Mechanical systems subjected to generalized nonholonomic constraints

We study mechanical systems subject to constraint functions that can be dependent at some points and independent at the rest. Such systems are modelled by means of generalized codistributions. We discuss how the constraint force can transmit an impulse to the motion at the points of dependence and derive an explicit formula to obtain the ``post-impact'' momentum in terms of the ``pre-impact'' momentum.Comment: 24 pages, no figure

Integrable Rosochatius deformations of higher-order constrained flows and the soliton hierarchy with self-consistent sources

We propose a systematic method to generalize the integrable Rosochatius deformations for finite dimensional integrable Hamiltonian systems to integrable Rosochatius deformations for infinite dimensional integrable equations. Infinite number of the integrable Rosochatius deformed higher-order constrained flows of some soliton hierarchies, which includes the generalized integrable H$\acute{e}$non-Heiles system, and the integrable Rosochatius deformations of the KdV hierarchy with self-consistent sources, of the AKNS hierarchy with self-consistent sources and of the mKdV hierarchy with self-consistent sources as well as their Lax representations are presented.Comment: 18 pages. to appear in J. Phys. A: Math. Ge

A Simple and Efficient Method for the Partial Synthesis of Pure (3<i>R</i>,3’<i>S</i>)-Astaxanthin from (3<i>R</i>,3’<i>R</i>,6’<i>R</i>)-Lutein and Lutein Esters via (3<i>R</i>,3’<i>S</i>)-Zeaxanthin and Theoretical Study of Their Formation Mechanisms

Carotenoids are natural compounds that have important roles in promoting and maintaining human health. Synthetic astaxanthin is a highly requested product by the aquaculture industry, but natural astaxanthin is not. Various strategies have been developed to synthesize this carotenoid. Nonetheless, these approaches have not only provided limited global yields, but its main commercial source also carries several health risks for humans. In this contribution, the one-pot base-catalyzed reaction of (3R,3&#8217;R,6&#8217;R)-lutein (1) esters has resulted in a successful isomerization process to easily obtain up to 95% meso-zeaxanthin (2), which in turn is oxidized to (3R,3&#8217;S)-astaxanthin (3) with a global yield of 68%. The same oxidation performed with UV irradiation (365 nm) for 5 min provided the highest global yield (76%). These chemical transformations have also been achieved with a significant reduction of the health risks associated with its potential human consumption. Furthermore, this is the first time only one of the configurational isomers has been obtained semisynthetically. The poorly understood formation mechanisms of these two compounds were also investigated using Density-Functional Theory (DFT) calculations. These theoretical studies revealed that the isomerization involves a base-catalyzed deprotonation at C-6&#8217;, followed by C-4&#8217; protonation, while the oxidation occurs via free radical mechanisms

Sensibilizar la mirada hacia el adulto mayor

El objetivo del Proyecto de Aplicación Profesional CÓDIGO es lograr la construcción de una imagen más justa e incluyente de los adultos mayores a través del análisis e interpretación de la imagen del adulto mayor, de actividades de inmersión teórica e investigación etnográfica y de la producción de imágenes que los represente más justa y dignamente. El proceso de inmersión teórica se hizo basado en autores como Guber, Corona, Enríquez, Flick, y Carrillo y Cuarenta, mientras que para realizar el acercamiento a un escenario asilado, se contó con el apoyo del Instituto Jalisciense del Adulto Mayor (IJAM) y se visitaban escenarios alternos en los que se detectó la presencia de adultos mayores con la intención de contar con un panorama más amplio sobre los tipos de vejez