The generalized Calogero–Bogoyavlenskii–Schiff equation (GCBSE) is examined and analyzed in this paper. It has several applications in plasma physics and soliton theory, where it forecasts the soliton wave propagation profiles. In order to obtain the analytically exact solitons, the model under consideration is a nonlinear partial differential equation that is turned into an ordinary differential equation by using the next traveling wave transformation. The new extended direct algebraic technique and the modified auxiliary equation method are applied to the generalized Calogero–Bogoyavlenskii–Schiff equation to get new solitary wave profiles. As a result, novel and generalized analytical wave solutions are acquired in which singular solutions, mixed singular solutions, mixed complex solitary shock solutions, mixed shock singular solutions, mixed periodic solutions, mixed trigonometric solutions, mixed hyperbolic solutions, and periodic solutions are included with numerous soliton families. The propagation of the acquired soliton solution is graphically presented in contour, two- and three-dimensional visualization by selecting appropriate parametric values. It is graphically demonstrated how wave number impacts the obtained traveling wave structures.

This study reports the synthesis of copper–zinc binary oxide coupled cadmium tungstate through a simple bio-precipitation method followed by calcination at 600 °C and its adsorption application. The characterization analysis reveals that the prepared composite has low particles size (nano-range), high porosity, and functional groups on the surface. The calcination of sample at 600 °C causes some essential function groups to disappear on the surface. Prepared composite was found to be effective adsorptive material to treat Congo red dye in aqueous solution. 2.5 g L⁻¹ dose of adsorbent could remove more than 99% Congo red dye from 10 mg L⁻¹ solution and more than 80% Congo red dye from 60 mg L⁻¹ aqueous solution. The maximum adsorption capacity of present adsorbent was calculated to be 19.6 mg Congo red per gram of adsorbent. Isotherms analysis suggested a physio-chemical adsorption process. Thermodynamic analysis revealed a exothermic and feasible adsorption process. Adsorption rate was well explained by pseudo second order kinetics. The rate determining step was intra-particle diffusion evaluated from the Weber-Morris plot. To assess the adsorption performance of present adsorbent for Congo red dye the partition coefficient and adsorption equilibrium capacity were compared with other adsorbents. The partition coefficient and adsorption equilibrium values for 10 mg L⁻¹ aqueous solution were found to be approximately 83.3 mg g⁻¹ µM⁻¹ and 4.0 mg g⁻¹ at 30 °C and 7.0 pH using 2.5 g L⁻¹ adsorbent. The value of partition coefficient was found to be higher than previous reported zinc oxide coupled cadmium tungstate having partition coefficient = as 21.4 mg g⁻¹ µM⁻¹ at 30 °C and 7.0 pH using 2.0 g L⁻¹ adsorbent. These results suggested that present adsorption technology is efficient for wastewater treatment.

All solid-state room-temperature lithium-sulfur (Li-S) batteries have gained increasing attention due to their ability to eliminate the polysulfides shuttle effects and the safety dangers associated with the liquid electrolytes. Herein, a novel composite solid-state electrolyte, which is nickel-tungsten carbides (NiWC) over mesoporous silica (SBA-15) filled polyethylene oxide (PEO), was developed and investigated for Li-S batteries. The filler minimizes the crystallinity of the PEO and increases the ionic conductivity of the electrolyte, resulting in lowering the AC impedance of electrolyte composite from 26,256 ohm to 2416 ohm and to 5734 ohm after adding the electrolyte material with Ni/W ratios of 1:1 and 9:1, respectively. A high initial specific capacity of 1305 mAh g⁻¹ and a capacity retention of 66.7% after 8 cycles at C/10 was obtained at room temperature after adding NiWC/SBA-15 with a Ni/W ratio of 1:1. This novel composite solid-state electrolyte shows a remarkable long-term performance at high current rates (1, 2, 4, and 5C) and rate capabilities at 0.1, 0.2, 0.5, 1, 2, 4 and back to 0.1C. The battery was able to recover 77% of the initial specific capacity at 0.1C. The materials were characterized by XRD and SEM-EDX to study the crystallinity and elemental distributions, respectively.

In this paper, we propose a mathematical model to describe the influence of the SARS-CoV-2 virus with correlated sources of randomness and with vaccination. The total human population is divided into three groups susceptible, infected, and recovered. Each population group of the model is assumed to be subject to various types of randomness. We develop the correlated stochastic model by considering correlated Brownian motions for the population groups. As the environmental reservoir plays a weighty role in the transmission of the SARS-CoV-2 virus, our model encompasses a fourth stochastic differential equation representing the reservoir. Moreover, the vaccination of susceptible is also considered. Once the correlated stochastic model, the existence and uniqueness of a positive solution are discussed to show the problem’s feasibility. The SARS-CoV-2 extinction, as well as persistency, are also examined, and sufficient conditions resulted from our investigation. The theoretical results are supported through numerical/graphical findings.

This study introduces an innovative way to use calcium oxide (CaO) derived from mussel shells as a catalyst support for biodiesel production. Several transition metals, including Ni, Ag, Mo, Co, and W were loaded on the aforementioned support to synthesize mono-metallic and bi-metallic catalysts using the wet impregnation method. Microwave technology was utilized to accelerate reactions and improve efficiency. Characterization techniques such as BET, SEM/EDX, and XRD confirmed the successful incorporation of metals into the catalyst structure. The prepared catalysts, Mussel(Ni), Mussel(Ni-W), Mussel(Ni-Ag), Mussel(Ni-Mo), and Mussel(Ni-Co), were evaluated to investigate the catalytic performance for biodiesel production from corn oil under different conditions such as microwave powers, catalyst loadings, reaction times, and methanol-to-oil ratios. The combination of mussel-derived catalysts with microwave technology resulted in reduced reaction times and 100% selectivity under conditions of 1.5% catalyst loading, 10 min reaction time, and a methanol-to-oil ratio of 15:1, showcasing the synergistic effects of transition metals. This study highlights the potential of mussel-shell-derived catalysts as a cost-effective and sustainable solution for biodiesel production. By reducing reliance on conventional methods, these findings contribute to clean energy advancements and offer a scalable, environmentally friendly pathway for renewable fuel synthesis.