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abstract: C*-algebras of categories of paths were introduced by Spielberg in 2014 and generalize C*-algebras of higher rank graphs. An approximately finite dimensional (AF) C*-algebra is one which is isomorphic to an inductive limit of finite dimensional C*-algebras. In 2012, D.G. Evans and A. Sims proposed an analogue of a cycle for higher rank graphs and show that the lack of such an object is necessary for the associated C*-algebra to be AF. Here, I give a class of examples of categories of paths whose associated C*-algebras are Morita equivalent to a large number of periodic continued fraction AF algebras, first described by Effros and Shen in 1980. I then provide two examples which show that the analogue of cycles proposed by Evans and Sims is neither a necessary nor a sufficient condition for the C*-algebra of a category of paths to be AF. / Dissertation/Thesis / Doctoral Dissertation Mathematics 2020

Dans cette thèse, on définit et on étudie les notions de structure de Poisson et coïsotrope sur un champ dérivé, dans le contexte de la géométrie algébrique dérivée. On considère deux présentations différentes de structure de Poisson : la première est purement algébrique, alors que la deuxième est plus géométrique. On montre que les deux approches sont en fait équivalentes. On introduit aussi la notion de structure coïsotrope sur un morphisme de champs dérivés, encore une fois en présentant deux définitions équivalentes : la première est basée sur une généralisation appropriée de l'opérade Swiss-Cheese de Voronov, tandis que la deuxième est formulée en termes de champs de multivecteurs rélatifs. En particulier, on montre que le morphisme identité admet une unique structure coïsotrope ; cela produit une application d'oubli des structures de Poisson n-décalées aux structures de Poisson (n-1)-décalées. On montre aussi que l'intersection de deux morphismes coïsotropes dans un champ de Poisson n-décalée est naturellement equipée d'une structure de Poisson (n-1)-décalée canonique. En outre, on fournit une équivalence entre l'espace de structures coïsotropes non-dégénérées et l'espace des structures Lagrangiennes en géométrie dérivée, introduites dans les travaux de Pantev-Toën-Vaquié-Vezzosi. / In this thesis, we define and study Poisson and coisotropic structures on derived stacks in the framework of derived algebraic geometry. We consider two possible presentations of Poisson structures of different flavour: the first one is purely algebraic, while the second is more geometric. We show that the two approaches are in fact equivalent. We also introduce the notion of coisotropic structure on a morphism between derived stacks, once again presenting two equivalent definitions: one of them involves an appropriate generalization of the Swiss Cheese operad of Voronov, while the other is expressed in terms of relative polyvector fields. In particular, we show that the identity morphism carries a unique coisotropic structure; in turn, this gives rise to a non-trivial forgetful map from n-shifted Poisson structures to (n-1)-shifted Poisson structures. We also prove that the intersection of two coisotropic morphisms inside a n-shifted Poisson stack is naturally equipped with a canonical (n-1)-shifted Poisson structure. Moreover, we provide an equivalence between the space of non-degenerate coisotropic structures and the space of Lagrangian structures in derived geometry, as introduced in the work of Pantev-Toën-Vaquié-Vezzosi.

Cette thèse est consacrée à l'étude des interactions entre les structures homotopiques en théorie des catégories et les modèles catégoriques de la théorie des types de Martin-Löf. Le mémoire s'articule selon trois axes: les bifibrationos de Quillen, les catégories homotopiques des bifibrations de Quillen, et les tribus généralisées. Le premier axe définit une nouvelle notion de bifibration classifiant les pseudo foncteurs avec de bonnes propriétés depuis un catégorie de modèles et à valeurs dans la 2-catégorie des catégories de modèles et adjonctions de Quillen entre elles. En particulier on montre comment équipper d'une structure de modèle la construction de Grothendieck d'un tel pseudo foncteur. Le théorème principal de cette partie est une caractérisation des bonnes propriétés qu'un pseudo foncteur doit posséder pour supporter cette structure de catégorie de modèles sur sa construction de Grothendieck. En ce sens, on améliore les deux théorèmes précédemment existants dans la littérature qui ne donnent que des conditions suffisantes alors que nous donnons des conditions nécessaires et suffisantes. Le second axe se concentre sur le foncteur induit entre les catégories homotopiques des catégories de modèles mises en oeuvre dans une bifibration de Quillen. On y prouve que cette localization peut se faire en deux étapes au moyen d'un quotient homotopique à la Quillen itéré. De manière à rendre cette opération rigoureuse, on a besoin de travailler dans un cadre légèrement plus large que celui imaginé par Quillen : en se basant sur le travail d'Egger, on utilise des catégories de modèles sans nécessairement tous les (co)égalisateurs. Le chapitre de prérequis sert précisément à reconstruire la théorie basique des l'algèbre homotopique à la Quillen dans ce cadre élargi. Les structures mis à nu dans cette partie imposent de considérer des versions "homotopique" des poussés en avant et des tirés en arrière qu'on trouve habituellement dans les (op)fibrations de Grothendieck. C'est le point de départ pour le troisième axe, dans lequel on définit une nouvelle structure, appelée tribu relative, qui permet d'axiomatiser des versions homotopiques de la notion de flèche cartésienne et cocartésienne. Cela est obtenu en réinterprétant les (op)fibrations de Grothendieck en termes de problèmes de relèvement. L'outil principal dans cette partie est une version relative des systèmes de factorisation stricts ou faibles usuels. Cela nous permet en particulier d'expérimenter un nouveau demodèle de la théorie des types dépendants intentionnelle dans lequelles types identités sont donnés par l'exact analogue homotopique du prédicat d'égalité dans les hyperdoctrines de Lawvere. / This thesis is concerned with the study of the interplay between homotopical structures and categorical model of Martin-Löf's dependent type theory. The memoir revolves around three big topics: Quillen bifibrations, homotopy categories of Quillen bifibrations, and generalized tribes. The first axis defines a new notion of bifibrations, that classifies correctly behaved pseudo functors from a model category to the 2-category of model categories and Quillen adjunctions between them. In particular it endows the Grothendieck construction of such a pseudo functor with a model structure. The main theorem of this section acts as a charaterization of the well-behaved pseudo functors that tolerates this "model Gothendieck construction". In that respect, we improve the two previously known theorems on the subject in the litterature that only give sufficient conditions by designing necessary and sufficient conditions. The second axis deals with the functors induced between the homotopy categories of the model categories involved in a Quillen bifibration. We prove that this localization can be performed in two steps, by means of Quillen's construction of the homotopy category in an iterated fashion. To that extent we need a slightly larger framework for model categories than the one originally given by Quillen: following Egger's intuitions we chose not to require the existence of equalizers and coequalizers in our model categories. The background chapter makes sure that every usual fact of basichomotopical algebra holds also in that more general framework. The structures that are highlighted in that chapter call for the design of notions of "homotopical pushforward" and "homotopical pullback". This is achieved by the last axis: we design a structure, called relative tribe, that allows for a homotopical version of cocartesian morphisms by reinterpreting Grothendieck (op)fibrations in terms of lifting problems. The crucial tool in this last chapter is given by a relative version of orthogonal and weak factorization systems. This allows for a tentative design of a new model of intentional type theory where the identity types are given by the exact homotopical counterpart of the usual definition of the equality predicate in Lawvere's hyperdoctrines

In tasks with more than one path to succeed, it is possible that participants’ strategies vary and therefore, participants should not be analyzed as a homogeneous group. This thesis investigates individual differences in a two-dimensional categorization task with redundancy (i.e., a task where any of the two dimensions by itself suffices for perfect performance). Individual differences in learned knowledge and used knowledge are considered and studied. Participants first performed a categorization task with redundancy (training phase), and afterward were asked to do categorizations in which the previously redundant knowledge becomes decisive (testing phase). Using the data from the testing phase, dimension(s) learned by each participant were determined and the response patterns of each participant in the training phase was used to determine which dimension(s) were used. The used knowledge was assessed using two separate analyses, both of which look at accuracy and response time patterns, but in different ways. Analysis 1 uses iterative decision bound modeling and RT-distance hypothesis and Analysis 2 uses the stochastic version of general recognition theory. In Analysis 1, more errors and slower response times close to a decision bound perpendicular to a dimension indicate that a participant is using that dimension. Analysis 2 goes a step further and in addition to determining which dimension(s) are used, specifies in what way they were used (i.e., identifying the strategy of each participant). Possible strategies are described heuristically (unidimensional, time efficient and conservative) and then each heuristic is translated into a drift diffusion model by the unique way that strategy is assumed to affect trial-by-trial difficulty of the task. Finally, a model selection criterion is used to pick the strategy that is used by each participant.

This is a critical and comparative study that examines the blossoming and maturation of the Sesotho sa Leboa (Northern Sotho) Young Adult (YA) novella from the canon of novels in that language. The periods under examination are divided into three decades, namely, 1940–1949, 1950-1959 and 1960-1969. Taking into account the significant research done by scholars in Sesotho sa Leboa, very little is known about YA literature and in particular, the Young Adult novella (novelette or novel). This somewhat confusing sub-genre is clarified and dissected by literary theorists from different orientations and traditions (schools of thought). It is envisaged that this research work will help language practitioners in Sesotho sa Leboa, and other languages to make informed decisions about the classification of the sub-genre in terms of its literary elements. Defining the age cohort of the young adult has also been, and still is, a hotly debated terrain. Arguably, the problem stems from diverse societies trying to provide a uniform definition of a global community. In many instances, the age definition of ‘who is the young adult’ seems to be more complex and political in nature. In the final analysis, the study provides guidelines for the literary evaluation of texts for use in secondary schools, tertiary institutions and for the selection of books for libraries. Novice writers, in comparison with their predecessors, will also become more conversant with the requirements of the sub-genre. For this reason, Sesotho sa Leboa literature will continue to grow and develop in all facets in relation to quality, insight and world view. / Afrikaans: Hierdie is 'n kritiese en vergelykende studie wat die bloei en volwassenheid van die Sesotho sa Leboa (Noord-Sotho) jong volwassene (YA) novelle vanuit die kanon van romans in daardie taal ondersoek. Die periodes wat ondersoek word, word in drie dekades verdeel, naamlik 1940–1949, 1950-1959 en 1960-1969. Met inagneming van die beduidende navorsing wat wetenskaplikes in Sesotho sa Leboa gedoen het, is daar baie min bekend oor jong volwassene-literatuur en veral die novelle van jong volwassene romans. Hierdie ietwat verwarrende subgenre word deur literêre teoretici uit verskillende oriëntasies en tradisies (denkrigtings) verhelder en gedissekteer. Daar word voorsien dat hierdie navorsingswerk taalpraktisyns in Sesotho sa Leboa en ander tale sal help om ingeligte besluite te neem oor die klassifikasie van die subgenre in terme van die literêre elemente daarvan. Die definisie van die ouderdomsgroep van die jong volwassene was, en is nog steeds, 'n baie gedebatteerde terrein. Die probleem spruit waarskynlik uit uiteenlopende samelewings wat probeer om 'n eenvormige definisie van 'n wêreldgemeenskap te gee. In baie gevalle,lyk die definisie van 'wie die jong volwassene' is, meer kompleks en polities van aard. Uiteindelik bied die studie riglyne vir die literêre evaluering van tekste wat gebruik kan word in sekondêre skole, tersiêre instellings en vir die keuse van boeke vir biblioteke. Beginnersskrywers, in vergelyking met hul voorgangers, sal ook meer vertroud raak met die vereistes van die subgenre. Om hierdie rede sal die literatuur van Sesotho sa Leboa aanhou groei en ontwikkel in alle fasette in verhouding tot kwaliteit, insig en wêreldbeskouing. / Thesis (DLitt)--University of Pretoria, 2020. / African Languages / DLitt / Unrestricted

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This diploma thesis deals with a design of single-engine, multi-purpose, transport airplane in Normal category, given by CS/FAR 23. Design is created in highest constructional and technological accordance with L 410 airplane series. Thesis determines airplanes conceptual layout, basic dimensions, basic weight and center of gravity analysis, aerodynamic and aerostatic foundation, flight performances and airplane properties. Thesis arranges various versions of cabin layouts and describes power plant installation and landing gear construction. Results of the thesis shows, that this design is advantageous in various aspects. Design is comparable with competition from perspective of its performances. Financial analysis showed, that costs of development are returnable in relatively low amount of sold airplanes, for a prices, that are lower than a prices, competition is selling similar airplanes for. Moreover, costs of maintenance are expected to be low, as a consequence of using only one engine unit.

Diese Arbeit beschäftigt sich mit der Speziestheorie aus Mochizukis Beweis(versuch) der abc-Vermutung. Es wird ein Standpunkt eingeführt, der Parallelen zwischen der Kategorientheorie und der Speziestheorie aufzeigt und es werden so die Besonderheiten der Speziestheorie herausgearbeitet. In der Speziestheorie möchte man Konstruktionen ausführen, welche von keinen Auswahlen abhängen. Dieses Problem wird in einem allgemeinen Kontext für universelle Morphismen gelöst. An Beispielen wird die in der Arbeit behandelte Theorie erklärt.

The main goal of this thesis was to implement a functional programming (FP) library named Funk that extends C# with support for concepts present in functional programming languages, such as F# and Scala. Funk utilizes many functional programming concepts, including immutability, pattern matching, and various types of monads, together with stronger typing. Introduction of these concepts into C# helps in avoiding many runtime errors and boilerplate code, and it also lets developers write C# code in a declarative rather than in an imperative way, making the day-to-day software development easier and less error-prone. Additionally, the thesis analyzes and compares Funk with existing functional programming libraries such as Language-ext and FuncSharp. Finally, it analyzes the new features of C# 8, which include nullable reference types and pattern matching and compares them with the functionalities of the Funk library.