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 main purpose of the research is to demonstrate the importance of the insurance sector in the economy through its role in providing security for all economic sectors and thus stimulating the gross domestic product and reducing dependence on the output of the oil sector, which may expose the Iraqi economy to several problems and imbalances, I have found that there is a great weakness in the role of the insurance sector in Iraq at the level of government, companies and individuals, and the reason for this is the lack of policies supporting the insurance sector and the lack of work in the strategy of economic diversity and the decrease of security awareness by individuals so became Developing the sector to ensure the urgent need
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The subject of the information technology system ( ITS ) of the important issues And contemporary thought in management, and various types of organizations seeking to apply and try to
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In this paper solar radiation was studied over a region of Baghdad (Latitude 33.3o and longitude 44.4o). The two parts of global solar radiation: diffuse and direct solar radiation were estimated depending on the clearance index of measured data (Average Monthly mean global solar radiation). Metrological data of measured (average monthly mean diffuse and direct solar radiation) were used to comparison the results and show the agreement between them. Results are determined by applying Liu and Jordan two models (1960). Excel 2007program is used in calculation, graphics and comparison the results.
Abstract
The research aims to determine the nature of the Iraqi market in terms of banking financial stability and the extent impact of the operational efficiency on it, Accordingly, chosen 15 relational banks were chosen as an intentional sample that could represent the Iraqi banking system for the period 2010-2020. The operational efficiency variable was measured according to the data envelope model, and banking financial stability used CAMELS model which includes five indicators (capital adequacy, asset quality, management quality, profitability, and liquidity), so for testing the research hypotheses used the random regression model by adopting the S
... Show MoreThe high cost of chemical analysis of water has necessitated various researches into finding alternative method of determining portable water quality. This paper is aimed at modelling the turbidity value as a water quality parameter. Mathematical models for turbidity removal were developed based on the relationships between water turbidity and other water criteria. Results showed that the turbidity of water is the cumulative effect of the individual parameters/factors affecting the system. A model equation for the evaluation and prediction of a clarifier’s performance was developed:
Model: T = T0(-1.36729 + 0.037101∙10λpH + 0.048928t + 0.00741387∙alk)
The developed model will aid the predictiv
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Public debt has posed a major challenge to both developing and developed countries, which has focused attention on the optimal limits (threshold of debt) and its determinants.
The study examines the effect of the Public bank debt on the foreign reserves and the work of the foreign reserve as a limitation on the process of bank debt (part of the internal debt) for the period (2017-2004), in addition to finding the type and nature of the relationship between them according to the hypotheses of the study, Public bank debt and foreign reserves.
The study was based on data from the Iraqi banking sector, which showed that Iraq has a foreign reserve in line with internat
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In this paper, an algorithm is suggested to train a single layer feedforward neural network to function as a heteroassociative memory. This algorithm enhances the ability of the memory to recall the stored patterns when partially described noisy inputs patterns are presented. The algorithm relies on adapting the standard delta rule by introducing new terms, first order term and second order term to it. Results show that the heteroassociative neural network trained with this algorithm perfectly recalls the desired stored pattern when 1.6% and 3.2% special partially described noisy inputs patterns are presented.
This research aims to develop new spectrophotometric analytical method to determine drug compound Salbutamol by reaction it with ferric chloride in presence potassium ferricyanide in acid median to formation of Prussian blue complex to determine it by uv-vis spectrophotmetric at wavelengths rang(700-750)nm . Study the optimal experimental condition for determination drug and found the follows: 1- Volume of(10M) H2SO4 to determine of drug is 1.5 ml . 2- Volume and concentration of K3Fe(CN)6 is 1.5 ml ,0.2% . 3- Volume and concentration of FeCl3 is 2.5ml , 0.2%. 4- Temperature has been found 80 . 5- Reaction time is 15 minute . 6- Order of addition is (drug + K3Fe(CN)6+ FeCl3 + acid) . Concentration rang (0.025-5 ppm) , limit detecti
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