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.
In this paper, the theoretical cross section in pre-equilibrium nuclear reaction has been studied for the reaction at energy 22.4 MeV. Ericson’s formula of partial level density PLD and their corrections (William’s correction and spin correction) have been substituted in the theoretical cross section and compared with the experimental data for nucleus. It has been found that the theoretical cross section with one-component PLD from Ericson’s formula when doesn’t agree with the experimental value and when . There is little agreement only at the high value of energy range with the experimental cross section. The theoretical cross section that depends on the one-component William's formula and on-component corrected to spi
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This research aims at identifying the system of applying the QRcode system for acquisition of chemistry by first class female students studying at intermediate schools knowledge and its effect on creative thinking. The research sample consisted of (63) female students in one of the intermediate schools in Baghdad/Iraq using two equivalents experimental and control groups. The scientific context used was based on the chemistry text book related to the periodic table, (Metals) for the first group of students and Alkaline metals,Nonmetals, Metalloides) for the second group. The research methodology employed consisted of the followings :Measuring students acquisition using (35) issues. The results were verified for their face validity and obtai
... Show More<span lang="EN-US">We are living in the 21<sup>st</sup> century, an era of acquiring necessity in one click. As we, all know that technology is continuously reviving to stay ahead of advancements taking place in this world of making things easier for mankind. Technology has been putting his part in introducing different projects as we have used the field programmable gate arrays (FPGAs) development board of low cost and programmable logic done by the new evolvable cyclone software is optimized for specific energy based on Altera Cyclone II (EP2C5T144) through which we can control the speed of any electronic device or any Motor Control IP product targeted for the fan and pump. Altera Cyclone FPGAs’ is a board thro
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The activity of Adhatoda vasica crude plants extracts against B.thuringiensis bacteria was determined by MIC test and sensitivity test which showed no response of this type of bacteria against extracts .The interference between the effect of hot and cold aqueous extracts and Bacillus thuringiensis bacteria for controlling the population of fig moth when males and females released before treatment under control condithion was gave a highly percentage of larval mortality which reached to 100% in (B.t. + hot aqueous extract ) and 97.3% in (B.t + coldaqueous extract ) after two weeks of treatment when concentration of 50% of aqueous extracts and 5×10?1of Bacillus thuringiensis bacteria but when the insect (males & females) released after
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The differential cross section for the Rhodium and Tantalum has been calculated by using the Cross Section Calculations (CSC) in range of energy(1keV-1MeV) . This calculations based on the programming of the Klein-Nashina and Rayleigh Equations. Atomic form factors as well as the coherent functions in Fortran90 language Machine proved very fast an accurate results and the possibility of application of such model to obtain the total coefficient for any elements or compounds.
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The performance of a synergistic combination of electrocoagulation (EC) and electro-oxidation (EO) for oilfield wastewater treatment has been studied. The effect of operative variables such as current density, pH, and electrolyte concentration on the reduction of chemical oxygen demand (COD) was studied and optimized based on Response Surface Methodology (RSM). The results showed that the current density had the highest impact on the COD removal with a contribution of 64.07% while pH, NaCl addition and other interactions affects account for only 34.67%. The optimized operating parameters were a current density of 26.77 mA/cm2 and a pH of 7.6 with no addition of NaCl which results in a COD removal efficiency of 93.43% and a specific energy c
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The five-a- Side Soccer for simple mental disability is as interesting and caring as many other sporting events. Therefore, the researchers believe that their basic skills tests are compatible with then level of the tested individuals in terms of age and mental ability. As a means of selecting those who are qualified to practice this game in a simple way, the problem of research has been identified in the design and standardization of two scoring skills that belong to this category and are approved by the training staff during the initial selection process. The research community is determined by people with mental disabilities who belong to the governmental and private institutes and the Special Olympics Union in Baghdad and for the year 2
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