In this paper the modified trapezoidal rule is presented for solving Volterra linear Integral Equations (V.I.E) of the second kind and we noticed that this procedure is effective in solving the equations. Two examples are given with their comparison tables to answer the validity of the procedure.

Shatt al-Arab is the only navigational artery in Iraq, extending from the city of Qurna to its mouth in the Arabian Gulf at the city of Al-Fao within the governorate of Basrah for a length of approximately 204 km. Its width ranges from 400 m to 2000 m, and its depth ranges from 8 m to 20 m. The southern part of it, 93 km long from Umm al-Rassas Island to Ras al-Bisha, represents the international border between Iraq and Iran, where the Thalweg line represents the border between the two countries, which is the deepest point in the riverbed (according to the 1975 Algiers Agreement). The western bank (the Iraqi side) within the common border of Shatt al-Arab is subject to continuous erosion, which leads to the shifting of t

The importance of Public Relations activity has increased during the last half of the last century as a specialized and modern administrative function in most institutions. It has, moreover, become an integral part of activities of those institutions of various types, due to its pivotal role in building its reputation and drawing a good mental image among its audiences, as well as its influential and basic role in maintaining communication and the communication between its members at its various levels and their job tasks to ensure the greatest amount of understanding and to enhance trust between them. This is why public relations activity has become indispensable in all institutions, and without it, it is difficult to achieve any coordi

 A New developed technique to estimate the necessary six elastic constants of homogeneous laminate of special orthotropic properties are presented in this paper for the first time. The new approach utilizes the elasto-static deflection behavior of composite cantilever beam employing the famous theory of Timoshenko. Three extracted strips of the composite plate are tested for measuring the bending deflection at two locations. Each strip is associated to a preferred principal axis and the deflection is measured in two orthogonal planes of the beam domain. A total of five trails of testing is accomplished and the numerical results of the stiffness coefficients are evaluated correctly under the contribution of the macromechanic

The objective of this paper was to study the laser spot welding process of low carbon steel sheet. The investigations were based on analytical and finite element analyses. The analytical analysis was focused on a consistent set of equations representing interaction of the laser beam with materials. The numerical analysis based on 3-D finite element analysis of heat flow during laser spot welding taken into account the temperature dependence of the physical properties and latent heat of transformations using ANSYS code V.10.0 to simulate the laser welding process. The effect of laser operating parameters on the results of the temperature profile were studied in addition to the effect on thermal stresses  and dimensions of the laser w

This paper deals with constructing mixed probability distribution from mixing exponential

Comparative taxonomic study has been compeleted for the species of the. genus Centaurium Hill. of Iraq. So the morphological characters were studied comparatively for the first time form Iraqi materials. Stems, leaves ,infloresences and reproductive organs characters were a good taxonomic importance. Geographical distrtribution has been done for the species of the genus in addition to the environment information. The results were presented with schedules, tables, maps and micrographs. Taxonomic key for the species separation was also presented.