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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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Preparation and Physical Properties of Doped CdBa 2-x Sr x Ca 2 Cu 3 O 8+δ Compound
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Sun Jan 01 2012
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The First Scientific Conference The Collage Of Education For Pure Sciences 2012
Synthesis, Spectroscopic and Biological Studies of some metal ions complexes with 2-hydroxy-N-pyridin-2-yl methyl-acetamide
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The ligand 2-Hydroxy-N-pyridin-2-ylmethyl-acetamide(L) has been prepared from reaction of 2-(aminomethyl)pyridin with chloroacetic acid (1:1).It has been characterized by elemental analysis (C,H,N) ,'H, 13 C-NMR, IR and electronic spectra. The complexes of divalent (Co,Ni,Cu,Zn,Cd and Hg) ions and trivalent(Cr) ion have been synthesized and characterized by IR, electronic spectra, molar conductivity, atomic absorption and molar ratio (Ni 2+) complex. The analytical studies for the complexes show; octahedral for (Cr 3+),square planar for (Cu 2+) and (Co,Ni Zn, Cd and Hg) tetrahedral geometries. The study of biological activity of the ligand (L) and its complexes (Co,Ni,Cu,Cd,Hg) in two deferent concentration (1and5) mg/ml showed various acti

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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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synthesis, Composition, Spectral, Geometry and Antibacterial Applications ofMn(||),Ni(||),Co(||),Cu(||) and Hg(||) schiff Base complexes of N2O2 mixed donor with 1,10-phenanthroline
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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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Inelastic electron scattering form factors involving the second excited 2+ level in the isotopes 50,54,52Cr
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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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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 spectroscopyand 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 tridentate ligand, connecting Cu (

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