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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
Thu Nov 01 2018
Journal Name
Journal Of Economics And Administrative Sciences
Use A State Space Model and Forecast House Prices in Baghdad.
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The purchase of a home and access to housing is one of the most important requirements for the life of the individual and the stability of living and the development of the prices of houses in general and in Baghdad in particular affected by several factors, including the basic area of the house, the age of the house, the neighborhood in which the housing is available and the basic services, Where the statistical model SSM model was used to model house prices over a period of time from 2000 to 2018 and forecast until 2025 The research is concerned with enhancing the importance of this model and describing it as a standard and important compared to the models used in the analysis of time series after obtaining the

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Publication Date
Fri Jun 01 2018
Journal Name
Arpn Journal Of Engineering And Applied
Product development from 3D scanner To CNC machine in reverse engineering
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The purpose of this article is to introduce reverse engineering procedure (REP). It can achieved by developing an industrial mechanical product that had no design schemes throughout the 3D-Scanners. The aim of getting a geometric CAD model from 3D scanner is to present physical model. Generally, this used in specific applications, like commercial plan and manufacturing tasks. Having a digital data as stereolithography (STL) format. Converting the point cloud be can developed as a work in programming by producing triangles between focuses, a procedure known as triangulation. Then it could be easy to manufacture parts unknown documentation and transferred the information to CNC-machines. In this work, modification was proposed and used in RE

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Publication Date
Sat Nov 02 2013
Journal Name
International Journal Of Computer Applications
Mixed Transforms Generated by Tensor Product and Applied in Data Processing
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Finding orthogonal matrices in different sizes is very complex and important because it can be used in different applications like image processing and communications (eg CDMA and OFDM). In this paper we introduce a new method to find orthogonal matrices by using tensor products between two or more orthogonal matrices of real and imaginary numbers with applying it in images and communication signals processing. The output matrices will be orthogonal matrices too and the processing by our new method is very easy compared to other classical methods those use basic proofs. The results are normal and acceptable in communication signals and images but it needs more research works.

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Publication Date
Thu Jan 01 2015
Journal Name
Journal Of Nanomaterials
Comparative Studies on Thermal Performance of Conic Cut Twist Tape Inserts with SiO<sub>2</sub>and TiO<sub>2</sub>Nanofluids
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This paper presents a comparison study on thermal performance conic cut twist tape inserts in laminar flow of nanofluids through a constant heat fluxed tube. Three tape configurations, namely, quadrant cut twisted tape (QCT), parabolic half cut twisted tape (PCT), and triangular cut twisted (VCT) of twist ratioy= 2.93 and cut depthde= 0.5 cm were used with 1% and 2% volume concentration of SiO2/water and TiO

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Publication Date
Tue Oct 01 2024
Journal Name
Journal Of Physics: Conference Series
An Effect of Al on the Properties of ZnIn<sub>2</sub>Se<sub>4</sub> Thin Film
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Abstract<p>Zinc-indium-selenide ZnIn<sub>2</sub>Se<sub>4</sub> (ZIS) ternary chalcopyrite thin film on glass with a 500 nm thickness was fabricated by using the thermal evaporation system with a pressure of approximately 2.5×10<sup>−5</sup> mbar and a deposition rate of 12 Å/s. The effect of aluminum (Al) doping with 0.02 and 0.04 ratios on the structural and optical properties of film was examined. The utilization of X-ray diffraction (XRD) was employed to showcase the influence of aluminum doping on structural properties. XRD shows that thin ZIS-pure, Al-doped films at RT are polycrystalline with tetragonal structure and preferred (112) orientation. Where the </p> ... Show More
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Publication Date
Wed Aug 30 2023
Journal Name
Al-kindy College Medical Journal
Investigating the Effect of Genetic Polymorphisms of Deiodinase Type 2 on Levothyroxine Dose Requirements in Patients with Hypothyroidism
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Background: Hypothyroidism is the most abundant thyroid disorder worldwide. For decades, levothyroxine was the main effective pharmacological treatment for hypothyroidism. A variety of factors can influence levothyroxine dose, such as genetic variations. Studying the impact of genetic polymorphisms on the administration of medications was risen remarkably. Different genetic variations were investigated that might affect levothyroxine dose requirements, especially the deiodinase enzymes.  Deiodinase type 2 genetic polymorphisms’ impact on levothyroxine dose was studied in different populations. Objective: To examine the association of the two single nucleotide polymorphism (SNP)s of deiodinase type 2 (rs225013 and rs225014) and le

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Publication Date
Thu Oct 01 2009
Journal Name
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Effect of isovalent substitution and Quenching on the Transition Temperature of (Bi1-xPbx)2(Sr1-yBay)2Ca2Cu3O10+δ
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A high Tc superconductor with a nominal composition
(Bi1-xPbx)2(Sr1-yBay)2Ca2Cu3O10+δ for (0 £ x £ 0.5) and (0 £ y £ 0.5) was prepared by
a solid state reaction method. The effect of the substitution of Pb for Bi and Ba for Sr and
quenching temperature on the superconductivity has been investigated to obtain the
optimum conditions for the formation and stabilization of the high Tc phase (2223).
The results showed that the optimum sintering temperature for the pure composition is
equal to 875°C and the sintering time is equal to 240h with heating and cooling rate of
60°C/h . Our results indicated that a small amount of (Ba = 0.1) could raise the transition
temperature (Tc), but enhancing Ba to 0.4 has raised

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Publication Date
Wed Aug 30 2023
Journal Name
Al-kindy College Medical Journal
Investigating the Effect of Genetic Polymorphisms of Deiodinase Type 2 on Levothyroxine Dose Requirements in Patients with Hypothyroidism
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Background: Hypothyroidism is the most abundant thyroid disorder worldwide. For decades, levothyroxine was the main effective pharmacological treatment for hypothyroidism. A variety of factors can influence levothyroxine dose, such as genetic variations. Studying the impact of genetic polymorphisms on the administration of medications was risen remarkably. Different genetic variations were investigated that might affect levothyroxine dose requirements, especially the deiodinase enzymes.  Deiodinase type 2 genetic polymorphisms’ impact on levothyroxine dose was studied in different populations.

Objective: To examine the association of the two single nucleotide polymorphism (SNP)s of deiodinase t

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Publication Date
Sun Mar 02 2008
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Calculations of Signal to Noise Ratio (SNR) for Free Space Optical Communication Systems
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In this paper, we calculate and measure the SNR theoretically and experimental for digital full duplex optical communication systems for different ranges in free space, the system consists of transmitter and receiver in each side. The semiconductor laser (pointer) was used as a carrier wave in free space with the specification is 5mW power and 650nm wavelength. The type of optical detector was used a PIN with area 1mm2 and responsively 0.4A/W for this wavelength. The results show a high quality optical communication system for different range from (300-1300)m with different bit rat (60-140)kbit/sec is achieved with best values of the signal to noise ratio (SNR).

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Publication Date
Thu May 18 2023
Journal Name
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Place Identity in Defining Urban Space of Border Rivers in Historical City Centres
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In the city, building space could transform to be as place, because architecture does not include only traditional values such as housing, human protection, stability, etc, but could carry other dimensions beyond the housing or building occupancy or develop urban design. Rivers had vision in motion as a way to show dynamic processes in its flowing slowly, which are simply measured in time and the life of citizens. The research consider the river path in traditional cities as Alley connecting the spaces of the city ... old Baghdad was characterized by this property and it is look like Venice in the past, while traditional European cities were able to preserve this property till now, and capable to take transformation of the city with deve

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