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.
Objective: to assess the predictive value of Doppler imaging of the uterine artery in the identification of early intrauterine abnormal pregnancy as compared to a normal intrauterine pregnancy. Subjects and methods: one hundred and twenty pregnant ladies, at their 6-12 weeks of gestation, with a singleton pregnancy were included in this population-based case-control study. Thirty women with a missed miscarriage, 30 with hydatidiform mole, 30 with a blighted ovum, and 30 as a control group, without risk factors, underwent Doppler interrogation of the uterine arteries. Resistive index (RI), pulsatility index (PI), and the systolic/diastolic ratio (S/D) were measured for both sides. The t-test, or ANOVA test when appropriate, was
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Poly vinyl alcohol has been studied for its ability to form crystallites by using annealing method. Semicrystalline films of poly vinyl alcohol (PVA) were prepared by casting 11.5 wt. % and 13 wt. % PVA aqueous solution onto glass slides at annealing temperature range 90 -120°C and duration time 15- 60 minute. This allowed the macromolecules to form crystallites, small regions of folded and compacted chains separated by amorphous regions where single PVA chain may pass through several of these crystallites. Degree of crystallinity of PVA films (hydrogels) was determined by method of density; on the other hand the swelling behavior was conducted by the determination of water uptake, wet degree of crystallinity, gel fraction and solubilit
... Show MoreScleral acrylic resin is widely used to synthesize ocular prosthesis. However, the properties of this material change over time, thus requiring the prosthesis to be refabricated. Many studies were conducted to improve these properties by reinforcing this material with nanoparticles. This study aims to evaluate the effect of silver nanoparticle powder on the mechanical properties (transverse flexural strength, impact strength, shear bond strength, surface microhardness, and surface roughness) of scleral acrylic resin used for ocular prostheses. Two concentrations were selected from the pilot study and evaluated for their effects on scleral acrylic resin properties. According to the pilot study, 0.01 and 0.02wt% AgNPs powder improved
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According to Chandra Survey Observatory Near-Asteroid Belt Comets, the solar wind's contact with the comet produces a variety of spectral characteristics. The study of X-ray spectra produced by charge exchange is presented here. The spectrum of a comet can reveal a lot about its composition. This study has concentrated on the elemental abundance in six different comets, including 17P/Holmes, C/1999T1, C/2013A1, 9p/Temple1, and 103p/Hartley2 (NEAT). Numerous aspects of the comet's dynamics allow it to behave in a unique manner as it gets closer to the Near-Asteroid Belt. These characteristics are being examined, and some studies are still ongoing. The computations allow us to observe, for instance, how the composition of
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This paper deals with the subject of demarcating as appropriate scientific techniques to rationalize consumption and to control segments of the society for the technical conduct of its handling of the product depending on the mix of elements (product and the volume of demand, Price, promotion and distribution), but inverse manner designed to adjust the working condition of balance between supply and demand and to ensure that rates continue in the marketing process properly, and therefore the research aims to shed light on some of the practices that reflect the Demarketing techniques, As well as the statement of the reality of attitudes towards the practice of those techniques through a sample survey of officials in Baghdad company for so
... Show MoreThe inhibitive action of Reactive Red (RR31) dye against corrosion of carbon steel in 1M acetic acid solution has been studied using gravimetric method at temperature ranged (288-318)K. The antibacterial activity for the different concentrations of RR31 dye against different bacterial species was studied. The experimental data indicates that this dye acts as a potential inhibitor for carbon-steel in acetic acid medium and the protection efficiency increase with increasing (RR31) dye. The adsorption of (RR31) dye on the carbon steel surface was found to follow Langmuir adsorption isotherm. Thermodynamic data for the adsorption process such as Gibbs free energy change ∆Gads, enthalpy change ∆Hads, and entropy change ∆Sads were estima
... Show MoreTo avoid the negative effects due to inflexibility of the domestic production inresponse to the increase in government consumption expenditure leads to more imports to meet the increase in domestic demand resulting from the increase in government consumption expenditure. Since the Iraqi economy economy yield unilateral depends on oil revenues to finance spending, and the fact government consumer spending is a progressive high flexibility the increase in overall revenues, while being a regressive flexibility is very low in the event of reduced public revenues, and therefore lead to a deficit in the current account position. And that caused the deficit for imbalance are the disruption of the
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The monogenean Gyrodactylus taimeni Ergens, 1971 was recorded in this study for the first time in Iraq from gills of the common carp Cyprinus carpio Linnaeus, 1758. The description and measurements of this parasite as well as illustration were given. In addition, a list of species of Gyrodactylus so far recorded from C. carpio in Iraq is also included together with a list of all other hosts recorded for each gyrodactylid species.
Represents a supervisory and oversight role of the Central Bank towards finding a sober banking sector, as the procedures , regulations and laws that the Central Bank insists on its implementation with the utmost precision, and that was to protect depositors and shareholders' class basis rights, but it is in the interest of the bank in the end, as it seeks to improve the performance of commercial banks and vaccinated against falling into the blunders, they also contribute to building a sober and stable banking sector and security contributes to the welfare and employment optimization of economic resources, and treatment of research (and the presence of banks decline in financial performance, according to financial performance indic
... Show MoreThe rental activity receives "significant" interest from accounting organizations interested in issuing accounting standards worldwide, such as the Financial Accounting Standards Board (FASB), the International Accounting Standards Board (IASB). As leases represents an important source of finance for economic units as an alternative to financing assets through purchase or borrowing. Professional organizations have focused on addressing the situation of extra-budgetary funding through which the lessee hides many leases that are classified as financing without It shows in the budget, which gives an incorrect picture of the reality of the financial situation of economic unity, IASB has issued IFRS 16, which terminates off- Balance s
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