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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 Mar 28 2017
Journal Name
Iraqi Journal Of Pharmaceutical Sciences ( P-issn 1683 - 3597 E-issn 2521 - 3512)
Synthesis and Preliminary Antimicrobial Study of 2-Amino-5-Mercapto-1,3,4-Thiadiazole Derivatives
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Nitrogen heterocycles are of a special interest because they constitute an important class of natural and non natural products, many of which exhibit useful biological activities.Among these nitrogen heterocycles are 1, 3, 4-thiadiazole containing compounds. The therapeutic effects of these derivatives have been well studied for a number of pathological conditions including inflammation, pain, or hypertension. Moreover, synthesis of thiadiazoles has attracted wide-spread attention due to their diverse applications as antibacterial, anticancer, antifungal anti-inflammatory and antidepressant agents.According to this information’s new derivatives of 1, 3, 4-thiadiazole were designed and synthesized and in the hope of having some act

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Publication Date
Mon Mar 22 2010
Journal Name
Al- Mustansiriya J. Sci
Synthesis of New Amides and Schiff Bases derived From 2-Amino-1,3,4- Oxadiazole
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New compounds of amids [IV]a-e and Schiff bases [V]f-h derived from 2-amino-1,3,4-oxadiazoles [III] were synthesized and characterized by physical and spectraldata.2-Aamino-1,3,4-oxadiazoles was prepared by the action of bromine on acorresponding semicarbazide [II]( which was prepared by reaction of dialdehyde [I]with semicarbazide hydrochloride ) in the presence of sodium acetate , followed byan intramolecular cyclization . (PDF) Synthesis of New Amides and Schiff Bases derived From 2-Amino -1,3,4- Oxadiazole. Available from: https://www.researchgate.net/publication/326679206_Synthesis_of_New_Amides_and_Schiff_Bases_derived_From_2-Amino_-134-_Oxadiazole [accessed Nov 15 2023].

Publication Date
Wed May 11 2011
Journal Name
Tikrit Journal Of Pure Science
Isolation and partial purification malatase isoenzymes from urine of type 2 diabetic patients
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This study was performd on 50 urine specimens of patients with type 2 diabetes, in addition, 50 normal specimens were investigated as control group. The activity rate of maltase in patients (6.40±2.17) I.U/ml and activity rate of maltase in normal (0.44±0.20)I.U/ml. The results of the study reveal that maltase activity of type 2 diabetes patient's urine shows significant increase (P<0.01) compare to normal.

Publication Date
Sat Dec 01 2012
Journal Name
Journal Of Engineering And Development
Comparison Study of (urinary & serum) AST Activity from Patients with type 2 diabetes
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Aspartate aminotransferase was purified from urine and serum of patients with type 2 diabetes in a 2 steps procedure involving dialysis bag and sephadex G-25 gel filtration (column chromatography). The enzyme was purified 346.23 fold with 1467% yield and 3.46 fold with 142.85% yield in urine and serum of patients with type 2 diabetes respectively. The purified enzyme showed single peak. The results of this study revealed that AST activity of type 2 diabetes urine and serum increased significantly (p<0.001) compared with control group.

Publication Date
Fri Feb 08 2019
Journal Name
Iraqi Journal Of Laser
Laser Induced Fluorescence Spectroscopy of Decamethylrhenocene ( - C5 Me5)2 Re in Supersonic Jet
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In this paper we report the use of supersonic jet laser induced fluorescence (LIF) spectroscopy to facilitate the study of the spectra of some organometallic sandwich compounds particularly the metallocenes. The charge-transfer processes within these compounds, especially ligand to metal charge transfer within decamethylrhenocene ( - C5 Me5)2 Re were of particular interest. The spectrum shows a high degree of structures, indicating that there are several levels populated and these molecules are able to undergo many possible transitions

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Publication Date
Mon Sep 11 2017
Journal Name
Journal Of Molecular Cell Biology
Sustained activation of P2X7 induces MMP-2-evoked cleavage and functional purinoceptor inhibition
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Publication Date
Thu Jul 01 2021
Journal Name
Eurasian Chemical Communications
Synthesis of new heterocyclic derivatives from 2-furyl methanethiol and study their applications
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In this research, cyclic compounds derived from 2- furfural mercaptan (oxazole, triazoles) were synthesized, and their biological efficacy was measured and compared with standard drugs. Also, their effectiveness as anti-oxidant was measured and compared with ascorbic acid as a standard substance. Some of the synthesized compounds were deduced with good efficacy. © 2021 Sami Publishing Company. All rights reserved

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Scopus
Publication Date
Tue Nov 02 2021
Journal Name
Indonesian Journal Of Chemistry
Preparation and Characterization of New Tetra-Dentate N&lt;sub&gt;2&lt;/sub&gt;O&lt;sub&gt;2&lt;/sub&gt; Schiff Base with Some of Metal Ions Complexes
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This study describes preparation a new series of tetra-dentate N2O2 dinuclear complexes Cr(III), Co(II)and Cu(II) of the Schiff base 2-[5-(2-hydroxy-phenyl)-1,3,4-thiadiazol-2-ylimino]-methyl-naphthalen-1-ol], (LH2) derived from 1-hydroxy-naphthalene-2-carbaldehyde with 2-amino-5-(2-hydroxy-phenyl)-1,3,4-thiadiazole. These ligands were characterized by FT-IR, UV-Vis, Mass spectra, elemental analysis, and 1H-NMR. All prepared complexes have been characterized by conductance measurement, magnetic susceptibility, electronic spectra, infrared spectrum, thermal Analysis (TGA), and metal analysis by atomic absorption. The stoichiometry of metal to ligand, magnetic susceptibility, and electronic spectra measurements show an octahedral geom

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Publication Date
Tue Aug 02 2022
Journal Name
Ijhs
The association between polymorphism of TCF7L2 gene rs12255372 G/T and type 2 diabetes mellitus in Iraqi women suffering from menopause
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Type 2 diabetes mellitus (T2DM) became the most prevalent health problem. Almost half of the world's people are ignorant that have diabetes. Menopause occurs as an important alteration in women through which take place the change in sex hormones, distribution in fat،s body, and metabolism, altogether which participate in the metabolism disease such as type 2 diabetes mellitus. Several studies have appeared the association between the TCF7L2 gene and different diseases like type 2 diabetes mellitus (T2DM). This study aimed to detect the relation of the genetic variation polymorphism for the TCF7L2 gene (rs12255372 G/T) in Iraqi women menopausal with T2DM. The outcomes indicated the increased levels of biochemical characteristics including H

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Publication Date
Mon Apr 04 2011
Journal Name
Ibn Al-haitham J.for Pure &appl.sci
Anew Spectrophotometric Method For The Determination of La (III) With 3-Hydroxy -4-(2-hydroxy –Phenyl azo)Naphthalene -1-Sulfonic Acid
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A simple, rapid and sensitive spectrophotometric method has been proposed for the determination of La (III) using 3-hydroxy -4-(2-hydroxy-phenyl azo) naphthalene -1- sulfonic acid as a chromogenic reagent. This method is based on the formation of a red-pink colored complex, upon the reaction of La(III) with the reagent in an alkaline medium (pH= 9.50), having a maximum absorbance at 459 nm. Beer's law is valid in the concentration range 0.512 µg.ml-1 with a Sandell's sensitivity value of 0.0188 µg.cm-2 and molar absorptivity of 7376.12 L.mol-1.cm-1. The stoichiometric composition of the chelate is 1:3. The effect of the presence of different cations as interferants in the determination of La(III) under the given optimum conditions wer

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