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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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Mon Aug 01 2022
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Al-, Ga-, and In-decorated BP nanotubes as chemical sensors for 2-chloroethanol
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B3LYP density functional is utilized for probing the effect of decorating Al, Ga, and In on the sensing performance of a boron phosphide nanotube (BPNT) in detecting the 2-chloroethanol (CHE) molecule. We predict that the interaction of pure BPNT with CHE is physisorption, and the sensing response (SR) of BPNT is approximately 6.3. The adsorption energy of CHE is about − 26.3 to − 91.1, − 96.6, and − 100.3 kJ/mol, when the Al, Ga, and In metals are decorated on the BPNT surface, respectively. This indicates that the decorated metals significantly strength the interaction. Also, the corresponding SR meaningfully rises to 19.4, 41.0, and 93.4, indicating that by increasing the atomic number of metals, the sensitivity i

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Mon Nov 06 2017
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International Conference On Technologies And Materials For Renewable Energy, Environment And Sustainability, Tmrees17, 21-24 April 2017, Beirut Lebanon
HgBa2 Can-1CunO2n+2+δ Superconducting thin films Prepared by Pulsed Laser Deposition
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In the present work, HgBa2Can-1CunO2n+2+δ superconducting thin films with (100) nm thickness were (n=1, 2 and 3) prepared by Pulsed Laser Deposition technique on glass substrate at R.T (300) K, have been synthesize. The effect of Cu content on the structural, surface morphology, optical and electrical properties of HgBa2Can-1CunO2n+2+δ films were investigated and analyzed. The results of XRD analysis show that all samples are polycrystalline structure with orthorhombic phase, the change of Cu concentration in samples produce changes in the mass density, lattice parameter and the ratio (c/a). AFM techniques were used to examine the surface morphology of HgBa2Can-1CunO2n+2+δ superconducting films, the study showed the values of surface rou

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Sat Dec 01 2018
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" أنعكاس تبني المعيار المحاسبي الدولي رقم ( 2 ) للقطاع العام على بيان التدفق النقدي "
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يعد بيان التدفق النقدي من البيانات المهمة الصادرة من الوحدات الحكومية غير الهادفة للربح، بعد تبنيها معايير IPSASs ، مما يوفر معلومات اوسع تلبي حاجات المستخدمين لأتخاذ القرارات المناسبة . أذ يتضمن بيان التدفق النقدي بموجب المعيار رقم ( 2 ) التدفقات النقدية حسب الأنشطة التشغيلية و الاستثمارية والتمويلية ، وهذا لا ينسجم مع مخرجات النظام المحاسبي الحكومي العراقي . وان هدف البحث هو  التعرف

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Publication Date
Sun Jan 19 2020
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
Effect flexibility of the Strategic human resources in improvement operational performance: "Survey study of views of a sample of managers, engineers and technicians in the Baghdad south 2/Station directorate of Electricity"
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The research attempts to diagnose the level of the effect of human resources flexibility (employees skills flexibility, employees behaviors flexibility, and human resource practice flexibility) in the south al-rusafa directorate of a power  station one of the formations and the Ministry of Electricity, and impact of a range of variables related to the performance operational, namely, (efficiency, effectiveness)recognizing the importance of the subjects studied,& because of the importance of expected results of the field under consideration,researcher selected a sample of size (121) engineers and technicians of workers in the directorate. Was my hypotheses the major search of a relationship and impact between human resources flex

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Wed Oct 01 2008
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Topical therapy of acne vulgaris using 2% tea lotion in comparison with 5% zinc sulphate solution.
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Thu Feb 01 2018
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Publication Date
Thu Oct 01 2020
Journal Name
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Spectral and Electrical Characteristics of Nanostructured NiO/TiO 2 Heterojunction Fabricated by DC Reactive Magnetron Sputtering
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In this work, p-n junctions were fabricated from highly-pure nanostructured NiO and TiO2 thin films deposited on glass substrates by dc reactive magnetron sputtering technique. The structural characterization showed that the prepared multilayer NiO/TiO2 thin film structures were highly pure as no traces for other compounds than NiO and TiO2 were observed. It was found that the absorption of NiO-on-TiO2 structure is higher than that of the TiO2-on-NiO. Also, the NiO/TiO2 heterojunctions exhibit typical electrical characteristics, higher ideality factor and better spectral responsivity when compared to those fabricated from the same materials by the same technique and with larger particle size and lower structural purity.

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Publication Date
Sun Sep 01 2013
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Spectrophotometric Determination of Bismuth(III) with 4-(2-pyridylazo) Resorcinol-Application to Waters and Veterinary Preparation
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This paper describes the development of a simple spectrophotometric determination of bismuth III with 4-(2-pyridylazo) resorcinol (PAR) in aqueous solution in the presence of cetypyridinium chloride surfactant at pH 5 which exhibits maximum absorption at 532 nm. Beer's law is obeyed over the range 5-200 µg/25 mL. i.e. 0.2-8 ppm with a molar absorptivity of 3×104 l.mol-1.cm-1 and Sandell's sensitivity index of 0.0069 µg.cm-2. The method has been applied successfully in the determination of Bi (III) in waters and veterinary preparation.

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Publication Date
Sun Mar 02 2008
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Comparative sensitivity of two freshwater snail Melanopsis nodosa and Bulinus truncatus to 2, 4-D pesticide
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The molluscicidal effects of herbicide 2, 4-D were studied against tow species of freshwater snail Bulinus truncatus and Melanopsis nodosa by short term experiments. Calculated values of lethal concentrations (LC50 and LC100) were maid to two spices for different period of time 24hr, 48hr, 72hr and 96hr. The study had showed that the herbicide 2, 4-D was toxic against the tow species. The toxicity of the herbicide was low or unknown in low concentrations in the first period of exposure 24and 48hr to two spices but it increase gradually with increase period of exposure. The spice of B.truncatus was more tolerant than the M.nodosa. All the individual of M nodosa was death while in B.truncatus the complete death was not appear until finish the

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