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 variation in wing morphological features was investigated using geometric morphometric technique of the Sand Fly from two Iraqi provinces Babylon and Diyala . We distributed eleven landmarks on the wings of Sand Fly species. By using the centroid size and shape together, all species were clearly distinguished. It is clear from these results that the wing analysis is an essential method for future geometric morphometry studies to distinguish the species of Sand Flies in Iraq.
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The current study was carried out at the Fields belongs of Horticulture Department, Collage of Agricultural Engineering Science, University of Baghdad, Al-Jadiriyah for the spring season 2016 -2017 to study the effect for inoculation mycorrhizae and folair application with bio stimulators and their interaction in the growth characters of (local okra ptera). A factorial experiment (2 in randomized complete block design (RCBD), the experiment included (12) treatment Distributed in three replicates. The three factors used in this experiment included . The inoculation with control (C) Mycorrhizae ( M ) , Biozyme (B ) ( B1 2cm3.L-1), ( B2 4cm1-.L-1) , Phosphalas (P) (P 2cm3.L-1), ( M + B1), ( M + B2), (P +
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This research aims to find how three different types of mouthwashes affect the depth of artificial white spot lesions. Teeth with various depths of white spot lesions were immersed in either splat mouthwash, Biorepair mouthwash, Sensodyne mouthwash, or artificial saliva (control)twice daily for one minute for 4 weeks and 8 weeks at 37°C. After this immersion procedure, lesion depth was measured using a diagnosed pen score. A one-way analysis of variance, Dunnett T3 and Tukey's post hoc α = .05 were used to analyze the testing data. Splat mouthwash enhanced the WSL remineralization and made the lowest ΔF compared with other mouthwashes in shallow and deep enamel after 4 and 8 weeks of treatment. In the repair groups, after 4 weeks
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The present study was Conducted to evaluate the effect of amixture of three species of arbuscular mycorrhizal fungi ( Glomus etunicatum , G. leptotichum and Rhizophagus intraradices ) in Influence on the percentage of the components of NPK and protein of tomato leaves and roots infected with Fusarium oxysporum f.sp. Lycopersici wich cause Fusarial wilt disease , planted for 8 weeks in the presence of the organic matter ( peatmose) , using pot cultures in aplastic green house , Results indicated significant increase in the percentage of the elements of NK and protein of tomato leaves and roots In the control treatment (C), While the percentage of the element P was after infection with the pathogen 4 weaks after mycorrhizal colonization in al
... Show MoreAbstract The present study was Conducted to evaluate the effect of amixture of three species of arbuscular mycorrhizal fungi ( Glomus etunicatum , G. leptotichum and Rhizophagus intraradices ) in Influence on the percentage of the components of NPK and protein of tomato leaves and roots infected with Fusarium oxysporum f.sp. Lycopersici wich cause Fusarial wilt disease , planted for 8 weeks in the presence of the organic matter ( peatmose) , using pot cultures in aplastic green house , Results indicated significant increase in the percentage of the elements of NK and protein of tomato leaves and roots In the control treatment (C), While the percentage of the element P was after infection with the pathogen 4 weaks after mycorrhiza
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Background: Spices and herbs have been used by many cultures to enhance the flavor and aroma of food and for their medicinal value. Black cardamom is one of these spices widely used in cooking because of its unique taste and powerful flavor. The aim of study was to test the effect of black cardamom on Mutans Streptococci in comparison to chlorhexidine gluconate (0.2%) and de-ionized water. Materials and methods: Dried fruits of black cardamom were extracted by using alcohol (70% ethanol). Saliva was collected from seven volunteers. Agar well technique with different concentrations of black cardamom extracts was used to test the sensitivities of Mutans Streptococci, as well black cardamom extracts effect on viable counts of Mutans Streptococ
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