Orientador: Sergio Antonio Tozoni / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-24T12:51:29Z (GMT). No. of bitstreams: 1 Reis_HenriqueCostados_M.pdf: 703227 bytes, checksum: eb7b033a2901dc0b4b5f4219968ab619 (MD5) Previous issue date: 2014 / Resumo: Essa dissertação tem como objetivo principal estudar estimativas superiores e inferiores de n-larguras de classes de Sobolev sobre a esfera unitária d-dimensional real. No primeiro capítulo, é realizado um estudo de alguns resultados básicos sobre os espaços Lp. No segundo capítulo, é realizado um estudo sobre algumas funções definidas na esfera d-dimensional real tais como os harmônicos esféricos e os harmônicos zonais e também são estudadas estimativas para médias de Levy de algumas normas especiais definidas no espaço euclidiano n-dimensional. O terceiro capítulo é o último e mais importante. Nele são estudadas estimativas superiores e inferiores para n-larguras de Kolmogorov das classes de Sobolev de funções definidas na esfera. Várias dessas estimativas são assintoticamente exatas em termos de ordem / Abstract: The main purpose of this work is to study upper and lower bounds for n-widths of Sobolev classes on the d-dimensional real unit sphere. In the first chapter, it is studied some basic results about Lp spaces. In the second chapter, it is studied some functions defined on the d-dimensional real sphere such as spherical harmonics and zonal harmonics and also it is studied estimates for Levy means of some special norms defined on the n-dimensional Euclidean space. The third chapter is the last and the most important. In this chapter, it is studied Kolmogorov n-widths of Sobolev classes of functions defined on the sphere. Many of these estimates are asymptotically sharp in the sense of order / Mestrado / Matematica / Mestre em Matemática

This thesis compared tooth widths, arch widths, and arch lengths; their differences between males and females, and changes from early mixed dentitions to adult dentitions. Comparing subjects who were known to have Angle Class I normal occlusion in their permanent dentitions to subjects who were known to be Class I or Class II crowded malocclusions in their permanent dentitions. These comparisons can only be achieved utilizing data from a longitudinal study, such as the Iowa Growth Study. Dental casts in the early mixed dentition (average age of 8.85 years) and in the adult dentition (average age 15.45 years) taken from subjects who did not receive orthodontic treatment during or in the dates prior to data collection were measured for this study. The casts utilized were from the Iowa Growth Study; all of the subjects were of European descent. The longitudinal sample of casts in the Iowa Growth study were made from white dental stone poured into alginate impressions from 1946 until 1960. The objectives of this study were to compare individual tooth widths, mean sum tooth widths, arch widths, arch length segments, and arch perimeters of Class I Normal (CIN) and Class I and II crowded dentitions (CD) in the early mixed (MD) and permanent (PD) dentitions to explore new methods of predicting crowding. The goal was to evaluate the significance of differences between MD and PD for tooth widths, arch lengths, and arch widths in both arches of CIN and CD subjects to determine values that may be useful for MD space analysis. Thirty males and thirty females from the Iowa Growth Study with CIN and CD occlusions were selected from the longitudinal study. Casts of MD and PD subjects were double measured with digital calipers by both the primary and secondary investigators. The average of each investigator's two measurements were used to determine measurement error. All other statistical analysis was based on the mean measurements taken by CPW. Descriptive statistics were computed. The normal non-crowded and crowded samples were compared with two-sample t-test, and changes from MD to PD with paired-sample t-test. Examiner measurement errors were tested with intra-class correlation coefficients. When the mean sums of MD and PD tooth widths were compared, using data from all 60 subjects, the CD group had a significantly greater mean sum of tooth widths than the CIN group. In both genders, crowded dentitions had significantly greater mean sum of tooth widths than CIN's for both the maxilla and mandible in MD and PD. When the mean sums of the arch lengths [Perimeters] were compared using data from all 60 subjects, the arch perimeters of the CD and CIN samples did not differ. It was concluded that total arch lengths Perimeters] were not significant indicators for crowding. Gender comparisons: Within the CIN group, males had numerically larger tooth width sums and arch length sums than females. The sum of maxillary and mandibular tooth widths for CIN's and CD (both males and females) mandibular tooth widths for CIN's and CD (both males and females pooled together and sexes separately. In the MD stage the mean sum of maxillary and mandibular arch lengths in the MD were significantly greater than those in the PD, because arch perimeters decrease during the transition from mixed to permanent dentitions. In summary, the results of this research thesis study showed that the sum of tooth widths in both arches had a significant association with dental crowding. In contrast, the sum of arch lengths [perimeter in both arches] did not differ between the normal and crowded samples. Additional analysis of the measurements taken in this thesis research project, the individual arch length segments, especially the canine and posterior arch length segments in the right and left sides of the lower arch in the mixed dentition casts, and their relation to the sum of the widths of the lower permanent canines and premolars in the normal and crowded malocclusions may give us important information about the development of crowded malocclusions.

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The Texas Department of Transportation (TxDOT) uses precast, prestressed concrete panels (PCPs) as stay-in-place formwork for most bridges built in Texas. The PCPs are placed on the top flanges of adjacent girders and topped with a 4-in. cast-in-place (CIP) slab. This thesis is directed towards identifying and quantifying the serviceability implications of reducing the deck reinforcement across the interior spans of CIP-PCP decks. The goal of this research is to understand how the PCPs influence cracking and crack control in the CIP slab and to make recommendations to optimize the top mat reinforcement accordingly. Several tests were conducted to evaluate the performance of different top mat reinforcement arrangements for ability to control crack widths across PCP joints. The longitudinal reinforcement was tested using a constant bending moment test, a point load test, and several direct tension tests. Because of difficulty with the CIP-PCP interface during the longitudinal tests, direct tension tests of the CIP slab only were used to compare the transverse reinforcement alternatives. Prior to testing, various top mat design alternatives were evaluated through pre-test calculations for crack widths. Standard reinforcing bars and welded wire reinforcement were considered for the design alternatives. During this study, it was found that the tensile strength of the CIP slab is critical to controlling transverse crack widths. The CIP-PCP interface is difficult to simulate in the laboratory because of inherent eccentricities that result from the test specimen geometry and loading conditions. Furthermore, the constraint and boundary conditions of CIP-PCP bridge decks are difficult to simulate in the laboratory. Based on the results of this testing program, it seems imprudent to reduce the longitudinal reinforcement across the interior spans of CIP-PCP decks. The transverse reinforcement, however, may be reduced using welded wire reinforcement across the interior spans of CIP-PCP decks without compromising longitudinal crack width control. A reduced standard reinforcing bar option may also be considered, but a slight increase in longitudinal crack widths should be expected. / text

Measurements of line width parameters for eleven rotational transitions of type (J -- J + 1) of SO2 were made and are reported herein. The line width quantum number (J) trend was obtained. The microwave spectrograph used for these measurements of line width is described. Operational methods to operate the spectrograph are presented and discussed, with particular attention given to how to measure the line width. Suggestions for future avenues of probing this molecule to ascertain the non-uniform behavior of the line width parameter over the quantum number and frequency range are given.

This paper presents an analysis of tree-ring growth patterns of male and female Fraxinus mandshurica trees from 1931 to 2007. The specific object was to study the response of radial growth to climate variables separately for male and female trees. The results show that the growth patterns in the two genders were similar during the mid-1950s to 1970s but different in the periods 1931–1940s and 1980–2007. In the period 1980–2007, the mean sensitivity and mean widths of the tree rings were significantly different between the genders (p < 0.05). The climate-growth response in female and male trees was also different. Female trees are sensitive to precipitation in November of the previous year, whereas male trees respond to mean temperature in November of the previous year. The results confirm that climatic sensitivity in male and female trees of dioecious species is different, yet this difference is not stable through time.

In this paper we consider sequences of best approximation. We first examine the rho best approximation function and its applications, through an example in approximation theory and two new examples in calculating n-widths. We then further discuss approximation theory by examining a modern proof of Weierstrass's Theorem using Dirac sequences, and providing a new proof of Chebyshev's Equioscillation Theorem, inspired by the de La Vallee Poussin Theorem. Finally, we examine the limits of approximation theorem by looking at Bernstein Lethargy theorem, and a modern generalization to infinite-dimensional subspaces. We all note that smooth functions are bounded by Jackson's Inequalities, but see a newer proof that a single non-differentiable point can make functions again susceptible to lethargic rates of convergence.

Magister Scientiae Dentium - MSc(Dent) / BACKGROUND: Plaster models form an integral part of the traditional orthodontic records. They are necessary for diagnosis and treatment planning, case presentations as well as for the evaluation of treatment progress. The accuracy of the measurements taken for space assessment is crucial prior to treatment planning. The introduction of digital models overcomes some problems experienced with plaster models. Digital models have shown to be an acceptable alternative for plaster models. AIM: The aim of the study was to determine the accuracy of traditional measurement techniques when compared to the CAD/ CAM measurements in the assessment of tooth widths and arch perimeter from plaster models. METHOD: The mesio-distal tooth widths and arch perimeter of thirty archived plaster models were measured using a digital caliper to the nearest 0.01 mm and divider to the nearest 0.1 mm. Corresponding digital models were produced by scanning them with a CAD/CAM (InEos X5) and space analysis completed by measurements using InEos Blue software. Measurements were repeated after 1 week from the initial measurement. The methods were compared using descriptive analysis (mean difference and standard deviation). RESULTS: The operator reliability was high for digital models as well as the plaster models when the measurement tool was the digital caliper (analyzed using the Pearson correlation coefficient in the paired t-test). The mean values of tooth widths measurements of CAD/CAM, digital caliper and divider were 6.82 (±0.04), 6.94 (± 0.04) and 7.11 (± 0.04). There was a significant difference between the measurements made by the CAD/CAM and the divider. Additionally significant differences between the measurements by digital caliper and divider measurements (p < 0.05) were observed. No significant difference was found when comparing CAD/CAM to digital caliper. Positive correlation was displayed between CAD/CAM, digital caliper and the divider, but the measurements completed with the digital caliper had the highest correlation with the CAD/CAM. The difference was not significant between the aforementioned measurement tools (p > 0.05). Arch perimeter measurements showed no statistical significant difference between CAD/CAM, digital caliper and divider (p < 0.05). CONCLUSION: Archived plaster models stored as records can be converted to digital models as it will have the same accuracy of measurements. The value of doing a space analysis with the CAD/CAM system can be performed with similar reliability on the digital models as a caliper on plaster models.

The threshold characteristics of multimode laser oscillators are considered in detail, and a new model is given for semiconductor diode lasers. Analytical expressions and numerical solutions are obtained for mode amplitudes, and over-all spectral characteristics of lasers operating above and below threshold. The theoretical results are i n agreement with experimental data. The band-ta-band absorption is included in the model and i t ' s effect is studied on the mixed broadening.

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