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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
Sun Jan 20 2019
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Text Classification Based on Weighted Extreme Learning Machine
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The huge amount of documents in the internet led to the rapid need of text classification (TC). TC is used to organize these text documents. In this research paper, a new model is based on Extreme Machine learning (EML) is used. The proposed model consists of many phases including: preprocessing, feature extraction, Multiple Linear Regression (MLR) and ELM. The basic idea of the proposed model is built upon the calculation of feature weights by using MLR. These feature weights with the extracted features introduced as an input to the ELM that produced weighted Extreme Learning Machine (WELM). The results showed   a great competence of the proposed WELM compared to the ELM. 

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Crossref (3)
Crossref
Publication Date
Sun Jun 06 2010
Journal Name
Baghdad Science Journal
Algebraic Coincidence Periods Of Self – Maps Of A Rational Exterior Space Of Rank 2
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Let f and g be a self – maps of a rational exterior space . A natural number m is called a minimal coincidence period of maps f and g if f^m and g^m have a coincidence point which is not coincidence by any earlier iterates. This paper presents a complete description of the set of algebraic coincidence periods for self - maps of a rational exterior space which has rank 2 .

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Crossref
Publication Date
Thu May 11 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
The Construction and Reverse Construction of the Complete Arcs in the Projective 3-Space Over Galois Field GF(2)
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  The main purpose of this work is to find the complete arcs in the projective 3-space over Galois field GF(2), which is denoted by PG(3,2), by two methods and then we compare between the two methods

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Publication Date
Tue Dec 01 2020
Journal Name
Baghdad Science Journal
Partial Sums of Some Fractional Operators of Bounded Turning: Partial Sums of Some Fractional Operators
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            In this paper, several conditions are put in order to compose the sequence of partial sums ,  and  of the fractional operators of analytic univalent functions ,  and   of bounded turning which are bounded turning too.

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Publication Date
Mon May 22 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
On Fuzzy Internal Direct Product
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The main aim of this paper is to introduce the concept of a Fuzzy Internal Direct Product of fuzzy subgroups of group . We study some properties and prove some theorems about this concept ,which is very important and interesting of fuzzy groups and very useful in applications of fuzzy mathematics in general and especially in fuzzy groups.

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Publication Date
Sun Jun 01 2014
Journal Name
Baghdad Science Journal
Study of the Inter-Particle Expectation Values for Inter and Outer Shell: Khalil H. Al-Bayati|Ban H. Al-Asaad|Baidaa S. H.
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In this research the Inter-Particle Expectation Values have been studied for atomics Helium (He) and Beryllium (Be) also for He-like ions, Be-like ions (Li-1, B+1? Li+1, Be+2, B+3) by using Hartree-Fock wave functions, We compared the results to some ions which have the same atomic number from each group with atomic number, We compared the results with published calculations to the last studied .

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Publication Date
Sun Dec 07 2008
Journal Name
Baghdad Science Journal
ON CERTAIN SUB-SPACE OF X
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The study of properties of space of entire functions of several complex variables was initiated by Kamthan [4] using the topological properties of the space. We have introduced in this paper the sub-space of space of entire functions of several complex variables which is studied by Kamthan.

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Crossref
Publication Date
Fri Dec 01 2023
Journal Name
Chemical Methodologies
Investigations on TiO<inf>2</inf>-NiO@In<inf>2</inf>O<inf>3</inf> Nanocomposite Thin Films (NCTFs) for Gas Sensing: Synthesis, Physical Characterization, and Detection of NO<inf>2</inf> and H<inf>2</inf>S Gas Sensors
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Scopus
Publication Date
Sun Oct 03 2010
Journal Name
Baghdad Science Journal
On Semi-p-Compact Space
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Publication Date
Thu Apr 08 2021
Journal Name
Journal Of Interdisciplinary Mathematics
On regular δ-semi.open space
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It is shown that if a subset of a topological space (χ, τ) is δ-semi.closed, then it is semi.closed. By use this fact, we introduce the concept regularity of a topological space (χ, τ) via δ-semi.open sets. Many properties and results were investigated and studied. In addition we study some maps that preserve the δ-semi.regularity of spaces.

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