Health benefits of pistachios consumption

The health benefits of nuts, mainly in relation to the improvement of dysmetabolic conditions such as obesity, type 2 diabetes mellitus and the related cardiovascular diseases, have been widely demonstrated. Compared to other nuts, pistachios have a lower fat and caloric content, and contain the highest levels of unsaturated fatty acids, potassium, γ-tocopherol, phytosterols and xanthophyll carotenoids, all substances that are well known for their antioxidant and anti-inflammatory actions. This variety of nutrients contributes to the growing body of evidence that the consumption of pistachios improves health, leading to a greater potential of healthy antioxidant and anti-inflammatory activity, glycemic control, and endothelial function. The present review examines the nutrients and phytochemicals present in pistachios as well as the potential health benefits of including pistachios in a diet.     

Partial characterizations of clique-perfect and coordinated graphs: Superclasses of triangle-free graphs

A graph G is clique-perfect if the cardinality of a maximum clique-independent set of H equals the cardinality of a minimum clique-transversal of H, for every induced subgraph H of G. A graph G is coordinated if the minimum number of colors that can be assigned to the cliques of H in such a way that no two cliques with non-empty intersection receive the same color equals the maximum number of cliques of H with a common vertex, for every induced subgraph H of G. Coordinated graphs are a subclass of perfect graphs. The complete lists of minimal forbidden induced subgraphs for the classes of clique-perfect and coordinated graphs are not known, but some partial characterizations have been obtained. In this paper, we characterize clique-perfect and coordinated graphs by minimal forbidden induced subgraphs when the graph is either paw-free or {gem, W₄, bull}-free, both superclasses of triangle-free graphs.     

Computer-assisted proofs of special function identities related to Poisson integrals

As a by-product of his work, E. Symeonidis obtained in (Comment. Math. Univ. Carol. 44(3):437–460, 2003) indirect proofs of two interesting special function identities involving Gegenbauer polynomials. In (Muldoon, 2004 ) the question of direct proofs was posed. We answer this question by presenting proofs obtained with the help of computer algebra algorithms based on WZ theory.     

Partial characterizations of coordinated graphs: line graphs and complements of forests

A graph G is coordinated if the minimum number of colors that can be assigned to the cliques of H in such a way that no two cliques with non-empty intersection receive the same color is equal to the maximum number of cliques of H with a common vertex, for every induced subgraph H of G. Coordinated graphs are a subclass of perfect graphs. The list of minimal forbidden induced subgraphs for the class of coordinated graphs is not known. In this paper, we present a partial result in this direction, that is, we characterize coordinated graphs by minimal forbidden induced subgraphs when the graph is either a line graph, or the complement of a forest. F. Bonomo, F. Soulignac, and G. Sueiro’s research partially supported by UBACyT Grant X184 (Argentina), and CNPq under PROSUL project Proc. 490333/2004-4 (Brazil). The research of G. Durán is partially supported by FONDECyT Grant 1080286 and Millennium Science Institute “Complex Engineering Systems” (Chile), and CNPq under PROSUL project Proc. 490333/2004-4 (Brazil).     

Strong solutions to a parabolic equation with linear growth with respect to the gradient variable

In this paper we prove existence and uniqueness of strong solutions to the homogeneous Neumann problem associated to a parabolic equation with linear growth with respect to the gradient variable. This equation is a generalization of the time-dependent minimal surface equation. Existence and regularity in time of the solution is proved by means of a suitable pseudoparabolic relaxed approximation of the equation and a passage to the limit.     

Weighted Composition Operators from H ∞ to the Bloch Space of a Bounded Homogeneous Domain

Let D be a bounded homogeneous domain in ℂ ⁿ . In this paper, we study the bounded and the compact weighted composition operators mapping the Hardy space H ^∞(D) into the Bloch space of D. We characterize the bounded weighted composition operators, provide operator norm estimates, and give sufficient conditions for compactness. We prove that these conditions are necessary in the case of the unit ball and the polydisk. We then show that if D is a bounded symmetric domain, the bounded multiplication operators from H ^∞(D) to the Bloch space of D are the operators whose symbol is bounded.     

EFFECT OF THYMINE DIMER INTRODUCTION IN A 21 BASE PAIR OLIGONUCLEOTIDE

Abstract— It is well known that the pyrimidine dimers are the main damage produced by UV radiation on the DNA structure. However, while studies on the photoproduct structure have been carried out extensively, uncertainties still exist on the implication that a single damaging event has on the overall conformation. In particular, the extension of the damage influence on the polynucleotide chain is a matter of debate. This problem is especially important to understanding some steps of the repair mechanisms. In this study we performed a chemical-physical characterization of 21 base pair oligonucleotides containing a single thymine dimer in one strand. Thermodynamic parameters were determined by means of thermal denaturation experiments, and static fluorescence measurements were performed to unequivocally define the primary structure-conformation relationship in this specific case. We used hydroxyl radicals, produced by means of γ-irradiation of the sample solution, to detect fine structure changes. Our data show that the introduction of a single thymine dimer might cause only a slight distortion of the helix geometry, as judged by the evaluation of the enthalpic and the entropic terms and by the small changes observed in the binding of ethidium bromide to DNA. The modifications in the sugar phosphate backbone subsequent to the damaging event are especially evident, near the thymine dimer, toward the 5'-end direction in the strand containing the dimer.     

Partial characterizations of clique-perfect graphs I: Subclasses of claw-free graphs

A clique-transversal of a graph G is a subset of vertices that meets all the cliques of G. A clique-independent set is a collection of pairwise vertex-disjoint cliques. The clique-transversal number and clique-independence number of G are the sizes of a minimum clique-transversal and a maximum clique-independent set of G, respectively. A graph G is clique-perfect if these two numbers are equal for every induced subgraph of G. The list of minimal forbidden induced subgraphs for the class of clique-perfect graphs is not known. In this paper, we present a partial result in this direction; that is, we characterize clique-perfect graphs by a restricted list of forbidden induced subgraphs when the graph belongs to two different subclasses of claw-free graphs.