In a connected graph , the distance function between each pair of two vertices from a set vertex  is the shortest distance between them and the vertex degree  denoted by  is the number of edges which are incident to the vertex  The Schultz and modified Schultz polynomials of  are have defined as:

 respectively, where the summations are taken over all unordered pairs of distinct vertices in  and  is the distance between  and  in  The general forms of Schultz and modified Schultz polynomials shall be found and indices of the edge – identification chain and ring – square graphs in the present work.

In this research, an analysis for the standard Hueckel edge detection algorithm behaviour by using three dimensional representations for the edge goodness criterion is presents after applying it on a real high texture satellite image, where the edge goodness criterion is analysis statistically. The Hueckel edge detection algorithm showed a forward exponential relationship between the execution time with the used disk radius. Hueckel restrictions that mentioned in his papers are adopted in this research. A discussion for the resultant edge shape and malformation is presented, since this is the first practical study of applying Hueckel edge detection algorithm on a real high texture image containing ramp edges (satellite image).

 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

Many approaches of different complexity already exist to edge detection in
color images. Nevertheless, the question remains of how different are the results
when employing computational costly techniques instead of simple ones. This
paper presents a comparative study on two approaches to color edge detection to
reduce noise in image. The approaches are based on the Sobel operator and the
Laplace operator. Furthermore, an efficient algorithm for implementing the two
operators is presented. The operators have been applied to real images. The results
are presented in this paper. It is shown that the quality of the results increases by
using second derivative operator (Laplace operator). And noise reduced in a good

As modern radiotherapy technology advances, radiation dose and dose distribution have improved significantly. As part of a natural evolution, there has recently been renewed interest in therapy, particularly in the use of heavy charged particles, because these types of radiation serve theoretical advantages in all biological and physical aspects. The interactions of alpha particle with matter were studied and the stopping powers of alpha particle with Breast Tissue were calculated by using Beth-Bloch equation, Zeigler's formula and SRIM software, also the Range and Liner Energy Transfer (LET) and Breast Thickness As well as Dose and Dose equivalent for this particle were calculated by using Mat lab language for (0.01-200) MeV alpha ene

The bauxite produced from Al-Ga 'ara area in Al-Enbar containing 50.4 wt. percentages Al₂O₃ was used for a- alumina production.                                                                                                

For α-alumina pro

Nuclear medicine is important for both diagnosis and treatment. The most common treatment for diseases is radiation therapy used against cancer. The radiation intensity of the treatment is often less than its ability to cause damage, so radiation must be carefully controlled. The interactions of alpha particle with matter were studied and the stopping powers of alpha particle with ovary tissue were calculated using Beth-Bloch equation, Zeigler’s formula and SRIM Software also the range and Liner Energy Transfer (LET) and ovary thickness as well as dose and dose equivalent for this particle were calculated by using Matlab language for (0.01-200) MeV alpha energy.

In this paper We introduce some new types of almost bi-periodic points in topological bitransfprmation groups and thier effects on some types of minimaliy in topological dynamics