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 industrial production sector has an important role in the national economy of the advanced countries as well as the developing ones to get higher levels for their economy . We in Iraq , just like most of the develpoing countries , our economy still suffers of great shortage in this active sector in spite of the repeated statements about the desire of activating the contribution of this sector in the national economy . The industrial sector in Iraq suffers in general of many problems , especially the public industrial sector (manufacturing) . These problems have been existed because of the unnatural conditions that Iraq has passed during the previous decades especially in the political and security sides . which reflecte
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A legal discourse in the Qur’an and Sunnah is almost devoid of the use of one of the general formulas, and due to its frequent rotation in the tongue of the legislator, the formulas may overlap their members in apparently contradictory provisions, which makes the individual from the general members appear to the beholder to be covered by two contradictory provisions, and this research came to present what might happen to him The legal text interpreter of weighting between the two opposing texts is the strength of the generality that is established by the generality formula, so the two strongest formulas in the inclusion of its members outweigh the weaker of them and precede them, and the research decided that the formulas vary
... Show MoreThe research problem focused through the researcher's experience in the gymnastics game and the lack of use of educational models that give the student an important role in the educational process, so it became necessary to identify the type of prevailing style for students, and the need for diversity in the use of educational models based on scientific theories, including the Daniel Document model. Based on three theories of learning, which are structural, behavioral, and meaningful learning. The research aimed to identify the effect of using the Daniel model for people with two types of brain control (left and right) to learn the skill of the Cartwheel in artistic gymnastics for students of the second stage. The researcher used the experi
... Show MoreThe study aims to identify the degree of Tabuk University practices to raise the intellectual awareness of students through scientific research, as well as to identify the degree of Tabuk University practicing to raise the intellectual awareness through the educational process (faculty member – activities). The study also seeks to identify the degree of Tabuk University practicing to raise the intellectual awareness of students through community service and university media. The study is descriptive in nature that employed the questionnaire as a tool in collecting data. Total of (540) students were chosen randomly from different colleges at universities of Tabuk to form the study sample. The results showed that faculty member has pract
... Show MoreThe research aims to identify the relationship between spatial ability and the physical structure of concepts to the students of the Faculty of Education for Pure Sciences / Ibn al-Haitham، research involved students from the third class / morning study for the year 2011/2012 totaling (98) male and female students ،distributed into three groups which were selected randomly . The number of students (26 males and females) represented research sample after excluding repeaters and absentees، the research included two tests ; one test of spatial ability، which included (20) items and other test the physical structure of concepts، which included (12) items distributed into four domains ، the first (linking b
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The construction sector consumes large amounts of energy during the lifetime of a building. This consumption starts with manufacturing and transferring building materials to the sites and demolishing this building after a long time of occupying it. The topic of energy conservation and finding the solution inside the building spaces become an important and urgent necessity. It is known that the roof is exposed to a high amount of thermal loads compared to other elements in a building envelope, so this needs some solutions and treatments to control the flow of the heat through them. These solutions and treatments may be achieved by using nanomaterials. Recently, nanomaterials have high properties, so that this made them go
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The research aims at conducting a follow-up evaluation of a number of strategic projects implemented by the Directorate of Public Municipalities, one of the Ministry of Construction, Housing and Municipalities and Public Works. The sample included (35) varied strategic projects implemented in most Iraqi governorates. Buildings, municipal buildings, minarets, massacres, multi-story parking, paving and rehabilitation of streets and residential neighborhoods. The difference between the actual and planned times and costs of these projects was then measured and analyzed. These projects were used as a tool for collecting data and information. The questionnaire included four axes, each representing one of the parties to the project, whi
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