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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
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
Thu Apr 06 2023
Journal Name
Materials Science Forum
Study of the Effect of Ce &lt;sup&gt;3+&lt;/sup&gt; on the Gas Sensitivity and Magnetic Properties of Cu&lt;sub&gt;x&lt;/sub&gt;Ce&lt;sub&gt;0.3-X&lt;/sub&gt;Ni&lt;sub&gt;0.7&lt;/sub&gt;Fe&lt;sub&gt;2&lt;/sub&gt;O&lt;sub&gt;4&lt;/sub&gt; Ferrite Nanoparticles
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This study includes the preparation of the ferrite nanoparticles CuxCe0.3-XNi0.7Fe2O4 (where: x = 0, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3) using the sol-gel (auto combustion) method, and citric acid was used as a fuel for combustion. The results of the tests conducted by X-ray diffraction (XRD), emitting-field scanning electron microscopy (FE-SEM), energy-dispersive X-ray analyzer (EDX), and Vibration Sample Magnetic Device (VSM) showed that the compound has a face-centered cubic structure, and the lattice constant is increased with increasing Cu ion. On the other hand, the compound has apparent porosity and spherical particles, and t

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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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Publication Date
Fri Jan 20 2023
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
The Completion of Generalized 2-Inner Product Spaces
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A complete metric space is a well-known concept. Kreyszig shows that every non-complete metric space  can be developed into a complete metric space , referred to as completion of .

We use the b-Cauchy sequence to form  which “is the set of all b-Cauchy sequences equivalence classes”. After that, we prove  to be a 2-normed space. Then, we construct an isometric by defining the function from  to ; thus  and  are isometric, where  is the subset of  composed of the equivalence classes that contains constant b-Cauchy sequences. Finally, we prove that  is dense in ,  is complete and the uniqueness of  is up to isometrics

 

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Publication Date
Fri Dec 01 2023
Journal Name
Physical Chemistry Research
Thermophysical Study of Ethylene Glycol + H<inf>2</inf>O and Ethylene Glycol + (DMF/H<inf>2</inf>O) at 298.15 K
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n this research, some thermophysical properties of ethylene glycol with water (H2O) and two solvent mixtures dimethylformamide/ water (DMF + H2O) were studied. The densities (ρ) and viscosities (η) of ethylene glycol in water and a mixed solvent dimethylformamide (DMF + H2O) were determined at 298.15 K, t and a range of concentrations from 0.1 to1.0 molar. The ρ and η values were subsequently used to calculate the thermodynamics of mixing including the apparent molar volume (ϕv), partial molar volume (ϕvo) at infinite dilution. The solute-solute interaction is presented by Sv results from the equation ∅_v=ϕ_v^o+S_v √m. The values of viscosity (B) coefficients and Falkenhagen coefficient(A) of the Jone-Dole equation and Gibbs free

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