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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
Wed Jan 01 2025
Journal Name
Eastern Ukrainian Medical Journal
IMPACT OF HIGHLY SELECTIVE VERSUS RELATIVELY SELECTIVE COX2 INHIBITORS ON INSULIN SENSITIVITY IN IRAQI PATIENTS DIAGNOSED WITH TYPE 2 DIABETES
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Background: A worldwide health epidemic, type 2 diabetes mellitus was significantly influenced by chronic inflammation, which led to increased insulin resistance (IR). The most widely practiced form of therapy used to control musculoskeletal pain in people with diabetes is non-steroidal anti-inflammatory drugs (NSAIDs), which provide their action by inhibiting cyclooxygenase enzyme (COX). COX1, COX2, and COX3 are distinct isoforms of the cyclooxygenase enzyme. The potential anti-inflammatory benefits of cyclooxygenase-2 (COX-2) inhibitors, both selective and non-selective, have been investigated concerning the management of type 2 diabetes patients. Objective: the purpose of this research is to explore the impact of highly selective

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Publication Date
Wed Sep 02 2020
Journal Name
Indonesian Journal Of Chemistry
Synthesis, Characterization and Biological Efficacies from Some New Dinuclear Metal Complexes for Base 3-(3,4-Dihydroxy-phenyl)-2-[(2-hydroxy-3-methylperoxy-benzylidene)-amino]-2-methyl Propionic Acid
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The reaction of methyldopa with o-vanillin in refluxing ethanol afforded Schiff base and characterized through physical analysis with a number of spectra also the study of biological activity. The geometry of the Schiff base was identified through using (C.H.N) analysis, Mass, 1H-NMR, FT-IR, UV-Vis spectroscopy. Metal complexes of Cr3+, Mn2+, Co2+, Ni2+, Cu2+, Zn2+, Cd2+ and Hg2+ with Schiff base have been prepared in the molar ratio 2:1 (Metal:L), (L = Schiff base ligand) except Hg2+ at molar ratio 1:1 (Hg:L). The prepared complexes were characterized by using Mass, FT-IR and UV-Vis spectral studies, on other than magnetic properties and flame atomic absorption, conductivity measurements. According to the results a dinuclear octahe

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Publication Date
Wed Sep 02 2020
Journal Name
Indonesian Journal Of Chemistry
Synthesis, Characterization and Biological Efficacies from Some New Dinuclear Metal Complexes for Base 3-(3,4-Dihydroxy-phenyl)-2-[(2-hydroxy-3-methylperoxy-benzylidene)-amino]-2-methyl Propionic Acid
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The reaction of methyldopa with o-vanillin in refluxing ethanol afforded Schiff base and characterized through physical analysis with a number of spectra also the study of biological activity. The geometry of the Schiff base was identified through using (C.H.N) analysis, Mass, 1H-NMR, FT-IR, UV-Vis spectroscopy. Metal complexes of Cr3+, Mn2+, Co2+, Ni2+, Cu2+, Zn2+, Cd2+ and Hg2+ with Schiff base have been prepared in the molar ratio 2:1 (Metal:L), (L = Schiff base ligand) except Hg2+ at molar ratio 1:1 (Hg:L). The prepared complexes were characterized by using Mass, FT-IR and UV-Vis spectral studies, on other than magnetic properties and flame atomic absorption, conductivity measurements. According to the results a dinuclear octahedral geo

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Publication Date
Thu Mar 08 2018
Journal Name
Iosr Journal Of Applied Chemistry
synthesis, Composition, Spectral, Geometry and Antibacterial Applications ofMn(||),Ni(||),Co(||),Cu(||) and Hg(||) schiff Base complexes of N2O2 mixed donor with 1,10-phenanthroline
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synthesis, Composition, Spectral, Geometry and Antibacterial Applications ofMn(||),Ni(||),Co(||),Cu(||) and Hg(||) schiff Base complexes of N2O2 mixed donor with 1,10-phenanthroline

Publication Date
Sun Dec 18 2022
Journal Name
Journal Of The College Of Basic Education
A (k,ℓ) Span in Three Dimensional Projective Space PG(3,p) Over Galois Field where p=4
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الغرض من هذا العمل هو دراسة الفضاء الإسقاطي ثلاثي الأبعاد PG (3، P) حيث p = 4 باستخدام المعادلات الجبرية وجدنا النقاط والخطوط والمستويات وفي هذا الفضاء نبني (k، ℓ) -span وهي مجموعة من خطوط k لا يتقاطع اثنان منها. نثبت أن الحد الأقصى للكمال (k، ℓ) -span في PG (3،4) هو (17، ℓ) -span ، وهو ما يساوي جميع نقاط المساحة التي تسمى السبريد.

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Publication Date
Thu Oct 25 2018
Journal Name
Journal Of Optical Communications
320 Gbps Free Space Optic Communication System Deploying Ultra Dense Wavelength Division Multiplexing and Polarization Mode Division Multiplexing
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Abstract<p>This work aims to investigate the integrated ultra-dense wavelength division multiplexing (UDWDM) and polarization division multiplexing (PDM) schemes incorporated in the free space optic (FSO) communication system. Erbium-doped fiber amplifiers (EDFAs) are used as post and pre-amplifiers in the proposed UDWDM–PDM–FSO system to boost the transmission power for increasing the distance. Thirty-two channels are transported over the FSO link to realize the total data transmission of 160 and 320 Gbps with 0.08 and 0.1 nm channel spacing, respectively. Results are also reported with non-return to zero modulation schemes. The performance of the proposed UDWDM–PDM–FSO transmission sys</p> ... Show More
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Publication Date
Mon Feb 04 2019
Journal Name
Iraqi Journal Of Physics
Inelastic electron scattering form factors involving the second excited 2+ level in the isotopes 50,54,52Cr
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An expression for the transition charge density is investigated where the deformation in nuclear collective modes is taken into consideration besides the shell model transition density. The inelastic longitudinal form factors C2 calculated using this transition charge density with excitation of the levels for Cr54,52,50 nuclei. In this work, the core polarization transition density is evaluated by adopting the shape of Tassie model together with the derived form of the ground state two-body charge density distributions (2BCDD's). It is noticed that the core polarization effects which represent the collective modes are essential in obtaining a remarkable agreement between the calculated inelastic longitudinal F(q)'s and those of experimen

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Publication Date
Tue Nov 30 2021
Journal Name
Indian Journal Of Forensic Medicine & Toxicology
The role of vitamin D3 in improving lipid profile in type 2 diabetes patients with
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Publication Date
Sun Jun 01 2014
Journal Name
Baghdad Science Journal
Levels of Glucose-6-phosphate Dehydrogenase in Type 1 Diabetes Mellitus patients with Nephropathy and Cardiovascular disease complication: Perry H. Saifullah|Saad M. Nida|Israa B. Raoof
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The aim of this study is to evaluate oxidative stress in diabetes mellitus (DM) Type1 by the measurement of Glucose-6-phosphate Dehydrogenase (G-6-PD), an enzyme expressed in human RBCs, is important in the generation of reduced glutathione which is the key product in oxidative stress controls. The Study was carried on 80 samples of blood and serum of National Diabetes Center (NDC). The study groups under fasting conditions and they divided as:20 samples of diabetes mellitus patients without complications and 20 samples of diabetes mellitus with cardiovascular (CV) complications and 20 samples of diabetes mellitus with Nephropathy (Neph) complications compared with 20 control group with average age (13-67) years.. The results sh

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Publication Date
Wed Jun 16 2021
Journal Name
Biochemical And Cellular Archives
Synthesis, characterization and pharmaceutical studies of schiff base from 2-pyrrolidinone derivative and imidazole-2-carboxaldehyde and corresponding complexes with Metal (||)
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Synthesis, characterization and pharmaceutical studies of schiff base from 2-pyrrolidinone derivative and imidazole-2-carboxaldehyde and corresponding complexes with Metal (||)