Introdução: O hábito de fumar causa inúmeros prejuízos à saúde, entre os quais aumenta o risco de disfunção endotelial. Atualmente, o método mais utilizado para a avaliação não invasiva da função vascular, é a dilatação mediada por fluxo da artéria braquial: através da ultrassonografia. Objetivos: Avaliar em que tempo ocorre à máxima dilatação, e se existe diferença na avaliação da função endotelial avaliada pela ultrassonografia ao comparar quatro grupos de mulheres (gestantes ou não e fumantes ou não). Métodos Estudo transversal no qual foi realizada a mensuração do diâmetro da artéria braquial em repouso e em quatro tempos após estímulo (30, 60, 90 e 120 segundos) em quatro grupos de mulheres entre 20 e 30 anos de idade, incluindo gestantes entre 24 e 28 semanas de idade gestacional: gestantes não fumantes (N=47), gestantes fumantes (N=33), mulheres não fumantes (N=34) e mulheres fumantes (N=19), resultando em 133 avaliações. Resultados: Dados antropométricos, idade, paridade e idade gestacional não houve diferença significativa nos grupos estudados, bem como, os níveis de pressão arterial diastólica (PAD) (mmHg) e índice de massa corporal. Uma diferença significativa foi observada entre o número de cigarros consumidos por semana entre gestantes e não gestantes (p=0,04). A DMF foi maior entre as gestantes não fumantes em comparação às fumantes (11,50 ± 5,77 vs. 8,74 ± 4,83; p=0,03) como também no grupo de não gestantes não fumantes em comparação as fumantes (10,52 ± 4,76 vs. 7,21 ± 5,57; p=0,03). Ambas com diferença significativa em relação ao grupo controle. Em relação à avaliação da dilatação nos diferentes tempos, esta foi máxima para todos os grupos no tempo 60 segundos após a desinsuflação. Uma diferença significante foi observada em todos os tempos e entre todos os grupos. Conclusões: A máxima dilatação mediada por fluxo foi observada 60 segundos, após o estímulo em todos os grupos. O hábito de fumar parece levar a disfunção endotelial, tanto em mulheres gestantes quanto em não gestantes, o que foi demonstrado por uma menor dilatação mediada por fluxo nas fumantes. / There is innumerous health problems associated with smoking habits, among them an increased risk of endothelial dysfunction. Currently, the most used method for noninvasive evaluation of vascular function is flow-mediated dilatation (FMD) of the brachial artery determined by ultrasonography. Objectives: To determine at what time the maximum dilatation occurs and whether there is a difference in the evaluation of endothelial function determined by ultrasonography when comparing four groups of women (pregnant smokers and pregnant no smokers, and non-pregnant smokers and non-pregnant no-smokers). Methods This cross sectional study included a total of 133 women. The women were divided into 4 groups non-smoking pregnant women (N=47), smoking pregnant women (N=33), non-smoking women (N=34), and smoking pregnant women (N=19). The diameter of the brachial artery was measured at five times (rest, after a stimulus (30, 60, 90 and 120 seconds). Results: Anthropometric data, age, parity, gestational age, diastolic blood pressure (DBP) and body mass index did not differ significantly between groups. A significant difference was observed in the number of cigarettes smoked per week between pregnant women and non-pregnant women (p=0.04). The FMD was greater among non-smoking pregnant women compared to smoking pregnant women (11.50 ± 5.77 vs. 8.74 ± 4.83; p=0.03) and also among non-smoking non-pregnant women compared to smoking non-pregnant women (10.52 ± 4.76 vs. 7.21 ± 5.57; p=0.03). The difference was significant in both cases. Regarding the evaluation of dilation at the different time points, the maximum value was obtained for all groups at the 60 second time point after disinsufflation. A significant difference was observed at all times and between all groups. Conclusions: Maximum FMD was observed 60 seconds after the stimulus in all groups. The smoking habit seems to lead to endothelial dysfunction both in pregnant and non-pregnant women, as demonstrated by the lower FMD among smokers.

There are two primary sources of motivation for the contents of this thesis. The first is an effort to generalize classical dilation theory, a brief history of which is given in Section 2.1. The second source of motivation is the study of the representation theory of tensor algebras associated to C*-correspondences; these concepts are discussed in Sections 2.2 and 2.4. Although seemingly unrelated, there is a close connection between these two motivating theories. The link between classical dilation theory and the representation theory of tensor algebras over C*-correspondences was established by Muhly and Solel in their 1998 paper Tensor Algebras over C*-Correspondences: Representations, Dilations, and C*-Envelopes. In that paper, the authors not only introduced the concept of (operator-theoretic) tensor algebras – non-selfadjoint operator algebras that generalize algebraic tensor algebras – but they also developed the representation theory of these algebras. In order to do so, they introduced and made extensive use of a generalized dilation theory for contractions on Hilbert space. In analogy with classical dilation theory, they developed notions of “isometric dilation” and “coisometric extension” for completely contractive representations of the tensor algebra. The process of forming isometric dilations proceeded smoothly, but constructing coisometric extensions proved more problematic. In contrast to the classical case, Muhly and Solel showed that there is a high degree of nonuniqueness involved when building coisometric extensions. This lack of uniqueness proved to be an impediment to developing a full generalization of the dilation and model theories of Sz.-Nagy and Foias. In this thesis, we introduce a way to manage the ambiguities that arise when forming coisometric extensions. More specifically, we show that the notion of a transfer operator from classical dynamics can be adapted to this setting, and we prove that when a transfer operator is fixed in advance, every completely contractive representation of the tensor algebra admits a unique coisometric extension that respects the transfer operator in a fashion that we describe in Chapter 5. We also prove a commutant lifting theorem in the context of coisometric extensions.

The Discrete Element Method was first introduced by Cundall and Strack (1979) to model granular soils within the context of geotechnical engineering. The material is modeled as a random assembly of discrete elements. Each particle interacts with neighboring particles through contact forces that can be built up and broken at any time. The particles were modeled as discs in 2-D or as spheres in 3-D. Research studies have been conducted to improve the simulation of actual grain shapes. Ashmawy et al. (2003) developed the overlapping rigid clusters (ORC) method to accurately model irregular particle shapes. The idea relies on clumping a number of overlapping discs such that their coincides with that of the actual particle. In this dissertation, experimental verification program is presented. An experimental setup was built and model-grains were manufactured in the laboratory. A numerical simulation for the experimental test was carried out. The numerical and experimental results were compared qualitatively and quantitatively. A good agreement was observed within small displacements ranges. However, results were considerably different at large displacements. Numerical results utilizing the ORC method were closer to the experimental results than those of discs. A sequential and operator-independent procedure, which relies on the ORC concept, was developed. Identical inertial properties between the actual particle and the model were ensured. The new procedure was implemented for rounded and angular particles. The effect of particle shape and angularity on the strength and dilatancy characteristics of granular soils was investigated. A modified shape factor, which relies on the work introduced by Sukumaran and Ashmawy (2001), was developed. A series of pure shear testing simulations was performed on different shape and angularity particle groups. Angularity had a remarkable effect on strength and dilatancy properties compared to shape. The effect of interparticle friction on dilatancy was studied. An attempt was made to use an equivalent interparticle friction to model different particle shapes. It was concluded that there is no one-to-one equivalency between interparticle friction and shape or angularity. Instead, the interparticle friction must be continuously altered as a function of confining pressure and void ratio to achieve the required effect.

This thesis consists of studies in the separate fields of operator algebras and non-associative algebras. Two natural operator algebra structures, A ⊗_max B and A ⊗_min B, exist on the tensor product of two given unital operator algebras A and B. Because of the different properties enjoyed by the two tensor products in connection to dilation theory, it is of interest to know when they coincide (completely isometrically). Motivated by earlier work due to Paulsen and Power, we provide conditions relating an operator algebra B and another family {C_i}_i of operator algebras under which, for any operator algebra A, the equality A ⊗_max B = A ⊗_min B either implies, or is implied by, the equalities A ⊗_max C_i = A ⊗_min C_i for every i. These results can be applied to the setting of a discrete group G pre-ordered by a subsemigroup G⁺, where B ⊆ C*_r(G) is the subalgebra of the reduced group C*-algebra of G generated by G⁺, and C_i = A(Q_i) are digraph algebras defined by considering certain pre-ordered subsets Q_i of G. The 16-dimensional algebra A₄ of real sedenions is obtained by applying the Cayley-Dickson doubling process to the real division algebra of octonions. The classification of subalgebras of A₄ up to conjugacy (i.e. by the action of the automorphism group of A₄) was completed in a previous investigation, except for the collection of those subalgebras which are isomorphic to the quaternions. We present a classification of quaternion subalgebras up to conjugacy.

The endothelium plays an essential role in the regulation of vascular homeostasis and a state of endothelial dysfunction, which develops in the presence of cardiovascular risk factors, may contribute to the development and progression of cardiovascular disease. As such, the measurement of endothelial function, beyond being an experimental tool, may serve as an important tool to complement current risk assessment algorithms in the identification of high-risk patients. Flow-mediated dilation (FMD) is a non-invasive measure of peripheral conduit artery endothelial function that holds great promise. Presently, FMD suffers from methodological heterogeneity and a poor understanding of the various biological components involved in eliciting the dilatory response to a given shear stimulus. We compared both traditional and alternative methods of arterial diameter characterization with regards to their repeatability, nitric oxide-dependency, and their sensitivity in distinguishing between normal and dysfunctional endothelial responses. Our findings emphasize the importance of continuous arterial diameter measurement and suggest that the time to peak FMD is not a useful adjunctive measure of the FMD response. Given that endothelial dysfunction may be of clinical importance, strategies to correct it or prevent it from occurring may be of benefit. The 3-hydroxy-3-methylglutaryl coenzyme A inhibitors are agents that have demonstrated marked cholesterol-independent, endothelial-protective effects. We investigated the ability of rosuvastatin and atorvastatin to protect against endothelial dysfunction associated with ischemia and reperfusion (IR) injury, and chronic nitrate therapy. Using the FMD technique, we demonstrated, for the first time in humans, that acute rosuvastatin administration protects against IR-induced conduit artery endothelial dysfunction. Additionally, we demonstrated that this effect likely occurred by a cyclooxygenase-2-dependent mechanism, which may provide mechanistic insight into the observed cardio-toxicity with cyclooxygenase-2 inhibitors. In contrast, we observed that this endothelial-protective effect was lost upon sustained rosuvastatin administration, which may have important implications regarding the generation of sustained cardioprotective phenotypes. Finally, we demonstrated that atorvastatin co-administration prevented the development of tolerance and endothelial dysfunction associated with continuous transdermal nitroglycerin therapy in humans, likely through an antioxidant mechanism. Future studies are needed in disease patients to determine whether the concept of nitrate tolerance needs reconsideration in the presence of vascular-protective agents.

The endothelium plays an essential role in the regulation of vascular homeostasis and a state of endothelial dysfunction, which develops in the presence of cardiovascular risk factors, may contribute to the development and progression of cardiovascular disease. As such, the measurement of endothelial function, beyond being an experimental tool, may serve as an important tool to complement current risk assessment algorithms in the identification of high-risk patients. Flow-mediated dilation (FMD) is a non-invasive measure of peripheral conduit artery endothelial function that holds great promise. Presently, FMD suffers from methodological heterogeneity and a poor understanding of the various biological components involved in eliciting the dilatory response to a given shear stimulus. We compared both traditional and alternative methods of arterial diameter characterization with regards to their repeatability, nitric oxide-dependency, and their sensitivity in distinguishing between normal and dysfunctional endothelial responses. Our findings emphasize the importance of continuous arterial diameter measurement and suggest that the time to peak FMD is not a useful adjunctive measure of the FMD response. Given that endothelial dysfunction may be of clinical importance, strategies to correct it or prevent it from occurring may be of benefit. The 3-hydroxy-3-methylglutaryl coenzyme A inhibitors are agents that have demonstrated marked cholesterol-independent, endothelial-protective effects. We investigated the ability of rosuvastatin and atorvastatin to protect against endothelial dysfunction associated with ischemia and reperfusion (IR) injury, and chronic nitrate therapy. Using the FMD technique, we demonstrated, for the first time in humans, that acute rosuvastatin administration protects against IR-induced conduit artery endothelial dysfunction. Additionally, we demonstrated that this effect likely occurred by a cyclooxygenase-2-dependent mechanism, which may provide mechanistic insight into the observed cardio-toxicity with cyclooxygenase-2 inhibitors. In contrast, we observed that this endothelial-protective effect was lost upon sustained rosuvastatin administration, which may have important implications regarding the generation of sustained cardioprotective phenotypes. Finally, we demonstrated that atorvastatin co-administration prevented the development of tolerance and endothelial dysfunction associated with continuous transdermal nitroglycerin therapy in humans, likely through an antioxidant mechanism. Future studies are needed in disease patients to determine whether the concept of nitrate tolerance needs reconsideration in the presence of vascular-protective agents.

In this thesis, a method to calculate scaling function coefficients for a new bi-orthogonal wavelet family derived directly from an impulse response waveform is presented. In literature, the Daubechies wavelets (DB wavelet) and the Morlet wavelet are the most commonly used wavelets for the dyadic wavelet transform (DWT) and the continuous wavelet transform (CWT), respectively. For a specific vibration signal processing application, a wavelet basis that is similar or is derived directly from the signal being studied proves to be superior to the commonly used wavelet basis. To assure a wavelet basis has a direct relationship to the signal being studied, a new formula is proposed to calculate coefficients which capture the characteristics of an impulse response waveform. The calculated coefficients are then used to develop a new bi-orthogonal wavelet family.

We show that results on the characterization of admissible quantizations, which have been derived in Potzelberger [3], have to be modified in case the probability distribution has linear components. Furthermore, we provide an example, where the limit of optimal quantizations is not admissible. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

Let P be a Borel probability measure on Rd. We characterize the maximal elements p E M(P,m) with respect to the Bishop-De Leeuw order, where p E M(P, m) if and only if p P and [supp(p)] m. The results obtained have important consequences for statistical inference, such as tests of homogeneity or multivariate cluster analysis and for the theory of comparison of experiments. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

In this thesis, we examine quasiconformal mappings in Rn. We begin by proving basic properties of the modulus of curve families. We then give the geometric, analytic,and metric space definitions of quasiconformal maps and show their equivalence. We conclude with several computational examples.