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.

Transverse target single-spin asymmetry in inclusive electroproduction of charged pions and kaons

Single-spin asymmetries were investigated in inclusive electroproduction of charged pions and kaons from transversely polarized protons at the HERMES experiment. The asymmetries were studied as a function of the azimuthal angle psi about the beam direction between the target-spin direction and the hadron production plane, the transverse hadron momentum P-T relative to the direction of the incident beam, and the Feynman variable x(F). The sin psi* amplitudes are positive for pi(+) and K+ slightly negative for pi(-) and consistent with zero for K-, with particular P-T but weak x(F) dependences. Especially large asymmetries are observed for two small subsamples of events, where also the scattered electron was recorded by the spectrometer. (C) 2013 The Authors. Published by Elsevier B.V. All rights reserved.

Convergence Properties and Fixed Points of Two General Iterative Schemes with Composed Maps in Banach Spaces with Applications to Guaranteed Global Stability

This paper investigates the boundedness and convergence properties of two general iterative processes which involve sequences of self-mappings on either complete metric or Banach spaces. The sequences of self-mappings considered in the first iterative scheme are constructed by linear combinations of a set of self-mappings, each of them being a weighted version of a certain primary self-mapping on the same space. The sequences of self-mappings of the second iterative scheme are powers of an iteration-dependent scaled version of the primary self-mapping. Some applications are also given to the important problem of global stability of a class of extended nonlinear polytopic-type parameterizations of certain dynamic systems.

Brca1 is expressed in human microglia and is dysregulated in human and animal model of ALS

Background: There is growing evidence that microglia are key players in the pathological process of amyotrophic lateral sclerosis (ALS). It is suggested that microglia have a dual role in motoneurone degeneration through the release of both neuroprotective and neurotoxic factors. Results: To identify candidate genes that may be involved in ALS pathology we have analysed at early symptomatic age (P90), the molecular signature of microglia from the lumbar region of the spinal cord of hSOD1(G93A) mice, the most widely used animal model of ALS. We first identified unique hSOD1(G93A) microglia transcriptomic profile that, in addition to more classical processes such as chemotaxis and immune response, pointed toward the potential involvement of the tumour suppressor gene breast cancer susceptibility gene 1 (Brca1). Secondly, comparison with our previous data on hSOD1(G93A) motoneurone gene profile substantiated the putative contribution of Brca1 in ALS. Finally, we established that Brca1 protein is specifically expressed in human spinal microglia and is up-regulated in ALS patients. Conclusions: Overall, our data provide new insights into the pathogenic concept of a non-cell-autonomous disease and the involvement of microglia in ALS. Importantly, the identification of Brca1 as a novel microglial marker and as possible contributor in both human and animal model of ALS may represent a valid therapeutic target. Moreover, our data points toward novel research strategies such as investigating the role of oncogenic proteins in neurodegenerative diseases.

On the Stability and Equilibrium Points of Multistaged SI (n) R Epidemic Models

This paper relies on the concept of next generation matrix defined ad hoc for a new proposed extended SEIR model referred to as SI(n)R-model to study its stability. The model includes n successive stages of infectious subpopulations, each one acting at the exposed subpopulation of the next infectious stage in a cascade global disposal where each infectious population acts as the exposed subpopulation of the next infectious stage. The model also has internal delays which characterize the time intervals of the coupling of the susceptible dynamics with the infectious populations of the various cascade infectious stages. Since the susceptible subpopulation is common, and then unique, to all the infectious stages, its coupled dynamic action on each of those stages is modeled with an increasing delay as the infectious stage index increases from 1 to n. The physical interpretation of the model is that the dynamics of the disease exhibits different stages in which the infectivity and the mortality rates vary as the individual numbers go through the process of recovery, each stage with a characteristic average time.