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.
These deposits take many forms like current acc, deposits in order to growth and serve national economy Various in varicose perspectives .
The problem of this paper its concern with un applied the mathematical models that used in profitability analysis of current acc , and deposits in view of risk, profit efficiency and financial leverage for this reason the paper discussion use the cumulate mathematical model to solve these problem, that content three variables that be used to measuring profitability by consequent replacement method by stable base and by moving base for 2007 – 2009 applied the data collect from Iraq middle east bank. &nbs
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Background: Oral SCC is a complex malignancy where environmental factors, viral infections and genetic alterations most likely interact, and thus give rise to the malignant condition. The HSP70 play a direct role in apoptosis inhibition by aligning the improved integrity of a cell’s proteins with the improved chances of that particular cell’s survival.P21 gene produces p21 protein which is a potent cyclin-dependent kinase inhibitor that plays a significant role in carcinogenesis. The aims of the study were to evaluate and compare the immun-histochemical expression of the HSP70 and cell cycle protein p21in NOM, OED, and OSCC. Correlate both marker expressions with each other. Materials and methods: Forty six formalin-fixed, par
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Objectives: To determine the effectiveness of the instructional program on patients’ knowledge about home safety while receiving anti-cancer treatment at Al- Karama Teaching Hospital in Al-Kut City.
Methodology: A quasi-experimental design is conducted through the application of a pre-test and post-test approach for the study and control groups from February 5th, 2020 to April 25th, 2020. A non–probability (purposive) sample of (50) patients treated at the Blood Disease and Oncology Center is selected and divided into two groups. Each group contains (25) patients as control and study groups. An instrument is constructed that is comprised of two parts; t
... Show MoreSYNTHESIS, CHARACTERIZATION, STRUCTURAL, THERMAL, POM STUDIES, ANTIMICROBIAL AND DNA CLEAVAGE ACTIVITY OF A NEW SCHIFF BASE-AZO LIGAND AND ITS COMPLEXATION WITH SELECTED METAL IONS
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A new Mannich base ligand was prepared by reacting the 2-chloro.-N-(5-mercapto-1, 3, 4-thiadazol -2-yl) acetamide and Piperidine in the presence (formaldehyde) (L) ligand. A series of ligand complexes were prepared from (L) with the metal ion Co (II), Ni (II), Cu (II), Pd (II), Pt (IV), and Au (III). Various spectroscopic techniques such as C.H.N.S, FTIR, UV-VIS, , 1HNMR, 13CNMR, Magnetic moment, and molar conductivity successfully characterize the obtained compounds. The M: L ratio was determined using the molar ratio method in solution. All prepared compounds' antibacterial and antifungal activity was studied against two types of bacteria and one type of fungi at a rate of 0.02M. The standard ΔH° f and ΔEb of the ligands an
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New Schiff base and their Mn(II),Co(II),Ni(II), Cu(II) and Hg(II) complexes formed by the condensation of O-phathaldehyde and ethylene diamine (2:1) to give ligand (L1) in the first step ,then the ligand (L1) with 2- aminophenol (1:2) to give ligand (L2) were prepared by classic addition through microwave method . These compounds (Ligands and complexes) have been diagnosed electronic spectra, FT-IR,1H-&13C-NMR (only ligand), magnetic susceptibility, elemental microanalysis and molar conductance measurements. Analytical values displayed that all the complexes appeared (metal: ligand) (1:1) ratio with the six chelation. All the compounds appear a high activity versus four types of bacteria such as; (Escherichia coli), (Sta
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حضرت معقدات كل من الفنادايل, الخارصين, النحاس والكادميوم بتكافؤهم الثنائي والذهب بتكافؤه الثلاثي بأستخدام صبغة ازوجديدة (6،4،2-ثلاثي هيدروكسي-3-((3-هيدروكسي فنيل) ثنائي زينيل ) فنيل ) ايثان-1-اون المحضرة من ملح الديازونيوم مع ٦,٤,٢- ثلاثي هيدروكسي اسيتوفينون بعد عزل (E)-1-(2,4,6-trihydroxy-3-((3-hydroxyphenyl)diazenyl)phenyl)ethan-1-one تم تشخيصها بواسطة الطرق الطيفية المتاحة والتقنيات التشخيصية لكل من التحليل الدقيق للعناصرواطياف كل من ال
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The new azo dye was synthesized via the reaction of the diazonium salt form of 3-aminophenol with 2-hydroxyquinoline. This dye was then used to access a series of complexes with the chlorides of manganese, iron, zinc, cadmium, and vanadium sulfate. The prepared ligand and its complexes were characterized by FT-IR spectroscopy, UV-visible spectroscopy, mass spectrometry, thermogravimetric analysis, differential scanning calorimeter, and microelemental analysis. Conductivity, magnetic susceptibility, metal content, and chlorine content of the complexes were also measured. The ligand and cadmium complex were identified using1H NMR and 13C NMR spectroscopy. The results showed that the shape of the ligand is a trigonal planner, and the c
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This study aimed to fabricate a curcumin@platinum nanohybrid (CUR@Pt NPs) through a green tea–based synthesis method and to evaluate its various functions, including antioxidant, burn-healing, and selective anticancer activities against PANC-1 pancreatic cancer cells. Green tea polyphenols served as natural reducing and stabilizing agents, facilitating an eco-friendly, single-step manufacturing process. Physicochemical characterization confirmed successful nanohybrid formation: a CUR@Pt band appeared at 457 nm in the UV–Vis spectrum, XRD displayed crystalline platinum peaks at 2θ = 46.9°, and 67.0°, matching the (200), and (220) planes, respectively, and TEM images showed well-dispersed spherical nanoparticles with an average siz
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