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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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Sun Jan 01 2023
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Photocatalytic degradation of Congo red dye using magnetic silica-coated Ag2WO4/Ag2S as Type I heterojunction photocatalyst: Stability and mechanisms studies
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In the present study, magnet silica-coated Ag2WO4/Ag2S nanocomposites (FOSOAWAS) were fabricated via a multistep method to address the drawbacks related to single photocatalysts (pure Ag2WO4 and pure Ag2S) and to clarify the significant influence of semiconductor heterojunction on the enhancement of visible-light-driven organic degradation. Different techniques were performed to investigate the elemental composition, morphology, magnetic and photoelectrochemical properties of the fabricated FOSOAWAS photocatalyst. The FOSOAWAS photocatalyst (1 g/L) exhibited excellent photodegradation efficiency (99.5%) against Congo red dye (CR = 20 ppm) after 140 min of visible-light illumination. This result confirmed the ability of the heterojunction be

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Fri Aug 18 2023
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Synthesis, characterization, and antimicrobial evaluation of new Schiff bases derived from vanillic acid conjugated to heterocyclic 4H-1,2,4-triazole-3-thiol
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A multistep synthesis was established for the preparation of a new vanillic acid-1, 2, 4-1triazole-3-thiol conjugate (4). Finally, several aromatized aldehydes reacted with compound (4) to produce Schiff bases derivatives (5–11). The purpose of this research is to prepare new vanillic acid derivatives with 1, 2, 4-triazole-3-thiol heterocyclic ring structures and to evaluate their antimicrobial activity in a preliminary assessment. Fourier-transform infrared (FT-IR) and proton nuclear magnetic resonance spectroscopy (1H-NMR) were used to verify the structures of the newly synthesized compounds. all the final synthesized compounds (

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Detection, purification and characterization of a bacteriocin produced by Bacillus subtilis NK16 exhibits a significant antimicrobial activity against clinical Staphylococcus spp.
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Bacteriocin is an important antimicrobial peptide that can be used in industrial and medical fields due to its characteristics of antibacterial, food preservation and anticancer activities. Fifty isolates of Bacillus sp were collected from different soil samples which were already recognized via morphological and biochemical identification process. The isolates were screened for bacteriocin production effective against Staphylococcus spp in order to select the highest producing isolate. The isolate NK16 showed the maximum bacteriocin production (80 AU/ml) which was further characterized as Bacillus subtilis NK 16 through using API identification system (API 20E and API 50CHB). Then, next step was to detect the optimal conditions for maximum

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Effects of wind, global warming and fear in a disease-induced Hassell-Varley predator-prey model through Caputo fractional order derivative
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Potential effects of miR‑146 expression in relation to malondialdehyde as a biomarker for oxidative damage in patients with breast cancer
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Thu Oct 01 2020
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Chemical-Free Greywater Treatment Using Aeration, Sedimentation, Followed by Granular Activated Carbon Filter (GAC) -A Case Study of Baghdad city household
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Greywater is a possible water source that can be improved for meeting the quality required for irrigation. Treatment of greywater can range from uncomplicated coarse filtration to advanced biological treatment. This article presents a simple design of a small scale greywater treatment plant, which is a series of physical and natural processes including screening, aeration, sedimentation, and filtration using granular activated carbon filter and differentiates its performance with sand filter. The performance of these units with the dual filter media of (activated carbon with sand) in treatment of greywater from Iraqi house in Baghdad city during 2019 and that collected from several points including washbasins, kitchen si

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Wed Jan 29 2020
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Neutrophil/lymphocyte and platelet/lymphocyte ratios as potential markers of disease activity in patients with Ankylosing spondylitis: a case-control study
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Abstract<sec> <title>Background

The neutrophil/ lymphocyte ratio (NLR) and platelet/lymphocyte ratio (PLR) have the potential to be inflammatory markers that reflect the activity of many inflammatory diseases. The aim of this study was to evaluate the NLR and PLR as potential markers of disease activity in patients with ankylosing spondylitis.

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The study involved 132 patients with ankylosing spondylitis and 81 healthy controls matched in terms of age and gender. Their sociodemographic data, disease activity scores using the Bath Ankylosing

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Preparation, <i>In-vitro, Ex-vivo</i>, and Pharmacokinetic Study of Lasmiditan as Intranasal Nanoemulsion-based <i>In Situ</i> Gel
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Lasmiditan (LAS) is a recently developed antimigraine drug and was approved in October, 2019 for the treatment of acute migraines; however, it suffers from low oral bioavailability, which is around 40%.

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This study aimed to improve the LAS bioavailability via formulation as nanoemulsionbased in situ gel (NEIG) given intranasally and then compare the traditional aqueous-LASsuspension (AQS) with the two successful intranasal prepared formulations (NEIG 2 and NEIG 5) in order to determine its relative bioavailability (F-relative) via using rabbits.

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Comparative Study of Genomic DNA Extraction Protocols from Whole Blood for P53 Gene Polymorphism in Persons with and without Prostate Cancer
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In latest decades, genetic methods have developed into a potent tool in a number of life-attaching applications. In research looking at demographic genetic diversity, QTL detection, marker-assisted selection, and food traceability, DNA-based technologies like PCR are being employed more and more. These approaches call for extraction procedures that provide efficient nucleic acid extraction and the elimination of PCR inhibitors. The first and most important stage in molecular biology is the extraction of DNA from cells. For a molecular scientist, the high quality and integrity of the isolated DNA as well as the extraction method's ease of use and affordability are crucial factors. The present study was designed to establish a simple, fast

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In diabetes, impaired wound healing and other tissue abnormalities are considered major concerns. Many factorsaffect the time and quality of wound healing. One of the purposes of medical sciences is wound healing in a short time withreduced side effects. The herbal products are more precious in both prophylaxis as well as curative in delayed diabetic woundhealing activity when compared to synthetic drugs.A wide range of evidence has shown that capers plant possesses differentbiological effects, including antioxidant, anticancer and antibacterial effects. Phytochemical analysis shows thatC. spinosahashigh quantities of bioactive constituents, including polyphenolic compounds, which are responsible for its health-promotingeffects. The healing

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