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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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Fri Aug 20 2021
Journal Name
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The Influence of No-Core Fiber Length on the Sensitivity in Fiber Optic Strain Sensor
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The influence of sensing element length of no-core fiber strain sensor has been studied and experimentally demonstrated, four different lengths of 125 μm diameter no-core fiber is fused between two standard single-mode fibers and bi-directionally strained, the highest obtained sensitivity was around 16.37 pm με -1 which was exhibited in the shortest no-core fiber segment, to the best of our knowledge this is the first study of the influence of no-core fiber strain sensors length on sensor sensitivity. The proposed sensor can be used in many opto-mechanical applications such as, structural health monitoring, aerospace vehicles and airplane components monitoring.

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Thu Apr 07 2022
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The impact of monetary policy on monetary stability in Iraq for the period (2004-2018)
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Monetary policy is an important part of the economic policy to influence the monetary aspect of stabilization, for this reason the research will seek to clarify the extent of the impact of monetary policy in achieving monetary stability in Iraq during the chosen research period, because the Iraqi economy suffers from monetary instability due to political and security turmoil, Therefore, an effective and effective monetary policy is required in terms of reducing inflationary pressures to reach the required monetary stability, in order to create the appropriate monetary environment for the work of the economic and productive sectors. Thus, the research adopted a basic hypothesis that monetary policy in Iraq has a clear impact on achieving mon

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Publication Date
Sun Apr 01 2018
Journal Name
Journal Of Economics And Administrative Sciences
"The Impact of International Public Sector Accounting Standards (IPSASs) on the Public Budget in Iraq"
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     The aim of the research is to determine the impact of the Iraqi public budget on IPSASs by conducting the questionnaire; the research was based on the hypothesis that "there is an impact of the adoption of the International Accounting Standards in the general budget of Iraq”. The research concluded that the government accounting system closely interferes with the general budget at all stages. The shifting towards the accrual basis is the first element of the reform package towards reaching the reform of the state budget. Without reforming government accounting, it is almost impossible to develop the budget. IPSASs are a recognized reference to the assessment and development of governmen

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Publication Date
Sat Sep 30 2023
Journal Name
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The effect of cognitive sharing on strategic anxiety: Analytical research into the Iraqi Airways Company
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The current research aims to test the effect of knowledge sharing in its dimensions represented by(individual dimension, organizational dimension, and technological dimension), In reducing the strategic Anxiety of Iraqi Airways, In view of the importance of the two variables for the company from the perspective of society and the sample resulting from directing various organizational phenomena to reduce its strategic Anxiety, As a goal, it should be viewed from multifaceted perspectives(uncertainty, relational disorder, competitive disorder, resource depletion), And it was embodied by choosing the descriptive, exploratory approach, as it is the most appropriate in that aspect, so that the research questionnaire is one of solid scientific

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Publication Date
Sun Jul 02 2017
Journal Name
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The Effect of Lead Time Strategy on the First Intermediate Class Pupils' Achievement in Geography
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The study aims at finding out the effect of the lead time strategy on the first intermediate class pupils' achievement in geography The partial experimental design of two groups, experimental and control, with pre-post tests is used. The sample is represented in (73) female pupils. The sample is divided into two groups (37) experimental group and (36) control one. The sam ple is selected from first intermediate class pupils ( Al Batol intermediate school for girls) Baghdad Al-karkh-3, for academic year 2015-2016 The researcher has equalized the two groups in several variables: the previous achievement tests, intelligence, age in months, the scores of geography test of first course

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Publication Date
Fri Oct 19 2018
Journal Name
Journal Of Economics And Administrative Sciences
Integrated Marketing Communication and Its Effect on the revitalization of The Marketing Performance Field Research
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The research topic was chosen because of the importance of communication in organizations in general and the marketing  process in particular. Without communication, the organization can not live and continue ,The problem of study diagnosis the reduction in sales in the company of plant oils in some its classes and weakness in differentiation and its reputation at market in spit if having good products with standardized features And lack of customer communication channels, also the company does not have any whole view about the concept of marketing communication, Therefore, This sudy aimed ro define to know the type of relationship between the extent of the impact of the integrated marketing

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Sun May 10 2015
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Intellectual Reflections of the Cubical Arts on the Iraqi Contemporary Pottery Art: أحمد جعفر حسين
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The current study discusses one of the most important modern schools in art, and it studies its impact on contemporary Iraqi art, particularly in the art of pottery because of its association to the utilitarian function. However, this study demonstrated that pottery is a unique art, which has exceeded the limits of this function. In addition, pottery has a great role in changing the view and understanding of it. Therefore, this art assists in achieving the concepts, philosophies, and values among other fine arts branches.The most prominent issues in this article is dealing with reflections of the cubical arts on the Iraqi contemporary pottery art by through the works of the most prominent contemporary artists such as (Saad Shakir, SHania

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Thu May 14 2020
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Visual Pollution and its Impact on the Aesthetics: The Town of Eizariya as a Model
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This study seeks to shed light on the aspects of visual pollution and its impact on the aesthetics of the town of Al-Eizariya known to suffer from the phenomenon. In order to identify the real causes of the problem which develops in various forms and patterns, threatening not only the aesthetic appearance of the towns, but also causes the emergence of new problems and phenomena that will have negative repercussions on the population. The researcher uses the analytical descriptive method to analyze the phenomenon of visual pollution in terms of reality, development, manifestations and spread and uses photos which document the visual pollution and its impact on the aesthetics of the known. The study concluded the existence of a strong rela

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Publication Date
Fri Jun 30 2023
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the effect of the semantic map strategy on predictive thinking among fifth grade femal students
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Publication Date
Tue Dec 31 2019
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The Effect of Disclosure and Transparency Criteria In Saudi Banks on The Financial Ratios Indicators
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The study aimed to measure the effect of applying the disclosure and transparency standards criteria adopted by the Saudi Arabian Monetary Authority on improving performance indicators in the Saudi banking sector, by measuring the extent of the impact of the bank's financial indicators represented by liquidity, profitability and return on assets in Saudi banks by applying the criteria of disclosure and transparency, which is one of the Main principles in the list of governance, which was approved by the Saudi Arabian Monetary Authority. The analytical approach was followed to achieve the goal of the study, as the financial statements of Saudi banks were analyzed during a period of 8-year to test four hypotheses related to measuri

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