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.
Objectives: to evaluate patient knowledge with hemodialysis and to determine the effectiveness of Self-regulation Fluid Program on Patients with hemodialysis self-efficacy for fluid adherence in Al-Diwaniyah Teaching Hospital.
Methodology: A quasi-experimental design (two group design: pre-test and post-test) was used. This study was conducted in Al-Diwaniya Teaching Hospital for the period from (15th of October 2018 to 20th of May 2019) on a non-probability (purposive) sample consisting of (60 patients) treatment in hemodialysis units. A questionnaire was built as a data collection tool and consisted of four parts:
First part: Demographic characteristics of the pati
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The study of cohomology groups is one of the most intensive and exciting researches that arises from algebraic topology. Particularly, the dimension of cohomology groups is a highly useful invariant which plays a rigorous role in the geometric classification of associative algebras. This work focuses on the applications of low dimensional cohomology groups. In this regards, the cohomology groups of degree zero and degree one of nilpotent associative algebras in dimension four are described in matrix form.
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Solubility problem of many of effective pharmaceutical molecules are still one of the major obstacle in theformulation of such molecules. Candesartan cilexetil (CC) is angiotensin II receptor antagonist with very low water solubility and this result in low and variable bioavailability. Self- emulsifying drug delivery system (SEDDS) showed promising result in overcoming solubility problem of many drug molecules. CC was prepared as SEDDS by using novel combination of two surfactants (tween 80 and cremophore EL) and tetraglycol as cosurfactant, in addition to the use of triacetin as oil. Different tests were performed in order to confirm the stability of the final product which includes thermodynamic study, determination of self-emulsificat
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Key-frame selection plays an important role in facial expression recognition systems. It helps in selecting the most representative frames that capture the different poses of the face. The effect of the number of selected keyframes has been studied in this paper to find its impact on the final accuracy of the emotion recognition system. Dynamic and static information is employed to select the most effective key-frames of the facial video with a short response time. Firstly, the absolute difference between the successive frames is used to reduce the number of frames and select the candidate ones which then contribute to the clustering process. The static-based information of the reduced sets of frames is then given to the fuzzy C-Means algor
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Methods: 112 placentae samples were investigated during the period from August 2007 to August 2008 under light microscopefor mother aged 15 - 45 years old.Results: It was found that normal placental shapes had no correlation to mother age, while abnormal shapes were found more inyoung age groups. The better placental measured parameters were found in mother age 20-24 years. The percentages ofabnormal umbilical cord insertion were very high compared to other studies. Babies’ gender had a correlation with theplacental thickness; male babies have thicker placentae than females. Male babies have longer umbilical cords with widerdiameter than females. Light microscope picture showed the chorionic villi with isolated fetal blood vessel were hig
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