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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 May 29 2019
Journal Name
Iraqi Journal Of Physics
The effect of the cold atmospheric plasma on the number of platelets
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This study includes the direct influence of (single & multi) dose of Cold Atmospheric Plasma (CAP) on the no. of platelets for mice for different exposure time (15, 30, 60, and 120) sec. the influence of CAP on mice was measured after 1, 2, 3, 7, and 14 day from exposure.
The results obtained in this study indicate that the effect of low doses of CAP on platelets was stimulatory effect in the first few hours from exposure (1day) but the high dose was inhibitory, It was found that after two weeks of exposure that the number of platelets became normal comparable to the control one, and this indicates that plasma effect was removed after this period.

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Publication Date
Wed Dec 30 2020
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
The impact of voluntary corporate disclosure on tax planning: The impact of voluntary corporate disclosure on tax planning
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The attention of civil society organizations, governments and international non-governmental organizations in recent years has focused on the acute practices adopted by companies with the aim of reducing the tax burden, and the results of these practices have a negative impact on the tax revenues that the state uses to finance public needsThe aim of the research is to measure the impact of the voluntary disclosure of companies on tax planning for the period from 2011 to 2015 and the research community is in the General Tax Authority. The research sample is 6 companies within the private sector in the financial, banking, insurance and industrial fields. The research was based on a special model to measure the optional disclosure,

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Publication Date
Wed Dec 30 2015
Journal Name
College Of Islamic Sciences
The position of the Egyptian public opinion on the Mibi revolution
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The study of the subject of (Egyptian public opinion on the Libyan revolution) came to reveal the role of Egyptian public opinion in mobilizing and solidarity for the masses. With the events witnessed by the Arab countries before the revolution, this was evident by the people 's attitudes towards the tripartite aggression against Egypt in 1956, and the June 1967 war, and the most recent what the Egyptian people showed towards the Libyan revolution. The Egyptian press followed the completion of the arms deal with France and revealed the ability of the Libyan negotiator to achieve moral gain, supported by Egyptian support to thwart the United States intentions to arm "Israel" similarly. The Egyptian people expressed a love for peace and su

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Publication Date
Wed Mar 10 2021
Journal Name
Baghdad Science Journal
study the effects of the polluted waste water on the environment
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to study the discribrion and the pollution in the environment in the south of baghdad samples of waste water from industrail units using the mercury in its process also

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Publication Date
Sun Jan 01 2023
Journal Name
The Egyptian Journal Of Hospital Medicine
Evaluation of Interleukin-18 Serum Concentration and Gene Polymorphism (Rs1946518) in A Sample of Type-2 Diabetes Mellitus Patients from Iraq.
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Background Type two diabetes (T2DM) is characterized by insufficient insulin production and secretion. Additionally, the body develops insulin resistance which affects 90–95% of diabetics. Complex cytokines, receptors, genetic pathways, and the immune system are involved in T2DM. Interleukin-18 (IL-18) is one of the inflammatory cytokines associated with Type 2 diabetes. Environmental and genetic variables, including genetic polymorphisms, can increase T2DM risk and its consequences. Single nucleotide gene polymorphisms (SNPs) are important risk factors for diabetes that can be used to find the disease early and treat it better. Objective This study aimed to determine the levels of IL-18 in the serum of Iraqi patients with Type 2 diabetes

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Publication Date
Mon May 01 2017
Journal Name
Baghdad Science Journal
Synthesis and Spectroscopic Studies of some Divalent Metall Ion Complexes of 3-(4-hydroxyphenyl)-2-(3-(4-nitrobenzoyl) thioureido) propanoic acid
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3-(4-hydroxyphenyl)-2-(3-(4-nitrobenzoyl) thioureido) propanoic acid (HNP) a new ligand was synthesized by reaction of Tyrosine with (4-Nitrobenzoyl isothiocyanate) by using acetone as a solvent. The prepared ligand (HNP) has been characterized by elemental analysis (CHNS), infrared (FT-IR), electronic spectral (Ultraviolet visible) and(1H,13C-Nuclear Magnetic Resonance) spectra. Some Divalent metal ion complexes of (HNP) were prepared and spectroscopic studies by Fourier transform infrared (FTIR), electronic spectral(UV-Vis), molar conductance, magnetic susceptibility and atomic absorption. The results measured showed the formula of six prepared complexes were [M (HNP)2] (M+2 = Manganese, Cobalt, Nickel, Znic, Cadmium and Mercury),from the

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Publication Date
Sun Mar 05 2017
Journal Name
Baghdad Science Journal
Synthesis of Some Mixed ligands Complexes of (2-hydroxy benzaldine)-4-amino Antipyrine and 1,10-phenanthroline and Studying their antibacterial activity
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Complexes from the ligand (2-hydroxy benzaldine)-4-aminoantipyrine with some transition metal ions V(l?),Cr(lll),Fe(lll) and Co(ll) were prepared in the presence of the co-ligand 1,10-phenanthroline in alcoholic medium. These compounds were characterized by the available techniques: FT-IR ,UV-Visible ,magnetic susceptibility, Flame atomic absorption technique as well as elemental analysis and conductivity mesurments .From these spectral studies, a square pyramidal structure proposed for V(IV) complex and an octahedral geometry for Cr(III),Fe(III) and Co(II) complexes. The biological activity of the ligands and their complexes were evaluated by a gar plate diffusion technique against three human pathogenic bacterial strains: Pseudomonas ae

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Publication Date
Sun Sep 03 2017
Journal Name
Baghdad Science Journal
Synthesis and Spectroscopic Studies of some Divalent Metall Ion Complexes of 3-(4-hydroxyphenyl)-2-(3-(4-nitrobenzoyl) thioureido) propanoic acid
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Publication Date
Wed Mar 10 2021
Journal Name
Baghdad Science Journal
Production of fibrinolytic protease from various fungal isolates and species 2.Determination of optimum conditions for enzyme production from Pleurotus ostreatus
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The optimum conditions for production of fibrinolytic protease from an edible mushroom Pleurotus ostreatus grown on the solid medium , Sus medium, composed of Sus wastes (produced from extracted medicinal plant Glycyrrhiza glabra) were determined. Addition of 5% of Soya bean seeds meal in Sus medium recorded a maximum fibrinolytic protease activity resulting in 7.7 units / ml. The optimum moisture content of Sus medium supplemented with 5% Soya bean seeds meal was 60% resulting in 7.2 units / ml.Pleurotus ostreatus produced a maximum fibrinolytic protease activity when the spawn rate,pH of medium and incubation temperature were 2,6 and 30°C, respectively. The maximum fibrinolytic protease activity was 7.6 units / ml when incubat

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Publication Date
Mon Oct 03 2022
Journal Name
Physica Scripta
Radiation shielding properties of Cd-Bi-Pb-Zn-borate glasses: influence of Bi<sub>2</sub>O<sub>3</sub> activation
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Abstract<p>We report the detail characterizations and <italic>γ</italic>-radiation protecting characteristics of some new types of cadmium (Cd)-bismuth (Bi)-lead (Pb)-zinc (Zn)-borate glasses of the form (70-x)B<sub>2</sub>O<sub>3</sub>-10ZnO-10PbO-10CdO-xBi<sub>2</sub>O<sub>3</sub> (with x = 0 to 20 mol%) synthesized via melt-quenching process. The influence of various Bi<sub>2</sub>O<sub>3</sub> contents on the <italic>γ</italic>-radiation shielding traits of the obtained glass samples was evaluated by exposing them at different <italic>γ</italic>-ray energies (0.356, 0.662, 1.173, and 1.33 MeV) whic</p> ... Show More
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