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.
Abstract
The main question raised in this paper is: Is it possible to translate the ‘genre’
of Quran? And if this ‘genre’ is Quran specific, a ‘genre’ of its own, i.e. a unique one,
how can the Quranic text be translated from Arabic into English or any other
language? This question has been raising a lot of controversy among translation
theorists, linguists, philosophers and scholars of Islam and specialists in the sciences
of Arabic language let alone Quran exegetes. Scholars of the Arabic language and
scholars of Islam have argued that because of the genre of Quran is the genre of (ijaz),
translatability can never be possible. Equivalence, thus, cannot be achieved especially
if we know that so far
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 MoreThe study aimed at identifying the role of the Faculty of Education in the community service in light of vision of the Kingdom 2030 from the faculty members’ point of view at the University of Jeddah. The study used a descriptive method through a questionnaire administered to a sample of the faculty members.It concluded that the role of the College in serving the community is the development of the right habits in the family and the importance of establishing bridges of cooperation between the Faculty of Education and the surrounding environment and teaching special education teachers how to apply some methods of measurement to determine the needs of students with disabilities. The results also pointed out that there are no statistical
... Show MorePrecision irrigation applications are used to optimize the use of water resources, by controlling plant water requirements through using different systems according to soil moisture and plant growth periods. In precision irrigation, different rates of irrigation water are applied to different places of the land in comparison with traditional irrigation methods. Thus the cost of irrigation water is reduced. As a result of the fact that precise irrigation can be used and applied in all irrigation systems, it spreads rapidly in all irrigation systems. The purpose of the Precision Agriculture Technology System (precision irrigation) , is to apply the required level of irrigation according to agricultural inputs to the specified location , by us
... Show MoreRegression testing being expensive, requires optimization notion. Typically, the optimization of test cases results in selecting a reduced set or subset of test cases or prioritizing the test cases to detect potential faults at an earlier phase. Many former studies revealed the heuristic-dependent mechanism to attain optimality while reducing or prioritizing test cases. Nevertheless, those studies were deprived of systematic procedures to manage tied test cases issue. Moreover, evolutionary algorithms such as the genetic process often help in depleting test cases, together with a concurrent decrease in computational runtime. However, when examining the fault detection capacity along with other parameters, is required, the method falls sh
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Java is a high-level , third generation programming language were introduced Javaoptics Open Source Physics (OSP) as a new simulation for design one of the most important interference optical coating called antireflection coating. It is recent developments in deign thin-film coatings. (OSP) shows multiple beam interferences from a parallel dielectric thin film and the evolution of reflection factors. It is simple to use and efficiently also can serve educational purposes. The obtained results have been compared with needle method
Experts of Psychology and education emphasized that childhood is one of the most important stages in the formation of human personality, and the most influential in his public life, especially the stage in which he lives within his family, which must provide him with the requirements of healthy growth of physical, emotional, moral and social. Emotional-social connection of the child to his family, is especially important in determining the characteristics of his social character, in accordance with the norms and values prevailing in society. This requires the child to be cared for and cared for, and to deal with him in a healthy social manner. So as to achieve positive growth and harmony in the process of social control in internal
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