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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
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
Wed Feb 01 2023
Journal Name
Baghdad Science Journal
Efficient Approach for Solving (2+1) D- Differential Equations
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     In this article, a new efficient approach is presented to solve a type of partial differential equations, such (2+1)-dimensional differential equations non-linear, and nonhomogeneous. The procedure of the new approach is suggested to solve important types of differential equations and get accurate analytic solutions i.e., exact solutions. The effectiveness of the suggested approach based on its properties compared with other approaches has been used to solve this type of differential equations such as the Adomain decomposition method, homotopy perturbation method, homotopy analysis method, and variation iteration method. The advantage of the present method has been illustrated by some examples.

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Publication Date
Wed Mar 29 2017
Journal Name
Iraqi Journal Of Pharmaceutical Sciences ( P-issn 1683 - 3597 E-issn 2521 - 3512)
Association between Gallstones and Diabetics Type 2 Iraqi Patients
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Gallstone disease is one of the most common complications among diabetic patients especially type 2 DM. Till now, there is no specific and certain factor that explain the incidence of gallstones among type 2 diabetic patients and many risk factors are taken collectively to estimate its intensity and severity compared to non diabetic counter parts. This clinical study was designed to evaluate and report the incidence and severity of gallstones among type 2 diabetics and non diabetics regarding certain factors. 20 diabetic females and 20 diabetic males were collected as patients′ group and have had gallstones while 20 females and 20 males who have had gallstones without diabetes mellitus type 2 were collected as controls′ group

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Publication Date
Fri Nov 18 2005
Journal Name
Acta Crystallographica Section E
Bis(μ3-4-bromo­phenyl­imido)tris­(tricarbonyl­ruthenium)(2 Ru—Ru)
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The title compound, [Ru3(μ3-NC6H4Br)2(CO)9], is a V-shaped triruthenium cluster, each side of the V being face-capped by a 4-bromo­phenyl­imide ligand. Each Ru atom is also ligated by three terminal carbonyl ligands. There are two molecules in the asymmetric unit with minor conformational differences.

Publication Date
Sun Dec 15 2019
Journal Name
Journal Of Baghdad College Of Dentistry
Angiopoietin-2 Immunohistochemical Expression in Oral Squamous cell Carcinoma
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Background: There are various secreted proteins affecting the prognosis of oral squamous cell carcinoma (OSCC) and one of them is Angiopoietin-2(Ang-2) which is thought to have an essential role in the development and progression of the tumor. Aim of the study: This study was conducted to determine the expression of (Ang-2) in (OSCC) to assess its correlations with clinicopathological parameters of the tumor. Material and Methods: 36 formalin- fixed, paraffin- embedded tissue blocks histologically diagnosed as OSCC were examined for Ang-2 immunohistochemical expression semi quantitively. Results: The expression of Ang-2 was significantly associated with histopathological grade (P value=0.023), while there is no significant association wi

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Publication Date
Sat Jun 30 2012
Journal Name
Al-kindy College Medical Journal
Assessment of Neck Circumference Measurement among Type 2 Diabetic Patients in Identifying: Obesity and the Likelihood of Developing Metabolic syndrome.
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Background: Obesity is an evolving major health problem in both developed and developing countries. Traditional obesity indices as body mass index, waist circumference, waist-hip-ratio are well known measures to identify obese subjects, however, neck circumference as an index of upper-body obesity was found to be a simple and time-saving screening measure that can be used to identify obesity and the likelihood of developing metabolic syndrome in type 2 diabetic patients.
Aim: to investigate the relationship of neck circumference (NC) to obesity and metabolic syndrome in Iraqi subjects with type 2 diabetes.
Methods: The study group included 90 type 2 diabetic subjects (48 men and 42 women) aged 30-68 years. The subjects were those w

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Publication Date
Fri Aug 25 2017
Journal Name
Oriental Journal Of Chemistry
Relationship Between the structure of Newly Synthesized derivatives of 1,3,4-oxadiazole Containing 2-Methylphenol and their Antioxidant and Antibacterial Activities
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1, 3, 4-oxadiazole-5-thion ring (2) successfully formed at position six of 2-methylphenol and five of their thioalkyl (3a-e). Furthermore 6-(5-(Aryl)-1, 3, 4-oxadiazol-2-yl)-2-methylphenol (5a-i) were formed at position six by two method. The first method was from cyclization their correspondinghydrazones (4a-e) of 2-hydroxy-3-methylbenzohydrazide (1) using bromine in glacial acetic acid. The second method was from cyclization the hydrazide with aryl carboxylic acid in the presence of phosphorusoxy chloride. The newly synthesized compounds were characterized from their IR, NMR and mass spectra. The antioxidant properties of these compounds were screened by 2, 2-Diphenyl-1-picrylhydrazide (DPPH) and ferric reducing antioxidant power (FRAP) a

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Publication Date
Mon Jul 01 2024
Journal Name
Russian Journal Of Organic Chemistry
Synthesis and Study of the Biological Activity of New Compounds Derived from 4-(5-Phenyl-1,3,4-oxadiazole-2-yl)aniline
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Publication Date
Mon Jan 01 2024
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Journal Of Clinical And Experimental Dentistry
Eradication of mature biofilm from the isthmus region using Er, Cr: YSGG Laser as an activator of 2% chlorhexidine gluconate
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Publication Date
Fri Aug 25 2017
Journal Name
Oriental Journal Of Chemistry
Relationship Between the structure of Newly Synthesized derivatives of 1,3,4-oxadiazole Containing 2-Methylphenol and their Antioxidant and Antibacterial Activities
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1,3,4-oxadiazole-5-thion ring (2) successfully formed at position six of 2-methylphenol and five of their thioalkyl (3a-e). Furthermore 6-(5-(Aryl)-1,3,4-oxadiazol-2-yl)-2-methylphenol (5a-i) were formed at position six by two method. The first method was from cyclization their corresponding hydrazones (4a-e) of 2-hydroxy-3-methylbenzohydrazide (1) using bromine in glacial acetic acid. The second method was from cyclization the hydrazide with aryl carboxylic acid in the presence of phosphorusoxy chloride. The newly synthesized compounds were characterized from their IR, NMR and mass spectra. The antioxidant properties of these compounds were screened by 2,2-Diphenyl-1-picrylhydrazide (DPPH) and ferric reducing antioxidant power (FRAP) assay

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Scopus (12)
Crossref (4)
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