In this master thesis it is analyzed the system of four partial fluxions of the primary row of differential equations the row of which dwindles at the point of p+1, when p = 0. The system of partial fluxions of differential equations has been solved through the modified technique of summarized degree rows. Two cases were explored: general and when the system’s ratios initial matrix is a special structure matrix. The solutions of the system dependence on the ratios, which are near partial fluxions of the searched function, were explored. There were designed four families of the detached solutions and proved that each of them depends on one optional function of y and z variables. The structure of system of solutions at the malformation points depends not only on x degree, but also on y and z variables. There is no such type of malformation in the theory of dwindle simple differential equations, therefore this analyzed dwindle of the system of partial fluxion of differential equations is called quasi-regular malformation. Keywords: differential equation, partial derivation, quasi-regular malformation.

Abstract This study used an exploratory research focus to investigate if making electricity consumption public and subject to social norms and networks resulted in consumption decreases for households in Milton, Ontario. In the first phase, Milton Hydro identified customers who fell within an average annual electricity consumption category and these customers were invited to participate by mail. Due to lack of participant uptake, cold-calling, targeting of service and faith groups and commuters, and snowball sampling were employed to obtain a total participant size of 17. The second phase saw participants grouped according to social network type (occupational, faith group, etc) and exposed to approval or disapproval indicators within their group about their daily electricity consumption rates via an on-line ‘energy pool’. There were five main groups: one of neighbours, one of members of a faith group, one of members of a company, one of strangers and one of a control group. Group members saw other members’ indicators with the exception of the control group, whose indicators were privately delivered. All group’s electricity consumption was tracked through daily smart meter readings. Participants also had the option of commenting on each other’s electricity use via an online ‘comment box’. In the third phase participants were asked to participate in a questionnaire to assess: 1) the perceived efficacy of the intervention; 2) perceptions of electricity consumption; and 3) the influence of the group on these perceptions. This sequential methodology was chosen for its ability to “...explain significant (or non-significant) results, outlier results, or surprising results” (Cresswell, 2006, p. 72). The findings of this exploratory research seem to suggest the following: 1) that publicity or group type does not seem to affect electricity consumption in comparative electricity consumption feedback for this study; 2) that participants used injunctive norms to comment on their electricity consumption but directed these comments solely at themselves; and 3) that the stronger the relationships in the group, the more likely participants were to engage with the website through checking it and commenting on it. This study may be useful to those in the fields of: 1) electricity conservation who wish to leverage feedback technologies; 2) social networks who wish to better understand how tie strength interacts with social norms and; 3) those in social marketing who wish to develop norm-based campaigns.

Using a quasi-experimental design, the author examined the effects of the Professional Development School Partnerships Deliver Success educational model on student academic achievement in science and mathematics in 12 high-needs, urban elementary, middle, and high schools in the southeastern United States. Student achievement was measured for first to eighth grade students by the State Criterion-Referenced Competency Test and for 11th-grade students by the State High School Graduation Test. 6 ANOVAs were used to compare baseline and year 1 performance data. Student ethnicity was used to disaggregate the data to investigate the extent, if any, to which achievement gaps narrowed. For the different ethnic groups, the small changes in proportion passing across the first year of implementation were not correlated with mean scale score changes as measured by Hedges’s g effect sizes. This result has national implications for the No Child Left Behind Act of 2001 policy in terms of reporting results. Three of the 6 ANOVAs showed significant change in achievement means for the PDS schools when using PDS school data only. However, when data from both PDS and matched comparison schools were analyzed, the overall results indicated no statistically significant gains in mathematics and science means for the professional development schools in relation to the comparison schools for the first year of professional development school implementation.

Le turnover au sein des organisations, à un faible niveau, peut être bénéfique pour le renouvellement des ressources. Mais en atteignant des sommets, il perturbe l'organisation et oblige à une gestion de l'immédiat, nuisible pour la performance des hommes et de l'entreprise. Le groupe Veolia Transport souffre de cet aléa organisationnel de manière récurrente, quand le cœur de son activité est basé sur la délégation de service public, où la qualité des hommes est gage de la performance de l'organisation. En appui de cet impératif qualitatif, le groupe promeut une politique générale de formation ambitieuse afin d'intégrer, professionnaliser et fidéliser ses collaborateurs. Le fer de lance de cette politique est l'alternance, la formation diplômante en alternance. Dès lors, l'alternance impacte-t-elle à la baisse le turnover ? À travers une démarche proche d'un design quasi-expérimental, mobilisant une enquête dite longitudinale par questionnaire et l'appui d'un groupe de contrôle je teste, sur les exploitants du groupe en France, un design théorique explicatif de la relation alternance-turnover, par le prisme de l'implication organisationnelle. En proposant une définition gestionnaire de l'alternance, mes résultats démontrent le développement d'une relation dialectique individu-organisation par l'alternance, conditionnée par la mise en exergue d'un contrat psychologique fort et d'un double tutorat organisationnel. En croisant mes résultats avec 18 entretiens dits de validation, il ressort que l'alternance développe une socialisation organisationnelle partielle, en raison de la difficulté à comprendre pleinement son rôle en fin de cursus. Un glissement de la fonction tutorale en un système tutoral apparait, où la communauté de travail aide à l'apprentissage du métier, quand le supérieur-tuteur conserve un rôle de mentor. Enfin, l'alternance possède un effet positif sur l'intention de quitter, en créant les conditions du développement de l'implication organisationnelle, à la condition d'une gestion dédiée. Dans ce dessein, je propose la mise en place d'une gestion spécifique des alternants, en ne considérant plus l'alternance comme un outil de formation mais comme un outil de gestion des ressources humaines, créateur de potentiels.

In this thesis we study the asymptotic behaviour of the solution of a discrete time renewal equation depending on a small perturbation parameter. In particular, we construct asymptotic expansions for the solution of the renewal equation and related quantities. The results are applied to studies of quasi-stationary phenomena for regenerative processes and asymptotics of ruin probabilities for a discrete time analogue of the Cramér-Lundberg risk model.

La thèse comporte deux parties. La première traite de la convergence vers l'équilibre de flots de gradients discrets ou plus généralement de discrétisations d'un système autonome admettant une fonction de Lyapunov. En se plaçant dans une cadre pour lequel les olutions du problème continu converge vers un état stationnaire en temps grand, il est démontré sous des hypothèses générale que le système discret a la même propriété. Ce résultat conduit à des conclusions nouvelles sur le comportement en temps grand de schémas numériques anciens. La seconde partie concerne la simulation numérique de particules en suspension dans un fluide visqueux. Il est montré que les méthodes utilisées actuellement pour simuler l'interaction hydrodynamique entre particules perdent de leur précision quand de grandes forces non-hydrodynamiques sont en jeu et que au moins deux particules sont proches l'une de l'autre. Ce cas survient, dans le contexte de l'ingénierie biomédicale, lors de la conception de nano-robots capables de nager. Cette perte de précision est due au caractère singulier de l'écoulement de Stokes dans les zones de presque contact. Une nouvelle méthode est introduite ici. Des expérimentations numériques sont effectuées pour mettre en évidence sa grande précision.

This thesis deals with the question of what resources are necessary and sufficient for quantum computational speedup. In particular, we study what resources are required to promote fault tolerant stabilizer computation to universal quantum computation. In this context we discover a remarkable connection between the possibility of quantum computational speedup and negativity in the discrete Wigner function, which is a particular distinguished quasi-probability representation for quantum theory. This connection allows us to establish a number of important results related to magic state computation, an important model for fault tolerant quantum computation using stabilizer operations supplemented by the ability to prepare noisy non-stabilizer ancilla states. In particular, we resolve in the negative the open problem of whether every non-stabilizer resource suffices to promote computation with stabilizer operations to universal quantum computation. Moreover, by casting magic state computation as resource theory we are able to quantify how useful ancilla resource states are for quantum computation, which allows us to give bounds on the required resources. In this context we discover that the sum of the negative entries of the discrete Wigner representation of a state is a measure of its usefulness for quantum computation. This gives a precise, quantitative meaning to the negativity of a quasi-probability representation, thereby resolving the 80 year debate as to whether this quantity is a meaningful indicator of quantum behaviour. We believe that the techniques we develop here will be widely applicable in quantum theory, particularly in the context of resource theories.

The issue of eddy currents induced by the rapid switching of magnetic field gradients is a long-standing problem in magnetic resonance imaging. A new method for dealing with this problem is presented whereby spatial harmonic components of the magnetic field are continuously sensed, through their temporal rates of change, and corrected. In this way, the effects of the eddy currents on multiple spatial harmonic components of the magnetic field can be detected and corrections applied during the rise time of the gradients. Sensing the temporal changes in each spatial harmonic is made possible with specially designed detection coils. However to make the design of these coils possible, general relationships between the spatial harmonics of the field, scalar potential, and vector potential are found within the quasi-static approximation. These relationships allow the vector potential to be found from the field – an inverse curl operation – and may be of use beyond the specific problem of detection coil design. Using the detection coils as sensors, methods are developed for designing a negative feedback system to control the eddy current effects and optimizing that system with respect to image noise and distortion. The design methods are successfully tested in a series of proof-of-principle experiments which lead to a discussion of how to incorporate similar designs into an operational MRI.

This thesis analyzes different light localization phenomena in waveguide arrays. We report on the observation of quasi-Bloch oscillations, a new type of dynamic localization in the spatial evolution of light in curved, coupled optical waveguides. The delocalization and final relocalization of an optical beam in a waveguide array is shown by spatially resolving the optical intensity at various propagation distances. Through comparison to different structures, quasi-Bloch oscillations are shown to be robust beyond the nearest-neighbor tight-binding approximation.

This thesis analyzes different light localization phenomena in waveguide arrays. We report on the observation of quasi-Bloch oscillations, a new type of dynamic localization in the spatial evolution of light in curved, coupled optical waveguides. The delocalization and final relocalization of an optical beam in a waveguide array is shown by spatially resolving the optical intensity at various propagation distances. Through comparison to different structures, quasi-Bloch oscillations are shown to be robust beyond the nearest-neighbor tight-binding approximation.