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 molluscicidal effects of herbicide 2, 4-D were studied against tow species of freshwater snail Bulinus truncatus and Melanopsis nodosa by short term experiments. Calculated values of lethal concentrations (LC50 and LC100) were maid to two spices for different period of time 24hr, 48hr, 72hr and 96hr. The study had showed that the herbicide 2, 4-D was toxic against the tow species. The toxicity of the herbicide was low or unknown in low concentrations in the first period of exposure 24and 48hr to two spices but it increase gradually with increase period of exposure. The spice of B.truncatus was more tolerant than the M.nodosa. All the individual of M nodosa was death while in B.truncatus the complete death was not appear until finish the
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Background: Osteoporosis is one of the major public health problems from which more and more people in the world are suffering. There is evidence suggesting that osteoporosis knowledge is one contributor to osteoporosis preventive behavior. Aim of the Study: To assess the knowledge regarding osteoporosis risk factors, prevention, and management in women of reproductive ages. To identify any association between knowledge and studied factors.
Abstract. This work presents a detailed design of a three-jointed tendon-driven robot finger with a cam/pulleys transmission and joint Variable Stiffness Actuator (VSA). The finger motion configuration is obtained by deriving the cam/pulleys transmission profile as a mathematical solution that is then implemented to achieve contact force isotropy on the phalanges. A VSA is proposed, in which three VSAs are designed to act as a muscle in joint space to provide firm grasping. As a mechatronic approach, a suitable type and number of force sensors and actuators are designed to sense the touch, actuate the finger, and tune the VSAs. The torque of the VSAs is controlled utilizing a designed Multi Input Multi Output (MIMO) fuzzy controll
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Background: Salivary biomarkers, a non-invasive alternative method to serum and tissue based biomarkers and it is consider as an effective modality for early diagnosis. Salivary microRNA 21, a nucleotide biomarker, was reported to increase in patients with oral squamous cell carcinoma. This study was conducted to measure the fold change of microRNA 21 in stimulated saliva and to study its association with smoking and occurrence of oral squamous cell carcinoma. Materials and methods: A 20 patients with oral squamous cell carcinoma who used to be smokers was included in addition to 40 control subjects (20 smokers and 20 non- smokers health looking subjects). Stimulated saliva was collected under standardized condition. Salivary microRNA 21 wa
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In this research various of 2,5-disubstituted 1,3,4-oxadiazole (Schiff base, oxo-thiazolidine , and other compounds) were synthesized from 2,5-di(4,4?- amino-1,3,4-oxadiazole ) which use quently synthesized from mixture of 4-amino benzoic acid and hydrazine in the presence of polyphosphorus acid. The synthesized compounds were characterized by using some Spectral data (UV, FT-IR, and 1H-NMR).
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ABSTRACT Background: Polycystic ovary syndrome (PCOS) is one of the most common endocrine disorders affecting women in their reproductive age.It is characterized by anovulation or oligo-ovulation and hyperandrogensim.Androgen excess is the central defect in polycystic ovary syndrome. It is a complex disorder affects general health in addition to oral health.This study aimed to assess the gingival health status among a group of women with polycystic ovary syndrome as well as to estimate the levels of salivaryfree testosterone in unstimulated saliva in relation to gingival health condition. Materials and methods: Sixty two women with an age range 20-25 years old and with a body mass index range18.5-24.9 (normal weight) were included in this s
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In this research, 5- membered heterocyclic compounds as oxazolidine-5-one J1-J5 derivatives were prepared using primary aromatic amine, aromatic carbonyl compounds and chloroacetic acid. By combining primary aromatic amines and aromatic carbonyl compounds, Schiff's bases were synthesized. Schiff bases are used with the chloroacetic acid compound to prepare oxazolidine-5-one J1-J5 derivatives. The compounds J1-J5 were described using NMR spectroscopy and FT-IR. .The biological efficacy was evaluated according to maximum inhibitory concentrations (MICs) toward Staphyloccoccus aureus and Esherichia coli. The best MIC was 210 μg ml-1 for J4 against the two pathogenic bacteria, while J1, J4, and J1 did not show any inhibitory effect against all
... Show MoreThe target of this study was to study the natural phytochemical components of the head (capsule) of Cynara scolymus cultivated in Iraq. The head (capsule) of plant was extracted by maceration in70% ethanol for 72 hours, and fractioned by hexane, chloroform and ethyl acetate. Preliminary qualitative phytochemical screening was performed on the ethyl acetate fraction for capsule was revealed the presence of flavonoid and aromatic acids. These were examined by (high -performance liquid chromatography) (HPLC diodarray), (high- performance thin-layer chromatography)(HPTLC).
Flavonoids were isolated by preparative layer chromatography and aromatic acid was isolated by preparative high-
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