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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
Sun May 01 2022
Journal Name
Journal Of Ecological Engineering
Ability of Response Surface Methodology to Optimize Photocatalytic Degradation of Amoxicillin from Aqueous Solutions Using Immobilized TiO&lt;sub&gt;2&lt;/sub&gt;/Sand
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Publication Date
Sun Dec 01 2013
Journal Name
Baghdad Science Journal
Detection of Anti-Helicopacter pylori IgG Antibody, Anti-GAD antibody, Anti-Beta islets cell in a sample of serum with type-2 Diabetes mellitus patients
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We have investigated twenty five patients with type-2 diabetes mellitus aged (35-60) years and fifteen healthy persons as control group to detect Anti-Helicobacter pylori IgG antibody. All studied groups were carried out to measure fasting blood sugar, anti- Glutamic acid decarboxylase (GAD), anti-? islets cells antibody by IFAT, Anti-H. pylori IgG antibody by ELISA technique. There was significant elevation in the concentration of fasting blood sugar than in control group (P < 0.05), the patients had negative results for anti-GAD antibody and anti- ? islets cells antibody, there were significant differences (P < 0.05) of anti-H. pylori IgG antibody in 28 % of patients had type-2 diabetes than control group. This lead to suggestion that typ

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Publication Date
Mon Jan 11 2016
Journal Name
مجلة كلية التربية الاساسية
Synthesis and Characterization of Some Metal Complexes of [4- chloro-N- 1,5-dimethy l-3-oxo-2- phenyl-2,3-dihydro-1H-pyrazol-4- ylcarbamothioyl(benzamide)
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A new ligand [4-chloro-N-(1,5-dimethyl-3-oxo-2-phenyl-2,3- dihydro-1H-pyrazol-4-ylcarb amothioyl) benzamide] (CAP) was synthesized by reaction of P-ChloroBenzoyl isothio cyanate with 4- aminoantipyrine,The ligand was characterized by micro elemental analysis C.H.N.S.,FT-IR,UV-Vis and1H13CNMR spectra, some transition metals complex of this ligand were prepared and characterized by FT-IR, UV-Vis spectra, conductivity measurements, magnetic susceptibility and atomic absorption. From the obtained results the molecular formula of all prepared complexes were [M(CAP)2(H2O)2]Cl2(M+2 =Mn, Co, Ni, Cu, Zn, Cd and Hg),the proposed geometrical structure for all complexes were octahedral

Publication Date
Wed May 01 2024
Journal Name
Journal Of Physics: Conference Series
Analyze the Structure and Electrical Properties of PbBr<sub>2</sub> Ca<sub>1.9</sub>Sb<sub>0.1</sub>Cu<sub>3</sub>O<sub>8+</sub> <sub>δ</sub> Superconducting Gamma Irradiation
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The purpose of the current work was to evaluate the effect of Radiation of Gamma on the superconducting characteristics of the compound PbBr2Ca1.9Sb0.1Cu3O8+δ utilizing a 137Cs source at doses of 10, 15, and 20MRad. Solid state reaction technology was used to prepare the samples. Before and after irradiation, X-ray diffraction (XRD) and superconductor properties were examined. Results indicated that the tetragonal structure of our chemical corresponds to the Pb-1223 phase with an increase in the ratio c/a as a result of gamma irradiation. (Tc (onset) ) and on set temperature Tc (offset)) were also dropping from 113 to the 85.6 K and 129.5 to 97 K, respectively, for a transition temperatu

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Publication Date
Mon Sep 30 2013
Journal Name
Iraqi Journal Of Chemical And Petroleum Engineering
Effect of Additives on the Properties of Different Types of Greases
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The aim of this research is to study the influence of additives on the properties of soap greases, such as lithium, calcium, sodium, lithium-calcium grease, by adding varies additives, such as graphite, molybdenum disulfide, carbon black, corrosion inhibitor, and extreme pressure.
These additives have been added to grease to obtain the best percentages that improve the properties of grease such as load carrying, wear resistance, corrosion resistance, drop point, and penetration.
The results showed the best weight percentages to all types of grease which give good properties are 1.5% extreme pressure additive, 3% graphite, 1% molybdenum disulfide, 2.5% carbon black.
The other hand, the best weight percentage for corrosion inhibit

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Publication Date
Sun Jan 01 2023
Journal Name
Journal Of Advanced Biotechnology And Experimental Therapeutics
Kidney injury molecule-1 and cystatin C as early biomarkers for renal dysfunction in Iraqi type 2 diabetes mellitus patients
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Diabetic kidney disease (DKD) is caused by a variety of processes. As a result, one biomarker is insufficient to represent the complete process. This study Evaluate the diagnostic value of serum kidney injury molecule-1(KIM-1) and cystatin C (CysC) as early biochemical markers of DKD and predictive their sensitivities and specificities as biomarkers of nephropathy in Iraqi type 2 diabetic (T2DM) patients. This cross-sectional study include 161 T2DM patients from Diabetes and Endocrinology Center at Merjan medical city in Babylon. Patients divided according to urinary albumin creatinine ratio(ACR) (Group1:ACR≤30mg/g,Group2:ACR>30mg/g). Random spot urine and fasting blood samples were taken from each patient and urinary ACR, bloo

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Publication Date
Fri Oct 04 2024
Journal Name
Chemical Review And Letters
Newly designed 2-(aminomethyl)benzimidazole derivatives as possible tyrosine kinase inhibitors: synthesis, characterization, preliminary cytotoxic evaluation and in Silico studies
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Publication Date
Fri Nov 01 2019
Journal Name
Iop Conference Series: Earth And Environmental Science
The role of low concentrations of some sulfuric antioxidants on the semen characteristics of rams
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Abstract<p>This study aims to investigate the effect of low concentrations of sulfuric antioxidants on sperm of rams. This study was conducted in the field of sheep and goats of the Department of Livestock in the collage of Agricultural Engineering Sciences, University of Baghdad. The semen was collected using the artificial vagina at weekly rate (Pooled semen) and was subjected to different tests and then was divided into seven treatments but different concentrations of cysteine (0.5, 1mM) and glutathione (0.5, 1mM) and taurine (0.5, 1mM).The sample of the semen was diluted with Tris dilution (10: 1). The results showed that the low concentrations of glutathione, cysteine and taurine resulted i</p> ... Show More
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Publication Date
Thu Dec 01 2016
Journal Name
Journal Of Economics And Administrative Sciences
The impact of financial reporting of earnings per share on the quality of financial reporting
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This research deals with the case of the Iraqi joint-stock companies listed on the Iraq Stock Exchange study in terms of compliance with the requirements of IAS 33 "Earnings per share" and the research problem Alrtash concentrated in a statement the commitment of those companies the requirements of the International Standard 33, which may adversely affect the quality of financial reporting where and in particular the quality of accounting information and content of the primary and secondary characteristics make them be of interest to the decisions of its users, so the aim of this research to the statement of financial reporting earnings per share on the quality of financial reporting in listed shareholding in Iraq Stock Exchange

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Publication Date
Sun Sep 30 2001
Journal Name
Iraqi Journal Of Chemical And Petroleum Engineering
The Effect of MFI of High-Density Polyethylene on the Mathematical Modeling of Tensile Characteristic
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