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https://repository.sspu.edu.ua/handle/123456789/397

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4-вимірні вектори в СТВ
(2011) Мороз Іван Олексійович; Moroz Ivan Oleksiiovych; Іваній Володимир Степанович; Ivanii Volodymyr Stepanovych; Холодов Роман Іванович; Kholodov Roman Ivanovych
Вивчення явищ, які протікають з великими швидкостями, вимагає врахування скінченності швидкості передачі взаємодії. Це, спільно з вимогою інваріантності законів всіх явищ по відношенню до зміни системи відліку, приводить до необхідності нерозривного розгляду простору і часу та введення єдиного об’єкту, у якому протікають всі процеси в природі – чотиривимірного простору-часу.
Cloud-based Service GeoGebra and its Use in the Educational Process: the BYOD-approach
(2019) Семеніхіна Олена Володимирівна; Друшляк Марина Григорівна; Бондаренко Юлія Анатоліївна; Кондратюк Світлана Миколаївна; Дегтярьова Неля Валентинівна; Semenikhina Olena Volodymyrivna; Drushliak Maryna Hryhorivna; Bondarenko Yuliia Anatoliivna; Kondratiuk Svitlana Mykolaivna; Dehtiarova Nelia Valentynivna
The authors propose one of the possible ways to solve the problem of insufficient number of computers in public educational institutions and limited access to computer classes in Ukraine. Such a way is the introduction of the BYOD-approach (Bring Your Own Device) in the learning process. The authors specify the content and correlation of the concepts of "information technologies", "computer technologies", "cloud technologies" to determine the type of service GeoGebra. The authors propose different ways of using the GeoGebra service. They are studied to prepare future math teachers for the use of modern information (digital) technologies in professional activities.
Computer Mathematical Tools: Practical Experience of Learning to Use Them
(2014) Semenikhina Olena Volodymyrivna; Семеніхіна Олена Володимирівна; Drushliak Maryna Hryhorivna; Друшляк Марина Григорівна
The article contains general information about the use of specialized mathematics software in the preparation of math teachers. The authors indicate the reasons to study the mathematics software. In particular, they analyze the possibility of presenting basic mathematical courses using mathematical computer tools from both a teacher and a student, argue in favour of using software instead of traditional paper-and-board style. The special course of the study of mathematics software (main tasks of the course are disclosed; knowledge and skills that students should possess on completion of their studies are dedicated; content of computer workshop is detailed) is briefly described. Also the authors give a detailed solution and its methodic basis of typical problem with the use of the SCM Maple. The typical errors which made by students in the use of specialized mathematics packages are characterized. Author’s own experience of teaching computer workshop of the study of mathematical computer tools by the students of Sumy State Pedagogical Makarenko University is presented and analyzed.
Computer Tools “Trace” and “Locus” in Dynamic Mathematics Software
(2014) Drushliak Maryna Hryhorivna; Друшляк Марина Григорівна
The article describes the results of use of tools "Trace" and "Locus" in dynamic mathematics software. Examples of solutions of stereometric locus problems to construct static traces in software GeoGebra5.0, Cabri3D and plane geometry problems to construct both static traces and traces that are perceived as independent dynamic objects in software MathKit and GeoGebra are given. Attention is focuses on the differences of the actions of these tools. Author notes the possibility of forming a logical and constructive thinking with their use.
Computer Visualization of Logic Elements of the Information System Based on PROTEUS
(2019) Shamonia Volodymyr Hryhorovych; Semenikhina Olena Volodymyrivna; Drushliak Maryna Hryhorivna; Lynnyk Serhii Ivanovych; Шамоня Володимир Григорович; Семеніхіна Олена Володимирівна; Друшляк Марина Григорівна; Линник Сергій Іванович
The article considers the possibility of a computer visualization of the code decoder work in Proteus, which is used in a laboratory workshop when studying the topic "Digital logic" of the discipline "Architecture of Information Systems" (the field of study “12 Information technologies” and “01 Education, 014 Secondary education. Computer science”). Modelling and simulation dur-ing the laboratory work contribute to the awareness of the importance of visual-ization as a means of positive impact on the level of future IT-specialists’ edu-cational achievements. This was confirmed by the analysis of the obtained re-sults at the significance level of 0.05 according to Student’s test.
Conditions of Dedekindness of Generalized Norms in Non-periodic Groups
(2019) Lukashova Tetiana Dmytrivna; Drushliak Maryna Hryhorivna; Lyman Fedir Mykolaiovych; Лукашова Тетяна Дмитрівна; Друшляк Марина Григорівна; Лиман Федір Миколайович
The authors consider generalized norms for different systems of infinite and noncyclic subgroups in nonperiodic groups. Relations between these norms are established. The conditions under which the given norms are Dedekind, in particular, central, are studied.
Constructing Geometrical Models of Spherical Analogs of the Involute of a Circle and Cycloid
(Eastern-European Journal of Enterprise Technologies, 2023) Nesvidomin A.; Pylypaka S.; Volina T.; Kalenyk Mykhailo Viktorovych; Shuliak I.; Semirnenko Y.; Tarelnyk N.; Hryshchenko I.; Kholodniak Y.; Sierykh L.; Несвідомін А.; Пилипака С.; Воліна Т.; Каленик Михайло Вікторович; Шуляк І.; Семірненко Ю.; Тарельник Н.; Грищенко І.; Холодняк Ю.; Сєрих Л.
The common properties of images on a plane and a sphere are considered in the scientific works by scientists-designers of spherical mechanisms. This is due to the fact that the plane and the sphere share common geometric parameters. They include constancy at all points of the Gaussian curve, which has a zero value for a plane and a positive value for a sphere. Figures belonging to them can slide freely on both surfaces. With unlimited growth of the radius of the sphere, its limited section approaches the plane, and the spherical shape transforms into a plane. Thus, a loxodrome that crosses all meridians at a constant angle is transformed into a logarithmic spiral that intersects at a constant angle the radius vectors that come from the pole. The tooth profile of cylindrical gears is outlined by the involute of a circle. A spherical involute is used for the corresponding bevel gears. Other spherical curves are also known, which are analogs of flat ones. The formation of a cycloid and an involute of a circle are associated with the mutual rolling of a line segment with each of these figures. If the segment is fixed and the circle rolls along it, then the point of the circle describes the cycloid. In the case of a stationary circle along which a segment is rolled, the point of the segment will execute the involute. To move to the spherical analogs of these curves, it is necessary to replace the circle with a cone, and the straight line with a plane. The spherical prototype of the cycloid will be the trajectory of the point of the base of the cone, which rolls along the plane, that is, along the sweep of the cone. The sweep of a cone is a sector, the radius of the limiting circle of which is equal to the generating cone. If this sweep, like a section of a plane, is rolled around a fixed cone, when its top coincides with the center of the sector, then the point of the limiting radius of the sector will execute a spherical involute. This paper analytically implements these two motions and reports the parametric equations of the spherical analogs of the circle involute and the cycloid
Cтруктура и свойства полимерных композитов и нанокомпозитов, подвергнутых термомагнитной обработке
(2015) Стадник Олександр Дмитрович; Stadnyk Oleksandr Dmytrovych; Мороз Іван Олексійович; Moroz Ivan Oleksiiovych; Медведовська Оксана Геннадіївна; Medvedovska Oksana Hennadiivna; Білик Володимир Миколайович; Bilyk Volodymyr Mykolaiovych
В работе исследовано воздействие термомагнитной обработки на структуру и свойства полимерных композиционных материалов, на основе эпоксидно-диановой смолы, поливинилиденфторида, полиэтилена, поли-4-метилпентена-1. В качестве наполнителей использовали порошки: электролитическое железо, карбонильный никель и нанокобальт. Определено значение температуры плавления и кристаллизации, а также диапазон температур плавления (кристаллизации). Установлена зависимость степени кристалличности, коэрцитивной силы и остаточной намагниченности полимерных композиционных материалов от концентрации наполнителя и условий обработки.
Dynamic Mathematics Software as a Necessary Component of Modern-Math-Teachers Preparation in Ukraine
(2016) Semenikhina Olena Volodymyrivna; Семеніхіна Олена Володимирівна; Drushliak Maryna Hryhorivna; Друшляк Марина Григорівна
The article discusses the relevance of the study of dynamic Mathematics software by future math teachers in Ukraine. The focus is on the requirement, not only to know about specialized dynamic software, but also to be able to organize an effective learning process with its usage. The arguments for the organization of special courses in the study of dynamic Mathematics software are based on the need to demonstrate the skills of usage of modern Mathematics software. The authors describe their own experience of teaching the course at A. S. Makarenko Sumy State Pedagogical University (Ukraine), which is included in the curricula as variable course of math-teacher preparation, in particular, the successive changes of the content of the course, due to constant and rapid development of Information Technology, during all periods of learning.
Finite 2-Groups with a Non-Dedekind Non-Metacyclic Norm of Abelian Non-Cyclic Subgroups
(2019) Lyman Fedir Mykolaiovych; Лиман Федір Миколайович; Lukashova Tetiana Dmytrivna; Лукашова Тетяна Дмитрівна; Drushliak Maryna Hryhorivna; Друшляк Марина Григорівна
The authors study ﬁnite 2-groups with non-Dedekind non-metacyclic norm of Abelian non-cyclic subgroups depending on the cyclicness or the noncyclicness of the center of a group G. The norm is deﬁned as the intersection of the normalizers of Abelian non-cyclic subgroups of G. It is found out that such 2-groups are cyclic extensions of their norms of Abelian non-cyclic subgroups. Their structure is described.
Generalized Norms of Groups
(2016) Drushliak Maryna Hryhorivna; Друшляк Марина Григорівна; Lukashova Tetiana Dmytrivna; Лукашова Тетяна Дмитрівна; Lyman Fedir Mykolaiovych; Лиман Федір Миколайович
In this survey paper the authors have tried to specify all the known results concerning the norms of the group and its generalizations. Special attention is paid to the analysis of their own research of different generalized norms, particularly the norm of non-cyclic subgroups, the norm of Abelian non-cyclic subgroups, the norm of infinite subgroups, the norm of infinite Abelian subgroups and the norm of other systems of Abelian subgroups.
On Computer Support of the Course “Fundamentals of Microelectronics” by Specialized Software: the Results of the Pedagogical Experiment
(2020) Semenikhina Olena Volodymyrivna; Drushliak Maryna Hryhorivna; Lynnyk Serhii Ivanovych; Kyryliuk Hanna; Kharchenko Inna Ivanivna; Honcharenko Olena; Семеніхіна Олена Володимирівна; Друшляк Марина Григорівна; Линник Сергій Іванович; Кирилюк Ганна; Харченко Інна Іванівна; Гончаренко Олена
The awareness of the ideas about the work of modern computers is important for the future IT-specialists’ preparation. Processes occurring in the middle of the computing system are based on the work of the physical devices, the modeling of which is advisable to carry out in simulation software. The authors consider the problem of choosing simulation software of physical processes. The experience of teaching a microelectronics course allowed to choose two simulation software: Proteus and Multisim. The pedagogical experiment on the choice of the optimal simulation software to support the course of microelectronics, which is studied by future ITspecialists and computer science teachers, was conducted based on Makarenko Sumy State Pedagogical University (Ukraine). The comparative analysis of the individual characteristics of the simulation software prefers Proteus. However, the results of the pedagogical experiment confirm the feasibility of attracting Multisim.
On Finite 2-Groups With Non-Dedekind Norm of Abelian Non-Cyclic Subgroups
(2016) Lyman Fedir Mykolaiovych; Лиман Федір Миколайович; Lukashova Tetiana Dmytrivna; Лукашова Тетяна Дмитрівна; Drushliak Maryna Hryhorivna; Друшляк Марина Григорівна
The authors study finite 2-groups with the cyclic center and non-metacyclic non-Dedekind norm of Ab elian non-cyclic subgroups. It is found out that such groups are cyclic or metacyclic extensions of their norms of Abelian non-cyclic subgroups. Their structure is described.
On Groups With the Minimal Condition for Non-Invariant Decomposable Abelian Subgroups
(2006) Lyman Fedir Mykolaiovych; Лиман Федір Миколайович; Drushliak Maryna Hryhorivna; Друшляк Марина Григорівна
The infinite groups, in which there is no any infinite descending chain of non-invariant decomposable abelian subgroups (md-groups)are studied. Infinite groups with the minimal condition for non-invariant abelian subgroups, infinite groups with the condition of normality for all decomposable abelian subgroups and others belong to the class of md-groups. The complete description of infinite locally finite and locally soluble non-periodic md-groups is given, the connection of the class of md-groups with other classes of groups are investigated.
On the Non-cyclic Norm in Non-periodic Groups
(2020) Lukashova Tetiana Dmytrivna; Lyman Fedir Mykolaiovych; Drushliak Maryna Hryhorivna; Лукашова Тетяна Дмитрівна; Лиман Федір Миколайович; Друшляк Марина Григорівна
The authors study non-periodic locally soluble by finite groups with the non-Dedekind norm of non-cyclic subgroups, which is the intersection of normalizes of all non-cyclic subgroups of a group. It is found that all non-cyclic subgroups are normal in these groups. Their structure is described.
On the Norm of Decomposable Subgroups in Locally Finite Groups
(2015) Lyman Fedir Mykolaiovych; Лиман Федір Миколайович; Lukashova Tetiana Dmytrivna; Лукашова Тетяна Дмитрівна
We study the relationships between the norm of decomposable subgroups and the norm of Abelian non- cyclic subgroups in the class of locally finite groups. We also describe some properties of periodic lo- cally nilpotent groups in which the norm of decomposable subgroups is a non-Dedekind norm.
On the Norm of Decomposable Subgroups in Nonperiodic Groups
(2016) Lyman Fedir Mykolaiovych; Лиман Федір Миколайович; Lukashova Tetiana Dmytrivna; Лукашова Тетяна Дмитрівна
We study the relationships between the properties of nonperiodic groups and the norms of their de- composable subgroups. In particular, we analyze the influence of restrictions imposed on the norm of decomposable subgroups on the properties of the group in the case where this norm is non-Dedekind. We also describe the structure of nonperiodic locally nilpotent groups for which the indicated norm is non-Dedekind. Moreover, some relations between the norm of noncyclic Abelian subgroups and the norm of decomposable subgroups are established.
On the Results of a Study of the Willingness and the Readiness to Use Dynamic Mathematics Software by Future Math Teachers
(2015) Semenikhina Olena Volodymyrivna; Семеніхіна Олена Володимирівна; Drushliak Maryna Hryhorivna; Друшляк Марина Григорівна
The article presents the results of pedagogical research on the willingness and the psychological readiness to use dynamic mathematics software by future math teachers. We used nonparametric method for dependent samples – the McNemar’s test. The hypothesis, that the study of Special course on the use of dynamic mathematics software for future teachers has a positive impact on the willingness and the psychological readiness to use such software in their own professional activities, is confirmed at the significance level of 0.05. Additionally, the results of the experiment on the willingness and the readiness to support the teaching of some subjects (algebra, planimetry, solid geometry and analysis) with dynamic mathematics software and the willingness and the readiness to use some dynamic mathematics software (Gran (Gran1, Gran2d, Gran3d), GeoGebra, Сabri, MathKit, DG, GS) by Ukrainian math teachers is given.
Open Educational Resources as a Trend of Modern Education
(2019) Семеніхіна Олена Володимирівна; Друшляк Марина Григорівна; Бондаренко Юлія Анатоліївна; Кондратюк Світлана Миколаївна; Іонова Ірина Миколаївна; Semenikhina Olena Volodymyrivna; Drushliak Maryna Hryhorivna; Bondarenko Yuliia Anatoliivna; Kondratiuk Svitlana Mykolaivna; Ionova Iryna Mykolaivna
The article presents the results of the study of open educational resources in mathematical disciplines. The purpose of the article is to summarize the experience of teaching mathematical courses based on quantitative analysis of the corresponding open educational resources and determination of ways of using such resources in the conditions of Ukrainian universities. The definition of open educational resources and their specific features are specified, in particular, support of different formats for presentation of materials, their publication under conditions of an open license, provision of free access, the possibility of modification of materials by other users. The analysis of the number of open educational resources Coursera, Edx, Udemy, and INTUIT has revealed that the bulk of mathematical courses in relation to others is not large, which suggests a reduction in young people's interest in purely mathematical disciplines. At the same time, it was noted that the presence of such resources on the site of the university contributes to the formation of its positive image within the country and the world. The own experience of studying mathematical online courses on Analytical Geometry, Linear Algebra, Geometry and Mathematical Philosophy is described.
Organization of Experimental Computing in GeoGebra 5.0 in Solving Problems of Probability Theory
(2015) Semenikhina Olena Volodymyrivna; Drushliak Maryna Hryhorivna; Семеніхіна Олена Володимирівна; Друшляк Марина Григорівна
The article analyzes the use of various mathematics software in the study of stochastic. The idea of dynamic visualization of the results of random experiments on the example of the classical problem of the meeting, which can be solved in two ways: using statistical definition of probability, which is based on random experiments, and traditionally using the geometric definition of probability. Some tasks, on the base of which the idea of visualization of the results of random experiments can be implemented, are offered with instructions.

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