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.
Producing pseudo-random numbers (PRN) with high performance is one of the important issues that attract many researchers today. This paper suggests pseudo-random number generator models that integrate Hopfield Neural Network (HNN) with fuzzy logic system to improve the randomness of the Hopfield Pseudo-random generator. The fuzzy logic system has been introduced to control the update of HNN parameters. The proposed model is compared with three state-ofthe-art baselines the results analysis using National Institute of Standards and Technology (NIST) statistical test and ENT test shows that the projected model is statistically significant in comparison to the baselines and this demonstrates the competency of neuro-fuzzy based model to produce
... Show MoreThis research aims at answering many questions raised by the research problem concerning the view of the organizations under consideration for the concept of smart leadership and its most important dimensions, as well as the view of crisis management and its concept and most important methods through research objectives that define and clarify the smart leadership with its dimensions and methods of crisis management.
For the purpose of reaching the results of the research and testing the assumptions about the relationship between smart leadership and methods of crisis management, the researcher adopted a questionnaire, designed especially to be a criterion for the research, as the main tool for data coll
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The effect of smoking, age and exposure duration in pesticide risk groups were studied > Groups were all men and included farmers (25), pesticide sellers (25), pesticides manufacture workers (Al-Tark factory for agricultural pesticide production) (25), Control group (25) were from Baghdad university staff (living in Baghdad city) > The cytogenetic parameters studied were Chromosomal aberrations (CA), induction of micronuclei (Mn)formation .Results revealed that smoking synergized pesticides exposure in induction of structural CAs in all groups with significant differences (P<0.01) and the worst effect recorded in workers , the increment was more than folds the level of control group (0.68) for the non smokers and was 5.78 times (control gr
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Nonlinear time series analysis is one of the most complex problems ; especially the nonlinear autoregressive with exogenous variable (NARX) .Then ; the problem of model identification and the correct orders determination considered the most important problem in the analysis of time series . In this paper , we proposed splines estimation method for model identification , then we used three criterions for the correct orders determination. Where ; proposed method used to estimate the additive splines for model identification , And the rank determination depends on the additive property to avoid the problem of curse dimensionally . The proposed method is one of the nonparametric methods , and the simulation results give a
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The ABO blood group system is highly polymorphic, with more than 20 distinct sub-groups; study findings are usually related to ABO phenotype, but rarely to the ABO genotype and animal models are unsatisfactory because their antigen glycosylation structure is different from humans. Both the ABO and Rh blood group systems have been associated with a number of diseases, but this is more likely related to the presence or absence of these tissue antigens throughout the body and not directly or primarily related to their presence on RBCs. A total of fifty-two 52 patients without complication of DMII, two hundred sixteen 216 patients with complication of DMII and seventy-one 71 person as healthy control were included in the study. The resu
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Writing as a female playwright in theatre gives a deeper depiction of woman’s real- self. Beth Henley has succeeded in providing a new realist vision of women’s abilities to face their inevitable tragic fates and how to conquer their despair. In Crimes of the Heart, the playwright uses certain method to present the development of the heroines’ characters through blending the tragic events with a comic frame. In fact, Henley focuses on the simple humorous activities more that the importance of the tragic event to present her vision of how to survive and face the crisis of life.
Crimes of the Heart is a play that is concerned about three sisters whose lives are headed in distinctly different directions; howe
... Show MoreWorld statistics proved that the most of work dangerous accidents, which causes death, are occurred in the construction works. These accidents related to many causes such as loss of workers experience and ignoring rules of safety requirements, especially young workers. Due to the risk of accidents that may occur in the site of work, the idea of this study crystallized to show the relationship between the age of worker and number of injuries and accidents, to identify the causes of these injuries, and to put the appropriate solutions to avoid or reduce the risk of work injuries. Also, the research shows the main principles of safety requirements to forming a clear picture about the subject of the study. A questioner form was prepared to c
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This research aims to introduce a new technique-off-site and self-form segmental concrete masonry arches fabrication, without the need of construction formwork or centering. The innovative construction method in the current study encompasses two construction materials forms the self-form masonry arches, wedge-shape plain concrete voussoirs, and carbon fiber-reinforced polymer (CFRP) composites. The employment of CFRP fabrics was for two main reasons: bonding the voussoirs and forming the masonry arches. In addition, CFRP proved to be efficient for strengthening the extrados of the arch rings under service loadings. An experimental test was conducted on four sophisticated masonry arch specimens. The research parameters were the Keystone thic
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The experiment was conducted at the period from 20th Dec. 2015 to 30th Mar. 2016 to know the effect of growth medium and nodes number on the acclimatization success of tissue propagated potatoes seedlings (Burrin class) and study some plant physiological properties. The first experiment involved testing growth media: loam, peat moss, and perlite with different portions (1:1) to plant tissue propagated potato tubers, while the second experiment involved testing the nodes number where 9, 8, 7, 6, and 5 plant nodes were chosen. Results of the first experiment showed the superiority of the culture media of peat moss + perlite to other culture media by giving the higher values of shoot system studied properties: plant height, branches number, le
... Show MoreSelf- curing is the potential of lightweight aggregate to absorption great amount of water thru mixing which prominently can moves to the paste during hydration process. Self- curing empowers a water to be distributes more evenly act out the cross section. Whereas, the external curing water is only able to penetrate several millimetres into concrete with low water cement ratio. Brick dust accumulates in the demolish site creates serious environmental contamination. This study investigates the effect of brick dust recovered from construction site on the Properties of mortar cured in three curing conditions. Mortar in this study produced using BD as cement additive with (2, 4, 6, and 8) % by weight of cement. BD was used a
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