<p> The principal object of this study is to find weak and strong type estimates concerning functions in weighted Lp spaces and their maximal functions. We also apply these results to the study of convolution integrals. </p> / Thesis / Master of Science (MSc)

No description available.

Let <b>X</b> be a compact Hausdorff space and <b>A</b> a uniform algebra on <b>X</b>. Let if be an isometric unital representation that maps <b>A</b> into bounded linear operators on a Hilbert space. This research investigated that there is a one-to-one correspondence between the collection of maximal sets of antisymmetry for <b>A</b> and that of maximal projections of antisymmetry for π (<b>A</b>) under the extension of π if π satisfies a certain regularity property. / Ph. D.

O principal objetivo deste trabalho é apresentar um estudo sistemático da teoria dos espaços topológicos resolúveis e irresolúveis. Enfocaremos diversas propriedades inerentes aos mesmos, incluindo uma exposição meticulosa de técnicas utilizadas na construção de espaços topológicos irresolúveis e sem pontos isolados. Dado um cardinal \\kappa > 1, exibiremos exemplos de espaços topológicos que são \\kappa-resolúveis, mas que não são \\kappa^{+}-resolúveis. Mostraremos, ainda, que se um espaço topológico for n-resolúvel, para todo número natural n, o mesmo será \\omega-resolúvel. Provaremos, contudo, que se \\lambda é um cardinal tal que \\omega < cf(\\lambda) = \\lambda, existe um espaço topológico que é \\mu-resolúvel, para todo cardinal \\mu < \\lambda, mas que não é \\lambda-resolúvel. O cerne desta dissertação refere-se à construção, em ZFC, de um subespaço enumerável, denso e submaximal de 2^c. / The main purpose of this work is to study the theory of resolvable and irresolvable topological spaces. We shall introduce many properties of these spaces and we shall give special attention to some techniques used in the construction of irresolvable topological spaces without isolated points. Given a cardinal \\kappa > 1, we will present some examples of topological spaces which are \\kappa-resolvable, but not \\kappa^{+}-resolvable. Besides, we will show that if a topological space is n-resolvable, for every natural number n > 1, then it is \\omega-resolvable too. Nevertheless, we shall prove that if \\lambda is a cardinal with \\omega < cf(\\lambda) = \\lambda, there is a topological space which is \\mu-resolvable, for each cardinal \\mu < \\lambda, but that is not \\lambda-resolvable. The backbone of this dissertation is the construction, in ZFC, of a countable, dense and submaximal subspaces of 2^c.

O principal objetivo deste trabalho é apresentar um estudo sistemático da teoria dos espaços topológicos resolúveis e irresolúveis. Enfocaremos diversas propriedades inerentes aos mesmos, incluindo uma exposição meticulosa de técnicas utilizadas na construção de espaços topológicos irresolúveis e sem pontos isolados. Dado um cardinal \\kappa > 1, exibiremos exemplos de espaços topológicos que são \\kappa-resolúveis, mas que não são \\kappa^{+}-resolúveis. Mostraremos, ainda, que se um espaço topológico for n-resolúvel, para todo número natural n, o mesmo será \\omega-resolúvel. Provaremos, contudo, que se \\lambda é um cardinal tal que \\omega < cf(\\lambda) = \\lambda, existe um espaço topológico que é \\mu-resolúvel, para todo cardinal \\mu < \\lambda, mas que não é \\lambda-resolúvel. O cerne desta dissertação refere-se à construção, em ZFC, de um subespaço enumerável, denso e submaximal de 2^c. / The main purpose of this work is to study the theory of resolvable and irresolvable topological spaces. We shall introduce many properties of these spaces and we shall give special attention to some techniques used in the construction of irresolvable topological spaces without isolated points. Given a cardinal \\kappa > 1, we will present some examples of topological spaces which are \\kappa-resolvable, but not \\kappa^{+}-resolvable. Besides, we will show that if a topological space is n-resolvable, for every natural number n > 1, then it is \\omega-resolvable too. Nevertheless, we shall prove that if \\lambda is a cardinal with \\omega < cf(\\lambda) = \\lambda, there is a topological space which is \\mu-resolvable, for each cardinal \\mu < \\lambda, but that is not \\lambda-resolvable. The backbone of this dissertation is the construction, in ZFC, of a countable, dense and submaximal subspaces of 2^c.

Syfte och frågeställningar Syftet med den här studien var att undersöka den aeroba fysiska aktivitetsnivån hos gymnasieungdomar på Bygg- och anläggningsprogrammet under skoldagar som innehöll teorilektioner, praktiska lektioner, idrottslektioner och raster. Frågan som ställdes var: Hur ser den fysiska aktivitetsnivån ut under teorilektioner, praktiska lektioner och lektioner i idrott och hälsa samt under raster hos gymnasieelever på Bygg- och anläggningsprogrammet. Metod I studien deltog 9 pojkar i åldern 16 år, längd 174-192cm och vikt 51-91kg. Den test som genomförts är 5 Minuters Pyramid Test (5MPT) och registrering av aerob fysisk belastning gjordes med hjärtfrekvensmätningar. 5MPT är ett skytteltest som är fem minuter långt, där försökspersonen tar sig fram och tillbaka mellan två stolpar och så snabbt som möjligt passerarfram och tillbaka över en vertikal pyramidformad trappramp (sträcka 5,5 meter). Antalet vändor, skattad ansträngning samt hjärtfrekvens (HF) registrerades. Utvecklad power (effekt) erhölls genom produkten av kroppsmassa, gravitation, antal vändor, höjd på högsta plinten (0,53 m) dividerat med total tiden i 5MPT. Utifrån 5MPT kunde beräknad VO2 max samt Power/kg (W/kg) beräknas för försökspersonen. Testet med hjärtfrekvensregistrering gick till så att eleverna under en skolvecka hela skoldagen bar en pulsklocka med förtejpad urtavla och ett elektrodbälte. De tryckte på händelsemarkering vid rast och när lektionen startade igen. Eleverna förde dagbok där de beskrev vad de gjort under dagen.  Resultat För samtliga försökspersoner kan man se en genomgående trend avseende fysisk belastningsnivå uttryckt som hjärtfrekvens vilket syns i följande resultat. Den högsta pulsen uppnåddes under idrottslektionerna med en genomsnittlig hjärtfrekvens på ca 140 slag/min, den näst högsta under de praktiska lektionerna med 94 slag/min. Därnäst följde rasterna med 83 slag/min och lägst utslag visades under teorilektionerna med en genomsnittlig hjärtfrekvens på ca 80 slag/min. Försökspersonerna utnyttjade ca 30 % av sin maximala syreupptagningsförmåga under de praktiska lektionerna. Slutsats Den här studien har visat att det är under undervisningen i idrott och hälsa och delvis på de praktiska lektionerna som en högre aktivitetsnivå mätt i hjärtfrekvens kan noteras hos försökspersonerna. Studien indikerar också att försökspersonerna utsätts för relativt hög fysisk belastning. Ca 30 % av den maximala syreupptagningsförmågan utnyttjas vid en skoldag med praktiska lektioner. / Aim The aim of the study was to investigate the aerobic physical activity level of high school students who study to become building workers during school days which consist of theory classes, practical classes, physical education classes and pauses. The question to be answered was: How was the aerobic physical activity level during theory classes, practical classes, physical education classes and pauses for high school students in a program for building workers. Method In this study participated 9 boys aged 16, length 174-192 cm and weight 51-91 kg. The test that has been carried out was 5 Minutes Pyramid Test (5MPT). In addition heart rate was measured during the school day. The 5MPT is a 5-minute-shuttle test, in which the participant moves back and forth in a short interval (5.5 m) over boxes (highest height 0.53 m) formed like a pyramid. Power in the pyramid test (5MPT POWER) was calculated as the product of numbers of laps, body mass, gravity and highest box level divided by time. From 5 MPT VO2 max and Power/kg (W/kg) were calculated for the participants. The participant’s heart rates were measured during a week the whole school day by means of a heart monitor with the monitor display taped over and an electrode belt. They pushed a button on the clock to mark when they had pauses and when the classes started again. The participants wrote in a diary what they had done during each day. Results The results show that for each of the participants the same trend considering aerobic physical load level expressed in heart rate in the following results. The highest pulse rate was obtained during the physical education lessons 140 beats/min followed by practical lessons 94 beats/min, pauses 83 beats/min and theory lessons 80 beats/min. The participants are using approximately 30 % of their maximal oxygen uptake during a day with practical lessons. Conclusions This study shows that it is during physical education lessons and to some extent during practical lessons in building construction, a higher activity level measured in heart rate can be noticed in the participants. The study indicates that the participants are exposed to a relative high physical workload. Roughly 30 % of maximal oxygen uptake is used during a day of practical lessons.

CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / Este trabalho à baseado no artigo "Uniquely Covered Groups" de M. A. Brodie, que investiga grupos finitos que possuem uma Ãnica cobertura irredundante por subgrupos prÃprios. O resultado principal obtido por M. A. Brodie assegura que um grupo finito e nÃo nilpotente G à unicamente coberto se, e somente se, G/Z(G) à um grupo nÃo abeliano de ordem pq, onde p e q sÃo primos distantes e {x,Z(G) à cÃclico para todo x â G. Nosso propÃsito à apresentar a demonstraÃÃo e uma aplicaÃÃo deste teorema. / This work is based on the article "Uniquely Covered Groups" due to M. A. Brodie, which investigates finite groups that have a single irredundante coveraging by subgroups. The main result obtained by M. A. Brodie asserts that a non-nilpotent finite group G is uniquely covered if and only if, G/Z(G) is a non-Abelian group of order pq, where p and q are distinct primes and {x,Z(G) is cyclic for every x â G. Our purpose is to present the proof and application of this theorem.

The aim of this thesis was to investigate the extent of peripheral and central components in the development of fatigue during maximal exercise. Fatigue during maximal and supramaximal exercise has traditionally been modelled from the peripheral context of an inadequate capacity to supply metabolic substrate to the contracting muscles to meet the increased energy demand. However, there are a number of observations that are not compatible with the peripheral fatigue model but which support a reduced central drive during exercise acting to prevent organ failure that might occur should the work be continued at the same intensity. Candidates for the role of “exercise stopper” have been identified as mechanical forces, teleoanticipation, cardiovascular capacity and dyspnoea. We explored these various possibilities in order to determine the most likely cause of exercise cessation during high intensity exercise.The development of a plateau in oxygen consumption during maximal incremental exercise has traditionally been used as evidence that an oxygen deficiency in the exercising muscles causes the termination of exercise. However, the incidence of this “plateau phenomenon” depends largely on mode of exercise, testing protocol and sampling frequency. The aim of this study was to examine whether the development of the “plateau phenomenon” is an artefact of pedalling cadence. In the first study nine healthy individuals performed in random order a maximal incremental ramp test (0.5 W.s-1) on four occasions at a fixed cadence of 60, 80 or 100 rpm and at a self-selected cadence. Oxygen consumption (VO2), CO2 production (VCO2), minute ventilation (VE) and heart rate were measured throughout each trial and averaged over 30 s. Cadence was recorded every second. Neither VO2max nor peak power output were different between trials. Submaximum VO2, VCO2 and VE were not influenced by cadence. A plateau in oxygen consumption was observed in 14% of the trials. Cadence declined significantly towards the end of the self-selected cadence trial (p < 0.05). This ramp protocol produces a low incidence of the “plateau phenomenon” and the measured physiological variables are unaffected by cadence. Furthermore, only one subject displayed this phenomenon on more than one occasion. This confirms that the “plateau phenomenon” is an artefact of the testing protocol. The significant fall in cadence in anticipation of exercise termination during the self-selected cadence trial indicates the presence of a neural regulation, which would lead to a “plateau phenomenon” in those cycle tests in which the work rate is cadence-dependent.The purpose of the second study was to assess whether pacing strategies are adopted during supramaximal exercise bouts lasting longer than 30 s. Eight healthy males performed six Wingate Anaerobic Tests (WAnT). Subjects were informed that they were performing four 30 s WAnT and a 33 s and 36 s WAnT. However, they actually completed two trials of 30, 33 and 36 s each. Temporal feedback in the deception trials was manipulated so that subjects were unaware of the time discrepancy. Power output (PO) was determined from the angular displacement of the flywheel and averaged over 3 s. The peak power (PPI), mean power (MPI) and fatigue (FI) indices were calculated for each trial. Power output was similar for all trials up to 30 s. However, at 36 s the PO was significantly lower in the 36 s deception trial compared to the 36 s informed trial (392 ± 32 W vs 470 ± 88 W) (p < 0.001). The MPI was significantly lower in the 36 s trials (714 ± 76 W and 713 ± 78 W) compared to the 30 s trials (745 ± 65 W and 764 ± 82 W) although they were not different at 30 s (764 ± 83 W and 755 ± 79 W). The significant reduction in FI was greatest in the 36 s deception trial. In conclusion, the significant reduction in PO in the last six seconds of the 36 second deception trial, but not in the 36 second informed trial, indicates the presence of a pre-programmed 30 second “end point” based on the anticipated exercise duration from previous experience. Furthermore the similarity in pacing strategy in all informed trials suggests that the pacing strategy is centrally regulated and is independent of the total work to be performed.Athletes adopt a pacing strategy to delay fatigue and optimise athletic performance. However, many current theories of the regulation of muscle function during exercise do not adequately explain all observed features of such pacing strategies. We studied power output, oxygen consumption and muscle recruitment strategies during successive 4km cycling time trials to determine whether alterations in muscle recruitment by the central nervous system could explain the observed pacing strategies. Seven, highly trained cyclists performed three consecutive 4 km time trial intervals, each separated by 17 minutes. Subjects were instructed to perform each trial in the fastest time possible, but were given no feedback other than distance covered. Integrated electromyographic (iEMG) readings were measured at peak power output and for 90 s before the end of each trial. Subjects reach a VO2max in each interval. Time taken to complete the first and third intervals was similar. Peak power output was highest in the first interval but average power output, oxygen consumption, heart rate and postexercise plasma lactate concentrations were not different between intervals. Power output and iEMG activity rose similarly during the final 60 s in all intervals but were not different between trials. The similar pacing strategies in successive intervals and the parallel increase in iEMG and power output towards the end of each interval suggests that these pacing strategies could not have been controlled by peripheral mechanisms. Rather, these findings are compatible with the action of a centrally regulated that are recruited and de-recruited during exercise. The extent to which peripheral feedback influences recruitment patterns could not be determined from these experiments.The fourth study examined whether the supplementation of inspired air with a hyperoxic mixture results in a dose-dependent increase in peak work rate and maximal oxygen consumption (VO2max) during a ramp test to volitional exhaustion. To avoid the methodological disadvantages associated with breathing the gas mixtures from mixing bags, the trials were performed in a sealed chamber in which the oxygen fraction (FIO2) in the ambient air was altered and subjects were able to inhale directly from the environment. The three oxygen fractions in which the subjects exercised were 21% (room air), 35 or 60%. Arterial blood sampling occurred at rest and every 3 min during the trial. The blood was analysed for the partial pressure of oxygen (pO2), and carbon dioxide (pCO2); pH; oxygen saturation (sO2); haemoglobin saturation (O2Hb); and lactate concentrations. Expired gas and heart rate were measured continuously. Arterial sO2 and O2Hb were elevated in both hyperoxic conditions and did not fall throughout either trial. However in the normoxic trial sO2 and O2Hb declined over the duration of the trial. Lactate concentrations and pH were similar between all trials. VO2max was significantly higher with an FIO2 of 35 and 60% but was not different between hyperoxic conditions. Maximal ventilation (VEmax), carbon dioxide production (VCO2max) and heart rate were similar for all trials. Peak power output was increased in the trained athletes in the 60% FIO2 trial. Since the plateau phenomenon occurred infrequently in all trial (~9%) and the effect of hyperoxia on performance was less than the changes in blood oxygen carrying capacity, we conclude that hyperoxia improved exercise performance not solely by increasing oxygen delivery to the exercising muscles.In order to be able to directly compare the results from studies using different equipment it is important to know the interchangeability of the results from the machines. The fifth study tested the reliability and interchangeability of the two automated metabolic gas analyser systems that would be used in this series of studies at a range of submaximal workloads. Eight highly trained cyclists performed two incremental submaximal cycle ergometer tests. For each session either a Schiller CS-200 or a Vmax Series 229 automated gas analyser was used for expired gas analysis. Data for oxygen consumption (VO2), CO2 production (VCO2), minute ventilation (VE) and respiratory exchange ration (RER) were averaged for each of the five stages (200, 250, 275, 300 and 325 W). The VO2, VE and RER were similar between trials at all workloads. However, VCO2 was significantly lower in the Schiller trial at workloads above 200 W (p < 0.05). Although there was a significant correlation between the two automated systems for the measured parameters (VO2 = 0.78; VCO2 = 0.80; VE = 0.82; RER = 0.72) (p < 0.05), a Bland-Altman plot revealed that the limits of agreement between the two systems were unacceptably large (VO2 = 0.53 to 1.30 L.min-1; VCO2 = 0.55 to 0.64 L.min-1; VE = -22.3 to 30.3 L.min-1; RER = - 0.03 to 0.13). The co-efficient of variation within the analysers was insignificant for both systems. Both the systems provide reliable measures of expired gas parameters. However, care should be taken in directly comparing studies that have used the two different systems due to the poor agreement between the systems.The factors causing the termination of maximal exercise at sea level are unknown. A widely held view is that skeletal muscle anaerobiosis consequent to an inadequate oxygen delivery to the exercising muscles limits exercise. However, there is also evidence that respiratory muscle fatigue at the high ventilatory volumes achieved during maximal exercise delivery and respiratory muscle work on maximal exercise performance, we exercised 8 highly trained cyclists in a pressure-sealed chamber in which O2 concentrations were manipulated and helium (He) was substituted for nitrogen in the ambient air in order to reduce the work of breathing during exercise. This system ensured that external inspiratory and expiratory resistance was minimised and identical in all experimental conditions and approximated conditions present during usual exercise. During trials with O2 enriched ambient air the peak work rate increased (451 ± 58 W vs. 429 ± 59 W). Neither maximum nor submaximal oxygen consumption was altered in FIO2 of 35% (5.0 ± 0.6 l.min-1) compared to 21% (4.9 ± 0.7 l.min- 1). Substituting helium for nitrogen had no additional effect on work (453 ± 56 W) or VO2max (4.9 ± 0.7 l.min-1) beyond those observed for the hyperoxic conditions. Although submaximum VE was reduced with helium, VEmax was unchanged. Since exercise was terminated at the same peak work rate (± 5 W) in the two hyperoxic conditions we postulate that the actual work rate may be the sensed variable that determines maximal exercise performance. The findings from these studies suggest that the maintenance of physiological homeostasis and the avoidance of organ and cellular damage are of fundamental importance during maximal exercise. This is achieved through central regulation of work output based, possibly, on afferent information from the mechanoreceptors in the exercising skeletal muscles or alternatively, the extent of motor unit recruitment during maximal exercise may be hardwired in the central nervous system in a system of feed-forward control.

In this thesis, we study the following three types of periodic string patterns and some of their variants. Firstly, we consider maximal d-repetitions. These are substrings that are at least 2+d times as long as their minimum period. Secondly, we consider 3-cadences. These are arithmetic subsequence of three equal characters. Lastly, we consider maximal pairs. These are pairs of identical substrings. Maximal d-repetitions and maximal pairs of uncompressed strings are already well-researched. However, no non-trivial upper bound for distinct occurrences of these patterns that take the compressed size of the underlying strings into account were known prior to this research. We provide upper bounds for several variants of these two patterns that depend on the compressed size of the string, the logarithm of the string's length, the highest allowed power and d. These results also lead to upper bounds and new insights for the compacted directed acyclic word graph and the run-length encoded Burrows-Wheeler transform. We prove that cadences with three elements can be efficiently counted in uncompressed strings and can even be efficiently detected on grammar-compressed binary strings. We also show that even slightly more difficult variants of this problem are already NP-hard on compressed strings. Along the way, we extend the underlying geometry of the convolution from rectangles to arbitrary polygons. We also prove that this non-rectangular convolution can still be efficiently computed.:1 Introduction 2 Preliminaries 3 Non-Rectangular Convolution 4 Alphabet Reduction 39 5 Maximal (Sub-)Repetitions 6 Cadences 7 Maximal Pairs A Propositions

Background Since anthropometric variables are critical to the creation of pulmonary nomograms for FVC, FEV1, and other volumes and capacities, it is logical that anthropometric variables also influence the values of the maximal respiratory pressures (MRPs). Since nomograms are race-specific, it is important that tribe-specific tables of normal maximal inspiratory pressure (MIP) and maximal expiratory pressure (MEP) be developed. To date normal tables for MRPs do not exist for Navajo children. Objective Therefore the purpose of this study was to derive MRP normative reference values for Navajo children in the age range of 6-14 years. Methods - Participants and Measurements A cross-sectional study was undertaken with a representative sample of 534 healthy children, ages 6-14 years, attending Navajo Nation elementary schools in Arizona. MIP and MEP were measured. Results Test results from 275 girls and 259 boys met American Thoracic Society quality control standards and showed that MRPs all increased with height. Mean MIP in cm H2O was 77 for boys and 67 for girls with lower limits of 44 and 40, respectively. Mean MEP in cm H2O was 75 for boys and 66 for girls with the lower limits of 42 and 38, respectively. Conclusion Since the data were collected from the population of interest, the resulting MIP and MEP reference equations should be used when testing Navajo children ages 6-14 years.