On critical values of L-functions of potentially automorphic motives

In this paper we prove a version of Deligne's conjecture for potentially automorphic motives, twisted by certain algebraic Hecke characters. The Hecke characters are chosen in such a way that we can use automorphic methods in the context of totally definite unitary groups.Comment: 24 page

Families of Bianchi modular symbols: critical base-change p-adic L-functions and p-adic Artin formalism

Let $K$ be an imaginary quadratic field. In this article, we study the eigenvariety for GL(2)/K, proving an etaleness result for the weight map at non-critical classical points and a smoothness result at base-change classical points. We give three main applications of this; let $f$ be a regular $p$-stabilised newform of weight $k$ at least 2 without CM by $K$. (1) We construct a two-variable $p$-adic $L$-function attached to the base-change of $f$ to $K$ under assumptions on $f$ that we conjecture always hold, in particular making no assumption on the slope of $f$. (2) We construct three-variable $p$-adic $L$-functions over the eigenvariety interpolating the $p$-adic $L$-functions of classical base-change Bianchi cusp forms in families. (3) We prove that these base-change $p$-adic $L$-functions satisfy a $p$-adic Artin formalism result, that is, they factorise in the same way as the classical $L$-function under Artin formalism. In an appendix, Carl Wang-Erickson describes a base-change deformation functor and gives a characterisation of its Zariski tangent space.Comment: 26 pages, with a 3 page appendix by Carl Wang-Erickson. Comments welcome! Changes for v5: added contents, minor changes to exposition. v4: corrected funding acknowledgements. v3: This version has a new introduction, has been reorganised and greatly shortened, and incorporates minor corrections. v2: minor correction

Acid-catalyzed Disproportionation of 3 and 4-Methylcyclohexene in Various Sulfuric Acid Concentrations

Abstract: Experiments were conducted to verify a mechanism for the formation of cyclohexenyl cations from 3 and 4-methylcyclohexenes. Three concentrations of sulfuric acid were subjected to various concentrations of sulfuric acid: 80, 89 and 96% (w/w). For 3-methylcyclohexene, at the 89 and 96% concentrations, the reaction did not occur. The results showed that the region for experimentation is between 78 and 83% (w/w) sulfuric acid. For 4-methylcyclohexene, all but the highest concentration was successful in evaluating the spectra for possible cation formations. These small-scale experiments along with the data collected will hopefully lead to future research to gain a better understanding of the mechanism of cyclohexenyl cations

THE AMERICAN CORRECTIONAL HEALTHCARE SYSTEM IS AILING: TECHNOLOGY INNOVATION AS A PRESCRIPTION FOR PENAL SYSTEM HEALTHCARE DELIVERY

The U.S. corrections industry has a history of poor inmate healthcare delivery, with penal-system reform advocates and other stakeholders highlighting these failures. Inmates receiving poor medical and psychiatric care behind jail walls experience greater difficulty becoming self-sufficient, and this situation contributes to the nation’s recidivism problem. Caring for inmates is often a neglected proposition and because of this, the U.S. courts impose legal requirements that inmates receive healthcare. Access to quality healthcare specialists for inmates led the penal system to investigate and implement use of telehealth during the 1990s. This thesis investigates how the evolving field of telehealth and emerging technologies may contribute to improved inmate healthcare in the future. A myriad of factors discussed in the thesis pose as challenges to implementing innovations that could improve penal system healthcare. For all the challenges confronting corrections administrators and criminal reform advocates, the corrections system is at a crossroads, as there is potential to modernize jail facilities and use technology to improve the safety and healthcare of inmates, corrections officers and those who render care. Investing in technology infrastructure that supports emerging technologies could also facilitate simpler integration of future innovations that address suicide, mental illness and other medical health maladies that would otherwise go unaddressed.Civilian, Dallas Fire-Rescue DepartmentApproved for public release. Distribution is unlimited

The Holographic Disorder-Driven Superconductor-Metal Transition

We implement the effects of disorder on a holographic superconductor by introducing a random chemical potential on the boundary. We demonstrate explicitly that increasing disorder leads to the formation of islands where the superconducting order is enhanced and subsequently to the transition to a metal. We study the behavior of the superfluid density and of the conductivity as a function of the strength of disorder. We find explanations for various marked features in the conductivities in terms of hydrodynamic quasi-normal modes of the holographic superconductors. These identifications plus a particular disorder-dependent spectral weight shift in the conductivity point to a signature of the Higgs mode in the context of disordered holographic superconductors. We observe that the behavior of the order parameter close to the transition is not mean-field type as in the clean case, rather we find robust agreement with $\exp(- A\, |T-T_c|^{-\nu})$, with $\nu =1.03\pm 0.02$ for this disorder-driven smeared transition.Comment: 7 pages, 8 figures. v2: minor improvements of the Higgs mode and smeared phase transition discussions. Typos corrected. Published versio

Holographic s+p Superconductors

We study the phase diagram of a holographic model realizing a U(2) global symmetry on the boundary and show that at low temperature a phase with both scalar s and vector p condensates exists. This is the s+p-wave phase where the global U(2) symmetry and also the spatial rotational symmetry are spontaneously broken. By studying the free energy we show that this phase is preferred when it exists. We also consider unbalanced configurations where a second chemical potential is turned on. They present a rich phase diagram characterized by the competition and coexistence of the s and p order parameters.Comment: 6 pages, 4 figures; v3: published version, clarifications and references adde

Holographic p-wave Superconductor with Disorder

We implement the effects of disorder on a holographic p-wave superconductor by introducing a random chemical potential which defines the local energy of the charge carriers. Since there are various possibilities for the orientation of the vector order parameter, we explore the behaviour of the condensate in the parallel and perpendicular directions to the introduced disorder. We clarify the nature of various branches representing competing solutions and construct the disordered phase diagram. We find that moderate disorder enhances superconductivity as determined by the value of the condensate. Though we mostly focus on uncorrelated noise, we also consider a disorder characterized by its spectral properties and study in detail its influence on the spectral properties of the condensate and charge density. We find fairly universal responses of the resulting power spectra characterized by linear functions of the disorder power spectrum.Fil: Arean, Daniel. Instituto Max Planck de Física; AlemaniaFil: Pando Zayas, Leopoldo. University of Michigan; Estados UnidosFil: Salazar, Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; ArgentinaFil: Scardicchio, Antonello. The Abdus Salam. International Centre for Theoretical Physics; Italia. Columbia University; Estados Unidos. Princeton University; Estados Unido

A Dirty Holographic Superconductor

We study the effects of disorder on a holographic superconductor by introducing a random chemical potential on the boundary. We consider various realizations of disorder and find that the critical temperature for superconductivity is enhanced. We also present evidence for a precise form of renormalization in this system. Namely, when the random chemical potential is characterized by a Fourier spectrum of the form $k^{-2\alpha}$ we find that the spectra of the condensate and the charge density are again power-laws, whose exponents are accurately and universally governed by linear functions of $\alpha$.Comment: 5 pages, 8 figures. v3: discussion improved, references added, typos corrected, results unchange