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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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Tue Mar 30 2021
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Synthesis, Characterization and Biological Activity Evaluation of Some Pyrazoles, Thiazoles and Oxazoles Derived from 2-Mercaptoaniline
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    Synthesis of 2-mercaptobenzothiazole (A1) is performed from the reaction of  o-aminothiophenol and carbon disulfide CS2 in ethanol under basic condition. Compound (A1)  is reacted with chloro acetyl chloride to give compound (A2). Hydrazide acid compound (A3) is obtained from the reaction of compound (A2) with  hydrazine hydrate in ethanol under reflux in the presence of glacial acetic acid .The reaction of hydrazide acid compound (A3) with ethyl acetoacetate gives pyrazole compound (A4). The new hydrazone  compound (A5) was prepared from the reaction of compound (A3) with  benzaldehyde. Reaction of compound

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Evaluation of angiopoietin-2 level in patients with multiple myeloma at presentation and in remission state
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The study aimed to assess the level of ANG‑2 in MM patients at diagnosis and in remission state and elaborate on its correlation with interleukin‑6 (IL‑6) and beta‑2 microglobulin (B2M) levels. Sixty MM patients; 20 newly diagnosed (ND), and 40 patients in remission were included. Twenty healthy individuals were included as a control group. Plasma levels of ANG‑2, B2M, and IL‑6 were tested by enzyme‑lin ked immunosorbent assay. There are significant statistical differences between ND patients and those in remission in hemoglobin, neutrophil count, blood urea, serum creatinine, glomerular filtration rate, B2M, IL6, and ANG‑2 (P = 0.001, 0.033, 0.005, 0.001, 0.001, 0.001, 0.004, and 0.001, respectively). ANG‑2 showed signifi

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Topical therapy of acne vulgaris using 2% tea lotion in comparison with 5% zinc sulphate solution
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The impact of governance on the reputation of the organization
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The current study aims to determine the extent of SOMO's interest in governance and whether this interest is sufficient to be reflected in enhancing its organizational reputation, and the field of research was in the oil marketing company SOMO. (109), (105) questionnaires were distributed, (94) forms and (11) forms were not retrieved, and the valid questionnaires had reached (91). The analytical and descriptive approach was used for the study, and the current research has found a positive impact of government on the reputation of the organization, and this research demonstrated the existence of the proposed relationship and the impact between governance and the reputation of the organization.

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Publication Date
Sun Mar 01 2015
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Preparation and Spectral Characterization of New Azo Imidazole Ligand 2-[(2`-Cyano Phenyl) Azo]-4,5-Diphenyl Imidazole and its Complexes with Co(II), Ni(II), Cu(II), Zn(II), Cd(II) and Hg (II) Ions
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The preparation and spectral characterization of complexes for Co(II), Ni(II), Cu(II), Cd(II), Zn(II) and Hg(II) ions with new organic heterocyclic azo imidazole dye as ligand 2-[(2`-cyano phenyl) azo ]-4,5-diphenyl imidazole ) (2-CyBAI) were prepared by reacting a dizonium salt solution of 2-cyano aniline with 4,5-diphenyl imidazole in alkaline ethanolic solution .These complexes were characterized spectroscopically by infrared and electronic spectra along with elemental analysis‚ molar conductance and magnetic susceptibility measurements. The data show that the ligand behaves a bidantate and coordinates to the metal ion via nitrogen atom of azo and with imidazole N3 atom. Octahedral environment is suggested for all metal complex

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Thu Dec 31 2020
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The Chinese Economy and its impact on international trade (Study on the role of the port of Gwadar)
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China's economic policy and its huge capabilities operate according to an expansion strategy, especially in investing foreign projects, as the past ten years have witnessed a major development in the elements of comprehensive strength, especially in the economic field, in 2014 China launched the largest initiative in the world, represented by the Belt and Road Project (BRI), which links nearly 70 countries, through this project, a very important region has emerged, which is (the port of cadres) in Pakistan, as China has headed towards that region and given the highest importance that is in its interest in the first place regardless of the great Pakistani interest, This is consistent with its future aspirations, especially after breaking

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Publication Date
Sun Jun 05 2016
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Preparation and Physico-Chemical Investigation Studies for the of Mn(II),Co(II),Ni(II) and Cu(II) Metal Complexes with Ligand 2- Hydroxybenzaldine Urea
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Some of metal compounds have been synthesized of record ligand from aldehid interaction of a substance which is salicyladehyde with another material which is urea. During the analysis of the metal component, The prepared complexes were characterized by elemental analysis, IR ,UV-visible , conductivity and magnetic susceptibility measurements. this confirms the ratio[1:1] between the metal and ligand. It is found that theortical values agree with practical values All the studied complexes are suggested as an octahedral stereochemistry.

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Publication Date
Sat Oct 01 2016
Journal Name
Journal Of Economics And Administrative Sciences
The Intellectual Capital And Its Revenues On The Investment Applied Research On Sample of Banks Listed on In The Iraq Stocks Exchange
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Abstract

      The changes that happened in the environment of  business have great effects upon organizations with different activities specially the banks  which requires the existence of an able opinion  resources can adapt with the changes . Accordingly importance put upon  intellectual  capital which become one of the basic resources for organizations and one of success and growth elements with the availability of expertise , skills and capability of making  essential changes in different process due to the presentation of innovations and creations of the to support banks activities .Therefore the intellectual  capital represents the more r

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Publication Date
Mon Feb 01 2021
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Investigations on the Impact of Using Elliptic Groynes on the Flow in Open Channels
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This paper presents a numerical simulation of the flow around elliptic groynes by using CFD ‎software. The flow was simulated in a flume with 4m long, 0.4m wide, ‎and 0.175m ‎high ‎‎with a constant bed slope. Moreover, the first Groyne placed at 1m from the flow ‎‎inlet with a ‎constant the Groyne height of 10cm and a 1cm thickness, and the ‎width of Groynes equals ‎7cm‎. A submergence ratio of the elliptic Groynes of 75% was assumed, corresponding to a discharge of ‎0.0057‎m3/sec. The CFD ‎model showed a good ability to simulate the flow ‎around ‎Groynes with ‎ good accuracy. The results of ‎CFD software showed that when using double elliptic Groy

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