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.
Suggestion Plan for the Reclassification of U.N Publications in Central Library
This study attempts to determine the necessary teaching competencies for teachers and the level of their importance in the development of their performance professionally and scientifically, and the progress towards a better future to achieve an effective level. Accordingly, the research community consists of the morning-preparatory schools for boys at the General Directorate of Education of Baghdad \ Rusafa2. The study sample included (68) teachers constituted 88.31% of the total community of teachers. As for the research tools, the researcher adopted the descriptive method by using the observation method in which the researcher prepared a list of teaching. For verifying the re
... Show MoreThe main objective of present work is to describe the feasibility of friction stir welding (FSW) for
joining of low carbon steel with dimensions (3 mm X 80 mm X 150 mm). A matrix (3×3) of welding
parameters (welding speed and tool rotational speed) was used to see influence of each parameter on
properties of welded joint .Series of (FSW) experiments were conducted using CNC milling machine
utilizing the wide range of rotational speed and transverse speed of the machine. Effect of welding
parameters on mechanical properties of weld joints were investigated using different mechanical tests
including (tensile and microhardness tests ). Micro structural change during (FSW) process was
studied and different welding zones
The research aims to find ways to minimize the use of quantities of chemical fertilizers in agriculture in order to get to an environment that is free of contaminants. Magnetized water technology used in the experience of planting seeds of tomatoes Thomson type to obtain a higher efficiency to absorb fertilizer NRK in the protected environment of the period from February to June. Magnetized water system used locally made levels Gaues (4800,2500,1500) concentrations of 50 to 100% for each level and the rate of (4) replicates, and results indicated that the severity of the magnet (4800 Gaues) and a concentration of 50% gave the highest percentage of tomato fruit size and intensity ( 1500 Gaues) and a concentration of 100% did not give any inc
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The aim of the current research is to verify the effect of the cognitive modeling strategy on the achievement of the chemistry course for the students of the first intermediate grade. To achieve the objective of the research, the null hypothesis was formulated via cognitive modeling strategy. The results showed that the experimental group's students performed better than the students in the control group. In the light of the results, the researchers concluded: The impact of the cognitive modeling strategy in the achievement of students of first intermediate grade in chemistry.
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Obiovisly that the holy thresholds are directly related to Islam and Muslims and related to the general culture of the Islamic peoples. In terms of architecture, it is considered a distinctive architectural scene that reviews the history of this origin and its architectural styles. Recently, with the increase in the number of pilgrims and visitors to the holy shrines, there is a need to develop and expand the buildings and provide them with services and introduce modern technology. The building of the holy thresholds consists of a number of functional design indicators: The general problem of research is that there is no clear theoretical framework for the design indicators for the development of the holy shrines according to the functio
... Show MoreGypseous soil is considered as a problematic soil for embankment construction, however, implementation of emulsified asphalt as a stabilization agent could be a proper solution for enhancing its properties as a subgrade soil. In this work, the sustainability of asphalt stabilized soil has been assessed in terms of its resistance to cyclic (freezing-thawing) and (heating-cooling) processes. Specimens have been prepared at optimum fluid content (moisture and emulsion) and tested under direct shear stresses while subjected to 30 cycles of (freezing-thawing) and (heating-cooling). Both of dry and soaked testing conditions have been implemented. Data have been observed after each 10 cycles, and compared with that of reference mix. It was conclud
... Show MoreThe study aimed at clarifying the contradictions of the general industrial companies despite the investment allocations and the government investment expenditure on manufacturing activities under the so- called rehabilitation programs. However, this did not contribute to a certain extent in the growth and industrial leap in the direction of developing the activities of the sector Industrial sector in Iraq because of the lack of adoption of a number of basic principles towards the need to take priority of investment in the field of manufacturing and industrial decision-making in the restructuring of industry according to the priorities of investment in light of the international industrial trend, Tosmarah available to the manufact
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Background: Asthma is one of the most common chronic respiratory diseases in the world, standing for the most frequent cause for hospitalization and emergency cases. Respiratory viruses are the most triggering cause. Aim: To assess the role of viral infections, especially COVID-19, in the pathogenesis of asthma initiation and exacerbations. Method: Electronic search was done for the manuscripts focusing on asthma as a risk factor for complications after COVID-19 infection. The outcomes were titles, materials, methods and classified studies related or not related to the review study. Three hundred publications were identified and only ten studies were selected for analysis. Seven studies were review, one retrospective, one longitudin
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