Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2014-10-30T14:24:27Z No. of bitstreams: 2 Dissertação - Roussian Di Ramos Alves Gaioso - 2014.pdf: 6127790 bytes, checksum: 9990f791c0f9abaee7e3e03e4cdc8ee4 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2014-10-30T14:29:29Z (GMT) No. of bitstreams: 2 Dissertação - Roussian Di Ramos Alves Gaioso - 2014.pdf: 6127790 bytes, checksum: 9990f791c0f9abaee7e3e03e4cdc8ee4 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2014-10-30T14:29:29Z (GMT). No. of bitstreams: 2 Dissertação - Roussian Di Ramos Alves Gaioso - 2014.pdf: 6127790 bytes, checksum: 9990f791c0f9abaee7e3e03e4cdc8ee4 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2014-08-08 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / This paper presents a Graphics Processing Unit (GPU) based parallels implementations for the All Pairs Shortest Paths and Transitive Closure problems in graph. The implementations are based on the main sequential algorithms and takes full advantage of the highly multithreaded architecture of current manycore GPUs. Our solutions reduces the communication between CPU and GPU, improves the Streaming Multiprocessors (SMs) utilization, and makes intensive use of coalesced memory access to optimize graph data access. The advantages of the proposed implementations are demonstrated for several graphs randomly generated using the widely known graph library GTgraph. Graphs containing thousands of vertices and different edges densities, varying from sparse to complete graphs, were generated and used in the experiments. Our results confirm that GPU implementations can be competitive even for graph algorithms whose memory accesses and work distribution are both irregular and data-dependent. Keywords / Este trabalho apresenta implementações paralelas baseadas em Graphics Processing Unit (GPU) para os problemas da identificação dos caminhos mínimos entre todos os pares de vértices e do fecho transitivo em um grafo. As implementações são baseadas nos principais algoritmos sequenciais e tiram o máximo proveito da arquitetura multithreaded das GPUs atuais. Nossa solução reduz a comunicação entre a Central Processing Unit (CPU) e a GPU, melhora a utilização dos Streaming Multiprocessors (SMs) e faz um uso intensivo de acesso aglutinado em memória para otimizar o acesso de dados do grafo. As vantagens dessas implementações propostas são demonstradas por vários grafos gerados aleatoriamente utilizando a ferramenta GTgraph. Grafos contendo milhares de vértices foram gerados e utilizados nos experimentos. Nossos resultados confirmam que implementações baseadas em GPU podem ser viáveis mesmo para algoritmos de grafos cujo acessos à memória e distribuição de trabalho são irregulares e causam dependência de dados.

MA (Xitsonga) / Ehansi Ka Senthara ya M. E. R. Mathivha ya Tindzimi ta Afrika Vutshila na Mfuwo / Xikongomelonkulu xa ndzavisiso lowu i ku xopaxopa maendli mo susa ma xiendliwa xin’we eka Xitsonga hi ku kongomisa eka tindlela leti ma tirhaka hatona exivulweni. Xikongomelo lexi xi aviwa hi marhavi manharhu. Rhavi ro sungula ri kongomana na ku xopaxopa maendli mo susa lama paluxaka mukhuva na mbuyelo hi xikongomelo xo kumisisa michumu leyi nga tirhaka tanihi tiagumente ta nhlokomhaka na tiagumente ta swiendliwa, xikan’we na ku lavisisa michumu leyi nga tirhaka tanihi switirho swa maendli mo susa. Rhavi ra vumbirhi rona ri langutana na ku lavisisa maendli mo susa ma xiendliwa xin’we lama paluxaka mukhuva na mbuyelo lama tirheke eswivulweni ma ri na swivulwana swa mahlanganisi swa xivangelo, xikongomelo na xipimelo. Kasi rhavi ra vunharhu ri tirhana no kambisisa tinhlamuselo/mitirho ya xisemantiki leyi nyikiwaka tiagumemnte hi maendli mo susa ma xiendliwa xin’we lama paluxaka mukhuva na mbuyelo. Eka ndzavisiso lowu ku tirhisiwa thiyori ya vunongoti, ku nga thiyori leyi kongomanaka na ndlela leyi vanhu va twisisaka xiswona marito. Mhaka leyi endlekaka eka thiyori leyi, hi leswi vanhu va twisisaka xiswona marito emiehleketweni ya vona eka leswi ma vulaka swona hi ku angarhela. Swiphemu swa nkoka leswi thiyori leyi yi jikajikaka eka swona i nhlokomhaka leyi nga xiendli xa leswi susiwaka, riendli leri hlamuselaka leswi susiwaka na hilaha swi susiwaka hakona, xiendliwa lexi khumbekaka hileswi vuriwaka hi riendli, na xilandzelandzhaku lexi nga vaka ndhawu, xitirho na swin’wana ni swin’wana. Ndzavisiso lowu wu endliwa hi ku landzelela maendlelo ma nkoka, laha ku nga na maendlelo mambirhi mo kongoma ehansi ka wona; ku nga mo tirhisa ntlawa wo karhi wa vavulavuri va Xitsonga lava nga xiyayiya swivulwa leswi mulavisisi a swi vumbeke leswi vaka swi tirhisile maendli mo susa. Mulavisisi u lulamisile papila ra swivutiso leri longoloxeke swivulwa leswi a lavaka leswaku vavulavuri lava va swi xiyayiya ku xiya loko swi twala kumbe swi nga twali na maendlelo ma nxopaxopo wa vundzeni bya tsalwa lama tirhisiwaka ku xopaxopa swivulwa leswi nga tirhisiwa tanihi mahungu ya ndzavisiso lowu. / NRF

Tato práce představuje nové metody pro verifikaci programů pracujících s neomezenými celočíslenými proměnnými, konkrétně metody pro analýzu dosažitelnosti a~konečnosti. Většina těchto metod je založena na akceleračních technikách, které počítají tranzitivní uzávěry cyklů programu. V práci je nejprve představen algoritmus pro akceleraci několika tříd celočíselných relací. Tento algoritmus je až o čtyři řády rychlejší než existující techniky. Z teoretického hlediska práce dokazuje, že uvažované třídy relací jsou periodické a~poskytuje tudíž jednotné řešení prolému akcelerace. Práce dále představuje semi-algoritmus pro analýzu dosažitelnosti celočíselných programů, který sleduje relace mezi proměnnými programu a~aplikuje akcelerační techniky za účelem modulárního výpočtu souhrnů procedur. Dále je v práci navržen alternativní algoritmus pro analýzu dosažitelnosti, který integruje predikátovou abstrakci s accelerací s cílem zvýšit pravděpodobnost konvergence výpočtu. Provedené experimenty ukazují, že oba algoritmy lze úspěšně aplikovat k verifikaci programů, na kterých předchozí metody selhávaly. Práce se rovněž zabývá problémem konečnosti běhu programů a~dokazuje, že tento problém je rozhodnutelný pro několik tříd celočíselných relací. Pro některé z těchto tříd relací je v práci navržen algoritmus, který v polynomiálním čase vypočítá množinu všech konfigurací programu, z nichž existuje nekonečný běh. Tento algoritmus je integrován do metody, která analyzuje konečnost běhů celočíselných programů. Efektivnost této metody je demonstrována na několika netriviálních celočíselných programech.

The purpose of this thesis is to examine idiomatic structures with ki in the ki-wo [transitive verb] and ki-ga [intransitive verb] constructions. It is argued that for Japanese language learners, it is crucial to be able to understand and produce ki idioms, because they are frequently used in everyday speech. There are often misconceptions regarding ki in the West for those who are fans of Japanese culture due to the influence of martial arts and anime, which paint ki as a spiritual energy that can be controlled and developed. However, upon examining the above mentioned idiomatic structures with ki, it is clear that ki can be expressed as both controllable by the subject of ki (transitive), as well as a thing that acts of its own accord and is spontaneous (intransitive). This thesis somewhat corroborates the studies of W. M. Jacobson, Zoe Pei Sui Luk , and Yoshihiko Ikegami by arguing that intransitive constructions are often used in Japanese, and examining both transitive and intransitive expressions with ki is significant to understanding the meanings produced in ki expressions. It is hoped that analyzing 37 transitive and intransitive idiomatic structures with ki will help Japanese language learners not only understand the syntactic and semantic aspects of transitivity in the Japanese language, but also to help these L2 learners conceptualize the abstract noun ki, which can be defined in so many different ways in a dictionary.

Made available in DSpace on 2016-04-28T19:59:04Z (GMT). No. of bitstreams: 1 Flavia Regina Oliveira Leao.pdf: 1078930 bytes, checksum: 82670d39a47c0fa85a8a7818f1fc4e5c (MD5) Previous issue date: 2007-10-04 / Secretaria da Educação do Estado de São Paulo / This dissertative work promotes a stylistic-literary approach between two short stories from the Portuguese Literature, from the nineteenth century  Singularidades de uma rapariga loura, by Eça de Queiroz, and Manuel Maçores, by Trindade Coelho  through the comparative description of the construction of their characters. As they are transitory and transitive between two realities, the romantic and the realistic, we have defined our objectives which consists of differentiating the treatement that is dedicated to them, based on the ficcional techniques used by their respective narrators in their ficccional projects: the manking and the unmasking. In particular, we analyse the role of the transformation of the indirect speech into the direct one, and the lexical choice as a complementary technique, keeping in mind that this analysis led us to the reading of alternatives in the critical space of the relation narrator and character. In the first chapter, studies of Ernesto Da Cal, Wayne Booth, Mikhail Bakhtin and Jean Starobinski, among others, assisted us in presenting the narrator-character discursive play, in Singularidades de uma rapariga loura, short story that keeps in itself the complexity of the structure between being and seeming in the ficcional context in discursive revelation. In the second chapter, we resort to Segolin s contemporary studies, in order to prove the autonomy that the character achieves by means of narrating technique, in Manuel Maçores, a handmade work which revealed the transitivity of the character from Romantism to Realism, by using the critical space in the narrative setting. In the third chapter, with theoretical supporters as Lukács and Barthes, we deal with the differentiation of the language in the composition of the Portuguese realistic short story that favored the drawing of a parallel between the transitive characters in Singularidades de uma rapariga loura and Manuel Maçores. We conclude, therefore, that the operational variations occured in the narrator-character s distance provoke a diversion in the characters voices in a perspective that takes the tale to the platform of a potential educational novel, under a methodological dominance in the act of permutation, which we believe that contributes to a higher level of social singularity of the Portuguese short story in a historical moment of transformation / Este trabalho dissertativo promove uma aproximação estilístico-literária entre dois contos da Literatura Portuguesa, do século XIX  Singularidades de uma rapariga loura, de Eça de Queiroz, e Manuel Maçores, de Trindade Coelho , através da descrição comparativa da construção de suas personagens. Sabendo-as transitórias e transitivas entre duas realidades, a romântica e a realista, definimos nosso objetivo que consiste em diferenciar o tratamento que lhes é dedicado, a partir das técnicas ficcionais utilizadas pelos respectivos narradores em seus projetos ficcionais: o mascaramento e o desvelamento. Em particular, analisamos o papel da transformação do discurso indireto em discurso direto, e a escolha lexical como técnica complementar, sabendo que essa análise nos conduziu à leitura de alternativas no espaço crítico da relação narrador e personagem. No primeiro capítulo, estudos de Ernesto Da Cal, Wayne Booth, Mikhail Bakhtin e Jean Starobinski, entre outros, auxiliaram-nos na apresentação do jogo discursivo narrador-personagem, em Singularidades de uma rapariga loura, conto que reserva em si a complexidade da estruturação entre o ser e o parecer no contexto ficcional em revelação discursiva. No segundo capítulo, recorremos aos estudos contemporâneos de Segolin, para comprovar a autonomia que a personagem logra por meio da técnica do narrar, em Manuel Maçores, trabalho artesanal esse que nos revelou a transitividade da personagem do romantismo para o realismo, pela via do espaço crítico no cenário narrativo. No terceiro capítulo, com suportes teóricos como Lukács e Barthes, lidamos com a diferenciação da linguagem na composição do conto realista português, o que nos favoreceu o traçado de um paralelo entre as personagens transitivas em Singularidades de uma rapariga loura e Manuel Maçores. Concluímos, portanto, que as variações operacionais ocorridas no distanciamento narrador-personagem provocam desvios nas vozes das personagens em uma perspectiva que lança o conto para o estrado de um possível romance de formação, sob uma dominante metodológica em ato de permuta, e que julgamos contribuir para um maior grau de singularização social do conto português em histórico momento de transformação

Cette dissertation se divise en deux parties, distinctes mais connexes, qui sont le reflet de la cotutelle. Nous étudions et résolvons des problèmes concernant d'une part la combinatoire des mots dans un contexte abélien et d'autre part des problèmes de couverture dans des graphes. Chaque question fait l'objet d'un chapitre. En combinatoire des mots, le premier problème considéré s'intéresse à la régularité des suites au sens défini par Allouche et Shallit. Nous montrons qu'une suite qui satisfait une certaine propriété de symétrie est 2-régulière. Ensuite, nous appliquons ce théorème pour montrer que les fonctions de complexité 2-abélienne du mot de Thue--Morse ainsi que du mot appelé ''period-doubling'' sont 2-régulières. Les calculs et arguments développés dans ces démonstrations s'inscrivent dans un schéma plus général que nous espérons pouvoir utiliser à nouveau pour prouver d'autres résultats de régularité. Le deuxième problème poursuit le développement de la notion de mot de retour abélien introduite par Puzynina et Zamboni. Nous obtenons une caractérisation des mots sturmiens avec un intercepte non nul en termes du cardinal (fini ou non) de l'ensemble des mots de retour abélien par rapport à tous les préfixes. Nous décrivons cet ensemble pour Fibonacci ainsi que pour Thue--Morse (bien que cela ne soit pas un mot sturmien). Nous étudions la relation existante entre la complexité abélienne et le cardinal de cet ensemble. En théorie des graphes, le premier problème considéré traite des codes identifiants dans les graphes. Ces codes ont été introduits par Karpovsky, Chakrabarty et Levitin pour modéliser un problème de détection de défaillance dans des réseaux multiprocesseurs. Le rapport entre la taille optimale d'un code identifiant et la taille optimale du relâchement fractionnaire d'un code identifiant est comprise entre 1 et 2 ln(|V|)+1 où V est l'ensemble des sommets du graphe. Nous nous concentrons sur les graphes sommet-transitifs, car nous pouvons y calculer précisément la solution fractionnaire. Nous exhibons des familles infinies, appelées quadrangles généralisés, de graphes sommet-transitifs pour lesquelles les solutions entière et fractionnaire sont de l'ordre |V|^k avec k dans {1/4, 1/3, 2/5}. Le second problème concerne les (r,a,b)-codes couvrants de la grille infinie déjà étudiés par Axenovich et Puzynina. Nous introduisons la notion de 2-coloriages constants de graphes pondérés et nous les étudions dans le cas de quatre cycles pondérés particuliers. Nous présentons une méthode permettant de lier ces 2-coloriages aux codes couvrants. Enfin, nous déterminons les valeurs exactes des constantes a et b de tout (r,a,b)-code couvrant de la grille infinie avec |a-b|>4. Il s'agit d'une extension d'un théorème d'Axenovich. / This dissertation is divided into two (distinct but connected) parts that reflect the joint PhD. We study and we solve several questions regarding on the one hand combinatorics on words in an abelian context and on the other hand covering problems in graphs. Each particular problem is the topic of a chapter. In combinatorics on words, the first problem considered focuses on the 2-regularity of sequences in the sense of Allouche and Shallit. We prove that a sequence satisfying a certain symmetry property is 2-regular. Then we apply this theorem to show that the 2-abelian complexity functions of the Thue--Morse word and the period-doubling word are 2-regular. The computation and arguments leading to these results fit into a quite general scheme that we hope can be used again to prove additional regularity results. The second question concerns the notion of return words up to abelian equivalence, introduced by Puzynina and Zamboni. We obtain a characterization of Sturmian words with non-zero intercept in terms of the finiteness of the set of abelian return words to all prefixes. We describe this set of abelian returns for the Fibonacci word but also for the Thue-Morse word (which is not Sturmian). We investigate the relationship existing between the abelian complexity and the finiteness of this set. In graph theory, the first problem considered deals with identifying codes in graphs. These codes were introduced by Karpovsky, Chakrabarty and Levitin to model fault-diagnosis in multiprocessor systems. The ratio between the optimal size of an identifying code and the optimal size of a fractional relaxation of an identifying code is between 1 and 2 ln(|V|)+1 where V is the vertex set of the graph. We focus on vertex-transitive graphs, since we can compute the exact fractional solution for them. We exhibit infinite families, called generalized quadrangles, of vertex-transitive graphs with integer and fractional identifying codes of order |V|^k with k in {1/4,1/3,2/5}. The second problem concerns (r,a,b)-covering codes of the infinite grid already studied by Axenovich and Puzynina. We introduce the notion of constant 2-labellings of weighted graphs and study them in four particular weighted cycles. We present a method to link these labellings with covering codes. Finally, we determine the precise values of the constants a and b of any (r,a,b)-covering code of the infinite grid with |a-b|>4. This is an extension of a theorem of Axenovich.

In this thesis, the main objects of study are probability measures on the isomorphism classes of countable, connected rooted graphs. An important class of such measures is formed by unimodular measures, which satisfy a certain equation, sometimes referred to as the intrinsic mass transport principle. The so-called law of a finite graph is an example of a unimodular measure. We say that a measure is sustained by a countable graph if the set of rooted connected components of the graph has full measure. We demonstrate several new results involving sustained unimodular measures, and provide thorough arguments for known ones. In particular, we give a criterion for unimodularity on connected graphs, deduce that connected graphs sustain at most one unimodular measure, and prove that unimodular measures sustained by disconnected graphs are convex combinations. Furthermore, we discuss weak limits of laws of finite graphs, and construct counterexamples to seemingly reasonable conjectures.

Cette dissertation se divise en deux parties, distinctes mais connexes, qui sont le reflet de la cotutelle. Nous étudions et résolvons des problèmes concernant d'une part la combinatoire des mots dans un contexte abélien et d'autre part des problèmes de couverture dans des graphes. Chaque question fait l'objet d'un chapitre. En combinatoire des mots, le premier problème considéré s'intéresse à la régularité des suites au sens défini par Allouche et Shallit. Nous montrons qu'une suite qui satisfait une certaine propriété de symétrie est 2-régulière. Ensuite, nous appliquons ce théorème pour montrer que les fonctions de complexité 2-abélienne du mot de Thue--Morse ainsi que du mot appelé ''period-doubling'' sont 2-régulières. Les calculs et arguments développés dans ces démonstrations s'inscrivent dans un schéma plus général que nous espérons pouvoir utiliser à nouveau pour prouver d'autres résultats de régularité. Le deuxième problème poursuit le développement de la notion de mot de retour abélien introduite par Puzynina et Zamboni. Nous obtenons une caractérisation des mots sturmiens avec un intercepte non nul en termes du cardinal (fini ou non) de l'ensemble des mots de retour abélien par rapport à tous les préfixes. Nous décrivons cet ensemble pour Fibonacci ainsi que pour Thue--Morse (bien que cela ne soit pas un mot sturmien). Nous étudions la relation existante entre la complexité abélienne et le cardinal de cet ensemble. En théorie des graphes, le premier problème considéré traite des codes identifiants dans les graphes. Ces codes ont été introduits par Karpovsky, Chakrabarty et Levitin pour modéliser un problème de détection de défaillance dans des réseaux multiprocesseurs. Le rapport entre la taille optimale d'un code identifiant et la taille optimale du relâchement fractionnaire d'un code identifiant est comprise entre 1 et 2 ln(|V|)+1 où V est l'ensemble des sommets du graphe. Nous nous concentrons sur les graphes sommet-transitifs, car nous pouvons y calculer précisément la solution fractionnaire. Nous exhibons des familles infinies, appelées quadrangles généralisés, de graphes sommet-transitifs pour lesquelles les solutions entière et fractionnaire sont de l'ordre |V|^k avec k dans {1/4, 1/3, 2/5}. Le second problème concerne les (r,a,b)-codes couvrants de la grille infinie déjà étudiés par Axenovich et Puzynina. Nous introduisons la notion de 2-coloriages constants de graphes pondérés et nous les étudions dans le cas de quatre cycles pondérés particuliers. Nous présentons une méthode permettant de lier ces 2-coloriages aux codes couvrants. Enfin, nous déterminons les valeurs exactes des constantes a et b de tout (r,a,b)-code couvrant de la grille infinie avec |a-b|>4. Il s'agit d'une extension d'un théorème d'Axenovich. / This dissertation is divided into two (distinct but connected) parts that reflect the joint PhD. We study and we solve several questions regarding on the one hand combinatorics on words in an abelian context and on the other hand covering problems in graphs. Each particular problem is the topic of a chapter. In combinatorics on words, the first problem considered focuses on the 2-regularity of sequences in the sense of Allouche and Shallit. We prove that a sequence satisfying a certain symmetry property is 2-regular. Then we apply this theorem to show that the 2-abelian complexity functions of the Thue--Morse word and the period-doubling word are 2-regular. The computation and arguments leading to these results fit into a quite general scheme that we hope can be used again to prove additional regularity results. The second question concerns the notion of return words up to abelian equivalence, introduced by Puzynina and Zamboni. We obtain a characterization of Sturmian words with non-zero intercept in terms of the finiteness of the set of abelian return words to all prefixes. We describe this set of abelian returns for the Fibonacci word but also for the Thue-Morse word (which is not Sturmian). We investigate the relationship existing between the abelian complexity and the finiteness of this set. In graph theory, the first problem considered deals with identifying codes in graphs. These codes were introduced by Karpovsky, Chakrabarty and Levitin to model fault-diagnosis in multiprocessor systems. The ratio between the optimal size of an identifying code and the optimal size of a fractional relaxation of an identifying code is between 1 and 2 ln(|V|)+1 where V is the vertex set of the graph. We focus on vertex-transitive graphs, since we can compute the exact fractional solution for them. We exhibit infinite families, called generalized quadrangles, of vertex-transitive graphs with integer and fractional identifying codes of order |V|^k with k in {1/4,1/3,2/5}. The second problem concerns (r,a,b)-covering codes of the infinite grid already studied by Axenovich and Puzynina. We introduce the notion of constant 2-labellings of weighted graphs and study them in four particular weighted cycles. We present a method to link these labellings with covering codes. Finally, we determine the precise values of the constants a and b of any (r,a,b)-covering code of the infinite grid with |a-b|>4. This is an extension of a theorem of Axenovich.

Cette thèse traite des phénomènes liés aux mathématiques financières et économiques. Elle est composée de deux sujets de recherche indépendants. La première partie est consacrée à deux contributions au problème de Merton. Pour commencer, nous étudions le problème de l’investissement optimal et de la consommation de Merton dans le cas de marchés discrets dans un horizon infini. Nous supposons qu’il y a des frictions sur les marchés en raison de la perte due aux échanges financières. Ces frictions sont modélisées par des fonctions de pénalités non linéaires où les modèles classiques de coût de transactions étudiés par Magill et Constantinides [31] et les marchés illiquides étudiés par Cetin, Jarrow et Protter dans [6] sont inclus dans cette formulation. Dans ce contexte, la région de solvabilité est définie en tenant compte de cette fonction de pénalité et chaque investisseur doit maximiser son utilité, dérivée de la consommation. Nous donnons la programmation dynamique du modèle et nous prouvons l’existence et l’unicité de la fonction valeur. Des stratégies optimales d’investissement et de consommation sont également construites. Ensuite, nous étendons le modèle de Merton à un problème à plusieurs investisseurs. Notre approche consiste à construire un modèle d’équilibre général déterministe dynamique. Nous prouvons ensuite l’existence d’un équilibre du problème qui est un ensemble de contrôles composés de processus de consommation et de portefeuille, ainsi que les processus de prix qui en découlent afin que la politique de consommation de chaque investisseur maximise son profil. Les résultats obtenus dans cette partie étendent principalement les résultats récemment obtenus par Chebbi et Soner [10] ainsi qu’aux d’autres résultats obtenus dans ce cadre dans la littérature. Dans la deuxième partie, nous traitons le problème de l’existence d’un équilibre d’une économie de production avec des ensembles d’allocations réalisables non-bornés où les consommateurs peuvent avoir des préférences non-transitives non-complètes. Nous introduisons une propriété asymptotique sur les préférences pour les consommations réalisables afin de prouver l’existence d’un équilibre. Nous montrons que cette condition est vraie lorsque l’ensemble des allocations réalisables est compact ou aussi lorsque les préférences sont représentées par des fonctions d’utilité dans le cas où l’ensemble des niveaux d’utilité rationnels individuels réalisables est compact. Cette hypothèse généralise la condition de CPP de Allouch [1] et couvre l’exemple de Page et al. [40] lorsque les niveaux d’utilité disponibles définis ne sont pas compacts. Nous étendons donc les résultats existants dans la littérature avec des ensembles réalisables non bornés de deux façons en ajoutant la production et en prenant en compte des préférences générales. / This PhD dissertation studies two independent research topics dealing with phenomena issues from financial and economic mathematics.This thesis is organized in two parts. The first part is devoted to two contributions tothe Merton problem. First, we investigate the problem of optimal investment and consumption of Merton in the case of discrete markets in an infinite horizon. We suppose that there is frictions in the markets due to loss in trading. These frictions are modeled through nonlinear penalty functions and the classical transaction cost studied by Magill and Constantinides in [31] and illiquidity models studied by Cetin, Jarrow and Protter in [6] are included in this formulation. In this context, the solvency region is defined taking into account this penalty function and every investigator have to maximize his utility, that is derived from consumption, in this region. We give the dynamic programming ofthe model and we prove the existence and uniqueness of the value function. Optimalinvestment and consumption strategies are constructed as well. We second extend the Merton model to a multi-investors problem. Our approach is to construct a dynamic deterministic general equilibrium model. We then provide the existence of equilibrium of the problem which is a set of controls that is composed of consumption and portfolio processes, as well as the resulting price processes so that each investor’s consumption policy maximizes his lifetime expected. The results obtained in this part extends mainly the results recently obtained by Chebbi and Soner [10] and other corresponding results in the litterature.The second part of this thesis deals with the problem of the existence of an equilibrium of a production economy with unbounded attainable allocations sets where the consumers may have non-complete non-transitive preferences. We introduce an asymptotic property on preferences for the attainable consumptions in order to prove the existence of an equilibrium. We show that this condition holds true if the set of attainable allocations is compact or, when preferences are representable by utility functions, if the set of attainable individually rational utility levels is compact. This assumption generalizes the CPP condition of Allouch [1] and covers the example of Page et al. [40] when the attainable utility levels set is not compact. So we extend the previous existence results with unbounded attainable sets in two ways by adding a production sector and considering general preferences.

In this thesis, the main objects of study are probability measures on the isomorphism classes of countable, connected rooted graphs. An important class of such measures is formed by unimodular measures, which satisfy a certain equation, sometimes referred to as the intrinsic mass transport principle. The so-called law of a finite graph is an example of a unimodular measure. We say that a measure is sustained by a countable graph if the set of rooted connected components of the graph has full measure. We demonstrate several new results involving sustained unimodular measures, and provide thorough arguments for known ones. In particular, we give a criterion for unimodularity on connected graphs, deduce that connected graphs sustain at most one unimodular measure, and prove that unimodular measures sustained by disconnected graphs are convex combinations. Furthermore, we discuss weak limits of laws of finite graphs, and construct counterexamples to seemingly reasonable conjectures.