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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
Sat May 20 2023
Journal Name
Baghdad Science Journal
Synthesis, Characterization and Anticancer Activity of Chitosan Schiff Base / PVP Gold Nano Composite in Treating Esophageal Cancer Cell Line
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In the present paper, chitosan Schiff base has been synthesized from chitosan’s reaction with the salicyldehyde. The AuNPs was manufacture by extract of onion peels as a reducing agent. The Au NPs that have been prepared were characterized through the UV-vis spectroscopy, XRD analyses and SEM microscopy. The polymer blends of the chitosan Schiff base / PVP has been prepared through using the approach of solution casting. Chitosan Schiff base / PVP Au nano-composites was prepared. Nano composites and polymer blends have been characterized by FTIR which confirm the formation of Schiff base by revealing a new band of absorption at 1651cm-1 as a result of the (C=N) imine group. SEM, DSC and TGA confirms the thermal stability of the pr

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Publication Date
Fri Aug 09 2024
Journal Name
The Egyptian Journal Of Neurology, Psychiatry And Neurosurgery
Patterns and sociodemographic characteristics of substance abuse among hepatitis C virus-infected patients in Iraq: a cross-sectional study
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Abstract<sec> <title>Background

Substance use disorders are a widely recognized problem among hepatitis C-infected patients; moreover, substance abuse by intravenous injection is a common mode of transmission of the hepatitis C virus worldwide. The frequency of substance use disorders and their relation to hepatitis C infection are still unknown in Iraq. This cross-sectional study, conducted among a sample of hepatitis C- infected patients attending the Gastrointestinal Tract Center in Baghdad Medical City, aimed to examine the prevalence of substance use disorders, the sociodemographic characteristics of the abusers, and the relation between intravenous

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Publication Date
Tue Jun 20 2023
Journal Name
Baghdad Science Journal
Insulin Like Growth Factor Binding Protein 7 as a Novel Diagnostic Marker in Sera of Iraqi Patients with Acromegaly
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The purpose of this study was to measure serum levels of insulin-like growth factor-binding protein (IGFBP7), Insulin-like Growth Factor 1 (IGF-1), Growth Hormone (GH), Interleukin 6 (IL-6) and insulin in acromegaly patients and healthy controls. The acromegaly group had 60 patients, while the population group had 30 people who had never had acromegaly before. The concentration of IGFBP7, IGF-1, GH, IL-6, and insulin were determined. The results of the present study indicate that IGFBP7 level in the acromegaly group was significantly lower (1.690.07 ng/mL vs. 2.740.12 ng/mL, respectively, p = 0.001). IGF-1, GH, IL-6, and insulin concentrations were also significantly higher in acromegaly patients. The diagnostic accuracy (2.194) was exce

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Publication Date
Sat Feb 01 2020
Journal Name
Journal Of Green Engineering
Water distribution and interference of wetting front in stratified soil under a continues and an intermittent subsurface drip irrigation
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Publication Date
Thu Apr 20 2023
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Evaluation of Adiponectin, Irisin, Vitamin D Levels and Their Relation in Iraqi Patients with Non alcoholic Fatty Liver Disease
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Non-alcoholic fatty liver disease (NAFLD) is one of chronic liver and defines by fat accumulation ≥5% in liver which can progresses to non-alcoholic steatohepatitis (NASH). NAFLD related to obesity as well as non obese individuals. Adiponectin is a cytokine secreted from adipose tissue involved NAFLD pathogenesis and liked with obesity. Irisin is a myokine, has a convenient effect against metabolic diseases such as obesity, disylipemia diabetes type 2 and reversed liver steatosis and may be related with NAFLD.  Vitamin D is one of the fat soluble vitamins and more precisely as a pro-hormone through its metabolite (1,25(OH)2 cholecalciferol) the major steroid hormone. After the skin exposure to the light, vitamin D undergoes to

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Publication Date
Sun Nov 01 2020
Journal Name
Iop Conference Series: Materials Science And Engineering
Thermophysical properties of [EMIM][BF<sub>4</sub>] and [HMIM][PF<sub>6</sub>] imidazolium ionic liquids with MWCNTs
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Abstract<p>In this study, several ionanofluids (INFs) were prepared in order to study their efficiency as a cooling medium at 25 °C. The two-step technique is used to prepare ionanofluid (INF) by dispersing multi-walled carbon nanotubes (MWCNTs) in two concentrations 0.5 and 1 wt% in ionic liquid (IL). Two types of ionic liquids (ILs) were used: hydrophilic represented by 1-ethyl-3-methylimidazolium tetrafluoroborate [EMIM][BF<sub>4</sub>] and hydrophobic represented by 1-hexyl-3-methylimidazolium hexafluorophosphate [HMIM][PF<sub>6</sub>]. The thermophysical properties of the prepared INFs including thermal conductivity (TC), density and viscosity were measured experimental</p> ... Show More
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Publication Date
Mon Aug 01 2022
Journal Name
Journal Of Engineering
Production of Load Bearing Concrete Masonry Units (blocks) From Green Concrete Containing Plastic Waste and Nano Silica Sand Powder
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Industrial development has recently increased, including that of plastic industries. Since plastic has a very long analytical life, it will cause environmental pollution, so studies have resorted to reusing recycled waste plastic (sustainable plastic) to produce environmentally friendly concrete (green concrete). In this research, producing environmentally friendly load-bearing concrete masonry units (blocks) was considered where five concrete mixtures were compressed at the blocks producing machine. The cement content reduced from 400 kg/m3 (B-400) to 300 kg/m3 (B-300) then to 200 kg/m3 (B-200). While (B-380) was produced using 380 kg/m3 cement and 20 kg/m3 nano-sil

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Publication Date
Sat Apr 01 2023
Journal Name
Baghdad Science Journal
Equilibrium, Kinetic, and Thermodynamic Study of Removing Methyl Orange Dye from Aqueous Solution Using Zizphus spina-christi Leaf Powder
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In this study, Zizphus spina-christi leaf powder was applied for the adsorption of methyl orange. The effect of different operating parameters on the Batch Process adsorption was investigated such as solution pH (2-12), effect of contact time (0-60 min.), initial dye concentration (2-20 mg/L), effect of adsorbent dosage (0-4.5 g) and effect of temperature (20-50ᵒC). The results show a maximum removal rate and adsorption capacity (%R= 23.146, qe = 2.778 mg/g) at pH = 2 and equilibrium was reached at 40 min. The pseudo- second-order kinetics were found to be best fit for the removal process (R2 = 0.997). Different isotherm models (Langmuir, Freundlich, Dubini-Radushkevich,Temkin)  were applied in this stud

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Publication Date
Fri Dec 01 2023
Journal Name
Applied Energy
Deep clustering of Lagrangian trajectory for multi-task learning to energy saving in intelligent buildings using cooperative multi-agent
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The intelligent buildings provided various incentives to get highly inefficient energy-saving caused by the non-stationary building environments. In the presence of such dynamic excitation with higher levels of nonlinearity and coupling effect of temperature and humidity, the HVAC system transitions from underdamped to overdamped indoor conditions. This led to the promotion of highly inefficient energy use and fluctuating indoor thermal comfort. To address these concerns, this study develops a novel framework based on deep clustering of lagrangian trajectories for multi-task learning (DCLTML) and adding a pre-cooling coil in the air handling unit (AHU) to alleviate a coupling issue. The proposed DCLTML exhibits great overall control and is

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Publication Date
Fri Dec 01 2023
Journal Name
Materials Today Sustainability
Structure and performance of polyvinylchloride microfiltration membranes improved by green silicon oxide nanoparticles for oil-in-water emulsion separation
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