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.
Most studies indicated that the values of atmospheric variables have changed from their general rates due to pollution or global warming etc. Hence, the research indicates the changes of direct solar radiation values over a whole century i.e. from 1900 to 2000 depending on registered data for four cities, namely (Mosul - Baghdad - Rutba - Basra. Moreover, attemptsto correlate the direct solar radiation with the temperature values have been recorded over that period. The results showed that there is a decreasing pattern of radiation quantities over time throughout the study period, where the value of direct radiation over the city of Baghdad 5550 w/m2 was recorded in the year 1900, but this ratio decreased cle
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Most vegetation’s are Land cover (LC) for the globe, and there is an increased attention to plants since they represent an element of balance to natural ecology and maintain the natural balance of rapid changes due to systematic and random human uses, including the subject of the current study (Bassia eriophora ) Which represent an essential part of the United Nations system for land cover classification (LCCS), developed by the World Food Organization (FAO) and the world Organization for environmental program (UNEP), to observe basic environmental elements with modern techniques. Although this plant is distributed all over Iraq, we found that this plant exists primarily in the middle
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Granular carbon can be used after conventional filtration of suspended matter or, as a combination of filtration - adsorption medium. The choice of equipment depends on the severity of the organic removal problem, the availability of existing equipment, and the desired improvement of adsorption condition.
Design calculations on dechlorination by granular - carbon filters considering the effects of flow rate, pH , contact time, head loss and bed expansion in backwashing , particle size, and physical characteristics were considered assuming the absence of bacteria or any organic interface .
Background: Abdominoplasty is one of the commonest surgical procedures that performed for those patients who had skin laxity, strive and muscle rectur diastasis. Combined using of liposuction and abdominoplasty it can give better result than traditional abdominoplasty with fear complications. Patient and Method: A total number of 25 female patients with age ranging between 27-55 years were underwent lipoabdominoplasty. With extensive liposuction of abdominal wall and selective undermining together with muscle plication. All of our patients had body mass index more than 30. Patients satisfaction and complication were documented postoperatively. Result: All of our patients had no Major complications and the postoperative period passed unevent
... Show MoreIn this research, the preparation of a chemically activated carbon from date stones by using electric and microwave assisted K2CO3 activation was studied. The effect of radiation power, radiation time, and impregnation ratio on the yield and Iodine number on the activated carbons was investigated. The activated carbon characterizations were examined by its surface area, pore structure analysis, bulk density, moisture content, ash content, iodine number, FTIR, and scanning electron microscopy (SEM). The adsorption capacity was also studied by adsorption of fluoroquinolones antibiotics, CIP, NOR, and LEVO, by the prepared activated carbon.
... Show MoreReprehensible during the period of human life ,particular in child hood and after weaning
baby,analmeating habits have acquired his remaining life time and here high Iights,the role of
the mother in the childs education,dietar habits, and health methods and what is beneficial to
his health and in sufficien quantities for the baby .brooze trails are learned by the childin the
home with animportant and significant role in the future,inacht.aaralgame course wisely,after
becoming more in dependent in its delision-making an choices beyond the control of parents.
The present study aimed to message measure the awareness of food the mother and her role in
the development of food awareness sons, and its relation ship with som
This study comes as: The responsibility of the Iraqi newspapers in promoting the political culture inside society, an analytical study in newspapers: Al-Sabah, Al-Ittihad, Al-Aalam for 2/ 3/ 2013 to 31/ 3/ 2013 to spot light on the extent to which the three mentioned newspapers are compliance with the promotion of the political culture inside society which is seen as one of the essential requirements for the success and promotion of the democratic process inside society.
The study aims to: finding out the extent to which these newspapers are compliance with their responsibility in the promoting the political culture inside society; knowing the nature of their role in pr
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In this research the Inter-Particle Expectation Values have been studied for atomics Helium (He) and Beryllium (Be) also for He-like ions, Be-like ions (Li-1, B+1? Li+1, Be+2, B+3) by using Hartree-Fock wave functions, We compared the results to some ions which have the same atomic number from each group with atomic number, We compared the results with published calculations to the last studied .
This research aims to analyze the indicators of spatial variation in the guide of health field in both Al-Adhamiyah and Rusafa districts according to the environmental and administrative units in 2016. The analysis was done by groups of health guide indicators. The objectives of the study were to identify the spatial variation of health services and assess the health situation for families following the environmental and administrative units of the studied area. Such objectives can be done by specifying the extent of the families’ consent to the type of services, measuring the cases of deprivation, and identifying the most deprived areas. The study has finally concluded that there is a clear spatial variation between the indicators and
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Abstract:
The models of time series often suffer from the problem of the existence of outliers that accompany the data collection process for many reasons, their existence may have a significant impact on the estimation of the parameters of the studied model. Access to highly efficient estimators is one of the most important stages of statistical analysis, And it is therefore important to choose the appropriate methods to obtain good estimators. The aim of this research is to compare the ordinary estimators and the robust estimators of the estimation of the parameters of
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