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Generally, stochastic functional differential equations (SFDEs) pose a challenge as they often lack explicit exact solutions. Consequently, it becomes necessary to seek certain favorable conditions under which numerical solutions can converge towards the exact solutions. This article aims to delve into the convergence analysis of solutions for stochastic functional differential equations by employing the framework of G-Brownian motion. To establish the goal, we find a set of useful monotone type conditions and work within the space C r ((− ∞ , 0 ] ; R n) . The investigation conducted in this article confirms the mean square boundedness of solutions. Furthermore, this study enables us to compute both L G 2 and exponential estimates. [ABSTRACT FROM AUTHOR]

This research concentrates on the analysis of meromorphic mappings. We derived several important results for value distribution of specific difference polynomials of meromorphic mappings, which generalize the work of Laine and Yang. In addition, we proved uniqueness theorems of meromorphic mappings. The difference polynomials of these functions have the same fixed points or share a nonzero value. This extends the research work of Qi, Yang and Liu, where they used the finite ordered meromorphic mappings. [ABSTRACT FROM AUTHOR]

The present study focuses on fabrication of magnetic activated carbon (M-AC) using tire waste and its potential investigation for adsorption of Cr (VI) from wastewater. The composite material (M-AC) was synthesized by pyrolysis followed by in situ magnetization method, and characterized by FTIR, FESEM, EDX, and XRD analysis. The maximum adsorption of Cr (VI) ion over composite adsorbent was found (~99.5%) to occur at pH 2, sample volume 10 mL, adsorbent dose 100 mg, contact time 30 min. The adsorption process was endothermic, feasible, spontaneous, and was found to follow pseudo second order of the reaction. The Cr ion could be completely desorbed (~99.3%) from the composite adsorbent by using 20 mL of 2 M NaOH solution. The composite adsorbent was regenerated by continuous adsorption and desorption for 5 consecutive cycles by using 10 mL 0.1 M HCl solution. M-AC also performed well in case of tannery wastewater by removing about 97% of Cr (VI). [ABSTRACT FROM AUTHOR]

Herein, we report the synthesis of magnetic nanoparticle (MNP)-reduced graphene oxide (rGO) and polymethylmethacrylate (PMMA) composite (MNPs/rGO/PMMA) as adsorbent via an in situ fabrication strategy and, in turn, the application for adsorptive removal and recovery of Cr(VI) from tannery wastewater. The composite material was characterized via XRD, FTIR and SEM analyses. Under batch mode experiments, the composite achieved maximum adsorption of the Cr(VI) ion (99.53 ± 1.4%, i.e., 1636.49 mg of Cr(VI)/150 mg of adsorbent) at pH 2, adsorbent dose of 150 mg/10 mL of solution and 30 min of contact time. The adsorption process was endothermic, feasible and spontaneous and followed a pseudo-2nd order kinetic model. The Cr ions were completely desorbed (99.32 ± 2%) from the composite using 30 mL of NaOH solution (2M); hence, the composite exhibited high efficiency for five consecutive cycles without prominent loss in activity. The adsorbent was washed with distilled water and diluted HCl (0.1M), then dried under vacuum at 60 °C for reuse. The XRD analysis confirmed the synthesis and incorporation of magnetic iron oxide at 2θ of 30.38°, 35.5°, 43.22° and 57.36°, respectively, and graphene oxide (GO) at 25.5°. The FTIR analysids revealed that the composite retained the configurations of the individual components, whereas the SEM analysis indicated that the magnetic Fe 3 O 4 -NPs (MNPs) dispersed on the surface of the PMMA/rGO sheets. To anticipate the behavior of breakthrough, the Thomas and Yoon-Nelson models were applied to fixed-bed column data, which indicated good agreement with the experimental data. This study evaluates useful reference information for designing a cost-effective and easy-to-use adsorbent for the efficient removal of Cr(VI) from wastewater. Therefore, it can be envisioned as an alternative approach for a variety of unexplored industrial-level operations.

The present study focuses on fabrication of magnetic activated carbon (M-AC) using tire waste and its potential investigation for adsorption of Cr (VI) from wastewater. The composite material (M-AC) was synthesized by pyrolysis followed by in situ magnetization method, and characterized by FTIR, FESEM, EDX, and XRD analysis. The maximum adsorption of Cr (VI) ion over composite adsorbent was found (~99.5%) to occur at pH 2, sample volume 10 mL, adsorbent dose 100 mg, contact time 30 min. The adsorption process was endothermic, feasible, spontaneous, and was found to follow pseudo second order of the reaction. The Cr ion could be completely desorbed (~99.3%) from the composite adsorbent by using 20 mL of 2 M NaOH solution. The composite adsorbent was regenerated by continuous adsorption and desorption for 5 consecutive cycles by using 10 mL 0.1 M HCl solution. M-AC also performed well in case of tannery wastewater by removing about 97% of Cr (VI).