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.
Video streaming is widely available nowadays. Moreover, since the pandemic hit all across the globe, many people stayed home and used streaming services for news, education, and entertainment. However, when streaming in session, user Quality of Experience (QoE) is unsatisfied with the video content selection while streaming on smartphone devices. Users are often irritated by unpredictable video quality format displays on their smartphone devices. In this paper, we proposed a framework video selection scheme that targets to increase QoE user satisfaction. We used a video content selection algorithm to map the video selection that satisfies the user the most regarding streaming quality. Video Content Selection (VCS) are classified in
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Learn new methods of teaching mathematics contribute to raising the level of pupils to acquire mathematical concepts primary stage
Attempt advancement in the level of mathematics teaching for the better through the use of modern teaching strategies. The research aims at the progress in the acquisition of mathematical concepts schoolgirls after subjecting the fourth grade to teach in active learning strategies, the number of research sample (60) schoolgirl, by (30) schoolgirl experimental group and 30 pupils of the control group. Clear from the results shown the presence of a statistically significant difference between the acquisition of concepts of schoolgirls two groups (experimental and control) for the benefit of pupils of the exp
The control of prostheses and their complexities is one of the greatest challenges limiting wide amputees’ use of upper limb prostheses. The main challenges include the difficulty of extracting signals for controlling the prostheses, limited number of degrees of freedom (DoF), and cost-prohibitive for complex controlling systems. In this study, a real-time hybrid control system, based on electromyography (EMG) and voice commands (VC) is designed to render the prosthesis more dexterous with the ability to accomplish amputee’s daily activities proficiently. The voice and EMG systems were combined in three proposed hybrid strategies, each strategy had different number of movements depending on the combination protocol between voic
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In this work, an explicit formula for a class of Bi-Bazilevic univalent functions involving differential operator is given, as well as the determination of upper bounds for the general Taylor-Maclaurin coefficient of a functions belong to this class, are established Faber polynomials are used as a coordinated system to study the geometry of the manifold of coefficients for these functions. Also determining bounds for the first two coefficients of such functions.
In certain cases, our initial estimates improve some of the coefficient bounds and link them to earlier thoughtful results that are published earlier.
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A field experiment was carried out at University of Baghdad, College of Agricultural Engineering Sciences during fall season of 2020 and spring season of 2021. This study was aimed evaluate the effect of the organic fertilizer and boron foliar on the yield of potatoes for processing. The factorial experiment (5*4) within RCBD and three replicates. The organic fertilizer as palm peat at four levels (0, 12, 24 and 36 ton. ha-1) in addition to the chemical fertilizer recommendation treatment. Boron at four Concentrations 0, 100, 150 and 200 mg. L-1 . The results revealed significant different among application of organic fertilizer at the level of 24 ton. ha-1 and the foliar application of boron at a concentration of 100 mg. L-1 in the
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Diyala river is the most important tributaries in Iraq, this river suffering from pollution, therefore, this research aimed to predict organic pollutants that represented by biological oxygen demand BOD, and inorganic pollutants that represented by total dissolved solids TDS for Diyala river in Iraq, the data used in this research were collected for the period from 2011-2016 for the last station in the river known as D17, before the river meeting Tigris river in Baghdad city. Analysis Neural Network ANN was used in order to find the mathematical models, the parameters used to predict BOD were seven parameters EC, Alk, Cl, K, TH, NO3, DO, after removing the less importance parameters. While the parameters that used to predict TDS were fourte
... Show MoreThe purpose of this paper is to model and forecast the white oil during the period (2012-2019) using volatility GARCH-class. After showing that squared returns of white oil have a significant long memory in the volatility, the return series based on fractional GARCH models are estimated and forecasted for the mean and volatility by quasi maximum likelihood QML as a traditional method. While the competition includes machine learning approaches using Support Vector Regression (SVR). Results showed that the best appropriate model among many other models to forecast the volatility, depending on the lowest value of Akaike information criterion and Schwartz information criterion, also the parameters must be significant. In addition, the residuals
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The rapid change in economic is a serious challenge facing all countries around the world, even developed ones. This challenge is increasing as the world enters the age of knowledge in which different knowledge and technologies have emerged and the distance between the emergence of scientific knowledge and its actual application on the ground has been reduced as well as the growing role of science and technology in community development. One of the most important technology amongst these technologies is nanotechnology, where this technology plays a major role in the development of products and modern devices and reduces cost with quality improvement. This technology is cross-cultural, requires a comprehensive knowledge structure and depe
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