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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
Sun Aug 30 2020
Journal Name
Journal Of Economics And Administrative Sciences
The effect of the environmental management system on the clean production strategy / case study in Middle Refineries Company
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The aim of this research is to measure and analyze the gap between the actual reality and the requirements of the environmental management system in the middle refineries company/refinery cycle according to ISO14001: 2015, as well as to measure the availability of a clean production strategy and test the relationship and impact between the availability of the requirements of the standard and a clean production strategy for the actual reality in the company.

The research problem was determined by the extent to which the requirements of the environmental management system are applied according to ISO14001: 2015 in the middle refineries company? To what extent are the required clean production strategies ava

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Crossref
Publication Date
Wed Jan 08 2025
Journal Name
Journal Of Al-rafidain University College For Sciences ( Print Issn: 1681-6870 ,online Issn: 2790-2293 )
Utilizing the Error Correction Model to Investigate the Impact of Fluctuations in Bank Deposits on the Money Supply
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This paper assesses the impact of changes and fluctuations in bank deposits on the money supply in Iraq. Employing  the research constructs an Error Correction Model (ECM) using  monthly time series data from 2010 to 2015. The analysis begins with  the Phillips-Perron unit root test to ascertain the stationarity of the  time series and the Engle and Granger cointegration test to examine  the existence of a long-term relationship. Nonparametric regression functions are estimated using two methods: Smoothing Spline and M-smoothing. The results indicate that the  M-smoothing approach is the most effective, achieving the shortest adjustment period and the highest adjustment ratio for short-term disturbances, thereby facilitating a return

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Tue Jan 01 2019
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The effect of the -Zahorik- model on acquiring grammatical concepts among students of the College of Administration and Economics/University of Baghdad
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Publication Date
Thu Apr 30 2020
Journal Name
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The Effect of organizational stress on the Performance of professor at the Faculty of Economics and Commercial Sciences / University of Djelfa / Algeria
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The present study aims at identifying the effect of organizational pressure with its aspects (management, work team, nature and conditions of work, external environment) on job performance in all its dimensions (commitment and effort made, capabilities and the rapidity of performance, motivation and job satisfaction, work environment) for the university teacher at the Faculty of Economics, Commercial and Management Sciences at the University of Djelfa, Algeria.

     In this research, the descriptive analytical approach is used. Data was collected through the distribution of a questionnaire to a sample that included 130 permanent teachers before being analyzed using the (SPSS) statisti

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Publication Date
Sun Jul 09 2023
Journal Name
Journal Of Engineering
The Effect of Age and occupation on the Type and the Number of workers injuries in construction sector in Iraq
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World statistics proved that the most of work dangerous accidents, which causes death, are occurred in the construction works. These accidents related to many causes such as loss of workers experience and ignoring rules of safety requirements, especially young workers. Due to the risk of accidents that may occur in the site of work, the idea of this study crystallized to show the relationship between the age of worker and number of injuries and accidents, to identify the causes of these injuries, and to put the appropriate solutions to avoid or reduce the risk of work injuries. Also, the research shows the main principles of safety requirements to forming a clear picture about the subject of the study. A questioner form was prepared to c

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Thu Jun 30 2011
Journal Name
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The Effect of the Solution Heat Treatment on the Mechanical Properties of Aluminum-Copper Alloy (2024-T3) Using Rolling Process
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The effect of solution heat treatment on the mechanical properties of Aluminum-Copper alloy. (2024-T3) by the rolling process is investigated. The solution heat treatment was implemented by heating the sheets to 480 C° and quenching them by water; then forming by rolling for many passes. And then natural aging is done for one month. Mechanical properties (tensile strength and hardness) are evaluated and the results are compared with the metal without treatment during the rolling process. ANSYS analysis is used to show the stresses distribution in the sheet during the rolling process.  It has been seen that good mechanical properties are evident in the alloy without heat treatment due to the strain hardening and also the mechanical

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Publication Date
Sun Dec 31 2023
Journal Name
College Of Islamic Sciences
The relationship between the rule of mental improvement and ugliness and the objectives of Sharia And its impact on rulings
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The research addresses a fundamental Islamic jurisprudential Purposeful issue, which is (Sharia), and to indicate the impact of this on Islamic jurisprudence, deriving rulings and extracting purposes, and to repel the illusion that this issue is only doctrinal, and clarifying the aspects of similarities and links between them by explaining the origin of deriving the purposes of Islamic Law (Sharia) through the meanings and wisdom learned from the texts and the explanation of the rulings. The rulings of Islamic Law (Sharia) have urged bringing benefits and repelling harms, and that the path to do so is reason and its production. I began the research by defining the purposes of Islamic Law (Sharia), then defining the rule of rational right

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Publication Date
Sat Jan 01 2022
Journal Name
International Journal Of Economics And Finance Studies
THE IMPACT OF THE AUDIT COMMITTEE AND AUDIT TEAM CHARACTERISTICS ON THE AUDIT QUALITY: MEDIATING IMPACT OF EFFECTIVE AUDIT PROCESS
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Publication Date
Tue Dec 10 2024
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The Effect of Resistance Training Using Elastic Bands on the Developmentof Specific Endurance and Performance of the Oji-mata Skill
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t: - Sports training in itself is a means, not an end. It is the core process that involves using exercises to provide an opportunity for athletes to perform their duties with the highest level of efficiency by developing and enhancing their capabilities and potential, using them to gain the greatest benefit for themselves and, consequently, for their team. This requires the selection of various methods and different means of training, focusing on specific physical and skill-related aspects. Therefore, training plans should take into account individual differences between players. Many researchers and experts in the field of sports in general, and combat sports in particular, emphasize the importance of having a holistic approach in the tra

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Wed Jan 05 2022
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The effect of single superset exercises on the maximum strength of the limb muscles in bodybuilding for players (Classic Physique).
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HR Ghanim, GA Abdulhassan, International Journal of Early Childhood Special Education, 2022

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