The concept of the order sum graph associated with a finite group based on the order of the group and order of group elements is introduced. Some of the properties and characteristics such as size, chromatic number, domination number, diameter, circumference, independence number, clique number, vertex connectivity, spectra, and Laplacian spectra of the order sum graph are determined. Characterizations of the order sum graph to be complete, perfect, etc. are also obtained.

We used to think of grammar as the bones of the language and vocabulary as the flesh to be added given that language consisted largely of life generated chunks of lexis. This “skeleton image” has been proverbially used to refer to that central feature of lexis named collocation- an idea that for the first 15 years of language study and analysis gave a moment‟s thought to English classroom material and methodology.
The work of John Sinclair, Dave Willis, Ron Carter, Michael McCarthy, Michael Lewis, and many others have all contributed to the way teachers today approach the area of lexis and what it means in the teaching/learning process of the language. This also seems to have incorporated lexical ideas into the teaching mechanis

An energy and exergy thermodynamic analysis using EES program was done for a domestic refrigerator working with R-134a using vapor compression refrigeration cycle. The analysis deals with the system component, i.e. compressor, condenser, evaporator and the expansion device. The analysis depends on the entropy generation minimization approach to improve the refrigerator performance by exploring the optimum design points. These design points were derived from three different theories governing the entropy generation minimization using exergy analyzing method. These theories were first applied to find the optimum balance between the hot inner condenser area and the cold inner evaporator area of the refrigerator and between

A new definition of a graph called Pure graph of a ring denote Pur(R) was presented , where the vertices of the graph represent the elements of R such that there is an edge between the two vertices ???? and ???? if and only if ????=???????? ???????? ????=????????, denoted by pur(R) . In this work we studied some new properties of pur(R) finally we defined the complement of pur(R) and studied some of it is properties

This paper generalizes and improves the results of Margenstren, by proving that the number of -practical numbers  which is defined by   has a lower bound in terms of . This bound is more sharper than Mangenstern bound when  Further general results are given for the existence of -practical numbers, by proving that the interval contains a -practical for all

In this paper, various aspects of smart grids are described. These aspects include the components of smart grids, the detailed functions of the smart energy meters within the smart grids and their effects on increasing the awareness, the advantages and disadvantages of smart grids, and the requirements of utilizing smart grids. To put some light on the difference between smart grids and traditional utility grids, some aspects of the traditional utility grids are covered in this paper as well.

Iraq has a huge network of pipelines, transport crude oil and final hydrocarbon products as well as portable water. These networks are exposed to extensive damage due to the underground corrosion processes unless suitable protection techniques are used. In this paper we collect the information of cathodic protection for pipeline in practical fields (Oil Group in Al Doura), to obtain data base to understand and optimize the design which is made by simulation for the environmental factors and cathodic protection variables also soil resistivity using wenner four terminal methods for survey sites; and soil pH investigations were recorded for these selected fields were within 7-8, and recording the anodes voltage and its related currents for

Abstract

Magnetic abrasive finishing (MAF) is one of the advanced finishing processes, which produces a high level of surface quality and is primarily controlled by a magnetic field. This paper study the effect of the magnetic abrasive finishing system on the material removal rate (MRR) and surface roughness (Ra) in terms of magnetic abrasive finishing system for eight of input parameters, and three levels according to Taguchi array (L27) and using the regression model to analysis the output (results). These parameters are the (Poles geometry angle, Gap between the two magnetic poles, Grain size powder, Doze of the ferromagnetic abrasive powder, DC current, Workpiece velocity, Magnetic poles velocity, and Finishi