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 civil engineering field currently focus on sustainable development. It is important to develop new sustainable and economic generations of concrete, using eco-friendly materials in the construction industry with a fair amount of costs and minimizing the impact upon the environment by reducing CO2 emissions from the cement industry as a whole while still obtaining high cement quality and strength. The main objective of this research is to clarify the mechanical behavior and ability to use Portland limestone cement in producing self compacted concrete, due to the beneficious effec of the limestone cement economically and enviromently. The research investigates the effect of using steel and polymer meshs as reinforcement, where the results
... Show MoreThe hydroconversion of Iraqi light straight run naphtha was studied on zeolite catalyst. 0.3wt.%Pt/HMOR catalyst was prepared locally and used in the present work. The hydroconversion performed on a continuous fixed-bed laboratory reaction unit. Experiments were performed in the temperature range of 200 to 350°C, pressure range of 3 to 15 bars, LHSV range of 0.5-2.5h-1, and the hydrogen to naphtha ratio of 300.
The results show that the hydroconversion of Iraqi light straight naphtha increases with increase in reaction temperature and decreases with increase in LHSV.
High octane number isomers were formed at low temperature of 240°C. The selectivity of hydroisomerization improved by increasing reaction pressu
... Show MoreThe research aimed at designing teaching sessions using the self-scheduling strategy with a competitive style in learning handball as well as identifying differences between pre and post tests in both groups in learning short and long passes in handball. The researchers used the experimental method on 2nd-grade secondary school students. The researchers concluded using the self-scheduling strategy due to its positive effect on learning short and long handball passes in handball. Finally, the researchers recommended applying strategies and styles in teaching different school levels as well as making similar studies using teaching strategies and styles for learning handball skills in students.
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Background: The anterior loop of mental nerve is commonly described as that part of the neurovascular bundle that transverses anterior and inferior to the mental foramen only to loop back to exit the mental foramen. The aim of the study is to evaluate the incidence and extension of anterior loop of mental nerve by using digital panoramic imaging system to avoid nerve damage during different surgical procedures in dentistry. Materials and Method: Panoramic image was taken for all 400 patients and stored in the computer. Then Horizontal and Vertical for the anterior loop extension when exist was measured and recorded in a special case sheet prepared for each subject. Results: Results indicated that out of 400 patients there were only 25 pat
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The study aims to know the nature of the expected relationship between market share management strategies and the variation in the performance of the shares of a number of Iraqi industrial companies listed in the Iraqi Stock Exchange. For the period (2005-2018) in the light of both the monthly closing prices and sales volume during the research period, the (Panel Data) method was relied on through a stylistic test (fixed effects model and random effects model), and the results determined the need to adopt the fixed effects model method for sample data and test Assumptions, the results showed the positive impact of market share according to its strategies on the performance of stocks according to its studied indicators (Treynor index
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The demand for single photon sources in quantum key distribution (QKD) systems has necessitated the use of weak coherent pulses (WCPs) characterized by a Poissonian distribution. Ensuring security against eavesdropping attacks requires keeping the mean photon number (µ) small and known to legitimate partners. However, accurately determining µ poses challenges due to discrepancies between theoretical calculations and practical implementation. This paper introduces two experiments. The first experiment involves theoretical calculations of µ using several filters to generate the WCPs. The second experiment utilizes a variable attenuator to generate the WCPs, and the value of µ was estimated from the photons detected by the BB
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The major aim of this research is study the effect of the type of lightweight aggregate (Porcelinite and Thermostone), type and ratio of the pozzolanic material(SF and HRM) and the use of different ratios of w/cm ratio(0.32 and 0.35) on the properties of SCLWC in the fresh and hardened state. SF and HRM are used in three percentage 5%,10%, and 15% as a partial replacement by weight of
cement for all types of SCLWC. The requirements of self-compatibility for SCC are fulfilled by using the high performance superplasticizer (G51) at 1.2liter per 100 kg of cement. The values of air dry density and compressive strength at age of 28 days within the limits of structural lightweight concrete. The air dry density and compressive strength at a
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A preventing shield for neutrons and gamma rays was designed using alternate layers of water and iron with pre-fixed dimensions in order to study the possibility of attenuating both neutrons and gamma-rays. ANISN CODE was prepared and adapted for the shield calculation using radiation doses calculation: Two groups of cross-section were used for each of neutrons and gamma-rays that rely on the one – dimensional transport equation using discrete ordinate's method, and through transforming cross-section values to values that are independent on the number of groups. The memory size required for the applied code was reduced and the results obtained were in agreement with those of standard acceptable document samples of cross –section, this a
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