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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
Sat May 01 2021
Journal Name
Journal Of Physics: Conference Series
Metal Complexes of Multidentate N<sub>2</sub>S<sub>2</sub> Heterocyclic Schiff-base Ligands;Formation, Structural Characterisation and Biological Activity
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Abstract<p>The synthesis of ligands with N<sub>2</sub>S<sub>2</sub> donor sets that include imine, an amide, thioether, thiolate moieties and their metal complexes were achieved. The new Schiff-base ligands; N-(2-((2,4-diphenyl-3-azabicyclo[3.3.1]nonan-9-ylidene)amino)ethyl)-2-((2-mercaptoethyl)thio)-acetamide (H<sub>2</sub>L<sup>1</sup>) and N-(2-((2,4-di-p-tolyl-3-azabicyclo[3.3.1]nonan-9-ylidene)amino)ethyl)-2-((2-mercaptoethyl)thio) acetamide (H2L<sup>2</sup>) were obtained from the reaction of amine precursors with 1,4-dithian-2-one in the presence of triethylamine as a base in the CHCl3 medium. Complexes of the general formula K<sub>2<</sub></p> ... Show More
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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)
Comparative Study between Oral Hypoglycemic Drugs Repaglinide, Glibenclamide and Rosiglitazone on Some Biochemical Parameters in Type 2 Diabetic Patients
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Type 2 diabetes mellitus is often characterized by hyperglycemia as a result of increased insulin resistance in hepatic/peripheral tissues and pancreactic B-cell dysfunction. Approximately 92% of patients with type 2 diabetes mellitus demonstrate insulin resistance, however hyperglycemia is always a consequence of insulin deficiency. This study was done on 120 patients newly diagnosed diabetes type 2 characterized by dyslipidemia that is increased triglycerides and decreased HDL. Hypoglycemia and weight gain are common problem with oral sulfonyl urea drugs. In this work three different oral hypoglycemic drugs repaglinide and glibenclamide (insulin secretagogues) and rosiglitazone (insulin sensitizer) were used for treatment of patients w

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Publication Date
Mon Jan 15 2018
Journal Name
Scientific Reports
Tuning charge carrier transport and optical birefringence in liquid-crystalline thin films: A new design space for organic light-emitting diodes
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Abstract<p>Liquid-crystalline organic semiconductors exhibit unique properties that make them highly interesting for organic optoelectronic applications. Their optical and electrical anisotropies and the possibility to control the alignment of the liquid-crystalline semiconductor allow not only to optimize charge carrier transport, but to tune the optical property of organic thin-film devices as well. In this study, the molecular orientation in a liquid-crystalline semiconductor film is tuned by a novel blading process as well as by different annealing protocols. The altered alignment is verified by cross-polarized optical microscopy and spectroscopic ellipsometry. It is shown that a change in alignment of the </p> ... Show More
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Publication Date
Sat Aug 15 2015
Journal Name
Chemistry And Materials Research
Synthesis and Characterization of 3, 5-Dimethyl-2-(4-nitrophenyl azo)-Phenol Complexes with Co (II) and Ni (II) and Study Its Effect on the Activity of Ach Enzyme (invitro)
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Publication Date
Wed Jun 30 2010
Journal Name
Al-kindy College Medical Journal
Frozen Shoulder in Type 2 Diabetes Mellitus
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Background: Frozen shoulder affects 2-5% of the
general population, and around 10-30% of diabetic
patients. It affect mainly the non-dominant shoulder,
and has more incidence in patients with poor
glycemic control.
Objective: To detect the incidence of frozen
shoulder in type 2 diabetic patients attending the
Specialized Center for Endocrinology and Diabetes
in Baghdad.Patients and methods: One hundred
patients with frozen shoulder were included in the
study from a total number of 580 type 2 diabetics
over a period of six months. 70 patients were
females and 30 patient were males. All were
investigated for fasting blood
glucose and HbA1c.
Results: The non-dominant shoulder was
involved in

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Publication Date
Thu Aug 16 2012
Journal Name
Journal Of Chemical And Pharmaceutical Research
Synthesis, Characterization, Schiff Base Phenyl 2-(2-hydroxybenzylidenamino)benzoate and its complexes with LaIII,Cr III and Pr III
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The aim of the work is the synthesis and characterization of the tridentate Schiff base (HL) containing (N and O) as donor atoms type (ONO). The ligand is: (HL) phenyl 2-(2-hydroxybenzylidenamino)benzoate . This ligand was prepared by the reaction of (phenyl 2-aminobenzoate) with salicylaldehyde under reflux in ethanol and few drops of glacial acetic acid which gave the ligand (HL). The prepared ligand was characterized by (FT IR,UV–Vis) spectroscopy, Elemental analysis of carbon, hydrogen and nitrogen (C.H.N.) and melting point. The ligand was reacted with some metal ions under reflux in ethanol with (1 metal :2 ligand )mole ratio which gave complexes of the general formula: [M(L)2]Cl , M = Cr III La III and , Pr III Products were found

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Publication Date
Sun Nov 01 2020
Journal Name
Iop Conference Series: Materials Science And Engineering
SnO<sub>2</sub> doped In<sub>2</sub>O<sub>3</sub> thin films as reducing gas sensors
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Summery<p>This research includes description of the x-ray diffraction, morphology and sensing measurements of SnO<sub>2</sub> doped In<sub>2</sub>O<sub>3</sub> thin films synthesized by pulsed laser deposition method on glass and silicon wafer substrates. In2O3:SnO2 powders were obtained by mixing In2O3 with SnO2 in the desired ratio, and calcination the at temperature 1273 K for 5 hours. SnO<sub>2</sub> doped In<sub>2</sub>O<sub>3</sub> thin films with different ratios (0, 0.01, 0.03, 0.05, 0.07, and 0.09% wt.) were prepared using pulsed laser deposition method. The structural investigation using X-ray diffraction revealed that the mai</p> ... Show More
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Publication Date
Sat Jul 01 2017
Journal Name
Energy Procedia
HgBa 2 Ca n-1 Cu n O 2n+2+δ Superconducting thin films Prepared by Pulsed Laser Deposition
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Publication Date
Sun Sep 01 2013
Journal Name
Baghdad Science Journal
Synthesis, Spectral Studies, and Theoretical Treatment of New Ni(II),and Co(II) Complexes of Bidenetate Ligands 2-Benzamido Benzothiazole ,and 2-Actamido Benzothiazole
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New metal complexes of the ligands 2-benzamido benzothiazole(B1), and 2-actamido benzothiazole(B2) with metal ions Ni(II),and Co(II) were prepared in alcoholic medium. The prepared complexes were characterized by FT-IR and electronic spectroscopy, Magnetic susceptibility, Flame Atomic Absorption technique as well as elemental analysis and conductivity measurement. From the spectral studies, an octahedral monomer structure proposed for Ni(II) complexes, and a tetrahedral monomer structure for Co(II)complexes.Semi-empirical methods (PM3,and ZINDO/1)were carried out to evaluate the heat formation( ?H?f)binding energy(?Eb) and dipole moment(µ)for all metal complexes. Also vibration frequencies, Electrostatic potential, HOMO and LUMO

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Publication Date
Sat Jan 23 2016
Journal Name
Journal University Of Kerbala
Synthesis and Characterization of Some Metal Complexes of [2-chloro-N-(1,5-dimethyl-3-oxo-2-phenyl-2,3-dihydro-1Hpyrazol-4-ylcarbamothioyl)acetamide] (L)
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A new ligand [ 2-chloro-N- (1,5-dimethyl-3-oxo-2-phenyl-2,3-dihydro -1H-pyrazol- 4- ylcarbamothioyl)acetamide](L) was synthesized by reacting the Chloro acetyl isothiocyanate with 4-aminoantipyrine,The ligand was characterized by(C HNS) elemental microanalysis and the spectral measurements including Uv-Vis ,IR ,1H and13C NMR spectra, some transition metals complex of this ligand were prepared and characterized by Uv-Vis, FT-IR spectra, conductivity measurements, magnetic susceptibility and atomic absorption. From the obtained results the molecular formula of all prepared complexes were [M(L)2(H2O)2]Cl2 (M+2 =Mn, Co, Ni, Cu, Zn, Cd and Hg),the proposed geometrical structure for all complexes were octahedra