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 .

An advertisement is a form of communication intended to promote the sale of a product or service, influence public opinion, gain political support, or to elicit some other response. It consists of various type, including style, target audience, geographic scope, medium, or purpose. An advertisement should catch a person's attention and quickly create a memorable impression. The main aim of the present paper is to investigate the phonological problems of translating English international TV advertisements into Arabic. It deals with the most common and popular TV advertisements. The importance of such advertisements lies not in its information content rather than in the achievement of the desired impact on the receivers. When translating such

Let G be a graph, each edge e of which is given a weight w(e). The shortest path problem is a path of minimum weight connecting two specified vertices a and b, and from it we have a pre-topology. Furthermore, we study the restriction and separators in pre-topology generated by the shortest path problems. Finally, we study the rate of liaison in pre-topology between two subgraphs. It is formally shown that the new distance measure is a metric

The purpose of this paper is to solve the stochastic demand for the unbalanced transport problem using heuristic algorithms to obtain the optimum solution, by minimizing the costs of transporting the gasoline product for the Oil Products Distribution Company of the Iraqi Ministry of Oil. The most important conclusions that were reached are the results prove the possibility of solving the random transportation problem when the demand is uncertain by the stochastic programming model. The most obvious finding to emerge from this work is that the genetic algorithm was able to address the problems of unbalanced transport, And the possibility of applying the model approved by the oil products distribution company in the Iraqi Ministry of Oil to m

     In this paper, the Adomian decomposition method (ADM) is successfully applied to find the approximate solutions for the system of fuzzy Fredholm integral equations (SFFIEs) and we also study the convergence of the technique. A consistent way to reduce the size of the computation is given to reach the exact solution. One of the best methods adopted to determine the behavior of the approximate solutions. Finally, the problems that have been addressed confirm the validity of the method  applied in this research using a comparison by combining numerical methods such as the Trapezoidal rule and Simpson rule with ADM.

The aim of this article is to solve the Volterra-Fredholm integro-differential equations of fractional order numerically by using the shifted Jacobi polynomial collocation method. The Jacobi polynomial and collocation method properties are presented. This technique is used to convert the problem into the solution of linear algebraic equations. The fractional derivatives are considered in the Caputo sense. Numerical examples are given to show the accuracy and reliability of the proposed technique.

A (k,n)-arc A in a finite projective plane PG(2,q) over Galois field GF(q), q=pⁿ for same prime number p and some integer n≥2, is a set of k points, no n+1 of which are collinear.  A (k,n)-arc is complete if it is not contained in a(k+1,n)-arc.  In this paper, the maximum complete (k,n)-arcs, n=2,3 in PG(2,4) can be constructed from the equation of the conic.