Institute of Mathematics
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Item type:Publication, Space-time description of atoms, part I: Electronic structures, dark matter, and g-factors of electron, muon and tau(World Scientific Publishing Company, 2024-06-17)Kostadin TrenčevskiThe description of atoms is based on 3D time and some relativistic effects about spinning bodies have been published previously. The time displacement of the electrons also plays an important role. While the principal quantum number n refers to the angular momentum nℏ observed by external observer, the azimuth quantum number l refers to the angular momentum lℏ observed from the electron itself. The intrinsic angular momentum observed by the electron is ±ℏ/2 according to Stern–Gerlach experiment, but the angular momentum observed by external observer is about α^2ℏ/4. The magnetic quantum numbers are deduced from the mentioned effects and the trajectories of electrons are non-probabilistic and geometrically well determined. The spin quantum number indicates the time arrow toward the future or toward the past. So, the electrons with opposite time arrows can be grouped in pairs, where the nucleus is in the middle. Descriptions of the dark matter particles and the electrons are given. Using the value α=1/137.035999166 suggested from the QED, the g-factors of the electron and muon are ge=−2.002319304361166; gμ=−2.002331839354934, which give excellent agreements with the experiments. So, if we equalize the formulas for g-factor from QED and this approach, it determines the theoretical value of α, without experiment. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Statistical Literacy of Undergraduate Students Before Taking the Introductory Statistics Course(Сојуз на математичари на Македонија, 2023) - Some of the metrics are blocked by yourconsent settings
Item type:Publication, SCALE INVARIANT STOCHASTIC GRADIENT METHOD WITH MOMENTUM(Matematichki Bilten, Union of Mathematicians of Macedonia, 2023) - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Assessment of the Environmental Gamma Dose Rate in Macedonia(Technical Faculty “Mihajlo Pupin”, Zrenjanin & Faculty of Sciences and Mathematics, Niš, 2024-10)Lambe Barandovski, Robert Šajn, Trajče Stafilov, Aneta Gacovska – BarandovskaAssessment of the environmental gamma dose rate in Macedonia was conducted in 2010, 2015, and 2020 to establish baseline data of the gamma dose rate and observe potential changes over time. For the purpose, the gamma dose rate was measured at 68 locations in 2010, and 72 location in 2015 and 2020 using a portable dosimeter positioned 1 m above the ground surface. The gamma dose rates in the country were in the range 53 - 340 nSv/h in 2010, 38 - 360 nSv/h in 2015 and 41 - 300 nSv/h in 2020. It was found that the reason for a variation in the measured values is due to the geological factors and geological formations which are different in different parts of the country. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, FUZZY IDEALS IN (n + k, n)-SEMIGROUPS(Union of Mathematicians of Macedonia, 2022)Valentina Miovska, Delcho Leshkovski, Vesna Celakoska-JordanovaIn this paper we introduce the concepts of fuzzy subset of vector valued groupoid (semigroup), as well as fuzzy subgroupoid, fuzzy subsemigroup, fuzzy i-ideal (ideal) and bi-ideal of vector valued groupoid (semigroup), investigate their properties and present suitable examples. Prime and fuzzy prime, semiprime and fuzzy semiprime subsets of vector valued groupoids are defined and their properties are investigated. We characterize the Green's relations J_{i} on a vector valued semigroup S in terms of fuzzy subsets. Green's relations J_{i}^{F} on S are suitably defined and it is shown that they coincide with the relation J_{i} on S. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Everlasting educational reforms on the road to quality and permanent knowledge or…(Proceedings of Science, 2023-10-02)Lambe Barandovski, Vera Zoroska, Aneta Gacovska - BarandovskaThe Macedonian educational system is under continuous reforms and changes made to the syllabuses and methods of teaching. In the last two decades, almost every aspect of teaching mathematics and physics in primary school has been changed. The last three major changes cover different approaches: coordinated teaching in 2008, curriculum changes towards research methods and problem solving in learning and teaching - according to the Cambridge International Examinations Center in 2016, and the newest concept according to the European Strategy 2020 (based on six dimensions: quality, inclusion and gender equality, green and digital transitions, teachers, higher education, a stronger Europe in the world) and the new Action Plan for Digital Education 2021-2027 (with initiatives for high quality, inclusive and accessible digital education in Europe). Different opinions appeared in public, mostly among teachers and parents, for and against the „new ways” in education. Hereby some of the arguments for and against will be presented, problems and questions will be stressed out and curriculum differences will be shown. Are we losing the chance for laying the foundations of mathematics and physics while walking on the road to digitalization? Are we ready as a country to embrace the new social challenges? Have we done enough research before introducing the new concepts, do we know if we are professionally, materially and mentally ready to let the „digital books“ and „interculturalism“ on a small door in the classrooms? Finally, yes, the freedom in finding personal creative ways of teaching and using open-source material is great, so is stimulating critical thinking among students. But is the majority of the population ready to trade the classical textbooks for digital ones? Has there been continuing professional education for teacher in the classroom to be ready to grasp the new concept? Are we ready for this kind of transition in education as a way for a complete social transition? - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Determining Value at Risk using Extreme Value Theory on a Financial Data Set(Union of Mathematicians of Macedonia, 2023-11-28)Stevo Gjorgiev, Aneta Gacovska - BarandovskaExtreme value theory has a wide range of applications. The paper considers application of extreme value theory in the area of nancial ows. Our data set has been processed using two di erent methods, block maxima and peak over the threshold method. We compare the obtained results for the risk measures and draw conclusions on the behavior of the nancial ows for di erent time intervals. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Attitudes Towards Reproduction and Creating a Family Among Albanian Women—The Case of Arachinovo Municipality, North Macedonia(Springer, 2024-03-17)Biljana Apostolovska Toshevska, Mirjanka Madjevikj, Marija Ljakoska, Aneta Gacovska BarandovskaThe place people live can determine whom they meet, the partners they choose, the level of education they accomplish, the income they earn, and the options available to them and their families. It also affects life habits, customs, and affects attitudes regarding reproduction, and creating a family. The municipality of Arachinovo with all its characteristics and specifics, especially the attitudes of women toward reproduction and creating a family is very challenging to study. Located around 12 km from the capital city center, this municipality stands out in terms of birth rates, and ethnic and religious homogeneity. Data for the main analyses in the paper were obtained by a field survey conducted in April and May of 2020. The survey included a little over 60 women of reproductive age, divided into three age groups. For the analysis of the variance of the means of the three chosen groups, standard statistical tests were used, while the one-way ANOVA test was used for testing seven hypotheses for the equality of the means of the three independent specimens. A chi-squared test of independence of a pair of random variables based on observations was made, for the whole sample, according to the considered questions. The research and the gained results are expected to contribute to the creation of appropriate economic, social, and demographic policies, which will enable greater inclusion of women in the educational process, the labor force, and society, and will raise awareness about their role and place in the family. - 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 $2^*$.