Applied Mathematics and Control Sciences

We consider a system with uniform oscillatory elements, namely, two massive loads (inert-inertial system). The possibility of occurrence of such a system free of harmonic oscillations which, as in the conventional oscillatory systems is caused by that its elements are opposite character reactivity. The oscillating system with homogeneous (inert) components opposite reactivity is achieved by summing the spatial shift (p/2) and phase shift (p/2). The inert-inertial oscillator there is a mutual exchange between the kinetic energies of loads. Unlike traditional vibration systems free vibration frequency oscillatory systems with homogeneous elements do not depend on the system parameters and determined solely by the initial conditions, so that they can make available to any harmonic oscillations initially set frequency.

In the article the algorithm of surface’s construction on the basis of a construct-parametrical method of a shaping by immersion of any line in congruence is considered. The parametrical equations of coordination of space by helix and ellipses, on the basis of which u -, v - and w -congruences are defined, are received. The surfaces of the resulting congruences are visualized. The general structure of surfaces is determined.

Space-search problem classification system is create for retail opening. Classification criterions is location, quality of retail, the target audience, category of commodities and the type of problem to be solve: search the place of a new commercial real estate object; choice of premises on the first and basement stores of the existing apartment houses for transfer to category of the non-residential premise and the subsequent placement of commercial real estate object; the choice of the room among the existing commercial real estate objects. For the solution of the tasks answering a question "Where we build and/or opening a commercial real estate object?", the models belonging to the class of gravitational can be used. However, for the task solution of optimum location search for a construction and/or opening a commercial real estate object with set quality, focused on a specific target audience with a specified trade segment, these models cannot be use. Solution to these problems is competence retail specialists. Shop at home is object for research this publication. Meaningful, conceptual and mathematical problems definition is represented for the search optimal location for open or/and building corner shop. Mathematical model based on Huff’s modification model; it designed for measure commercial object consumer attractiveness.

The aim of this work is to identify prerequisites crises. The subject of research were the main macroeconomic indicators of the Russian Federation in the years of crisis, such as GDP, the dollar price of oil, inflation, unemployment. In the course of work we were considered the three main indicators of the Russian Federation crises: the crisis of 1998, the 2009 crisis and the crisis of 2014-2105 years, and also examined the causes of them. During the work they were calculated correlation coefficients of oil and the dollar in times of crisis, and revealed the basic laws. The study, paired regression equations were formulated for oil rates and the ruble exchange rate against the dollar, and for GDP and inflation, GDP and unemployment. As a result, we identified the major predictors of crises.

Discusses the advantages of using “information approach” to modeling the regional real estate market. Shows the importance of considering the influence of mega-, macro-and meso-economic factors when building computer models of market, suitable for analysis and forecasting of the market value of residential properties, and mass cadastral valuation, the underlying effective tax system to more fairly distribute the tax burden. In addition, mining models “what if” allows you to see how changes in the key pricing factors will affect the market value of objects, what is the decision support aimed at the development of the real estate market. It is concluded that such models can be embedded in a monitoring system of the housing market and updates inventory tables real estate regions in real time, when change of the economic situation in the region, the country and the world entails an automatic update of inventory data.