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.
(26)
(23)
Estimating multivariate location and scatter with both affine equivariance and positive break down has always been difficult. Awell-known estimator which satisfies both properties is the Minimum volume Ellipsoid Estimator (MVE) Computing the exact (MVE) is often not feasible, so one usually resorts to an approximate Algorithm. In the regression setup, algorithm for positive-break down estimators like Least Median of squares typically recomputed the intercept at each step, to improve the result. This approach is called intercept adjustment. In this paper we show that a similar technique, called location adjustment, Can be applied to the (MVE). For this purpose we use the Minimum Volume Ball (MVB). In order
... Show More
The Dagum Regression Model, introduced to address limitations in traditional econometric models, provides enhanced flexibility for analyzing data characterized by heavy tails and asymmetry, which is common in income and wealth distributions. This paper develops and applies the Dagum model, demonstrating its advantages over other distributions such as the Log-Normal and Gamma distributions. The model's parameters are estimated using Maximum Likelihood Estimation (MLE) and the Method of Moments (MoM). A simulation study evaluates both methods' performance across various sample sizes, showing that MoM tends to offer more robust and precise estimates, particularly in small samples. These findings provide valuable insights into the ana
... Show MoreThe study of the characteristics of the heritage fabric is one of the important things in studies of conservation and rehabilitative use. There are three main elements of rehabilitation and they are considered the basis for achieving the rehabilitation process and these elements are (development, sustainability, participation) and that the first item addressed in the research is heritage and urban fabric in heritage areas where characteristics have been studied And a problem, while the second term is rehabilitation, where the concept of rehabilitation, the types and causes of the process of rehabilitation and the benefits and qualifications that affect the urban fabric that are represented (social, economic, religious and political) were
... Show MoreThe purpose of this paper is to identifying some of the physical, kinetic and electrical capabilities of the working muscles of patients with simple hemiplegic cerebral palsy, preparation of special exercises (rehabilitation and water) accompanied by symmetrical electrical stimulation in the rehabilitation of working muscles for patients with simple hemiplegic cerebral palsy, and identifying the effect of exercises, especially (rehabilitation and water), accompanied by symmetrical electrical stimulation, on some physical, kinetic and electrical capabilities in rehabilitating working muscles for patients with simple hemiplegic cerebral palsy. The researcher used the experimental approach with a one-group design with two pre and post-tests du
... Show MoreThe aim of the current research is to identify the impact of the SWOT strategy on developing systemic intelligence among students of the Ibn Rushd College of Education for Human Sciences University of Baghdad / College of Education Ibn Rushd for Human Sciences. The current research community consists of (8590) male and female students, divided into (7) departments. The current research relied on one of the partial control designs, which is the design of non-random groups: experimental group and a control group with a pre and post-test. As for the research tool, It was represented by Tourmanin’s Systemic Intelligence Scale (2012) of (50) items that measure the eight components of systemic intelligence. The results of the Mann Whitney te
... Show MoreThis paper was conducted to identifying the body growth averages for the infants of the age (3-6) months and their relation with brest (natural ) or artificial feeding The results showed that the higher percentage was for the infants with the natural feeding in comparison with those of the artificial or mixed feeding. Also there was a clear increase in the average of the body growth for those with the natural feeding and such results were closer to the standard criterion. While the averages of body growth for those with the artificial or mixed feeding were low. In addition, it was clear that the averages of body growth of the i
... Show More
Results showed that the optimum conditions for production of inulunase from isolate Kluyveromyces marxianus AY2 by submerged culture could be achieved by using inulin as carbon source at a concentration of 2% with mixture of yeast extract and ammonium sulphate in a ratio of 1:1 in a concentration of 1% at initial pH 5.5 after incubation for 42 hours at 30ºC.
Abstract
This research aims to identify the availability of the elements of the concept of citizenship, to identify the distribution ratios of the outputs of the musical skills curriculum at the levels of educational goals associated with the elements of the concept of citizenship in the guides of teachers of musical skills for grades (12-1) in the Sultanate of Oman. A content analysis card was designed to include the teacher’s guides of musical skills for grades (12-1), which included the outputs, according to the grades with the identification of the elements of citizenship (identity, belonging, rights, participation). The results of the research revealed that the percentage of inclusion of citizenship values
... Show More