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.
The increase globally fossil fuel consumption as it represents the main source of energy around the world, and the sources of heavy oil more than light, different techniques were used to reduce the viscosity and increase mobility of heavy crude oil. this study focusing on the experimental tests and modeling with Back Feed Forward Artificial Neural Network (BFF-ANN) of the dilution technique to reduce a heavy oil viscosity that was collected from the south- Iraq oil fields using organic solvents, organic diluents with different weight percentage (5, 10 and 20 wt.% ) of (n-heptane, toluene, and a mixture of different ratio
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Prodigiosin is a ‘natural red pigment produced by Serratia marcescens which exhibits immunosuppressive and anticancer properties in addition to antimicrobial activities. This work presents an attempt to maximize the production of prodigiosin by two different strategies: one factor at time (OFAT) and statistical optimization. The result of OFAT revealed that sucrose and peptone were the best carbon and nitrogen sources for pigment production with concentration of prodigiosin of about 135 mg/ L. This value was increased to 331.6mg/ L with an optimized ratio of C/N (60:40) and reached 356.8 with pH 6 and 2% inoculum size at end of classical optimization. Statistical experimental design based on Response surface methodology was co
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G-system composed of three isolates G3 ( Bacillus),G12 ( Arthrobacter )and G27 ( Brevibacterium) was used to detect the mutagenicity of the anticancer drug, cyclophosphamide (CP) under conditions similar to that used for standard mutagen, Nitrosoguanidine (NTG). The CP effected the survival fraction of isolates after treatment for 15 mins using gradual increasing concentrations, but at less extent comparing to NTG. The mutagenic effect of CP was at higher level than that of NTG when using streptomycin as a genetic marker, but the situation was reversed when using rifampicin resistant as a report marker. The latter effect appeared upon recording the mutagen efficiency (ie., number of induced mutants/microgram of mutagen). Measuring the R
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Abstract
This research aims to study the reflection of accounting for contingent assets and liabilities and provisions on Faithful Representation characteristic of accounting information, To achieve this goal has been questionnaire design has been distributed to research sample, which consists of (50) li
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The objective of this work is to study the influence of end milling cutting process parameters, tool material and geometry on multi-response outputs for 4032 Al-alloy. This can be done by proposing an approach that combines Taguchi method with grey relational analysis. Three cutting parameters have been selected (spindle speed, feed rate and cut depth) with three levels for each parameter. Three tools with different materials and geometry have been also used to design the experimental tests and runs based on matrix L9. The end milling process with several output characteristics is solved using a grey relational analysis. The results of analysis of variance (ANOVA) showed that the major influencing parameters on multi-objective response w
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The question of estimation took a great interest in some engineering, statistical applications, various applied, human sciences, the methods provided by it helped to identify and accurately the many random processes.
In this paper, methods were used through which the reliability function, risk function, and estimation of the distribution parameters were used, and the methods are (Moment Method, Maximum Likelihood Method), where an experimental study was conducted using a simulation method for the purpose of comparing the methods to show which of these methods are competent in practical application This is based on the observations generated from the Rayleigh logarithmic distribution (RL) with sample sizes
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Nanoceria have shown numerous unique characteristics, such as biocompatibility and are excellent agents for biological applications. The aim of this study is to investigate cerium oxide nanoparticles for 2, 2- diphenyl-1-picryl-hydrazyl-hydrate (DPPH) free radical scavenging activity and their ability to offer protection against ionizing radiation. In vitro antioxidant activity study of nanoceria particles has shown good free radical scavenging activity for DPPH radical assayed within a concentration range of 0.01 to 0.05 g/l, at higher concentrations of nanoparticles showed reverse trend in absorbance and inhibition indicating this finite rang of concentration is suitable for scavenging free radicals, also nanoparticles were found to ha
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Abstract This study investigated the treatment of textile wastewater contaminated with Acid Black 210 dye (AB210) using zinc oxide nanoparticles (ZnO NPs) through adsorption and photocatalytic techniques. ZnO NPs were synthesized using a green synthesis process involving eucalyptus leaves as reducing and capping agents. The synthesized ZnO NPs were characterized using UV-Vis spectroscopy, SEM, EDAX, XRD, BET, Zeta potential, and FTIR techniques. The BET analysis revealed a specific surface area and total pore volume of 26.318 m2/g. SEM images confirmed the crystalline and spherical nature of the particles, with a particle size of 73.4 nm. A photoreactor was designed to facilitate the photo-degradation process. The study investigated the inf
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