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.
Experimental research was carried out on eight reinforced concrete beams to study the embedded length of the longitudinal reinforcement. Six beams were casted using self compacted concrete, and the two other beams were casted using normal concrete. The test was carried out on beams subjected to two point loads. The strain and the slip of the main reinforcement have been measured by using grooves placed during casting the beams at certain places. The measured strain used to calculate the longitudinal stresses (bond stress) surrounding the bar reinforcement, The study was investigated the using of self compacted concrete SCC on the embedded length of reinforcing bars, and comparing the results with normal concrete. The test results show th
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The massive growth of the automotive industry and the development of vehicles use lead to produce a huge amount of waste tire rubber. Rubber tires are non-biodegradable, resulting in environmental problems such as fire risks. In this search, the flexural behavior of steel fiber reinforced self-compacting concrete (SFRSCC) beams containing different percentages and sizes of waste tire rubbers were studied and compared them with the flexural behavior of SCC and SFRSCC. Micro steel fiber (straight type) with aspect ratio 65 was used in mixes. The replacement of coarse and fine aggregate was 20% and 10% with chip and crumb rubber. Also, the replacement of limestone dust and silica fume was 50%, 25%, and 12% with ground rubbe
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The present study deals with the optimum design of self supporting steel communication towers. A special technique is used to represent the tower as an equivalent hollow tapered beam with variable cross section. Then this method is employed to find the best layout of the tower among prespecified configurations. The formulation of the problem is applied to four types of tower layout
with K and X brace, with equal and unequal panels. The objective function is the total weight of the tower. The variables are the base and the top dimensions, the number of panels for the tower and member's cross section areas. The formulations of design constraints are based on the requirements of EIA and ANSI codes for allowable stresses in the members
This study focused on the improvement of the quality of gasoline and enhancing its octane number by the reduction of n-paraffins using zeolite 5A. This study was made using batch and continuous mode. The parameters which affected the n-paraffin removal efficiency for each mode were studied. Temperature (30 and 40 ˚C) and mixing time up to 120 min for different amounts of zeolite ranging (10-60 g) were investigated in a batch mode. A maximum removal efficiency of 64% was obtained using 60 g of zeolite at 30 ˚C after a mixing time 120 min. The effect of feed flow rate (0.3-0.8 l/hr) and bed height (10-20 cm) were also studied in a continuous mode. The equilibrium isotherm study was made using different amounts of zeolite (2-20 g) and the
... Show MoreThe importance of this research is due to its importance goals, Which are about the attempt of researchers to investigate the probability of depending on businesses, environments to transform organizations, performance in away that enhance the leading role of organizations in their environments , and through views of a number of the staff working in the foundation of technical institutes in Mosul. .
After deciding the methodology of the study that ,in one hand ,performs the goals of the study , and achieving a suitable theoretical framework to present the concepts of businesses, environments and the leadin
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This research aims to identify the effective role of self-managed teams in the quality of service performance in the directorate of Ramadi municipality. The problematic nature of our research involves this main question of the effective role of self-managed teams in the Municipality of Ramadi in improving the services of performance quality to the beneficiaries from the Directorate service. The importance of this study lies in the role played by the work teams in the organizations that excel in their field, the attendant of the changes in the leadership, administrative roles of the institutions, and teams leaders, will be achieved by the self-managed teams in improving the quality of the service provided by the institution to whi
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The research aims to reveal the professional self and the school climate among the educational counselors. The research problem is crystallized in the following:
1-Identifying the professional level of the educational counselors.
2- Knowing the level of the school climate with the educational counselors.
3- Are there statistically significant differences in the professional self and the school climate between the educational counselors of different gender (male / female)?
4- Is there a relationship between the professional self and the school climate of the research sample?
To answer these questions, the research was conducted on educational counselors in secondary schools in the district of Falluj
... Show MoreA case-control study was performed to examine age, gender, and ABO blood groups in 1014 Iraqi hospitalized cases with Coronavirus disease 2019 (COVID-19) and 901 blood donors (control group). The infection was molecularly diagnosed by detecting coronavirus RNA in nasal swabs of patients.
Mean age was significantly elevated in cases compared to controls (48.2 ± 13.8
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Abstract
The present investigation aimed to formulate a liquid self-microemulsifying drug delivery system (SMEDDS) of tacrolimus to enhance its oral bioavailability by improving its dispersibility and dissolution rate. Four liquid SMEDDS were prepared using maisine CC as oil phase, labrasol ALF as surfactant and transcutol HP as co-surfactant based on the solubility studies of tacrolimus in these components. The phase behavior of the components and the area of microemulsion were evaluated using pseudoternary phase diagrams. The formulations were also assessed for thermodynamic stability, robustness to dilution, self-emulsification time, drug content, globule size and polydispersity index. The prepared SMEDDS formulations exhibi
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