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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
Sat Jan 01 2022
Journal Name
Proceeding Of The 1st International Conference On Advanced Research In Pure And Applied Science (icarpas2021): Third Annual Conference Of Al-muthanna University/college Of Science
Efficient approach for solving high order (2+1)D-differential equation
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Publication Date
Mon Apr 01 2019
Journal Name
Iraqi Journal Of Biotechnology
The Promising Anti-Tumor Impact of Newcastle Disease Virus Expressing IL-2 and P53 Genes in Many Cancer Cell Lines In vitro
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Abstract: Recombinant Newcastle disease virus (rNDV) has shown an anticancer effect in preclinical studies, but has never been tested in a lung cancer models. In this study we explored the anticancer activity of genetically modified NDV expressing IL-2-P53 (rClone30–IL-2-P53) in lung cancer model. We have cloned IL-2 and P53 genes and inserted them in the viral genome of New Castle Disease Virus to create a genetically modified rNDV- IL-2-P53 virus and tested the anti-tumor activity of the new virus in vitro on different types of cancer cell lines by MTT assay. TheIL-2 and P53 gene were successfully cloned and inserted into the viral genome by using a Mlu I and Sfi I endonucleases, viral vector was constructed correctly and successf

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Publication Date
Tue Jan 01 2019
Journal Name
International Journal Of Pharmaceutical Research
New method for the evaluation of propranolol with phosphotungstic acidvialong distance chasing photometer (NAG-ADF-300-2) using continuous flow injection analysis
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A new, simple and sensitive method was used forevaluation of propranolol withphosphotungstic acidto prove the efficiency, reliability and repeatability of the long distance chasing photometer (NAG-ADF-300-2) using continuous flow injection analysis. The method is based on reaction between propranolol and phosphotungstic acid in an aqueous medium to obtain a yellow precipitate. Optimum parameters was studied to increase the sensitivity for developed method. A linear range for calibration graph was 0.007-13 mmol/L for cell A and 5-15 mmol/L for cell B, and LOD 207.4792 ng/160 µL and 1.2449 µg/160 µL respectively to cell A and cell B with correlation coefficient (r) 0.9988 for cell A, 0.9996 for cell B, RSD% was lower than 1%, (n=8) for the

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Publication Date
Sun Dec 03 2017
Journal Name
Baghdad Science Journal
Synthesis and Characterization of Some Metal Complexes of [4-Methoxy-N-(pyrimidine-2-ylcarbamothioyl)benzamide]
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A new ligand [4-Methoxy -N-(pyrimidine-2-ylcarbamothioyl) benzamide] (MPB) was synthesized by reactioniofi(4-Methoxyibenzoyliisothiocyanate)withi(2-aminopyri-midine). The Ligand was characterized by elemental micro analysis (C.H.N.S),(FT-IR) (UV- Vis) and (1Hi,13CNMR)spectra. Some transition metals complexes of this ligand were prepared and characterized by (FT-IR, UV-Vis) spectra conductivity measurements magnetic susceptibility and atomic absorption. From the obtained results the molecular formula of all complexes was suggested to be [M(MPB)2Cl2] (M+2i=Cu, Mn, Co ,Ni ,Zn ,Cd and Hg),the proposed geometrical structure for all complexes was an octahedral.

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Publication Date
Sun Sep 01 2013
Journal Name
Baghdad Science Journal
Spectroscopic Characterization and Antimicrobial Activities of Some Heavy Metals Complexes of 2-hydroxy phenyl piperonalidene
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An antibacterial and antifungal piperonal-derived compound and its Rh(III), Pd(II), Pt(IV), and Cd(II) metal complexes were synthesized and characterized by spectroscopic methods, conductivity, metal analyses and magnetic moment measurements. The nature of the complexes formed in ethanolic solution was studied following the molar ratio method. From the spectral studies, octahedral geometry was suggested for rhodium (III) and platinum (IV) complexes, while a square planer structure was suggested for palladium (II) complex and a tetrahedral geometry for cadmium (II) complex. Structural geometries of these compounds were also suggested in gas phase by using hyperchem-8 program for the molecular mechanics and semi-empirical calculations.

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Publication Date
Tue Aug 05 2014
Journal Name
International Journal Of Engineering Sciences & Research Technology
Synthesis and Characterization of Some New Metal Complexes 2-(4-nitrophenyl azo)-2,4- dimethylphenol.
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The Ligand 2-(4-nitrophenyl azo)-2,4-dimethylphenol derived from 4-nitroaniline and 2,4-dimethylphenol was synthesized. The prepared ligand was identified by FT-IR and UV-Vis spectroscopic techniques. Treatment of the ligand with the following metal ions ( CuII , ZnII ,CdII and HgII) in aqueous ethanol with a 1:2 M:L ratio. Characterization of these compounds has been done on the basis of FT-IR and UV-Vis, as well as magnetic susceptibility and conductivity measurements. On the basis of physicochemical data tetrahedral geometries were assigned for the complexes.

Publication Date
Tue Jan 01 2013
Journal Name
Baghdad Science Journal
Detection of Type 2 Diabetes Mellitus in Serum from Women with Polycystic Ovarian Syndrome
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Polycystic ovary syndrome (PCOS) is one of the most common endocrine disorder. To determine the metabolic disorders in women with PCOS, (25) women with PCOS ages (15 - 47) years have been investigated and compared with (20) healthy individuals. All the studied groups were carried out to measure fasting blood sugar, (anti-GAD Ab, anti β-islet cell Ab by IFAT) and measured insulin level by ELISA. There was significant elevation in the concentration of fasting blood sugar than in control groups (p ≤ 0.05) and there was negative results for anti-GAD Ab and anti β-islet cell Ab by IFAT test for serum of women with PCOS, while there was significant differences in the insulin level for women with PCOS compared with control groups (p ≤ 0.05),

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Publication Date
Sun Sep 01 2013
Journal Name
Baghdad Science Journal
Synthesis of substituted (oxazepine, Diazepine, tetrazde) via Schiff Bases for 2- Aminobenzo Thaizole Derivatives
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This work includs synthesis of several Schiff bases by condensation of 6- methoxy – 2- amino benzothiazole with some aldehydes and ketones (2- hydroxyl benzaldehyde, 4- hydroxyl benzaldehyde, 4- N,N –dimethy amino acetophenone, benzophenone) to abtain schiff bases (1-5). These schiff bases were found to react with phthalate anhydride to give oxazepine derivatives (6-10) that were reacted with primary aromatic amines to give Diazepine derivatives (11-15). Besides, we prepared new tetrazole derivatives (16-20) from the reaction of the prepared Schiff bases with sodium azide in the prepared compounds that were characterized by physical properties, FT-IR and some of the 1H-NMR and 13C –NMR spectroscopy.

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Publication Date
Wed May 28 2025
Journal Name
Oxidation Communications
ESTIMATION OF GALECTIN-3 IN TYPE-2 DIABETIC PATIENTS AFTER VACCINATED AGAINST COVID-19"
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The rapid spread of the COVID-19 coronavirus in 2019 infected many people, primarily affecting the respiratory system. Both COVID-19 and type 2 diabetes have been associated with numerous risks that have become life-threatening. The study studied the link between galectin levels and some clinical characteristics in Iraqis with type 2 diabetes and COVID-19 against those without diabetes. The study included 120 patients and healthy men. Three groups were formed for this study depending on the initial mutant cell line: 80 samples of individuals with type 2 diabetes, aged 40–60 years, with and without COVID-19, were included in each of the first and second groups. The control group consisted of 40 research participants who were matched for ag

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Publication Date
Sun Mar 01 2009
Journal Name
Baghdad Science Journal
A Study of structural and electrical properties ofCuIn (Sex Te1-x) 2 thin films
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structural and electrical of CuIn (Sex Te1-x)2

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