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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 Dec 31 2015
Journal Name
Al-khwarizmi Engineering Journal
Experimental Study on the Effect of Insertion of Copper Lessing Rings in Phase Change Material (PCM) on the Performance of Thermal Energy Storage Unit
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Abstract

One of the most suitable materials to be used in latent heat thermal energy storage system (LHTES) are Phase change materials, but a problem of slow melting and solidification processes made many researchers focusing on how to improve their thermal properties. This experimental work concerned with the enhancing of thermal conductivity of phase change material. The enhancing method was by the addition of copper Lessing rings in phase change material (paraffin wax). The effect of diameter for the used rings was studied by using two different diameters (0.5 cm and 1cm). Also, three volumetric percentages of rings addition (3%, 6% and 10%) were tested for each diameter. The discharging process was done with

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Publication Date
Wed Jan 10 2018
Journal Name
Al–bahith Al–a'alami
Using of digital media and its effect on constructing the value system of Iraqi society (Field study on a sample of the audience for the city of Baghdad model)
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With the great development in the field of the Internet, the talk about the new media and its implications began, And its interactive services have made the future of media material sometimes participating in it and manufacturing it at other times,
the public is seeking information and choosing the appropriate ones, as well as exchanging messages with the sender after what the role of the receiver is just receiving information only.
This study aims to demonstrate the effects of using digital media in various forms and types to construct the value system of Iraqi society through the identification of the following aims:
Identify the most popular digital media for the Iraqi public in their daily lives on the Internet.
Identify

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Crossref
Publication Date
Wed Dec 13 2017
Journal Name
Al-khwarizmi Engineering Journal
Numerical Simulation of the Collector Angle Effect on the Performance of the Solar Chimney Power Plant
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Sloped solar chimney system is a solar chimney power plant with a sloped collector. Practically, the sloped collector can function as a chimney, then the chimney height can be reduced and the construction cost would be reduced.The continuity, Naver-stockes, energy and radiation transfer equations have been solved and carried out by Fluent software. The governing equations are solved for incompressible, 3-D, steady, turbulent standard model with Boussiuesq approximation  to develop for the sloped solar chimney system in this study and evaluate the performance of solar chimney power plant  in Baghdad city of Iraq numerically by Fluent (14) software with orking conditions such as solar radiation intensity (30

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Publication Date
Thu Jun 30 2022
Journal Name
Association Of Arab Universities Journal Of Engineering Sciences
The effect of soaking and wetting on the properties of the gypsum soil treated with polyurethane
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the shear strength parameters of the treated and untreated gypsum soil under the effect of four soaking and drying cycles has studied in this paper, moreover examined the effect of wetting and drying cycles on the collapse potential of the soil and comparing between the behavior of the treated and untreated gypsum soil under the effect of the two conditions. Gypsum soil sample brought from Sawa lake in Al Muthana governorate with the content of gypsum 65.5%, the polyurethane polymer (PP) was used with different percentages 3, 6, and 10% to enhance the mechanical properties of gypsum soil, model was prepared to achieve four soaking and drying cycle to the samples before testing, this model consists of an Aluminum plate base with dimensions 7

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Publication Date
Fri Dec 01 2017
Journal Name
Journal Of Economics And Administrative Sciences
“The impact of the critical factors for the transfer of knowledge on opportunities and strategic success”
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The current research discusses “The impact of the critical factors for the transfer of knowledge on opportunities and strategic success ", the attention have been increased on knowledge transfer and strategic success subjects because on being one of the important and contemporary issues, which have a significant impact on the existence of organizations and its future. The research aims to identify the critical factors for knowledge transfer in private high education environment which enables (the college community surveyed) to achieve strategic success, also the research sought to answer questions related to research problem by testing a number of major and minor hypothes in impact, in order to test the hypotheses I used a fiel

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Publication Date
Wed Apr 01 2020
Journal Name
Journal Of Economics And Administrative Sciences
The effect of credit risk indicators on the profitability of banks in the Arab gulf countries
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The purpose of this study is to investigate the effect of credit risk indicators on the Arab Gulf countries' banks Profitability over the period of 2015 to 2017.  The banking credit risk was calculated using non-performing loans ratio affecting banks profitability indicators like net income and by using fixed effect and random effect model analyses, the study found that increasing in non-performing loans ratio will decrease the net income in gulf banks, the study also found that personal loans represent the largest share of loans granted in gulf banks. Also, the study recommends the importance of developing the capabilities of credit departments in commercial banks in dealing with bad loans, and studying the financial statem

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Crossref
Publication Date
Thu Dec 26 2019
Journal Name
Bulletin Of The Iraq Natural History Museum (p-issn: 1017-8678 , E-issn: 2311-9799)
THE EFFECTS OF TEMPERATURE AND MOISTURE STRESS CONTENT ON THE EXTENSIVE CULTIVATION OF THE OYSTER MUSHROOM
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    Oyster mushroom (Pleurotus ostreatus (Jacq. ex Fr.) P. Kumm.) is involved in the destruction of dead wood which is the main place of settlement of several living organisms. After humification, dead wood also becomes an important component of forest soils.

 

    The purpose of the research is to study temperature and moisture conditions of extensive cultivation of oyster mushrooms on various wood substrates. To accomplish this goal, the following tasks were set: to determine the amount of effective stress temperatures and moisture content of substrates and their influence on the appearance of fruiting bodies of the oyster mushroom; to study the features of the extensive culti

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Scopus Crossref
Publication Date
Sun Jul 28 2024
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The Effect of the Audit Value on the Value Relevance of Accounting Information for Economic Units
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Abstract The study aims to clarify the value of auditing economic units and how it can be measured, which is one of the most important challenges to matching the Value Relevance of Accounting Information. The problem of the study was identified with questions that revolve around the extent to which it is possible to measure the value of auditing in Iraqi economic units and the extent to which the value of auditing affects the adequacy of accounting information. Through reviewing the studies discussing this topic, it was found that auditing can provide value through the performance of the auditor and adding value to the economic unit subject to audit. The study recommended the need to study the situational factors of auditing, whether exter

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Publication Date
Wed Jan 01 2014
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The effect of the self-scheduling strategy on the chemistry achievement of first intermediate female students
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Publication Date
Thu Dec 31 2020
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
The efficiency of the tax examiner and its impact on reducing the risk of tax evasion
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The research dealt with the effect of the tax examiner's efficiency in detecting tax evasion, as the research problem dealt with tax evasion, especially in Iraq, for many reasons and factors, including those related to tax administration represented in administrative corruption and the complexity of procedures in the tax accounting process and failure to achieve justice in the tax treatment, including the taxpayer himself, as he tries to evade for reasons Related to the level of tax awareness, loss of confidence in the tax administration, and reasons related to the state's inability to manage the services file well and its ability to achieve the set goals, This reflected negatively on the emergence of some of the consequences of

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