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.
Background: Blood group system and the ability to taste phenylthiocarbamide (PTC) are the most studied traits in human genetics which have been extensively used in describing genetic variations among human populations around the world that may had an effect on dental caries. The aims of present study were to investigate the caries experience among students with different bitter taste threshold in relation to blood type. Materials and Methods: The sample of present study includes dental students female aged19-21 years. The diagnosis of dental caries was done according to the criteria of Manjia et al, 1989 recording decayed lesion by severity (D1-4) MFS. Furthermore, bitter taste sensitivity was measured according to PTC (phenylthiocarbamid
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The current study is designed to investigate the histological and immunohistochemical characteristics of the thyroid gland in adult male Sciurus anamalus. This study found that the thyroid gland of the Caucasian squirrel is located in the neck area, below the larynx, on both sides of the trachea. It has two lobes (right and left) with cylindrical shape. The histological studies revealed that the thyroid gland is surrounded by a capsule which consists of connective tissue and forming of two layers which are outer layer and inner layer, and a layer of adipose tissue appears overlapping the outer layer. The inner tissue of the gland consists of follicles with different shapes and sizes, and is lined with simple cuboidal epithelial tissue (foll
... Show MoreThis study describes the preparation of a new bidentate Schiff base derived from the condensation of Isatin-3-hydrazone with 2-acetylthiophene and the preparation of new series of complexes with a good yield. The prepared ligand was characterized by IR, UV-Vis, C.H.N.S elemental analysis, 1H and 13C NMR, LC-Mass spectroscopy, and physical measurements. Its complexes were analyzed by C.H.N.S elemental analyses, UV-Vis., FTIR, NMR, LC-Mass Spectra, atomic absorption spectroscopy, magnetic susceptibility, and conductivity measurements The results from spectroscopy and measurement studies showed that the ligand coordinated to the metal ion as a bidentate ligand via oxygen and nitrogen, forming an octahedral geometry around it. In vitro antimicr
... Show MoreThis study reports on natural convection heat transfer in a square enclosure of length (L=20 cm) with a saturated porous medium (solid glass beads) having same fluid (air) at lower horizontal layer and free air fill in the rest of the cavity's space. The experimental work has been performed under the effects of heating from bottom by constant heat flux q=150,300,450,600 W/m2 for four porous layers thickness Hp (2.5,5,7.5,1) cm and three heaters length δ(20,14,7) cm. The top enclosure wall was good insulated and the two side walls were symmetrically cooled at constant temperature. Four layers of porous media with small porosity, Rayleigh number range (60.354 - 241.41) and (Da) 3.025x10-8 has been investigated. The obtained data of temperatu
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A specific, sensitive and new simple method was used for the determination of methyldopa in pure and pharmaceutical formulations by using continuous flow injection analysis. This method is based on formation of ion pair compound between methyldopa and potassium hexacyanoferrate in acidic medium to obtain a yellow precipitate complex using long distance chasing photometer (NAG-ADF-300-2). The linear range for calibration graph was 0.05-35 mmol/L for cell A and 0.05-25 mmol/L for cell B, and LOD 1.4292 µg /200 µL for both cells with correlation coefficient (r) 0.9981 for cell A and 0.9994 for cell B, RSD% was lower than 0.5 % for n=8 for. The results were compared with classical method UV-Spectrophotometric at λ max=280 nm and turbi
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Adhesion (type 1 fimbriae) and host defense avoidance mechanisms (capsule or lipopolysaccharide) have been shown to be prevalent in Escherichia coli isolates associated with urinary tract infections. In this work, 50 uropathogenic Escherichia coli (UPEC) isolated from children with urinary tract infections were genotypically characterized by polymerase chain reaction (PCR) assay. We used two genes; fimH and kpsMTII, both of them previously identified in uropathogenic E.coli (UPEC) isolates. The PCR assay results identified fimH (90.0)% and kpsMTII (72.0)% isolates. In the present study, was also demonstrated that these genes may be included in both or one of them within a single isolate.
Background and Aim. Coronary artery disease (CAD) is a major risk factor for the progression to heart failure (HF), which is associated with an increase in left ventricular volume (LVV). This study aims to measure ventricular function and myocardial perfusion imaging markers of the left side of the heart, which can be performed with injection of a 99mTc at stress and rest by using single-photonemission-computed-tomography (SPECT). Subject and methods. The study included 121 patients with CAD, comprising 53 females and 68 males with ages between 25 to 88 years and 265 healthy subjects comprising 84 males and 181 females. All patients and healthy subjects volunteered to participate in this study. They were classified according to
... Show MoreBackground: The aim of this study was to determine phototoxic effect of visible blue light on anaerobic periodontal pathogens namely Aggregatibacter actinomycetemcomitans and Porphyromonas gingivalis. Materials and methods: Strains of Aggregatibacter actinomycetemcomitans and Porphyromonas gingivalis were isolated from pockets of systemically healthy patients aged between 35-55 years old with pocket depths of 5-6 mm, the bacteria cultured on special blood Agar plates solid media, then subjected to visible blue light emitted from commercially available light cure devise (LED curing light); that emits blue light (400-500nm) of 1000mw energy at different periods of time exposures, then the CFU of each plate was measured by direct colony count
... Show MoreThe present study aimed to investigate the anatomy, histology, and immunohistochemistry of parathyroid gland in two Iraqi mammals (Weasel, Herpestes javanicus and Long-ear hedgehog, Hemiechinus auritus) as a comparative study. A total of (20) animal for each species were used in the present study. Animals collected were immediately anesthesia and dissected to get the parathyroid gland. Methods of Humason and Bancroft and Stevens were employed for histological techniques. Different stains were used (Hematoxylin- Eosin stain-(H & E), Periodic Acid Schiff stain-(PAS), Azan stain, and Methyl Blue stain-(MB)) for staining the histological sections. Anti-calcitonin, code140778 marker used for immune-histochemical study. Results of the present stu
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