Cantilever beams are used in many crucial applications in machinery and construction. For example, the airplane wing, the microscopic probe for atomic force measurement, the tower crane overhang and twin overhang folding bridge are typical examples of cantilever beams. The current research aims to develop an analytical solution for the free vibration problem of cantilever beams. The dynamic response of AISI 304 beam represented by the natural frequencies was determined under different working surrounding temperatures ((-100 ℃ to 400 ℃)). A Matlab code was developed to achieve the analytical solution results, considering the effect of some beam geometrical dimensions. The developed analytical solution has been verified successfully wi

    In this paper, the finite difference method is used to solve fractional hyperbolic partial differential equations, by modifying the associated explicit and implicit difference methods used to solve fractional  partial differential equation. A comparison with the exact solution is presented and the results are given in tabulated form in order to give a good comparison with the exact solution

The CdS quantum dots were prepared by chemical reaction
of cadmium oleylamine (Cd –oleylamine complex) with the
sulfite-oleylamine (S-oleylamine) with 1:6 mole ratios. The
optical properties structure and spectroscopy of the product
quantum dot were studied. The results show the dependence of the
optical properties on the crystal dimension and the formation of
the trap states in the energy band gap.

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.

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.

In this paper, a method based on modified adomian decomposition method for solving Seventh order integro-differential equations (MADM). The distinctive feature of the method is that it can be used to find the analytic solution without transformation of boundary value problems. To test the efficiency of the method presented two examples are solved by proposed method.

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

This paper focuses on the optimization of drilling parameters by utilizing “Taguchi method” to obtain the minimum surface roughness. Nine drilling experiments were performed on Al 5050 alloy using high speed steel twist drills. Three drilling parameters (feed rates, cutting speeds, and cutting tools) were used as control factors, and L9 (3³) “orthogonal array” was specified for the experimental trials. Signal to Noise (S/N) Ratio and “Analysis of Variance” (ANOVA) were utilized to set the optimum control factors which minimized the surface roughness. The results were tested with the aid of statistical software package MINITAB-17. After the experimental trails, the tool diameter was found as the most important facto