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.
Statistical methods of forecasting have applied with the intention of constructing a model to predict the number of the old aged people in retirement homes in Iraq. They were based on the monthly data of old aged people in Baghdad and the governorates except for the Kurdistan region from 2016 to 2019. Using BoxJenkins methodology, the stationarity of the series was examined. The appropriate model order was determined, the parameters were estimated, the significance was tested, adequacy of the model was checked, and then the best model of prediction was used. The best model for forecasting according to criteria of (Normalized BIC, MAPE, RMSE) is ARIMA (0, 1, 2)
The research study and analysis of the integration of marketing communications and their impact on the marketing performance of a number of telecom companies, as included in the research problem to know the role of marketing communications community in achieving sales and market share, profitability and customer satisfaction. The importance of research begins to be the right choice for the elements of marketing communications, lead to savings in time, effort and money and create a more idea about the effectiveness of the application of the concept of integration. The research to determine the role of marketing communications in promoting the integration of the marketing performance of companies in the field of sales and marke
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The investment portfolio of financial instruments & banking relatively new in the banking sector & the world of investment &capital markets in spite of its importance & its advantages in terms of the nature of the diversity of investment instruments as well as reduce the risk of investment & its contribution to the revitalization of the banks & the financial market , economic, &characterized by developments accelerated under information & communications technology , as is the portfolio tool vehicle of investment tools that provide for people who want to invest & they can not manag
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Statistical methods of forecasting have applied with the intention of constructing a model to predict the number of the old aged people in retirement homes in Iraq. They were based on the monthly data of old aged people in Baghdad and the governorates except for the Kurdistan region from 2016 to 2019. Using Box-Jenkins methodology, the stationarity of the series was examined. The appropriate model order was determined, the parameters were estimated, the significance was tested, adequacy of the model was checked, and then the best model of prediction was used. The best model for forecasting according to criteria of (Normalized BIC, MAPE, RMSE) is ARIMA (0, 1, 2).
Improved oral bioavailability of lipophilic substances can be achieved using self-emulsifying drug delivery systems. However, because the properties of self-emulsifying are greatly influenced by surfactant amount and type, type of oil used, droplet size, charge, cosolvents, and physiological variables, the synthesis of self-emulsifying is highly complex; consequently, only a small number of excipient self-emulsifying formulations has been developed so far for clinical use. This study reports a highly effective procedure for developing self-emulsifying formulations using a novel approach based on the hydrophilic-lipophilic difference theory. Microemulsion characteristics, such as the constituents and amounts of oil and surfactant electrolyte
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A simple setup of random number generator is proposed. The random number generation is based on the shot-noise fluctuations in a p-i-n photodiode. These fluctuations that are defined as shot noise are based on a stationary random process whose statistical properties reflect Poisson statistics associated with photon streams. It has its origin in the quantum nature of light and it is related to vacuum fluctuations. Two photodiodes were used and their shot noise fluctuations were subtracted. The difference was applied to a comparator to obtain the random sequence.
Abstract The purpose of this study, teach the art of performing Olympic lifts (snatch and, clean and jerk) using the two methods are instructional (self-learning associated with the model) and (reverse style of partial way). Identify the effectiveness of these methods in learning the art of performance and style of the best Olympic lifting in the learning and retention of novice for Olympic lifts. The research sample consisted of 16 lifters were selected purposively representing specialist center for the care of athletic talent to weightlifting for ages 14 years. The sample was divided into two experimental, Each group (8) eight weightlifters. The experimental group used the style of the first self-learning associated with the m
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Basic orientation is to look at identifying conceptual perspective to market self-research and descriptive, as has the marketing theme for the same attention in the practical side before endo scopic In recent years, is marketing an integrated and holistic included many areas not limited to the marketing of goods and services, and even included the marketing of religion, politics and individuals for themselves, as the awareness and concepts that seep into the soul of man from its inception until his arrival to the stage of owning a level of skills or expertise, scientific or all of those things degrees mixed with ambition and aspiration for self-realization takes way to search for opportunities or created, often observe individual
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