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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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.
This study has been conducted to examin the effect of sodium propionate at different level of 0.03,0.06,0.10% on the number of bacteria and mold and to extend the storage life of laboratory processed biscuit. The results indicated that the use of 0.10% sodium propionate prolonged the storage peroid until the third month, while the use of 0.20% sodium propionate showed no growth of bacteria up to six month of storage, three types of bacteria has been isolated from processed biscuit, namely, Staphylococcus aureus, Bacillus cereus, Esherichia coli. using 0.10% sodium propionate showed no growth of mold up to three month of storage ,while using of 0.15 % and 0.20% sodium propionate prevent the growth
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This study has been conducted to examin the effect of potassium sorbate at different level of 0.03,0.06,0.10% on the number of bacteria and mold and to extend the storage life of laboratory processed biscuit. The results indicated that the use of 0.03% potassium sorbate prolonged the storage peroid until the third month .three types of bacteria has been isolated from processed biscuit, namely, Staphylococcus aureus, Bacillus cereus, Esherichia coli using 0.06% potassium sorbate showed no growth of bacteria up to six month of storage ,while using of 0.03% and 0.06% potassium sorbate prevent the growth of mold up to three and six months of storage respectively. Both Aspergillus and Penicillium were isolated from the processed biscuit.
الذات والتحصيل الدراسي . وقد استخدمت الباحثة المنهج الوصفي التحليلي، وبلغت عينة الدراسة (500) طالبًا وطالبة، تم اختيارهم بالطريقة الطبقية العشوائية وهي تمثل (15%) من مجتمع الدراسة البالغ (3328) طالباً وطالبة من طلبة المرحلة الإعدادية واستخدمت الباحثة مقياسين تم بناء مقياس لقياس الجوهر والمظهر وتبني مقياس فاعلية الذات بعد إن قامت بترجمته وتعريبه وجعله ملائم للبيئة العراقية، كم تم استخراج درجات التحصيل الدراسي للع
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Background: This in vitro study was carried out to evaluate the effects of various veneering dentin ceramic thicknesses and repeated firings on the color of lithium disilicate glass-ceramic (IPS e.max Press) and zirconium-oxide (IPS ZirCAD) all-ceramic systems, measured by clinical spectrophotometers (Easyshade Advance 4.0) . Materials and methods: The 72specimens cube-shaped have the dimension of about 11 mm in width, 14 mm in length, 1mm in thickness, these cores divided into 3 groups according to the type of material each group have (24)core specimens. Each group had been divided into three sub-groups (each having 8 specimens) according to veneering with dentin ceramic thicknesses: as 0.5, 1, or 2 mm (n=8). IPS e.max press and ZirCAD c
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