### Book chapter

## The Kantorovich Problem and Wasserstein Metric in the Theory of Belief Functions

The aim of this paper is to show that the Kantorovich problem, well known in models of economics and very intensively studied in probability theory in recent years, can be viewed as the basis of some constructions in the theory of belief functions. We demonstrate this by analyzing specialization relation for finitely defined belief functions and belief functions defined on reals. In addition, for such belief functions, we consider the Wasserstein metric and study its connections to disjunctions of belief functions.

### In book

The paper deals with the engineering training problems in the field of information and communication technologies (ICT). It analyzes the content and relationship of ICT educational and professional standards, formulates a number of engineering education problems under a two-level system of personnel training and proposes their solutions.

The paper estimates productivity agglomeration effects for manufacturing plants located within the Russian urban agglomeration. The last was defined as a central city and other towns located within the distance of 50 km from the central city. The data employed is the survey data collected by HSE in the year of 2009. We estimated the multilevel models. The results imply that location within the urban agglomeration is always significantly and positively associated with the higher productivity of the manufacturing plants, while local economic diversification provides an explanation for the power of agglomeration forces. The city size affects positively the productivity only outside urban agglomerations, thus providing evidence that specialization and interaction of economic agents in the dense economic space allow to overcome the negative side of location in a small town.

Article contains methodological analysis of improvements of professional training specialists in criminal justice. Author proposes problem approach towards various elements of criminal law.

This article gives a survey of recent research related to the Monge-Kantorovich problem. Principle results are presented on the existence of solutions and their properties both in the Monge optimal transportation problem and the Kantorovich optimal plan problem, along with results on the connections between both problems and the cases when they are equivalent. Diverse applications of these problems in non-linear analysis, probability theory, and differential geometry are discussed.

The article is devoted to the trends and determinants of the transformation of Russian regions' industrial specialization during the period of economic growth. Using the methodology of statistic and econometric analysis it is tested whether the tendency of diversification dominates the tendency of regions’ industrial specialization in 1997-2004 and whether there is a convergence of Russian regions' industrial structures. The considered factors of industries' development in a particular location include the initial industrial structure, inter- and intraregional technologic links between industries, quality of investment climate, R&D potential, international competition.

In the paper we argue that aggregation rules in the theory of belief functions should be in accordance with underlying decision models, i.e. aggregation produced in conjunctive manner has to produce the order embedded to the union of partial orders constructed in each source of information; and if we take models based on imprecise probabilities, then such aggregation exists if the intersection of underlying credal sets is not empty. In the opposite case there is contradiction in information and the justifiable functional to measure it is the functional giving the smallest contradiction by applying all possible conjunctive rules. We give also the axiomatics of this contradiction measure.

This chaper refers to the problem of low productivity and weak competitive stand of plants located in small and particulalry small specialized towns as compared to firms in bigger and more diversified locations. The findingds imply that the urban size and density of economic space, as well as its excessive sectoral specialization significantly reduce the firm competitiveness. Yet, the sectoral structure matters: textile and garmet plants in small towms are most vulnerable. Minimal diversification of economic structure and sufficient scale economy at the plant level allow to reduce the negative effects of the urban size.