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.
Zinc, Copper, Selenium, Magnesium, Manganese, Chromium, Iron, Nickel, Cobalt, Vanadium and Germanium were determined by atomic absorption spectrophotometer (AAS) in blood serum of patients with rheumatoid arthritis, (30) patients (14male and 16female) with age range (37-60) years compared with normal tensive control. The analysis of results showed that the mean value of concentration (Magnesium, Manganese and Nickel) were significantly higher in patients with rheumatoid arthritis compared to that of healthy, while the mean levels of serum (Zinc, Copper, Selenium, Chromium, Iron, Cobalt and Germanium) were significantly lower than controls. There were no significant changes in overall mean concentration of serum Vanadium in patients
... Show More
(2)
In this study, iron oxide nanoparticles (α-Fe₂O₃ NPs) were prepared using a readily available chili pepper plant extract from local markets. This study aims to evaluate the magnetic properties of α-Fe₂O₃ prepared in green chemistry from Capsicum plant extract. After several simple preparatory steps, such as washing and cutting, they were treated with an inorganic complex (potassium hexacyanoferrate) (K3[Fe(CN)₆]). In the first analytical step, the in vitro detection of the plant extract solution after reaction with the potassium hexacyanoferrate (III) complex revealed characteristic adsorption bands of the cyanide group, which disappeared upon complexation. The iron oxide NPs were characterized using various methods, including X
... Show MoreAbstract
The aim of this work is to create a power control system for wind turbines based on fuzzy logic. Three power control loop was considered including: changing the pitch angle of the blade, changing the length of the blade and turning the nacelle. The stochastic law was given for changes and instant inaccurate assessment of wind conditions changes. Two different algorithms were used for fuzzy inference in the control loop, the Mamdani and Larsen algorithms. These two different algorithms are materialized and developed in this study in Matlab-Fuzzy logic toolbox which has been practically implemented using necessary intelligent control system in electrical engineerin
... Show More
(1)
A Geographic Information System (GIS) is a computerized database management system for accumulating, storage, retrieval, analysis, and display spatial data. In general, GIS contains two broad categories of information, geo-referenced spatial data and attribute data. Geo-referenced spatial data define objects that have an orientation and relationship in two or three-dimensional space, while attribute data is qualitative data that can be counted for recording and analysis. The main aim of this research is to reveal the role of GIS technology in the enhancement of bridge maintenance management system components such as the output results, and make it more interpretable through dynamic colour coding and more sophisticated vi
... Show More
(3)
Two types of monofloral Malaysian honey (Gelam and Nenas) were analyzed to determine their antioxidant activities and total phenolic and flavonoid contents, with and without gamma irradiation. Our results showed that both types of honey can scavenge free radicals and exhibit high antioxidant-reducing power; however, Gelam honey exhibited higher antioxidant activity (p < 0.05) than Nenas honey, which is in good correlation (r = 0.9899) with its phenolic contents. Interestingly, we also noted that both irradiated honeys have higher antioxidant activities and total phenolic and flavonoid contents compared to nonirradiated honeys by Folin-Ciocalteu and UV-spectrophotometry methods, respectively. However, HPLC analysis for phenolic co
... Show More
(74)
The corrosion of carbon steel in single phase (water with 0.1N NaCl ) and two immiscible phases (kerosene-water) using turbulently agitated system is investigated. The experiments are carried out for Reynolds number (Re) range of 38000 to 95000 corresponding to rotational velocities from 600 to 1400 rpm using circular disk turbine agitator at 40 0C. In two-phase system test runs are carried out in aqueous phase (water) concentrations of 1 % vol., 5 % vol., 8% vol., and 16% vol. mixed with kerosene at various Re. The effect of Reynolds number (Re), percent of dispersed phase, dispersed drops diameter, and number of drops per unit volume on the corrosion rate is investigated and discussed. Test runs are carried out using two types of
... Show More
(2)
(8)
Beryllium Zinc Oxide (BexZn1-xO) ternary nano thin films were deposited using the pulsed laser deposition (PLD) technique under a vacuum condition of 10-3 torr at room temperature on glass substrates with different films thicknesses, (300, 600 and 900 nm). UV-Vis spectra study found the optical band gap for Be0.2Zn0.8O to be (3.42, 3.51 and 3.65 eV) for the (300, 600 and 900nm) film thicknesses, respectively which is larger than the value of zinc oxide ZnO (3.36eV) and smaller than that of beryllium oxide BeO (10.6eV). While the X-ray diffraction (XRD) pattern analysis of ZnO, BeO and Be 0.2 Zn 0.8 O powder and nano-thin films indicated a hexa
... Show More
(1)