Volterra – Fredholm integral equations (VFIEs) have a massive interest from researchers recently. The current study suggests a collocation method for the mixed Volterra - Fredholm integral equations (MVFIEs)."A point interpolation collocation method is considered by combining the radial and polynomial basis functions using collocation points". The main purpose of the radial and polynomial basis functions is to overcome the singularity that could associate with the collocation methods. The obtained interpolation function passes through all Scattered Point in a domain and therefore, the Delta function property is the shape of the functions. The exact solution of selective solutions was compared with the results obtained

The aim of this paper is to present a method for solving high order ordinary differential equations with two point's boundary condition, we propose semi-analytic technique using two-point oscillatory interpolation to construct polynomial solution. The original problem is concerned using two-point oscillatory interpolation with the fit equal numbers of derivatives at the end points of an interval [0 , 1] . Also, many examples are presented to demonstrate the applicability, accuracy and efficiency of the method by comparing with conventional methods.

a porentioncsisteve has been carried out of the corrosion behavior of inconel(600) in chloride ions (Cl) over the tempreatures 293 over the temperatures 308K in both the dcacrated and the alloy

Pulsed laser ablation in liquid (PLAL) has become an increasingly important technique for metals production and metal oxides nanoparticles (NPs) and others. This technique has its many advantages compared with other conventional techniques (physical and chemical). This work was devoted for production of zirconia (ZrO2) nanoparticles via PLAL technique from a solid zirconium target immersed in a wet environment in order to study the effect of this environment on the optical properties and structure of ZrO2 nanoparticles. The solutions which used for this purpose is distilled water (D.W). The produces NPs were characterized by mean of many tests such as UV-visible (UV-Vis.), transmission electron microscope (TEM) and Z-Potential. The UV-Vis.

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

In this paper, the theoretical cross section in pre-equilibrium nuclear reaction has been studied for the reaction  at energy 22.4 MeV. Ericson’s formula of partial level density PLD and their corrections (William’s correction and spin correction) have been substituted  in the theoretical cross section and compared with the experimental data for  nucleus. It has been found that the theoretical cross section with one-component PLD from Ericson’s formula when  doesn’t agree with the experimental value and when . There is little agreement only at the high value of energy range with  the experimental cross section. The theoretical cross section that depends on the one-component William's formula and on-component corrected to spi

Abstract The surface of kaolin was diagnosed by an AFM and the results were shown The height of the highest peak reached by a quantity of Kaolin ‎surface is 2.5 µm, the granules, and their diameter with an average diameter of 666.1nm. Using Kaolin's adsorption properties, erythrosine was removed of its aqueous solution. It was determined that the maximal dye adsorption ranged 36.53–40.61%. ‎‎‎‎The results of using the Freundlich, Langmuir, and Temkin adsorption isotherms revealed that at temperatures of (298,308,318) K, the Freundlich model was followed, the Langmuir model did not match, and the Temkin model could only be partially applied. There is also physical adsorption. One of the three kinetic models of the