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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 May 01 2024
Journal Name
Biology
Lysophosphatidylcholine Acetyltransferase 2 (LPCAT2) Influences the Gene Expression of the Lipopolysaccharide Receptor Complex in Infected RAW264.7 Macrophages, Depending on the E. coli Lipopolysaccharide Serotype
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Escherichia coli (E. coli) is a frequent gram-negative bacterium that causes nosocomial infections, affecting more than 100 million patients annually worldwide. Bacterial lipopolysaccharide (LPS) from E. coli binds to toll-like receptor 4 (TLR4) and its co-receptor’s cluster of differentiation protein 14 (CD14) and myeloid differentiation factor 2 (MD2), collectively known as the LPS receptor complex. LPCAT2 participates in lipid-raft assembly by phospholipid remodelling. Previous research has proven that LPCAT2 co-localises in lipid rafts with TLR4 and regulates macrophage inflammatory response. However, no published evidence exists of the influence of LPCAT2 on the gene expression of the LPS receptor complex induced by smooth or rough b

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Publication Date
Sun Aug 15 2021
Journal Name
Al-qadisiyah Journal Of Pure Science Vol.(26) Issue (special Issue Num.4) (2021) Pp. 30–33
Accounts for the groups (2, ), = 41 and 43
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Publication Date
Tue Mar 30 2021
Journal Name
Journal Of Interdisciplinary Mathematics
Computations for the special linear group (2, 49)
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Publication Date
Sun Nov 01 2020
Journal Name
Journal Of Physics: Conference Series
Laser Irradiation Effect on The Optical Properties of CoO<sub>2</sub>Thin Films deposited via Semi-Computerized Spraying System
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Abstract<p>In this paper deals with the effect laser irradiation on the optical properties of cobalt oxide (CoO<sub>2</sub>) thin films and that was prepared using semi computerized spray pyrolysis technique. The films deposited on glass substrate using such as an ideal value concentration of (0.02)M with a total volume of 100 ml. With substrate temperature was (350 C), spray rate (15 ml/min).The XRD diffraction given polycrystalline nature with Crystal system trigonal (hexagonal axes). The obtained films were irradiated by continuous green laser (532.8 nm) with power 140 mW for different time periods is 10 min,20min and 30min. The result was that the optical properties of cobalt oxide thin films affe</p> ... Show More
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Publication Date
Sun Aug 30 2020
Journal Name
Journal Of Economics And Administrative Sciences
Improve operational performance by simulating the Holonic manufacturing system A case study at the rubber product plant in Al-Najaf Al-Ashraf
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The research aims to improve operational performance through the application of the Holonic Manufacturing System (HMS) in the rubber products factory in Najaf. The problem was diagnosed with the weakness of the manufacturing system in the factory to meet customers' demands on time within the available resources of machines and workers, which led to time delays of Processing and delivery, increased costs, and reduced flexibility in the factory, A case study methodology used to identify the reality of the manufacturing system and the actual operational performance in the factory. The simulation was used to represent the proposed (HMS) by using (Excel 2010) based on the actual data and calculate the operational performance measures

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Publication Date
Sun Dec 06 2009
Journal Name
Baghdad Science Journal
Best estimation for the Reliability of 2-parameter Weibull Distribution
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This Research Tries To Investigate The Problem Of Estimating The Reliability Of Two Parameter Weibull Distribution,By Using Maximum Likelihood Method, And White Method. The Comparison Is done Through Simulation Process Depending On Three Choices Of Models (?=0.8 , ß=0.9) , (?=1.2 , ß=1.5) and (?=2.5 , ß=2). And Sample Size n=10 , 70, 150 We Use the Statistical Criterion Based On the Mean Square Error (MSE) For Comparison Amongst The Methods.

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Publication Date
Wed Dec 01 2021
Journal Name
Baghdad Science Journal
New Common Fixed Points for Total Asymptotically Nonexpansive Mapping in CAT(0) Space
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      Strong and ∆-convergence for a two-step iteration process utilizing asymptotically nonexpansive and total asymptotically nonexpansive noneslf mappings in the CAT(0) spaces have been studied. As well, several strong convergence theorems under semi-compact and condition (M) have been proved. Our results improve and extend numerous familiar results from the existing literature.

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Publication Date
Fri May 31 2024
Journal Name
Journal Of Interdisciplinary Mathematics
Fibrewise locally micro sliceable and fibrewise locally micro-section able micro-topological space
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The primary objective of this research be to develop a novel thought of fibrewise micro—topological spaces over B. We present the notions from fibrewise micro closed, fibrewise micro open, fibrewise locally micro sliceable, and fibrewise locally micro-section able micro topological spaces over B. Moreover, we define these concepts and back them up with proof and some micro topological characteristics connected to these ideas, including studies and fibrewise locally micro sliceable and fibrewise locally micro-section able micro topological spaces, making it ideal for applications where high-performance processing is needed. This paper will explore the features and benefits of fibrewise locally micro-sliceable and fibrewise locally

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Publication Date
Thu Mar 30 2017
Journal Name
Iraqi Journal Of Pharmaceutical Sciences ( P-issn 1683 - 3597 E-issn 2521 - 3512)
The Effect of Long Term use of Glibenclamide on Serum and Urinary Sodium and Potassium Level in Type 2 DM Patients
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         Long-term use of sulfonylureas including chlorpropamide, is known to potentiate the antidiuretic action of arginine vasopressin (AVP), predisposing to hyponatremia.The present study was designed to evaluate the effect of long term use of glibenclamide on serum and urinary levels of sodium and potassium in Type 2 DM patients in Iraqi DM centers. Ninety eight patients with Type 2 DM who were maintained on different doses of glibenclamide for at least 1 year, attending the centre for Diabetes and Endocrinology in Al-Rusafa, Baghdad, were enrolled in the study, in addition to 15 normal healthy subjects. Patients were allocated into three groups according to the dose of glibenc

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Publication Date
Tue Nov 03 2015
Journal Name
Journal Of Natural Sciences Research
Implementation of remote sensing for vegetation studying using vegetation indices and automatic feature space plot
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