Le travail qui suit comporte quatre chapitres : le premier est centré autour de la propriété de mélange faible pour les échanges d'intervalles et flots de translation. On y présente des résultats obtenus avec Artur Avila qui renforcent des résultats précédents dus à Artur Avila et Giovanni Forni. Le deuxième chapitre est consacré à un travail en commun avec Zhiyuan Zhang et concerne les propriétés d'ergodicité et d'accessibilité stables pour des systèmes partiellement hyperboliques de dimension centrale au moins égale à deux. On montre que sous des hypothèses de cohérence dynamique, center bunching et pincement fort, la propriété d'accessibilité stable est dense en topologie C^r, r>1, et même prévalente au sens de Kolmogorov. Dans le troisième chapitre, on expose les résultats d'un travail réalisé en collaboration avec Julie Déserti, consacré à l'étude d'une famille à un paramètre d'automorphismes polynomiaux de C^3 ; on montre que de nouveaux phénomènes apparaissent par rapport à ce qui était connu dans le cas de la dimension deux. En particulier, on étudie les vitesses d'échappement à l'infini, en montrant qu'une transition s'opère pour une certaine valeur du paramètre. Le dernier chapitre est issu d'un travail en collaboration avec Jiangong You, Zhiyan Zhao et Qi Zhou ; on s'intéresse à des estimées asymptotiques sur la taille des trous spectraux des opérateurs de Schrödinger quasi-périodiques dans le cadre analytique. On obtient des bornes supérieures exponentielles dans le régime sous-critique, ce qui renforce un résultat précédent de Sana Ben Hadj Amor. Dans le cas particulier des opérateurs presque Mathieu, on montre également des bornes inférieures exponentielles, qui donnent des estimées quantitatives en lien avec le problème dit "des dix Martinis". Comme conséquences de nos résultats, on présente des applications à l'homogénéité du spectre de tels opérateurs ainsi qu'à la conjecture de Deift. / The following work contains four chapters: the first one is centered around the weak mixing property for interval exchange transformations and translation flows. It is based on the results obtained together with Artur Avila which strengthen previous results due to Artur Avila and Giovanni Forni. The second chapter is dedicated to a joint work with Zhiyuan Zhang, in which we study the properties of stable ergodicity and accessibility for partially hyperbolic systems with center dimension at least two. We show that for dynamically coherent partially hyperbolic diffeomorphisms and under certain assumptions of center bunching and strong pinching, the property of stable accessibility is dense in C^r topology, r>1, and even prevalent in the sense of Kolmogorov. In the third chapter, we explain the results obtained together with Julie Déserti on the properties of a one-parameter family of polynomial automorphisms of C^3; we show that new behaviours can be observed in comparison with the two-dimensional case. In particular, we study the escape speed of points to infinity and show that a transition exists for a certain value of the parameter. The last chapter is based on a joint work with Jiangong You, Zhiyan Zhao and Qi Zhou; we get asymptotic estimates on the size of spectral gaps for quasi-periodic Schrödinger operators in the analytic case. We obtain exponential upper bounds in the subcritical regime, which strengthens a previous result due to Sana Ben Hadj Amor. In the particular case of almost Mathieu operators, we also show exponential lower bounds, which provides quantitative estimates in connection with the so-called "Dry ten Martinis problem". As consequences of our results, we show applications to the homogeneity of the spectrum of such operators, and to Deift's conjecture.

Dans cette thèse, nous nous intéressons à l'arithmétique de certains corps de fonctions. Nous cherchons à établir dans un premier temps des théorèmes de dualité arithmétique sur ces corps, pour les appliquer ensuite à l'étude des points rationnels sur certaines variétés algébriques. Dans les trois premiers chapitres, nous travaillons sur le corps des fonctions d'une courbe sur un corps local supérieur (comme Qp, Qp((t)), C((t)) ou C((t))((u))). Dans le premier chapitre, nous établissons sur un tel corps des théorèmes de dualité arithmétique « à la Poitou-Tate » pour les modules finis, les tores, et même pour certains complexes de tores. Nous montrons aussi l'existence, sous certaines hypothèses, de certaines portions des suites exactes de Poitou-Tate correspondantes. Ces résultats sont appliqués dans le deuxième chapitre à l'étude du principe local-global pour les algèbres simples centrales, de l'approximation faible pour les tores, et des obstructions au principe local-global pour les torseurs sous des groupes linéaires connexes. Dans le troisième chapitre, nous nous penchons sur les variétés abéliennes et établissons des théorèmes de dualité arithmétique « à la Cassels-Tate ». Cela demande aussi de mener une étude fine des variétés abéliennes sur les corps locaux supérieurs. Dans le quatrième et dernier chapitre, nous travaillons sur les corps des fractions de certaines algèbres locales normales de dimension 2 (typiquement C((x, y)) ou Fp((x, y))). Nous établissons d'abord un théorème de dualité en cohomologie étale « à la Artin-Verdier » dans ce contexte. Cela nous permet ensuite de montrer des théorèmes de dualité arithmétique en cohomologie galoisienne « à la Poitou-Tate » pour les modules finis et les tores. Nous appliquons finalement ces résultats à l'étude de l'approximation faible pour les tores et des obstructions au principe local-global pour les torseurs sous des groupes linéaires connexes. / In this thesis, we are interested in the arithmetic of some function fields. We first want to establish arithmetic duality theorems over those fields, in order to apply them afterwards to the study of rational points on algebraic varieties. In the first three chapters, we work on the function field of a curve defined over a higher-dimensional local field (such as Qp, Qp((t)), C((t)) or C((t))((u))). In the first chapter, we establish "Poitou-Tate type" arithmetic duality theorems over such fields for finite modules, tori and even some complexes of tori. We also prove the existence, under some hypothesis, of parts of the corresponding Poitou-Tate exact sequences. These results are applied in the second chapter to the study of the local-global principle for central simple algebras, of weak approximation for tori, and of obstructions to local-global principle for torsors under connected linear algebraic groups. In the third chapter, we are interested in abelian varieties and we establish "Cassels-Tate type" arithmetic duality theorems. To do so, we also need to carry out a precise study of abelian varieties over higher-dimensional local fields. In the fourth and last chapter, we work on the field of fractions of some 2-dimensional normal local algebras (such as C((x, y)) or Fp((x, y))). We first establish in this context an "Artin-Verdier type" duality theorem in étale cohomology. This allows us to prove "Poitou-Tate type" arithmetic duality theorems in Galois cohomology for finite modules and tori. In the end, we apply these results to the study of weak approximation for tori and of obstructions to local-global principle for torsors under connected linear algebraic groups.

Durant les dernières décennies, la désintégration induite par une boucle $b o sgamma$, a attiré beaucoup d'attention à cause de sa sensibilité potentielle à la nouvelle physique. Dans le model standard, les transitions $b o sgamma_{L(R)}$ et $overline{b} o overline{s}gamma_{R(L)}$ sont proportionnelles aux coefficients de Wilson $C_7(C'_7)$.La désintégration $B o Kpipigamma$ offre à travers l'analyse angulaire un observable P impaire ($lambda$) et à traversle mélange $B-overline{B}$ un observable CP impaire ($S_{ho Kgamma}$) tous deux étants sensibles au rapport $C'_7/C_7approx m_s/m_b$. La difficulté principale étant que $lambda$ et $S_{ho Kgamma}$ sont accompagnés par un facteur de dilution provenant de la désintégration forte. Ce travail est centré sur l'éstimation et la modélisation de ces facteurs de dilution. La transition $B o Kpipigamma$ se produit en tant quetrois désintégrations successives.La transition faible $B o K_{res}gamma$ est suivie par la désintégration forte en trois corps de la résonance kaonic $K_{res} o Kpipi$ via trois états intermediaires distincts $ho K$, $K^*pi$ et $kappapi$.L'observable $S_{ho Kgamma}$ est accessible avec l'état final $K^0pi^+pi^-gamma$, mais la présence de $K^{*pm}pi^mp$ et $kappa^pmpi^mp$, n'étants pas état propre de CP, induit le facteur de dilution $D$.Pour résoudre ce problème, nous dérivons l'expression de $D$ en fonction des ondes partielles $ho K$, $K^*pi$ et $kappapi$ et en incluant les résonances kaonic $K_1(1270/1400), K^*(1410)$ et $K_2^*(1430)$. Afin de calculer le facteur de dilution, les ondes partielles peuvent être extraites avec l'état final $K^{pm}pi^{mp}pi^{pm}gamma$, où la sensibilité expérimentale est plus élevée. Ensuite, nous proposons une nouvelle méthode, indépendante du model, pour déterminer $D$, qui consiste a extraire le facteur de dilution independamment de $S_{ho Kgamma}$ en utilisant des états finaux avec un pion neutre tels que $K^+pi^-pi^0gamma$. En exploitant des données existantes avec $m_{Kpipi} <1.8;$GeV$/c^2$, nous obtenons $D=0.92pm0.17$.Lorsque l'on considère juste $K_1(1270/1400)$ et $K^*(1410)$, $lambda$ peut être extrait de la distribution angulaire and de Dalitz avec une précision de l'ordre de $pm 10%$ pour un echantillon de $5.10^3$ évènements générés à l'aide de la méthode Monté Carlo. Mais cela demande une bonne connaissance de différentes quantités importantes pour la désintégration forte telles que l'angle de mélange de $K_1$, les rapports de branchement individuel $B o K_{res}gamma$ et les phases relatives. Nous montrons que certains de ces paramètres et $lambda$ peuvent être simultanément ajustés avec une perte de précision de juste quelques pourcents. Puis nous dérivons comment, en utilisant seulement la distribution angulaire, il est possible d'annuler partiellement les contributions provenants de la désintégration forte afin d'obtenir une limite inférieure pour $|lambda|$. / Over the last decades, the loop induced decay $b o sgamma$ has attracted a considerable amount of attention due to its potential sensitivity to new physics. In the standard model, the processes $b o sgamma_{L(R)}$ and $overline{b} o overline{s}gamma_{R(L)}$ are proportional to the Wilson coefficients $C_7(C'_7)$. The decay $B o Kpipigamma$ provides via angular analysis a parity odd observable ($lambda$) and via $B-overline{B}$ mixing a CP odd observable ($S_{ho Kgamma}$) both sensitive to the ratio $C'_7/C_7approx m_s/m_b$. The main issue is that both $lambda$ and $S_{ho Kgamma}$ are accompanied by a dilution factor originating from the strong decay. This work is focused on the estimation and modelisation of those dilution factors.The transition $B o Kpipigamma$ occurs as three subsequent decays. The weak process $B o K_{res}gamma$ is followed by the strong 3-body decay of the kaonic resonance $K_{res} o Kpipi$ via three distinct intermediate states $ho K$, $K^*pi$ and $kappapi$.The observable $S_{ho Kgamma}$ is accessible with the final state $K^0pi^+pi^-gamma$, but the presence of non CP eigenstates $K^{*pm}pi^mp$ and $kappa^pmpi^mp$ induce the dilution factor $D$.To deal with this inconvenience, we derive the expression of $D$ in terms of the partial waves $ho K$, $K^*pi$ and $kappapi$ and including the koanic resonances $K_1(1270/1400), K^*(1410)$ and $K_2^*(1430)$. The partial waves can then be fitted using the final state $K^{pm}pi^{mp}pi^{pm}gamma$, where the experimental sensitivity is higher, in order the compute the dilution factor. Then we propose a new model independent method to determine $D$, which consist in extracting the dilution factor independently of $S_{ho Kgamma}$ using final states with one neutral pion such as $K^+pi^-pi^0gamma$. Exploiting existing data with $m_{Kpipi} <1.8;$GeV$/c^2$, we obtained $D=0.92pm0.17$.When considering only $K_1(1270/1400)$ and $K^*(1410)$, fitting the angular and Dalitz plot distribution allows to extract $lambda$ with an accuracy of the order of $pm 10%$ for a sample of $5.10^3$ Monte Carlo generated events. But this require a good knowledge of different quantities of importance in the strong decay such as the $K_1$ mixing angle, individual $B o K_{res}gamma$ branching ratios and relative phases. We show that some of those parameters can simultaneously fitted with $lambda$ with a loss of accuracy of just a few percent. We derive how, using only the angular distribution, one can partially cancel contribution from the strong decay and obtain a lower bound on $|lambda|$.

Per- and polyfluorinated substances (PFAS) are compounds that consist of a carbon chainbackbone that is partially or entirely fluorinated, with an addition of a functional group. SomePFAS are known as persistent organic pollutants (POPs) and have therefore been drawing a lot ofattention as well as increased concerns. PFAS have been detected in humans, wildlife and theenvironment and some have exhibited toxic effects such as hepatotoxicity, immunotoxicity,reproductive toxicity and endocrine disruption as well as being persistent and bioaccumulative.Serum, plasma and whole blood have been used as biomonitoring matrices in many studies toevaluate human exposure to PFAS. Restrictions have been applied to some PFAS, but thesecompounds are still ubiquitous. This study will investigate the performance (recovery, matrixeffect (ME) in terms of intra-/inter-day repeatability) of ion-pair extraction (IPE) and solid phaseextraction with weak anion exchange (SPE-WAX). The extraction methods were adapted fromliterature and 13 PFAS were selected for this work based on prior biomonitoring studies. Thetarget PFAS content was analyzed with liquid chromatography coupled with tandem massspectrometry (LC-MS/MS). The extraction methods were also compared for extractableorganofluorine (EOF) extraction in terms of blank levels as well as the amount extracted withdifferent methods; the EOF content was measured with combustion ion chromatography (CIC).The EOF levels were used to estimate the amount of unidentified organofluorine (UOF), to avoidunderestimating potential health hazards. Samples extracted using IPE had an average ionizationenhancement of 9%, while SPE-WAX showed an average ionization suppression of -1%. SPEWAXshowed higher average recoveries for procedural blanks (78%), horse serum (96%) andhuman serum (95%) in comparison to IPE (69%, 36%, 88%, respectively). The CIC analysis forEOF content was observed to be below MDL (&lt;50 ng/mL F) with some contaminations observedin the procedural blanks.

This diploma thesis is concerned with the numerical analysis of welded aluminim structures. In these structures, there are significant decreases in the mechanical properties at the area of the weld and in the heat affected zone as a result of welding. Within this thesis, simulations of quasi-statically loaded welded joints made from EN AW-6082 T6 alloy were performed to investigate the load capacity and ductility of these joints. Computations were performed using a programme system based on an explicit finite element method. To describe material anisotrophy, a nonlinear material model called the Weak texture model was chosen. Material properties of the weld and the heat affected zone were considered to be different from base material. The required material parameters were adopted from available literature, however, material tests and indetification procedure of these parameters were described. In comparison with the experimental data, the results of the numerical simulations showed a relatively good ability of models to capture load capacity of studied welded joints. Nevertheless, due to mesh sensitivity of models caused by localization of deformation, it was not possible to determine ductility of these joints.

La loi du 5 mars 2007 relative à la protection juridique des majeurs a fait de la question de la protection de la personne et de son autonomie une ligne directrice. La conciliation de cette double injonction paradoxale - protéger et rendre autonome - confère un cadre humaniste à la loi. Pour rendre la capacité au majeur sans pour autant nier la fonction protectrice des mesures, la protection juridique obéit à des « grands principes». Ces principes permettent d'adapter la protection à la vulnérabilité de la personne et, en outre, de lui laisser des libertés, des capacités. La protection se rénove ainsi sous le concept de durabilité. Ce concept consiste à améliorer les capacités individuelles des personnes vulnérables. L'existence du concept de durabilité se manifeste donc dans le champ de protection des personnes vulnérables et l'expression de ce concept, parce qu'il tend à favoriser l'autonomie de ces dernières, leur assure un soutien. Le concept de durabilité, appliqué dans le champ de protection des personnes vulnérables, a d'abord germé en droit des majeurs protégés. Pourtant, la vulnérabilité rayonne au­delà de ce cercle étroit. Depuis la réforme du 10 février 2016, la vulnérabilité a été prise en compte en droit commun des contrats. La référence à la vulnérabilité permet de démontrer que ce n'est qu'à certaines conditions qu'on admet l'application des normes protectrices. Ces normes, telles qu'elles ont évolué avec les lois récentes, traduisent une appréhension nouvelle de la protection sous le prisme de la «durabilité». L'expression de la protection durable se manifeste particulièrement dans le droit des majeurs protégés qui en est le berceau. Des mécanismes tendent en effet à favoriser l'expression de la volonté de la personne et donc son autonomie afin de l'associer le plus possible aux décisions la concernant. La personne est ainsi intégrée dans le processus décisionnel. On découvre aujourd'hui les traces d'une protection durable en droit commun des contrats, le droit des contrats et le droit des majeurs protégés comportant des mécanismes destinés à permettre le rétablissement de l'autonomie de la personne. / The article of law dated 5 March 2007 regarding legal protection of adults has raised a guideline the issue of protection and autonomy of the protected persons. Conciliation of this double paradoxical injunction - protecting and empowering - gives the law a humanist framework. In order to give capability back to the person of full age without denying protective fonction of measures, legal protection obeys "guiding principles". These principles enable adjustment of protection depending on the person 's vulnerability and, in addition, allow him to keep his freedom and abilities. Protection is renewed under the concept of durability, by improving individual capacities of vulnerable persons. The existence of the concept of durability manifests in the fields of protection of the vulnerable persons and in the expression of the concept, as it tends towards the development of the vulnerable person in the autonomy and providing them with support. The concept of sustainable, applied in the field of protection of vulnerable people, was first germinated in law of protected adults. However, vulnerability shines beyond this narrow circle. Since reform of 10 February 2016, vulnerability has been taken into account in the Common Contract Law. Reference to vulnerability makes it possible to demonstrate that it is only under certain conditions that the application of protective standards is accepted. These standards, which have evolved through recent legislation, reflect a new apprehension of protection under the prism of the " durability ". The expression of sustainable protection is manifested particularly in the law of protected adults which is its beginnings. Mechanisms tend in fact to favour expression of the will of the person and therefore his autonomy in order to make him take part as much as possible in decisions which concem him. The person is thus integrated into the decision-making process. We can now discover traces of a sustainable protection in the Common Contract Law, law of contracts and right of protected adults thus including mechanisms designed to restore of the person's autonomy.

The aim of this work is to make some investigations concerning duality for multiobjective optimization problems. In order to do this we study first the duality for scalar optimization problems by using the conjugacy approach. This allows us to attach three different dual problems to a primal one. We examine the relations between the optimal objective values of the duals and verify, under some appropriate assumptions, the existence of strong duality. Closely related to the strong duality we derive the optimality conditions for each of these three duals. By means of these considerations, we study the duality for two vector optimization problems, namely, a convex multiobjective problem with cone inequality constraints and a special fractional programming problem with linear inequality constraints. To each of these vector problems we associate a scalar primal and study the duality for it. The structure of both scalar duals give us an idea about how to construct a multiobjective dual. The existence of weak and strong duality is also shown. We conclude our investigations by making an analysis over different duality concepts in multiobjective optimization. To a general multiobjective problem with cone inequality constraints we introduce other six different duals for which we prove weak as well as strong duality assertions. Afterwards, we derive some inclusion results for the image sets and, respectively, for the maximal elements sets of the image sets of these problems. Moreover, we show under which conditions they become identical. A general scheme containing the relations between the six multiobjective duals and some other duals mentioned in the literature is derived. / Das Ziel dieser Arbeit ist die Durchführung einiger Untersuchungen bezüglich der Dualität für Mehrzieloptimierungsaufgaben. Zu diesem Zweck wird als erstes mit Hilfe des so genannten konjugierten Verfahrens die Dualität für skalare Optimierungsaufgaben untersucht. Das erlaubt uns zu einer primalen Aufgabe drei unterschiedliche duale Aufgaben zuzuordnen. Wir betrachten die Beziehungen zwischen den optimalen Zielfunktionswerten der drei Dualaufgaben und untersuchen die Existenz der starken Dualität unter naheliegenden Annahmen. Im Zusammenhang mit der starken Dualität leiten wir für jede dieser Dualaufgaben die Optimalitätsbedingungen her. Die obengenannten Ergebnisse werden beim Studium der Dualität für zwei Vektoroptimierungsaufgaben angewandt, und zwar für die konvexe Mehrzieloptimierungsaufgabe mit Kegel-Ungleichungen als Nebenbedingungen und für eine spezielle Quotientenoptimierungsaufgabe mit linearen Ungleichungen als Nebenbedingungen. Wir assoziieren zu jeder dieser vektoriellen Aufgaben eine skalare Aufgabe für welche die Dualität betrachtet wird. Die Formulierung der beiden skalaren Dualaufgaben führt uns zu der Konstruktion der Mehrzieloptimierungsaufgabe. Die Existenz von schwacher und starker Dualität wird bewiesen. Wir schliessen unsere Untersuchungen ab, indem wir eine Analyse von verschiedenen Dualitätskonzepten in der Mehrzieloptimierung durchführen. Zu einer allgemeinen Mehrzieloptimierungsaufgabe mit Kegel-Ungleichungen als Nebenbedingungen werden sechs verschiedene Dualaufgaben eingeführt, für die sowohl schwache als auch starke Dualitätsaussagen gezeigt werden. Danach leiten wir verschiedene Beziehungen zwischen den Bildmengen, bzw., zwischen den Mengen der maximalen Elemente dieser Bildmengen der sechs Dualaufgaben her. Dazu zeigen wir unter welchen Bedingungen werden diese Mengen identisch. Ein allgemeines Schema das die Beziehungen zwischen den sechs dualen Mehrzieloptimierungsaufgaben und andere Dualaufgaben aus der Literatur enthält, wird dargestellt.

As the title already suggests the aim of the present work is to present Farkas - type results for inequality systems involving convex and/or non - convex functions. To be able to give the desired results, we treat optimization problems which involve convex and composed convex functions or non - convex functions like DC functions or fractions. To be able to use the fruitful Fenchel - Lagrange duality approach, to the primal problem we attach an equivalent problem which is a convex optimization problem. After giving a dual problem to the problem we initially treat, we provide weak necessary conditions which secure strong duality, i.e., the case when the optimal objective value of the primal problem coincides with the optimal objective value of the dual problem and, moreover, the dual problem has an optimal solution. Further, two ideas are followed. Firstly, using the weak and strong duality between the primal problem and the dual problem, we are able to give necessary and sufficient optimality conditions for the optimal solutions of the primal problem. Secondly, provided that no duality gap lies between the primal problem and its Fenchel - Lagrange - type dual we are able to demonstrate some Farkas - type results and thus to underline once more the connections between the theorems of the alternative and the theory of duality. One statement of the above mentioned Farkas - type results is characterized using only epigraphs of functions. We conclude our investigations by providing necessary and sufficient optimality conditions for a multiobjective programming problem involving composed convex functions. Using the well-known linear scalarization to the primal multiobjective program a family of scalar optimization problems is attached. Further to each of these scalar problems the Fenchel - Lagrange dual problem is determined. Making use of the weak and strong duality between the scalarized problem and its dual the desired optimality conditions are proved. Moreover, the way the dual problem of the scalarized problem looks like gives us an idea about how to construct a vector dual problem to the initial one. Further weak and strong vector duality assertions are provided.

In the first part of this thesis, we generalize a coding theorem and a converse of Kadota and Wyner (1972) to abstract channels with time structure. As a main contribution we prove the coding theorem for a significantly weaker condition on the channel output memory, called total ergodicity for block-i.i.d. inputs. We achieve this result mainly by introducing an alternative characterization of information rate capacity. We show that the ψ-mixing condition (asymptotic output-memorylessness), used by Kadota and Wyner, is quite restrictive, in particular for the important class of Gaussian channels. In fact, we prove that for Gaussian channels the ψ-mixing condition is equivalent to finite output memory. Moreover, we derive a weak converse for all stationary channels with time structure. Intersymbol interference as well as input constraints are taken into account in a flexible way. Due to the direct use of outer measures and a derivation of an adequate version of Feinstein’s lemma we are able to avoid the standard extension of the channel input σ-algebra and obtain a more transparent derivation. We aim at a presentation from an operational perspective and consider an abstract framework, which enables us to treat discrete- and continuous-time channels in a unified way. In the second part, we systematically analyze infinite output memory conditions for abstract channels with time structure. We exploit the connections to the rich field of strongly mixing random processes to derive a hierarchy for the nonequivalent infinite channel output memory conditions in terms of a sequence of implications. The ergodic-theoretic memory condition used in the proof of the coding theorem and the ψ-mixing condition employed by Kadota and Wyner (1972) are shown to be part of this taxonomy. In addition, we specify conditions for the channel under which memory properties of a random process are invariant when the process is passed through the channel. In the last part, we investigate cascade and integration channels with regard to mixing conditions as well as properties required in the context of the coding theorem. The results are useful to study many physically relevant channel models and allow a component-based analysis of the overall channel. We consider a number of examples including composed models and deterministic as well as random filter channels. Finally, an application of strong mixing conditions from statistical signal processing involving the Fourier transform of stationary random sequences is discussed and a list of further applications is given. / Im ersten Teil der Arbeit wird ein Kodierungstheorem und ein dazugehöriges Umkehrtheorem von Kadota und Wyner (1972) für abstrakte Kanäle mit Zeitstruktur verallgemeinert. Als wesentlichster Beitrag wird das Kodierungstheorem für eine signifikant schwächere Bedingung an das Kanalausgangsgedächtnis bewiesen, die sogenannte totale Ergodizität für block-i.i.d. Eingaben. Dieses Ergebnis wird hauptsächlich durch eine alternative Charakterisierung der Informationsratenkapazität erreicht. Es wird gezeigt, dass die von Kadota und Wyner verwendete ψ-Mischungsbedingung (asymptotische Gedächtnislosigkeit am Kanalausgang) recht einschränkend ist, insbesondere für die wichtige Klasse der Gaußkanäle. In der Tat, für Gaußkanäle wird bewiesen, dass die ψ-Mischungsbedingung äquivalent zu endlichem Gedächtnis am Kanalausgang ist. Darüber hinaus wird eine schwache Umkehrung für alle stationären Kanäle mit Zeitstruktur bewiesen. Sowohl Intersymbolinterferenz als auch Eingabebeschränkungen werden in allgemeiner und flexibler Form berücksichtigt. Aufgrund der direkten Verwendung von äußeren Maßen und der Herleitung einer angepassten Version von Feinsteins Lemma ist es möglich, auf die Standarderweiterung der σ-Algebra am Kanaleingang zu verzichten, wodurch die Darstellungen transparenter und einfacher werden. Angestrebt wird eine operationelle Perspektive. Die Verwendung eines abstrakten Modells erlaubt dabei die einheitliche Betrachtung von zeitdiskreten und zeitstetigen Kanälen. Für abstrakte Kanäle mit Zeitstruktur werden im zweiten Teil der Arbeit Bedingungen für ein unendliches Gedächtnis am Kanalausgang systematisch analysiert. Unter Ausnutzung der Zusammenhänge zu dem umfassenden Gebiet der stark mischenden zufälligen Prozesse wird eine Hierarchie in Form einer Folge von Implikationen zwischen den verschiedenen Gedächtnisvarianten hergeleitet. Die im Beweis des Kodierungstheorems verwendete ergodentheoretische Gedächtniseigenschaft und die ψ-Mischungsbedingung von Kadota und Wyner (1972) sind dabei Bestandteil der hergeleiteten Systematik. Weiterhin werden Bedingungen für den Kanal spezifiziert, unter denen Eigenschaften von zufälligen Prozessen am Kanaleingang bei einer Transformation durch den Kanal erhalten bleiben. Im letzten Teil der Arbeit werden sowohl Integrationskanäle als auch Hintereinanderschaltungen von Kanälen in Bezug auf Mischungsbedingungen sowie weitere für das Kodierungstheorem relevante Kanaleigenschaften analysiert. Die erzielten Ergebnisse sind nützlich bei der Untersuchung vieler physikalisch relevanter Kanalmodelle und erlauben eine komponentenbasierte Betrachtung zusammengesetzter Kanäle. Es wird eine Reihe von Beispielen untersucht, einschließlich deterministischer Kanäle, zufälliger Filter und daraus zusammengesetzter Modelle. Abschließend werden Anwendungen aus weiteren Gebieten, beispielsweise der statistischen Signalverarbeitung, diskutiert. Insbesondere die Fourier-Transformation stationärer zufälliger Prozesse wird im Zusammenhang mit starken Mischungsbedingungen betrachtet.

Results of psychological experiments have shown that humans make assumptions, which are not necessarily valid, that they are influenced by their background knowledge and that they reason non-monotonically. These observations show that classical logic does not seem to be adequate for modeling human reasoning. Instead of assuming that humans do not reason logically at all, we take the view that humans do not reason classical logically. Our goal is to model episodes of human reasoning and for this purpose we investigate the so-called Weak Completion Semantics. The Weak Completion Semantics is a Logic Programming approach and considers the least model of the weak completion of logic programs under the three-valued Łukasiewicz logic. As the Weak Completion Semantics is relatively new and has not yet been extensively investigated, we first motivate why this approach is interesting for modeling human reasoning. After that, we show the formal correspondence to the already established Stable Model Semantics and Well-founded Semantics. Next, we present an extension with an additional context operator, that allows us to express negation as failure. Finally, we propose a contextual abductive reasoning approach, in which the context of observations is relevant. Some properties do not hold anymore under this extension. Besides discussing the well-known psychological experiments Byrne’s suppression task and Wason’s selection task, we investigate an experiment in spatial reasoning, an experiment in syllogistic reasoning and an experiment that examines the belief-bias effect. We show that the results of these experiments can be adequately modeled under the Weak Completion Semantics. A result which stands out here, is the outcome of modeling the syllogistic reasoning experiment, as we have a higher prediction match with the participants’ answers than any of twelve current cognitive theories. We present an abstract evaluation system for conditionals and discuss well-known examples from the literature. We show that in this system, conditionals can be evaluated in various ways and we put up the hypothesis that humans use a particular evaluation strategy, namely that they prefer abduction to revision. We also discuss how relevance plays a role in the evaluation process of conditionals. For this purpose we propose a semantic definition of relevance and justify why this is preferable to a exclusively syntactic definition. Finally, we show that our system is more general than another system, which has recently been presented in the literature. Altogether, this thesis shows one possible path on bridging the gap between Cognitive Science and Computational Logic. We investigated findings from psychological experiments and modeled their results within one formal approach, the Weak Completion Semantics. Furthermore, we proposed a general evaluation system for conditionals, for which we suggest a specific evaluation strategy. Yet, the outcome cannot be seen as the ultimate solution but delivers a starting point for new open questions in both areas.