In this paper the modified trapezoidal rule is presented for solving Volterra linear Integral Equations (V.I.E) of the second kind and we noticed that this procedure is effective in solving the equations. Two examples are given with their comparison tables to answer the validity of the procedure.

The aim of this paper is to propose a reliable iterative method for resolving many types of Volterra - Fredholm Integro - Differential Equations of the second kind with initial conditions. The series solutions of the problems under consideration are obtained by means of the iterative method. Four various problems are resolved with high accuracy to make evident the enforcement of the iterative method on such type of integro differential equations. Results were compared with the exact solution which exhibits that this technique was compatible with the right solutions, simple, effective and easy for solving such problems. To evaluate the results in an iterative process the MATLAB is used as a math program for the calculations.

Decision making is vital and important activity in field operations research ,engineering ,administration science and economic science with any industrial or service company or organization because the core of management process as well as improve him performance . The research includes decision making process when the objective function is fraction function and solve models fraction programming by using some fraction programming methods and using goal programming method aid programming ( win QSB )and the results explain the effect use the goal programming method in decision making process when the objective function is
fraction .

in this paper the collocation method will be solve ordinary differential equations of retarted arguments also some examples are presented in order to illustrate this approach

A UV-Vis spectrophotometry method was developed for the determination of metoclopramide hydrochloride in pure and several pharmaceutical preparations, such as Permosan tablets, Meclodin syrups, and Plasil ampoules. The method is based on the diazotization reaction of metoclopramide hydrochloride with sodium nitrate and hydrochloric acid to yield the diazonium salt, which is then reacted with 3,5-dimethyl phenol in the presence of sodium hydroxide to form a yellow azo dye. Calibration curves were linear in the range from 0.3 to 6.5 µg/mL, with a correlation coefficient of 0.9993. The limits of detection and quantification were determined and found to be 0.18 and 0.61 µg/mL, respectively. Accuracy and precision were also determined b

PMMA (Poly methyl methacrylate) is considered one of the most commonly used materials in denture base fabrication due to its ideal properties. Although, a major problem with this resin is the frequent fractures due to heavy chewing forces which lead to early crack and fracture in clinical use. The addition of nanoparticles as filler performed in this study to enhance its selected mechanical properties. The Nano-additive effect investigated in normal circumstances and under a different temperature during water exposure. First, tests applied on the prepared samples at room temperature and then after exposure to water bath at (20, 40, 60) C^° respectively. SEM, PSD, EDX were utilized for samples evaluation in this study. Flexural

Electrochemical corrosion of hydroxyapatite (HAP) coated performance depends on various parameters like applied potential, time, thickness and sintering temperature. Thus, the optimum parameters required for the development of stable HAP coatings was found by using electrophoretic deposition (EPD) technique. This study discusses the results obtained from open circuit potential-time measurements (OCP-time), potentiodynamic polarisation and immersion tests for all alloy samples done under varying experimental conditions, so that the optimum coating parameters can be established. The ageing studies of the coated samples were carried out by immersing them in Ringer’s solution for a period of 30 days indicates the importance of stable HAP c

Exploring the B-Spline Transform for Estimating Lévy Process Parameters: Applications in Finance and Biomodeling Exploring the B-Spline Transform for Estimating Lévy Process Parameters: Applications in Finance and Biomodeling Letters in Biomathematics · Jul 7, 2025Letters in Biomathematics · Jul 7, 2025 Show publication This paper, presents the application of the B-spline transform as an effective and precise technique for estimating key parameters i.e., drift, volatility, and jump intensity for Lévy processes. Lévy processes are powerful tools for representing phenomena with continuous trends with abrupt changes. The proposed approach is validated through a simulated biological case study on animal migration in which movements are mo

In this work, composite materials were prepared by mixing different concentrations of ferrites with polyacrylonitrile (PAN) polymer. Using the electrospinning technique, these composites were deposited on a p-type silicon wafer. The prepared samples demonstrated nanofibers in both pure PAN polymers and their composites with ferrite. Prior to examining the humidity sensing effectiveness with a percentage of relative humidity at a frequency of 10 kHz, based on ambient temperature and a relative humidity range of 50–100%, the composite nanofibers demonstrated stronger humidity sensing compared to the pure PAN nanofibers, which demonstrated a powerful resistance response. More precisely, the PAN@ferrite nanocomposite showed a broad adsorption