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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
Wed Jan 01 2025
Journal Name
Medical Journal Of Babylon
Study Effect of Periostin Level in Obese Iraqi Females Patients with Type 2 Diabetes Mellitus
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Abstract<sec> <title>Background:

Obesity has been connected to a higher risk of acquiring a number of diseases, including cancer, type 2 diabetes mellitus (T2DM), hypertension, and cardiovascular disease. Periostin is a crucial regulator of the growth and maintenance of bones, teeth, and the heart.

Objectives:

The aim of the study was to estimate the level of (periostin, glycated hemoglobin [HbA1c], fasting serum [FBG], total cholesterol [TC], high-density lipoprotein [HDL], low-density lipoprotein [LDL], and triglycerides [TG]) in diabetic Ira

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Publication Date
Fri Jan 01 2016
Journal Name
Der Pharmacia Lettre
Synthesis, characterization and anticonvulsant evaluation of new derivatives derived from 5-methoxy-2-mercapto benzimidazole
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A new series of 5-methoxy-2-mercapto benzimidazole derivatives were synthesized by the reaction of 5-methoxy- 2-mercaptobenzimidazole with chloroacetic acid and affords 2-((5-methoxy-1H-benzo[d]imidazol-2-yl)thio) acetic acid (1),which on cyclization with acetic anhydride and pyridine gives 7- methoxybenzo[4,5]imidazo[2,1-b]thiazol- 3(2H)-one(2), which on condensation with different aryl aldehydes in the presence of anhydrous sodium acetate in glacial acetic acid, furnishes a arylidene thiazolidinone. The purity of the synthesized compounds was confirmed by melting point and TLC.The structures were established by different spectral analysis such as FTIR,1HNMR, and CHN analysis. The newly synthesized compounds (3a-d) were in vivo evaluated f

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Scopus
Publication Date
Wed Jan 01 2025
Journal Name
Medical Journal Of Babylon
Study Effect of Periostin Level in Obese Iraqi Females Patients with Type 2 Diabetes Mellitus
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Abstract<sec> <title>Background:

Obesity has been connected to a higher risk of acquiring a number of diseases, including cancer, type 2 diabetes mellitus (T2DM), hypertension, and cardiovascular disease. Periostin is a crucial regulator of the growth and maintenance of bones, teeth, and the heart.

Objectives:

The aim of the study was to estimate the level of (periostin, glycated hemoglobin [HbA1c], fasting serum [FBG], total cholesterol [TC], high-density lipoprotein [HDL], low-density lipoprotein [LDL], and triglycerides [TG]) in diabetic Ira

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Publication Date
Thu Nov 19 2020
Journal Name
Iop Conference Series: Materials Science And Engineering
Structural, morphological and optical properties of spray pyrolysis TiO<sub>2</sub>:GO nano films
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Thin films of pure and doped nano titanium dioxide (TiO2) were prepared using a chemical pyrolysis technique (CPS), with different nanosize graphene oxide (GO) concentrations in the range (3-9)wt%. The structural, morphological andoptical characteristics of these films were investigated. X-ray diffraction (XRD) technique measurements revealed that the structure properties of TiO2have polycrystalline structure with anatase phase. AFM analysis showed the grain size of TiO2 films with different concentrations was decreased after doping with high concentration of GO ratio. Roughness of these films decreased too after adding of GO impurity for all films from (7.65-5.6)nm except 5wt% percentage where increased to 13.7nm. Optical

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Publication Date
Mon Jul 27 2026
Journal Name
Aip Conference Proceedings
Synthesis, study antimicrobial and antioxidant activity of new 2-mercapto quinazolinone derivatives containing azetidinone ring
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Publication Date
Wed Jun 01 2022
Journal Name
Res Militaris
The impact of the Corona pandemic on the financial performance of companies listed on the Iraqi Stock Exchange
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This research aims to demonstrate the nature and concept of the Corona pandemic, its implications for the global economy, and the management and performance of companies in particular. Additionally, the research intends to measure the impact of the Corona pandemic on companies' financial performance. Listed on the Iraqi Stock Exchange, which has finished compiling its year-end financial statements for 2019-2020. The investigation arrived at several findings, the most significant of which was that most businesses were not prepared for such a crisis technologically or to develop human resources to deal with this pandemic. In addition, most companies experienced a decrease in their financial performance as a direct result of the Corona pandemi

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Scopus
Publication Date
Sat Sep 01 2018
Journal Name
Polyhedron
Novel dichloro (bis {2-[1-(4-methylphenyl)-1H-1, 2, 3-triazol-4-yl-κN3] pyridine-κN}) metal (II) coordination compounds of seven transition metals (Mn, Fe, Co, Ni, Cu, Zn and Cd)
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Publication Date
Sun Feb 28 2021
Journal Name
Journal Of Economics And Administrative Sciences
The effect of increasing the volume of debt on the volume of trading (applied research on a sample of private banks listed on the Iraq Stock Exchange)
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This research worked on identifying the effect of increasing the volume of indebtedness by companies listed on the Iraq Stock Exchange on the trading volume of those companies, and this research included some theoretical concepts related to both debt financing and trading volume, and it represents the research community of the joint-stock companies listed in The Iraq Stock Exchange (the banking sector). As for the research sample, it was deliberately chosen represented by companies with continuous trading without stopping, which reached 10 joint-stock companies, and the period of research was extended during the period 2011-2015, and a set of indicators and financial methods were used In measuring research v

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Publication Date
Sun Jan 19 2020
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
Effect flexibility of the Strategic human resources in improvement operational performance: "Survey study of views of a sample of managers, engineers and technicians in the Baghdad south 2/Station directorate of Electricity"
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The research attempts to diagnose the level of the effect of human resources flexibility (employees skills flexibility, employees behaviors flexibility, and human resource practice flexibility) in the south al-rusafa directorate of a power  station one of the formations and the Ministry of Electricity, and impact of a range of variables related to the performance operational, namely, (efficiency, effectiveness)recognizing the importance of the subjects studied,& because of the importance of expected results of the field under consideration,researcher selected a sample of size (121) engineers and technicians of workers in the directorate. Was my hypotheses the major search of a relationship and impact between human resources flex

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Publication Date
Sun Jun 01 2014
Journal Name
Baghdad Science Journal
The effect of Nitrofurantoin on liver on Albino mice
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the current study Included, evaluation the impact of Nitrofurantoin drug on liver in albino mice, 128 male albino mice have been used . Animals treared with (150,200 Mg/Kg) for 8 weeks . NFI caused histological changes in liver represented by , swelling of hepatocytes, disappearance of radial arrangement , vaculation of liver cells , increasing of kupffer cells and appearance of giant cells. NFT caused Congestion of blood vessels and infiltration of inflammatory cells in liver in all used concentrations.

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