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.
Abstract
financial market occupy very important place in the economic activity all over the world countris, and its importance increased with considerable technological progress in the world of transportation ,communications and information where its impact have spread over the whole world, which led to link the international economy in a kind of international relations so that the open policy became the prevailing trend in national and regional economies within the framework of the new world order.
the international economy has faced the financial crisis, global, that hit all world economies although the United States is the center of the crisis and the starting spark for it w
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In this study, we focused on the random coefficient estimation of the general regression and Swamy models of panel data. By using this type of data, the data give a better chance of obtaining a better method and better indicators. Entropy's methods have been used to estimate random coefficients for the general regression and Swamy of the panel data which were presented in two ways: the first represents the maximum dual Entropy and the second is general maximum Entropy in which a comparison between them have been done by using simulation to choose the optimal methods.
The results have been compared by using mean squares error and mean absolute percentage error to different cases in term of correlation valu
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The educational sector is one of the important sectors in the world, and it is considered one of the means of community development. In addition, it is one of the means of making the country’s renaissance and devel-opment because it represents the factory of thinking minds that make change. There is no doubt that this sector is the same as any other sector. The deficit in the studied scientific planning has been prolonged, which led to its deterioration, and the problems of education remain diverse and inherited from previous time periods, where the hierarchical cluster analysis was used on postgraduate students in universities in Iraq, except for Kurdistan region, and the number of universities that were included in the study was
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The research topic is summarized in the importance of studying the measuring the extent of the university youth’s exposure in the Emirati Society to those series and the resulting achieved satisfaction. The most important results and recommendations of the study are as follows: a high rate of the respondents’, sample individuals, exposure to the dubbed Turkish series since it is evident that almost three-fourths of the study individuals watch the dubbed Turkish series,.”. The most significant positive aspects of the dubbed Turkish series are: “they focus on the most important tourist attractions in Turkey” and “ improving the audience›s knowledge and information on the traditions of the Turkish society”. The most apparent
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The present research aims to test the effect of cognitive complexity as an independent variable in organizational agility as a responsive variable among the leaders working at the headquarters of the Iraqi Petroleum Products Distribution Company.
To conclude a number of recommendations that contribute in the organizational agility in the company, and due to the importance of this research in public organizations and its notable role in community organizations. The research was carried out on a random sample of 101 individuals out of a total of 308, which represents the high leaders in the company (general managers, head of departments, and division officials). A questionnaire was used as information
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Background: Plantar heel pain is a clinical syndrome characterized by pain and tenderness beneath the heel which is typically worse in the morning and improves after the first few steps in the day. It is a common and frequently disabling clinical complaint that may be caused by a broad spectrum of osseous or soft tissue disorders.
Objective: To evaluate the effectiveness of an operation of multiple drilling of calcaneum for resistant plantar heel pain syndrome.
Methods: During the period from November 2012 to August 2016, 17 patients (17heels) were enrolled in a cohort clinical study at the orthopedic unit in AL-Sheikh Zayed and Al-Wassity Hospitals.
The information required for construction quantities surveying is not only generated by various participants in different construction phases but also stored in different forms including graphics, text, tables, or various combinations of the three. To report a bill of quantities (BOQ), the project manager has to continuously excerpt information from various resources and record it on papers. Without adequate staff and time, this repetitive and tedious process is difficult for the project manager to handle properly and thus reduces the effectiveness and the accuracy of the quantities surveying process which creates problems during the design, tender, and construction supervision of construction projects for designers and contractors pract
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Background: Plantar heel pain is a clinical syndrome characterized by pain and tenderness beneath the heel which is typically worse in the morning and improves after the first few steps in the day. It is a common and frequently disabling clinical complaint that may be caused by a broad spectrum of osseous or soft tissue disorders. Objective: To evaluate the effectiveness of an operation of multiple drilling of calcaneum for resistant plantar heel pain syndrome. Methods: During the period from November 2012 to August 2016, 17 patients (17heels) were enrolled in a cohort clinical study at the orthopedic unit in AL-Sheikh Zayed and AlWassity Hospitals. Result: Drilling of the calcaneum is a simple procedure achieving 70.6% cure in resistant as
... Show MoreMicrobial fuel cell is a device that uses the microorganism metabolism for the production of electricity under specific operating conditions. Double chamber microbial fuel cell was tested for the use of two cheap electrode materials copper and aluminum for the production of electricity under different operating conditions. The investigated conditions were concentration of microorganism (yeast) (0.5- 2 g/l), solutions temperature (33-45 oC) and concentration of glucose as a substrate (1.5- 6 g/l). The results demonstrated that copper electrode exhibit good performance while the performance of aluminum is poor. The electricity is generated with and without the addition of substrate. Addition of glucose substrate
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This work aims to investigate the tensile and compression strengths of heat- cured acrylic resin denture base material by adding styrene-butadiene (S- B) to polymethyl methacrylate (PMMA). The most well- known issue in prosthodontic practice is fracture of a denture base. All samples were a blend of (90%, 80%) PMMA and (10%, 20%) S- B powder melted in Oxolane (Tetra hydro furan). These samples were chopped down into specimens of dimensions 100x10x2.5mm to carry out the requirements of tensile tests. The compression strength test specimens were shaped into a cylinder with dimensions of 12.7mm in diameter and 20mm in length. The experimental results show a significant increase in both tensile and compression strengths when compared to cont
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