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.
A simple, fast, inexpensive and sensitive method has been proposed to screen and optimize experimental factors that effecting the determination of phenylephrine hydrochloride (PHE.HCl) in pure and pharmaceutical formulations. The method is based on the development of brown-colored charge transfer (CT) complex with p-Bromanil (p-Br) in an alkaline medium (pH=9) with 1.07 min after heating at 80 °C. ‘Design of Experiments’ (DOE) employing ‘Central Composite Face Centered Design’ (CCF) and ‘Response Surface Methodology’ (RSM) were applied as an improvement to traditional ‘One Variable at Time’ (OVAT) approach to evaluate the effects of variations in selected factors (volume of 5×10-3 M p-Br, heating time, and temperature) on
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The heritage of the human peoples remains a beacon of data, after renewed awareness of them, open to their propositions, which are born from the womb of intertwined elements of customs, knowledge, arts, and literature ... Misleading the reception process, it may be something intriguing to identify with caution with the text sample selected by the current search procedures prepared according to the adoption of a descriptive therapist in a three-dimensional approach, as well as a comprehensive textual reference for that specific communication dimension within Anthology Andalusian - Moroccan poetry in the book of pleasure in the perception of the five senses Tahdib ibn Manzoor (d. 711 e) from the origin of Tivashi (d. 651 e) Tagged: Separat
... Show MoreThe research aims to show the impact that the information of the supporting bodies can have and its dimensions represented by (information credibility, efficiency and effectiveness of information, cooperation with the tax administration, obligating the taxpayer, accuracy and completeness of information and the appropriate time) in tax inventory, as well as clarifying the moral differences in The response of the surveyed sample according to the personal variables represented by (gender, educational attainment, scientific specialization, job title, years of service), and the descriptive analytical approach was adopted and in light of it, the questionnaire was designed as a main tool in collecting data from the sample of (80)
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The research paper deals with the role of the place making in eco-tourism through a review of international experiences in the eco-tourism industry and its contribution to advancing the reality of tourism there, and attracting the largest number of tourists. The study is divided into five axes: the first is a study of related concepts, and the second is a study of global experiences, which included three countries: (South Bank (Gabriel's Wharf) - London, Rotterdam in the Netherlands, and dealt with each of Happy Streets and Kendrick Mills, and then the Perak River tourist corridor - Malaysia). As for the third axis, it is concerned with analyzing these experiences to reach th
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As the bit rate of fiber optic transmission systems is increased to more than , the system will suffer from an important random phenomena, which is called polarization mode dispersion. This phenomenon contributes effectively to: increasing pulse width, power decreasing, time jittering, and shape distortion. The time jittering means that the pulse center will shift to left or right. So that, time jittering leads to interference between neighboring pulses. On the other hand, increasing bit period will prevent the possibility of sending high rates. In this paper, an accurate mathematical analysis to increase the rates of transmission, which contain all physical random variables that contribute to determine the transmission rates, is presen
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Intrusion detection systems detect attacks inside computers and networks, where the detection of the attacks must be in fast time and high rate. Various methods proposed achieved high detection rate, this was done either by improving the algorithm or hybridizing with another algorithm. However, they are suffering from the time, especially after the improvement of the algorithm and dealing with large traffic data. On the other hand, past researches have been successfully applied to the DNA sequences detection approaches for intrusion detection system; the achieved detection rate results were very low, on other hand, the processing time was fast. Also, feature selection used to reduce the computation and complexity lead to speed up the system
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In this paper, a robust adaptive sliding mode controller is designed for a mobile platform trajectory tracking. The mobile platform is an example of a nonholonomic mechanical system. The presence of holonomic constraints reduces the number of degree of freedom that represents the system model, while the nonholonomic constraints reduce the differentiable degree of freedom. The mathematical model was derived here for the mobile platform, considering the existence of one holonomic and two nonholonomic constraints imposed on system dynamics. The partial feedback linearization method was used to get the input-output relation, where the output is the error functions between the position of a certain point on the platform
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