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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
Mon Dec 30 2019
Journal Name
Iraqi Journal Of Chemical And Petroleum Engineering
Experimental Study of Iraqi Light Naphtha Isomerization over Ni-Pt/H-Mordenite
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Hydroisomerization of Iraqi light naphtha was studied on prepared Ni-Pt/H-mordenite catalyst at a temperature range of 220-300°C, hydrogen to hydrocarbon molar ratio of 3.7, liquid hourly space velocity (LHSV) 1 hr-1 and at atmospheric pressure.

The result shows that the hydrisomerization of light naphtha increases with the increase in reaction temperature at constant LHSV. However, above 270 0C the isomers formation decreases and the reaction is shifted towards the hydrocracking reaction, a higher octane number of naphtha was formed at 270 °C.

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Publication Date
Fri Apr 01 2022
Journal Name
Baghdad Science Journal
Positive Definiteness of Symmetric Rank 1 (H-Version) Update for Unconstrained Optimization
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Several attempts have been made to modify the quasi-Newton condition in order to obtain rapid convergence with complete properties (symmetric and positive definite) of the inverse of  Hessian matrix (second derivative of the objective function). There are many unconstrained optimization methods that do not generate positive definiteness of the inverse of Hessian matrix. One of those methods is the symmetric rank 1( H-version) update (SR1 update), where this update satisfies the quasi-Newton condition and the symmetric property of inverse of Hessian matrix, but does not preserve the positive definite property of the inverse of Hessian matrix where the initial inverse of Hessian matrix is positive definiteness. The positive definite prope

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Publication Date
Sun Jun 01 2008
Journal Name
Baghdad Science Journal
Studying of the complexes product of the nerve agent Soman with the Butyrylcholinesterase and Acetylcholinesterase Enzymes
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Cholinesterases are among the most efficient enzymes known. They are divided into two groups: acetylcholinesterase (AChE) involved in the hydrolysis of the neurotransimitter acetylcholine, and butyrylcholinesterase (BChE) of unknown function. Several crystal structures of the former have shown that the active site is located at the bottom of a deep and narrow gorge. Human BChE has attracted attention because it can hydrolyze toxic esters and nerve agents. Here we analyze the complexes of cholinesterase with soman by describing the 3D geometry of the complex, the active site, the changes happened through the inhibition and provide a description for the mechanism of inhibition. Soman undergoes degradation in the active site of the AChE and B

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Publication Date
Mon Mar 25 2019
Journal Name
Al-academy
The Effectiveness of Implication in New Formulations of the Contemporary Industrial Product: زياد حاتم حربي
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  The current research aims at transforming the concept of implication from the rhetoric into the industrial design in order to have a new term (the design implication) in which the industrial designer takes all or part of another's design to imply his design in it and acknowledge that, and if he did not do so, it would be (design theft) parallel to the literary plagiarism.
In order to show the potentials of the industrial design in the production of new formulations of the industrial products forms, as the design is the carrier of language that addresses the recipients, it is possible to use the implication as a the tool of literature in the design and as a design strategy as it is one of the concepts that takes its course in e

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Publication Date
Fri Jun 30 2023
Journal Name
International Journal Of Intelligent Engineering And Systems
DeepFake Detection Improvement for Images Based on a Proposed Method for Local Binary Pattern of the Multiple-Channel Color Space
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DeepFake is a concern for celebrities and everyone because it is simple to create. DeepFake images, especially high-quality ones, are difficult to detect using people, local descriptors, and current approaches. On the other hand, video manipulation detection is more accessible than an image, which many state-of-the-art systems offer. Moreover, the detection of video manipulation depends entirely on its detection through images. Many worked on DeepFake detection in images, but they had complex mathematical calculations in preprocessing steps, and many limitations, including that the face must be in front, the eyes have to be open, and the mouth should be open with the appearance of teeth, etc. Also, the accuracy of their counterfeit detectio

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Publication Date
Sun Jun 11 2017
Journal Name
Al-academy
Directorial Vision Between The Closed And Open In The Iraqi Theater Space
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This research deals with the concept of space in the theatrical performance and how the director works between two different spaces, the closed space and the open space. The question was how to use space according to the director's vision in the presentation. The problem of the research was whether the director of the Iraqi filmmaker could see the variable in the architectural space Or the place or space within the exhibition between open and closed, through the formation of the vision of the external components of intellectual and aesthetic and aesthetic, and impact on the relationship between the actor and the recipient to produce a new aesthetic space, and then the purpose of research and importance and limits and terminology The seco

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Publication Date
Sun May 26 2019
Journal Name
Iraqi Journal Of Science
Bayesian Estimation for Two Parameters of Gamma Distribution under Generalized Weighted Loss Function
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This paper deals with, Bayesian estimation of the parameters of Gamma distribution under Generalized Weighted loss function, based on Gamma and Exponential priors for the shape and scale parameters, respectively. Moment, Maximum likelihood estimators and Lindley’s approximation have been used effectively in Bayesian estimation. Based on Monte Carlo simulation method, those estimators are compared in terms of the mean squared errors (MSE’s).

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Publication Date
Wed Mar 15 2023
Journal Name
Al-academy
Kinetic diversity and its effectiveness in the formal variables of industrial product design
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The formal diversity in designs is achieved by creating shapes and lines with a distinct movement pattern, which are preceded by mental processes. The greatest source of diversity in design in general and industrial design in particular is the creation of multiple directions for the completion of designs and the diversification of intellectual proposals for the design idea. The human activity that takes place around us in various fields of life takes place due to the diversity of movement in the form of the design product and its effectiveness through the dynamic diversity in the form, which differs in the methods of designing and showing it. He invents material value as a distinct artistic product that he owns A specific form or system

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Publication Date
Fri Mar 04 2022
Journal Name
Environmental Science And Pollution Research
Geographically weighted regression model for physical, social, and economic factors affecting the COVID-19 pandemic spreading
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Abstract<p>This study aims to analyze the spatial distribution of the epidemic spread and the role of the physical, social, and economic characteristics in this spreading. A geographically weighted regression (GWR) model was built within a GIS environment using infection data monitored by the Iraqi Ministry of Health records for 10 months from March to December 2020. The factors adopted in this model are the size of urban interaction areas and human gatherings, movement level and accessibility, and the volume of public services and facilities that attract people. The results show that it would be possible to deal with each administrative unit in proportion to its circumstances in light of the factors that appe</p> ... Show More
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Publication Date
Mon Dec 20 2021
Journal Name
Bulletin Of The Iraq Natural History Museum (p-issn: 1017-8678 , E-issn: 2311-9799)
IMPACT OF THARTHAR ARM WATER ON COMPOSITION AND DIVERSITY OF COPEPODA IN TIGRIS RIVER, NORTH OF BAGHDAD CITY, IRAQ
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This study is considered to be the first on this sector of Tigris River after 2003, to evaluate the effect of Tharthar Arm on the composition and diversity of Copepoda in Tigris River. Six sampling sites were selected; two on the Tharthar Arm and four sites along the Tigris River, one before the confluence as a control site and the others downstream the confluence; thirty-five copepod taxa were recorded, 34 taxa in the Tigris River and 25 taxa in the Tharthar Arm.
The highest density of Copepoda was in site 2 at Tharthar Arm was 265584.2 Ind./m3 lead to an increasing in Copepoda density in Tigris River from 63878.2 Ind./m3 in site 1 before the confluence to 127198.3 Ind./m3 in site 4 immediately downstream the confluence. Also, the me

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