On LpL^p--LqL^q trace inequalities

We give necessary and sufficient conditions in order that inequalities of the type $$\| T_K f\|_{L^q(d\mu)}\leq C \|f\|_{L^p(d\sigma)}, \qquad f \in L^p(d\sigma),$$ hold for a class of integral operators $T_K f(x) = \int_{R^n} K(x, y) f(y) d \sigma(y)$ with nonnegative kernels, and measures $d \mu$ and $d\sigma$ on $\R^n$, in the case where $p>q>0$ and $p>1$. An important model is provided by the dyadic integral operator with kernel $K_{\mathcal D}(x, y) \sum_{Q\in{\mathcal D}} K(Q) \chi_Q(x) \chi_Q(y)$, where $\mathcal D=\{Q\}$ is the family of all dyadic cubes in $\R^n$, and $K(Q)$ are arbitrary nonnegative constants associated with $Q \in{\mathcal D}$. The corresponding continuous versions are deduced from their dyadic counterparts. In particular, we show that, for the convolution operator $T_k f = k\star f$ with positive radially decreasing kernel $k(|x-y|)$, the trace inequality $$\| T_k f\|_{L^q(d\mu)}\leq C \|f\|_{L^p(d x)}, \qquad f \in L^p(dx),$$ holds if and only if ${\mathcal W}_{k}[\mu] \in L^s (d\mu)$, where $s = {\frac{q(p-1)}{p-q}}$. Here ${\mathcal W}_{k}[\mu]$ is a nonlinear Wolff potential defined by ${\mathcal W}_{k}[\mu](x)=\int_0^{+\infty} k(r) \bar{k}(r)^{\frac 1 {p-1}} \mu (B(x,r))^{\frac 1{p-1}} r^{n-1} dr,$ and $\bar{k}(r)=\frac1{r^n}\int_0^r k(t) t^{n-1} dt$. Analogous inequalities for $1\le q < p$ were characterized earlier by the authors using a different method which is not applicable when $q<1$

Multistationary and Oscillatory Modes of Free Radicals Generation by the Mitochondrial Respiratory Chain Revealed by a Bifurcation Analysis

The mitochondrial electron transport chain transforms energy satisfying cellular demand and generates reactive oxygen species (ROS) that act as metabolic signals or destructive factors. Therefore, knowledge of the possible modes and bifurcations of electron transport that affect ROS signaling provides insight into the interrelationship of mitochondrial respiration with cellular metabolism. Here, a bifurcation analysis of a sequence of the electron transport chain models of increasing complexity was used to analyze the contribution of individual components to the modes of respiratory chain behavior. Our algorithm constructed models as large systems of ordinary differential equations describing the time evolution of the distribution of redox states of the respiratory complexes. The most complete model of the respiratory chain and linked metabolic reactions predicted that condensed mitochondria produce more ROS at low succinate concentration and less ROS at high succinate levels than swelled mitochondria. This prediction was validated by measuring ROS production under various swelling conditions. A numerical bifurcation analysis revealed qualitatively different types of multistationary behavior and sustained oscillations in the parameter space near a region that was previously found to describe the behavior of isolated mitochondria. The oscillations in transmembrane potential and ROS generation, observed in living cells were reproduced in the model that includes interaction of respiratory complexes with the reactions of TCA cycle. Whereas multistationarity is an internal characteristic of the respiratory chain, the functional link of respiration with central metabolism creates oscillations, which can be understood as a means of auto-regulation of cell metabolism. © 2012 Selivanov et al

Repensar la educación y la pedagogía: algunas reflexiones críticas

Certainly it becomes necessary to reflect on the school not only as a place of permanent cultural construction, influenced by multiple relationships, but also on how it becomes the place where these connections band together and set up new ones. In every analysis on education and pedagogies, it must not be left behind the fact that curricular designs explicit and condition the school practices. Likewise, these outlines also determine the intentionality of the teaching practices. These ideas constitute the basis guiding the reflections of this investigation, which more than appearing as theoretical issues, are actually visualized like practical possibilities. The arguments that are expressed here gather the most significant concerns conveyed by the authors. They account for the approximate outcome of the reading and the reflection on the personal teaching practice gained within the university classrooms and the experience of working with high school students.Recibido 1 de noviembre, 2007 • Aprobado 20 de marzo, 2008 &nbsp; Reflexionar sobre la escuela como un lugar de construcción cultural permanente, influida por múltiples relaciones; pero, a la vez, como el lugar donde éstas se mediatizan y se construyen otras nuevas, se torna necesario. Valorar que los diseños curriculares explicitan y condicionan las prácticas escolares, y determinan, en buena medida, la intencionalidad de las prácticas pedagógicas es una cuestión que no se debe dejar de lado, en cualquier análisis sobre la educación y la pedagogía. Estas ideas constituyen los ejes sobre los cuales se articulan las reflexiones de este escrito, las cuales, lejos de plantearse, sólo como cuestiones, puramente, teóricas, se visualizan como posibilidades prácticas. Los argumentos que aquí se expresan recogen las preocupaciones, más importantes, de los autores, y constituyen el resultado aproximado de la lectura y la reflexión sobre la práctica pedagógica personal, desde las aulas universitarias y la experiencia de trabajar con jóvenes de secundaria

Local and global behaviour of nonlinear equations with natural growth terms

This paper concerns a study of the pointwise behaviour of positive solutions to certain quasi-linear elliptic equations with natural growth terms, under minimal regularity assumptions on the underlying coefficients. Our primary results consist of optimal pointwise estimates for positive solutions of such equations in terms of two local Wolff's potentials.Comment: In memory of Professor Nigel Kalto

Desarrollo de un producto con base en fibra de zanahoria deshidratada para comedores escolares

Introducción: La fibra dietética procedente de la zanahoria, es una fuente de betacaroteno, precursor de vitamina A. Nutrientes indispensables en la alimentación, pues participan en variadas y diferentes funciones como antioxidantes, inmunidad, visión nocturna y en los niños (as) es fundamental, para su crecimiento y desarrollo. Metodología: Se desarrollaron tres formulaciones de repostería (quequitos), con fibra de zanahoria como uno de sus ingredientes, los sabores fueron: Nº1 naranja, Nº2: banano con almendra y Nº3: chocolate. Para determinar la aceptabilidad y palatabilidad, se realizó un “Focus Group” con niños escolares de edades entre 7 y 9 años. Resultados: Se encontró que la fibra de zanahoria aportó a las tres formulaciones, volumen, peso, y cantidades importantes de fibra 2,3 a 2,6 gramos y de ß carotenos 660 mcg, para un aproximado de 137 mcg de vitamina A o Equivalentes de Retinol, por porción de 40 gramos. La formulación de naranja, fue la más beneficiada en sabor, color y aroma; en la de chocolate, la fibra influyó negativamente en el sabor, mientras que en la de banano con almendra, afectó el color y proporcionó una textura húmeda que comprometió la vida útil del producto. Un 53% de los niños participantes eligió la formulación de naranja como favorito por su sabor. La investigación demostró que este producto es una alternativa novedosa de un alimento funcional, que permite mejorar la variedad y enriquecer la dieta de los niños (as) en el servicio de comidas servidas de los comedores escolares del país. También, se puede aprovechar a este sub producto de proceso “fibra de zanahoria” para desarrollar alimentos gustosos para el consumidor y beneficiosos en cuanto a su calidad nutricional. Se recomienda determinar la vida útil del producto y el diseño de un empaque que permita un adecuado manejo para la distribución y conservación del producto final. Objetivo general: Desarrollar un producto a base de fibra de zanahoria deshidratada, agradable al paladar, que permita variar y complementar la calidad nutricional de la dieta servida a los niños (as) que asisten a los comedores escolares

Information theory in the study of anisotropic radiation

Information theory is used to perform a thermodynamic study of non equilibrium anisotropic radiation. We limit our analysis to a second-order truncation of the moments, obtaining a distribution function which leads to a natural closure of the hierarchy of radiative transfer equations in the so-called variable Eddington factor scheme. Some Eddington factors appearing in the literature can be recovered as particular cases of our two-parameter Eddington factor. We focus our attention in the study of the thermodynamic properties of such systems and relate it to recent nonequilibrium thermodynamic theories. Finally we comment the possibility of introducing a nonequilibrium chemical potential for photons.Comment: 1 eps figure upon request by e-mail, to appear in Journal of Physics

Differentially Expressed Proteins in Primary Endothelial Cells Derived From Patients With Acute Myocardial Infarction

Endothelial dysfunction is one of the primary factors in the onset and progression of atherothrombosis resulting in acute myocardial infarction (AMI). However, the pathological and cellular mechanisms of endothelial dysfunction in AMI have not been systematically studied. Protein expression profiling in combination with a protein network analysis was used by the mass spectrometry-based label-free quantification approach. This identified and quantified 2246 proteins, of which 335 were differentially regulated in coronary arterial endothelial cells from patients with AMI compared with controls. The differentially regulated protein profiles reveal the alteration of (1) metabolism of RNA, (2) platelet activation, signaling, and aggregation, (3) neutrophil degranulation, (4) metabolism of amino acids and derivatives, (5) cellular responses to stress, and (6) response to elevated platelet cytosolic Ca2+ pathways. Increased production of oxidants and decreased production of antioxidant biomarkers as well as downregulation of proteins with antioxidant properties suggests a role for oxidative stress in mediating endothelial dysfunction during AMI. In conclusion, this is the first quantitative proteomics study to evaluate the cellular mechanisms of endothelial dysfunction in patients with AMI. A better understanding of the endothelial proteome and pathophysiology of AMI may lead to the identification of new drug targets

Optimization of Xanthatin Extraction from Xanthium spinosum L. and its cytotoxic, anti-angiogenesis and antiviral properties

The aqueous extraction of the sesquiterpene lactone xanthatin from Xanthium spinosum L. favours the conversion of xanthinium to xanthatin via the loss of acetic acid. The cytotoxic (Hep-G2 and L1210 human cell lines) and antiviral activities of isolated xanthatin are established. This natural compound shows significant cytotoxicity against the Hep-G2 cell line and our experimental results reveal its strong anti-angiogenesis capacity in vitro. The structure of xanthatin is determined by spectroscopic methods and for the first time confirmed by X-ray diffraction