Fixed and Best Proximity Points of Cyclic Jointly Accretive and Contractive Self-Mappings

p(>= 2)-cyclic and contractive self-mappings on a set of subsets of a metric space which are simultaneously accretive on the whole metric space are investigated. The joint fulfilment of the p-cyclic contractiveness and accretive properties is formulated as well as potential relationships with cyclic self-mappings in order to be Kannan self-mappings. The existence and uniqueness of best proximity points and fixed points is also investigated as well as some related properties of composed self-mappings from the union of any two adjacent subsets, belonging to the initial set of subsets, to themselves.

On Best Proximity Point Theorems and Fixed Point Theorems for p-Cyclic Hybrid Self-Mappings in Banach Spaces

This paper relies on the study of fixed points and best proximity points of a class of so-called generalized point-dependent (K-Lambda)hybrid p-cyclic self-mappings relative to a Bregman distance Df, associated with a Gâteaux differentiable proper strictly convex function f in a smooth Banach space, where the real functions Lambda and K quantify the point-to-point hybrid and nonexpansive (or contractive) characteristics of the Bregman distance for points associated with the iterations through the cyclic self-mapping.Weak convergence results to weak cluster points are obtained for certain average sequences constructed with the iterates of the cyclic hybrid self-mappings.

Intracellular Ca2+ release through ryanodine receptors contributes to AMPA receptor-mediated mitochondrial dysfunction and ER stress in oligodendrocytes

Overactivation of ionotropic glutamate receptors in oligodendrocytes induces cytosolic Ca2+ overload and excitotoxic death, a process that contributes to demyelination and multiple sclerosis. Excitotoxic insults cause well-characterized mitochondrial alterations and endoplasmic reticulum (ER) dysfunction, which is not fully understood. In this study, we analyzed the contribution of ER-Ca2+ release through ryanodine receptors (RyRs) and inositol triphosphate receptors (IP(3)Rs) to excitotoxicity in oligodendrocytes in vitro. First, we observed that oligodendrocytes express all previously characterized RyRs and IP(3)Rs. Blockade of Ca2+-induced Ca2+ release by TMB-8 following alpha-amino-3-hydroxyl-5-methyl-4-isoxazole-propionate (AMPA) receptor-mediated insults attenuated both oligodendrocyte death and cytosolic Ca2+ overload. In turn, RyR inhibition by ryanodine reduced as well the Ca2+ overload whereas IP3R inhibition was ineffective. Furthermore, AMPA-triggered mitochondrial membrane depolarization, oxidative stress and activation of caspase-3, which in all instances was diminished by RyR inhibition. In addition, we observed that AMPA induced an ER stress response as revealed by alpha subunit of the eukaryotic initiation factor 2 alpha phosphorylation, overexpression of GRP chaperones and RyR-dependent cleavage of caspase-12. Finally, attenuating ER stress with salubrinal protected oligodendrocytes from AMPA excitotoxicity. Together, these results show that Ca2+ release through RyRs contributes to cytosolic Ca2+ overload, mitochondrial dysfunction, ER stress and cell death following AMPA receptor-mediated excitotoxicity in oligodendrocytes. Cell Death and Disease (2010) 1, e54; doi:10.1038/cddis.2010.31; published online 15 July 2010

The promoter of cell growth- and RNA protection-associated SND1 gene is activated by endoplasmic reticulum stress in human hepatoma cells

Background: Staphyloccocal nuclease domain-containing protein 1 (SND1) is involved in the regulation of gene expression and RNA protection. While numerous studies have established that SND1 protein expression is modulated by cellular stresses associated with tumor growth, hypoxia, inflammation, heat- shock and oxidative conditions, little is known about the factors responsible for SND1 expression. Here, we have approached this question by analyzing the transcriptional response of human SND1 gene to pharmacological endoplasmic reticulum (ER) stress in liver cancer cells. Results: We provide first evidence that SND1 promoter activity is increased in human liver cancer cells upon exposure to thapsigargin or tunicamycin or by ectopic expression of ATF6, a crucial transcription factor in the unfolded protein response triggered by ER stress. Deletion analysis of the 5'-flanking region of SND1 promoter identified maximal activation in fragment (-934, +221), which contains most of the predicted ER stress response elements in proximal promoter. Quantitative real- time PCR revealed a near 3 fold increase in SND1 mRNA expression by either of the stress- inducers; whereas SND1 protein was maximally upregulated (3.4-fold) in cells exposed to tunicamycin, a protein glycosylation inhibitor. Conclusion: Promoter activity of the cell growth- and RNA-protection associated SND1 gene is up-regulated by ER stress in human hepatoma cells.

An Embedded Stress Sensor for Concrete SHM Based on Amorphous Ferromagnetic Microwires

A new smart concrete aggregate design as a candidate for applications in structural health monitoring (SHM) of critical elements in civil infrastructure is proposed. The cement-based stress/strain sensor was developed by utilizing the stress/strain sensing properties of a magnetic microwire embedded in cement-based composite (MMCC). This is a contact-less type sensor that measures variations of magnetic properties resulting from stress variations. Sensors made of these materials can be designed to satisfy the specific demand for an economic way to monitor concrete infrastructure health. For this purpose, we embedded a thin magnetic microwire in the core of a cement-based cylinder, which was inserted into the concrete specimen under study as an extra aggregate. The experimental results show that the embedded MMCC sensor is capable of measuring internal compressive stress around the range of 1-30 MPa. Two stress sensing properties of the embedded sensor under uniaxial compression were studied: the peak amplitude and peak position of magnetic switching field. The sensitivity values for the amplitude and position within the measured range were 5 mV/MPa and 2.5 mu s/MPa, respectively.

Approximate Best Proximity Points of Cyclic Self-maps in Metric Spaces and Cyclic Asymptotic Regularity

3rd International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE) Madrid, AUG 28-31, 2014 / editado por Vagenas, EC; Vlachos, DS; Bastos, C; Hofer, T; Kominis, Y; Kosmas, O; LeLay, G; DePadova, P; Rode, B; Suraud, E; Varga, K

On contractive cyclic fuzzy maps in metric spaces and some related results on fuzzy best proximity points and fuzzy fixed points

This paper investigates some properties of cyclic fuzzy maps in metric spaces. The convergence of distances as well as that of sequences being generated as iterates defined by a class of contractive cyclic fuzzy mapping to fuzzy best proximity points of (non-necessarily intersecting adjacent subsets) of the cyclic disposal is studied. An extension is given for the case when the images of the points of a class of contractive cyclic fuzzy mappings restricted to a particular subset of the cyclic disposal are allowed to lie either in the same subset or in its next adjacent one.