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.
This research aimed to identify the structural model of the relationship between emotional creativity and self-efficacy among male and female students of the preparatory year at Tabuk University. The current study adopted the descriptive correlational approach, as it is appropriate to the nature of the study. The study tools contained (60) items that measure the relationship between emotional creativity and self-efficacy among the male and female students of the preparatory year at Tabuk University. The study sample was chosen by the stratified random method of the study community, where the study sample reached (183) male and female students of the preparatory year at the University of Tabuk. The results of the study showed that there a
... Show MoreVarious activities taking place within the city of Baghdad have significantly contributed to organic pollution in Rivers Tigris and Diyala. The present study aimed to assess some physical, chemical and biological aspects of six sites on Rivers Tigris and Diyala as they flow through the city of Baghdad. Monthly samples were collected for the period January to December, 2005. Marked differences in the physical and chemical characteristics of water were noted between the two rivers’ sites. Average values during the study period of dissolved oxygen, biochemical oxygen demand, particulate organic matter, nitrate, phosphate and total dissolved solids for Tigris and Diyala were 7.8,4.7; 2.4,10.4; 350.1,921.4;7.8,13.9;1.2,4.8;814,2176 mg / l re
... Show More
(1)
This research aims to find out "the effectiveness of the self-questioning strategy in the achievement of students Phase III institutes of teacher preparation and decision-making in chemistry." The researcher follows approach quasi-experimental with a post-test, and the sample consisted of (27) from " Teachers Training Institute-AL-Byaa "in Directorate of Education Baghdad Karkh / 2 students divided into two unequal groups: experimental its number (14) students studied using reciprocal teaching strategy and control its number (13) students have studied in the usual way.The two groups were equivalent extraneous variables.
The researcher was prepare achievement test consist of 40 items was the adoption of a measure of decision-makin
... Show MoreThis research aims to identify the effectiveness of counseling by using the technique of self-talkin developing the habits of mind among middle school students by testing important hypotheses, and choosing the experimental design for the two groups (experimental - control). The classification of "Costa & Kallick" was adopted to measure the habits of the mind, and the scale consisted of (64) items, and after confirming the psychometric properties of the scale, the researcher applied it to the research sample (487) students from middle school students. One of the students who got the lowest marks after answering the scale. purpose of applying the experiment. He divided them into two groups, one of them is experimental (10) students, as
... Show More
The aim of the current research is to identify the self-control of kindergarten teachers as well as to identify the significance of the differences according to a variable (years of service, academic achievement, specialization). Its final paragraphs consist of (35) paragraphs, and its psychometric properties were verified and the tool was applied to a sample of (400) teachers chosen randomly from kindergarten teachers affiliated to the General Directorates of Education in Baghdad, Rusafa, and Karkh for the academic year 2019-2020
In light of the objectives of the current research, the following results were reached
- The current research sample is from kindergarten teachers with self-contro
- There are diffe
In this publication, several six coordinate bridged-polymeric metal complexes are reported. The reaction of 4,4`-dipyridine with ethyl chloroacetate in mole ratio of 1:2 gave the multidentate carboxylate ligand bis(N-carboxylatomethyl)-4,4`-dipyridinium). The reaction of the ligand with metal chloride and sodium azide resulted in the formation of the required polymeric complexes. Upon complex formation, the carboxylato ligand behaves as a neutral multidantate species. The mode of bonding and overall geometry of the complexes were determined through physicochemical and spectroscopic methods. These studies revealed octahedral geometry about metal centres and complexes of the general formula [Cr2(L)(N3)4]Cl2.H2O, Na2[Ag2(L)(N3)4].H2O and [M2(L
... Show MoreThe grasping stability of robotic manipulators is crucial to enable autonomous manipulation in an environment where robots are facing obstacles in their route, where abrupt changes in the robot’s speed are induced. These speed variations will produce forces affecting the robotic manipulator, hence its grasping stability. In this research, the grasping stability of a robotic manipulator that functions according to a frictional self-locking mechanism is investigated statically and dynamically. Both theoretical and experimental results showed that the grasped object size, weight, and its orientation inside the gripper have a great effect on grasping stability. Both the theoretical and experimental results indicated that the grasping object p
... Show More
The interest in Multi social skills and self-concept is extremely important for many of the scholars of education and psychology has taken a great deal in their writings and their interests as they see that social skills training is to make sure of the same, and that whenever enable the individual from acquiring social skills whenever asserted itself.The research aims know social skills and self-concept and their relationship to the children Riyadh age (4-6 years), and the research sample consisted of(200) boys and girls from kindergarten in the city of Baghdad Bjanbey Rusafa second and Karkh second.And to the objectives of the research realized the researcher has built two measures of social skills a
... Show More
(13)
(10)
Surface water flow samples were collected with distances downstream over Saqlawiya main drain whose stretch of about 24.5 km. The drain travels through different land use pattern, before, flowing into Tigris River. Eight sampling points were carefully
selected downstream the channel during dry season. The examined water parameters were pH, NH3, NO3, PO= 4, BOD5, COD, TDS, S.S, Cl-, SO= 4, Na+ , Ca+2, Mg+2, and Oil and Grease. Descriptive and inferential methods through finding the best curve fit correlation were employed in the study to test the strength of the association between water chemical characteristics and distance downstream the channel. A comparison of the values of chemical parameters at the Al-Saqlawiya Drain-Tigris Riv