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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 Dec 01 2011
Journal Name
Journal Of Economics And Administrative Sciences
Dynamic algorithm (DRBLTS) and potentially weighted (WBP) to estimate hippocampal regression parameters using a techniqueBootstrap (comparative study)
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Bootstrap is one of an important re-sampling technique which has given the attention of  researches recently. The presence of outliers in the original data set may cause serious problem to the classical bootstrap when the percentage of outliers are higher than the original one. Many methods are proposed to overcome this problem such  Dynamic Robust Bootstrap for LTS (DRBLTS) and Weighted Bootstrap with Probability (WBP). This paper try to show the accuracy of parameters estimation by comparison the results of both methods. The bias , MSE and RMSE are considered. The criterion of the accuracy is based on the RMSE value since the method that provide us RMSE value smaller than other is con

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Publication Date
Tue Apr 11 2023
Journal Name
Indonesian Journal Of Chemistry
Synthesis of Co (ll), Ni (ll), Cu (ll), Pd (ll), and Pt (lV) Complexes with 14, 15, 34, 35-Tetrahydro-11 H, 31 H-4, 8-diaza-1,3 (3,4)-ditriazola-2,6 (1,4)-dibenzenacyclooctaphane-4,7-dien-15, 35-dithione, and the Thermal Stability of Polyvinyl Chloride Modified Complexes
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In the current endeavor, a new Schiff base of 14,15,34,35-tetrahydro-11H,31H-4,8-diaza-1,3(3,4)-ditriazola-2,6(1,4)-dibenzenacyclooctaphane-4,7-dien-15,35-dithione was synthesized. The new symmetrical Schiff base (Q) was employed as a ligand to produce new complexes comprising Co(II), Ni(II), Cu(II), Pd(II), and Pt(II) metal-ions at a ratio of 2:1 (Metal:ligand). There have been new ligands and their complexes validated by (FTIR), (UV-visible), 1H-NMR, 13C-NMR, CHNS, and FAA spectroscopy, Thermogravimetric analysis (TG), Molar conductivity, and Magnetic susceptibility. The photostabilization technique to enhance the polymer was also used. The ligand Q and its complexes were mixed in 0.5% w/w of polyvinyl chloride in tetrahydrofuran

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Publication Date
Wed Jun 28 2017
Journal Name
Proceedings Of The 2017 Acm Conference On Innovation And Technology In Computer Science Education
Media Literacy as a By-Product of Collaborative Video Production by CS Students
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Understanding, promoting, and teaching media literacy is an important societal challenge. STEM educators are increasingly looking to incorporate 21st century skills such as media literacy into core subject education. In this paper we investigate how undergraduate Computer Science (CS) students can learn media literacy as a by-product of collaborative video tutorial production. The paper presents a study of 34 third-year CS undergraduates who, as part of their learning, were each asked to produce three video tutorials on Raspberry Pi programming, using a collaborative video production tool for mobile phones (Bootlegger). We provide results of both quantitative and qualitative analysis of the production process and resulting video tutorials,

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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
Sun Mar 07 2010
Journal Name
Baghdad Science Journal
Synthesis and Polymerization of Poly Acryl Imide and One of Their Derivatives Then Curing the Product with Alkyl Halide
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The present work involved four steps: First step include reaction of acrylamide ,N-?-Methylen-bis(acryl amide) and N-tert Butyl acryl amide with poly acryloyl chloride in the presence of triethyl amine (Et3N) as catalyst, the second step include homopolymerization of all products of the first step by using benzoyl peroxide(BPO) as initiator in (80-90)Co in the presence of Nitrogen gas(N2). In the third step the poly acrylimide which prepare in second step was convert into potassium salt by using alcoholic potassium hydroxide solution. Fourth step include Alkylation of the prepared polymeric salts in third step by react it with different alkyl halides(benzyl chloride, allylbromide , methyl iodide) by using DMF as solvent for(10-12) hours.

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Crossref
Publication Date
Wed Jan 01 2020
Journal Name
Periodicals Of Engineering And Natural Sciences
Comparing traditional estimators and the estimators of (PSO) algorithm for some growth models of gross domestic product in Iraq
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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
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 t

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Publication Date
Thu Oct 01 2009
Journal Name
Iraqi Journal Of Physics
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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