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 performance of the pavement in terms of vehicle safety and tire wear is affected by the friction behavior of the pavement. To highlight the main characteristics that affect the production of better friction resistance of the pavement surface in this work. The micro-texture and macro-texture of the asphalt surface of Baghdad Airport highway were studied using two methods: (sand patch method and the British pendulum test). The sand patch was examined by drawing sand grains of a specific volume, while the micro-texture was analyzed using a BPT under dry and wet surface conditions. All data obtained from the two examinations were analyzed and modelled statistically using SPSS 25 software. Results show that skid resistance of pavemen
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The main objective of present work is to describe the feasibility of friction stir welding (FSW) for
joining of low carbon steel with dimensions (3 mm X 80 mm X 150 mm). A matrix (3×3) of welding
parameters (welding speed and tool rotational speed) was used to see influence of each parameter on
properties of welded joint .Series of (FSW) experiments were conducted using CNC milling machine
utilizing the wide range of rotational speed and transverse speed of the machine. Effect of welding
parameters on mechanical properties of weld joints were investigated using different mechanical tests
including (tensile and microhardness tests ). Micro structural change during (FSW) process was
studied and different welding zones
The aim of the current research is to verify the effect of the cognitive modeling strategy on the achievement of the chemistry course for the students of the first intermediate grade. To achieve the objective of the research, the null hypothesis was formulated via cognitive modeling strategy. The results showed that the experimental group's students performed better than the students in the control group. In the light of the results, the researchers concluded: The impact of the cognitive modeling strategy in the achievement of students of first intermediate grade in chemistry.
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This study attempts to determine the necessary teaching competencies for teachers and the level of their importance in the development of their performance professionally and scientifically, and the progress towards a better future to achieve an effective level. Accordingly, the research community consists of the morning-preparatory schools for boys at the General Directorate of Education of Baghdad \ Rusafa2. The study sample included (68) teachers constituted 88.31% of the total community of teachers. As for the research tools, the researcher adopted the descriptive method by using the observation method in which the researcher prepared a list of teaching. For verifying the re
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Cold plasma is a relatively low temperature gas, so this feature enables us to use cold plasma to treat thermally sensitive materials including polymers and biologic tissues. In this research, the non-thermal plasma system is designed with diameter (3 mm, 10 mm) Argon at atmospheric pressure as well as to be suitable for use in medical and biotechnological applications.
The thermal description of this system was studied and we observed the effect of the diameter of the plasma needle on the plasma, when the plasma needle slot is increased the plasma temperature decrease, as well as the effect of the voltages applied to the temperature of the plasma, where the temperature increasing with increasing the applied voltage . Results showed t
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Background: Asthma is one of the most common chronic respiratory diseases in the world, standing for the most frequent cause for hospitalization and emergency cases. Respiratory viruses are the most triggering cause. Aim: To assess the role of viral infections, especially COVID-19, in the pathogenesis of asthma initiation and exacerbations. Method: Electronic search was done for the manuscripts focusing on asthma as a risk factor for complications after COVID-19 infection. The outcomes were titles, materials, methods and classified studies related or not related to the review study. Three hundred publications were identified and only ten studies were selected for analysis. Seven studies were review, one retrospective, one longitudin
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My study here is about the (possible for itself) features especially in the (Alashaira) opinion, also I touch to the other logicians opinions, I clarified these features concisely in the preface to be clear in front of the reader, I made it in two studies and five subjects.I talked about the meaning of the existence in the ((possible for itself) theme, and I clarified its types in the logicians and the philosophers' opinions, through which the existence and the nonexistence are equal in it, as it cannot be existed nor be nonsexist unless with a separated reason, and there is no necessity to oblige its existence, or its nonexistence is impossible.Then I talked about the outweighing of the (possible for itself) as one side of the exi
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