In this paper, the homotopy perturbation method (HPM) is presented for treating a linear system of second-kind mixed Volterra-Fredholm integral equations. The method is based on constructing the series whose summation is the solution of the considered system. Convergence of constructed series is discussed and its proof is given; also, the error estimation is obtained. Algorithm is suggested and applied on several examples and the results are computed by using MATLAB (R2015a). To show the accuracy of the results and the effectiveness of the method, the approximate solutions of some examples are compared with the exact solution by computing the absolute errors.

This manuscript presents several applications for solving special kinds of ordinary and partial differential equations using iteration methods such as Adomian decomposition method (ADM), Variation iterative method (VIM) and Taylor series method. These methods can be applied as well as to solve nonperturbed problems and 3rd order parabolic PDEs with variable coefficient. Moreover, we compare the results using ADM, VIM and Taylor series method. These methods are a commination of the two initial conditions.

In this paper we prove the boundedness of the solutions and their derivatives of the second order ordinary differential equation x ?+f(x) x ?+g(x)=u(t), under certain conditions on f,g and u. Our results are generalization of those given in [1].

In this research is estimated the function of reliability dynamic of multi state systems  and their compounds and for three types of systems (serial, parallel, 2-out-of-3) and about two states (Failure and repair) depending on calculating the structur function allow to describing the behavior of

         In this paper, developed Jungck contractive mappings into fuzzy Jungck contractive and proved  fuzzy fixed point for some types of generalize fuzzy Jungck contractive mappings.

The aims of this study are to explore the commercial artifacts in the following three kinds of vegetables oils, Nigella Sativa, Trigonella foenum-graecum Linn,and Zingiber officinale. These oils have been very popular medicinal plants which are commonly used in traditional medicine .These commercial oils have been compared with the extracts of these plants.
The physical properties of extracts and commercial oils of these plants have been stuied. We observed that the refractive index of the plants matches and non-significant, while specific gravity of Nigella Sativa has similar specific gravity in both extracts and commercial oil in contrast with Trigonella foenum Linn,and Zingiber officinale and we found significant difference (P&lt

   The main focus of this research is to examine the Travelling Salesman Problem (TSP) and the methods used to solve this problem where this problem is considered as one of the combinatorial optimization problems which met wide publicity and attention from the researches for to it's simple formulation and important applications and engagement to the rest of combinatorial problems , which is based on finding the optimal path through known number of cities where the salesman visits each city only once before returning to the city of departure n this research , the benefits  of( FMOLP)   algorithm is employed as one of the best methods to solve the (TSP) problem and the application of the algorithm in conjun

The study deals with the issue of multi-choice linear mathematical programming. The right side of the constraints will be multi-choice. However, the issue of multi-purpose mathematical programming can not be solved directly through linear or nonlinear techniques. The idea is to transform this matter into a normal linear problem and solve it In this research, a simple technique is introduced that enables us to deal with this issue as regular linear programming. The idea is to introduce a number of binary variables And its use to create a linear combination gives one parameter was used multiple. As well as the options of linear programming model to maximize profits to the General Company for Plastic Industries product irrigation sy

The changes that happen in training progress especially in skill side demands tests researchers found poorness for patterns to special tests in defending skills against shooting although applying these tests on other samples without considering the age , so the problem of research came controlling the tests of defense against shooting that serve juniors players and match the original society to serve the basketball game . The research sample chosen for juniors players for Baghdad clubs in season (2011-2012) the sample numbered (82) players represented (7) clubs that their percentage (82%) , after gaining the data processed statically and we reached to conclusion that : defending tests against shooting applied first time in Iraq in Iraq envi

In this work, we introduce a new kind of perfect mappings, namely j-perfect mappings and j-ω-perfect mappings. Furthermore we devoted to study the relationship between j-perfect mappings and j-ω-perfect mappings. Finally, certain theorems and characterization concerning these concepts are studied; j = , δ, α, pre, b, β