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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 Oct 02 2014
Journal Name
Journal Of The Islamic University College
The image of the family in dubbed Turkish series and their potential impact on Iraqi youth
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Since the nineties of the last century, Iraqi youth have been exposed to Mexican soap operas dubbed into classical Arabic, and the stories and ideas presented by these series were almost new to all the minds of the youth at that time, a culture completely different from the culture we have of social relations, and since the number of episodes was more than Of the 100 episodes, exposure to these series has left young people confused by the addiction to all their ideas and stories. They differ from the foreign films (mostly American) that we used to watch, and they only take two hours (at most). These films contain diverse stories and may be forgotten. Memory includes events and characters in their entirety at times, and you may remember th

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Fri Apr 01 2022
Journal Name
Baghdad Science Journal
Study the Efficiency of Two Concentrations from Algae Cladophora glomerata Extract on the Giardia lamblia parasite
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Giardia lamblia parasite was isolated from the diarrhea samples of patients with Giardiasis dysentery and was developed in HSP media, four mice groups have been used to find in vivo efficacy of two concentrations (128,256) mg/ml of chlorophorm extracts from Cladophora glomerata algae against Giardia lamblia parasite  as compared with (Flagyl) by measuring several biochemical markers as ( GPT and GOT) enzymes ,sodium ,potassium and iron concentration as well as counting the number of parasitic cysts in each mice groups. The results demonstrate that levels of GPTA GOT enzymes have been decreased in mice treated with algal extract. As for the concentration of the Sodium, Potassium and Iron increased in mice treat

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Publication Date
Tue Mar 01 2011
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
The effect of differentiation strategy on achieve competitive advantage: survey comparison between the companies maintenance service
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Is to obtain competitive advantage legitimate objective pursued by all organizations to achieve, because they live today in environments of rapid change and dynamic in order to meet the demands of the customer changing as well as intense competition between the organizations, which requires them to get the location of competitive markets in order to do this will remain to do the building and strengthening competitive advantage to be able to achieve, but that this feature is not easy and is not only through the identification and use of a successful strategy for a competitive standard and then manage it successfully. Hence the research problem of determining the sources of differentiation strategy and its impact on the dimensions of compe

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Publication Date
Wed Aug 08 2012
Journal Name
Arabian Journal Of Geosciences
Chemical and physical control processes on the development of caves in the Injana Formation, Central Iraq
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Publication Date
Wed Dec 25 2019
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
Non-interest income and its impact on the profits of the Iraqi banking sector: (Comparative study)
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     In this study,  has been discussed the issue of non-interest income and its impact on the Iraqi banking sector profit for the period between (2008-2017) as it was the main objective of the study is to find the relationship between the non-interest income and the profits of the banking sector in order to know  the size of the sector's dependence on non-interest income As well as an analysis of its profitability compared to selected countries, And to test hypotheses, the financial ratios and some statistical tests to determine the stability of the time series such as the test (Correlegram , Dickey -Fuller (depending on the statistical program (E-Views V8) and a simple linear regression method by (Minitab

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Publication Date
Tue Oct 23 2018
Journal Name
Journal Of Economics And Administrative Sciences
The Effect of Dividend Policy on Earnings Quality in The Companies listed in Iraq Stock Exchange
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The dividends is one of difficult and important decisions taken by the administration in the economic units, because this decision has a direct impact on the investor and economic unit, so the main objective of any investor is achieve earnings, as well as information borne by dividends about the earnings quality of the economic unit and the level and efficiency of management to achieving earnings.

The research aims at explaining the effect of the dividends policy on the earnings quality in the companies listed in the Iraq Stock Exchange. The Miller model was used to measu

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Crossref
Publication Date
Wed Sep 01 2010
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
Global Financial crisis and its impact on the performance of the Emerging Stock Exchange: الاردن نموذجا
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The research aims to explain the reality and the roots of the problem financial crisis and its impact on the performance of the Amman Stock Exchange, by testing three hypotheses, the first and the second relates to the performance of the Amman Stock Exchange and its sectors before and after the financial crisis. And the third examined the relationship between indirect foreign investment and the performance of Amman Stock Exchange.
     Hypothesis testing results of the first and second pointed to the existence of statistically significant differences for the performance of the stock market in general and in particular their performance for the period before and after the financial crisis. The third hypothesis resu

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Publication Date
Thu Oct 30 2025
Journal Name
Al-nahrain Journal For Engineering Sciences
The Effect of Magnetic Abrasive Finishing on the Flat Surface for Ferromagnetic and non-Ferromagnetic materials
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Magnetic Abrasive Finishing (MAF) is an advanced finishing method, which improves the quality of surfaces and performance of the products. The finishing technology for flat surfaces by MAF method is very economical in manufacturing fields an electromagnetic inductor was designed and manufactured for flat surface finishing formed in vertical milling machine. Magnetic abrasive powder was also produced under controlled condition. There are various parameters, such as the coil current, working gap, the volume of powder portion and feed rate, that are known to have a large impact on surface quality. This paper describes how Taguchi design of experiments is applied to find out important parameters influencing the surface quality generated during

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Publication Date
Fri Sep 30 2022
Journal Name
Journal Of Economics And Administrative Sciences
Estimation of Reliability through the Wiener Degradation Process Based on the Genetic Algorithm to Estimating Parameters
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      In this paper, the researcher suggested using the Genetic algorithm method to estimate the parameters of the Wiener degradation process,  where it is based on the Wiener process in order to estimate the reliability of high-efficiency products, due to the difficulty of estimating the reliability of them using traditional techniques that depend only on the failure times of products. Monte Carlo simulation has been applied for the purpose of proving the efficiency of the proposed method in estimating parameters; it was compared with the method of the maximum likelihood estimation. The results were that the Genetic algorithm method is the best based on the AMSE comparison criterion, then the reliab

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Publication Date
Sat Jul 08 2017
Journal Name
Iraqi Journal Of Pharmaceutical Sciences ( P-issn 1683 - 3597 E-issn 2521 - 3512)
The Effect of Coumarin Derivatives(compounds) on the Vibrio cholerae Isolates from Different Clinical Iraqi Sources
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From a large number of bacterial samples collected from different hospital in Iraq in central  health laboratory ,only ten isolates were identified primary as Vibrio. A number of  morphology and biochemical test were carried out to complete this identification that showed all bacterial isolates were related to Vibrio cholerae .In this study  all Vibrio isolates were investigated for Bio typing and the result showed that all (10) isolate were related to (Eltor biotypes) .Also, the susceptibility test towards eight antibiotics were carried  out .

Results shows that  ciprofloxacin , Norfloxacin, Erythromycin, Ampicillin,  ceftriaxone  and Amikacin were the most effective

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