Challenges and search for sustainable ways of territories’ development cause serious concern to authorities around the globe. The choice of methodological approaches for assessment and monitoring, indicators for sustainability criteria, as well as the ways of their processing are an important conceptual basis that provides effective facilitation of the administered territories development. The study is aimed at finding and analyzing the existing approaches and tools for territorial development monitoring, as well as elaboration of methodological and procedural framework for assessing the territories sustainability to solve social and economic problems. Herewith, in the authors’ opinion, the main conceptual and methodological prerequisite that distinguishes the proposed approach, should take into account the effects of interregional and intersectoral interaction or, in other words, the effects of cluster transfers. It has been revealed that there is still no consensus among the scientific works’ authors not only concerning theoretical aspects, but also on methodological issues of the monitoring procedure and tools for assessing the development sustainability, especially in the context of cluster approach. The analysis of the main methodological approaches to assessing the sustainable development of various levels systems (national and regional economies, territories, industries, enterprises and products) is given in the paper. Systematization of the approaches and tools used by scientists from different countries, as well as international organizations and institutions, has been carried out. Advantages, disadvantages and limitations for the practical application of the selected methodological approaches are indicated. The essence of the TOPSIS method as a tool for assessing the sustainability of the territories’ development, taking into account the multiplicative effects of interregional and intersectoral interaction is given. It has been shown that it is the cluster approach that acts as an effective tool for managing the sustainable development of territorial systems

We emphasize intertwining relations as a universal tool in constructing onedimensional quasi-exactly solvable operators and offer their possible generalization to the multidimensional case. Considered examples include all quasi-exactly solvable operators with invariant subspaces of monomials. We show that the simplest case of generalized intertwining relations allows to naturally relate quasi-exactly solvable operators with two invariant monomial subspaces to a nonlinear parasupersymmetry of second order. Quantum-mechanical systems with linear and nonlinear supersymmetry are discussed from the viewpoint of quasi-exact solvability. We construct such a general system with a cubic supersymmetry and argue that quantum-mechanical systems with nonlinear supersymmetry of fourth order and higher are generally not quasi-exactly solvable. Besides, we construct two examples of quasi-exactly solvable operators with invariant subspaces which cannot be reduced to monomial spaces. *

results that are connected to highly effective creation, storage, distribution, and usage of information. It also supplemented them with a new sense of proclaiming information on the most valuable resources as well as provision of free and continuous interaction of economic subjects À the highest priority of socioeconomic systems.

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