A proof of the conjecture of Cohen and Mullen on sums of primitive roots

We prove that for all $q>61$, every non-zero element in the finite field $\mathbb{F}_{q}$ can be written as a linear combination of two primitive roots of $\mathbb{F}_{q}$. This resolves a conjecture posed by Cohen and Mullen.Comment: 8 pages; to appear in Mathematics of Computatio

On Grosswald's conjecture on primitive roots

Grosswald's conjecture is that $g(p)$, the least primitive root modulo $p$, satisfies $g(p) \leq \sqrt{p} - 2$ for all $p>409$. We make progress towards this conjecture by proving that $g(p) \leq \sqrt{p} -2$ for all $409<p< 2.5\times 10^{15}$ and for all $p>3.67\times 10^{71}$.Comment: 7 page

On consecutive primitive elements in a finite field

For $q$ an odd prime power with $q>169$ we prove that there are always three consecutive primitive elements in the finite field $\mathbb{F}_{q}$. Indeed, there are precisely eleven values of $q \leq 169$ for which this is false. For $4\leq n \leq 8$ we present conjectures on the size of $q_{0}(n)$ such that $q>q_{0}(n)$ guarantees the existence of $n$ consecutive primitive elements in $\mathbb{F}_{q}$, provided that $\mathbb{F}_{q}$ has characteristic at least~$n$. Finally, we improve the upper bound on $q_{0}(n)$ for all $n\geq 3$.Comment: 10 pages, 2 table

Breathing feedback system with wearable textile sensors

Breathing exercises form an essential part of the treatment for respiratory illnesses such as cystic fibrosis. Ideally these exercises should be performed on a daily basis. This paper presents an interactive system using a wearable textile sensor to monitor breathing patterns. A graphical user interface provides visual real-time feedback to patients. The aim of the system is to encourage the correct performance of prescribed breathing exercises by monitoring the rate and the depth of breathing. The system is straightforward to use, low-cost and can be installed easily within a clinical setting or in the home. Monitoring the user with a wearable sensor gives real-time feedback to the user as they perform the exercise, allowing them to perform the exercises independently. There is also potential for remote monitoring where the user’s overall performance over time can be assessed by a clinician

Experimental verification of position-dependent angular-momentum selection rules for absorption of twisted light by a bound electron

We analyze the multipole excitation of atoms with twisted light, i.e, by a vortex light field that carries orbital angular momentum. A single trapped 40Ca+ ion serves as a localized and positioned probe of the exciting field. We drive the transition and observe the relative strengths of different transitions, depending on the ion's transversal position with respect to the center of the vortex light field. On the other hand, transition amplitudes are calculated for a twisted light field in form of a Bessel beam, a Bessel-Gauss and a Laguerre-Gauss mode. Analyzing experimental obtained transition amplitudes we find agreement with the theoretical predictions at a level of better than 3%. Finally, we propose measurement schemes with two-ion crystals to enhance the sensing accuracy of vortex modes in future experiments.Fil: Afanasev, Andrei. The George Washington University; Estados UnidosFil: Carlson, Carl E.. College of William and Mary; Estados UnidosFil: Schmiegelow, Christian Tomás. Johannes Gutenberg University Mainz. Institute of Physics; Alemania. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Schulz, Jonas. Johannes Gutenberg University Mainz. Institute of Physics; AlemaniaFil: Schmidt-kaler, Ferdinand. Johannes Gutenberg University Mainz. Institute of Physics; AlemaniaFil: Solyanik, Maria. The George Washington University; Estados Unido

Los humos del mercedario: el postre americano de 'La villana de Vallecas'

El estudio de cómo se representan en las obras áureas algunos objetos de la vida cotidiana, como el tabaco, avanza la comprensión de las mismas, como es el caso de 'La villana de Vallecas', de Tirso de Molina. Utilizando la dicha comedia y fuentes tratadísticas de la época, este artículo muestra que el tabaco –como el chocolate– fue objeto de la fascinación del mercedario, que vio en él un ambiguo símbolo del Nuevo Mundo, del consumismo avant la lettre y de la sensualidad. The study of how some everyday objects, such as tobacco, are represented in Golden Age works contributes to our understanding of these works, as is the case with Tirso de Molina’s 'La villana de Vallecas'. Utilizing sources including this comedy and contemporary treatises, this article shows that tobacco –like chocolate– was an object of fascination for the Mercedarian, who saw in it an ambiguous symbol of the New World, of consumerism avant la lettre, and of sensuality