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 aim of this study was Identifying the relation of coordination and kinesthetic perception with artistic performance level in gymnastics skills for students in second class from the college of physical education/ university of Baghdad/ Al - jadreia .The searchers have been used the descriptive method in scanning style .The subject of this search has been taken (45) female - student in second class from the college of physical education/ university of Baghdad . The searchers have reached into specific conclusions concerning with statistic analysis about immoral joint relation between sensitive- kinetic coincidence and realization and with Artistic Performance Level in Gymnastics Skills for Women for second class .The an important recommen
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To decrease the dependency of producing high octane number gasoline on the catalytic processes in petroleum refineries and to increase the gasoline pool, the effect of adding a suggested formula of composite blending octane number enhancer to motor gasoline composed of a mixture of oxygenated materials (ethanol and ether) and aromatic materials (toluene and xylene) was investigated by design of experiments made by Mini Tab 15 statistical software. The original gasoline before addition of the octane number blending enhancer has a value of (79) research octane number (RON). The design of experiments which study the optimum volumetric percentages of the four variables, ethanol, toluene, and ether and xylene materials leads
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The process of identifying the region is not an easy process when compared with other operations within the attribute or similarity. It is also not difficult if the process of identifying the region is based on the standard and standard indicators in its calculation. The latter requires the availability of numerical and relative data for the data of each case Any indicator or measure is included in the legal process
The adoption of many mathematical concepts contributes to the construction of models of sports and the population can be interpreted to explain the movement and growth of the population lead to proper planning to manage the requirements of the population and meet their needs of providing education or providing medical services, health and others. In this study, the number of births in the Governorate of Basrah for the period (1998-2050) is estimated to be based on the assumption that the population of the visually impaired is a stable society. If the rate of growth is (0.0492), some demographic indicators are important for maintaining the average age of women at pregnancy (27.817). Each woman will give birth (3.74) female birth d
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The present study aimed to assess the impact of seed Rhizobia treatment and potyvirus inoculation on bacterial nodulation and nitrogen fixation in cowpeas. The plants were infected with the virus two weeks post-germination. Nodules were present on the roots of plants treated with Rhizobia; however, almost no nodules were detected on untreated plants. The average number of nodules per plant on virus-inoculated plants was significantly lower than the average number per noninoculated plant. The virus caused a substantial decrease in the weight of nodules also. The study revealed that the presence of Rhizobia resulted in a significant rise in nitrogen content in the foliage. Specifically, the nitrogen percentage increased from 1.29% in plants n
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The main objective of this study is to describe the preparation of topographic maps using the Surfer software. A total of 159 regularly distributed Ground Control Points (GCPs) were collected with the use of the Differential Global Positioning System (DGPS). Seven methods (Contour Map, Post Map, 3D Surface Map, 3D Wireframe Maps, Grid Vector-1 Map, Color Relief Map, and Shaded Relief Maps) at the Surfer environment were used to prepare the topographic maps at the Mukhtar Village near the Al-Fallujah City. Contour lines with other features were superimposed on the DEM layer, which refers to the topography of the terrain inside this study area. The accuracy of the database's results was estimated, essential maps were given, and the re
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Introduction to Medical Physics for Pharmacy Students and Medical Groups - ISBNiraq.org
The general objective of the research is to better understand changes in land cover and their impact on climatic factors by measuring changes in land cover for the Baghdad city for the period 1999-2021 and evaluating changes in land cover and measuring changes in climatic factors (relative humidity and evaporation). This study from 1999 to 2021 and in two different seasons: the April of the growing season and August the dry season. When using the supervised classification method to determine the differences, the results showed remarkable changes, the study showed the spatial variations in LC from 1999 to 2021 as follows: increase in the vegetation and water bodies during April and decrease this in August while the soil and built up decreas
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