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 Russian foreign policy of the post-cold-war era faced dilemmas in the light of the international and regional realities of the disintegration of the Soviet Union and the formation of a new unipolar international order led by the United States of America. Thus, Russian foreign policy-making was divided over the nature of the foreign policy to be followed. The achievement of the Russian goals, especially as the objectives of Russian foreign policy have been set within the framework of trying to regain the status and leading role, as well as the establishment of some fundamental changes to be consistent with the new international situation of the post-one The Russian Federation has adopted in the sphere of its foreign policy to the vari
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The effect of using three different interpolation methods (nearest neighbour, linear and non-linear) on a 3D sinogram to restore the missing data due to using angular difference greater than 1° (considered as optimum 3D sinogram) is presented. Two reconstruction methods are adopted in this study, the back-projection method and Fourier slice theorem method, from the results the second reconstruction proven to be a promising reconstruction with the linear interpolation method when the angular difference is less than 20°.
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Linguistic research according to modern curricula:
It is one of the important matters that occupy the ideas of those concerned with linguistic studies, whether Arabic or otherwise. Recent years have witnessed the advancement of this methodological approach, and books and studies in Arabic have been written on important, multifaceted issues, of grammatical and linguistic origins, and their balance with new developments and ideas attracted mostly from Western studies.
The comparative approach - as they call it - is one of the modern approaches that is based on balancing a language with other sisters belonging to its family, to reach similarities and differences between them, and to know the c
In the spreading of the Internet, mobile smart devices, and interactive websites such as YouTube, the educational video becomes more widespread and deliberative among users. The reasons for its spread are the prevalence of technologies, cheap cost, and easy to use. However, these products often lack to the distinction in video production. By following videos of an educational channel on YouTube, some comments found to discuss the lack of the content presented to motivate the learners, which lead to reduce the viewers of the videos. Therefore, there is an important decision to find general standards for the design and production of educational videos. A list of standards has been drawn up to help those interested in producing educational
... Show MoreIf the sovereignty of the state is reflected in the taxation of its citizens, this sovereignty can not be completed and completed only if it works on its part to collect its debts, whether voluntary or compulsory, and the debt of the debt arises from the will of the individual and the will of the state alone, The existing management of seizure and collection is based on an unequal relationship between the State and the debtor from which the obligation arises. Naturally, this relationship has obligations and rights on both parties. The researcher used a set of studies and previous research, books and other sources related to the subject of research. This was done through the theoretical and practical aspects, which focused on direct and i
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The aim of the research is to shed light on the dimensions of the strategic lens and its impact on achieving the pioneer tax performance and represented by the dimensions (strategic direction, growth, pilot indicator, renewal and modernization, efficiency and effectiveness) in the General Tax Authority. The questionnaire was adopted as a tool to collect data and information from the adult sample They are (91) who are on the site (Assistant Director General, Head of Division, First Division Deputy, Second Division Deputy, Division Officer, Division Officer Associate) The statistical program (SPSS) has been used to calculate (the mean, the standard deviation, the correlation coefficient, the difference coefficient, the F test, the
... Show MoreThe study aimed to reveal the extent of the first intermediate grade science curriculum focus on the national values, health, environmental, economic values, in the light of the education policy in the Kingdom of Saudi Arabia, in addition to present a proposed vision to strengthen it in the science curriculum for the first intermediate grade. The study was applied to the two books student and the two books of activity on the first-second semesters for the academic year 1441 AH. To analyze the curriculum content, the study used a verified card prepared by the researchers and a criterion for interpreting percentages. The study reached the following results: environmental values ranked first with a concentration of (43%), i.e. with an avera
... Show MoreOil industry played a major role in delineating the course and type o development in both imported and exported Arabic countries alike where its revenues has perform an essential role in forming programs and plans of development on both national and international level in addition to anticipation of future consuming.
Iraq, as an oil producer country with a revenues –based economy depends on oil in building its economy totally including its infrastructure having a the greatest conformed reservoir which make the government budget depends largely on oil revenues where its strategic importance lies in funding all aspects of expenders as it is considered the prime source of foreign currency. The chall
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This work was conducted to study the ability of locally prepared Zeolite NaY for the reduction of sulfur compounds from Iraqi natural gas by a continuous mode adsorption unit. Zeolite Y was hydrothermally synthesized using abundant kaolin clay as aluminum precursor. Characterization was made using chemical analysis, XRD and BET surface area. Results of the adsorption experiments showed that zeolite Y is an active adsorbent for removal H2S from natural gas and other gas streams. The effect of temperature was found inversely related to the removal efficiency. Increasing bed height was found to increase the removal efficiency at constant flow rate of natural gas. The adsorption capacity was evaluated and its maximum uptake was 5.345 mg H2S/g z
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