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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Water has a great self-generating capacity that can neutralize the polluting interventions carried out by humans. However, if human activities continue this uncontrolled and unsustainable exploitation of this resource, this regenerating capacity shall fail and it will be jeopardized definitively. Shatt Al-Arab River in South of Iraq. It has an active role in providing water for irrigation, industry, domestic use and a commercial gateway to Iraq. in the last five years Shatt Al-Arab suffered from a rise in pollutants due to the severe decline in sewage networks, irregular networks and pesticide products, as well as the outputs of factories and companies that find their way to water sources and lead to a widespread collapse of water quality.
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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
... Show MoreThe aim of our work is to develop a new type of games which are related to (D, WD, LD) compactness of topological groups. We used an infinite game that corresponds to our work. Also, we used an alternating game in which the response of the second player depends on the choice of the first one. Many results of winning and losing strategies have been studied, consistent with the nature of the topological groups. As well as, we presented some topological groups, which fail to have winning strategies and we give some illustrated examples. Finally, the effect of functions on the aforementioned compactness strategies was studied.
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In the beta decay process, a neutron converts into a proton, or vice versa, so the atom in this process changes to a more stable isobar. Bethe-Weizsäcker used a quasi-experimental formula in the present study to find the most stable isobar for isobaric groups of mass nuclides (A=165-175). In a group of isobars, there are two methods of calculating the most stable isobar. The most stable isobar represents the lowest parabola value by calculating the binding energy value (B.E) for each nuclide in this family, and then drawing these binding energy values as a function of the atomic number (Z) in order to obtain the mass parabolas, the second method is by calculating the atomic number value of the most stable isobar (ZA). The results show
... Show MoreIntroduction to Medical and Biological Statistics for Pharmacy Students and Medical Groups (Undergraduate & Postgraduate) - ISBNiraq.org
Hepatitis B is an inflammation of the liver that caused by Hepatitis B virus (HBV) which is DNA virus that infects the human and some kinds of animals such as chimpanzees and birds. This disease considered as the major disease of mankind and a serious global public health problem. HBsAg, HBeAg, HBcAb, HBeAb and HBsAb are markers used to detect the presence and the stage of infection. The current study included (181) individuals from both sexes, (137) males and (44) females. By ratio 3.11: 1.The mean age of patients 2.4033 ± 0.83519 (range 18-73) years as follows < 20 (11.6%), 21–40 (47.5%), 41–60 (29.8%) and > 60 (11.0%) . These patients are 73 (40.4%) Blood donors from Central Blood Bank, 88 (48.6%) Chronic kidney failure at Ibn –
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In this paper, a self-tuning adaptive neural controller strategy for unknown nonlinear system is presented. The system considered is described by an unknown NARMA-L2 model and a feedforward neural network is used to learn the model with two stages. The first stage is learned off-line with two configuration serial-parallel model & parallel model to ensure that model output is equal to actual output of the system & to find the jacobain of the system. Which appears to be of critical importance parameter as it is used for the feedback controller and the second stage is learned on-line to modify the weights of the model in order to control the variable parameters that will occur to the system. A back propagation neural network is appl
... Show MoreIn this paper, a simulation model and practical testbed for green Internet of Things (IoT) edge devices are proposed based on solar harvester with constant voltage-maximum power point tracking (CV-MPPT) technique. Billions of connected edge devices represent the essential part of the IoT through the IP-enabled sensor networks based on IPv6 over Low power Wireless Personal Area Network (6LoWPAN). In traditional IoT edge devices, the stored energy in the non-rechargeable battery determines the node lifetime while it is being depleted with time. Therefore, purchasing billions of such batteries is costly and must be disposed of efficiently. This paper is aimed at simulating and implementing a new class of green IoT edge devices that can report
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Imam al - Karji replies to some Islamic groups
In his book the jokes of the Koran