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.
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The tax base is one of the bases of the technical organizing of taxes, and that a good selection of the tax base effects the outcome of the tax and its fairness, and with the expansion of the tax range results a dangerous phenomenon called tax evasion, which became threaten the economies of countries and this phenomenon prevents the achievement of the state to its economic, political and social objectives which seeks to resolve this phenomenon and identifying all human and material potential and realize the real reasons that lie behind it. The researcher found that tax authorities are weak in terms of it the technical material and financial abilities, the analysis of data show that then is a significant reve
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Mammals are under threat worldwide due to deforestation, hunting, and other human activities. In Iraq, a total of 93 species of wild mammals have been recorded including species with global conservation concern. Bamo Mountain is situated within the Zagros Mountains in northern Iraq which is a suitable habitat for wild mammals. Due to scarcity of the field survey efforts and cryptic behavior, monitoring of the wild mammals fauna in Zagros Mountain seems challenging. Therefore, we used a camera trap which seems to be an ideal way to determine species diversity of wild mammals in Bamo Mountain. Moreover, interviews with local villagers were performed. The mammalian diversity of Bamo Mountain is not fully explored but seemed threatened by lo
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The bank deposits is fuel banking activity and raw material products for the commercial bank and the basis of its activity and its lifetime So the bank, which seeks to continue the successful development of the volume of cash deposits has translated the work of the bank to meet the needs of different sectors by providing the necessary funding, and from this point of view was the research problem a lack of interest departments of banking services to commercial banks as a means for the development of electronic cash deposits have, and which represents the basis for the supplier commercial bank fund.
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Abstract:
The issues related to foreign trade is a broad field for discussions and captures the interest of economists for their contribution to the process of economic development in the economies of the countries, especially developing ones. The imports of goods and services in foreign trade constitute an important part of the local by which the economy gets goods and services that the economy cannot produce because of the incompetent base of production. Further, the demand function of imports occupied a good deal of the attention of researchers in the field of international economics for which agricultural imports constitute an important part. The reason for the interest in the subject is due to its im
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