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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.

Let X and Y be Banach spaces. Let f: Ω → Y be a Frèchet differentiable function on an open subset Ω of X and F be a set-valued mapping with closed graph. Consider the following generalized equation problem: 0 in f(x)+ F(x). In the present paper, we study a variant of Newton's method for solving generalized equation (1) and analyze semilocal and local convergence of this method under weaker conditions than those considered by Jean-Alexis and Piètrus [13]. In fact, we show that the variant of Newton's method is superlinearly convergent when the Frèchet derivative of f is (L,p)-Hölder continuous and (f+F)^-1 is Lipzchitz-like at a reference point. Moreover, applications of this method to a nonlinear programming problem and a variational inequality are given. Numerical experiments are provided which illustrate the theoretical results.

Analysis of the success of reforestation after a fire is the most important task of forestry. For these purposes, in the summer of 2021, aerial photography was carried out from a Phantom 4 pro UAV (Unmanned Aerial Vehicle) of a 15-year-old burnt-out (2006) along the north-western border of the Botanical Garden of Petrozavodsk State University (Republic of Karelia). In addition to this, a full-scale survey was carried out at the registration sites. Before the forest fire, rocky Scots pine ( Pinus sylvestris L.) trees grew. The work was carried out in order to assess the state of natural renewal after a fire along rocky outcrops by combining the processing of aerial photography data with field surveys. As a result of photogrammetric processing, an orthophotomap with a spatial resolution of 4.6 cm/pix, a height map and three-dimensional point clouds were reconstructed. To analyze the quantitative distribution of the territory according to the species composition, the trees were pinned on the orthophotomap according to the registration areas of field surveys, as a result of which the quantitative distribution of tree species was determined in the ratio of 64 % Scots pine and 23 % of drooping birch ( Betula pendula Roth) (other species were not identified). Field surveys showed that after the fire, a viable young stand of mixed composition with a predominance of Scots pine (71% of the total number of tree species) was formed. In addition to Scots pine, drooping birch (22 %), aspen ( Populus tremula L.) and gray alder ( Alnus incana (L.) Moench) (3.5 % each) participate in the formation of young stands on this burned-out area. These indicators are consistent with the analysis of the orthomosaic of the area (the error is less than 10 %). When comparing the height of plants on three-dimensional clouds of points with field measurements, it was possible to reliably determine only the height of plants for a large generally accepted category (> 1.5 m). The maximum height of Scots pine trees in the study area is 6 m, and the average values varied from 3.5 to 4.5 m, which indicates the success of reforestation after burning on rocky outcrops.