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.
Incremental forming is a flexible sheet metal forming process which is performed by utilizing simple tools to locally deform a sheet of metal along a predefined tool path without using of dies. This work presents the single point incremental forming process for producing pyramid geometry and studies the effect of tool geometry, tool diameter, and spindle speed on the residual stresses. The residual stresses were measured by ORIONRKS 6000 test measuring instrument. This instrument was used with four angles of (0º,15º,30º, and 45º) and the average value of residual stresses was determined, the value of the residual stress in the original blanks was (10.626 MPa). The X-ray diffraction technology was used to measure the residual stresses
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Otitis media with effusion (OME) is a common disease especially among young children (before school age) and it is one of the common causes of acquired hearing loss in childhood. Pediatric patients with OME are usually undernourished. The purpose of this study is to determine whether the serum levels of trace elements (zinc, copper, magnesium, iron) have a role in the development of OME in children. This study carried out on 55 children and subdivided them into two groups. Group 1 (patient group) consist of 30 children suffering from OME and group 2 (control group) included 25 apparently healthy children. Serum levels of zinc, copper, magnesium and iron were measured for both groups. Comparison the results between the two groups showed t
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Background: Breast cancer is the commonest type of malignancy worldwide and in Iraq. It is a serious disease that affects the general health and cause systemic changes that affect the physical and chemical properties of saliva leading to adverse effects on oral health. This study was conducted toassess the tumor marker CA15-3 and selected elements in saliva and their relation to oral health status among breast cancer patients compared to control group. Materials and Methods: The total sample consisted of 60 women aged 35-45 years. 30 women were newly diagnosed with breast cancer before taking any treatment and surgery (study group) and 30 women without clinical signs and symptoms of breast cancer as a control group. Dental caries was record
... Show MoreMore than 450 distinct types of human papilloma virus recognized via recent molecular techniques. The low and high oncogenic risk-HPV genotypes have an association with a variety of benign and malignant tumors in the oropharyngeal and nasopharyngeal localizations. This study aimed to determine the rate of DNA detection of HPV genotype 6/11 in non-oncologic nasopharyngeal and palatine tonsillar tissues from pediatric patients subjected to adeno-tonsillectomies. A total number of 64 tissue specimens enrolled; 44 non-oncologic nasopharyngeal and palatine hypertrophied tissue specimens from 22 pediatric patients sustained combined adeno-tonsillectomies and compared to 20 nasal trimmed tissues with unremarkable pathological changes (in
... Show MoreThe biological activities of some ternary nickel complexes with a Schiff base obtained from 4-dimethylaminobenzaldehyde and 2-aminophenol have been reported. The Schiff base ( HL1) acts as a primary ligand whereas, anthranilic acid ( HL2), 2-nitroaniline ( HL3), alanine ( HL4) and histidine ( HL5) act as secondary ligand or co-ligand. The anticancer activity of these compounds was studied against human colon carcinoma (HCT-116), human hepatocellular liver carcinoma (HEPG-2) and human breast carcinoma (MCF-7) cell lines. As per the results, the compounds were active against the cell lines. The antioxidant activity of the same compounds was evaluated using DPPH (1,1-diphenyl-2-picryl-hydrazyl) radical scavenging and compared with ascorbic aci
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The purpose of our study was to develop Dabigatran Etexilate loaded nanostructured lipid carriers (DE-NLCs) using Glyceryl monostearate and Oleic acid as lipid matrix, and to estimate the potential of the developed delivery system to improve oral absorption of low bioavailability drug, different Oleic acid ratios effect on particle size, zeta potential, entrapment efficiency and loading capacity were studied, the optimized DE-NLCs shows a particle size within the nanorange, the zeta potential (ZP) was 33.81±0.73mV with drug entrapment efficiency (EE%) of 92.42±2.31% and a loading capacity (DL%) of 7.69±0.17%. about 92% of drug was released in 24hr in a controlled manner, the ex-vivo intestinal p
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This study was aimed to investigate the role of crud alcoholic extract of Lallemantia royleana seeds in reducing the hepatotoxicity and side effect of rifadin drug in liver. The animals (40 mice) were divided into four groups, the first group was treated with normal saline (0.9%) for 28 days as a control and the second group was treated with rifadin (1.5 mg/kg/day) for 28 days and third group was treated with acoholic extract of Lallemantia royleana seeds (1% w/v) for 28 days, while the forth group was treated with alcoholic extract of seeds alone for 5 days and with alcoholic extract and rifadin for 28 days, so the total period of this group is 33
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This investigation reports application of a mesoporous nanomaterial based on dicationic ionic liquid bonded to amorphous silica, namely nano-N,N,N′,N′-tetramethyl-N-(silican-propyl)-N′-sulfo-ethane-1,2-diaminium chloride (nano-[TSPSED][Cl]2), as an extremely effectual and recoverable catalyst for the generation of bis(pyrazolyl)methanes and pyrazolopyranopyrimidines in solvent-free conditions. In both synthetic protocols, the performance of this catalyst was very useful and general and presented attractive features including short reaction times with high yields, reasonable turnover frequency and turnover number values, easy workup, high performance under mild conditions, recoverability and reusability in 5 consecutive runs without lo
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Mixed ligand metal complexes of CrIII, FeIII,II, NiII and CuII have been synthesized using 5-chlorosalicylic acid (5-CSA) as a primary ligand and L-Valine (L-Val) as secondary ligand. The metal complexes have been characterized by elemental analysis, electrical conductance, magnetic susceptibility measurements and spectral studies. The electrical conductance studies of the complexes indicate their electrolytic nature. Magnetic susceptibility measurements revealed paramagnetic nature of the all complexes. Bonding