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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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Effect of nanomaterials on the durability of hot mix asphalt
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Thu Apr 14 2016
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Bio--genetics Journal
Correlation of Her-2/neu gene amplification by FISH and CISH with clinicopathological parameter of Iraqi breast carcinoma patients at central public health laboratories
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The objective of the study: is to investigate the correlations between the HER2 neu gene status with the clinicopathological parameters of infiltrative breast carcinoma. A total of seventy four Iraqi breast cancer patients were collected from one center (Department of Public Health) paraffin blocks were collected from histopathology department central public health laboratories, Bagdad, Iraq from 2014-2015. The cases which has been taken included invasive ductal and invasive lobular carcinoma type Women age were ranged from 24-80 years old. Evaluation of Her-2/neu gene amplification status was done using FISH and CISH techniques that showed a significant correlations with clinicopathological parameters.

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Sun Apr 01 2018
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Al–bahith Al–a'alami
Investment of Propaganda in Al-Rafidain and Al- Sharqiya News Channels: Content Analysis of News Bulletins from 1/12/2016 to 29/2/2016
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The technological developments in the field of communication have witnessed considerable impact in the variables which exist in following up and conveying the events which link it’s meaning to political implications. This makes a number of satellite channels depend on the techniques of propaganda and use them in the news bulletins to achieve political aims and ends related to its formational directives where those channels allotted a considerable time in its programming transmission map to concentrate on the security and political status to complete the image of the informational scene according to the logic of its propaganda and styles in processing news for daily events.The technological developments in the field of communication hav

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Sat Jul 01 2023
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Journal Of Accounting And Financial Studies ( Jafs )
The impact of the practice of professional doubt on the quality of the auditor's performance in Iraq: بحث استطلاعي
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              Due to the increasing interest in the quality of auditing by writers, researchers and regulators of the auditing profession. The matter necessitated a statement of the extent to which the auditor practices professional skepticism, because of its significant impact in discovering errors and material misrepresentations contained in the financial statements in order to give the financial community confidence in them and the success of the audit process. The research aims to clarify the concept and importance of the practice of professional skepticism and its effect on the quality of the auditor's performance in Iraq. To achieve the research objectives, the two re

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The Impact of Climate Change on the Increase in the Frequency of Drought in the Eastern Region of Iraq
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Aim: This abstract aims to highlight the critical nature of climate change as a pressing challenge facing humanity in the 21st century. It underscores the severe consequences it poses to essential facets of human existence, including water and energy resources, agricultural production, and the broader environmental systems. Method: The abstract primarily utilizes a descriptive approach to emphasize the impact of climate change on the Middle East, particularly the Arab region. It relies on a review of existing knowledge and data related to climate change and its effects on ecosystems and drought patterns. Results: The abstract outlines the direct and indirect repercussions of climate change on human life and the environment. It draws atten

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Publication Date
Sat Dec 31 2022
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College Of Islamic Sciences
The effect of changing the grammatical ruling in the Qur’anic readings on changing the jurisprudential ruling
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 The study aimed to show the jurisprudential impact of the multiplicity of directing the syntactic movement of the Qur’anic readings, and it was based on the inductive, descriptive and analytical approach. , such as the difference in explaining the ruling on washing the feet, and the one who meditates on the Qur’anic readings notices in it a picture of the Qur’anic miracles, and this is what is manifested by the brevity of the speech. Collapse the research, and the research tried to trace the Qur’anic readings, contained in the verses, and the readings were limited to what is related to the explanatory meaning mentioned by the commentators, by clarifying the explanatory relationship between the Qur’anic readings and the me

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Publication Date
Thu Mar 30 2017
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Iraqi Journal Of Pharmaceutical Sciences ( P-issn 1683 - 3597 E-issn 2521 - 3512)
The Effect of Chronic Renal Failure on Thyroid Hormones
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       Chronic renal failure (CRF) affects thyroid function in multiple ways, including low circulating thyroid hormone concentration, altered peripheral hormone metabolism, disturbed binding to carrier proteins, possible reduction in tissue thyroid hormone content, and increased iodine store in thyroid glands.The target of study is to find a relationship between chronic renal failure and thyroid function.In addition, we tried to study the effect of CRF on serum creatinine dependent on the level of thyroid hormones (T3 and T4) and thyroid stimulating hormones(TSH). Forty patients with chronic renal failure (20 male, 20 female) were enrolled in this study in addition to forty healthy individual as control gro

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Fri Jun 08 2012
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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
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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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CONCENTRATIONS OF SILYMARIN ON THE RUMEN ACTIVITIES IN LAMBS
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Silymarin is derived from the milk thistle plant, and possesses numerous pharmacological actions, including hepatoprotective, anti-inflammatory, antioxidant, and anticancer properties. The aim of the study was to the determination of influence different concentrations of Silymarin on the rumen performance in 30 local lambs (divided into three groups of 10 lambs each). In the first and second groups, 420 and 210 mg kg-1 of silymarin were administered for 8 weeks, and the third group was the control, which received normal saline solution. The parameters evaluated included the level of volatile fatty acids (VFAs), ammonia and pH in the rumen. Furthermore, the in vitro digestibility of ash, protein, fat and dry matter was investigated.

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