5,200 research outputs found

    Automorphic forms and rational homology 3–spheres

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    We investigate a question of Cooper adjacent to the Virtual Haken Conjecture. Assuming certain conjectures in number theory, we show that there exist hyperbolic rational homology 3–spheres with arbitrarily large injectivity radius. These examples come from a tower of abelian covers of an explicit arithmetic 3–manifold. The conjectures we must assume are the Generalized Riemann Hypothesis and a mild strengthening of results of Taylor et al on part of the Langlands Program for GL2 of an imaginary quadratic field. The proof of this theorem involves ruling out the existence of an irreducible two dimensional Galois representation rho of Gal(Qbar/Qsqrt-2) satisfying certain prescribed ramification conditions. In contrast to similar questions of this form, rho is allowed to have arbitrary ramification at some prime pi of Z[sqrt -2]. In the next paper in this volume, Boston and Ellenberg apply pro–p techniques to our examples and show that our result is true unconditionally. Here, we give additional examples where their techniques apply, including some non-arithmetic examples. Finally, we investigate the congruence covers of twist-knot orbifolds. Our experimental evidence suggests that these topologically similar orbifolds have rather different behavior depending on whether or not they are arithmetic. In particular, the congruence covers of the non-arithmetic orbifolds have a paucity of homology

    The effect of the hog-corn ratio on swine production in Iowa

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    Correlations between the interfacial chemistry and current-voltage behavior of n-GaAs/liquid junctions

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    Correlations between the surface chemistry of etched, (100) oriented n-GaAs electrodes and their subsequent photoelectrochemical behavior have been probed by high-resolution x-ray photoelectron spectroscopy. GaAs photoanodes were chemically treated to prepare either an oxide-free near stoichiometric surface, a surface enriched in zero-valent arsenic (As0), or a substrate-oxide terminated surface. The current-voltage (I-V) behavior of each surface type was subsequently monitored in contact with several electrolytes

    For His Mother\u27s Sake

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    https://digitalcommons.library.umaine.edu/mmb-vp/4601/thumbnail.jp

    Exploring Forecast Models for Day of Launch Winds

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    The Lived Experience of Beginning Teachers Defining their Pedagogical Way of Being

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    This hermeneutic phenomenological study explores the lived experience of beginning teachers defining their pedagogical way of being. Many beginning teachers have found frustration and disillusionment during their first year in the classroom, leading to high levels of attrition. Those beginning teachers who remain in the classroom may develop a way of being that opposes how they are as an individual and that pulls them further from the students in their care. How do the individuals who experience this phenomenon make meaning of that experience? What insights about the preparation and support of beginning teachers can be drawn from these experiences? This research is conducted in the tradition of hermeneutic phenomenology, grounded in the work of philosophers such as Heidegger (1962), Gadamer (2006/1975), and Merleau-Ponty (1962). Drawing from these philosophers, van Manen (1997) provides a detailed process used to conduct this form of research. This methodology serves to uncover the essences of this phenomenon, eliciting lived experience through hermeneutic conversation. To uncover the nature of the lived experience of beginning teachers defining their pedagogical way of being, six participants were recruited from urban, suburban, and rural secondary public schools in a south central county in Pennsylvania. The phenomenological text from this study not only reiterates the often noted "challenges" inherent in the first year experience, but also identifies a language of beginning. I seek to understand this language by connecting it to the three Buddhist ways of being, which guides my questioning of the "basics" of the beginning teaching experience, offering a new way of being in the flowing language of becoming. The experiences shared by the participants in this study uncovered many insights that may assist those charged with the care of beginning teachers during the periods of pre-service "formation" and in-service "orientation." I suggest the importance of "reflective conversations" to elicit the language of beginning, facilitated by a caring mentor. As the languages of "blockheadedness" and "splitheadedness" emerge, varying supports may be implemented to permit reflection and growth
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