Dans cette thèse, nous nous intéressons à differentes colorations des sommets d’un graphe et aux homomorphismes de graphes. Nous nous intéressons plus spécialement aux graphes planaires et aux graphes peu denses. Nous considérons la coloration propre des sommets, la coloration acyclique, la coloration étoilée, lak-forêt-coloration, la coloration fractionnaire et la version par liste de la plupart de ces concepts.Dans le Chapitre 2, nous cherchons des conditions suffisantes de 3-liste colorabilité des graphes planaires. Ces conditions sont exprimées en termes de sous-graphes interdits et nos résultats impliquent plusieurs résultats connus.La notion de la coloration acyclique par liste des graphes planaires a été introduite par Borodin, Fon-Der Flaass, Kostochka, Raspaud, et Sopena. Ils ont conjecturé que tout graphe planaire est acycliquement 5-liste coloriable. Dans le Chapitre 3, on obtient des conditions suffisantes pour qu’un graphe planaire admette une k-coloration acyclique par liste avec k 2 f3; 4; 5g.Dans le Chapitre 4, nous montrons que tout graphe subcubique est 6-étoilé coloriable.D’autre part, Fertin, Raspaud et Reed ont montré que le graphe de Wagner ne peut pas être 5-étoilé-coloriable. Ce fait implique que notre résultat est optimal. De plus, nous obtenons des nouvelles bornes supérieures sur la choisissabilité étoilé d’un graphe planaire subcubique de maille donnée.Une k-forêt-coloration d’un graphe G est une application ¼ de l’ensemble des sommets V (G) de G dans l’ensemble de couleurs 1; 2; ¢ ¢ ¢ ; k telle que chaque classede couleur induit une forêt. Le sommet-arboricité de G est le plus petit entier ktel que G a k-forêt-coloration. Dans le Chapitre 5, nous prouvons une conjecture de Raspaud et Wang affirmant que tout graphe planaire sans triangles intersectants admet une sommet-arboricité au plus 2.Enfin, au Chapitre 6, nous nous concentrons sur le problème d’homomorphisme des graphes peu denses dans le graphe de Petersen. Plus précisément, nous prouvons que tout graphe sans triangles ayant un degré moyen maximum moins de 5=2 admet un homomorphisme dans le graphe de Petersen. En outre, nous montrons que la borne sur le degré moyen maximum est la meilleure possible. / In this thesis, we are interested in various vertex coloring and homomorphism problems of graphs with special emphasis on planar graphs and sparsegraphs. We consider proper vertex coloring, acyclic coloring, star coloring, forestcoloring, fractional coloring and the list version of most of these concepts.In Chapter 2, we consider the problem of finding sufficient conditions for a planargraph to be 3-choosable. These conditions are expressed in terms of forbiddensubgraphs and our results extend several known results.The notion of acyclic list coloring of planar graphs was introduced by Borodin,Fon-Der Flaass, Kostochka, Raspaud, and Sopena. They conjectured that everyplanar graph is acyclically 5-choosable. In Chapter 3, we obtain some sufficientconditions for planar graphs to be acyclically k-choosable with k 2 f3; 4; 5g.In Chapter 4, we prove that every subcubic graph is 6-star-colorable. On theother hand, Fertin, Raspaud and Reed showed that the Wagner graph cannot be5-star-colorable. This fact implies that our result is best possible. Moreover, weobtain new upper bounds on star choosability of planar subcubic graphs with givengirth.A k-forest-coloring of a graph G is a mapping ¼ from V (G) to the set f1; ¢ ¢ ¢ ; kgsuch that each color class induces a forest. The vertex-arboricity of G is the smallestinteger k such that G has a k-forest-coloring. In Chapter 5, we prove a conjecture ofRaspaud and Wang asserting that every planar graph without intersecting triangleshas vertex-arboricity at most 2.Finally, in Chapter 6, we focus on the homomorphism problems of sparse graphsto the Petersen graph. More precisely, we prove that every triangle-free graph withmaximum average degree less than 5=2 admits a homomorphism to the Petersengraph. Moreover, we show that the bound on the maximum average degree in ourresult is best possible.

Current practice in U.S. underground coal mine high-voltage distribution systems is to attempt to limit ground fault current to 25 Amperes and de-energize the circuit at 10 Amperes. However, the significant amount of system capacitance due to the use of shielded cables can cause ground fault current to be two or three times the intended ground fault limit. Consequently, this practice can cause several issues such as ground fault currents significantly exceeding the neutral grounding resistor current limit, loss of relay selectivity in the distribution system, and transient overvoltages in certain ground fault situations. These issues are solved to some extent by using a resonance grounded system, currently used in some other countries. However, a shortcoming of traditional resonance grounded systems is the inability to deal with the harmonic components existing in ground fault current. With the increasing use of nonlinear sources such as variable frequency drives, the proportion of harmonic components in ground fault current can be significant. Consequently, although the fundamental component can be almost fully compensated in a traditional resonance grounded system, the harmonic components can still be large enough to maintain arcing and cause personal injury and equipment damage. In this dissertation, a novel method is developed to perform real-time prediction of the harmonics in ground fault currents. Methods for neutralizing the ground fault current harmonics and identifying ground fault location are also developed. Results indicate that the combination of traditional high-resistance grounding and active current injection to neutralize harmonics in the ground fault has the potential to significantly reduce the total ground fault current and reduce arc and flash hazards during ground faults in high voltage distribution systems.

The purpose of this essay is to analyze how the Trojan prince Paris is described in the Iliad and in the movie Troy in regard to love and bravery. Thereafter an analysis of the similarities and differences between the Iliad and the movie Troy will be made. There will also be a discussion why there are differences between an epic story which was made for over two thousand years ago and a modern movie made in the twenty-first century. The differences will be based on the perspective ancient Greek culture versus filmmaking of the twenty-first century. The method that has been used is narrative analysis where the primary data, the Iliad and the movie Troy, have been interpreted.                         The Trojan prince Paris is described as a young, handsome man driven by his passion for Helen. Because of his passion for Helen he started a war and sacrificed thousands of men of Troy for her sake. The study showed that Paris was described in both the Iliad and the movie Troy as a coward, although some of his actions were brave. One reason why there are differences between the Iliad and the movie Troy is Wolfgang Petersen’s decision to remove the interference of the gods but other reasons are also discussed in the essay.

Die Ausstellung und die Broschüre mit dem Titel „arbeiten. sprechen. spielen. feiern.“ laden dazu ein, anhand fotografischer Quellen einen kritischen Blick auf die Praxis der Reformpädagogik im 20. Jahrhundert zu werfen und neue Impulse für die eigene Beschäftigung mit diesen Ansätzen aufzunehmen. Sie richtet sich insbesondere an Studierende des Lehramtes, an angehende und aktive Lehrer, an Wissenschaftler in den Bereichen Historische Bildungsforschung, Erziehungswissenschaft und Schulpädagogik sowie an Interessierte aus Berufen der pädagogischen Praxis. Darüber hinaus ist die Ausstellung so konzipiert, dass sie für universitäre Lehrveranstaltungen, z. B. für Einführungen in das wissenschaftliche Arbeiten, genutzt werden kann. Sie möchte dementsprechend das Vorhaben unterstützen, Kenntnisse der Fotoanalyse zu vermitteln, um somit grundlegende Kompetenzen im wissenschaftlichen Arbeiten mit der Quelle Foto aufzubauen. / The exhibition and the brochure with the title “working. speaking. playing. celebrating.” encourages taking a critical look at the practice of the progressive educational movement in the 20th century and provides a new impetus for taking up practical experience with this pedagogical approach by oneself. It is especially aimed at students to become a teacher, future and regular teachers, scientists in the fields of Historical Educational Research, Education and School Pedagogy, as well as other interested educators in practice. Furthermore, the exhibition is designed in a way that it can be used for lectures at university, e.g. for the introduction of scientific work. Consequently, it supports the idea of conveying knowledge of photographic analysis to build up basic competences in the scientific work of photos used as sources.

The rural power grid has traditionally mostly consisted of overhead power lines. In recent years the trend has been to replace the overhead lines with cables instead. The reason is that overhead lines are relatively vulnerable, strong winds and storms can cause trees and branches to fall over the power lines and cause a phase to ground fault. This will then trip the ground fault relays and disconnect the faulty power line. A cable grid is not vulnerable in the same way, and could be considered a solution to make the power grid more reliable. A cable grid does come whit other types of problems instead. It generates about 50 times more phase to ground capacitance compared with the same length of overhead lines. When a phase to ground fault occurs the capacitance in the healthy phases will generate a current to ground and then through the fault. On average a cable grid generates about 2 A per kilometer. Large cable grids can therefore cause very large capacitive currents to flow through the fault.  To counter this, a reactor is placed between the neutral point of the transformer and ground. When a phase to ground fault occurs, the reactor will generate an inductive current which is in the opposite phase compared to the capacitive current. This current will flow through the faulty line and cancel out the capacitive current. In a perfectly tuned power grid the only component left in the fault is a smaller resistive current. Large cable grids will require a large reactor to generate the large inductive current, which might need to flow over a great distance in the grid to reach the fault location. To reduce the inductive current from the central reactor, it is possible to install smaller local reactors in the grid. These will then in the event of a phase to ground fault generate a part of the inductive current, which will reduce the currents from the central reactor. This report will look at the factors related to grounding systems and how these factors affect the ground fault currents. The purpose of the report is to give recommendations to Umeå Energi on where in their grid they should install additional local reactors and also which factors they should consider when doing future expansions and rebuilds of their power grid.

Die Ausstellung und die Broschüre mit dem Titel „arbeiten. sprechen. spielen. feiern.“ laden dazu ein, anhand fotografischer Quellen einen kritischen Blick auf die Praxis der Reformpädagogik im 20. Jahrhundert zu werfen und neue Impulse für die eigene Beschäftigung mit diesen Ansätzen aufzunehmen. Sie richtet sich insbesondere an Studierende des Lehramtes, an angehende und aktive Lehrer, an Wissenschaftler in den Bereichen Historische Bildungsforschung, Erziehungswissenschaft und Schulpädagogik sowie an Interessierte aus Berufen der pädagogischen Praxis. Darüber hinaus ist die Ausstellung so konzipiert, dass sie für universitäre Lehrveranstaltungen, z. B. für Einführungen in das wissenschaftliche Arbeiten, genutzt werden kann. Sie möchte dementsprechend das Vorhaben unterstützen, Kenntnisse der Fotoanalyse zu vermitteln, um somit grundlegende Kompetenzen im wissenschaftlichen Arbeiten mit der Quelle Foto aufzubauen. / The exhibition and the brochure with the title “working. speaking. playing. celebrating.” encourages taking a critical look at the practice of the progressive educational movement in the 20th century and provides a new impetus for taking up practical experience with this pedagogical approach by oneself. It is especially aimed at students to become a teacher, future and regular teachers, scientists in the fields of Historical Educational Research, Education and School Pedagogy, as well as other interested educators in practice. Furthermore, the exhibition is designed in a way that it can be used for lectures at university, e.g. for the introduction of scientific work. Consequently, it supports the idea of conveying knowledge of photographic analysis to build up basic competences in the scientific work of photos used as sources.

<p>In 2004 <em>Troy</em> was released in movie theatres worldwide and almost immediately sparked up discussions on film’s relation to the ancient epic of Homer.</p><p> The main purpose of this paper is to see the connection between <em>Troy</em> and Homer’s <em>The Iliad</em> – motion pictures’ only officially credited source of inspiration. By using comparative method and intertextual approach I try to see how a literary piece, for centuries recited and cherished by the highest academic circles is remodelled to fit the taste of a mass public. How <em>The Iliad</em> mutates to be a marketable product.</p><p>   I discuss the changes of the plot that were introduced in <em>Troy</em> and try to see those changes as an outcome of mutation process. Apart from the plot, the notion of a hero is also discussed: how the definition of hero changed through time? To illustrate the changes, two main heroes – Achilles and Hector are discussed, yet again using the comparative method.</p><p>   By approaching <em>Troy</em> and <em>The Iliad</em> as two separate cultural products (I did not view <em>Troy</em><em> </em>as a documentary on <em>The Iliad</em>) I was able to connect them. I could see that the essence of the literary work and the film appears to be the same. It shows that the ancient Greek values, especially those, related to warfare and heroism, have definitely survived long enough to penetrate the modern thought.</p>

In 2004 Troy was released in movie theatres worldwide and almost immediately sparked up discussions on film’s relation to the ancient epic of Homer.  The main purpose of this paper is to see the connection between Troy and Homer’s The Iliad – motion pictures’ only officially credited source of inspiration. By using comparative method and intertextual approach I try to see how a literary piece, for centuries recited and cherished by the highest academic circles is remodelled to fit the taste of a mass public. How The Iliad mutates to be a marketable product.    I discuss the changes of the plot that were introduced in Troy and try to see those changes as an outcome of mutation process. Apart from the plot, the notion of a hero is also discussed: how the definition of hero changed through time? To illustrate the changes, two main heroes – Achilles and Hector are discussed, yet again using the comparative method.    By approaching Troy and The Iliad as two separate cultural products (I did not view Troy as a documentary on The Iliad) I was able to connect them. I could see that the essence of the literary work and the film appears to be the same. It shows that the ancient Greek values, especially those, related to warfare and heroism, have definitely survived long enough to penetrate the modern thought.

This thesis deals with the concept of education of German pedagogue and university professor Peter Petersen, on the basis of which he elaborated and verified a pedagogical concept called the Jenaplan, which is a synthesis of different lines of the international reform educational movement of the beginning of the last century. It's only ten years left, and one centuries since the first verification of this concept at the practice school of university of Jena and the first book publication of The Small Jena-Plan (Der kleine Jena- Plan, 1927). Yet it is still a challenge that encourages thinking about changes in the work of a regular school. Still again, he questions the stereotypes and serves as a contemporary model of the school as a workshop of humanity. The first chapter deal with the historical background of the reform educational movement and the basic features of reform pedagogy. The second chapter describes the life of Peter Petersen. The third chapter is devoted to the basic elements of Petersen's pedagogy and the principles of the Jenaplan school. The fourth chapter forms the core of the theoretical part of the work and, on the basis of quotes from Petersen's writings, describes and interprets its concept of pedagogical anthropology, which is the starting point for education to humanity. The fifth...

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