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MRbmuIoBVTCNdQwCLKT9
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
Tue Jan 01 2019
Journal Name
Indian Journal Of Public Health Research &amp; Development
Effect of <i>Olea europea</i> L Extraction and TiO<sub>2</sub> Nanoparticles against <i>Pseudomonas aeruginosa</i>
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Publication Date
Fri Jun 03 2022
Journal Name
Annals Of Parasitology
Genotyping and evaluation of interleukin-10 and soluble HLA-G in abortion due to toxoplasmosis and HSV-2 infections
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Abortion is a condition that occurs due to one of the pathological injuries, often one of the members of the TORCH is the real cause. The current study aimed to investigate the impact of toxoplasmosis, HSV-2 infections with abortion, and also, the identification of immunogenetics marker (interleukin-10) that may be associated with abortion. Anti-Toxoplasma IgG, IgM, Herpes simplex virus-2 IgM, human soluble leukocyte antigen class I–G and interleukin10 were estimated by ELISA technique, while the expression of IL-10 gene was investigated by using the real-time PCR. The results showed that among aborted women the rate of anti-Toxoplasma and HSV-2 IgM antibodies occurred within the age groups (21–30) years and (31–40) years 32(100.0%) a

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Publication Date
Wed Dec 30 2020
Journal Name
Iraqi Journal Of Pharmaceutical Sciences ( P-issn 1683 - 3597 E-issn 2521 - 3512)
Association of Retinol Binding Protein- 4 (RBP4) with Glycemia, Dyslipidemia, Hypertension, and Obesity in Type 2 Diabetic Iraqi Patients
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Abstract:

Background: Retinol binding protein 4 (RBP4), an adipokine that participate in a lipid metabolism or insulin resistance through a complex regulatory network. Recently, RBP4 was reported to be associated with many cardiovascular diseases (CVDs) risk factors in patients of type 2 diabetes mellitus (T2DM). This study aims to study the correlation of  serum RBP4 with some markers of glycemic control, dyslipidemia, hypertension and obesity in T2DM Iraqi patients.

Subjects and Methods: one hundred fifty participants were enrolled in this coss-sectional study, 120 of participants were T2DM patients and 30 were apparently healthy individuals to serve as control gro

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Publication Date
Fri Mar 10 2017
Journal Name
Superconductor Science And Technology
Conceptual designs of conduction cooled MgB<sub>2</sub> magnets for 1.5 and 3.0 T full body MRI systems
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Publication Date
Wed Mar 10 2021
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Baghdad Science Journal
the effect of doping ratio on the opical properties
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the films of cdse pure and doped with copper ratio glass substrate effect od cucomcentration technique thikness doped with copper is an anonmg and the density of state increases

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Publication Date
Fri Dec 30 2016
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International Journal Of Advanced Research In Biological Sciences (ijarbs)
The effect of obesity on the periodontal health status
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Publication Date
Sat Feb 28 2026
Journal Name
Al–bahith Al–a'alami
The Common Discourse of The Arab tweeters on Normalization
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The study aimes to analyze the discourse of Arab tweeters regarding the normalization of Arab-Israeli relations on the social media site (Twitter).
Study Methodology: The study relay on the survey method, using the comprehensive survey method, and this research is one of the descriptive types that aim to describe the phenomenon in a qualitative way, and discuss it through the method of in-depth analysis, in addition to using the tools of (discourse analysis).
Study sample: A sample of (8686) tweets for (7425) tweeters, which was posted on Twitter during the period from 15/9 to 30/9/2020, on the issue of normalizing Arab-Israeli relations.
Study tools: The data study was collected using the data mining tool from social networks (

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Thu Jun 21 2012
Journal Name
J Bagh Coll Dent
Dental caries in relation to oral infections and feeding types among children aged 2-5 years
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Publication Date
Fri Dec 30 2011
Journal Name
Al-kindy College Medical Journal
None anticipated bacterial urinary tract infections in type 2 diabetic patients relative to duration and angiopathies
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Background: Diabetes mellitus is a well
known metabolic and vascular illness associated
with high incidence of bacterial urinary tract
infections especially in diabetic complications
including both micro and macro-vascular types.
Objective: To study the incidence of bacterial
urinary tract infections in type 2 diabetic
patients, the type of micro-organism responsible
in relation to age, sex of patients, duration of the
disease & related micro & macrovascular
diabetic complications.
Methods: A prospective study of the diabetic
patients including 40 males with mean age of
54(±9) years and 50 females, mean age of 51(±7)
years and duration of the and sex matched
controls (27 males and 33

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Publication Date
Sun Dec 03 2023
Journal Name
2023 Ieee International Conference On Energy Technologies For Future Grids (etfg)
Optimal Hybrid Type-2 Fuzzy-PID Controller for Blade Pitch Angle in Horizontal-axis Wind Turbines
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In the modern world, wind turbine (WT) has become the largest source of renewable energy. The horizontal-axis wind turbine (HAWT) has higher efficiency than the vertical-axis wind turbine (VAWT). The blade pitch angle (BPA) of WT is controlled to increase output power generation over the rated wind speed. This paper proposes an accurate controller for BPA in a 500-kw HAWT. Three types of controllers have been applied and compared to find the best controller: PID controller (PIDC), fuzzy logic type-2 controller (T2FLC), and hybrid type-2 fuzzy-PID controller (T2FPIDC). This paper has been used Mamdani and Sugeno fuzzy inference systems (FIS) to find the best inference system for WT controllers. Furthermore, genetic algorithm (GA) and particl

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