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.
Water saturation is the most significant characteristic for reservoir characterization in order to assess oil reserves; this paper reviewed the concepts and applications of both classic and new approaches to determine water saturation. so, this work guides the reader to realize and distinguish between various strategies to obtain an appropriate water saturation value from electrical logging in both resistivity and dielectric has been studied, and the most well-known models in clean and shaly formation have been demonstrated. The Nuclear Magnetic Resonance in conventional and nonconventional reservoirs has been reviewed and understood as the major feature of this approach to estimate Water Saturation based on T2 distribution. Artific
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Ondansetron HCl (OND) is a potent antiemetic drug used for control of nausea and vomiting associated with cancer chemotherapy. It exhibits only 60 – 70 % of oral bioavailability due to first pass metabolism and has a relative short half-life of 3-5 hours. Poor bioavailability not only leads to the frequent dosing but also shows very poor patient adherence. Hence, in the present study an approach has been made to develop OND nanoparticles using eudragit® RS100 and eudragit® RL100 polymer to control release of OND for transdermal delivery and to improve patient compliance.
Six formulas of OND nanoparticles were prepared using nanoprecipitation technique. The particles sizes and zeta potential were measured
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The research focuses on determination of best location of high elevated tank using the required head of pump as a measure for this purpose. Five types of network were used to find the effect of the variation in the discharge and the node elevation on the best location. The most weakness point was determined for each network. Preliminary tank locations were chosen for test along the primary pipe with same interval distance. For each location, the water elevation in tank and pump head was calculated at each hour depending on the pump head that required to achieve the minimum pressure at the most weakness point. Then, the sum of pump heads through the day was determined. The results proved that there is a most economical lo
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In this paper, an Integral Backstepping Controller (IBC) is designed and optimized for full control, of rotational and translational dynamics, of an unmanned Quadcopter (QC). Before designing the controller, a mathematical model for the QC is developed in a form appropriate for the IBC design. Due to the underactuated property of the QC, it is possible to control the QC Cartesian positions (X, Y, and Z) and the yaw angle through ordering the desired values for them. As for the pitch and roll angles, they are generated by the position controllers. Backstepping Controller (BC) is a practical nonlinear control scheme based on Lyapunov design approach, which can, therefore, guarantee the convergence of the position tracking
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Epithelial mesenchymal transition (EMT) is a process comprising cellular and molecular events which result in cells shifting from an epithelial to a mesenchymal phenotype. Periodontitis is a destructive chronic disease of the periodontium initiated in response to a dysbiotic microbiome, and dominated by Gram-negative bacteria in the subgingival niches accompanied by an aberrant immune response in susceptible subjects. Both EMT and periodontitis share common risk factors and drivers, including Gram-negative bacteria, excess inflammatory cytokine production, smoking, oxidative stress and diabetes mellitus. In addition, periodontitis is characterized by down-regulation of key epithelial markers such as E-cadherin together with up-regulation of
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This research work aims to the determination of molybdenum (VI) ion via the formation of peroxy molybdenum compounds which has red-brown colour with absorbance wave length at 455nm for the system of ammonia solution-hydrogen peroxide-molybdenum (VI) using a completely newly developed microphotometer based on the ON-Line measurement. Variation of responses expressed in millivolt. A correlation coefficient of 0.9925 for the range of 2.5-150 ?g.ml-1 with percentage linearity of 98.50%. A detection limit of 0.25 ?g.ml-1 was obtained. All physical and chemical variable were optimized interferences of cation and anion were studied classical method of measurement were done and compared well with newly on-line measurements. Application for the use
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In this work we prepared some schiff bases by condensation urea and benzaldehyde or its derevative ( bromo benzaldehyde or hydroxy benzaldehyde ) as ( 1 : 1 ) mole ( urea : benzaldehyde or its substitution ) to prepare compounds ( A1 , B1 , C1 , D1 , E1 , F1 , G1 ) and ( 1 : 2 ) mole ( urea : benzaldehyde or its substitution ) to prepare compounds ( A2 , B2 , C2 , D2 , E1 , F2 , G2 ) . The prepared compounds identified spectroscopic by infrared spectroscopy FT-IR and Thin layer chromotography T.L.C . The force constant calculated from the wave number for the carbonyl stretching from FT-IR chart and by using the following equation K = 4?2C2?'2? The change in double bond order for carbonyl deteremined in according with some past re
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