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.
Design and build a center basins new p-type four mirrors were studied its effect on all parameters evaluating the performance of the solar cell silicon in the absence of a cooling system is switched on and noted that the efficiency of the performance Hzzh cell increased from 11.94 to 21 without cooling either with cooling has increased the efficiency of the
This study aimed at identifying the counseling needs for classroom teachers specialization in
Jerash university. The sample of the study consisted (112) students. To achieve this goal a
scale with (39) items was built by the researcher, this scale has four domains they are as
follows; family, social, psychological and academic domain. The results of this study showed
that counseling needs obtain the heighest average. As well as, the results of the study revealed
that there were statistical differences in favor of gender and teaching year variable. Finally the
study stated a list of recommendations.
The reactions of ozone with 2,3-Dimethyl-2-Butene (CH3)2C=C(CH3)2 and 1,3-Butadiene CH2=CHCH=CH2 have been investigated under atmospheric conditions at 298±3K in air using both relative and absolute rate techniques, and the measured rate coefficients are found to be in good agreement in both techniques used. The obtained results show the addition of ozone to the double bond in these compounds and how it acts as function of the methyl group substituent situated on the double bond. The yields of all the main products have been determined using FTIR and GC-FID and the product studies of these reactions establish a very good idea for the decomposition pathways for the primary formed compounds (ozonides) and give a good information for the effe
... Show More
Objective: To determine the effect of instructional program on infertile women's knowledge regarding
diagnostic and therapeutic intervention for infertility.
Methodology: Non-probability (purposive sample) of (100) infertile women, who visit Kamal Al-Samaraee Hospital/
fertility and IVF center. The data are collected through the use of constructed questionnaire, which included:
demographic characteristics, social status, previous medical history, reproductive status, sexual status and questions
regarding women’s knowledge about infertility. Instrument validity and reliability was determined. Data were
collected through the use of questionnaire, the application of the instructional program was done for the study group<
Through the early childhood and after the ablactating the child learns acquired food habbits that might studying with him throughout his life. Here the parents role arises: teaching the child the sound food habits and hygienic styles and whatever beneficial to the health and with the sufficient quantities for the body. In this way the experiences the child learns at home will be of great help in his future life in choosing the suitable food after becoming more dependent in making his decisions and choices away from his parents. The results in this study showed that the averages of the children’s consumption of the high energy foods in comparison with the other highest consumption average , after that comes the con sumption of soft drills
... Show More
Objectives To tailor composites of polyethylene–hydroxyapatite to function as a new intracanal post for the restoration of endodontically treated teeth (ETT). Methods Silanated hydroxyapatite (HA) and zirconium dioxide (ZrO2) filled low-density polyethylene (LDPE) composites were fabricated by a melt extrusion process and characterised using infrared spectroscopy (FTIR), differential scanning calorimetry (DSC) and dynamic mechanical analysis (DMA). The flexural strength and modulus were determined in dry state and post ageing in simulated body fluid and fractured surfaces analysed by SEM. The water uptake and radiographic appearance of the experimental composites were also measured and compared with a commercially known endodontic fibre
... Show More
(3)
(12)
(10)
Elastic electron scattering form factors, charge density distributions and charge,neutron and matter root mean square (rms) radii for P24PMg, P28PSi and P32PS nuclei arestudied using the effect of occupation numbers. Single-particle radial wave functionsof harmonic-oscillators (HO) potential are used. In general, the results of elasticcharge form factors showed good agreement with experimental data. The occupationnumbers are taken to reproduce the quantities mentioned above. The inclusion ofoccupation numbers enhances the form factors to become closer to the data. For thecalculated charge density distributions, the results show good agreement withexperimental data except the fail to produce the hump in the central region for P28PSinucleus.
... Show MoreBackground: C-reactive protein (CRP) is an acute phase protein that its plasma levels increase after trauma or surgery so it is used as an indicator for the level of inflammation after surgery. The objective of this study is to investigate pre- and post-operative levels of CRP in three types of oral surgical interventions (Apicoectomy, Impaction, and Impacted teeth exposure). Materials and Methods: A total number of (48) healthy individuals aged (20-60) years who needed oral surgical intervention for either (removal of impacted third molars, exposure of an impacted canine, or Apicoectomy). A 4ml venous blood was obtained from each patient at two occasions (pre-operatively at the day of operation and post-operatively after 48 hours), then ce
... Show More
(1)