Approximation theory is a fundamental tool in order to study the representation theory of a ring R. Roughly speaking, it consists in determining suitable additive or abelian subcategories of the whole module category Mod-R with nice enough functorial properties. For example, torsion theory is a well suited incarnation of approximation theory. Of course, such an idea has been generalised to the additive setting itself, so that both Mod-R and other interesting categories related with R may be linked functorially. By the seminal work of Beilinson, Bernstein and Deligne (1982), the derived category of the ring turns out to admit useful torsion theories, called t-structures: they are pairs of full subcategories of D(R) whose intersection, called the heart, is always an abelian category. The so-called standard t-structure of D(R) has as its heart the module category Mod-R itself. Since then a lot of results devoted to the module theoretic characterisation of the hearts have been achieved, providing evidence of the usefulness of the t-structures in the representation theory of R. In 2020, following a research line promoted by many other authors, Saorin and Stovicek proved that the heart of any compactly generated t-structure is always a locally finitely presented Grothendieck categories (actually, this is true for any t-structure in a triangulated category with coproducts). Essentially, this means that the hearts of D(R) come equipped with a finiteness condition miming that one valid in Mod-R. In the present thesis we tackle the problem of characterising when the hearts of certain compactly generated t-structures of a commutative ring are even locally coherent. In this commutative context, after the works of Neeman and Alonso, Jeremias and Saorin, compactly generated t-structures turned out to be very interesting over a noetherian ring, for they are in bijection with the Thomason filtrations of the prime spectrum. In other words, they are classified by geometric objects, moreover their constituent subcategories have a precise cohomological description. However, if the ascending chain condition lacks, such classification is somehow partial, though provided by Hrbek. The crucial point is that the constituents of the t-structures have a different description w.r.t. that available in the noetherian setting, yet if one copies the latter for an arbitrary ring still obtains a t-structure, but it is not clear whether it must be compactly generated. Consequently, pursuing the study of the local coherence of the hearts given by a Thomason filtration, we ended by considering two t-structures. Our technique in order to face the lack of the ascending chain condition relies on a further approximation of the hearts by means of suitable torsion theories. The main results of the thesis are the following: we prove that for the so-called weakly bounded below Thomason filtrations the two t-structures have the same heart (therefore it is always locally finitely presented), and we show that they coincide if and only they are both compactly generated. Moreover, we achieve a complete characterisation of the local coherence for the hearts of the Thomason filtrations of finite length.

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The overreaching goal of this paper is to investigate the existence and uniqueness of weak solution of a semilinear parabolic equation with double nonlocality in space and in time variables that naturally arises while modeling a biological nano-sensor in the chaotic dynamics of a polymer chain. In fact, the problem under consideration involves a symmetric integrodifferential operator of Lévy type and a term called the interaction potential, that depends on the time-integral of the solution over the entire interval of solving the problem. Owing to the Galerkin approximation, the existence and uniqueness of a weak solution of the nonlocal complement value problem is proven for small time under fair conditions on the interaction potential.

Recently, due to the increasing adoption of distributed energy resource (DER) technologies including battery energy storage (BES) and electric vehicle (EV) systems, bidirectional power converters are becoming more popular. These converters are broadly utilized as interface devices and provide a bidirectional power flow in applications where the primary power supply can both supply and receive energy. A dc capacitor, called the dc-link, is an important component of such bidirectional converters. For a wide range of applications, the converter is required to control the dc-link voltage. Commonly, a proportional-integrating (PI) controller is used by the dc capacitor voltage controller to generate a set-point for the inner current controller. This approach tightly regulates the dc-link voltage to a given value. The research presented in this dissertation shows that such an approach compromises the stability margins of the converter for reverse power flow and weak grid conditions. It is shown that by allowing a small variation of dc capacitor voltage in proportion to the amount of power flowing through the converter, the stability and robustness margins are improved. This approach also simplifies the design process and can be applied to both dc/dc and dc/ac (single-phase and three-phase) converters. Moreover, it grants an inherent power sharing capability when multiple converters share the same dc-link terminals; removing the need to a communication link between parallel converters. The proposed controller is equipped with a current limiting mechanism to protect the converter during low-voltage/over-current transients. Detailed analyses, simulations, comparisons, and experimental results are included to illustrate the effectiveness of the proposed control approach. To mathematically establish the properties of the proposed method in a single-phase dc/ac application, this dissertation also derives a new and systematic modeling approach for a grid-connected bidirectional single-phase inverter controlled in stationary frame. Implementing the control system in the stationary frame has advantages over rotating frame. However, the combination of dc and ac state variables and nonlinearities make its stability analysis challenging. In the proposed model, an imaginary subsystem is properly generated and augmented to allow a full transformation to a synchronous rotating frame. The proposed modeling strategy is modular and has a closed form which facilitates further extensions. It is successfully used to demonstrate enhanced stability margins of the proposed controller.

I detta examensarbete utforskas kollektiva boendeformer som socialt hållbara lösningar i framväxande urbana miljöer förankrat i ett gestaltningsförslag. Det finns en efterfrågan på bostadsmarknaden av kollektiva boendeformer följt av strukturella förändringar i samhället, minskade hushållsstorlekar och människans behov av social interaktion. Teoridelen utgör ett teoretiskt ramverk för studiens fokus på kollektiva boendeformer, med hjälp av teoretiska principer och empirisk forskning kring kollektiva boenden, individens behov av autonomi och gemenskap, samt hur rumslig utformning påverkar social interaktion. För att undersöka detta har studien genomfört en litteratursökning, intervju med bostadsforskare och fallstudier av kollektiv i Malmö. Arbetet baseras på en Inquiry by Design metod som möjliggör en flexibel arbetsmetod. I resultatet presenteras insikter från intervjun och fallstudierna, analyser av rumsliga designaspekter, och sammanfattande slutsatser som formulerar designkriterier för ett gestaltningsförslag av ett framtida kollektivboende. Diskussionen placerar forskningsfynden i kontext till aktuella utmaningar inom bostadsmarknaden, betonar vikten av mellanmänskliga relationer i kollektiv, och föreslår en förlängning av "den tredje platsen" som en integrerad del av hemmet. / In this thesis, collective housing forms are explored as socially sustainable solutions in emerging urban environments, anchored in a design proposal. There is a demand in the housing market for collective living arrangements due to structural changes in society, decreasing household sizes, and the human need for social interaction. The theoretical framework of the study focuses on collective housing forms, drawing on theoretical principles and empirical research on collective living, individual needs for autonomy and community, and how spatial design influences social interaction. To investigate this, the study conducts a literature review, an interview with a housing researcher and case studies of collective housing in Malmö. The work is based on an Inquiry by Design method, enabling a flexible approach. The results present insights from the interview and case studies, analyses of spatial design aspects, and summarizing conclusions that result in a design criteria for a proposal of future collective housing forms. The discussion contextualizes the research findings within current challenges in the housing market, emphasizing the importance of interpersonal relationships in collective housing forms, and suggests an extension of the "the third place" as an integrated part of the home.

Il presente lavoro offre un’analisi linguistica dell’implicito nei racconti "Drakon" [Il drago], "Peščera" [La caverna] e "Mamaj", scritti da Evgenij Zamjatin tra il 1918 e il 1920 e noti come ciclo di Pietrogrado. Il tema è motivato sia dalle caratteristiche di questi testi, in cui il riferimento al contesto post-rivoluzionario e la critica alla rivoluzione sono molto chiari, ma del tutto impliciti, e il lettore può solo inferirli partendo dal testo e dalla conoscenza del contesto condiviso con lo scrittore, sia dallo studio degli scritti di Zamjatin sulla prosa, in cui emerge che l’implicito è uno degli strumenti principali con cui egli realizza la sua concezione di opera letteraria, frutto della cooperazione fra autore e lettore. Per l’analisi abbiamo utilizzato gli strumenti offerti dalla teoria della pertinenza, elaborata a partire dagli anni Ottanta da Dan Sperber e Deirdre Wilson, e più precisamente i concetti di implicatura ed esplicatura; essi risultano particolarmente produttivi rispetto a quelli della retorica tradizionale, i quali illuminano la fattura del testo, ma non spiegano come da essa il lettore arrivi a comprenderlo e interpretarlo, come avvenga, cioè, la collaborazione creativa che Zamjatin pone al centro della propria estetica. / The present work offers a linguistic analysis of implicitness in the stories "Drakon" [The Dragon], "Peščera" [The Cave] and "Mamaj", written by Yevgeny Zamyatin between 1918 and 1920 and known as his Petrograd cycle of stories. This topic is justified not only by the peculiarities of these texts, whose reference to post-revolutionary context and criticism of revolution are very clear but quite implicit, and the reader can only infer them from the text and the context he shares with the writer, but also by what Zamyatin stated in his essays on prose, where implicitness is one of the main instruments for achieving his idea of literary work as the result of the cooperation between author and reader. The analysis proceeds by applying the elements provided by the relevance theory which has been developed by Dan Sperber and Deirdre Wilson since the eighties, and particularly that of implicature and explicature; they are more fruitful than traditional rhetorical categories, which shed light on the way Zamyatin’s texts are built, but do not explain how the reader understands and interprets them, that is, how the creative cooperation pointed out in Zamyatin’s aesthetics takes place.

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.