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.
Mindfulness is considered a process to draw an image of the active event and to creat new social varieties which leaves the individuals open to modernity and to be sensitive towards the context. in contrast, when individuals act with less attention, they need to be more determined concerning the varieties and events of the past . and as a result , they become unaware of the characteristics that creat the individual condition .The problem of the current study is represented in asking about the nature of the possible relationship between mindfulness and self-regulated learning within specific demographic frame of an importantsocial category represented in university students where no previous researches nor theories have agreed on the natu
... Show MoreSelf-criticism is that a person confronts himself with his mistakes in order to reform and develop them for the better, motivate them and inspire hope in them to push them forward and continue to give in this life. The Holy Qur’an teaches us, through the models it cited in its verses, that this is through repentance, a feeling of remorse, and a determination to leave mistakes, and quit disobedience and sins, etc., and all this is done through constructive criticism, and at the same time, one must realize his strengths. , in order to succeed in preserving it and employing it in the right path that pleases God, His Messenger, himself and his society. This has been explained through an introduction, two topics and a conclusion, and God is t
... Show MoreThis study aims to identify the forgiveness level among gifted students and its relation to the self-awareness. The study sample consisted of (207) students were randomly chosen, they are integrated in secondary schools in Abha / Saudi Arabia. The correlative, analytical descriptive method was adopted. Two scales were adopted by the researcher: The forgiveness scale prepared by Rye et al (2001) which translated to Arabic by Al-Mahasneh (2017) and the self-awareness scale which prepared by Al-Ghezwani (2017). The study results indicated the following: the forgiveness level among the talented students was high, the self-awareness level among talented students was high, and there is a positive statistically significant relationship
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This study aimed to show the extent of compliance with the income taxpayer to provide tax returns and increase the speed of collection of these taxes in addition to increasing confidence in Income Tax department and reduce the number of cases transferred to the courts and promote taxpayer awareness in charge of the importance of self-assessment system, and study sought to investigate the effect of the existence of records documents, technical audit, and computational audit and documentary audit on income tax collections in Jordan, from the point of viewof Jordanian income tax auditors ,results shows there's a strong relation between these variables and Income Tax collections.
This paper is devoted to investigate the effect of internal curing technique on the properties of self-compacting concrete. In this study, self-compacting concrete is produced by using limestone powder as partial replacement by weight of cement with percentage of (5%), sand is partially replaced by volume with saturated fine lightweight aggregate which is thermostone aggregate as internal curing material in three percentages of (5%, 10%, 15%) for self-compacting concrete, and the use of two external curing conditions which are water and air. The experimental work was divided into three parts: in the first part, the workability tests of fresh self-compacting concrete were conducted. The second part included conducting compressive str
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The aim of present study was to develop solid and liquid self-microemulsifying drug delivery system of poorly water soluble drug mebendazole using Aerosil 200 as solid carrier. Microemulsions are clear, stable, isotropic liquid mixtures of oil, water and surfactant, frequently in combination with a co-surfactant having droplet size range usually in the range of 20-250 nm. Oleic acid, tween 80 and polypropylene glycol were selected as oil, surfactant and co-surfactant respectively and for preparation of stable SMEDDS, micro emulsion region was identified by constructing pseudo ternary phase diagram containing different proportion of surfactant: co-surfactant (1:1, 2:1 and 3:1), oil and water. In brief S/ CoS mix means su
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The aim of this study is to identify the effectiveness of a rational, emotional, behavioral program in developing self-efficacy to reduce the level of Burnout in 20 teachers of students with autism disorder in Jazan, Saudi Arabia. The proposed program included 12 training sessions. The researcher found that the proposed program has contributed significantly to the development of self-efficacy and reduce the level of Burnout for the targeted subject in this study.
The study aims to follow modern methods in teaching rhythmic gymnastics skills by directing learners to develop their perceptions and absorb what the world deals with today and develop intelligence among learners, the researchers searched for the strengths of the learner by providing them with an opportunity to form their kinetic formation, hence the problem came by introducing a method of self-intelligence and social to guide the learner in the search for ways and solutions to overcome boredom and economy Time and effort in the educational process in learning and give them the freedom to express their ideas And their skills and here came the role of social and self-intelligence to teach the individual and collective kinetic formati
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Purpose This study was design to investigate of Purpose This study was design to investigate of P. aeruginosa, an example of Gram-negative bacteria, in seven primary and secondary schools of Baghdad city, and the effects of Ethanol and Dettol of P. aeruginosa biofilm. Design/methodology/approach Seventy swabs were collected from seven primary and secondary schools of Baghdad city, Iraq, during November -December 2022. Swabs were collected from classes desk, doors handles, students hands and water taps. Standard microbiological testing methods were used on the samples for isolation and identification. The ability of bacteria to form biofilm and the effects of Ethanol and Dettol on “preformed” biofilms was examined by microtiter plate wi
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