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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 Jan 26 2006
Journal Name
Acta Crystallographica Section E
(OC-6-13)-Bis[5-bromo-2-(4-bromo­phenyl­diazenyl)phen­yl]dicarbonyl­ruthenium(II) with mutually transN-donor atoms
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The title compound, [Ru(C12H7Br2N2)2(CO)2], possesses a distorted octa­hedral environment about the Ru atom, with two cyclo­metallated 4,4′-dibromo­azobenzene ligands and two mutually cis carbonyl ligands. The donor atoms are arranged such that the N atoms are mutually trans and the aryl C atoms are trans to carbonyl ligands.

Publication Date
Sun Mar 07 2010
Journal Name
Baghdad Science Journal
Relation between Serum Leptin, Lipid Profiles and other biomarkers levels in patients with type 2 diabetic nephropathy
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Background: In advanced diabetes mellitus, serum levels of the most hormones are altered due to several interplaying mechanisms. Objective: To assess the relation of serum leptin and lipid profile in type 2 diabetic nephropathy. Patients and Method: Serum leptin levels and its relation to lipid profile were estimated in 62 patients with type 2 diabetic nephropathy attending the National Diabetes Center in Al- Mustansiriya University, and (26) healthy individuals considered as control group. The diabetic patients were classified into three groups, (24) pathients with normoalbuminuria (21) patients with microalbuminuria and (17) patients with macroalbuminuria. Fasting plasma glucose, serum creatinine, Hb A1c %, lipid profile (Total c

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Publication Date
Sun Oct 01 2023
Journal Name
Medical Journal Of Babylon
Urokinase-type plasminogen activator receptor as a predictive marker for cardiac disease among type 2 diabetic patients
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Abstract<sec> <title>Background:

Type 2 diabetes mellitus is a progressive and chronic disease manifested by β-cell dysfunction and improved insulin resistance. Higher levels of urokinase-type plasminogen activator receptors have been found to predict morbidity and mortality among diabetic patients with cardiac disease.

Objective:

This study aims to explore the role of serum urokinase-type plasminogen activator receptor levels as a prognostic marker among type 2 diabetic Iraqi patients.

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Publication Date
Tue May 01 2018
Journal Name
Journal Of Physics: Conference Series
Study electron transport coefficients for Ar, O<sub>2</sub> and their mixtures by using EEDF program
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Publication Date
Wed Jan 01 2020
Journal Name
Proceedings Of The 2020 2nd International Conference On Sustainable Manufacturing, Materials And Technologies
The impact of toxicant on the food chain ecological model
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Publication Date
Mon Feb 04 2019
Journal Name
Journal Of The College Of Education For Women
The archaeological and religious sites on the city of Babylon
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The archaeological and religious sites play a prominent role in the rest of the other tourist activities as cultural and spiritual needs that can not be dispensed with. Archaeological sites represent cultural origins of the nation. Religious sites represent the state of man's orientation to God in places of worship . The focus was on the city of Babylon because it is an ancient city and tourist because of its characteristics and elements. The importance of the city of Babylon is illustrated by highlighting its archeological and religious status through its geographical distribution. This gives the subject special importance for the purpose of knowing the city's important sites. And come out with a number of results and a set of recommend

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Publication Date
Thu Jun 30 2022
Journal Name
Anbar Journal Of Agricultural Sciences
THE EFFECT OF PESTICIDES ON THE ENVIRONMENT AND LIVING ORGANISMS
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The current report dealt with the effect of pesticides on the ecosystem through their impact on soil, water, and microorganisms and their impact on human health. As well as this study dealt with the biodegradation process of pesticides and the organisms involved in this process, even some previous studies proved that Bacillus spp. And Pseudomonas sp. Bacteria is the most efficient in the biodegradation of pesticides, at the same time, other previous studies dealt with the environmental factors that affect the biodegradation process of pesticides. It proved that each of the incubation periods, pH, and temperature have different effects on biodegradation. Most of the studies indicated that the best incubation period for biodegradation is 7-8

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Publication Date
Wed Dec 30 2015
Journal Name
College Of Islamic Sciences
The impact of Arab civilization   On the first century AH
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The influx of Arab Qahtani and Nizari tribes continued to the countries of Baluchistan and the Levant in pre-Islamic times until the Levant became open to the Arab-Islamic tide during the first century AH. The Islamic Orient until the early Islamic Arab Army reached the western borders of China. What we will see in the folds of the search.

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Publication Date
Wed Jan 01 2020
Journal Name
Technologies And Materials For Renewable Energy, Environment And Sustainability: Tmrees20
Studying the effect of the annealing on Ag2Se thin film
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Publication Date
Wed Mar 30 2016
Journal Name
College Of Islamic Sciences
Methods of Quran inference On the existence of the Creator of sleep
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The issue, the existence of God Almighty, and the creativity of the universes including the whale, and assets and how diversified, and faith in him and his lordship and divinity, is a delicate issue, and very important and dangerous, and it occupied human thought old and new, and still occupy it until God takes the land and on it. Many complex issues of thought, behavior, and ethics have resulted in the belief of many communities in the existence of the Almighty, having ruled their minds, depicting their beliefs and distancing their thoughts about slippage and abuse. When they looked at the wonders of creatures and the minutes of the assets, they thought about the planetary and astronomical motion systems. His existence was denied by ath

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