In this work I study the well-posedness of the Cauchy problem associated with the coupled Schrödinger equations with quadratic nonlinearities, which appears modeling problems in nonlinear optics. I obtain the local well-posedness for data in Sobolev spaces with low regularity. To obtain the local theory, I prove new bilinear estimates for the coupling terms of the system in the continuous case. Concerning global results, in the continuous case, I establish the global well-posedness in H s (R) × H s (R), for some negatives indexes s. The proof of the global result uses the I-method introduced by Colliander, Keel, Staffilani, Takaoka and Tao.

A dengue é um dos graves problemas de saúde pública mundial. O Nordeste do Brasil (NEB) possui um clima e ambiente urbano ideal para a proliferação do mosquito Aedes (aegypti e albopictus), vetor da doença. O Estado de Alagoas, principalmente a sua capital, tem epidemias da doença de forma frequente. Portanto, o objetivo deste estudo é avaliar a aplicação de Rede Neural Artificial (RNA) nos casos notificados de dengue (CND) nas regiões administrativas (RA) de Maceió. As RAs são divididas em: RA1, RA2, RA3, RA4, RA5, RA6, RA7 e RA8. Os CND foram submetidos a RNA não linear autorregressiva (NAR) – (RNA-NAR). O período de estudo foi de 2011 a 2020. Os resultados obtidos de CND se destacaram em anos específicos (2012, 2013, 2017, 2018 e 2020), por outro lado houve superestimativas das previsões via RNA. Em algumas RAs houve subnotificações e, por isso interferiu nos resultados das previsões. A RNA-NAR foi validada, visto que a maioria das previsões apresentou correlação positiva e com resposta aos dados observados, exceto as RAs com subnotificações. O uso da RNA é adequado no alerta e previsão da donça, onde tal instrumento pode ser usado em ações preventivas de controle da doença.

This study aimed to evaluate the performance of the Weather Research and Forecasting (WRF) mesoscale model in the simulation of wind speed in the semiarid region of Northeast Brazil (NEB). The accuracy of the simulations was determined by comparing between forecast (WRF) and observed (OBS) values with an average every 10 minutes. The measurements were made in a 100 m high anemometric tower during the execution of the Project Previsão do Vento em Parques Eólicos do Nordeste Brasileiro – PVPN. The tower was installed in a flat semiarid location in Craíbas, Alagoas - NEB. The period analyzed was five months (2015/03/01 to 2015/07/31). The analysis was performed using descriptive statistics (DS) including central and dispersion measures; bivariate statistics (BS) that includes the correlations (Pearson, Kendall and Spearman) with a t-Student hypothesis test to verify the representativeness of the correlations, and errors statistics (ES) with equations to verify the effectiveness of the simulation; Simple Linear Regression (SLR); Normal and Weibull probability density function (PDF); Principal Component Analysis (PCA). In addition to the temporal assessment of wind speed, temporal distribution of the average daily cycle (ADC), boxplot, scatterplot (1:1) and relative frequency distribution. The results showed that the simulation made by the WRF model reproduced well the daily temporal evolution of the wind in the studied period with a small tendency of underestimation. These results indicate the potential of the WRF model in the modeling of wind speed for the region studied and can contribute to the production of wind energy.

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