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MRbmuIoBVTCNdQwCLKT9
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
Sat May 01 2021
Journal Name
Journal Of Physics: Conference Series
The substitutions of Strontium by yttrium and their effects on Bi<sub>2</sub>Sr<sub>2</sub>-<sub>x</sub>Y<sub>x</sub>Ca<sub>2</sub>Cu<sub>3</sub>O<sub>10</sub>+<sub>δ</sub> superconducting compound
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Abstract<p>Superconducting compound Bi<sub>2</sub>Sr2-<sub>x</sub>Y<sub>x</sub>Ca<sub>2</sub>Cu<sub>3</sub>O<sub>10+δ</sub> were Synthesized by method of solid state reaction, at 1033 K for 160 hours temperature of the sintering at normal atmospheric pressure where substitutions Yttrium oxide with Strontium. When Y2O3 concentration (0.0, 0.1, 0.2, 0.3, 0.4 and 0.5). All specimens of Bi<sub>2</sub>Sr<sub>2</sub>Ca<sub>2</sub>Cu<sub>3</sub>O<sub>10+δ</sub> superconducting compounds were examined. The resistivity of electrical was checked by the four point probe technique, It was found th</p> ... Show More
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Publication Date
Mon Dec 29 1997
Journal Name
كلية العلوم للبنات
Synthesis And Studies Of Complexes Of Some Elements With 2-Mercaptohiazole (2-HMBT)
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Synthesis And Studies Of Complexes Of Some Elements With 2-Mercaptohiazole (2-HMBT)

Publication Date
Mon Apr 01 2024
Journal Name
Indonesian Journal Of Chemistry
Synthesis, Structure and Biological Activity Studies of New Metal Ion Complexes Based on 3-[(3-Hydroxynaphthalene-2-yl-ethylidene)-hydrazono]-1,3-dihydro-indol-2-one
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In the present study, a novel ligand (L) made of 2-hydroxynaphthaldehyde and 3-hydrazone-1,3-dihydro-indole-2-one(3-[(3-hydroxynaphthalen-2-yl-ethylidene)-hydrazono]-1,3-dihydro-indol-2-one). The ligand was characterized by FTIR, UV-vis, mass, 1H-NMR, 13C-NMR, and CHN elemental analysis. New complexes of this ligand were created by treating methanol and a drop of DMF solution of the produced ligand with the hydrated metal salts of Mn(II), Co(II), Ni(II), Cu(II), and Zn(II) in a molar ratio of 2:1 (L:M). As a result, complexes have been emerged and identified FTIR, UV-vis, C.H.N., chloride-containing, molar conductance, magnetic susceptibility, and atomic absorption. The characterization result for each complex indicated complexes wi

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Publication Date
Fri Feb 20 2026
Journal Name
Journal Of Baghdad College Of Dentistry
Effect of Periodontal Therapy on Serum and Salivary Interleukin-2 Levels in Chronic Periodontitis
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Background: Interleukine-2 is a multifunctional cytokine, considered a central regulator of host resistance against a variety of pathogens and has been recently demonstrated to exert an active role in the pathogenesis of periodontal diseases. The purpose of this study was to evaluate the effect of scaling and root planning on level of IL-2 in serum and saliva of patients with chronic generalized periodontitis, in relation to clinical parameters. Materials and Methods: A total of 50 subjects were enrolled, of which 25 had chronic generalized periodontitis and 25 periodontally healthy subjects as control. The clinical parameters included: gingival index, pocket probing depth, clinical attachment level and bleeding on probing. The level of

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Publication Date
Fri May 31 2024
Journal Name
Journal Of Interdisciplinary Mathematics
Fibrewise locally micro sliceable and fibrewise locally micro-section able micro-topological space
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The primary objective of this research be to develop a novel thought of fibrewise micro—topological spaces over B. We present the notions from fibrewise micro closed, fibrewise micro open, fibrewise locally micro sliceable, and fibrewise locally micro-section able micro topological spaces over B. Moreover, we define these concepts and back them up with proof and some micro topological characteristics connected to these ideas, including studies and fibrewise locally micro sliceable and fibrewise locally micro-section able micro topological spaces, making it ideal for applications where high-performance processing is needed. This paper will explore the features and benefits of fibrewise locally micro-sliceable and fibrewise locally

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Publication Date
Wed Dec 01 2021
Journal Name
Baghdad Science Journal
New Common Fixed Points for Total Asymptotically Nonexpansive Mapping in CAT(0) Space
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      Strong and ∆-convergence for a two-step iteration process utilizing asymptotically nonexpansive and total asymptotically nonexpansive noneslf mappings in the CAT(0) spaces have been studied. As well, several strong convergence theorems under semi-compact and condition (M) have been proved. Our results improve and extend numerous familiar results from the existing literature.

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Publication Date
Tue Nov 03 2015
Journal Name
Journal Of Natural Sciences Research
Implementation of remote sensing for vegetation studying using vegetation indices and automatic feature space plot
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Publication Date
Fri Dec 19 2014
Journal Name
Al-mustansiriyah
Synthesis, Spectroscopic and Antibacterial Studies of N (2-amino phenyl)-N-((pyridine-2-yl) methyl) Benzene-1, 2-Diamine Complexes
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Publication Date
Tue Sep 15 2020
Journal Name
Al-academy
Communication and Outreach and their Relation to Industrial Product Circulation: حنان غازي صالح
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  With the increase of the huge developments that the world witnesses day after day, the contemporary designer tried to reveal his abilities in development and coping with transitions in all types of design discourses such as the functional and technical discourses, and the numerous means of communications included in these discourses and their influence over the recipient, because they carry perceptible, tangible or implicit vocabulary that influences the recipient's relation with the circulation of the industrial product through the effectiveness of numerous means of communication contained in the design products represented by the functional, formal, aesthetic, and technical communication. In order to highlight the importance of

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Publication Date
Fri Jul 21 2023
Journal Name
Journal Of Engineering
ADJUSTING OFF – CENTERING PROCESS FOR A BLOW MOLDED PLASTIC PRODUCT BY USE OF WINQSB SOFTWARE
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In most manufacturing processes, and in spite of statistical control, several process capability indices refer to non conformance of the true mean (µc ) from the target mean ( µT ), and the variation is also high. In this paper, data have been analyzed and studied for a blow molded plastic product (Zahi Bottle) (ZB). WinQSB software was used to facilitate the statistical process control, and process capability analysis and some of capability indices. The relationship between different process capability indices and the true mean of the process were represented, and then with the standard deviation (σ ), of achievement of process capability value that can reduce the standard deviation value and improve production out of theoretical con

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