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.
In this work, ZnO quantum dots (Q.dots) and nanorods were prepared. ZnO quantum dots were prepared by self-assembly method of zinc acetate solution with KOH solution, while ZnO nanorods were prepared by hydrothermal method of zinc nitrate hexahydrate Zn (NO3)2.6H2O with hexamethy lenetetramin (HMT) C6H12N4. The optical , structural and spectroscopic properties of the product quantum dot were studied. The results show the dependence of the optical properties on the crystal dimension and the formation of the trap states in the energy band gap. The deep levels emission was studied for n-ZnO and p-ZnO. The preparation ZnO nanorods show semiconductor behavior of p-type, which is a difficult process by doping because native defects.
Background: Self-medication is a practice or action taken by individuals for themselves in order to achieve and maintain health, as well as to avoid and protect against disease. The aim of this study is to evaluate the knowledge, attitudes, and practice of self-medication among medical students at Sudan International University.
Subjects & Methods: This was a prospective study that involved 288 out of 1000 students in the Faculty of Medicine at Sudan International University. Data were collected using a self-administered questionnaire from January to March 2022 to evaluate the self-medication knowledge, attitude, and practice among first, second, and third-ye
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Internal curing is a method that has been advised to decrease the primary age cracking, mainly of concrete mixes using low (water to cementitious materials - w/cm) ratios corresponding to the self-compacting concrete-(SCC). This research aims to study the effect of the internal curing using saturated lightweight aggregate- (LWA) on the steel reinforcing corrosion in SCC. In this research, crushed bricks or thermostone were partially replaced by (20%) by the weight of sand and volumetrically measured. The results showed that the steel reinforcement of internally cured concrete showed a slight increase in corrosion up to 300 days of exposure to the saline solution (containing 3.5% NaCl). The ability of using the crushed bricks or thermostone
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This research aims to analyze the intellectual and civilizational regression that afflicted Iraqi and Arab society due to political and religious tyranny and internal conflicts, which was reflected in the deterioration of human rights values and the absence of equality and justice in dealing with the other religiously, which affected the reluctance of members of religious groups to interact with their national societies and then migrate to Outside, which contributed to a double loss, in terms of the loss of these societies by productive and effective national competencies, and in terms of distorting the image of Islam. The research stressed that the first treatments of this phenomenon are the consolidation of the values of citize
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The current research aims to identify the level of parental treatment methods tolerance, hostility, strictness, and warmth, as well as the level of self-efficacy among middle school students. Moreover, it aims to identify the correlation relationship between the variables of parental treatment methods and self-efficacy among middle school students. The research sample included (150) middle school students. For achieving the objectives of the current research, the researchers adopted a scale of parental treatment methods prepared by (Zughair, 2006), and a scale of self-efficacy prepared by (Youssef, 2016), which were applied in their final form to the research sample. The research reached the following results: parents use a low-level hos
... Show MoreBackground: Myocardial infarction (MI) is distinguished by the necrosis of myocardial cells as a result of substantial and prolonged ischemia. Anxiety, problems sleeping, and feelings of depression are some of the most common psychosocial consequences of having a myocardial infarction. Aim: The purpose of this study is to evaluate the effects of post-myocardial infarction on patients' levels of anxiety, depression, and quality of sleep. Method: The collection of data from 94 individuals with MI was carried out according to a descriptive cross-sectional design. Sleep quality, depression, and anxiety were evaluated using standard questionnaires. Results: 69.1% of the participants reported having trouble getting quality sleep. The perc
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Abstract The goal of current study was to identify the relationship between addiction of self-images (Selfie) and personality disorder of narcissus, and the difference of significance the relationship between addiction self-images (selfie) and personality disorder narcissus at students of Mustansiriya university, addiction self- images (selfie) defined: a photograph that one has taken of oneself, typically one taken with a smartphone or webcam and shared via social media, edit and down lowed to social networking sites, and over time, the replacement of normal life virtual world, which is accompanied by a lack of a sense of time, and the formation of repeated patterns increase the risk of social and personal problems. To achieve the goals
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