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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 Dec 01 2020
Journal Name
Systematic Reviews In Pharmacy
A Study On The Effects Of Risk Factors On The Pathology And The Development Of Breast Cancer In Iraqi Women
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Breast cancer is one of the most important malignant diseases all over the world. The incidence of breast cancer is increasing around the world and it is still the leading cause of cancer mortality An Approximately 1.3 million new cases were diagnosed worldwide last year. With areas rising increasing, risk factors for breast cancer including obesity, early menarche, alcohol and smoking, environmental contamination and reduced or late birth rates become more prevalent. In Iraq, breast cancer ranks first among types of cancers diagnosed in women. This study was conducted on one hundred twenty women with breast cancer that was evaluated and investigated for the possible role of the risk factors on the development of breast cancer in females. T

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Fri Feb 08 2008
Journal Name
Al-mustansiriyah
Synthesis and Spectral Studies of the Transition Metals (Co(II), Ni(II), Cu(II), Cd(II), Hg(II) and Pb(II)) with aniline-2-thio methylene chloridecomplexes.
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Mon Mar 23 2020
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A Assessment of long distance chasing photometer (NAG-ADF-300-2) by estimating the drug atenolol with ammonium molybdate via continuous flow injection analysis: drug atenolol a
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     Atenolol was used with ammonium molybdate to prove the efficiency, reliability and repeatability of the long distance chasing photometer (NAG-ADF-300-2) using continuous flow injection analysis. The method is based on reaction between atenolol and ammonium molybdate in an aqueous medium to obtain a dark brown precipitate. Optimum parameters was studied to increase the sensitivity for developed method. A linear range for calibration graph was 0.1-3.5 mmol/L for cell A and 0.3-3.5 mmol/L for cell B, and LOD 133.1680 ng/100 µL and 532.6720 ng/100 µL for cell A and cell B respectively with correlation coefficient (r) 0.9910 for cell A and 0.9901 for cell B, RSD% was lower than 1%, (n=8) for the determination of ate

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Publication Date
Mon Sep 20 2021
Journal Name
Key Engineering Materials
Effect of Partial Substitution of Sr by Ba on the Structural Properties of Tl&lt;sub&gt;0.8&lt;/sub&gt;Ni&lt;sub&gt;0.2&lt;/sub&gt;Sr&lt;sub&gt;2-x&lt;/sub&gt;Br&lt;sub&gt;x&lt;/sub&gt;Ca&lt;sub&gt;2&lt;/sub&gt;Cu&lt;sub&gt;3&lt;/sub&gt;O&lt;sub&gt;9-δ&lt;/sub&gt; System
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In this manuscript, the effect of substituting strontium with barium on the structural properties of Tl0.8Ni0.2Sr2-xBrxCa2Cu3O9-δcompound with x= 0, 0.2, 0.4, have been studied. Samples were prepared using solid state reaction technique, suitable oxides alternatives of Pb2O3, CaO, BaO and CuO with 99.99% purity as raw materials and then mixed. They were prepared in the form of discs with a diameter of 1.5 cm and a thickness of (0.2-0.3) cm under pressures 7 tons / cm2, and the samples were sintered at a constant temperature o

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Wed Feb 19 2020
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International Journal Of Development In Social Sciences And Humanities
The Effect of Context on the Comprehension of English Idioms
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Publication Date
Thu Dec 01 2011
Journal Name
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The Effect of Shear on the Properties of Rigid PVC
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The rheological and fusion behavior of polyvinyl chloride (PVC) compounds plays a dominant role in
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The Impact of Coronavirus on the Implementation of Contractual Obligations
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The global health crisis resulting from the spread of the Corona virus, which the World Health Organization described on January 30, 2020 as a public health emergency of international concern, then returned to describe it as a pandemic on March 11, 2020, and the measures and procedures taken by government authorities in different countries of the world, whether at the highest level of imposing a comprehensive curfew or what is called globally home quarantine and thus disrupting all sectors and activities in the state, whether public or private (with the exception of some sectors such as the health, media and security sectors), or at a lower level than that, such as reducing work rates in different sectors by rates that vary from one country

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Publication Date
Fri Sep 01 2023
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The Impact of Smoking on the Complications of Acute Appendicitis
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Abstract<p> Introduction The pathophysiology of appendicitis likely stems from obstruction of the appendiceal orifice leading to an increase in intraluminal and intramural pressure, resulting in small vessel occlusion and lymphatic stasis. Organ supplied by an end artery, such as the appendix, are more prone to the deleterious effects of arterial occlusion. The continuous cigarette smoking might be associated with a greater risk for developing atherosclerosis.</p><p> Objectives The aim is to evaluate the effect of cigarette smoking on the incidence of complications of acute appendicitis.</p><p> Methods Patients suffered from symptoms and signs suggesting a</p> ... Show More
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The role of angiotensin converting enzyme (insertion)/(deletion) and angiotensin II type 1 receptor (A1166C) gene polymorphisms in antiproteinuric effect of ACE inhibitors in type 2 diabetic Iraqi patients
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The angiotensin converting enzyme (ACE) I\D gene polymorphism influences the blood ACE enzyme activity. Renoprotective effect of ACE inhibitors (ACEIs) varies among patients due to genetic variation, particularly in Renin-Angiotensin-Aldosterone System genes. This study investigates the genetic variations of ACE I\D and AGT1RA1166C gene polymorphisms in the antiproteinuric effect of ACEI therapy in type 2 diabetes mellitus (T2DM) patients. This is a cross-sectional study that included 76 T2DM patients who are ACEI users, divided into two groups: T2DM without diabetic kidney disease (DKD) included 31 patients, and T2DM with DKD included 45 patients. Urine samples were taken for measurement of urine albumin and creatinine, then calcul

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