LpL^p-boundedness properties for the maximal operators for semigroups associated with Bessel and Laguerre operators

In this paper we prove that the generalized (in the sense of Caffarelli and Calder\'on) maximal operators associated with heat semigroups for Bessel and Laguerre operators are weak type (1,1). Our results include other known ones and our proofs are simpler than the ones for the known special cases.Comment: 8 page

Comparison of solar radio and EUV synoptic limb charts during the present solar maximum

The present solar cycle is particular in many aspects: it had a delayed rising phase, it is the weakest of the last 100 years, and it presents two peaks separated by more than one year. To understand the impact of these characteristics on the solar chromosphere and coronal dynamics, images from a wide wavelength range are needed. In this work we use the 17~GHz radio continuum, formed in the upper chromosphere and the EUV lines 304 and 171~{\AA}, that come from the transition region (He II) and the corona (Fe IX, X), respectively. We analyze daily images at 304 and 171~{\AA} obtained by the Atmospheric Imaging Assembly (AIA). The 17~GHz maps were obtained by the Nobeyama Radioheliograph (NoRH). To construct synoptic limb charts, we calculated the mean emission of delimited limb areas with 100" wide and angular separation of $5^\circ$. At the equatorial region, the results show an hemispheric asymmetry of the solar activity. The northern hemisphere dominance is coincident with the first sunspot number peak, whereas the second peak occurs concurrently with the increase in the activity at the south. The polar emission reflects the presence of coronal holes at both EUV wavelengths, moreover, the 17~GHz polar brightenings can be associated with the coronal holes. Until 2013, both EUV coronal holes and radio polar brightenings were more predominant at the south pole. Since then they have not been apparent in the north, but thus appear in the beginning of 2015 in the south as observed in the synoptic charts. This work strengthens the association between coronal holes and the 17~GHz polar brightenings as it is evident in the synoptic limb charts, in agreement with previous case study papers. The enhancement of the radio brightness in coronal holes is explained by the presence of bright patches closely associated with the presence of intense unipolar magnetic fields.Comment: 6 pages, 5 figures. Acccepted for publication in Astronomy & Astrophysic

Exploring a rheonomic system

A simple and illustrative rheonomic system is explored in the Lagrangian formalism. The difference between Jacobi's integral and energy is highlighted. A sharp contrast with remarks found in the literature is pointed out. The non-conservative system possess a Lagrangian not explicitly dependent on time and consequently there is a Jacobi's integral. The Lagrange undetermined multiplier method is used as a complement to obtain a few interesting conclusion

Association of radio polar cap brightening with bright patches and coronal holes

Radio-bright regions near the solar poles are frequently observed in Nobeyama Radioheliograph (NoRH) maps at 17 GHz, and often in association with coronal holes. However, the origin of these polar brightening has not been established yet. We propose that small magnetic loops are the source of these bright patches, and present modeling results that reproduce the main observational characteristics of the polar brightening within coronal holes at 17 GHz. The simulations were carried out by calculating the radio emission of the small loops, with several temperature and density profiles, within a 2D coronal hole atmospheric model. If located at high latitudes, the size of the simulated bright patches are much smaller than the beam size and they present the instrument beam size when observed. The larger bright patches can be generated by a great number of small magnetic loops unresolved by the NoRH beam. Loop models that reproduce bright patches contain denser and hotter plasma near the upper chromosphere and lower corona. On the other hand, loops with increased plasma density and temperature only in the corona do not contribute to the emission at 17 GHz. This could explain the absence of a one-to-one association between the 17 GHz bright patches and those observed in extreme ultraviolet. Moreover, the emission arising from small magnetic loops located close to the limb may merge with the usual limb brightening profile, increasing its brightness temperature and width.Comment: 8 pages, 6 figures, 1 table. Accepted for publication in The Astrophysical Journa

Eficiência da adubação residual com rochas brasileiras para a cultura da soja.

O objetivo deste trabalho foi avaliar a eficiência agronômica residual de rochas como fertilizantes multinutrientes no desenvolvimento e no estado nutricional da soja cultivada em sucessão ao girassol. O experimento foi executado em casa-devegetação, em vasos contendo 3 kg dos solos com características distintas, um Latossolo Vermelho distroférrico (LVdf) e um Neossolo Quartzarênico (NQ). Os tratamentos foram dispostos no esquema fatorial (solos x fontes) e delineamento em blocos casualizados, com quatro repetições. Além de uma testemunha não adubada, testaram-se as fontes de potássio, arenito vulcânico, brecha alcalina, carbonatito, biotita xisto, ultramáfica alcalina e a fonte padrão de potássio, cloreto de potássio, aplicadas na dose de 150 mg kg-1 de K2O por ocasião da semeadura do girassol. Cultivaram-se duas plantas de soja BRS 232 por vaso, as quais foram coletadas no estádio de florescimento pleno para a avaliação da produção de matéria seca da parte aérea, além dos teores de macro e micronutrientes nos tecidos. As rochas ultramáfica alcalina e biotita xisto apresentaram os maiores índices de eficiência agronômica residual para a produção de matéria seca pela soja. As rochas diferem na capacidade de disponibilização de nutrientes às plantas em função da composição mineralógica e apresentam características de fertilizantes multinutrientes, o que deve ser considerado no cálculo de balanço da adubação