CHARACTEIZATIONS OF WOVENT g-FRAMES AND WEAVING g-FRAMES IN HILBERT SPACESS AND C^(*)-MODULES

In this paper,using Parseval frames we generalize Sun’s results to g-frames in Hilbert C^(*)-modules.Moreover,for g-frames in Hilbert spaces,we present some characterizations in terms of a family of frames,not only for orthonormal bases.Also,we have a note about a comment and a relation in the proof of Proposition 5.3 in[D.Li et al.,On weaving g-frames for Hilbert spaces,Complex Analysis and Operator Theory,2020].Finally,we have some results for g-Riesz bases,woven and P-woven g-frames.

APPROXIMATE DUALITY OF g-FRAMES IN HILBERT SPACES

In this article, we introduce and characterize approximate duality for g-frames. We get some important properties and applications of approximate duals. We also obtain some new results in approximate duality of frames, and generalize some of the known results in approximate duality of frames to g-frames. We also get some results for fusion frames, and perturbation of approximately dual g-frames. We show that approximate duals are stable under small perturbations and they are useful for erasures and reconstruction.

Brain-derived neurotrophic factor in patients with advanced age-related macular degeneration

AIM: To investigate the serum level of the brain derived neurotrophic factor (BDNF) in age -related macular degeneration (AMD) and healthy control subjects. The disruption in the tight balance of neuroinflammatory and neuroprotective processes in an immune -privileged site like retina is proposed to contribute to the pathogenesis of AMD. One of the main neuroprotective mediators in the central nervous system Is BDNF with its serum level notably affected in several neurodegenerative disorders. METHODS: Thirty-six patients'with AMD and 36 age-matched controls were enrolled in this study. The serum level of BDNF was measured using the enzyme -linked immunosorbent assay method. Results were analyzed to compare case and control values. Comparisons were also made between the BDNF level of wet- vsdry-AMD, and male vs female patients and controls. Analysis of variance (ANOVA) and Student's t-test were employed to analyze the data. RESULTS: The mean BDNF levels in AMD group were significantly higher than the control group. Furthermore, our analysis revealed greater BDNF values in all AMD subgroups compared to controls (P=0.004, 0.005, 0.001 and 0.02 for male wet-AMD, male dry-AMD, female wetAMD and female dry-AMD vscontrols, respectively). The BDNF level however did not vary between wet- and dryAMD patients (P=0.74). While within-group comparisons in males and females of AMD and control groups did not show any difference in BDNF (P=0.16, 0.64 and 0.85 for wet -AMD, dry -AMD and control groups, respectively), between -group data showed a higher mean BDNF in both male and female AMD subjects than their peer controls. CONCLUSION: This study demonstrated that the serum BDNF level is different in patients with AMD as compared to subjects without AMD. Future attempts should be done to unravel beneficial or deleterious effect of this neurotrophin in the pathogenesis of AMD.