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.
This research investigated the effect of adding two groups of reinforcement materials, including bioactive materials Hydroxyapatite (HA) and halloysite nanoclay and bioinert materials Alumina (AL2O3) and Zirconia (ZrO2), each of them with various weight ratios (1,2,3,4 &5)% to the polymer matrix PMMA. The best ratios were selected, and then a hybrid was preparing Composite red from the best ratios from each group. Thermal properties, including thermal conductivity and Thermomechanical Analysis (TMA) technology, have been studied. The results showed that adding 3% Hydroxyapatite (HA) and 5% halloysite nanoclay to the polymethacrylate (PMMA) mer leads to an increase in thermal conductivity. It was also found from the Thermomechanical Analysis
... Show MoreThe Khabour reservoir, Ordovician, Lower Paleozoic, Akkas gas field which is considered one of the main sandstone reservoirs in the west of Iraq. Researchers face difficulties in recognizing sandstone reservoirs since they are virtually always tight and heterogeneous. This paper is associated with the geological modeling of a gas-bearing reservoir that containing condensate appears while production when bottom hole pressure declines below the dew point. By defining the lithology and evaluating the petrophysical parameters of this complicated reservoir, a geological model for the reservoir is being built by using CMG BUILDER software (GEM tool) to create a static model. The petrophysical properties of a reservoir were computed using
... Show MoreThe nuclear structure of 38Ar, 59Co, 124Sn, 146Nd, 153Eu and 203Tl target nuclei used in technology for nuclear batteries have been investigation, in order that, these nuclei are very interesting for radioisotope thermo-electric generator (RTG) space studies and for betavoltaic battery microelectronic systems. The single particle radial density distribution, the corresponding root mean square radii (rms), neutron skin thicknesses and binding energies have been investigated within the framework of Hartree-Fock Approximation with Skyrme interaction. The bremsstrahlung spectrums produced by absorption of beta particles in betavoltaic process and backscattered p
... Show MoreUrinary tract infection is a bacterial infection that often affects the bladder and thus the urinary system. E. coli is one of the leading uropathogenic bacteria that cause urinary tract infections. Uropathogenic E. coli is highly effective and successful in causing urinary tract infections through biofilm formation and urothelial cell invasion mechanisms. Other organisms that cause urinary tract infections include members of the Enterobacteriaceae family, streptococci and staphylococci species and perch. In addition, K.penumoniae is another important gram-negative bacterium that causes urinary tract infections. With the PCR technique, unseen bacterial species can be detected using standard clinical microbiology methods. In this study, the
... Show MoreThe objective of the study is to demonstrate the predictive ability is better between the logistic regression model and Linear Discriminant function using the original data first and then the Home vehicles to reduce the dimensions of the variables for data and socio-economic survey of the family to the province of Baghdad in 2012 and included a sample of 615 observation with 13 variable, 12 of them is an explanatory variable and the depended variable is number of workers and the unemployed.
Was conducted to compare the two methods above and it became clear by comparing the logistic regression model best of a Linear Discriminant function written
... Show MoreIn this study, polymeric coating was developed by incorporating nano graphene in the polymer blend with applications to oil storage tanks. The oil storage tanks samples were brought from the oil Pipeline Company / Doura refinery in Baghdad. The coating polymer was formed with a blend (epoxy resin and repcoat ZR). The proportion of mixing the mixture was 3:1:1 epoxy resin 21.06 gm: repcoat ZR 10.53 gm: hardener 10.53 gm. The blend/graphene was prepared using in stui-polymerization method with different weight percentage 1, 3, 5, and 7 wt % added to blend. The resulting solution was put in a glass tube on a magnetic stirrer for one hour at a temperature of 40 °C. The result of contact angle and wate
... Show MoreThe current research aims to build a training program for chemistry teachers based on the knowledge economy and its impact on the productive thinking of their students. To achieve the objectives of the research, the following hypothesis was formulated:
There is no statistically significant difference at (0.05) level of significance between the average grades of the students participating in the training program according to the knowledge economy and the average grades of the students who did not participate in the training program in the test of productive thinking. The study sample consisted of (288) second intermediate grade students divided into (152) for the control group
... Show MoreThis research aims to know the effectiveness of teaching with a proposed strategy according to the common Knowledge construction modelin mathematical proficiency among students of the second middle class. The researchers adopted the method of the experimental approach, as the experimental design was used for two independent and equal groups with a post-test. The experiment was applied to a sample consisting of (83) students divided into two groups: an experimental comprising (42) students and a control group, the second comprising (41) students., from Badr Shaker Al-Sayyab Intermediate School for Boys, for the first semester of the academic year (2021-2022), the two groups were rewarded in four variables: (chronological age calculated in mo
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