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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
Fri Mar 28 2025
Journal Name
Journal Of Physical Education
The effect of the four-pillar strategy on the performance of the transmission and preparation skills in volleyball
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The aim of the research is to prepare practical volleyball lessons by using the four pillars strategy for middle school students, and to identify the effect of the four pillars strategy in performing the transmission and volleyball skills in the second intermediate students, to assume that the two researchers assume that there are no statistically significant differences between the results of my skill performance tests Sending and preparing tribal and remote volleyball for the experimental and controlled groups, and there are no statistically significant differences between the results of the performance of the transmission and preparation skills of the volleyball between the two experimental and control groups, and the research co

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Publication Date
Tue Oct 23 2018
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Journal Of Economics And Administrative Sciences
“The impact of using the of the Government Finance Statistics Manual (GFSM) on The General Budget in Iraq”
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This research is aiming  to analyze the impacts of the current budget in Iraq by using  the Government Finance Statistics Manual (GFSM) , the research is based on hypothesis: (There is an impact on the using of the Government Finance Statistics Manual (GFSM) In public budget in Iraq) .This hypothesis was demonstrated by using the questionnaire, a number of conclusions were reached, the most important being the lack of terminology adopted in the government accounting system and the Iraqi financial and accounting manual as a result of their adoption of the monetary basis for the lack of accounting terminology that meets t

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Sat Sep 30 2023
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Journal Of Accounting And Financial Studies ( Jafs )
The use of green accounting information systems in the oil sector and its impact on reporting on sustainability - an applied study
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Abstract

                  The research seeks to shed light on green accounting information systems, analyze them, identify sustainability reporting and how to improve it, as well as study the importance of the Iraqi oil sector, analyze it, and work on applying green accounting information systems in order to improve the quality of sustainability reporting. Oil as a branch of the General Corporation for the Distribution of Oil and Gas Products to apply the practical aspect and prove the hypothesis of the research. Explaining the company's role in improving environmental conditions

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Publication Date
Wed Jan 02 2019
Journal Name
Journal Of Educational And Psychological Researches
A training program for chemistry teachers based on the knowledge economy and its impact on the productive thinking of their students
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       The current research aims to build a training program for chemistry teachers based on the knowledge economy and its impact on the productive thinking of their students. To achieve the objectives of the research, the following hypothesis was formulated:

   There is no statistically significant difference at (0.05) level of significance between the average grades of the students participating in the training program according to the knowledge economy and the average grades of the students who did not participate in the training program in the test of productive thinking. The study sample consisted of (288) second intermediate grade students divided into (152) for the control group

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Publication Date
Sat Jul 01 2023
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
The impact of financing structure on bank profits : Applied research on a sample of commercial banks listed in the Iraq Stock Exchange for the period (2011-2020)
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The research aims to identify the concept of financing structure and what are the determinants that affect it and the goals achieved by financing in commercial banks in addition to the sources upon which the financing structure depends consisting of internal financing sources and external financing sources and their connection to the profits of commercial banks. Baghdad, Khaleeji Commercial Bank) registered in the Iraq Stock Exchange during the period for the years (2011-2020) published in the Iraq Stock Exchange from and the research relied on financial analysis tools to analyze the independent variable the following financing structure (the ratio of equity to total assets, the ratio of deposits to Total liabilities, the ratio of loans

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Publication Date
Sat Mar 25 2023
Journal Name
International Journal Of Drug Delivery Technology
Preparation, Characterization, Antioxidant and Antibacterial Studies of New Metal (II) Complexes with Schiff Base for 3-amino-1-phenyl-2- pyrazoline-5-one
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A new ligand complexes have been synthesis from reaction of metal ions of Mn(II), Co(II), Ni(II), Cu(II), Zn(II), Cd(II), Hg(II), Pd(II) and Pt(II) with schiff base LH. 5-[(2-Hydroxy-naphthalen-1-ylmethylene)-amino]-2-phenyl-2,4-dihydro-pyrazol-3-one, this ligand was characterized by Fourier transform infrared (FTIR), UV-vis, 1H, 13CNMR, and mass spectra. All complexes were characterized by techniques micro analysis C.H.N, UV-vis and FTIR spectral studies, atomic absorption, chloride content, molar conductivity measurements and magnetic susceptibility. The ligand acts as bidentate, coordination through nitrogen atom from azomethin group and deprotonated phenolic oxygen atom. The spectroscopic and analytical measurements showed that

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Publication Date
Thu Feb 16 2023
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Iraqi Journal Of Pharmaceutical Sciences ( P-issn 1683 - 3597 E-issn 2521 - 3512)
A Novel Single Nucleotide Polymorphism of Interleukin-10 Gene is Linked to Type 2 Diabetes Mellitus in Iraqi Patients with Toxoplasmosis(Conference Paper )#
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Type 2 diabetes mellitus (T2DM) is a chronic disorder that is a serious health concern all over the globe, it is linked to Interleukin-10 (IL-10) single nucleotide polymorphisms (SNPs) at the promoter region. On the other hand, diabetes influences the cellular and humoral immunity predisposing the patient to a variety of opportunistic parasites one of them is Toxoplasma gondii (T. gondii), which may infect any nucleated cell, including pancreatic cells. The purpose of this research was to explore the association of IL-10 genetic polymorphisms with T2DM and latent toxoplasmosis among Iraqi patients with T2DM. Fifty-five and fifty-eight venous blood samples were taken from T2DM patients and age-matched non-diabetic person

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Publication Date
Thu Jan 01 2009
Journal Name
Ibn Al-haitham Journal For Pure And Applied Science
Complexeation Behavior of CoII, NiII, CuII, ZnII, and CdII Ions Toward Schiff Base Derived From 2, 4-Dihydroxy Benzaldehyde and O-Phenylene Diamin
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The aim of this work covers the synthesis and characterization of the new tertra dentate ligand (H4L) containing (N and O) as donor set atoms kind (N2O2) where: H4L=Bis-1,2 (2,4- dihydroxybenzylediene phylinediamine . The preparation of ligand contains reaction 2, 4 - Dihydroxy benzaldehyde and o-phenylene diamine . Schiff base was reacted with some metal ions in the presence of methanol to give the complexes in the general formula [M (H2L)] where: MII = Co, Ni, Cu, Zn, Cd. All compounds were characterized by spectroscopic methods I.R , U.V.-Vis, metal content and molar conductivity measurements, showed that the complexes are non-electrolyte. The proposed geometry for all of the proposed complexes was a tetrahedral while Ni complex was squa

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Wed Nov 01 2017
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DFT + U and ab initio atomistic thermodynamics approache for mixed transitional metallic oxides: A case study of CoCu 2 O 3 surface terminations
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This study develops a systematic density functional theory alongside on-site Coulomb interaction correction (DFT + U) and ab initio atomistic thermodynamics approachs for ternary (or mixed transitional metal oxides), expressed in three reservoirs. As a case study, among notable multiple metal oxides, synthesized CoCu2O3 exhibits favourable properties towards applications in solar, thermal and catalytic processes. This progressive contribution applies DFT + U and atomistic thermodynamic approaches to examine the structure and relative stability of CoCu2O3 surfaces. Twenty-five surfaces along the [001], [010], [100], [011], [101], [110] and [111] low-Miller-indices, with varying surface-termination configurations were selected in this study.

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Publication Date
Wed Jul 08 2009
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Complexeation Behavior of CoII, NiII, CuII, ZnII, and CdII Ions Toward Schiff Base Derived From 2, 4 -Dihydroxy Benzaldehyde and O-Phenylene Diamine
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bstract The aim of this work covers the synthesis and characterization of the new tertra dentate ligand (H4L) containing (N and O) as donor set atoms kind (N2O2) where: H4L=Bis-1,2 (2,4- dihydroxybenzylediene phylinediamine . The preparation of ligand contains reaction 2, 4 - Dihydroxy benzaldehyde and o-phenylene diamine . Schiff base was reacted with some metal ions in the presence of methanol to give the complexes in the general formula [M (H2L)] where: MII = Co, Ni, Cu, Zn, Cd. All compounds were characterized by spectroscopic methods I.R , U.V.-Vis, metal content and molar conductivity measurements, showed that the complexes are non-electrolyte. The proposed geometry for all of the proposed complexes was a tetrahedral while Ni complex

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