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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
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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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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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
Thu Jun 30 2022
Journal Name
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The Impact of Governance Mechanisms on the Accounting Disclosure of the Sustainable Development of Iraqi Economic Units
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The research aims to demonstrate the impact of governance mechanisms on the quality of financial reports in the light of the accounting disclosure for sustainable development represented in (accounting disclosure for economic development, accounting disclosure for environmental development, and accounting disclosure for social development) in a sample of banks listed in the Iraq Stock Exchange.

Governance mechanisms were measured by evaluating and analyzing the mechanisms in banks for the research sample consisting of (15) banks, based on the governance guide issued by the Central Bank, as well as the banks’ financial reports for the years 2016 -2018, and the dimensions of accounting disclosure for sust

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Crossref (2)
Crossref
Publication Date
Fri Jun 08 2012
Journal Name
Journal Of The College Of Basic Education
Study the adsorption of diphenhydramine – HCl on Iraqi bauxite
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Drug overdose and poisoning are common clinical problems and could occur with Diphenhydramine hydrochloride (DFH) (one of anti histaminic drug ). It therefore important to study the adsorption of the DFH on pharmaceutical adsorbents which could serve as possible antidotes for the emergency treatment of DFH overdose or poisoning when they occur. The rate and extent of adsorption of DFH on some pharmaceutical adsorbents, bauxite were investigated spectra photometrically also the effect temperature, pH, presence of sucrose as additive have been studied as well, adsorbent's weight and partical size.The equilibrium adsorption contact times were determined for clay surface. Adsorption isotherms have been analyzed by the freundlich model. The appa

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Publication Date
Tue Aug 15 2023
Journal Name
Journal Of Economics And Administrative Sciences
The Influence of Customer Knowledge Management on Sustainable Promotion
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This research has investigated the effect of the customer knowledge management CKM in sustainable promotion SP. The research conducted a quantitative method on a sample of employees in the Al-Furat State Company for Chemical Industries affiliated / the Ministry of Industry and Minerals in Iraq. The research’s problem presented a set of questions, one of the most important was (is there a relation and impact between the dimensions of customer knowledge management and sustainable promotion). The aim of the research is to identify the extent to which customer knowledge management activities are applied in understudy organization. This research adopted the questionnaire as a main instrument to collect information from (140) participants in

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Crossref
Publication Date
Wed Jan 11 2023
Journal Name
J. Of Kirkuk Univ. For Agri. Sci.
THE HARMFUL CONSEQUENCES OF HEAT STRESS ON CHICKENS INDUSTRY
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This article dealt with identifying the importance of heat stress in poultry flocks and the damages resulting from the production of eggs and meat and the spread of pathogens, in addition to that ways to mitigate the harmful effects of heat stress, including physiological, nutritional, engineering and genetics, in order to ensure preservation of the product and reduce damages

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