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1.
Szeged indeks povezav, pi indeks in wienerjev indeks povezav benzenoidnih sistemov
Doroteja Štunf, 2017, magistrsko delo

Opis: Magistrska naloga obravnava benzenoidne sisteme. Predstavljena je uporaba teorije grafov v kemiji in s tem uporabna povezava med kemijo in matematiko. V uvodnih poglavjih so zato predstavljeni osnovni pojmi teorije grafov in kemijski pojmi, ki so potrebni za razumevanje nadaljnje snovi. Benzenoidni sistemi so zanimivi za raziskovanje, saj predstavljajo skupino kemijskih spojin imenovano benzenoidni ogljikovodiki. V nadaljevanju naloge so podane osnovne lastnosti in definicije benzenoidnih sistemov. V uvodu osrednjega dela so navedene definicije Wienerjevega, Szeged in PI indeksa za poljubne in nato še za utežene grafe. Sledi vpeljava vseh treh indeksov povezav s predstavitvijo algoritmov za njihov izračun v linearni časovni zahtevnosti, ki je v nalogi tudi dokazana. Za lažje razumevanje so dodani primeri izračuna na izbranem primeru benzenoidnega sistema.
Ključne besede: benzenoidni sistem, topološki indeks, Wienerjev indeks povezav, Szeged indeks povezav, PI indeks, uteženi graf, elementarni razrez, kvocientno drevo, linearna časovna zahtevnost
Objavljeno: 09.01.2018; Ogledov: 28; Prenosov: 3
.pdf Celotno besedilo (1,09 MB)

2.
Strukturne lastnosti resonančnih grafov tubulenov in fulerenov
Niko Tratnik, 2017, doktorska disertacija

Opis: Doktorska disertacija obravnava predvsem resonančne grafe tubulenov in fulerenov. V prvem poglavju so predstavljeni nekateri že znani rezultati o resonančnih grafih, prav tako pa je podana struktura doktorske disertacije. V naslednjem poglavju so definirani nekateri osnovni pojmi teorije grafov, ki jih potrebujemo v preostalih poglavjih. V tretjem poglavju so predstavljene tri pomembne družine kemijskih struktur, to so benzenoidni sistemi, tubuleni in fulereni. Omenjene družine predstavljajo molekule, ki jih imenujemo benzenoidni ogljikovodiki, ogljikove nanocevke in fulereni. V četrtem poglavju je najprej pokazana povezava med Kekuléjevimi strukturami določene molekule ter popolnimi prirejanji ustreznega kemijskega grafa. V nadaljevanju poglavja je definiran resonančni graf benzenoidnega sistema, tubulena in fulerena. Glavni namen tega koncepta je modeliranje interakcij med posameznimi Kekuléjevimi strukturami molekule. Nato se lotimo raziskovanja osnovnih lastnosti resonančnih grafov. Pokazano je, da je resonančni graf tubulena ali fulerena dvodelni graf, vsaka njegova povezana komponenta pa je bodisi pot bodisi graf z ožino štiri. Prav tako dokažemo, da je 2-jedro vsake povezane komponente resonančnega grafa širokega tubulena ali fulerena, ki ni pot, vedno 2-povezan graf. Nato podamo primer neskončne družine tubulenov, katerih resonančni grafi niso povezani. Na koncu poglavja definiramo resonančni graf za katerikoli graf, ki je vložen na zaprto ploskev. Dokažemo tudi, da so taki resonančni grafi inducirani podgrafi hiperkock. V petem poglavju definiramo Zhang-Zhangov polinom, ki je namenjen štetju posebnih struktur, imenovanih Clarova pokritja. Dokazano je, da je Zhang-Zhangov polinom grafa, vloženega na zaprto ploskev, enak polinomu kock ustreznega resonančnega grafa. Ta rezultat posplošuje podobne rezultate za benzenoidne sisteme, tubulene in fulerene. Na koncu se ukvarjamo s strukturo distributivne mreže resonančnih grafov. Dokazano je, da je vsaka povezana komponenta resonančnega grafa tubulena graf pokritja neke distributivne mreže. Prav tako pokažemo, da je vsaka povezana komponenta resonančnega grafa tubulena medianski graf, njen graf blokov pa je pot. Nazadnje podamo primer fulerena, katerega resonančni graf ni graf pokritja nobene distributivne mreže.
Ključne besede: benzenoidni sistem, ogljikova nanocevka, tubulen, fuleren, resonančni graf, Z-transformirani graf, Clarovo pokritje, Zhang-Zhangov polinom, polinom kock, distributivna mreža, medianski graf, graf blokov, grafi na ploskvah
Objavljeno: 09.01.2018; Ogledov: 25; Prenosov: 4
.pdf Celotno besedilo (1,40 MB)

3.
Fizikalne lastnosti intermetalne katalizatorske spojine ZnPd
Arbresha Hölbl, 2017, magistrsko delo

Opis: Kataliza se uporablja v znanosti in tehnologiji za spreminjanje poteka kemijskih reakcij preko znižanja aktivacijske energije, ki je potrebna za reakcijo. Najpreprostejši katalizator dobimo, če vzamemo kovinski element brez podlage. Slabost take izbire je zelo omejeno število elementov, ki so katalitsko aktivni za dano kemijsko reakcijo. Alternativni materiali za heterogeno katalizo so strukturno urejene intermetalne spojine. Gre za spojine iz dveh ali več kovinskih elementov, ki se nahajajo levo ali v okolici Zintlove črte v periodnem sistemu elementov. Njihova struktura je popolnoma ali delno urejena in se razlikuje od strukture elementov, ki tvorijo spojino. Stabilnost intermetalnih spojin med kemijsko reakcijo je povezana z njihovo elektronsko in geometrijsko strukturo. Prednost uporabe intermetalnih spojin za katalizo je možnost izbire elektronske in geometrijske strukture. Intermetalne spojine lahko razpadejo pred ali med katalizo, tako da iz njih nastane katalizator z veliko aktivno površino. Intermetalne spojine lahko nastanejo tudi med kemijsko reakcijo pri reakciji med aktivno kovino in podlago ali med različnimi materiali s podlago. V izogib tem težavam je bil nedavno sprejet pristop, da se kot stabilne katalizatorje brez podlage uporablja intermetalne spojine z urejeno kristalno strukturo. V Magistrskem delu smo opravili karakterizacijo vzorca ZnPd s pomočjo mikroskopije SEM, ki je bila izvedena na Kemijskem institutu v Ljubljani. Ostale meritve so bile izvedene na Institutu »Jožef Stefan« v Ljubljani. Z napravo PPMS (angl. Physical Property Measurement System) proizvajalca Quantum Design smo izmerili fizikalne lastnosti ZnPd. Pri določanju magnetnega stanja vzorca pa smo uporabili magnetometer MPMS (angl. Magnetic Property Measurement System) XL-5 proizvajalca Quantum Design. V Magistrskem delu smo prav tako dopolnili nedavne študije fizikalnih lastnostih intermetalnih katalizatorjev GaPd in InPd.
Ključne besede: kataliza, katalizator, kompleksne kovinske spojine, intermetalne spojine, paladij, specifična toplota, električna upornost, magnetizacija, magnetna susceptibilnost
Objavljeno: 21.12.2017; Ogledov: 19; Prenosov: 2
.pdf Celotno besedilo (2,35 MB)

4.
Young pedagogical centre with extensive experience and knowledge
Boris Aberšek, 2009, izvirni znanstveni članek

Opis: The contributions gathered in this publication have been prepared within the framework of the Pedagogical Center (PC) of the Faculty of Natural Sciences and Mathematics (FNM) at the University of Maribor, which might seem to be a young center since it has only been established in 2009, nevertheless, the extensive experience and knowledge of its faculty tell a story of a much more established institution. “Pedagogical” is a defining term indicting that the center's activities are focused primarily on pedagogical programmes at FNM and on educating teachers at all levels in the broadest sense of the word. Pedagogical center FNM is a pedagogical research unit, that supports all natural science, mathematical and technology programmes at both the Faculty of Natural Sciences and Mathematics, as well as the entire University of Maribor, especially the teaching programmes, since after the separation of the large Faculty of Education into three entities - FNM being one of them - its “colour” as well as educational and historical core have been lost. Teacher education at FNM lost previous value and has become much less emphasised than it was the case with its predecessor institution the Faculty of Education. Thus the main aim of the center is to give back to the faculty a part of its previous “colour” as well as to promote and develop educational sciences and their interdisciplinary integration that will certainly mean a step towards guaranteeing quality of work as well as quality of education for all students.
Ključne besede: education, sciences education, technical education, quality enhancement
Objavljeno: 19.12.2017; Ogledov: 19; Prenosov: 0
.pdf Celotno besedilo (639,76 KB)

5.
What is the tendency in biology virtual field trips?
Miro Puhek, Matej Perše, Andrej Šorgo, 2012, izvirni znanstveni članek

Opis: There is no doubt any more that virtual worlds are suitable for school environment. It was shown by various researchers that they can contribute in supplying students with additional information, help them to visualise subjects, respond with answer on demand or even in some cases supplement the real materials. Based on the real experience, the virtual field trail Walk on Maribor Island was developed for biology and natural science classes in lower secondary school. The trail is presented through eight exercises that differentiate not only in theme, but also in difficultness, fun, background idea etc. In spring 2011, 133 eighth grade students worked on the virtual field trail during the biology class. After the work on exercises, students were asked to analyse the exercises regarding the level of difficultness, level of interest and level of proficiency. The main aim of the study was to present the tendency in biology virtual field trips that should be taken into consideration before the development of new exercises.
Ključne besede: education, biology teaching, field trip, field work
Objavljeno: 19.12.2017; Ogledov: 33; Prenosov: 0
.pdf Celotno besedilo (919,81 KB)

6.
Using chemical models for developing natural science competences in teaching chemistry
Darinka Sikošek, Mateja Žuželj, 2013, izvirni znanstveni članek

Opis: Chemical models are indispensable tool in chemistry class and enable secondary school pupils to develop complex thought processes and spatial concepts, both of which are necessary to improve their understanding of chemical concepts. In this research, special emphasis is given to complex competencies not only their acquisition, but rather how pupils develop them. For this purpose, a learning strategy has been developed, called learning by self-generating chemical models. Pupils learn individually on their own models, which are made from easily accessible, low-cost materials. The impact of workable models was investigated (assembly of commercial models and production of self-made models) on the (1) learning success using simple molecule shapes and (2) the degree of competence development which realized through the implemented activities. The study involved first-year secondary school-pupils, defined as self-creators of paper- and -wire models (experimental group) and assemblers of commercial models (called the control group). The appearance of the molecules being studied took the form of geometric shapes and structures, which pupils present by making of ball-, called wire-models from plasticine and wire or paper created, called paper models. Based on the results of statistical processing of the data, we found that self-creation of models (as an innovative approach) leads to better understanding and to subsequently sustained knowledge for the pupil. It should also be noted that pupils who were self-generators in comparisons to those who merely assembled the models, generally developed many complex skills in the areas of problem solving, practical competence, mathematical competence and critical thinking skills. The knowledge so acquired was also better understood.
Ključne besede: education, chemical models, competencies, chemistry, self-made models
Objavljeno: 19.12.2017; Ogledov: 16; Prenosov: 0
.pdf Celotno besedilo (734,46 KB)

7.
The challenges of complete informatization of education
Magdalena Šverc, Igor Pesek, Andrej Flogie, 2014, izvirni znanstveni članek

Opis: Since the methods of teaching and learning are currently changing, Slovenian society is challenged to respond. Ministries responsible for the development of the educational system encourage informatization of education by launching strategically oriented tenders. This research presents three such projects, which together propose guidelines on how to further develop the Slovenian educational system with an emphasis on the introduction of information and communication technologies into everyday life in Slovenian schools at all levels (teaching, learning, management, etc.). There are three main areas that are covered: (1) technical assistance and support, (2) development and deployment of e-learning materials and e-textbooks and (3) teacher training. Using these approaches it would be possible to achieve an increase in digital competences and a change in our pedagogical paradigm. Results show a better motivation, communication and improved teamwork among students. This is a consequence of changes in the way of thinking and teaching by both teachers and other school participants, especially the headmasters who put the student in the centre of activities. The whole process of school informatization depends on a coherent development of various fields. The focus is on a change of pedagogical paradigm and the consequential teacher and managerial staff training.
Ključne besede: e-competent school, e-competent teacher, e-textbooks, innovative 1:1 pedagogy
Objavljeno: 19.12.2017; Ogledov: 25; Prenosov: 0
.pdf Celotno besedilo (1,16 MB)

8.
The architecture of a school system according to the theory of dynamical systems
Boris Aberšek, Janez Bregant, 2012, izvirni znanstveni članek

Opis: From the experience of recent years it seems clear that the existing educational system, as a whole, is perceived as an ailing system that fails to meet the needs of a major portion of the society it serves. Every aspect of the educational process must be studied and reconsidered in the light of new and different societal expectations. In the last decades we started with one school reform after the other, but it looks now that these changes had no positive impact whatsoever. Even worse, the school system was damaged afterwards. In this paper we will explore some possibilities how to improve it without facing these consequences. The main idea is, as a result of our latest research, that mathematical methods for describing and simulating could be very useful for predicting and simulating school systems without using a long term and complex empirical experimentation. The paper introduces the correlation between the dynamical mathematical calculus and the educational school system and elaborates to some extent the basic idea of using the former to predict the latter.
Ključne besede: architecture, mathematical modelling, school systems, dynamical systems
Objavljeno: 19.12.2017; Ogledov: 19; Prenosov: 0
.pdf Celotno besedilo (802,07 KB)

9.
Teaching with analogies
Boris Aberšek, 2016, kratki znanstveni prispevek

Opis: As disciplines reach maturity, a dynamic meta-structure is needed, which facilitates merging and new divisions of disciplines. Under such a meta-structure, the disciplines propel the evolution of knowledge, but adapt themselves when driving forces emerge sufficient to provoke their adaptation (Suarez-Orozco, Satin-Bajaj, 2010). This means that on the science, technology, engineering and math (STEM) education must give transdisciplinary view (Flogie, Aberšek, 2015). Science-education research studies and STEM teachers’ classroom experiences have shown that analogies and transdisciplinar point of view, when used properly, can help make science concepts meaningful to students.
Ključne besede: education, analogies, teaching
Objavljeno: 19.12.2017; Ogledov: 20; Prenosov: 1
.pdf Celotno besedilo (449,10 KB)

10.
Teaching complex fields of soft matter, proposal of a new liquid crystal analogy
Uroš Jagodič, Jacob Staines, Samo Kralj, Robert Repnik, 2014, izvirni znanstveni članek

Opis: The key reason behind the richness of different structures and patterns displayed in nature is the universal mechanism of symmetry breaking. It shapes configurations at all length scales encountered in universe. Structures reached via symmetry breaking transitions are commonly described in terms of order parameter fields. One of the simplest systems where symmetry breaking concepts have already been explored in detail, are various liquid crystal (LC) phases. The reason behind this is rich variety of structures exhibited by LCs and their convenient experimental accessibility. Consequently, a wide spectrum of different theoretical tools have been developed in LCs. In this contribution the orientational ordering of housing block in San Francisco, which we choose as a typical large-city representative, was studied. Following nematic LC analogy we determine the local degree of ordering. The structural pattern of the city displays a domain-type pattern. The average degree of ordering within a domain strongly correlates with crime rate within it. Therefore, the results confirm an intuitive expectation that structures define properties. This model can be used as a helpful tool in education as it provides a way of understanding complex topics with the help of well-known every day phenomena.
Ključne besede: education, liquid crystals, modelling, order parameter
Objavljeno: 19.12.2017; Ogledov: 19; Prenosov: 0
.pdf Celotno besedilo (2,32 MB)

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