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.
An experiment was conducted in pots under field conditions during fall seasons of 2017 and 2018. This study aimed to improve a weak growth of seedlings under salt stress in sorghum. Three factors were studied. 1st factor was three cultivars (Inqath, Rabeh, and Buhoth70). 2nd factor was seed priming (primed and unprimed seed). Seed were primed by soaking for 12 hours in a solution containing 300 + 70 mg L−1 of gibberellic (GA3) and salicylic (SA) acids, respectively. 3rd factor was irrigation with saline water (6, 9 and 12 dS m−1) resulting from dissolving sodium chloride in distilled water in addition to control treatment (distilled water). Randomized complete block design was used with four replications. In both seasons: the results sh
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One of the critical factors for dental implant success is accurate clinical and radiological assessment. Cone-beam computed tomography systems (CBCT) allow surgeons to determine the quality and quantity before surgery, aiding in treatment planning. This study highlights the importance of such an assessment Materials and Methods A total of 40 patients were referred to CBCT scanning for pre-dental implant assessment in the Oral and Maxillofacial Radiology department at Al-Shaheed Gazi Al Hariri Hospital from 2021 to 2022. The patients were between 18 and 50 years old. All data were analyzed with on-demand 3D software (Kavo OP 3D: Cone Beam 3D imaging Germany). Results: Regarding the ridge shape: In the upper anterior and posterior regions, th
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Abstract:
Background: Retinol binding protein 4 (RBP4), an adipokine that participate in a lipid metabolism or insulin resistance through a complex regulatory network. Recently, RBP4 was reported to be associated with many cardiovascular diseases (CVDs) risk factors in patients of type 2 diabetes mellitus (T2DM). This study aims to study the correlation of serum RBP4 with some markers of glycemic control, dyslipidemia, hypertension and obesity in T2DM Iraqi patients.
Subjects and Methods: one hundred fifty participants were enrolled in this coss-sectional study, 120 of participants were T2DM patients and 30 were apparently healthy individuals to serve as control gro
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The objective of study was determining the most prevalent Salmonella spp. and their antimicrobial susceptibility in broilers and laying chickens and their feed and drinking water in five chicken farms in Karbala, Iraq over the period from August to October 2020. A total of 289 samples, including 217 cloaca swabs, 46 water and 26 feed samples were collected. Salmonella spp. was identified firstly by routine diagnostic methods, followed by applying the API 20E kit, the Vitek2 system, and serology. There was significant differences in Salmonella prevalence among different types of samples, mainly cloaca swabs reported a high isolation rate (21.7%). In contrast, feed samples were completely free of contamination. The highest rate of isolation w
... Show MoreObjectives: This study aimed to evaluate the therapeutic potential effects of ascorbic acid or and pyridoxine on diabetic renal microalbumiuria. Methods: This was a cross-sectional study on patients with diabetes mellitus at Al-Yarmouk teaching hospital from January to December 2012, Iraq-Baghdad. Twenty one patients with diabetes mellitus (D.M), 8 IDDM and 13 IDDM were selected from, the duration of disease were ranged from 2-12 years for both type (10 females and 11males) and all enrolled patients ages were ranged from 28-65years. The concentration of total protein in urine was calculated by a biuret colorimetric assay and the urine creatinine level was measured by a modified Jaffe test. Statistical analysis: results are expressed as mean
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New simple and sensitive spectrophotometric methods for the determination of paracetamol in aqueous medium were developed. The first method is based on coupling of paracetamol with p-amino-2-hydroxy sodium benzoate (AHB) in the presence of sodium periodate, as oxidizing agent, to form a brownish-orange compound which shows a λmax at 470 nm. The molar absorptivity (εmax) of the colored product was found to be (3371) l. mole1. cm-1 and Sandel’s index 0.0449 μg. cm-2. The method follows Beer’s law in the concentration range of 12.5-500.0 μg of paracetamol in a final volume of 25 ml (0.5-20.0) μg. ml-1 with relative standard deviation percent (RSD%) ranged between 0.26-4.71% and accuracy, expressed by recovery percent, 95-106% for five
... Show MoreBackground:sThe aims of this study were to evaluate and compare the ability of three different techniques to obdurate simulated lateral canals, evaluate the effect of the main canal curvature on obturation of lateral canals and compare the gutta-percha penetration between coronal and apical lateral canals. Materials and methods: Resin blocks with 30 straight and 30 curved were used in this study. Each canal has two parallel lateral canals. The main canal has 0.3 mm apical diameter and 0.04 taper. The canals were divided into six groups according to canal curvature and obturation techniques used (n=10): Groups C1 and C2: straight and curved canals obturated with continuous wave technique using E&Q masterTM system. Groups O1 and O2: straight
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