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

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

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

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

Data Privacy and Dignitary Privacy: Google Spain, the Right To Be Forgotten, and the Construction of the Public Sphere

The 2014 decision of the European Court of Justice in Google Spain controversially held that the fair information practices set forth in European Union (EU) Directive 95/46/EC (Directive) require that Google remove from search results links to websites that contain true information. Google Spain held that the Directive gives persons a “right to be forgotten.” At stake in Google Spain are values that involve both privacy and freedom of expression. Google Spain badly analyzes both. With regard to the latter, Google Spain fails to recognize that the circulation of texts of common interest among strangers makes possible the emergence of a “public” capable of forming the “public opinion” that is essential for democratic self-governance. As the rise of American newspapers in the nineteenth and twentieth centuries demonstrates, the press underwrites the public sphere by creating a structure of communication both responsive to public curiosity and independent of the content of any particular news story. Google, even though it is not itself an author, sustains the contemporary virtual public sphere by creating an analogous structure of communication. With regard to privacy values, EU law, like the laws of many nations, recognizes two distinct forms of privacy. The first is data privacy, which is protected by the fair information practices contained in the Directive. These practices regulate the processing of personal information to ensure (among other things) that such information is used only for the specified purposes for which it has been legally gathered. Data privacy operates according to an instrumental logic, and it seeks to endow persons with “control” over their personal data. Data subjects need not demonstrate harm in order to establish violations of data privacy. The second form of privacy recognized by EU law is dignitary privacy. Article 7 of the Charter of Fundamental Rights of the European Union protects the dignity of persons by regulating inappropriate communications that threaten to degrade, humiliate, or mortify them. Dignitary privacy follows a normative logic designed to prevent harm to personality caused by the violation of civility rules. There are the same privacy values as those safeguarded by the American tort of public disclosure of private facts. Throughout the world, courts protect dignitary privacy by balancing the harm that a communication may cause to personality against legitimate public interests in the communication. The instrumental logic of data privacy is inapplicable to public discourse, which is why the Directive contains derogations for journalistic activities. The communicative action characteristic of the public sphere is made up of intersubjective dialogue, which is antithetical both to the instrumental rationality of data privacy and to its aspiration to ensure individual control of personal information. Because the Google search engine underwrites the public sphere in which public discourse takes place, Google Spain should not have applied fair information practices to Google searches. But the Google Spain opinion also invokes Article 7, and in the end the decision creates doctrinal rules that are roughly approximate to those used to protect dignitary privacy. The Google Spain opinion is thus deeply confused about the kind of privacy it wishes to protect. It is impossible to ascertain whether the decision seeks to protect data privacy or dignitary privacy. Google Spain is ultimately pushed in the direction of dignitary privacy because data privacy is incompatible with public discourse, whereas dignitary privacy may be reconciled with the requirements of public discourse. Insofar as freedom of expression is valued because it fosters democratic self-government, public discourse cannot serve as an effective instrument of self-determination without a modicum of civility. Yet the Google Spain decision recognizes dignitary privacy only in a rudimentary and unsatisfactory way. If it had more clearly focused on the requirements of dignitary privacy, Google Spain would not so sharply have distinguished Google links from the underlying websites to which they refer. Google Spain would not have blithely outsourced the enforcement of the right to be forgotten to a private corporation like Google

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