Sumer Journal for Pure Science

This paper presents new results concerning coincidence and common fixed points in the setting of fuzzy Fréchet spaces, making essential use of the triangular inequality inherent in such spaces.to illustrate the applicability of the theoretical results, a concrete example is provided. Moreover, the established findings are employed to investigate a class of fuzzy differential equations, where we demonstrate the existence and uniqueness of a common fixed point for a triplet of operators. This fixed point corresponds to the unique solution of associated fuzzy differential system. The proposed approach opens new perspectives in the study of fuzzy dynamic systems and may serve as a foundation for extending similar results to broader classes of compatibility conditions and fuzzy differential models.

In this paper, the influence of removing three holes called L3 nanocavities to achieve a high quality factor (Q-factor) of two-dimensional photonic crystal (2D-PC) and its optical properties were investigated. There are two important factors that are modified to obtain a high quality factor, which are changing the hole size, and after that, hole shifting. Next, the effect of organic-semiconductor materials on the cavity photoluminescence (PL) photonic crystal (PC) was studied. Fabrication techniques to create the photonic crystal L3 nano-cavity are described. In addition, the impact of the deposited organic-semiconductor emitter spectrum on the electromagnetic field intensity within the L3 nanocavity was measured using photoluminescence spectroscopy. Finally, the hole size of the (2D-PC) nanocavities and its lattice constant were characterized utilizing scanning electron microscope (SEM).

In this study CeO2 NPs were successfully prepared via the hydrothermal method and influence of pH on the properties . The prepared nano-sized particles were characterized using various techniques including: Ultraviolet-Visible (UV–Vis) spectroscopy, X-ray diffraction (XRD), Field Emission Scanning Electron Microscopy (FESEM), Energy-Dispersive X-ray spectroscopy (EDX). The (UV–Vis) spectra showed the absorption peak changing from 335 nm to 298 nm with increasing pH value from 7 to 11, indicating the occurrence of a blue shift, which is a prior indication of the decrease in the grain size of CeO2 nanoparticles with increasing pH value. The XRD pattern of CeO2 NPs reveals the fluorite cubic structure, the crystallite size changes with an increase in pH value. According to FETEM image analysis, the average CeO2 particle size decreases from35.85 to 20.65 nm with increasing pH value from 7 to 11. Energy Dispersive X-ray analysis (EDX) was utilized to determine the constituent elements of CeO2 NPs mixture.