Gerasimenko S.A., Pavlenko A.N.
ON THE PRESENTATION OF THE SECTION “ANALYTICAL GEOMETRY” IN ENGINEERING DIRECTIONS OF BACHELOR DEGREE COURSES IN FULL-TIME/CORRESPONDENCE FORMS OF STUDY ^{[№ 1 ' 2024]}
Currently, the main trends in higher education reform naturally lead to a significant reduction in the proportion of classroom lessons in the educational process, which has an extremely negative effect on the study of mathematical cycle disciplines due to their abstraction and often cumbersome presentation of the material. Thus, there is a need of increasing the effectiveness of contact work and strengthening the role of independent work of students. The above mentioned is also typical when studying the section “Analytical Geometry” in engineering bachelor courses, especially in full-time and correspondence studies. In order to increase the effectiveness of learning this section, a new applied approach to the study of analytical geometry in engineering bachelor courses in full-time and correspondence education is proposed, consisting in 1) consideration of the main tasks of analytical geometry based on natural science and technical specifications that arouse the interest of students and the relevance of which is beyond doubt, 2) the use of interdisciplinary connections with special disciplines, as well as with the history of natural science and technology, 3) moving the study of a significant part of the section “Analytical Geometry” to the independent work. To increase the effectiveness of the use of the considered approach, it is advisable to use relevant methodological support. As the latter, it is appropriate to use textbooks, collections of tasks and individual tasks, posters and 3d models, interactive guidelines integrated with applications written in high-level languages, generators of typical problems, etc.

Gerasimenko S.A., Pavlenko A.N.
ON UNIFICATION OF MULTIPLE, CURVILINEAR AND SURFACE INTEGRALS PRESENTATION IN ENGINEERING DIRECTIONS OF UNDERGRADUATE STUDIES ^{[№ 1 ' 2023]}
In modern world, the up-to-date trends in reforming of higher education lead to a significant reduction of classroom activities in the educational process, which extremely negatively affects the study of disciplines of the mathematical cycle due to their abstractness and often complexity of material presentation. Thus, there is a necessity to increase the efficiency of contact work and to widen the role of unsupervised work of students. This problem is especially evident in the study of the topic “Integral calculus for functions of several variables” in the engineering directions of undergraduate studies.
One of the factors that contribute to increasing the efficiency of contact and unsupervised work is the unification of the educational material presentation related to this topic.
In this article, we suggest a new approach to the study of multiple, curvilinear and surface integrals in the engineering directions of undergraduate studies, which include a unified parallel consideration of these integrals when using: 1) a preliminary revision of the topic “Defined integral” and the study of new material on this basis, 2) interdisciplinary connections, 3) information technologies.
It is advisable to use appropriate methodical support to improve the effectiveness of this approach. As the latter, it is appropriate to use tutorials, problem books and individual tasks, posters and 3d models, interactive guidelines integrated with applications, written in high-level languages, generators of typical tasks, etc.

Gerasimenko S.A., Pavlenko A.N.
DEDUCTIVE-EMPIRICAL APPROACH TO THE STUDY OF MATHEMATICAL CYCLE DISCIPLINES IN NATURAL SCIENCE COURSE IN MATHCAD ^{[№ 2 ' 2021]}
Nowadays, the main trends in the reform of higher education naturally lead to a significant decrease of classes in the educational process, which negatively affects the study of the disciplines of the mathematical cycle due to their abstraction and often complexity of material presentation. Thus, there is a need to increase the effectiveness of contact work and to strengthen the role of independent study of students.
One of the factors contributing to improving the effectiveness of contact work is the preliminary propedeutic independent study of the material when applying the empirical component of the deductive-empirical approach to teaching higher mathematics.
The proposed new deductive-empirical approach to the organization of non-auditory independent work in the study of the disciplines of the mathematical cycle by students of natural sciences should include the following directions/stages: 1) providing historical information on the empirical approach to solve mathematical problems arising in solving natural science and technical problems, 2) experiments leading to the expediency of introducing new concepts and experiments illustrating definitions, 3) empirical justification of difficult-to-prove and not obviously feasible theorems, 4) application of experimental method to find numerical values of quantities, 5) use of the experimental method to illustrate and check the results of solving a problem, 6) monitoring the effectiveness of applying a deductive-empirical approach to teaching mathematics.
To increase the efficiency of propedeutic independent study, it is necessary to use appropriate methodological support. And the last (depending on the section being studied), you can use interactive methodological guidelines integrated with applications written in various high-level languages, emulators of devices for conducting mathematical experiments, etc.
Thus, students of natural sciences should study mathematical disciplines in the inextricable unity of the traditional deductive presentation of educational material with an empirical approach to learning with the wide use of interactive technologies.

Gerasimenko S.A., Pavlenko A.N.
ORGANIZATION OF THE MATHEMATICAL CYCLE DISCIPLINES PROPAEDEUTIC STUDY OF NATURAL SCIENTIFIC AND ENGINEERING DIRECTIONS ^{[№ 2 ' 2020]}
Currently, the main trends in the reform of higher education naturally lead to a significant reduction of the part of classroom studies in the educational process, which is extremely negative for the study of the mathematical cycle disciplines due to their abstraction and often cumbersome presentation of the material. Thus, there is a need to increase the effectiveness of contact work and to strengthen the role of students’ independent work.
One of the factors contributing to an increase in the effectiveness of contact work is independent propaedeutic consideration of the material under study.
The approach to organizing extracurricular independent work in the propaedeutic study of the mathematical cycle disciplines by students of natural sciences and engineering should include the following steps: recalling the facts previously studied, presenting the natural science (engineering) applications in their historical retrospective and presenting the main ideas of this section. The latter is supposed to be performed the most clearly, with the maximum use of interdiscipline relations.
To increase the effectiveness of propaedeutic independent work, it is advisable to use appropriate methodological support. As the latter (depending on the section under study), you can use interactive study guide integrated with applications written in various high-level languages, presentations, educational films and study guide in written form.
Thus, the preliminary acquaintance with the new mathematical section should be during extracurricular independent work with the widespread use of interactive teaching technologies.

Gerasimenko S.A., Pavlenko A.N., Pikhtilkova O.A.
ABOUT SOME ASPECTS OF ORGANIZATION OF INDEPENDENT WORK ON THE DISCIPLINES OF THE MATHEMATICAL CYCLE STUDENTS OF NATURAL SCIENTIFIC DIRECTIONS ^{[№ 8 ' 2017]}
Currently, the main trends of reform of higher education naturally leads to a significant reduction in the proportion of classrooms in the educational process, and as a consequence, to a sharp increase of a role of independent work of students. Full improving the efficiency of the latter is a necessary condition for better learning of students of educational material. Approach to the organization of classroom independent work at studying of mathematical disciplines cycle students of science and engineering should include the following stages: a demonstration of practical application have been studied on the lecture method; independent decision students the same tasks, generated with the help of information technologies; automatic verification of the correctness of the decision of tasks and conclusions on the basis of the assimilation of educational material each student. To enhance effective learning of mathematics and to organize the operational control of independent work, it is advisable to use interactive guidelines, integrated with applications written in different high level languages. The contents of the online guidance: explanation of the basics of the method, giving concrete samples of application using multimedia technologies; generated with the help of information technology options of the model jobs; tasks of a creative nature with elements of research work. Thus, students receive the first skills of independent work should take place in the classroom under the guidance of a teacher, require reliable and timely monitoring of independent work, appropriate use of information technology to reduce the burden on the teacher.

Beregovaya N.G., Gerasimenko V.V., Molchanov S.A., Morozov M.M.
OUTLOOK RECYCLING SPENT TYPE ZEOLITE NAX ORENBURG GAS CHEMICAL COMPLEX ^{[№ 10 ' 2015]}
NaH type zeolites used in industry for drying and deep fine purification of gases and liquids, for the separation of gaseous and liquid mixtures, separation of a mixture of hydrocarbons in a cryogenic air separation plant. Used zeolites Orenburg gas chemical complex is placed on authorized landfill gas production management and refers to the IV and V classes of hazard. Zeolites are unusable production waste. The paper presents experimental data on the reuse of waste zeolites. Laboratory studies were carried out on the basis of a branch of Gubkin Russian State University of Oil and Gas in Orenburg. A variant of asphalt production with the introduction of the grain portion of these zeolites. On the basis of the experiments selected the optimal component composition of the experimental asphalt. A variant of the use of waste zeolites — putting them in the concrete mix as a placeholder. It was found optimal amount of spent zeolite added to the composition of the resulting samples. A technique for obtaining samples of concrete mixtures and their composition. Determine their strength properties, such as water saturation, swelling, tensile strength, and coefficient of frost-grade asphalt and concrete strength. Depending on the strength of the samples revealed the content of the waste in their composition zeolite the possibility of using zeolites in agriculture. The developed technology allows to relieve the landfill and reduce the environmental burden on the region. Implementation of the proposed technologies in production will be accompanied by extra profit.

Gerasimenko S.A., Rustanov A.R., Shchipkova N.N.
ANALOGS IDENTITIES GRAY FOR TENSOR CONHARMONIC CURVATURE AC-MANIFOLDS OF CLASS C₁₁ ^{[№ 9 ' 2015]}
The main objective is to study the geometry of the curvature tensor conharmonic AC-class varieties C₁₁. For this purpose, the following two problems are solved: 1) get contact analogues identities Gray conharmonic curvature tensor introduced in consideration of Ishi; 2) on the basis of these identities to isolate and study the subclasses of AC-class varieties C₁₁. The paper identified three classes of almost contact metric manifolds class C₁₁, named as GK₁-, GK₂- and GK₃-manifolds. In Theorem 1 we obtain conditions on the curvature tensor components conharmonic on the space of the associated G-structure in which almost contact metric structure belongs to a class C₁₁ selected classes. Theorem 2 is proved that the variety of AC-class C₁₁ is GK₃-manifold and the GK₂-manifold. In Theorem 3 proved that AC-manifold of class C₁₁, which is GK₁-manifold is a manifold with Einstein's cosmological constant. In particular, in the case of completeness and continuity is compact and has a finite fundamental group. Finally, in Theorem 4 is proved that the variety of AC-class C₁₁ dimension greater than 5 is GK₁-manifold if and only if it is Ricci flat manifold.

Rustanov A.R., Gerasimenko S.A., Shchipkova N.N.
THE GEOMETRY OF TENSOR CONHARMONIC CURVATURE AC-MANIFOLDS OF CLASS C₁₁ ^{[№ 9 ' 2015]}
The main objective is to study the geometry of the curvature tensor conharmonic almost contact metric manifolds class C₁₁. To this end, following tasks: 1) calculate the basic essential components of curvature tensor conharmonic space of the associated G-structure; 2) explore conharmonic flat manifolds of class C₁₁; 3) get the identities satisfied by the curvature tensor conharmonic AC-class varieties C₁₁; 4) select and explore some subclasses of AC-class varieties C₁₁ of differential-geometric invariants of the second order. The paper addressed these problems. We prove the following theorem. Theorem 1: conharmonic flat AC-manifold of class C₁₁ is Ricci-flat manifold. Theorem 2: conharmonic flat AC-manifold of class C₁₁ is a manifold of Einstein. Theorem 3: conharmonic flat AC-manifold of class C₁₁ is a flat manifold. Theorem 4: AC-manifold of class C₁₁ is a manifold of class K₁ if and only if the AC-manifold of class C₁₁ is Ricci-flat manifold. Theorem 5: AC-manifold of class C₁₁ is a manifold of class K₂ if and only if the AC-manifold of class C₁₁ is Ricci-flat manifold. Theorem 6: AC-manifold of class C₁₁ is a manifold of class K₃ if and only if the AC-manifold of class C₁₁ is a flat manifold. Theorem 7: AC-manifold of class C₁₁, a manifold of class K₄ is a manifold of class Einstein's cosmological constant. In particular, in the case of completeness and continuity is compact and has a finite fundamental group. Theorem 8. AC-manifold of class C₁₁ dimension greater than 5 is K₄-manifold if and only if it is Ricci flat manifold.

Gerasimenko T.I.
ETHNOS AND CULTURE: INTERPRETATION OF TERMS AND APPROACHES TO THE STUDY ^{[№ 6 ' 2015]}
In the modern science, there is no unity in understanding of the phenomena of "ethnos" and "culture", although the problem has been investigated for a long time. In the representation of different scientific traditions and schools the views on the nature, feature set, the relationships between these concepts differ. In the context of a burst of scientific interest in issues of ethnicity and ethnic culture in response to globalization and the growth of intercultural communication studies ethnicities and cultures are extremely relevant. It is necessary to streamline the conceptual and methodological apparatus of interdisciplinary projects. The main directions of the Western ethno-cultural studies (European tradition, American Scientific School) are analyzed in the article. The Russian scientists' views evolution on the subject of the study has been analyzed. The basic concepts and approaches to their description have been described: primordialist (objectivist), postmodern (constructivist, instrumentalist) and practical. Ethno-constitutive and ethno-differentiating features have been divided and systematized. Hierarchization of ethnic groups has been shown. Correlation of such concepts as "diaspora", "ethnic communities" or "ethnic fraternities", "ethno-cultural group", "regional ethno-cultural group", "etniya", "people" has been described. The definition of ethnic culture has been given, its structure has been shown. Ethnos and ethnic culture — the notions are close, but not identical. Ethnic culture and the culture of ethnic groups are distinguished. Ethnic culture has several levels: household, professional, mass, as a rule internationalized. The article analyzes the formation at different levels in the development of intra ethnic cultural differences, including the regional and ethnic cultural similarities. Transformation of ethnic culture is influenced by various factors, including different parts ethnicity urbanization and westernization, geographical position, landscape, proximity to other ethnic groups, mutual complementarities. Ethnic and cultural differentiation is also affected by the age structure of the population, the level of economic development, especially the organization of the economy and others.

Gerasimenko T.I., Zaloznaya G.M., Chmyshenko E.G., Tikhonov N.B.
INVESTMENT BASICS OF INDUSTRIAL INFRASTRUCTURE IN THE REGION ^{[№ 4 ' 2015]}
Financing of development of production infrastructure is carried out at the expense of own (profit, depreciation) and the raised funds (the credits of banks, budgetary funds, means from other sources). It is established that, first of all, strengthening of a role of stability of manufacturing enterprises in implementation of investment process in production infrastructure of the region is observed. In the Orenburg region the share of own means in structure of investments into fixed capital decreased from 72 % in 2000 to 66,2 % in 2013, but 39,6 % of investments are formed at the expense of profit. This value is maximum for the last 13 years. Thus, development of production infrastructure of specific orientation everything is more carried out at the expense of manufacturing enterprises and more and more depends on their stability. It is also important to emphasize that by 2013. participation of public authorities of regional level in implementation of projects of production infrastructure was sharply reduced. In the Orenburg region influence of the enterprises of mining on investment development of production infrastructure is adult. At the enterprises of fuel and energy complex process of investment development is the most dynamic in relation to other objects of economy of the region. At the same time development of production infrastructure didn't lead yet to the solution of the problems facing the enterprises that reflects insufficient productivity of the existing infrastructure development of the region. As for sources of means, in the Orenburg region reorientation of economy to use of short-term financial investments is observed that considerably reduces possibilities of medium-term and long-term planning and management in the sphere of development of production infrastructure. In the region there is a growth of foreign investments which main part is aimed at the development of the sphere of an exchange and is to a lesser extent focused on activization of the production sphere. The increase in investment activity in the region at the expense of means of the regional budget will lead to growth of investments from the federal budget.

Lapaev S.P., Gerasimenko T.I., Chmyshenko E.G., Tikhonov N.B.
MODERN ORGANIZATIONAL AND ECONOMIC SUPPORT OF THE DEVELOPMENT OF INDUSTRIAL INFRASTRUCTURE IN THE REGION ^{[№ 4 ' 2015]}
The development of industrial infrastructure in the region requires the formation of an appropriate organizational and economic support of this process. The most important form of enhancing development of industrial infrastructure is a public-private partnership (PPP). The Russian Federation has formed a sufficient legal framework for the development of public-private partnership, operates a single entity to support the implementation of projects based on PPP — State Corporation "Bank for Development and Foreign Economic Affairs (Vnesheconombank). In the Orenburg region now PPP is used mainly for the development of social infrastructure and to a small extent — the production. From 9 infrastructure projects based on PPP in the Orenburg region, only one project is aimed at the development of geographically-oriented industrial infrastructure — reconstruction of highway Ilek — Tashla — Sobolev. At the same time in other regions of the Russian Federation has considerable experience in the use of PPPs for the development of industrial infrastructure. The leaders are the following regions: St. Petersburg, North and Far East federal districts. The most common forms of organizational and economic support for the development of industrial infrastructure are business — incubators, innovation centers, research and educational complexes and investment centers. In the Orenburg region created a significant number of organizations focused on the development of industrial infrastructure: State Non-Profit Organization "Orenburg Regional Fund for Small Business", a non-profit organization "guarantee fund for small and medium-sized enterprises of the Orenburg region" nonprofit organization "Foundation for Promotion of investments in entities Small and medium-sized enterprises in the Orenburg region "and others. However, the effectiveness of the use of the organizational and economic support for the development of industrial infrastructure in the region is insufficient. To support the development of industrial infrastructure, various financial instruments: the reduced rate of income tax exemptions on property tax, rental property, investment tax credit, and others. But their use is not sufficiently effective. In our country, the coordination of infrastructure development of the region to implement a single body — Autonomous Nonprofit Organization "Agency of strategic initiatives to promote new projects," but in the functions of this structure is not highlighted the need for accelerated development of the productive infrastructure to enhance the region's economy, which has a negative effect on handling the process. To solve the problems of production infrastructure in the regions, a network of corporate development, municipalities are formed investment sites that may become the new direction of the organizational and economic support for the development of industrial infrastructure. The problem is that all forms of organizational and economic support for the development of industrial infrastructure in the region have been used in the economy of each region and municipality.

Gerasimenko T.I., Semenov E.A.
ECONOMIC-GEOGRAPHICAL AND GEOPOLITICAL POSITION AS INTEGRAL SPATIAL CATEGORY ^{[№ 1 ' 2015]}
The role of economic-geographical and geopolitical position in the development of territories is extremely high; it is not a coincidence that there exists the term "pressure of location" or "positional pressure", introduced by B.B. Rodomanov. The positional principle lies as a fundamental one in geography. Properties of economic-geographical and geopolitical position as the important integral spatial category, their peculiarities allow estimating the location of a particular region or a country in the geo-economic and geopolitical space. EGP and GPP are not only important categories; they underlie some central teachings of the economic and geographical science. Classical scholars of Russian economic geography — N.N. Baransky, V.V. Pokshishevsky, I.M. Maergoiz — developed the foundations of the doctrine of EGP and methods of its evaluation. The doctrine was further developed in the works of contemporary authors, being reflected in the submitted article. Considering these categories is necessary when creating strategies for socio-economic development of territories and territorial planning schemes, as well as the choice of geopolitical and geo-economic preferences. In addition to such important elements of EGP as transport and geographical, industrial and geographical, recreational and geographical, geo-demographic and other characteristics, such new features as financial and geographical, innovative and geographical, agglomerative and geographical position take on special significance in terms of modern post-industrial economy, the rise of globalization and integration, modernization and diffusion of innovations, economic space compression, increasing importance of institutional factors and mobility production. The main properties of geographic location are, first of all, its historic character. It is subject to the dynamics under the influence of various factors. Secondly, it is potential (probabilistic) nature of EGP, which gives opportunities for development, but does not predetermine it. Thirdly, the remote nature of EGP optimizes logistics schemes. The influence on the EGP and GLP on territorial structure, the nature and direction of the external socio-economic relations in the region is great.

Gerasimenko T.I., Zolnikova J.F.
HISTORY OF DISCOVERY AND EXPLORATION OF MINERAL SPRINGS IN THE REGION CAUCASIAN MINERAL WATERS IN THE FIRST QUARTER OF THE XIX CENTURY ^{[№ 6 ' 2014]}
This article analyzes one of the stages of the history of exploration of mineral springs resort in the region Caucasian Mineral Waters — first quarter of the XIX century. The features of the test phase, shows activity of scientists from different fields of knowledge in the study region.

Gerasimenko S.A., Gamova N.A., Zubova I.K., Ostraya O.V.
ON THE DIRECTIONS OF EDUCATIONAL ACTIVITY IN HIGH SCHOOL (ON AN EXAMPLE OF THE ORENBURG STATE UNIVERSITY) ^{[№ 2 ' 2014]}
The article reflects the experience of teachers in the Faculty of Mathematics and organizing educational activities, presents the structure, functions, principles and the role of educational activity in the formation of socially mature personality.

Gerasimenko T.I., Lapaeva M.G.
FORMATION TRANS-BORDER REGIONS IN THE CONTEXT OF HISTORICAL-GEOGRAPHICAL FEATURES OF THE INTERACTION ^{[№ 2 ' 2012]}
The article shows the role of the regional development in historical-geographical aspects in the era of globalization. Global and regional development is two sides of single process. Aggravation of global problems stressed the actuality and importance of regional studies. The offset and blur the boundaries are global trend in the era of globalization. The result of trans-border interaction is formation of trans-border regions as parts of multi-layer system. Ethno-cultural space is one of the important subsystems of system.