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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
Sun Feb 01 2026
Journal Name
Journal Of Baghdad College Of Dentistry
Early and delayed effect of 2% chlorhexidine on the shear bond strength of composite restorative material to dentin using a total etch adhesive
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Background: Lack of durability of the bond of the dental adhesive systems to tooth structure is one of the most important problems in tooth colored restorative work. This in vitro study was performed to evaluate the effect of 2% chlorhexidine gluconate(CHX) on dentin bond strength by using total etch adhesive system at twenty-four hours and three months of water storage. Material and methods:A flat dentin surface was prepared for forty sound human maxillary premolar teeth which were acid etched with 36% phosphoric acid gel after being divided randomly into four groups of ten teeth each according to storage time and CHX application, theCHX was applied for 60 seconds before adhesive application for groups I and III which were tested after twe

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Publication Date
Fri Feb 01 2019
Journal Name
Journal Of Physics: Conference Series
Manufacturing and studying the effect of partial substitution on the properties of the compound Bi<sub>2-x</sub> Ag<sub>x</sub>Sr<sub>1.9</sub>Ba<sub>0.1</sub>Ca<sub>2</sub>Cu<sub>3</sub>O<sub>10+δ</sub> superconductors.
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Publication Date
Sun Mar 04 2018
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Baghdad Science Journal
Synthesis and Characterization of a Molecularly Imprinted Polymer for Diclofenac Sodium Using (2-vinylpyridine and 2-hydroxyethyl metha acrylate) as the Complexing Monomer
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Four electrodes were synthesized based on molecularly imprinted polymers (MIPs). Two MIPs were prepared by using the diclofenac sodium (DFS) as the template, 2-hydroxy ethyl metha acrylate(2-HEMA) and 2-vinyl pyridine(2-VP) as monomers as well as divinyl benzene and benzoyl peroxide as cross linker and initiator respectively. The same composition used for prepared non-imprinted polymers (NIPs) but without the template (diclofenac sodium). To prepared the membranes electrodes used different plasticizers in PVC matrix such as: tris(2-ethyl hexyl) phosphate (TEHP), tri butyl phosphate (TBP), bis(2-ethyl hexyl) adipate (BEHA) and tritolyl phosphate (TTP). The characteristics studied the slop, detection limit, life time and linearity range of DF

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Publication Date
Wed Oct 17 2018
Journal Name
Journal Of Economics And Administrative Sciences
the role of marketing intelligence in promoting new product policies.a sample survey of workers in a number of mineral water plants in dohuk governorate
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Marketing Intelligence is one of the important methods of collecting information about competitors ' products and changes in customers ' tastes and needs that contribute to determining the policies to be followed in product development.

The problem of research, which seeks to be answered by the extent to which the companies in question have the appropriate and effective mechanisms to develop their products, and the nature of the relationship between the components of marketing intelligence and new product development policies. The importance of research is determined by the importance of obtaining important and necessary information to make the appropriate decision on the development of the new product an

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Publication Date
Mon Feb 13 2023
Journal Name
Journal: Aip Conference
Composition, Depiction, Antibacterial, Antioxidant, and Cytotoxicity activities studies of A New Nano-Sized Binuclear Metal (II) Schiff Base complexes
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Abstract In the current contribution, a novel binuclear nickel(II) and zinc(II) complexes were prepared from a hexadentate ligand prepared via condensation of 3,3'-Bipyridine-6,6'-dicarbaldehyde , 2-amino-5-chlorobenzaldehyde and 2-Aminophenol .The symmetric ligand (H2DTPE) and its metal complexes were illustrated utilizing various techniques of physicochemical containing magnetic moment, analytical analysis and spectroscopy of mass, IR, 13C and 1H NMR, TGA and UV-Vis. The particles of MO Nanoscale were created from the labeled complex applying the ways of pyrolysis and utilizing methods of XRD, FT-IR, and FE-SEM, that specified close compatibility with the typical pattern for nanoparticles of NiO, ZnO and appeared the reasonable size in

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Publication Date
Wed Jan 17 2018
Journal Name
Journal Of Applied Chemistry
Synthesis, Composition, Spectral, Geometryand AntibacterialApplicationsof MnII, NiII, CoII, CuII and HgIIcomplexes of N2O2-mixed donor Schiff Basewith 1,10-phenanthroline
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Publication Date
Thu Feb 29 2024
Journal Name
International Journal Of Design &amp; Nature And Ecodynamics
Artificial Neural Network Assessment of Groundwater Quality for Agricultural Use in Babylon City: An Evaluation of Salinity and Ionic Composition
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Publication Date
Sun Sep 05 2010
Journal Name
Baghdad Science Journal
Composition operator induced by ?(z) = sz + t for which |s|?1, |t|<1 and |s|+|t|?1
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We study in this paper the composition operator that is induced by ?(z) = sz + t. We give a characterization of the adjoint of composiotion operators generated by self-maps of the unit ball of form ?(z) = sz + t for which |s|?1, |t|<1 and |s|+|t|?1. In fact we prove that the adjoint is a product of toeplitz operators and composition operator. Also, we have studied the compactness of C? and give some other partial results.

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Publication Date
Wed Mar 10 2021
Journal Name
Baghdad Science Journal
synthesis and characterization of 2 hydroxy
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diasotiation compondnds sulphate upon with melting elemental aryl been used in his mouth for a while of studied

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Publication Date
Sat Jun 12 2021
Journal Name
Biochemical And Cellular Archives
EFFECT OF SINGLE ORAL DOSE OF FUMONISIN B1 ON IMMUNOHISTOCHEMICAL EXPRESSION OF TLR-2 AND 4 IN MICE
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Fumonisin B1 is toxic secondary metabolites compound produced by Fusarium spp. on maize and maize products causes health problems to human and animal. Therefore, this research is planned to study the effect of FB1 on the expression of TLR-2 & 4 in liver and kidney cells of mice. Four group of male mice were orally administrated with single dose of FB1 toxin as the following: 0 ppb, 800 ppb, 1200 ppb and 1600 ppb. After two weeks all animals were sacrificed, liver and kidney autopsies were taken and the level of TLR-2 & 4 detected in each four group by immunohistochemistry technique (IHC). According to the IHC examination of groups (1, 2, 3 and 4) strong expression of TLR2 in liver and kidney were (0%, 33.3%, 100%, 100%), respectively. This

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