Diese Arbeit untersucht vollständige Zeichenkettenfrequenzverteilungen natürlichsprachiger Texte auf ihren linguistischen und anwendungsbezogenen Gehalt. Im ersten Teil wird auf dieser Datengrundlage ein unüberwachtes Lernverfahren entwickelt, das Texte in Morpheme zerlegt. Die Zerlegung geht von der Satzebene aus und verwendet jegliche vorhandene Kontextinformation. Es ergibt sich ein sprachunabhängiger Algorithmus, der die gefundenen Morpheme teilweise zu Baumstrukturen zusammenordnet. Die Evaluation der Ergebnisse mit Hilfe statistischer Modelle ermöglicht die Identifizierung auch kleiner Performanzunterschiede. Diese sind einer linguistischen Interpretation zugänglich. Der zweite Teil der Arbeit besteht aus stilometrischen Untersuchungen anhand eines Textähnlichkeitsmaßes, das ebenfalls auf vollständigen Zeichenkettenfrequenzen beruht. Das Textähnlichkeitsmaß wird in verschiedenen Varianten definiert und anhand vielfältiger stilometrischer Fragestellungen und auf Grundlage unterschiedlicher Korpora ausgewertet. Dabei ist ein wiederholter Vergleich mit der Performanz bisheriger Forschungsansäzte möglich. Die Performanz moderner Maschinenlernverfahren kann mit dem hier vorgestellten konzeptuell einfacheren Verfahren reproduziert werden. Während die Segmentierung in Morpheme ein lokaler Vorgang ist, besteht Stilometrie im globalen Vergleich von Texten. Daher bietet die Untersuchung dieser zwei unverbunden scheinenden Fragestellungen sich gegenseitig ergänzende Perspektiven auf die untersuchten Häufigkeitsdaten. Darüber hinaus zeigt die Diskussion der rezipierten Literatur zu beiden Themen ihre Verbindungen durch verwandte Konzepte und Denkansätze auf. Aus der Gesamtheit der empirischen Untersuchungen zu beiden Fragestellungen kann abgeleitet werden, dass den längeren und damit selteneren Zeichenketten wesentlich mehr Informationsgehalt innewohnt, als in der bisherigen Forschung gemeinhin angenommen wird. / This thesis investigates the linguistic and application specific content of complete character substring frequency distributions of natural language texts. The first part develops on this basis an unsupervised learning algorithm for segmenting text into morphemes. The segmentation starts from the sentence level and uses all available context information. The result is a language independent algorithm which arranges the found morphemes partly into tree like structures. The evaluation of the output using advanced statistical modelling allows for identifying even very small performance differences. These are accessible to linguistic interpretation. The second part of the thesis consists of stylometric investigations by means of a text similarity measure also rooted in complete substring frequency statistics. The similarity measure is defined in different variants and evaluated for various stylometric tasks and on the basis of diverse corpora. In most of the case studies the presented method can be compared with publicly available performance figures of previous research. The high performance of modern machine learning methods is reproduced by the considerably simpler algorithm developed in this thesis. While the segmentation into morphemes is a local process, stylometry consists in the global comparison of texts. For this reason investigating of these two seemingly unconnected problems offers complementary perspectives on the explored frequency data. The discussion of the recieved litarature concerning both subjects additionally shows their connectedness by related concepts and approaches. It can be deduced from the totality of the empirical studies on text segmentation and stylometry conducted in this thesis that the long and rare character sequences contain considerably more information then assumed in previous research.

Die Strukturen in Lösung dreier unterschiedlich modifizierter DNA Doppelstränge wurden mittels NMR Spektroskopie gelöst. Sie alle besitzen polare Sonden im Zentrum der Helix, welche sensitiv für die nähere Umgebung sind. Ihr Schmelzverhalten wurde mit Hilfe einer neuen Methode charakterisiert, welche komplette Absorptionsspektren in Kombination mit Singularwertzerlegung (SVD) nutzt. Letztere erlaubt die Analyse der Spektren als Ganzes, die notwendig ist um der Blauverschiebung des Sondensignals zu folgen, welche durch die zuvor genannte Sensitivität zur Umgebung verursacht wird. Auf diese Weise kann der Schmelzprozess des Duplex lokal und global beschrieben werden. Die erste Modifikation, 2-Hydroxy-7-Carboxyfluoren (HCF), wurde gegenüber einer abasischen Seite platziert, um sterische Spannungen zu vermeiden. Die NMR Spektroskopie deckte zwei gleichverteilte Konformationen auf, da die Rotation des HCF Chromophors nur durch die Stapelwechselwirkung innerhalb der Helix unterbunden wird. Der zweite Doppelstrang enthält ein über R-Glycerol gebundenes 6-Hydroxychinolinium (6HQ) gegenüber Cytosin. Der Einbau von 6HQ als Mononukleotid einer Glykolnukleinsäure (GNA) ist ein strukturelles Alleinstellungsmerkmal. Bisher sind nur Kristallstrukturen von vollständiger GNA bekannt, daher ist die Struktur in Lösung dieses Doppelstranges von generellem Interesse. Die geringe Größe von R-Glycerol stört das Rückgrat des 6HQ-Stranges, welche eine von der helikalen Achse abweichende Stapelachse für die drei zentralen Basen verursacht. Die letzte Modifikation ist ein künstliches Basenpaar bestehend aus 4-Aminophthalimid (4AP) und 2,4-Diaminopyrimidin (DAP). Anstatt der gewünschten drei Wasserstoffbrücken wurden zwei Strukturen, die entweder eine oder zwei Wasserstoffbrücken beinhalten, beobachtet, welche durch die Verbindung von 4AP zur 2’-Deoxyribofuranose erklärt werden können. / The solution structures of three differently modified DNA double strands were solved by NMR spectroscopy. They all incorporate polarity probes in the center of the helix that are sensitive to the immediate environment. Their melting behavior was characterized by a new method that utilizes complete absorption spectra in combination with Singular Value Decomposition (SVD). The latter allows to analyze the spectra in their entirety, which is required to follow the blue shift of the probe signal that is caused by the aforementioned sensitivity to the environment. In this way the duplex melting process is characterized in local and global terms.The first modification, 2-hydroxy-7-carboxyfluorene (HCF), is placed opposite an abasic site to avoid steric strain. NMR spectroscopy revealed two equally distributed conformations, since rotation of the HCF chromophore is only hindered by stacking interactions inside the helix. The second double strand comprises R-glycerol linked 6-hydroxyquinolinium (6HQ) opposite cytosine. The incorporation of 6HQ as glycol nucleic acid (GNA) mononucleotide is a unique structural feature. Until now, only crystal structures of full GNA backbone duplexes are known, so the solution structure of this double strand is of general interest. The small size of R-glycerol disturbs the backbone of the 6HQ strand, which causes a stacking axis that differs from the helical long axis for the three central bases. The last modification is an artificial base pair made of 4-aminophthalimide (4AP) and 2,4-diaminopyrimidine (DAP). Instead of the desired three hydrogen bonds, two structures containing either a single or two hydrogen bonds are observed that can be explained by the linkage of 4AP to 2’-deoxyribofuranose.

Este trabalho analisa três estratégias de hedge de opção, buscando identificar a importância da escolha da estratégia para a obtenção de um bom desempenho do hedge. O conceito de hedge é analisado de forma retrospectiva e uma teoria geral de hedge é apresentada. Em seguida são descritos alguns estudos comparativos de desempenho de estratégias de hedge de opção e suas metodologias de implementação. Para esta análise comparativa são selecionadas três estratégias de hedge de opção de compra do tipo européia: a primeira utiliza o modelo Black-Scholes-Merton de precificação de opções, a segunda utiliza uma solução de programação dinâmica para hedge dinâmico multiperiódico e a terceira utiliza um modelo GARCH para precificação de opções. As estratégias são comentadas e comparadas do ponto de vista de suas premissas teóricas e por meio de testes comparativos de desempenho. O desempenho das estratégias é comparado sob uma perspectiva dinâmicamente ajustada, multiperiódica e autofinanciável. Os dados para comparação de desempenho são gerados por simulação e o desempenho é avaliado pelos erros absolutos médios e erros quadráticos médios, resultantes na carteira de hedge. São feitas ainda considerações a respeito de alternativas de estimação e suas implicações no desempenho das estratégias. / This work analyzes three option hedging strategies, to identify the importance of choosing a strategy in order to achieve a good hedging performance. A retrospective analysis of the concept of hedging is conducted and a general hedging theory is presented. Following, some comparative papers of hedging performance and their implementation methodologies are described. For the present comparative analysis, three hedging strategies for European options have been selected: the first one based on the Black-Scholes-Merton model for option pricing, the second one based on a dynamic programming solution for dynamic multiperiod hedging and the third one based on a GARCH model for option pricing. The strategies are compared under their theoric premisses and through comparative performance testes. The performances of the strategies are compared under a dynamically adjusted multiperiodic and self-financing perspective. Data for performance comparison are generated by simulation and performance is evaluated by mean absolute errors and mean squared errors resulting on the hedging portfolio. An analysis is also done regarding estimation approaches and their implications over the performance of the strategies.

<p>The research work carried out in this thesis is aimed&nbsp;&nbsp; at fuzzifying algebraic and relational structures in the framework of Ω-sets, where Ω is a complete lattice.<br />Therefore we attempt to synthesis universal algebra and fuzzy set theory. Our&nbsp; investigations of Ω-algebraic structures are based on Ω-valued equality, satisability of identities and cut techniques. We introduce Ω-algebras, Ω-valued congruences,&nbsp; corresponding quotient&nbsp; Ω-valued-algebras and&nbsp; Ω-valued homomorphisms and we investigate connections among these notions. We prove that there is an Ω-valued homomorphism from an Ω-algebra to the corresponding quotient Ω-algebra. The kernel<br />of an Ω-valued homomorphism is an Ω-valued congruence. When dealing with cut structures, we prove that an Ω-valued homomorphism determines classical homomorphisms among the corresponding quotient structures over cut&nbsp; subalgebras. In addition, an&nbsp; Ω-valued congruence determines a closure system of classical congruences on cut subalgebras. In addition, identities are preserved under Ω-valued homomorphisms. Therefore in the framework of Ω-sets we were able to introduce Ω-attice both as an ordered and algebraic structures. By this Ω-poset is defined as an Ω-set equipped with&nbsp; Ω-valued order which is&nbsp; antisymmetric with respect to the corresponding Ω-valued equality. Thus defining the notion of pseudo-infimum and pseudo-supremum we obtained the definition of Ω-lattice as an ordered structure. It is also defined that the an Ω-lattice as an algebra is a bi-groupoid equipped with an Ω-valued equality fulfilling some particular lattice Ω-theoretical formulas. Thus using axiom of choice we proved that the two approaches are equivalent. Then we also introduced the notion of complete Ω-lattice based on Ω-lattice. It was defined as a generalization of the classical complete lattice.<br />We proved results that characterizes Ω-structures and many other interesting results.<br />Also the connection between Ω-algebra and the notion of weak congruences is presented.<br />We conclude with what we feel are most interesting areas for future work.</p> / <p>Tema ovog rada je fazifikovanje algebarskih i relacijskih struktura u okviru omega- skupova, gdeje Ω kompletna mreza. U radu se bavimo sintezom oblasti univerzalne algebre i teorije rasplinutih (fazi) skupova. Na&scaron;a istraživanja omega-algebarskih struktura bazirana su na omega-vrednosnoj jednakosti,zadovoljivosti identiteta i tehnici rada sa nivoima. U radu uvodimo omega-algebre,omega-vrednosne kongruencije, odgovarajuće omega-strukture, i omega-vrednosne homomorfizme i istražujemo veze izmedju ovih pojmova. Dokazujemo da postoji Ω -vrednosni homomorfizam iz Ω -algebre na odgovarajuću količničku Ω -algebru. Jezgro Ω -vrednosnog homomorfizma je Ω- vrednosna kongruencija. U vezi sa nivoima struktura, dokazujemo da Ω -vrednosni homomorfizam odredjuje klasične homomorfizme na odgovarajućim količničkim strukturama preko nivoa podalgebri. Osim toga, Ω-vrednosna kongruencija odredjuje sistem zatvaranja klasične kongruencije na nivo podalgebrama. Dalje, identiteti su očuvani u Ω- vrednosnim homomorfnim slikama.U nastavku smo u okviru Ω-skupova uveli Ω-mreže kao uredjene skupove i kao algebre i dokazali ekvivalenciju ovih pojmova. Ω-poset je definisan kao Ω -relacija koja je antisimetrična i tranzitivna u odnosu na odgovarajuću Ω-vrednosnu jednakost. Definisani su pojmovi pseudo-infimuma i pseudo-supremuma i tako smo dobili definiciju Ω-mreže kao uredjene strukture. Takodje je definisana Ω-mreža kao algebra, u ovim kontekstu nosač te strukture je bi-grupoid koji je saglasan sa Ω-vrednosnom jednako&scaron;ću i ispunjava neke mrežno-teorijske formule. Koristeći aksiom izbora dokazali smo da su dva pristupa ekvivalentna. Dalje smo uveli i pojam potpune Ω-mreže kao uop&scaron;tenje klasične potpune mreže. Dokazali smo jo&scaron; neke rezultate koji karakteri&scaron;u Ω-strukture.Data je i veza izmedju Ω-algebre i pojma slabih kongruencija.Na kraju je dat prikaz pravaca daljih istrazivanja.</p>

<p>In this work a comparative analysis of several approaches to fuzzy algebraic structures and comparison of previous approaches to the recent one developed at University of&nbsp; Novi Sad has been done. Special attention is paid to reducts and expansions of algebraic structures in fuzzy settings. Besides mentioning all the relevant algebras and properties developed in this setting, particular new algebras and properties are developed and investigated. Some new structures, in particular Omega Boolean algebras, Omega Boolean lattices and Omega Boolean rings are developed in the framework of omega structures. Equivalences among these structures are elaborated in details. Transfers from Omega groupoids to Omega groups and back are demonstrated. Moreover, normal subgroups are introduced in a particular way. Their connections to congruences are elaborated in this settings. Subgroups, congruences and normal subgroups are investigated for Ω-groups. These are latticevalued algebraic structures, defined on crisp algebras which are not necessarily groups, and in which the classical equality is replaced by a lattice-valued one. A normal Ω-subgroup is defined as a particular class in an Ω-congruence. Our main result is that the quotient groups over cuts of a normal Ω- subgroup of an Ω-group G, are classical normal subgroups of the corresponding quotient groups over G. We also describe the minimal normal Ω-subgroup of an Ω-group, and some other constructions related to Ω-valued congruences.Further results that are obtained are theorems that connect various approaches of fuzzy algebraic structures. A special notion of a generalized lattice valued Boolean algebra is introduced. The universe of this structure is an algebra with two binary, an unary and two nullary operations (as usual), but which is not a crisp Boolean algebra in general. A main element in our approach is a fuzzy&nbsp; quivalence relation such that the Boolean algebras identities are approximately satisfied related to the considered fuzzy equivalence. Main properties of the new introduced notions are proved, and a connection with the notion of a structure of a generalized fuzzy lattice is provided.</p> / <p>Ovaj rad bavi se komparativnom analizom različitih pristupa rasplinutim (fazi) algebarskim strukturama i odnosom tih struktura sa odgovarajućim klasičnim&nbsp;&nbsp; algebrama. Posebna pažnja posvećena je poredenju postojećih pristupa ovom&nbsp;&nbsp; problemu sa novim tehnikama i pojmovima nedavno razvijenim na Univerzitetu u Novom Sadu. U okviru ove analize, proučavana su i pro&scaron;irenja kao i redukti algebarskih struktura u kontekstu rasplinutih algebri. Brojne važne konkretne algebarske strukture istraživane su u ovom kontekstu, a neke nove uvedene su i ispitane. Bavili smo se detaljnim istrazivanjima Ω-grupa, sa stanovista kongruencija, normalnih podgrupa i veze sa klasicnim grupama. Nove strukture koje su u radu uvedene u posebnom delu, istrazene su sa aspekta svojstava i medusobne ekvivalentnosti. To su Ω-Bulove algebre, kao i odgo-varajuce mreže i Bulovi prsteni. Uspostavljena je uzajamna ekvivalentnost tih struktura analogno odnosima u klasičnoj algebri. U osnovi na&scaron;e konstrukcije su mrežno vrednosne algebarske strukture denisane na klasičnim algebrama koje ne zadovoljavaju nužno identitete ispunjene na odgovarajucim klasičnim strukturama (Bulove algebre, prsteni, grupe itd.), već su to samo algebre istog tipa. Klasična jednakost zamenjena je posebnom kompatibilnom rasplinutom (mrežno-vrednosnom) relacijom ekvivalencije. Na navedeni nacin i u cilju koji je u osnovi teze (poredenja sa postojecim pristupima u ovoj naucnoj oblasti) proucavane su (vec denisane)&nbsp; Ω-grupe. U nasim istraživanju uvedene su odgovarajuće normalne podgrupe. Uspostavljena je i istražena njihova veza sa Ω-kongruencijama. Normalna podgrupa&nbsp; Ω-grupe definisana je kao posebna&nbsp; klasa Ω-kongruencije. Jedan od rezultata u ovom delu je da su količničke grupe definisane pomocu nivoa Ω-jednakosti klasične normalne podgrupe odgovarajućih količničkih podgrupa polazne&nbsp; -grupe. I u ovom slučaju osnovna&nbsp; struktura na kojoj je denisana Ω-grupa je grupoid, ne nužno grupa. Opisane su osobine najmanje normalne podgrupe u terminima Ω-kongruencija, a date su i neke konstrukcije&nbsp; Ω-kongruencija.</p><p>Rezultati koji su izloženi u nastavku povezuju različite pristupe nekim mrežno- vrednosnim strukturama. Ω-Bulova algebra je uvedena na strukturi sa dve binarne, unarnom i dve nularne operacije, ali za koju se ne zahteva ispunjenost klasičnih aksioma. Identiteti za Bulove algebre važe kao mrežno-teoretske formule u odnosu na mrežno-vrednosnu jednakost. Klasicne Bulove algebre ih zadovoljavaju, ali obratno ne vazi: iz tih formula ne slede standardne aksiome za Bulove algebre. Na analogan nacin uveden je i&nbsp; Ω-Bulov prsten. Glavna svojstva ovih struktura su opisana. Osnovna osobina je da se klasične Bulove algebre odnosno Bulovi prsteni javljaju kao količničke strukture na nivoima Ω -jednakosti. Veza ove strukture sa Ω-Bulovom mrežom je pokazana.</p><p>Kao ilustracija ovih istraživanja, u radu je navedeno vi&scaron;e primera.</p>

This item contains the agenda, minutes, and attachments for the Faculty Senate meeting on this date. There may be additional materials from the meeting available at the Faculty Center.

This research project explores whether the delivery of positive psychology interventions in the workplace through an employee assistance program (EAP) can improve employees’ authentic happiness/flourishing as well as decrease symptoms of depression. A small convenience sample of 13 Manitoba public school educators accessing employee assistance were recruited for a quasi-experimental research design. Nine participants were randomly assigned to the experimental group and the remaining participants assigned to the control. Experimental group members participated in a six session psychoeducational, experiential, and process-oriented positive psychotherapy group that met once a week over six weeks. Experimental group participants’ scores on the authentic happiness/flourishing measure increased by a statistically significant 9% and depression scores decreased by a statistically significant 45% from pre-intervention to one month post-intervention. The study’s findings therefore provide promising confirmation that positive psychology interventions delivered through EAPs can make a meaningful difference as both secondary prevention and primary enhancement strategies in the workplace.

Les maladies cardio-vasculaires sont la première cause de mortalité dans le monde. L’hypertrophie cardiaque est un processus de remodelage provoqué par une surcharge de travail du muscle cardiaque afin de mieux répondre à la demande de l’organisme. Bien que bénéfique à court terme, une hypertrophie trop accentuée conduira à long terme, à une insuffisance cardiaque. L’hypertrophie est associée à un remodelage électrique qui conduit généralement à un allongement du potentiel d’action, une des causes des arythmies ventriculaires et de la mort subite. Généralement, le mécanisme causal est la fibrillation ventriculaire, un trouble du rythme irréversible dont les mécanismes sont complexes et méconnus. Si les conséquences fonctionnelles in vitro des mutations génétiques ou du remodelage ionique sont relativement simples à étudier ou à prévoir, leur rôle dans les mécanismes des troubles du rythme in vivo sont plus difficiles à appréhender. Parmi les nombreux modèles animaux développés pour la recherche sur les troubles du rythme, la souris est de plus en plus utilisée en raison de notre capacité à muter, invalider ou sur-exprimer les gènes d'intérêt chez ces animaux. L'objectif de mon travail de thèse était de mieux comprendre le rôle des canaux ioniques en physiopathologie cardiaque, en particulier dans la survenue des troubles du rythme in vivo. Ces travaux ont permis d'améliorer notre connaissance du rôle des anomalies génétiques impliquant des canaux ioniques et du remodelage ionique dans la physiopathologie des troubles du rythme et pourrait ainsi ouvrir de nouvelles perspectives thérapeutiques dans le traitement anti-remodelage cardiaque et la prévention de la mort subite. / Cardiovascular disease is the leading cause of death in the world each year. If no action is taken to improve cardiovascular health and current trends continue, WHO estimates that 25% more healthy life years will be lost to cardiovascular disease globally by 2020. Cardiac hypertrophy is the consequence of an excessive workload of the heart muscle leading to cardiac remodeling process. As the workload increases, the ventricular walls grow thicker, lose elasticity and eventually may fail to pump with as much force as a healthy heart. Furthermore, hypertrophied myocardium is not physiologically normal and may confer a predisposition to potentially fatal arrhythmias. Generally, the causal mechanism is ventricular fibrillation, a cardiac rhythm disorder which is irreversible but the pathophysiological mechanisms are complex and poorly understood. The functional consequences of mutations or ionic remodeling are relatively simple to study in vitro, but their role in the pathophysiology of arrhythmias in vivo is more difficult to grasp. Among the different animal models developed in cardiac arrhythmias research, the mouse is increasingly used because of our ability to mutate, knock-out or over-express genes of interest. The objective of my thesis was to study the role of ion channels in physiology as well as cardiac pathophysiology, particularly in the involvement of the occurrence of cardiac arrhythmias in vivo. This thesis will improve our understanding of the role of genetic abnormalities involving ionic remodeling in the pathogenesis of the heart and may also open new therapeutic perspectives in the treatment of cardiac remodeling as well as sudden cardiac death. / Thèse en cotutelle avec Université de Nantes - Pays de La Loire - France (2005-2010)

This research project explores whether the delivery of positive psychology interventions in the workplace through an employee assistance program (EAP) can improve employees’ authentic happiness/flourishing as well as decrease symptoms of depression. A small convenience sample of 13 Manitoba public school educators accessing employee assistance were recruited for a quasi-experimental research design. Nine participants were randomly assigned to the experimental group and the remaining participants assigned to the control. Experimental group members participated in a six session psychoeducational, experiential, and process-oriented positive psychotherapy group that met once a week over six weeks. Experimental group participants’ scores on the authentic happiness/flourishing measure increased by a statistically significant 9% and depression scores decreased by a statistically significant 45% from pre-intervention to one month post-intervention. The study’s findings therefore provide promising confirmation that positive psychology interventions delivered through EAPs can make a meaningful difference as both secondary prevention and primary enhancement strategies in the workplace.

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.