Let be a non-trivial simple graph. A dominating set in a graph is a set of vertices such that every vertex not in the set is adjacent to at least one vertex in the set. A subset is a minimum neighborhood dominating set if is a dominating set and if for every holds. The minimum cardinality of the minimum neighborhood dominating set of a graph is called as minimum neighborhood dominating number and it is denoted by . A minimum neighborhood dominating set is a dominating set where the intersection of the neighborhoods of all vertices in the set is as small as possible, (i.e., ). The minimum neighborhood dominating number, denoted by , is the minimum cardinality of a minimum neighborhood dominating set. In other words, it is the smallest number of vertices needed to form a minimum neighborhood-dominating set. The concept of minimum neighborhood dominating set is related to the study of the structure and properties of graphs and is used in various fields such as computer science, operations research, and network design. A minimum neighborhood dominating set is also useful in the study of graph theory and has applications in areas such as network design and control theory. This concept is a variation of the traditional dominating set problem and adds an extra constraint on the intersection of the neighborhoods of the vertices in the set. It is also an NP-hard problem. The main aim of this paper is to study the minimum neighborhood domination number of the split graph of some of the graphs.
The research aims to investigate the possibility of joint auditing in improving the market value of Iraqi companies listed on the Iraq Stock Exchange. The sample was represented by 10 Iraqi companies listed in the Iraq market for the period from 2014-2017 (2 years before implementation and 2 years after implementation) and the research was based on the idea that joint auditing enhances investor confidence and raises their level of security as a result of providing quality and reliable reports, and thus This indicates good news in the market that reflects on the performance of stocks and the market value of companies that adopt joint auditing. The results of the analysis indicate an improvement in the market value, but this improv
... Show MoreThis research aims at building a proposed training program according to the self-regulated strategies for the mathematics teachers and to identify the effect of this program on relational Mathematics of teachers. The sample of the research was (60) Math teachers; (30) teachers as experimental group and (30) teachers as control group. The results of the current research reacheded that the proposed training program according to some self-managed learning strategies, meets the needs of trainees with remarkable effectiveness to improve the level of their teaching performance to achieve the desired goals. Training teacher according to self-managed learning strategies is effective in bringing about the transition of training to their students
... Show MoreThe main parameters and methods influencing the removal of Gentian Violet (GV) dye from aqueous media were investigated using a stachy plant in this study. The surface of the stachy plant was determined using FTIR spectra. Adsorption is influenced by the adsorbent's characteristic groups. The research took into account the usual conditions for GV dye adsorption by the stachy plant, such as the impact of contact time. Mass dosage , after 0.3 g the amount of adsorbed dye declines. Study pH and ionic strength, the results obtained showed that at pH 3 the largest adsorption of (GV) was seen, while at pH 9, the lowest adsorption was observed at 298 K, the adsorption kinetics and equilibrium constants were achieved, and the equilibr
... Show MoreThe catalytic cracking of three feeds of extract lubricating oil, that produced as a by-product from the process of furfural extraction of lubricating oil base stock in AL-Dura refinery at different operating condition, were carried out at a fixed bed laboratory reactor. The initial boiling point for these feeds was 140 ºC for sample (1), 86 ºC for sample (2) and 80 ºC for sample (3). The catalytic cracking processes were carried out at temperature range 325-400 ºC and initially at atmospheric pressure after 30 minutes over 9.88 % HY-zeolite catalyst load. The comparison between the conversion at different operating conditions of catalytic cracking processes indicates that a high yield was obtained at 375°C, according to gasoline pr
... Show MoreSimulation of free convection heat transfer in a square enclosure induced by heated thin plate is represented numerically. All the enclosure walls have constant temperature lower than the plate’s temperature. The flow is assumed to be two-dimensional. The discretized equations were solved stream function, vorticity, and energy equations by finite difference method using explicit technique and Successive Over- Relaxation method. The study was performed for different values of Rayleigh number ranging from 103 to 105 for different angle position of heated thin plate(0°, 45°, 90°). Air was chosen as a working fluid (Pr = 0.71). Aspect ratio of center of plate to the parallel left wall A2
... Show MoreThis research deals with a part of our heritage and Arab culture, which is the poetry of contemporary Islamic poets, especially the poetry that was said in the mother in contemporary Islamic poetry, when extrapolating the offices of some contemporary Islamic poets found a clear presence of the mother, and during the search for the subject or its I found that the subject did not receive research and study, although the bureaus of contemporary Islamic poets included in it a huge amount of verses in which they stood at the mother Pharthua, and expressed their feelings and emotions towards them, and accordingly this research tagged (mother in contemporary Islamic poetry _ Dr Artistic models in models of contemporary Islamic poetry) to stand
... Show MoreThis work deals with thermal cracking of heavy vacuum gas oil which produced from the top of vacuum distillation unit at Al- DURA refinery, by continuous process. An experimental laboratory plant scale was constructed in laboratories of chemical engineering department, Al-Nahrain University and Baghdad University. The thermal cracking process was carried out at temperature ranges between 460-560oC and atmospheric pressure with liquid hourly space velocity (LHSV) equal to 15hr-1.The liquid product from thermal cracking unit was distilled by atmospheric distillation device according to ASTM D-86 in order to achieve two fractions, below 220oC as a gasoline fraction and above 220oC as light cycle o
... Show MoreThe purpose of this study is to demonstrate a simple high sensitivity vapor sensor for propanol ((CH3)2CHOH). A free space gap was employed in two arms of a Mach-Zehnder interferometer to serve as the sensing mechanism by adding propanol volume (0.2, 0.4, 0.6, 0.8, and 1) ml and to set the phase reference with a physical spacing of (0.5, 1, 1.5, and 2) mm. The propagation constant of transmitted light in the Mach-Zehnder interferometer’s gap changes due to the small variation in the refractive index inside sensing arm that will further shift the optical phase of the signal. Experimental results indicated that the highest sensitivity of propanol was about 0.0275 nm/ml in different liquid volume while highest phase shift was 0.182×103 i
... Show MoreThis study aims to reveal the similarities and differences between Iraqi and Malay university learners and their genders in producing the supportive moves of criticism. To this end, 30 Iraqi and 30 Malay university learners have participated in this study. A Discourse Completion Test (DCT) and a Focus Group Interview (FGI) are conducted to elicit responses from the participants. Nguyen’s (2005) classification of criticism supportive moves is adapted to code the data. The data are analysed qualitatively and quantitatively. Overall, the findings unveil that both groups use similar categories of supportive moves, but Iraqis produce more of these devices than Malays in their criticisms. Although both females and males of both groups use id
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Praise be to God, Lord of the worlds, and prayers and peace be upon the most honorable of the prophets and messengers, our master Muhammad, and on the good God and his righteous companions.
For the most truthful hadith is the Book of God Almighty, and the best guidance is the guidance of the Prophet, may God bless him and grant him peace. If any)). Our good predecessor took care of collecting what they were able to collect and arrange from the words of the prophecy issued by our master Muhammad, peace and blessings be upon him, and wrote works on them including forms of support, parts, dictionaries, and mosques. About me, if any, in order to re