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 research aims to develop a proposed mechanism for financial reporting on sustainable investment that takes the specificity of these investments.
To achieve this goal, the researcher used (what if scenario) where the future financial statements were prepared for the year 2026, after completion of the sustainable project and operation, as the project requires four years to be completed.
The researcher relied on the results of the researchers collected from various modern sources relevant to the research topic and published on the internet, and the financial data and information obtained to assess the reality of the company's activity and its environmental, social, and economic i
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QA Sarhan, University of Anbar Sport and Physical Education Sciences, 2019
Acting on the Holy Qur’an by contemplating its meanings, stopping at its commands and prohibitions, and everything in it that guides us to truth and mercy. The Holy Qur’an includes it for various purposes in one verse, and there is no doubt that this is part of the perfection of this great book, and one of the sciences of the fundamentalists is the indication of the context, and it is a great science of high rank, and it is one of the most important things that lead to the correct understanding of the miraculous and decisive book of God Almighty, and one of the best meanings of the Qur’an It was not from the context of the verses, and from here it can be said that the indication of the context is one of the origins of deriving lega
... Show MoreA study carried out in quail’s field owned by the Department of Animal production/ Collage of Agriculture / Tikrit University. For the period 14/ 5/ 2016 to 4/ 6/ 2016 in order to study the effect of adding Curcuma longa - to the diet of quails - on some productive and physiological characteristics of the Japanese quail birds bred for meat production. Using (48) quail birds which are two weeks old provided by Department of Agricultural Research. The birds were divided randomly after weighing them into three treatments; four replicate treatments for (4 bird/ replicate). The treatments as follows: (T1) control group (fed diet without any supplement), second (T2) and third (T3) groups were fed diet supplemental 4.5 and 9g Curcuma powder /
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In this research, a number of the western al-Anbar clays (red iron clays, Attapulgite) were modified by treating them thermally with a temperature of 650oC. After that, these clays reflux with sodium hydroxide 5% for 1 hour by using microwave as a power supply. The research included fractionation alqayaira crude oil the fractionation included removing the asphaltene by precipitation from the crude using a simple paraffin solvent (normal hexane) as a non-soluble substance. After that it was filtered using the ash-free filter paper 42, the dissolved part, maltinate, was taken, drying a temperature of 75oC and weight, and to find the percentage of the two parts. Malatine was divided into three main parts (paraf
... Show MoreBackground: Maxillary first premolar with wide MOD cavity more susceptible to fracture. The aim of this study was to assess the influence of cavity design for cusp coverage on the fracture resistance of weakened maxillary first premolar restored with CAD/CAM hybrid ceramic versus nanohybide composite. Materials and Methods: Fifty six intact maxillary first premolars of approximately comparable sizes were divided into seven groups eight for each: Group A: Intact teeth (control group); Group B: teeth prepared for MOD inlay; Group C: teeth prepared for MOD onlay covering the lingual cusp; Group D: teeth prepared for MOD covering buccal and lingual cusps ,the previous three groups indirectly restored with nanohybrid composite (3M ESPE Z 250 X
... Show MoreIn this research a new system identification algorithm is presented for obtaining an optimal set of mathematical models for system with perturbed coefficients, then this algorithm is applied practically by an “On Line System Identification Circuit”, based on real time speed response data of a permanent magnet DC motor. Such set of mathematical models represents the physical plant against all variation which may exist in its parameters, and forms a strong mathematical foundation for stability and performance analysis in control theory problems.
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Hydroponics is the cultivation of plants by utilizing water without using soil which emphasizes the fulfillment of the nutritional needs of plants. This research has introduced smart hydroponic system that enables regular monitoring of every aspect to maintain the pH values, water, temperature, and soil. Nevertheless, there is a lack of knowledge that can systematically represent the current research. The proposed study suggests a systematic literature review of smart hydroponics system to overcome this limitation. This systematic literature review will assist practitioners draw on existing literature and propose new solutions based on available knowledge in the smart hydroponic system. The outcomes of this paper can assist future r
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