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, PROPRETIES OF THE K-TH UPPER ORDER STATISTICS PROCESS THROUGH AN EXAMPLE(Union of Mathematicians of Macedonia, 2019)Aneta Gacovska-BarandovskaThe author has previously considered the asymptotic be havior of upper order statistics with central rank of a sample with deterministic size and of randomly indexed upper order statistics. In this paper, by using regular norming time-space changes, a theoretical example has been constructed in order to illustrate some of the ob tained properties of the k-th upper order statistics process. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, On limit laws for central order statistics under power normalization(Bulgarian Academy of Sciences, Institute of Mathematics and Informatics, 2015)Elisaveta I. Pancheva, Aneta Gacovska-BarandovskaSmirnov (1949) derived four limit classes of distributions for linearly normalized central order statistics. In this paper we investigate the possible limit distributions of the k-th upper order statistics with central rank using regular power norming sequences and obtain twelve limit classes. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Asymptotic behavior of central order statistics under monotone normalization(Elsevier, SIAM, 2014)Pancheva, E.I. Gacovska, A.Smirnov [Trudy Mat. Inst. Steklov., 25 (1949), pp. 3-60 (in Russian); Amer. Math. Transl., 67 (1952) (in English)] derived four limit types of distributions for linearly normalized central order statistics under the weak convergence. In this paper we investigate the possible limit distributions of the kth upper order statistics with central rank using monotone regular norming sequences and obtain 13 possible types. - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Randomly Indexed Central Order Statistics(Bulgarian Academy of Sciences, 2013)Gacovska, Aneta Pancheva, Elisaveta I.In our paper from 2012 we have considered the upper order statistics with central rank of sample with deterministic size. Here we investigate the asymptotic behaviour of randomly indexed upper order statistics using regular norming time-space changes. - 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?