Number theorists believe that primes play a central role in Number theory and that solving problems related to primes could lead to the resolution of many other unsolved conjectures, including the prime k-tuples conjecture. This paper aims to demonstrate the existence of this conjecture for admissible k-tuples in a positive proportion. The authors achieved this by refining the methods of “Goldston, Pintz and Yildirim” and “James Maynard” for studying bounded gaps between primes and prime k-tuples. These refinements enabled to overcome the previous limitations and restrictions and to show that for a positive proportion of admissible k-tuples, there is the existence of the prime k-tuples conjecture holding for each “k”. The sig

In this paper, we study the growth of solutions of the second order linear complex differential equations  insuring that any nontrivial solutions are of infinite order. It is assumed that the coefficients satisfy the extremal condition for Yang’s inequality and the extremal condition for Denjoy’s conjecture. The other condition is that one of the coefficients itself is a solution of the differential equation .

The purpose of this paper is to apply different transportation models in their minimum and maximum values by finding starting basic feasible solution and finding the optimal solution. The requirements of transportation models were presented with one of their applications in the case of minimizing the objective function, which was conducted by the researcher as real data, which took place one month in 2015, in one of the poultry farms for the production of eggs

Abstract

Objective(s): The study aims to measure the effectiveness of the program on removing dead tissue for burn patients by testing the nurses before the program in addition to testing them again after implementing the educational program.

Methodology: The study is quantitative in nature (one experimental) and will employ pre- and post-testing techniques between October 17, 2020 and March 20, 2022. A non-probability (purposive) sample of 24 nurses working in the Azadi Teaching Hospital's Burns and Plastic Surgery Center was chosen. The experimental survey of nursing practice, a literature review, scientific records, and previous research were all taken into considerat

Objective(s):        The study aims to evaluate the information of the elderly about personal hygiene , and to find out the relationship between residents of geriatric-care homes knowledge and their demographic characteristics .

Methodology:      A quasi-experimental design study is conducted at geriatric home  in Al Cyelakh  Geriatric Care Home. The study was started at between November 20, 2021, and March 1, 2023. randomly sample of (30) elderly  in geriatric home were studied . Data were collected throughout the utilization of the adopted questionnaire and interview technique. The questionnaire was consists of (40) items related to concerned personal hygiene geriatrics persons, t

Consider a simple graph   on vertices and edges together with a total  labeling . Then ρ is called total edge irregular labeling if there exists a one-to-one correspondence, say  defined by  for all  where  Also, the value  is said to be the edge weight of . The total edge irregularity strength of the graph G is indicated by  and is the least  for which G admits   edge irregular h-labeling.  In this article,   for some common graph families are examined. In addition, an open problem is solved affirmatively.

The study aimed to identify the perceptions of social studies teachers in the Governorate of Muscat about the importance of employing the skills of the twenty-first century in teaching. The study employed a qualitative approach. The two researchers used an analytical approach based on the Grounded Theory, the data was gathered through semi-structured interviews with (15) male and female teachers. The results indicated that social studies teachers relate the twenty-first-century skills more to improving students’ achievement level in the subject, while they see that these skills have less influence in developing students’ communication skills and cooperation with their peers. In light of the results of the study, the two researchers r

The research problem is clearly deficient suffered by the internal audit function in all institutions of Iraq, as a result of the lack of sponsor organizations for this profession and there is no law or local legislation determine its powers and its responsibilities and scope of work As well as the lack of interest of senior management in economic units that function, as it focuses its work on the scope of financial and accounting matters only So required to rebuild this function in line with the current developments as well as the lack of a framework that defines the strategy of this function, and it came the idea of research to find out how to create a regulatory method for re-strategic construction of the internal audit function depen

 Improving speaking skills of Iraqi EFL students was the main purpose of the current research. Thirty EFL students were selected as the research participants for achieving this aim. All students completed the pretest and then spent the next 25 weeks meeting for 90 minutes each to present their nine lectures, answer difficult questions, and get feedback on their use of language in context. Progressive-tests, posttests and delayed post-tests followed every three courses. The researcher utilized SPSS 22 to anal Analyze the data descriptively and inferentially after doing an ANOVA on repeated measurements. It has been shown that using the ideas of sociocultural theory in the classroom has an important and positive impact on students of

 An edge dominating set    of a graph  is said to be an odd (even) sum degree edge dominating set (osded (esded) - set) of G if the sum of the degree of all edges in X is an odd (even) number. The odd (even) sum degree edge domination number  is the minimum cardinality taken over all odd (even) sum degree edge dominating sets of G and is defined as zero if no such odd (even) sum degree edge dominating set exists in G. In this paper, the odd (even) sum degree domination concept is extended on the co-dominating set E-T of a graph G, where T is an edge dominating set of G.  The corresponding parameters co-odd (even) sum degree edge dominating set, co-odd (even) sum degree edge domination number and co-odd (even) sum degree edge domin