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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
Sat Jun 01 2024
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Study of The Effect of Concentration on The Efficiency of The Sensitive N749-TiO2 Solar Cell
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In this research, we studied the effect of concentration carriers on the efficiency of the N749-TiO2 heterogeneous solar cell based on quantum electron transfer theory using a donor-acceptor scenario. The photoelectric properties of the N749-TiO2 interfaces in dye sensitized solar cells DSSCs are calculated using the J-V curves. For the 〖(CH_3)〗_3 COH solvent, the N749-TiO2 heterogeneous solar cell shows that the concentration carrier together with the strength coupling are the main factors affecting the current density, fill factor and efficiency. The current density and current increase as the concentration increases and the strength coupling increases as the N749-TiO2 heterogeneous in solar cell. However, the efficiency is more sens

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Fri Jul 01 2016
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The Impact Of Application Of Jit In The Banking Sector On The Quality Of Banking Service
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Abstract 

          The research the impact of the application of some of the production system tools in the specified time, which can be adapted in the service sectors (banking sector) over the improvement and increase the quality of banking services, and highlights the research problem in the low quality of banking services provided to customers because of the reliance on traditional banking systems in the provision of services Because of the lack keep pace with global developments in the banking industry, and the goal of research is to clarify the applicability of the production system in the time specified in the service sector and th

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Wed Jun 29 2022
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The impact of the internet of things on information institutions from the perspective of library employees
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Wed May 31 2017
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Construction Policies on Campus An Analytical Study of the Policy of Construction Planning on Kufa Campus
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     University Campuses, as any lively physical entity, is subject to continuous variation due to . growth, development and change. This reality covers the existing or futuristic additives or  additions, consecutively these changes may have a strong sensation of disorientation as a result of formatic changes in buildings, or in movement paths. And it epitomized the research problem to "the need for knowledge to clarify the impact of intellectual and executive policy in achieving coherence, functional and space organization of the elements of the university urban environment and in the stages of future growth and change,"  the search targeted "to highlight the study of constraction politics on campus Bmqomad

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Mon Aug 01 2022
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EVALUATION OF THE TOXICITY OF DELTAMETHRIN INSECTICIDE ON SOME HEMATOLOGICAL PARAMETERS AND OXIDATIVE STRESS ON MICE
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Laboratory Study on the Effect of Water-Cement Ratio on Strength Characteristics of Jet Grouting Columns
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Jet grouting is one of the most widely applied soil improvement techniques. It is suitable for most geotechnical problems, including improving bearing capacity, decreasing settlement, forming seals, and stabilizing slopes. One of the difficulties faced by designers is determining the strength and geometry of elements created using this method. Jet grouted soil-cement columns in soil are a complicated issue because they are dependent on a number of parameters such as soil type, grout and water flow rate, rotation and lifting speed of monitor, nozzle jetting force, and water to cement ratio of slurry. This paper discusses the effect of the water-cement ratio on the physical and mechanical characteristics of soilcrete. In t

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Publication Date
Tue Jun 01 2021
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Effect of Environmental Factors on the Accuracy of a Quality Inspection System Based on Transfer Learning
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In this research, a study is introduced on the effect of several environmental factors on the performance of an already constructed quality inspection system, which was designed using a transfer learning approach based on convolutional neural networks. The system comprised two sets of layers, transferred layers set from an already trained model (DenseNet121) and a custom classification layers set. It was designed to discriminate between damaged and undamaged helical gears according to the configuration of the gear regardless to its dimensions, and the model showed good performance discriminating between the two products at ideal conditions of high-resolution images. So, this study aimed at testing the system performance at poo

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Publication Date
Tue Jun 01 2021
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Al-khwarizmi Engineering Journal
Effect of Environmental Factors on the Accuracy of a Quality Inspection System Based on Transfer Learning
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In this research, a study is introduced on the effect of several environmental factors on the performance of an already constructed quality inspection system, which was designed using a transfer learning approach based on convolutional neural networks. The system comprised two sets of layers, transferred layers set from an already trained model (DenseNet121) and a custom classification layers set. It was designed to discriminate between damaged and undamaged helical gears according to the configuration of the gear regardless to its dimensions, and the model showed good performance discriminating between the two products at ideal conditions of high-resolution images.

So, this study aimed at testing the system performance at poor s

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Publication Date
Wed Jan 03 2024
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The consumption of fresh fruits has increased nowadays due to the lifestyle of the consumers. Maintaining the quality and nutritional value of cut fruits during storage is difficult compared to whole fruits. Deterioration of internal and external quality usually occurs in freshly harvested fruits. It is necessary to use different techniques to maintain the quality and increase the shelf life of the freshly cut product. This research studied the effect of treating apple slices with cold plasma once and with filtered water again on quality characteristics (hardness, moisture content, sugar content, carbohydrate content, and color) after being stored for five days. The best treatment was determined using two different pressures of the plasma j

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Spectrophotometric Determination of Micro Amount of Chromium (III) Using Sodium 4-((4,5-diphenyl-imidazol-2-yl)diazenyl)-3-hydroxynaphthalene-1-sulfonate in the Presence of Surfactant, Study of Thermodynamic Functions and Their Analytical Applications
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          Using sodium4-((4,5-diphenyl-imidazol-2-yl)diazenyl)-3-hydroxynaphthalene-1-sulfonate (SDPIHN) as a chromogenic reagent in presence of non-ionic surfactant (Triton x-100) to estimate the chromium(III)  ion if the wavelength of this reagent 463 nm to form a dark greenish-brown complex in wavelength 586 nm at pH=10,the complex was stable for longer than 24 hours. Beer's low, molar absorptivity 0.244×104L.mol-1.cm-1, and Sandal's sensitivity 0.021 µg/cm2 are all observed in the concentration range 1-11 µg/mL. The limits of detection (LOD) and limit of quantification (LOQ), respectively, were 0.117 µg/mL and 0.385µg/mL. (mole ratio technique, job's method) were employed to

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