Typed Angularly Decorated Planar Rooted Trees and Ω-Rota-Baxter Algebras

As a generalization of Rota–Baxter algebras, the concept of an Ω-Rota–Baxter could also be regarded as an algebraic abstraction of the integral analysis. In this paper, we introduce the concept of an Ω-dendriform algebra and show the relationship between Ω-Rota–Baxter algebras and Ω-dendriform algebras. Then, we provide a multiplication recursion definition of typed, angularly decorated rooted trees. Finally, we construct the free Ω-Rota–Baxter algebra by typed, angularly decorated rooted trees.

КОМПЛЕКСНЫЙ АНАЛИЗ СОСТОЯНИЯ РЕГИОНАЛЬНОЙ СОЦИО-ЭКОЛОГО-ЭКОНОМИЧЕСКОЙ СИСТЕМЫ (НА ПРИМЕРЕ НИЖЕГОРОДСКОЙ ОБЛАСТИ)

In order to assess the state of affairs in a region with account for the economic, socio-demographic and environmental aspects, to find out the causes of backwardness, and to work out ameliorating measures, it is reasonable to regard each administrative-territorial unit (ATU) as an integral socio-environmentally-economic system (SEES). ATUs in the Nizhegorodskaya Oblast were chosen to evaluate the suggested approach to integral analysis of SEES conditions and developmental degree. The approach implies calculating the values of the generalized desirability function (GDF) and their assessment using principal components and SWOT analyses. The calculated GDF values for the years 2016–2018 made it possible to distinguish leaders and outsiders among ATUs. Among all ATUs, 78% fall into the two lower classes of GDF gradation, which means that conditions are poor there. The results were confirmed by statistical analysis and were interpreted analytically using SWOT analysis. The suggested methodology makes it possible to distinguish “pain spots” and “points of increase” and correct decision making aimed to promote sustainable development at a regional level.

A new method for monitoring wells productivity index dynamics

А method for monitoring wells productivity index dynamics from the moment of its start-ups is proposed. It allows detecting candidates for conducting well tests (WT) and well interventions for the increase of a daily production. The method is based on an integral analysis using pressure maps and well tests. Application of this method on the Salym group of oilfields has allowed concluding about wells stock status, about productivity index dynamics in time, also to make an assumption about the reasons for its change. The analysis showed that productivity index relative changes in horizontal wells lower than in slanted wells.

Study current oil-gas saturation according to the geophysical logging data in Pirallahi adasy field

The paper studies the current distribution of oil-gas saturation in the reservoirs of Kirmaki and Lower Kirmaki suits in Pirallahi adasy field according to the integral analysis using the results of field, geological, geophysical well logging, as well as those of laboratory investigations. For studying the heterogeneity of sections, the changes of reservoir parameters according to the logging data interpretation have been analyzed. Based on comparative analysis of data interpretation for old and new wells (PNNL and other logging measurements), the areas maintained productivity in research region have been revealed and the sites for new well drilling and residual oil extraction recommended as well.