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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 Jan 01 2022
Journal Name
Journal Of The Mechanical Behavior Of Materials
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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Publication Date
Mon Feb 04 2019
Journal Name
Journal Of The College Of Education For Women
Some Methodological Notes on Ibn Al-Jezri Book: Ghayat Al-Nihaya (The Aim of the End): Some Methodological Notes on Ibn Al-Jezri Book: Ghayat Al-Nihaya (The Aim of the End)
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Abstract
Dame Ngaio Edith Marsh (1899-1982), a writer of detective fiction, was born
at Christchurch, New Zealand. Her hero, Chief Detective Inspector Roderick Alleyn,
appears in her first novel, A Man Lay Dead (1934), and in subsequent novels
including Death and the Dancing Footman (1942). She wrote twenty detective novels.
The Dancing Footman, Thomas, listening to a playful song from the smokingroom's
radio where William lay dead after being killed by his brother, Nicholas,
provides the most suspected guest at Highfold with badly needed alibi. The murderer,
Nicholas, plans an almost perfect crime, but the dance of this footman spoils his
scheme. When Alleyn and his group of policemen stage a show in which the

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Publication Date
Tue Dec 01 2020
Journal Name
Journal Of Engineering
Impact of Induction Motor Faults on the Basic Parameters' Values
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Unlike fault diagnosis approaches based on the direct analysis of current and voltage signals, this paper proposes a diagnosis of induction motor faults through monitoring the variations in motor's parameters when it is subjected to an open circuit or short circuit faults. These parameters include stator and rotor resistances, self-inductances, and mutual inductance. The genetic algorithm and the trust-region method are used for the estimation process. Simulation results confirm the efficiency of both the genetic algorithm and the trust-region method in estimating the motor parameters; however, better performance in terms of estimation time is obtained when the trust-region method is adopted. The results also show the po

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Publication Date
Tue Jul 02 2019
Journal Name
Sudan Journal Of Medical Sciences
Positive and Negative Effects of the Commensal Bacteria on Carcinogenesis
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Background: Cancer is a lethal disease that results from a multifactorial process. Progression into carcinogenesis and an abnormal cell proliferation can occur due to the micro and macro environment as well as genetic mutations and modifications. In this review, cancer and the microbiota – mainly bacteria that inhabit the tumour tissue – have been discussed. The positive and negative impacts of the commensal bacteria on tumours being protective or carcinogenic agents, respectively, and their strategies have also been described. Methods: Related published articles written in English language were searched from Google Scholar, PubMed, Mendeley suggestions, as well as Google search using a combination of the keywords ‘Microbiota, commens

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Publication Date
Thu Mar 12 2020
Journal Name
Al-khwarizmi Engineering Journal
The Influence of ProcessVariables for MillingSculptured Surfaces on Surface Roughness
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Increasing the variety of products that are being designed with sculptured surfaces, efficient machining of these surfaces has become more important in many manufacturing industries. The objective of the present work is the investigation of milling parameters for the sculptured surfacesthat effecting of surface roughness during machining of Al-alloy. The machining operation implemented on C-TEK CNC milling machine. The influence of the selected variables on the chosen characteristics have been accomplished using Taguchi design approach, also ANOVA had been utilized to evaluate the contributionsof each parameter on proc

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Publication Date
Tue Jun 14 2016
Journal Name
Al-academy
The impact of modern global art movements on Graphic Design
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The significant shift in the Fine Arts, who led the avant-garde movements and creative which appeared in the modern, specifically in the mid-nineteenth century and early twentieth century era path, embodied in a clear show of new aesthetic value rejects traditional methods put in shape and color qualities She described the movements subjectivity or no formal, was intended to determine the direct function of expression and speech language in the visual arts away from the representation and simulation of reality was accompanied by the appearance of those fine movements directed towards a global approach to design carries features and clear in its organizations formalism of the most important move away from the symmetry and the adoption of

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Publication Date
Tue Jun 18 2024
Journal Name
Al-bahir
Organization of Traffic on the Main Streets Microcontroller Traffic Lights
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Publication Date
Sat Jan 01 2022
Journal Name
Aip Conference Proceedings
The effect of different flooding ratio on Al-Shuwaija marsh
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In this research, the effect of changing the flood level of Al-Shuwaija marsh was studied using the geographic information systems, specifically the QGIS program, and the STRM digital elevation model with a spatial analysis accuracy of 28 meters, was used to study the marsh. The hydraulic factors that characterize the marsh and affecting on the flooding such as the ranks of the water channels feeding the marsh and the degree of slope and flat areas in it are studied. The area of immersion water, the mean depth, and the accumulated water volume are calculated for each immersion level, thereby, this study finds the safe immersion level for this marsh was determined.

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Publication Date
Sat Jul 01 2017
Journal Name
Energy Procedia
The effect of sunlight on medium density polyethylene Water pipes
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Publication Date
Sat Oct 01 2011
Journal Name
Journal Of Engineering
THE EFFECT OF CUTOFF WALL ANGLE ON SEEPAGE UNDER DAMS
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Flow of water under concrete dams generates uplift pressure under the dam, which may cause the dam to function improperly, in addition to the exit gradient that may cause piping if exceeded a safe value. Cutoff walls usually used to minimize the effect of flow under dams. It is required to
1)minimize the flow quantity to conserve water in the reservoir, it is also required to
2)minimize the uplift pressure under the dam to maintain stability of the dam, and it is required to

3) minimize the exit gradient to prevent quick condition to occur at the toe of the dam where piping may occur and may cause erosion of the soil. Varying the angle of cutoff walls affects its influence on the factors aforementioned that are required to

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