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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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Sat Jan 01 2022
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Impact of eccentricity and depth-to-breadth ratio on the behavior of skirt foundation rested on dry gypseous soil
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Abstract<p>Gypseous soils are considered one of the most problematic soils. The skirted foundation is an alternative technology that works to improve the bearing capacity and reduce settlement. This paper investigates the use of square skirted foundations resting on gypseous soil subjected to concentric and eccentric vertical load with eccentricity values of 4, 8, and 17 mm in 16 experimental model tests. To obtain the results by using this type of foundation, a small-scale physical model was designed to obtain the load–settlement behavior of the square skirted foundation; the dimension of the square footing is 100 mm × 100 mm with 1 mm thickness, the skirt depth (<italic>D</italic></p> ... Show More
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E-learning is a necessity imposed by the Corona pandemic, which has disrupted various educational institutions in the world, but some of these institutions have not been affected and education has continued with them, due to their flexible educational system that was able to employ technology in the continuity of the educational process in the so-called e-learning, because It has characteristics that make it the most suitable alternative to avoid the consequences of the Corona pandemic and its damage to the educational process, as e-learning is one of the modern methods that contribute to enhancing the effectiveness of the learner, and enabling him to assume greater responsibility compared to traditional education, so the learner becomes

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the aspect of the radiation superposed on the soliton pulse propagated in single mode optical fiber
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Sat Feb 20 2021
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The tourism industry, with its two sides (recreational and religious), is one of the important investment fields in Iraq, it is represented Iraq as the second economic source after the oil sector. So a need for serious efforts to develop the tourism sector and maintain its sustainability. This paper will be one of the important contributions in this field; the paper aims to explore the extent of the impact of the sustainable strategy on the level of overall performance in the Iraqi tourism sector. The field of research was some Iraqi tourist institutions at Iraqi tourism, Which covers the field of study on the one side, and can be studied on the other side, for the developing study methodology and organizing its main parts, the research pap

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The effect of creating knowledge according to the model (Nonaka &amp; Takeuchi, 1995) on organizational ambidexterity: A study on a sample of Iraqi private banks
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Purpose - This study relies on the descriptive and analytical approach through collecting and analyzing the necessary data, as this approach focuses on polling the opinions of the research sample and its directions, and aims to develop a model that studies the relationship between knowledge creation and organizational ambidexterity in Iraqi private banks and verifying its validity experimentally. Design / Methodology / Introduction - A survey was conducted through a questionnaire form to collect data from a sample of (113) managers in private commercial banks. In addition, this study used the AMOS program and the ready-to-use statistical program package (SPSS V.25) to test the proposed hypotheses of the theoretical model experimentally. Res

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There are many techniques that can be used to estimate the spray quality traits such as the spray coverage, droplet density, droplet count, and droplet diameter. One of the most common techniques is to use water sensitive papers (WSP) as a spray collector on field conditions and analyzing them using several software. However, possible merger of some droplets could occur after they deposit on WSP, and this could affect the accuracy of the results. In this research, image processing technique was used for better estimation of the spray traits, and to overcome the problem of droplet merger. The droplets were classified as non-merged and merged droplets based on their roundness, then the merged droplets were separated based on the average non-m

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