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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 Mar 01 2012
Journal Name
Journal Of Economics And Administrative Sciences
The Impact of Intellectual trends on the nature of the Economic Structure of Iraq
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The Impact of Intellectual trends on the nature of the Economic Structure of Iraq

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Publication Date
Tue Sep 01 2015
Journal Name
2015 Ieee International Circuits And Systems Symposium (icsys)
Investigating the impact of on-chip interconnection noise on Dynamic Thermal Management efficiency
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Dynamic Thermal Management (DTM) emerged as a solution to address the reliability challenges with thermal hotspots and unbalanced temperatures. DTM efficiency is highly affected by the accuracy of the temperature information presented to the DTM manager. This work aims to investigate the effect of inaccuracy caused by the deep sub-micron (DSM) noise during the transmission of temperature information to the manager on DTM efficiency. A simulation framework has been developed and results show up to 38% DTM performance degradation and 18% unattended cycles in emergency temperature under DSM noise. The finding highlights the importance of further research in providing reliable on-chip data transmission in DTM application.

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Sat Feb 01 2025
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On the Impact of Lacing Reinforcement Arrangement on Reinforced Concrete Deep Beams Performance
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The optimum design is characterized by structural concrete components that can sustain loads well beyond the yielding stage. This is often accomplished by a fulfilled ductility index, which is greatly influenced by the arrangement of the shear reinforcement. The current study investigates the impact of the shear reinforcement arrangement on the structural response of the deep beams using a variety of parameters, including the type of shear reinforcement, the number of lacing bars, and the lacing arrangement pattern. It was found that lacing reinforcement, as opposed to vertical stirrups, enhanced the overall structural response of deep beams, as evidenced by test results showing increases in ultimate loads, yielding, and cracking of

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Publication Date
Sat Feb 01 2025
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Civil Engineering Journal
On the Impact of Lacing Reinforcement Arrangement on Reinforced Concrete Deep Beams Performance
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The optimum design is characterized by structural concrete components that can sustain loads well beyond the yielding stage. This is often accomplished by a fulfilled ductility index, which is greatly influenced by the arrangement of the shear reinforcement. The current study investigates the impact of the shear reinforcement arrangement on the structural response of the deep beams using a variety of parameters, including the type of shear reinforcement, the number of lacing bars, and the lacing arrangement pattern. It was found that lacing reinforcement, as opposed to vertical stirrups, enhanced the overall structural response of deep beams, as evidenced by test results showing increases in ultimate loads, yielding, and cracking of

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Publication Date
Sat Feb 01 2025
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Civil Engineering Journal
On the Impact of Lacing Reinforcement Arrangement on Reinforced Concrete Deep Beams Performance
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The optimum design is characterized by structural concrete components that can sustain loads well beyond the yielding stage. This is often accomplished by a fulfilled ductility index, which is greatly influenced by the arrangement of the shear reinforcement. The current study investigates the impact of the shear reinforcement arrangement on the structural response of the deep beams using a variety of parameters, including the type of shear reinforcement, the number of lacing bars, and the lacing arrangement pattern. It was found that lacing reinforcement, as opposed to vertical stirrups, enhanced the overall structural response of deep beams, as evidenced by test results showing increases in ultimate loads, yielding, and cracking of

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Publication Date
Sat Feb 01 2025
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On the Impact of Lacing Reinforcement Arrangement on Reinforced Concrete Deep Beams Performance
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The optimum design is characterized by structural concrete components that can sustain loads well beyond the yielding stage. This is often accomplished by a fulfilled ductility index, which is greatly influenced by the arrangement of the shear reinforcement. The current study investigates the impact of the shear reinforcement arrangement on the structural response of the deep beams using a variety of parameters, including the type of shear reinforcement, the number of lacing bars, and the lacing arrangement pattern. It was found that lacing reinforcement, as opposed to vertical stirrups, enhanced the overall structural response of deep beams, as evidenced by test results showing increases in ultimate loads, yielding, and cracking of

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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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Publication Date
Fri Jan 01 1999
Journal Name
University Of Baghdad
On the Equiconvergence Theorem
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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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Sun Sep 01 2013
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Synthesis and biological studies for some heterocyclic compounds derived from 2-Morpholino-1,8- naphthyridine-4-carboxylic acid
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New heterocyclic compounds derived from 2-Morpholino-1,8-naphthyridine-4-carboxylic acid such as oxadiazolo, thiadiazolo – thione and triazolo-thione have been prepared and characterized on the basis of IR and 1H NMR spectra data. The hydrizide compound was utilized as a starting material for preparing of these compounds. The second part of this study involves the biological studies of some of these naphthyridine derivatives by using three different kinds of bacteria namely: Staphylococcus aureus, Pseudomonas aeruglnosa and Escherichia coli. The data indicated that some of these compounds have a good activity against the tested bacteria in comparison to antibiotics.

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