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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
Mon Aug 31 2020
Journal Name
Bmc Oral Health
The success of using 2% lidocaine in pain removal during extraction of mandibular premolars: a prospective clinical study
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Abstract<sec><title>Background

The purpose of this study was to evaluate the anesthetic effectiveness of a buccal infiltration technique combined with local massage (using 2% lidocaine) in the extraction of mandibular premolars to be utilized as an alternative to the conventional inferior alveolar nerve block.

Methods

Patients eligible included any subject with a clinical indication for tooth extraction of the mandibular 1st or 2nd premolars. All patients were anesthetized buccally by local infiltration technique followed by an external pressure applied for 1 min directly over the injection area. In each case, another local

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Publication Date
Sun Mar 18 2018
Journal Name
International Journal Of Pharmaceutical Quality Assurance
The Role of Soluble L-Selectin with Polymorphism in Iraqi Arabs Patients with Diabetes Mellitus Type 2
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Diabetes mellitus type 2 [DMT2] is a disturbance of metabolism and complex diseases influenced by environmental, genetic agents, and linked with inflammation, happens when the pancreas either does not use the insulin as it should or the body does not make enough insulin, lead to insulin resistance [IR] alongside with gradual loss of ß-cell secretory ability. The aim of this study was to investigate the role of soluble L-selectin (sL-selectin) in diabetes mellitus type 2 patients in Iraqi Arabs patient. Study includes seventy six Iraqi Arabs patients (male and female) having newly diagnosed type 2 diabetes mellitus (T2DM), with Fifty three Iraqi Arabs healthy subjects matched in age, sex and ethnic group. Patients and healthy subjec

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Publication Date
Fri Apr 01 2022
Journal Name
Baghdad Science Journal
The Cut-off Values of Triglycerides - Glucose Index for Metabolic Syndrome Associated with Type 2 Diabetes Mellitus
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       The co-occurrence of metabolic syndrome with type 2 diabetes mellitus (T2DM) will potentiate the morbidity and mortality that may be associated with each case. Fasting triglycerides-glucose index (TyG index) has been recommended as a useful marker to predict metabolic syndrome. Our study aimed to introduce gender-specific cut-off values of triglycerides- glucose index   for diagnosing metabolic syndrome associated with type 2 diabetes mellitus. The data were collected from Baghdad hospitals between May - December 2019. The number of eligible participants was 424. National cholesterol education program, Adult Treatment Panel III criteria were used to define metabolic syndrome. Measurement of fasting blood glucose, lipid pro

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Publication Date
Sat Sep 28 2019
Journal Name
Asian Journal Of Chemistry
Preparation, Spectroscopic Characterization and Theoretical Studies of Transition Metal Complexes with 1-[(2-(1H-indol-3-yl)ethylimino)methyl]naphthalene-2-ol Ligand
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A new Schiff base [1-((2-(1H-indol-3-yl)ethylimino)methyl)naphthalene-2-ol] (HL) has been synthesized by condensing (2-hydroxy-1-naphthaldehyde) with (2-(1H-indol-3-yl)ethylamine). In turn, its transition metal complexes were prepared having the general formula; [Pt(IV)Cl2(L)2], [Re(V)Cl2(L)2]Cl and [Pd(L)2], 2K[M(II)Cl2(L)2] where M(II) = Co, Ni, Cu] are reported. Ligand as well as metal complexes are characterized by spectroscopic techniques such as FT-IR, UV-visible, 13C & 1H NMR, mass, elemental analysis. The results suggested that the ligand behaves like a bidentate ligand for all the synthesized complexes. On the other hand, theoretical studies of the ligand as well its metal complexes were conducted at gas phase using Hyp

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Publication Date
Tue Jun 14 2011
Journal Name
Journal Of Education
Synthesis and Characterization Complexes of 2- Thiotolylurea with Matel Salts.
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Complexes of some metal ions with 2-thiotolylurea were prepared in ethanolic medium using (1:1) (Metal : Ligand) ratio yielded series of neutral complexes as the general formula [M(L)Cl2]. The prepared complexes were identified by atomic absorption FT.IR, UV-Visble spectra, molar conductivity and magnetic properties. From the above data the tetrahedral structure was suggested for all complexes.

Publication Date
Sun Apr 30 2023
Journal Name
Al-kindy College Medical Journal
SARS-CoV-2 and other Coronaviruses: A matter of variations
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Since the appearance of COVID-19 disease as an epidemic and pandemic disease, many studies are performed to uncover the genetic nature of the newly discovered coronavirus with unique clinical features. The last three human coronavirus outbreaks, SARS-CoV, MERS-CoV and SARS-CoV-2 are caused by Beta-Coronaviruses. Horizontal genetic materials transfer was proven from one coronavirus to the other coronavirus of non-human origin like infectious bronchitis virus (IBV) of avian. Horizontal genetic materials transfer was also from non-corona viruses like astroviruses and equine rhinovirus (ERV-2) or from coronavirus-unrelated viruses, like influenza virus type C. However, SARS-CoV-2 is identical to SARS-CoV and MERS-CoV. Interestingly, Wuhan ci

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Publication Date
Sun Jun 06 2010
Journal Name
Baghdad Science Journal
Synthesis of Some Heterocyclic Compounds derived from 2-mercapto pyrimidine
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In this work 2-hydrazino pyrimidine (1) was prepared from 2-mercapto pyrimidine with hydrazine hydrate. Treatment of (1) with active methylene compounds gave 2-(3,5-dimethyl -1 H – Pyrazole-1-yl) pyrimidine , whereas the reaction of (1) with carboxylic anhydride namely maleic anhydride or 1,2,3,6-tetra hydro phthalic anhydride yielded 1-Pyrimidine-2-yl-1,2-dihydro pyridazine-3,6-dione (3) and 2 – Pyrimidin -2-yl -2,3,4 a ,5,8 a – hexahydro phthalazine 1,4 – dione (4) . Reaction of (1) with phenyl isothiocyanate and ethyl chloro acetate afforded 3-Phenyl-1,3-thiazolidine-2,4-dione-2( pyrimidine -2- yl hydrazone (6) Azomethine (7-10) were prepared through condensation of (1) with aromatic aldehydes or ketones, then comp

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Publication Date
Thu Mar 30 2017
Journal Name
Iraqi Journal Of Pharmaceutical Sciences ( P-issn 1683 - 3597 E-issn 2521 - 3512)
Preliminary Cytotoxic Study of Some Novel Furo-2-quinolone Compounds
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In this research, new series of Furo-2-quinolone [FQ] compounds have been synthesized. These novel [FQ] compounds were prepared from coumarin derivatives (Furocoumarins: psoralen and isopsoralen).Identifications of these FQ compounds were performed by using infrared spectrum (I.R), Ultraviolet spectrum (U.V) and Nuclear Magnetic Resonance spectrum (H1-NMR) besides some physical data. The cytotoxic screening involves ;using HEP-2 cell line which gave differential responses against tested compounds : 4,6 Dimethyl furo[2, 3-g] coumarin (C1), 1-(2`, 4`, Dimethoxy benzylideneimino)-2,6-dimethyl Furo [2, 3-g] quinoline-2-one (C3) and the angular psoralen of the same derivative

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Publication Date
Sun Mar 01 2009
Journal Name
Baghdad Science Journal
Synthesis of Some New 1,2,4-Triazoles Derived from 2-Mercaptobenzimidazole
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New 1,2,4-triazole derivatives of 2-mercaptobenzimidazole (MB) are reported. Ethyl (benzimidazole-2-yl thio) acetate (1) has been prepared by condensing 2-mercaptobenzimidazole with ethylchloroacetate. The ester (1) on reacting with hydrazine hydrate gave the corresponding acetohydrazide(2)which was reacted separately with phenylisocyanate and phenylisothiocyanate, followed by ring closure in an alkaline medium giving 3-[(benzimidazole-2-yl thio) methyl]-4-phenyl-1,2,4-triazole-5-ol and 3-[(benzimidazole-2-yl thio) methyl]-4-phenyl-1,2,4-triazole-5-thiol respectively (6,7). Reaction of acetohydrazide (2) with CS2 and ethanol/KOH, gave dithiocarbazate salt (8). Cyclization of (8) with hydrazine hydrate gave 3-[(benzimi

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Publication Date
Wed Mar 10 2021
Journal Name
Baghdad Science Journal
Hard-soft interacation of 2-mercaptobenzonathol with some metal ions
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Was appointed acid steady disintegration of organic EkandThe results proved that organic Allicand acting and Konnh solid baseBy Tgrav Pearson has possible account Maamat hardness and softness of organic Ekand

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