Moduli for Pairs of Elliptic Curves with Isomorphic N-torsion

We study the moduli surface for pairs of elliptic curves together with an isomorphism between their N-torsion groups. The Weil pairing gives a "determinant" map from this moduli surface to (Z/NZ)*; its fibers are the components of the surface. We define spaces of modular forms on these components and Hecke correspondences between them, and study how those spaces of modular forms behave as modules for the Hecke algebra. We discover that the component with determinant -1 is somehow the "dominant" one; we characterize the difference between its spaces of modular forms and the spaces of modular forms on the other components using forms with complex multiplication. Finally, we show some simplifications that arise when N is prime, including a complete determination of such CM-forms, and give numerical examples.Comment: 30 page

Quantum wideband traveling-wave analysis of a degenerate parametric amplifier

We develop a wideband traveling-wave formalism for analyzing quantum mechanically a degenerate parametric amplifier. The formalism is based on spatial differential equations-spatial Langevin equations-that propagate temporal Fourier components of the field operators through the nonlinear medium. In addition to the parametric nonlinearity, the Langevin equations include absorption and associated fluctuations, dispersion (phase mismatching), and pump quantum fluctuations. We analyze the dominant effects of phase mismatching and pump quantum fluctuations on the squeezing produced by a degenerate parametric amplifier

A multimedia tutorial shell with qualitative assessment in biology

The project is developing methods to produce multimedia tutorials relatively quickly and cheaply, using a generic software shell suitable for any subject area. The shell is a version of one produced originally as part of the HEFC-funded TLTP initiative by the Biodiversity Consortium. Tutorials presented in the shell will provide the student with a structured learning experience that will allow their initial knowledge level or their knowledge acquisition and progress to be qualitatively and quantitatively assessed. Where areas of weakness are revealed by the assessment, students will be advised to study particular parts of the tutorial in order to improve their understanding

Microbial carbon sources on the shelf and slope of the northwestern Gulf of Mexico

Over the past five years, gas chromatography/combustion/isotope ratio mass spectrometry (GC/C/IRMS) analyses of phospholipid fatty acids (PLFAs) has been increasingly used to link organic matter (OM) sources with sedimentary bacteria. This technique has been applied across diverse estuarine and coastal sediments, including lower Laguna Madre, TX, an oligotrophic, coastal lagoon dominated by a single OM source, seagrasses; shelf stations, a eutrophic coastal region receiving multiple sources of OM, hypoxic regions that occur seasonally and deep slope and abyssal plain sediments of the Gulf of Mexico (GOM). Previous reports using the Laguna Madre data as examples, have been used to make comparisons of PLFA 16:0 and PLFA 15:0 isotope ratios and PLFA 16:0 and total organic carbon isotope ratios. Deviations from the 1:1 line in the former indicate living or recently senescent sources of organic matter are not predominantly bacterial. Deviations from the 1:1 line in the latter indicate living or recently senescent sources of organic matter differ isotopically from detrital or older OM in sediments. Prior to the work of Goni et al. (1998), carbon isotope ratios of OM in GOM sediments were interpreted as marine in origin. Based on a series of geochemical measurements, Goni et al. suggested that GOM sediments are largely composed of terrestrial organic carbon (OCterr). Furthermore, They went on to show that shelf and slope sediments were primarily C3 and C4 respectively. I report on the preferential utilization of autochthonous OM by sedimentary bacteria at the sediment surface and the shift to recalcitrant, terrestrially derived OM with depth

Putting off and putting on: an examination of character information in Colossians 3.1-17 and the spiritualities created in the process

The majority of academic study on the epistle to the Colossians focuses primarily on issues related to Christology, the identification of the heresy that threatened the church, or the ongoing debate surrounding authorship of the epistle. Current research leaves several lacunae in the broader understanding of the writer’s intent with the Colossian epistle. There is very little attention given to the existence of a process by which the Colossian believers can mature in Christ and face any theologically aberrant teachings with a growing faith and solid doctrine. There is also a gap in the research within the field of Christian spirituality regarding the application of specific principles of spirituality to sacred canonical texts and early Christian writings. This thesis seeks to fill these research gaps through the use of socio-rhetorical strategies and principles of Christian spirituality. The primary text for this research is the pericope of Colossians 3.1-17. The research on the epistle examines the pericope for an embedded process of character transformation by which the Colossian believers grow towards Christlikeness. As the Colossians grow in maturity, their lived experience of God changes. There are spiritualities embedded within the text that begin to impact the growth of the believers through the embodiment of the text. The identification of these spiritualities as well as the process of character transformation allows for the filling of research gaps and a richer understanding of the epistle writer’s intent.Philosophy, Practical and Systematic TheologyD. Phil. (Theology

Semantic Shift in Old English and Old Saxon Identity Terms

Christianity substantially altered Germanic life during the early Middle Ages. However, no large-scale studies have attempted to visualize Christianization through macroscopic semantic trends, nor have any studies used Old Saxon as a control group to help illustrate the role of Christianity in less obvious semantic contexts. The core question of this project, then, revolves around semantic corpora and their role in clarifying sociocultural phenomena: how can a cross-section of Old Saxon and Old English semantics help clarify Christianity\u27s role in re-shaping early medieval Germanic identity? This study uses corpus linguistics, post-colonial/historical theory, and Digital Humanities approaches to schematize the processes underlying the semantic shift of eight Old English/Old Saxon lexeme pairs—ambiht/ambaht, facen/fekan, gædeling/gaduling, hosp–hosc/hosk, geneat/ginot, scyldig/skuldig, þegn/thegan, and wlanc/wlank—that illustrate how the Anglo-Saxons and Continental Saxons re-interpreted their social and moral “Self” between ca.600 CE and ca.1100 CE. This study obtained quantitative and qualitative sample data primarily from the Dictionary of Old English Electronic Corpus (DOEEC) and TITUS Texts. To establish a semantic baseline, data collection began with Latin/vernacular glosses and ended with larger works of early Germanic literature, including the Old English Beowulf and Old Saxon Heliand. To better systematize semantic observations, the sample lexemes were organized into two groups: “Social Roles” and “Personal Qualities.” The Old English and Old Saxon conclusions yielded three key observations: First, in the “Social Roles,” the transition from reciprocal exchange to autocratic kingship correlated to the naturalization of Christian hierarchy; second, in the “Personal Qualities,” new Christian moral concepts like the sin of superbia introduced semantic gaps that necessitated the reassignment of preexisting lexemes, resulting in semantic hybridization, specialization, and the subversion of Germanic pride; third, Christianity\u27s preference for the unseen occasioned a shift from material to spiritual representations of salvation. These findings have significance for future research on Old English/Old Saxon semantic shift, the relative and absolute dating of Old English/Old Saxon literature, and hybrid digital/analog approaches to philology