هناك دائما حاجة إلى طريقة فعالة لتوليد حل عددي أكثر دقة للمعادلات التكاملية ذات النواة المفردة أو المفردة الضعيفة لأن الطرق العددية لها محدودة. في هذه الدراسة ، تم حل المعادلات التكاملية ذات النواة المفردة أو المفردة الضعيفة باستخدام طريقة متعددة حدود برنولي. الهدف الرئيسي من هذه الدراسة هو ايجاد حل تقريبي لمثل هذه المشاكل في شكل متعددة الحدود في سلسلة من الخطوات المباشرة. أيضا ، تم افتراض أن مقام النواة

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 we proposed a new method for selecting a smoothing parameter in kernel estimator to estimate a nonparametric regression function in the presence of missing values. The proposed method is based on work on the golden ratio and Surah AL-E-Imran in the Qur'an. Simulation experiments were conducted to study a small sample behavior. The results proved the superiority the proposed on the competition method for selecting smoothing parameter.

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

          In the present research, a crane frame has been investigated by using finite element method. The damage is simulated by reducing the stiffness of assumed elements with ratios (10% and 20 %) in mid- span of the vertical column in crane frame. The cracked beam with a one-edge and non-propagating crack has been used. Six cases of damage are modeled for crane frame and by introducing cracked elements at different locations with ratio of depth of crack to the height of the beam (a/h) 0.1, 0.20. A FEM program coded in Matlab 6.5 was used to model the numerical simulation of the damage scenarios. The results showed a decreasing in the five natural frequencies from undamaged beam which means

 A New developed technique to estimate the necessary six elastic constants of homogeneous laminate of special orthotropic properties are presented in this paper for the first time. The new approach utilizes the elasto-static deflection behavior of composite cantilever beam employing the famous theory of Timoshenko. Three extracted strips of the composite plate are tested for measuring the bending deflection at two locations. Each strip is associated to a preferred principal axis and the deflection is measured in two orthogonal planes of the beam domain. A total of five trails of testing is accomplished and the numerical results of the stiffness coefficients are evaluated correctly under the contribution of the macromechanic

Trace Elements (Cd, Pb, Cu, Zn, Ni) level were examined in hair of donors from industrial areas, cities and village, and in permanent contact with a polluted workplace environment in lattakia. Hair sample were analyzed for their contents of the trace elements by inductivity coupled plasma- mass spectrometer (ICP- MS). It was found that the contents of (Cd, Pb, Cu, Zn, Ni) in the hair were significantly higher in the industrial areas and cities, while in the village had the lower concentration of elements. Correlation coefficients between the levels of the elements in hair found in this study showed that hair is a good indicator of Environmental Pollution.

In this paper , an efficient new procedure is proposed to modify third –order iterative method obtained by Rostom and Fuad [Saeed. R. K. and Khthr. F.W. New third –order iterative method for solving nonlinear equations. J. Appl. Sci .7(2011): 916-921] , using three steps based on Newton equation , finite difference method and linear interpolation. Analysis of convergence is given to show the efficiency and the performance of the new method for solving nonlinear equations. The efficiency of the new method is demonstrated by numerical examples.