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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
Fri Feb 08 2019
Journal Name
Journal Of The College Of Education For Women
The Theory of Vital Space - Theoretical Study of Geopolitical Dimensions, Targets and Means (USA) Case Study
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The concept of forming the living space in the American strategic thought has an
important position it is regarded as an strategic movement that it supports the American
United States with the huge capabilities in its own concern that enables it to approach of
American administration , we find that of different historical periods it works to establish that
the geopolitical dimension which is accompanied with the ability of American response for
the evens that in its own turn enables the American united states to seize the growing chances
in the global strategic environment This study includes five chapters :
- Chapter one: The idea of living space.
- Chapter two: Geopolitical dimension of living space theory.
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Publication Date
Sun Jan 01 2017
Journal Name
Ursus
Community composition of Ixodid ticks parasitizing American black bears in Missouri, USA
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Publication Date
Mon Mar 15 2021
Journal Name
Al-academy
Design Technologies in Promoting the Advertisement for National Product: وسام عبد الامير كريم المالكي
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The current research is concerned with studying the variables in the promotion process which influence the advertisement design structure, as the accomplished design and construction process is subject to many variables, whether they were intellectual or technological, internal or external variables. These variables may overlap in order to get a comprehensive system for the artistic configuration, that any design in its content reaches the highest levels of perfection is connected to the extent of its compliance with and approximation to these variables, that is why we find their reflections deeply rooted in the individual's mind, especially the designer artist who is influenced by everything surrounding him forming knowledge systems res

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Publication Date
Wed May 18 2016
Journal Name
Al-academy
Abstraction and exaggeration formalism and its reflection in the industrial product: نور عباس حسين
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This study deals with the reality of the design of a washing machine automation available in the markets Mahlah.otata importance of this issue is through the development of technological and technical exploited for the benefit of the consumer and always seeking perfection in industrial product through providing comfort to the user and reduce fatigue and the effort and time-saving as well. On this basis, the research aims of this study put the foundations for the development of design automation washer. The boundaries of the study were products company LG producing Sna2012.uahtot this study on five chapters included Allvsal first importance of research and the need for a mechanism in addition to Alchuklh research objectives and Hdodh.ama

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Publication Date
Wed May 01 2024
Journal Name
Journal Of Physics: Conference Series
Study of The Effect of Concentration on The Efficiency of The Sensitive N749-TiO<sub>2</sub> Solar Cell
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Abstract<p>In this research, we studied the effect of concentration carriers on the efficiency of the N749-TiO<sub>2</sub> heterogeneous solar cell based on quantum electron transfer theory using a donor-acceptor scenario. The photoelectric properties of the N749-TiO<sub>2</sub> interfaces in dye sensitized solar cells DSSCs are calculated using the J-V curves. For the (CH3)3COH solvent, the N749-TiO<sub>2</sub> heterogeneous solar cell shows that the concentration carrier together with the strength coupling are the main factors affecting the current density, fill factor and efficiency. The current density and current increase as the concentration increases and the </p> ... Show More
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Publication Date
Mon Apr 03 2023
Journal Name
Journal Of Educational And Psychological Researches
The Effectiveness of Using Cubing Technique in the Iraqi EFL Secondary Students' Composition Writing, Vocabulary, and Meta-Cognitive Awareness
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Abstract

The aim of this research is to determine how well the Cubing Technique affects the Iraqi EFL students' composition writing, vocabulary, and meta-cognitive awareness of writing strategies. The sample of (64) secondary-school female students in the fifth grade is drawn from two classrooms and split into two equal groups: the experimental group and the control group, each of which consists of (32) students. A quasi-experimental design is applied. The performance test and Meta-cognitive Writing Strategies questionnaire are given as a pre-test for equalizing the two groups after ensuring their validity and reliability. Then, they are administrated as a posttest in both groups. According to the results, the si

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Publication Date
Tue Jul 01 2014
Journal Name
Political Sciences Journal
Political events in Iraq after 2003 and the impact of belonging and awareness in contemporary Iraqi composition
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الاحداث السياسية في العراق بعد 2003 وأثر الانتماء والوعي في التشكيل العراقي المعاصر

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Publication Date
Thu Dec 15 2022
Journal Name
Al-academy
Philosophy of values and its epistemological representations in industrial product design
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The research dealt with the concepts of the philosophy of values ​​and its epistemological variables according to specific propositions represented in their scientific approaches to value theory in the field of industrial design. As the epistemological propositions of the theory of values ​​were dealt with based on the epistemological fields that dealt with the concept and what values ​​are, starting with the modernist propositions and postmodern, passing through the propositions of sociological and psychological thought, which was a prelude to extracting the concepts of value theory and adopting it in the field of industrial product design. The epistemological approaches to value theory in industrial product design were repr

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Publication Date
Wed Jan 01 2020
Journal Name
Periodicals Of Engineering And Natural Sciences
Solving multicollinearity problem of gross domestic product using ridge regression method
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This study is dedicated to solving multicollinearity problem for the general linear model by using Ridge regression method. The basic formulation of this method and suggested forms for Ridge parameter is applied to the Gross Domestic Product data in Iraq. This data has normal distribution. The best linear regression model is obtained after solving multicollinearity problem with the suggesting of 10 k value.

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Scopus
Publication Date
Thu Sep 01 2011
Journal Name
Journal Of Economics And Administrative Sciences
The use of the methods of the lower squares and the smaller squares weighted in the estimation of the parameters and design of the sample acceptance schemesFor general exponential distribution
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The acceptance sampling plans for generalized exponential distribution, when life time experiment is truncated at a pre-determined time are provided in this article. The two parameters (α, λ), (Scale parameters and Shape parameters) are estimated by LSE, WLSE and the Best Estimator’s for various samples sizes are used to find the ratio of true mean time to a pre-determined, and are used to find the smallest possible sample size required to ensure the producer’s risks, with a pre-fixed probability (1 - P*). The result of estimations and of sampling plans is provided in tables.

Key words: Generalized Exponential Distribution, Acceptance Sampling Plan, and Consumer’s and Producer Risks

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