Some extremal functions in Fourier analysis, III

We obtain the best approximation in $L^1(\R)$, by entire functions of exponential type, for a class of even functions that includes $e^{-\lambda|x|}$, where $\lambda >0$, $\log |x|$ and $|x|^{\alpha}$, where $-1 < \alpha < 1$. We also give periodic versions of these results where the approximating functions are trigonometric polynomials of bounded degree.Comment: 26 pages. Submitte

Efectos del proceso de secado sobre la composición en ácidos grasos, perfil fenólico, tocoferoles y actividad antioxidante de almendras barú (Dipteryx alata Vog.)

This study carried out a chromatographic and spectrophotometric characterization of the bioactive compounds, antioxidants, phenolics, tocopherols, sterols and fatty acids of baru almonds “in natura” and submitted to drying processes. It was determined that baru “in natura” almonds presented high levels of phenolic compounds, vitamin C, antioxidants, phenolics, sterols, total monounsaturated fatty acids and low thrombogenic, and atherogenic indexes. During the process of drying it at 65 °C for 30 minutes, a decrease was noted in the levels of caffeic acid, chlorogenic acid, anthocyanins, p-coumaric acid, ferulic acid, o-coumaric acid, quercetin, and polyunsaturated fatty acids. The same condition resulted in an increase in the levels of gallic acid, rutin, catechin, trans-cinnamic acid, vanillin, m-coumaric acid, tocopherols, monounsaturated fatty acids and antioxidant activity (ORAC and DPPH). When submitted to a temperature of 105 ºC for 30 minutes the same behavior was seen with a reduction in the vitamin C and ORAC contents and increased presence of flavonoids.Este estudio realizó una caracterización cromatográfica y espectrofotométrica de la presencia de compuestos bioactivos, antioxidantes, fenólicos, tocoferoles, esteroles y ácidos grasos en almendras del tipo baru “in natura” y sometidos a procesos de secado. Se detectó, en la almendra de baru “in natura”, altos contenidos de compuestos fenólicos, vitamina C, antioxidantes fenólicos, esteroles, ácidos grasos monoinsaturados totales y bajos índices de trombogénicos y aterogénicos. Durante el proceso de secado a 65 °C durante 30 minutos, se observó una disminución en los niveles de ácido cafeíco, ácido clorogénico, antocianinas, ácido p-cumárico, ácido ferúlico, ácido o-cumárico, quercetina y ácidos grasos poliinsaturados. De la misma manera se observó un aumento en los niveles de ácido gálico, rutina, catequina, ácido trans-cinámico, vanilina, ácido m-cumárico, tocoferoles, ácidos grasos monoinsaturados y actividad antioxidante (ORAC y DPPH). Cuando se sometió a una temperatura de 105 °C durante 30 minutos, presentó el mismo comportamiento, sin embargo, influyó en la reducción del contenido de vitamina C y ORAC y aumentó la presencia de flavonoides

Towards a quantum universe

In this short review we study the state of the art of the great problems in cosmology and their interrelationships. The reconciliation of these problems passes undoubtedly through the idea of a quantum universe.Comment: 7 pages, Accepted for publication in Astrophysics & Space Scienc