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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 Jan 01 2022
Journal Name
Proceeding Of The 1st International Conference On Advanced Research In Pure And Applied Science (icarpas2021): Third Annual Conference Of Al-muthanna University/college Of Science
Interleukin 2−330 single nucleotide polymorphism association with type 1 diabetes in Iraqi patients
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Type 1 diabetes (T1D) is an autoimmune disease with chronic nature resulting from a combination of both factors genetic and environmental. The genetic contributors of T1D among Iraqis are unexplored enough. The study aimed to shed a light on the contribution between genetic variation of interleukin2 (IL2) gene to T1D as a risk influencer in a sample of Iraqi patients. The association between IL2−330 polymorphism (rs2069762) was investigated in 322 Iraqis (78 T1D patients and 244 volunteers as controls). Genotyping for the haplotypes using polymerase chain reaction test – specific sequence primer (PCR-SSP) for (GG, GT, and TT) genotypes corresponding to (G and T) alleles were performed. A significant association revealed a decreased freq

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Publication Date
Sat Apr 01 2023
Journal Name
Journal Of Applied Hematology
Molecular Alterations in IDH 1/2 Genes among Iraqi Adult Acute Myeloid Leukemia Patients
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BACKGROUND:

The recurrent somatic variations in IDH1/2 genes in AML play imperative roles in epigenetic dysregulation and the pathogenesis of AML, which could be useful prognostic markers for risk stratification.

AIM:

The aim of the study was to detect the frequency of R132 mutations in the IDH1 gene and R140Q mutation in the IDH2 gene with their treatment outcomes.

PATIENTS
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Tue Jan 01 2019
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Diabetes &amp; Metabolic Syndrome: Clinical Research &amp; Reviews
Nephrotic range proteinuria; does it predict lung involvement in patients with type 2 diabetes
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Tue Jan 01 2019
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Nephrotic range proteinuria; does it predict lung involvement in patients with type 2 diabetes
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Publication Date
Sun Sep 07 2008
Journal Name
Baghdad Science Journal
Chromosomal aberrations and N-ras activation in human larynx carcinoma cell line Hep-2.
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In the present study, cytogenetic and molecular techniques were conducted to detect the chromosomal aneuploidy and the involvement of N and H genes in squamous larynx carcinoma cell line Hep-2.Our results showed that numerical and structural abnormalities were involved in larynx cancer Hep-2.The total number of chromosomes ranging from tripolyploidy in passage187to more than that in passage207.The more frequent chromosomes involved in numerical aberrations were chromosomes1,7,16,17 and 18. Structural chromosomal aberrations were also detected.Deletion of short arm was detected in chromosome 1(del 1p) and the long arm of chromosome 1(del 1q)and 6(del 6q).Gaining on short arms were also recorded in chromosomes 3(3p+) and 12(12p+).At the mole

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Thu Apr 18 2019
Journal Name
Al-kindy College Medical Journal
Iron Chelation Therapy in Sickle Cell/Beta Thalassemia Syndrome, a 2 years’ Extension Study
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Publication Date
Sat May 30 2026
Journal Name
Iraqi Journal Of Science
Leucine-rich alpha-2-glycoprotein-1 as a Potential biomarker for polycystic ovary syndrome
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     Polycystic ovary syndrome (PCOS) is a common endocrine disorder affecting women of reproductive age, characterized by anovulatory, infertility and metabolic disturbances. This study aimed to assess the diagnostic accuracy of Leucine-rich alpha-2-glycoprotein-1 (LRG1) and xanthine oxidase (XO) activity as novel biomarkers for PCOS, as well as to explore the relationship between LRG1 and XO activity across different groups. A total of 150 married women, aged 18-46 years were enrolled and divided into three groups: 50 with PCOS under treatment, 50 PCOS without treatment conditions shared by women with polycystic ovary conditions, and 50 healthy women. Serum samples were analysed to measure LRG1, xanthine oxidase (XO) activity,

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Publication Date
Wed May 13 2009
Journal Name
Journal Of Planner And Development
Urban creep on the green areas and its environmental effects on the city of Baghdad
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he planning process is generally aimed at developing the city and making it meet the needs of different citizens. The green areas constitute one of the basic needs of the city and with the rapid and unusual growth in the size of cities, especially in the third world countries, which is often embodied in capitals. Which was achieved as a result of many reasons, including political, economic and social and even enshrined through some of the decisions that were issued and the city of Baghdad, but a clear example of these cities. The city and the environment are inseparable terms. The city is where people spend their lives and their daily experiences, and the environment is the center in w

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Publication Date
Fri Jun 01 2018
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
The tax planning and its effect on the investment: On sample of Iraqi Contribution Company
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The importance of the current study  lies in the  importance of the  Tax policy that  being considered one of the most important tools working on fulfilling  the  social,  financial  and economic  goals  and improving  the investment environment  in the country  to become  having the ability to  activate the  national economy. The current study  has  referred  that  (  Has  the  tax planning  practiced by  the Iraqi  contribution  companies  led to increase  the  far-term tax  outcome through  getting  benefit of   the monetary  funds  and expansion in&nbs

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Publication Date
Sat Feb 02 2019
Journal Name
Journal Of The College Of Education For Women
The Effect of Arab Environment on the Artist's Works August Renoir: The Effect of Arab Environment on the Artist's Works August Renoir
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Abstract:
This study is considerated one of many Studies above the standing of
the Islamic Arab nation which was chosen by God from other nations all over
the world . Some of these nations used to come to the Arab nation to take
whatever useful for them from the beginning of history till now . The
researcher deals in this study with a French artist who is well-know as
August Renoir . He traveled to Algeria and lived there . He was
influenced by the Islamic culture.
The study include. from chapter . chapter one deals with the framework of
programming (out line ) . Chapter two deals with the theoretical framework .
It includes five sections. Deals with the Islamic drawings(Arabesque) . section
three deals w

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