On the compositum of all degree d extensions of a number field

Let k be a number field, and denote by k^[d] the compositum of all degree d extensions of k in a fixed algebraic closure. We first consider the question of whether all algebraic extensions of k of degree less than d lie in k^[d]. We show that this occurs if and only if d < 5. Secondly, we consider the question of whether there exists a constant c such that if K/k is a finite subextension of k^[d], then K is generated over k by elements of degree at most c. This was previously considered by Checcoli. We show that such a constant exists if and only if d < 3. This question becomes more interesting when one restricts attention to Galois extensions K/k. In this setting, we derive certain divisibility conditions on d under which such a constant does not exist. If d is prime, we prove that all finite Galois subextensions of k^[d] are generated over k by elements of degree at most d.Comment: 14 pages, 2 figure

Being Bad in a Video Game can Make Us Morally Sensitive

Several researchers have demonstrated that the virtual behaviors committed in a video game can elicit feelings of guilt. Researchers have proposed that such guilt could have prosocial consequences. However, this proposition has not been supported with empirical evidence. The current study examined this issue in a 2 2 (video game play vs. real world recollection guilt vs. control) experiment. Participants were first randomly assigned to either play a video game or complete a memory recall task. Next, participants were randomly assigned to either a guilt-inducing condition (game play as a terrorist/recall of acts that induce guilt) or a control condition (game play as a UN soldier/recall of acts that do not induce guilt). Results of the study indicate several important findings. First, the current results replicate previous research indicating that immoral virtual behaviors are capable of eliciting guilt. Second, and more importantly, the guilt elicited by game play led to intuition-specific increases in the salience of violated moral foundations. These findings indicate that committing "immoral" virtual behaviors in a video game can lead to increased moral sensitivity of the player. The potential prosocial benefits of these findings are discussed.Advertisin

Heights and infinite algebraic extensions of the rationals

textThis dissertation contains a number of results on properties of infinite algebraic extensions of the rational field, all of which have a view toward the study of heights in diophantine geometry. We investigate whether subextensions of extensions generated by roots of polynomials of a given degree are themselves generated by polynomials of small degree, a problem motivated by the study of heights. We discuss a relative version of the Bogomolov property (the absence of small points) for extensions of fields of algebraic numbers. We describe the relationship between the Bogomolov property and the structure of the multiplicative group. Finally, we describe some results on height lower bounds which can be interpreted as diophantine approximation results in the multiplicative group.Mathematic

Characterizing mood management as need satisfaction: The effects of intrinsic needs on selective exposure and mood repair

This study attempted to (a) extend traditional mood management theory research by investigating the influence of the intrinsic needs for competence and autonomy on selective exposure to video games and (b) test the influence of satisfying these needs on resultant mood repair. An experiment varied satisfaction of competence and autonomy needs using false feedback. Subjects then selected media that varied in level of user demand. Measures of need satisfaction were taken before and after media selection. Results demonstrated that (a) thwarted intrinsic needs significantly predict the choice of video games with different levels of user demand and (b) the satisfaction of these needs predicts enjoyment. Findings indicate that mood management can result from mood repair through need satisfaction. © 2012 International Communication Association

Remarks on diophantine approximation in the multiplicative group and generalized Lehmer problems

Non UBCUnreviewedAuthor affiliation: University of WisconsinPostdoctora