Le modèle de dimères, également connu sous le nom de modèle de couplage parfait, est un modèle probabiliste introduit à l'origine dans la mécanique statistique. Une configuration de dimères d'un graphe est un sous-ensemble des arêtes tel que chaque sommet est incident à exactement une arête. Un poids est attribué à chaque arête et la probabilité d'une configuration est proportionnelle au produit des poids des arêtes présentes. Dans cette thèse, nous étudions principalement deux modèles qui sont liés au modèle de dimères, et plus particulièrement leur comportements limites. Le premier est le modèle des forêts couvrantes enracinées sur des cycles (CRSF) sur le tore, qui sont en bijection avec les configurations de dimères via la bijection de Temperley. Dans la limite quand la taille du tore tend vers l'infini, la mesure sur les CRSF converge vers une mesure de Gibbs ergodique sur le plan tout entier. Nous étudions la connectivité de l'objet limite, prouvons qu'elle est déterminée par le changement de hauteur moyen de la mesure de Gibbs ergodique et donnons un diagramme de phase. Le second est le modèle de perles, un processus ponctuel sur $\mathbb{Z}\times\mathbb{R}$ qui peut être considéré comme une limite à l'échelle du modèle de dimères sur un réseau hexagonal. Nous formulons et prouvons un principe variationnel similaire à celui du modèle dimère \cite{CKP01}, qui indique qu'à la limite de l'échelle, la fonction de hauteur normalisée d'une configuration de perles converge en probabilité vers une surface $h_0$ qui maximise une certaine fonctionnelle qui s'appelle "entropie". Nous prouvons également que la forme limite $h_0$ est une limite de l'échelle des formes limites de modèles de dimères. Il existe une correspondance entre configurations de perles et (skew) tableaux de Young standard, qui préserve la mesure uniforme sur les deux ensembles. Le principe variationnel du modèle de perles implique une forme limite d'un tableau de Young standard aléatoire. Ce résultat généralise celui de \cite{PR}. Nous dérivons également l'existence d'une courbe arctique d'un processus ponctuel discret qui encode les tableaux standard, defini dans \cite{Rom}. / The dimer model, also known as the perfect matching model, is a probabilistic model originally introduced in statistical mechanics. A dimer configuration of a graph is a subset of the edges such that every vertex is incident to exactly one edge of the subset. A weight is assigned to every edge, and the probability of a configuration is proportional to the product of the weights of the edges present. In this thesis we mainly study two related models and in particular their limiting behavior. The first one is the model of cycle-rooted-spanning-forests (CRSF) on tori, which is in bijection with toroidal dimer configurations via Temperley's bijection. This gives rise to a measure on CRSF. In the limit that the size of torus tends to infinity, the CRSF measure tends to an ergodic Gibbs measure on the whole plane. We study the connectivity property of the limiting object, prove that it is determined by the average height change of the limiting ergodic Gibbs measure and give a phase diagram. The second one is the bead model, a random point field on $\mathbb{Z}\times\mathbb{R}$ which can be viewed as a scaling limit of dimer model on a hexagon lattice. We formulate and prove a variational principle similar to that of the dimer model \cite{CKP01}, which states that in the scaling limit, the normalized height function of a uniformly chosen random bead configuration lies in an arbitrarily small neighborhood of a surface $h_0$ that maximizes some functional which we call as entropy. We also prove that the limit shape $h_0$ is a scaling limit of the limit shapes of a properly chosen sequence of dimer models. There is a map form bead configurations to standard tableaux of a (skew) Young diagram, and the map is measure preserving if both sides take uniform measures. The variational principle of the bead model yields the existence of the limit shape of a random standard Young tableau, which generalizes the result of \cite{PR}. We derive also the existence of an arctic curve of a discrete point process that encodes the standard tableaux, raised in \cite{Rom}.

We investigate the famous Laguerre–Pólya class of entire functions and its subclass, the Laguerre–Pólya class of type I. The functions from these classes can be expressed in terms of the Hadamard Canonical Factorization (see Chapter 1, Definition 1.2 and 1.3). The prominent theorem by E. Laguerre and G. Pólya gives a complete description of the Laguerre–Pólya class and the Laguerre–Pólya class of type I, showing that these classes are the respective closures in the topology of uniform convergence on compact sets of the set of real polynomials having only real zeros (that is, the set of so-called hyperbolic polynomials) and the set of real polynomials having only real negative zeros. Both the Laguerre–Pólya class and the Laguerre–Pólya class of type I play an essential role in complex analysis. For the properties and characterizations of these classes, see, for example, [31] by A. Eremenko, [40] by I.I. Hirschman and D.V. Widder, [43] by S. Karlin, [57] by B.Ja. Levin, [66, Chapter 2] by N. Obreschkov, and [74] by G. Pólya and G. Szegö. In the thesis, we study entire functions with positive coefficients and with the monotonic sequence of their second quotients of Taylor coefficients. We find necessary and sufficient conditions under which such functions belong to the Laguerre–Pólya class (or the Laguerre–Pólya class of type I).:List of symbols Introduction 1 Background of research 1 1.1 The Laguerre–Pólya class .................... 1 1.2 The quotients of Taylor coefficients ............... 3 1.3 Hutchinson’s constant ...................... 4 1.4 Multiplier sequences ....................... 4 1.5 Apolar polynomials........................ 8 1.6 The partial theta function .................... 10 1.7 Decreasing second quotients ................... 13 1.8 Increasing second quotients ................... 14 2 A necessary condition for an entire function with the increasing second quotients of Taylor coefficients to belong to the Laguerre–Pólya class 15 2.1 Proof of Theorem 2.1....................... 16 2.2 The q-Kummer function ..................... 29 2.3 Proof of Theorem 2.10 ...................... 31 2.4 Proof of Theorem 2.11 ...................... 43 3 Closest to zero roots and the second quotients of Taylor coefficients of entire functions from the Laguerre–Pólya I class 49 3.1 Proof of Statement 3.1 ...................... 50 3.2 Proof of Theorem 3.2....................... 53 3.3 Proof of Theorem 3.4....................... 61 3.4 Proof of Theorem 3.6....................... 66 4 Entire functions from the Laguerre–Pólya I class having the increasing second quotients of Taylor coefficients 69 4.1 Proof of Theorem 4.1....................... 70 4.2 Proof of Theorem 4.3....................... 76 5 Number of real zeros of real entire functions with a non-decreasing sequence of the second quotients of Taylor coefficients 81 5.1 Proof of Theorem 5.1....................... 82 5.2 Proof of Corollary 5.2....................... 88 5.3 Proof of Theorem 5.4....................... 88 6 Further questions 95 Acknowledgements 97 Selbständigkeitserklärung 101 Curriculum Vitae 103 Bibliography 107

This exploratory qualitative case study provides a description of the Glencree Centre for Peace and Reconciliation’s practice in addressing deep-rooted conflict, from the Republic of Ireland. This research grew out of practical problems from the field of conflict resolution in Canada, in particular interest-based mediation, in addressing deep-rooted conflict. Using an extended epistemology, data is harvested from praxis to create naturalistic generalizations: guidelines for addressing deep-rooted conflict. The research findings are the result of a synthesis of three data sources: interviews with facilitators from Glencree, textual data, and nearly five months of onsite observation. The main themes derived from the research include: Glencree’s Diverse Practice; Glencree’s Approach to Conflict; Glencree’s Identity; Glencree’s Approach to Deep-Rooted Conflict; and Implementing Glencree’s Approach. This study is intended as a snapshot in time of a set of dynamic and emergent ideas addressing conflict in practice. Through an inductive research design, findings from praxis are related to theory from the field of conflict resolution. In addition, implications for addressing deep-rooted conflict are identified, including Glencree’s emphasis on the need for flexibility as a characteristic for conflict work, and an underlying worldview incorporating aspects of dynamic systems theory and chaos theory.

This exploratory qualitative case study provides a description of the Glencree Centre for Peace and Reconciliation’s practice in addressing deep-rooted conflict, from the Republic of Ireland. This research grew out of practical problems from the field of conflict resolution in Canada, in particular interest-based mediation, in addressing deep-rooted conflict. Using an extended epistemology, data is harvested from praxis to create naturalistic generalizations: guidelines for addressing deep-rooted conflict. The research findings are the result of a synthesis of three data sources: interviews with facilitators from Glencree, textual data, and nearly five months of onsite observation. The main themes derived from the research include: Glencree’s Diverse Practice; Glencree’s Approach to Conflict; Glencree’s Identity; Glencree’s Approach to Deep-Rooted Conflict; and Implementing Glencree’s Approach. This study is intended as a snapshot in time of a set of dynamic and emergent ideas addressing conflict in practice. Through an inductive research design, findings from praxis are related to theory from the field of conflict resolution. In addition, implications for addressing deep-rooted conflict are identified, including Glencree’s emphasis on the need for flexibility as a characteristic for conflict work, and an underlying worldview incorporating aspects of dynamic systems theory and chaos theory.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / A cana-de-açúcar (Saccharum spp) é uma cultura em expansão no Brasil, necessitando de práticas que aumentem a produtividade nos diferentes ecossistemas do país. Dessa forma, o presente trabalho, teve como objetivo avaliar o crescimento inicial e a tolerância à seca da variedade de cana-de-açúcar RB92579 com a aplicação de bioestimulantes e enraizadores. Para isso, foi realizado um experimento em casa de vegetação, em delineamento inteiramente casualizado. Os tratamentos utilizados foram: T1 Controle; T2 - AIB (Ácido Indolbutírico), na concentração de 1000 mg.L-1; T3 - B+Zn (Bórax, 10 Kg por hectare + Sulfato de Zinco, 20 Kg por hectare); T4 - Triptofano, 7,2 Kg por hectare; T5 - (Kymon Plus®, 1,0 L por hectare + Potamol® 0,5 L por hectare) e T6 - Stimulate®, 0,5 L por hectare. Aos 41 e 124 DAP foram coletados dados morfológicos e de biomassa para análise do crescimento inicial da planta. Aos 117 dias após o plantio foi suspensa a rega por 36 horas para avaliar o efeito dos bioestimulantes e enraizadores em mitigar o efeito do estresse hídrico. A aplicação de AIB e Stimulate® proporcionaram maiores taxas de crescimento e acúmulo de biomassa. A aplicação de Ubyfol e Stimulate® proporcionaram maiores trocas gasosas na ausência de estresse hídrico e aumentaram a eficiência quântica efetiva do PSII mesmo quando a plantas estavam sob estresse hídrico, quando comparadas com o controle. Em plantas sob estresse hídrico moderado, a aplicação de Stimulate® proporcionou a manutenção de maiores taxas de fotossíntese, transpiração e condutância estomática. O experimento deve ser repetido em campo para verificar se esses resultados se traduzem em aumento da produtividade tanto na condição de sequeiro como na condição irrigada.

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.

This dissertation asserts that the tortuous relationship Spanish American literature had with cosmopolitanism since the Wars of Independence reached a turning point towards the end of the second half of the twentieth century. While the literary production of the nineteenth and most of the twentieth century was centred on the Spanish American nation and the continent, contemporary literature has become increasingly deterritorialized, and has begun to present narrative worlds and discuss issues that transcend this circumscribed universe. The discerning of this articulation of global issues in contemporary literature – which I contend is predicated on the concept of cosmopolitanism – is the primary objective of this investigation. The five novels examined here are Elena Poniatowska’s La “Flor de Lis” (1988), Mario Vargas Llosa’s El Paraíso en la otra esquina (2003) and El sueño del celta (2010), and Jorge Volpi’s El fin de la locura (2003) and No será la Tierra (2006). This study aims to describe and assess an evolving perspective on the treatment of cosmopolitanism in Spanish America. I trace the shift from the previous generations’ main preoccupation with aesthetic cosmopolitanism, which sought to engage Latin American literary discourse with the Western canon, to what I identify as the current political implication of the concept. To this end, I show that whereas mid-twentieth century authors displaced cosmopolitanism in favour of more politically expedient concepts, authors now plot it in their novels as a means of discussing issues of identity and citizenship in an increasingly globalized world.

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.