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.
OpenStreetMap (OSM) is the world’s biggest publicly licensed geographic data collection. Because OSM is rapidly being used in a wide range of applications, researchers have focused their efforts on determining its quality. The OSM buildings data quality is still ambiguous, due to the limitations, and a few researchers have evaluated the OSM buildings data quality through difficulties where the authoritative data are not obtainable. The focus of this research is to analyze and assess the accuracy of OSM buildings including completeness, and positional accuracy methods. Two different study areas in Baghdad city-Iraq have been investigated: Al-Rasheed and Al-Karrada. The process of the (OSM) data evaluation involved identifying the correspon
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Among the different passive techniques heat pipe heat exchanger (HPHE) seems to be the most effective one for energy saving in heating ventilation and air conditioning system (HVAC). The applications for nanofluids with high conductivity are favorable to increase the thermal performance in HPHE. Even though the nanofluid has the higher heat conduction coefficient that dispels more heat theoretically but the higher concentration will make clustering .Clustering is a problem that must be solved before nanofluids can be considered for long-term practical uses. Results showed that the maximum value of relative power is 0.13 mW at nanofluid compared with other concentrations due to the low density of nanofluid at this concentration. For highe
... Show MoreReduction has been linked visually in art since man began making functional and aesthetic forms, and this beginning can be identified with cave paintings. Reduction is one of the clearest indications of intellectual presence in aesthetic experience. Modernism was greatly supported by the great transformations that the intellectual movement witnessed in the world in general and in Europe in particular. There, and their transfer of European artistic experiences, and the reflection of this influence in their aesthetic sculptures, and for this reason the researchers find that the study of the aesthetic references of the reductive forms in the Iraqi sculptural experience represents a great importance in the study of the history of contem
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Due to the deterioration of water quality within the last few years because of the increase of water consumption and the waste water production and disposal into the river The water quality in both surface and ground water resources was negatively affected .The concept of water quality index is used as a tool for water quality classification in Tigris River within Baghdad City .Twenty two parameters of pollution were selected to measure the water quality indices of Tigris river within Baghdad city .Those parameters were measured during (2000-2004)as average monthly values ,three water treatment plants were selected out of the eight water treatment plants that exist along the river.Al Kharkh water treatment plant to reflect the water quality
... Show MoreIn this study predication of crop coefficient (Kc) values through growing season for cucumber plant was conducted. A field experiment was carried out at AL Yusufiyah Township, in the Governorate of Baghdad, (latitude: 33°09' N, longitude: 44°24' E, and altitude: 34 m) in medium loam soil. The plant was cultivated inside the greenhouse under subsurface trickle irrigation system with soil water retention technology (SWRT) during the growing season 2017. Crop coefficient values were guessed from the direct method of measurements of daily crop evapotranspiration, while reference evapotranspiration was obtained from Agricultural Meteorology Project - Station of Baghdad - Abu-Ghraib. The obtained results were showed that crop coeffici
... Show MoreDue to the easily access to the satellite images, Google Earth (GE) images have become more popular than other online virtual globes. However, the popularity of GE is not an indication of its accuracy. A considerable amount of literature has been published on evaluating the positional accuracy of GE data; however there are few studies which have investigated the subject of improving the GE accuracy. In this paper, a practical method for enhancing the horizontal positional accuracy of GE is suggested by establishing ten reference points, in University of Baghdad main campus, using different Global Navigation Satellite System (GNSS) observation techniques: Rapid Static, Post-Processing Kinematic, and Network. Then, the GE image for the study
... Show MorePurpose: The concept of complete street is one of the modern trends concerned with diversifying means of transportation and reducing the disadvantages of mechanical transportation modes. This paper discusses the role of complete streets can play in developing the urban environment in the Alyarmok District of Baghdad. Method/design/approach: The linear regression method used to analyze the opinions of 100 respondents surveyed in the study area in order to find the relationship between the urban environment and the complete street elements. Theoretical framework: The Modern trends in urban planning aim to find alternatives to the policies of traditional transportation planning that focus on vehicular mobi
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Implementation of TSFS (Transposition, Substitution, Folding, and Shifting) algorithm as an encryption algorithm in database security had limitations in character set and the number of keys used. The proposed cryptosystem is based on making some enhancements on the phases of TSFS encryption algorithm by computing the determinant of the keys matrices which affects the implementation of the algorithm phases. These changes showed high security to the database against different types of security attacks by achieving both goals of confusion and diffusion.
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