Gauss Sums, Stickelberger's Theorem, and the Gras Conjecture for Ray Class Groups

Let $k$ be a real abelian number field and $p$ an odd prime not dividing $[k:\mathbb{Q}]$. For a natural number $d$, let $E_d$ denote the group of units of $k$ congruent to $1$ modulo $d$, $C_d$ the subgroup of $d$-circular units of $E_d$, and $\mathfrak{C}(d)$ the ray class group of modulus $d$. Let $\rho$ be an irreducible character of $G=\mathrm{Gal}(k/\mathbb{Q})$ over $\mathbb{Q}_p$ and $e_{\rho} \in \mathbb{Z}_p[G]$ the corresponding idempotent. We show that if the ramification index of $p$ in $k$ is less than $p-1$, then $|e_{\rho} \mathrm{Syl}_p(E_d/C_d) | = |e_{\rho} \mathrm{Syl}_p(\mathfrak{C}_d)|$ where $\mathfrak{C}_d$ is the part of $\mathfrak{C}(d)$ where $G$ acts non-trivially. This is a ray class version of the Gras Conjecture. In the case when $p \mid [k:\mathbb{Q}]$, similar but slightly less precise results are obtained. In particular, beginning with what could be considered a Gauss sum for real fields, we construct explicit Galois annihilators of $\mathrm{Syl}_p(\mathfrak{C}_{\mathfrak{a}})$ akin to the classical Stickelberger Theorem

Characterization of a 50kW Inductively Coupled Plasma Torch for Testing of Ablative Thermal Protection Materials Using Non-Air Gases

Thermal protection systems have been a major area of study since the advent of space flight, but recent efforts towards crewed spaceflight missions have placed a new importance on the development of such systems. The 50 kW Inductively Coupled Plasma (ICP) Torch Facility at The University of Texas at Austin allows for rapid testing of high-temperature aerospace materials essential to the development of thermal protection systems in planetary re-entry applications. This ICP Torch Facility has been previously characterized using air as the test gas. However, planets of interest for future exploration have atmospheric compositions that differ from air, so testing heat shield materials in the presence of other gases is critical. To address this disparity between tested and actual environment, the current work characterizes the torch using various combinations of argon, CO2, and N2 by determining its operational range at various power settings, mass flow rates, and mixtures these gases. At each setting, the cold-wall heat flux is also measured to determine the range the torch is able to provide. Measurements indicate that using pure Ar gives the torch the largest operating range with regard to power setting and gas injection mass flow rate, and mixing argon into other gases drastically increases the stable operating range compared to the pure gas. Pure CO2 does not form a stable plasma discharge, but a mixture of 50% argon and 50% CO2 (by mass) provides stable operation up to 40 slpm total gas flow rate with a maximum heat flux of 98 W/cm2. Smaller percentages of CO2 allow the cold-wall heat flux to be increased to 110 W/cm2. Pure N2 forms a stable plasma discharge, but the operating range is very limited, providing stable operation up to 20 slpm total gas flow rate with a maximum heat flux of 110 W/cm2.Aerospace Engineering and Engineering Mechanic

Social network profiles as information sources for adolescents' offline relations

This paper presents the results of a study concerning the use of online profile pages by adolescents to know more about “offline” friends and acquaintances. Previous research has indicated that social networking sites (SNSs) are used to gather information on new online contacts. However, several studies have demonstrated a substantial overlap between offline and online social networks. Hence, we question whether online connections are meaningful in gathering information on offline friends and acquaintances. First, the results indicate that a combination of passive uncertainty reduction (monitoring a target’s profile) and interactive uncertainty reduction (communication through the target’s profile) explains a considerable amount of variance in the level of uncertainty about both friends and acquaintances. More specifically, adolescents generally get to know much more about their acquaintances. Second, the results of online uncertainty reduction positively affect the degree of self-disclosure, which is imperative in building a solid friend relation. Furthermore, we find that uncertainty reduction strategies positively mediate the effect of social anxiety on the level of certainty about friends. This implies that socially anxious teenagers benefit from SNSs by getting the conditions right to build a more solid relation with their friends. Hence, we conclude that SNSs play a substantial role in today’s adolescents’ everyday interpersonal communication

Bottom-up radio: creating a new media format using living lab research

This study resulted in the creation of a new media format for urban youth, adopting a living lab-approach, as current studies have shown that this group is currently not reached with the contemporary media offer. Living lab research is a state-of-the art methodology that aims at involving end-users in the innovation process over a longer time span, combining both quantitative and qualitative research techniques and tools. In a first phase, a panel of urban youngsters was created using an intake survey (N=290). These data were analyzed resulting in three distinct types of urban youngsters. In a second phase, a qualitative research trajectory was organized in order to refine the three profiles and get an insight in their media use, digital skills, media preferences and needs with regards to the current media offer. Research methods during this phase included diary studies, participatory observation during workshops and probe research. In a third phase, co-creation sessions were organized with youngsters from the urban panel in order to get feedback on a concept that was iteratively developed during the first two phases of the project. Results show that mobile devices and social media are important for these urban youngsters and that most of these youngsters have quite some creative skills. Radio seems to be a less popular medium, although they spend a significant amount of time listening to music. Further, results show that these youngsters are in need of a platform which stimulates community building and offers a space to express their creativity. A third requirement for the development of a new media format that would meet the needs of these youngers is a format that provides space for local elements and niche markets. This all resulted in the launch of Chase, an urban, crowdsourced radio station

Evaluation of the game development process of a location-based mobile game

There is a growing interest of government bodies and NGOs in using (serious) video games in awareness campaigns. Until now, however, little was known on how to set up such a campaign so as to effectively cater to the needs of different stakeholders including the target audience. Hence designing, developing and translating a game for educational purposes whilst balancing between fun and learning is a complex process, this paper aims to evaluate this by presenting a methodological framework for involving stakeholders in the design and development of a game-based awareness campaign based on a user-centered software design methodology and assesses its effectiveness in a concrete use case: the development of the location-based mobile game City Jam. The goal was to develop a game-based road safety campaign to confront adolescents with road traffic situations with the aim to positively influence road safety attitude and behavior. Mobile technologies offer new opportunities to embed digital game based learning by in different contexts. Given the nature of the road safety campaign, a location-based game format was chosen, aiming to facilitate learning by means of an extended three-way interaction (human interaction, game and context). Different user-centered design methods were deployed throughout several phases of the game development process: In phase one (the opportunity identification) a literature review was performed to investigate relevant fields for the game’s goal. In phase two (the game concept development) expert interviews and a focus groups were conducted with relevant stakeholders and in phase three (the game concept design) co-design sessions and a focus group resulted in a game design document. In phase four (game development and testing) the beta version of City jam was developed and tested in an iterative field testing design and resulted in the final game. Results obtained throughout the game development process provided us the opportunity to evaluate several major aspects. Firstly the impact of stakeholder involvement on the different phases of the design process and the final product resulted in a game that was tailored to the preferences and needs of the target group. Secondly translating the game concept into practice, such as game elements, proposed educational game elements, were evaluated based on the usability, playability principles and social and technological aspects. Benefits and challenges of user-centered design methods are discussed and how budget constraints and differing desired outcomes of different stakeholders challenge but also enrich the process