In the article simulation models of the formation conditions of the nanotechnology diffusion as a basis for modernization of existing plants are proposed and tested. The poll of industrial enterprises managers in Sverdlovsk region has revealed latent demand for nanotechnology development; nanodevices, mastered by other companies; composite materials; technical systems, implementing new physical and chemical properties. As a result of modeling (based on Weidlich nonlinear models) there were identified the forces of the cooperative and antagonistic effects, direct and indirect influence of the pace and conditions of technology development at various levels. The model of nanotechnology promotion is also obtained and tested.

The questions related to the evaluation of industrial modernization possibilities of nanotechnology are reviewed in this paper, restrictive barriers are marked, the author's typology of levels of nanotechnological developments' interaction provided. The author shows models which formalize the diffusion of nanotechnology - a model of technological dynamics and a model of nanotechnologøñôä modernization. A large part of the paper is devoted to methodological approaches to the assessment of synergistic effects of nanotechnology, such as technological roadmaps, the analysis of external effects, optional theory and dynamic analysis of market structure. A new typology of interaction levels between nanotechnology and industrial operating systems, taking into account the direction and depth of their interaction, is suggested. Three types of functions of nanotechnological developments are highlighted: addition, substitution and field construction. A matrix of levels and types of interaction of nanotechnology to their functions is constructed and a model of interaction between nanotechnology and traditional technologies as well. The bases for evaluating the synergetic effect of nanotechnology are technological roadmaps, which possible scenarios are reflected in the modified inter-sectoral balance. Using roadmaps for evaluating the effects of nanotechnology will not only review the likely scenarios and their potential profitability, but also help to choose the optimal path in terms of resource cost and socio-economic, fiscal and environmental performance of nanotechnologies. Synergetic effects are conditioned by additional benefits or costs of socio-economic system due to changes in its structure, so the effects can be evaluated through positive or negative externalities. The synergistic effect of nanotechnology can be defined as the non-vicarious quantitative market effect for subjects who are not participating in the creation or consumption of nanotechnology. For the evaluation of synergistic effects of nanotechnology implementation, an optional theory can be used; in particular, such parameters as an option on the timing of the project, the option to reject the project, the option to carry out sequential investment, the option for the extension, the option to decline and the option to suspension can be used.

In the article, the need for the coordinated development hi-tech economic sectors with development of industrial production as a whole is proved. It is shown that structural and technological heterogeneity of Ural creates essential barriers of modernization of less profitable branches. The increasing value of the spatial factor of development of the country as a whole, particular federation subjects of Russia and municipalities is proved. It is shown that spatial gaps do not allow to use the capacity of the available Russian territory localized within regions, and separate municipalities. The problem of finding the rational compromise in resources’ distribution between the purposes of policy of structural and technological modernization and policy of maintenance of the current social and economic stability is brought into focus. Trends of territorial-sectoral location of objects of new construction and modernization in Sverdlovsk region during 2000-2012 are revealed. The assessment of the relative attractiveness of territories for definition of effective location of objects of new construction and modernization of existing industry taking into account functional use of territories and integration estimates on leading components is carried out. Methodological provisions are developed, and methodical tools of formation of the regional Scheme of the location of objects of modernization and new construction are offered. On the example of Sverdlovsk region, the offers on the creation new vacancies and modernizations of operating workplaces according to the economic activity and administrative districts during the period up to 2020 are developed.

The main purpose of the article is to validate the mathematical models describing the innovative response in the industrial regions. The article gives a deep analysis of trends in the development of the Russian industrial regions, puts forward and tests the following hypotheses: the hypothesis of uneven economic development of different types of industrial regions (regions, strengthening its industrial status, new industrial regions and regions of deindustrialization), the hypothesis of the development identity of certain types of industrial regions, the hypothesis of the catalytic role of the state in the dynamics of innovation, the hypothesis of the existence of the resonance innovation in the economic system. The authors propose the innovative resonance methodology, show the conditions for the resonance in the economic system, describe the types of resonant response. The main methods used are: resonance effects, reproductive techniques and methods of economic-mathematical modelling. In the paper, the authors propose a mathematical formalization of the innovative resonance mechanism in the regional industrial system, which includes: a) the development model of investment by industry and reproductive sectors; b) the dynamic diversified (multi-sectoral) model of reproduction; c) the model of the adaptive management of the innovative self-development of regional industrial system; d) the model of the stability of innovation dynamics and extended reproduction. The authors study the innovative response in the industrial regions of Russia. In the context of innovation resonance, the authors examined the functional industrial policies of a typical industrial region and the resonant responses associated with its implementation. The results of the study presented in the paper can be used in the justification of the mechanisms of the regional industrial policy, as well as for the assessment of the regulatory impact of the existing legal acts.