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 study investigates the impacts of climate change (CC) on the emergence and proliferation of fungal pathogens, with a particular focus on global food security and the potential of medicinal plants and their by-products as sustainable mitigation strategies. Through a systematic literature review of articles published up to 2024, we analyze how CC exacerbates the spread and severity of fungal diseases in crops, leading to significant agricultural losses and threats to food availability. The findings highlight that, alongside conventional approaches such as genetic resistance and precision farming, bioactive compounds derived from medicinal plants and their by-products offer promising, eco-friendly alternatives for the management of fungal
... Show MoreBACKGROUND: Hospital training courses for pharmacy students were required to prepare students to meet the challenges of real-world hospital work. AIM: Because there have been few studies on the efficacy of such courses, we aimed to recognize recent graduates’ perceptions, benefits, and factors influencing the quality of hospital training courses for pharmacy students. METHODS: A qualitative study using a phenomenology approach was conducted in 2022 and included several hospitals in Baghdad, Iraq, using in-depth face-to-face individual-based semi-structured interviews. Until saturation, a convenient sample of recently graduated pharmacists was included. The obtained data were analyzed using a thematic content analysis approach
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The aim of this study to identify the effect of using two strategies for active learning ( Jigsaw Strategy & Problems Solving) in learning some balanced beam's skills in artistic gymnastics for women , as well as to identify the best of the three methods (jigsaw strategy , problems solving and the traditional method) in learning some skills balance beam , the research has used the experimental methodology, and the subject included the students of the college of Physical Education and Sports Sciences / University of Baghdad / third grade and by the lot was selected (10) students for each group of groups Search three and The statistical package for social sciences (SPSS) was used means, the standard deviation and the (T.test), the one way a n
... Show MoreThis research a study model of linear regression problem of autocorrelation of random error is spread when a normal distribution as used in linear regression analysis for relationship between variables and through this relationship can predict the value of a variable with the values of other variables, and was comparing methods (method of least squares, method of the average un-weighted, Thiel method and Laplace method) using the mean square error (MSE) boxes and simulation and the study included fore sizes of samples (15, 30, 60, 100). The results showed that the least-squares method is best, applying the fore methods of buckwheat production data and the cultivated area of the provinces of Iraq for years (2010), (2011), (2012),
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Hospitals are part of the service organizations and most importantly at the level of individuals because they are tied to the people health and their daily lives , the nursing service is one of the important services provided by hospitals, and nurses are the human resource that offers this service, from this standpoint the idea of research came to prepare work Scheduling for nurses in a scientific way to improve performance operational for their services and provide efficient service available 24 hours a day, the research use one of the modern and scientific rules of scheduling its “schedule of
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Objective: This study aimed to investigate the relationship between high blood pressure and
different variables, such as (weight, smoking, amount of salt and water taken daily, and number
of hours of natural sleep per person) for young people.
Methodology: The study was conducted on students at the student community of the Technical
Institute in Baquba and the University of Diyala during the period from September 2015
until June 2016. The patients ranged in age from 18-24 years. All data were collected through
a questionnaire that included the main reasons and periodic follow-up of the disease.
Results: The total number of samples was 450.The results showed that 33% of all samples
have high blood pressure. The rel
The problem of multi assembly line balancing appears as one of the most prominent and complex type of problem. The research problem of this dissertation is concerned with choosing the suitable method that includes the nature of the processes of the multi assembly type of the sewing line at factory no. (7). The State Company for Leather Manufacturing. The sewing line currently suffers from idle times at work stations which resulted in low production levels that do not meet the production plans. The authors have devised a flexible simulation model which uses the uniform distribution to generate task time for each shoe type produced by the factory. The simulation of the multi assembly line was based on assigni
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Abstract
Electrical magnate was designed and constructed, the optimum Magnetic flux and the effect of time on the physical properties of the alkaline (magnetic water) produced from the bottled drinking water [the total dissolved solids (TDS) or the electrical conductivity, and pH] were studied, to simulate ZamZam water in Mekka Saudi Arabia. Also, the efficiency of magnetic field from this designed electrical magnate in decreasing the TDS of sea water (of 1500 ppm NaCl Content), to convert it to water suitable for irrigation (TDS<1000 ppm) was investigated in this work.The results show that the magnetic flux from our designed electrical magnate in the range of (0.013- 0.08) Tesla and 30 minut
... Show MoreThe research aimed to modeling a structural equation for tourist attraction factors in Asir Region. The research population is the people in the region, and a simple random sample of 332 individuals were selected. The factor analysis as a reliable statistical method in this phenomenon was used to modeling and testing the structural model of tourism, and analyzing the data by using SPSS and AMOS statistical computerized programs. The study reached a number of results, the most important of them are: the tourist attraction factors model consists of five factors which explain 69.3% of the total variance. These are: the provision of tourist services, social and historic factors, mountains, weather and natural parks. And the differenc
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