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

After the designs for the house plan and the facade plan are completed, the construction implementation stages are proceeded. Below: Fig. 1 design Determining the plot of land, the building area and the spaces, and drawing the map by a specialized technical authority (engineer or engineering office) depending on the dimensions of the plot for example, building maps of 100 meters 5 by 20. Keywords: how, to, build, house

This paper is concerned with introducing and studying the new approximation operators based on a finite family of d. g. 'swhich are the core concept in this paper. In addition, we study generalization of some Pawlak's concepts and we offer generalize the definition of accuracy measure of approximations by using a finite family of d. g. 's.

Water flow into unsaturated porous media is governed by the Richards’ partial differential equation expressing the mass conservation and Darcy’s laws. The Richards’ equation may be written in three forms,where the dependent variable is pressure head or moisture content, and the constitutive relationships between water content and pressure head allow for conversion of one form into the other. In the present paper, the “moisture-based" form of Richards’ equation is linearized by applying Kirchhoff’s transformation, which
combines the soil water diffusivity and soil water content. Then the similarity method is used to obtain the analytical solution of wetting front position. This exact solution is obtained by means of Lie’s

The study's primary purpose is to explore an appropriate way of monitoring and assessing water depths using the satellite remote sensing technique of the Al Habbaniyah Lake in Iraq. This research studied the experience-conditions (thresholds) of different bands for multi-temporal satellite image data with different satellite image sensors (Landsat 5-TM, and EO1-ALI) for the same region, to recognize regions of water depths. The threshold values are taken that to separate the Al Habbaniyah Lake to the required depths (shallow, deep, and very deep), as a supervised method. A three-dimension feature space plot had used to represent these regions. The relationship of the mean values of the three separated water regions with all TM and A