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, the construction of Hermite wavelets functions and their operational matrix of integration is presented. The Hermite wavelets method is applied to solve nth order Volterra integro diferential equations (VIDE) by expanding the unknown functions, as series in terms of Hermite wavelets with unknown coefficients. Finally, two examples are given

In this paper, we have been used the Hermite interpolation method to solve second order regular boundary value problems for singular ordinary differential equations. The suggest method applied after divided the domain into many subdomains then used Hermite interpolation on each subdomain, the solution of the equation is equal to summation of the solution in each subdomain. Finally, we gave many examples to illustrate the suggested method and its efficiency.

In this article four samples of HgBa₂Ca₂Cu_2.4Ag_0.6O_8+δ were prepared and irradiated with different doses of gamma radiation 6, 8 and 10 Mrad. The effects of gamma irradiation on structure of HgBa₂Ca₂Cu_2.4Ag_0.6O_8+δ samples were characterized using X-ray diffraction. It was concluded that there effect on structure by gamma irradiation. Scherrer, crystallization, and Williamson equations were applied based on the X-ray diffraction diagram and for all gamma doses, to calculate crystal size, strain, and degree of crystallinity. I

The goal of this paper is to design a robust controller for controlling a pendulum
system. The control of nonlinear systems is a common problem that is facing the researchers in control systems design. The Sliding Mode Controller (SMC) is the best solution for controlling a nonlinear system. The classical SMC consists from two phases. The first phase is the reaching phase and the second is the sliding phase. The SMC suffers from the chattering phenomenon which is considered as a severe problem and undesirable property. It is a zigzag motion along the switching surface. In this paper, the chattering is reduced by using a saturation function instead of sign function. In spite of SMC is a good method for controlling a nonlinear system b

The theory of Multi-Criteria Decision Making (MCDM) was introduced in the second half of the twentieth century and aids the decision maker to resolve problems when interacting criteria are involved and need to be evaluated.  In this paper, we apply MCDM on the problem of the best drug for rheumatoid arthritis disease. Then, we solve the MCDM problem via -Sugeno measure and the Choquet integral to provide realistic values in the process of selecting the most appropriate drug. The approach confirms the proper interpretation of multi-criteria decision making in the drug ranking for rheumatoid arthritis.

In computer vision, visual object tracking is a significant task for monitoring
applications. Tracking of object type is a matching trouble. In object tracking, one
main difficulty is to select features and build models which are convenient for
distinguishing and tracing the target. The suggested system for continuous features
descriptor and matching in video has three steps. Firstly, apply wavelet transform on
image using Haar filter. Secondly interest points were detected from wavelet image
using features from accelerated segment test (FAST) corner detection. Thirdly those
points were descripted using Speeded Up Robust Features (SURF). The algorithm
of Speeded Up Robust Features (SURF) has been employed and impl

In this study, we report a statistical study for the relationship between coronal mass ejections (CMEs) and sunspot number (SSN) that were registered during the period 2008-2017 for the solar cycle 24. SSN was extracted from Sunspot Index and Long-term Solar Observations (SILSO), while CMEs number from observations made by the Large Angle and Spectrometric Coronagraph (LASCO) on board the Solar and Heliospheric Observatory mission (SOHO). The present period was adopted to conduct the investigation and obtain the mutual correlation between SSN and CMEs. The relationship between CME, the speed of halo CME, and partial halo CMEs for solar cycle 24 were studied. The analysis of results indicated that the average speed of halo CMEs is almost

In this paper, a robust adaptive sliding mode controller is designed for a mobile platform trajectory tracking.  The mobile platform is an example of a nonholonomic mechanical system. The presence of holonomic constraints reduces the number of degree of freedom that represents the system model, while the nonholonomic constraints reduce the differentiable degree of freedom. The mathematical model was derived here for the mobile platform, considering the existence of one holonomic and two nonholonomic constraints imposed on system dynamics. The partial feedback linearization method was used to get the input-output relation, where the output is the error functions between the position of a certain point on the platform

In this article, the nonlinear problem of Jeffery-Hamel flow has been solved analytically and numerically by using reliable iterative and numerical methods. The approximate solutions obtained by using the Daftardar-Jafari method namely (DJM), Temimi-Ansari method namely (TAM) and Banach contraction method namely (BCM). The obtained solutions are discussed numerically, in comparison with other numerical solutions obtained from the fourth order Runge-Kutta (RK4), Euler and previous analytic methods available in literature. In addition, the convergence of the proposed methods is given based on the Banach fixed point theorem. The results reveal that the presented methods are reliable, effective and applicable to solve other nonlinear problems.