This research aims to solve the problem of selection using clustering algorithm, in this research optimal portfolio is formation using the single index model, and the real data are consisting from the stocks Iraqi Stock Exchange in the period 1/1/2007 to 31/12/2019. because the data series have missing values ,we used the two-stage missing value compensation method, the knowledge gap was inability the portfolio models to reduce The estimation error , inaccuracy of the cut-off rate and the Treynor ratio combine stocks into the portfolio that caused to decline in their performance, all these problems required employing clustering technic to data mining and regrouping it within clusters with similar characteristics to outperform the portfolio

This paper introduces some properties of separation axioms called α -feeble regular and α -feeble normal spaces (which are weaker than the usual axioms) by using elements of graph which are the essential parts of our α -topological spaces that we study them. Also, it presents some dependent concepts and studies their properties and some relationships between them.

In this paper we show that if ? Xi is monotonically T2-space then each Xi is monotonically T2-space, too. Moreover, we show that if ? Xi is monotonically normal space then each Xi is monotonically normal space, too. Among these results we give a new proof to show that the monotonically T2-space property and monotonically normal space property are hereditary property and topologically property and give an example of T2-space but not monotonically T2-space.

The samples were collected monthly crustaceans Mjmafah foot of two stations in tributary Zab down and two others in the Tigris River for one year with effect from November 2001 until October 2002 recorded during the study period the current 41 units taxonomic and were higher density of Mjmafah foot Guy Tigris River before the mouth of the tributary

In this research we study the effect of UV radiation on pure PC samples and doped samples with plasticizer (DOP) for different exposure times (6, 12, 18, 24h). The study have been made on the change in the IR spectra causes by the UV radiation on both kinds of samples, besides the morphology changes were also studied by the optical microscope. From the results we conclude that the increasing of exposure causes the elaboration of CO₂ and C₂ gases.