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.
In this study, phosphorescence analysis (KPA) is used for determining soil collected from the Tigris River from Al- Karrada and Bab Al-Sharq in Baghdad and samples were taken from rainwater collected from Al-Rashad, Al-Obeidi, Al-Dora and Al-Sadr City in Baghdad. The measurements were carried out by the Iraqi Ministry of Health and Environment, in the Radiation Protection Center. The collection, removal and evaporation of the samples ranged from January to the end of March 2018. The results show the presents of concentration of 238U and 235U in soil samples and the rainwater samples. The conclusion of this work is the concentration of uranium in soil samples is more than recommendations by ICRP value of 1.9 μg /l. While all water sample
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Abstract A descriptive (cross sectional) study was conducted to assess psychosocial domain of quality of life for (100) women who had hysterectomy for non malignant indications during 6-12 months post operative. The study carried out in both consultation clinics of Al-Elwiya Maternity Hospital and Baghdad Teaching Hospital from January 5th 2003 to July 10th 2003). The results of the study show that hysterectomy achieved a highly successful outcome in terms of psychological and social adjustments for hysterectomies women, a highly significant differences between quality of life (QoL) and some of demographic cha
Objective: This study aimed to assessing new suggested technique of Physical Growth Curves (PGC) charts in
children under two years old of a non-probability sample.
Methodology: A non-probability sample of size (420) children under two years selected from 12 Primary
Health Care Centers in Diyala governorate during the period from 15th Nov. 2010 to 13th Mar. 2011
according to admix of a different properties together in one chart/or growth curve chart included in at least
weight, Height, and Head circumference.
Results: the results showed different properties that can be admix together in one chart/or growth curve
chart included in at least weight, Height, and Head circumference. And to overtake the problem of the norm
Many problems are facing the installation of piles group in laboratory testing and the errors in results of load and settlement are measured experimentally may be happened due to select inadequate method of installation of piles group. There are three main methods of installation in-flight, pre-jacking and hammering methods. In order to find the correction factor between these methods the laboratory model tests were conducted on small-scale models. The parameters studied were the methods of installation (in-flight, pre-jacking and hammering method), the number of piles and in sandy soil in loose state. The results of experimental work show that the increase in the number of piles value led to increase in load carrying ca
... Show MoreThe differential protection of power transformers appears to be more difficult than any type of protection for any other part or element in a power system. Such difficulties arise from the existence of the magnetizing inrush phenomenon. Therefore, it is necessary to recognize between inrush current and the current arise from internal faults. In this paper, two approaches based on wavelet packet transform (WPT) and S-transform (ST) are applied to recognize different types of currents following in the transformer. In WPT approach, the selection of optimal mother wavelet and the optimal number of resolution is carried out using minimum description length (MDL) criteria before taking the decision for the extraction features from the WPT tree
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An innovative two-step noncatalytic esterifcation technique was proposed to synthesize alkyl esters from free fatty acids simulated in waste cooking oil, as a pretreatment process for biodiesel production, without adding any catalyst under normal conditions of pressure and temperature. The efect of methanol:oil molar ratio, reaction time, mixing rate, and reaction temperature were investigated. The results confrmed that the conversion of the reaction was increased when increasing the methanol molar ratio and decreased in prolonged reaction temperature. High conversion (94.545%) was successfully achieved at optimized conditions of 115:1, 65:1 methanol:oil molar ratio in the frst step and second step, respectively, other conditions i
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In this paper, three types of epoxy-based coatings (Polyamide, pure Polyamine, and Polyamine reinforced by glass-flake) used as a lining for potable water tanks were studied using experimental and finite element methods. Tensile, impact, and fatigue tests were conducted on uncoated and coated AISI 316 stainless steel. The test results show that the applied epoxy based coating improves the mechanical properties, increases of fatigue crack resistance, and enhance the dynamic fracture toughness. The fatigue crack propagation is influenced by the compositions of epoxy coating, and the glass-flake improves the coating resistance to fatigue crack propagation compared to other types.
(2)
This paper presents L1-adaptive controller for controlling uncertain parameters and time-varying unknown parameters to control the position of a DC servomotor. For the purpose of comparison, the effectiveness of L1-adaptive controller for position control of studied servomotor has been examined and compared with another adaptive controller; Model Reference Adaptive Controller (MRAC). Robustness of both L1-adaptive controller and model reference adaptive controller to different input reference signals and different structures of uncertainty were studied. Three different types of input signals are taken into account; ramp, step and sinusoidal. The L1-adaptive controller ensured uniformly bounded
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