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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
Tue Jan 01 2019
Journal Name
In Indian Journal Of Public Health Research And Development
The Significance of p53, Bcl-2, and HER-2/neu Protein Expression in Iraqi Females Breast Cancer Cell Line (AMJ13)
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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 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
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 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
Fri Sep 30 2011
Journal Name
Al-khwarizmi Engineering Journal
Composition and Temperature Dependence of Excess Volume of Heavy Oil-Stocks Mixtures + (Gas oil or Toluene or Reformate)
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Binary mixtures of three, heavy oil-stocks was subjected to density measurements at temperatures of 30, 35 and 40 °C. and precise data was acquired on the volumetric behavior of these systems. The results are reported in terms of equations for excess specific volumes of mixtures. The heavy oil-stocks used were of good varity, namely 40 stock, 60 stock, and 150 stock. The lightest one is 40 stock with °API gravity 33.69 while 60 stock is a middle type and 150 stock is a heavy one, with °API gravity 27.74 and 23.79 respectively. Temperatures in the range of 30-40 °C have a minor effect on excess volume of heavy oil-stock binary mixture thus, insignificant expansion or shrinkage is observed by increasing the temperature this effect beco

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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 May 01 2018
Journal Name
Journal Of Physics: Conference Series
The partial substitution of copper with nickel oxide on the Structural and electrical properties of HgBa<sub>2</sub> Ca<sub>2</sub> Cu<sub>3x</sub>Ni<sub>x</sub> O<sub>8+δ</sub> superconducting compound
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Publication Date
Thu May 28 2020
Journal Name
Iraqi Journal Of Science
The Association Between IL-2 Gene (RS2069763 (Single Nucleotide Polymorphism and Type 2 Diabetes Mellitus in Iraqi Patients
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This research attempts to find the association between single nucleotide polymorphism (SNP) of IL2+166 gene (rs2069763) and type 2 diabetes mellitus (T2DM) in a sample of Iraqi patients. A total of 44 patients and 55 apparently healthy volunteers were genotyped for the SNP using polymerase chain reaction test. Three genotypes (GG, GT, and TT) corresponding to two alleles (G and T) were found to have SNP. Both study groups’ genotypes had a good agreement for the analysis of Hardy-Weinberg Equilibrium. The results revealed increased frequencies between the observed and expected GG and TT genotypes and IL2+166 SNP T allele in T2DM  patients (40.9 vs. 40.0 %; OR = 1.04; 95% CI, 0.47 - 2.31), whereas the values in the control group were

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