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MRbmuIoBVTCNdQwCLKT9
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
Tue Nov 18 2025
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The Responsibility of the Iraqi Journalism in Promoting Political Culture in Society: (An Analytical Study in Newspapers: Al-Sabah, Al-Ittihad, Al-Aalam for 2/ 3/ 2013 - 31/ 3/ 2013)
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This study comes as: The responsibility of the Iraqi newspapers in promoting  the political culture inside society, an analytical study in newspapers: Al-Sabah, Al-Ittihad, Al-Aalam for 2/ 3/ 2013 to 31/ 3/ 2013 to spot light on the extent to which the three mentioned newspapers are compliance with the promotion  of the political culture inside society which is seen as one of the essential requirements for the success and promotion of the democratic process inside society.

The study aims to: finding out the extent to which these newspapers are compliance with their responsibility in the promoting the political culture inside society; knowing the nature of their role in pr

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Publication Date
Sat Oct 01 2016
Journal Name
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The Intellectual Capital And Its Revenues On The Investment Applied Research On Sample of Banks Listed on In The Iraq Stocks Exchange
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Abstract

      The changes that happened in the environment of  business have great effects upon organizations with different activities specially the banks  which requires the existence of an able opinion  resources can adapt with the changes . Accordingly importance put upon  intellectual  capital which become one of the basic resources for organizations and one of success and growth elements with the availability of expertise , skills and capability of making  essential changes in different process due to the presentation of innovations and creations of the to support banks activities .Therefore the intellectual  capital represents the more r

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Mon Feb 01 2021
Journal Name
Journal Of Engineering
Investigations on the Impact of Using Elliptic Groynes on the Flow in Open Channels
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This paper presents a numerical simulation of the flow around elliptic groynes by using CFD ‎software. The flow was simulated in a flume with 4m long, 0.4m wide, ‎and 0.175m ‎high ‎‎with a constant bed slope. Moreover, the first Groyne placed at 1m from the flow ‎‎inlet with a ‎constant the Groyne height of 10cm and a 1cm thickness, and the ‎width of Groynes equals ‎7cm‎. A submergence ratio of the elliptic Groynes of 75% was assumed, corresponding to a discharge of ‎0.0057‎m3/sec. The CFD ‎model showed a good ability to simulate the flow ‎around ‎Groynes with ‎ good accuracy. The results of ‎CFD software showed that when using double elliptic Groy

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Publication Date
Sat Apr 25 2020
Journal Name
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THE EFFECT OF CAPITAL ADEQUACY AND ASSET QUALITY ON THE VALUE OF THE BANK AN APPLIED STUDY ON A SAMPLE OF IRAQI BANKS LISTED ON THE IRAQ STOCK EXCHANGE
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As the banking sector is a strong influence on the country's economic growth,The solid financial well-being of anybank does not mean only a guarantee for its investors, It is also important for both owners and workers and for theeconomy in all its joints.The elements of capital adequacy and quality of assets are important to the functioning of thebanking business.In this study, the research sample included four private banks. Quarterly data were used for the period(2011 - 2018).Moreover, data is also collected from articles, papers, the World Wide Web (the Internet) and specializedinternational journals.In this research, an effort was made to try to find out the effect of (the ratio of the capital owned todeposits on the value of the bank),

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Publication Date
Sun Aug 30 2020
Journal Name
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The Effect of Brainstorming on audit Quality and its Reflection on Detecting the Risk of Fraud
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Brainstorming is one of the fundamental and necessary concepts for practicing the auditing profession, as auditing standards encouraged the implementation of brainstorming sessions to reach reasonable assurance about the validity of the evidence and information obtained by the auditor to detect fraud, as the implementation of brainstorming sessions and the practice of professional suspicion during the audit process lead to increase the quality of auditing and thus raise the financial community's confidence in the auditing profession again after it was exposed to several crises that led to the financial community losing confidence in the auditing profession.

The research aims to explain the effect of brain

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Crossref
Publication Date
Fri Oct 30 2020
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The Effect of Brainstorming on audit Quality and its Reflection on Detecting the Risk of Fraud
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Brainstorming is one of the fundamental and necessary concepts for practising the auditing profession, as auditing standards encouraged the implementation of brainstorming sessions to reach reasonable assurance about the validity of the evidence and information obtained by the auditor to detect fraud, as the implementation of brainstorming sessions and the practice of professional suspicion during the audit process lead To increase the quality of auditing and thus raise the financial community's confidence in the auditing profession again after it was exposed to several crises that led to the financial community losing confidence in the auditing profession.

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Tue Sep 08 2020
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Silver Nanoparticles and their Role in Gene Expression of Motility Gene motB and Repression of AI-2-Controlled Gene
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Antibiotic resistance is the capability of the strains to resist or protect themselves from the effects of an antibiotic. Such a resistance towards the current antimicrobials leads to the search of novel antimicrobials. Nanotechnology has been promising in different field of science and among it is the use of nanoparticles as antibacterial agents. The gastrointestinal tract seems to be the primary reservoir of uropathogenic E.coli (UPEC) in humans. UPEC strains harbour the urinary tract and cause urinary tract infection. They cause serious ailments in terms of humans. They develop resistance and increase their virulence by forming biofilms. They also show a remarkable locomotory movement with the aid of autoinducer controlled ge

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Evaluation of interleukin-9 serum level and gene polymorphism in a sample of Iraqi type 2 diabetic mellitus patients
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Background: Diabetic mellitus (DM) is a collection of metabolic disorder identified by hyperglycemia. The heterogeneous etiology includes defects either in insulin secretion, or in insulin action, or the both. In addition to the distraction in carbohydrate, fat and protein metabolism. Inflammatory reaction that caused by many pro-inflammatory cytokines play a central role in the pathogenicity of T2DM, these cytokines can enhance insulin resistance which led to impaired glucose homeostasis. Subjects: The study included 75 patients (38 males and 37 females) suffering from T2DM with age mean ± SE 52.30 ± 1.60, and 70 individuals as healthy controls (35 males and 35 females) with age mean ± SE 48.88 ± 0.64. Evaluation of immunological marke

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Synthesis ,characterization and antibacterial activity of mixed ligand complexes of some metals with 1-nitroso-2-naphthol and Lphenylalanine
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Publication Date
Sat Dec 01 2012
Journal Name
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Microwave assisted synthesis of new heterocyclic compounds: 1, 2, 3-triazoles and tetrazoles and study of their biological activity
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The work includes synthesis of 1,2,3-triazoles via click conditions and using the microwave irradiation starting from two synthesized azides: 2,3,4,6-tetra-O-acetyl-β-D-glucopyranosyl azide (5) and perfluorobutylethyl azide (10) and different terminal alkynes. It also includes microwave enhanced synthesis of tetrazoles via the reaction of two synthesized azides i.e., perfluorobutylethyl azide (10) and 1,5-diazidopentane (13) with benzoyl cyanide. Most of the prepared compounds have been characterized by: TLC, FT-IR, 1H NMR, 13C NMR, LC-MS and microelemental analysis