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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
Mon Mar 01 2010
Journal Name
Iraqi J Pharm Sci,
Synthesis, Characterization and Antibacterial Activities of Ligand Type N2O4 Schiff base and its Novel Complexes with Co(II), Ni(II), Cu(II) and Zn(II) ions
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The reaction of 2-amino benzoic acid with 1,2-dichloroethane under reflux in methanol and KOH as a base to gave the precursor [H4L]. The precursor under reflux and drops of CH3COOH which reacted with (2mole) from salicycaldehyde in methanol to gave a new type N2O4 ligand [H2L], this ligand was reacted with (MCl2) Where [M= Co (II), Ni(II), Cu(II) and Zn(II)] in (1:1) ratio at reflux in methanol using KOH as a base, to give complexes of the general formula [M(L)]. All compounds have been characterized by spectroscopic methods [1H NMR ( just to the ligand), FTIR, uv-vis, atomic absorption], melting point, conductivity, chloride content, as well as magnetic susceptibility measurements. From the above data, the proposed molecular structu

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Publication Date
Wed Aug 19 2020
Journal Name
Revista De Chimie
Synthesis, Characterization and Biological Evaluation of Cr(III), Fe(III), Co(II), Ni(II), Zn(II) and Cd(II) Complexes Using an Azo Dye as Ligand
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Azo ligand 11-(4-methoxyphenyl azo)-6-oxo-5,6-dihydro-benzo[4,5] imidazo[1,2-c] quinazoline-9-carboixylic acid was derived from 4-methoxyaniline and 6-oxo-5,6-dihydro-benzo[4,5]imidazo[1,2-c]quinazoline-9-carboxylic acid. The presence of azo dye was identified by elemental analysis and spectroscopic methods (FT-IR and UV-Vis). The compounds formed have been identified by using atomic absorption in flame, FT.IR, UV-Vis spectrometry magnetic susceptibility and conductivity. In order to evaluate the antibacterial efficiency of ligand and its complexes used in this study three species of bacteria were also examined. Ligand and its complexes showed good bacterial efficiencies. From the obtained data, an octahedral geometry was proposed for all p

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Publication Date
Wed Oct 25 2017
Journal Name
Oriental Journal Of Chemistry
Synthesis and Antioxidant Ability of Some New 6-amino-7H- [1,2,4]triazolo[3,4-b][1,3,4]thiadiazin-3-yl) Derivatives Bearing 2,6-Dimethoxy-4-(methoxymethyl)Phenol Moiety
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Publication Date
Sat Sep 23 2017
Journal Name
Oriental Journal Of Chemistry
Synthesis and Antioxidant Ability of some new 6-amino-7H- [1,2,4]triazolo[3,4-b][1,3,4]thiadiazin-3-yl) derivatives bearing 2,6-dimethoxy-4-(methoxymethyl)phenol moiety
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Compound 4-(((6-amino-7H-[1, 2, 4] triazolo [3, 4-b][1, 3, 4] thiadiazin-3-yl) methoxy) methyl)-2, 6-dimethoxyphenol (6) was synthesized by multi steps. The corresponding acetonitrile thioalkyl (7) was cyclized by refluxing with acetic acid to afford 4-(((6-amino-7H-[1, 2, 4] triazolo [3, 4-b][1, 3, 4] thiadiazin-3-yl) methoxy) methyl)-2, 6-dimethoxyphenol (8). Two new series of 4-(((6-(3-(4-aryl) thioureido)-7H-[1, 2, 4] triazolo [3, 4-b][1, 3, 4] thiadiazin-3-yl) methoxy) methyl)-2, 6-dimethoxyphenol (9a-c) and of 4-(((6-(substitutedbenzamido) 7H-[1, 2, 4] triazolo [3, 4-b][1, 3, 4] thiadiazin-3-yl) methoxy) methyl)-2, 6-dimethoxyphenol (10a-c) were synthesized as new derivatives for fused 1, 2, 4-trizaole-thiadiazine (8). The antioxidant

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Publication Date
Mon Jan 01 2024
Journal Name
Journal Of The College Of Languages (jcl)
فارسی Practical application of Jean René Ladmiral's model in translation from Arabic to Persian: کاربست عملی الگوی ژان رنه لادمیرال در ترجمه از عربی به فارسی
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Translation is a dynamic and living process that cannot be considered equal to the original text and requires the appropriate structure, language, thought and culture of the target language, and the translator's intellectual, linguistic and cultural influences inadvertently penetrate into the translated text. It causes heterogeneity of the destination text with the source text.

Admiral's theory is trying to help by providing components and suggested approaches to resolve these inconsistencies. In the meantime, in addition to the mission of putting words together, the translator must sometimes sit in the position of the reader and judge and evaluate the translated text in order to understand its shortcomings and try to correct it a

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Publication Date
Tue Jul 01 2014
Journal Name
Bulletin Of The Iraq Natural History Museum (p-issn: 1017-8678 , E-issn: 2311-9799)
A DESCRIPTION STUDY OF TWO LOCAL FISH HIMRI CARASOBARBUS LUTEUS (Heckel, 1843)(CYPRINIFORMES: CYPRINIDAE) AND HISHNI LIZA ABU (Heckel, 1843) (MUGILOIDEI : MUGILIDAE) BY BONES STAINING METHOD
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    Two local fish Himri Carasobarbus luteus (Heckel, 1843)  and Hishni Liza abu (Heckel, 1843) were stained with Alizarin Red and featured some anatomical qualities which cleared the difference of the muscular and skeletal fabric for each fish. Since clear Histologic differences appeared in these two species, it was intended from this study the possibility of adopting a diagnosis between local fish species by staining bones and tissues.

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Publication Date
Fri Jul 28 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Structural and Spectroscopic Study of Novel Tetradentate Macrocyclic Ligand Type N4 and It’s Complexes with CrIII, MnII, FeII, CoII, NiII ,CuII, PdII and CdII
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   Ethylenediamine was reacted in the first step with 2,5 – hexandion to produce the precursor [A] , then [A] was reacted with diethylmalonate to give the new tetradentate macrocyclic Ligand [H2L].This Ligand was reacted with some metal ions in ethanol to give a series of new metal complexes of the general formula [M(HnL)X]m  ( where : M= CrIII  ,      n = 0 ,  X= Cl2 , m= -1 ;  M = MnII , FeII , NiII , CuII ,      n = 1 , X= Cl2 , m = -1 ;  M = CoII , n = 0 ,       X = Cl , m = -1 ; M = PdII , n = 0 , X=0 , m = 0  ; M = CdII , n = 2 , X = 0 ,     m = +2 .  All compounds were characterize

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Publication Date
Wed Feb 01 2023
Journal Name
Health Science Reports
Diagnostic potential of salivary interleukin‐17, RANKL, and OPG to differentiate between periodontal health and disease and discriminate stable and unstable periodontitis: A case‐control study
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Abstract<sec><title>Background and Aims

Limitations of the conventional diagnostic techniques urged researchers to seek novel methods to predict, diagnose, and monitor periodontal disease. Use of the biomarkers available in oral fluids could be a revolutionary surrogate for the manual probing/diagnostic radiograph. Several salivary biomarkers have the potential to accurately discriminate periodontal health and disease. This study aimed to determine the diagnostic sensitivity and specificity of salivary interleukin (IL)‐17, receptor activator of nuclear factor‐κB ligand (RANKL), osteoprotegerin (OPG), RANKL/OPG for differentiating (1) periodontal health from disease and (2) stable a

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Publication Date
Mon Dec 25 2017
Journal Name
Biomedical And Pharmacology Journal
Evaluation of Crestal Bone Loss and Alkaline Phosphatase Level in Saliva According To Different Flap Designs in Single-Tooth Dental Implant Surgery (A Clinical Comparative Study)
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Publication Date
Tue Jun 01 2021
Journal Name
Journal Of The College Of Languages (jcl)
Hidden messages in (Pour un oui ou pour un non) of Nathalie Sarraute: Les messages cachés dans "Pour un oui ou pour un non" de Nathalie Sarraute
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       The implicit is the narrative technique used to give indirect hidden messages. To read between the lines means to understand the implicit meaning that is not directly indicated. This technique is expressed in two forms: the hypothesis and the implications of linguistic and non-linguistic rules. Nathalie Sarraute’s "Pour un oui ou pour un non" states this narrative method through her character’s verbal and non-verbal dialogue. The present paper discusses the implicit method and shows the reason behind which  the author uses it in her play "Pour un oui ou pour un non".

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