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.
Abstract: This study was aimed to investigate the effect of two doses of pregabalin (PGB) on hormonal level and sexual activity in female albino rats. Ninety female rats with age (9-10 weeks) and weight (200±20 g) were divided into three major groups of thirty rats. First group was considered as control G1, the second G2 and third G3 groups were exposed to PGB into two doses 150, and 300 mg/kg body weight per day respectively. Each major group was divided into three subgroups (subgroup A, B, and C of each has ten rats), the treatments last for one month for subgroup A, two months for subgroup B, and three months for subgroup C. Five rats from each subgroup were placed separately into two breeding cages with two isolated males and wait
... Show MoreNonlinear diffraction patterns can be obtained by focusing a laser beam through a thin slice of the material. Here, we investigated experimentally the formation of the far field nonlinear diffraction patterns of cw laser beam at 532 nm passing through a quartz cuvette containing multi-wall carbon nanotubes (MWCNT's) suspended in acetone and in DI water at concentrations of 0.030.wt.%, 0.045 wt.%, 0.060 wt.%, and 0.075 wt.%. Our results show that increasing the concentration of both types of suspensions (MWCNTs in acetone and MWCNTs DI water) led to increase in the number of pattern rings which indicates an increase in their nonlinear refractive indices. Moreover, MWCNTs DI water suspension at a concentration of 0.075 wt. % was more effic
... Show MoreThis study aimed to show the extent of compliance with the income taxpayer to provide tax returns and increase the speed of collection of these taxes in addition to increasing confidence in Income Tax department and reduce the number of cases transferred to the courts and promote taxpayer awareness in charge of the importance of system self-assessment, and study sought to investigate the effect of the existence of records documents, technical audit, and computational audit and documentary audit on income tax collections in Jordan, from the point of view of Jordanian income tax auditors ,results shows there's a strong relation between these variables and Income Tax collections.
Objective(s): to assess the effectiveness of educational program on improving diabetic foot self-efficacy concerning managing their feet. Methodology: A descriptive analytic (quasi – experimental) design study was carried out at Diabetic and Endocrinology Center in Baghdad- Rusafa Sector from 2nd of May 2017, to27th June 2018. Non-probability sample of (80) male and female diabetic patients were selected. The study instruments consisted of two major parts: first
The current research aims to identify the level of extension of the sense of self and the cognitive style (complexity - simplification) among university students, as well as the significance of the difference according to gender (males - females), as well as the correlation between the two variables, and in order to verify this, the researcher has constructed The measure of the extension of the sense of self based on the theory of Alport 1961, as the number of its final paragraphs reached (28) paragraphs, and the cognitive style scale (complexity - simplification) prepared by (Abdullah 2017) was adopted, as the scale consisted of (32) paragraphs in its final form. To verify their psychometric properties, and the two tools were applied to
... Show MorePurpose :This study seeks to provide the point of view stands on the marketing performance of the banks in the context of Dynamic Equilibrium of marketing. It aims to develop a prototype of measuring marketing performance under the umbrella of marketing dynamic prototype, embodied of the strategic alliance and competition, and the laws and legislation, and to explore any of the dimensions more effective in achieving performance. This study aims to discusses the importance of the Dynamic Equilibrium of marketing and it role in achieving the marketing performance <
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This cross-sectional, questionnaire-based study evaluated the knowledge, attitude and practice towards breast cancer and breast self-examination [BSE] among 387 [302 females and 85 males] educated Iraqis affiliated to 2 Iraqi universities. The participants were categorized into 3 occupations: student [71.3%], teaching staff [10.3%] and administrative staff [18.3%]. About half of the participants had a low knowledge score [< 50%]; only 14.3% were graded as [Good] and above. Almost 75% of the participants believed that the best way to control breast cancer was through early detection and other possible preventive measures. Most participants [90.9%] had heard of BSE, the main source of informatio
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This thesis aims to study the effect of addition polymer materials on mechanical properties of self-compacting concrete, and also to assess the influence of petroleum products (kerosene and gas oil) on mechanical properties of polymer modified self-compacting concrete (PMSCC) after different exposure periods of (30 ,60 ,90 ,and 180 days).
Two type of curing are used; 28 days in water for SCC and 2 days in water followed 26 days in air for PMSCC.
The test results show that the PMSCC (15% P/C ratio) which is exposed to oil products recorded a lower deterioration in compressive strength's values than reference concrete. The percentages of reduction in compressive strength values of PMSCC (15% P/C ratio) was
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The negative impact of oral diseases on the function, economy, and general health of the population is well‐documented. In the last decades, evidence linking increased expression of depression and oral diseases/conditions has significantly increased. The aim of this study is to assess the association between oral disease/conditions and self‐reported symptoms of depression individuals.
A specially designed questionnaire was distributed via social media for 1 week. It consisted of two main sections; the first section was dedicated to collect demographic variables and self‐reported symptoms
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