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The NAUK group (Advanced Learning Blocks group http://www.nauk.si) is engaged in the development of theoretical and practical concepts of ICT use in all levels of education. Recently, the proposed introduction of electronic textbooks (e-textbooks) has become a major topic nationwide in Slovenia. There are multiple dilemmas to be solved, e.g. what a modern e-textbook is, what it should include, in what way should it differ from conventional textbooks, what tools and technologies should be used for its creation, etc. This paper attempts to make recommendations, which we believe should be followed by all the authors of e-textbooks. V okviru skupine NAUK (Napredne Učne Kocke http://www.nauk.si) se ukvarjamo z razvojem tako teoretičnih kot praktičnih izhodišč na področju uporabe IKT v izobraževalnem procesu na vseh nivojih. V zadnjem času je v Sloveniji zelo v ospredju problematika elektronskih učbenikov (e-učbenikov). Rešiti bo potrebno več dilem: kakšen naj bo sodoben e-učbenik, kakšne naj bodo njegove značilnosti, kaj mora vsebovati, v čem se razlikuje od klasičnega učbenika, katera orodja in tehnologije uporabiti za izdelavo itd. V prispevku smo poskusili predstaviti nekaj priporočil, za katere menimo, da naj bi jih upoštevali vsi avtorji e-učbenikov.

DEDI stands for the Digital Encyclopaedia of natural and Cultural Heritage in Slovenia which was a result of two prototype research and development projects DEDI and DEDI II in the period between 2008 and 2010. The two projects were co-financed by the Ministry of Higher Education, Science and Technology and the European Regional Development Fund in the frame of research and development projects e-content and e-services. DEDI is the first attempt of multimediarich digital representation of Slovenian natural and cultural heritage on a common web site offering verifiable, qualitative and complex content to a wide range of general public. Digital content (text, video records, audio records, photographs) is enriched by 2-dimensional and/or 3-dimensional visualisation of geographical data or even by 4-dimensional models with time component. 4D models combine 3D models with the time dimension. Thus it is possible to simulate the past, the current and the future condition of natural and cultural heritage objects, their changes, growth, deterioration or oscillation. 3D and 4D models are more explanatory, plastic and attractive to the unprofessional public thus increasingthe interest in the digital encyclopaedia. Technological solutions for the project were developed by the consortium partners in the field of web technologies who succeeded to locate all immovable natural and cultural heritage objects. The Google maps web platform is normally used for 2D representations but it is often too complex to represent a large amount of data. In order to meet the needs of the digital encyclopaedia data need to be structured and linked which is one of the main advantages of Geopedia, an interactive atlas which enables active user participation in adding and editing information on Slovenia. A 3D visualisation tool Gaea+ is used for real time visualisation of 3D models offering user-friendly presentation of any geospatial information and an interactive walk-through allowing users to move in 3D space. Many advanced DEDI files (dynamic multimedia representations or dediteka) of some natural and cultural objects of national importance were created. An advanced dediteka combines several object representation into interactive non-linear stories and upgrade them in various ways. The advanced dediteka "The story of Martin Krpan and his age" is a digitised story of Martin Krpan written in 1858 by Fran Levstik enriched by the audio record. The user can read a story and listen to the Slovenian language of the Levstik´s time.Two main digitisation criteria of equal importance were used for the selection of natural and cultural heritage objects: geographical area and the content value. The article describes a 4D simulation of the urban growth of Ljubljana and the virtual reconstruction of the Žiga Zois study room. 4D simulation of the growth of Ljubljana is based on historical and contemporary sources, i.e. 3D visualisation with time component. It is based on old city plans, digitised terrain model, national topographic maps, contemporary city plan and cadastre. 3D terrain models of buildings are enriched by a city plan of a specific period of time. The historical growth of the city is represented by a 2D dynamic map with floor plans and isochrones. 3D scanned exterior of the Žiga Zois Mansion is represented as well as a part of the interior with the virtual reconstruction of his study room where the collection of minerals was kept. Some specimens are 3D scanned. A few items of his literary opus are digitised, too. V okviru projekta Digitalne enciklopedije naravne in kulturne dediščine na Slovenskem, DEDI II, je bil prikaz digitalnih vsebin običajnih formatov (tekst, video, zvočni zapis in fotografija) obogaten z geografsko informacijo, ki je hkrati prikazana dvo- in/ali trirazsežnostno, lahko pa tudi štirirazsežnostno s časovno komponento. 4D modeli prikazujejo 3D modele objektov v času, kar pomeni, da lahko simuliramo pretekla, sedanja in prihodnja stanja objektov, njihovo spreminjanje, rast, upadanje ali nihanja. 3D in 4D modeli povečajo nazornost, plastičnost in privlačnost prikaza objektov laičnim uporabnikom, s tem pa se poveča zanimanje za enciklopedijo. V prispevku sta podrobneje predstavljena 4D simulacija rasti mesta Ljubljane in virtualna rekonstrukcija kabineta Žige Zoisa. Za Ljubljano je narejena 4D simulacija rasti mesta na osnovi zgodovinskih in sodobnih virov, tj. 3D prostorski prikaz s časovno komponento. Kot vir so uporabljeni stari načrti Ljubljane, digitalni model reliefa, državne topografske karte in sodobni mestni načrti ter podatki katastra stavb. Stavbe so prikazane tridimenzionalno na modelu reliefa , ki je za vsako dobo razvoja mesta prekrit s karto tistega obdobja. Rast mesta je dvodimenzionalno dinamično prikazana tudi na karti s prikazom naraščanja števila tlorisnih prikazov stavb in z izohronami rasti mesta. Za Zoisovo palačo je izdelan 3D prikaz skenirane zunanjosti ter del notranjosti hiše z virtualno rekonstrukcijo njegovega kabineta, v katerega je umeščena zbirka mineralov. Nekaj primerkov iz zbirke je tudi 3D skeniranih, prav tako je digitaliziranih nekaj del iz Zoisove pisne zapuščine.

The project entitled "Digital encyclopaedia of Slovenian natural and cultural heritage" (DEDI II) has been evolved as a prototype research and development project (2009-2010). It represents the first attempt of multimedia-rich digital representation of Slovenian natural and cultural heritage by the means of interdisciplinary work of different cultural and educational institutions. Verifiable, qualitative and complex content of four types of heritage is co-located on a common site (immovable, movable, vivid and natural heritage) with the goal to promote the heritage and educate the general public, as well as to encourage the public to create tomorrow's heritage. A new detailed thesaurus was constructed enabling the classification of different kinds of heritage.It merges the established and newly created taxonomies of each type of heritage. To ensure the quality of published contents, the professional Editorial Board has been established. The National and University Library of Slovenia (NUK), one of the fundamental institutions for collecting and keeping the written cultural heritage of Slovenia, has already participated in the conception of the first project scheme. In the second part of the DEDI project, NUK contributed a number of digitalized books selected on the basis of their historical and literary importance. Digitalized books were published on the DEDI portal under the movable cultural heritage taxonomy. Projekt Digitalna enciklopedija naravne in kulturne dediščine na Slovenskem (DEDI II) je prototipni raziskovalno-razvojni projekt (2009-2010) in predstavlja prvi poskus večmedijske digitalne predstavitve slovenske naravne in kulturne dediščine in interdisciplinarno združuje delo različnih kulturnih in izobraževalnih institucij, s čimer so bile na enem mestu zbrane verodostojne, kakovostne in kompleksne vsebine štirih vrst dediščine (nepremične, premične, žive kulturne ter naravne) z namenom, izobraževati in približati dediščino najširši javnosti in jo spodbuditi k soustvarjanju jutrišnje dediščine. Za potrebe projekta je bil narejen podroben tezaver dediščine, ki združuje do sedaj znane in na novo dopolnjene taksonomije za posamezne vrste de-diščine. Ustanovljena je bila strokovna uredniška skupina, ki skrbi za kakovost objavljenih vsebin. Narodna in univerzitetna knjižnica (NUK) je kot ena temeljnih ustanov za hranjenje in zbiranje slovenske pisne kulturne dediščine sodelovala že pri zasnovi pilotnega projekta DEDI, v nadaljevalnem projektu pa je z digitalizacijo pomembnih zgodovinskih in literarnih del v okviru premične dediščine prispevala k primerni zastopanosti virtualne knjige na spletnem portalu DEDI.

Avtorji učnih e-gradiv, namenjenih učiteljem, vse prevečkrat pripravijo le-te v obliki monolitnih blokov, sestavljenih na način, kot so običajni tekstovni delovni zvezki. To zahteva, da jih učitelj uporabi kot celoto, na točno predpisan način. A ker je učitelj posrednik med učnim gradivom in učencem, je on tisti, ki mora narediti izbor gradiv in jih kombinirati na ustrezen način. E-gradiva naj bodo zato pripravljena na fleksibilen način. Zakaj ne izrabiti možnosti, ki jih ponujajo nove tehnologije, in učitelju vsaj ponuditi možnost, da gradivo pripravi ustrezno svojim in učenčevimm potrebam. V procesu izdelave izobraževalnih e-gradiv, ki je v Sloveniji v zadnjih letih močno porastlo zaradi različnih razpisov na to tematiko, se je vedno bolj zapostavljalo učitelja in vpeljevalo dvosmerno relacijo med avtorjem gradiva ter uporabnikom - učencem. Cilj projekta nauk je zato izgradnja naprednih učnih vsebin, ki učitelju dajejo možnost prilagajanja, saj le-ta najbolj ve, kaj potrebuje pri pouku. V prispevku tako srečamo izkušnje iz preteklih let, predstavimo možne scenarije uporabe repozitorijev učnih gradiv ter na osnovah zgrajenega portala nauk.si.

The article presents the website of the Digital Heritage Encyclopaedia called DEDI, which introduces new concepts to the protection and presentation of heritage to the general public. DEDI provides support to scientific-research activities, learning and cultural development, strengthens the national identity, and contributes to Slovenia's recognisability and competitiveness. The encyclopaedia's principal value lies in its integrated presentation of the four types of heritage in one place. Special attention is dedicated to e-learning, the use of the digital encyclopaedia for educational purpose, and the active parcitipation of the widest public - all in the spirit of our motto that we can only preserve what we know. Predmet prispevka je predstavite spletnege mesta Digitalne enciklopedije dediščine - DEDI, ki prinaša nove koncepte na področju varovanja in predstavljanja dediščine najširši javnosti. DEDI zagotavlja podporo znanstveno-raziskovalnemu delu, učenju, kulturnemu razvoju, utrjuje narodno identiteto ter prispeva k prepoznavnosti in konkurenčnosti Slovenije. Vrednost digitalne enciklopedije vidimo predvsem v enovitem prikazu štirih vrst dediščine na enem mestu. Posebna pozornost je namenjena e-učenju oziroma uporabi digitalne enciklopedije v izobraževalne namene ter aktivni udeležbi najširše javnosti, saj sledimo geslu, da lahko ohranjamo samo tisto, kar poznamo.

The doctoral thesis describes problems concerning graphs that can be represented in the Euclidean plane (or k-space) in such a way, that vertices are represented as points in the plane (k-space) and edges as line segments of unit lengths. Problems are observed from a computational and a mathematical point of view. In the first part of the thesis the (already known, mainly mathematical) theory of unit-distance graph representations is presented; at the same time the terminology of the results is unified and several propositions are proved. First computer aided attempts to generate small graphs with a unit-distance representation are discussed. In the following chapter the well-known graph products of k-dimensional unit-distance graphs are studied; the chapter summarizes the results from [58]. The third chapter disproves the wrong assumption that Heawood graph is not a unit-distance graph, by providing the unit-distance coordinatization of it. In the fourth chapter all degenerate unit-distance representations of the Petersen graph in the Euclidean plane are presented and some relationships among them are observed; see [57]. In the following chapter generalized Petersen graphs and I-graphs are observed. Necessary and sufficient conditions for two I-graphs to be isomorphic are given. As a corollary it is shown that a large subclass of I-graphs can be drawn with unit-distances in the Euclidean plane by using the representation with a rotational symmetry. Conjectures concerning unit-distance coordinatizations and highly-degenerate unit-distance representations of I-graphs are stated and verified for all I-graphs up to 2000 vertices. In the sixth chapter the decision problems that ask about the existence of a degenerate k-dimensional unit-distance representation or coordinatization of a given graph are shown to be NP-complete. In the last chapter of the thesis a heuristics that draws a given graph in the Euclidean plane by minimizing the quotient of the longest and the shortest edge length is presented; see SPE algorithm in [1]. The dilation coefficient of a graph is introduced and theoretically obtained bounds for the dilation coefficient of a complete graph are given. The calculated upper bounds for the dilation coefficients of complete graphs are compared to the values obtained by three graph-drawing algorithms, see [62].

U prvom dijelu diplomskog rada, dana su teoretska i praktična gledišta na konstrukcijske čelike sa posebnim osvrtom na čelike za poboljšavanje i cementiranje. Iz te grupe za potrebe ovog rada odabrana su četiri tipa čelika i to dva tipa ugljičnih (C15E i C45E) i dva tipa legiranih (20MnCr5 i 42CrMo4) konstrukcijskih čelika za poboljšavanje i cementiranje. Iz dostupne literature prikupljeni su podaci o njihovim kemijskim i mehaničkim svojstvima. opisani su postupci za poboljšavanje i cementiranje kako općenito tako i za navedene čelike. kao uvod u laboratorijska mjerenja opisani su mehanizmi transformacija tj. faznih pretvorbi u čvrstom stanju čistog željeza i konstrukcijskih čelika sa naglaskom na transformaciju  ' (BCC rešetka) u  ' (FCC rešetka) područje. U praktičnom dijelu pomoću dilatometra vršeno je mjerenje točaka transformacije na 12 uzoraka navedenih čelika. Opisana je svrha postupka i parametri mjerenja a dat je i detaljan opis mjernog uređaja. Dilatacijski dijagrami su analizirani i iz njih se očitane temperature transformacije točaka Ac1 i Ac3, utjecaj kemijskog sastava, kao i neke pojave na pojedinim uzorcima zadanih čelika. Dobiveni podaci obrađeni su i uspoređeni sa podacima iz poznate literature te su doneseni određeni zaključci opisani u poglavlju 7.

Some novel results on the first and second Zagreb index and on the Estrada index are presented.