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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 Sgrafitto’s technique and its impacts on the contemporary ceramic art
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The current study deals with one of the ancient and modern techniques of ceramic art, which has evolved dramatically. This technique is interested in the muddy Body and its coloring, rather than interesting in the coloring of the layer on the surface of the glass port on the ceramic object. It is classified as ceramic techniques of the single heartburn, where use many coloring oxides. As well as, the use of (Pigment), which is often made of metal compounds, or metal oxides such as iron and manganese, copper and cobalt and more others.
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Wed Jan 02 2019
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PROPOSED STANDARDS FOR EVALUATING THE EDUCATIONAL VIDEO ON THE SOCIAL MEDIA
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In the spreading of the Internet, mobile smart devices, and interactive websites such as YouTube, the educational video becomes more widespread and deliberative among users. The reasons for its spread are the prevalence of technologies, cheap cost, and easy to use. However, these products often lack to the distinction in video production. By following videos of an educational channel on YouTube, some comments found to discuss the lack of the content presented to motivate the learners, which lead to reduce the viewers of the videos. Therefore, there is an important decision to find general standards for the design and production of educational videos. A list of standards has been drawn up to help those interested in producing educational

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The interpolation effect on the spare sinogram for 3D image reconstruction
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The effect of using three different interpolation methods (nearest neighbour, linear and non-linear) on a 3D sinogram to restore the missing data due to using angular difference greater than 1° (considered as optimum 3D sinogram) is presented. Two reconstruction methods are adopted in this study, the back-projection method and Fourier slice theorem method, from the results the second reconstruction proven to be a promising reconstruction with the linear interpolation method when the angular difference is less than 20°.

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Thu Mar 01 2018
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THE PROBLEM OF TRANSLATING METAPHOR IN AN ARTISTIC TEXT (ON THE MATERIAL OF RUSSIAN AND ARABIC LANGUAGES)
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Mechanisms of Social Change in the Era of Digital Communication and its Effects on the Communicative Message
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The assessment of a river water’ quality is an essential procedure of monitor programs and is used to collect basic environmental data. The management of integrated water resources in a sustainable method is also necessary to allow future generations to meet their water needs. The main objective of this research is to assess the effect of the Diyala River on Tigris River water quality using Geographic Information System (GIS) technique. Water samples have been collected monthly from November 2017 to April 2018 from four selected locations in Tigris and Diyala Rivers using the grab sampling method. Fourteen parameters were studied which are Turbidity, pH, Dissolved Oxygen, Biological Oxygen Demand, Electrical Conductivi

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The research aims to determine optimal urban planning and design indicators of the urban clusters form in hot arid zones through studying of three urban areas in Baghdad, analyzing their urban indicators which include floor area ratio (FAR), urban clusters height, building density or land coverage, green areas, paved areas, shading ratio and how they affect urban temperature. The research reached the conclusion that air outdoor temperature on urban areas affected primarily by shadows casted on the ground, the effect of shaded area equals (5) times the effect of paved areas and (3.7) times the effect of green areas, this means that increasing urban clusters height in hot arid zones could minimize air outdoor temperature, building

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