Representations of the conformal Lie algebra in the space of tensor densities on the sphere

Let ${\mathcal F}_\lambda(\mathbb{S}^n)$ be the space of tensor densities on $\mathbb{S}^n$ of degree $\lambda$. We consider this space as an induced module of the nonunitary spherical series of the group $\mathrm{SO}_0(n+1,1)$ and classify $(\mathrm{so}(n+1,1),\mathrm{SO}(n+1))$-sim$unitary submodules of${\mathcal F}_\lambda(\mathbb{S}^n)$as a function of$\lambda$.Comment: Published by JNMP at http://www.sm.luth.se/math/JNMP

Mental Health in Collegiate Student Athletes Post-Injury: Triangulating Services at Western Oregon University

Collegiate student athletes are in a vulnerable age group for many mental health concerns, and many athlete-specific stressors such as injury heighten these conditions. In addition to the physical ramifications of injury, student athletes often experience psychological reactions to injury such as depression, anxiety, identity loss, disordered eating, and substance abuse. To support the needs of injured student athletes, the NCAA Mental Health Best Practices guide states that student athletes should have easy access to mental health care providers of multiple disciplines through a cohesive network of coaches, the athletic department, athletic trainers, team doctors, and certified counselors working together for the athlete’s wellbeing. Consequently, my thesis aimed to investigate ways to triangulate these sources at Western Oregon University (WOU) to better support the needs of student athletes following injury. To achieve this goal, I compiled peer-reviewed literature on mental health in collegiate student athletes post-injury, interviewed members of the athletic department, athletic training staff, and counselors at the Student Health and Counseling Center (SHCC), and made recommendations to the University regarding policies and procedures they can implement to better support the needs of injured student athletes at WOU

Does GRID Alternatives Impact Greenhouse Gas Emissions Reduction Targets in Central Coast Climate Action Plans?

As of March 2016, GRID Alternatives’ 179 solar electric system installations on low-income housing contributed 103 metric tons of carbon (MT CO2e) emissions reduction for the climate action plans’ Energy or Renewable Energy climate action measures that pertain to solar electric installations in the cities of: Arroyo Grande, Atascadero, Paso Robles, and San Luis Obispo and San Luis Obispo County. In 2007, the San Luis Obispo County Air Pollution Control District (APCD) created a team of government agencies to design climate action plans (CAP) that met the emission reduction goals set out by AB 32 and the 2008 Climate Change Scoping Plan (Rincon Consultants, 2014, p. 1-2). Each CAP outlines its greenhouse gas (GHG) baseline emissions and GHG emissions reduction targets in metric tons of carbon (MT CO2e) and identifies climate action measures to reach GHG emissions reduction targets. The climate action measure that pertains to Energy or Renewable Energy, specifically solar electric system installations, is examined in this study. GRID Alternatives, a non-profit solar installer that implements its Solar Affordable Housing Program, was selected by the California Public Utilities Commission (CPUC) in 2008, to serve as the statewide program manager for the California Solar Initiative’s $108 million incentive program called the Single-family Affordable Solar Homes (SASH) program, which is the country\u27s first dedicated solar rebate program for low-income families (GRID, 2016a, p. 2). In 2010, GRID Alternatives opened its Central Coast office in Atascadero to serve five central coast counties and tracks CO2 emission reductions for each installation. My objective is to determine the impact that GRID Alternatives’ solar electric installations in the cities of Arroyo Grande, Atascadero, Paso Robles, and San Luis Obispo and in San Luis Obispo County have on their respective CAPs’ GHG emissions reduction targets for the Energy or Renewable Energy climate action measure that pertains to solar electric installations

Fighting Child Pornography: A Review of Legal and Technological Developments

In our digitally connected world, the law is arguably behind the technological developments of the Internet age. While this causes many issues for law enforcement, it is of particular concern in the area of child pornography in the United States. With the wide availability of technologies such as digital cameras, peer-to-peer file sharing, strong encryption, Internet anonymizers and cloud computing, the creation and distribution of child pornography has become more widespread. Simultaneously, fighting the growth of this crime has become more difficult. This paper explores the development of both the legal and technological environments surrounding digital child pornography. In doing so, we cover the complications that court decisions have given law enforcement who are trying to investigate and prosecute child pornographers. We then provide a review of the technologies used in this crime and the forensic challenges that cloud computing creates for law enforcement. We note that both legal and technological developments since the 1990s seem to be working to the advantage of users and sellers of child pornography. Before concluding, we provide a discussion and offer observations regarding this subject

Scalar Field Theory on Non-commutative Snyder Space-Time

We construct a scalar field theory on the Snyder non-commutative space-time. The symmetry underlying the Snyder geometry is deformed at the co-algebraic level only, while its Poincar\'e algebra is undeformed. The Lorentz sector is undeformed at both algebraic and co-algebraic level, but the co-product for momenta (defining the star-product) is non-co-associative. The Snyder-deformed Poincar\'e group is described by a non-co-associative Hopf algebra. The definition of the interacting theory in terms of a non-associative star-product is thus questionable. We avoid the non-associativity by the use of a space-time picture based on the concept of realization of a non-commutative geometry. The two main results we obtain are: (i) the generic (namely for any realization) construction of the co-algebraic sector underlying the Snyder geometry and (ii) the definition of a non-ambiguous self interacting scalar field theory on this space-time. The first order correction terms of the corresponding Lagrangian are explicitly computed. The possibility to derive Noether charges for the Snyder space-time is also discussed.Comment: 10 pages; v2: introduction rewritten, co-algebraic analysis improved, references added; to appear in PR

Antiferromagnetism and charged vortices in high-Tc superconductors

The effect of the long-range Coulomb interaction on charge accumulation in antiferromagnetic vortices in high-Tc superconductors is studied within a Bogoliubov-de Gennes mean-field model of competing antiferromagnetic and d-wave superconducting orders. Antiferromagnetism is found to be associated with an accumulation of charge in the vortex core, even in the presence of the long-range Coulomb interaction. The manifestation of Pi-triplet pairing in the presence of coexisting dSC and AFM order, and the intriguing appearance of one-dimensional stripe-like ordering are discussed. The local density of states (LDOS) in the vortex core is calculated and is found to be in excellent qualitative agreement with experimental data.Comment: 14 pages, 8 figures, 2 column RevTex4 PRB forma

On the scattering theory of the classical hyperbolic C(n) Sutherland model

In this paper we study the scattering theory of the classical hyperbolic Sutherland model associated with the C(n) root system. We prove that for any values of the coupling constants the scattering map has a factorized form. As a byproduct of our analysis, we propose a Lax matrix for the rational C(n) Ruijsenaars-Schneider-van Diejen model with two independent coupling constants, thereby setting the stage to establish the duality between the hyperbolic C(n) Sutherland and the rational C(n) Ruijsenaars-Schneider-van Diejen models.Comment: 15 page

Decomposition of time-covariant operations on quantum systems with continuous and/or discrete energy spectrum

Every completely positive map G that commutes which the Hamiltonian time evolution is an integral or sum over (densely defined) CP-maps G_\sigma where \sigma is the energy that is transferred to or taken from the environment. If the spectrum is non-degenerated each G_\sigma is a dephasing channel followed by an energy shift. The dephasing is given by the Hadamard product of the density operator with a (formally defined) positive operator. The Kraus operator of the energy shift is a partial isometry which defines a translation on R with respect to a non-translation-invariant measure. As an example, I calculate this decomposition explicitly for the rotation invariant gaussian channel on a single mode. I address the question under what conditions a covariant channel destroys superpositions between mutually orthogonal states on the same orbit. For channels which allow mutually orthogonal output states on the same orbit, a lower bound on the quantum capacity is derived using the Fourier transform of the CP-map-valued measure (G_\sigma).Comment: latex, 33 pages, domains of unbounded operators are now explicitly specified. Presentation more detailed. Implementing the shift after the dephasing is sometimes more convenien