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.
A revolution called information revolution has recently invaded the world. It is Currently considered one of the most important properties of development to the countries of the world The criteria provided by computers such as accuracy, speed, time saving Storage and restore have led them to be widely used in economy, industry, agriculture, communications, etc., as well as being the major finder of reengineering the operations of innovation. The use of computers in the preparation of budgets will lead to achieve accuracy. Since, the operation draws upon the statistic and quantity estimations about budget items, the computerized balance sheet may save time and effort of preparing mathematical equations annually. According to the problem o
... Show Moreم. د. ولاء طارق حميد, Al. Qadisiya journal for the Sciences of Physical Education, 2017
The paper aims to identify the impact of discrete realization strategy in the development of reflective thinking among students: (males/females) of Qur'an and Islamic education departments for the course of Islamic jurisprudence according to the variability of sex. The researcher used the experimental approach and adopted an experimental determination with a set part of the two groups (experimental and controlled). He selected the sample deliberately which consists of (147) students spread over four classes (experimental males/ experimental females/ controlled males/ controlled females), and it took last for an academic year of (2010-2011). He, then, prepared a post test to measure the reflective thinking with his five skills (skill of o
... Show MoreThe studying trying to determine the role of Strategic Intelligence on the Process of Green Manufacturing of Sample of Mineral water factories at Dahuk city. The study submit a theoretical frame of Strategic Intelligence and Green Manufacturing, a supposed sample, had been set to reverye the nature of the relations and effect in the study Varity, the study depend on group of the main and branch concurring with the relations and effect between the Strategic Intelligence and Green Manufacturing to answer the following questions about research to problems:
What are the relationships and effects between stra
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The study aims to build a proposed training program for school leaders in the Sultanate of Oman on the planning practices of the Kaufman model in light of the needs and challenges of reality. It also aims to identify the challenges facing school leaders in practicing the stages of strategic planning. To achieve these objectives, the study adopted the descriptive approach due to its suitability to the nature of the study. A questionnaire was used to collect the needed data. The study sample included (225) individuals from school principals, their assistants and senior teachers in post-basic education in the Sultanate of Oman. After processing the data statistically, the study concluded that the reality of planning practices for school lea
... Show MoreThis growing interest of the international scientific specialized commissions is due to the role that the audit committee can play, as one of companies’ governance tools, to increase the accuracy and transparency of the financial information disclosed by the companies, through its oversight role on the process of preparing financial reports, its supervision on the internal audit function within the companies, and supporting its independency, as well as coordinating the efforts between the internal control unites and the external auditor represented by the (Board of Supreme Audit) to clear the observations and irregularities in order to reduce the fraud cases.
This research was built on an applied sample of audit committee works
... Show MoreThe research sought to demonstrate the effectiveness of monetary policy in banking stability by measuring the impact of monetary policy in the composite index of banking stability in Iraq for the period 2010/2017, as the stability of the financial system is one of the main objectives that the Central Bank is keen to achieve along with other objectives to ensure the performance Effective for all economic units, this is what prompted the central banks to give more attention in ensuring the safety, durability and stability of their financial systems, and the increasing interest by the Central Bank of Iraq in the subject of financial stability stems from its responsibility in ensuring a sound and stable financial system. Maintain it and mini
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