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.
يعد علم التدريب الرياضي الحديث عملية تربوية علمية مبنية على اسس صحيحة هدفها وصول اللاعبين الى التكامل في الاداء الفني وهذا يتم عن طريق التأثير المنظم والدقيق بواسطة استعمال التمارين البدنية التي تحدث تغيرات خاصة في عمل اعضاء واجهزة جسم الرياضي والتي بدورها تؤدي الى رفع كفاءة الاعضاء والاجهزة لتحقيق الانجازات الرياضية العالية ولقد استعملت الباحثتان اسلوب حديث من اساليب التدريب الرياضي من اجل تطوير تحم
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There are many problems facing the economic entities as a result of its mass production &variation of its products , the matter which had increased the need & importance of cost accounting which is regarded a main tool for the managerial control.
The actual costing system is unable to meet the contemporary management needs ,so the Standard costing system appear to provide the management with required information to perform its functions by the best use& way.
This research aims to determine the standard cost for the direct material for oil extraction activity by applying it in the north oil company.
Abstract
The study aims to reveal the level of inclusion of citizenship values in the English language textbooks (We Can) series for elementary education in the Kingdom of Saudi Arabia. To achieve this objective, the "content analysis" methodology was used. A content analysis card was designed to include (6) main areas of citizenship values, it consisted of (28) sub-indicators of citizenship values that were supposed to be included in the English language textbook series (We Can) for elementary education. The study sample consisted of all the English language textbooks (We Can) series for elementary education, which consisted of (6) textbooks, two for each class. The results of the study indicated that there is a
... Show More“Child of today is a man of the future" this slogan is one of the most popular logos of international organizations and institutions that dealing with human beings needs in general and children needs in particular, whether these needs are educational, health, social, or economic. Children require special care and extra legal protection, since the child-raising is not the Child’s own issue, but it's the issue of the society in which he/she would integrate.
As the education and language skillsacquisition primarily associated with hearing, because human being receives most of the skills and knowledge through the hearing; that imitate sounds and learn how to speak isacquired only by hearing, so therefore the hearing - impairedchi
... Show MoreAbstract---The aim of the current research is to identify the level of logical reasoning skills in chemistry students at the Faculty of Education for Pure Sciences/ Ibn Al-Haytham for the academic year (2021-2022). The differences in their level of skills according to the gender variable (males and females) and the academic stages (first- second - third - fourth). The descriptive approach was adopted because it corresponds to the nature of the research objectives. The research sample consisted of (400 )students selected in a relatively random stratified way. The researcher constructed a logical reasoning test, which includes (6) sub-skills , which is (proportional - probabilistic- synthetic- deductive- logic- variable adjustment). The psych
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The process of soil classification in Iraq for industrial purposes is important topics that need to be extensive and specialized studies. In order for the advancement of reality service and industrial in our dear country, that a lot of scientific research touched upon the soil classification in the agricultural, commercial and other fields. No source and research can be found that touched upon the classification of land for industrial purposes directly. In this research specialized programs have been used such as geographic information system software The geographical information system permits the study of local distribution of phenomena, activities and the aims that can be determined in the loca
The technology in continuous and quick development, that reflects in all parts of our life and interred both scientific and practical fields. Marketing is one of them, a customer’s way to deal with choosing and demanding the product deferent from the traditional way. Some of the buying processes are electronic now, therefore the current research is identifying the digital channels that entered the world of marketing and influenced the activities and types that fall under this name and how it affects in positioning strategy, which is how to install the product or brand in the mind of the customer and was dimensions (brand identity, brand personality, brand communication, brand awareness, brand image), The researcher took t
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Abstract
It is clear to everyone how important it is to implement transactions electronically, as it facilitates the provision of services to beneficiaries, whether individuals or institutions, to achieve many benefits that are not exclusive to the beneficiary or the applicant, but extends to the governmental and international bodies. And the number of users has reached millions since its emergence in 1995, because the concepts of electronic transactions have great advantages for the economy in general and the banking sector in particular, so cooperation in various fields with the aim of becoming an information society has become paramount, It allows customers to pay money to any company they want t
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The great importance of training made it as an investment for the organization, and assert the Quality of performance which support it by prepare the employee to the Current and future Jobs . The Research problem a rounded about How to measure the impact of training based on (ISO 10015) and its effect on the Quality of performance , How to evaluation the results of training to attained the training goals . The Research aims to find out the effects of application of international standard guidelines (ISO 10015) to attained the quality of audit work achieved in the Federal Board of Supreme Audit. The Research sought to achieve a number of objectives cognitive and applied on the basis of four key assumptions, and other su
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