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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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Wed May 08 2019
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IMPROVING SENSITIVITY OF In 2 O 3 AGAINST NO 2 TOXIC GAS BY LOADING TIN OXIDE
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The paper discusses the structural and optical properties of In 2 O 3 and In 2 O 3-SnO 2 gas sensor thin films were deposited on glass and silicon substrates and grown by irradiation of assistant microwave on seeded layer nucleated using spin coating technique. The X-ray diffraction revealed a polycrystalline nature of the cubic structure. Atomic Force Microscopy (AFM) used for morphology analysis that shown the grain size of the prepared thin film is less than 100 nm, surface roughness and root mean square for In 2 O 3 where increased after loading SnO 2 , this addition is a challenge in gas sensing application. Sensitivity of In 2 O 3 thin film against NO 2 toxic gas is 35% at 300 o C. Sensing properties were improved after adding Tin Oxi

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Wed Jul 28 2021
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Synthesis, Characterization, and Biological Studies of New Complexes Derived from 2-(1H-Benzimidazol-2-yl) Aniline
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Thu Mar 30 2017
Journal Name
Iraqi Journal Of Pharmaceutical Sciences ( P-issn 1683 - 3597 E-issn 2521 - 3512)
Effects of Interleukin-2 (IL-2) and Interleukin-6 (IL-6) in Recurrent Spontaneous Abortion (RSA)
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         Recurrent Spontaneous Abortion (RSA) is the most painful experience for couples expecting a child. This study aimed to determine the relevance of IL-2 and IL-6 in recurrent spontaneous abortion (RSA).  Serum samples were collected from 90 women attend Al Kadhmiya teaching hospital in Baghdad. 60 women (first group) had recurrent abortion the women were negative for rubella virus, herpes simplex virus and toxplasma gondii. And they were negative from bacterial infection eg. Niesseria gonorrhea and Chlamydia trachomatis. The histopathological tests for fetus abnormalities were negative in this group, and 30 women (second group) with successful pregnancy (normal delivery). All samples we

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Publication Date
Sat Oct 01 2022
Journal Name
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Study structure and optical properties of Ag2Se, Ag2Se0. 8Te0. 2 and Ag2Se0. 8S0. 2 thin films
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Silver sulfide and the thin films Ag2Se0.8Te0.2 and Ag2Se0.8S0.2 created by the thermal evaporation process on glass with a thickness of 350 nm were examined for their structural and optical properties. These films were made at a temperature of 300 K. According to the X-ray diffraction investigation, the films are polycrystalline and have an initial orthorhombic phase. Using X-ray diffraction research, the crystallization orientations of Ag2Se and Ag2Se0.8Te0.2 & Ag2Se0.8S0.2 (23.304, 49.91) were discovered (XRD). As (Ag2Se and Ag2Se0.8Te0.2 & Ag2Se0.8S0.2) absorption coefficient fell from (470-774) nm, the optical band gap increased (2.15 & 2 & 2.25eV). For instance, the characteristics of thin films made of Ag2Se0.8Te0.2 and Ag2Se0.8S0.2

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Publication Date
Sun Dec 24 2023
Journal Name
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Structural, Characterization, Biological and Studying the Enzyme Activity of some transition metal complexes with 4- )(2- hydroxy phenyl imino) methyl) -2, 6-dimethoxy phenol
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A new Schiff bases ligand 4- ((2-hyolroxy phenylimino) methyl) -2, 6-dimethoxyphenol  derived from condensation of 2- amino phenol with 4-hydroxy -3, 5-dimethoxy benzaldehyde have been synthesized and characterized by  spectroscopy,  spectra, Mass spectrum and elemental microanalysis (C.H.N). Metal Complexes with ions have been also synthesized and characterized spectroscopic methods  spectroscopy, flame atomic absorption, molar conductivity measurements and magnetic susceptibility. These studies indicate that the moler ratio  for the complexes. The complexes  showed characteristics octahedral geometry with the (O,N) ligand coordinated in bidentate mode while with  showed square planer. The enzyme activity of the ligand and i

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Publication Date
Sun Jan 26 2020
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Synthesis, Characterization of 2-azido-4-(azido (2-azido-2-( azido carbonyl)-1,3-dioxoian-4-yl)methyl)– 5-((R-azido (hydroxyl) methyl- 1,3-dioxole-2-carbonyl azide. ethanol. hydrate (L-AZD) with Some Metal Complexes
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The reaction oisolated and characterized by elemental analysis (C,H,N) , 1H-NMR, mass spectra and Fourier transform (Ft-IR). The reaction of the (L-AZD) with: [VO(II), Cr(III), Mn(II), Co(II), Ni(II), Cu(II), Zn(II), Cd(II) and Hg(II)], has been investigated and was isolated as tri nuclear cluster and characterized by: Ft-IR, U. v- Visible, electrical conductivity, magnetic susceptibilities at 25 Co, atomic absorption and molar ratio. Spectroscopic evidence showed that the binding of metal ions were through azide and carbonyl moieties resulting in a six- coordinating metal ions in [Cr (III), Mn (II), Co (II) and Ni (II)]. The Vo (II), Cu (II), Zn (II), Cd (II) and Hg (II) were coordinated through azide group only forming square pyramidal

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Fri Dec 31 2021
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Hong-Ou-Mandel Dip Measurements of Two Independent Weak Coherent Pulses for Free Space Quantum Key Distribution Systems
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Preparation of identical independent photons is the core of many quantum applications such as entanglement swapping and entangling process. In this work, Hong-Ou-Mandel experiment was performed to evaluate the degree of indistinguishability between independent photons generated from two independent weak coherent sources working at 640 nm. The visibility was 46%, close to the theoretical limit of 50%. The implemented setup can be adopted in quantum key distribution experiments carried out with free space as the channel link, as all the devices and components used are operative in the visible range of the electromagnetic spectrum.

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Publication Date
Thu Mar 30 2017
Journal Name
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Crossref (2)
Crossref
Publication Date
Mon Nov 01 2010
Journal Name
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Correction of Spherical Aberration of an Immersion Lens Operating Under Space Charge Effect Described by a 2nd Order Equation
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The present work represents a theoretical study for the correction of spherical aberration of an immersion lens of axial symmetry operating under the effect of space charge, represented by a second order function and preassigned magnification conditions in a focusing of high current ion beams. The space charge depends strongly on the value of the ionic beam current which is found to be very effective and represents an important factor effecting the value of spherical aberration .The distribution of the space charge was measured from knowing it's density .It is effect on the trajectory of the ion beam was studied. To obtain the trajectories of the charged particles which satisfy the preassined potential the axial electrostatic potential w

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Mon Apr 14 2014
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Synthesis and Characterization of Some O-[2-{''2-Substituted Aryl (''1,''3,''4 thiadiazolyl) ['3,'4-b]-'1,'2,'4- Triazolyl]-Ethyl]-p- chlorobenzald oxime Derivatives
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In this study new derivatives of O-[2-{''2-Substituted Aryl (''1,''3,''4 thiadiazolyl) ['3,'4-b]-'1,'2,'4- Triazolyl]-Ethyl]-p- chlorobenzald oxime (6-11)have been synthesized from the starting material p-chloro – E- benzaldoxime 1.Compound 2 was synthesized by the reaction of p-chloro – E- benzaldoxime with ethyl acrylate in basic medium. Refluxing compound 2 with hydrazine hydrate in ethanol absolute afforded 3. Derivative 4 was prepared by the reaction of 3 with carbon disulphide, treated of compound 4 with hydrazine hydrate gave 5. The derivatives (6-11) were prepared by the reaction of 5 with different substitutesof aromatic acids. The structures of these compounds were characterized from their melting points, infrared spectroscopy

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