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 concept of sustainability is one of the modern concepts that influenced the quality of the urban plans for the cities, through the interest in the environmental and social aspects as well as the economic aspect and the need to balance to achieve sustainable development.
The research aims to identify the most prominent methods of sustainable urban land use planning and the strategies developed within these approaches to achieve sustainable development. The research started from the problem of a knowledge gap in adopting sustainable approaches and strategies when planning urban land uses for the holy city of Karbala.
In the theoretical aspect, the concepts of sustainable development, sustainable planning methodologies a
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A field experiment was conducted to grow the wheat crop during the fall season 2020 in Karbala province, north of Ain Al-Tamr District in two locations of different textures and parent materials. The first site (calcareous soil) with a sandy loam texture, is located at (44° 40′ 37′) east longitude and (32° 41′ 34′) north latitude, at an altitude of 32 m above sea level, and an area of 20 hectares. As for the second location (gypsum soil) with a loam texture, it is located at a longitude (45° 41′ 39′) east and a latitude (33° 43′ 34′ north) and at an altitude of 33 m above sea level and an area of 20 hectares. To find out the effect of different tillage systems on water productivity and wheat yield under center pivot irri
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The bodies responsible for the organization of accounting in the world seek to keep abreast of repaid development, by provide the information required by users, which they need to make efficient decision that return them to the desired benefits, and avoid the risks they could face if they made their decision based on misleading information, or insufficient, or not accurate, Hence, the IASB has undertaken to review the standards, and make the necessary adjustment and clarifications to remove the ambiguities that some of the paragraphs may have in IFRS issued.
And the Iraqi Central Bank obliges banks to convert from local accounting standards to apply IFRS only a step towards keeping pace with developments
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Two dwarf snakes were discovered, Eirenis thospitis Schmidtler & Lanza from Sereen mountain, north east of Arbil and E. rothii Jan from Saffin mountain North of Arbil city North of Iraqi Kurdistan. Supported by description and important notes on variation. In addition summarized list for 9 species of the genus Eirenis Jan in Iraq is also presented.
This piece of research work aims to study one of the most difficult reaction and determination due to continuous and rapid variation of reaction products and the reactants. As molybdenum (VI) aid in the decomposition of hydrogen peroxide in alkaline medium of ammomia, thus means a continuous liberation of oxygen which cuases and in a continuous manner a distraction in the measurement process. On this basis pyrogallol was used to absorbe all liberated oxygen and the result is an a clean undisturbed signals. Molybdenum (VI) was determined in the range of 4-100 ?g.ml-1 with percentage linearity of 99.8% or (4-300 ?g.ml-1 with 94.4%) while L.O.D. was 3.5 ?g.ml-1. Interferring ions (cations and anions) were studied and their main effect was red
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The challenges facing today's multi-customer and this is due to the multiplicity of products and speed in launching new products so search came to reveal the reveal the of the new product classification standards through a relationship (good products, low interest products, useful products and products desired) and the customer emotionally blackmail through deportation (fear, obligation and guilt). dentified the problem of the research in several questions focused on the nature of the relationship between the variables of research, and for that outline supposedly to search it expresses the head of one hypothesis and branched out of which four hypotheses subset, but in order to ensure the validity of the ass
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This research introduces a developed analytical method to determine the nominal and maximum tensile stress and investigate the stress concentration factor. The required tooth fillets parametric equations and gears dimensions have been reformulated to take into account the asymmetric fillets radiuses, asymmetric pressure angle, and profile shifting non-standard modifications. An analytical technique has been developed for the determination of tooth weakest section location for standard, asymmetric fillet radiuses, asymmetric pressure angle and profile shifted involute helical and spur gears. Moreover, an analytical equation to evaluate gear tooth-loading angle at any radial distance on the involute profile of spur and hel
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The aim of this study to identify patterns of cerebral control (right and left) for second grade students in the collage of physical education and sports science of the University of Baghdad, as well as identify the definition of theThe Effect of Using the Bybee Strategy(5ES) according to Brain Control Patterns in Learning a Kinetic Series on Floor exercises in Artistic Gymnastics for menمجلة الرياضة المعاصرةالمجلد 19 العدد 1 عام 2020effect using the (Bybee) strategy (5ES) according to brain control patterns inlearning a Kinetic series on floor exercises In artistic gymnastics for men, andidentify the best combination between the four research groups learn, use Finderexperimental method research sample consi
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The research aims to shed light on the obstacles that hinder the use of taxpayers' commercial books covered by provisions of the amended commercial book-keeping system No. 2 of 1985 and ways to address these obstacles. On this basis, the main null hypothesis was formulated that there is no statistically significant relationship between the obstacles to the adoption of the commercial books and taxable income.
The research data were collected on the base of three applied case studies of registered taxpayers in the General Commission of Taxes, GCT, together with the use of a questionnaire distributed to a sample of taxpayers ( companies ). The collected data were analyzed, the result were presented and the hypothesis was
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