In this paper we use non-polynomial spline functions to develop numerical methods to approximate the solution of 2nd kind Volterra integral equations. Numerical examples are presented to illustrate the applications of these method, and to compare the computed results with other known methods.

In this study, a new technique is considered for solving linear fractional Volterra-Fredholm integro-differential equations (LFVFIDE's) with fractional derivative qualified in the Caputo sense. The method is established in three types of Lagrange polynomials (LP’s), Original Lagrange polynomial (OLP), Barycentric Lagrange polynomial (BLP), and Modified Lagrange polynomial (MLP). General Algorithm is suggested and examples are included to get the best effectiveness, and implementation of these types. Also, as special case fractional differential equation is taken to evaluate the validity of the proposed method. Finally, a comparison between the proposed method and other methods are taken to present the effectiveness of the proposal meth

Cooling towers is one of the most important unit in industry, they are used to dispose heat from cooling media used in the integrated units. The choice of the cooling media plays recently an important rule due to fresh-water scarcity. The use of saline as a cooling media become of growing interest, but the corrosion problem has to be taken in consideration. In this study the simultaneous effect of cooling tower operation parameters on the corrosion rate of mild-steel is considered. The role of NaCl content is found to be pronounced more than the working solution temperature and flowrate. The corrosion of mild-steel in these studied factors had shown an interesting result especially with the NaCl% content. Firstly, there was an increase in t

This study explores eggshell waste as a low-cost, eco-friendly adsorbent for removing Aniline Blue dye from water. Batch and continuous experiments under various conditions showed effective performance. FTIR and SEM analyses confirmed porosity and functional groups. The adsorption followed the Sips isotherm and pseudo-first-order kinetics. The porous calcium carbonate structure enhanced dye removal. Thermodynamic results indicated an endothermic and spontaneous process. Lower flow rates improved performance in fixed-bed columns. The study supporting environmentally friendly solutions aligned with the Sustainable Development Goals (SDGs).

For the first time Iron tungstate semiconductor oxides films (FeWO4) was successfully synthesized simply by advanced controlled chemical spray pyrolysis technique, via employed double nozzle instead of single nozzle using tungstic acid and iron nitrate solutions at three different compositions and spray separately at same time on heated silicone (n-type) substrate at 600 °C, followed by annealing treatment for one hour at 500 °C. The crystal structure, microstructure and morphology properties of prepared films were studied by X-ray diffraction analysis (XRD), electron Scanning Electron Microscopy (SEM) and Atomic Force Microscopy (AFM) respectively. According to characterization techniques, a material of well-crystallized monoclinic ph

In this work, multilayer nanostructures were prepared from two metal oxide thin films by dc reactive magnetron sputtering technique. These metal oxide were nickel oxide (NiO) and titanium dioxide (TiO2). The prepared nanostructures showed high structural purity as confirmed by the spectroscopic and structural characterization tests, mainly FTIR, XRD and EDX. This feature may be attributed to the fine control of operation parameters of dc reactive magnetron sputtering system as well as the preparation conditions using the same system. The nanostructures prepared in this work can be successfully used for the fabrication of nanodevices for photonics and optoelectronics requiring highly-pure nanomaterials.

Cadmium oxide thin films were prepared by D.C magnetron plasma sputtering using different voltages (700, 800, 900, 1000, 1100 and 1200) Volt. The Cadmium oxide structural properties using XRD analysis for just a voltage of 1200 volt at room temperature after annealing in different temperatures (523 and 623) K were studied .The results show that the films prepared at room temperature have some peaks belong to cadmium element along the directions (002), (100), (102) and (103) while the other peaks along the directions of (111), (200) and (222) belong to cadmium oxide. Annealed samples display only cadmium oxide peaks. Also, the spectroscopic properties of plasma diagnostic for CdO thin films were determined and the results show that the el

Zinc oxide thin films were deposited by chemical spray pyrolysis onto glass substrates which are held at a temperature of 673 K. Some structural, electrical, optical and gas sensing properties of films were studied. The resistance of ZnO thin film exhibits a change of magnitude as the ambient gas is cycled from air to oxygen and nitrogen dioxide