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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
Tue Oct 01 2024
Journal Name
Journal Of Physics: Conference Series
An Effect of Al on the Properties of ZnIn<sub>2</sub>Se<sub>4</sub> Thin Film
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Abstract<p>Zinc-indium-selenide ZnIn<sub>2</sub>Se<sub>4</sub> (ZIS) ternary chalcopyrite thin film on glass with a 500 nm thickness was fabricated by using the thermal evaporation system with a pressure of approximately 2.5×10<sup>−5</sup> mbar and a deposition rate of 12 Å/s. The effect of aluminum (Al) doping with 0.02 and 0.04 ratios on the structural and optical properties of film was examined. The utilization of X-ray diffraction (XRD) was employed to showcase the influence of aluminum doping on structural properties. XRD shows that thin ZIS-pure, Al-doped films at RT are polycrystalline with tetragonal structure and preferred (112) orientation. Where the </p> ... Show More
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Publication Date
Wed Jun 28 2017
Journal Name
Proceedings Of The 2017 Acm Conference On Innovation And Technology In Computer Science Education
Media Literacy as a By-Product of Collaborative Video Production by CS Students
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Understanding, promoting, and teaching media literacy is an important societal challenge. STEM educators are increasingly looking to incorporate 21st century skills such as media literacy into core subject education. In this paper we investigate how undergraduate Computer Science (CS) students can learn media literacy as a by-product of collaborative video tutorial production. The paper presents a study of 34 third-year CS undergraduates who, as part of their learning, were each asked to produce three video tutorials on Raspberry Pi programming, using a collaborative video production tool for mobile phones (Bootlegger). We provide results of both quantitative and qualitative analysis of the production process and resulting video tutorials,

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Publication Date
Thu Jan 01 2015
Journal Name
Journal Of Nanomaterials
Comparative Studies on Thermal Performance of Conic Cut Twist Tape Inserts with SiO<sub>2</sub>and TiO<sub>2</sub>Nanofluids
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This paper presents a comparison study on thermal performance conic cut twist tape inserts in laminar flow of nanofluids through a constant heat fluxed tube. Three tape configurations, namely, quadrant cut twisted tape (QCT), parabolic half cut twisted tape (PCT), and triangular cut twisted (VCT) of twist ratioy= 2.93 and cut depthde= 0.5 cm were used with 1% and 2% volume concentration of SiO2/water and TiO

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Publication Date
Tue Apr 11 2023
Journal Name
Indonesian Journal Of Chemistry
Synthesis of Co (ll), Ni (ll), Cu (ll), Pd (ll), and Pt (lV) Complexes with 14, 15, 34, 35-Tetrahydro-11 H, 31 H-4, 8-diaza-1,3 (3,4)-ditriazola-2,6 (1,4)-dibenzenacyclooctaphane-4,7-dien-15, 35-dithione, and the Thermal Stability of Polyvinyl Chloride Modified Complexes
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In the current endeavor, a new Schiff base of 14,15,34,35-tetrahydro-11H,31H-4,8-diaza-1,3(3,4)-ditriazola-2,6(1,4)-dibenzenacyclooctaphane-4,7-dien-15,35-dithione was synthesized. The new symmetrical Schiff base (Q) was employed as a ligand to produce new complexes comprising Co(II), Ni(II), Cu(II), Pd(II), and Pt(II) metal-ions at a ratio of 2:1 (Metal:ligand). There have been new ligands and their complexes validated by (FTIR), (UV-visible), 1H-NMR, 13C-NMR, CHNS, and FAA spectroscopy, Thermogravimetric analysis (TG), Molar conductivity, and Magnetic susceptibility. The photostabilization technique to enhance the polymer was also used. The ligand Q and its complexes were mixed in 0.5% w/w of polyvinyl chloride in tetrahydrofuran

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Publication Date
Thu Nov 17 2011
Journal Name
Environmental Earth Sciences
Geochemistry and mineralogical composition of the airborne particles of sand dunes and dust storms settled in Iraq and their environmental impacts
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Publication Date
Tue Feb 01 2022
Journal Name
Baghdad Science Journal
Numerical Solution for Linear State Space Systems using Haar Wavelets Method
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In this research, Haar wavelets method has been utilized to approximate a numerical solution for Linear state space systems. The solution technique is used Haar wavelet functions and Haar wavelet operational matrix with the operation to transform the state space system into a system of linear algebraic equations which can be resolved by MATLAB over an interval from 0 to . The exactness of the state variables can be enhanced by increasing the Haar wavelet resolution. The method has been applied for different examples and the simulation results have been illustrated in graphics and compared with the exact solution.

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Publication Date
Mon Aug 01 2022
Journal Name
Baghdad Science Journal
Subgroups and Orbits by Companion Matrix in Three Dimensional Projective Space
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The aim of this paper is to construct cyclic subgroups of the projective general linear group over  from the companion matrix, and then form caps of various degrees in . Geometric properties of these caps as secant distributions and index distributions are given and determined if they are complete. Also, partitioned of  into disjoint lines is discussed.

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Publication Date
Thu Nov 01 2018
Journal Name
Journal Of Economics And Administrative Sciences
Use A State Space Model and Forecast House Prices in Baghdad.
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The purchase of a home and access to housing is one of the most important requirements for the life of the individual and the stability of living and the development of the prices of houses in general and in Baghdad in particular affected by several factors, including the basic area of the house, the age of the house, the neighborhood in which the housing is available and the basic services, Where the statistical model SSM model was used to model house prices over a period of time from 2000 to 2018 and forecast until 2025 The research is concerned with enhancing the importance of this model and describing it as a standard and important compared to the models used in the analysis of time series after obtaining the

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Publication Date
Fri Dec 15 2023
Journal Name
Al-academy
Design contexts in interior space design (sewing workshops as a model)
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The topic of context is one of the important topics, which was mentioned as a concept in several fields and different fields, and there were many points of view that defined that concept.
He specified the title of the research (design contexts in the design of the interior space), as the research sought to identify the concept of context in the interior design of the spaces of sewing workshops. The research was divided into four chapters:
The first chapter, which consists of the methodological framework, the problem of research and the need for it, the importance of research, the goal and limits of research for sewing workshops for vocational schools from (2020-2021).
The second chapter: consists of previous studies and the theo

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Publication Date
Tue Nov 30 2021
Journal Name
Iraqi Geological Journal
Ore Petrography, Mineralogical and Chemical Composition of New Iron Meteorite (Al-Sherqat Meteorite) from Iraq
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The meteorite with a single total mass of 630 gm as a visible meteorite has fallen on 22 March 2021, at 10:00 a.m. in Al-Sherqat subdistrict within Salah Al-Din, northern Iraq; and therefore, was named Al-Sherqat meteorite by the authors. It is characterized by a uniform structure of coherent and medium degree of malleability. It is of a well-crystalline structure and not homogeneous in composition. The Al-Sherqat meteorite is composed of metallic phases of 7.6 gm/cm3 density exhibiting an oriented intergrowth of kamacite (α-FeNi) with taenite showing a Widmanstätten pattern on an etched polished section with the finest octahedrite kamacite bandwidth of less than 0.2 mm. It is composed of Fe (86.9 wt%), Ni (9.63 wt%), P (1.31 wt%)

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