Institute of Mathematics
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Item type:Publication, Topological transitivity of algebraically recurrent sets(Academy of Sciences and Arts of Bosnia and Herzegovina, 2024)Shoptrajanov, MartinIn this paper we will discuss the connection between topological transitivity and recurrence of G-flows acting on a compact metric space X. We will prove that the T T -property of the set of all algebraically recurrent points AR(ϕ) implies chain recurrent properties of the whole space and hence improve some of the results from [6]. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, ДЕМОГРАФСКИТЕ ПРОМЕНИ НИЗ ПРИЗМАТА НА МАТЕМАТИЧКИТЕ МОДЕЛИ(Природно-математички факултет - Скопје, 2020-09-02)Aneta Gacovska Barandovska - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Students’ ability to use geometry knowledge in solving problems of geometrical optics(Taylor & Francis, International Journal of Mathematical Education in Science and Technology, 2023-03-20)Aneta Gacovska Barandovska, Boce Mitrevski, Lambe BarandovskiProblem-solving is an essential part of teaching, learning, and assessment of physics and mathematics. The continuing educational reforms have a deep impact on everyday teaching as well as working with talented students. In the Macedonian educational system, the curricula do not explicitly point out the connection between mathematics and physics, but findings show that if the students do not understand the connection, they have problems adopting the knowledge. The gap that appears in applying geometry subsists even among talented students. When solving problems of geometrical optics, besides physics, it is inevitable that students use the standard geometrical apparatus. Even when the basics of physics are well known, possible mathematical mistakes often lead to wrong results in the given problems in physics. Here we demonstrate such an example of a selected problem from Macedonian state competitions in physics. The case study investigates two samples of students, 18 primary school students and 67 high school students, involved in State physics competitions in the year 2016. The selected problems have similar demands. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Global Scheme of the basic interactions and their geometrical interpretations(Faculty of Natural Sciences and Mathematics, University of Nis, Serbia, 2023)Kostadin TrenchevskiOur space-time consists of three 3-dimensional spaces: space $S$, space rotations $SR$ and time $T$. First are considered the basic possible 4 cases for exchange among them: 1. $r\rightarrow s$, 2. $s\rightarrow r$, 3. $r\rightarrow t$, and 4. $s\rightarrow t$, where $s\in S$, $r\in SR$, and $t\in T$. Analogous to the affine group of translations and rotations ${\cal A}$, it is considered a space group $G_s$ of $6\times 6$ matrices, which is isomorphic to the group $Spin(4)$. The space metric observed by the particles is found. Further are considered 4 generalized exchanges $1^*$, $2^*$, $3^*$ and $4^*$, induced by the cases 1, 2, 3, and 4. The case $1^*$ leads to the electro-weak interaction, and it is a consequence of non-commutativity between one translation and one rotation in the space group $G_s$. The case $2^*$ leads to the strong interaction, and it is a consequence of non-commutativity between two translations in the space group $G_s$. It leads also to the galactic acceleration which is observed at the periphery of each galaxy, and now we do not need dark matter in order to explain the motion of the distant stars in the galaxies. The case $3^*$ leads to electromagnetic interaction, and it is a consequence of non-commutativity between one translation and one rotation in the affine group ${\cal A}$. The case $4^*$ leads to gravitational interaction and it is a consequence of non-commutativity between one translation and one "radial translation" in the affine group ${\cal A}$. The corresponding accelerations are deduced and for a fixed space positions they are of type ${\bf a}={\rm rot}(\vec{\varphi})$ (gauge invariant), but the quantum and wave effects are neglected. It is also predicted a new gravity-weak interaction, which belongs to the case $2^*$.