Water pollution remains a pressing global environmental concern, with the textile industry recognized as a major contributor to both water consumption and contamination, particularly through the release of synthetic dyes. Therefore, the development of efficient treatment technologies targeting dye pollutants in textile wastewater is imperative. In this study, a ternary Ag/ZnO/g-C3N4 nanocomposite was successfully synthesized via an ultrasonication-assisted method with Ag content variation (2 mol
Stochastic optimal control problems are commonly formulated as optimization problems constrained by stochastic dynamical systems, whose value functions satisfy Hamilton–Jacobi–Bellman (HJB) equations. Owing to their strong nonlinearity and high dimensionality, closed-form solutions of HJB equations are rarely available, thereby motivating the development of robust and highly accurate numerical methods. This research introduces two hybrid spectral–collocation strategies for the numerical solution of stochastic HJB equations, constructed from different combinations of orthogonal polynomial bases. The first strategy utilizes shifted Chebyshev polynomials for time approximation and fractional-order Legendre polynomials for state approximation, while the second utilizes shifted Legendre polynomials in time and fractional-order Chebyshev polynomials in state. A convergence analysis is developed within the Caputo fractional derivative framework to justify the proposed methods and to establish the associated error estimates. The resulting nonlinear algebraic system is then solved using the collocation method. Numerical simulations, including an application to a resource extraction model, confirm that the proposed methods attain a high level of accuracy and exhibit convergence rates in strong agreement with the theoretical predictions. These results demonstrate that the developed hybrid spectral–collocation frameworks constitute reliable and efficient tools for addressing stochastic optimal control problems based on HJB equations.
Hydrogen, a zero-carbon energy source with high energy density, is widely used in Proton Exchange Membrane Fuel Cells (PEMFC), where Membrane Electrode Assembly (MEA) plays an important role. This study examines the fabrication of MEAs using the Catalyst Coated Membrane (CCM) technique by airbrush spray and ultrasonic spray methods, using Pt/C catalysts on activated carbon from kepok banana peel (soft carbon) and carbon nanotubes (CNT). Activated carbon soaked with 1M NaOH for 3 hours showed a surface area of 163.075 m²/g, exceeding that of CNTs (101.466 m²/g). The Pt/C catalyst with 1M3H-1 configuration achieved the highest Pt content (52.99 wt%). The ultrasonic spray ensured an even distribution of the catalyst, with a power density of 0.167 mW/cm² (1M3H-1) achieved faster. Although the airbrush spray reaches 0.889 mW/cm² (CNT1), the time required is longer, making the ultrasonic spray more efficient.
SS316L material exhibits superior corrosion resistance. The two grade compositions, comprising nickel and molybdenum, enable the alloy to resist acids and chlorides without degradation. Due to its exceptional corrosion resistance, both metals are among the few classified as "marine grade stainless steels." Gas Tungsten Arc Welding (GTAW) is executed to guarantee sufficient corrosion resistance during installation. This study analyzes the outcomes of welding ER316LSi as a filler material with SS316L base metal, focusing on microstructure, EDAX analysis, and corrosion rate. This study did not perform hardness testing. This study will indicate welding variables for future research on specific applications, utilizing various weld blades and current parameters. Corrosion testing, encompassing Tafel and Electrochemical Impedance Spectroscopy, indicates that the SS316LSi weld metal will yield a higher degree of ferrite development in the weld region. The welding temperature significantly influences the ferrite structures. The corrosion rates for each electrolyte solution are as follows: for the seawater electrolyte solution, a current of 110A yields a rate of 8.39857 x 10 -6 mpy, 120A results in 7.09315 x 10 -6 mpy, and 130A produces a rate of 7.85427 x 10 -6 mpy. The MgCl 2 electrolyte solution exhibits a concentration of 110A = 7.2195 × 10 -6 mpy, a current of 120A = 7.2156 × 10 -6 mpy, and a current of 130A = 7.1406 × 10 -6 mpy. The corrosion resistance at a current of 120 amperes is greater in seawater conditions than at a current of 130 amperes in MgCl2 solutions. The corrosion rate and reductions in Fe, Mo, Cr, and Mn following 14 days of immersion testing in sewage and MgCl2 are the reasons that low-heat-input or solid-phase bonding techniques can significantly enhance pitting resistance compromised by welding.
Abstract This work investigates the Laplacian spectrum and energy conservation associated with the linear wave equation on a tetrahedron-shaped quantum graph under Neumann–Kirchhoff vertex conditions. Using spectral analysis and the secular determinant formulation, we derive the explicit dependence of the eigenvalues on the topology of the graph. We further demonstrate that the total wave energy, defined as the sum of kinetic and potential components over all edges, remains conserved in time, indicating the absence of dissipation due to symmetry and vertex conditions. These results clarify the relationship between graph geometry, Laplacian spectra, and stable wave dynamics, and provide insight into resonance phenomena and wave propagation in quantum graph structures relevant to mathematical physics.
