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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
Thu Jun 30 2016
Journal Name
Iraqi Journal Of Chemical And Petroleum Engineering
The Effect of Asphaltene on the Stability of Iraqi Water in Crude Oil Emulsions
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In the present work, asphaltenes and resins separated from emulsion samples collected from two Iraqi oil wells, Nafut Kana (Nk) and Basrah were used to study the emulsion stability. The effect of oil resins to asphaltene (R/A) ratio, pH of the aqueous phase, addition of paraffinic solvent (n-heptane), aromatic solvent (toluene), and blend of both (heptol) in various proportions on the stability of emulsions had been investigated. The conditions of experiments were specified as an agitation speed of 1000 rpm for 30 minutes, heating at 50 °C, and water content of 30%.  The results showed that as the R/A ratio increases, the emulsion will be unstable and the amount of water separated from emulsion increases. It was noticed that the em

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Publication Date
Fri Nov 15 2024
Journal Name
Iraqi Journal Of Science
The Impact of Partial Solar Eclipse on the Observation of Neutral Hydrogen Emission Line
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The research involves examining the influence of partial solar eclipse on the strength of neutral hydrogen from the Sun. Baghdad University Radio Telescope (BURT) was used to monitor the partial solar eclipse on the 25th of October, 2022. Radio observations from the Sun were recorded from 11:30 AM to 03:36 PM. This means that the HI emission from the Sun was recorded before, during and after the event. It was noticed, that at the moment of maximum eclipse, ~ 46% of the Sun’s disk was covered by the Moon. For the purpose of this research, the solar radio wave intensity was monitored and the solar flux density was determined at different times, i.e. before, during and after the partial solar eclipse. The obtained results showed that

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Publication Date
Sat Oct 01 2011
Journal Name
Iraqi Journal Of Physics
The Role of Annealing Temperature on the Optical Properties of Thermally Deposited CdTe Films
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A polycrystalline CdTe film has been prepared by thermal evaporation technique on glass substrate at substrate temperature 423 K with 1.0 m thicknesses. The film was heated at various annealing temperature under vacuum (Ta =473, 523 and K). Some of physical properties of prepared films such as structural and optical properties were investigated. The patterns of X-ray diffraction analysis showed that the structure of CdTe powder and all films were polycrystalline and consist of a mixture of cubic and hexagonal phases and preferred orientation at (111) direction.
The optical measurements showed that un annealed and annealed CdTe films had direct energy gap (Eg). The Eg increased with increasing Ta. The refractive index and the real p

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Publication Date
Fri Dec 01 2023
Journal Name
Asian Pacific Journal Of Cancer Prevention
Effect of Laetrile Vinblastine Combination on the Proliferation of the Hela Cancer Cell Line
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Publication Date
Fri Feb 01 2019
Journal Name
Journal Of Economics And Administrative Sciences
Reflecting the Faithful economic representation of accounting practices on the quality of accounting information
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Where the accounting system in Iraq is still using many of these accounting practices according to the legal requirements to measure assets and liabilities away from the measurement that results in information representing the economic essence and represent honestly the financial situation and financial performance and future cash flows, and the needs of users of financial reports to useful accounting information adopted The International Accounting Standards Board (IASB) represents the true representation of accounting information in accordance with the concept of economic substance, which is the basis for the preparation and development of international accounting standards, and because accounting is part of the

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Crossref
Publication Date
Thu Sep 07 2023
Journal Name
Journal Of Higher Education Theory And Practice
THE CONCEPTUAL FRAMEWORK OF THE CULTURE OF PEACE AND ITS IMPLICATIONS ON SUSTAINABLE DEVELOPMENT
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The issue of peace, renunciation of violence, and acceptance of the other is one of the vital issues that rose to the top of the list of priorities at the end of the last century and the beginning of the new millennium of the conscience of the Iraqi people by spreading the culture of peace. In this context, we seek during this research to identify the concept of the culture of peace and its impact on sustainable development, and to draw a set of results and suggestions to consolidate this culture in our Iraqi society as an obligation of sustainable development.

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Publication Date
Sun Sep 01 2019
Journal Name
Al-khwarizmi Engineering Journal
The Effect of Wind Velocity on the Suppression of Composite Wing Airfoil NACA 0012
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The first studies on shocks and vibrations were carried out at the beginning of the 1930s to improve the behavior of buildings during earthquakes. Vibration tests on aircraft were developed from 1940 to verify the resistance of parts and equipments prior to their first use. Flutter is a well-known example of dynamic aero elasticity, where when oscillation of structure interacted with unsteady aerodynamic forces the flutter will occur. Vibration on any structure without damping means that self-harmonic oscillation will occur, and in most cases the oscillation may start to increase until structural failure. This behavior is very similar to resonance phenomena if only the oscillation is being studied as a vibration case. In vibration suppre

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Publication Date
Wed Oct 01 2014
Journal Name
Al–bahith Al–a'alami
The Arts of Media Writing / An Empirical Study on the Privacy of Media Writing
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Media writing is accuracy writing. Clarity and concision are its predominant features. It is a writing that goes straight to the essence because it has no time to waste. Furthermore, it must be as accurate as scientific writing. It is destined for the average reader and has to be understood by everyone. However, it can be as elegant as literary writing. The variety in its forms of expression does not prevent media writing from having its own amplitude.

In short, this study is a practical approach that aims at studying different kinds of writing styles and identifying the specificity of media writing using some patterns and examples

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Crossref
Publication Date
Sun Feb 17 2019
Journal Name
Iraqi Journal Of Physics
A study of the solvent effect on the low temperature spectra of benzoanthracene molecules
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been taken at room temperature down to liquid nitrogen temperature (77K). Polar and nonpolar solvents have been used to study the solvent effect on the absorption and fluorescence spectra of solute molecules. Some of the spectroscopic parameters have been determined as functions of solvent polarity and temperature. The results indicate that the band width FWHM increases with increasing the solvent polarity and temperature, while the peak emission cross section decreases with increasing of solvent polarity and decreases with increasing the temperatures. Clear vibrational structure spectra of benzoanthracene molecules have been observed in Nonane and Hexane solvents at 77K.

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Crossref
Publication Date
Tue Feb 18 2025
Journal Name
Proceedings Of The 3rd International Conference On Engineering And Innovative Technology
Study the effect of nano vibration amplitude on the electromagnetic interaction of CMC structure
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Vibration is a source of energy that can be beneficial or harmful based on the application. Vibration can affect the function of any structure; however, Ceramic matrix composite (CMC) is one of these structures. Whereby less studies have been concentrated on study its function specially when electromagnetic wave (microwave) exposed on its surface to perform its designed function. To address this concept, SiC composite has been fabricated which is designed to have a transparent characteristics to microwave. External vibration had been applied on its surface to monitor how much influence could nanoscale amplitude vibration damage the microwave interaction. The source of vibration was applied from piezoelectric and the vibration was monitored

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