Eigenvalues in Spectral Gaps of a Perturbed Periodic Manifold

We consider a non-compact Riemannian periodic manifold such that the corresponding Laplacian has a spectral gap. By continuously perturbing the periodic metric locally we can prove the existence of eigenvalues in a gap. A lower bound on the number of eigenvalue branches crossing a fixed level is established in terms of a discrete eigenvalue problem. Furthermore, we discuss examples of perturbations leading to infinitely many eigenvalue branches coming from above resp. finitely many branches coming from below.Comment: 30 pages, 3 eps-figures, LaTe

A Qualitative Study of the Effects of the University of Arkansas Autism Support Program

Abstract Individuals who have been diagnosed with autism spectrum disorder are often united by the following characteristics: difficulty communicating and interacting with others, inhibited ability to function socially, difficulty functioning academically or at work, and trouble transitioning to independent lifestyles (Lord, 2013). The purpose of this study was to determine how undergraduate students with Autism Spectrum Disorder perceive the helpfulness of the University of Arkansas Autism Support Program in the following areas: reducing college- related stress, facilitating academic success, facilitating social success, and preparing individuals for independent adult roles. In short, the study sought to determine the effects of the University of Arkansas Autism Support Program on participating undergraduate students with Autism Spectrum Disorder. Data was collected via a paper and pencil questionnaire and an oral interview for undergraduate members of the University of Arkansas Autism Support Program to complete. The results of this study are beneficial to any individual who has a connection to autism in academia (i.e. students with autism spectrum disorders, autism support program employees, peers, professors, researchers, family members, etc.) and provides useful qualitative data on the strengths and weaknesses of one of many college-level autism support programs through the eyes of participating students

Racah Polynomials and Recoupling Schemes of su(1,1)\mathfrak{su}(1,1)

The connection between the recoupling scheme of four copies of $\mathfrak{su}(1,1)$, the generic superintegrable system on the 3 sphere, and bivariate Racah polynomials is identified. The Racah polynomials are presented as connection coefficients between eigenfunctions separated in different spherical coordinate systems and equivalently as different irreducible decompositions of the tensor product representations. As a consequence of the model, an extension of the quadratic algebra ${\rm QR}(3)$ is given. It is shown that this algebra closes only with the inclusion of an additional shift operator, beyond the eigenvalue operators for the bivariate Racah polynomials, whose polynomial eigenfunctions are determined. The duality between the variables and the degrees, and hence the bispectrality of the polynomials, is interpreted in terms of expansion coefficients of the separated solutions

Note on 'N-pseudoreductions' of the KP hierarchy

The group-theoretical side of N-pseudoreductions is discussed. The resulting equations are shown to be easy transformations of the N-KdV hierarch

Spectral convergence of non-compact quasi-one-dimensional spaces

We consider a family of non-compact manifolds X_\eps (``graph-like manifolds'') approaching a metric graph $X_0$ and establish convergence results of the related natural operators, namely the (Neumann) Laplacian \laplacian {X_\eps} and the generalised Neumann (Kirchhoff) Laplacian \laplacian {X_0} on the metric graph. In particular, we show the norm convergence of the resolvents, spectral projections and eigenfunctions. As a consequence, the essential and the discrete spectrum converge as well. Neither the manifolds nor the metric graph need to be compact, we only need some natural uniformity assumptions. We provide examples of manifolds having spectral gaps in the essential spectrum, discrete eigenvalues in the gaps or even manifolds approaching a fractal spectrum. The convergence results will be given in a completely abstract setting dealing with operators acting in different spaces, applicable also in other geometric situations.Comment: some references added, still 36 pages, 4 figure

Promise Arizona: Building Immigrant Political Power

This case study investigates the history and accomplishments of one organization that is making considerable strides in advancing the values and political interests of the Latino community. Beginning in 2010, Promise Arizona (PAZ) and Promise Arizona in Action (PAZ en Acción) work to empower Latinos and the immigrant community to flex their civic muscle through community organizing and political action. This case study provides a snapshot of the organization's formation, growth, and organizing initiatives and explores what strategies have been central to its success. It is one model of how grassroots organizing can contribute to achieving immigration rights

The Vermilion River basin : an inventory of the region's resources

published or submitted for publicatio