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.
Background: Cardiopulmonary resuscitation (CPR) is a technique or procedure that combined chest compression and rescue breathing to maintain enough circulation that prevents brain damage until other essential steps are taken to control the main cause of cardiac and respiratory arrest. The health care personnel should be qualified in the performing of cardiopulmonary resuscitation (CPR) to improve the survival rate of the victims. Therefore; it is necessary to use new methods for learning [1]. Objectives: the study aims to compare the effectiveness of self-instructional teaching strategy and traditional teaching approach on student’s knowledge toward cardiopulmonary resuscitation. Methods: A randomized comparative trial (RCT) design was ca
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The purpose of this paper is to identifying the level of skill self-esteem of the young tennis players in the Governorate of Baghdad, identifying some aspects of attention (acuteness, concentration, and diversion of attention) among the young tennis players of the Baghdad governorate, and identify the skills of serve and serve spiking in tennis by young tennis players in Baghdad governorate. The researchers used the descriptive approach in the correlative relations style for its suitability and the research problem. the research sample was chosen in a deliberate way from the youth team players in tennis for the Governorate of Baghdad and the participants in the 2021-2022 sports season, whose number is (20) male players and (4) young playe
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The aim of the research is to evaluate the practice of banking departments for strategic foresight represented by its dimensions (environmental scanning, future vision, scenarios, reconfiguration) and its relationship to the organizational brilliance represented by dimensions (brilliance of leadership, brilliance of service and innovation, brilliance of knowledge, brilliance of employees), as the research was applied in A number of private Iraqi commercial banks represented by (Baghdad, Iraqi Investment, Iraqi Middle East Investment, Commercial Gulf, Ashur International Investment, Al Mansour Investment, Via Iraq Invest
... Show MoreThe research aims to identify the effect of the training program that is based on integrating futuristic thinking skills with classroom interaction patterns on mathematics teachers in order to provide their students with creative solution skills. The research sample consisted of 31teachers (15 teachers for the experimental group and 16 for the control groups). The researcher developed a measure for the academic self-efficacy consisting of (39) items. Its validity, reliability, coefficient of difficulty and discriminatory power were estimated. To analyze the findings, the researcher adopted the Mann-Whitney (U) test and the effect size, and the findings were as follows: There is a statistically significant difference at the significance leve
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MM ABDUL-WAHHAB, SA AHMED, International Journal of Pharmaceutical Research, 2020 - Cited by 2
Background׃ Halitosis is a common condition and is most often caused by a buildup of bacteria in the mouth because of gum disease, food, or plaque. It can result in anxiety among those affected, it is also associated with depression and symptoms of obsessive compulsive disorder. The aim of this study isto assess the prevalence of self-reported halitosis and associated factors (dental plaque, gingival condition and dental caries) in 15 years old male students in Karbala city in Iraq. Additionally, we studied adolescents’ concern with their own breath and whether anyone had ever told them that they had halitosis. Methods׃ A cross sectional observational survey was conducted to15 years old high school students from public and p
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This research is carried out to investigate the behavior of self-compacting concrete (SCC) two-way slabs with central square opening under uniformly distributed loads. The experimental part of this research is based on casting and testing six SCC simply supported square slabs having the same dimentions and reinforcement. One of these slabs was cast without opening as a control slab. While, the other five slabs having opening ratios (OR) of 2.78%, 6.25%, 11.11%, 17.36% and 25.00%. From the experimental results it is found that the maximum percentage decrease in cracking and ultimate uniform loads were 31.82% and 12.17% compared to control slab for opening ratios (OR
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