The set of all (n×n) non-singular matrices over the field F this set forms a group under the operation of matrix multiplication. This group is called the general linear group of dimension  over the field F, denoted by . The determinant of these matrices is a homomorphism from  into F* and the kernel of this homomorphism was the special linear group and denoted by  Thus  is the subgroup of  which contains all matrices of determinant one.

The rational valued characters of the rational representations written as a linear combination of the induced characters for the groups  discuss in this paper and find the Artin indicator for this group after study the rational valued characters of the rational representations and the induce

The current work aims to evaluate the association between genetic mutations in thymidylate synthetase (TYMS gene in exon1 and partial regions of promotor and intron 1 [877 bp, 657,220–658,096 bp]) and the therapeutic outcomes for rheumatoid arthritis (RA) Iraqi patients. An observational cross-sectional study involving 95 RA patients with established RA patients based on their methotrexate treatment responsiveness. Genetic sequencing of the TYMS gene was performed for all patients according to the instruction manuals of the sequencing company (Macrogen Inc. Geumchen, South Korea). Four polymorphisms were identified by sequencing 95 randomly selected patients in the noncoding region of TYMS

In the era of the digital economy, public organizations need to consolidation the capabilities of entrepreneurial alertness to reduce the risks of sudden transformations and changes, and to find effective mechanisms to discover and invest in environmental opportunities proactively, as this concern has become a knowledge gap in public sector institutions, the current research aims to identify the role of digital competence in influencing on entrepreneurial alertness in the Central Bank of Iraq (CBI), the descriptive analytical approach was used as a research method to describe and analyze the main research variables. digital competence as an explanatory variable includes three dimensions: digital infrastructure, digital integration, and d

The aquatic Heptageniidae family of Ava-sheen branch (Greater Zab Tributary) in Duhok Governorate/ Iraq was studied. Samples were collected using Surber stream sampler to study their diagnostic morphological characteristics and molecular phylogenetic profile using a nuclear gene 16s ribosomal RNA. The morphological and molecular identification supported that the three species, Epeorus longimanus, Heptagenia elegantula and Ephemerella cornutus belong to Heptageniidae family, while the molecular results also confirmed the monophyletic origin of these three genera.

Hyperlipidemia is one of the most important factors leading to atherosclerosis and heart disease, therefore, this study conducted to examine the effect of two newly synthesized compounds[3-(5(ethylthio)-1,3,4-thiadiazol-2-yl)-2,3-dihydro-2-(3-nitrophenyl)benzo[1-3-e] thiazin-4-one (I) and 5(4dimethyl amino) benzylidene amino)-1,3,4-thiadiazole-2-thiol(II)] on the activities of creatine kinase(CK) and 3-hydroxy-3-methylglutaryl- CoA reductase (HMGR) in male Wister mice . Also to determine the type of inhibition of these compounds on the above enzymes .The study was carried out on sixty male Wister mice aged seven to eight weeks their weight ranged(180-200 g) . The mice were grouped as: group(1): control group (12 mice).Group(2):consisted

The study aims to investigate the degree of student teachers at Sultan Qaboos University acquired skills in teaching Arabic via a virtual micro-teaching lab, as well as to reveal the difficulties they faced and their development proposals. To do this, the researchers developed a questionnaire divided into four dimensions: planning, implementation, evaluation, and

ethical values for the teaching profession, in addition to two open-ended questions to identify difficulties and suggestions. It was administered to (30) student teachers. The results revealed that the average degree of student-teacher acquisition of skills was high in its four dimensions. It ranged between (39.2) to (82.2), while the overall average was (56.2).

The aim of this research is to construct a three-dimensional maritime transport model to transport nonhomogeneous goods (k) and different transport modes (v) from their sources (i) to their destinations (j), while limiting the optimum quantities v ijk x to be transported at the lowest possible cost v ijk c and time v ijk t using the heuristic algorithm, Transport problems have been widely studied in computer science and process research and are one of the main problems of transport problems that are usually used to reduce the cost or times of transport of goods with a number of sources and a number of destinations and by means of transport to meet the conditions of supply and demand. Transport models are a key tool in logistics an

The researcher is one of the workers in university sports student activities, as he noticed that there is a diversity in the use of leadership patterns among managers of student activities in Iraqi universities between one director and another, which leads to the impact of these leadership styles on performance, positive or negative, in the level of human relations and the achievement of results. The researcher adopted the descriptive method in the survey method with relational relationships. The research sample consisted of (184) sports coaches who represent (27) universities and governmental and private colleges. To achieve the research objectives, the researcher used the Statistical Package for Social Sciences (Spss). To extract.statisti

     In this work, the electrostatic probe was utilized to estimate the density of electrons for plasma generated around reentry vehicles that have a geometrically blunt nose at high-altitude. The thermocouple uses to measured electron temperature, which is equal to the temperature of the gas, on board the MAC spacecraft. In the spacecraft backflow field, electrostatic probe measurements were taken at five separate regions 1 to 5 cm from the body of the spacecraft. Over an altitude range of 90 to 50 km with an electron density of 10⁸ to 10¹² 1/cm³, respectively. The measured electron temperature ranged from 0.05 to 0.9 electron volts and the maximum re-entry velocity of the spacecraft was about 7048 m

Each sport has its own energy requirements that differ from the energy requirements of other sports, and a different method is used in each of them, so the trainer must first rely on the principle of privacy in training first, that is, privacy according to the working energy system, that is, he defines the controlling energy system In that event, and how the muscles use the available energy to perform according to the energy production systems. As we find the serving skill is the first volleyball skill with which the team starts the match in order to be able to gain points directly, through knowledge it turns out that there is a weakness in the skill performance, especially the skill of serving and being The key to victory for volle