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.
The purpose of this study was to measure serum levels of insulin-like growth factor-binding protein (IGFBP7), Insulin-like Growth Factor 1 (IGF-1), Growth Hormone (GH), Interleukin 6 (IL-6) and insulin in acromegaly patients and healthy controls. The acromegaly group had 60 patients, while the population group had 30 people who had never had acromegaly before. The concentration of IGFBP7, IGF-1, GH, IL-6, and insulin were determined. The results of the present study indicate that IGFBP7 level in the acromegaly group was significantly lower (1.690.07 ng/mL vs. 2.740.12 ng/mL, respectively, p = 0.001). IGF-1, GH, IL-6, and insulin concentrations were also significantly higher in acromegaly patients. The diagnostic accuracy (2.194) was exce
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Aphelenchus avenae was isolated from the wheat crown in Summel distract- Duhok, Kurdistan region-Iraq infected by a crown rot disease which is caused by Fusarium spp; wheat's crown culturing on Potato Dextrose Agar (PDA) and incubating at 25°C A. avenae was found associated with fungal culture which meant that fungal nematode was parasitic on crown rot fungi on wheat crown, this species was described for the first time in Iraq.
Fungal Nematode incubated with Fusarium graminearum, F. oxysporum and Verticillium dahliae reproduce in both solid and liquid media, best results of nematode reproduction were recorded on F. graminearum followed by F. oxy
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A simple, environmental friendly and selective sample preparation technique employing porous membrane protected micro-solid phase extraction (μ-SPE) loaded with molecularly imprinted polymer (MIP) for the determination of ochratoxin A (OTA) is described. After the extraction, the analyte was desorbed using ultrasonication and was analyzed using high performance liquid chromatography. Under the optimized conditions, the detection limits of OTA for coffee, grape juice and urine were 0.06 ng g−1, 0.02 and 0.02 ng mL−1, respectively while the quantification limits were 0.19 ng g−1, 0.06 and 0.08 ng mL−1, respectively. The recoveries of OTA from coffee spiked at 1, 25 and 50 ng g−1, grape juice and urine samples at 1, 25 and 50 ng mL
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In the present paper, chitosan Schiff base has been synthesized from chitosan’s reaction with the salicyldehyde. The AuNPs was manufacture by extract of onion peels as a reducing agent. The Au NPs that have been prepared were characterized through the UV-vis spectroscopy, XRD analyses and SEM microscopy. The polymer blends of the chitosan Schiff base / PVP has been prepared through using the approach of solution casting. Chitosan Schiff base / PVP Au nano-composites was prepared. Nano composites and polymer blends have been characterized by FTIR which confirm the formation of Schiff base by revealing a new band of absorption at 1651cm-1 as a result of the (C=N) imine group. SEM, DSC and TGA confirms the thermal stability of
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Two series of 1,3,4-oxadiazole derivatives at the sixth position of the 2,4-di-
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The purpose of my thesis is to synthesis two new bidentate ligands which were used to prepare series of metal complexes by reacting the ligands with (M+2 = Mn, Co, Ni, Cu, Cd and Hg) Succinyl chloride was used as starting material to synthesis two bidentate ligands (L1) and (L2) by reaction it with 4-chloroaniline (L1) and (4-aminoacetophenone) (L2) in dichloromethane as a solvent, that are: (L1) = N1,N4-bis (4-chloro phenyl ) succinamide (L2) =N1,N4-bis(4-acetylphenyl)succinamide The new ligands were characterize by using spectroscopic study (Fourier-transform infrared spectroscopy (FT-IR), electronic spectra ( UV-Vis) ,nuclear magnetic resonance(1H,13C-NMR), Mass spectra
... Show MoreAn 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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