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

Disorder and the effective Mn-Mn exchange interaction in Ga1−x_{1-x}Mnx_xAs diluted magnetic semiconductors

We perform a theoretical study, using {\it ab initio} total energy density-functional calculations, of the effects of disorder on the $Mn-Mn$ exchange interactions for $Ga_{1-x}Mn_xAs$ diluted semiconductors. For a 128 atoms supercell, we consider a variety of configurations with 2, 3 and 4 Mn atoms, which correspond to concentrations of 3.1%, 4.7%, and 6.3%, respectively. In this way, the disorder is intrinsically considered in the calculations. Using a Heisenberg Hamiltonian to map the magnetic excitations, and {\it ab initio} total energy calculations, we obtain the effective \JMn, from first ($n=1$) all the way up to sixth ($n=6$) neighbors. Calculated results show a clear dependence in the magnitudes of the \JMn with the Mn concentration $x$. Also, configurational disorder and/or clustering effects lead to large dispersions in the Mn-Mn exchange interactions, in the case of fixed Mn concentration. Moreover, theoretical results for the ground-state total energies for several configurations indicate the importance of a proper consideration of disorder in treating temperature and annealing effects

Diferenciação genética entre procedências de açaizeiro por marcadores RAPD e SSR.

Diferenciação genética refere-se à distribuição da variabilidade entre e dentro de populações, procedências ou outros tipos de agrupamentos. Seu conhecimento é importante para estabelecer estratégias de coleta, conservação e manejo de germoplasma de qualquer espécie. Neste trabalho, avaliou-se a diferenciação genética entre procedências de açaizeiro que compõem a coleção da Embrapa Amazônia Oriental, por meio de marcadores RAPD e SSR. Para tanto, foram utilizados DNAs de 107 acessos, representantes de 17 regiões geográficas diferentes e utilizados em PCR com 28 primers RAPD e sete primers SSR. Os dados foram submetidos à análise de variância molecular (AMOVA) com estrutura hierárquica desbalanceada. Altos níveis de diferenciação genética foram registrados entre procedências, com 0,301 para o marcador dominante e 0,242 para o co-dominante. Para os dois marcadores, a AMOVA apresentou grande variabilidade dentro das procedências (acima de 69%). O pequeno tamanho amostral das procedências do Maranhão pode ter contribuído para a diferenciação significativa entre procedências. Os dados obtidos por esses marcadores foram concordantes quanto à distribuição da variação genética entre e dentro de procedências dessa palmeira

Inflammasome activation by NLRP1 and NLRC4 in patients with coronary stenosis

Objective and design: We performed an experimental, analytical and prospective study to evaluate the systemic activation of inflammasome in atherosclerosis\u2019 patients, in order to shed light into responsible mechanisms for plaque formation. Subjects: We included sixty individuals distributed into 3 groups: 2 groups based on the report from the angiography (severe lesions - SL and primary lesions - PL) and 1 group enclosing healthy individuals (HC). Methods: The expression assays of inflammasome genes NLRP1, NLRC4, CASP-1 and IL-1\u3b2 were performed using Real Time qPCR, with specific Taqman Assays. IL-1\u3b2 serum levels were analysed by commercial kit. Were applied the Shapiro-Wilk and Student's T-test as statistical tests. Statistical significance was set to p 64 0.05. Results: Upregulation of NLRP1 (+3.47 FC, p = 0.0001), NLRC4 (+7.06 FC, p = 6.792 7 10 1209) and IL-1\u3b2 (+2.43 FC, p = 0.005) was observed in all atherosclerosis patients when compared to HC. According to stenosis severity, patients with primary lesions showed upregulation of inflammasome genes NLRP1 (+2.87 FC, p = 0.0008), NLRC4 (+6.34 FC, p = 4.134 7 10-07) and IL-1\u3b2 (+3.39 FC, p = 0.0012) with respect to the HC group. No statistical difference was found in IL-1\u3b2 serum levels according the assessed groups. Conclusions: Inflammasome activation in atherosclerosis's patients can be systemic altered and may be triggered by NLRP1 and NLRC4 receptors. IL-1\u3b2 gene expression was identified in our study as an important systemic detectable marker of plaque severity

Intralobar pulmonary sequestration: diagnostic expertise

An obese 22-year-old man with a history of recurrent respiratory infections presented to the emergency room with left pleuritic chest pain, productive cough with mucupurulent sputum and an axillary temperature of 37.7°C. Blood work showed elevated inflammatory parameters and chest X-ray was relevant for heterogeneous infiltration in the left base and opacity of the left costophrenic angle. An angio-CT scan revealed areas of bilateral consolidation with presence of an arterial branch originating from the aorta to the collected area of the left lower lobe, consistent with a respiratory infection grafted on a intralobar pulmonary sequestration of the left lung base. The infectious process was treated and the patient was planned for a lower left lobectomy

Efeito do espaçamento nos caracteres agronômicos da mamona, cultivar Al Guarany 2002.

O objetivo do trabalho foi avaliar o efeito do espaçamento entre plantas e do estande final sobre alguns caracteres agronômicos da cultivar AL Guarany 2002, na safra 2010/11 em Pelotas/RS