Нови резултати за некои класи повеќелисни функции

Оваа докторска дисертација е од комплексанта анализа, поконкретно, од геометриската теорија на функциите и пред се од теоријата на повеќелисните, а е опфатена и теоријата на еднолисните функции. Дисертацијата содржи нови оригинални резултати кои се составен дел на четири трудови. Истражувањата се насочени кон наоѓање на врски помеѓу некои класи на повеќелисни функции изразени преку импликации кои содржат неравенства. Понатаму, тие се насочени кон разгледување на израз за повеќелисни функции проучуван од Silverman за еднолисни. Дадени се и нови критериуми за ограничено вртење со помош на модулот и реалниот дел на линеарната комбинација на f'(z) и f(z)/z, т.е., на \alpha f'(z)+\beta f(z)/z. Дисертацијата е завршена со идеи за понатамошни истражувања

CA18232 - Mathematical models for interacting dynamics on networks (MAT-DYN-NET)

Many physical, biological, chemical, financial or even social phenomena can be described by dynamical systems. It is quite common that the dynamics arises as a compound effect of the interaction between subsystems in which case we speak about coupled systems. This Action shall study such interactions in particular cases from three points of view: 1. the abstract approach to the theory behind these systems, 2. applications of the abstract theory to coupled structures like networks, neighbouring domains divided by permeable membranes, possibly non-homogeneous simplicial complexes, etc., 3. modelling real-life situations within this framework. The purpose of this Action is to bring together leading groups in Europe working on a range of issues connected with modelling and analysing mathematical models for dynamical systems on networks. It aims to develop a semigroup approach to various (non-)linear dynamical systems on networks as well as numerical methods based on modern variational methods and applying them to road traffic, biological systems, and further real-life models. The Action also explores the possibility of estimating solutions and long time behaviour of these systems by collecting basic combinatorial information about underlying networks

An optimization model for medical personnel scheduling during pandemic

During a pandemic, the medical staff have a problem in dealing with the care of hospitalized patients. This paper aims to find solution of the problem of medical personnel scheduling in a covid centre during Covid- 19 pandemic. Covid centers face up with a problem how the employees should be organize throughout the working day. In this talk, we intend to minimize the number of medical personnel who must be on duty during the weeks when the number of infected is high. So, the staff work schedule must be the best possible so they will optimize all available resources and in the same time will satisfy all operational constraints

Case Study: Which math topics students have a problem with when they start university studying

After graduating from high school, many high school students decide to continue their studies. The decision of what they want to be and what they will study is made by some of them a long time ago, but for some there is hesitation until the last moment. Due to some reasons, there are some of them who decide to continue their education at the technical faculty, even though they have problems with the topics they have learned in mathematics subjects. It happens to almost every new generation of students. That led us to research to find a solution and change that practice. In this paper, a questionnaire has been prepared for students in first study year from technical faculties with questions with which we want to see which mathematical topics students have the most problems with, i.e., facing difficulties in solving tasks. Research results are given by statistical analysis. Then, a conclusion from the results is drawn. Finally, in the end of the paper, a possible solution for the identified problematic topics is stated

Statistical Analysis of Knowledge for Topic Complex Numbers of Students From the First Academic Year

Students who decide to study at a technical faculty must be well prepared for all mathematical topics. Many of the students, at the beginning of their studies when they encounter math problems with complex numbers, face difficulties in solving them, even though they have already studied complex numbers in high school. In this paper an analysis of the knowledge of the topic complex numbers, of the newly enrolled students at the technical faculties at University Goce Delchev Shtip, is made. The need for such an analysis was realized a few years ago when it was observed how first year students had problems when complex numbers were mentioned. With an appropriate statistical analysis, we wanted to assess how well the students know how to solve problems with complex numbers, what they find most problematic when learning the subject of complex numbers and what difficulties they face. Based on the results of the analysis, we will offer a solution to overcome the problems that students face when solving problems with complex numbers

Analysis of student achievements in teaching matrix using Geogebra software

The achievement of students after completion of teaching process in each subject is what is quite important for both professors and students. This research deals with the analysis of students' achievements for the topic matrices, in a “traditional” way and teaching enriched with free software. The introduction of software in the teaching process as “modernized” approach to teaching aims to increase student activity, to raise the teaching process to a higher level, to raise a student’s achievements and to motivate students to learn more independently

Using Excel to predict and compare the grade in Mathematics by simplelinear regression model

In this paper was used simple linear regression model to predict and compare the final grade of the students in subject of Mathematics from department of Technical Sciences. Data’s were collected from students of two Universities:University "Mother Teresa" in Skopje and University "Goce Delcev" – Stip. The model was based on the data of students' scores in three tests: 1st periodical exam, 2nd periodical exam and final examination. This analyze was carried out by simple linear regression model. For obtaining our results was used Excel. In this paper also have been given the graphical representations of ours analysis and in the end have been given some conclusions based on the results

Solving tasks from the topic plane equation using GeoGebra

Every new generation of students have difficulties with learning mathematical subjects. The success in Mathematics is getting lower and lower, not only in Macedonia but also on global level. Mathematical materials that contain only problems with solutions without their visual representation are hardly acceptable for many students. So, visualization plays an important role in the process of teaching mathematics subjects. In this paper, we will present the solution of examples of plane equation and, by using free software, visualization of that solution is made. For solving several examples, we are going to use the Computer Algebra System (CAS) in GeoGebra

Предности и недостатоци при изведување online настава по математика

Наставниот процес и начинот на изведување и одржување на наставата се најважни за продуцирање на образовани, таленирани и способни експерти во која и да било област. Доста време наставата во универзитетите и училиштата се одвиваше на класичен начин во предавална, амфитеатар или училница. Новини кои се воведува со тек на годините беа дигитализацијата, примената на интернетот, користење на платформата е-учење и слично. Ковид 19 пандемијата наложи целосна промена на тој класичен начин на спроведување на наставата т.е. ја донесе потребата од воведување и спроведување на online настава. Целта на оваа студија е да се согледат придобивките и недостатоците од реализрање online настава по математика во образовните инситуции

The importance of IT technologies in education in pandemic time

The emergence of a pandemic is not something new in the world. There also have been pandemics in the past. The global covid 19 pandemics has been around for a long time. People all over the world are slowly adapting to the changes and life styles imposed by the Corona virus and after a year and a half of living with that virus they have accepted all the challenges and got used to the new way of life. In the paper we described the functioning of the educational process during the pandemic with Covid 19 virus, more precisely, an analysis of the way the classes we hold during the pandemic is given. Emphasis on the application of IT technologies for successful implementation of teaching and achieving excellent results from students is placed. Finally, a conclusion in which we want to emphasize the importance of the application of IT technologies in education during and after the end of the virus is given, in order to emphasize the advantages of their use. We achieve all this by comparing the educational process in a time of pandemic using IT tools and without IT technologies