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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 Apr 18 2019
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Al-kindy College Medical Journal
Prevalence of H pylori in obese attending Obesity therapy Unit
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Background: Obesity is an increasing health problem in developed countries and has grown into a major global epidemic. Recent studies suggested colonization of the stomach by Hpylori might affect gastric expression of appetite- and satiety-related hormone and patients cured of H pylori infection gained weight. Obesity and Helicobacter pylori (H. pylori) are important because of the problems they lead and their frequency of occurrence.

Objectives: To find out the prevalence of H. pylori infection in obese.

Type of the study:A cross-sectional study

Methods: A total of 32 obese female admitted to the study. Body mass indices (BMI) of all subjects wer

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Tue Dec 03 2024
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The Time Machine: Scientific Advances and Social Milieus in H. G. Well's Vision of the Future
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Thu Jun 30 2022
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The Effectiveness of Monetary Policy in Neutralizing Oil Price Fluctuations on the Gross Domestic Product in Iraq for the Period (1990-2019)
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The research aimed to measure the reality of monetary policy and its role in neutralizing the impact of fluctuations in total domestic oil prices, through the most important monetary policy variable (money supply). An example of this is using a simple technique in the previous example, turning it into a straightforward user interface by (Judd and Kunee). After estimating the impact of the policy with the domestic gross domestic oil prices in Iraq, the effect of fluctuations in the domestic gross domestic oil prices in the simple regression model, while the morale of oil prices was not proven with a negative sign, while the morale of money supply and their impact on the increase of the domestic was proven in the multiple regressio

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Tue May 01 2018
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Fibrewise soft ideal topological space
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Wed Jan 01 2020
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<i>Insilico</i> and <i>in vitro</i> Approach for Design, Synthesis, and Anti-proliferative Activity of Novel Derivatives of 5-(4-Aminophenyl)-4-Substituted Phenyl-2, 4-Dihydro-3<i>H</i>-1, 2, 4-Triazole-3-Thione
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Sun Feb 28 2021
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Effects of Macroeconomic Variables on Gross Domestic Product in Saudi Arabia using ARDL model for the period 1993-2019
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This paper analyses the relationship between selected macroeconomic variables and gross domestic product (GDP) in Saudi Arabia for the period 1993-2019. Specifically, it measures the effects of interest rate, oil price, inflation rate, budget deficit and money supply on the GDP of Saudi Arabia. The method employs in this paper is based on a descriptive analysis approach and ARDL model through the Bounds testing approach to cointegration. The results of the research reveal that the budget deficit, oil price and money supply have positive significant effects on GDP, while other variables have no effects on GDP and turned out to be insignificant. The findings suggest that both fiscal and monetary policies should be fo

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Publication Date
Mon May 11 2020
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A Theoretical Investigation on Chemical Bonding of the Bridged Hydride Triruthenium Cluster: [Ru3 (μ-H)( μ3-κ2-Hamphox-N,N)(CO)9]
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Ruthenium-Ruthenium and Ruthenium–ligand interactions in the triruthenium "[Ru3(μ-H)(μ3-κ2-Hamphox-N,N)(CO)9]" cluster are studied at DFT level of theory. The topological indices are evaluated in term of QTAIM (quantum theory of atoms in molecule). The computed topological parameters are in agreement with related transition metal complexes documented in the research papers. The QTAIM analysis of the bridged core part, i.e., Ru3H, analysis shows that there is no bond path and bond critical point (chemical bonding) between Ru(2) and Ru(3). Nevertheless, a non-negligible delocalization index for this non-bonding interaction is calculated

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Fri Sep 15 2023
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Employing digital marketing through communication in promoting the commercial product
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In recent years, the means of communication have achieved a great generality that made them occupy, in a short time, the first ranks among the most widely used social networks in the world, due to the many services and advantages offered by this network to its users. It has led to a leap in the field of visual communication, especially since it relies mainly on the image Its dimensions make it a means of communication and transfer of ideas and meanings between the peoples of the world, and it also allows the inclusion of digital advertising content using multimedia with a degree of professionalism in other social networks, which allowed the various segments of society the opportunity to invest this network in their businesses of differen

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The Aestheticof Balance And Its Relationship To The Design of The Industrial Product Shape
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The study tagged: (The aesthetics of balance and its relationship to the design of the body of the industrial product) discussed the role of balance in the design of industrial products of different shapes, colors and sizes, as well as their function. Based on the research problem that was determined by the following question: What is the relationship between balance and the design of the body of the industrial product? The aim of the research is to: reveal the statement of the effectiveness of the balance in the design of the industrial product body.
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