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.
3D models delivered from digital photogrammetric techniques have massively increased and developed to meet the requirements of many applications. The reliability of these models is basically dependent on the data processing cycle and the adopted tool solution in addition to data quality. Agisoft PhotoScan is a professional image-based 3D modelling software, which seeks to create orderly, precise n 3D content from fixed images. It works with arbitrary images those qualified in both controlled and uncontrolled conditions. Following the recommendations of many users all around the globe, Agisoft PhotoScan, has become an important source to generate precise 3D data for different applications. How reliable is this data for accurate 3D mo
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The current research aims to diagnose the type and level of influence of social media, whose dimensions are represented by (attitudes towards social media marketing, knowledge and use of social media, influence on the Internet and social media, following up on social media) on customer behavior in its dimensions (attracting attention, raising Interest, desire creation, customer response), and the research sought to answer questions related to the research problem by testing the main hypotheses to explore correlations and influence between the two variables, and to achieve research hypothesis tests, the field study was used, as the research sample reached (135) individuals from the director and the assistant director And marketing personnel
... Show MoreDue to severe scouring, many bridges failed worldwide. Therefore, the safety of the existing bridge (after contrition) mainly depends on the continuous monitoring of local scour at the substructure. However, the bridge's safety before construction mainly depends on the consideration of local scour estimation at the bridge substructure. Estimating the local scour at the bridge piers is usually done using the available formulae. Almost all the formulae used in estimating local scour at the bridge piers were derived from laboratory data. It is essential to test the performance of proposed local scour formulae using field data. In this study, the performance of selected bridge scours estimation formulae was validated and sta
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Chromatographic and spectrophotometric methods for the estimation of mebendazole in
pharmaceutical products were developed. The flow injection method was based on the oxidation of
mebendazole by a known excess of sodium hypochlorite at pH=9.5. The excess sodium hypochlorite is then
reacted with chloranilic acid (CAA) to bleach out its color. The absorbance of the excess CAA was recorded
at 530 nm. The method is fast, simple, selective, and sensitive. The chromatographic method was carried out
on a Varian C18 column. The mobile phase was a mixture of acetonitrile (ACN), methanol (MeOH), water
and triethylamine (TEA), (56% ACN, 20% MeOH, 23.5% H2O, 0.5% TEA, v/v), adjusted to pH = 3.0 with
1.0 M hy
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The consumption of fossil fuels has caused many challenges, including environmental and climate damage, global warming, and rising energy costs, which has prompted seeking to substitute other alternative sources. The current study explored the microwave pyrolysis of Albizia branches to assess its potential to produce all forms of fuel (solid, liquid, gas), time savings, and effective thermal heat transfer. The impact of the critical parameters on the quantity and quality of the biofuel generation, including time, power levels, biomass weight, and particle size, were investigated. The results revealed that the best bio-oil production was 76% at a power level of 450 W and 20 g of biomass. Additionally, low power levels led to enhanced
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In order to promote sustainable steel-concrete composite structures, special shear connectors that can facilitate deconstruction are needed. A lockbolt demountable shear connector (LB-DSC), including a grout-filled steel tube embedded in the concrete slab and fastened to a geometrically compatible partial-thread bolt, which is bolted on the steel section's top flange of a composite beam, was proposed. The main drawback of previous similar demountable bolts is the sudden slip of the bolt inside its hole. This bolt has a locked conical seat lug that is secured inside a predrilled compatible counter-sunk hole in the steel section's flange to provide a non-slip bolt-flange connection. Deconstruction is achieved by demounting the tube from the t
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Polyethersulfone (PES) ultrafiltration membrane blending NaX zeolite crystals as a hydrophilic additive was examined for zinc (II) and lead ions Pb (II) removal from aqueous solutions. The effect of NaX zeolite content on the permeation flux and removal efficiency was studied. The results showed that adding zeolite to the polymer matrix enhanced the permeation flux. The permeation flux of all the zeolite/PES matrix membranes was higher than the pristine membrane. No significant improvement was observed in the removal of Zn (II) ions using all prepared membranes as the removal percentage did not raise above 29.2%. However, the removal percentage of Pb (II) ions was enhanced to 97% using a membrane containing 0.9%wt. zeolite. Also, it was
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