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.
Background: Platelet-rich fibrin (PRF) is a simple, low cost and minimally invasive way to obtain a natural concentration of autologous growth factors and is currently being widely experimented in different fields of medicine for its ability to aid the regeneration of tissue with a low healing potential. Fields of application are sports medicine, orthopedics, dentistry, dermatology, ophthalmology, plastic and maxillofacial surgery, etc. The rationale for using platelets in so many fields for the treatment of different tissues is because PLTs constitute a reservoir of critical GFs and cytokines, which may govern and regulate the tissue healing process that is quite similar in all kinds of tissues. Materials and Methods: Screw titanium implan
... Show More<em>The aim of the research is to set a set of BioKinematic variables for the step of crossing barriers (3–6–9) in a 110-meter barrier for young runners. The researchers concluded the study by interpreting and discussing the results that the most important variables must be relied upon when training and selecting runners that got the best saturation on their factors: 1-The first factor which refers to the total distance of the plan to pass the third barrier + the total distance of the plan to pass the ninth barrier + the total distance Plan to cross the sixth barrier. 2-The second factor which refers to the total vertical speed before passing the third barrier + the total vertical speed before the sixth barrier + the total vertica
... Show MoreThis paper aims to verify the existence of relationships between product innovation and the reputation of the organization. The study problem is that the State Organization for Marketing of Oil (SOMO) system is inflexible in terms of marketing procedures and needs innovative, unconventional methods in innovating its products and improving performance. The reputation of the organization. The importance of the study lies in that it is an attempt to raise the interest of SOMO in its approach to the research variables in order to enhance its competitive position in the future and improve the marketing business environment, which contributes to enhancing the reputation of the organization by product innovation. The study sample
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The research depth and dimensions of the problem of environmental pollution resulting from the combustion of fuel used in electric power generators, especially in the summer and you are the national electric power supplied by almost non-existent state where this problem is a local phenomenon that has serious dimensions to human health, as well as the possibility of using a the tax system tools of b (environmental taxes) to reduce these pollutants, so the search is aimed at the types of gases emitted from burning fuel electric generators operating in the province of Baghdad and then measure the amount of environmental pollution as well as compared to the amount of some of these gases, which is more risk to humans with permitted by the Wor
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Representing banking supervision An important function performed by the Iraqi Central Bank, in order to achieve stability in the financial and banking system, and safeguard the rights of depositors, investors and other targets, and to realize the Iraqi Central Bank banking supervision actors on banks, there must be an awareness of regulatory bank's existing control and subject them, as well as the role of banking oversight interested in spreading this awareness.
So sought search to find out the role played by the Iraqi Central Bank in raising awareness of the regulatory banking between the parties to the regulatory process, through the presentation and analysis of the legal framework for banking supervision and awareness supervisory
Is hardly day expire without hearing the news either Abuse Managementthe accounting standards or the existence of serious misstatements by someauditors.Which caused the demanding of many companies in the recent republication of the financial statements and the re-announcement of its financialresults. Such acts raise questioning about the role that should be played by theauditors, prompting agencies responsible for setting auditing standards to takeTo throw increasingly responsibility on the auditors in order to interest risksfraud The Risks of Fraud in their review of the financial statements.also The Public Company Accounting Oversight Board in the U.S.called about the need of owning the Certified Public Accountants those whoaudits for
... Show MoreThe study aims at knowing the actual uses of instructional technology in teaching history subject in the colleges of education for humanities from the college staff members' perspectives and their attitudes towards it. The sample of the study consisted of (24) instructors from the Colleges of Education for the Humanities, the College of Basic Education- Haditha and the College of Education for Women, the study used the descriptive method, and the questionnaire was consisted of (50) items, and the psychometric properties of the instrument of the study were extracted. The researchers used the appropriate statistical means to analyze the data, and the results of the study showed the following: the teaching staff attitudes towards the use of
... Show MoreAbstract Lateral Epicondylitis (LE) which has been referred to as the Tennis Elbow as well is a lesion affecting common tendinous origins of wrist extensors due to chronic overuse injury that results in damaging common extensor tendons which join forearm extensor muscles to humerus. The aim of the present evidence-based clinical statement is reviewing scientific evidences for efficacy of a variety of the rehabilitation methods, chronic lateral epicondylitis management. It is focused upon treating chronic lateral epicondylitis and the latest developments in physiotherapy area for managing chronic lateral epicondylitis. Due to the fact that primary physical impairments in the LE are decreased is the strength of the grip, fundamentally due to
... Show MoreBesides the role of state institutions that come in the forefront of their priorities and obligations to provide security and development of the economy and reduce the unemployment rate and the reduction of inflation and improving education, health and others, the Community Partnership At frames what has become known as the institutions of society civil-with the state does not eliminate the role, but rather complements its role ; it is the role of civil society partner and an extension of the role of the state in the face of challenges and crises, but it may be sometimes a race role in addressing social, political and economic issues of the role played by the state, not complementary.
The highlighting the specificity of the relationsh
This research theme of the pressures of work , which is one of the important topics in order to recognize the reality of( influencing the pressures of work in the performance of employees in the General Company for Vegetable Oil Industry in Baghdad )through the statement of the existence of the correlation and influence whether or not the statement of the strength of this relationship and its impact in the case of its existence has been provided as part of my Search for variables and their removal in front of the Sub- scientific aspect has been the distribution of the questionnaire on a sample of( 62) people working in the company Mint distributors on several sections where.
Formed resolution of two sets
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