American youth are leaving organized religion at historical levels. Given that religious and political similarity (consensual solidarity) tends to strengthen affectual solidarity (emotional connection) in parent-adolescent dyads, decreasing adolescent religiousness and increasing political disagreements may threaten family social cohesion. However, during adolescence, youth empathy skills tend to increase and adolescents’ conflict with their parents tends to eventually subside. Based on principles outlined in intergenerational family solidarity theory, I hypothesized that adolescent empathy skills and authoritative parenting style would buffer the negative relational effects of religious and political discrepancies within the parent-adolescent relationship. I used Waves 2-4 (referred to as Times 1-3) of parent-adolescent data drawn from the Family Foundations of Youth Development study (Time 2 N = 1764 families) to understand patterns of discrepancy using a person-centered analysis. As a first step in latent profile analysis, I enumerated five distinct classes in Time 2 using the indicators of religious and political identities and social cohesion at both Times 2 and 3, alongside the covariates of adolescent empathy, parenting styles, and demographic controls. Next, I labeled the five classes as follows: Class 1 – Less Religious Parents Politically Mixed (26% of the sample, n = 665); Class 2 – More Religious Parents Moderate Conservative (26% of the sample, n = 399); Class 3 – Both Somewhat Religious Conservative (20% of the sample, n = 254); Class 4 – Least Religious Adolescents Politically Mixed (14% of the sample, n = 236); and Class 5 – More Religious Adolescents Very Conservative (14% of the sample, n = 210). Finally, I compared the five classes on the longitudinal distal outcome of social cohesion at Time 3. The Less Religious Parents Politically Mixed families predicted significantly less social cohesion while the Both Somewhat Religious Conservative families predicted significantly higher social cohesion from Time 2 to 3.

We present the notions of uniform distribution and discrepancy of sequences contained in the unit interval, as well as an important application of discrepancy in numerical integration by way of the quasi-Monte Carlo method. Some fundamental (and other interesting) results with regards to these notions are presented, along with some detalied and instructive examples and comparisons (some of which not often provided by the literature). We go on to analytical and numerical investigations of the asymptotic behaviour of the discrepancy (in particular for the van der Corput-sequence), and for the general error estimates of the quasi-Monte Carlo method. Using the discoveries from these investigations, we give a conditional proof of the van der Corput theorem. Furthermore, we illustrate that by using low discrepancy sequences (such as the vdC-sequence), a rather fast convergence rate of the quasi-Monte Carlo method may still be achieved, even for situations in which the famous theoretical result, the Koksma inequality, hasbeen rendered unusable. / Vi presenterar begreppen likformig distribution och diskrepans hos talföljder på enhetsintervallet, såväl som en viktig tillämpning av diskrepans inom numerisk integration via kvasi-Monte Carlo metoden. Några fundamentala (och andra intressanta) resultat presenteras med avseende på dessa begrepp, tillsammans med några detaljerade och instruktiva exempel och jämförelser (varav några sällan presenterade i litteraturen). Vi går vidare med analytiska och numeriska undersökningar av det asymptotiska beteendet hos diskrepansen (särskilt för van der Corput-följden), såväl som för den allmänna feluppskattningen hos kvasi-Monte Carlo metoden. Utifrån upptäckterna från dessa undersökningar ger vi ett villkorligt bevis av van der Corput's sats, samt illustrerar att man genom att använda lågdiskrepanstalföljder (som van der Corput-följden) fortfarande kan uppnå tämligen snabb konvergenshastighet för kvasi-Monte Carlo metoden. Detta även för situationer där de kända teoretiska resultatet, Koksma's olikhet, är oandvändbart.

Doctor of Philosophy / Department of Mathematics / Alexander G. Ramm / Several methods for a stable solution to the equation $F(u)=f$ have been developed. Here $F:H\to H$ is an operator in a Hilbert space $H$, and we assume that noisy data $f_\delta$, $\|f_\delta-f\|\le \delta$, are given in place of the exact data $f$. When $F$ is a linear bounded operator, two versions of the Dynamical Systems Method (DSM) with stopping rules of Discrepancy Principle type are proposed and justified mathematically. When $F$ is a non-linear monotone operator, various versions of the DSM are studied. A Discrepancy Principle for solving the equation is formulated and justified. Several versions of the DSM for solving the equation are formulated. These methods consist of a Newton-type method, a gradient-type method, and a simple iteration method. A priori and a posteriori choices of stopping rules for these methods are proposed and justified. Convergence of the solutions, obtained by these methods, to the minimal norm solution to the equation $F(u)=f$ is proved. Iterative schemes with a posteriori choices of stopping rule corresponding to the proposed DSM are formulated. Convergence of these iterative schemes to a solution to the equation $F(u)=f$ is proved. This dissertation consists of six chapters which are based on joint papers by the author and his advisor Prof. Alexander G. Ramm. These papers are published in different journals. The first two chapters deal with equations with linear and bounded operators and the last four chapters deal with non-linear equations with monotone operators.

In the first part of this thesis we transfer a result of Guillopé et al. concerning the number of zeros of the Selberg zeta function for convex cocompact Schottky groups to the setting of certain types of graph directed Markov systems (GDMS). For these systems the zeta function will be a type of Ruelle zeta function. We show that for a finitely generated primitive conformal GDMS S, which satisfies the strong separation condition (SSC) and the nestedness condition (NC), we have for each c>0 that the following holds, for each w \in\$C$ with Re(w)>-c, |\Im(w)|>1 and for all k \in\$N$ sufficiently large: log | zeta(w) | <<e {delta(S).log(Im|w|)} and card{w \in\ Q(k) | zeta(w)=0} << k {delta(S)}. Here, Q(k)\subset\%C$ denotes a certain box of height k, and delta(S) refers to the Hausdorff dimension of the limit set of S. In the second part of this thesis we show that in any dimension m \in\$N$ there are GDMSs for which the Hausdorff dimension of the uniformly radial limit set is equal to a given arbitrary number d \in\(0,m) and the Hausdorff dimension of the Jørgensen limit set is equal to a given arbitrary number j \in\ [0,m). Furthermore, we derive various relations between the exponents of convergence and the Hausdorff dimensions of certain different types of limit sets for iterated function systems (IFS), GDMSs, pseudo GDMSs and normal subsystems of finitely generated GDMSs. Finally, we apply our results to Kleinian groups and generalise a result of Patterson by showing that in any dimension m \in\$N$ there are Kleinian groups for which the Hausdorff dimension of their uniformly radial limit set is less than a given arbitrary number d \in\ (0,m) and the Hausdorff dimension of their Jørgensen limit set is equal to a given arbitrary number j \in\ [0,m).

Importance sampling is a well known variance reduction technique for Monte Carlo simulation. For quasi-Monte Carlo integration with low discrepancy sequences it was neglected in the literature although it is easy to see that it can reduce the variation of the integrand for many important integration problems. For lattice rules importance sampling is of highest importance as it can be used to obtain a smooth periodic integrand. Thus the convergence of the integration procedure is accelerated. This can clearly speed up QMC algorithms for integration problems up to dimensions 10 to 12. (author's abstract) / Series: Research Report Series / Department of Statistics and Mathematics

The dissertation consists of two parts. The first part is devoted to results in Discrepancy Theory. We consider geometric discrepancy in higher dimensions (d > 2) and obtain estimates in Exponential Orlicz Spaces. We establish a series of dichotomy-type results for the discrepancy function which state that if the L¹ norm of the discrepancy function is too small (smaller than the conjectural bound), then the discrepancy function has to be very large in some other function space.The second part of the thesis is devoted to results in Additive Combinatorics. For a set with small doubling an order-preserving Freiman 2-isomorphism is constructed which maps the set to a dense subset of an interval. We also present several applications.

Purpose: Previous research has highlighted that dysfunctional customer behaviour is commonplace in service exchange interactions. However, most research has focused on what forms of dysfunctional behaviours that are prevalent in a face-to-face context. Instead of focusing on traditional face-to-face interactions, this thesis will address and consider dysfunctional customer behaviour in a live chat support context. Moreover, the reason why certain behaviours are perceived as dysfunctional in an online context will also be discussed from a role discrepancy perspective. Methodology: The methodological approach relies on a qualitative case study of the online casino company LeoVegas. The research is carried out by conducting ten semi-structured interviews with the firm's live chat customer-contact employees. The interviews were conducted via the video chat application Skype. Findings: The findings highlight five customer behaviour categories that the respondents perceived as dysfunctional. The employees thought these behaviours violated the rules and norms of the service script. However, the data implied role discrepancies between the employees and customers, where the customers and the employees had different views of the service script. The reason for these discrepancies were due to customer ignorance of reading the terms and conditions, which the employees and LeoVegas recognized as the service script. This resulted in customer violations of the service scripts which the employees perceived as dysfunctional customer behaviour. Originality/Contribution:The thesis contributes with five employee perceived categories of dysfunctional customer behaviour in a relative unstudied online support context. A theoretical contribution of the study is the introduction of a new perception of dysfunctional customer behaviour, with the researchers arguing that dysfunctional customer behaviour is not about customers violating the service script but rather that there is a role discrepancy between the customers and the employees. This leads to an important managerial implication, that managers need to ensure role congruence between employees and customers so that role discrepancy may be avoided.

Previous research has found that maternal depression is predictive of adolescents’ aggression. The present study examined three mechanisms believed to account for this relation: parenting practices, family functioning, and informant discrepancy. The data for this study are from the Multisite Violence Prevention Project which collected data from a high-risk sample of sixth grade students, parents, and core teachers. A within-subjects analysis of variance examined the association between maternal depression and informant discrepancy. Structural equation modeling compared the relation between maternal depression and adolescents’ aggression as a function of parenting practices and family functioning. Results indicated that maternal depression was related to adolescents’ aggression and moderated the degree of the discrepancy between reports of aggression. Results indicated that the relation between maternal depression and mother-report of adolescents’ aggression was mediated by parenting practices and family functioning, with parenting practices mediating the relation over and beyond family functioning.

Introduction: L’ostéogenèse imparfaite (OI) est un désordre de collagène héréditaire caractérisé par du tissu conjonctif défectueux avec une incidence de 1 sur 20 000 naissances. Il y a une surreprésentation marquée des malocclusions de Classe III, une occlusion croisée antérieure et postérieure dans la population d’OI. L’objectif principal de cette recherche est d’évaluer si la sévérité des malocclusions présente chez les patients atteints d’OI est proportionnelle à la gravité du syndrome. L’objectif secondaire de cette recherche est d’évaluer si la sévérité de la malocclusion augmente avec l’âge. Matériels et méthodes: Étude rétrospective d’observation effectuée par calcul du Discrepancy Index (DI) de 56 modèles dentaires de patients atteints d’OI. Les résultats du DI ont été comparés à trois variables qui caractérisent la gravité du syndrome: type de OI, type génétique et le Z-score de la grandeur de chaque patient. En outre, l’analyse longitudinale d’un sous-ensemble de 20 modèles a été faite pour déterminer si la sévérité de la malocclusion augmente avec le temps. Résultats: La médiane du DI était de 33,5 [1, 109]. Le DI est plus augmenté chez les patients atteints d’un type de OI plus sévère (p = 0,001) ainsi chez les patients avec un Z-score de grandeur plus bas (p <0,0001). L'analyse longitudinale a démontré une augmentation statistiquement significative de DI au fil du temps. (p=0.05) Conclusion: La malocclusion des patients atteints d’OI semble liée à la gravité de ce syndrome. En outre, la sévérité de la malocclusion semble augmenter avec l'âge. / Introduction: Osteogenesis imperfecta (OI) is an inherited collagen disorder characterized by defective connective tissue with an incidence of 1 in 20,000 births. There is a marked over-representation of Class III malocclusion, negative overjet and lateral openbite in the OI population. Objectives: Primary objective is to evaluate whether the severity of the malocclusions present in OI patients is proportional to the severity of the syndrome. Secondary objective is to evaluate whether the malocclusion severity increases with age. Methods: Retrospective observational study performed by calculating the Discrepancy Index (DI) of 56 dental casts of patients with mild to severe OI. DI scores were compared to three variables that characterize the severity of the syndrome: OI type, genetic type and height z-score of each patient. In addition, longitudinal analysis of a subset of 20 OI casts was done to determine whether the malocclusion increases in severity with time. Results: The median DI score was 33.5 [1, 109]. The DI score increased with increasing severity of OI type (p=0.001) and decreasing height z-score (p<0.0001). In addition, longitudinal analysis of 20 OI patients demonstrated a statistically significant increase in DI over time (p=0.05). Conclusion: The malocclusion characteristic of OI patients seems linked to the severity of the syndrome. In addition, the malocclusion severity seems to increase with age.

O objetivo neste estudo foi avaliar a reprodutibilidade quantitativa dos modelos tridimensionais gerados por meio de imagens de tomografia volumétrica de feixe cônico, obtidos por dois tomógrafos volumétricos NEWTOM 9000 DVT (i- (Quantitative Radiology, Verona, Itália) e i-CAT (Imaging Sciencies Int. Hatfield, Pensilvânia. Estados Unidos da América), submetidos à inspeção de engenharia reversa. Uma mandíbula macerada foi digitalizada por meio do SCANNER 3D VIVID 910, com precisão de 0,01 mm, associado à fotometria digital, sendo utilizado o software GEOMAGIC STUDIO, e assim obteve-se um modelo considerado padrão ouro. Posteriormente realizamos o exame de tomografia volumétrica de feixe cônico, na mesma mandíbula nos dois tomógrafos volumétricos, obtendo-se assim os modelos virtuais tridimensionais. Por meio de um alinhamento das geometrias do padrão ouro com os modelos virtuais resultantes da tomografia do aparelho NEWTOM 9000 DVT e do i-CAT, foram observadas as possíveis discrepâncias. Concluímos que estas alterações encontradas após a análise quantitativa das diversas regiões foram menores nas imagens adquiridas pelo tomógrafo volumétrico de feixe cônico modelo i-CAT, e portanto possibilitam a geração de modelos de prototipagem rápida de melhor qualidade. / The purpose of this study was to evaluate the quantitative reproductability of the 3d models created using CT images. The images used were obtained from two different cone beam tomographs: NEWTOM 9000 DVT (Quantitative Radiology, Verona, Italy) and i-CAT ( Imaging Sciences Int., Hatfield, EUA) and then inspected through reverse engineering processing software. A dry mandible was digitalized using a 3D Scanner VIVID 910 and the GEOMAGIC STUDIO software to obtain a 0,01mm precision model considered to be our gold standard. Two distinct 3D virtual models were then created after submitting the same dry mandible to a cone beam exam on both tomographs (NEWTOM and i-Cat). Possible discrepancies between the 3D models and the gold standard were analyzed through and alignment of their geometries. After evaluating the discrepancies at the different sites of the models, we concluded that the virtual model obtained using the i-Cat tomograph images was more accurate and therefore of greater quality.