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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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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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Fri May 01 2015
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Use of non-Conventional Material to Remove Cu+2 ions from Aqueous Solutions using Chemical Coagulation
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Coagulation - flocculation are basic chemical engineering method in the treatment of metal-bearing industrial wastewater because it removes colloidal particles, some soluble compounds and very fine solid suspensions initially present in the wastewater by destabilization and formation of flocs. This research was conducted to study the feasibility of using natural coagulant such as okra and mallow and chemical coagulant such as alum for removing Cu and increase the removal efficiency and reduce the turbidity of treated water. Fourier transform Infrared (FTIR) was carried out for okra and mallow before and after coagulant to determine their type of functional groups. Carbonyl and hydroxyl functional groups on the surface of

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Sun Oct 21 2018
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Background: Several studies suggested that skeletal system is adversely affected by diabetes and is associated with increased risk of osteoporosis and fragility fractures  

Objectives: The study was a case-control study that designed to assess the level of bone turnover markers (BTMs) among patients with type 2 diabetes mellitus (T2DM) and to investigate the effect of body weight and diabetic control on the level of bone turnover

Type of the study: Cross- sectional study.

Methods: The present study included 100 postmenopausal women with type 2 diabetes mellitus. Sixty-six non-diabetic postmenopausal women were enrolled as a control. Fasting b

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Background: Chronic hyperglycemia causes diabetic nephropathy(DN), which is a typical microvascular complication of type 2 diabetes mellitus. The pathogenesis of DN is not fully understanding. The inflammation may possess a significant role in the progression of DN in diabetic patients. Method: The study accomplished at teaching laboratories of medical city, Baghdad, Iraq. It was included 50uncontrolled diabetic type 2 patients with nephropathy, age range (40-78) years and 42 controlled diabetics type 2 without nephropathy, age range (35 - 52) years as a control group. The participants divided in to two groups according to HbA1c measurement which is described as follows: < 7.5% of HbA1c describes controlled diabetes, and > 9% of HbA1c

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Synthesis, Characterization and Investigation Liquid Crystalline, Properties of 1, 2, 3-triazole Derivatives via Cycloaddition Reaction
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The new of compounds synthesized by sequence reactions starting from a reaction of 3-phenylenediamine or 4-phenylenediamine with chloroacetyl chloride to produce the compounds [I]a,b, then the compounds[I]a,b reacted with sodium azide to yield compounds[II]a,b that reacted 1,3-dipolarcycloaddition reaction with acrylic acid to give compounds [III]a,b these compounds reacted with methanol led to ester compounds[IV]a,b then reacted with hydrazine to give acid hydrazide [V]a,b . Finally compounds [V]a,b reacted with aromatic aldehydes to product shiff bases derivatives. The compounds characterized by mp. , IR, 1HNMR in addition to mass spectroscopy for some of them the liquid crystals properties were studied by using polarized optical microsco

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