The financial market plays an important role in influencing the economic sectors, including the private industrial sector, through the provision of capital and transfer from savers to investors for the purpose of establishing or expanding projects. Therefore, the financial market is one of the important tools in stimulating the economy in general and the industrial sector in particular, Through the inclusion of industrial companies in the financial market and the introduction of industrial shares to the public, and then provide the necessary funding to stimulate the private industrial sector, Iraq is one of the oil-dependent countries on the oil sector mainly, which lacks industrial production, which is from Are the sectors that

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 An edge dominating set    of a graph  is said to be an odd (even) sum degree edge dominating set (osded (esded) - set) of G if the sum of the degree of all edges in X is an odd (even) number. The odd (even) sum degree edge domination number  is the minimum cardinality taken over all odd (even) sum degree edge dominating sets of G and is defined as zero if no such odd (even) sum degree edge dominating set exists in G. In this paper, the odd (even) sum degree domination concept is extended on the co-dominating set E-T of a graph G, where T is an edge dominating set of G.  The corresponding parameters co-odd (even) sum degree edge dominating set, co-odd (even) sum degree edge domination number and co-odd (even) sum degree edge domin

     Numerical simulations were carried out to evaluate the effects of different aberrations modes on the performance of optical system, when observing and imaging the solar surface. Karhunen-Loeve aberrations modes were simulated as a wave front error in the aperture function of the optical system. To identify and apply the appropriate rectification that removes or reduces various types of aberration, their attribute must be firstly determined and quantitatively described. Wave aberration function is well suitable for this purpose because it fully characterizes the progressive effect of the optical system on the wave front passing through the aperture. The Karhunen-Loeve polynomials for circular aperture were used to

The aim of this paper is to employ the fractional shifted Legendre polynomials (FSLPs) in the matrix form to approximate the fractional derivatives and find the numerical solutions of the one-dimensional space-fractional bioheat equation (SFBHE). The Caputo formula was utilized to approximate the fractional derivative. The proposed methodology applied for two examples showed its usefulness and efficiency. The numerical results showed that the utilized technique is very efficacious with high accuracy and good convergence.

This study presents a practical method for solving fractional order delay variational problems. The fractional derivative is given in the Caputo sense. The suggested approach is based on the Laplace transform and the shifted Legendre polynomials by approximating the candidate function by the shifted Legendre series with unknown coefficients yet to be determined. The proposed method converts the fractional order delay variational problem into a set of (n ＋ 1) algebraic equations, where the solution to the resultant equation provides us the unknown coefficients of the terminated series that have been utilized to approximate the solution to the considered variational problem. Illustrative examples are given to show that the recommended appro