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.
The effect of using grinded rocks of (quartzite and porcelanite) as powder of (10 and 20) % replacement by weight of cement for self-compacting concrete slabs was investigated in this study. Five slabs with 15 concrete cubes were tested experimentally at 28 days to study the compressive strength, ultimate load, ultimate deflection, ductility, crack load and steel strain. The test results show that, the compressive strength improvement when replacement of local rock powder reached to (7.3, 4.22) % for (10 and 20) % quartzite powder and (11.3, 16.1) % for (10 and 20) % porcelanite powder, respectively compared to the reference specimen. The ultimate load percentage increase for slabs with (10 and 20) % rep
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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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Prediction of the structural response of reinforced concrete to the time-dependent, creep and shrinkage, volume changes is complex. Creep is usually determined by measuring the change, with time, in the strain of specimens subjected to a constant stress and stored under appropriate conditions. This paper brings into view the development of creep strain for four self-compacting concrete mixes: A40, AL40, B60 and BL60 (where 40 and 60 represent the compressive strength level at 28 days and L indicates to Portlandlimestone cement). Specimens were put under sustained load and exposed to controlled conditions in a creep chamber (ASTM C512). The test results showed that normal strength Portland-limestone mixes have yielded lower ultimate c
... 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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The current research aims to shed light on the Global Reporting Initiative (GRI), which helps to report financial and non-financial information by economic units in general and listed on the Iraq Stock Exchange in particular. The research was based on a main premise that apply the criteria of the Global Reporting Initiative (GRI) would provide useful information to users to help them make appropriate decisions. To achieve the goal of the research, the descriptive analysis method was used, and quantitative analysis was used. At the level of the descriptive analysis method, a desk survey was conducted. As for the quantitative analysis, it relied on applied data through a questionnaire form (Questioners) as a research tool, and the
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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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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 MoreAn edge dominating set of a graph is said to be an odd (even) sum degree edge dominating set (osded (esded) - set) of G if the sum of the degree of all edges in X is an odd (even) number. The odd (even) sum degree edge domination number is the minimum cardinality taken over all odd (even) sum degree edge dominating sets of G and is defined as zero if no such odd (even) sum degree edge dominating set exists in G. In this paper, the odd (even) sum degree domination concept is extended on the co-dominating set E-T of a graph G, where T is an edge dominating set of G. The corresponding parameters co-odd (even) sum degree edge dominating set, co-odd (even) sum degree edge domination number and co-odd (even) sum degree edge domin
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This study focuses on the impact of technology on creating a dystopian world as presented by the English playwright Caryl Churchill in her play A Number (2002). This dramatic work came as a reaction to the most crucial and valuable turning point in the scientific achievements of human engineering, namely, the cloning of the sheep called Dolly. Therefore, A Number is a play that presents an analytical stage for imagining the biotechnological and scientific future. This dramatic vignette captures the playwright’s fears towards the abnormal progress of technology and science and how far such technological progress affects human relationships and identity. It also portrays how technological progress results in the feeling of a lack of
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