Rubber Bands, Pursuit Games and Shy Couplings

In this paper, we consider pursuit-evasion and probabilistic consequences of some geometric notions for bounded and suitably regular domains in Euclidean space that are CAT(kappa) for some kappa > 0. These geometric notions are useful for analyzing the related problems of (a) existence/nonexistence of successful evasion strategies for the Man in Lion and Man problems, and (b) existence/nonexistence of shy couplings for reflected Brownian motions. They involve properties of rubber bands and the extent to which a loop in the domain in question can be deformed to a point without, in between, increasing its loop length. The existence of a stable rubber band will imply the existence of a successful evasion strategy but, if all loops in the domain are well-contractible, then no successful evasion strategy will exist and there can be no co-adapted shy coupling. For example, there can be no shy couplings in bounded and suitably regular star-shaped domains and so, in this setting, any two reflected Brownian motions must almost surely make arbitrarily close encounters as t tends to infinity.Comment: 48 pages, 8 figure

The oenological interest of fumaric acid: Stop malolactic fermentation and preserve the freshness of wines

ABSTRACT One of the problems related to the increase in average temperatures in the wine-growing regions is the lower accumulation of organic acids in the berries. Wine freshness depends to a great extent on its acidity. Herein, the effectiveness of fumaric acid to inhibit malolactic fermentation or to stop it once initiated is evaluated in order to preserve the malic acid content. Different doses of fumaric acid and SO2 were tested. The ability of these compounds to inhibit bacterial development and stop the malic acid degradation was testedonaredwineofthevarietyVitisviniferaL.cv.Tempranillowhosemalicacidcontentwassetat1.5g/L. The control wine inoculated with 6 log CFU/mL of Oenococcus oeni finished the malolactic fermentation in 12 days. However, the use of doses equal to or greater than 300mg/L of fumaric acid delayed the onset of malolactic fermentation for more than 50 days with little degradation of malic acid. In addition, fumaric acid proved to be effective in stopping malolactic fermentation already started where the bacterial count was 7 log CFU/mL. Fumaric acid can be considered as a potent inhibitor of malolactic fermentation

An asymmetric BODIPY triad with panchromatic absorption for high-performance red-edge laser emission

© The Royal Society of Chemistry 2015. A rational design of an unprecedented asymmetric cassette triad based entirely on BODIPY chromophores allows efficient light harvesting over the UV-vis spectral region, leading to a bright and stable red-edge laser emission via efficient energy-transfer processes.Peer Reviewe

Uniqueness and Nondegeneracy of Ground States for (−Δ)sQ+Q−Qα+1=0(-\Delta)^s Q + Q - Q^{\alpha+1} = 0 in R\mathbb{R}

We prove uniqueness of ground state solutions $Q = Q(|x|) \geq 0$ for the nonlinear equation $(-\Delta)^s Q + Q - Q^{\alpha+1}= 0$ in $\mathbb{R}$, where $0 < s < 1$ and $0 < \alpha < \frac{4s}{1-2s}$ for $s < 1/2$ and $0 < \alpha < \infty$ for $s \geq 1/2$. Here $(-\Delta)^s$ denotes the fractional Laplacian in one dimension. In particular, we generalize (by completely different techniques) the specific uniqueness result obtained by Amick and Toland for $s=1/2$ and $\alpha=1$ in [Acta Math., \textbf{167} (1991), 107--126]. As a technical key result in this paper, we show that the associated linearized operator $L_+ = (-\Delta)^s + 1 - (\alpha+1) Q^\alpha$ is nondegenerate; i.\,e., its kernel satisfies $\mathrm{ker}\, L_+ = \mathrm{span}\, \{Q'\}$. This result about $L_+$ proves a spectral assumption, which plays a central role for the stability of solitary waves and blowup analysis for nonlinear dispersive PDEs with fractional Laplacians, such as the generalized Benjamin-Ono (BO) and Benjamin-Bona-Mahony (BBM) water wave equations.Comment: 45 page

Separation of Oligosaccharides from Lotus Seeds via Medium-pressure Liquid Chromatography Coupled with ELSD and DAD

peer-reviewedLotus seeds were identified by the Ministry of Public Health of China as both food and medicine. One general function of lotus seeds is to improve intestinal health. However, to date, studies evaluating the relationship between bioactive compounds in lotus seeds and the physiological activity of the intestine are limited. In the present study, by using medium pressure liquid chromatography coupled with evaporative light-scattering detector and diode-array detector, five oligosaccharides were isolated and their structures were further characterized by electrospray ionization-mass spectrometry and gas chromatography-mass spectrometry. In vitro testing determined that LOS3-1 and LOS4 elicited relatively good proliferative effects on Lactobacillus delbrueckii subsp. bulgaricus. These results indicated a structure-function relationship between the physiological activity of oligosaccharides in lotus seeds and the number of probiotics applied, thus providing room for improvement of this particular feature. Intestinal probiotics may potentially become a new effective drug target for the regulation of immunity

Comparison of exit time moment spectra for extrinsic metric balls

We prove explicit upper and lower bounds for the L1-moment spectra for the Brownian motion exit time from extrinsic metric balls of submanifolds Pm in ambient Riemannian spaces Nn. We assume that P and N both have controlled radial curvatures (mean curvature and sectional curvature, respectively) as viewed from a pole in N. The bounds for the exit moment spectra are given in terms of the corresponding spectra for geodesic metric balls in suitably warped product model spaces. The bounds are sharp in the sense that equalities are obtained in characteristic cases. As a corollary we also obtain new intrinsic comparison results for the exit time spectra for metric balls in the ambient manifolds Nn themselves

Fortalecimiento de la estructura de Llamas Honey como empresa familiar

El presente documento expone de manera detallada y estructurada el proyecto que se desarrolló en conjunto con pequeños productores de la localidad del Salvador, municipio de Tequila y la Fundación Beckmann. El desarrollo del plan de trabajo sucede de manera particular con Llamas Honey, una empresa ubicada en El Salvador, Tequila, donde una familia dedicada a la apicultura, busca fortalecer y crecer su negocio, a través de la consolidación de una estructura administrativa que garantice la profesionalización de sus procesos, la definición del empaque y embalaje de sus productos y que a su vez, permita la optimización en los tiempos de producción, trayendo como consecuencia la colocación de la marca en puntos de venta en Tequila y dentro de la Zona Metropolitana de Guadalajara (ZMG) así como la posibilidad de expansión mediante nuevas redes de envíos a toda la República Mexicana. Después de analizar la situación actual de la empresa familiar, se definió un objetivo general que se fundamenta en las necesidades reales percibidas a través de los actores y que da seguimiento al trabajo previo realizado en semestres anteriores.ITESO, A.C

Prevention of diet-induced obesity by apple polyphenols in Wistar rats through regulation of adipocyte gene expression and DNA methylation patterns

This study was conducted to determine the mechanisms implicated in the beneficial effects of apple polyphenols (APs) against diet-induced obesity in Wistar rats, described in a previous study from our group. Supplementation of high-fat sucrose diet with AP prevented adiposity increase by inhibition of adipocyte hypertrophy. Rats supplemented with AP exhibited improved glucose tolerance while adipocytes isolated from these rats showed an enhanced lipolytic response to isoproterenol. AP intake led to reduced Lep, Plin, and sterol regulatory element binding transcription factor 1 (Srebf1) mRNA levels and increased aquaporin 7 (Aqp7), adipocyte enhancer binding protein 1 (Aebp1), and peroxisome proliferator-activated receptor gamma co-activator 1 alpha (Ppargc1a) mRNA levels in epididymal adipocytes. In addition, we found different methylation patterns of Aqp7, Lep, Ppargc1a, and Srebf1 promoters in adipocytes from apple-supplemented rats compared to high-fat sucrose fed rats. The administration of AP protects against body weight gain and fat deposition and improves glucose tolerance in rats. We propose that AP exerts the antiobesity effects through the regulation of genes involved in adipogenesis, lipolysis, and fatty acid oxidation, in a process that could be mediated in part by epigenetic mechanisms

Evaluación fisicoquímica y capacidad antioxidante de chiltepín silvestre de Nuevo León, México.

La demanda del chile piquín por sus amplios atributos, además de su importancia socioeconómica como recurso natural en las áreas rurales y su potencial como nueva opción productiva en el noreste de México, ha motivado la realización de varios estudios. Por lo anterior en este trabajo se realizó una evaluación fisicoquímica y actividad antioxidante de chiltepín silvestre de Nuevo León, México. Se tuvieron seis tratamientos, con base en los tres sitios de colecta y dos índices de madurez. Se determinaron las siguientes variables de estudio; peso, largo ancho, pH, °Brix, acidez titulable, color y actividad antioxidante por DPPH. El diseño experimental utilizado fue completamente al azar y la prueba de comparaciones de medias de Tukey (p≤ 0.05). El mayor peso y tamaño se observó en los frutos de chiltepín verdes, mientras que los valores más altos de luminosidad e intensidad se observaron en los frutos de chiltepín rojos. En relación al contenido de sólidos solubles totales y acidez titulable los frutos de chiltepín rojo presentaron el mayor contenido en relación a los frutos de chiltepín verdes. Sin embargo la mayor actividad antioxidante se encontró en los frutos de chiltepín verdes