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.

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

DAIRMD Professor Hayder R. Al-Hamamy, **Professor Adil A. Noaimi, **Dr. Ihsan A. Al-Turfy, IOSR Journal of Dental and Medical Sciences (IOSR-JDMS), 2015

In the present study, multi-walled carbon nanotubes (MWCNTs) with outside diameters of< 8 nm and 20−30 nm were covalently functionalized with β-Alanine using a novel synthesis procedure. The functionalization process was proved successful using Raman spectroscopy, FTIR, and TEM. Utilizing the two-step method with ultrasonication, the MWCNTs treated with β-Alanine (Ala-MWCNTs) with weight concentrations of 0.025%, 0.05%, 0.075%, and 0.1% were dispersed in distilled water to prepare water-based nanofluids. The aqueous colloidal dispersions of pristine MWCNTs were unstable. While for Ala-MWCNTs and after> 50 days from preparation, higher colloidal stability was obtained up to relative concentration of 0.955 and 0.939 for the 0.075-wt% samp

The research work was conducted to investigate the effect of oral administration of water extract of black pepper at doses of (1, 5) mg/kg body weight for two weeks daily by determining the genotoxic effect (mitotic index), evaluation of immunological effect (IgG, IgM, IgA, C3, C4) and measuring fertility hormones (follicles stimulation hormone/FSH, lutenising hormone/LH) levels with histopathological examinations of female albino swiss mice ovaries in comparison with control (normal saline). A clear effect in increasing mitotic activity was reveled for both doses in comparison with control. Results also showed a significant increase in the value of the all immunological parameters at both doses in comparison with control. Also obvious rais

Abstract in English  The aim of this study is to identify the effectiveness of rehabilitation exercises in conjunction with aquatic therapy for those suffering from sacroiliitis in football players. The researcher used the experimental approach, using the experimental design (pre-measurement, post-measurement). Similar to the objectives and procedures of the research, the researcher assumed the following: the existence of significant differences. Statistics between pre- and post-measurements in variables in favor of post-measurement for the following variables (degree of pain and level of balance). The experimental approach was used with a pre- and post-measurement design on one group of football players with sacroiliitis, nu

Binary mixtures of three heavy oil-stocks had been subjected to density measurments. The data had been aquired on the volumetric behaviour of these systems. The heavy oil-stocks used were of good varity, namely 40 stock , 60 stock, and 150 stock, 40 stock is the lightest one with the API gravity 33.7 while 60 stock is middle type and 150 stock is heavy one, with API gravity 27.7 and 23.8 respectively. Stocks with Kerosene or Xylene for non-ideal mixtures for which excess volume can be positive or  negative. Mixture of heavy-oil stocks with paraffinic spike (Kerosene) show negative excess volume. While, aromatic rings results a lower positive excess volume, as shown in Xylene when blending with 40 stock and 60 stock but a negati