The set of all (n×n) non-singular matrices over the field F. And 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 rationally valued characters of the rational representations are written as a linear combination of the induced characters for the groups discussed in this paper. We find the Artin indicator for this group after studying the rationally valued characters of the rational

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 legal protection of the human genome is an ethical issue related to the future of human existence.  After the disclosure of the human genetic map, scientific practices and research related to the human genome increased, especially the negative applications of genetic engineering that violates basic human rights, especially the right to human dignity, and pose real challenges to the existence and diversity of  Present and future generations. Therefore, the existence of legal rules at the national and international levels is an absolute necessity to prohibit these threats and to arrange civil and criminal liability for those who violate them.

          The she/teacher is considered one of the basics of the educational process for its essential role in education and teaching the kindergarten child, thus  its lack to construct social relations in side the kindergarten environment working in it regarded one of the shortcoming factors she is suffering from which should be manipulated, because it could effect its enthusiasm to work in the kindergarten according to what has mentioned, the researcher presents the following objective:-

• Identifying level of social enhancement for the kindergarten teachers via the test of the following hypothesis:-

The concern of this article is the calculation of an upper bound of second Hankel determinant for the subclasses of functions defined by Al-Oboudi differential operator in the unit disc. To study special cases of the results of this article, we give particular values to the parameters A, B and λ

     In this paper, ZnO NPs were prepared using D.C high-voltage and high frequency with an output of 6 kHz at two different preparation times preparation (10,12) minutes. Transmission electron microscopy (TEM) with (FE-SEM) was used to examine the homogenous, compact, and dense surface of the zinc oxide nanoparticles created with apparent grain size determined by (XRD), XRD results explain that the increase of the preparation time from 10 minutes to 12-minute caused an increase in crystallite size. In addition, FE-SEM showed that the increase in the ZnO NPs cluster distribution with particle size increases with increasing the preparation time. AFM was also utilized to determine the degree of cooperation between the surfaces of the z