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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
Tue Feb 20 2024
Journal Name
Baghdad Science Journal
Some Results about Acts over Monoid and Bounded Linear Operators
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This study delves into the properties of the associated act V over the monoid S of sinshT. It examines the relationship between faithful, finitely generated, and separated acts, as well as their connections to one-to-one and onto operators. Additionally, the correlation between acts over a monoid and modules over a ring is explored. Specifically, it is established that  functions as an act over S if and only if  functions as module, where T represents a nilpotent operator. Furthermore, it is proved that when T is onto operator and  is finitely generated, is guaranteed to be finite-dimensional. Prove that for any bounded operator the following,  is acting over S if and only if  is a module where T is a nilpotent operator, is a

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Publication Date
Sat May 01 2021
Journal Name
Journal Of Physics: Conference Series
Three Weighted Residuals Methods for Solving the Nonlinear Thin Film Flow Problem
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Abstract<p>In this paper, the methods of weighted residuals: Collocation Method (CM), Least Squares Method (LSM) and Galerkin Method (GM) are used to solve the thin film flow (TFF) equation. The weighted residual methods were implemented to get an approximate solution to the TFF equation. The accuracy of the obtained results is checked by calculating the maximum error remainder functions (MER). Moreover, the outcomes were examined in comparison with the 4<sup>th</sup>-order Runge-Kutta method (RK4) and good agreements have been achieved. All the evaluations have been successfully implemented by using the computer system Mathematica®10.</p>
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Publication Date
Wed Mar 15 2023
Journal Name
Al-academy
Scenography and the effectiveness of meaning in the theatrical space
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The elements of theater formation that fall within the spatial experience of the scenography of the show, which the directors work in in the imaginary theater, are important and have an aesthetic, intellectual and cognitive dimension, working to highlight reality in an aesthetic image surrounding space and space. And its relationship to the distinct, multiple and variable spaces above the stage, to produce theatrical signals and endless meanings through the possibility of infinite reconfiguration of the theater's space and its public and private space through the distribution of a group of blocks within the scenic image.
I dealt with in the first chapter (the methodological framework), which includes the research problem identified

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Publication Date
Fri Feb 15 2019
Journal Name
Route Educational & Social Science Journal
The effect of the 4-H model on self-regulated learning and life skills for female chemistry students in the second intermediate year
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Sun Sep 01 2013
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Archives Des Sciences
Convex Approximation in Terms of Fractional Weighted Moduli of Smoothness
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This paper deals with founding an estimation of best approximation of unbounded functions which satisfied weighted Lipschitz condition with respect to the convex polynomials by means of weighted moduli of smoothness of fractional order  , ( , ) p f t . In addition we prove some properties of weighted moduli of smoothness of fractional order.

Publication Date
Mon Jan 28 2013
Journal Name
Spie Proceedings
Enhancement of security for free space optics based on reconfigurable chaotic technique
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Free Space Optical (FSO) technology offers highly directional, high bandwidth communication channels. This technology can provide fiber-like data rate over short distances. In order to improve security associated with data transmission in FSO networks, a secure communication method based on chaotic technique is presented. In this paper, we have turned our focus on a specific class of piece wise linear one-dimensional chaotic maps. Simulation results indicate that this approach has the advantage of possessing excellent correlation property. In this paper we examine the security vulnerabilities of single FSO links and propose a solution to this problem by implementing the chaotic signal generator “reconfigurable tent map”. As synchronizat

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Publication Date
Wed May 17 2023
Journal Name
Journal Of Engineering
Comparison of the Combining Methods Used In Space Diversity
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The basic concept of diversity; where two or more inputs at the receiver are used to get uncorrelated signals. The aim of this paper is an attempt to compare some possible combinations of diversity reception and MLSE detection techniques. Various diversity combining techniques can be distinguished: Equal Gain Combining (EGC), Maximal Ratio Combining (MRC), Selection Combining and Selection Switching Combining (SS).The simulation results shows that the MRC give better performance than the other types of combining (about 1 dB compare with EGC and 2.5~3 dB compare with selection and selection switching combining).

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Publication Date
Sun Sep 07 2014
Journal Name
Baghdad Science Journal
Composition of fish assemblage in the East Hammar marsh, southern Iraq
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The fish assemblage in the East Hammar marsh was studied during December 2009 to May 2010. The fish fauna of the marsh consisted of 17 native, 23 marine (49%) and seven alien species. The dominant species were Liza abu (14.6%), Carassius auratus (13.4%) and Thryssa mystax (11.2%). The resident species formed 44.7%, occasional species 36.1% and seasonal species 19.2% of the total number of fish species. Fish species diversity index ranged from 1.28 to 2.61, richness from 1.98 to 4.50 and evenness from 0.45 to 0.78. Salinity ranged from 1.45 to 7.74‰. The increase in the proportion of marine species (49%) in the fish assemblage due to marine waters progress from Arabian Gulf had an impact on the values of ecological indices and the

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Publication Date
Mon Nov 09 2015
Journal Name
Iraqi Journal Of Market Research And Consumer Protection
The effect of different thermal treatments and pH on the stability of a glycyrrhizin which Product from the licorice plant, Glycyrrhiza glabra L: The effect of different thermal treatments and pH on the stability of a glycyrrhizin which Product from the licorice plant, Glycyrrhiza glabra L
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The plant licorice is considered important plants as nutritionally and medically and economically, as a rich in phytochemical, vitamins and minerals, and being widely available, Research indicated the presence of many nutrients such as (proteins, Carbohydrates, vitamins and minerals) as well as presence of Glycyrrhizin which responsible of sweet taste, that allowing the possibility to use it as natural intensity sweetener with few calories in Sweetening of many food. This research is aimed to study the Stability of Glycyrrhizin toward the various manufacturing conditions such as (thermal treatment, pH of foods and microwaves), so three factorial experiments was implemented to find out the Stability as following: 100C° - 121C° - Microwa

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Publication Date
Sun Dec 10 2017
Journal Name
Al-academy
The ideological effect in the in Interior space structure
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Design system often generated relationship within the frame work of their concept of interior design a system or more can be created between design relationships within this concept in the structure of its internal space product. Through the division of all to it parts to reveal the hidden places and stages of composition and their relationship and interdependence between them. And then re- composition of all its parts, doth in the deign process at the initial stages or in the processes of treatments that are necessary after the completion of design and circulation. To be able to use other events close to the first events designed for them. In terms of idea logical in fluency and its social, economic, cultural and political dimension. As

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