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Mards Workshop Proceedings
2020, proceedings of professional or unreviewed scientific conference contributions

Abstract: The collection contains contributions by authors who were presented at a workshop within the Erasmus + project MARDS in Maribor, at the University of Maribor.
Keywords: doctoral study, higher education, e-learning, distance learning, study evaluation
Published: 25.11.2020; Views: 173; Downloads: 18
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Distance-based Invariants and Measures in Graphs
Aleksander Kelenc, 2019, doctoral dissertation

Abstract: This doctoral dissertation is concerned with aspects on distance related topics in graphs. We study three main topics, namely a recently introduced measure called the Hausdorff distance of graphs and two new graph invariants - the edge metric dimension and the mixed metric dimension of graphs. All three topics are part of the metric graph theory since they are tightly connected with the basic concept of distance between two vertices of a graph. The Hausdorff distance is a relatively new measure of the similarity of graphs. The notion of the Hausdorff distance considers a special kind of common subgraph of the compared graphs and depends on the structural properties outside of the common subgraph. We study the Hausdorff distance between certain families of graphs that often appear in chemical graph theory. Next to a few results for general graphs, we determine formulae for the distance between paths and cycles. Previously, there was no known efficient algorithm for the problem of determining the Hausdorff distance between two trees, and in this dissertation we present a polynomial-time algorithm for it. The algorithm is recursive and it utilizes the divide and conquer technique. As a subtask it also uses a procedure that is based on the well-known graph algorithm for finding a maximum bipartite matching. The edge metric dimension is a graph invariant that deals with distinguishing the edges of a graph. Let $G=(V(G),E(G))$ be a connected graph, let $w \in V(G)$ be a vertex, and let $e=uv \in E(G)$ be an edge. The distance between the vertex $w$ and the edge $e$ is given by $d_G(e,w)=\min\{d_G(u,w),d_G(v,w)\}$. A vertex $w \in V(G)$ distinguishes two edges $e_1,e_2 \in E(G)$ if $d_G(w,e_1) \ne d_G(w,e_2)$. A set $S$ of vertices in a connected graph $G$ is an edge metric generator of $G$ if every two distinct edges of $G$ are distinguished by some vertex of $S$. The smallest cardinality of an edge metric generator of $G$ is called the edge metric dimension and is denoted by $dim_e(G)$. The concept of the edge metric dimension is new. We study its mathematical properties. We make a comparison between the edge metric dimension and the standard metric dimension of graphs while presenting some realization results concerning the two. We prove that computing the edge metric dimension of connected graphs is NP-hard and give some approximation results. Moreover, we present bounds and closed formulae for the edge metric dimension of several classes of graphs. The mixed metric dimension is a graph invariant similar to the edge metric dimension that deals with distinguishing the elements (vertices and edges) of a graph. A vertex $w \in V(G)$ distinguishes two elements of a graph $x,y \in E(G)\cup V(G)$ if $d_G(w,x) \ne d_G(w,y)$. A set $S$ of vertices in a connected graph $G$ is a mixed metric generator of $G$ if every two elements $x,y \in E(G) \cup V(G)$ of $G$, where $x \neq y$, are distinguished by some vertex of $S$. The smallest cardinality of a mixed metric generator of $G$ is called the mixed metric dimension and is denoted by $dim_m(G)$. In this dissertation, we consider the structure of mixed metric generators and characterize graphs for which the mixed metric dimension equals the trivial lower and upper bounds. We also give results on the mixed metric dimension of certain families of graphs and present an upper bound with respect to the girth of a graph. Finally, we prove that the problem of determining the mixed metric dimension of a graph is NP-hard in the general case.
Keywords: Hausdorff distance, distance between graphs, graph algorithms, trees, graph similarity, edge metric dimension, edge metric generator, mixed metric dimension, metric dimension
Published: 03.08.2020; Views: 415; Downloads: 68
.pdf Full text (800,48 KB)

Critical setback distance for a footing resting on slopes
Rajesh Prashad Shukla, Ravi Sankar Jakka, 2017, original scientific article

Abstract: Structures are often constructed on slopes in hilly regions, which results in a lack of soil support on the sloping side of the footings. This causes a reduction in the bearing capacity of the footings. Though there are number of studies about foundations on slopes, most of these studies are confined to surface footings only (i.e., without the depth of embedment). Furthermore, there is no consensus in the literature over the influence of the setback distance on bearing capacity. This paper presents the results of finite-element analyses on a strip footing resting on stable slopes. A very large number of possible soil slopes with different footing depths were analysed. From the results it is found that the critical setback distance increases with an increase in the internal friction angle of soil, the depth of the footing and the slope gradient. The critical setback distance is varying between 2 to 4 times the footing width for soils with a low internal friction angle, while it is more than 10 times the footing width for soils with a higher internal friction angle. A regression equation is also developed based on the outcomes of the study. The developed equation is able to predict the influence of various parameters affecting the bearing capacity of a footing resting over the slopes. The results are compared with earlier experimental and numerical studies.
Keywords: bearing capacity ratio, cohesionless soil, footing, setback distance, slopes
Published: 18.06.2018; Views: 551; Downloads: 53
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Smart e-testing
Marjan Krašna, Tomaž Bratina, Branko Kaučič, 2012, original scientific article

Abstract: A decade of experience with e-learning material production gives significant trends overview. From the perspective of ICT evolution this means very long time. E-learning is always closely coupled to ICT but with the distinction - it always lags behind the advancement in ICT. Among many unknown issues one thing is certain - e-learning permanently changes. From the past experiences prediction of immediate future e-learning is possible but the prediction for longer time is less accurate. In the article chronological e-learning achievements and their connections are presented in order to give an overview of trends in e-learning in Slovenia. But despite of the detailed past knowledge fundamental prediction error of e-learning future developments was made. Today's hot topics are not better e-learning materials, not even broad application of interactive boards but e-testing. Possible immediate future of e-learning is therefore application of intelligent e-testing systems. Intelligent computer assisted testing (CAT) is not the new topic in e-learning. It is object of many researches but it is not suitable for teachers. It is way too complicated for teachers to apply it successfully in their work. E-learning development process for intelligent computer assisted test production that suits teachers' competences is prepared and explained in the article.
Keywords: distance learning, knowledge assessment, learning management system
Published: 19.12.2017; Views: 509; Downloads: 67
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E-learning materials for social science students
Marjan Krašna, Tomaž Bratina, 2014, original scientific article

Abstract: Today's student population is rightfully categorized as digital natives. From the beginning of their education, they used ICT. The technological gadgets, internet, and social networks are like a glove to them. Such generation of students require more than just textbooks. In the 2013 University of Maribor establish a task force for e-learning materials development. The goal was to identify the optimal technological, didactical and financial approach to the long process of e-learning materials development. Members of the task force have many workshops presenting different views, acquired experiences from their previous projects, technological constraints, prediction, etc. During these workshops it was decided it would be the best to prepare different types of e-learning materials and test them by the students. From their feedbacks we could set the guidelines for large scale production. At the Faculty of Arts, Faculty of Natural Sciences and Mathematics and Faculty of Education students needs to acquire also the digital competences to become successful teachers. For special didactics study programs different types of e-learning materials were produced with different technological approach. The concept was to upgrade the previous deliverables (PowerPoint slides) and narrate them. Narrated slides would enable students to refresh their lectures and should be used as blended e-learning materials. Narrations were prepared in different format: textual narration, voice narration and video narration. But later it was decided that these types are not enough and a mix of narratives (integrated multimedia learning materials) could be used on individual slides depending on the content of the slide. Students first receive the lecture in the classroom and in the same week they need to study associated e-learning materials and write their review of corresponding e-learning materials. In their review students were required to log the required time for studying the e-learning materials; benefits and drawbacks; potential improvement of e-learning materials; and open text of impression of using e-learning materials. Effectiveness and outcomes were tested with the electronic quizzes. Students were highly motivated with these new types of learning materials and provide us valuable feedback. Most efficient were text narrated learning materials, but the favourite was integrated multimedia learning materials. Video and audio narrations take them more time to study since they were constrained with the speed of speech of the recorded lecturer.
Keywords: design, distance learning, e-learning, learning materials, validation, verification
Published: 15.12.2017; Views: 931; Downloads: 89
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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: 714; Downloads: 128
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Corroborating a modification of the Wiener index
Ivan Gutman, Janez Žerovnik, 2002, short scientific article

Abstract: In a recent work [Chem. Phys. Lett. 333 (2001) 319-321] Nikolić, Trinajstić, and Randie put forward a novel modification ▫$^m$▫W of the Wiener index. We now show that ▫$^m$▫W possesses the basic properties required by a topological index to be acceptable as a measure of the extent of branching of the carbon-atom skeleton of the respective molecule (and therefore to be a structure-descriptor, potentially applicable in QSPR and QSAR studies). 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 mw(Pn) < mW(Tn) < mW(Sn). We also show how the concept of the modified Wiener index can be extended to weighted molecular graphs.
Keywords: graph theory, distance, molecular graphs, modified Wiener index, weigted modified Wiener index, branching, chemical graph theory
Published: 05.07.2017; Views: 553; Downloads: 57
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On acyclic colorings of direct products
Simon Špacapan, Aleksandra Tepeh, 2008, original scientific article

Abstract: A coloring of a graph ▫$G$▫ is an acyclic coloring if the union of any two color classes induces a forest. It is proved that the acyclic chromatic number of direct product of two trees ▫$T_1$▫ and ▫$T_2$▫ equals ▫$\min\{ \Delta(T_1) + 1, \Delta(T_2) + 1\}$▫. We also prove that the acyclic chromatic number of direct product of two complete graphs ▫$K_m$▫ and ▫$K_n$▫ is ▫$mn-m-2$▫, where ▫$m \ge n \ge 4$▫. Several bounds for the acyclic chromatic number of direct products are given and in connection to this some questions are raised.
Keywords: mathematics, graph theory, coloring, acyclic coloring, distance-two coloring, direct product
Published: 31.03.2017; Views: 384; Downloads: 62
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Mitja Toplak, 2015, undergraduate thesis

Abstract: Diplomsko delo predstavlja razvoj mobilne aplikacije, namenjene promociji in predstavitvi adrenalinskih športov v Sloveniji. Predstavi potek od ideje, raziskave trga in preučevanja konkurence, do samega programskega razvoja na mobilni platformi Android. Raziskuje druge, že obstoječe načine predstavitve tovrstnih športov, pri čem se osredotoča na prikaz informacij o posameznih destinacijah. Po analizi je izdelan model aplikacije, postavljeni so cilji, oblikovan je uporabniški vmesnik in potrebne funkcionalnosti. Sledi predstavitev razvoja aplikacije v razvijalskem okolju Android Studio. Po zaključku implementacije sta prikazana testiranje in objava aplikacije v spletni trgovini Google Play. Pri tem je opisano, kako uspešno prikazovati in ponujati informacije končnemu uporabniku.
Keywords: Android, ekstremni športi, adrenalinski športi, turizem, Google maps, Google Query Language, Google directions API, Google distance Matrix
Published: 14.10.2015; Views: 779; Downloads: 98
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Distance education models and new communication trends in education
Ivan Gerlič, 2007, original scientific article

Abstract: Last decade's technological development in the field of information technology has boosted the range of varieties of its use in the distance education and given new dimensions to this type of education. Distance-learning nowadays is practised by several theory's, each differing from the other in its formal access, in the analyse of its teaching and learning materials, in its ways and range of counselling and the range of its communication with the participants, as well as in its didactic concept of preparing and forming learning materials, etc. Distance education is important criterion for new communication trends in education. Therefore it shall be covered more thoroughly in this work.
Keywords: vzgoja in izobraževanje, izobraževanje na daljavo, učenje na daljavo, modeli učenja, didaktični modeli, komunikacijski modeli, spletno izobraževanje, education, distance education, distance learning, teaching models, didactic models, communication models, web-based education
Published: 10.07.2015; Views: 1081; Downloads: 56
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