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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 Dec 06 2015
Journal Name
Baghdad Science Journal
Synthesis and Characterization of Some Metal Complexes with their Sulfamethoxazoleand 4,4'-dimethyl-2,2'-bipyridyl and study Cytotoxic Effect on Hep-2 Cell Line
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The ligand 4-amino-N-(5-methylisoxazole-3-yl)-benzene-sulfonamide(L1) (as a chelating ligand) was treated with Pd(II),Pt (IV) and Au(III) ions in alcoholic medium in order to prepare a series of new metal complexes. Mixed ligand complexes of this primary ligand were prepared in alcoholic medium in presence of the co-ligand 4,4'-dimethyl-2,2'-bipyridyl(L2) with Cu(II) ,Pd(II) and Au(III) ions. The complexes were characterized in solid state using flame atomic absorption, elemental analysis C.H.N.S, FT-IR, UV-Vis Spectroscopy, conductivity and magnetic susceptibility measurements. The nature of some complexes formed in ethanolic solution has been studied following the molar ratio method, also stability constant was studied and the complexes f

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Publication Date
Tue Mar 30 2021
Journal Name
Iraqi Journal Of Science
Electrochemical Polymerization and Biological Activity of 4-(Nicotinamido)-4-Oxo-2-Butenoic Acid as An Anticorrosion Coating on A 316L Stainless Steel Surface
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In this study, poly4-(nicotinamido)-4-oxo-2-butenoic acid (PNOE) was prepared by the electro polymerization of 4-(nicotinamido)-4-oxo-2-butenoic acid (NOE) monomer on a 316 stainless steel (St.St) which acts as an anticorrosion coating.  Fourier transforms infrared (FTIR), atomic force microscopy (AFM), scanning electron microscopy (SEM), and cyclic voltammetry were used to diagnose the structure and the properties of the prepared polymer layer. The corrosion behavior of the uncoated and coated 316  St.St were evaluated by using an electro chemical polarization technique in 0.2 M hydrochloric acid  solution as a corrosive medium at a temperature range of 293 to 323 K. Nano materials, such as nano ZnO and graphene were added in di

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Publication Date
Tue Jan 01 2013
Journal Name
Chemical And Process Engineering Research
Synthesis and Characterization of Complexes of Schiff Base [1, 2-Diphenyl -2- 2-{[1-(3-Amino-Phenyl)-Ethylidene]-Hydrazono Methyl}-Phenol] with Mn(II), Fe(II), Co(II), Cu(II), Zn(II), Cd(II), Ni(II), and Hg(II) Ions
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The new tridentate Schiff base ligand (HL)namely 2-{[1-(3-amino-phenyl)-ethylidene]-hydrazono methyl}- phenol containing (N N O)as donors atoms was prepared in two steps:Step (1): By the reaction of 3- aminoacetophenone with hydrazine monohydrate under reflux in methanol and drops of glacial acetic acid gave the intermediate compound 3-(1- hydrazono ethyl)-phenol amine.Step (2): By the reaction of 3-(1-hydrazono ethyl)-phenol amine with salicyaldehyde under reflux in methanol, gave the ligand (HL).The prepared ligand was characterized by I.R, U.V-Vis,1H- 13C NMR spectra and melting point and reacted with some metal ions under reflux in methanol with (1:1) ratio gave complexes of the general formula: [MClL]. Where: M= Mn(II), Fe(II), Co(II),

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Publication Date
Sat Nov 01 2014
Journal Name
Journal Of Cosmetics, Dermatological Sciences And Applications
Therapeutic evaluation of 2% tea lotion in comparison with 5% zinc sulfate solution in the treatment of acne rosacea
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KE Sharquie, AA Noaimi, SA Al-Hashimy, MM Al-Salih, Journal of Cosmetics, Dermatological Sciences and Applications, 2014 - Cited by 12

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Publication Date
Tue Oct 24 2023
Journal Name
Chemical Engineering &amp; Technology
Electrodeposition of Manganese Dioxide under Different Conditions: Application of MnO<sub>2</sub>/Carbon Fibers in the Electrosorption Process
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Abstract<p>Anodic electrodeposition was used to synthesize a composite electrode of nanostructured manganese dioxide/carbon fiber (CF) galvanostatically. Different characterization results of the nanostructured MnO<sub>2</sub> were obtained by varying the H<sub>2</sub>SO<sub>4</sub> concentration and the current density. Field emission scanning electron microscopy, X‐ray diffraction, and atomic force microscopy were utilized to characterize the prepared composite electrodes. The best conditions were: 0.3 mA cm<sup>−2</sup> current density and 0.64 M H<sub>2</sub>SO<sub>4</sub> concentration. The electrosorption performance of the MnO<sub></sub></p> ... Show More
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Publication Date
Tue Jul 01 2025
Journal Name
Journal Of The Faculty Of Medicine Baghdad
Clinical Diagnostic Value of Stromelysin-2 and Highly Sensitive-Cardiac Troponin I in the Severity of Coronary Artery Obstruction
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Background: Coronary artery disease is a leading cause of death worldwide. Troponin is released into blood from patients with reversible myocardial ischemia. Stromelysin-2 is also involved in the development and progression of atherosclerosis by tissue remodeling and degradation of extracellular matrix proteins.Objectives: To investigate the role of serum high-sensitive cardiac troponin I (hs-cTn I) and Stromelysin-2 (Str-2) in the diagnosis and determination of the severity of coronary artery obstruction.Methods: This cross-sectional study was conducted on 125 subjects undergoing coronary angiography for suspicion of coronary artery disease in Baghdad Teaching Hospital/ Medical City complex/ Baghdad/ Iraq by the Department of Bioch

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Publication Date
Mon Jul 01 2019
Journal Name
Journal Of Physics: Conference Series
Effect of Nickel Substitution On Structural and Electrical Properties of Hg<sub>0.5</sub>Pb<sub>0.5</sub>Ba<sub>2</sub>Ca<sub>2</sub>Cu<sub>3-y</sub>Ni<sub>y</sub>O<sub>8+δ</sub> Superconductor Composite
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Abstract<p>six specimens of the Hg<sub>0.5</sub>Pb<sub>0.5</sub>Ba<sub>2</sub>Ca<sub>2</sub>Cu<sub>3-y</sub> <italic>Ni<sub>y</sub> </italic>O<sub>8+δ</sub> (y=0.2,0.4,0.6,0.8,1.0) superconducting compound were prepared by solid state reaction method, with sintering temperature equal to 1123K for 24 hours. The electrical resistivity was examined by the four probe technique, It was found that all the specimens have metallic behavior and increasing the critical temperature with increasing nickel concentration. The optimum critical temperature T<sub>c</sub> was found equal </p> ... Show More
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Publication Date
Sun Dec 01 2013
Journal Name
The Iraqi Postgraduate Medical Journal
Comparative Study Between Glimepiride and Glibenclamide in the Treatment of Type 2 Diabetic Patients in Al-Yarmouk Hospital
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Comparative Study Between Glimepiride and Glibenclamide in the Treatment of Type 2 Diabetic Patients in Al-Yarmouk Hospital

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Publication Date
Thu Aug 28 2014
Journal Name
Iraqi National Journal Of Chemistry The Editorial Board
The New C-2,C-3 Substituted Heterocyclic Derivatives of L-Ascorbic acid: Synthesis, Characterization, and Bacterial Activity
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New Schiff bases derivatives [IV]a-e is prepared via condensation of Derythroascorbic acid with p-substituted aldehydes in dry benzene. To obtain these derivatives, the 5,6-O-isopropylidene-L-ascorbic acid[I] was chosen as starting material, compound prepared from the reaction of L-ascorbic acid as starting material. Compound[I] was prepared from the reaction of L-ascorbic acid with dry acetone in the presence of hydrogen chloride. The esterification of hydroxyl groups at C-2 and C-3 positions with excess ofethyl α –chloroacetate in the presence of sodium acetate produce acorresebonding ester [II] , which was condensed with hydrazine hydrate to give new hydrazide [III] . The new Schiff bases [IV]a-e were synthesized by reaction of acid h

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Publication Date
Tue Aug 30 2022
Journal Name
Research Journal Of Pharmacy And Technology
The Distribution of ABO blood groups among type 2 Diabetes mellitus patients with or without Chronic Microvascular Complications
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The ABO blood group system is highly polymorphic, with more than 20 distinct sub-groups; study findings are usually related to ABO phenotype, but rarely to the ABO genotype and animal models are unsatisfactory because their antigen glycosylation structure is different from humans. Both the ABO and Rh blood group systems have been associated with a number of diseases, but this is more likely related to the presence or absence of these tissue antigens throughout the body and not directly or primarily related to their presence on RBCs. A total of fifty-two 52 patients without complication of DMII, two hundred sixteen 216 patients with complication of DMII and seventy-one 71 person as healthy control were included in the study. The resu

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