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.
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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Abstract
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 MoreRecent research looking for acknowledgment of strategically influence of Robinson and self question at progressing the reading comprehension for students of sixth class .
To achieve research goal so the researcher mentally chose primary sixth class at the school (Tashti the primary) that followed education directorate of province (Jamjamal)/Suliymania for the scholastic year 2012-2013 as application field for their experiment of boys' number reached to (95) (female and male)students in reality (32) of the first experimental group and (31) student (female and male) from controlled group, the researcher rewarded between of three variable groups (timing period, intelligence ,Kurdish language degr
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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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One of the important goals in the learning process is to be effective learning through the self-direction of the learner , because it has an impact on the effort of learners , it is better to be a learner responsible for learning and independent of the acquisition of knowledge ,
اذ اكدتكثيرAs many have confirmed منFrom الدراساتStudies والادبياتAnd literature انthat فشلالكثير The failure of many منFrom الطلبةStudents فيin a تنظيمgroup المعلوماتthe information ومعالجتهاAnd processed اثناءduring عمليةProcess تعلمهمLearn them لاNo يرجعReturns الىto me انخفاضdrop فيin a درجةDegree ذكائهمTheir intelligence اوor عدمNo
... Show MoreThis paper proposes a self organizing fuzzy controller as an enhancement level of the fuzzy controller. The adjustment mechanism provides explicit adaptation to tune and update the position of the output membership functions of the fuzzy controller. Simulation results show that this controller is capable of controlling a non-linear time varying system so that the performance of the system improves so as to reach the desired state in a less number of samples.
Self-repairing technology based on micro-capsules is an efficient solution for repairing cracked cementitious composites. Self-repairing based on microcapsules begins with the occurrence of cracks and develops by releasing self-repairing factors in the cracks located in concrete. Based on previous comprehensive studies, this paper provides an overview of various repairing factors and investigative methodologies. There has recently been a lack of consensus on the most efficient criteria for assessing self-repairing based on microcapsules and the smart solutions for improving capsule survival ratios during mixing. The most commonly utilized self-repairing efficiency assessment indicators are mechanical resistance and durab
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