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.
High-performance liquid chromatographic methods are used for the determination of water-soluble vitamins with UV-Vis. Detector. A reversed-phase high-performance liquid chromatographic has been developed for determination of water-soluble vitamins. Identification of compounds was achieved by comparing their retention times and UV spectra with those of standards solution. Separation was performed on a C18 column, using an isocratic 30% (v/v) acetonitril in dionozed water as mobile phase at pH 3.5 and flow rate 1.0m/min. The method provides low detection and quantification limits, good linearity in a large concentration interval and good precision. The detection limits ranged from 0.01 to 0.025µg/ml. The accuracy of the method was
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This experiment presented essential oils by GC/MS, pigment content, and their antioxidant activities as well as sensory evaluation of delight samples. Limonene (66.88%) was the most prevalent yield. The peels of clementine had DPPH and ABT Scavenging activity. All levels of pigment extract had better scores for all sensory values and recorded acceptable scores in terms of appearance, color, aroma, and overall acceptability compared to control delight. Besides, delight samples containing 15 mg astaxanthin pigment extract showed maximum sensory scores compared to other samples and control delight. On the other hand, the product was less acceptable to the panelists compared to control in the case of the addition of 3.75 mg astaxanthin pigme
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The virulent genes are the key players in the ability of the bacterium to cause disease. The products of such genes that facilitate the successful colonization and survival of the bacterium in or cause damage to the host are pathogenicity determinants. This study aimed to investigate the prevalence of virulence factors (esp, agg, gelE, CylA) in E. faecalis isolated from diverse human clinical collected in Iraqi patient , as well as to assess their ability to form biofilm and to determine their haemolytic and gelatinase activities. Thirty-two isolates of bacteria Enterococcus faecalis were obtained, including 15 isolates (46.87%) of the urine, 6 isolates (18.75%) for each of the stool and uterine secretions, and 5 isolates (15.62%) of the wo
... Show MoreCongenital valvular pulmonary stenosis accounts for 5-10% of all congenital heart disease. Balloon pulmonary valvuloplasty is a safe and effective method in reduction of moderate to severe valvular pulmonary stenosis. This retrospective study done in Hawler surgical specialty cardiac center on pediatric patients who had pulmonary valve stenosis (with echocardiographic peak gradient 2:50mmHg) and treated by balloon pulmonary valvuloplasty. A total of 178 cases were involved, 93(52.25%) patient was male and 85 (47.75%) patients was female. 160 patient (89.89%) were treated with single balloon method 18 patient (10.11%) were managed by double balloon method technique. Follow up period of these patients range from 1 year to 10 years (mean of 5.
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Background: Antimicrobial agents have been considered as having potential for the prevention of dental caries. This study aimed to test the effect of different concentrations of cardamom and black tea extracts on the sensitivity and growth of salivary mutans streptococci in comparison to chlorhexidine gluconate (0.2%) in vitro. Materials and methods: In this study. Mutans streptococci were isolated from saliva of 34 healthy people (aged between 22-40yrs). The bacteria was isolated, purifiedand diagnosed according to morphologicalcharacteristic and biochemical tests. Aqueous extracts of cardamom and black tea were prepared. Different concentrations of extracts were prepared and estimated in gm/ 100ml deionized water. The agar diffusion techn
... Show MoreThree mesoporous silica with different functional group were prepared by one-step synthesis based on the simultaneous hydrolysis and condensation of sodium silicate with organo - silane in the presence of template surfactant polydimethylsiloxane - polyethyleneoxide (PDMS - PEO). The prepared materials were characterized by Fourier transform infrared spectroscopy (FTIR), thermogravimetric analysis (TGA), atomic force microscopy (AFM) and nitrogen adsorption/desorption experiments. The results indicate that the preparation of methyl and phenyl functionalized silica were successful and the mass of methyl and phenyl groups bonded to the silica structure are 15, 38 mmol per gram silica. The average diameter of the silica particles are 103.51,
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Background: Although methotrexate (MTX) is a frequently used chemotherapy drug, its effectiveness is sometimes hampered by the drug's toxic consequences. Omega 7 is a monounsaturated fatty acid, with different anti-inflammatory, anti-diabetic anti-obesity applications, and its possible protective effects against MTX-induced blood toxicity were investigated in this study. Objective: Evaluation of possible protective effects of omega7 against MTX-induced blood toxicity. Methods: 30 mice were divided into five groups, the First group take liquid paraffin orallyfor 7 days for served as negative control and the second group take methotrexate (20mg/kg) intraperitoneallyto serve as a positive control,the third group takes omega 7 (100mg/kg
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