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.
Vocational education is the basis of contemporary educational movement that aims at satisfying human needs. Societies can develop their human resources via setting programs for the working class as an aspect of the comprehensive national development. Vocational education is the main source of technical cadres the Iraqi labor market requires of the vocational preparatory schools to provide after three years of schooling.
The vocational schools of the governorate of Basra have a number of problems that lead to the lack of proficiency of their graduates. This study is an attempt to identify these problems or obstacles
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يعد الاقتصاد الياباني احد اكبر الاقتصادات الرأسمالية المتقدمة ويحتل المرتبة الثالثة بعد الاقتصاد الأمريكي واقتصاد الاتحاد الاوربي من حيث حجم الناتج المحلي الإجمالي والذي يكاد يقترب من (5) تريليون دولار سنويا.
لقد ادت التطورات المتلاحقة التي شهدها الاقتصاد العالمي وخاصة في حقل التمويل الدولي خلال العشرين سنة الاخيرة الى تصاعد وارتفاع في حجم وحركه رؤوس الاموال الدولية على اوسع نطاق بحيث ا
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Objective: To identify the effect of the cube model on visual-spatial intelligence and learning the skill of spikinging in volleyball for female students, The researchers used the experimental method by designing two equivalent groups with pre- and post-measurements. Research methodology: The main research sample of (30) female students was selected from the research community represented by second-stage students in the College of Physical Education and Sports Sciences - University of Baghdad for the academic year (2024-2025). The sample was divided equally into two control and experimental groups. The researchers conducted the sample homogenization process and the equivalence process between the two groups in the variables of visua
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This study examines the relationship between the increase in the number of tourists coming to Tunisia and GDP during the period 1995-2017, using the methodology of joint integration, causal testing and error correction model. The research found the time series instability of the logarithm of the number of tourists coming to Tunisia and the output logarithm but after applying the first differences, these chains become stable, THUS these time series are integrated in the first differences. Using the Johansson method, we found the possibility of a simultaneous integration relationship between the logarithm of the number of tourists coming to Tunisia and the logarithm of GDP in Tunisia, and there is a causal relationship in one direc
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The method of analysis is one of the tools the coach to identify strengths andweaknesses of each player, and how to avoid mistakes that in the course ofperformance on the other hand, Voslob analysis is important for the player, as throughthe analysis will determine the capacity enjoyed by both the coach and player, as wellas being the possibility of progress in a scientific manner thoughtful, and also helps inthe evaluation of physical and skill level and tactical, psychological and trainingcapacity of the coach in order to avoid obstacles and make the coach is movingtowards the right track to improve the good level, and then an investigation tocomplete higher education.Hence the importance of research in the analysis of simple attack and n
... Show MoreIl semble que Khattabi était un linguiste, avec un endroit linguistique pour comprendre les textes de conversations et des mots étranges en particulier. Langue, et chacun avait ses arguments et ses preuves. Ses corrections incluaient la mélodie dans les mouvements, telle qu'une dilution plus serrée, la dilution de l'agitateur, le remplacement d'un autre mouvement, ou une autre rotation des mouvements, et le changement de structure morphologique du mot qui en résultait, ainsi que l'alerte sur les conséquences des lettres, Certaines de ces erreurs sont dues à la langue, et certaines sont considérées comme un type de déformation ou de fausse représentation connue de certains spécialistes, ce qui constitue un précédent louable
... Show MoreThe research aims to clarify the response of the GDP to the M1 shock. It includes access to the results using standard methods, where the standard model was built according to quarterly data using the program STATA 17. According to the joint integration model ARDL, the research found a long-term equilibrium positive for the relationship between GDP and the money supply in Iraq, as the change in the money supply by a certain percentage will lead to a change in GDP by about 71% of that percentage. In the event of a shock in the Iraqi economy, the impact of the M1 will differ from what it was before the shock, as the shock will increase its effectiveness towards GDP by about 10% more than before the shock. At the same time, the relationship
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(1)
Verbs are an important material in the construction of the sentence, as they are among the requirements of every sophisticated language, and in this regard, Ibn Al-Gothic (d. 367 AH): “Know that verbs are the origins of the buildings of most speech, and thus scholars called them buildings.” Verbs are the source of expression of the speakers’ ideas to represent the element of activity and movement, and with their knowledge We infer the meanings of Arabic words, and Ibn Al-Sarraj (d. 316 AH) defined it: “The verb denotes a meaning and a time, and that time is either past, present, or future.” Its letters are original and does not drop from its construction a letter in the conjugation of its conjugations, and it is in Arabic two type
... Show MoreVolcaniclastic rocks of Al Muqdadiya Formation (Pliocene) in Injana area, southern Hemrin anticline, NE of Iraq, were studied ( petrographically, physically, mineralogically and geochemically , as well as the engineering properties) to assess the suitability of volcaniclastic rocks to use them in industry as refractories. The results show that the physical and engineering properties change with the temperature change. The bulk density and the specific gravity increase by increasing temperature while the apparent porosity, water sorption and the linear shrinkage decrease. On the other hand the compressive strength increase by increasing temperature. The volcaniclastics have very low thermal conductivi
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