of unknown compactly supported refractive index (contrast) from L-2 with a fixed positive wave number. The proof is based on the new estimates for the Green-Faddeev function in L-infinity space. The main goal of this work is to prove a uniqueness result in the two- and three-dimensional cases and to discuss some possible constructive methods for solving the problem. Finally, we present some numerical examples to demonstrate the results in two dimensions. Published under license by AIP Publishing.Peer reviewe

About directions of overcoming of the modern crisis States of the economy of Russia

In the general methodical plan the offer on the organisation of system of the indicative analysis and regulation of volumes of output is proved and reveals and is industrial-economic activities the enterprises and the organisations of real sector of economy, as organizational tool of the permission of crisis positions in economy. In the concrete plan author's offers in directions and ways of overcoming of the modern crisis phenomena in economy of Russia are stated

ABOUT THE APPROACH AND METHOD OF DETERMINING THE VALUE OF ROYALTIES FOR THE DEVELOPMENT OF MINERALS

All business entities, regardless of their form of ownership, must obey established rules, when paying for the right to use licenses for inventions, renting films, publishing books, products, patents, innovations. The calculation of the amount of payment is carried out in accordance with the bilateral agreement. Calculating royalties, based on profits earned by an enterprise, has certain disadvantages. Many of the most diverse factors affect the volume of profit. The author’s approach and the method of determining the value of royalties for the development of mineral resources have been explained in the article. Their basis consists of: determining the value of economic rent as a result of the extraction and sale of mineral resources; ensuring, that mining companies receive income on their production capital at a level not lower than the average for the country’s economy as a whole

Wave packet evolution approach to ionization of hydrogen molecular ion by fast electrons

The multiply differential cross section of the ionization of hydrogen molecular ion by fast electron impact is calculated by a direct approach, which involves the reduction of the initial 6D Schr\"{o}dinger equation to a 3D evolution problem followed by the modeling of the wave packet dynamics. This approach avoids the use of stationary Coulomb two-centre functions of the continuous spectrum of the ejected electron which demands cumbersome calculations. The results obtained, after verification of the procedure in the case atomic hydrogen, reveal interesting mechanisms in the case of small scattering angles.Comment: 7 pages, 8 Postscript figure

The comparative evaluation of the operational performance of the economies of constituent entities of the Russian Federation

The article consideres the existing practice of the comparative assessment of effectiveness of the economies of constituent entities of the Russian Federation, reveals its shortcomings, and the factors causing them, factors causing them, including the shortcomings of the system and indicators of state statistical reporting and methods for their determination, as well as the consequences of these shortcomings in the system of internal economic and social-labor relations. The authors ’proposals are based on the following: adopting, as a generalized indicator of the economic efficiency of the functioning of the economies of administrative-territorial entities of the country, the indicator of gross domestic income generated in their territories, regardless of which of them are registered; changes in the basic provisions for determining in statistical accounting the volumes of the gross domestic product and gross income, excluding from their volumes the cost of services, that do not represent in their content the newly created value