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

Influence of vapor transport equilibration on the crystal quality and thermal-expansion coefficients of gamma-LiAlO2

gamma-LiAlO2 (LAO) single crystal has been grown by the Czochralski method. However, its quality was deteriorated due to lithium volatilization during the crystal growth. The full width at half maximum value drops from 116.9 to 44.2 arc sec after the LAO slice was treated by vapor transport equilibration at 1000, 1100, and 1200 degrees C/48 h in sequence. The treated slice shows higher optical transmission than the as-grown one in the measured wavelength range of 190-1900 nm, meanwhile, its absorption edge exhibits a blueshift. According to Raman spectra, the treated slice has homogeneous quality at different depths from surface to 0.01 mm. The expansion coefficient of the treated slice for a axis drops from 17.2398x10(-6)/degrees C to 16.5240x10(-6)/degrees C, and that for c axis drops from 10.7664x10(-6)/degrees C to 10.0786x10(-6)/degrees C.

A meta-analytic approach to quantifying scientific uncertainty in stock assessments

Quantifying scientific uncertainty when setting total allowable catch limits for fish stocks is a major challenge, but it is a requirement in the United States since changes to national fisheries legislation. Multiple sources of error are readily identifiable, including estimation error, model specification error, forecast error, and errors associated with the definition and estimation of reference points. Our focus here, however, is to quantify the influence of estimation error and model specification error on assessment outcomes. These are fundamental sources of uncertainty in developing scientific advice concerning appropriate catch levels and although a study of these two factors may not be inclusive, it is feasible with available information. For data-rich stock assessments conducted on the U.S. west coast we report approximate coefficients of variation in terminal biomass estimates from assessments based on inversion of the assessment of the model’s Hessian matrix (i.e., the asymptotic standard error). To summarize variation “among” stock assessments, as a proxy for model specification error, we characterize variation among multiple historical assessments of the same stock. Results indicate that for 17 groundfish and coastal pelagic species, the mean coefficient of variation of terminal biomass is 18%. In contrast, the coefficient of variation ascribable to model specification error (i.e., pooled among-assessment variation) is 37%. We show that if a precautionary probability of overfishing equal to 0.40 is adopted by managers, and only model specification error is considered, a 9% reduction in the overfishing catch level is indicated.