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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 Oct 01 2022
Journal Name
The Egyptian Journal Of Hospital Medicine
Study on Viral Infection and Related Parameters in A Sample of Diabetes Mellitus Type 2
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Publication Date
Sun Dec 09 2018
Journal Name
Baghdad Science Journal
Synthesis, Characterization of Poly Heterocyclic Compounds, and Effect on Cancer Cell (Hep-2) In vitro.
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A synthesis series of new heterocyclic derivatives (A2-A7) (pyrrole, pyridazine, oxazine and imidazol) derived from 4-acetyl-2,5-dichloro-1-(3,5-dinitrophenyl)-1H-pyrrole-3-carboxylate(A1) have been synthesised. Synthesis of compound (A2) by the reaction of starting material (A1) with hydroxyl amine hydrochloride in the presence of pyridine. Compound (A2) was reacted with hydrazine hydrate in dry benzene to give (A3) derivative. The compound )A3( deals with sodium nitrite to give diazonium salt, and the reaction diazonium salt with ethyl acetoacetate to produce compound (A4). To a mixture of compound (A4) and hydroxyl amine with sttired to yield (A5).Compound (A6) was prepared by reaction compound (A4) with thiosemicarbazide in presence

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Publication Date
Thu Jan 11 2018
Journal Name
Al-khwarizmi Engineering Journal
Control on a 2-D Wing Flutter Using an Adaptive Nonlinear Neural Controller
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An adaptive nonlinear neural controller to reduce the nonlinear flutter in 2-D wing is proposed in the paper. The nonlinearities in the system come from the quasi steady aerodynamic model and torsional spring in pitch direction. Time domain simulations are used to examine the dynamic aero elastic instabilities of the system (e.g. the onset of flutter and limit cycle oscillation, LCO). The structure of the controller consists of two models :the modified Elman neural network (MENN) and the feed forward multi-layer Perceptron (MLP). The MENN model is trained with off-line and on-line stages to guarantee that the outputs of the model accurately represent the plunge and pitch motion of the wing and this neural model acts as the identifier. Th

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Publication Date
Mon May 30 2022
Journal Name
The Journal Of Infection In Developing Countries
SARS-CoV-2 viral shedding and susceptibility: perspectives on gender and asymptomatic patients
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Despite efforts to contain and manage the SARS-CoV-2 outbreak which was declared a public health emergency of international concern in January 2020 by the World Health Organization (WHO), the COVID-19 pandemic still remains a major global challenge. Patients who display the classical symptoms of the infection are easily identified, tested, isolated and monitored. However, many cases of infected asymptomatic patients have been documented. These patients are not easily identified even though many evidences suggest that they can spread the virus to others. How and why these COVID-19 asymptomatic presentations occur remain unclear. The many theories and views are conjectural, and supporting evidences are still needed. In this review, we

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Publication Date
Wed Sep 15 2021
Journal Name
Al-academy
Processes directing the scenographic space in the Iraqi theatrical show Shakespeare texts as a model: فرحان عمران موسى - سماء محي عطية محمد
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The operative system of theatrical performance depends on the construction of the scenographic space, as it constitutes the most aesthetic effect of the recipient, and the body of the theatrical discourse that contains the signs of the show, and it comes as an embodiment of the directing vision of the show director, so most of the world directors resorted to attention to the output treatment to establish the scenographic space, and thus it possesses a contrast in The embodiment of the directing vision according to the stylistic and hermeneutical dimension of the director, so the two researchers found the importance of studying the topic, and the study came under the title (Directing Treatments of the Scenographic Space in the Iraqi Theat

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Publication Date
Mon Oct 01 2018
Journal Name
Journal Of Economics And Administrative Sciences
The effect of deficiencies in the standards and tools used for the management of the banking system in the emergence of the financial crisis by focusing on the Basel 1and 2
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The banking industry, as a result of the great challenges it faced, required continuous development of the principles of management, control and mechanisms used. The Basel Committee on Banking Supervision has played a leading role in legalizing many of these developments and has been able to contribute significantly to establishing a common framework for banking supervision, The central role in the various countries of the world is based on coordination between the various regulatory authorities and thinking about finding mechanisms to confront the risks faced by banks, recognizing the importance of the banking sector in the stability of domestic and international banking systems or the danger of this sector in the emergence of F

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Publication Date
Wed Oct 17 2018
Journal Name
Journal Of Economics And Administrative Sciences
the role of marketing intelligence in promoting new product policies.a sample survey of workers in a number of mineral water plants in dohuk governorate
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Marketing Intelligence is one of the important methods of collecting information about competitors ' products and changes in customers ' tastes and needs that contribute to determining the policies to be followed in product development.

The problem of research, which seeks to be answered by the extent to which the companies in question have the appropriate and effective mechanisms to develop their products, and the nature of the relationship between the components of marketing intelligence and new product development policies. The importance of research is determined by the importance of obtaining important and necessary information to make the appropriate decision on the development of the new product an

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Publication Date
Tue Jan 01 2019
Journal Name
Al-dhad Book Store And Publishing
Calculus part 2
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This book includes four main chapters: 1. Indefinite Integral. 2. Methods of Integration. 3. Definite Integral. 4. Multiple Integral. In addition to many examples and exercises for the purpose of acquiring the student's ability to think correctly in solving mathematical questions.

Publication Date
Sun Sep 01 2019
Journal Name
Journal Of Physics: Conference Series
Integral transforms defined by a new fractional class of analytic function in a complex Banach space
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Abstract<p>In this effort, we define a new class of fractional analytic functions containing functional parameters in the open unit disk. By employing this class, we introduce two types of fractional operators, differential and integral. The fractional differential operator is considered to be in the sense of Ruscheweyh differential operator, while the fractional integral operator is in the sense of Noor integral. The boundedness and compactness in a complex Banach space are discussed. Other studies are illustrated in the sequel.</p>
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Publication Date
Mon Mar 15 2021
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Al-academy
Icon, Symbol and Values of Functional and Aesthetic Communication in Industrial Product Design: زياد حاتم حربي العامري
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The icon and the symbol represent the constituents of the communication process, through their intellectual and philosophical concepts that have been addressed by the current research that it has touched upon their importance in conveying the design idea for the recipient and showing the specificity of each one of them in the communication process. The research problem has been limited by the following question: what are the communication roles that the symbol and the icon present for the user in designing the industrial product?
The research objective is to reveal the theoretical visualization that describes the icon and the symbol in the industrial product and its importance in the communication process through stating the of simil

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