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 study was carried out by reinforcing the resin matrix material
which was (Epoxy- Ep828) by useing Kevlar fibers and glass fibers type (E-gl ass) both or them in the form of woven roving and poly propylene tlbcrs in the form chopped strand mats. wi th (30%) volume fraction. Some mechan i cal properties of the were prepared composite specimens U ltraviolet radiation were stuied after being subjected to different weathering conditi ons i ncluded. Compression and hardness testing were carried out using Briel! method so as to compare between composite behavior i n the environments previously mentioned .
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... Show Moreسلمان، 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.
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 MoreY Adnan, H Atiyah, IH Neamah…, International Development Planning Review, 2024
In 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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The biggest problem of structural materials for fusion reactor is the damage caused by the fusion product neutrons to the structural material. If this problem is overcomed, an important milestone will be left behind in fusion energy. One of the important problems of the structural material is that nuclei forming the structural material interacting with fusion neutrons are transmuted to stable or radioactive nuclei via (n, x) (x; alpha, proton, gamma etc.) reactions. In particular, the concentration of helium gas in the structural material increases through deuteron- tritium (D-T) and (n, α) reactions, and this increase significantly changes the microstructure and the properties of the structural materials. T
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In this article, the lattice Boltzmann method with two relaxation time (TRT) for the D2Q9 model is used to investigate numerical results for 2D flow. The problem is performed to show the dissipation of the kinetic energy rate and its relationship with the enstrophy growth for 2D dipole wall collision. The investigation is carried out for normal collision and oblique incidents at an angle of . We prove the accuracy of moment -based boundary conditions with slip and Navier-Maxwell slip conditions to simulate this flow. These conditions are under the effect of Burnett-order stress conditions that are consistent with the discrete Boltzmann equation. Stable results are found by using this kind of boundary condition where d
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This paper set forth the spatial suitability of the informal settlement supposed to be distributed by the Iraqis government to poor people. The Iraqi government identified 9 locations of informal settlement in Baghdad city and acceptance it as a reality as a help for them to getting home. In this paper I discovered the suitability of those locations which one will be suitable more than others for living. The analysis process was applied using the GIS environment – spatial analysis. According to the results, It has been identified as the most important measures to identify which one of these areas suitable for development for housing by using some criteria (Distance from the city center, Proximity from transport routes, Proximity of high v
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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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