Math anxiety refers to the negative reaction that many people experience when placed in situations that require mathematical problem solving (Richardson & Suinn, 1972). This reaction can range from seemingly minor frustration to overwhelming emotional and physiological disruption (Ashcraft & Moore, 2009). In fact, it has been argued that math anxiety can be considered as a genuine phobia given that it is a state anxiety reaction, shows elevated cognitive and physiological arousal, and is a stimulus-learned fear (Faust, 1992). Math anxiety has been associated with many negative consequences, the most pertinent of which is poor achievement in math. This negative consequence is of central importance in today???s society as people???s mathematical abilities have been shown to strongly influence their employability, productivity, and earnings (Bishop, 1989; Bossiere, Knight, Sabot, 1985; Riviera-Batiz, 1992) A large literature exists demonstrating a negative relation between math anxiety and performance on complex math. That said, there is currently no published research (outside of that presented in this thesis) which investigates whether math anxiety is also related to the basic processes that serve as the foundations for that complex math. In this thesis I examine the relation between math anxiety and three of these basic processes that support complex mathematical problem solving. Specifically, in a series of experiments, I demonstrate that, in addition to their difficulties with complex math, high math anxious adults perform more poorly than their low math anxious peers on measures of counting (Experiments 1 and 2), numerical comparison (Experiment 3 and 4), and spatial processing (Experiment 5 and 6). My findings are then discussed with respect to their implications for our understanding of math anxiety and for potential remediation programs.

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The phenomenon where small numbers produce faster left than right responses and large numbers produce faster right than left responses (The SNARC effect) has been used as evidence for obligatory activations of magnitude. In two experiments, I used the SNARC effect to examine crosstalk using a psychological refractory period (PRP) paradigm. In Experiment 1, subjects made a parity judgment to the second number, while ignoring the first number in session 1 or performing a magnitude judgment on the number in session 2. In Experiment 2, subjects performed a magnitude judgment on the second number. They ignored the first number in session 1 or performed a parity judgment on the number in session 2. The results supported two conclusions. First, presentation of a number produced obligatory representations of magnitude even if the number was to be ignored. Second, early representations of magnitude resulted in crosstalk on processing of the subsequent number.

L'évolution de l'électronique de puissance ces dernières années a entraîné une augmentation de la densité de puissance et une diminution du coût des onduleurs de tension à modulation de largeur d'impulsion (MLI). Ces évolutions ont répandu l'utilisation de convertisseurs de puissance pour les applications de variateurs de vitesse ce qui a permis le développement du concept d' " avion plus électrique ". Ce concept consiste à remplacer un des vecteurs énergétiques (pneumatique ou hydraulique) par l'énergie électrique. Cependant, le développement du réseau électrique a entraîné une augmentation de la tension embarquée, ce qui a conduit à un vieillissement prématuré des équipements électriques embarqués. La forme de tension appliquée, appelée "modulation de largeur d'impulsion" (MLI), est constituée de trains d'impulsions. Avec l'application de ces impulsions, la tension n'est plus distribuée de manière homogène le long du bobinage. Dans ce cas, on pourra observer d'importantes différences de potentiel entre les spires d'une même phase voire entre deux phases du bobinage. En outre, un autre paramètre important provient du type d'enroulement des moteurs utilisés par l'industrie. L'enroulement aléatoire est la technique de bobinage la plus courante pour les moteurs basses tensions car cette méthode présente un faible coût. Le risque induit par ce type d'enroulement est que la première et une des dernières spires de la première bobine peuvent être proches l'une de l'autre. Dans ce cas, jusqu'à 80% de la tension sera supportée par quelques dizaines de microns d'émail, et les systèmes d'isolation existants ne sont pas dimensionnés pour résister à de telles contraintes. L'utilisation de longs câbles reliant l'onduleur au moteur peut aussi provoquer des surtensions importantes aux bornes du moteur. Ce phénomène s'explique par le fait que le câble se comporte comme une ligne de transmission qui n'est pas adaptée en termes d'impédance au bobinage du moteur. De plus, ces importantes différences de potentiel associées à de faibles pressions, présentes dans les zones dépressurisées de l'aéronef, peuvent entraîner l'apparition de décharges partielles. Les décharges partielles sont des décharges électriques qui court-circuitent partiellement l'intervalle entre deux conducteurs. Il existe de nombreuses méthodes de détection bien connues pour les tensions AC et DC, cependant, la détection sous tension de type MLI dans des moteurs basse tension est beaucoup plus complexe. Les signaux de décharge partielle sont en effet intégrés dans le bruit électromagnétique généré par la commutation. Le but de cette thèse est donc de développer un procédé de détection et un procédé de filtrage permettant une détection non intrusive et en fonctionnement (on-line) des décharges partielles dans le domaine aéronautique afin de qualifier les systèmes d'isolation électrique utilisés dans les aéronefs. / The development of power electronics in recent years has led to increase power density and to decrease pulse width modulation (PWM) voltage inverter cost. These developments have expanded the use of power converters for variable speed drive applications which enabled the development of the concept of "more electric aircraft". This concept consists in replacing one of energy carriers (pneumatic or hydraulic) with electrical energy. However, the deployment of electrical energy has increased the onboard voltage, which leads to premature aging of onboard electrical equipment. The shape of the PWM voltage consists of pulse trains. With the application of these pulses, the voltage is no longer homogeneously distributed along the coil. In this case, large differences in potential between the strands are present. In addition, another important parameter derived from the winding type motor used in industry. The random winding is the most common technique for low voltage motors due to its lower cost. The risk generated by this type of winding is that the first and the last turns of the first coil can be facing one another. In this case, up to 80% of the voltage will be supported by a few tens of microns of enamel, and existing insulation systems are not designed to withstand such severe constraints. The use of long cable connecting the inverter to the motor can also cause significant overvoltage at the motor terminals. This phenomenon is explained by the fact that the cable behaves as a transmission line to which the motor coils is not adapted in terms of impedance. In addition, these large potential differences associated with low pressures in the depressurized areas of the aircraft, may cause the occurrence of partial discharge. Partial discharges are electrical discharges that short-circuited partially the gap between two conductors. There are many detection methods well known under AC and DC voltage, however, in the case of the detection under PWM like voltage in low-voltage motors, the detection is much more complex. Partial discharge signals are embedded in the electromagnetic noise generated by the switching. The aim of this thesis is to develop a detection method and filtering method enabling a non-intrusive and an "on-line" partial discharges detection in the aeronautical field in order to qualify the electrical insulation systems used in aircraft.