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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
Thu Jan 01 2015
Journal Name
Ibn Al-haitham J. For Pure & Appl. Sci.
Synthesis and Characterization of Some Metal Complexes of [N-(1,5-dimethyl-3-oxo-2-phenyl-2,3-dihydro-1H-pyrazol- 4-ylcarbamothioyl) acetamide]
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A new ligand [N- (1,5- dimethyl -3- oxo- 2 – phenyl - 2 ,3 – dihydro -1H- pyrazol -4- ylcarbamothioyl) acetamide] (AAD) was synthesized by reaction of acetyl isothiocyanate with 4-aminoantipyrine, The ligand was characterized by micro elemental analysis C.H.N.S., FT-IR ,UV-Vis and 1H-13CNMR 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(AAD)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
Tue Dec 01 2015
Journal Name
Journal Of Al-nahrain University-science
Synthesis of Polyacrylamides from Derivatives 2-Aminobenzothiazole and also Preparation of Dibutylphthalate as a Plasticizer to Estimate Plasticization Behaviour for Prepared Polymers
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Publication Date
Sun Sep 01 2013
Journal Name
Baghdad Science Journal
Synthesis ,spectroscopic study of Antipyryl azo 2-Naphthol and use it as new reagent for determination of Co(II) and Cu(II)
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A simple ,accurate and sensitive spectrophotometric method has been developed the determination of Cobalt(II) and Cupper (II) .The method is based on the chelation of Co(II) and Cu(II) ions with 4-(4´-pyrazolon azo) -2-Naphthol(APAN) in aqueous medium . The complexes have a maximum absorption at (513) and (506) nm and ? max 0.531×10 4 and 0.12×10 5 L.mol -1.cm -1 for Co(II) and Cu(II) respectively .The reagent and two complexes have been prepared in ethanolic solution.The stoichiometry of both complexes were found to be 1:2 (metal :legend) .The effects of various cations and anions on Co(II) and Cu(II) determination have been investigated .The stability constants and standard deviations for Co(II) and Cu(II) 0.291 x107 ,0.909X108 L.mol

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Publication Date
Wed Jan 30 2013
Journal Name
Al-kindy College Medical Journal
Over expression of Her- 2 neu in ovarian surface epithelial carcinoma in a sample of Iraqi patient at Al-kindy Teaching Hospital.
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Background: Although expression of the HER-
2/neuoncogene may be of some prognostic importance
in advanced ovarian cancer, its role in early-stage
disease has not been established. The current study
examined the prevalence and significance of HER-
2/neu expression in different grades of different types
of surface epithelial ovarian carcinoma.
Methods: Thirty eight female patients with surface
epithelial ovarian cancer were included in this study.
The blocks of corresponding formalin fixed, paraffinembedded
ovarian biopsies were retrieved from the
archives and hematoxylin-eosin slides of each ovarian
biopsy were reviewed and marked their grades of
differentiation , then a new sections from each sampl

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Publication Date
Wed Feb 15 2023
Journal Name
Environmental Technology
Bio-synthesis of TiO<sub>2</sub> using grape leaves extract and its application for photocatalytic degradation of ibuprofen from aqueous solution
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Publication Date
Wed Sep 27 2023
Journal Name
Iraqi Journal Of Pharmaceutical Sciences ( P-issn 1683 - 3597 E-issn 2521 - 3512)
Assessment of Serum Levels of Advanced Oxidation Protein Products in Type 2 Diabetic Patients with and without Retinopathy Taking Different Antidiabetic Treatments
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The goal of this study was to investigate the protein peroxidation role by measuring serum levels of advanced oxidation protein products (AOPP) in type 2 diabetic patients with or without retinopathy and comparing them to controls to see if circulating AOPP levels can be used as a detection biomarker for DR. And see which of the two widely used antidiabetic treatment groups had the most impact on this oxidative stress marker. The groups were divided into two subgroups: 1) 70 type 2 diabetic patients (36 male, 34 female), 35 with diabetic retinopathy (DR) and 35 with no evidence of DR, and 2) non-diabetic controls (11 male, 9 female) were chosen from Ibn AL-Haitham Hospital for Ophthalmology and a Specialized Center for Endocrinology and Dia

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Crossref (2)
Scopus Crossref
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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Crossref
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
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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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Crossref
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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