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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
Sun Feb 28 2021
Journal Name
Journal Of Economics And Administrative Sciences
Determine The Factors Affecting Product Quality Using FMEA Analysis: A Case Study in Al Zawraa State Company
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The research aims to identify the factors that affect the quality of the product by using the Failure Mode and Effect Analysis (FMEA) tool and to suggest measures to reduce the deviations or defects in the production process. I used the case study approach to reach its goals, and the air filter product line was chosen in the air filters factory of Al-Zawraa General Company. The research sample was due to the emergence of many defects of different impact and the continuing demand for the product. I collected data and information from the factory records for two years (2018-2019) and used a scheme Pareto Fishbone Diagram as well as an FMEA tool to analyze data and generate results.

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Crossref
Publication Date
Fri Jan 01 2016
Journal Name
Iosr Journal Of Applied Physics (iosr-jap)
Influence of concentration on the structural, optical and electrical properties of TiO 2 : CuO thin film Fabricate by PLD
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In this work, Titanium oxide thin films doped with different concentration of CuO (0,5,10, 15,20) %wt were prepared by pulse laser deposition(PLD) technique on glass substrates at room temperature with constant deposition parameter such as : pulse (Nd:YAG), laser with λ=1064 nm, constant energy 800 mJ , repetition rate 6 Hz and No. of pulse (500). The structure , optical and electrical properties were studied . The results of X-ray diffraction( XRD) confirmed that the film grown by this technique have good crystalline tetragonal mixed anatase and rutile phase structure, The preferred orientation was along (110) direction for Rutile phase. The optical properties of the films were studied by UV-VIS spectrum in the range of (360-1100)

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Publication Date
Wed Jun 24 2020
Journal Name
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Studies on the Photostability of Polystyrene Films with New Metals Complex of 1, 2, 4-triazole-3-thione Derivate
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The new complexes including Cu(II), Co(II), Ni(II), Pt(IV), and Pd(II) metals with 4,4'-(((1E,1'E)-1,4-phenylenebis(methaneylylidene))bis(azaneylylidene))bis(5-(4-chlorophenyl)-4H-1,2,4-triazole-3-thione) have been synthesized of utilizing us polystyrene (PS) photostability. The supplement (0,5 w / v%) was for the production of polystyrene ( PS) in the form of tetrahydrofuran (THF). Polystyrene films were exposing irradiation (250 – 380 nm) absorption light intensity of 6.02 x 10-9 ein dm-3 s-1 at room temperature, through the changes that occur to each of viscosity average molecular weight (Mv), main chain scission (S), degree of polymerization (DPn), weight loss %, hydroxyl index (lOH), carbonyl index (ICo) determined the photo stabiliz

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Scopus
Publication Date
Tue Oct 01 2013
Journal Name
Journal Of Economics And Administrative Sciences
Analysis of the causal relationship between the gross fixed capital formation and gross domestic product for the agricultural sector for the period 1980 -2010
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Despite Iraq's possession of the energies material, human and agricultural resources and great economic but that contribution of the agricultural sector in the total gross fixed capital formation and gross domestic product in the Iraqi economy remained low and declining continuously since the nineties of the last century, as well as the inability of agricultural production to meet the country's needs of food . The food gap increased strategic food crops until it reached 1049 thousand tons in 2010. On this basis, there is a need to study and analysis the behavior of the function of  gross fixed capital format

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Crossref
Publication Date
Sat Dec 01 2018
Journal Name
Journal Of Economics And Administrative Sciences
The Physical Evidence Of The Product And Its Impact In Attracting The Customer AField research for a sample of private medical clinics in Maysan
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Abstract

     The current research problem includes a variety of research motivations to serve the private health sector, which is witnessing a great competition from internal and external environments. In this regard, private medical clinics are increasingly seeking to attract and retain customers through the quality of their service offerings represented by health services. Innovative and effective marketing methods to improve performance and stay in competition, by relying on the physical evidence of the product as a component of the marketing mix of services and its role in particular in packaging and supporting the health service with concrete evidence that affects the customer an

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Publication Date
Tue Dec 05 2023
Journal Name
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Ecofriendly Control for Stored-Product Pest, Oryzaephilus surinamensis (Order: Coleoptera, Family: Silvanidae)
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Dates are considered one of the most important foods consumed in Arab countries. Dates are commonly infested with the sawtoothed grain beetle, Oryzaephilus surinamensis. Consequently, the date yield, quantity, and quality (economic value and seed viability) are negatively affected. This study was designed to investigate the effectiveness of air evacuation as eco-friendly and safe control method against adult O. surinamensis. Insects were obtained from the infested date purchased from a private store in sakaka city, Aljouf region, Saudi Arabia. Air evacuation (using a vacuum pump) and food deprivation were applied to O. surinamensis, and insect mortality was observed daily in comparison with the control group (a

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Publication Date
Tue Sep 15 2020
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Identity Attributes and Strategies in Industrial Product Design: وليد محمد مهدي عيسى
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The research discussed the role of interrelationships between the product attributes and the individual identity of the brand and the user, starting from reviewing the identity concepts in the general design propositions and the identity from the industrial design perspective, and highlighting the role of the attributes in identifying the individual identity of the product, which would enable the user to adopt them to be representative of his identity, starting from identifying the importance of the identity being characterized by three major elements: innovating products in the user's viewpoint, viewing the user's environment, the methodology of the design language, and identifying the identity attributes in the industrial product start

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Publication Date
Wed Mar 01 2023
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Existence of Fixed Points for Expansive Mappings in Complete Strong Altering JS-metric space
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The paper aims at initiating and exploring the concept of extended metric known as the Strong Altering JS-metric, a stronger version of the Altering JS-metric. The interrelation of Strong Altering JS-metric with the b-metric and dislocated metric has been analyzed and some examples have been provided. Certain theorems on fixed points for expansive self-mappings in the setting of complete Strong Altering JS-metric space have also been discussed.

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Publication Date
Tue Nov 06 2018
Journal Name
Iraqi National Journal Of Nursing Specialties
Factors Affecting Birth Space Interval of Women Who Are Attending Primary Health Care Centers
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Objective: The aim of this study is to determine the factors affecting birth space interval in a sample of women.
Methodology: A cross-sectional study conducted in primary health centers in Al-Tahade and Al- Shak Omar in
Baghdad city. Data were collected by direct interview using questionnaire especially prepared for the study.
Sample size was (415) women in age group (20-40) years who were chosen randomly.
Results: Analysis of data shows highest rate of women (31.8%) had a birth space interval of (8-12) months
followed by (26.7%) had a birth space interval of (19-24) months, (20.2%) had a birth space interval of (>24)
months and (16.1%) had a birth space interval of (13-18) months respectively, while lower rate of w

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Publication Date
Mon Nov 01 2010
Journal Name
Iraqi Journal Of Physics
Determination of Skip Entry Trajectories for Space Vehicles at Circular and Super Circular Speeds
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The study of entry and reentry dynamics for space vehicles is very important, particularly for manned vehicles and vehicles which is carry important devices and which can be used again. There are three types for entry dynamic, ballistics entry, glide entry and skip entry. The skip entry is used in this work for describing entry dynamics and determining trajectory. The inertia coordinate system is used to derive equations of motion and determines initial condition for skip entry. The velocity and drag force for entry vehicle, where generate it during entry into earth’s atmosphere are calculated in this work. Also the deceleration during descending and determining entry angles, velocities ratio and altitude ratio have been studied. The c

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