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MRbmuIoBVTCNdQwCLKT9
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
Sun Mar 01 2020
Journal Name
Iop Conference Series: Materials Science And Engineering
Spectral fluctuations in <sup>24</sup>Mg nucleus using the framework of the nuclear shell model
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Abstract<p>Random matrix theory is used to study the chaotic properties in nuclear energy spectrum of the <sup>24</sup>Mg nucleus. The excitation energies (which are the main object of this study) are obtained via performing shell model calculations using the OXBASH computer code together with an effective interaction of Wildenthal (W) in the isospin formalism. The <sup>24</sup>Mg nucleus is assumed to have an inert <sup>16</sup>O core with 8 nucleons (4protons and 4neutrons) move in the 1d<sub>5/2</sub>, 2s<sub>1/2</sub> and 1d<sub>3/2</sub> orbitals. The spectral fluctuations are studied by two statistical measures: the nearest neighb</p> ... Show More
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Publication Date
Thu Jan 01 2026
Journal Name
Rsc Advances
A dual-angle optoelectronic flow injection platform for ferrous ion (Fe <sup>2+</sup> ) determination using blue LED excitation and solar cell detection
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A new optoelectronic flow injection method is proposed for the determination of ferrous ions (Fe 2+ ) based on thiocyanate complexation to form a deep-red FeSCN 2+ complex.

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Publication Date
Wed Dec 01 2021
Journal Name
Journal Of Physics: Conference Series
The effect of left ventricle ischemia severity on cardiac performance appeared on ejection fraction using radioactive TC <sup>99m</sup> MIBI in comparison with echocardiography
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Abstract<p>Ischemic heart disease is a major causes of heart failure. Heart failure patients have predominantly left ventricular dysfunction (systolic or diastolic dysfunction, or both). Acute heart failure is most commonly caused by reduced myocardial contractility, and increased LV stiffness. We performed echocardiography and gated SPECT with Tc<sup>99m</sup> MIBI within 263 patients and 166 normal individuals. Left ventricular end systolic volume (LVESV), left ventricular end diastolic volume (LVEDV), and left ventricular ejection fraction (LVEF) were measured. For all degrees of ischemia, there was a significant difference between ejection fraction values measured by SPECT and echo</p> ... Show More
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Publication Date
Thu Sep 28 2017
Journal Name
Medycyna Pracy
MTS-6 detectors calibration by using &lt;sup&gt;239&lt;/sup&gt;Pu-Be neutron source
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Publication Date
Fri Aug 12 2022
Journal Name
Surgical Neurology International
“The most inspiring and mind-blowing meetings ever:” Highlights of the 15<sup>th</sup> SNI Baghdad Neurosurgery Online Meeting, from Participants’ Perspectives
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Background:

Education by lectures has been standard for 100 years or more. Given the 21st century technology, people can connect with others around the world instantly, electronically. With the pandemic, teaching changed to one-way information transfer with the loss of interpersonal learning experience. SNI® and now SNI Digital have been experimenting with different forms of communication to transfer information.

Methods:

Using an interactive education model, a meeting for neurosurgeons in Baghdad was held for students, residents, and neurosurgeons

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Publication Date
Thu Oct 08 2020
Journal Name
British Journal Of Pharmacology
Protective effects of Δ<sup>9</sup>‐tetrahydrocannabinol against enterotoxin‐induced acute respiratory distress syndrome are mediated by modulation of microbiota
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Background and Purpose

Staphylococcal enterotoxin‐B (SEB) is one of the most potent bacterial superantigens that exerts profound toxic effects by inducing a cytokine storm. Inhaled SEB can cause acute respiratory distress syndrome (ARDS), which is often fatal and with no effective treatments.

Experimental Approach

Efficacy of Δ9‐tetrahydrocannabinol (THC) was tested in a mouse model of SEB‐mediated ARDS, in which lung inflammation, alterations in gut/lung microbiota and production of short‐chain fatty acids (SCFAs) was measured. Gene dysregulation of lung epithelial cells was studied by transcriptome arrays. F

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Publication Date
Mon Jan 01 2024
Journal Name
Computers, Materials &amp; Continua
Improving Video Watermarking through Galois Field &lt;i&gt;GF&lt;/i&gt;(2&lt;sup&gt;4&lt;/sup&gt;) Multiplication Tables with Diverse Irreducible Polynomials and Adaptive Techniques
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Publication Date
Sun Jan 01 2017
Journal Name
Dalton Transactions
Mangiferin functionalized radioactive gold nanoparticles (MGF-<sup>198</sup>AuNPs) in prostate tumor therapy: green nanotechnology for production, in vivo tumor retention and evaluation of therapeutic efficacy
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We report here an innovative feature of green nanotechnology-focused work showing that mangiferin—a glucose functionalized xanthonoid, found in abundance in mango peels—serves dual roles of chemical reduction and in situ encapsulation, to produce gold nanoparticles with optimum in vivo stability and tumor specific characteristics. The interaction of mangiferin with a Au-198 gold precursor affords MGF-198AuNPs as the beta emissions of Au-198 provide unique advantages for tumor therapy while gamma rays are used for the quantitative estimation of gold within the tumors and various organs. The laminin receptor specificity of mangiferin affords specific accumulation of therapeutic payloads of this new therapeutic agent within prostate tumors

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Publication Date
Mon Nov 25 2024
Journal Name
Iraqi Journal For Computer Science And Matgematics
Posinormality of Operators Treated by Weyl's Theorem on Unbounded Hilbert Space
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Hamiltonians, momentum operators, and other quantum-mechanical perceptible take the form of self-adjoint operators when understood in quantized physical schemes. Unbounded and self-adjoint recognition are required in the situation of positive measurements. The selection of the proper Hilbert space(s) and the selection of the self-adjoint extension must be made in order for this to operate. In this effort, we define a new extension positive measure depending on the measurable field of nonzero positive self-adjoint operator in unbounded Hilbert space of analytic functions of complex variables. Consequently, we define an extension norm in the same space. We show several new properties of the suggested operator and its adjoin operator. These pr

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Publication Date
Sun Dec 10 2017
Journal Name
Al-academy
The Composition of design according to norm renovation in the interior design space
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The interior spaces represent a true reflection of the concepts and values ​​of humanity and requirements; were interested in current research ongoing changes that have occurred in those human values ​​and requirements over time, even pat each time warp its values ​​and its own requirements. Those changes, which receive Bdilalha the spaces linked by a renewal which guarantees the interior design of the spaces of sustainability and bio-coordinated. Launched search from an initial perception that those associated with the changes of the spaces through time that have not been subject to examination and supervision, they will constitute a continuing threat of losing the ties with the past under the pretext of modernization and mo

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