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.
Genetic variation was studied in 22 local and imported samples collected from local Iraqi market by using Single sequence repeat (SSR-PCR). Six primers set were used in this study. These primers produced 33 bands. Molecular weights of these bands ranged between 100 bp to 1500 bp. The number of polymorphic bands is 24, whereas the number of monomorphic bands is 9. The results of Dendrogram of the studied samples depended on SSR-PCR results by using Jaccard coefficient for genetic similarity was distributed the samples into 10 groups. This Dendrogram revealed a higher similarity between Iraqi/Balad green bell pepper and Iraqi/Yousifia green bell pepper with 1 value. This value is the highest between samples in comparison with lowest values (0
... Show MoreBACKGROUND: Chronic prostatitis/chronic pelvic pain syndrome (CP/CPPS) is common, yet no curative treatment identified. Cinnamon is a herbal substance, which has many applications in medicine. AIM: The aim of the study was to study the effect of cinnamon on patients with chronic pelvic pain syndrome. METHODS: Sixty patients with documented CP/CPPS randomized into two groups during 2018 and 2019 in Baghdad. The first group received 60 capsules each contained 1 g of cinnamon. The other group received 60 capsules each contained 1 g of sugar powder (placebo). All the patients instructed to take one capsule twice daily for 1 month. National Institutes of Health-Chronic Prostatitis Symptom Index (NIH-CPSI) was reported for bot
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Abstract
Objective (s): To evaluate reasons for partial compliance and non-compliance to the
routine childhood vaccination schedule in Al-Karkh district
Methodology: Descriptive study , using the evaluation approach, is carried throughout the present study to determine the reasons for the Routine Childhood Vaccination at health care sectors and primary health care centers at Al-Karkh District in Baghdad City, Convenient, non-probability, sample of (90) mother who are recruited from health care sectors at Al-Karkh District in Baghdad City. All mothers, who ha
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The ground state proton, neutron, and matter density distributions and corresponding root-mean-square radii (rms) of the unstable neutron-rich
22C exotic nucleus are investigated by two-frequency shell model (TFSM) approach. The single-particle wave functions of harmonic-oscillator (HO)
potential are used with two oscillator parameters bcore and bhalo. According to this model, the core nucleons of 20C are assumed to move in the model
space of spsdpf. Shell model calculations are performed with (0+2)hw truncations using Warburton-Brown psd-shell (WBP) interaction. The outer (halo) two neutrons in 22C are assumed to move in HASP (H. Hasper) model space (2s1/2, 1d3/2, 2p3/2, and 1f7/2 orbits) using the HASP interaction. The halo st
A faunistic review of the genus Chaitophorus Koch, 1854, including four species in Iraq is given; the distribution data of each species and their hosts have been recorded. In this investigation the poplar leaf aphid Ch. populialbae (Boyer de Fonscolombe, 1841) is recorded here for the first time in Iraq on popular trees Populus euphratica Oliv. during the period from November 2016 to April 2017 in Baghdad province.
A brief description for apterous viviparous female of this species is given; and a key to the species of the genus Chaitophorus is constricted.
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A simple, accurate, and cost-efficient UV-Visible spectrophotometric method has been developed for the determination of naphazoline nitrate (NPZ) in pure and pharmaceutical formulations. The suggested method was based on the nucleophilic substitution reaction of NPZ with 1,2-naphthoquinone-4-sulfonate sodium salt in alkaline medium at 80°C to form an orange/red-colored product of maximum absorption (λmax) at 483 nm. The stoichiometry of the reaction was determined via Job's method and limiting logarithmic method, and the mechanism of the reaction was postulated. Under the optimal conditions of the reaction, Beerʼs law was obeyed within the concentration range 0.5–50 μg/mL, the molar absorptivity value (ε) was 5766.5 L × mol–1 × c
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In this work, excess properties (eg excess molar volume (VE), excess viscosity (ȠE), excess Gibbs free energy of activation of viscos flow (ΔG* E) and molar refraction changes (ΔnD) of binary solvent mixtures of tetrahydrofurfuryl alcohol (THFA) with aromatic hydrocarbons (benzene, toluene and p-xylene) have been calculated. This was achieved by determining the physical properties including density ρ, viscosity Ƞ and refraction index nD of liquid mixtures at 298.15 K. Results of the excess parameters and deviation functions for the binary solvent mixtures at 298.15 K have been discussed by molecular interactions that occur in these mixtures. Generally, parameters showed negative values and have been found to fit well to Redlich-Kister
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