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.
Introduction: Inadequate pain assessment and management is a problem in hospitalized patients that impairs their wellbeing. Intensive care unit nurses’ pain practices are affected by several barriers and enablers. Objectives: The objectives of this study were to determine the level of nurses’ practices and perceived barriers related to pain assessment in critically ill patients. Methodology: A cross-sectional design study was used. Purposive sampling technique was employed, including 100 nurses recruited from 8 intensive care units in Baghdad city, Iraq. The study was conducted from September 1st to October 20th, 2022. The pain assessment and management for critically ill patients survey was used to collect data. Descriptive sta
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Bipedal robotic mechanisms are unstable due to the unilateral contact passive joint between the sole and the ground. Hierarchical control layers are crucial for creating walking patterns, stabilizing locomotion, and ensuring correct angular trajectories for bipedal joints due to the system’s various degrees of freedom. This work provides a hierarchical control scheme for a bipedal robot that focuses on balance (stabilization) and low-level tracking control while considering flexible joints. The stabilization control method uses the Newton–Euler formulation to establish a mathematical relationship between the zero-moment point (ZMP) and the center of mass (COM), resulting in highly nonlinear and coupled dynamic equations. Adaptiv
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Background The appropriate disposal of medication is a well-recognized issue that has convened growing recognition in several contexts. Insufficient awareness relating to appropriate methods for the disposal of unneeded medicine may result in notable consequences. The current research was conducted among the public in Iraq with the aim of examining their knowledge, attitude, and practices regarding the proper disposal of unused and expired medicines. Methods The present study used an observational cross-sectional design that was community-based. The data were obtained from using an online questionnaire. The study sample included people of diverse genders, regardless of their race or occupational status. The study mandated that all pa
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Anemia of chronic disease (ACD) and iron deficiency anemia (IDA) are the two most important types of anemia in rheumatoid arthritis (RA). Functional iron deficiency in ACD can be attributed to overexpression of the main iron regulatory hormone hepcidin leading to diversion of iron from the circulation into storage sites resulting in iron-restricted erythropoiesis. The aim is to investigate the role of circulating hepcidin and to uncover the frequency of IDA in RA. The study included 51 patients with RA. Complete blood counts, serum iron, total iron binding capacity, ferritin, and hepcidin- 25 were assessed. ACD was found in 37.3% of patients, IDA in 11.8%, and combined (ACD/IDA) in 17.6%. Serum hepcidin was higher in ACD than in con
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The cement slurry is a mixture of cement, water and additives which is established at the surface for injecting inside hole. The compressive strength is considered the most important properties of slurry for testing the slurry reliability and is the ability of slurry to resist deformation and formation fluids. Compressive strength is governed by the sort of raw materials that include additives, cement structure, and exposure circumstances. In this work, we use micro silica like pozzolanic materials. Silica fume is very fine noncrystalline substantial. Silica fume can be utilized like material for supplemental cementations for increasing the compressive strength and durability of cement. Silica fume has very fine particles size less
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The incidence of disease and damage will increase, if environmental control and acceptable management practices are not provided during the rearing period. Ascites affect young broilers with rapid growth, and the most critical factor in causing ascites syndrome is the lack of oxygen in body tissues (hypoxia). This research aimed to investigate the effect of olive leaves hydroalcoholic extract and probiotics (LactoFeed) on experimental ascites caused by levothyroxine in male broiler chickens. The present study was an interventional type, and for its implementation, a single-factor design was used in eight groups with 3 replicates. Data were analyzed based on a one-way analysis of variance. Blood parameters of male chick
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Aims: This study was conducted to assess the effect of the addition of yttrium oxide (Y2O3) nanoparticles on the tensile bond strength, tear strength, shore A hardness, and surface roughness of soft-denture lining material. Materials and Methods: Y2O3 NPs with 1.5 and 2 wt.% were added into acrylic-based heat-cured soft-denture liner. A total of 120 specimens were prepared and divided into four groups according to the test to be performed (tensile bond strength, tear strength, surface hardness, and surface roughness). Results: There was a highly significant increase in tensile bond strength between the soft liner and the acrylic denture base, tear strength, and hardness at both concentrations as compared to the control group, whereas ther
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