The metric dimension and dominating set are the concept of graph theory that can be developed in terms of the concept and its application in graph operations. One of some concepts in graph theory that combine these two concepts is resolving dominating number. In this paper, the definition of resolving dominating number is presented again as the term dominant metric dimension. The aims of this paper are to find the dominant metric dimension of some special graphs and corona product graphs of the connected graphs  and , for some special graphs  . The dominant metric dimension of  is denoted by  and the dominant metric dimension of corona product graph G and H is denoted by .

In this paper, we introduce an exponential of an operator defined on a Hilbert space H, and we study its properties and find some of properties of T inherited to exponential operator, so we study the spectrum of exponential operator e^T according to the operator T.

he effect of different cultural conditions on production of bioemulsifier from Serratia marcescens S10 was determined; different carbon and nitrogen sources were used such as: different oils include: edible (vegetable) oils (olive oil, sesame oil, sun flower oil and corn oil) and heavy oils (oil 150, oil 60, oil 40) as carbon sources and (NH4Cl, casein, (NH4)2SO4, peptone, tryptone, gelatin and yeast extract) as nitrogen sources were added to production media. Bioemulsifier was estimated by measuring the surface tension (S.T), emulsification activity (E.A) and emulsification index (E24%). The best results of bioemulsifier production from Serratia marcescens S10 were obtained at pH8 and incubated at 37ºC for 5days, using sesame oil

A computational investigation is carried out in the field of charged –particle optics with the aid of numerical analysis method using the personal computer. The work is concerned with the design of electron gun with space-charge effect. The Finite element method (FEM) used in the solution of Poison's equation for determine the axial potential distribution of the two-electrode immersion lens operated under zero magnification condition , and from the solution of the paraxial ray equation the optical properties such as the focal length , spherical and chromatic aberration coefficients are determined, also a calculation of the brightness and perveance for the lens. The electrodes geometry was determined in two and three dimensi

For a nonempty subset X of a group G and a positive integer m , the product of X , denoted by Xm ,is the set Xm = That is , Xm is the subset of G formed by considering all possible ordered products of m elements form X. In the symmetric group Sn, the class Cn (n odd positive integer) split into two conjugacy classes in An denoted Cn+ and Cn- . C+ and C- were used for these two parts of Cn. This work we prove that for some odd n ,the class C of 5- cycle in Sn has the property that = An n 7 and C+ has the property that each element of C+ is conjugate to its inverse, the square of each element of it is the element of C-, these results were used to prove that C+ C- = An exceptio

The present paper focuses on the nature of the different interactions between cometary nucleus and tail with solar wind. The dynamics of the comet will impose many features that provide unique behavior of the comet when entering the solar system. These features are reviewed in this paper and few investigations are made. The calculations made in this work represent the analysis and interpretation of the different features of the comet, such as perihelion and eccentricity dependence on the gas production rate, and the dependence of the latter on the composition of the comet nucleus. The dependences of the heliocentric, bow shock, contact surface, and stand-off distances with gas production rate for many types of comets that cover linear and n

This study delves into the properties of the associated act V over the monoid S of sinshT. It examines the relationship between faithful, finitely generated, and separated acts, as well as their connections to one-to-one and onto operators. Additionally, the correlation between acts over a monoid and modules over a ring is explored. Specifically, it is established that  functions as an act over S if and only if  functions as module, where T represents a nilpotent operator. Furthermore, it is proved that when T is onto operator and  is finitely generated, is guaranteed to be finite-dimensional. Prove that for any bounded operator the following,  is acting over S if and only if  is a module where T is a nilpotent operator, is a