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.
Background: Health education was put as one of the components of primary health care elements and was recognized as a fundamental tool to the attainment of health for all
Objective: To evaluate the Knowledge, attitude regarding health education & to find out if there is any association between the gathered data and certain variables (age, gender, educational level, occupation). Methods: A Cross-sectional study done at Al Mustansyryia Primary Health Care Center from the 1st of January to 1st of May 2016. All patients attending the Primary Health Care Centers who were above 18 years of age and willing to participate in the research (303) were included in t
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Silver sulfide and the thin films Ag2Se0.8Te0.2 and Ag2Se0.8S0.2 created by the thermal evaporation process on glass with a thickness of 350 nm were examined for their structural and optical properties. These films were made at a temperature of 300 K. According to the X-ray diffraction investigation, the films are polycrystalline and have an initial orthorhombic phase. Using X-ray diffraction research, the crystallization orientations of Ag2Se and Ag2Se0.8Te0.2 & Ag2Se0.8S0.2 (23.304, 49.91) were discovered (XRD). As (Ag2Se and Ag2Se0.8Te0.2 & Ag2Se0.8S0.2) absorption coefficient fell from (470-774) nm, the optical band gap increased (2.15 & 2 & 2.25eV). For instance, the characteristics of thin films made of Ag2Se0.8Te0.2 and Ag2Se0.8S0.2
... Show MoreIt is well known that petroleum refineries are considered the largest generator of oily sludge which may cause serious threats to the environment if disposed of without treatment. Throughout the present research, it can be said that a hybrid process including ultrasonic treatment coupled with froth floatation has been shown as a green efficient treatment of oily sludge waste from the bottom of crude oil tanks in Al-Daura refinery and able to get high yield of base oil recovery which is 65% at the optimum operating conditions (treatment time = 30 min, ultrasonic wave amplitude = 60 micron, and (solvent: oily sludge) ratio = 4). Experimental results showed that 83% of the solvent used was recovered meanwhile the main water
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An efficient networks’ energy consumption and Quality of Services (QoS) are considered the most important issues, to evaluate the route quality of the designed routing protocol in Wireless Sensor Networks (WSNs). This study is presented an evaluation performance technique to evaluate two routing protocols: Secure for Mobile Sink Node location using Dynamic Routing Protocol (SMSNDRP) and routing protocol that used K-means algorithm to form Data Gathered Path (KM-DGP), on small and large network with Group of Mobile Sinks (GMSs). The propose technique is based on QoS and sensor nodes’ energy consumption parameters to assess route quality and networks’ energy usage. The evaluation technique is conducted on two routing protocols i
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Background: Color stability of glass ionomers (GIs) could be affected by many factors such as pH and consumption of liquid medications like antibiotics. Most common antibiotics used during childhood are amoxicillin suspension (AM.S) and azithromycin suspension (AZ.S) which have acidic and basic pH respectively. Aim: to evaluate and compare the effect of AM.S and AZ.S on color stability of nano resin-modified GI. Methods: Thirty disc of nano resin-modified glass ionomer (2mm height x 4mm diameter) were divided into three groups (n=10 for each) and independently exposed to AM.S, AZ.S, and artificial saliva (A.S.). Color stability was evaluated in triplicate by VITA Easyshade® before and after three immersion protocols, repeated over
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Helicobacter pylori (H. Pylori) is one of the most common infectious human pathogens. H. pylori could induce inflammation, that causes illnesses and disorders of upper gastrointestinal which including peptic ulcer diseases, dyspepsia, gastroesophageal reflux disease and gastric mucosa-associated lymphoid tissue (MALT) lymphoma. It is important to use a better tolerated and greatly effective eradication regimen. In this study, 75 newly diagnosed adult patients with H. pylori infection were included and completed the study, they were allocated into three groups with three different treatment regimens for H. pylori eradications; Group A (25 patients) received oral standard clarithromycin-based tr
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Coupling reaction of 4-aminoantipyrene with 8-hydroxyqunoline gave the new bidentate azo ligand 5-(4-antipyrene azo)-8-hydroxyqunoline. Treatment of this ligand with the following metals ions (MnII, CoII, NiII, CuII and ZnII) in aqueous ethanol with a 1:2 M:L ratio yielded a series of neutral complexes of the general formula [M(L)2Cl2]. The prepared complexes were characterized using flame atomic absorption, FT.IR, UV-Vis spectroscopic as well as magnetic susceptibility and conductivity measurements. Chloride ion content were also evaluated by (Mohr Method). From above data, the proposed molecular structure for these complexes as octahedral geometry.
Rock type identification is very important task in Reservoir characterization in order to constrict robust reservoir models. There are several approaches have been introduced to define the rock type in reservoirs and each approach should relate the geological and petrophysical properties, such that each rock type is proportional to a unique hydraulic flow unit. A hydraulic flow unit is a reservoir zone that is laterally and vertically has similar flow and bedding characteristics. According to effect of rock type in reservoir performance, many empirical and statistical approaches introduced. In this paper Cluster Analysis technique is used to identify the rock groups in tertiary reservoir for Khabaz oil field by analyses variation o
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