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 object of this research is to determine the effect in the differences of the correlation pattern of the micro blogging on the educational attainment of computer science curriculum for 12th grade students. I will try to test the best suited correlation and I might use the demo curriculum as well to achieve its objectives , The research method that will be used in this research is the quantitative method where we will use a sample of 60 students divided into two groups ( correlate the micro blogging - adopted the sequence pattern of relating the micro blogging) As a result, we found out that there are quantitative differences among the two groups' median , The differences goes back to the main effect of the correlation pattern of the m
... Show MoreDocumentary Credit passes through many practical phases starting from Opening credit and matching documents and payment of the amount of credit……etc. It is worthy to mention that there are several aspects that are varied and differed from Bank to another one which can offer Competitive Advantage for the bank …This will be shown in this research.
For the purpose of achieving the objective of this research within the theoretical aspect, the researcher had seen and briefed several books and researches which are mainly related to the subject of the research.
As for the practical aspect, has included Questionnaire which included many questions that are fit and suitable to the hypotheses.
Research sample has
... Show MoreAs a result of the entry of multinationals companies in Iraq for investing in the joint projects through conducting agreements and contracts for work on important and strategic projects to get the necessary funds and various experiences which characterize the foreign participant sides that Iraq currently needs them and because of the non-applying the accounting processing stipulated in the unified accounting system in addition to the absence of a local accounting bases as well as the default of the participant contracts on indicating the accounting methods about those projects which are considered one of the bases that enables auditors in the public sector to depend on it, thus the research paper deals with studying an
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Abstract:
Central banks seek to control and supervise credit and follow it up effectively due to the high credit risks surrounding it that may lead to damage to banks, and may even lead to damage to the reputation and confidence of the banking system as a whole.
The main role of supervisory control is to control credit by controlling it from excessive expansion during periods of economic inflation or its revitalization and improvement and expansion of credit transactions in cases of economic recession, or when central banks desire to support the national economy or support a sector of various
... Show MoreRandom laser gain media is synthesized with different types of dye at the same concentration (1×10-3 M) as an active material and silicon dioxide NPs (silica SiO2) as scatter centers through the Sol-Gel technique. The prepared samples are tested with UV–Vis spectroscopy, Fluorescence Spectroscopy, Field Emission Scanning Electron Microscopy (FESEM), and Energy Dispersive X-ray Diffraction (EDX). The end result demonstrates that doped dyes with silica nanoparticles at a concentration of 0.0016 mol/ml have lower absorbance and higher fluorescence spectra than pure dyes. FESEM scans revealed that the morphology of nanocrystalline silica is clusters of nano-sized spherical particles in the range (25-67) nm. It is con
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The research aims to know (the effect of the pdeode strategy) in acquiring historical concepts among the fourth-grade literary female students in the history module. To achieve the goal of this research, the following null hypothesis was formulated. There is no statistically significant difference at the level of (0.05) between the average scores of the experimental group students, who study history according to the PDEODE strategy, and the average scores of the control group students who study the same module in the traditional way of the historical concepts acquisition test.The researcher chose the experimental method for the current research and adopted the experimental design of partial control with a post-test, which depends on the
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This research discusses one of the largest and most important issues of a doctrinal and philosophical dimension at the same time, which is the issue of man’s freedom to choose his actions, and thus his responsibility for those actions, by looking at the nature of these acts, their being and the origin of their creation. He showed that they were created in man by force, and that he was their original creator, and that they were among the creatures of the God Almighty God like others, but they are attributed to man through acquisition. So to the first saying went Jahmiyya or Jabariyya, and to the second saying went to fatalism in the past, and the existentialists shared with them in the modern era, and to the third saying went to the Sun
... Show MoreIn 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 MoreThe goal of current research to know the according of scientific values in the curriculum of chemistry sixth - grade science To achieve this goal wasa to build aalistaofa scientifica values toa be included in the curriculum of chemistry sixth - grade science after seeing a group of literature and previous studies, the list presented to a group of arbitrators and specialists in educational and psychological sciences and methods of teaching science, and curricula and teaching methods , Arbitrators and specialists have expressed their views and comments on the tool, and that the list was formed in final form (9) values Head of scientific includes ( 35) sub - value, then the researcher analyzed the chemistry curriculum for sixth grade Scient
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