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

In this study, condensation polymerization was used to synthesize a number of novel liquid crystal polymers with 1,3,4-oxadiazole rings based on melamine. The new synthesized polymers were characterized by Fourier transform infrared (FTIR) and proton nuclear magnetic resonance (1HNMR) spectroscopy. Differential scanning calorimetry (DSC) and optical polarization microscopy (OPM) were used to investigate their liquid crystalline properties. The results demonstrated that throughout a wide temperature range, most of the polymers exhibited columnar (CohX) and nematic (N) liquid crystalline phases.

       The current study aimed at identifying the impact of each of the full and part time summer enrichment programs on the performance of gifted students. Moreover, it aimed to study the difference between the full and part time programs on the performance of gifted students. The study sample consisted of (115) students from the full time programs and (137) students from the part time programs, they have been randomly selected from the gifted students participating in the full and part time summer enrichment programs. The researcher used the scale of student performance. The results indicated that there were statistically significant differences between the averages of the pre and post applications of the

This study aims to find the effect of water-cement ratio on the compressive strength of concrete by using ultrasonic pulse velocity test (UPVT). Over 230 standard cube specimens were used in this study, with dimensions of 150mm, and concrete cubes were cured in water at 20 °C. Also, the specimens used in the study were made of concrete with varied water-cement ratio contents from 0.48 to 0.59. The specimens were taken from Diyarbakir-Turkey concrete centers and tested at the structure and material science lab, civil engineering, faculty of engineering from Dicle University.  The UPV measurement and compressive strength tests were carried out at the concrete age of 28 days. Their UPV and compressive strength ranged

Kurdistan power system is expanded along years ago. The electrical power is transmitted through long transmission lines. The main problem of transmission lines is active and reactive power losses. It is important to solve this issue, unless, the most of electrical energy will lost over transmission system. In this study, High Voltage Direct Current links/bipolar connection were connected in a power system to reduce the power losses. The 132kV, 50 Hz, 36 buses Kurdistan power system is used as a study case. The load flow analysis was implemented by using ETAP.16 program in which Newton-Raphson method for three cases. The results show that the losses are reduced after inserted HVDC links.

    The emergence of COVID-19 has resulted in an unprecedented escalation in different aspects of human activities, including medical education. Students and educators across academic institutions have confronted various challenges in following the guidelines of protection against the disease on one hand and accomplishing learning curricula on the other hand. In this short view, we presented our experience in implementing e-learning to the undergraduate nursing students during the present COVID-19 pandemic emphasizing the learning content, barriers, and feedback of students and educators. We hope that this view will trigger the preparedness of nursing faculties in Iraq to deal with this new modality of learning and improve it should t