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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
Thu Mar 30 2017
Journal Name
Iraqi Journal Of Pharmaceutical Sciences ( P-issn 1683 - 3597 E-issn 2521 - 3512)
The Effect of Long Term use of Glibenclamide on Serum and Urinary Sodium and Potassium Level in Type 2 DM Patients
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         Long-term use of sulfonylureas including chlorpropamide, is known to potentiate the antidiuretic action of arginine vasopressin (AVP), predisposing to hyponatremia.The present study was designed to evaluate the effect of long term use of glibenclamide on serum and urinary levels of sodium and potassium in Type 2 DM patients in Iraqi DM centers. Ninety eight patients with Type 2 DM who were maintained on different doses of glibenclamide for at least 1 year, attending the centre for Diabetes and Endocrinology in Al-Rusafa, Baghdad, were enrolled in the study, in addition to 15 normal healthy subjects. Patients were allocated into three groups according to the dose of glibenc

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Publication Date
Tue May 01 2018
Journal Name
Journal Of Physics: Conference Series
The partial substitution of copper with nickel oxide on the Structural and electrical properties of HgBa<sub>2</sub> Ca<sub>2</sub> Cu<sub>3x</sub>Ni<sub>x</sub> O<sub>8+δ</sub> superconducting compound
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Publication Date
Thu May 28 2020
Journal Name
Iraqi Journal Of Science
The Association Between IL-2 Gene (RS2069763 (Single Nucleotide Polymorphism and Type 2 Diabetes Mellitus in Iraqi Patients
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This research attempts to find the association between single nucleotide polymorphism (SNP) of IL2+166 gene (rs2069763) and type 2 diabetes mellitus (T2DM) in a sample of Iraqi patients. A total of 44 patients and 55 apparently healthy volunteers were genotyped for the SNP using polymerase chain reaction test. Three genotypes (GG, GT, and TT) corresponding to two alleles (G and T) were found to have SNP. Both study groups’ genotypes had a good agreement for the analysis of Hardy-Weinberg Equilibrium. The results revealed increased frequencies between the observed and expected GG and TT genotypes and IL2+166 SNP T allele in T2DM  patients (40.9 vs. 40.0 %; OR = 1.04; 95% CI, 0.47 - 2.31), whereas the values in the control group were

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Publication Date
Fri Feb 01 2019
Journal Name
Journal Of Physics: Conference Series
Study the effect of gamma Irradiation on the Superconducting Properties of HgBaSrCa<sub>2</sub>Cu<sub>3</sub>O<sub>8+δ</sub>
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Publication Date
Sun Aug 30 2020
Journal Name
Journal Of Economics And Administrative Sciences
Improve operational performance by simulating the Holonic manufacturing system A case study at the rubber product plant in Al-Najaf Al-Ashraf
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The research aims to improve operational performance through the application of the Holonic Manufacturing System (HMS) in the rubber products factory in Najaf. The problem was diagnosed with the weakness of the manufacturing system in the factory to meet customers' demands on time within the available resources of machines and workers, which led to time delays of Processing and delivery, increased costs, and reduced flexibility in the factory, A case study methodology used to identify the reality of the manufacturing system and the actual operational performance in the factory. The simulation was used to represent the proposed (HMS) by using (Excel 2010) based on the actual data and calculate the operational performance measures

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Publication Date
Tue Feb 01 2022
Journal Name
International Journal Of Nanoscience
Study of the Transition State of SnO<sub>2</sub> Cluster with NO<sub>2</sub> Gas Molecule via Density Functional Theory
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Density functional theory (DFT) with B3LYP level and 6-311G[Formula: see text] basis sets for light atoms like N and O and SDD basis sets for heavy atoms like Sn is used to examine the interaction of tin dioxide nanocrystals with nitrogen dioxide as a function of temperature from 273[Formula: see text]K to 373[Formula: see text]K through a Gaussian 09W software program. Gibbs free energy, enthalpy, and entropy of activation and reaction are calculated. The situation of transition of SnO2 clusters toward nitrogen dioxide is investigated. According to the findings, the activation energy of SnO2 clusters with nitrogen dioxide increases as the temperature rises (in negative value). Gauss view 0

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Publication Date
Sun Sep 03 2017
Journal Name
Baghdad Science Journal
Kinetic and Mechanistic Studies for the Gas-phase Reaction of Ozone with 2, 3-Dimethyl-2-Butene and 1, 3-Butadiene
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The reactions of ozone with 2,3-Dimethyl-2-Butene (CH3)2C=C(CH3)2 and 1,3-Butadiene CH2=CHCH=CH2 have been investigated under atmospheric conditions at 298±3K in air using both relative and absolute rate techniques, and the measured rate coefficients are found to be in good agreement in both techniques used. The obtained results show the addition of ozone to the double bond in these compounds and how it acts as function of the methyl group substituent situated on the double bond. The yields of all the main products have been determined using FTIR and GC-FID and the product studies of these reactions establish a very good idea for the decomposition pathways for the primary formed compounds (ozonides) and give a good information for the effe

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Publication Date
Thu Nov 08 2018
Journal Name
Chemistry – A European Journal
Magnetic Shielding, Aromaticity, Antiaromaticity and Bonding in the Low‐Lying Electronic States of S <sub>2</sub> N <sub>2</sub>
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Aromaticity, antiaromaticity and chemical bonding in the ground (S0), first singlet excited (S1) and lowest triplet (T1) electronic states of disulfur dinitride, S2N2, were investigated by analysing the isotropic magnetic shielding, σiso(r), in the space surrounding the molecule for each electronic state. The σiso(r) values were calculated by state-optimized CASSCF/cc-pVTZ wave functions with 22 electrons in 16 orbitals constructed from gauge-including atomic orbitals (GIAOs). The S1 and T1 electronic states were confirmed as 11Au and 13B3u, respectively, through linear response CC3/aug-cc-pVTZ calculations of the vertical excitation energies for eight singlet (S1–S8) and eight triplet (T1–T8) electronic states. The aromaticities of S

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Publication Date
Sun Dec 25 2022
Journal Name
Iraqi Journal Of Pharmaceutical Sciences ( P-issn 1683 - 3597 E-issn 2521 - 3512)
Epicatechin product of Camellia sinensis leaves detection by thin layer chromatography and high performance liquid chromatography
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The current study performed in order to detect and quantify epicatechin in two tea samples of Camellia sinensis (black and green tea) by thin layer chromatography (TLC) and high performance liquid chromatography (HPLC). Extraction of epicatechin from black and green tea was done by using two different methods: maceration (cold extraction method) and decoction (hot extraction method). Qualitative and quantitative determinations of epicatechin in two tea samples were investigated. Epicatechin identification was made by utilizing preliminary chemical tests and TLC. This identification was also boosted by HPLC and then quantified epicatechin in all ethyl acetate fractions of two tea samples. This research revealed the existence of epica

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Publication Date
Mon Feb 13 2023
Journal Name
Aip Conference Proceedings
composition,depiction,antibacterial,antioxidant,and cytotoxicity activities studies of a new nano-sized binuclear metal(||) schiff base complexes
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composition,depiction,antibacterial,antioxidant,and cytotoxicity activities studies of a new nano-sized binuclear metal(||) schiff base complexes