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 mechanism for selecting the President of the Republic and his constitutional powers under the Constitution of the Republic of Iraq
The she/teacher is considered one of the basics of the educational process for its essential role in education and teaching the kindergarten child, thus its lack to construct social relations in side the kindergarten environment working in it regarded one of the shortcoming factors she is suffering from which should be manipulated, because it could effect its enthusiasm to work in the kindergarten according to what has mentioned, the researcher presents the following objective:-
- Identifying level of social enhancement for the kindergarten teachers via the test of the following hypothesis:-
سلمان، ندى نجيب. 2015. التباين المكاني السكان الأميين في الوطن العربي للمدة 1990-2009. مجلة آداب ذي قار،مج. 4، ع. 15، ص ص. 101-126.
Y Adnan, H Atiyah, IH Neamah…, International Development Planning Review, 2024
This research has been applied on 100 children (age 4 – 6 years) from three kindergartens distributed on basis of 43 children from the college of Education for women kindergarten (A) , 27 children from the governmental Al- Mustafa kindergarten (B) , and 30 children from the private Al – Baraom kindergarten (C) . Details concerning their school meals, already prepared at home , have been analyzed according to their dietary components taken from the tables of the dietary values .The statistical analysis results have shown no significant difference (p< 0.01) in the intake of energy , protein and thiamin between the children of A and C kindergartens while these children have significantly recieved higher amounts of the above nutrien
... Show MoreIn light of the limited sources of funding suffered by the Iraqi economy, it highlights the importance of enhancing the efficiency of public expenditure, and if the measurement of the efficiency of public expenditure and identify benchmarks first step of promoting efficiency, the adoption of scientific methods of analysis imperative in promoting the efficiency. Under this framework, the focus was on the methodologies used to measure the efficiency of public spending and supply analysis with trying statement strengths and weaknesses, and make use of it in the measurement of the efficiency of public spending in the Iraqi economy. As well as devise measurable indicators take into account the specificity of the Iraqi economy and the
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Distribution of light intensity in the flat photobioreactor for microalgae cultivation as a step design for production of bio-renewable energy was addressed in the current study. Five sizes of bioreactors with specific distances from the main light source were adopted as independent variables in experiential design model. The results showed that the bioreactor’s location according to the light source, determines the nature of light intensity distribution in the reactor body. However, the cross-section area plays an important role in determining the suitable location of reactor to achieve required light homogeneity. This area could change even the expected response of the light passing through the reactor if Beer-Lambert's law is adopted.
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The aerodynamic characteristics of the forward swept wing aircraft have been studied theoretically and an experimentally investigation for the wake field generated by this configuration have been carried out. Low order panel method with the Dirichlet boundary condition have been used to solve the case of the steady, inviscid and compressible flow. Two different panel method techniques have been employed: the source-doublet and the doublet method. The thickness for the various components was considered in the study. Prandtl-Glauert similarity rule has been used to account for the compressibility effects. Experimentally, a model was manufactured from wood with body length (290mm) and main wing span was (204mm). The primary objective of th
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