In this paper Volterra Runge-Kutta methods which include: method of order two and four will be applied to general nonlinear Volterra integral equations of the second kind. Moreover we study the convergent of the algorithms of Volterra Runge-Kutta methods. Finally, programs for each method are written in MATLAB language and a comparison between the two types has been made depending on the least square errors.

This paper introduces a non-conventional approach with multi-dimensional random sampling to solve a cocaine abuse model with statistical probability. The mean Latin hypercube finite difference (MLHFD) method is proposed for the first time via hybrid integration of the classical numerical finite difference (FD) formula with Latin hypercube sampling (LHS) technique to create a random distribution for the model parameters which are dependent on time [Formula: see text]. The LHS technique gives advantage to MLHFD method to produce fast variation of the parameters’ values via number of multidimensional simulations (100, 1000 and 5000). The generated Latin hypercube sample which is random or non-deterministic in nature is further integ

The way used to estimate the fuzzy reliability differs according to the nature of the information of failure time which has been dealt in this research.The information of failure times has no probable distribution to explain it , in addition it has fuzzy quality.The research includes fuzzy reliability estimation of three periods ,the first one from 1986 to 2013,the second one from 2013 to 2033 while the third one from 2033 to 2066 .Four failure time have been chosen to identify the membership function of fuzzy trapezoid represented in the pervious years after taking in consideration the estimation of most researchers, proffional    geologists and the technician who is incharge of maintaining of Mosul Dam project. B

      The objective of this research is employ the special cases of  function  trapezoid in the composition of fuzzy sets to make decision within the framework of the theory of games traditional to determine the best strategy for the mobile phone networks in the province of  Baghdad and Basra, has been the adoption of different periods of the  functions belonging to see the change happening in the matrix matches and the impact  that the strategies  and decision-making  available to each player and the impact on  societ

In this study, gold nanoparticles (AuNPs) were synthesized using a plasma jet system at different exposure times. Using ultraviolet, visible spectra, X-ray diffraction, the nanoparticles were characterized (XRD). A Plasmon surface resonance concentrated at 530, 540, and 533 nm for the prepared AuNPs. The pattern of XRD showed that the extreme peaks of the film reflect crystalline existence. The face-centered cubic structure of the gold nanoparticles was prepared for all samples, with an average crystallite size of 25-40 nm. The effect of AuNPs in vivo on liver function levels was measured. For all doses, we notice an increase in the ranks of liver function in the blood during the period of dosing, and it begins to decrease when the dosi

     In this paper, we introduce and discuss an extended subclass〖 Ą〗_p^*(λ,α,γ) of meromorphic multivalent functions involving Ruscheweyh derivative operator. Coefficients inequality, distortion theorems, closure theorem for this subclass are obtained.

Abstract
The research aims to build a training program to develop some executive functions for kindergarten children. To achieve this goal, the two researchers built the program according to the following steps:
1. Determining the general objective of the program.
2. Determining the behavioral objectives of the program.
3. Determining the included content in the program.
4. Implementing the content of the activities of the program.
5. Evaluating the Program.
The program included (12) training activities, the training activities included several items: the title of the activity, the time of implementation of the activity, the general objective of the activity, the procedural behavioral objective, the means and tools u

The aim of this work is to evaluate the onc-electron expectation values < r > from the radial electronic density funetion D(r) for different wave ?'unctions for the 2s state of Li atom. The wave functions used were published in 1963,174? and 1993 , respectavily. Using " " ' wave function as a Slater determinant has used the positioning technique for the analysis open shell system of Li (Is2 2s) State.