Absence of reflection as a function of the coupling constant

We consider solutions of the one-dimensional equation $-u'' +(Q+ \lambda V) u = 0$ where $Q: \mathbb{R} \to \mathbb{R}$ is locally integrable, $V : \mathbb{R} \to \mathbb{R}$ is integrable with supp$(V) \subset [0,1]$, and $\lambda \in \mathbb{R}$ is a coupling constant. Given a family of solutions $\{u_{\lambda} \}_{\lambda \in \mathbb{R}}$ which satisfy $u_{\lambda}(x) = u_0(x)$ for all $x<0$, we prove that the zeros of $b(\lambda) := W[u_0, u_{\lambda}]$, the Wronskian of $u_0$ and $u_{\lambda}$, form a discrete set unless $V \equiv 0$. Setting $Q(x) := -E$, one sees that a particular consequence of this result may be stated as: if the fixed energy scattering experiment $-u'' + \lambda V u = Eu$ gives rise to a reflection coefficient which vanishes on a set of couplings with an accumulation point, then $V \equiv 0$.Comment: To appear in Journal of Mathematical Physic

The Stellar Content of Obscured Galactic Giant HII Regions V: G333.1--0.4

We present high angular resolution near--infrared images of the obscured Galactic Giant HII (GHII) region G333.1--0.4 in which we detect an OB star cluster. For G333.1--0.4, we find OB stars and other massive objects in very early evolutionary stages, possibly still accreting. We obtained $K$--band spectra of three stars; two show O type photospheric features, while the third has no photospheric features but does show CO 2.3 $\mu$m band--head emission. This object is at least as hot as an early B type star based on its intrinsic luminosity and is surrounded by a circumstellar disc/envelope which produces near infrared excess emission. A number of other relatively bright cluster members also display excess emission in the $K$--band, indicative of disks/envelopes around young massive stars. Based upon the O star photometry and spectroscopy, the distance to the cluster is 2.6 $\pm$ 0.4 kpc, similar to a recently derived kinematic (near side) value. The slope of the $K$--band luminosity function is similar to those found in other young clusters. The mass function slope is more uncertain, and we find $-1.3 \pm 0.2 < \Gamma < -1.1 \pm 0.2$- for stars with M $> 5$ M$_\odot$ where the upper an lower limits are calculated independently for different assumptions regarding the excess emission of the individual massive stars. The number of Lyman continuum photons derived from the contribution of all massive stars in the cluster is 0.2 $\times$ $10^{50}$ $s^{-1}$ $< NLyc < 1.9$ $\times$ $10^{50}$ $s^{-1}$. The integrated cluster mass is 1.0 $\times$ $10^{3}$ $M_\odot < M_{cluster} < 1.3$ $\times$ $10^{3}$ $M_\odot$.Comment: 31 pages, including 12 figures and 3 tables. Accepted for publication in the A

Quasiperiodicity and non-computability in tilings

We study tilings of the plane that combine strong properties of different nature: combinatorial and algorithmic. We prove existence of a tile set that accepts only quasiperiodic and non-recursive tilings. Our construction is based on the fixed point construction; we improve this general technique and make it enforce the property of local regularity of tilings needed for quasiperiodicity. We prove also a stronger result: any effectively closed set can be recursively transformed into a tile set so that the Turing degrees of the resulted tilings consists exactly of the upper cone based on the Turing degrees of the later.Comment: v3: the version accepted to MFCS 201

Bright and dark states of light: The quantum origin of classical interference

Classical theory asserts that several electromagnetic waves cannot interact with matter if they interfere destructively to zero, whereas quantum mechanics predicts a nontrivial light-matter dynamics even when the average electric field vanishes. Here we show that in quantum optics classical interference emerges from collective bright and dark states of light, \textit{i.e.}, entangled superpositions of multi-mode photon-number states. This makes it possible to explain wave interference using the particle description of light and the superposition principle for linear systems.Comment: 5 pages, 1 figure

Anomalous behavior of trapping on a fractal scale-free network

It is known that the heterogeneity of scale-free networks helps enhancing the efficiency of trapping processes performed on them. In this paper, we show that transport efficiency is much lower in a fractal scale-free network than in non-fractal networks. To this end, we examine a simple random walk with a fixed trap at a given position on a fractal scale-free network. We calculate analytically the mean first-passage time (MFPT) as a measure of the efficiency for the trapping process, and obtain a closed-form expression for MFPT, which agrees with direct numerical calculations. We find that, in the limit of a large network order $V$, the MFPT $$ behaves superlinearly as $\sim V^{{3/2}}$ with an exponent 3/2 much larger than 1, which is in sharp contrast to the scaling $\sim V^{\theta}$ with $\theta \leq 1$, previously obtained for non-fractal scale-free networks. Our results indicate that the degree distribution of scale-free networks is not sufficient to characterize trapping processes taking place on them. Since various real-world networks are simultaneously scale-free and fractal, our results may shed light on the understanding of trapping processes running on real-life systems.Comment: 6 pages, 5 figures; Definitive version accepted for publication in EPL (Europhysics Letters

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

Diffusing-wave spectroscopy of nonergodic media

We introduce an elegant method which allows the application of diffusing-wave spectroscopy (DWS) to nonergodic, solid-like samples. The method is based on the idea that light transmitted through a sandwich of two turbid cells can be considered ergodic even though only the second cell is ergodic. If absorption and/or leakage of light take place at the interface between the cells, we establish a so-called "multiplication rule", which relates the intensity autocorrelation function of light transmitted through the double-cell sandwich to the autocorrelation functions of individual cells by a simple multiplication. To test the proposed method, we perform a series of DWS experiments using colloidal gels as model nonergodic media. Our experimental data are consistent with the theoretical predictions, allowing quantitative characterization of nonergodic media and demonstrating the validity of the proposed technique.Comment: RevTeX, 12 pages, 6 figures. Accepted for publication in Phys. Rev.