1. Hereditarnia 2019 : Book of Abstracts, Maribor, 21st & 22nd June, 20192019, 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 in DKUM: 13.12.2019; Views: 839; Downloads: 297
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2. Testing the sustainability of growth of the LJSEX in the January 2000 to May 2010 periodAleš 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 in DKUM: 22.01.2018; Views: 920; Downloads: 336
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3. Modernizing mathematics education in Slovenia : a teacher friendly approachBojan 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 in DKUM: 15.12.2017; Views: 1014; Downloads: 95
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4. Interactive e-learning materials in the mathematics classroom in SloveniaSamo 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 in DKUM: 15.12.2017; Views: 1315; Downloads: 86
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5. Ljubljana-Leoben graph theory seminar : Maribor, 13.-15. September, 2017. Book of abstracts2017, 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 in DKUM: 08.12.2017; Views: 1126; Downloads: 160
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6. Omega polynomial revisitedMircea 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 in DKUM: 24.08.2017; Views: 759; Downloads: 99
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7. Altered Wiener indicesDamir 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 in DKUM: 17.08.2017; Views: 849; Downloads: 108
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8. Wiener numbers of pericondensed benzenoid hydrocarbonsSandi 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 in DKUM: 05.07.2017; Views: 1095; Downloads: 153
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9. The Hosoya-Wiener polynomial of weighted treesBlaž 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 in DKUM: 05.07.2017; Views: 985; Downloads: 94
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