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.
Beta-lactam medications are among the commonly used antibiotics. These drugs kill germs by disrupting cell wall formation. This drug treats bacterial infections in numerous body sections. A new, quick, high-performance liquid chromatography approach has been developed and verified by the FDA and EMA for the simultaneous estimation of drugs in their medicinal and pure forms. This study deals with the determination of beta-lactam drugs (Amoxicillin, Ampicillin, Cephalexin, Cefotaxime, Cefoxitin, Cefamandole, Cephalothin, Piperacillin, Penicillin, Oxacillin, Cloxacillin, Nafcillin, Carbenicillin, Mezlocillin, Dicloxacillin) by a Reversed-Phase High-Performance Liquid Chromatography (RP-HPLC) technique based on an UV detector using a
... Show MoreThe concept of rehabilitation provided an essential richness in the conservation philosophy through sustaining buildings life and adapting them to the contemporary use through a vision which looks at the present and future . In Iraq , the existence of historical buildings and the traditional fabric in the cities required the urban development which enhanced the interests of planning and architectural fields especially the building rehabilitation which requires the architectural intervention , and all that led to elaborate the problem of research which is " The confusion in the concepts of monumental, historical and traditional buildings in Iraq, As well as The insufficient knowledge about rehabilitation and the acts related to it through
... Show MoreHuman resistin is an adipokine, with a possible link to coronary heart disease.A few studies were done about resistin in acute phase of ST-segment elevation myocardial infarction (STEMI) especially in Iraqi patients. Accordingly we design a study to investigate the association between resistin concentration and acute phase of STEMI in Iraqi patients.
The present study was carried out at Al-Yarmouk Teaching Hospital from December 2011 until June 2012. Serum resistin levels were measured in 50 patients with acute STEMI (mean age: 58.16 ± 11.73 years) at the first 12 hours of admission and 34 normal controls (mean age: 53.98 ± 15.46 years) matched for age, sex and other risk factors.
Resistin level in patients wi
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Bacopa monnieri L. (Scrophulariaceae), synoname is Herpestis monniera that provides bioactive compounds, especially triterpenoid saponins (Bacosides) which exhibits an important biological activities, like hypothyroidism, anticonvulsant, memory enhancing and antistress. Because there are no researches about B. monnieri L. plant that grow in Iraq, and there active compounds especially triterpenoid saponin (TS), and there effects. This study was detected the presence of (TS) in, and examined the cytotoxic and the antioxidant activity of these compounds in vitro. The study was included the extraction and identification of TS from the whole parts of B. monnieri L. by using three methods, and the best yield was analyzed by High Performance Liqui
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Environmentally friendly copper oxide nanoparticles (CuO NPs) were prepared with a green synthesis route via Anchusa strigosa L. Flowers extract. These nanoparticles were further characterized by FTIR, XRD and SEM techniques. Removing of Gongo red from water was applied successfully by using synthesized CuO NPs which used as an adsorbent material. It was validated that the CuO NPs eliminate Congo red by means of adsorption, and the best efficiency of adsorption was gained at pH (3). The maximum adsorption capacity of CuO NPs for Congo red was observed at (35) mg/g. The equilibrium information for adsorption have been outfitted to the Langmuir, Freundlich, Temkin and Halsey adsorption isot
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In this research, annealed nanostructured ZnO catalyst water putrefaction system was built using sun light and different wavelength lasers as stimulating light sources to enhance photocatalytic degradation activity of methylene blue (MB) dye as a model based on interfacial charges transfer. The structural, crystallite size, morphological, particle size, optical properties and degradation ability of annealed nanostructured ZnO were characterized by X-Ray Diffraction (XRD), Atomic Force Microscopy (AFM) and UV-VIS Spectrometer, respectively. XRD results demonstrated a pure crystalline hexagonal wurtzite with crystalline size equal to 23 nm. From AFM results, the average particle size was 79.25nm. All MB samples and MB with annealed nanostr
... Show MoreA rapid high performance liquid chromatography method for the determination of sphinganine (Sa) and sphingosine (So) in urine samples by employing a silica-based monolithic column is described. The samples were first extracted using ethyl acetate and derivatized using ortho-phthaldialdehyde in the presence of 2-mercaptoethanol. C20 sphinganine was used as internal standard. Under the optimized conditions, separation was achieved using a mixture of methanol:water (93:7, v/v), column temperature at 30°C, flow rate of 1 mL min−1, and an injection volume of 10 μL. Good linearity was obtained for Sa and So over the concentration range 20–500 ng mL−1(correlation coefficients ≥0.9978). The detection limits were 0.45 ng mL−1 for Sa and
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