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.

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.

Systems on Chips (SoCs) architecture complexity is result of integrating a large numbers of cores in a single chip. The approaches should address the systems particular challenges such as reliability, performance, and power constraints. Monitoring became a necessary part for testing, debugging and performance evaluations of SoCs at run time, as On-chip monitoring is employed to provide environmental information, such as temperature, voltage, and error data. Real-time system validation is done by exploiting the monitoring to determine the proper operation of a system within the designed parameters. The paper explains the common monitoring operations in SoCs, showing the functionality of thermal, voltage and soft error monitors. The different

In this study, a brand-new graph definition known Associate graph of a ring R denote Ass(R) is present, where the graph’s vertices stand in for R’s elements s.t, any two vertices α and β  merage by an edge if and only if α = rβ and β = sα. In this paper, we investigated some new property of Ass (R)  are studied., the complement of Ass (R) is finally defined and a few of its characteristics are researched.

The aim of this paper is to study the Zariski topology of a commutative KU-algebra. Firstly, we introduce new concepts of a KU-algebra, such as KU-lattice, involutory ideal and prime ideal and investigate some basic properties of these concepts. Secondly, the notion of the topology spectrum of a commutative KU-algebra is studied and several properties of this topology are provided. Also, we study the continuous map of this topological space.

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

The current research includes a look at the participation of Iraqi women in the combat roles, which starts from the assumption of the democratic transition that must be led - in one of its aspect - until the army or the military foundation to become a "citizen army," the matter which is represented a demand increasingly needed in the experiences of Democratic transformation that facing serious security challenges such as in Iraq, this means that the army or security foundation - which is involved in counterterrorism - should not reflect a specific group in society , and hence embody the most important democratic principles, which are equality and equal opportunities, especially gender equality. On the other hand, the influence of armed conf

Rheumatoid arthritis (RA) is a chronic inflammatory disease associated with decreased antioxidant state .This study aim to investigate the status of oxidant/antioxidant in a sample of  Iraqi patients with RA and the role of peroxynitrite and its natural scavenger uric acid in them .This case-controlled study was conducted at Baghdad teaching hospital /Baghdad from December 2010-May 2011 . Twenty-five patients with mean age 39 years and 25 apparently healthy subject as controls with mean age 29 years were included in the study .Investigations include estimation of serum levels of nitric oxide (NO)  ,peroxynitrite (PN) , malondialdehyde (MDA)  , and uric acid (UA) .Serum PN levels were significantly elevated in RA patients a