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.
Abstract
The current research aims to reveal the extent to which all scoring rubrics data for the electronic work file conform to the partial estimation model according to the number of assumed dimensions. The study sample consisted of (356) female students. The study concluded that the list with the one-dimensional assumption is more appropriate than the multi-dimensional assumption, The current research recommends preparing unified correction rules for the different methods of performance evaluation in the basic courses. It also suggests the importance of conducting studies aimed at examining the appropriateness of different evaluation methods for models of response theory to the
... Show MoreThe current research tackles the self-efficacy and its relation to the cognitive assessment for the daily disturbances for the University of Baghdad students. Two criteria have been adopted to achieve the objectives of the research. The sample of this study consists of 200 male and female students who were chosen randomly. The data were analyzed statistically, revealing that the university students owned their own self-efficacy as well as a cognitive assessment for the daily disturbances and they recognized them as self-threatening. The results also indicated the existence of a prediction activity in the field of the cognitive assessment to the daily disturbances selection. In light of the acquired results, the study recommends the neces
... Show MoreAbstract The study aimed at reviewing translation theories proposed to address problems in translation studies. To the end, translation theories and their applications were reviewed in different studies with a focus on issues such as critical discourse analysis, cultural specific items and collocation translation.
The study aims to find out the extent to which several Iraqi institutional accreditation standards (governance and administration, scientific research, curricula) are applied in two public universities (Baghdad and Middle Technical University) and two private universities (Uruk and Al-Mansour College) by diagnosing strengths and weaknesses and proposing a mechanism and procedures to help educational institution aims to reduce or eliminate the gap. The study stems from the extent of application of several Iraqi institutional accreditation standards represented as it was worked on through observation and field coexistence to reach scientific and practical facts. The method of case study and comparison betwe
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The current research aims to identify the Vocational Self of the educational counselors as well as to identify the significant difference in the professional self according to the gender variable (male-female). The researcher adopted the scale of al-hasani (2015), which consisted of (34) items. It was applied to a sample of (300) school counselors (male-female) who were randomly selected from the six directorates in the Baghdad governorate for the academic year 2020/2021. The results showed that the research sample of educational counselors has a vocational self-concept. There are no statistically significant differences in the vocational self-concept between males and females among the educational counselors.
The current research aims to identify the possible self of university students and the differences in the level of possible self of students in terms of gender, specialization (scientific-humanitarian), and the interaction between them. In order to achieve the objectives of the current research, the two researchers have prepared a scale of the possible self, based on the theory (Markus and Nurius, 1986). The research tool was applied to a sample of (400) male and female students who were selected through a random stratified method from Al-Mustansiriya University students/morning studies for the academic year (2019-2020). The researcher reached the following results: the research sample has a high level of possible self; there is a differ
... Show MoreAl- belenoby , Andalusian obscure poet .I choose to study poetic rhythm in this poetic and the appropriateness of with what rhythm touring in his self to give beautiful meaning raise to receiver to put the hands of continental placements creativity in poetry .I divided my research into ideas are presented in a sequential manner , I started researching with poetic rhyme than rhyme they represent the form of the poem, they represent the external form of the poem and their music that farm the general concept then the rhetorical styles that represent the internal form of the poem and it music that the listener works and enjoying it part by part all this led to the put the hands of the receiver placement creativity in Belenoby Poet.&nbs
... Show MoreThe primary function of commercial banks is the process of converting liquid liabilities such as deposits to illiquid assets, (also known as a loan), liquid assets, (aka cash and cash equivalent) in a balanced manner between liquid and illiquid assets, that guaranteed the preservation of the rights of depositors and the bank and not by converting liquid liabilities into liquid assets in a very large percentage. This comes from its role as depository and intermediary institutions between supply and demand, therefore, we find that the high indicators of bank liquidity and solvency may reflect a misleading picture of the status of commercial banks, to some extent in terms of the strength of their balance sheets and
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