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

A GIT interpretration of the Harder-Narasimhan filtration

An unstable torsion free sheaf on a smooth projective variety gives a GIT unstable point in certain Quot scheme. To a GIT unstable point, Kempf associates a "maximally destabilizing" 1-parameter subgroup, and this induces a filtration of the torsion free sheaf. We show that this filtration coincides with the Harder-Narasimhan filtration.Comment: 19 pages; Comments of the referees and references added. The construction for holomorphic pairs (Sections 6 and 7 from previous version) will appear in a further publication. To appear in Rev. Mat Complutens

Dynamic relaxation of a liquid cavity under amorphous boundary conditions

The growth of cooperatively rearranging regions was invoked long ago by Adam and Gibbs to explain the slowing down of glass-forming liquids. The lack of knowledge about the nature of the growing order, though, complicates the definition of an appropriate correlation function. One option is the point-to-set correlation function, which measures the spatial span of the influence of amorphous boundary conditions on a confined system. By using a swap Monte Carlo algorithm we measure the equilibration time of a liquid droplet bounded by amorphous boundary conditions in a model glass-former at low temperature, and we show that the cavity relaxation time increases with the size of the droplet, saturating to the bulk value when the droplet outgrows the point-to-set correlation length. This fact supports the idea that the point-to-set correlation length is the natural size of the cooperatively rearranging regions. On the other hand, the cavity relaxation time computed by a standard, nonswap dynamics, has the opposite behavior, showing a very steep increase when the cavity size is decreased. We try to reconcile this difference by discussing the possible hybridization between MCT and activated processes, and by introducing a new kind of amorphous boundary conditions, inspired by the concept of frozen external state as an alternative to the commonly used frozen external configuration.Comment: Completely rewritten version. After the first submission it was realized that swap and nonswap dynamics results are qualitatively different. This version reports the results of both dynamics and discusses the different behaviors. 17 pages, 18 figure

Revisão e atualização da listagem de espécies de aves registradas na planície do Pantanal.

Este trabalho teve como objetivo atualizar a listagem das espécies de aves já registradas no Pantanal. Uma lista preliminar baseada em informações de literatura foi complementada com comunicações pessoais de ornitólogos que visitaram a região. Somente localidades situadas na planície inundável (de acordo com cartas do DSG em escala 1:100 000) foram consideradas. Um total de 470 espécies já foi registrado na planície, representando um aumento de cerca de 34% à riqueza de espécies anteriormente creditada a esse bioma. Deste total, 379 espécies tiveram exemplares coletados e depositados em coleções do Brasil e do exterior. Das 91 espécies restantes (registradas por observação direta, captura e/ou vocalização), 46 estão presentes em duas ou mais publicações, 26 em apenas uma e dezenove espécies resultaram de comunicações pessoais. O Pantanal não apresenta endemismos. Inventários são realizados nessa região desde o século XIX e localizam-se em pontos mais acessíveis, próximos a cidades, grandes rios ou rodovias. Grandes lacunas são evidentes no centro, em toda porção leste, no sul e na porção noroeste. Novos inventários e pesquisas em coleções de museus poderão resultar em acréscimos a esta listagem, além de confirmar ou desconsiderar registros de ocorrência duvidosa.bitstream/item/37413/1/BP39.pd

Alignment of the CLIC BDS

Aligning the CLIC Beam Delivery System faces two major challenges, the tight tolerances for the emittance preservation and its strong non-linear beam dynamics. For these reasons conventional beam-based alignment techniques, like dispersion free steering, are only partially successful and need to be followed by optimization algorithms based on other observables, like beam sizes

Triaxial Angular Momentum Projection and Configuration Mixing calculations with the Gogny force

We present the first implementation in the $(\beta,\gamma)$ plane of the generator coordinate method with full triaxial angular momentum and particle number projected wave functions using the Gogny force. Technical details about the performance of the method and the convergence of the results both in the symmetry restoration and the configuration mixing parts are discussed in detail. We apply the method to the study of $^{24}$Mg, the calculated energies of excited states as well as the transition probabilities are compared to the available experimental data showing a good overall agreement. In addition, we present the RVAMPIR approach which provides a good description of the ground and gamma bands in the absence of strong mixing.Comment: 40 pages,14 figure

Adsorption and catalytic activity of glucose oxidase accumulated on OTCE upon the application of external potential

This article describes the adsorption of glucose oxidase (GOx) onto optically transparent carbon electrodes (OTCE) under the effect of applied potential and the analysis of the enzymatic activity of the resulting GOx/OTCE substrates. In order to avoid electrochemical interferences with the enzyme redox center, control electrochemical experiments were performed using flavin adenine dinucleotide (FAD) and GOx/OTCE substrates. Then, the enzyme adsorption experiments were carried out as a function of the potential applied (ranged from the open circuit potential to +950. mV), the pH solution, the concentration of enzyme, and the ionic strength on the environment. The experimental results demonstrated that an increase in the adsorbed amount of GOx on the OTCE can be achieved when the potential was applied. Although the increase in the adsorbed amount was examined as a function of the potential, a maximum enzymatic activity was observed in the GOx/OTCE substrate achieved at +800. mV. These experiments suggest that although an increase in the amount of enzyme adsorbed can be obtained by the application of an external potential to the electrode, the magnitude of such potential can produce detrimental effects in the conformation of the adsorbed protein and should be carefully considered. As such, the article describes a simple and rational approach to increase the amount of enzyme adsorbed on a surface and can be applied to improve the sensitivity of a variety of biosensors.Fil: Benavidez, Tomás Enrique. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Investigaciones en Físico-química de Córdoba. Universidad Nacional de Córdoba. Facultad de Ciencias Químicas. Instituto de Investigaciones en Físico-química de Córdoba; Argentina. University of Texas; Estados UnidosFil: Torrente, Daniel. University of Texas; Estados UnidosFil: Marucho, Marcelo. University of Texas; Estados UnidosFil: Garcia, Carlos D.. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Investigaciones en Físico-química de Córdoba. Universidad Nacional de Córdoba. Facultad de Ciencias Químicas. Instituto de Investigaciones en Físico-química de Córdoba; Argentina. University of Texas; Estados Unido

A weakly non-hydrostatic shallow model for dry granular flows

A non-hydrostatic depth-averaged model for dry granular flows is proposed, taking into account vertical acceleration. A variable friction coefficient based on the $\mu(I)$ rheology is considered. The model is obtained from an asymptotic analysis in a local reference system, where the non-hydrostatic contribution is supposed to be small compared to the hydrostatic one. The non-hydrostatic counterpart of the pressure may be written as the sum of two terms: one corresponding to the stress tensor and the other to the vertical acceleration. The model introduced here is weakly non-hydrostatic, in the sense that the non-hydrostatic contribution related to the stress tensor is not taken into account due to its complex implementation. A simple and efficient numerical scheme is proposed. It consists of a three-step splitting procedure, and it is based on a hydrostatic reconstruction. Two key points are: (i) the friction force has to be taken into account before solving the non-hydrostatic pressure. Otherwise, the incompressibility condition is not ensured; (ii) both the hydrostatic and the non-hydrostatic pressure are taken into account when dealing with the friction force. The model and numerical scheme are then validated based on several numerical tests, including laboratory experiments of granular collapse. The influence of non-hydrostatic terms and of the choice of the coordinate system (Cartesian or local) is analyzed. We show that non-hydrostatic models are less sensitive to the choice of the coordinate system. In general, the non-hydrostatic model introduced here much better reproduces granular collapse experiments compared to hydrostatic models. An important result is that the simulated mass profiles up to the deposit and the front velocity are greatly improved. As expected, the influence of the non-hydrostatic pressure is shown to be larger for small values of the slope