On the Rate of Convergence for a Characteristic of Multidimensional Birth-Death Process

We consider a multidimensional inhomogeneous birth-death process (BDP) and obtain bounds on the rate of convergence for the corresponding one-dimensional processes

Prediction of some peroxidase functions in Arabidopsis thaliana L. By bioinformatic search

Peroxidases of class III are common in various organisms. They are involved in lignin biosynthesis and plant protection against stressors. Peroxidases are presented in many isoforms, whose role is not always clear. The aim of this study is to analyze the amino acid sequences of reference peroxidases with known functions and peroxidases from Arabidopsis thaliana L. whose functions are unknown and to consider their putative roles in lignin biosynthesis. The structural and functional organization of peroxidases was analyzed by bioinformatical methods applied to open Internet sources. Seven reference peroxidases were chosen from four plant species: Zinnia sp., Armoracia rusticana P.G. Gaertn., Lycopersicon esculentum L. N Populus alba L. Twenty-four amino acid sequences of homologous peroxidases from A. thaliana were selected for the analyses with the BLAST service. Their molecular weights and isoelectric points were calculated. Multiple alignments of amino acid sequences and phylogenetic analysis were done. Sites of binding to monolignol substrates were identified in seven peroxidases from A. thaliana, and the enzymes were assigned to the groups of S- or G-peroxidases. Amino acid replacements in the primary structures of peroxidases were analyzed. Peroxidases from A. thaliana were clustered with reference peroxidases. They formed six clusters on the phylogenetic tree, three of which contained only A. thaliana peroxidases. Peroxidases within each cluster had similar molecular weights and isoelectric points, common localization of expression, and similar functions. Thus, the use of bioinformatics, databases, and published data bring us to assumptions as to the functions of several A. thaliana class III peroxidases. AtPrx39 peroxidase was shown to be affine to sinapyl alcohol; AtPrx54, to p-coumaryl and coniferyl alcohols. They are likely to participate in lignin biosynthesis. © Tugbaeva A.S., Ermoshin A.A., Kiseleva I.S., 2019

M.Yu. Lermontov and A.A. Velyaminov: History of Relations and Views on Caucasian Question

Based on the analysis of archival documents and literary texts, a comparative analysis is conducted of the similar ideas expressed by poet M.Yu. Lermontov and General A.A. Velyaminov regarding Russian-Caucasian relations. Their history of interaction is reconstructed through the identification of contemporary witnesses, analysis of the poet's letters, and determination of their shared circle of acquaintances. The hypothesis is put forward that they were acquainted before 1837, when Lermontov came under Velyaminov’s direct command. The influence of Velyaminov on Lermontov’s early works is demonstrated. Additionally, an overlooked essay by A.A. Velyaminov entitled “History of the Caucasus” is introduced into scholarly circulation, which provides a detailed chronicle of the Caucasus from prehistoric times to the present day. Through the study of Velyaminov’s publicistic works, a better understanding is gained of the origins and development of Lermontov’s Caucasian historiosophy in the context of messianic ideas prevalent in society during the 1830s due to Russia’s actions on its eastern borders. The shared belief of both Lermontov and Velyaminov in the peacemaking role of the Russian Empire is revealed. These newly discovered materials contribute to a more comprehensive understanding of the formation of Lermontov’s historical thinking in regards to his perception of Russian-Caucasian relations

Caucasus in Context: M.Yu. Lermontov’s Reflections on Man and Fate of History

The article examines the specificity of Lermontov’s vision and depiction of the Caucasus world. It reconstructs Lermontov's philosophy of history in the context of the Caucasian War. The study reveals the cultural and historical conditioning of the poet’s imagery and ideas, and the dominant values of the Caucasian world in his artistic heritage. The article focuses on how Lermontov portrays the everyday existence of the highlanders, whose images he sees as representing the natural man in both his attractiveness and his corrupt passions. By depicting the Caucasus world in its natural and cultural uniqueness, Lermontov highlights elements of the highlander's mentality that are close to his own, and notes the convergence of Russian and Caucasian cultures. Reproducing the cultural traditions of the peoples of the North Caucasus, the poet reflects on the interaction between their clan relationships, individualistic elements, and Islamic cultural traditions. The hypothesis of the study is related to the dynamics of Lermontov’s depiction of the significance of Islam in the life of the peoples of the North Caucasus. In his early Caucasian poems, Islam appears as an external attribute of highlander life that has little impact on their consciousness, merging with their clan tradition. In his later works, however, Lermontov begins to understand Islam in its cultural and political function, which, when combined with highlander independence, can contribute to productive state interaction between Russians and the indigenous peoples of the Caucasus

Lermontov’s Sketch “Russia Has no Past...” in Context of “Eastern Question”: to Problem of Poet’s Artistic Historiosophy

The subject of the study was the content of Lermontov’s autograph “Russia has no past...” from the “Notebook donated by V. F. Odoevsky” in the aspect of the poet’s historical views. The purpose of the article is connected with the establishment of the historical and cultural genesis of the text and the clarification of its meaning in the context of Lermontov’s work, Russian-Caucasian interaction, as well as the historiosophical concepts of the first third of the 19th century. The research methodology is connected with textological, historical-genetic, cultural-historical, comparative-historical approaches to text analysis. The specific tools are the description of the autograph, as well as the preparation of a textological passport that reflects the technical aspects of the handwritten text. Lermontov’s note is presented in the context of a dialogue with contemporaries and folklore tradition. The historical and literary context of Lermontov’s note, its allusions to the facts of sociohistorical thought and images of Russian literature emphasize Lermontov’s patriotism. As a result of the study, Lermontov’s protoPan-Slavic concept was reconstructed, which correlates with ideas about the ways of Russia’s development as a great power. The conclusion of the study was the understanding of Lermontov’s sketch “Russia has no past...” as an emanation of the poet’s reflections on relations between Russia and the Caucasus in the aspect of the “Eastern question”

TOOLKIT FOR SELECTING TECHNOLOGY AS A TRANSFER OBJECT UNDER MULTI-CRITERIA CONDITIONS

The article analyzes the features of the development of small and medium-sized enterprises (SMEs) in the context of the COVID-19 pandemic. There revealed the negative trends associated with the disproportionality of the sectoral structure of the business and the low enterprises’ innovative activity. The key measures of state support for entrepreneurship taken by the Government of the Russian Federation in the period 2020–2021 are considered. The expediency of stimulating small and medium-sized businesses to participate in the process of technology transfer is determined, based on which the main purpose of the study is formulated, associated with the formation of economic and mathematical tools for choosing a technology for further implementation in the practice of SMEs. The research substantiates the expediency of using the fuzzy-multiple simplified method of analysis of hierarchies by Saaty for choosing technological solutions from a finite number of available alternatives, taking into account the interests of small and medium-sized businesses. The proposed approach makes it possible to increase the degree of validity of management decisions by reducing the volume of metamathematical operations and reducing the impact of subjectivism

ИНСТРУМЕНТАРИЙ ВЫБОРА ТЕХНОЛОГИИ КАК ОБЪЕКТА ТРАНСФЕРА В УСЛОВИЯХ МНОГОКРИТЕРИАЛЬНОСТИ

The article analyzes the features of the development of small and medium-sized enterprises (SMEs) in the context of the COVID-19 pandemic. There revealed the negative trends associated with the disproportionality of the sectoral structure of the business and the low enterprises’ innovative activity. The key measures of state support for entrepreneurship taken by the Government of the Russian Federation in the period 2020–2021 are considered. The expediency of stimulating small and medium-sized businesses to participate in the process of technology transfer is determined, based on which the main purpose of the study is formulated, associated with the formation of economic and mathematical tools for choosing a technology for further implementation in the practice of SMEs. The research substantiates the expediency of using the fuzzy-multiple simplified method of analysis of hierarchies by Saaty for choosing technological solutions from a finite number of available alternatives, taking into account the interests of small and medium-sized businesses. The proposed approach makes it possible to increase the degree of validity of management decisions by reducing the volume of metamathematical operations and reducing the impact of subjectivism.В статье проведен анализ особенностей развития малого и среднего предпринимательства (МСП) в условиях пандемии СOVID-19. Выявлены негативные тенденции, связанные с диспропорциональностью отраслевой структуры бизнеса и низкой инновационной активностью предприятий. Рассмотрены ключевые меры государственной поддержки предпринимательства, предпринятые Правительством Российской Федерации в период2020–2021 годов. Определена целесообразность стимулирования субъектов малого и среднего предпринимательства к участию в процессе трансферта технологий, на основании чего сформулирована основная цель исследования, связанная с формированием экономико-математического инструментария выбора технологии для дальнейшего внедрения в практику деятельности МСП. Обоснована целесообразность применения нечетко-множественного упрощенного метода анализа иерархий Саати при осуществлении выбора технологических решений из конечного числа имеющихся альтернатив с учетом интересов субъектов малого и среднего предпринимательства. Предложенный подход позволяет повысить степень обоснованности управленческих решений при сокращении объема метаматематических операций и снижении влияния субъективизма

Theory of differential inclusions and its application in mechanics

The following chapter deals with systems of differential equations with discontinuous right-hand sides. The key question is how to define the solutions of such systems. The most adequate approach is to treat discontinuous systems as systems with multivalued right-hand sides (differential inclusions). In this work three well-known definitions of solution of discontinuous system are considered. We will demonstrate the difference between these definitions and their application to different mechanical problems. Mathematical models of drilling systems with discontinuous friction torque characteristics are considered. Here, opposite to classical Coulomb symmetric friction law, the friction torque characteristic is asymmetrical. Problem of sudden load change is studied. Analytical methods of investigation of systems with such asymmetrical friction based on the use of Lyapunov functions are demonstrated. The Watt governor and Chua system are considered to show different aspects of computer modeling of discontinuous systems

Biochemical Responses to the Long-Term Impact of Copper Sulfate (CuSO4) in Tobacco Plants

Metabolic changes under stress are often studied in short-term experiments, revealing rapid responses in gene expression, enzyme activity, and the amount of antioxidants. In a long-term experiment, it is possible to identify adaptive changes in both primary and secondary metabolism. In this study, we characterized the physiological state of tobacco plants and assessed the amount and spectrum of phenolic compounds and the lignification of axial organs under excess copper stress in a long-term experiment (40 days). Plants were treated with 100 and 300 μM CuSO4, as well as a control (Knop solution). Copper accumulation, the size and anatomical structure of organs, stress markers, and the activity of antioxidant enzymes were studied. Lignin content was determined with the cysteine-assisted sulfuric method (CASA), and the metabolite profile and phenolic spectrum were determined with UHPLC-MS and thin-layer chromatography (TLC). Cu2+ mainly accumulated in the roots and, to a lesser extent, in the shoots. Copper sulfate (100 μM) slightly stimulated stem and leaf growth. A higher concentration (300 μM) caused oxidative stress; H2O2 content, superoxide dismutase (SOD), and guaiacol peroxidase (GPOX) activity increased in roots, and malondialdehyde (MDA) increased in all organs. The deposition of lignin increased in the roots and stems compared with the control. The content of free phenolics, which could be used as substrates for lignification, declined. The proportions of ferulic, cinnamic, and p-coumaric acids in the hydrolysate of bound phenolics were higher, and they tended toward additional lignification. The metabolic profile changed in both roots and stems at both concentrations, and changed in leaves only at a concentration of 300 μM. Thus, changes in the phenolic spectrum and the enhanced lignification of cell walls in the metaxylem of axial (root and stem) organs in tobacco can be considered important metabolic responses to stress caused by excess CuSO4. © 2023 by the authors.Russian Science Foundation, RSF: 22-24-00817This research was supported by the Russian Science Foundation, project no. 22-24-00817, https://rscf.ru/project/22-24-00817/ accessed on 4 September 2023