In a connected graph , the distance function between each pair of two vertices from a set vertex  is the shortest distance between them and the vertex degree  denoted by  is the number of edges which are incident to the vertex  The Schultz and modified Schultz polynomials of  are have defined as:

 respectively, where the summations are taken over all unordered pairs of distinct vertices in  and  is the distance between  and  in  The general forms of Schultz and modified Schultz polynomials shall be found and indices of the edge – identification chain and ring – square graphs in the present work.

Objective: The research aimed to develop a scale for students' logical reasoning in football, prepare educational exercises for the idea filtering strategy and its application in physical education football lessons on outdoor fields, and identify its impact on logical reasoning and performance in the skills of forward shooting from dribbling and from side passes in football. Research methodology: The experimental method was adopted with a two-group design (experimental and control) with (58) students randomly selected and divided into the two groups, representing (65.909%). The researchers used (120) students to develop the scale under study, employing systematic steps and various sequential statistical analyses. They also prepared

The current research aims to know the extent of the impact of performance evaluation in its dimensions as an explanatory variable in the behavioural and attitudinal work outputs with its dimensions as a response variable in order to reach appropriate solutions through which the University of Fallujah seeks to achieve its goal in the process of diagnosing the axes of strength and to benefit from them in the process of strengthening the status and sobriety of the academic position of the professor and the researcher relied on The descriptive and analytical approach in carrying out this study, and data was collected from university professors, including leaders, heads of departments and divisions, who numbered (97) teachers. And fie

The current research aims to train students to take benefit of their studies to analyze and taste the artistic works as one of the most important components of the academic structure for students specializing in visual arts; then to activate this during training them the methods of teaching. Consequently, the capabilities of mind maps were employed as a tool that would be through freeing each student to analyze a model of artistic work and think about his analytical principles according to what he knows. Then, a start-up with a new stage revolves around the possibility of transforming this analysis into a teaching style by thinking about how the student would do. The same person who undertook the technical analysis should offer this work

This study tries to clear the correlation and association between asthma, obesity and leptin levels. Also it will work to indicate the main risk factors which play role in the elevation of leptin level within asthmatic patients.  This is a case control study conducted on (38) asthmatic patients and (20) healthy control who were closely similar by age, gender and BMI. The main statistical tests used were student t test, linear regression test and correlation test. Significance was set at P < 0.05. Sampling method used for this study was convenience sampling method.  The main results of this study show a significant association and positive correlation between age (old age  â‰¥ 40 ye

New Schiff base and their Mn(II),Co(II),Ni(II), Cu(II) and Hg(II) complexes formed by the condensation of O-phathaldehyde and ethylene diamine (2:1) to give ligand (L1) in the first step ,then the ligand (L1) with 2- aminophenol (1:2) to give ligand (L2) were prepared by classic addition through microwave method . These compounds (Ligands and complexes) have been diagnosed electronic spectra, FT-IR,1H-&13C-NMR (only ligand), magnetic susceptibility, elemental microanalysis and molar conductance measurements. Analytical values displayed that all the complexes appeared (metal: ligand) (1:1) ratio with the six chelation. All the compounds appear a high activity versus four types of bacteria such as; (Escherichia coli), (Sta

The clinical spectrum of cutaneous leishmaniasis (CL), an intracellular parasitic pathogen, ranges from a single sore healing to chronic crusty lesions with a manifestation of treatment resistance. The complicated interaction between Leishmania bodies and the early immune response, including innate and adaptive mechanisms, determines the evolution of nodules. This study examined the levels of the chemoattractant interleukin 8 (IL-8), pro-inflammatory nitric oxide (NO), and immunoregulatory macrophage inhibitory factor (MIF) in the serum of subjects recently diagnosed with cutaneous leishmaniasis, in parallel with patients being monitored during consecutive sodium stibogluconate (Pentostam) treatment. A total of 161 serum samples of newly di

This paper offers a postcolonial analysis of Sudanese author Tayeb Salih's novel Season of Migration to the North (1966), emphasizing the interplay between indigenous and colonial narratives. The analysis centers on the protagonist, Mustafa Sa'eed, who embodies its essence. The character of Mustafa Saeed represents the intricate interplay between colonial and indigenous elements. This research employs Edward Said's postcolonial concept, Contrapuntal Reading (1993), which underscores the interconnection of the histories of colonizers and the colonized through the portrayal of Mustafa Saeed's character, focusing on the mechanisms of colonial power, such as cultural hegemony, identity manipulation, and the resistance of the colonized.

Through the researchers' acquaintance with the previous studies, the problem was identified as that the preparation of training curricula in all its units must be based on accurate scientific foundations. Positively affect the type of attack and its implication in the presence of correlational relations, whether direct or indirect, i.e., precedence in training and in preparing units Therefore, the researcher decided to build a causal model to know the relationships to show the best model of the direct straight attack. The study aimed to build a causal model for the most important physical measurements and kinetic capabilities of the direct straight attack in the research sample. The two researchers used the descriptive approach in t