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.
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The purpose of the study is the city of Baghdad, the capital of Iraq, was chosen to study the spectral reflection of the land cover and to determine the changes taking place in the areas of the main features of the city using the temporal resolution of multispectral bands of the satellite Landsat 5 and 8 for MSS and OLI sensors respectively belonging to NASA and for the period 1999-2021, and calculating the increase and decrease in the basic features of Baghdad. The main conclusions of the study were, This study from 1999 to 2021 and in two different seasons: the Spring of the growing season and Summer the dry season. When using the supervised classification method to determine the differences, the results showed remarkable changes. Where h
... Show MoreThe present work presents design and implementation of an automated two-axis solar tracking system using local materials with minimum cost, light weight and reliable structure. The tracking system consists of two parts, mechanical units (fixed and moving parts) and control units (four LDR sensors and Arduino UNO microcontroller to control two DC servomotors). The tracking system was fitted and assembled together with a parabolic trough solar concentrator (PTSC) system to move it according to information come from the sensors so as to keep the PTSC always perpendicular to sun rays. The experimental tests have been done on the PTSC system to investigate its thermal performance in two cases, with tracking system (case 1) and without trackin
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This research paper tries to show the significance of the narrative structure in the television advertisement and its connotations. The researchers chose the annual advertisement of Zain Mobile Telecommunication Company for the year 2020, which shed light on the global Corona pandemic crisis. The idea of the advertisement won wide approval as it focused on the suffering that everyone is witnessing like medical and security personnel in particular, and family relationships consequences.
In addition to the positive global interaction with the message presented by the Company in these exceptional circumstances. The advertisement, which lasted for 2.35 minutes, exceeded 13 million views in a short period of time. This prompted us to choos
The research aims to shed light on the obstacles that hinder the use of taxpayers' commercial books covered by provisions of the amended commercial book-keeping system No. 2 of 1985 and ways to address these obstacles. On this basis, the main null hypothesis was formulated that there is no statistically significant relationship between the obstacles to the adoption of the commercial books and taxable income.
The research data were collected on the base of three applied case studies of registered taxpayers in the General Commission of Taxes, GCT, together with the use of a questionnaire distributed to a sample of taxpayers ( companies ). The collected data were analyzed, the result were presented and the hypothesis was
... Show MoreInform the people of the Enlightenment including what was said in detail
In photography
For Mohammed Hashim bin Ahmed footy famous Balva Hashim (Tel: 1349 e)
Background: Tap waters play an important role in fulfilling the people needs for drinking and domestic purposes. Contaminate the tap water with different pollutants has become an issue of great concern for 90% of people who are depended on the tap water as the main source of drinking. Pollutants can make their way easily into the delivering pipes which suffer from the leaking resulting in decreasing the quality of water. Objective: Therefore, assess the water quality for drinking purpose by calculating the water quality index is an important tool to ascertain whether the water is suitable for human consumption or not. Methods: In the present work, the water quality of the Al-Salam, western region of Baghdad city, Iraq was investigated for 7
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The aim of this study to identify patterns of cerebral control (right and left) for second grade students in the collage of physical education and sports science of the University of Baghdad, as well as identify the definition of theThe Effect of Using the Bybee Strategy(5ES) according to Brain Control Patterns in Learning a Kinetic Series on Floor exercises in Artistic Gymnastics for menمجلة الرياضة المعاصرةالمجلد 19 العدد 1 عام 2020effect using the (Bybee) strategy (5ES) according to brain control patterns inlearning a Kinetic series on floor exercises In artistic gymnastics for men, andidentify the best combination between the four research groups learn, use Finderexperimental method research sample consi
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