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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
Fri Dec 01 2023
Journal Name
Baghdad Science Journal
Determining ACE-2 Level and Some Relevant Biochemical Parameters and studying the effect of Gender in Iraqi Diabetic Patients with Glomeruli and Renal Tubules Fibrosis as Early Prediction Marker
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     Diabetic kidney disease is an illness of the glomerulus that interferes with the glomerular filtration barrier (GFB), which is worked to enable kidney to selective purification of water and solutes in addition to limiting the movement of large macromolecules such as albumin. In the glomerular endothelium, mesangial cells, foot cells, and the brush border of the proximal tubules, ACE-2 is expressed and that the kidneys represent the highest-expressing region of this enzyme. Thus, the current study aimed to evaluate ACE-2 level in this case compared to healthy condition. The study Conducted with 120 male and female ranging in age (30-65) years old. Ninety patients with type 2 diabetes subdivided into three groups on the basis of A

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Publication Date
Fri Jan 01 2021
Journal Name
Plant Archives
STUDY OF THE EFFECT OF SPEED, DEPTH OF THE CULTIVATION AND THE NUMBER OF TIMES THE SPRING – LOADED CULTIVATOR PASSES ON SOME TECHNICAL PARAMETERS OF THE CULTIVATOR AND ON WEED CONTROL
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Publication Date
Fri Jan 15 2021
Journal Name
Plant Archives
STUDY OF THE EFFECT OF SPEED, DEPTH OF THE CULTIVATION AND THE NUMBER OF TIMES THE SPRING – LOADED CULTIVATOR PASSES ON SOME TECHNICAL PARAMETERS OF THE CULTIVATOR AND ON WEED CONTRO
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Publication Date
Tue Feb 05 2019
Journal Name
Journal Of The College Of Education For Women
The Scientific Journals in the websites of the colleges of University of Baghdad on the web
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The aim of the research is the knowing of the academic Scientific Journals of the colleges of University of Baghdad , through searching in the University of Baghdad website and the websites of colleges and thus studying the presentation of these journals in those website , and this is done by surfing the main pages of the websites for the colleges included in the research , and by analyzing the research made a menu for all the academic Scientific Journals for all institutes of the University of Baghdad , which simplifies the way for the researchers to publish these researches in the specific journals for their specialties .

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Publication Date
Sun Dec 06 2015
Journal Name
Baghdad Science Journal
The Effect of The Electrochemical Deposition Potential Variation on The Coating of Hydroxyatite on Commertialy pure Titanium (CpTi) and Ti-6Al-4V Alloy
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In this research we investigated the corrosion behavior of the commertialy pure titanium and Ti-6Al-4V alloy that coated with hydroxyapatite by electrochemical deposition with applied voltage (6,9,12) Volt from aqueous solution containing Ca(NO3)2.H2O =7.0 gm/l , (NH4)2HPO4 =3.5 gm/l , Na(NO3)2 = 8.5 gm/l in order to improve the bonding strength of hydroxyapetite and medical metals and alloys and increasing the biocompatibility. The coating layer morphology was investigated by XRD, Optical microscope , and SEM tests, the corrosio tests was made by use senthesys simulated body fluid (SBF) , and we found that the propreate voltage for coatint on Ti was 9 Volt and for Ti-6Al-4Vwas12Volt.

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Publication Date
Sun Dec 16 2018
Journal Name
Al-academy
The Impact of the Use of Piano on the Development of Musical Possibilities of Violinists
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This research is to take advantage of the performance capabilities which the piano has become famous with and transfer the impact of that advantage to the possibilities of playing the violin. The research aims to introduce the effect of using the piano on the development of the violinists' musical potential. The research, in its literature, focuses on the interpretation of the impact on the possibility of both instruments (piano and violin) in two main sections: the piano (its origin, potential and role in music) and the violin (its origin, potential and role in music). The procedures of the research consisted of presenting a special analysis of a questionnaire consisting of a number of questions presented by the researcher to her resear

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Publication Date
Fri Nov 01 2019
Journal Name
Biochemical And Cellular Archives
ASSOCIATION OF SERUM INSULIN-LIKE GROWTH FACTOR-1 WITH OBESITY IN TYPE 2 DIABETIC IRAQI PATIENTS AND ACUTE RENAL FAILURE
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ABSTRACT : Diabetes mellitus stands for a set of metabolic diseases that if they are not managed, they can initiate threatening life problems. This study hypothesizes that insulin-like growth factor-1 level can be used as a biomarker for early diagnosing renal problems in patients with type 2 diabetic disease. This study included 30 recently identified type 2 diabetic patients with acute renal malfunction who had an entrance in National Diabetic Center,AL-Mustansiriyah University.They have beenin the Center from October 2018 up to end of April 2019. Their age range has been (40-62) years. Comprehensive clinical investigationhas beencompleted for each patient to discount other diabetic complications like cardiac, neurologic and eye complicat

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Publication Date
Wed May 24 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Science
Direct and Indirect Spectrophotometric Determination of Paracetamol in Pharmaceutical Preparations By Oxidative Coupling With p-Amino-2-hydroxy Sodium Benzoate
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New simple and sensitive spectrophotometric methods for the determination of paracetamol in aqueous medium were developed. The first method is based on coupling of paracetamol with p-amino-2-hydroxy sodium benzoate (AHB) in the presence of sodium periodate, as oxidizing agent, to form a brownish-orange compound which shows a λmax at 470 nm. The molar absorptivity (εmax) of the colored product was found to be (3371) l. mole1. cm-1 and Sandel’s index 0.0449 μg. cm-2. The method follows Beer’s law in the concentration range of 12.5-500.0 μg of paracetamol in a final volume of 25 ml (0.5-20.0) μg. ml-1 with relative standard deviation percent (RSD%) ranged between 0.26-4.71% and accuracy, expressed by recovery percent, 95-106% for five

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Publication Date
Sun Jan 20 2019
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Synthesis, Antibacterial and Antifungal Activities for Novel Derivatives of 2,2'-(((1-benzylbenzoimidazol-2-yl)methyl)azanediyl)bis(ethan-1-ol)
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The compound 2,2'-(((1H-benzo(d)imidazol-2-yl)methyl)azanediyl)bis(ethan-1-ol) was reacted with benzyl bromide to afford compound (1) which used as row material to prepare a series of compounds through condensation reaction, the starting compound were reacted with tosyl chloride to protect the OH group  to afford compound 2, then reacted benzyl bromide to produce compound (2), then the compound (2) treated with three compounds ( 2-mercaptobenzthiazole, 2-mercaptobenimidazol and 2-chloromethyl benzimidazole) to form compounds 3a,b, 4a,b and 5a,b respectively. In the another step the click reaction of compound 2,2'-(((1H-benzo(d)imidazol-2-yl)methyl)azanediyl)bis(ethan-1-ol) with Propargyl bromide produce compound  6  which reacted

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Publication Date
Mon Nov 01 2021
Journal Name
Journal Of Physics: Conference Series
Neural Network Model for Synthesis of Thermally Sprayed (AI/AI<sub>2</sub>O<sub>3</sub>) Composite Protective Coatings
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Abstract<p>Al<sub>2</sub>O<sub>3</sub> and Al<sub>2</sub>O<sub>3</sub>–Al composite coatings were deposited on steel specimens using Oxy-acetylene gas thermal spray gun. Alumina was mixed with Aluminum in six groups of concentrations (0, 5, 10,12,15 and 20% ) Al2O3, Specimens were tested for corrosion using Potentiodynamic polarization technique. Further tests were conducted for the effect of temperature on polarization curve and the hardness tests for the coated specimens. At first, Modelling was carried out using MINITAB-19, least square method, as a 2nd degree nonlinear model, bad results were achieved because of the high nonlinearity. Better result w</p> ... Show More
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