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.
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This research aims at calculating the optimum cutting condition for various types of machining methods, assisted by computers, (the computer program in this research is designed to solve linear programs; the program is written in v. basic language). The program obtains the results automatically, this occur through entering the preliminary information about the work piece and the operating condition, the program makes the calculation actually by solving a group of experimental relations, depending on the type of machining method (turning, milling, drilling). The program was transferred to package and group of windows to facilitate the use; it will automatically print the initial input and optimal solution, and thus reduce the effort and t
... Show MoreThe derivatives formed after the successive acetylation, esterification and nitration reactions to cholic, deoxycholic, and taurocholic acids were identified to be of the following general strucure: Colt, Where RI=NO3, OH, 0=, or CH3COO. R2=H, NO3, OH, 0-=, or CH3COO. R3=H, NO3,01-1, 0=, or CH3COO. R4=OH, NH(CH2)2S03Na, NH(CH2)2S03H, or OMe. By using U.V-visible and I.R spectrophotometry . The number of hydroxyl groups was determined, purity was checked from T.L.C, Most of these derivatives will find pharmaceutical application.
Interface evaluation has been the subject of extensive study and research in human-computer interaction (HCI). It is a crucial tool for promoting the idea that user engagement with computers should resemble casual conversations and interactions between individuals, according to specialists in the field. Researchers in the HCI field initially focused on making various computer interfaces more usable, thus improving the user experience. This study's objectives were to evaluate and enhance the user interface of the University of Baghdad's implementation of an online academic management system using the effectiveness, time-based efficiency, and satisfaction rates that comply with the task questionnaire process. We made a variety of interfaces f
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The mechanism of hydrogen (H2) gas sensor in the range of 50-200 ppm of RF-sputtered annealed zinc oxide (ZnO) and without annealing was studied. The X-ray Diffraction( XRD) results showed that the Zn metal was completely converted to ZnO with a polycrystalline structure. The I–V characteristics of the device (PT/ZnO/Pt) measured at room temperature before and after annealing at 450 oC for4h, from which a linear relationship has been observed. The sensors had a maximum response to H2 at 350 oC for annealing ZnO and showed stable behavior for detecting H2 gases in the range of 50 to 200 ppm. The annealed film exhibited hig |
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Prediction of accurate values of residual entropy (SR) is necessary step for the
calculation of the entropy. In this paper, different equations of state were tested for the
available 2791 experimental data points of 20 pure superheated vapor compounds (14
pure nonpolar compounds + 6 pure polar compounds). The Average Absolute
Deviation (AAD) for SR of 2791 experimental data points of the all 20 pure
compounds (nonpolar and polar) when using equations of Lee-Kesler, Peng-
Robinson, Virial truncated to second and to third terms, and Soave-Redlich-Kwong
were 4.0591, 4.5849, 4.9686, 5.0350, and 4.3084 J/mol.K respectively. It was found
from these results that the Lee-Kesler equation was the best (more accurate) one
Objective(s):To evaluate the quality of life among secondary and to find out the relationship between students'quality of life and their socio-demographic characteristics of age, gender, residence, marital status, father's and mother's education, and family financial status in Kirkuk City. Methodology: A cross-sectional study is conducted on (100) studentwho are boys and girls aged(13 to 24) years old. These subjects are studying at secondary schools in Kirkuk City.The study is carried out at secondary schools in Kirkuk City from 7th July 7th 2014 to May 7th 2015. A questionnaire is constructed for the purpose
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Project deal with the study of the suitability of the planning standards of the select sites for sports facilities for the holy city of Karbala and the extent of convergence and divergence between these standards and points of strength and weakness in each of these standards.
It was found that there was a lack of the role given to the sports as a kind of luxury does not deserve to spend money and efforts, and was then incorporated with a lot of entertainment services by planners.
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