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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 Jun 01 2017
Journal Name
Research Journal Of Pharmaceutical, Biological And Chemical Sciences
Synthesis, Characterization and antibacterial activity of mixed ligands complexes of some metal ions with 2-aminophenol and tributylphosphine
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Four metal complexes mixed ligand of 2-aminophenol (2-AP) and tributylphosphine (PBu3) were produced in aqueous ethanol with (1:2:2) (M:2-AP:PBu3). The prepared complexes were identified by using flame atomic absorption, FT.IR and UV-Vis spectroscopic methods as well as magnetic susceptibility and conductivity measurements. In addition antibacterial activity of the two ligands and mixed ligand complexes oboist three species of bacteria were also examined. The ligands and their complexes show good bacterial activities. From the obtained data the octahedral geometry was suggested for all prepared complexes. Keywords: Mixed ligand complexes, spectral studies, 2-aminophenol, tributylphosphine.

Publication Date
Fri Mar 01 2024
Journal Name
Baghdad Science Journal
Synthesis and Characterization of New 2-amino-5-chlorobenzothiazole Derivatives Containing Different Types of Heterocyclic as Antifungal Activity
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Nine new compounds of 2-amino-5-chlorobenzothiazole derivatives were synthesized. These new compounds were formed through the reaction of 2-amino-5-chlorobenzothiazole 1 with ethyl chloroacetate and KOH, which gave an ester derivative 2, followed by refluxing compound 2 with hydrazine hydrate to afford hydrazide derivative 3. The reaction of compound 3 with CS2 and KOH gave 1,3,4-oxadiazole-2-thiol derivative 4, and then the reaction of compound 2 with thiosemicarbazide to produce compound 5  then treated it with 4%NaOH led to ring closure to provide 1,2,4-triazole-3-thiol derivative

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Publication Date
Fri Jul 24 2020
Journal Name
Al-kindy College Medical Journal
A review study of targeting of AAK1 and JAK1/2 using baricitinib in COVID-19 infected human cells
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     The outbreak of a current public health coronavirus 2019 disease is a causative agent of a serious acute respiratory syndrome and even death. COVID-19 has exposed to multi-suggested pharmaceutical agents to control this global disease. Baricitinib, a well-known antirheumatic agent, was one of them. This article reviews the likely pros and cons of baricitinib in attenuation of COVID-19 based on the mechanism of drug action as well as its pharmacokinetics. The inhibitory effect of baricitinib on receptor mediated endocytosis promoter, AKK1, and on JAK-STAT signaling pathway is benefacial in inhibition of both viral assembling and inflammation. Also, its pharmacokinetic has encouraged the physicians toward the drug

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Publication Date
Tue Jan 01 2019
Journal Name
Baghdad Science Journal
Synthesis of new five-membered hetrocyclic compounds from 2-furfuryl mercaptan derivative and evaluation of their biological activity
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A theoretical and protection study was conducted of the corrosion behavior of carbon steel surface with different concentrations of the derivative (Quinolin-2-one), namly (1-Amino-4,7-dimethyl-6-nitro-1H-quinolin-2-one (ADNQ2O)). Theoretically, Density Functional Theory (DFT) of B3LYP/ 6-311++G (2d, 2p) level was used to calculate the optimized geometry, physical properties and chemical inhibition parameters, with the local reactivity to predict both the reactive centers and to locate the possible sites of nucleophilic and electrophilic attacks, in vacuum, and in two solvents (DMSO and H2O), all at the equilibrium geometry. Experimentally, the inhibition efficiencies (%IE) in the saline solution (of 3.5%) NaCl were studied using potentiomet

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Publication Date
Mon Feb 04 2019
Journal Name
Journal Of The College Of Education For Women
The Study of Traffic on The Roads The Governorate Of Karbala
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The study of traffic on the roads the governorate of Karbala, Where is the study of traffic on the roads measure is necessary to determine the extent of the road and highlighting the importance of its role in the transfer of individuals from original to destination as well as the importance of the region that attracted its movement. This research aims to analyze the traffic in the governorate of Karbala through the study and analysis of surveys of traffic that were made in the governorate. Based on this analysis, it has been reached to identify volumes of the traffic and its density and how the roads are efficient and accommodating these volumes, the results of the traffic survey of the studied roads in the area of the study have shown t

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Publication Date
Fri Jan 01 2021
Journal Name
Journal Of Economics And Administrative Sciences
The effect of strategic alignment on the reputation of the organization
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The current study aims to determine the extent of SOMO's interest in strategic alignment operations and whether this interest is sufficient to be reflected in enhancing its organizational reputation. The field of research was in the oil marketing company SOMO. The managers in the top management within this company were targeted and the questionnaire was used as a data collection tool. The study population (109), (105) questionnaires were distributed, (94) questionnaires and (11) questionnaires were not retrieved, and the valid questionnaires had reached (91) and the analytical and descriptive approach was used for the study, the current research found to find A direct relationship and a positive effect of strategic

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Publication Date
Sun Nov 24 2024
Journal Name
Polymer-plastics Technology And Materials
Li <sub>2</sub> CO <sub>3</sub> as a Modifier for PVA/PVP/PEG Blend Polymer Electrolytes: Effects on Structural Integrity, Electrical Performance, Thermal Behavior and Optical Properties
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Publication Date
Sun Dec 15 2019
Journal Name
Journal Of Baghdad College Of Dentistry
Association of a genetic variant (rs689466) of Cyclooxygenase-2 gene with chronic periodontitis in a sample of Iraqi population
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Background: periodontitis is a chronic inflammatory disease causing destruction of the tooth supporting structures, initiated by dental plaque and modified by environmental and genetic risk factors. Cyclooxygenase-2 (COX-2) enzyme is responsible for the production of prostaglandin E2, an important mediator in the chronic periodontitis (CP) pathogenesis. Polymorphisms in COX-2 gene have linked to CP in different populations. Aim: To study the association between Cyclooxygenase-2 single nucleotide polymorphism rs689466 (-1195A/G SNP) and chronic periodontitis in a sample of Iraqi population. Methods: One hundred Iraqi subjects divided into two groups: case group consisted of 70 CP patient (35 males and 35 females) with age range 30-55 year

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Publication Date
Sun Jul 01 2018
Journal Name
Journal Of Global Pharma Technology
Synthesis of New 2, 4, 5-triphenyl imidazole Derivatives Derived from benzoin and Studying their Biological Activity
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compound [1] was formed from the reaction of benzoin and benzaldehyde in the presence of ammonia, which was reacted with sodium hydride in DMF to obtain imidazole salt. This salt was reacted with adipoyl chloride to give compound [2]. Acid hydrazide derivative [3] was obtained from the reaction of compound [2] with hydrazine hydrate. After that Shiff bases [4-9] have been synthesized from the reaction of compound [3] with different aromatic aldehydes. These new formed compounds were diagnosed by 13C-NMR, 1H-NMR for some of them (in Ahl-Albate University in Jordan) and FT-IR spectroscopy (In Baghdad University). All of the prepared products have been studied their biological activities toward two kinds of bacteria. These products show

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Publication Date
Sun Jun 05 2016
Journal Name
Baghdad Science Journal
Evaluation of Serum Malondialdehyde, Glutathione and Lipid Profile Levels in Iraqi Females with Type 2 Diabetes Mellitus
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This study is carried out on patients with type 2 diabetes mellitus to assess the lipid profile, malondialdehyde and glutathione. Our study is concerned with 51 (Iraqi Arab females) patients of type 2 diabetes mellitus compared with 31 control subjects unified in age, sex and ethnic background. Lipid profile is measured by using commercially available kits, while the serum MDA and glutathione levels are measured by means of sandwich ELISA test using commercially available kits. Serum MDA is significantly higher (P<0.001) while glutathione is significantly lower (P<0.001) in type 2 diabetic patients when compared to the control. The normal levels of MDA (3.82 ± 0.77n mol/ml) and GSH (2.23 ± 0.54 µg/ml) recorded for the non-diabetic female

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