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.
This research aims to identify the effectiveness of counseling by using the technique of self-talkin developing the habits of mind among middle school students by testing important hypotheses, and choosing the experimental design for the two groups (experimental - control). The classification of "Costa & Kallick" was adopted to measure the habits of the mind, and the scale consisted of (64) items, and after confirming the psychometric properties of the scale, the researcher applied it to the research sample (487) students from middle school students. One of the students who got the lowest marks after answering the scale. purpose of applying the experiment. He divided them into two groups, one of them is experimental (10) students, as
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The current research aims to evaluate liquidity (as an independent variable) to improve the bank’s profitability (as a dependent variable ), by the bank’s ability to maximize its profits from its business results without excessive bank’s liquidity, so that may affect negatively affects the bank’s reputation and it’s dealers confidence in facing their financial obligations. and this may lead trying to come out among other recommendations including contributing to obtain, the bank’s ability to achieve liquidity balance to maximize its profits. This research has been applied to the sample induced intentionally by choosing three Iraqi private banks. The researcher used financial indicators to assess the bank’s liq
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Due to the energy crisis and the stringent environmental regulations, diesel engines are offering good hope for automotive vehicles. However, a lot of work is needed to reduce the diesel exhaust emissions and give the way for full utilization of the diesel fuel’s excellent characteristics.
A kind of cetane number improver has been proposed and tested to be used with diesel fuel as ameans of reducing exhaust emissions. The addition of (2-ethylhexyl nitrate) was designed to raise fuel cetane number to three stages, 50, 52 and 55 compared to the used conventional diesel fuel whose CN was 48.5. The addition of CN improver results in the decre
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Self-compacted concrete (SCC) is a highly flowable concrete, with no segregation which can be spread into place by filling the structures framework and permeate the reinforcement without any compaction or mechanical consolidation ACI 237R-14. One of the most important problems faced by concrete industry in Iraq and Gulf Arab land is deterioration due to internal sulfate attack (ISA) that causes damage of concrete and consequently reduces its compressive strength, increases expansion and may lead to its cracking and destruction. The experimental program was focused to study two ordinary Portland cements with different chemical composition with (5, 10 and 15) % percentage of high reactivity metakaoline (HRM)
... Show MoreObjective(s): The aim of this study is to assess the impact of social phobia upon self-esteem of nursing
collegians.
Methodology: A Cross-sectional study is carried out at University of Baghdad, Karkuk, Thi-Qar, and Kufa,
colleges of nursing from Feb 8
th
, 2011 to Sep. 25th, 2011. A sample of all first class nursing collegians (N=330)
were selected from a probability sample of nursing colleges by dividing Iraq to three geographical areas (South,
North, and Middle Euphrates) in addition to Baghdad. The data were collected through the use of selfadministered
technique as a mean for data collection, by using a questionnaire that consists of three parts:
First part was the socio-demographic data form; the second o
Social protection meets different aspects of the needs of vulnerable groups, such as the economic, health, education, and family relations and ties in the Iraqi society. This is because vulnerable groups have suffered from social and economic influences that have negative implications on the social reality as a whole. Poverty is a case in point, which paved the way to frequent setbacks that have led to social structure instability. Accordingly, the present study aims to examine the role and effect of the Net of Social Protection Program in equally distributing social protection to curb or mitigate any negative consequnces that might happen to the poor segments and vulnerable people, who are succeptible to shocks, such as: the orphans, un
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Objectives: Dickkopf-1 (DKK-1) is WNT/b-catenin pathway antagonist which plays a detrimental role in the development of diabetic retinopathy (DR). This research aimed to assess serum DKK-1 levels in diabetic patients who have and have not developed DR and, compare them with the control subjects finding out whether we can use it as an indicator for DR early diagnosis and to find out which one of the widely used two groups of antidiabetic treatments had the greater effect on this biomarker and hence on the progression of DR. Methods: The study participants were divided into two subgroups: First, 70 patients (36 male, 34 female) with type 2 diabetes mellitus, among them 35 patients diagnosed with DR and 35 with no evidence of DR, and s
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