In this paper, we study the effect of group homomorphism on the chain of level subgroups of fuzzy groups. We prove a necessary and sufficient conditions under which the chains of level subgroups of homomorphic images of an a arbitrary fuzzy group can be obtained from that of the fuzzy groups . Also, we find the chains of level subgroups of homomorphic images and pre-images of arbitrary fuzzy groups

        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 main objective of this study is to understand the work of the pile caps made of lightweight aerated foam concrete and study the many factors affecting the ability and the capacity of the shear. The study was done by analyzing previous practical and theoretical experiences on the reinforced concrete pile caps. The previous practical results indicated that all specimens failed by shear diagonal compression or tension modes except one specimen that failed flexural-shear mode. Based on test specimens' practical results and behavior, some theoretical methods for estimating the ultimate strength of reinforced concrete pile caps have been recommended, some of which evolved into the design documents available on the subject.

       The present study conducted on 30 female patients with osteoarthritis OA a attending Baghdad teaching hospital, in addition to 30 healthy females, all subjects were (35-65) year's old .Parameters were measured in the sera of patients group and healthy groups were interleukin -8 (IL-8) and high sensitivity C-reactive protein (hs-CRP).The results revealed a higher significant in all parameters of patients sera compared to healthy groups. Conclusion was obtained that IL-8 and hs- CRP were a markers or player inflammatory disease like osteoarthritis nodal  

Background: Obesity and dental caries are multifactorial diseases related to poor eating habits and show a close relationship with the sociodemographic characteristics of individuals presenting these diseases. This research aimed to investigate the severity of dental caries among group of obese boys aged 12 year in relation to salivary interleukin-6 (IL-6) and C-reactive protein (CRP) of unstimulated whole saliva in comparison with normal weighted boys of the same age. Materials and Methods: The study group included 40 obese boys, with an age of 12 year. The control group included 40 normal weighted boys of the same age. The total sample involved for nutritional status assessment using Body Mass Index specific for age and gender according t

An interpretive (structural and stratigraphic) study of the two,-dimensional seismic, data of East Nasiriya area (30 km to the south east of Nasiriya oil field within Thi-Qar province, southeastern Iraq) was carried out using Petrel 2017 program. The study area has an importance due to its location between many oil fields, but still without exploration of oil wells. Twenty five seismic lines were used, date back to different types of seismic surveys conducted in the region at different time periods.  Also, the seismic velocity surveys of the nearest wells to oil fields, such as Nasiriya-1 and Subba-8, in addition to their sonic and density logs were used. A synthetic seismogram with a good matching with the seismic section was achie