Let/. It :0 ---0 G be any two self maps of a compact connected oriented Lie group G. In this paper, for each positive integer k , we associate an integer with fk,hi . We relate this number with Lefschetz coincidence number. We deduce that for any two differentiable maps f, there exists a positive integer k such that k 5.2+1 , and there is a point x C G such that ft (x) = (x) , where A is the rank of G . Introduction Let G be an n-dimensional com -pact connected Lie group with multip-lication p ( .e 44:0 xG--+G such that p ( x , y) = x.y ) and unit e . Let [G, G] be the set of homotopy classes of maps G G . Given two maps f , f G ---• Jollowing [3], we write f. f 'to denote the map G-.Gdefined by 01.11® =A/WO= fiat® ,sea Given a point g EC and a differ-entiable map F: G G , write GA to denote the tangent space of G at g [4,p.10] , and denote by d x F the linear map rig F :Tx0 T, (x)G induced by F , it is called the differential of Fat g [4,p.22]. Let LA, Rx :0 G be respec-tively the left translation Lx(i)=4..(g,e) , and the right translation Rx(1)./..(gcg). Then there is a natural homomorphism Ad ,the adjoin representation, from G to GL(G•), (the group of nonsingular linear transformations of Qdefined as follows:- Ad(g)= deRe, od,Lx. Note that d xRc, ad.; =d(4,( Lx(e)))0 de; =d.(4, 04)=4(40 Re) = d(4(4, (e)))0 (44, =d ar, o (44, . Since G is connected , the image of Ad belongs to the connected component of G(G)containing the identity,i.e. for each g E 0, detAd(g) > 0 . By Exercise Al • Dr.-Prof.-Department of Mathematics- College of Science- University of Baghdad. •• Dr.-Department of Mathematics- College of Science for Woman- University of Baghdad.
The research aims to reveal the professional self and the school climate among the educational counselors. The research problem is crystallized in the following:
1-Identifying the professional level of the educational counselors.
2- Knowing the level of the school climate with the educational counselors.
3- Are there statistically significant differences in the professional self and the school climate between the educational counselors of different gender (male / female)?
4- Is there a relationship between the professional self and the school climate of the research sample?
To answer these questions, the research was conducted on educational counselors in secondary schools in the district of Falluj
... Show MoreThis research aims to identify the effective role of self-managed teams in the quality of service performance in the directorate of Ramadi municipality. The problematic nature of our research involves this main question of the effective role of self-managed teams in the Municipality of Ramadi in improving the services of performance quality to the beneficiaries from the Directorate service. The importance of this study lies in the role played by the work teams in the organizations that excel in their field, the attendant of the changes in the leadership, administrative roles of the institutions, and teams leaders, will be achieved by the self-managed teams in improving the quality of the service provided by the institution to whi
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Targeted current research study of the relationship between guilt and self-consciousness and consisted of the research community of students from the open educational college, as has been selected students in the Department of Counseling and psychological science department and the researcher used guilt, prepared Scale (Ansari, 2003), and the measure of selfawareness prepared (Shammari 0.2000), and extracted his Alsekoumtria characteristics, Fastkhrjt alternatives after a presentation to a group of experts and specialists in the field of psychological counseling psychology, education, science and psychological validity and reliability Alvakronbach manner and retesting reaching reliability coefficient of guilt ((0.85) and awarenes
... Show MoreThe study aims to identify the level of cognitive beliefs, as well as to identify the level of self-organized learning strategies among intermediate school students. The study also aims to identify the differences in the level of self-organized learning strategies among intermediate school students in term of gender, branch (scientific, literary). In order to achieve the research objectives, the researcher designed a scale to measure the cognitive beliefs. As for the scale of self-organized learning strategies, the researcher adopted a scale of (Pintrich et al. 1991), which was translated by (Izzat Abdelhamid, 1999) , For self-organized learning strategies, the sample consisted of (400) students from the research population, whic
... Show MoreIn the past years, the Algerian Economy has witnessed various monetary developments characterized by different monetary and banking reforms aimed by monetary authorities to achieve monetary stability and driving overall growth. It should be noted that there is evidence to initiate fundamental changes on the basis of which new monetary, financing and banking policy mechanisms must be formulated in Algeria by enhancing the pursuit of reforming the monetary system, in order to improve monetary and economic indicators.
The study a
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Social protection meets different aspects of the needs of vulnerable groups, such as the economic, health, education, and family relations and ties in the Iraqi society. This is because vulnerable groups have suffered from social and economic influences that have negative implications on the social reality as a whole. Poverty is a case in point, which paved the way to frequent setbacks that have led to social structure instability. Accordingly, the present study aims to examine the role and effect of the Net of Social Protection Program in equally distributing social protection to curb or mitigate any negative consequnces that might happen to the poor segments and vulnerable people, who are succeptible to shocks, such as: the orphans, un
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The importance of this research is due to its importance goals, Which are about the attempt of researchers to investigate the probability of depending on businesses, environments to transform organizations, performance in away that enhance the leading role of organizations in their environments , and through views of a number of the staff working in the foundation of technical institutes in Mosul. .
After deciding the methodology of the study that ,in one hand ,performs the goals of the study , and achieving a suitable theoretical framework to present the concepts of businesses, environments and the leadin
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Objectives: Dickkopf-1 (DKK-1) is WNT/b-catenin pathway antagonist which plays a detrimental role in the development of diabetic retinopathy (DR). This research aimed to assess serum DKK-1 levels in diabetic patients who have and have not developed DR and, compare them with the control subjects finding out whether we can use it as an indicator for DR early diagnosis and to find out which one of the widely used two groups of antidiabetic treatments had the greater effect on this biomarker and hence on the progression of DR. Methods: The study participants were divided into two subgroups: First, 70 patients (36 male, 34 female) with type 2 diabetes mellitus, among them 35 patients diagnosed with DR and 35 with no evidence of DR, and s
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