An approximate solution of the liner system of ntegral cquations fot both fredholm(SFIEs)and Volterra(SIES)types has been derived using taylor series expansion.The solusion is essentailly

This paper investigates an effective computational method (ECM) based on the standard polynomials used to solve some nonlinear initial and boundary value problems appeared in engineering and applied sciences. Moreover, the effective computational methods in this paper were improved by suitable orthogonal base functions, especially the Chebyshev, Bernoulli, and Laguerre polynomials, to obtain novel approximate solutions for some nonlinear problems. These base functions enable the nonlinear problem to be effectively converted into a nonlinear algebraic system of equations, which are then solved using Mathematica^®12. The improved effective computational methods (I-ECMs) have been implemented to solve three applications involving

   The aim of this work is to detect the best operating conditions that effect on the removal of Cu²⁺, Zn²⁺, and Ni²⁺ ions from aqueous solution using date pits in the batch adsorption experiments. The results have shown that the Al-zahdi Iraqi date pits demonstrated more efficient at certain values of operating conditions of adsorbent doses of 0.12 g/ml of aqueous solution, adsorption time 72 h, pH solution 5.5 ±0.2, shaking speed  300 rpm, and smallest adsorbent particle size needed for removal of metals.  At the same time the particle size of date pits has a little effect on the adsorption at low initial concentration of heavy metals. The adsorption of metals increases with increas

      A new approach presented in this study to determine the optimal edge detection threshold value. This approach is base on extracting small homogenous blocks from unequal mean targets. Then, from these blocks we generate small image with known edges (edges represent the lines between the contacted blocks). So, these simulated edges can be assumed as true edges .The true simulated edges, compared with the detected edges in the small generated image is done by using different thresholding values. The comparison based on computing mean square errors between the simulated edge image and the produced edge image from edge detector methods. The mean square error computed for the total edge image (Er), for edge regio

Linear regression is one of the most important statistical tools through which it is possible to know the relationship between the response variable and one variable (or more) of the independent variable(s), which is often used in various fields of science. Heteroscedastic is one of the linear regression problems, the effect of which leads to inaccurate conclusions. The problem of heteroscedastic may be accompanied by the presence of extreme outliers in the independent variables (High leverage points) (HLPs), the presence of (HLPs) in the data set result unrealistic estimates and misleading inferences. In this paper, we review some of the robust

  This paper studies the existence of  positive solutions for the following boundary value problem :-
 
 y(b) 0 α y(a) - β y(a) 0     bta             f(y) g(t) λy    
 
 
The solution procedure follows using the Fixed point theorem and obtains that this problem has at least one positive solution .Also,it determines (  ) Eigenvalue which would be needed to find the positive solution .