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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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Mon Apr 18 2022
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Effect of Varying AgNO3 and CS(NH2)2 Concentrations on Performance of Ag2S/ZnO NRs/ITO Photoanode
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This research focuses on improving the photoelectrochemical performance of binary heterostructure Ag2S/ZnO NRs/ITO by manipulating synthesis conditions, particularly the concentrations of sliver nitrate AgNO3 and thiourea CS(NH2)2. The photoelectrochemical performance of Ag2S/ZnO nanorods on indium tin oxide (ITO) nanocomposite was compared to pristine ZnO NRs/ITO photoanode. The hydrothermal technique, an eco-friendly, low-cost method, was used to successfully produce Ag2S/ZnO NRs at different concentrations of AgNO3 and CS(NH2)2. The obtained thin films were characterized using field emission scanning electron microscopy (FESEM), energy-dispersive X-ray spectroscopy (EDS), X-ray diffraction (XRD), ultraviolet-visible spectroscopy

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Sat Dec 31 2016
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A Comparison of Sagittal Sections of Short T1inversion Recovery and T2 Weighted Fast Spin Echo Magnetic Resonance Sequences for Detection of Multiple Sclerosis Spinal Cord Lesions
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Background: Multiple sclerosis is a chronic autoimmune inflammatory demyelinating disease of the central nervous system of unknown etiology. Different techniques and magnetic resonance image sequences are widely used and compared to each other to improve the detection of multiple sclerosis lesions in the spinal cord. Objective: To evaluate the ability of MRI short tau inversion recovery sequences in improvementof multiple sclerosis spinal cord lesion detection when compared to T2 weighted image sequences. Type of the study: A retrospective study. Methods: this study conducted from 15thAugust 2013 to 30thJune 2014 at Baghdad teaching hospital. 22 clinically definite MS patients with clinical features suggestive of spinal cord involvement,

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Sun Mar 04 2018
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Synthesis and Characterization of a Molecularly Imprinted Polymer for Diclofenac Sodium Using (2-vinylpyridine and 2-hydroxyethyl metha acrylate) as the Complexing Monomer
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Four electrodes were synthesized based on molecularly imprinted polymers (MIPs). Two MIPs were prepared by using the diclofenac sodium (DFS) as the template, 2-hydroxy ethyl metha acrylate(2-HEMA) and 2-vinyl pyridine(2-VP) as monomers as well as divinyl benzene and benzoyl peroxide as cross linker and initiator respectively. The same composition used for prepared non-imprinted polymers (NIPs) but without the template (diclofenac sodium). To prepared the membranes electrodes used different plasticizers in PVC matrix such as: tris(2-ethyl hexyl) phosphate (TEHP), tri butyl phosphate (TBP), bis(2-ethyl hexyl) adipate (BEHA) and tritolyl phosphate (TTP). The characteristics studied the slop, detection limit, life time and linearity range of DF

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Fri Jul 28 2023
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Tubular Magnetic Shielding Scan (TMSS): A New Technique for Molecular Space Exploration. (i) The Case of Aromaticity of Benzene and [<i>n</i>]Paracyclophanes
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Both traditional and novel techniques were employed in this work for magnetic shielding evaluation to shed new light on the magnetic and aromaticity properties of benzene and 12 [n]paracyclophanes with n = 3–14. Density functional theory (DFT) with the B3LYP functional and all-electron Jorge-ATZP and x2c-TZVPPall-s basis sets was utilized for geometry optimization and magnetic shielding calculations, respectively. Additionally, the 6-311+G(d,p) basis set was incorporated for the purpose of comparing the magnetic shielding results. In addition to traditional evaluations such as NICS/NICSzz-Scan, and 2D-3D σiso(r)/σzz(r) maps, two new techniques were implemented: bendable grids (BGs) and cylindrical grids (CGs) of ghost atoms (Bqs). BGs a

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Publication Date
Fri Jun 05 2026
Journal Name
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Assessment of tongue space area in a sample of Iraqi adults with class I dental and skeletal pattern
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Background: Lateral cephalometric radiography is commonly used as a standard tool in orthodontic assessment and treatment planning. This study aimed to determine the tongue and surrounding space area in a sample of Iraqi adults with class I dental and skeletal pattern. Materials and methods: The study included thirty healthy subjects (15 males and 15 females) with an age ranged between 23-34 years and class I dental and skeletal pattern with no history of any sleep related disorders. The assessed cephalometric measurement included length and height of the tongue and position of hyoid bone from cervical line. Descriptive statistics were obtained for the data. Genders difference was evaluated by independent sample t-test. Results: There wer

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Sat Jun 12 2021
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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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Synthesis, Characterization and Thermal Study of Some New Metal Ions Complexes with a New Azo 2-((2-(1H-Indol-2- yl)ethyl)diazinyl)-5-aminophenol
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This research includes the preparation of a new azo 2-((2-(1H-indol-2- yl)ethyl)diazinyl)-5-aminophenol, in which the diazonium salt of 2(1H– Indole–3yl)- ethylamine reacts with a compound 3-aminophenol, and complexes have been prepared with the ions of Ni (II), Pd(II), Pt(IV), and Au(III). The characteristics of compounds include F.A.A, (C. H .N and O), 1H & 13C-NMR, IR, LC-Mass , UV-Vis spectral, DSC/TGA curve, the measurements of magnetic, and molar conductance. Each complex has an amount of [1:1] [M:L] and does not contain electrolytes. Based on the obtained results, molecular structural and geometry have been octahedral geometry suggest of Pt(IV) complex and tetrahedral of Ni (II)complex, the square planar of both Pd(II) and Au(III

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Thu Aug 20 2020
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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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