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.
Electro-chemical Machining is significant process to remove metal with using anodic dissolution. Electro-chemical machining use to removed metal workpiece from (7025) aluminum alloy using Potassium chloride (KCl) solution .The tool used was made from copper. In this present the optimize processes input parameter use are( current, gap and electrolyte concentration) and surface roughness (Ra) as output .The experiments on electro-chemical machining with use current (30, 50, 70)A, gap (1.00, 1.25, 1.50) mm and electrolyte concentration (100, 200, 300) (g/L). The method (ANOVA) was used to limited the large influence factors affected on surface roughness and found the current was the large influence f
... Show MoreTrickle irrigation is a system for supplying filtered water and fertilizer directly into the soil and water and it is allowed to dissipate under low pressure in an exact predetermined pattern. An equation to estimate the wetted area of unsaturated soil with water uptake by roots is simulated numerically using the HYDRUS-2D/3D software. In this paper, two soil types, which were different in saturated hydraulic conductivity were used with two types of crops tomato and corn, different values of emitter discharge and initial volumetric soil moisture content were assumed. It was assumed that the water uptake by roots was presented as a continuous sink function and it was introduced into Richard's equation in the unsaturated z
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Fourier Transform-Infrared (FT-IR) spectroscopy was used to analyze gasoline engine oil (SAE 5W20) samples that were exposed to seven different oxidation times (0 h, 24 h, 48 h, 72 h, 96 h, 120 h, and 144 h) to determine the best wavenumbers and wavenumber ranges for the discrimination of the oxidation times. The thermal oxidation process generated oil samples with varying total base number (TBN) levels. Each wavenumber (400–3900 cm−1) and wavenumber ranges identified from the literature and this study were statistically analyzed to determine which wavenumbers and wavenumber ranges could discriminate among all oxidation times. Linear regression was used with the best wavenumbers and wavenumber ranges to predict oxidation time.
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In present project, new Schiff base of 4, 4'- (((1E, 1'E)-1,4-.phenylenebis- (methane-ylylidene))-bis-(azane-ylylidene)) bis-(5-(4-chlorophenyl) -4H -1,2,4-triazole-3-thione) (L3) has been synthesized by condensation of 4-amino-5-(4-chlorophenyl)-2,4-dihydro-3H-1,2,4-triazole-3-thione with benzene-1,4-dicarboxaldehyde. The new asymmetrical Schiff base (L3) used as a ligand to synthesize a new complex with Co(II), Ni(II), Cu(II), Pd(II), and Pt(IV) metal ions by 1:2 (Metal: ligand) ratio. New ligand and their complexes have been exanimated and Confirmed by Fourier-transform infrared (FT-IR), Ultraviolet-visible (UV-visible), Proton nuclear magnetic resonance (1HNMR), carbon13 nuclear magnetic resonance (13CNMR), carbon-hydrogen nitrogen sulf
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Introduction: Carrier-based gutta-percha is an effective method of root canal obturation creating a 3-dimensional filling; however, retrieval of the plastic carrier is relatively difficult, particularly with smaller sizes. The purpose of this study was to develop composite carriers consisting of polyethylene (PE), hydroxyapatite (HA), and strontium oxide (SrO) for carrier-based root canal obturation. Methods: Composite fibers of HA, PE, and SrO were fabricated in the shape of a carrier for delivering gutta-percha (GP) using a melt-extrusion process. The fibers were characterized using infrared spectroscopy and the thermal properties determined using differential scanning calorimetry. The elastic modulus and tensile strength tests were dete
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PMMA (Poly methyl methacrylate) is considered one of the most commonly used materials in denture base fabrication due to its ideal properties. Although, a major problem with this resin is the frequent fractures due to heavy chewing forces which lead to early crack and fracture in clinical use. The addition of nanoparticles as filler performed in this study to enhance its selected mechanical properties. The Nano-additive effect investigated in normal circumstances and under a different temperature during water exposure. First, tests applied on the prepared samples at room temperature and then after exposure to water bath at (20, 40, 60) C° respectively. SEM, PSD, EDX were utilized for samples evaluation in this study. Flexural
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An experimental and theoretical study has been done to investigate the thermal performance of different types of air solar collectors, In this work air solar collector with a dimensions of (120 cm x90 cm x12 cm) , was tested under climate condition of Baghdad city with a (43° tilt angel) by using the absorber plate (1.45 mm thickness, 115 cm height x 84 cm width), which was manufactured from iron painted with a black matt.
The experimental test deals with five types of absorber:-
Conventional smooth flat plate absorber , Finned absorber , Corrugated absorber plate, Iron wire mesh on absorber And matrix of porous media on absorber .
The hourly and average efficiency of the collectors
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