An innovative inertial extra-proximal gradient algorithm for solving convex optimization problems with application to image and signal processing.

This study introduces an innovative approach to address convex optimization problems, with a specific focus on applications in image and signal processing. The research aims to develop a self-adaptive extra proximal algorithm that incorporates an inertial term to effectively tackle challenges in convex optimization. The study's significance lies in its contribution to advancing optimization techniques in the realm of image deblurring and signal reconstruction. The proposed methodology involves creating a novel self-adaptive extra proximal algorithm, analyzing its convergence rigorously to ensure reliability and effectiveness. Numerical examples, including image deblurring and signal reconstruction tasks using only 10% of the original signal, illustrate the practical applicability and advantages of the algorithm. By introducing an inertial term within the extra proximal framework, the algorithm demonstrates potential for faster convergence and improved optimization outcomes, addressing real-world challenges of image enhancement and signal reconstruction. The algorithm's incorporation of an inertial term showcases its potential for faster convergence and improved optimization outcomes. This research significantly contributes to the field of optimization techniques, particularly in the context of image and signal processing applications.

Investigation of Three-Dimensional Condensation Film Problem over an Inclined Rotating Disk Using a Nonlinear Autoregressive Exogenous Model.

This paper analyzed the three-dimensional (3D) condensation film problem over an inclined rotating disk. The mathematical model of the problem is governed by nonlinear partial differential equations (NPDE's), which are reduced to the system of nonlinear ordinary differential equations (NODE's) using a similarity transformation. Furthermore, the system of NODEs is solved by the supervised machine learning strategy of the nonlinear autoregressive exogenous (NARX) neural network model with the Levenberg-Marquardt algorithm. The dimensionless profiles of velocity, acceleration, and temperature are investigated under the effect of variations in the Prandtl number and normalized thickness of the film. The results demonstrate that increasing the Prandtl number causes an increase in the fluid's temperature profile. The solutions obtained by the proposed algorithm are compared with the state-of-the-art techniques that show the accuracy of the approximate solutions by NARX-BLM. The mean percentage errors in the results by the proposed algorithm for Θ(η), Ψ(η), k(η), -s(η), and (θ(η)) are 0.0000180%, 0.000084%, 0.0000135%, 0.000075%, and 0.00026%, respectively. The values of performance indicators, such as mean square error and absolute errors, are approaching zero. Thus, it validates the worth and efficiency of the design scheme.

Hydrogeochemical evolution and assessment of groundwater quality in the Togo and Dahomeyan aquifers, Greater Accra Region, Ghana.

Groundwater quality is generally better than surface water quality but this is not sacrosanct because during recharge and abstraction, groundwater may be subjected to variations due to influence from natural and anthropogenic processes. The Togo and Dahomeyan aquifers are threatened by several anthropogenic activities like dumping of domestic and industrial wastes in open landfill sites. These activities can be sources of groundwater constituents and can pose adverse health effects on humans and the ecosystem but little is known about the hydrogeochemical characteristics of groundwater and its quality in the area. Therefore, the present study is aimed at unravelling the hydrogeochemical characteristics and quality of groundwater in the Togo and Dahomeyan aquifers in the Greater Accra Region of Ghana. A total of 37 groundwater samples were collected and analysed for the concentrations of major ions, minor ions, and trace elements. The results were used to compute water quality parameters like electrical conductivity, sodium adsorption ratio, sodium percent, and magnesium ratio to assess the quality of the water for irrigation purposes. Groundwater shows acidic to slightly alkaline pH and evolved from Mg-Na-HCO3, Ca-Na-Mg-HCO3, Na-Ca-Mg-HCO3-Cl to Na-Mg-Ca-HCO3 with other mixed water types, which reflect the local geology. Geochemical modelling indicates that groundwater is supersaturated with respect to goethite and hematite and saturated with respect to calcite, aragonite, and dolomite in some samples. Hydrochemical graphing and multivariate statistical analysis indicate that the chemistry of groundwater in the area is primarily controlled by an interplay of chemical weathering, mineral dissolution, ion exchange reactions, agricultural activities, and sewage disposal. The groundwater is not entirely suitable for drinking purposes because of high concentrations of EC, TDS, Na+, Cl-, F-, Fe, Mn, Pb, Cr, and Ni, which exceed their maximum permissible limits provided by the World Health Organization. The computed parameters for assessing the quality of the water for irrigation reveal that 64.9% of the samples are suitable for irrigation purposes. However, 35.1% of the samples show very high salinity and sodium hazard and thus, are unsuitable for irrigation purposes. Therefore, it is recommended that mixing of the high salinity and sodium water with low salinity and sodium water can improve crop yields.