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.

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.

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

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

γ-Al2O3–NPs were synthesized by a green synthesis process based on Boswellia carterii resin extract and aluminum sulphate in an alkaline medium. Boswellia carterii resin extract is a significant reducing and stabilizing agent for synthesizing γ-Al2O3–NPs.Several techniques, including Fourier–transform infrared (FT-IR), UV–visible spectroscopy, x-ray diffraction, electron microscopy (XRD), energy dispersive x-ray (EDX), scanning electron microscopy (SEM), Transmission electron microscopy (TEM), and atomic force microscopy (AFM), were utilized to investigate the final product. XRD and SEM confirmed a plate-like crystalline structure with an average size of 17.5 nm. FT-IR analysis identified aluminum oxide stretching vibrations (655,

A high-performance liquid chromatography method was employed for the quantitative determination of ascorbic acid (AA) which called vitamin C in three types of Iraqi citrus (orange mandarin and aurantium ) and to establish this goal , evaluation of ascorbic acid degradation is so important due to its significant criticality when exposure to ordinary atmospheric conditions. The chromatographic analysis of AA was carried out after their sequential elution with KH2PO4 ( as mobile phase) by reverse-phase HPLC technique with C8 column and UV detection at 214 nm. .Bad resolutions was appeared clearly for C8 column , so another alternative condition were carried out to improve the resolution by replacement of C8 by C18 column .Statistical treat

Thermal conductivity for epoxy composites filled with Al2O3 and Fe2O3 are
calculated, it found that increasing the weight ratio of Al2O3 and Fe2O3 lead to
increase in the values of thermal conductivity, but the epoxy composite filled with
Fe2O3, have values of thermal conductivity less than for epoxy composite filled with
Al2O3, for the same weight ratio. Also thermal conductivity calculated for epoxy
composites by contact to every two specimens (like sandwich) content same weight
ratio of alumina-oxide and ferrite-oxide, its found that the value of thermal
conductivity lays between the values of epoxy filled Al2O3 and of epoxy filled Fe2O3

Introduction:Serratia marcescens is a gram-negative pathogen of many species. Its pathogenicity and survival are linked to its capacity to build biofilms as well as its strong inherent resistance to antimicrobials and cleaning agents. Objectives: To analyse the impact of glyceryl trinitrate (GTN) on the gene expression of QS-related genes (rssB, rsmA,and pigP) of S. marcescens. Methodology: The broth microdilution technique estimated the bactericidal effectiveness of glyceryl trinitrate. The presence of rssB, rsmA,and pigP in S. marcescens isolates was detected using PCR. qRT-PCR was used to assess the effect of GTN on rssB, rsmA,and pigPgene expression. Results: The results demonstrated that GTN has no effect on S. marcesce

The aim of this paper is to present the numerical method for solving linear system of Fredholm integral equations, based on the Haar wavelet approach. Many test problems, for which the exact solution is known, are considered. Compare the results of suggested method with the results of another method (Trapezoidal method). Algorithm and program is written by Matlab vergion 7.

To obtain the approximate solution to Riccati matrix differential equations, a new variational iteration approach was ‎proposed, which is suggested to improve the accuracy and increase the convergence rate of the approximate solutons to the ‎exact solution. This technique was found to give very accurate results in a few number of iterations. In this paper, the ‎modified approaches were derived to give modified solutions of proposed and used and the convergence analysis to the exact ‎solution of the derived sequence of approximate solutions is also stated and proved. Two examples were also solved, which ‎shows the reliability and applicability of the proposed approach. ‎