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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 Feb 01 2019
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Journal Of Physics: Conference Series
Manufacturing and studying the effect of partial substitution on the properties of the compound Bi<sub>2-x</sub> Ag<sub>x</sub>Sr<sub>1.9</sub>Ba<sub>0.1</sub>Ca<sub>2</sub>Cu<sub>3</sub>O<sub>10+δ</sub> superconductors.
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Publication Date
Sat Feb 21 2026
Journal Name
Journal Of Baghdad College Of Dentistry
Early and delayed effect of 2% chlorhexidine on the shear bond strength of composite restorative material to dentin using a total etch adhesive
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Background: Lack of durability of the bond of the dental adhesive systems to tooth structure is one of the most important problems in tooth colored restorative work. This in vitro study was performed to evaluate the effect of 2% chlorhexidine gluconate(CHX) on dentin bond strength by using total etch adhesive system at twenty-four hours and three months of water storage. Material and methods:A flat dentin surface was prepared for forty sound human maxillary premolar teeth which were acid etched with 36% phosphoric acid gel after being divided randomly into four groups of ten teeth each according to storage time and CHX application, theCHX was applied for 60 seconds before adhesive application for groups I and III which were tested after twe

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Publication Date
Sun Sep 05 2010
Journal Name
Baghdad Science Journal
Composition operator induced by ?(z) = sz + t for which |s|?1, |t|<1 and |s|+|t|?1
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We study in this paper the composition operator that is induced by ?(z) = sz + t. We give a characterization of the adjoint of composiotion operators generated by self-maps of the unit ball of form ?(z) = sz + t for which |s|?1, |t|<1 and |s|+|t|?1. In fact we prove that the adjoint is a product of toeplitz operators and composition operator. Also, we have studied the compactness of C? and give some other partial results.

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Publication Date
Wed May 19 2010
Journal Name
Journal Of College Of Science, University Of Babylon
H-Point Standard Addition Method for Simultaneous Determination of Cimetidine and Erythromycin Ethylsuccinate Drugs Using Bromothymol Blue as a Chromogenic Complexing Agent
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The H-Point Standard Addition Method (H-PSAM) has been applied for spectrophotometric simultaneous determination of Cimetidine and Erythromycin ethylsuccinate using Bromothymol Blue (BTB) as a chromogenic complexing agent in a buffer solution at pH 5.5.

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Fri Apr 01 2016
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Journal Of Economics And Administrative Sciences
Application Tools Lean Six Sigma Definition and measurement phases in new product development. In the Electrical Industries State Company. case Study.
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methodology six sigma Help  to reduce defects by solving problems effectively, and works Lean to reduce losses through the flow of the manufacturing process and when integrating these two methodologies (Lean and six sigma), the methodology of Lean six sigma will form the entrance to the organizers of the optimization process and increase the quality and reduce lead times and costs . by focusing on the needs of the customer. this process uses statistical tools and techniques to analyze and improve processes.

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Wed Mar 10 2021
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synthesis and characterization of 2 hydroxy
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Publication Date
Sat Jun 12 2021
Journal Name
Biochemical And Cellular Archives
EFFECT OF SINGLE ORAL DOSE OF FUMONISIN B1 ON IMMUNOHISTOCHEMICAL EXPRESSION OF TLR-2 AND 4 IN MICE
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Fumonisin B1 is toxic secondary metabolites compound produced by Fusarium spp. on maize and maize products causes health problems to human and animal. Therefore, this research is planned to study the effect of FB1 on the expression of TLR-2 & 4 in liver and kidney cells of mice. Four group of male mice were orally administrated with single dose of FB1 toxin as the following: 0 ppb, 800 ppb, 1200 ppb and 1600 ppb. After two weeks all animals were sacrificed, liver and kidney autopsies were taken and the level of TLR-2 & 4 detected in each four group by immunohistochemistry technique (IHC). According to the IHC examination of groups (1, 2, 3 and 4) strong expression of TLR2 in liver and kidney were (0%, 33.3%, 100%, 100%), respectively. This

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Wed Jul 17 2024
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Healthcare
Impact of Nonsurgical Periodontal Treatment of Periodontitis Stages 2 and 3 on Oral Health-Related Quality of Life
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This study investigates the impact of nonsurgical periodontal treatment (NSPT) on oral health-related quality of life (OHRQoL) in patients with periodontitis stages (S)2 and S3, and the factors associated with the prediction of patient-reported outcomes. Periodontitis patients (n = 68) with moderately deep periodontal pockets were recruited. Responses to the Oral Health Impact Profile (OHIP)-14 questionnaire and clinical parameters including plaque index, bleeding on probing (BOP), probing pocket depth (PPD), and clinical attachment loss (CAL) were recorded. All patients received supra- and subgingival professional mechanical plaque removal. All clinical parameters and questionnaire responses were recorded again 3 months after NSPT.

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Publication Date
Thu Aug 20 2020
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Al-mustansiriyah Journal Of Science
The Importance of 2-AminoThiazole Schiff Bases as Antimicrobial and Anticancer Agents
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The pharmacophore 2-aminothiazole has an interesting role in pharmaceutical chemistry as this led to the synthesis of many types of compounds with diverse biological activity. Schiff base derivatives at the same time contribute to drug evolution importantly. In this review, the Schiff base derivatives of 2-aminothiazole formed and some of their metal complexes are being focused on, and the antimicrobial and anticancer activity of them is being illustrated.

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Publication Date
Thu Aug 20 2020
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Al-mustansiriyah Journal Of Science
The Importance of 2-AminoThiazole Schiff Bases as Antimicrobial and Anticancer Agents
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The pharmacophore 2-aminothiazole has an interesting role in pharmaceutical chemistry as this led to the synthesis of many types of compounds with diverse biological activity. Schiff base derivatives at the same time contribute to drug evolution importantly. In this review, the Schiff base derivatives of 2-aminothiazole formed and some of their metal complexes are being focused on, and the antimicrobial and anticancer activity of them is being illustrated.

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