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.

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 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

Background. “Polyetheretherketone (PEEK)” is a biocompatible, high-strength polymer that is well-suited for use in dental applications due to its unique properties. However, achieving good adhesion between PEEK and hydrophilic materials such as dental adhesives or cement can be challenging. Also, this hydrophobicity may affect the use of PEEK as an implant material. Surface treatment or conditioning is often necessary to improve surface properties. The piranha solution is the treatment of choice to be explored for this purpose. Methods. PEEK disks of 10 mm diameter and 2 mm thickness were used in this study. Those samples were divided into five groups (each group has five samples). The first is the control group, in which no

In this study, Zizphus spina-christi leaf powder was applied for the adsorption of methyl orange. The effect of different operating parameters on the Batch Process adsorption was investigated such as solution pH (2-12), effect of contact time (0-60 min.), initial dye concentration (2-20 mg/L), effect of adsorbent dosage (0-4.5 g) and effect of temperature (20-50ᵒC). The results show a maximum removal rate and adsorption capacity (%R= 23.146, q_e = 2.778 mg/g) at pH = 2 and equilibrium was reached at 40 min. The pseudo- second-order kinetics were found to be best fit for the removal process (R² = 0.997). Different isotherm models (Langmuir, Freundlich, Dubini-Radushkevich,Temkin)  were applied in this stud

The investigation of determining solutions for the Diophantine equation  over the Gaussian integer ring for the specific case of  is discussed. The discussion includes various preliminary results later used to build the resolvent theory of the Diophantine equation studied. Our findings show the existence of infinitely many solutions. Since the analytical method used here is based on simple algebraic properties, it can be easily generalized to study the behavior and the conditions for the existence of solutions to other Diophantine equations, allowing a deeper understanding, even when no general solution is known.

The galvanic corrosion of the (Cu - Fe), (Cu - Zn) and (Fe - Zn) couples have been investigated in 3.5% NaCl solution, 40ºC, different velocities (Re = 5000, 10000 and 15000) and different area ratio’s of cathode to anode (AR= 0.5,1 and 2), by using commercial metal pipe (cylindrical tube).The Zero Resistance Ammeter has been used to measure the galvanic current (Ig) and galvanic potential (Eg) with time. The galvanic current density increases with increasing velocity (Re) and the area ratio (AR). The galvanic potential (Eg) is shifted to less negative with increasing velocity (Re) and the area ratio (AR). A statistical relations for the galvanic current density and galvanic potential as a function of (Re). and the area ratio had been

Studied the effect of foliar fertilizers Alaongrin results showed that spraying fertilizer Alaongrin and Fertilizers and Ministry of Agriculture and rack licorice extract every three weeks after thirty days from planting seedlings

One of the most common public liver diseases over the world is fatty liver which contain alcoholic and non-alcoholic fatty liver. One-fourth among general population are impact Non-Alcoholic Fatty Liver Disease (NAFLD) in the worldwide.Retinol binding protein 4 (RBP4) is known as an adipokine, mainly synthesized and secreted from the liver and form adipose tissues. RBP4 acts as a transporter and specifically bound to retinol from liver to others tissues. Visfatin is an adipocytokine and mainly produced from visceral fat tissue, skeletal muscles as well as liver. Vitamin A absorbed, transported as retinyl esters to the liver then hydrolyzed to the retinol form and storage in hepatic stellate cells (HSCs) after reesterified with rigly