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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 Mar 25 2023
Journal Name
International Journal Of Drug Delivery Technology
The Probable Association between Type 2 Diabetes Mellitus and Toxoplasma gondii Infection
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Background: Type 2 diabetes mellitus (T2DM) is a chronic disorder that constitutes a major health problem worldwide. Toxoplasma gondii is an intracellular parasite that may infect any nucleated cell. Toxoplasmosis is becoming a worldwide health threat, infecting 30–50% of the world’s human population. The studies that have been undertaken to investigate the link between T. gondii infection and diabetes have shown contradictory fi ndings. This research aimed to look at the possible link between T2DM and T. gondii infection. Methods and Subjects: The enzyme-linked immunosorbent assay (ELISA) approach was used to screen for T. gondii IgM and IgG antibodies in 69 patients with T2DM and 92 seemingly healthy persons as controls. Resul

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Publication Date
Fri Apr 03 2020
Journal Name
Technology Reports Of Kansai University
Results for Some Groups of PSL (2, F)
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Publication Date
Wed Jan 01 2020
Journal Name
Medeniyet Medical Journal
SARS-CoV-2: A Piece of Bad News
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A shocking third species emerged from a family of coronaviruses (CoV) in late 2019 following viruses causing SARS (Severe Acute Respiratory Syndrome-CoV) in 2003 and MERS (Middle East Respiratory Syndrome-CoV) in 2012; it’s a novel coronavirus now called severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2; formerly called 2019-nCoV). First emerging in China, it has spread rapidly across the globe, giving rise to significant social and economic costs and imposing severe strain on healthcare systems. Since many attempts to control viral spread has been futile, the only old practice of containment including city lockdown and social distancing are working to some extent. Unfortunately, specific antiviral drugs and vaccines remain u

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Publication Date
Sun Dec 18 2022
Journal Name
Journal Of The College Of Basic Education
A (k,ℓ) Span in Three Dimensional Projective Space PG(3,p) Over Galois Field where p=4
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الغرض من هذا العمل هو دراسة الفضاء الإسقاطي ثلاثي الأبعاد PG (3، P) حيث p = 4 باستخدام المعادلات الجبرية وجدنا النقاط والخطوط والمستويات وفي هذا الفضاء نبني (k، ℓ) -span وهي مجموعة من خطوط k لا يتقاطع اثنان منها. نثبت أن الحد الأقصى للكمال (k، ℓ) -span في PG (3،4) هو (17، ℓ) -span ، وهو ما يساوي جميع نقاط المساحة التي تسمى السبريد.

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Publication Date
Thu Oct 25 2018
Journal Name
Journal Of Optical Communications
320 Gbps Free Space Optic Communication System Deploying Ultra Dense Wavelength Division Multiplexing and Polarization Mode Division Multiplexing
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Abstract<p>This work aims to investigate the integrated ultra-dense wavelength division multiplexing (UDWDM) and polarization division multiplexing (PDM) schemes incorporated in the free space optic (FSO) communication system. Erbium-doped fiber amplifiers (EDFAs) are used as post and pre-amplifiers in the proposed UDWDM–PDM–FSO system to boost the transmission power for increasing the distance. Thirty-two channels are transported over the FSO link to realize the total data transmission of 160 and 320 Gbps with 0.08 and 0.1 nm channel spacing, respectively. Results are also reported with non-return to zero modulation schemes. The performance of the proposed UDWDM–PDM–FSO transmission sys</p> ... Show More
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Publication Date
Fri Jul 29 2022
Journal Name
Journal Of Environmental Science And Health, Part A
Comparing the efficiency of N-doped TiO<sub>2</sub> and commercial TiO<sub>2</sub> as photo catalysts for amoxicillin and ciprofloxacin photo-degradation under solar irradiation
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Publication Date
Sun Jun 05 2016
Journal Name
Baghdad Science Journal
Synthesis and characterization Studies of Metal Complexes with Schiff base derived from 4-[5-(2-hydoxy-phenyl)-[1,3,4-oxadiazol-2-ylimino methyl]-1,5-dimethyl-2-phenyl-1,2-dihydro-pyrazol-3-one
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New metal complexes of the ligand 4-[5-(2-hydoxy-phenyl)-[1,3,4- oxadiazol -2-ylimino methyl]-1,5-dimethyl-2-phenyl-1,2-dihydro-pyrazol-3-one (L) with the metal ions Co(II), Ni(II), Cu(II) and Zn(II) were prepared in alcoholic medium. The Schiff base was synthesized through condensate of [4-antipyrincarboxaldehyde] with[2-amino-5-(2-hydroxy-phenyl-1,3,4- oxadiazol] in alcoholic medium . Two tetradentate Schiff base ligand were used for complexation upon two metal ions of Co2+, Ni2+, Cu2+ and Zn2+ as dineucler formula M2L2.4H2O. The metal complexes were characterized by FTIR Spectroscopy, electronic Spectroscopy, elemental analysis, magnetic susceptidbility measurements, and also the ligand was characterized by 1H-NMR spectra, and m

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Publication Date
Mon Mar 02 2015
Journal Name
Chemistry And Materials Research
Synthesis and Characterization of 3,5-Dimethyl-2- (4-nitrophenyl azo)-PhenolComplexes with Co(II) and Ni(II) and Study Its Effect on the Activity of AchEnzyme(invitro)
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Transition metal complexes of Co(II) and Ni(II) with azo dye 3,5-dimethyl-2-(4-nitrophenylazo)-phenol derived from 4-nitoaniline and3,5-dimethylphenol were synthesized. Characterization of these compounds has been done on the basis of elemental analysis,electronic data, FT-IR,UV-Vis and 1 HNMR, as well as magnetic susceptibility and conductivity measurements. The nature of thecomplexes formed were studies following the mole ratio and continuous variation methods, Beer ' s law obeyed over a concentrationrange (1x10 -4 - 3x10 -4 M). High molar absorbtivity of the complex solutions were observed. From the analytical data, thestoichiomerty of the complexes has been found to be 1:2 (Metal:ligand). On the basis of physicochemical data tetrahedral

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Publication Date
Sat Oct 28 2023
Journal Name
Baghdad Science Journal
Synthesis, Characterization of New Metal Complexes of Co (II), Cu (II), Cd (II) and Ru (III) from azo ligand 5-((2-(1H-indol-2-yl)ethyl) diazinyl)-2- aminophenol, Thermal and Antioxidant Studies
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A novel metal complexes Cu (II), Co (II), Cd (II), Ru (III) from azo ligand 5-((2-(1H-indol-2-yl)
ethyl) diazinyl)-2-aminophenol were synthesized by simple substitution of tryptamine with 2-aminophenol.
Structures of all the newly synthesized compounds were characterized by FT IR, UV-Vis, Mass spectroscopy
and elemental analysis. In addition measurements of magnetic moments, molar conductance and atomic
absorption. Then study their thermal stability by using TGA and DSC curves. The DCS curve was used to
calculate the thermodynamic parameters ΔH, ΔS and Δ G. Analytical information showed that all complexes
achieve a metal:ligand ratio of [1:1]. In all complex examinations, the Ligand performs as a tri

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Publication Date
Fri Aug 27 2021
Journal Name
Journal Of Craniofacial Surgery
The Effects of Local Alendronate With or Without Recombinant Human Bone Morphogenetic Protein 2 on Dental Implant Stability and Marginal Bone Level: A Randomized Controlled Study
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The aim of this study was to evaluate the effects of local application of bisphosphonate gel and recombinant human bone morphogenic protein 2 gel, on titanium dental implant stability and marginal bone level. Twenty-seven patients with upper and lower missing posterior tooth/teeth were included in the study with a total of 71 implants that were used for rehabilitation. The implants were randomly divided into 4 groups: 3 study groups and 1 control. Group1; local application of bisphosphonate gel, group 2; local application of recombinant human bone morphogenic protein 2 gel, group 3; local application of a mixed formula of both gels. The gel application was immediately preimplant insertion, group 4; implant insertion without application of a

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