In this paper, the Magnetohydrodynamic (MHD) for Williamson fluid with varying temperature and concentration in an inclined channel with variable viscosity has been examined. The perturbation technique in terms of the Weissenberg number  to obtain explicit forms for the velocity field has been used. All the solutions of physical parameters of the Darcy parameter , Reynolds number , Peclet number  and Magnetic parameter  are discussed under the different values as shown in plots.

The purpose of this paper is to apply different transportation models in their minimum and maximum values by finding starting basic feasible solution and finding the optimal solution. The requirements of transportation models were presented with one of their applications in the case of minimizing the objective function, which was conducted by the researcher as real data, which took place one month in 2015, in one of the poultry farms for the production of eggs

Aims to find out the (Extent of mathematics teachers' appreciation of the mathematical problem `multiple solutions) Research sample consisted of (100) mathematics teachers distributed on the General Directorates of Education in Baghdad (Rusafa 1/2/3) and (Karkh 1/2/ 3) There was two research approach which are: The first - two different answers of students to the same issue where teachers must assess each answer and explain which one the teacher will accept and why? The second - Different solutions of students' to the same issue, including wrong answers , Teachers should correct the answers and give them final grades (0-10). Descriptive and analytical Approch was used in this research methodology And zero hypotheses, which are as f

in this paper sufficient conditions of oscillation of all of nonlinear second order neutral differential eqiation and sifficient conditions for nonoscillatory soloitions to onverage to zero are obtained

The toxicity effect of some heavy metals (Lead, Cadmium, Copper, and Zinc) on the growth of alga Scenedesmus dimorphus which belongs to the Division of Chlorophyta was studied and depended on the total cell number . The growth rate and doubling time were also calculated accordingly in present of absent of the the heavy metals . There were differences in toxic effects of the metals (p<0.05) . The growth was decreased gradually with alga when exposured to Lead at 15,20 and 25 mg/l in comparison with the control , mean while 30 mg/l caused an acute decrease in growth . Treating the alga with 0.05,0.1,0.5 mg/l concentration of Cadmium the number of cells decreased while at 1 mg/l the effect was more pronounced . As for Copper the conc

This paper contains an equivalent statements of a pre-  space, where  are considered subsets of with the product topology. An equivalence relation between the preclosed set  and a pre-  space, and a relation between a pre-  space and the preclosed set  with some conditions on a function  are found. In addition, we have proved that the graph  of  is preclosed in if  is a pre-  space, where the equivalence relation  on  is open.

     On the other hand, we introduce the definition of a pre-stable ( pre-stable) set by depending on the concept of a pre-neighborhood, where we get that every stable set is pre-stable. Moreover, we obtain that