On Atkin and Swinnerton-Dyer Congruence Relations (2)

In this paper we give an example of a noncongruence subgroup whose three-dimensional space of cusp forms of weight 3 has the following properties. For each of the four residue classes of odd primes modulo 8 there is a basis whose Fourier coefficients at infinity satisfy a three-term Atkin and Swinnerton-Dyer congruence relation, which is the $p$-adic analogue of the three-term recursion satisfied by the coefficients of classical Hecke eigen forms. We also show that there is an automorphic $L$-function over $\mathbb Q$ whose local factors agree with those of the $l$-adic Scholl representations attached to the space of noncongruence cusp forms.Comment: Last version, to appear on Math Annale

Matrix elements of four-quark operators and \Delta L=2 hyperon decays

The study of neutrinoless double beta decays of nuclei and hyperons require the calculation of hadronic matrix elements of local four-quark operators that change the total charge by two units \Delta Q=2 . Using a low energy effective Lagrangian that induces these transitions, we compute these hadronic matrix elements in the framework of the MIT bag model. As an illustrative example we evaluate the amplitude and transition rate of \Sigma- -> p e- e-, a decay process that violates lepton number by two units (\Delta L=2). The relevant matrix element is evaluated without assuming the usual factorization approximation of the four-quark operators and the results obtained in both approaches are compared.Comment: 13 pages, 2 .eps figure

Modified dispersion relations and black hole physics

A modified formulation of energy-momentum relation is proposed in the context of doubly special relativity. We investigate its impact on black hole physics. It turns out that such modification will give corrections to both the temperature and the entropy of black holes. In particular this modified dispersion relation also changes the picture of Hawking radiation greatly when the size of black holes approaching the Planck scale. It can prevent black holes from total evaporation, as a result providing a plausible mechanism to treat the remnant of black holes as a candidate for dark matter.Comment: 4 pages, Revtex. Final version to appear in PR

Maximal violation of Clauser-Horne-Shimony-Holt inequality for four-level systems

Clauser-Horne-Shimony-Holt inequality for bipartite systems of 4-dimension is studied in detail by employing the unbiased eight-port beam splitters measurements. The uniform formulae for the maximum and minimum values of this inequality for such measurements are obtained. Based on these formulae, we show that an optimal non-maximally entangled state is about 6% more resistant to noise than the maximally entangled one. We also give the optimal state and the optimal angles which are important for experimental realization.Comment: 7 pages, three table

Bridging Education and Engineering Students through a Wind Energy-Focused Community Engagement Project

Regional growth in offshore wind energy development, changes to the state’s K-12 science standards, and a desire to deepen undergraduate student learning coalesced to inspire an interdisciplinary community engagement project bridging university courses in engineering and education. The project consists of three main activities: a professional development event for local fourth grade teachers, five classroom lessons designed and taught by undergraduate engineering and education majors, and a final celebration event, all focused around the topics of wind energy and engineering design. This spring, the project was carried out for the third consecutive year, though each year’s implementation has been unique due to the timing of the onset of COVID-19. Analysis of responses from the Teaching Engineering Self-Efficacy Scale and an end-of-semester course survey demonstrate growth in student learning and transferrable skills from participating in the semester-long project. Additionally, exploration of students’ narrative work provides a richness to further understanding their growth and challenges they confronted. This interdisciplinary community engagement project will continue into future years, with improvements informed by the findings of this work, most notably with the hope of returning to a fully in-person delivery of lessons to fourth-graders

Teaching Wind Energy to Engineering and Education Undergraduates Through Community Engagement

Rhode Island\u27s adoption of the Next Generation Science Standards in 2013 [1] established a pressing need to provide elementary schools with support for integrating engineering in our local district\u27s classrooms. Wind energy was identified as an appropriate instructional topic, both for its relevance to Rhode Island [2], and for its strength as a tool for studying the engineering design process. Education and engineering undergraduates collaborated to educate local fourth graders about engineering design and wind energy. While supporting the need for engineering education in the community, this project also deepened learning for both education and engineering students at Roger Williams University