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

This paper presents a hybrid approach for solving null values problem; it hybridizes rough set theory with intelligent swarm algorithm. The proposed approach is a supervised learning model. A large set of complete data called learning data is used to find the decision rule sets that then have been used in solving the incomplete data problem. The intelligent swarm algorithm is used for feature selection which represents bees algorithm as heuristic search algorithm combined with rough set theory as evaluation function. Also another feature selection algorithm called ID3 is presented, it works as statistical algorithm instead of intelligent algorithm. A comparison between those two approaches is made in their performance for null values estima

The musical templates are the fundamental reason for admiration and interest among a lot of cultural and societal medias because of the beauty of it's melodic value, where a lot of Iraqi singing and music specialists and composers try to consolidate daily life idea and translate it into music in a manner that preserve the template and rhythm horizontally and vertically, through the involvement of the scientific and philosophical concepts and theories of modern thought to reach the recipient,, as is the theory of form (Gestalt), one of the most important theories that stretched to their interpretations to the field in general art and in music science, especially, as an area that can be manifested as partial components template music, conn

In the present research synthesis and study of biological activity a series of new polymers modified of chitosan with compounds containing azo group. Beginning diazonium salt produced from 3,3'-dimethyl-[1,1'-biphenyl]-4,4'-diamine reacted with concentrated HCl acid and sodium nitrite. The coupling reaction between diazonium salt with substituted aromatic aldehyde to produce Azo derivatives )1-6(. Azo Schiff bases Chitosan )7-12( were synthesized by condensation of Chitosan with Azo derivatives )1-6( in ethanol with some drops of glacial acetic acid. The structural modifications of Chitosan ring (linked to a bioactive azo moiety) were expected to give new derivatives )7-12( with a diverse range of biological functions. These compounds' st

 في البحث الحالي تم تحضير ودراسة النشاط الحيوي لسلسلة من البوليمرات الجديدة المحورة  من الكيتوسان مع مركبات تحتوي على مجموعة الآزو. في البداية تم تحضير ملح الديازونيوم من  تفاعل  3,3'-dimethyl-[1,1'-biphenyl]-4,4'-diamine مع حامض الهيدروكلوريك المركز ونتريت الصوديوم .ثم تفاعل  الازدواج بين ملح  الديازونيوم مع الديهايدات اروماتية معوضة  لإنتاج مشتقات الازو (1-6). ازو شف بيس كيتوسان((12-7 والتي حضرت من تفاعل الكيتوسان مع مشتقات

The x-ray fluorescence (XRF) of Znpc molecule with (flow of Ar) and Znpc molecule with (grow in N2) showed two peaks at (8.5and 9.5 Kv) referring to orbital transition ) K?-shell & K?-shell) respectively. The study of x-ray diffraction (XRD) where it was observed good growth of the crystal structure as a needle by the sublimation technique with a ?-phase of (monoclinic structure ) . Using Bragg equation the value of the interdistance of the crystalline plane (d-value) were calculated. We noticed good similarity with like once in the American Standards for Testing Material (ASTM) .Powder Diffraction File (PDF) Program was used to ensure the information obtained from (ASTM) . The output of (PDF) was compared with celn program, where the val

   The aim of this paper is to introduce and study new class of fuzzy function called fuzzy semi pre homeomorphism in a fuzzy topological space by utilizing fuzzy semi pre-open sets. Therefore, some of their characterization has been proved; In addition to that we define, study and develop corresponding to new class of fuzzy semi pre homeomorphism in fuzzy topological spaces using this new class of functions.