A consistent estimator for spectral density matrix of a discrete time periodically correlated process

 In this article, we introduce a weighted periodogram in the class of smoothed periodograms as a consistent estimator for the spectral density matrix of a periodically correlated process. We derive its limiting distribution that appears to be a certain finite linear combination of Wishart distribution. We also provide numerical derivations for our smoothed periodogram and exhibit its asymptotic consistency using simulated data. In this article, we introduce a weighted periodogram in the class of smoothed periodograms as a consistent estimator for the spectral density matrix of a periodically correlated process. We derive its limiting distribution that appears to be a certain finite linear combination of Wishart distribution. We also provide numerical derivations for our smoothed periodogram and exhibit its asymptotic consistency using simulated data

A detailed electronic-scale DFT simulation and a response surface methodology for the removal of Fe (III) ions from aqueous solutions

At significant concentrations, Fe (III) is toxic and may cause industrial and human health problems. Iron ions and compounds reacting with oxygen can be critical in producing oxygen radicals and peroxides that can damage DNA. Adsorption is a critical chemical process that is widely used to remove heavy metals. In this study, the Hummers method was used to prepare graphene oxide, which was then used as an adsorbent in the adsorption process of iron ions. Graphene oxide was characterized using IR, SEM, and AFM. The most important parameters influencing the adsorption of Fe (III) ions (adsorbent mass, contact time, and pH) were investigated. The process optimization was performed using the Box–Behnken Design under response surface methodology by Minitab Version 19. According to response surface analysis, the experimental data fit the quadratic model perfectly. The experimental results indicated that GO has significant potential as an adsorbent for removing Fe (III). With a pH of 3.0, an adsorbent weight of 0.15 g, and a contact time of 90.0 minutes for an initial Fe (III) concentration of 20 mg/L, the predicted maximum removal ratio of Fe (III) ions was 100% during process optimization. Furthermore, kinetic and isotherm studies were conducted. Apart from the experiments, detailed density functional theory simulations were successfully used to investigate the interactions and possible adsorption of water-solvated Fe (III) cation onto model GO adsorbents. The simulated results demonstrated that cationic Fe (III)/water complexes have a high affinity for adsorption and binding to the GO surface.</p