Closed G2 forms and special metrics

170 p.

Best Proximity Points of Generalized Semicyclic Impulsive Self-Mappings: Applications to Impulsive Differential and Difference Equations

This paper is devoted to the study of convergence properties of distances between points and the existence and uniqueness of best proximity and fixed points of the so-called semicyclic impulsive self-mappings on the union of a number of nonempty subsets in metric spaces. The convergences of distances between consecutive iterated points are studied in metric spaces, while those associated with convergence to best proximity points are set in uniformly convex Banach spaces which are simultaneously complete metric spaces. The concept of semicyclic self-mappings generalizes the well-known one of cyclic ones in the sense that the iterated sequences built through such mappings are allowed to have images located in the same subset as their pre-image. The self-mappings under study might be in the most general case impulsive in the sense that they are composite mappings consisting of two self-mappings, and one of them is eventually discontinuous. Thus, the developed formalism can be applied to the study of stability of a class of impulsive differential equations and that of their discrete counterparts. Some application examples to impulsive differential equations are also given.

Advances in Nonlinear Complexity Analysis for Partial Differential Equations

1 p. -- [Editorial Material]

From social to political. New forms of mobilization and democratization. Conference proceedings

In the recent evolution of contemporary social movements three phases can be identified. The first phase is marked by the labour movement and the systemic importance attributed to the labour conflict in industrial societies. This conflict has been interpreted as a consequence of the shortcoming of social integration mechanisms by Emile Durkheim, as a rational conflict by entrepreneurs’ and workers’ interests by Max Wener, and as a central class struggle for the transformation of society by Karl Marx. The second phase in this development was led by the new social movements of the post-industrial society of the 1960s and 1970s’ students, women and environmentalist movements. Two new analytical perspectives have explained these movements’ meaning and actions. Resource mobilization theory (McAdam and Tilly) has focuses on rational attitudes and conflicts. Actionalist sociology, in turn, has identified the new protagonists of social conflicts that replaced the labour movement in postindustrial societies. The third phase emerges in a world characterized by the ascendance of markets, the increasingly prominent role of financial capital flows, the closure of communities, and fundamentalism. In this context, human rights and pro-democratization movements constitute alternatives to global domination and the systemic conditioning of individual and groups.

Centro de Acogida Inmediata –CAI- para víctimas de violencia de género: marco teórico

El presente documento hace parte del Proyecto Técnico “Centro de Acogida Inmediata –CAI- para víctimas de violencia de género”, elaborado para la Asociación BETA, Asociación para el Desarrollo de Proyectos de Intervención Social, presentado a la convocatoria del Departamento de Asuntos Sociales y de las Personas Mayores (Nº Expediente 2014//CONASP0148; CÓDIGO CPV: 85311000 Servicios de Asistencia Social con alojamiento).

Genotypes, Recombinant Forms, and Variants of Norovirus GII.4 in Gipuzkoa (Basque Country, Spain), 2009-2012

Background: Noroviruses (NoVs) are genetically diverse, with genogroup II-and within it-genotype 4 (GII.4) being the most prevalent cause of acute gastroenteritis worldwide. The aim of this study was to characterize genogroup II NoV causing acute gastroenteritis in the Basque Country (northern Spain) from 2009-2012. Methods: The presence of NoV RNA was investigated by reverse transcriptase-polymerase chain reaction (RT-PCR) in stool specimens from children younger than 15 years old with community-acquired acute gastroenteritis, and from hospitalized adults or elderly residents of nursing homes with acute gastroenteritis. For genotyping, the open reading frames ORF1 (encoding the polymerase) and ORF2 (encoding the major capsid protein) were partially amplified and sequenced. Recombinant strains were confirmed by PCR of the ORF1/ORF2 junction region. Results: NoV was detected in 16.0% (453/2826) of acute gastroenteritis episodes in children younger than 2 years, 9.9% (139/1407) in children from 2 to 14 years, and 35.8% (122/341) in adults. Of 317 NoVs characterized, 313 were genogroup II and four were genogroup I. The GII.4 variants Den Haag-2006b and New Orleans-2009 predominated in 2009 and 2010-2011, respectively. In 2012, the New Orleans-2009 variant was partially replaced by the Sydney-2012 variant (GII.Pe/GII.4) and New Orleans-2009/Sydney-2012 recombinant strains. The predominant capsid genotype in all age groups was GII.4, which was the only genotype detected in outbreaks. The second most frequent genotype was GII.3 (including the recently described recombination GII.P16/GII.3), which was detected almost exclusively in children. Conclusion: Nine different genotypes of NoV genogroup II were detected; among these, intergenotype recombinant strains represented an important part, highlighting the role of recombination in the evolution of NoVs. Detection of new NoV strains, not only GII.4 strains, shortly after their first detection in other parts of the world shows that many NoV strains can spread rapidly.

Hyers-Ulam-Rassias Stability of Functional Differential Systems with Point and Distributed Delays

This paper investigates stability and asymptotic properties of the error with respect to its nominal version of a nonlinear time-varying perturbed functional differential system subject to point, finite-distributed, and Volterra-type distributed delays associated with linear dynamics together with a class of nonlinear delayed dynamics. The boundedness of the error and its asymptotic convergence to zero are investigated with the results being obtained based on the Hyers-Ulam-Rassias analysis.

Differential Neuroprotective Effects of 5 '-Deoxy-5 '-Methylthioadenosine

Background: 5'-deoxy-5'-methylthioadenosine (MTA) is an endogenous compound produced through the metabolism of polyamines. The therapeutic potential of MTA has been assayed mainly in liver diseases and, more recently, in animal models of multiple sclerosis. The aim of this study was to determine the neuroprotective effect of this molecule in vitro and to assess whether MTA can cross the blood brain barrier (BBB) in order to also analyze its potential neuroprotective efficacy in vivo. Methods: Neuroprotection was assessed in vitro using models of excitotoxicity in primary neurons, mixed astrocyte-neuron and primary oligodendrocyte cultures. The capacity of MTA to cross the BBB was measured in an artificial membrane assay and using an in vitro cell model. Finally, in vivo tests were performed in models of hypoxic brain damage, Parkinson's disease and epilepsy. Results: MTA displays a wide array of neuroprotective activities against different insults in vitro. While the data from the two complementary approaches adopted indicate that MTA is likely to cross the BBB, the in vivo data showed that MTA may provide therapeutic benefits in specific circumstances. Whereas MTA reduced the neuronal cell death in pilocarpine-induced status epilepticus and the size of the lesion in global but not focal ischemic brain damage, it was ineffective in preserving dopaminergic neurons of the substantia nigra in the 1-methyl-4-phenyl-1,2,3,6-tetrahydro-pyridine (MPTP)-mice model. However, in this model of Parkinson's disease the combined administration of MTA and an A(2A) adenosine receptor antagonist did produce significant neuroprotection in this brain region. Conclusion: MTA may potentially offer therapeutic neuroprotection.

Differential activity of GSK-3 isoforms regulates NF-kappa B and TRAIL- or TNF alpha induced apoptosis in pancreatic cancer cells

While TRAIL is a promising anticancer agent due to its ability to selectively induce apoptosis in neoplastic cells, many tumors, including pancreatic ductal adenocarcinoma (PDA), display intrinsic resistance, highlighting the need for TRAIL-sensitizing agents. Here we report that TRAIL-induced apoptosis in PDA cell lines is enhanced by pharmacological inhibition of glycogen synthase kinase-3 (GSK-3) or by shRNA-mediated depletion of either GSK-3 alpha or GSK-3 beta. In contrast, depletion of GSK-3 beta, but not GSK-3 alpha, sensitized PDA cell lines to TNF alpha-induced cell death. Further experiments demonstrated that TNF alpha-stimulated I kappa B alpha phosphorylation and degradation as well as p65 nuclear translocation were normal in GSK-3 beta-deficient MEFs. Nonetheless, inhibition of GSK-3 beta function in MEFs or PDA cell lines impaired the expression of the NF-kappa B target genes Bcl-xL and cIAP2, but not I kappa B alpha. Significantly, the expression of Bcl-xL and cIAP2 could be reestablished by expression of GSK-3 beta targeted to the nucleus but not GSK-3 beta targeted to the cytoplasm, suggesting that GSK-3 beta regulates NF-kappa B function within the nucleus. Consistent with this notion, chromatin immunoprecipitation demonstrated that GSK-3 inhibition resulted in either decreased p65 binding to the promoter of BIR3, which encodes cIAP2, or increased p50 binding as well as recruitment of SIRT1 and HDAC3 to the promoter of BCL2L1, which encodes Bcl-xL. Importantly, depletion of Bcl-xL but not cIAP2, mimicked the sensitizing effect of GSK-3 inhibition on TRAIL-induced apoptosis, whereas Bcl-xL overexpression ameliorated the sensitization by GSK-3 inhibition. These results not only suggest that GSK-3 beta overexpression and nuclear localization contribute to TNF alpha and TRAIL resistance via anti-apoptotic NF-kappa B genes such as Bcl-xL, but also provide a rationale for further exploration of GSK-3 inhibitors combined with TRAIL for the treatment of PDA.

Approximate Solutions by Truncated Taylor Series Expansions of Nonlinear Differential Equations and Related Shadowing Property with Applications

This paper investigates the errors of the solutions as well as the shadowing property of a class of nonlinear differential equations which possess unique solutions on a certain interval for any admissible initial condition. The class of differential equations is assumed to be approximated by well-posed truncated Taylor series expansions up to a certain order obtained about certain, in general nonperiodic, sampling points t(i) is an element of [t(0), t(J)] for i = 0, 1, . . . , J of the solution. Two examples are provided.

Distribution theory and fundamental solutions of differential operators

The objective of this dissertation is to study the theory of distributions and some of its applications. Certain concepts which we would include in the theory of distributions nowadays have been widely used in several fields of mathematics and physics. It was Dirac who first introduced the delta function as we know it, in an attempt to keep a convenient notation in his works in quantum mechanics. Their work contributed to open a new path in mathematics, as new objects, similar to functions but not of their same nature, were being used systematically. Distributions are believed to have been first formally introduced by the Soviet mathematician Sergei Sobolev and by Laurent Schwartz. The aim of this project is to show how distribution theory can be used to obtain what we call fundamental solutions of partial differential equations.