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 aim of this study was to assess the nutritional status for samples at the age of 17-15 years. These samples were taken from secondary schools and universities in Baghdad area, 123 of them were male and 261 were female. Data on weight, height and body mass index (BMI) were determined in each individual. Smaller sample of 215 individuals (male and female) from the original sample was taken in order to record their nutritional behavior and daily food intake during the 24 hours prior to the visit through personal meeting using special questionnaire. The results showed that the weight and the height were within the range of the people of neighboring Arab countries, who are in the same age. Beside 44.4- 55.95% of these samples were within t
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A field experiment was conducted in an agricultural field in Al-Hindia district, Karbala governorate in a silty clay soil during the year 2020. The research included a study of two factors, the first is the depth of plowing at two levels, namely 13 and 20 cm, which represented the main blocks. The second is the tire inflation pressure at two levels, namely (70 and 140 kPa), which represented the secondary blocks. Slippage percentage, field efficiency, leaf area, and 300 grain weight were studied. The experiment was carried out using a split-plot system under a Randomized complete block design, at three replications. The tillage depth of 13 cm exceeds/transcend by giving it the least slippage of (11.01%), the highest field efficiency of (50.
... Show MoreThe study's objective is to find out the difference between the scholar of the research sample in awareness Green nanotechnology on the scaleas a whole and in each of its fields. The research depended of (136) specimen mem and women scholars of the fourth stage scholars / Department of Chemistry at the College of Education for Pure Sciences / Ibn Al-Haytham in Iraq for (2022-2023 AD) for the morning and evening studies, (65%) of the scientific community, It was picked at random with relation to the research instrument. it was a measure of awareness of green nanotechnology of (40) items, distributed in three areas (cognitive, skillful, emotional), and its validity and reliability were verified. Data analysis was completed for utilizing the s
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Authentic materials are the most important tools that the teacher could use in class in order to make teaching go smoothly and effectively in transmitting the necessary knowledge to all students. This research has investigated experimentally the effect of using authentic materials in teaching English as a foreign Language, because a number of studies point out that the use of authentic materials is regarded a useful means to motivate learners, arouse their interest and expose them to the real language they will face in real life situations.
It is hypothesis that there is no statistical significance difference between the experimental group who taught English as a foreign language by using the authentic materials with those
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The current research aims at highlighting the role of engagement of a sample of employees who works in some of the Iraqi private banks in terms of their interaction , commitment and enthusiasm and the positive impact they own regarding their job and devote their efforts to achieve the core purpose which is customer loyalty. The problem was expressed through a number of intellectual and practical questions.
In order to achieve the aim of the research the quantitative analytical method was used depending on a questionnaire as a basic tool to collect research data and the qualitative survey method depending on semi-structured interviews which were distrib
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The wave functions of converted harmonic-oscillator in local scaling transformations are employed to evaluate charge distributions and elastic charge electron scattering form structures for 6,7Li, 9Be, 14,15N and 16O nuclei. The nuclear shell-model was fulfilled using Warburton-Brown psd-shell (WBP) interaction with truncation in model space. Very good agreements with the experimental data were obtained for the aforementioned quantities.
It has been an increase concern of scientific and professional accounting sides on disclosure especially after appearance of business firms and accounting development with its relationship to financial statements which are considered to be outputs of the activity results. The preparing of financial statements and auditing of those accounts according to normal principles and standards of accounting on both local and international levels. Accounting disclosure can be seen an importance through discover all fundamental and necessary information for proper supply. Therefore, the research will highlight on public companies commitment in Iraq for basis and standards which have taken disclosure in financial data. The conceptual frame of t
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