Two-probe study of hot carriers in reduced graphene oxide

The energy relaxation of carriers in reduced graphene oxide thin films is studied using optical pump-probe spectroscopy with two probes of different colors. We measure the time difference between peaks of the carrier density at each probing energy by measuring a time-resolved differential transmission and find that the carrier density at the lower probing energy peaks later than that at the higher probing energy. Also, we find that the peak time for the lower probing energy shifts from about 92 to 37 fs after the higher probing energy peak as the carrier density is increased from 1.5E12 to 3E13 per square centimeter, while no noticeable shift is observed in that for the higher probing energy. Assuming the carriers rapidly thermalize after excitation, this indicates that the optical phonon emission time decreases from about 50 to about 20 fs and the energy relaxation rate increases from 4 to 10 meV/fs. The observed density dependence is inconsistent with the phonon bottleneck effect.Comment: 10 pages, 4 figure

Optimal Relay Selection with Non-negligible Probing Time

In this paper an optimal relay selection algorithm with non-negligible probing time is proposed and analyzed for cooperative wireless networks. Relay selection has been introduced to solve the degraded bandwidth efficiency problem in cooperative communication. Yet complete information of relay channels often remain unavailable for complex networks which renders the optimal selection strategies impossible for transmission source without probing the relay channels. Particularly when the number of relay candidate is large, even though probing all relay channels guarantees the finding of the best relays at any time instant, the degradation of bandwidth efficiency due to non-negligible probing times, which was often neglected in past literature, is also significant. In this work, a stopping rule based relay selection strategy is determined for the source node to decide when to stop the probing process and choose one of the probed relays to cooperate with under wireless channels' stochastic uncertainties. This relay selection strategy is further shown to have a simple threshold structure. At the meantime, full diversity order and high bandwidth efficiency can be achieved simultaneously. Both analytical and simulation results are provided to verify the claims.Comment: 8 pages. ICC 201

Exploring the Relationship between K-8 Prospective Teachers’ Algebraic Thinking Proficiency and the Questions They Pose during Diagnostic Algebraic Thinking Interviews

In this study, we explored the relationship between prospective teachers’ algebraic thinking and the questions they posed during one-on-one diagnostic interviews that focused on investigating the algebraic thinking of middle school students. To do so, we evaluated prospective teachers’ algebraic thinking proficiency across 125 algebra-based tasks and we analyzed the characteristics of questions they posed during the interviews. We found that prospective teachers with lower algebraic thinking proficiency did not ask any probing questions. Instead, they either posed questions that simply accepted and affirmed student responses or posed questions that guided the students toward an answer without probing student thinking. In contrast, prospective teachers with higher algebraic thinking proficiency were able to pose probing questions to investigate student thinking or help students clarify their thinking. However, less than half of their questions were of this probing type. These results suggest that prospective teachers’ algebraic thinking proficiency is related to the types of questions they ask to explore the algebraic thinking of students. Implications for mathematics teacher education are discussed