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.
Abstraet
Students dropout from the Education has a negative phenomena on individual and society and even on different aspects of life especially on the economic aspect , Thus our research tries studying and analyzing the relation between the size of dropout and human development level in Iraq and as (research sample) the first decade of this century as a studying period, the study includes the dropout in Secondary schools and depending the formal records as a main source to evaluate the size of this problem in Iraq , which shows an increase in the size of dropout in this period in comparison with the last decades of the twentieth century, this produces a negative effect on human developme
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The current research aims to diagnose the type and level of influence of social media, whose dimensions are represented by (attitudes towards social media marketing, knowledge and use of social media, influence on the Internet and social media, following up on social media) on customer behavior in its dimensions (attracting attention, raising Interest, desire creation, customer response), and the research sought to answer questions related to the research problem by testing the main hypotheses to explore correlations and influence between the two variables, and to achieve research hypothesis tests, the field study was used, as the research sample reached (135) individuals from the director and the assistant director And marketing personnel
... Show MoreIn this study, the use of non-thermal plasma theory to remove toxic gases emitted from a vehicle was experimentally investigated. A non-thermal plasma reactor was constructed in the form of a cylindrical tube made of Pyrex glass. Two stainless steel rods were placed inside the tube to generate electric discharge and plasma condition, by connecting with a high voltage power supply (up to 40 kV). The reactor was used to remove the contaminants of a 1.25-liter 4-cylinder engine at ambient conditions. Several tests have been carried out for a ranging speed from 750 to 4,500 rpm of the engine and varying voltages from 0 to 32 kV. The gases entering the reactor were examined by a gas analyzer and the gases concentration ratio
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The preparation of the phenanthridine derivative compound was achieved by adopting an efficient one-pot synthetic approach. The condensation of an ethanolic mixture of benzaldehyde, cyclohexanone and ammonium acetate in a 2:1:1 mole ratio resulted in the formation of the title compound. Analytical and spectroscopic techniques were used to confirm the nature of the new compound. A mechanism for the formation of the phenanthridine moiety that is based on three steps has been suggested
We propose two simple, rapid, and convenient spectrophotometric methods which are described for the determination of cephalexin in bulk and its pharmaceutical preparations. They are based on the measurement of the flame atomic emission of potassium ion (in the first method) and colorimetric determination of the green colored solution at 610 nm formed after the reaction of cephalexin with potassium permanganate as an oxidant agent (in the second method) in basic medium. The working conditions of the methods are investigated and optimized. Beer's law plot shows a good correlation in the concentration range of 5-40?g ml-1. The detection limits are 2.573,2.814 ?g ml-1 for the flame emission photometric method and 1.844,2.016 ?g ml-1 for colo
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Background: Although underdeveloped in Iraq, telehealth was one tool used to continue health service provision during the COVID-19 pandemic. Aim: To assess women’s experiences and satisfaction with gynaecological and obstetric telehealth services in Iraq during the COVID-19 pandemic. Methods: Free telehealth services were provided by 4 obstetrician-gynaecologists associated with private clinics in 2020–2021. All patients who accessed the services between June 2020 and February 2021 were invited to complete a postconsultation survey on their experience and satisfaction with services. Results were analysed using descriptive statistics and logistic regression conducted using SPSS version 25. Results: A total of 151 (30.2%) women re
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Technique was used to retail for analyzing atom beryllium ion cathode of an atom lithium to six pairs of functions wave which two ?????? and the rest of the casing moderation and to analyze atom lithium ion Mob atom beryllium to three pairs of functions wave pair of casing and the rest of the casing moderation using function wave Hartree Fock and each casing email wascalculate expected values ??....