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.
The performance of job effectively requires narrowing the meaningful routine activities and attempting employing the job procedures in favor of public welfare through adding the green impact as well as removing them from the red tapes which reflect the firmness of procedures, to enable the job parties to make their job independently, and pushing them to gain priority in the competition layer. This is not attaining easily amidst the regulatory problems expressed by the complication of procedures, the thing which make identifying the problem of the study through the following question:
Should we make the complex of procedures and their firmness a way to adopt the idea of the green regulatory tapes supportin
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Abstract:
Since the railway transport sector is very important in many countries of the world, we have tried through this research to study the production function of this sector and to indicate the level of productivity under which it operates.
It was found through the estimation and analysis of the production function Kub - Duglas that the railway transport sector in Iraq suffers from a decline in the level of productivity, which was reflected in the deterioration of the level of services provided for the transport of passengers and goods. This led to the loss of the sector of importance in supporting the national economy and the reluctance of most passengers an
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The aim of the research is to identify the reality of administrative motivation for the deans of the faculties of physical education and sports sciences at the universities of Baghdad and Al-Mustansiriya from the point of download of the faculty members. The number of the exploratory sample was (7) faculty members, they were taken in a random way, while the rest of the sample number was (150) faculty members who considered the application sample for the scale, and the two researchers also adopted a questionnaire for the scale and it is applied to the Iraqi environment. phrase, which are phrases that are interrelated with the administrative leadership motivation in the faculties of physical education and sports sciences. The researchers did
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The current study aimed to identify the difficulties faced by the student in mathematics and possible proposals to address these difficulties. The study used a descriptive method also used the questionnaire to collect data and information were applied to a sample of (163) male and female teachers. The results of the study found that the degree of difficulties in learning mathematics for the fifth and sixth grades is high for some paragraphs and intermediate for other paragraphs, included the student's field. The results also revealed that there were no statistically significant differences at the level of significance (α = 0.05) between the responses of the members of the study sample from male and female teachers to the degree of diffi
... Show MoreThis research addresses the necessity due to the scarcity of historical studies in the field of sports, especially those indicating the activities and achievements of Arab countries in the Paralympic movement. This study aims to document the participation of Arab countries in the Paralympic Games, explore the prominent sports in which Arab athletes with disabilities participated, and analyze their achievements during the Paralympic Games from 2004 to 2012. The research methodology adopted an analytical, historical approach, collecting and analyzing data objectively through the official website of the International Paralympic Committee, in addition to scientific and historical sources from research papers, journals, and websites. The key fi
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The centers of cities and historical quarter are exposed to a severe threat to the values of the physical and legal urban environment as a result of the value deterioration and the emergence, emergence and spread of new values on the intellectual and urban context, which generates the loss of the urban environment for its spatio-temporal continuity, flexibility, adaptation and continuity, and thus urban obsolescence, Hence the problem of the research in “the lack of comprehensiveness of studies on the phenomenon of urban obsolescence and its impact on the decline in the values of the quality of the built environment in historic
... Show MoreThe developing countries, like our country Iraq suffer from deep comprehensive structural crisis, manifestations and a clear imbalance between the demand and the supply sides. The overall imbalance in the external balance. As a consequence, this caused the accumulation of foreign debts or failure in the implementation of economic development programs. The countries which are forced to resort to the International Monitoring Funds, and the World Bank for assistance and to express an opinion on policies that include restrictions controls that belong to the monetary, and fiscal side group, imposed on the economies crisis, as a condition for returning to normal which called reform programs. The organize of the events of radical changes in the
... Show MoreDeveloping smart city planning requires integrating various techniques, including geospatial techniques, building information models (BIM), information and communication technology (ICT), and artificial intelligence, for instance, three-dimensional (3D) building models, in enabling smart city applications. This study aims to comprehensively analyze the role and significance of geospatial techniques in smart city planning and implementation. The literature review encompasses (74) studies from diverse databases, examining relevant solutions and prototypes related to smart city planning. The focus highlights the requirements and preparation of geospatial techniques to support the transition to a smart city. The paper explores various aspects,
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