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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
Sat Feb 01 2025
Journal Name
Civil Engineering Journal
On the Impact of Lacing Reinforcement Arrangement on Reinforced Concrete Deep Beams Performance
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The optimum design is characterized by structural concrete components that can sustain loads well beyond the yielding stage. This is often accomplished by a fulfilled ductility index, which is greatly influenced by the arrangement of the shear reinforcement. The current study investigates the impact of the shear reinforcement arrangement on the structural response of the deep beams using a variety of parameters, including the type of shear reinforcement, the number of lacing bars, and the lacing arrangement pattern. It was found that lacing reinforcement, as opposed to vertical stirrups, enhanced the overall structural response of deep beams, as evidenced by test results showing increases in ultimate loads, yielding, and cracking of

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Publication Date
Sat Feb 01 2025
Journal Name
Civil Engineering Journal
On the Impact of Lacing Reinforcement Arrangement on Reinforced Concrete Deep Beams Performance
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The optimum design is characterized by structural concrete components that can sustain loads well beyond the yielding stage. This is often accomplished by a fulfilled ductility index, which is greatly influenced by the arrangement of the shear reinforcement. The current study investigates the impact of the shear reinforcement arrangement on the structural response of the deep beams using a variety of parameters, including the type of shear reinforcement, the number of lacing bars, and the lacing arrangement pattern. It was found that lacing reinforcement, as opposed to vertical stirrups, enhanced the overall structural response of deep beams, as evidenced by test results showing increases in ultimate loads, yielding, and cracking of

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Publication Date
Sun Jan 01 2017
Journal Name
البحوث التربوية والنفسية
The effect of a training program for chemistry teachers on matching both sides of the brain together on the academic achievement of their students
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Publication Date
Fri Sep 30 2022
Journal Name
College Of Islamic Sciences
The jurisprudential aspects of Imam Abu al-Fayyadh al-Basri And its impact on the Shafi’i school of thought, on the rulings of worship
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Summary of the jurisprudence research

  Praise be to God, Lord of the Worlds, and prayers and peace be upon the Master of the Messengers, our master Muhammad, and upon his pure family, and his ignorant and ignorant companions, and those who followed them in goodness until the Day of Judgment.

 Then:

 The many jurisprudential aspects that the Shafi’i imams said are of great importance, because these aspects are nothing but the opinions of venerable jurists who have reached a high degree of knowledge until they have become among the owners of faces. And among them are the Shafi’i jurists, the jurists may differ among themselves, either because there is no text about their imam in a

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Publication Date
Sun Mar 07 2010
Journal Name
Baghdad Science Journal
Relation between Serum Leptin, Lipid Profiles and other biomarkers levels in patients with type 2 diabetic nephropathy
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Background: In advanced diabetes mellitus, serum levels of the most hormones are altered due to several interplaying mechanisms. Objective: To assess the relation of serum leptin and lipid profile in type 2 diabetic nephropathy. Patients and Method: Serum leptin levels and its relation to lipid profile were estimated in 62 patients with type 2 diabetic nephropathy attending the National Diabetes Center in Al- Mustansiriya University, and (26) healthy individuals considered as control group. The diabetic patients were classified into three groups, (24) pathients with normoalbuminuria (21) patients with microalbuminuria and (17) patients with macroalbuminuria. Fasting plasma glucose, serum creatinine, Hb A1c %, lipid profile (Total c

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Publication Date
Thu Jan 26 2006
Journal Name
Acta Crystallographica Section E
(OC-6-13)-Bis[5-bromo-2-(4-bromo­phenyl­diazenyl)phen­yl]dicarbonyl­ruthenium(II) with mutually transN-donor atoms
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The title compound, [Ru(C12H7Br2N2)2(CO)2], possesses a distorted octa­hedral environment about the Ru atom, with two cyclo­metallated 4,4′-dibromo­azobenzene ligands and two mutually cis carbonyl ligands. The donor atoms are arranged such that the N atoms are mutually trans and the aryl C atoms are trans to carbonyl ligands.

Publication Date
Thu Mar 30 2023
Journal Name
Optics Continuum
Ultrafast lithium disilicate veneer debonding time assisted by a CO<sub>2</sub> laser with temperature control
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We report on using a CO2 (10.6 µm) laser to debond the lithium disilicate veneers. Sixty-four sound human premolar teeth and 64 veneer specimens were used in the study. The zigzag movement via CO2 laser handpiece along with an air-cooled jet to prevent temperature elevation above the necrosis temperature limit (5.5 C°) was applied. The optimal deboning irradiation time was super-fast, at about 5 seconds at 3 Watt CO2 laser power. It is 20 times less than any previously published work for veneers debonding. The enamel beneath the debonded veneers has been assessed by atomic force microscopy (AFM) and shear stress technique as criteria for the easiness of debonding. The

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Publication Date
Tue May 01 2018
Journal Name
Journal Of Physics: Conference Series
Study electron transport coefficients for Ar, O<sub>2</sub> and their mixtures by using EEDF program
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Publication Date
Fri Jan 01 2021
Journal Name
Turkish Journal Of Physiotherapy And Rehabilitation
SYNTHESIS, SPECTROSCOPIC, CHARACTERIZATION AND BIOLOGICAL STUDIES FOR NEW COMPLEXES WITH N1, N5-BIS (3-HYDROXYPHENYL)- 2-OXOPENTANEDIAMIDE
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New complexes have been prepared from the new ligand [N1,N5-bis(3-hydroxyphenyl)-2- oxopentanediamide] derived from 2-Oxoglutaric acid and 3-aminophenol. Accordingly its binudear Mn(II),Co(II),Ni(II),Pd(II) and VO(II) complexes were prepared.. These compounds have been characterized by FT-IR, UV-Vis,Mass, 1H-NMR spectra, TGA curve, Chloride containing ,Molar conductance and atomic absorption. The characterization results gave binuclear complexes and pentadentate coordination and tetrahedral geometry for each Cobalt, Nickel, Manganese and Copper complexes otherwise Palladium complex gave a square planar geometry and Vanadium complex gave a square pyramidal geometry and the ligand is tetradentate. The biological activities for the new compoun

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Publication Date
Sun Oct 01 2023
Journal Name
Medical Journal Of Babylon
Urokinase-type plasminogen activator receptor as a predictive marker for cardiac disease among type 2 diabetic patients
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Abstract<sec> <title>Background:

Type 2 diabetes mellitus is a progressive and chronic disease manifested by β-cell dysfunction and improved insulin resistance. Higher levels of urokinase-type plasminogen activator receptors have been found to predict morbidity and mortality among diabetic patients with cardiac disease.

Objective:

This study aims to explore the role of serum urokinase-type plasminogen activator receptor levels as a prognostic marker among type 2 diabetic Iraqi patients.

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