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 current research aimed to identify the cognitive-behavioral therapy on people with depression, through the following hypothesis (there are no statistically significant differences in the sample before and after cognitive-behavioral therapy). The importance of research is highlighted through the use of cognitive-behavioral therapy, to be used in treating depression, anxiety and fears by health institutions. It is also considered as a reference for psychological studies related to this topic to be added to our libraries that already suffer from a scarcity of this type of resources. The cognitive-behavioral therapy was used in the treatment of five male subjects.
The study revealed the existence of statistically significant diff
... Show MoreMedia and communication's research are varied in accordance to research approaches' variety which seeks to reach convergent social, psychological, political, economic, and technical point of views. Its main aim is to assimilate all the new variables in the communicative method, especially, social media sites research; concerning their methodology, tools and theories. It is due to their diverse - developed applications and their increased rates of public use becoming irreplaceable in our daily life. It is well reflected by their consequent impact on the the public beside their role in changing its views.
This clarifies the notable increase of scientific research that concern them manifesting the dialectical relations and interfere
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The current research aims to identify the achievement of goals and the significance of the differences in achieving goals according to the variable of gender (male-female), specialization (scientific-human), and the stage (Master-PhD) for postgraduate students. To achieve the goals of the current research, the researcher developed a scale of achieving goals that was built according to the theory of (Lock & Latham 1990), which was applied to a sample of (257) male and female students who were selected randomly with a proportional distribution for the academic year (2021-2022). The scale of achieving goals consists of (30) items. The current research found that the research sample of postgraduate students has achieved their goals in ge
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Permeability estimation is a vital step in reservoir engineering due to its effect on reservoir's characterization, planning for perforations, and economic efficiency of the reservoirs. The core and well-logging data are the main sources of permeability measuring and calculating respectively. There are multiple methods to predict permeability such as classic, empirical, and geostatistical methods. In this research, two statistical approaches have been applied and compared for permeability prediction: Multiple Linear Regression and Random Forest, given the (M) reservoir interval in the (BH) Oil Field in the northern part of Iraq. The dataset was separated into two subsets: Training and Testing in order to cross-validate the accuracy
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أن لعبة كرة السلة في تقدم وتطور مستمر حالها في ذلك حال الألعاب الرياضية الأخرى حيث أن الفضل في ذلك يعود إلى المعرفة بالعلوم المختلفة وكذلك البحث العلمي من اجل تحقيق نتائج متقدمة تنشدها معظم الدول ومنها العراق على الصعيد المحلي والعربي والدولي. ومما لاشك فيه أن متطلبات تطور مستوى نتائج القدرات البدنية في أيُة لعبة مرتبطة بالبرمجة والتخطيط الصحيح للمناهج التدريبية إذ تقودنا هذه الحقيقة إلى إجراء المزيد من الا
... Show Moreلا يزال المهتمون بلعبة كرة السلة يبحثون عن إيجاد الوسائل الأكثر أهمية وصولاً إلى ما تطمح إليه الدول لتحقيق افضل المستويات في نواحي اللعبة كافة من خلال التغلب على المعوقات التي تحول دون تقدمها إلى الأمام بالدراسة والبحث. ومن هذا المنطلق انصب البحث في ضرورة معالجة القصور الناتج عن عدم وجود المعايير ذات العلاقة باختبارات قدرات اللاعبين وعلى وفق مراكز اللعب ولا سيما المهارية الهجومية مما شكل ذلك ضعفاً في أعداد و
... Show MoreThis research aims at calculating the optimum cutting condition for various types of machining methods, assisted by computers, (the computer program in this research is designed to solve linear programs; the program is written in v. basic language). The program obtains the results automatically, this occur through entering the preliminary information about the work piece and the operating condition, the program makes the calculation actually by solving a group of experimental relations, depending on the type of machining method (turning, milling, drilling). The program was transferred to package and group of windows to facilitate the use; it will automatically print the initial input and optimal solution, and thus reduce the effort and t
... Show MoreProject deal with the study of the suitability of the planning standards of the select sites for sports facilities for the holy city of Karbala and the extent of convergence and divergence between these standards and points of strength and weakness in each of these standards.
It was found that there was a lack of the role given to the sports as a kind of luxury does not deserve to spend money and efforts, and was then incorporated with a lot of entertainment services by planners.
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