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.
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The musical sign was associated with the first appearances of acting that are based on human gestures and expressive and silent movements, and they contributed in accentuating and clarifying these gestures and explain their meanings and indications, and they remained with them until these gestures turned into artistic theatrical shows so that the musical sign would have many functions and constitute the main pillars for this kind of show.
The musical sign is a language not much different than the human language in the semiotic analysis. There has been an increased interest in it and its use in the mime shows by the graduates who realized its necessity and significance in the pantomime show intellectually, artistically and aesthetical
The principal concern of this study is Disjunct and Conjunct adverbials in the
English language. The study sets out to explore and clarify the types, nature and
structure of disjuncts and conjuncts. It also aims at testing student's performance to
evaluate the use and usage of the disjuncts and conjuncts in their written performance.
Two tests, accordingly, were given to some fifty students of at the Dept. of English, at
the college of languages (third and fourth stages) in the University of Sulaimani. The
hypothesis that the study was based on are those students use disjuncts and conjuncts
hardly enough in their writings and when doing so, they generally tend to stick only to
the most commonly used and familiar o
Dental caries (tooth decay) is one of the most prevalent infectious disease and although of multifactorial origin, Streptococcus mutans is considered the principal pathogen in its development (i.e. bacterial processes damage hard tooth structure (enamel, dentine and cementum), producing dental cavities (holes in the teeth). The bactericidal properties of the Nd:YAG laser has been researched analyzing its use in caries prevention and bacterial reduction. One hundred twenty five samples were collected from carious teeth and isolated bacteria were diagnosed using microscopic examination, culture, biochemical tests, and Api 20 strep system. The results of this study showed that a noticeable decrease in the viability of Streptococcus mutans w
... Show MoreThe paper presents the design of a system consisting of a solar panel with Single Input/Multiple Outputs (DC-DC) Buck Converter by using Simulink dialogue box tools in MATLAB software package for simulation the system. Maximum Power Point Tracking (MPPT) technique depending on Perturb and Observe (P&O) algorithm is used to control the output power of the converter and increase the efficiency of the system. The characteristics of the MSX-60 PV module is chosen in design of the system, whereas the electrical characteristics (P-V, I-V and P-I curves) for the module are achieved, that is affected by the solar radiation and temperature variations. The proposed design module has been found to be stable for any change in atmospheric tempera
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Background: Type 2 diabetes mellitus (T2DM) is considered a global disease as it affects over 150 million people worldwide, a number that is supposed to be doubled by 2025. High glucose levels, in vitro, appear to raise the extent of LDL oxidation, and glycated LDL is more prone to oxidative modification.Objective: To investigate the relationship between serum level of vitamin E and lipid profile in patients with type II DM.Methods: This study involved 28 patients suffering from type II DM diagnosed 1-4 years ago and with age ranged from 17 -60 years old, with different residence around Basra ; In addition to 56 apparently healthy persons matched in age and sex to the patients as a control group. The medical histories were taken and Gene
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