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.
Twenty binary liquid crystalline mixture diagrams were investigated with polarizing microscope and differential scanning calorimeter (DSC). Four binary mixture diagrams were constructed to identify the smectic phase which is found to be the same in all components of the homologous series (4-n-alkoxy -2, 3, 5, 6-tetra methyl-4-n-alkoxy azo benzene) (nPA4M). The fifth binary mixture diagram was between the (6PA4M) and the reference liquid crystal compound, terephthlylidene-bis (4-n-butylanaline) (TBAA) to identify the type of smectic mesophase of these compounds, and the results obtained were compared with the literature. To study the effect of the 4 methyl lateral groups on the thermotropic behavior of the (nPA4M) homol
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The current research aims to identify the effectiveness of concept maps in the academic achievement of the art of elegance and fashion for third vocational students. The current research is a quasi-experimental one. The research sample consisted of (74) female students in Al-Saydiyah secondary school for girls, they were divided into two groups: the experimental group and the control group. The following hypothesis was developed: There are no statistically significant differences at the level (0.05) between the average scores of the students who studied the subject using concept maps and the average scores of the students who studied the subject in the traditional method in the post-achievement test. The
... Show MoreThe current paper focuses on the studying the forms of (even-even) nuclei for the heavy elements with mass numbers in the range from (A=226 - 252) for isotopes. This work will consist of studying deformation parameters which is deduced from the "Reduced Electric Transition Probability" which is in its turn dependent on the first Excited State . The "Intrinsic Electric Quadrupole Moments" (non-spherical charge distribution) were also calculated. In addition to that the Roots Mean Square Radii (Isotope Shift) are accounted for in order to compare them with the theoretical results.
The difference and variation in shapes of nuclei for the selected isotopes were detected using &
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This research aims to measure the effect of Self competency of the Managers in their behavior from the view point of the working individual in the organization since the behavior of managers is considered to be one of the essential variables in the organization which can affect the performance and the commitment of the working individual. the questioners was used to gather the data and the Iraqi Rail Road co. was the field of the study . and a random sample of (36) individual of the subordinates of the managers society of the study and used the (SPSS) statistical program was used in the analysis of the data of the research . the findings refer to the existence of a
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Scorpions and spiders belong to the class Arachnida in phylum Arthropoda. Scorpions are easily distinguished by median eyes on obvious the center of the carapace and have one pair, and lateral eyes have 2-8 in some species. Scorpions do not have good eyesight so the median eyes have always been simple and they are more sensitive than the lateral pairs. They have anterior median eyes (AME) with narrow field of view and pairs of lateral eyes (LE) with more sensitivity and response to light. Family Buthidae have 2-6 lateral eyes in Compsobuthus Mesobuthus, Hottentotta, while Vaejovidae, Chactidae and Chaerilidae have 2 pairs of lateral eyes. In addition, 3 pairs are found in Orthochirus and Androctonus. Spiders have six eyes in family Pholicid
... Show MoreUsed in the study especially calibrated Erwa to determine the number of neighborhood or the Alayoshi number of bacteria in the count modeling and casting method dishes in addition to using the drop method yielded significant results for a match between the methods used ..
In low-latitude areas less than 10° in latitude angle, the solar radiation that goes into the solar still increases as the cover slope approaches the latitude angle. However, the amount of water that is condensed and then falls toward the solar-still basin is also increased in this case. Consequently, the solar yield still is significantly decreased, and the accuracy of the prediction method is affected. This reduction in the yield and the accuracy of the prediction method is inversely proportional to the time in which the condensed water stays on the inner side of the condensing cover without collection because more drops will fall down into the basin of the solar-still. Different numbers of scraper motions per hour (NSM), that is
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Introduction/Aim. Roughly six percent of all malignancies diagnosed in children are malignant bone tumors. They have a dramatic effect on psychological status of children and their families. The aim of the study was to analyze the clinico-pathological features of bone tumors in Iraqi children and to assess response to treatment, outcome, and survival. Patients and methods. Over an eleven-year period, a retrospective study was done for children with bone tumors conducted on patients data that included a battery of pre-treatment investigations including a complete blood count, serum electrolyte, hepatic, and renal profile, bone marrow aspirate and biopsy, fine-needle aspiration, and imaging studies. Results. Data of 41 children with b
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