We study graph parameters arising from different types of colourings of random graphs, defined broadly as an assignment of colours to either the vertices or the edges of a graph. The chromatic number X(G) of a graph is the minimum number of colours required for a vertex colouring where no two adjacent vertices are coloured the same. Determining the chromatic number is one of the classic challenges in random graph theory. In Chapter 3, we give new upper and lower bounds for the chromatic number of the dense random graph G(n,p)) where p ∈ (0,1) is constant. These bounds are the first to match up to an additive term of order o(1) in the denominator, and in particular, they determine the average colour class size in an optimal colouring up to an additive term of order o(1). In Chapter 4, we study a related graph parameter called the equitable chromatic number. This is defined as the minimum number of colours needed for a vertex colouring where no two adjacent vertices are coloured the same and, additionally, all colour classes are as equal in size as possible. We prove one point concentration of the equitable chromatic number of the dense random graph G(n,m) with m = pn(n-1)/2, p < 1-1/e² constant, on a subsequence of the integers. We also show that whp, the dense random graph G(n,p) allows an almost equitable colouring with a near optimal number of colours. We call an edge colouring of a graph G a rainbow colouring if every pair of vertices is joined by a rainbow path, which is a path where no colour is repeated. The least number of colours where this is possible is called the rainbow connection number rc(G). Since its introduction in 2008 as a new way to quantify how well connected a given graph is, the rainbow connection number has attracted the attention of a great number of researchers. For any graph G, rc(G)≥diam(G), where diam(G) denotes the diameter. In Chapter 5, we will see that in the random graph G(n,p), rainbow connection number 2 is essentially equivalent to diameter 2. More specifically, we consider G ~ G(n,p) close to the diameter 2 threshold and show that whp rc(G) = diam(G) ∈ {2,3}. Furthermore, we show that in the random graph process, whp the hitting times of diameter 2 and of rainbow connection number 2 coincide. In Chapter 6, we investigate sharp thresholds for the property rc(G)≤=r where r is a fixed integer. The results of Chapter 6 imply that for r=2, the properties rc(G)≤=2 and diam(G)≤=2 share the same sharp threshold. For r≥3, the situation seems quite different. We propose an alternative threshold and prove that this is an upper bound for the sharp threshold for rc(G)≤=r where r≥3.

Le débat portant sur la relation entre la protection des droits de l'homme et la protection des investissements étrangers n’est pas nouveau. Quand cette dernière et la protection des droits de l'homme des peuples locaux s'opposent, quelle solution le régime du droit de l'investissement devrait-il proposer? Est-il possible d'inclure la protection des droits de l'homme des investisseurs étrangers dans le régime du droit international de l'investissement? Il faudrait trouver le moyen de rendre le régime du droit international de l'investissement compatible avec le régime du droit international des droits de l'homme. C'est le problème principal que cette thèse souhaite traiter. Je propose d'inclure la protection des droits de l'homme par le biais de la clause du traitement juste et équitable (TJE) dans les TBI. Le sens littéral du TJE est de donner aux investisseurs étrangers le traitement qu'ils méritent. Cela veut dire que l'on ne devrait leur donner ni plus ni moins que ce qu'ils méritent. On leur donne plus quand leur investissement est protégé sans que l'on accorde l'attention qui lui revient à la protection des droits de l'homme des peuples locaux. En même temps, les investisseurs étrangers méritent un environnement d'investissement dans lequel leurs droits de l'homme sont respectés. Pour l'argument de la cohérence, on a pu voir que le TJE était en général la mise en œuvre de l'état de droit. Les investisseurs étrangers méritent un environnement d'investissement où l'état de droit existe. L'état de droit inclut la protection des droits de l'homme. Les investisseurs étrangers méritent un environnement d'investissement où les droits de l'homme sont protégés. / The relationship between human rights protection and foreign investment protection has been an issue that has been widely discussed. When the foreign investment protection and the human rights protection of local people conflicts, how should the investment law regime solve the problem? Moreover, is it possible that foreign investors' human rights protection be included in the international investment law regime? The international investment law regime should find a way to make itself compatible with international human rights law regime. The aforementioned is the major issue that this thesis intends to address. I have proposed to include human rights protection through the fair and equitable treatment (FET) clause in BITs. The literal meaning of FET is to give foreign investors the treatment that they deserve. This means that foreign investors should not be given neither less than they deserve, nor more than they deserve. Foreign investors were given more than they deserve when their investment were protected without giving due regard to local people's human rights protection. Meanwhile, foreign investors deserve an investment environment where their human rights are protected. For the coherence argument, FET is generally the implementation of the rule of law. In its interpretation, there is a presupposed warrant. The warrant is "foreign investors deserve an investment environment where rule of law is implemented." Foreign investors deserve an investment environment where rule of law is implemented. Rule of law includes the protection of human rights. Foreign investors therefore deserve an investment environment where the protection of human rights is implemented.

Thesis (LLM. (Labour Law)) -- University of Limpopo, 2013 / This mini dissertation relates to the payment of divorce benefits to a former spouse upon divorce and recent amendments that have taken place in the Pension Funds Act 24 of 1956.Particular reference is made to the amendment of Section 37D.This amendment has brought about changes that will contribute positively to the development of South African Retirement Law. The discussion below deals with the unfairness to non-member former spouses before 1st November 2008. An analysis of pension interest taking into account relevant statutory provisions and case law will be dealt with as well. A classification between a member spouse and a former spouse in order to determine who is responsible to pay tax upon divorce. In terms of the Divorce Act 70 of 1979 the former spouse of a retirement fund on divorce could be awarded by the court a portion of the benefits that the member would have received had she/he resigned on the date of divorce. The former spouse was only entitled to receive that share when the member became entitled to a benefit in terms of the rules of the fund which states on his/her retirement or termination of membership which could have been many years after the date of the divorce. Dissolution of Customary marriages will also be discussed and the benefit a divorced spouse has at the dissolution of marriage.

This thesis is a qualitative study based on interviews conducted in early 2007 and aims at getting an understanding of the political environment from an opposition party’s point of view in Northern Sudan. The study is also trying to illustrate how good governance and democracy are building on each other and that good governance is a pre-requisite for democracy. In this perspective Sudan has a long way to go. The main assumption is that women are key to good governance and internal democracy and a democratic society. If the party excludes women, it can not be representative, participatory or equitable and inclusive. The thesis is therefore looking at the structures of one opposition party, the Umma Party, and women’s political participation in the party. This description is then analysed in light of Good Governance’s characteristics of participation, representativeness, equity and inclusiveness in the political society arena. The following questions were asked and answered: • What are the basic features of the political environment within which Sudanese opposition parties operate? • What are the leadership structures and decision making processes of the Umma Party in North Sudan? • How do women access these structures and processes? The main finding is that the Umma Party and Sudan do not fulfill the characteristics or the indicators to claim good governance or democracy – not within the party and not within the country.

<p>This thesis is a qualitative study based on interviews conducted in early 2007 and aims at getting an understanding of the political environment from an opposition party’s point of view in Northern Sudan.</p><p>The study is also trying to illustrate how good governance and democracy are building on each other and that good governance is a pre-requisite for democracy. In this perspective</p><p>Sudan has a long way to go. The main assumption is that women are key to good governance and internal democracy and a democratic society. If the party excludes women, it can not be representative, participatory or equitable and inclusive.</p><p>The thesis is therefore looking at the structures of one opposition party, the Umma Party, and women’s political participation in the party. This description is then analysed in light of Good Governance’s characteristics of participation, representativeness, equity and inclusiveness in the political society arena. The following questions were asked and answered:</p><p>• What are the basic features of the political environment within which Sudanese opposition parties operate?</p><p>• What are the leadership structures and decision making processes of the Umma Party in North Sudan?</p><p>• How do women access these structures and processes?</p><p>The main finding is that the Umma Party and Sudan do not fulfill the characteristics or the indicators to claim good governance or democracy – not within the party and not within the country.</p>

This dissertation analyses the implications of international investment law on host states’ legal ability to protect the environment, regulate sustainable use of natural resources, and develop new approaches to manage environmental risks and uncertainties. ‘Environmental policy space’ is found to be a useful term when exploring the regulatory autonomy in this context. On one hand, investment law aims to ensure stability of the investment environment. On the other hand, environmental law needs flexibility to react to the degradation of the environment. It is found that those different aims do not have to be in conflict. There are useful mechanisms in national environmental law which provide for accessible, transparent and predictable decisions for the private actor. These mechanisms can fulfill the aim of stability in investment law. It is, however, concluded that core provisions of international investment treaties risk to put constraints to environmental law in a variety of ways. To diminish these risks, states, when concluding investment treaties, should make clear that constraining environmental regulation is not compatible with the overarching aim of sustainable development. Furthermore, the interpretation of provisions of investment protection must respect principles and instruments of environmental law not to continue being unbalanced towards investor interests. It is also concluded that allowing for investor – state arbitration, without the investor exhausting local remedies, will ignore the important national administrative review system of public environmental measures.

The purpose of this study was to identify and describe the associations between systemic equity pedagogy (SEP) practices in highly diverse high schools and their students' science achievement and college readiness. This study focuses on science programs in ten highly diverse Texas high schools serving students who exhibit high science achievement and college readiness. According to the Policy Research Group in Science Education, only two percent of all culturally diverse high schools within the state of Texas demonstrate high science achievement and college readiness on state-tracked school-level indicators. Transforming a school context where achievement disparities exist among student groups in science classrooms necessitates that public school officials understand key factors, or “drivers,” and associated indicators contributing to SEP in programs. A model for programs is suggested using a framework for SEP based on data collected from ten highly successful, high diversity high schools. The following research questions address the research gap regarding indicators of SEP associated with high science achievement and college readiness in highly culturally diverse high schools. How do data from ten highly successful, high diversity high schools inform the development of a comprehensive SEP rubric? How do high achieving high schools of culturally diverse student populations score on a comprehensive SEP rubric? How do teachers’ perceptions toward implementing SEP practices vary in different schools? Three research papers detail the research of this dissertation. The purpose for the first paper is to increase understanding of indicators facilitating systemic and equitable teaching and learning practices, otherwise referred to as systemic equity pedagogy (SEP). Results of the study show indicators of a comprehensive SEP rubric. Together, 127 indicators, thirty categories, and eight SEP drivers form a model framing equitable teaching and learning practices associated with high science achievement and college readiness. In conclusion, indicators within the SEP rubric can be described as action-oriented descriptors that science teachers engage formally or informally in order to facilitate quality science education for all students. The purpose for paper two is to score equitable teaching and learning practices in highly successful high school science programs based on the SEP rubric. Findings reveals that implementation of various equitable teaching and learning practices vary across science programs and these practices can be described as both pedagogical and non-pedagogical. In conclusion, varying degrees of implementation exist for indicators in the SEP rubric. In paper three, the purpose is to understand science teachers’ attitude and approach toward implementing systemic teaching and learning practices. Results from this study provide scores that indicate science teachers’ perceptions of their approach to SEP. This study concludes by suggesting high achieving science programs may operate within a continuum for implementing equitable teaching and learning practices.

Title: Parameterized Complexity Author: Ondřej Suchý Department: Department of Applied Mathematics Advisor: Prof. RNDr. Jan Kratochvíl, CSc. Advisor's e-mail address: honza@kam.mff.cuni.cz Abstract: This thesis deals with the parameterized complexity of NP-hard graph problems. We explore the complexity of the problems in various scenarios, with respect to miscellaneous parameters and their combina- tions. Our aim is rather to classify in this multivariate manner whether the particular parameters make the problem fixed-parameter tractable or intractable than to present the algorithm achieving the best running time. In the questions we study typically the first-choice parameter is unsuccessful, in which case we propose to use less standard ones. The first family of problems investigated provides a common general- ization of many well known and studied domination and independence problems. Here we suggest using the dual parameterization and show that, in contrast to the standard solution-size, it can confine the in- evitable combinatorial explosion. Further studied problems are ana- logues of the Steiner problem in directed graphs. Here the parameter- ization by the number of terminals to be connected seems to be previ- ously unexplored in the directed setting. Unfortunately, the problems are shown to be...

Läsförståelse är en komplex färdighet beroende av flera samspelande förmågor. Lärares uppfattningar om hur läsförståelseundervisning kan utformas i praktiken i relation till elevers olika utvecklingsstadier är en avgörande faktor för elevers läsförståelseutveckling (Jönsson, 2007). I tidigare forskning framgår vilka förmågor som krävs för fullständig läsförståelse, och hur förmågorna kan undervisas i praktiken. Däremot saknas forskning om lärares uppfattningar av arbete med läsförståelse i klassrumskontext. Inte minst saknas lärares uppfattningar av arbete med läsförståelse ur ett helhetsperspektiv och hur lärarna går tillväga för att forma läsförståelsearbetet likvärdigt i relation till elevers skilda utvecklingsstadier. Syftet med föreliggande studie är därför att beskriva verksamma lågstadielärares uppfattningar om läsförståelseoch den undervisningspraktik som bedrivs för att utveckla elevers läsförståelse. Studiens syfte uppnås genom frågeställningarna: ·      Hur uppfattar verksamma lågstadielärare begreppet läsförståelse i F-3?  ·     Vilka arbetssätt beskriver och motiverar lågstadielärare att de använder för att utveckla elevers läsförståelse i F-3? ·     Vilka aspekter beskriver lågstadielärare som särskilt viktiga i samband med arbetssätt för läsförståelse i F-3?  Materialinsamlingen genomfördes genom tre semistrukturerade fokusgruppsintervjuer med sex verksamma lågstadielärare. Denna kvalitativa studie utgår från ett fokus på lärares uppfattningar. Studiens teoretiska utgångspunkt utgår från ett sociokulturellt perspektiv. I resultatet framgår att läsförståelse uppfattas som samspelande förmågor som inkluderar bland annat avkodning och inferensskapanden av textinnehållet. Resultatet visar lärarnas uppfattningar av arbetssätt för att utveckla läsförståelse, vilka motiveras och beskrivs i form av bland annat variationen av högläsning, textsamtal, en läsande klass, parläsning, och textkort. Arbetssätten beskrivs möjliggöra utveckling utifrån varierade kunskapsnivåer och utvecklingsstadier. I samband med arbetssätten har läraren en avgörande roll, där textval i relation till elevgrupp i samband med arbetssätten är en betydande faktor. / Reading comprehension is a complex skill depending on several interacting abilities. Teachers' perceptions of how reading comprehension teaching can be designed in practice relative to students' different developmental stages are a decisive factor for students' reading comprehension development (Jönsson, 2007). Previous research emphasizes which abilities are required for fully developed reading comprehension, and to some extent how these separate abilities can be taught in practice. However, there is a lack of research on teachers' perceptions regarding reading comprehension teaching in the classroom context. There is also a lack of research on teachers' perceptions of reading comprehension from a holistic perspective and how teachers create equitable reading comprehension teaching relative to students' different stages of development. The purpose of the present study is therefore to describe primary school teachers' perceptions of reading comprehension and the teaching practice that is conducted to develop students' reading comprehension. The purpose of the study is achieved through the questions:      ·      How does primary school teachers perceive the concept of reading comprehension in grades F-3? ·      What working methods do the primary school teachers describe and motivate that they use to develop students' reading comprehension in grades F-3? ·      What aspects do primary school teachers describe as particularly important in conjunction with working methods for reading comprehension in grades F-3? The data collection was carried out through three semi-structured focus group interviews with six primary school teachers. This qualitative study is focusing on teachers' perceptions. The theoretical framework of the study is based on a sociocultural perspective. The results show that reading comprehension is perceived as interacting abilities that include decoding and inference creation. The results show the teachers’ perceptions of working methods for developing reading comprehension, which are motivated and described by the variation of reading aloud, text talks, a reading class,reading in pairs, and text cards.The teachers describe that the working methods enable development based on varied levels of knowledge and stages of development. In connection with the working methods, the teacher has a decisive role, where text choice relative to the student group in connection with the working methods is a significant factor.

Likvärdig undervisning är en viktig del av svensk skola. Forskning visar däremot att målet med att bedriva en likvärdig undervisning är svår att genomföra i praktiken. Samtidigt som likvärdigheten försämras i svensk skola, verkar elevernas läsförståelse gå i samma riktning och fler är i lässvårigheter än tidigare.   Den här studien har som syfte att bidra med kunskap om likvärdighet i undervisning, med ett särskilt fokus på elever i lässvårigheter. Genom kvalitativa intervjuer med sex lärare på högstadiet undersöker studien hur lärare beskriver sina erfarenheter kring likvärdighet och vilka undervisningsstrategier de använder för att hjälpa elever i lässvårigheter bli delaktiga i läsundervisningen.   Resultatet visar att lärarna anser att likvärdig undervisning är svårt och att det inte finns tid att anpassa undervisningen efter varje enskild individ. Detta visar sig även när lärarna diskuterar läsundervisningen, där mycket fokus läggs vid att hjälpa elever i lässvårigheter. Resultatet visar även att lärarna ser ett ökat behov av att låta elever läsa mer skönlitteratur och att fler är i lässvårigheter än tidigare. Lärarna beskriver hur de använder olika undervisningsstrategier för att elever i lässvårigheter ska bli delaktiga i läsundervisningen. Studiens slutsats är att lärarna upplever att undervisningen inte är likvärdig, då den i större utsträckning anpassas efter elever i lässvårigheter. / Equitable teaching is an important part of the Swedish school system. Research on the other hand shows that equitable teaching is difficult to achieve in practice. At the same time as equity is deteriorating in Swedish school, students' reading comprehension also seems to be deteriorating and more people are having reading difficulties than before.   The purpose of this study is to contribute with knowledge about equitable teaching. Through qualitative interviews with six teachers in secondary school, the study examines how teachers describe their experiences of equity and which teaching strategies they use to help students with reading difficulties become included in reading instruction.  The results show that the teachers consider equitable teaching difficult and that there is no time to adapt the teaching to each individual. This is also apparent when the teachers discuss reading instruction, where a lot of focus is placed on helping students with reading difficulties. The results also show that the teachers see an increased need of letting students read more fiction and that more students are in reading difficulties then before. The teachers use different teaching strategies to make sure that students in reading difficulties are included in reading instruction. The study concludes that the teachers feel that the education is not equitable, as it to a greater extent is adapted to include students with reading difficulties.