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.
Aim: The reduction in the amount of marginal bone is the most important demand for the long term success of dental implants. This prospective clinical study was aimed to investigate the marginal bone loss of early loaded SLActive implants with different dimensions and surgical approaches. Materials and methods Fifteen patients aged from 18 to 60 years were divided into 2 groups (flapped and flapless approach) that underwent delayed implant placement protocol with SLActive implants. The marginal bone level was estimated by cone-beam computed tomography during three different periods: preoperatively, 8 weeks after surgery and 24 weeks after loading of the prosthesis. Results: The mean value of marginal bone level was not significantly chan
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This research concentrate on cultivated Iraqi Agave attenuata dried leaves and roots, because of little studies on this plant especially on the root that lead to the eager of study and comparison of phytochemical constituents between leaves and root. Extraction of bioactive constituents was carried out using several solvents with increasing polarity (n-hexane, ethyl acetate and methanol) by soxhlet apparatus. Steroidal saponins in Agave genus is well documented in many species, lightening the minds in this research on extraction method which is specific for steroidal saponins. Phytochemical screening was done by GC/MS for n-hexane fraction, qualitative and quantitative estimation of several bioactive constituents (caffe
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The purpose of this study is to investigate the histopathological response of dentinopulpal
response of human teeth to the Er: YAG laser cavity preparation in comparison with the conventional
class I cavity preparation. Thirty five sound human upper and lower first premolar teeth which were
needed to be extracted for orthodontic purposes were used in the study. Regarding to the method of
cavity preparation, the teeth were grouped into three groups; Group1; Control group which consists of
seven sound teeth without cavity preparation, Group2; Conventional cavity preparation group and group
3; Er: YAG laser cavity preparation group. Each of Group2 and3 consists of fourteen teeth that is
subdivided into: A. 7teeth that e
The use of male mothers fur c meat Fabro to learn Effect concentrations of ammonium chloride NH4CL and Bacarbonnat sodium NaHCO3 in drinking water by heat stress and Altsoam during heat stress on some of the qualities of productivity and Alvesrgih divided animals to 6 transactions, namely: - control without adding NH4CL, NaHCO3 and Altsoam (treatment 1) Altsoam-1200 of 7-4 weeks old chicken meat to heat patrol 25-34-25 .. 7 weeks old Weight was measured gravimetric vivo increase feed consumption
Objective: To find out the relationship between vaginal bleeding during third trimester and pregnancy outcomes. Methodology: A purposive sample is "Non-probability" of (100) women who had diagnostic vaginal bleeding during third trimester (27-40wk) of pregnancy, and who visited the Bint Al-Huda Hospital for the period from 15th Feb. to 17th May 2015.Validity and reliability of questionnaire are determined through pilot study. Descriptive and inferential statistical procedures were used to analyze the data, and the data were collected by using interview technique, constructed questionnaire has been desig
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four coordinated complexes for divalent metal ions : Mn, Fe, Co, Ni, Cu and Cd have been synthesized using bidentate Schiff base ligand type (NN)formed by the condensation of o-phenylenediamine , p- methylbenzadehyde and furfural in methanol. The ligand was reacted with divalent metal chloride forming complexes of the types :[M(L)Cl2] where : MII=Mn, Fe, Ni, Cu, and Cd . These new compounds were characterized by elemental analysis, spectroscopic methods (FT-IR, U.V-Vis, 1HNMR (for ligand only and atomic absorption) , magnetic susceptibility, chloride content along with conductivity measurement. These studies revealed that the geometry for all complexes about central metal ion is tetrahedral.
The article provides a comparative analysis of comparisons in Russian and Arabic, aimed at identifying their structural, typological, and functional-pragmatic features. The study is based on a systematic approach to the analysis of linguistic means of expressing comparisons in two differ- ent linguistic cultures. The article analyzes the main structural components of comparisons, their classification, and their cognitive and aesthetic functions. The results of the study demonstrate the deep cultural conditioning of comparative constructions and their important role in representing the specific features of the respective linguistic cultures.
The experiment was conducted in two stages: first stage: determination of the most effective dose of Cyperus rotundus tubers aquatic extract in male rats for 5 days, which was concentrated as (200 mg/kg body weight). The second stage was designed to observe and test the protective effects of C. rotundus tubers aquatic extract in the liver and kidney functions of male rats exposed to cadmium chloride poisoning (5 mg/kg bw) for 30 days. The animals were divided into (4) groups within each group (5) animals weighted (200-220g). The results of oral dose of cadmium chloride showed a significant increase of (P˂0.05) in the activity of both enzymes Alanine aminotransferas
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A novel Schiff base ligand [N1-benzylidenebenezene-1,2-diamine(L) = C20H16N2] was prepared through intensification of benzaldehyde (C6H5CHO) and O- amino aniline O-C6H4(NH2)2 in ethanol with 8-Hydroxyquinoline (8HQ) . Formed compounds were acquired of 1:1:2 molar proportion reactions for metal ions and ligands (L) and 2(8HQ) during reaction for MCl2 .nH2O salt products complexes conformable into the forms [M(L)(8HQ)2] ,where M = Mn(II),Co(II) and Ni(II). Whole the compounds were identified during the basis of their; FT-IR and U.V spectrum, melting point, molar conduct, identify of the percentage from the metal at the complexes via flame (AAS), C, H and N content of the Schiff base (L) and metal complexes were analysis and magnetic susceptib
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