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.
In this study, we fabricated nanofiltration membranes using the electrospinning technique, employing pure PAN and a mixed matrix of PAN/HPMC. The PAN nanofibrous membranes with a concentration of 13wt% were prepared and blended with different concentrations of HPMC in the solvent N, N-Dimethylformamide (DMF). We conducted a comprehensive analysis of these membranes' surface morphology, chemical composition, wettability, and porosity and compared the results. The findings indicated that the inclusion of HPMC in the PAN membranes led to a reduction in surface porosity and fiber size. The contact angle decreased, indicating increased surface hydrophilicity, which can enhance flux and reduce fouling tendencies. Subsequently, we evaluated the e
... Show MoreThe research aims to extrapolate the repercussions of the use of expert systems in the work of the external auditor on the quality of audit, as the research problem was that despite the use of these techniques in audit work, there is a problem related to the efficiency and effectiveness of these technological systems used in audit work, the feasibility of their use and the extent of their impact: The quality of the audit process.
The researchers adopted the questionnaire as a tool for collecting study data from a community composed of auditors in auditing offices and companies in Iraq, and the auditors of the Iraqi Federal Financial Supervision Bureau. The number of recovered and valid qu
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Ferrite with the general formula CuLayFe2-yO4 (where y=0.02, 0.04, 0.06, 0.08 and 0.1), were prepared by standard ceramic technique. The main cubic spinel structure phase for all samples was confirmed by x-ray diffraction patterns with the appearance of small amount of secondary phases. The lattice parameter results were 8.285-8.348 Å. X-ray density increased with La addition and showed values between 5.5826 – 5.7461gm/cm3. The Atomic Force Microscopy (AFM) showed that the average grain size was decreasing with the increase in La concentration. The Hall coefficient was found to be positive. It de |
Aim: The purpose of this study is to compare the effect of epineurotomy of median nerve with just division of the transverse carpal ligament in the treatment of carpal tunnel syndrome. Patients & Methods: We conducted a prospective, random study to evaluate the effect of epineurotomy on the outcome of operative treatment of established median-nerve compression in the carpal canal. Fifty hands (forty-four patients) were selected randomly into two groups: group I had a release of the transverse carpal ligament alone, and group II had a release and adjuvant epineurotomy of the median nerve. The groups were similar with regard to age group, gender, duration of symptoms, and preoperative physical findings. All patients had electrophysiological e
... Show MoreBuckling and free vibration analysis of laminated rectangular plates with uniform and non uniform distributed in-plane compressive loadings along two opposite edges is performed using the Ritz method. Classical laminated plate theory is adopted. The static component of the applied in- plane loading are assumed to vary according to uniform, parabolic or linear distributions. Initially, the plate membrane problem is solved using the Ritz method; subsequently, using Hamilton’s variational principle, linear homogeneous algebraic equations in terms of unknown are generated, the set of linear algebraic equations can be solved as an Eigen-value problem. Buckling loads for laminated plates with different combinations of bounda
... Show MoreThe dynamics of a single condensing two-phase bubble of two different dispersed-continuous systems were studied. The systems were, CCl4 - water and CCl4 - 100% glycerol. Cinephotography was used to determine the change in height, diameter and time. These results were used to determine the experimental rise velocity of the bubble, which was compared with a theoretical one based on some equations used. It was found that the velocity of the first system remained almost constant, while it decreased gradually for the second system.
The interest in calcium phosphates arises from the fact that bones contain a high percentage of mineralized calcium phosphate . In this study, pure and biocompatible hydroxyapatite (HAP) powder was successfully synthesized using hen’s egg shell as calcium source and phosphoric acid by precipitation method.The precipitate obtained was subjected to ripenning process for 24 hours, filtered, air dried, and calcined at temperatures of 400,800,900,and 1000 ºC.
X-Ray diffraction(XRD) technique was used to investigate the formation of HAP powder, XRD results revealed the HAP formation and also indicate no occurrence of secondary phases. Fourier Transform Infrared(FT-IR) spectrum shows the characterstic peaks for phosphate and hydroxyl grou
Receipt date:10/8/2019 acceptance date:18/12/2019 Publication date:31/12/2021
This work is licensed under a Creative Commons Attribution 4.0 International License.
This research is concerned with the concept of identity in general "Overall definition" and is not exposed to the classifications of identity or concepts that deal with their types and classifications, only the concept in terms of the initial picture as well as the views of thinkers on the proof of
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