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.
Focusing of Gaussian laser beam through nonlinear media can induce spatial self- phase modulation which forms a far field intensity pattern of concentric rings. The nonlinear refractive index change of material depends on the number of pattern rings. In this paper, a formation of tunable nonlinear refractive index change of hybrid functionalized carbon nanotubes/silver nanoparticles acetone suspensions (F-MWCNTs/Ag-NPs) at weight mixing ratio of 1:3 and volume fraction of 6x10-6 , 9x10-6 , and 18x10-6 using laser beam at wavelength of 473nm was investigated experimentally. The results showed that tunable nonlinear refractive indices were obtained and increasing of incident laser power density led to increase the nonlinear refractive inde
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the research discussed a stage of strategic management. The strategic of the evaluation of the proposed strategy through feedback is to ensure that it is implemented with the least possible variation. The research aims at evaluation a proposed strategy for the Ministry of Planning for the years 2018-2022 in line with the orientations of the state, taking into account the surrounding environmental conditions. It relies on scientific bases and steps to formulate the strategy The extent of the strategy suitability was tested through a set of statistical means and its objectivity was verified through a survey of a number of specialized experts who were selected in accordance with the principle
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The current research aims to determine the necessary linguistic competencies for Arabic language teachers of the preparatory stage (fourth grade preparatory), which were five main competencies: Arabic grammar competencies, literary competencies, cultural competencies, rhetorical competencies, and expression competencies. To achieve the objective of the research, the researcher developed a questionnaire as the main tool for collecting data based on literature, it consists of (28) items including the five main competencies. The questionnaire was administered to (60) male and female teachers at Al-Karkh's first Education Directorate in the city of Baghdad. The findings of the research indicated that Arabic language proficiency got the highe
... Show MoreThe State company for vegetable oils industry one of the most dynamic
companies in the Iraqi economy and is one of the companies manufacturing(food) that takes astrategic dimension and production within the concept of food security, this as well as to reduce dependence on imports and operation of national manpower.This study aims to describe the performance of the State company for vegetable oils industry for the period (2003-2007) which was characterized by economic and security instability of the country and give an accurate picture of their efficiency and their capacity to produce during this Period.
Providing Iraqi students with proficiency in English is the ultimate goal of the educational system which is a way of getting knowledge in the fields of arts, sciences, transferring knowledge and sciences to other communities. Therefore, conducting such a type of study is very important because the contents of English textbooks have a huge influence on learning of the students. Once the content of English textbooks contain errors as the correct one, this will effect on his/her learning. The present study is an attempt to evaluate the new course entitled “English for Iraq” for fifth grade students for secondary schools, by Olivia Johnston and Mark Farell. It aims to answer eleven questions relating to the following domains: strength, obj
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The development of a future mechanism for sustainable development in Iraq to meet the current and future challenges requires an analysis of the indicators of sustainable development. This research aims at presenting and analyzing the social care aspect and highlighting the important role of taxes with a focus on social sustainable development to determine the extent and direction of changes. Level of progress, the researcher concludes the weakness of the financial allocations to the Ministry of Labor and Social Affairs and in line with the large number of people who apply the conditions and controls, and recommends the researcher the necessity of participation of all segments of society between the public and private sector In terms of o
... Show MoreThe concept of quality of auditing profession comes on top of the concerns of the international business community and international institutions particularly now following the impact of the several failures and financial hardships suffered by the major companies in the recent collapse of money markets in some countries of the world and fear of their recurrence in the future.An observer of the local and international rules and standards (or principles) finds that these include such implications have direct or indirect effects on the performance of the service of the accountant and auditor, which should upgrade their professional performance in these services to a high level of quality so as to be in line with the requirements, principles
... Show MoreThe General Company for Iraqi Cement is regarded as one of the companies that contribute to support the Iraqi economy. It contributes to provide the material of cement which fulfils the consumer and investment need in the markets in competitive prices and not to resort to the importing of the cement from abroad. That would save a great share of the purchase parity of the poor sectors of society. The estimation of production function will contribute to putting the company.
The application functions of the standard production of benefit critical to clarify the actual relationship between production & its components, & allow to clarify the i
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The imbalances and economic problems which it face the countries, it is a result of international economic developments or changes or global crises such as deterioration in trade, sharp changes in oil prices, increasing global indebtedness, sharp changes in foreign exchange rates and other changes, all that, they affect the economic features of any country. and These influences vary from one country to another according to the rigidity of its economy and its potential in maneuvering with economic plans and actions that would reduce the impact or avoidance with minimal damage. Therefore, the countries that suffer from accumulated economic problems as a result of mismanagement and poor planning or suffe
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