Riesz potential versus fractional Laplacian

This paper starts by introducing the Grünwald–Letnikov derivative, the Riesz potential and the problem of generalizing the Laplacian. Based on these ideas, the generalizations of the Laplacian for 1D and 2D cases are studied. It is presented as a fractional version of the Cauchy–Riemann conditions and, finally, it is discussed with the n-dimensional Laplacian.

Riesz potential versus fractional Laplacian

This paper starts by introducing the Grünwald–Letnikov derivative, the Riesz potential and the problem of generalizing the Laplacian. Based on these ideas, the generalizations of the Laplacian for 1D and 2D cases are studied. It is presented as a fractional version of the Cauchy–Riemann conditions and, finally, it is discussed with the n-dimensional Laplacian.

Síntese de derivados de ácidos fenólicos e estudo da sua actividade antioxidante

A peroxidação lipídica, além de causar sérios danos no corpo humano, é a principal causa da deterioração dos alimentos afectando a sua cor, aroma e valor nutricional, o que conduz a uma diminuição do seu ciclo de vida. O fenómeno de oxidação pode ser retardado com recurso a antioxidantes, de origem natural ou sintética, que inibam a formação de espécies reactivas, ou que reajam com estas, formando posteriormente radicais com menor grau de reactividade. Nesta dissertação procedeu-se à síntese e elucidação estrutural de novos antioxidantes, derivados dos ácidos 3,4-diidroxibenzóico (PCA) e 3,4-diidroxifenilacético (DOPAC), e à avaliação da sua actividade anti-radicalar e antioxidante. Os novos antioxidantes sintetizados foram caracterizados usando RMN de 1H e de 13C, FTIR e EM-IE. A avaliação da actividade antioxidante foi realizada com base no método do radical 2,2- difenil-1-picrilhidrazilo (DPPH·) e por técnicas electroquímicas (voltametria de impulso diferencial e voltametria cíclica). Os resultados obtidos permitiram concluir que a eficácia anti-radicalar (AE) é determinada por aspectos da estrutura molecular dos compostos, nomeadamente pela presença de grupos hidroxilo no anel aromático e também de grupos extensores relativamente à posição do grupo carboxílico. Os resultados permitiram verificar que o DOPAC apresenta a mais elevada eficiência anti-radicalar dos compostos em estudo, incluindo o trolox e o ácido gálhico (compostos de referência). Com base nos resultados obtidos concluiu-se que, um menor potencial de oxidação conduz a uma melhor actividade anti-radicalar dos compostos. De facto, verificou-se para o PCA e respectivos ésteres o maior potencial de oxidação e também a menor eficiência anti-radicalar. Em contrapartida, os antioxidantes com maior eficiência anti-radicalar, DOPAC, trolox e ácido gálhico, apresentaram menor potencial de oxidação.

Simulation of the magnetic induction vector of a magnetic core to be used in FFC NMR relaxometry

This paper is a contribution for the assessment and comparison of magnet properties based on magnetic field characteristics particularly concerning the magnetic induction uniformity in the air gaps. For this aim, a solver was developed and implemented to determine the magnetic field of a magnetic core to be used in Fast Field Cycling (FFC) Nuclear Magnetic Resonance (NMR) relaxometry. The electromagnetic field computation is based on a 2D finite-element method (FEM) using both the scalar and the vector potential formulation. Results for the magnetic field lines and the magnetic induction vector in the air gap are presented. The target magnetic induction is 0.2 T, which is a typical requirement of the FFC NMR technique, which can be achieved with a magnetic core based on permanent magnets or coils. In addition, this application requires high magnetic induction uniformity. To achieve this goal, a solution including superconducting pieces is analyzed. Results are compared with a different FEM program.

Amygdala activation in response to 2D and 3D emotion-inducing stimuli

Studying changes in brain activation according to the valence of emotion-inducing stimuli is essential in the research on emotions. Due to the ecological potential of virtual reality, it is also important to examine whether brain activation in response to emotional stimuli can be modulated by the three-dimensional (3D) properties of the images. This study uses functional Magnetic Resonance Imaging to compare differences between 3D and standard (2D) visual stimuli in the activation of emotion-related brain areas. The stimuli were organized in three virtual-reality scenarios, each with a different emotional valence (pleasant, unpleasant and neutral). The scenarios were presented in a pseudo-randomized order in the two visualization modes to twelve healthy males. Data were analyzed through a GLM-based fixed effects procedure. Unpleasant and neutral stimuli activated the right amygdala more strongly when presented in 3D than in 2D. These results suggest that 3D stimuli, when used as “building blocks” for virtual environments, can induce increased emotional loading, as shown here through neuroimaging.