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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 Dec 31 2020
Journal Name
College Of Islamic Sciences
: Islamic law; perfection The rule of perfection in Islamic law and its impact on the creative construction of the individual and society: The rule of perfection in Islamic law and its impact on the creative construction of the individual and society
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This research explains to us the role of the Islamic religion in the issue of accuracy in speech and work, and how it is closely related to human production in his life, and Islam affirms that his idea is mainly reflected in his production, and how it affects the perception of the meaning of creativity. Therefore, our Islam affirmed the accuracy in every word or work we do to build a society in which people enjoy high quality in ethics and dedication in their work so that the Islamic system depends on humanity to preserve our rights on the other hand the research discusses the deliberate default and how it reflects on our production and how it makes it less good.

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Publication Date
Sun Jan 01 2023
Journal Name
International Journal Of Economics And Finance Studies
THE EFFECTS OF INFORMATION TECHNOLOGY ADOPTION ON THE FINANCIAL REPORTING: MODERATING ROLE OF AUDIT RISK
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Publication Date
Fri Sep 01 2023
Journal Name
Journal Of Engineering
Impact of Sulfate in the Sand on the Compressive Strength of Metakaolin-Based Geopolymer Mortar
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The advancement of cement alternatives in the construction materials industry is fundamental to sustainable development. Geopolymer is the optimal substitute for ordinary Portland cement, which produces 80% less CO2 emissions than ordinary Portland cement. Metakaolin was used as one of the raw materials in the geopolymerization process. This research examines the influence of three different percentages of sulfate (0.00038, 1.532, and 16.24) % in sand per molarity of NaOH on the compressive strength of metakaolin-based geopolymer mortar (MK-GPM). Samples were prepared with two different molarities (8M and 12M) and cured at room temperature. The best compressive strength value (56.98MPa) was recorded with 12M w

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Publication Date
Sat Jul 01 2023
Journal Name
Iop Conference Series: Earth And Environmental Science
A Statistical Analysis of the Effects of Afforestation on the Environment in Iraq (Northern Iraq)
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Abstract<p>The significance of the research conducted in northern Iraq comes despite the expansion of afforestation projects; yet, the suffering of the forests has increased due to their lack of scientific study, unpredictability of the climate, and adverse effects on the spread and growth of plant species Therefore, the goal of the study is to understand the effects of afforestation through a statistical analysis of plant diversity in northern Iraq and its distinctivenessThe analysis revealed that natural groupings had improved qualitatively more than other groups, particularly some dwindling species that are able to compete and occupy new areas. drought-prone vegetation, vegetation, and climat</p> ... Show More
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Publication Date
Wed Mar 10 2021
Journal Name
Baghdad Science Journal
Study the Effect of solvent on the Optical Properties Performance of active polymeric laser media
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The paper include studies the effect of solvent of dye doped in polymeric laser sample which manufactured in primo press way, which is used as an active (R6G) tunable dye lasers. The remarks show that, when the viscosity of the solvent (from Pure Water to Ethanol), for the same concentration and thickness of the performance polymeric sample is increased, the absorption spectrum is shifts towards the long wave length (red shift), & towards short wave length (blue shift) for fluorescence spectrum, also increased the quantum fluorescence yield. The best result we obtained for the quantum fluorescence yield is (0.882) with thickness (0.25mm) in Ethanol solvent in concentration (2*10-3mole/liter), while when we used the Pure Water as a solvent,

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Publication Date
Sat May 02 2015
Journal Name
التربية العلمية
the effect of a strategy on the reading compreheehension of first-yearinter intermediate school students
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Publication Date
Tue Feb 05 2019
Journal Name
Journal Of The College Of Education For Women
The value of work to the Elits of prophets and its influence on cultural construction
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Praise be to Allah and peace and blessings be upon our Prophet Muhammad and on his family and companions
Yet,
The prophets (peace be upon them) urged all thevalues and one of these is the value of work which is of a great importance, that all nations have gathered against us as the eaters gather at a bowl. One of the reasons of our weakness and the strength of our enemy is that we have neglected the value of work. And rather a large number of ignorant and uneducatedpeople started to believe that the means of living, triumph, gaining power, and establishing a civilization are given by Allah with neithergainingnoreffort from us. While we find in the past that Allah the Almighty narrated to us the story of Mary (Peace be upon her) and

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Publication Date
Tue Dec 01 2020
Journal Name
Al-khwarizmi Engineering Journal
Impact of using Double Layers Perforated Liners on the Acoustic Treatments of the Combustor Systems
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The response of the combustor’s liner to the air-flow that passes through it is the key reason for the combustion chambers noise, hence the instabilities of those chambers that decreases the mechanical efficiency of such sections, by increased its mechanical vibrations, which increases the failure rate created during originating of the cracks spreading by the shakes producing by the series of high-level frequencies. Accordingly, any work debating the impact of the context of liners in the combustion chamber can provide grasping for the combustion noise generated by the undesirable vibrations, and benefits the industrial firms to design an ideal production procedure which increases the lifespan of the combustor. The goal of this wo

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Publication Date
Sat Jan 01 2022
Journal Name
International Journal Of Clinical Dentistry
THE EFFECT OF A PROTECTIVE BARRIER ON THE SHEAR BOND STRENGTH OF DIFFERENT ORTHODONTIC BRACKETS
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Background and objectives: This study aimed at testing the effect of plastic sleeve or barrier, used to cover the guide of the light cure unit to prevent cross-infection, on the shear bond strength and site of bond failure of stainless steel and ceramic orthodontic brackets. Materials and methods: Forty orthodontic brackets; twenty stainless steel and twenty ceramic brackets bonded to forty extracted human maxillary first premolars using light cure adhesive cured with and without the use of a protective plastic barrier on the guide. Comparing the effect of this barrier on the shear bond strength and adhesive remnant index was performed using an independent t-test and Chi-square test. Results: The protective barrier had decreased the shear b

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Scopus
Publication Date
Sun Oct 17 2021
Journal Name
Iraqi Journal Of Physics
The effect of inorganic pigment on the tensile properties of polycarbonate irradiated with UV – light
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The effect of UV-light on the tensile properties of pure PC has been studied. It was shown that irradiation of PC undergo a drop in the tensile properties of 30 hour of exposure. The results of irradiated samples shows that the addition of ZnO and TiO2 with different percentages (0.5, 1, 1.5 %) will reduce the Young modulus and ultimate stress of PC/ZnO ,PC/ TiO2 composites

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