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The lack of generally accepted understanding of the essence of green tourism and the mechanism of switching tourism to green economy constitutes a scientific problem. By analyzing both domestic and foreign tourism clustering theory and practice, as well as the rapidly emerging green economy conception, we have managed to put forward a hypothesis about the possibility and expediency of integrating the processes of clustering and tourism ecologization, and the ability of a green tourism cluster to operate as one of the tools in the mechanism of green tourism transformation. The purposes of the study are as follows: to develop a conceptual model of a green tourism cluster as a tool for tourism ecologization, to identify possible influence of its activities on the processes of environmentally oriented transformation of the sectoral and regional economy. The study uses a methodological approach to greening tourism, integrating clustering and ecologization processes with a broad understanding of green economy as applied to the tourism sector. The paper concludes as we define and draw a conceptual model for the green tourism cluster. That includes the structure of a simulated system, participants, main internal and external connections, goals and principles of interaction, and expected system effects resulting from the green tourism cluster’s activity. Whether the cluster approach is applicable to the problem of tourism ecologization is poorly studied, which determines further prospects of research. The conceptualization of green tourism clusters will allow improving the efficiency of already established tourism clusters, ensuring their competitiveness by entering new, green markets, and creating regional-level entities actively transitioning to green economy.

This article examines the background and conditions for China’s Belt and Road Initiative, how it is perceived and reacted to in the world. We also present the results of the agreements reached by the Heads of State of Russia, Mongolia, and China. The article classifies 32 projects within the economic corridor, highlighting the most priority ones. A review of research done by scientists from these three countries in infrastructure development, regional integration, and interstate cooperation made it possible to determine the states’ potential and development levels in terms of financial and natural resource possession. In addition, we analyze and compare each party’s strategic interests and benefits from the economic corridor to be built, identify their peculiarities, and assess the existing mechanisms for trilateral cooperation. This work proves the need to work on interstate coordination mechanisms. Particular attention is paid to describing the essence, goals, and objectives of Mongolia’s Steppe Road national program, later renamed Path for Development, and the results of measures taken by the Mongolian government to create road transport infrastructure as part of the economic corridor. Examples of such measures are several road construction projects under the Path for Development, and the Tavan-Tolgoi - Gashuunsukhait and Tavan-Tolgoi - Zuunbayan railways. The problems of road transport infrastructure are related to the financial difficulties in refinancing the profits coming from the Ulaanbaatar Railbus, the lack of investment from the Asian Infrastructure Investment Bank and the Silk Road Fund, despite these financial institutions having decided to participate in financing road transport projects. There is criticism toward the fact that Chinese companies act as the principal contractors in the Mongolian-based projects financed by grant aid and a concessional loan from the Chinese government, while Mongolian ones are only involved as subcontractors. The Mongolian side has taken the initiative to attract investment from countries outside the set contracts or international financial institutions, which the other two parties, Russia and China, find disagreeable.

The article considers trends in the spatial development and regional policy of the Russian Federation in the last five years against the background of global trends, external challenges, and threats. It reveals the features of the “eastern vector" of Russia’s spatial development as a new element of its spatial policy and an important area of cross-border interactions. We show that the state support for Far Eastern investment projects and territories of priority development has dominated its implementation so far, whereas Siberia and its regions are practically excluded from this strategic initiative. Here we also examine the trends in national, inter-regional, and regional strategizing (as exemplified by the Strategy for the Spatial Development of Russia, the Strategy for Socio-Economic Development of the Angara-Yenisei Macroregion, as well as various growth and governance strategies and models for Novosibirsk and Kemerovo oblasts). By analyzing the statements of senior government officials, this paper gives an overview of recent strategic initiatives in public administration of spatial development processes. The conclusion justifies that, notwithstanding the extremely difficult growth conditions Russia underwent over the past five years, new strategic initiatives and trends gradually began to emerge, which have given grounds for cautious optimism about modernizing the country’s regional policy and spatial development.

The article presents new instrumental concepts for a class of the Gran- berg-type multiregional models, designated for studying how the three key features of an interregional system-equilibrium state, coalition stability, and openness-interdepend. Our computations illustrate fundamental differences in the properties of a closed interregional system and an open one.

It is shown that the algorithm for verifying congruence of square roots of Hermitian matrices proposed earlier by the author can be extended to the considerably more broad class of matrices whose cosquares are diagonalizable and have real spectra.

The present article deals with approximation results by means of the Lipschitz maximal function, Ditzian-Totik modulus of smoothness, and Lipschitz type space having two parameters for the summation-integral type operators defined by Mishra and Yadav [22]. Further, we determine the rate of convergence in terms of the derivative of bounded variation. To estimate the quantitative results of the defined operators, we establish quantitative Voronovskaya type and Gruss type theorems. Moreover; examples are given with graphical representation to support the main results.

This paper is devoted to constructing quadrature formulas for singular and hypersingular integrals evaluation. For evaluating the integrals with the weights (1- t )^γ₁(1+ t )^γ₂, γ₁, γ₂ > -1, defined on [-1,1], we have constructed quadrature formulas uniformly converging on [-1,1] to the original integral with the weights (1- t )^γ₁(1+ t )^γ₂, γ₁, γ₂ ≥ -1/2, and converging to the original integral for -1< t <1 with the weights (1- t )^γ₁(1+ t )^γ₂, γ₁, γ₂ > -1. In the latter case a sequence of quadrature formulas converges to evaluating integral uniformly on [-1+δ,1-δ], where δ > 0 is arbitrarily small. We propose a method for construction and error estimate of quadrature formulas for evaluating hypersingular integrals based on transformation of quadrature formulas for evaluation of singular integrals. We also propose a method of the error estimate for quadrature formulas for singular integrals evaluation based on the approximation theory methods. The results obtained were extended to hypersigular integrals.

In this manuscript, a new exponentially fitted operator strategy for solving a singularly perturbed parabolic partial differential equation with a right boundary layer is considered. We discretize the time variable using the implicit Euler approach and approximate the equation into first order delay differential equation with a small deviating argument using a Taylor series expansion. The two-point Gaussian quadrature formula and linear interpolation are implemented to obtain a tridiagonal system of equations. The tridiagonal system of equations is solved using the Thomas algorithm. Three numerical examples are considered to illustrate the efficiency of the present method and compared with the methods produced by different authors. Convergence of the method is analyzed. The absolute maximum error and rate of convergence are obtained for the model examples. The result shows that the present method is more accurate and ε-uniformly convergent for all ε ≤ h.

A matrix is said to be unitoid if it can be brought to diagonal form by a congruence transformation. We say that an algorithm is rational if it is finite and uses the arithmetic operations only. There exist rational methods designed for checking congruence of particular classes of unitoid matrices, for example, Hermitian, accretive, or dissipative matrices. We propose a rational algorithm for checking congruence of general unitoid matrices. The algorithm is heuristic in the sense that the user is required to set the values of two integral parameters M and N. The choice of these values depends on the available a priori information about the proximity of neighboring canonical angles of the matrices under checking.

Morphological characters of stigmas in 26 Asian and North American species of the genus Mertensia Roth (Boraginaceae) were studied using a scanning electron microscope. It is noted that there are 3 types of stigmas in the genus: flat, with a depression in the center; weakly or noticeably bi-lobed and spherical. In most species of the genus Mertensia, papillae have a short, barely noticeable stem and a lobed or spherical cap. We have designated this form of papillae with a new term - “modified lageniform” (modified bottle-shaped). For two species of the subgenus Steenhammera (Reichenb.) O.D. Nikif. characteristic papillae are “vermiform” (worm-like). The shape of the papillae confirms the earlier conclusion about the relationship of the North American species M. virginica (L.) G. Don fil. and Altai endemics M. bracteata (Willd. ex Schult. et Roem.) R. Kam. and M. meyeriana Macbride. It is shown that M. sibirica stands alone in the type sub-section of the Mertensia section, but shows kinship to the North American species M. arizonica Greene. In the species of the section Pterocarpeae Popov ex O.D. Nikif. papillae have a unique shape (4-8 multi-lobed deeply dissected caps with smooth surface), which confirms the validity of their inclusion in an separate section. In the section Alpinae O.D. Nikif. the papillae shape of the of M. lanceolata and M. longiflora differs from the other studied species of the section. It is shown that the features of papillae correlate with the features of the sectional and subsectional rank and can be used in the taxonomy of the genus.