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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
Sun Feb 03 2019
Journal Name
Journal Of The College Of Education For Women
The Role of the Family in investment Effect of the Mates in Evaluating the Childs Acceptance (2-5 years) of rich foods and inhancemenl rein for cement of the social love concepts: The Role of the Family in investment Effect of the Mates in Evaluating the Childs Acceptance (2-5 years) of rich foods and inhancemenl rein for cement of the social love concepts
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Abstract:
The aim of the present research is to evaluate the child’s nutritional
method (2-5 years old) which is based on his resistance of the food highly rich
with nutritional elements and his acceptance of the food of a low nutritional
value in addition to his having forbidden food with other mates and making
use of all mates when having food, in establishing the sound social values and
affection since child hood. The required statistical equation have been used
by the researcher namely (Z test).
The sample of the present study consists of (26) children who were selected
intentionally and randomly from the kindergartens of Al-Bayaa region and the
college of Education for women. The questionnaires were d

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Publication Date
Sun Dec 01 2024
Journal Name
Russian Journal Of General Chemistry
Synthesis, Characterization, and Biological Evaluation for New Derivatives Based on 2Сhloro-N-[4-(5-phenyl-1,3,4-oxadiazol-2-yl)phenyl]acetamide
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Publication Date
Sun Dec 01 2024
Journal Name
Russian Journal Of General Chemistry
Synthesis, Characterization, and Biological Evaluation for New Derivatives Based on 2Сhloro-N-[4-(5-phenyl-1,3,4-oxadiazol-2-yl)phenyl]acetamide
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Publication Date
Sun Dec 01 2024
Journal Name
Russian Journal Of General Chemistry
Synthesis, Characterization, and Biological Evaluation for New Derivatives Based on 2Сhloro-N-[4-(5-phenyl-1,3,4-oxadiazol-2-yl)phenyl]acetamide
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Publication Date
Thu Aug 11 2022
Journal Name
Chemical Papers
Surface tensiometry study of the interfacial phenomena in the mixed surfactant solutions of sodium di-2-ethylhexylsulfosuccinate (AOT) and hexadecyl benzylammonium chloride (HDBAC)
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Publication Date
Mon Dec 20 2021
Journal Name
Baghdad Science Journal
An Experimental Study of the Server-based Unfairness Solutions for the Cross-Protocol Scenario of Adaptive Streaming over HTTP/3 and HTTP/2
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Since the introduction of the HTTP/3, research has focused on evaluating its influences on the existing adaptive streaming over HTTP (HAS). Among these research, due to irrelevant transport protocols, the cross-protocol unfairness between the HAS over HTTP/3 (HAS/3) and HAS over HTTP/2 (HAS/2) has caught considerable attention. It has been found that the HAS/3 clients tend to request higher bitrates than the HAS/2 clients because the transport QUIC obtains higher bandwidth for its HAS/3 clients than the TCP for its HAS/2 clients. As the problem originates from the transport layer, it is likely that the server-based unfairness solutions can help the clients overcome such a problem. Therefore, in this paper, an experimental study of the se

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Publication Date
Fri Sep 25 2020
Journal Name
International Journal Of Drug Delivery Technology
Investigate Retention Behavior of 2-deoxycytidine in Hydrophilic Interaction Liquid Chromatography
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A hydrophilic interaction chromatography has been investigated to separate 2-deoxycytidine chosen for nucleoside. A small molecule with specific features for human serum samples was 2-deoxycytidine tested. 2-deoxycytidine has been applied to self-made stationary hydrophilic phases (ZIC1 and ZIC5). The deoxycytidine (dCD) retention was investigated with varying concentrations of sodium acetate buffer, acetonitrile%, and pH. The results confirmed the hydrophilicity of 2-deoxycytidine. The exchanger retention mechanism was studied taking into account 2-deoxycytidine used for describing the interaction of hydrophilic and cation. For both ZIC1 and ZIC5 exchangers, we described and discussed the influence of chromatographic conditions (co

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Publication Date
Sun Jun 01 2014
Journal Name
Baghdad Science Journal
Synthesis and Characterization of New heterocyclic Polyacrylamides from Derivatives 2-Aminobenzothiazole
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The present work involved preparation of new hetro cyclic polyacrylamides (1-9) using reaction of polyacryloyl chloride with 2-aminobenzothiazole which prepeard by thiocyanogen method in the presence of a suitable solvent and amount tri ethyl amine (Et3N) with heating. The structure confirmation of polymers were proved using FT-IR,1H-NMR,C13NMR and UV spectroscopy.Other physical properties including softening and melting points, and solubility of the polymers were also measured.

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Publication Date
Sun Jun 05 2011
Journal Name
Baghdad Science Journal
Synthesized azodyes of 2-amino-1, 3, 4- thiadiazole - 5 - thiol
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Several azo dyes were synthesized through coupling reaetion of some substituted phenols and B.naphthol with diazonium salt of 2- amino-1,3-4- thiadiazol -5- thiol. All the synthesized compounds during this work were characterized using some speetral data (F.TIRand UV)andM.P . 2-[4 --Hydroxy napthyl-azo ] -1,3,4-Thiadiazol -5-Thiol • 2- [2-- hydroxy –4- NO2 – phenyl- azo]- 1,3,4 - Thiadiazol –5-Thiol. • 2- [3--Amino-4-Hydroxy phenyl –azo]-1,3,4 - Thiadiazol –5-Thiol. . • 2-[2--Amino-4-Hydroxy phenyl -azo]-1,3,4 - Thiadiazol –5-Thiol . • 2- [3--Amino-6- Hydroxy phenyl -azo]-1,3,4 - Thiadiazol –5-Thiol. • 2-[2-- Hydroxy- 5 – chloro – Pheny - azo]- 1,3,4 - Thiadiazol –5-Thiol . • 2- [4-- Hydroxy phenyl -azo] -1,

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Publication Date
Tue Mar 01 2022
Journal Name
Malaysian Journal Of Medicine & Health Sciences
Detection of Iron and Ferritin in Diabetes Mellitus Type 2 Patients
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