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.
Hygienic engineering has dedicated a lot of time and energy to studying water filtration because of how important it is to human health. Thorough familiarity with the filtration process is essential for the design engineer to keep up with and profit from advances in filtering technology and equipment as the properties of raw water continue to change. Because it removes sediment, chemicals, odors, and microbes, filtration is an integral part of the water purification process. The most popular technique for treating surface water for municipal water supply is considered fast sand filtration, which can be achieved using either gravity or pressure sand filters. Predicting the performance of units in water treatment plants is a basic pri
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Integrated project delivery is collaboratively applying the skills and knowledge of all participants to optimize the project's results, increase owner value, decrease waste, and maximize efficiency during the design, fabrication, and construction processes. This study aims to determine IPD criteria positively impacting value engineering. To do this, the study has considered 9 main criteria according to PMP classification that already covers all project phases and 183 sub-criteria obtained from theoretical study and expert interviews (fieldwork). In this study, the SPSS (V26) program was used to analyze the main criteria and sub-criteria priorities from top to bottom according to their values of the Relative Importance In
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Sustainability is a major demand and need pursued by cities in all areas of life due to the environmental, social and economic gains they provide, especially in the field of city planning and urban renewal projects that aim to integrate the past, present and future.
The research aims to evaluate the Haifa Street renewal project, and Al-Shawaka district, one of the Baghdad districts located next to Al-Karkh, was elected by comparing the sustainability indicators of urban renewal with the reality of the situation through a field survey and questionnaire form and focusing on the social and economic impacts and environmental for the project on the study area. To reach the most important conclusions and recommendations
... Show MoreThe world is currently facing a medical crisis. The epidemic has affected millions of people around the world since its appearance. This situation needs an urgent solution. Most countries have used different solutions to stop the spread of the epidemic. The World Health Organization has imposed some rules that people should adhere. The rules are such, wearing masks, quarantining infected people and social distancing. Social distancing is one of the most important solutions that have given good results to confront the emerging virus. Several systems have been developed that use artificial intelligence and deep learning to track social distancing. In this study, a system based on deep learning has been proposed. The system includes monitor
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The marshes are one of the important environmental features affecting human and animal systems, so the studying of changes they undergo is one of the important topics. This study is concerned with the changes occurring in the Al Saadya marsh for the period from 1987 to 2017 exclusively in the winter season (the marshes’ revival season in Iraq revive). In order to inspect the changes in this marsh, we choose 7 years to cover the study period as a criterion years, namely 1987, 1990, 1995, 2000, 2007, 2014 and 2017. The “Maximum Likelihood” classifier was used to separate the stacked land cover features, where the minimum overall accuracy ratio that recorded for all years of study was 96%. The results revealed that Al-Saadya marsh went t
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The interesting of industrial sector and developing it after corner stone. It is important to build economic balanced and get behind and front linkage for transformative industrials, and this is important to get balanced.
The value of transformative industry sector is more important than other sectors in economy, and this is reflect the capital in industrial sector .Industry sector is larger than other sectors ,so it regards the motive which moving the economic wheel .
The problem :
The research treats reduction and retreat the ind
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This paper including a gravitational lens time delays study for a general family of lensing potentials, the popular singular isothermal elliptical potential (SIEP), and singular isothermal elliptical density distribution (SIED) but allows general angular structure. At first section there is an introduction for the selected observations from the gravitationally lensed systems. Then section two shows that the time delays for singular isothermal elliptical potential (SIEP) and singular isothermal elliptical density distributions (SIED) have a remarkably simple and elegant form, and that the result for Hubble constant estimations actually holds for a general family of potentials by combining the analytic results with data for the time dela
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The orbital motion and longitude for some Jupiter's satellites (Amaletha, Europa, Ganymede and Callisto) were calculated from two different locations Iraq and Syria. A program was designed, the input parameters were the desired year, month, day and the longitude of the location, the output parameters results were applied in form of a file, and this file includes the longitude, orbital motion, and local time of these satellites. A specific date 1-10-2013 was taken, the results of longitude was (20-336) º and orbital motion was (92-331) º for both Iraq and Syria location with observing time (05:24:14-15:18:10) for Iraq and (04:56:33-14:50:30) for Syria. The difference in time between the two locations was constant (00:45:00), these results
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In this research will be treated with a healthy phenomenon has a significant impact on different age groups in the community, but a phenomenon tonsillitis where they will be first Tawfiq model slope self moving averages seasonal ARMA Seasonal through systematic Xbox Cengnzla counter with rheumatoid tonsils in the city of Mosul, and for the period 2004-2009 with prediction of these numbers coming twelve months, has found that the specimen is the best representation of the data model is the phenomenon SARMA (1,1) * (2,1) 12 from the other side and explanatory variables using a maximum temperature and minimum temperature, sol