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 Political power in Lebanon is a fundamental objective of any political organization, whether political party or political group. Thus, there is a conflict of power. There are two kinds of political conflict that are differentiated by the idea of legitimacy. The competition is in the political system when the agreement between the social forces is considered legitimate, and the conflict is on the political system when the agreement between these forces ceases to be legitimate and Are working to topple it and seek to establish an alternative system. Therefore, the succession of power in Lebanon is a result of the competition and political conflict, which is in turn a result of the large number of regional and international players
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Historical concepts are among the concepts that are difficult to present to the pre-school child except by using modern techniques, as well as the difficulty of making visits to all historical monuments and going back to antiquity and the lack of studies in this area, therefore, we need an attractive medium that children love which is able to convey some abstract concepts that are difficult to teach to children using traditional methods, and among these activities that the kindergarten provides to children are the stories through which they develop their linguistic wealth, consolidate their religious and spiritual inclinations, refine their correct morals, and form their proper attitudes, knowledge and life concepts.
The
... Show MoreAcute toxicity is a step to evaluate the toxicity of a substance. Rutin is one of the flavonoid compounds with a variety of pharmacological effects. The aim of the study is to calculate the lethal dose that affect fifty percent of the mice used in the experiment (LD50). Thirty Swiss albino male and 30 non-pregnant female mice have been divided equally and randomly into 5 treated groups and one control group (n=5) Rutin has been administered with concentrations 5, 2.5.1.25,0.625 and 0.312 g/kg administered as a single dose intraperitoneally (IP) while the control group received 1% DMSO (IP). Animals were observed for any morbidity and mortality for 14 days. After 14 days the animal blood collected for biochemical and hem
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Praise be to God, who made the pegs of the earth and entrusted them with the task of keeping the earth from tilting, and prayers and peace be upon the one to whom the Qur’an was revealed, Muhammad, and upon his family and all his companions.
The topic of mountains is one of the important topics in human life, as God has associated great miracles with them that indicate the perfection of the power of God Almighty. God Almighty says: (And to the mountains, my palms have turned. This is worthy of every rational person to contemplate His signs, the Almighty, in this solid part and safety belt of the earth, in order to reveal the secrets of the mountains and uncover their treasures. The more the researcher studies the mountains and
... Show MoreLet M be a n-dimensional manifold. A C1- map f : M M is called transversal if for all m N the graph of fm intersect transversally the diagonal of MM at each point (x,x) such that x is fixed point of fm. We study the minimal set of periods of f(M per (f)), where M has the same homology of the complex projective space and the real projective space. For maps of degree one we study the more general case of (M per (f)) for the class of continuous self-maps, where M has the same homology of the n-dimensional sphere.
The execution phase of the project is most dangerous and the most drain on the resources during project life cycle, therefore, its need to monitor and control by specialists to exceeded obstructions and achieve the project goals. The study aims to detect the actual reasons behind mismanagement of the execution phase. The study begins with theoretical part, where it deals with the concepts of project, project selection, project management, and project processes. Field part consists of three techniques: 1- brainstorming, 2- open interviews with experts and 3- designed questionnaire (with 49 reason. These reasons result from brainstorming and interviewing with experts.), in order to find the real reasons behind misman
... Show MoreIraq has a range of small and large marshes, which can be divided into two groups, a group of marshes feeding water from the Tigris and Euphrates rivers, and a group of marshes fed by the seasonal valleys coming from the desert plateau and the aljazera plateau.
The marshes have go through major changes, some of them turning into industrial lakes to store the flood waters of the Tigris and Euphrates rivers. Others have been dried up and turned into agricultural land. Others have dried up and the water has been returned to them in less quantities than before.
The purpose of this research is to but light on the changes that have occurred in these marshes, with the mention of marshes turned into industrial lakes or agricultur
... Show MoreLogic is understood so far as a product perspective, either formal or informal. The topic is still, though interesting, imprecise, sketchy and problematic. Besides, the relevance of logic to linguistics has not been explained. This research focuses on dealing with logic as a product and a process. It introduces how logic is relevant to understanding language. Logic is surely not irrelevant to real human language. In this research, we coin 'logical pragmatics' to refer to "the structure of an argumentation and its parts used by the speaker for the purpose of persuasion to have an effect in the addressee and passive audience”. As such, the research mainly aims at providing a definition of "logical pragmatics" as well as developing an ide
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Background: Free radicals have been implicated in many pathological processes, including ischemia, inflammation, and malignancy. The free radicals may affect tissues damage by lipid
peroxidation which generate malondialdehyde (MDA) as a by byproduct of the reaction. The objective of this study is to examine the dynamics of lipid peroxidation in patients with
thyroid disorders using the measurement of malondialdehyde level as a marker for the degree of thyroid disorder.
Methods: Two hundred and forty five subjects were enrolled in this study. Hundred and ninety five were patients with different thyroid disorders (88 yperthyroidism, 63 hypothyroidism and 44 thyroid carcinoma) the remaining 50 subjects were
A total of 247 specimens of the Mallard were collected from Baghdad city and kut City and 154 specimens the collection was started from October1999