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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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Gastroprotective Activity of Ethyl-4-[(3,5-di-tert-butyl-2-hydroxybenzylidene) Amino]benzoate against Ethanol-Induced Gastric Mucosal Ulcer in Rats
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The Effect of Spatial Organization on the Sustainability of the Neighborhood Unit in the Residential Environment
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Spectrophotometric Determination of Micro Amount of Chromium (III) Using Sodium 4-((4,5-diphenyl-imidazol-2-yl)diazenyl)-3-hydroxynaphthalene-1-sulfonate in the Presence of Surfactant, Study of Thermodynamic Functions and Their Analytical Applications
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The achievement of world peace is a humanitarian demand that humanity has sought since its existence. Despite the international and regional efforts to achieve this demand, it is still reaching its desired ambitions if conflicts, contradictions, and internal and external wars continue to justify us clearly in terms of ethnic, religious and sectarian conflict. The revolution of informatics and the impact of globalization opened a new era of communication and openness and the negative and positive impact of others, which re-published and distributed values, ideas and new cultures Some of them carries extremist ideas urging violence and destruction and other abolition, it became necessary to follow policies and reward The culture of peace,

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The present study discusses the problem based learning in Iraqi classroom. This method aims to involve all learners in collaborative activities and it is learner-centered method. To fulfill the aims and verify the hypothesis which reads as follow” It is hypothesized that there is no statistically significant differences between the achievements of Experimental group and control group”. Thirty learners are selected to be the sample of present study.Mann-Whitney Test for two independent samples is used to analysis the results. The analysis shows that experimental group’s members who are taught according to problem based learning gets higher scores than the control group’s members who are taught according to traditional method. This

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Sat Oct 20 2018
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The effect of The Organizational Agility On High Performance ( Applied Search )
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The current research aims to know  the  reality of the  research's coefficients, to know  correlation and effectiveness  between  the  organizational  Agility  and high performance . The current research  has been applied on  the official banks , including  a sample of  senior administration  members  (120) ; besides , the research has used questionnaire  that being considered as the main tool for gathering  information  and data . It includes  59 questions  in addition to  the personal interviews  program  as to support  the questionnaire and to fulfill a great deal of reality. It has been anal

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The Authority and its impact on the prevention of Sharia rulings
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Praise be to God, Lord of the worlds, and prayers and peace be upon our master Muhammad and upon his family and companions.
And after:

      Muslim scholars have fought in the extent of regard to these interests, each according to his opinion and according to his evaluation, and his consideration of this interest, but it remains important that the legislation in them needs more precaution and caution against the predominance of passions, because the passions often decorate spoilers so they see an interest, so practical application must To realize the spirit of Islamic Sharia in its entirety of its rulings, and the preponderance between the interests and evils that prevail in our societies, which c

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The effects of devitrification on the lithium glass surface and microstructure
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Effect of the annealing and compositional on the Morphological and electrical
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Nanocrystalline TiO 2 and CuO doped TiO 2 thin films were successfully deposited on suitably cleaned glass substrate at constant room temperature and different concentrations of CuO (0.05,0.1,0.15,0.2) wt% using pulse laser deposition(PLD) technique at a constant deposition parameter such as : (pulse Nd:YAG laser with λ=1064 nm, constant energy 800 mJ, with repetition rate 6 Hz and No. of pulse (500). The films were annealed at different annealing temperatures 423K and 523 K. The effect of annealing on the morphological and electrical properties was studied. Surface morphology of the thin films has been studied by using atomic force microscopes which showed that the films have good crystalline and homogeneous surface. The Root M

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