Thesis (MSc)--University of Stellenbosch, 2000. / ENGLISH ABSTRACT: In this thesis we study the underlying mathematical principles of stationary subdivision, which can be regarded as an iterative recursion scheme for the generation of smooth curves and surfaces in computer graphics. An important tool for our work is Fourier analysis, from which we state some standard results, and give the proof of one non-standard result. Next, since cardinal spline functions have strong links with subdivision, we devote a chapter to this subject, proving also that the cardinal B-splines are refinable, and that the corresponding Euler-Frobenius polynomial has a certain zero structure which has important implications in our eventual applications. The concepts of a stationary subdivision scheme and its convergence are then introduced, with as motivating example the de Rahm-Chaikin algorithm. Standard results on convergence and regularity for the case of positive masks are quoted and graphically illustrated. Next, we introduce the concept of interpolatory stationary subdivision, in which case the limit curve contains all the original control points. We prove a certain set of sufficient conditions on the mask for convergence, at the same time also proving the existence and other salient properties of the associated refinable function. Next, we show how the analysis of a certain Bezout identity leads to the characterisation of a class of symmetric masks which satisfy the abovementioned sufficient conditions. Finally, we show that specific special cases of the Bezout identity yield convergent interpolatory symmetric subdivision schemes which are identical to choosing the corresponding mask coefficients equal to certain point evaluations of, respectively, a fundamental Lagrange interpolation polynomial and a fundamental cardinal spline interpolant. The latter procedure, which is known as the Deslauriers-Dubuc subdivision scheme in the case of a polynomial interpolant, has received attention in recent work, and our approach provides a convergence result for such schemes in a more general framework. Throughout the thesis, numerical illustrations of our results are provided by means of graphs. / AFRIKAANSE OPSOMMING: In hierdie tesis ondersoek ons die onderliggende wiskundige beginsels van stasionêre onderverdeling, wat beskou kan word as 'n iteratiewe rekursiewe skema vir die generering van gladde krommes en oppervlakke in rekenaargrafika. 'n Belangrike stuk gereedskap vir ons werk is Fourieranalise, waaruit ons sekere standaardresuJtate formuleer, en die bewys gee van een nie-standaard resultaat. Daarna, aangesien kardinale latfunksies sterk bande het met onderverdeling, wy ons 'n hoofstuk aan hierdie onderwerp, waarin ons ook bewys dat die kardinale B-Iatfunksies verfynbaar is, en dat die ooreenkomstige Euler-Frobenius polinoom 'n sekere nulpuntstruktuur het wat belangrike implikasies het in ons uiteindelike toepassings. Die konsepte van 'n stasionêre onderverdelingskema en die konvergensie daarvan word dan bekendgestel, met as motiverende voorbeeld die de Rahm-Chaikin algoritme. Standaardresultate oor konvergensie en regulariteit vir die geval van positiewe maskers word aangehaal en grafies geïllustreer. Vervolgens stelons die konsep van interpolerende stasionêre onderverdeling bekend, in welke geval die limietkromme al die oorspronklike kontrolepunte bevat. Ons bewys 'n sekere versameling van voldoende voorwaardes op die masker vir konvergensie, en bewys terselfdertyd die bestaan en ander toepaslike eienskappe van die ge-assosieerde verfynbare funksie. Daarna wys ons hoedat die analise van 'n sekere Bezout identiteit lei tot die karakterisering van 'n klas simmetriese maskers wat die bovermelde voldoende voorwaardes bevredig. Laastens wys ons dat spesifieke spesiale gevalle van die Bezout identiteit konvergente interpolerende simmetriese onderverdelingskemas lewer wat identies is daaraan om die ooreenkomstige maskerkoëffisientegelyk aan sekere puntevaluasies van, onderskeidelik, 'n fundamentele Lagrange interpolasiepolinoom en 'n kardinale latfunksie-interpolant te kies. Laasgenoemde prosedure, wat bekend staan as die Deslauriers-Dubuc onderverdelingskema in die geval van 'n polinoominterpolant, het aandag ontvang in onlangse werk, en ons benadering verskaf 'n konvergensieresultaat vir sulke skemas in 'n meer algemene raamwerk. Deurgaans in die tesis word numeriese illustrasies van ons resultate met behulp van grafieke verskaf.

Poly-proline-based chiral stationary phases are relatively new stationary phases and have shown to be competitive to other commercially available chiral stationary phases for high performance liquid chromatography (HPLC). The conformational studies, solvation properties and enantio-selective mechanism of this chiral stationary phase are the main focus of this thesis. Semi-flexible models are developed based on an extensive series of ab initio calculations for proline selectors from di- to hexa-proline and a series of six chiral analytes. Then molecular dynamics simulations are performed to study the solvation, conformational preferences at the interface, and the selectivity. The solvation and conformational preferences of poly-proline selectors at the interface are examined in a normal phase n-hexane/-2propanol and a reverse phase water/methanol solvent. We noticed a significant difference between conformational preferences of poly-proline chains in these solvents indicating the effect of solvent polarity and hydrogen bonding on the relative stabilities of poly-proline conformers. Solvent partitioning occurs at the interface and this creates a polarity gradient between the stationary phase and the bulk that encourages analyte docking at the interface. Hydrogen bonding to the poly-proline selectors is shown to be a function of solvent composition and poly-proline conformation at the interface. The selectivity of the poly-proline chains was studied by molecular dynamics simulations of chiral analytes docking into the interface. The selectivity factors for a set of enantiomers were predicted successfully. Enantio-resolution has been shown to mostly happen with hydrogen bonding to poly-proline carbonyl oxygens located close to the interface. Steric interactions and conformational flexibility of the analytes are also contributing factors for enantio-resolution. / Thesis (Ph.D, Chemistry) -- Queen's University, 2013-01-28 14:31:53.316

L’analyse vibratoire est l’une des principales méthodes pour le suivi et la maintenance des machines tournantes. Cette thèse s’inscrit dans cette thématique et en particulier dans le diagnostic des roulements en régime variable. L’objectif de la thèse est l’élaboration de capteurs logiciels. Ces derniers pourraient fournir un indicateur pertinent sur l’état de roulements défectueux à partir des signaux de vibrations de type aléatoire qu’ils génèrent dans les cas où ils sont mélangées à d’autres sources vibratoires provenant de défaut d’engrenages générant des signaux déterministes. Afin de diagnostiquer d’une façon efficace les cas d’avarie, il faut au préalable séparer le signal de vibration relatif à chaque source de vibration. En régime stationnaire, l’outil utilisé pour estimer la composante déterministe est la moyenne synchrone. En régime variable, la partie déterministe du signal de vibration évolue avec le régime même si l’enregistrement du signal de vibration est synchronisé avec la vitesse de rotation. Dès lors, cette composante ne devient plus périodique et son estimation par la moyenne synchrone classique devient inappropriée. Nous avons alors proposé une nouvelle approche qui consiste à caractériser les signaux de vibrations en régime variable en introduisant la notion de cyclo-non-stationnarité. Ceci nous a permis de développer un outil d'estimation des composantes déterministes du signal qui sont caractérisées par la cyclo-non-stationnarité d'ordre 1 et de développer un outil de caractérisation de la cyclo-non-stationnarité d'ordre 2 basé sur la synchronisation de la corrélation spectrale. Les performances de cet outil ont été testées avec succès sur des signaux synthétiques ainsi que sur des signaux réels. / Vibration analysis is one of the main methods for rotating machinery monitoring. The topic of this thesis is the diagnosis of rolling element bearings under varying rotating speed. The objective is the development of software sensors providing a relevant indicator of bearing condition monitoring from the vibration signal generated by the bearing. Often, rotating machinery is composed from gears and bearings. Gear faults generate deterministic components and bearing faults generate random components. To diagnose, the key point is to extract the vibration signal caused by bearing from the total vibration signal. In constant rotating speed condition, the used tool to estimate the deterministic component is the time synchronous averaging. In varying rotating speed, the signal becomes "cyclo-non-stationary". Therefore, the traditional synchronous averaging method becomes inappropriate and one needs to extend its definition and estimation process. In this thesis, we develop a new approach based on a decomposition of the vibration signal into a set of cyclo-non-stationary components. This allowed us to develop a tool for estimating the deterministic components of the signal which are characterized by cyclo-non-stationarity order 1 and to develop a tool for characterizing the cyclo-non-stationarity order 2 based on synchronized spectral correlation. The performance of this tool has been tested on synthetic signals and on real signals.

Master of Science / Department of Statistics / James W. Neill

by Wong Oi Ping. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 77-79). / Abstracts in English and Chinese. / Chapter 1 --- LP-minimizing and Stationary Sequences --- p.8 / Chapter 1.1 --- Residual function --- p.8 / Chapter 1.2 --- Minimizing sequences --- p.14 / Chapter 1.3 --- Stationary sequences --- p.17 / Chapter 1.4 --- On the equivalence of minimizing and stationary se- quence --- p.21 / Chapter 1.5 --- Complementarity conditions --- p.25 / Chapter 1.6 --- Subdifferential-based stationary sequence --- p.29 / Chapter 1.7 --- Convergence of an Iterative Algorithm --- p.32 / Chapter 2 --- Minimizing And Stationary Sequences In Nonsmooth Optimization --- p.38 / Chapter 2.1 --- Subdifferential --- p.38 / Chapter 2.2 --- Stationary and minimizing sequences --- p.40 / Chapter 2.3 --- C-convex and BC-convex function --- p.43 / Chapter 2.4 --- Minimizing sequences in terms of sublevel sets --- p.44 / Chapter 2.5 --- Critical function --- p.48 / Chapter 3 --- Optimization Conditions --- p.52 / Chapter 3.1 --- Introduction --- p.52 / Chapter 3.2 --- Second-order necessary and sufficient conditions with- out constraint --- p.55 / Chapter 3.3 --- The Lagrange and G-functions in constrained problems --- p.63 / Chapter 3.4 --- Second-order necessary conditions for constrained prob- lems --- p.73 / Chapter 3.5 --- Sufficient conditions for constrained problems --- p.74 / Bibliography

<p>Oxygen consumption and carbon dioxide production are usual measurements within the sports and training physiology. The same measurements are also common when it comes to establish the amount of energy that is used during work and to establish the intensity of work. The volume of oxygen that is consumed contra the volume of carbon dioxide that is produced can be used to calculate the metabolic rate within the human body. This calculation shows the percent relationship between carbohydrates and fat in the metabolism. </p><p>The first accurate method to measure the breathing gases for use in metabolic calculation was established in the early twenty century when the Douglas bag method was introduced. The expired air is collected in sealed bags and the volume of expired air is then analyzed when it comes to its content of oxygen and carbon dioxide. In our days several methods have been developed for automatic analysis of the breathing gases where the expired air is analyzed immediately by electronic instruments. </p><p>When it comes to the modern automatic instruments there are few scientific investigations about their reliability and that has raised questions about how accurate measurements they produce. One instrument is the Oxycon Stationary Pro which is used by Gymnastik- och Idrottshögskolan in Stockholm Sweden and several of the Swedish university hospital. In this report there has been done a practical comparison between the Douglas bag method and the automatic instrument Oxycon Stationary Pro. The comparison showed a great similarity when it come to the metabolic rate. When it comes to the respiratory gases however, the Oxycon Stationary Pro shows values up to five percent higher than the Douglas bag.</p>

Upon encountering stress conditions, cells must rapidly alter their gene expression and re-model their RNA complement to deal with the changing environment. As a consequence, both new RNA transcription as well as RNA degradation must take place. Accordingly, the RNA degradative machinery may adjust to the changes in RNA metabolism. Thus, a study of the response of the three major degradative exoribonucleases in Escherichia coli, polynucleotide phosphorylase, RNase II, and RNase R, to stress is of significant importance. RNase R, a processive 3' to 5' exoribonuclease, is unique among the known E. coli exoribonucleases in its ability to digest through RNAs containing extensive secondary structure without the aid of a helicase. In vivo, RNase R plays important roles in quality control of stable RNA, decay of mRNA with extensive repetitive extragenic palindromic (REP) sequences, cell-cycle regulated degradation of tmRNA in Caulobacter crescentus, as well as processing of rRNA under low temperature in P. syringae. In this dissertation, RNase R was shown to be unusual among the E. coli exoribonucleases in its dramatic response to a variety of stress conditions. Elevation of RNase R activity by as much as 10-fold was observed in response to entry into stationary phase, starvation and cold shock, and an ~3-fold increase was seen during growth in minimal medium compared to rich medium. The elevation in RNase R activity was associated with an increase in RNase R protein. Phenotypes of rnr mutants were also investigated, and RNase R was found to contribute to cell growth and viability. Further investigation of the regulation of RNase R during stress, primarily in stationary phase, revealed a novel regulation mechanism. Despite the large increase in RNase R protein and activity in stationary phase, rnr message actually decreased to only ~14% of its level in exponential phase. Further study revealed that RNase R is highly unstable in exponential phase and becomes stabilized during stationary phase, cold shock, and in minimal medium. Investigation of proteolysis on the unusual instability of RNase R indicated that both Lon and ClpXP play a role. In the absence of Lon, RNase R stability is increased ~10-fold. Based on these results, I propose that the increase in RNase R during stress is due to its enhanced stability under those conditions.

No description available.

The main focus of this thesis is on hydrophilic interaction chromatography (HILIC) and the preparation of stationary phases for HILIC. The mechanism of HILIC is also discussed; a large part of the discussion has been adapted from a review written by me and professor Irgum for the Journal of Separation Science (ref 34). By reevaluating the literature we have revealed that the notion of HILIC as simply partitioning chromatography needed modification. However, our interest in the HILIC mechanism was mainly inspired by the need to understand how to construct the optimal HILIC stationary phase. The ultimate stationary phase for HILIC is still not found. My theory is that a non-charged stationary phase capable of retaining a full hydration layer even at extreme acetonitrile (&gt; 85%) concentrations should give a HILIC stationary phase with a more pure partitioning retention behavior similar to that of a swollen C18 reversed phase. The preparation of a sorbitol methacrylate grafted silica stationary phase is one of our attempts at producing such a stationary phase. The preparation of such a grafted silica has been performed, but with huge difficulty and this work is still far from producing a column of commercial quality and reprodicibility. This thesis also discusses a new method for the initiation of atom transfer radical polymerization from chlorinated silica. This new grafting scheme theoretically results in a silica particle grafted with equally long polymer chains, anchored to the silica carrier by a hydrolytically stable silicon-carbon bond. The hydrolytic stability is especially important for HILIC stationary phases due to the high water concentration at the surface.

Oxygen consumption and carbon dioxide production are usual measurements within the sports and training physiology. The same measurements are also common when it comes to establish the amount of energy that is used during work and to establish the intensity of work. The volume of oxygen that is consumed contra the volume of carbon dioxide that is produced can be used to calculate the metabolic rate within the human body. This calculation shows the percent relationship between carbohydrates and fat in the metabolism. The first accurate method to measure the breathing gases for use in metabolic calculation was established in the early twenty century when the Douglas bag method was introduced. The expired air is collected in sealed bags and the volume of expired air is then analyzed when it comes to its content of oxygen and carbon dioxide. In our days several methods have been developed for automatic analysis of the breathing gases where the expired air is analyzed immediately by electronic instruments. When it comes to the modern automatic instruments there are few scientific investigations about their reliability and that has raised questions about how accurate measurements they produce. One instrument is the Oxycon Stationary Pro which is used by Gymnastik- och Idrottshögskolan in Stockholm Sweden and several of the Swedish university hospital. In this report there has been done a practical comparison between the Douglas bag method and the automatic instrument Oxycon Stationary Pro. The comparison showed a great similarity when it come to the metabolic rate. When it comes to the respiratory gases however, the Oxycon Stationary Pro shows values up to five percent higher than the Douglas bag.