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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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The Effect of Using Teaching Aid on the Development of Straight Forehand and Backhand Shot Performance in Lawn Tennis
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The problem of the research lies in finding aiding means that improve and facilitate learning artistic skills during the main part of a teaching sessions due to their great importance in developing the accuracy of forehand and backhand skills in tennis. Players are usually faced with difficulties at the beginning of learning due to lack of coordination in ball striking thus including a teaching aid will have a positive effect on learning some forehand and backhand skills. The research aimed at designing exercises using teaching aid in tennis as well as identifying the effect of these exercises on the accuracy of performing forehand and backhand shots in tennis. The researcher used the experimental method on (38) tennis players from Al Zewra

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The Influence of Rewards on Games Flow, Challenge, and Its Effects Towards the Engagement of Malaysian Digital Traditional Games
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Games engagement has become one of the main concerns in game industry. Early study revealed that Malaysian digital traditional games are suffering with the same issue due to several factors. One of it is the lack of the game itself. Although many Malaysian traditional games have been digitized, none of them has incorporated rewards despite its importance in games engagement. Realizing the importance of rewards in games engagement, one of Malaysian traditional Congkak has been chosen to be enhanced by incorporating rewards. Experiments have been conducted among 50 gamers among the Millennials. Prior interview, game demo and human test are conducted. Experiments focused on the influence of rewards on games flow, games challenge, and its ef

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Evaluation of the Influence of De-sanding (Recycling System) Process on the Pile Bearing Capacity Using Full Scale Models
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The present study investigates the effect of the de-sanding (recycling system) on the bearing capacity of the bored piles. Full-scale models were conducted on two groups of piles, the first group was implemented without using this system, and the second group was implemented using the recycling system. All piles were tested by static load test, considering the time factor for which the piles were implemented. The test results indicated a significant and clear difference in the bearing capacity of the piles when using this system. The use of the recycling system led to a significant increase in the bearing capacity of the piles by 50% or more. Thus it was possible to reduce the pile length by (15 % or more) thus, and implementation costs

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The Effect of Growth Medium and Nodes Number on the Acclimatization Success of Tissue Propagated Potatoes Seedlings Solanum tuberasum
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The experiment was conducted at the period from 20th Dec. 2015 to 30th Mar. 2016 to know the effect of growth medium and nodes number on the acclimatization success of tissue propagated potatoes seedlings (Burrin class) and study some plant physiological properties. The first experiment involved testing growth media: loam, peat moss, and perlite with different portions (1:1) to plant tissue propagated potato tubers, while the second experiment involved testing the nodes number where 9, 8, 7, 6, and 5 plant nodes were chosen. Results of the first experiment showed the superiority of the culture media of peat moss + perlite to other culture media by giving the higher values of shoot system studied properties: plant height, branches number, le

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EFFECT OF THE SUPPLEMENTATION OF THE LAYING QUAILS RATION WITHSESAME (SESAMUM INDICUM) SEEDS AND OIL ON EGG QUALITY TRAITS
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The aim of this study was to determine the influence of feeding diets containing different levels of sesame seeds and oil on the egg quality of laying quail. A total of 120, 10 weeks old, were randomly assigned to 1 of 5 dietary groups and fed for 12 weeks diets containing 0% sesame seeds + 0% sesame oil (control group; C) or 0.5% sesame oil (T1), 1% sesame oil (T2), 1% sesame seeds (T3), and 2% sesame seeds (T4).The study was terminated when the birds were 22 weeks of age. Egg quality characteristics involved in the present study were egg weight, yolk diameter, yolk height, yolk weight, albumen height, albumen weight,Haugh unit, shell weight, shell thickness, shell percentage, yolk percentage, and albumen percentage. The addition of sesame

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Wed Jun 29 2022
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On the Use of the First-Person Pronoun ‘we’ in Final-Year Master Projects of South Algerian EFL Students
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Evaluation of the Influence of De-sanding (Recycling System) Process on the Pile Bearing Capacity Using Full Scale Models
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This article aims to identify the views of media elites on citizen journalism, a new media genre that strays away from the foundations and ethics of professional journalism, thus calling for in-depth exploration and scrutiny into the genre and its commitment to the professional standards of journalism.

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