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.
Design of experiments (DOE) was made by Minitab software for the study of three factors used in the precipitation process of the Sodium Aluminate solution prepared from digestion of α-Al2O3 to determine the optimum conditions to a produce Boehmite which is used in production of ɤ-Al2O3 during drying and calcination processes, the factors are; the temperature of the sodium aluminate solution, concentration of HCl acid added for the precipitation and the pH of the solution at which the precipitation was ended. The design of the experiments leads to 18 experiments.
The results show that the optimum conditions for the precipitation of the sodium aluminate solution which
... Show MoreThe rapid developmemt of information technology and its use in all fields has a bositive influence on all fields , and financial markets have a share of this development through the use of an electronic trading system to settle transactions and enhance transparency and disclosure in all activities of these markets and stimulate their performance .
It is worth nothing that these revolutions remove the necessity for nonstop connection with persons through the internet or phone networks , novel knowledge decreases the charges of structure original transaction system and reducing the fences of new participants entry .
The development in transportations expertise allows for quicker or
... Show MoreAbstract
Magnetic abrasive finishing (MAF) is one of the advanced finishing processes, which produces a high level of surface quality and is primarily controlled by a magnetic field. This paper study the effect of the magnetic abrasive finishing system on the material removal rate (MRR) and surface roughness (Ra) in terms of magnetic abrasive finishing system for eight of input parameters, and three levels according to Taguchi array (L27) and using the regression model to analysis the output (results). These parameters are the (Poles geometry angle, Gap between the two magnetic poles, Grain size powder, Doze of the ferromagnetic abrasive powder, DC current, Workpiece velocity, Magnetic poles velocity, and Finishi
... Show MoreThe Iraqi economy has suffered for a long period of inflation because of the Iraq war and the resolutions and the sanctions that were imposed on Iraq, this phenomenon overshadowed at various aspects of the economy including the tax revenue that the State seeks to optimize the total income for the budget, the research covers the years 1990-2010, these years have been divided according to the country's economic variables.
The research adopted on econometrics analysis that is based on the information and data available on topics and has been using statistical methods to test functions are formulated.
Research concluded that rates of inflation and GDP impact is limited to direct taxation and indirect in current prices a
... Show MoreThe aim of this research is analysis the effect of the changes in (GDA, g, inflation) at average and standard economic curriculum in composition of the models, depending on SPSS program in analysis, and according to available date from central bank of Iraq and during the period from 2003 to 2018 and by using OLS and estimate of the equation and the results showed a statistical significance relation in incorporeal level 5% and the R2 value equal to 92.1 refer to the changes in independent variables explain 92% of changes of unemployment and the independent variables effect are very limit depend on estimated parameters in the model and respectively (0.986,0.229,-0.060), the research recommended necessity to active the inve
... Show MoreThis research aims at identifying the level of quality of University environment according to the viewpoint of female students taking the College of Sciences for Woman an example, as represented in the college units as registration unit and the unit of students' affairs, the curricula, instructors, study halls, the college library, scientific labs, computer access, stationary and photocopying services, health care center, the unit of artistic, cultural and sportive activity, the canteen, the college gardens, college buildings and equipment and bathrooms. To achieve the objectives of the research, the researcher prepared a questionnaire to identify the viewpoints of female students concerning the extent of the availability of the standards o
... Show MoreThe important factor in the success of construction projects is its ability to objective estimate of the cost of the project and adapt to the changes of the external environment, which is affected by a lot of elements and the requirements of the competitive environment. The faces of those projects are several problems in order to achieve particular goals. To overcome these difficulties has been the development of research in the last two decades and turn the focus on the role of the cost of project management, by providing information and assist management in planning and control of the budget among the main elements of the project, namely, (time-cost-quality),The research aims at the possibility of developing and implementing mechanisms
... Show More
(1)
The Anticyclone Merge affects Iraq’s climate clearly through its impact on the different climatic elements. where it appears while they pass through special and distinctive weather . and most of this affection appears in temperatures, Therefore, this research study the relationship between the repetition and the survival period of the Anticyclone Merge and temperature average by using coefficient correlation (Pearson) that shows there’s strong inverse relationship between the integration of Anticyclones and temperatures average. &nbs
... Show MoreThe research aims: to build a measure of the cognitive competence of coaches from the point of view of players of Iraqi Premier League volleyball clubs and extract scores and standard levels for it. In order to achieve the objectives of the research, the descriptive method was used using the survey method. As for the research sample, it was chosen intentionally, and was represented by volleyball players for the Premier League 2024-2025. The sample was divided into exploratory, constructive, and standardizing, and starting the construction procedures, which included finding the scientific foundations for the scale, in addition to extracting the modified standard score and levels for the sample of the main experiment for standardization. Amou
... Show More