Irreducibility of generalized Hermite-Laguerre Polynomials III

For a positive integer $n$ and a real number $\alpha$, the generalized Laguerre polynomials are defined by \begin{align*} L^{(\alpha)}_n(x)=\sum^n_{j=0}\frac{(n+\alpha)(n-1+\alpha)\cdots (j+1+\alpha)(-x)^j}{j!(n-j)!}. \end{align*} These orthogonal polynomials are solutions to Laguerre's Differential Equation which arises in the treatment of the harmonic oscillator in quantum mechanics. Schur studied these Laguerre polynomials for its interesting algebraic properties. He obtained irreducibility results of $L^{(\pm \frac{1}{2})}_n(x)$ and $L^{(\pm \frac{1}{2})}_n(x^2)$ and derived that the Hermite polynomials $H_{2n}(x)$ and $\frac{H_{2n+1}(x)}{x}$ are irreducible for each $n$. In this article, we extend Schur's result by showing that the family of Laguerre polynomials $L^{(q)}_n(x)$ and $L^{(q)}_n(x^d)$ with $q\in \{\pm \frac{1}{3}, \pm \frac{2}{3}, \pm \frac{1}{4}, \pm \frac{3}{4}\}$, where $d$ is the denominator of $q$, are irreducible for every $n$ except when $q=\frac{1}{4}, n=2$ where we give the complete factorization. In fact, we derive it from a more general result.Comment: Published in Journal of Number Theor

Analysis of the Importance of Extension in Accounting for the Post-Carboniferous Subsidence of the North Sea Basin

Post Carboniferous sedimentary deposition in the Central North Sea basins can be separated into three major periods: Permian, Triassic and mid-Jurassic through present. Most efforts to explain the basin within an extensional framework have concentrated on the post mid-Jurassic subsidence. These efforts have ignored the large amount of prior extension required to account for the observed crustal thinning and the substantial Permian and Triassic sediment fill. In addition the models predict a mid-Jurassic through early Cretaceous extension that significantly exceeds estimates of the horizontal displacement observed on high angle faults on multichannel seismic lines. We show in areas of minimal pre-Permian subsidence that adding two earlier phase extensions, one in the late Carboniferous through early Permian and the other in the Triassic produces a nearly horizontal late Carboniferous crustal thickness. The time-dependent extensional model required to account for the three periods of sediment deposition gives an excellent match to the observed subsidence history of the basement. We present an analysis of a recent seismic reflection line nm across the Central Graben in the vicinity of published refraction and well data. We show that the extension required in the third phase of the three phase model is compatible with the observed displacement on the high angle mid-Jurassic through early Cretaceous faults. However, we find no evidence for major extension either in the Triassic or late Carboniferous through early Permian.Institute for Geophysic

Meta-Objects in the IR: Using Sample Works as Training Tools

The University of Florida Institutional Repository (IR@UF) staff created sample works, such as a conference poster, that were loaded into the repository. The metadata of these items serve as a sample for users on how to describe similar items, and the objects themselves contain instructions on how to load items using the Self-Submittal tools

Opportunities and Challenges: Undergraduate Works in the IR@UF

The Institutional Repository at the University of Florida (IR@UF) is a platform and suite of services designed to provide access and preservation of scholarship generated by our institutional community. Most of our early efforts were directed at engaging faculty, staff and graduate students, which left our largest population, undergraduate students, under-served and under-represented. Over the past two years we have been pursued partnership opportunities with the Honors Program and the Center for Undergraduate Research, as well as seeking out additional opportunities to educate our undergraduate students about the IR@UF and solicit submissions. This presentation will provide an overview of these efforts, along with the challenges we have faced in incorporating this working into our IR, and future goals to better serve the needs of this segment of our institutional community

Culturally Responsive Teaching

Many classrooms, across all academic domains (reading, math, science, and social studies), are not culturally inclusive in terms of student race and ethnicity. As teachers, we can address this problem by promoting and incorporating culturally inclusive practices as we present subject content. Culturally responsive teaching promotes equitable student growth and development in the academic classroom. The primary purpose of this research was to build a website that shares culturally responsive teaching methods that educators can implement for their students. This online resource shares techniques for implementing an array of culturally diverse books into the curriculum, integrating cultural aspects into math and science concepts, and addressing the history of underserved groups. Culturally responsive teaching encourages students to connect their prior knowledge and experience to a curriculum that represents racial and ethnic diversity

Fragmentary Girls: Selective Expression on the Tumblr Platform

Empirically based on a series of focus groups with college-age women, this thesis examines how the affordances of anonymity and audience specificity facilitate both intimate personal expression and political participation on the Tumblr platform. In dialogue with literature on self disclosure and privacy, I seek to broaden our understanding of the mediated contexts that provide space for women’s voices online. The privacy afforded by Tumblr’s registration policies allows users more flexibility in terms of self-presentation than sites such as Facebook, which are necessarily linked to one’s offline identity through “real name only” policies. The use of pseudonyms contributes to a larger culture of anonymity on the platform, emboldening users to express themselves more freely and with less consequence. Specifically, Tumblr norms encourage the communication of emotions other than happiness or significant “life events” – instead providing a space for girls to express culturally devalued emotions such as sadness and anger. These kinds of intimate and cathartic expressions were made to an (imagined) audience of close friends and strangers in which parents and acquaintances were importantly absent. The reduced pressure of explanation, a limited (often like-minded) audience and the lowered-stakes of anonymity, are all also key features that encouraged feminist expression online. For focus group participants, the possibility of back-and-forth Facebook debates with relatives or former classmates kept them quiet. They described these interactions as exhausting, not as true conversations but as times when they needed to give long explanatory defenses as to why their concerns were issues at all. While debate is often assumed to be as a positive, constructive element of political discourse, this research calls into question the ways in which these ideals contribute to the silencing of women online and ask us to rethink what it means to say that “the personal is political.

Identifying Policy Trends: Institutional Repository Policy Survey Results

In 2016, the IR Manager at the University of Florida undertook a project to review existing policies of the IR@UF and complete an environmental scan of peer institutions to determine best practices in terms of IR Policies. Building on last year’s presentation which highlighted preliminary results of the 25-institution pilot survey (http://aquila.usm.edu/irday/2016/1/11/), this poster looks at the final results of the Institutional Repository Policy Survey. With over 95 respondents, the survey results identify trends in four core policy areas which may suggest best practices for those who are seeking to build an IR, or to conduct their own policy review