Le calcul du nombre chromatique et la détermination d'une colo- ration optimale des sommets d'un graphe sont des problèmes NP- difficiles en général. Ils peuvent cependant être résolus en temps po- lynomial dans les graphes parfaits. Par ailleurs, la perfection d'un graphe peut être décidée efficacement. Les graphes parfaits sont caractérisés par la structure de leur poly- tope des stables : les facettes non-triviales sont définies exclusivement par des inégalités de cliques. Réciproquement, une structure similaire des facettes du polytope des stables détermine-t-elle des propriétés combinatoires et algorithmiques intéressantes? Un graphe est h-parfait si les facettes non-triviales de son polytope des stables sont définies par des inégalités de cliques et de circuits impairs. On ne connaît que peu de résultats analogues au cas des graphes parfaits pour la h-perfection, et on ne sait pas si les problèmes sont NP-difficiles. Par exemple, les complexités algorithmiques de la re- connaissance des graphes h-parfaits et du calcul de leur nombre chro- matique sont toujours ouvertes. Par ailleurs, on ne dispose pas de borne sur la différence entre le nombre chromatique et la taille maxi- mum d'une clique d'un graphe h-parfait. Dans cette thèse, nous montrons tout d'abord que les opérations de t-mineurs conservent la h-perfection (ce qui fournit une extension non triviale d'un résultat de Gerards et Shepherd pour la t-perfection). De plus, nous prouvons qu'elles préservent la propriété de décompo- sition entière du polytope des stables. Nous utilisons ce résultat pour répondre négativement à une question de Shepherd sur les graphes h-parfaits 3-colorables. L'étude des graphes minimalement h-imparfaits (relativement aux t-mineurs) est liée à la recherche d'une caractérisation co-NP com- binatoire de la h-perfection. Nous faisons l'inventaire des exemples connus de tels graphes, donnons une description de leur polytope des stables et énonçons plusieurs conjectures à leur propos. D'autre part, nous montrons que le nombre chromatique (pondéré) de certains graphes h-parfaits peut être obtenu efficacement en ar- rondissant sa relaxation fractionnaire à l'entier supérieur. Ce résultat implique notamment un nouveau cas d'une conjecture de Goldberg et Seymour sur la coloration d'arêtes. Enfin, nous présentons un nouveau paramètre de graphe associé aux facettes du polytope des couplages et l'utilisons pour donner un algorithme simple et efficace de reconnaissance des graphes h- parfaits dans la classe des graphes adjoints. / Computing the chromatic number and finding an optimal coloring of a perfect graph can be done efficiently, whereas it is an NP-hard problem in general. Furthermore, testing perfection can be carried- out in polynomial-time. Perfect graphs are characterized by a minimal structure of their sta- ble set polytope: the non-trivial facets are defined by clique-inequalities only. Conversely, does a similar facet-structure for the stable set polytope imply nice combinatorial and algorithmic properties of the graph ? A graph is h-perfect if its stable set polytope is completely de- scribed by non-negativity, clique and odd-circuit inequalities. Statements analogous to the results on perfection are far from being understood for h-perfection, and negative results are missing. For ex- ample, testing h-perfection and determining the chromatic number of an h-perfect graph are unsolved. Besides, no upper bound is known on the gap between the chromatic and clique numbers of an h-perfect graph. Our first main result states that the operations of t-minors keep h- perfection (this is a non-trivial extension of a result of Gerards and Shepherd on t-perfect graphs). We show that it also keeps the Integer Decomposition Property of the stable set polytope, and use this to answer a question of Shepherd on 3-colorable h-perfect graphs in the negative. The study of minimally h-imperfect graphs with respect to t-minors may yield a combinatorial co-NP characterization of h-perfection. We review the currently known examples of such graphs, study their stable set polytope and state several conjectures on their structure. On the other hand, we show that the (weighted) chromatic number of certain h-perfect graphs can be obtained efficiently by rounding-up its fractional relaxation. This is related to conjectures of Goldberg and Seymour on edge-colorings. Finally, we introduce a new parameter on the complexity of the matching polytope and use it to give an efficient and elementary al- gorithm for testing h-perfection in line-graphs.

Qualitative properties of solutions to equations of fluid mechanics Mgr. Jakub Tichý Supervisor: doc. Mgr. Petr Kaplický, Ph.D. Department: Department of Mathematical Analysis Abstract This thesis is devoted to the boundary regularity of weak solutions to the system of nonlinear partial differential equations describing incompressible flows of a certain class of generalized Newtonian fluids in bounded domains. Equations of motion and continuity equation are complemented with perfect slip boundary conditions. For stationary generalized Stokes system in Rn with growth condi- tion described by N-function Φ the existence of the second derivatives of velocity and their regularity up to the boundary are shown. For the same system of equa- tions integrability of velocity gradients is proven. Lq estimates are obtained also for classical evolutionary Stokes system via interpolation-extrapolation scales. Hölder continuity of velocity gradients and pressure is shown for evolutionary generalized Navier-Stokes equations in R2 . Keywords Generalized Stokes and Navier - Stokes equations, incompressible fluids, perfect slip boundary conditions, regularity up to the boundary

O presente trabalho propõe-se analisar a industrialização do Brasil no contexto de mudanças econômicas e políticas no primeiro governo de Getúlio Vargas, de 1930 até 1945. Na literatura de economia brasileira com relação ao surgimento da indústria no Brasil, duas visões se contrapõem: de um lado, a industrialização como subproduto da intervenção do governo no setor cafeeiro; de outro, a industrialização intencionalmente promovida pelo governo. Com base em uma análise de equilíbrio em um jogo dinâmico de informação imperfeita, é evidenciada a racionalidade da criação de instituições para o desenvolvimento industrial na década de 1930. Este resultado de equilíbrio mostra as mudanças pela qual o Brasil passou a partir da década de 1930, com mudanças da estrutura tributária, educacional, financeira e relações de trabalho, ou seja, essa mudança institucional gerou campo fértil para o surgimento do processo de industrialização que caracterizou o primeiro governo Vargas e também mostra a intencionalidade desse governo, quando se observa a transformação do sistema tributário, de tal modo a ficar imune das oscilações econômicas externas e também as mudanças educacionais, que passou a incentivar o ensino primário, secundário e técnico profissionalizante, medidas essas feitas para atender o novo panorama econômico brasileiro. Outro ponto que corrobora o resultado do equilíbrio de Nash perfeito em subjogos é a perda da importância do setor cafeeiro no período que engloba o século XIX até o final do primeiro governo Vargas, onde as evidências mostram que os cafeicultores tinham, antes e durante a década de 1930, tendências a diversificarem investimentos por conta da perda da renda com o setor cafeicultor. / This study proposes to examine the industrialization of Brazil in the context of economic and political changes in the first government of Getulio Vargas, from 1930 until 1945. In the literature of the Brazilian economy with the coming of industry in Brazil, two visions are in opposition: on one hand, industrialization as a byproduct of government intervention in the coffee sector, on the other, deliberately promoted industrialization by the government. Based on an analysis of equilibrium in a dynamic game of imperfect information, rationality is evident from the creation of institutions for industrial development in the 1930s. The result shows the changes of equilibrium in which Brazil went from the 1930s, with changes in the tax structure, educational, financial and labor relations, that institutional change created fertile ground for the rise of industrialization that characterized the first Vargas government and also shows the intention of this government, when one observes the transformation of the tax system, so be immune to external economic fluctuations and also educational changes, which came to encourage the primary, secondary and technical vocational, measures designed to meet the new economic landscape of Brazil. Another point that confirms the outcome of the Nash equilibrium is perfect in subgame the loss of the importance of the coffee sector in the period that includes the nineteenth century until the end of the first Vargas government, where the evidence shows that farmers had, since the decade of 1930, to diversify investment trends due to the loss of income to the grower industry.

Le présent travail est une petite recherche sur l'apprentissage du français, et plus particulièrement sur l'alternance de l'imparfait et le passé composé parmi des suédophones. Le but du mémoire est de comprendre comment les apprenants appliquent la grammaire malgré la différence entre leur langue maternelle et la langue de l'apprentissage. L'étude part de la différence entre le français et le suédois. Le corpus se compose de dix récits au passé écrits par des étudiants des niveau trois et quatre du système scolaire suédois. Le titre de leur devoir était Un souvenir de mon enfance. Un exercice pris du manuel est aussi analysé. Le résultat montre que d'abord les suédophones apprennent à utiliser les verbes d'état à l'imparfait, puis les suédophones expérimentent avec l'aspect des verbes pour l’alternance entre l’imparfait et le passé composé En conclusion, l'alternance entre l'imparfait et le passé composé est un défi pour les suédophones, mais ce n'est pas un défi insurmontable. / The current piece of research is a study of how second language learners adapt to the distinction between imperfect and perfect in the narrative of past in the French language. The aim of the study is to find out how the learners adopt the grammar despite the difference between their native language and their learning language. The study describes the difference between Swedish and French. The corpus is defined, consisting of ten narratives by ten second language learners on the levels three and four in the Swedish school system. The title was Un souvenir de mon enfance. An exercise in the schoolbook is also analysed. The result shows that the students first learn how to use imperfect in sentences containing a state verb. Later the students attempt the aspect of the verb to practise the shift between the past tense and the perfect tense. In conclusion, the shift between perfect and imperfect is a challenge to the Swedish learner. However, it is not an unbridgeable gap.

O presente trabalho propõe-se analisar a industrialização do Brasil no contexto de mudanças econômicas e políticas no primeiro governo de Getúlio Vargas, de 1930 até 1945. Na literatura de economia brasileira com relação ao surgimento da indústria no Brasil, duas visões se contrapõem: de um lado, a industrialização como subproduto da intervenção do governo no setor cafeeiro; de outro, a industrialização intencionalmente promovida pelo governo. Com base em uma análise de equilíbrio em um jogo dinâmico de informação imperfeita, é evidenciada a racionalidade da criação de instituições para o desenvolvimento industrial na década de 1930. Este resultado de equilíbrio mostra as mudanças pela qual o Brasil passou a partir da década de 1930, com mudanças da estrutura tributária, educacional, financeira e relações de trabalho, ou seja, essa mudança institucional gerou campo fértil para o surgimento do processo de industrialização que caracterizou o primeiro governo Vargas e também mostra a intencionalidade desse governo, quando se observa a transformação do sistema tributário, de tal modo a ficar imune das oscilações econômicas externas e também as mudanças educacionais, que passou a incentivar o ensino primário, secundário e técnico profissionalizante, medidas essas feitas para atender o novo panorama econômico brasileiro. Outro ponto que corrobora o resultado do equilíbrio de Nash perfeito em subjogos é a perda da importância do setor cafeeiro no período que engloba o século XIX até o final do primeiro governo Vargas, onde as evidências mostram que os cafeicultores tinham, antes e durante a década de 1930, tendências a diversificarem investimentos por conta da perda da renda com o setor cafeicultor. / This study proposes to examine the industrialization of Brazil in the context of economic and political changes in the first government of Getulio Vargas, from 1930 until 1945. In the literature of the Brazilian economy with the coming of industry in Brazil, two visions are in opposition: on one hand, industrialization as a byproduct of government intervention in the coffee sector, on the other, deliberately promoted industrialization by the government. Based on an analysis of equilibrium in a dynamic game of imperfect information, rationality is evident from the creation of institutions for industrial development in the 1930s. The result shows the changes of equilibrium in which Brazil went from the 1930s, with changes in the tax structure, educational, financial and labor relations, that institutional change created fertile ground for the rise of industrialization that characterized the first Vargas government and also shows the intention of this government, when one observes the transformation of the tax system, so be immune to external economic fluctuations and also educational changes, which came to encourage the primary, secondary and technical vocational, measures designed to meet the new economic landscape of Brazil. Another point that confirms the outcome of the Nash equilibrium is perfect in subgame the loss of the importance of the coffee sector in the period that includes the nineteenth century until the end of the first Vargas government, where the evidence shows that farmers had, since the decade of 1930, to diversify investment trends due to the loss of income to the grower industry.

O presente trabalho propõe-se analisar a industrialização do Brasil no contexto de mudanças econômicas e políticas no primeiro governo de Getúlio Vargas, de 1930 até 1945. Na literatura de economia brasileira com relação ao surgimento da indústria no Brasil, duas visões se contrapõem: de um lado, a industrialização como subproduto da intervenção do governo no setor cafeeiro; de outro, a industrialização intencionalmente promovida pelo governo. Com base em uma análise de equilíbrio em um jogo dinâmico de informação imperfeita, é evidenciada a racionalidade da criação de instituições para o desenvolvimento industrial na década de 1930. Este resultado de equilíbrio mostra as mudanças pela qual o Brasil passou a partir da década de 1930, com mudanças da estrutura tributária, educacional, financeira e relações de trabalho, ou seja, essa mudança institucional gerou campo fértil para o surgimento do processo de industrialização que caracterizou o primeiro governo Vargas e também mostra a intencionalidade desse governo, quando se observa a transformação do sistema tributário, de tal modo a ficar imune das oscilações econômicas externas e também as mudanças educacionais, que passou a incentivar o ensino primário, secundário e técnico profissionalizante, medidas essas feitas para atender o novo panorama econômico brasileiro. Outro ponto que corrobora o resultado do equilíbrio de Nash perfeito em subjogos é a perda da importância do setor cafeeiro no período que engloba o século XIX até o final do primeiro governo Vargas, onde as evidências mostram que os cafeicultores tinham, antes e durante a década de 1930, tendências a diversificarem investimentos por conta da perda da renda com o setor cafeicultor. / This study proposes to examine the industrialization of Brazil in the context of economic and political changes in the first government of Getulio Vargas, from 1930 until 1945. In the literature of the Brazilian economy with the coming of industry in Brazil, two visions are in opposition: on one hand, industrialization as a byproduct of government intervention in the coffee sector, on the other, deliberately promoted industrialization by the government. Based on an analysis of equilibrium in a dynamic game of imperfect information, rationality is evident from the creation of institutions for industrial development in the 1930s. The result shows the changes of equilibrium in which Brazil went from the 1930s, with changes in the tax structure, educational, financial and labor relations, that institutional change created fertile ground for the rise of industrialization that characterized the first Vargas government and also shows the intention of this government, when one observes the transformation of the tax system, so be immune to external economic fluctuations and also educational changes, which came to encourage the primary, secondary and technical vocational, measures designed to meet the new economic landscape of Brazil. Another point that confirms the outcome of the Nash equilibrium is perfect in subgame the loss of the importance of the coffee sector in the period that includes the nineteenth century until the end of the first Vargas government, where the evidence shows that farmers had, since the decade of 1930, to diversify investment trends due to the loss of income to the grower industry.

In this thesis we study two probabilistic models defined on graphs: the Stochastic Block model and the Exponential Random Graph. Therefore, this thesis is divided in two parts. In the first part, we introduce the Krichevsky-Trofimov estimator for the number of communities in the Stochastic Block Model and prove its eventual almost sure convergence to the underlying number of communities, without assuming a known upper bound on that quantity. In the second part of this thesis we address the perfect simulation problem for the Exponential random graph model. We propose an algorithm based on the Coupling From The Past algorithm using a Glauber dynamics. This algorithm is efficient in the case of monotone models. We prove that this is the case for a subset of the parametric space. We also propose an algorithm based on the Backward and Forward algorithm that can be applied for monotone and non monotone models. We prove the existence of an upper bound for the expected running time of both algorithms. / Nessa tese estudamos dois modelos probabilísticos definidos em grafos: o modelo estocástico por blocos e o modelo de grafos exponenciais. Dessa forma, essa tese está dividida em duas partes. Na primeira parte nós propomos um estimador penalizado baseado na mistura de Krichevsky-Trofimov para o número de comunidades do modelo estocástico por blocos e provamos sua convergência quase certa sem considerar um limitante conhecido para o número de comunidades. Na segunda parte dessa tese nós abordamos o problema de simulação perfeita para o modelo de grafos aleatórios Exponenciais. Nós propomos um algoritmo de simulação perfeita baseado no algoritmo Coupling From the Past usando a dinâmica de Glauber. Esse algoritmo é eficiente apenas no caso em que o modelo é monotóno e nós provamos que esse é o caso para um subconjunto do espaço paramétrico. Nós também propomos um algoritmo de simulação perfeita baseado no algoritmo Backward and Forward que pode ser aplicado à modelos monótonos e não monótonos. Nós provamos a existência de um limitante superior para o número esperado de passos de ambos os algoritmos.

Este estudio investiga la enseñanza del pretérito perfecto compuesto en el aula de españolcomo lengua extranjera a nivel escolar en Suecia. El objetivo de esta monografía es ver sipuede ser beneficioso enseñar el pretérito perfecto compuesto mediante canciones en español,que incluyen el pretérito perfecto compuesto en sus versos, como recurso didáctico. Losparticipantes son treinta y cuatro alumnos, divididos en dos grupos, de ELE en el octavo yocho profesores de español. Este estudio se realiza mediante observaciones en clase, dospruebas para los alumnos y una encuesta entre los profesores.Los resultados del estudio muestran que los profesores que participan en el estudio consideranque la mayoría de sus alumnos tienen problemas para aprender el pretérito perfectocompuesto. Los resultados de las pruebas indican que los alumnos que hacen parte del primergrupo de estudio, que tuvieron una enseñanza inductiva con canciones en español,aumentaron su destreza para utilizar el pretérito perfecto compuesto tanto con los verbosregulares como con los irregulares. Los alumnos que hicieron parte del segundo grupo,quienes recibieron una enseñanza deductiva, aumentaron su destreza en usar/aplicar elpretérito perfecto compuesto menos que el primer grupo cuando trata de los verbosirregulares. Sin embargo, estos alumnos aprendieron utilizar el pretérito perfecto compuestocon los verbos regulares mejor que los del primer grupo.Además, nos indigamos si se presentaba una posible diferencia en relación con el interés y lamotivación para aprender entre chicos y chicas dado el tema romántico de las canciones. Losresultados muestran una ligera mayoría en los resultados de las alumnas. / This study investigates the teaching of the past perfect tense in the Swedish classroom ofSpanish as a foreign language. The purpose of this essay is to see if it is profitable to teach thepast perfect tense with songs in Spanish, which include the past perfect tense in the lyrics, asan educational resource. The participants are thirtyfour students, divided into two groups, inthe eight grade who study Spanish as a foreign language, and eight Spanish teachers. Thestudy was made through observations in class, two tests by the students and a survey with theteachers.The results of the study show that the teachers who participated in the study consider that themajority of their students have problems learning the past perfect tense. Furthermore, theresults show that the students who were part of the first group, who received an inductiveeducation including Spanish music, increased their abilities of using the past perfect tenseboth with regular and irregular verbs. The students who were part of the second group andwho learnt/were taught by means of the deductive approach increased their abilities to use thepast perfect tense less than the first group when it came to the irregular verbs. However, theylearnt to use the past perfect tense with regular verbs better than the first group.Furthermore, we also investigated if there were any differences according to the interest andthe motivation to learn between the boys and the girls. The results were slightly higher amongthe girls.

Dans cette thèse, nous nous intéressons à trois problèmes issus de l'informatique théorique, à savoir le placement de formes rectangulaires dans un conteneur (OPP), la coloration dite "forte" d'arêtes des graphes et les codes identifiants dans les graphes. L'OPP consiste à décider si un ensemble d'items rectangulaires peut être placé sans chevauchement dans un conteneur rectangulaire et sans dépassement des bords de celui-ci. Une contrainte supplémentaire est prise en compte, à savoir l'interdiction de rotation des items. Le problème est NP-difficile même dans le cas où le conteneur et les formes sont des carrés. Nous présentons un algorithme de résolution efficace basé sur une caractérisation du problème par des graphes d'intervalles, proposée par Fekete et Schepers. L'algorithme est exact et utilise les MPQ-arbres - structures de données qui encodent ces graphes de manière compacte tout en capturant leurs propriétés remarquables. Nous montrons les résultats expérimentaux de notre approche en les comparant aux performances d'autres algorithmes existants. L'étude de la coloration forte d'arêtes et des codes identifiants porte sur les aspects structurels et de calculabilité de ces deux problèmes. Dans le cas de la coloration forte d'arêtes nous nous intéressons plus particulièrement aux familles des graphes planaires et des graphes subcubiques. Nous montrons des bornes optimales pour l'indice chromatique fort des graphes subcubiques en fonction du degré moyen maximum et montrons que tout graphe planaire subcubique sans cycles induits de longueur 4 et 5 est coloriable avec neuf couleurs. Enfin nous confirmons la difficulté du problème de décision associé, en prouvant qu'il est NP-complet dans des sous-classes restreintes des graphes planaires subcubiques.La troisième partie de la thèse est consacrée aux codes identifiants. Nous proposons une caractérisation des graphes identifiables dont la cardinalité du code identifiant minimum ID est n-1, où n est l'ordre du graphe. Nous étudions la classe des graphes adjoints et nous prouvons des bornes inférieures et supérieures serrées pour le paramètre ID dans cette classe. Finalement, nous montrons qu'il existe un algorithme linéaire de calcul de ID dans la classe des graphes adjoints L(G) où G a une largeur arborescente bornée par une constante. En revanche nous nous apercevons que le problème est NP-complet dans des sous-classes très restreintes des graphes parfaits. / In this thesis we study three theoretical computer science problems, namely the orthogonal packing problem (OPP for short), strong edge-colouring and identifying codes.OPP consists in testing whether a set of rectangular items can be packed in a rectangular container without overlapping and without exceeding the borders of this container. An additional constraint is that the rotation of the items is not allowed. The problem is NP-hard even when the problem is reduced to packing squares in a square. We propose an exact algorithm for solving OPP efficiently using the characterization of the problem by interval graphs proposed by Fekete and Schepers. For this purpose we use some compact representation of interval graphs - MPQ-trees. We show experimental results of our approach by comparing them to the results of other algorithms known in the literature. we observe promising gains.The study of strong edge-colouring and identifying codes is focused on the structural and computational aspects of these combinatorial problems. In the case of strong edge-colouring we are interested in the families of planar graphs and subcubic graphs. We show optimal upper bounds for the strong chromatic index of subcubic graphs as a function of the maximum average degree. We also show that every planar subcubic graph without induced cycles of length 4 and 5 can be strong edge-coloured with at most nine colours. Finally, we confirm the difficulty of the problem by showing that it remains NP-complete even in some restricted classes of planar subcubic graphs.For the subject of identifying codes we propose a characterization of non-trivial graphs having maximum identifying code number ID, that is n-1, where n is the number of vertices. We study the case of line graphs and prove lower and upper bounds for ID parameter in this class. At last we investigate the complexity of the corresponding decision problem and show the existence of a linear algorithm for computing ID of the line graph L(G) where G has the size of the tree-width bounded by a constant. On the other hand, we show that the identifying code problem is NP-complete in various subclasses of planar graphs.

This thesis consists of three articles investigating the asymptotic behaviour of cosmological spacetimes with symmetries arising in Mathematical General Relativity. In Paper A and B, we consider spacetimes with Bianchi symmetry and where the matter model is that of a perfect fluid. We investigate the behaviour of such spacetimes close to the initial singularity ('Big Bang'). In Paper A, we prove that the Strong Cosmic Censorship conjecture holds in non-exceptional Bianchi class B spacetimes. Using expansion-normalised variables, we further show detailed asymptotic estimates. In Paper B, we prove similar estimates in the case of stiff fluids. In Paper C, we consider T2-symmetric spacetimes satisfying the Einstein equations for a non-linear scalar field. To given initial data, we show global existence and uniqueness of solutions to the corresponding differential equations for all future times. In the special case of a constant potential, a setting which is equivalent to a linear scalar field on a background with a positive cosmological constant, we investigate in detail the asymptotic behaviour towards the future. We prove that the Cosmic No-Hair conjecture holds for solutions satisfying an additional a priori estimate, an estimate which we show to hold in T3-Gowdy symmetry. / Denna avhandling består av tre artiklar som undersöker det asymptotiska beteendet hos kosmologiska rumstider med symmetrier som uppstår i Matematisk Allmän Relativitetsteori. I Artikel A och B studerar vi rumstider med Bianchi symmetri och där materiemodellen är en ideal fluid. Vi undersöker beteendet av sådana rumstider nära ursprungssingulariteten ('Big Bang'). I Artikel A bevisar vi att den Starka Kosmiska Censur-förmodan håller för icke-exceptionella Bianchi klass B-rumstider. Med hjälp av expansions-normaliserade variabler visar vi detaljerade asymptotiska uppskattningar. I Artikel B visar vi liknande uppskattningar för stela fluider. I Artikel C betraktar vi T2-symmetriska rumstider som uppfyller Einsteins ekvationer för ett icke-linjärt skalärfält. För givna begynnelsedata visar vi global existens och entydighet av lösningar till motsvarande differentialekvationer för all framtid. I det speciella fallet med en konstant potential, en situation som motsvarar ett linjärt skalärfält på en bakgrund med en positiv kosmologisk konstant, undersöker vi i detalj det asymptotiska beteendet mot framtiden. Vi visar att den Kosmiska Inget-Hår-förmodan håller för lösningar som uppfyller en ytterligare a priori uppskattning, en uppskattning som vi visar gäller i T3-Gowdy-symmetri. / <p>QC 20171220</p>