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The Product of Automorphic Weighted Composition Operators on Hardy Space H <sup>2</sup>
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Abstract<p>Let <inline-formula> <tex-math><?CDATA $n\in {\mathbb{N}},{p}_{i}\in {\rm{U}},{\alpha }_{{P}_{i}}(z)=\frac{{p}_{i}-z}{1-{\bar{p}}_{i}z}(z\in {\rm{U}})$?></tex-math> <math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mrow> <mi>n</mi> <mo>∈</mo> <mi>ℕ</mi> <mo>,</mo> <msub> <mi>p</mi> <mi>i</mi> </msub> <mo>∈</mo> <mi mathvariant="normal">U</mi> <mo>,</mo> <msub> <mi>α</mi> <mrow> <msub> <mi>P</mi> <mi>i</mi> </msub> </mrow> </msub> <mo stretchy="false">(</mo> <mi>z</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mfrac> <mrow> <msub> <mi>p</mi> <mi>i</mi> </msub> <mo>−</mo> <mi>z</mi> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <msub> <mover accent="true"> <mi>p</mi> <mo>¯</mo> </mover> <mi>i</mi> </msub> <mi>z</mi> </mrow> </mfrac> <mo stretchy="false">(</mo> <mi>z</mi> <mo>∈</mo> <mi mathvariant="normal">U</mi> <mo stretchy="false">)</mo> </mrow> </math> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JPCS_1530_1_012045_ieqn1.gif" xlink:type="simple"></inline-graphic> </inline-formula>, and let <inline-formula> <tex-math><?CDATA ${f}_{1}\in {H}^{\infty },i=1,\ldots,n$?></tex-math> <math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mrow> <msub> <mi>f</mi> <mn>1</mn> </msub> <mo>∈</mo> <msup> <mi>H</mi> <mi>∞</mi> </msup> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mi>n</mi> </mrow> </math> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JPCS_1530_1_012045_ieqn2.gif" xlink:type="simple"></inline-graphic> </inline-formula>. We discuss the relation between the points <italic>p<sub>i</sub> </italic> in U and the functions <italic>f<sub>i</sub> </italic> in U and the properties of the product of automorphic weighted composition operators <inline-formula> <tex-math><?CDATA ${W}_{{f}_{1},{\alpha }_{{p}_{1}}}\,{W}_{{f}_{2},{\alpha }_{{p}_{2}}}\ldots {W}_{{f}_{i},{\alpha }_{pi}}$?></tex-math> <math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mrow> <msub> <mi>W</mi> <mrow> <msub> <mi>f</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>α</mi> <mrow> <msub> <mi>p</mi> <mn>1</mn> </msub> </mrow> </msub> </mrow> </msub> <mspace width="0.25em"></mspace> <msub> <mi>W</mi> <mrow> <msub> <mi>f</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>α</mi> <mrow> <msub> <mi>p</mi> <mn>2</mn> </msub> </mrow> </msub> </mrow> </msub> <mo>…</mo> <msub> <mi>W</mi> <mrow> <msub> <mi>f</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>α</mi> <mrow> <mi>p</mi> <mi>i</mi> </mrow> </msub> </mrow> </msub> </mrow> </math> <inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JPCS_1530_1_012045_ieqn3.gif" xlink:type="simple"></inline-graphic> </inline-formula> on Hardy space H<sup>2</sup>. In fact, it is very nice connection between analytic function theory and operator theory. In this paper, we give the sufficient and necessary conditions to be normal, unitary, hermitian operator on <italic>H</italic> <sup>2</sup> and we shall present the shape of the numerical range of it.</p>
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Publication Date
Fri Jan 01 2021
Journal Name
Biochem. Cell. Arch.
SYNTHESIS AND CHARACTERIZATION OF SOME NEW METALS COMPLEXES OF 2-(3-ACETYLTHIOUREIDO)-3-PHENYLPROPANOIC ACID (APA)
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ABSTRACT : A new ligand [ 2- (3-acetylthioureido)-3-phenylpropanoic acid (APA) is synthesized by reaction of acetyl isothiocyanate with phenylalanine (1:1). It is characterized by micro elemental analysis (C.H.N.S.), FT-IR, (UV-Vis) and 1H and 13CNMR spectra. Some metals ions complexes of this ligand were prepared and characterized by FT-IR, UV-Visible spectra, conductivity measurements, magnetic susceptibility and atomic absorption. From results obtained, the following formula [M(APA)2] where M2+ = Mn, Co, Ni, Cu, Zn, Cd and Hg, the proposed molecular structure for these complexes as tetrahedral geometry, except copper complex is has square planer geometry.

Publication Date
Tue Jul 17 2018
Journal Name
Materials Research Express
Structural, electronic and thermodynamic properties of bulk and surfaces of terbium dioxide (TbO<sub>2</sub>)
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This contribution reports a comprehensive investigation into the structural, electronic and thermal properties of bulk and surface terbium dioxide (TbO2); a material that enjoys wide spectra of catalytic and optical applications. Our calculated lattice dimension of 5.36 Å agrees well with the corresponding experimental value at 5.22 Å. Density of states configuration of the bulk structure exhibits a semiconducting nature. Thermo-mechanical properties of bulk TbO2 were obtained based on the quasi-harmonic approximation formalism. Heat capacities, thermal expansions and bulk modulus of the bulk TbO2 were obtained under a wide range of temperatures and pressures. The dependency of these properties on operational pressure is very evident. Cle

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Publication Date
Sat Dec 01 2018
Journal Name
Journal Of Pharmaceutical Sciences And Research
Pryparation, characterization and biological activity of new derivatives of 2-biphenyl-3-aminomethylimidazo(1,2-a)pyrimidine
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New Fourteen compounds were synthesized in four steps. The first step included synthesis of 2-biphenyl fused ring of imidazo(1,2- a)pyrimidine from the reaction of 2-aminopyrimidine and biphenyl phenacyl bromide . The second step was introduced aldehyde group from the reaction of 2-biphenyl fused rings of imidazo(1,2-a)pyrimidine with POCl3 in presence of DMF and CHCl3. 3-Carbaladehyde derivatives of fused imidazo/pyrimidine was reacted with different aromatic amines to afford new Schiff bases. These new 3- imines derivatives was reduced by using sodiumborohydride to yield another new 3-aminomethyl-2-biphenyl imidazo (1,2-a)pyrimidine derivatives in moderate yield .Some new prepared compounds were identified by melting point, FT- IR , 13C-

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Publication Date
Wed Mar 10 2021
Journal Name
Baghdad Science Journal
Preparation of some azo compounds by diazotization and coupling of 2- amino -5 – thiol -1,3,4- thiadizaole
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2- amino -5- thiol-1,3,4- thiadiazole (S1) was prepared by cyclic locking of thiosemicarbazide in the presence of anhydrous sodium carbonate and CS2. diazotization of (S1) compound gave diazonium salt (S2) that reacts with different activated aromatic compounds to get the following azo compounds ,2 [(4- aminophenyl) diazenyl ] 1,3,4- thiazdiazole-5- thiol (S3) ,2-[4-amino- 1-naphthyl diazenyl] -1,3,4 – thiazdiazole-5-thiol (S4) , 3-amino-4-[(5- mercapto -1,3,4- thiadiazole -2-yl) diazenyl ] phenol(S5) ,1-[(5-mercapto-1,3,4-thiadiazole-2-yl) diazenyl] -2-naphthol (S6) , 5-{[4-(dimethylamino) phenyl] diazenyl}-1,3,4-thiadiazole-2- thiol(S7) ,5-{[4-(diethylamino) phenyl] diazenyl}-1,3,4- thiadiazole-2- thiol(S8) ,2- amino-5-[(5-mercapto-1,3

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Publication Date
Fri Sep 20 2024
Journal Name
Journal Of Nano Research
Impact of Copper Doping on Nanocrystalline SnO&lt;sub&gt;2&lt;/sub&gt; Thin Films Synthesized by Sol-Gel Coating and Chemical Bath Deposition for Gas Sensor Applications
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This work focuses on the preparation of pure nanocrystalline SnO2 and SnO2:Cu thin films on cleaned glass substrates utilizing a sol-gel spin coating and chemical bath deposition (CBD) procedures. The primary aim of this study is to investigate the possible use of these thin films in the context of gas sensor applications. The films underwent annealing in an air environment at a temperature of 500 C for duration of 60 minutes. The thickness of the film that was deposited may be estimated to be around 300 nm. The investigation included an examination of the structural, optical, electrical, and sensing characteristics, which were explored across various preparation circumstances, specifically focusing on varied

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Publication Date
Mon Oct 01 2018
Journal Name
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Fabrication of CdSe nanoparticles sensitized TiO 2 nanotube arrays via pulse electrodeposition for photoelectrochemical application
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Publication Date
Sun Dec 07 2014
Journal Name
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Estimation of Serum Osteocalcin Levels in Osteoporotic Postmenopausal Iraqi Women with Type 2 Diabetes Mellitus
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Background: Osteoporosis (OP) is a systemic disease characterized by low bone mass and micro architectural deterioration of bone tissue, resulting in an increased risk of fractures and has touched rampant proportions. Osteocalcin, one of the osteoblast-specific proteins, showed that its functions as a hormone improves glucose metabolism and reduces fat mass ratio. This study is aimed to estimate the osteocalcin and glucose level in blood serum of osteoporotic postmenopausal Women with and without Type 2 Diabetes.Materials and methods: 60 postmenopausal women with osteoporosis divided into two groups depending on with or without T2DM, 30 patients for each. Serum samples of 30 healthy postmenopausal women were collected as control group. Ost

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Publication Date
Thu Sep 26 2019
Journal Name
International Journal Of Pharmaceutical Research
Synthesis and identification of novel 2-thioxoimidazolidin- 4-one derivatives containing azo and ester groups
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The compounds 3-[4̄-(4˭-methoxybenzoyloxy) benzylideneamino]-2-thioxo-imidazolidine-4-one(3)aand 4-(1-(5-oxo- 2-thioxoimidazolidin-1-ylimino)ethyl)phenyl acetate(3)b were prepared from the reaction of aromatic aldehyde or ketone(1)a,bwith thiosemicarbazide to give aryl thiosemicarbazones(2)a,b ,followed by cyclization with ethylchloroacetate in the presence of fused sodium acetate. Treatment the compounds(3)a,bwith 4- hydroxybenzenediazoniumchloride yielded the correspondings4-((4-((4-hydroxyphenyl)diazenyl)-5-oxo-2- thioxoimidazolidin-1-ylimino)methyl)phenyl 4-methoxybenzoate(4)aand4-(1-(4-((4-hydroxyphenyl)diazenyl)-5-oxo-2- thioxoimidazolidin-1-ylimino)ethyl)phenyl acetate(4)b.The new 2-thioxo-imidazolidin-4-one with esters (5-7)a,b sy

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Publication Date
Mon Apr 01 2019
Journal Name
Biochemical And Cellular Archives
Prevalence of Hbv, Hcv and Hiv-1, 2 infections among patients in Saladin governorate, Iraq
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Hepatitis B and Hepatitis C viruses are the major health problem in the worldwide. In the Middle East, the prevalence of HBV in general population with the chronic infectionsis 2-5%,whereas the prevalence of HCV is about 1% in Arabian Gulf countries. World Health Organization (WHO) revealed that the risks of HBV and HCV transmissionas well as human immunodeficiency virus (HIV) through the transfusion of contaminated blood and blood products is high, because of the fragility of health services in these countries. Several viral diseases are transportby different modes like bloodtransfusion, sexual contact, and unsafe injections. The mostcommon blood-transmitted viruses are hepatitis B virus(HBV), hepatitis C virus (HCV) and humanimmunodeficie

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Publication Date
Sat Nov 04 2023
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Iraqi Journal Of Pharmaceutical Sciences( P-issn 1683 - 3597 E-issn 2521 - 3512)
Synthesis, Characterization, Anti-Inflammatory, and Antimicrobial Evaluation of New 2-Pyrazolines Derivatives Derived from Guaiacol
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Abstract:         Chalcones were used to synthesis series of 2-pyrazoline derivatives and evaluated their antimicrobial and anti-inflammatory activities        (E)-1,3-diphenylprop-2-en-1-one (1-5) were synthesized by Claisen-Schmidt Condensation method through the reaction of acetophenone with five various para substituted benzaldehyde in presence of KOH, the reaction monitoring by TLC and the result intermediates were checked by melting point and FT-IR Various 2-Pyrazoline derivatives were prepared by one pot reaction that involved the refluxing of (E)-1,3-diphenylprop-2-en-1-one (1–5) and Hydrazine monohydrate in the presence of glacial acetic acid for 24 hours at a temperature of (45–50) °C fo

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