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 basic idea of the Main Outfall Drain, MOD, was to construct a main channel to collect saline drained water of the irrigation projects within central and southern parts of Iraq and discharge it down to the Arabian Gulf. The MOD has a navigation lock structures near Addalmage Lake at station 299.4km. This structure is designed to ensure navigation within the MOD. The water level difference upstream the cross regulator and the downstream conjugation structure is about 9m. This head difference can be used to generate electrical power by constricting a low head power plant. This study aimed to utilize the head difference in navigation lock structures for power generation. Different operation condition an
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The digital camera which contain light unit inside it is useful with low illumination but not for high. For different intensity; the quality of the image will not stay good but it will have dark or low intensity so we can not change the contrast and the intensity in order to increase the losses information in the bright and the dark regions. . In this search we study the regular illumination on the images using the tungsten light by changing the intensities. The result appears that the tungsten light gives nearly far intensity for the three color bands(RGB) and the illuminated band(L).the result depend on the statistical properties which represented by the voltage ,power and intensities and the effect of this parameter on the digital
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The aim of this paper is to approximate multidimensional functions by using the type of Feedforward neural networks (FFNNs) which is called Greedy radial basis function neural networks (GRBFNNs). Also, we introduce a modification to the greedy algorithm which is used to train the greedy radial basis function neural networks. An error bound are introduced in Sobolev space. Finally, a comparison was made between the three algorithms (modified greedy algorithm, Backpropagation algorithm and the result is published in [16]).
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Abstract
The following research is marked by "social intelligence and its role in demonstration the potential abilities for individuals." The discussion dealt with the concepts of contemporary is very important because of their significant role in influencing the work of the Organization, as adopted link between the concepts of social intelligence and the potential role of the first to show the second .The research hypotheses tested in three health institutions in the city of Mosul, the research community is represented (Al-Salam Hospital and General Hospital and the son of ether), while the sample were the leaders of these institutio
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The study addressed the change in the nature of the land cover of the Al-Jadriya Twist area for the period from 1976-2024 with an area of (140 km2)and for a period of (48 years) based on satellite images and their analysis using geographic information systems. The main classifications of the area were reached (water cover, residential areas, vegetation cover, in addition to empty, unused areas). The extracted data indicate a decrease in the water cover and the change rate reached (-14.29) and the residential areas increased with a change rate of (28.26), while the vegetation cover rate was recorded from (45 km2) to (66 km2) and the empty areas had a change rate of (-78.57).
Earth cover of the city of Baghdad was studied exclusively within its administrative border during the period 1986-2019 using satellite scenes every five years, as Landsat TM5 and OLI8 satellite images were used. The land has been classified into ten subclasses according to the characteristics of the land cover and was classified using the Maximum Likelihood classifier. A study of the changing urban reality of the city of Baghdad during that period and the change of vegetation due to environmental factors, human influences and some human phenomena that affected the accuracy of the classification for some areas east of the city of Baghdad is presented. The year 2019 has been highlighted because of its privacy in changing the land cover of th
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In this paper, our purpose is to study the classical continuous optimal control (CCOC) for quaternary nonlinear parabolic boundary value problems (QNLPBVPs). The existence and uniqueness theorem (EUTh) for the quaternary state vector solution (QSVS) of the weak form (WF) for the QNLPBVPs with a given quaternary classical continuous control vector (QCCCV) is stated and proved via the Galerkin Method (GM) and the first compactness theorem under suitable assumptions(ASSUMS). Furthermore, the continuity operator for the existence theorem of a QCCCV dominated by the QNLPBVPs is stated and proved under suitable conditions.
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This study deals with knowing the public relations activities of the Integrity Commission for the year 2007, knowing the contents of these activities, knowing the contents of the advertisements that it published, whether the contents of the advertisements were convincing, and whether press photographs were used in these advertisements, as well as whether symbols and slogans were used. What language and words were used to address the recipient? 1- What feelings do the contents of advertisements arouse? 2- Research objectives: This research aims to answer the following questions: What are the public relations activities carried out by the Integrity Commission? B: Are the contents of the advertisements published by the Authority convincing to
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