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Geometric transformations play a pivotal role in computer graphics, determining the position and shape of objects. In machine learning, they are applied for processing and analyzing data, such as in images. In geometric surface modeling, they are utilized for the creation and transformation of three-dimensional forms. In physics, geometric transformations assist in describing the motion of objects in space and time. The aim of this work is to analyse and study the geometric transformation known as "oblique symmetry." Primarily, the article seeks to elucidate a number of important properties of this transformation, expanding the field of knowledge in perspective-affine correspondence. Throughout the study, the principal directions of oblique symmetry are identified, and their relationship with the axis and direction of the transformation is established. It is crucial to emphasise that the analysis makes it evident that the axis and the direction of symmetry are equivalent and interchangeable. Additionally, the article addresses the challenge of transforming an arbitrary ellipse, defined by its semi-axes, into a circle of equal area. In this context, a method is proposed to determine the axis and direction of oblique symmetry for a given ellipse. Based on the results obtained and the analysis conducted, the authors propose a geometric algorithm that provides the capacity to resolve positional problems in the field of descriptive geometry. This algorithm also offers a novel method for constructing ellipses with given semi-axes, which holds practical significance in various engineering and geometric issues. In the conclusion of the article, a specific example of applying the developed method is provided, clearly demonstrating its practical value and real capabilities in solving positional problems in the field of descriptive geometry. Moreover, directions for future research in the field of shape formation are suggested, utilising the "oblique symmetry" transformation in the spaces and .

The paper presents using of frame-by-frame animation of geometric constructions in the course "Descriptive Geometry" to present educational graphic material in a more accessible and visual form for students. Electronic support of descriptive geometry classes used at the Department of Engineering Graphics at Bauman Moscow State Technical University made in the technique of frame-by-frame animation in the format of presentations and electronic text publications is presented. The technique of creating frame-by-frame animation is described. Geometric constructions are performed using computer graphics systems, in layers; each layer contains one step of construction. When layers are showed on alternately, a number of graphic files are created, which are inserted in a certain sequence on presentation slides or on the pages of an electronic text publication. During the demonstration, a visualization of the course of geometric constructions is created on the screen. Teachers when giving lectures and practical classes use electronic support of classes, made in the format of presentations to demonstrate the course material on the screen in the classroom. The presentations contain graphic material in the technique of frame-by-frame animation and minimal text material; the teacher gives the necessary explanations. Electronic support of classes, made in the form of an electronic educational visual aid, is used for independent work of students. Unlike classroom presentations, in an electronic educational visual aid, the animation of geometric constructions is accompanied by a text step-by-step description of the sequence of solving geometric problems. The main advantage of using electronic training software made in frame-by-frame animation technology compared to traditional software is the visibility and the ability to consistently, step by step, understanding the course of graphic constructions, with the ability to go back and repeat the sequence at any stage.

The field theory is widely represented in spherical and cylindrical coordinate systems, since the mathematical apparatus of these coordinate systems is well studied. Field sources with more complex structures require new approaches to their study. The purpose of this study is to determine the correct coordination of space by normal conic coordinates. This is necessary in subsequent studies, the task of which will be to simplify the expressions for the characteristics of the field by introducing a special coordination of space, which reflect the shape of the source and/or sink of the field. For example, a field with a rectilinear source is more convenient to refer to cylindrical coordinates, and a field with a point source - to spherical coordinates. Basically, the use of field theory in the study of physical processes by methods of applied geometry is limited to two classical curvilinear systems, although their presentation in arbitrary curvilinear coordinates is known. We will distinguish between global and local coordinate systems. The global system, as well as the coordinates of a point in this system, will be denoted by x, y, z. She is unchanging. The local system, as well as the coordinates of a point in this system, will be denoted by t, u, v. Local system variable. At each point in space belonging to the area of existence of the system, the local coordinate system is defined

The article is exclusively applied and methodical in nature and is intended for the study of constructions in the section "Perspective". The paper considers the construction of the perspective of a straight line of the general position with the help of a picture trace and a vanishing point. In perspective, the traces of a straight line are the points of intersection with the picture and subject planes. Vanishing point – the perspective of an improper point of a straight line. The article discusses the picture trail, the vanishing point and the construction of a straight line segment by means of these perspective points. In textbooks for builders, such a task is not set at all and is not considered. Three authors have solutions in textbooks for architects: A.G. Klimukhin, Yu.I. Koroev and T.S. Timrot. However, they also have some disadvantages, which are discussed in this article. In the work proposed to the reader, such an arrangement of geometric components is performed that there is neither parallelism nor perpendicularity between them, that is, they are all located at acute angles to each other, which means that a general case of construction is proposed for consideration. So, we have a right angle only between the horizontal and frontal planes of projections, as well as between the picture and object (horizontal plane of projections) planes. The angles between the other geometric components are exceptionally sharp: a straight line of general position in the P1/P2 system is taken, it is also a straight line of general position in the P1/K system. Thus, the article considers, unlike other textbooks, the general case of a direct task.

The Institute of Oriental Manuscripts of the Russian Academy of Sciences (IOM RAS) has more than 100,000 manuscripts and xylographs in 60 Oriental languages. The Korean fund represents a small part of this collection, however the unique works of Korean culture stored in the IOM RAS are of interest to both researchers from the Republic of Korea and local Russian scientists. The article describes the difficulties of reading the text of the D-86 xylograph "Samseolgi jung" from the Manuscript Collection of the IOM RAS. The work highlights the main problems that a researcher may encounter when working with similar medieval sources of Korean culture written in the Korean alphabet (in Hangul). The author of the article analyzes some features of the Modern Korean language revealed in this xylograph and describes its differences from the language of the 15th century and from Contemporary Korean, using the study of texts written in Hangul in different centuries for comparison. Commented examples of the old orthography and different spelling variations of the same word are used to illustrate the peculiarities in the language of the source. This article also describes the features of writing the graphics of the text of the 19th century, which were not previously covered (in particular, the symbol of repetition of the previous syllable, which in its graphic form and function is similar to the repetition sign used in the Chinese language, and the abbreviation sign of the median predicative affix 고 /go/).

A report on the XII International scientific conference “Ancient Cultures of Mongolia, Baikal and Southern Siberia, and Northern China” held in Irkutsk by Irkutsk State University from September 25 to September 30 2023 is presented. Brief descriptions of the papers presented are given.

This article examines the notes of the prominent Russian mongolist of Polish origin Józef Kowalewski (1801–1878) in his “Diary of studies for 1832”, the manuscript of which is kept in the Department of Manuscripts of the Vilnius University Library. This diary entry has been previously published several times in the form of a facsimile. It is an excerpt in English from the annotation on the Chinese book Ming xin bao jian (明心寶鑑, Precious Mirror for the Enlightenment of the Mind) from the Protestant missionary magazine published in Malacca. The article clarifies and significantly supplements the previously published commentary on this entry, defines The Indo-Chinese Gleaner magazine as the source of the English annotation and William Milne (1785–1822) as its author. It is assumed that J. Kowalewski’s acquaintance with W. Milne’s note had determined later choice of Ming xin bao jian as a Chinese language teaching material at The Imperial Kazan University. The very fact of choosing this book by a Protestant missionary to be presented as an important manual on the Chinese language and the traditional worldview of the Chinese is discussed. The conclusion is made that, formally remaining in opposition to the earlier Catholic missionary work, Protestant preachers in assessing Ming xin bao jian were in consent with their predecessors.

The article is devoted to the study of new manuscript materials from the collection of the Institute of Oriental Manuscripts of the Russian Academy of Sciences on the relations between members of the Korean diplomatic mission and the Russian Orthodox Mission in Beijing. The letters, written in the first 20 years of the 19th century, contain correspondence between the members of the two countries' missions, which cannot be found in contemporary historical sources. This article is devoted to studying the addressee of the members of the Korean diplomatic mission, putting all the letters in order, and clarifying their historical value in the study of Sino-Russian-Korean relations on the eve of the modern time. The novelty of the study lies in the fact that these manuscripts, closely related to the activities of the great Russian sinologist N. Ya. Bichurin, have not been studied before. According to the content of these letters, Bichurin communicated with the Koreans on the model of educated Chinese people, and one of the purposes of communication between the envoys of the two countries was the acquisition of different information. The relevance of the study is caused by the growing scientific interest of scholars in new manuscript materials about the history of Russian sinology and Russian-Korean relations.

Bhartṛhari’s ontological teaching is usually identified with the concept of linguistic Absolute (Śabda-Brahman) and with the three levels of speech. However, in his main opus the ‘Vākyapadīya’, each of these concepts is mentioned only on a single occasion and in a brief manner. It is not a rare case that in different contexts Bhartṛhari considers language a mental construction, or conceptualization (kalpanā or vikalpa). The latter concept was introduced under the influence of Buddhist philosophy. The Buddhists who criticized ontological concepts of Brahmanic schools were Bhartṛhari’s main opponents, so he could appeal to vikalpa in order to avoid their criticism. The ontological status of the Absolute speech in the ‘Vākyapadīya’ remains unclear. Bhartṛhari does not address this question explicitly, however, the discussions on Śabda-Brahman in early Brahmanic works, as well as Somānanda’s critique of the philosophy of the Grammarians expressed in the ‘Śivadṛṣṭi’ give evidence that he did not straight-forwardly identify Brahman ‘endowed with linguistic nature’ (śabdatattva) with the ultimate Absolute (Parabrahman). On the contrary, in his ontological system the Supreme Speech is considered an ‘intermediate’ form of the Absolute. This view derives from the teaching of the ‘two Brahmans’ in the Early Upaniṣads. For Bhartṛhari, the lower Brahman might be the basis of the phenomena, while the ultimate Brahman is transcendent to the phenomenal world. Word or sound (śabda) understood as the essence of the Vedas and a means of concentration of mind belongs to the ‘lower’ Brahman, whereas the ultimate Brahman is devoid of phonic or linguistic characteristics.