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 study of improved model for measuring the total nuclear fusion cross section characteristics the D-D reaction may play an important role in deciding or determining the hot plasma parameters such as mean free path , the reaction rate , reactivity and energy for emitted neutrons or protons in our work we see the it is necessary to modify the empirical formulas included the total cross section in order to arrive or achieve good agreement with the international publish result.
The aim of this research is to identify the availability of visual thinking skills in the chemistry textbook scheduled for the third intermediate grade for the academic year (2020-2021) in the Republic of Iraq. The study sample consisted of all (85) images contained in the chemistry course for the third intermediate grade, which are (85) form using the curriculum. Analytical descriptive A list of visual thinking skills was prepared, and the unit of form was adopted as a unit of analysis and repetition as a unit of counting, and frequencies and percentages were used for statistical treatment, and validity and reliability were calculated. And using the Holste equation. The following results were reached: The skill
... Show MoreIn this paper, Bayes estimators of Poisson distribution have been derived by using two loss functions: the squared error loss function and the proposed exponential loss function in this study, based on different priors classified as the two different informative prior distributions represented by erlang and inverse levy prior distributions and non-informative prior for the shape parameter of Poisson distribution. The maximum likelihood estimator (MLE) of the Poisson distribution has also been derived. A simulation study has been fulfilled to compare the accuracy of the Bayes estimates with the corresponding maximum likelihood estimate (MLE) of the Poisson distribution based on the root mean squared error (RMSE) for different cases of the
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Monetary policy is an important part of the economic policy to influence the monetary aspect of stabilization, for this reason the research will seek to clarify the extent of the impact of monetary policy in achieving monetary stability in Iraq during the chosen research period, because the Iraqi economy suffers from monetary instability due to political and security turmoil, Therefore, an effective and effective monetary policy is required in terms of reducing inflationary pressures to reach the required monetary stability, in order to create the appropriate monetary environment for the work of the economic and productive sectors. Thus, the research adopted a basic hypothesis that monetary policy in Iraq has a clear impact on achieving mon
... Show MoreTheresearch took the spatial autoregressive model: SAR and spatial error model: SEM in an attempt to provide a practical evident that proves the importance of spatial analysis, with a particular focus on the importance of using regression models spatial andthat includes all of them spatial dependence, which we can test its presence or not by using Moran test. While ignoring this dependency may lead to the loss of important information about the phenomenon under research is reflected in the end on the strength of the statistical estimation power, as these models are the link between the usual regression models with time-series models. Spatial analysis had
... Show MoreThe aim of the research is to design a test with cognitive achievement through the use of the inverted class strategy for some basic soccer skills for gyms for first-average students, within the curriculum of the Ministry of Education, where the researcher used the experimental approach. For the same division (B) and the number of each group (10) students, i.e. the total total of the research sample (20) students, and the pre-test for the research sample was applied through the design of the test prepared by the research after which the educational program with the strategy was applied to the research sample and continued (8) weeks after Completion of the tutorial has been post-tested for the research sample, In it, he reached significant r
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The radial wave functions of the cosh potential within the three-body model of (Core+ 2n) have been employed to investigate the ground state properties such as the proton, neutron and matter densities and the associated rms radii of neutron-rich 6He, 11Li, 14Be, and 17B exotic nuclei. The density distributions of the core and two valence (halo) neutrons are described by the radial wave functions of the cosh potential. The obtained results provide the halo structure of the above exotic nuclei. Elastic electron scattering form factors of these halo nuclei are studied by the plane-wave Born approximation.
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Background: Extracorporeal Shock wave lithotripsy (ESWL) is widely used in treating patients with ureteralstones because it is effective, safe, and noninvasive. Based on factors such as size and the location of stones,there is a significant variation in the overall stone-free rate (SFR).Aim of the study: To evaluate the effect of ureteral wall thickness (UWT), stone attenuation, the time fromfirst attack of pain till first session of ESWL and stone/ rib density on the outcome of SWL in the treatmentof upper ureteral stones (UUS).Patient and methods: A prospective study when 127 patients with radio-opaque UUS ranging from 7 to 20mm and treated by ESWL were included in this study. The effect of (stone/ 12th rib) density by KUB, ureter
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