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Hereditarnia 2019
2019, other monographs and other completed works

Abstract: The booklet contains the abstracts of the talks given at the 22th Hereditarnia Workshop on Graph Properties that was held at the Faculty of Electrical Engineering and Computer Science in Maribor on 21st and 22nd of June, 2019. The workshop attracted 22 participants from 8 countries. All of the participants are researchers in di˙erent areas of graph theory, but at this event they all presented topics connected with (hereditary) graph properties. Themes of the talks encompass a wide range of contemporary graph theory research, notably, various types of graph colorings, graph domination, some graph dimensions matchings and graph products. Beside the abstracts of the plenary speaker (Roman Sotak) and three invited speakers (Tanja Gologranc, Michael A. Henning and Ismael G. Yero), the booklet also contains the abstracts of 7 contributed talks given at the event.
Keywords: mathematics, graph theory, Hereditarnia, Maribor, Slovenia
Published: 13.12.2019; Views: 386; Downloads: 138
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Influence of entrance exams results on foreign students in economics studies at University of Economics, Prague
Milos Maryska, Petr Doucek, 2018, review article

Abstract: Background and purpose: The purpose of the article is to analyse results of entrance exams and of regularly exams for foreign students in the Czech language undergraduate study programs at four faculties of University of Economics, Prague (UEP) with the intention to investigate the dependency between the results of Entrance exams from English and mathematics and (1) results of regularly exams during the study and between (2) completion rate of the study. Design/Methodology/Approach: We have analysed 4.381 records for applicants from foreign countries who applied for studies between years 2009 and 2015. We used standard statistics methods and the method of logistic regression in the form of logit model. Results: We identified weak statistical correlation between entrance exam results from mathematics and results of regular exams. The correlation coefficient varies between 0.078 – 0.283 for investigated faculties of UEP. The same indicator for English language exams presents better values and it varies between 0.218 – 0.312. If an entrance exam result is higher by one point, the probability of successful completion of studies is multiplied by values between 1.017 - 1.042 for individual faculty per one additional point. Conclusion: The results of the research in mathematics and English language show that excellent results in entrance exam cannot not guarantee successful regularly exams. Conclusion for the probability of completing studies is that the acceptable level of points for admission foreign students is between 150 and 170 points, depending on the faculty.
Keywords: knowledge, foreign student, university, english language, mathematics
Published: 10.10.2018; Views: 640; Downloads: 248
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Testing the sustainability of growth of the LJSEX in the January 2000 to May 2010 period
Aleš Ahčan, 2011, original scientific article

Abstract: In this paper we analyse the behaviour of the LJSEX, the main index of the Ljubljana Stock Exchange, in the period from January 2000 till May 2010. More precisely, we test for the presence of bubbles and antibubbles and try to determine whether or not a bubble could have been predicted (both the formation and the date of the bubble burst). Second, we also employ techniques used to model antibubbles to forecast the future behaviour of the LJSE index. Besides modelling index dynamics for the aforementioned period, we also seek to determine the factors that led to the bubble forming and later bursting. We find that the bubble could have been forecasted at least several months in advance. On the other hand, a very precise date of the crash seems harder to identify. By more closely analysing the interplay between interest rates, credit activity and the LJSEX, we conclude that there is a clear connection between decreasing interest rates, increased credit activity and the formation of a stock bubble. If there is a clear correlation between the early phase of a bubble and increased credit activity of the banking sector, the link between the end of the bubble and the restriction of credit activity is less pronounced. By fitting the extended antibubble model from (Johansen 1999a) we obtain the values of parameters that give us some indication of the future behaviour of the LJSEX. Based on these results we conclude that in the next few years we are likely to experience a period of increased volatility with no clear increasing or decreasing growth pattern.
Keywords: exchange, interest rate, business mathematics, calculations, models
Published: 22.01.2018; Views: 559; Downloads: 288
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Modernizing mathematics education in Slovenia
Bojan Hvala, 2009, original scientific article

Abstract: Nowadays, we are facing a large number of varied educational projects which aim to direct and modernize mathematics education. Many institutions (from university bodies and institutes to individual secondary and elementary schools, networks of schools and private enterprises) make an appearance on the project market and contribute their ideas. Such quantity can cause confusion among teachers. Encouraged by the article, a mathematician's lament, by Paul Lockhard, we present some simple principles for classroom work that, in our opinion, would enhance the efficiency of mathematics classes in the long term. Thus we try to help mathematics teachers build a strategy for a fruitful approach to the ideas, recommendations and advertisements on the educational market. Showing the respect towards the quality mathematics teachers and avoiding discouraging and confusing them are some of the leading ideas that we should pursue in our attempt to improve mathematics education. At the end, we also offer some recommendations about the teacher training system.
Keywords: education, mathematics education, pedagogical approach, ICT
Published: 15.12.2017; Views: 695; Downloads: 63
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Interactive e-learning materials in the mathematics classroom in Slovenia
Samo Repolusk, 2009, original scientific article

Abstract: This article presents the current development of e-learning in Slovenia, with an emphasis on the domestic E-um web portal (URL: www.e-um.si) for teaching mathematics in primary and secondary schools. Based on findings from recent scientific research, the strengths and weaknesses of e-learning materials in education, particularly in mathematics classes, are analyzed. We are particularly interested in the advantages and disadvantages of interactive e-learning materials in comparison to traditional learning materials as well as in the quality of the E-um web portal in comparison to similar educational web portals at home and abroad. Theoretical findings are tightly interwoven with examples of teaching practice using the E-um interactive materials.
Keywords: education, e-learning, blended learning, interactive e-learning, E-um, e-learning materials, mathematics, mathematics classes
Published: 15.12.2017; Views: 822; Downloads: 76
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Ljubljana-Leoben graph theory seminar
2017, other monographs and other completed works

Abstract: The booklet contains the abstracts of the talks given at the 30th Ljubljana-Leoben Graph Theory Seminar that was held at the Faculty of Natural Sciences and Mathematics in Maribor between 13-15 September, 2017. The seminar attracted more than 30 participants from eight countries, all of which are researchers in different areas of graph theory. The topics of the talks encompass a wide range of contemporary graph theory research, notably, various types of graph colorings (b-coloring, packing coloring, edge colorings), graph domination (rainbow domination, Grundy domination, graph security), distinguishing problems, algebraic graph theory, graph algorithms, chemical graph theory, coverings, matchings and also some classical extremal problems. Beside the abstracts of the four invited speakers (Csilla Bujtás, Premysl Holub, Jakub Przybyło, Zsolt Tuza), the booklet contains also the abstracts of 18 contributed talks given at the event.
Keywords: mathematics, discrete mathematics, graph theory, Ljubljana-Leoben seminar, Maribor, Slovenia
Published: 08.12.2017; Views: 653; Downloads: 85
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Omega polynomial revisited
Mircea V. Diudea, Sandi Klavžar, 2010, original scientific article

Abstract: Omega polynomial was proposed by Diudea (Omega Polynomial, Carpath. J. Math., 2006, 22, 43-47) to count the opposite topologically parallel edges in graphs, particularly to describe the polyhedral nanostructures. In this paper, the main definitions are re-analyzed and clear relations with other three related polynomials are established. These relations are supported by close formulas and appropriate examples.
Keywords: mathematics, chemical graph theory, counting polynomials, Ommega polynomial, Theta polynomial, Pi polynomial, PI index, Sadhana polynomial, Cluj-Ilmenau index, CI index
Published: 24.08.2017; Views: 463; Downloads: 69
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Altered Wiener indices
Damir Vukičević, Janez Žerovnik, 2005, original scientific article

Abstract: Recently Nikolić, Trinajstić and Randić put forward a novel modification ▫$^mW(G)$▫ of the Wiener number ▫$W(G)$▫, called modified Wiener index, which definition was generalized later by Gutman and the present authors. Here we study another class of modified indices defined as ▫$W_{min,λ}(G) = ∑(V(G)^λm_G(u,ν)^λ−m_G(u,ν)^{2λ})$▫ and show that some of the important properties of ▫$W(G)$▫, ▫$^mW(G)$▫ and ▫$^λW(G)$▫ are also properties of ▫$W_{min,λ}(G)$▫, valid for most values of the parameter λ. In particular, if ▫$T_n$▫ is any n-vertex tree, different from the n-vertex path ▫$P_n$▫ and the n-vertex star ▫$S_n$▫, then for any λ ≥ 1 or λ < 0, ▫$^W_{min,λ}(P_n) > W_{min,λ}(T_n)>W_{min,λ}(S_n)$▫. Thus for these values of the parameter λ, ▫$W_{min,λ}(G)$▫ provides a novel class of structure-descriptors, suitable for modeling branching-dependent properties of organic compounds, applicable in QSPR and QSAR studies. We also demonstrate that if trees are ordered with regard to ▫$W_{min,λ}(G)$▫ then, in the general case, this ordering is different for different λ.
Keywords: mathematics, chemical graph theory, Wiener index, modified Wiener index
Published: 17.08.2017; Views: 528; Downloads: 78
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Wiener numbers of pericondensed benzenoid hydrocarbons
Sandi Klavžar, Ivan Gutman, Amal Rajapakse, 1997, original scientific article

Abstract: Using a recently developed technique for the calculation of the Wiener number (W) of benzenoid systems, we determine explicit expressions for W for several homologous series of pericondensed benzenoid hydrocarbons. An elementary proof for the correctness of the used method is also included.
Keywords: mathematics, chemical graph theory, distance in graphs, Wiener number, benzenoids
Published: 05.07.2017; Views: 733; Downloads: 128
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The Hosoya-Wiener polynomial of weighted trees
Blaž Zmazek, Janez Žerovnik, 2007, original scientific article

Abstract: Formulas for the Wiener number and the Hosoya-Wiener polynomial of edge and vertex weighted graphs are given in terms of edge and path contributions. For a rooted tree, the Hosoya-Wiener polynomial is expressed as a sum of vertex contributions. Finally, a recursive formula for computing the Hosoya-Wiener polynomial of a weighted tree is given.
Keywords: mathematics, graph theory, Hosoya-Wiener polynomial, weighted tree, vertex weighted graphs
Published: 05.07.2017; Views: 600; Downloads: 60
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