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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
Thu Sep 15 2022
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Assessment of lipid profile with HbA1c in type 2 diabetic Iraqi patients
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Insulin-induced hyperglycemia is the hallmark of diabetes mellitus (DM), including various metabolic disorders. Diabetic people are more likely to develop dyslipidemia, hypertension, and obesity. Type 2 diabetes ‎(T2DM), the most common illness, is generally asymptomatic in its early stages and can go misdiagnosed for years. Diabetes screening may be beneficial in some cases since early identification and treatment can lessen the burden of diabetes and its consequences.‎ This study aimed to find the relationship between Glycated hemoglobin (HbA1c) ‎and lipid profile components in T2DM‎ patients. This descriptive-analytical and cross-sectional study was performed on the control group and T2DM patients in ‎Medical City in Baghdad be

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Publication Date
Wed Mar 16 2022
Journal Name
Journal Of Communicable Diseases
Immune Response among Different Types of SARS-CoV-2 Vaccines in Iraq
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Introduction: COVID-19 vaccine have been indicated to successfully decrease the hazard for symptomatic severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection furthermore associated hospitalisations. Objective: To study the immune response among different types of SARS-CoV-2 vaccines. Methods: This study includes 100 vaccinated individuals (43 Sinopharm, 30 AstraZeneca and 27 Pfizer) with one or two doses from different health centres in Baghdad. During the period from April 2021 to the end of May 2021, SARS-CoV-2 IgG and SARS-CoV-2 IgM levels were detected using AFIAS-6 device depending on FIA (Fluorescence Immunoassay) technique. Results: 93% of the cases were positive for IgG levels, and negative in 7% case

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Publication Date
Thu May 05 2022
Journal Name
Al-kindy College Medical Journal
Assessment of Lipid Profile among Sudanese patients with Type 2 Diabetes Mellitus
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Background: Diabetes mellitus is a major health issue that is one of the leading causes of cardiovascular disease. Recent studies have found a link between uncontrolled diabetes and cardiovascular disease, with dyslipidaemia predicting glycated-hemoglobin (HbA1c), which could be a major contributor to type 2 diabetes complications and etiology.

Objectives: The objective of present study was estimate lipid profiles among control and uncontrolled type 2 diabetic patients.

Subjects and Methods: Analytical case control based study, One hundred twenty participate were included in study, 70 patients with DM  as case group  refer to Abuagala Center and difference follow up diabetic center  and 50 non diabetic subjects taken as

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Wed Jan 15 2025
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State of type 2 diabetic Iraqi patients after hospitalization for COVID-19
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The coronavirus-19 (COVID-19) pandemic, triggered by the severe acute respiratory syndrome coronavirus 2, has affected over 100 million people and killed around 2 million individuals. One of the most common chronic illnesses in the world is diabetes, which greatly raises the risk of hospitalization and death for COVID-19 patients.

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This study aims to analyze the novel coronavirus's general characteristics and shed light on COVID-19 and its management in diabetic individuals by measuring some metabolic and inflammatory factors in type 2 diabetic pa

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Publication Date
Sun Dec 25 2022
Journal Name
International Journal Of Drug Delivery Technology
Synthesis of Few New Carrier Polymers Derived from 2-hydrazinylbenzo[d]thiazole
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2-hydrazinylbenzo[d]thiazole compound [1] is produced from reaction of 2-mercapto-benzothiazole with hydrazine hydride in ethanol. Compound [1] reacted with maleic anhydride in DMF to produce (Z)-4-(2-(benzo[d] thiazol-2yl) hydrazinyl)-4-oxobut-2-enoic acid [compound (2)]. While the treatment of compound [2] with the ammonium persulfate (NH4)2S2O8 (as the initiator) in order to produce compound [3], then compound [3] reacted with thionyl chloride in benzene to produce compound [4], finally compound [4] reaction with various drugs: cephalexin, amoxicillin, sulfamethizole, elecoxib obtained polymers [5–8]. The structure of synthesized compounds identified by spectral data: fourier transform infrared (FTIR) and proton nuclear magneti

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Publication Date
Sun Oct 01 2023
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Fabrication and Investigation of Structural, Optical and Dielectric Properties of ZnO:MnO 2 Composites
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In this work, (ZnO)1-x(MnO2)x compounds were synthesized with composition (x=0, 0.1, 0.2, 0.3, 0.4, and 0.5) of manganese oxide content using solid state reaction. Thin films were prepared from these compounds on glass substrates at room temperature using pulsed laser deposition method. The structure of the prepared compounds and thin films were analyzed using x-ray diffraction while the optical properties was measured using UV-visible spectrophotometry. It was found that the synthesized composites declared many peaks in the diffraction pattern which indicate polycrystalline structure with hexagonal wurtzite hexagonal structure of ZnO, and MnO2 and Mn2O3 secondary phases. A narrowing in the optical e

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Publication Date
Tue Jan 01 2019
Journal Name
Journal Of Pharmaceutical Sciences & Research
Determination of Some Biochemical Parameters of Acromegalic Patients with Type 2 Diabetes Mellitus.
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Background: Because of the disturbance in the pituitary gland, growth hormone (GH) secretion will be increased and, as a result, insulin-like growth factor 1 (IGF-1) secretion will be increase as well, leading to a chronic and rare disease called acromegaly disease. One of the most serious complications of acromycaly is diabetes. Insulin resistance, which causes diabetes, occurs in the body because of increased growth hormone secretion Objective: The aim of this work is to estimate some biochemical parameters. These parameters were not studied extensively in the literature such as BALP and LOX and the possibility of using LOX as a new biomarker for acromyalgic patients with diabetic. Patients and Methods: The study was performed on (25) mal

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Publication Date
Fri Oct 01 2021
Journal Name
International Journal Of Drug Delivery Technology
Synthesis and Preliminary Antimicrobial Activity Evaluation of New Amide Derivatives of 2-aminobenzothiazole
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Publication Date
Wed Mar 10 2021
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SYNTHESIS AND CHARACTERIZATION OF THE HEAVY METALS; AU (III) ,Pd (II),Pt(IV) Rh(III) COMPLEXES OF S –PROPYNYL 2 –THIOBENZIMIDAZOLE
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Complexes of Au(III) ,Pd (II) , Pt (IV ) and Rh(III) with S – propynyle -2- thiobenzimidazole (BENZA) have been prepared and characterized by IR and UV- Visible spectral methods in addition to magnetic and conductivity measurements and micro – elemental analysis (CHN).The probable structures of the new complexes have been suggested.

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Publication Date
Sun Dec 02 2012
Journal Name
Baghdad Science Journal
The Relation of IGF-1 and Insulin Resistance in a Sample of Iraqi Obese Type 2 Diabetic Patients with Macrovascular Disease
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Type 2 diabetes mellitus(T2DM) is a metabolic disease that is associated with an increased risk for atherosclerosis by 2-4 folds than in non- diabetics. In general population, low IGF-1 has been associated with higher prevalence of cardiovascular disease and mortality .This study aims to find out the relationship between IGF-1 level and other biochemical markers such as Homeostasis Model Assessment insulin resistance(HOMAIR) and Body Mass Index(BMI) in type 2 diabetic patients . This study includes (82) patients (40 females and 42 males) with age range (40-75) years,(34) non obese diabetic patients and (48) obese diabetic patients. The non obese individuals considered

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