The Taguchi Orthogonal Method was used in the study to improve biodiesel production from Jatropha oil in a single pot. This method predicted the conversion (%) from Jatropha oil transesterification by optimizing four critical process variables. Using the hydrothermal-sulphonation method, a special bio-functionalized catalyst made from agricultural waste, such as cocoa pods, eggshells, orange peels, and snail shells, was used to accelerate the reaction. The ideal conditions of MTOR (15:1), CW (3 wt%), RTime (60 minutes), and RT (65 ◦C) resulted in an optimal conversion of 95.20%. Furthermore, at MTOR of 15:1, CW of 2 Wt.%, RTime of 120 minutes, and RT of 60\(\mathrm{{}^\circ}\)C, a 99.08% product yield was obtained. Nine (9) experimental runs that assessed the FAME yield and the FFA conversion showed coefficients of variation (1.2000 and 0.1083), R\({}^{2}\) values (0.9821 and 0.9981), adjusted R\({}^{2}\) values (0.9641 and 0.9923), and projected R\(^{2}\) values (0.9091 and 0.9539), respectively. The goal of this research was to increase biodiesel yield from Jatropha oil by improving the attribute and conversion of the yielding transformation. The renewable fuel generated under peak conditions met the necessary conditions for manufacturing.

Adsorption of organic compounds on surfaces plays a decisive role in corrosion inhibition, especially on steel materials. The interaction of the sites on the organic molecule with the active sites on the surface remains a complex phenomenon that is very challenging to explain from purely experimental investigation. The integration of computational intelligence through computer algorithms and softwares reduces the laborious and time consuming trial and error stages of laboratory experiments. In this study, density functional theory was deployed to expound the adsorption of benzothiazole and four of its derivatives, namely: benzothiazol-2-ol (BZT-OH), benzothiazol-2-amine (BZT-NH\(_2\)), benzothiazol-2-carboxylic acid (BZT-COOH) and benzothiazol-2-thiol (BZT-SH) on Fe(110) surface. Energy and quantum chemical calculations were performed to determine the positions and orientations of molecular orbitals, molecular reactivity, most preferable sites for nucleophilic and electrophilic attack as well as potential adsorption sites. Molecular dynamics simulation were performed to understand the configuration of the adsorbed molecules on the surface and to predict the mechanism of adsorption. Results reveal that the adsorption sites were mostly domiciled around N, O and S atoms of the amine, carboxyl/hydroxyl and thiol groups, respectively. Adsorption energy decreased following the trend BTZ-COOH > BTZ-SH > BTZ-NH\(_2\) > BTZ > BTZ-OH whereas binding energy decreased following the trend BTZ-SH > BTZ-COOH > BTZ-OH > BTZ-NH\(_2\) > BTZ. Overall, adsorption of BTZ-COOH and BTZ-SH respectively was most enhanced and strongest on Fe(110) surface. All the studied molecules would exhibit good adsorption characteristics on steel surface, making them potential efficient ingredients for formulation of corrosion inhibitors.

Assessment of breast cancer at all stages is of great importance in medicine because in addition to predicting the growth rate, treatment planning must also be considered. In this study, the new maps named the M\(^{*}_{new}\)(k)-map besides a proper signal-to-noise ratio (SNR) under the corresponding theory as well as new parameters such as Ti and FWHM have been introduced to investigate breast cancer performance. In other words, a new function on the SNR from convolutional combination of the relaxation times in MRI as FD\(_{SNR}\) is suggested which utilizes Fourier transform and differentiating operator. This function may be computed for all T1- and T2- weighted images towards prediction of the growth rate of abnormal tissues. These maps and the parameters may contribute to better diagnosis of breast cancer.

This study explores the electro-magneto-hydrodynamic (EMHD) flow, heat and mass transfer of a Jeffrey nanofluid between two horizontal plates under the combined influence of electroosmotic flow (EOF), velocity slip, and an induced magnetic field. The base fluid is water with dispersed copper (Cu) nanoparticles. The governing nonlinear partial differential equations are solved using a finite difference method (FDM), complemented by an analytical approach via the method of undetermined coefficients. The results show that nanofluid velocity increases with higher Grashof numbers and permeability parameter, driven by buoyancy and porous medium effects. A magnetic field lowers fluid velocity but enhances the induced magnetic field near the lower wall; velocity slip reduces wall shear stress but increases velocity farther from the boundary; the Prandtl number improves heat transfer by reducing thermal diffusivity; the Darcy number facilitates flow through porous media; and an increase in Reynolds number sharpens the velocity profile and slightly enhances heat and mass transfer. These findings offer important insights into the coupled dynamics of EMHD nanofluid flow with potential applications in microfluidic and biomedical fields.

Classical graph theory represents pairwise relationships using vertices and edges, while hypergraphs extend this model by allowing hyperedges to join any number of vertices, enabling complex multi‐way connections. SuperHyperGraphs further generalize hypergraphs through iterated powerset constructions, capturing hierarchical relationships at multiple layers. Weighted and signed graph models assign numerical weights or positive/negative signs to edges, respectively, and these concepts have been lifted to hypergraphs and, more recently, to SuperHyperGraphs. In this paper, we systematically develop the definitions and core properties of weighted SuperHyperGraphs and signed SuperHyperGraphs. We provide detailed examples to illustrate their structure and discuss potential applications in modeling layered networks with quantitative and polarity annotations. Our results lay a foundation for future theoretical and algorithmic advances in this emerging area.

World Bank macrodata for every country on our planet indicate that national incomes per capita account for a significant portion of population disparity, and these incomes follow well-known distributions documented in the literature across almost all continents. Measuring and comparing disparity is a substantial task that requires assembling the relative nature of both small and large national incomes without distinctions. This is the primary reason we consider the Atkinson inequality index (in the continuous case) in this paper, which was developed towards the end of the 20th century to measure this disparity. Since then, a nonparametric estimator for the Atkinson index has not been developed; instead, a well-known classical discrete form has been utilized. This reliance on the classical form makes the estimation or measurement of economic inequalities relatively straightforward. In this paper, we construct a kernel estimator of the Atkinson inequality index and, by extension, that of its associated welfare function. We then establish their almost sure asymptotic convergence. Finally, we explore the performance of our estimators through a simulation study and draw conclusions about national incomes per capita on each continent, as well as globally, by making comparisons with the classical form based on World Bank staff estimates derived from sources and methods outlined in “The Changing Wealth of Nations”. The results obtained highlight the advantages of kernel-based measures and the sensitivity of the index concerning the aversion parameter.