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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
Wed Jan 15 2025
Journal Name
Human Antibodies
State of type 2 diabetic Iraqi patients after hospitalization for COVID-19
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Background

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.

Objective

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
Tue Apr 26 2022
Journal Name
International Journal Of Health Sciences
narrative review of nutritional status among iraqi adults with type 2 diabetes
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Type 2 diabetes is a global public health problem especially in middle east countries and Iraq has not spared from this pandemic. The prevalence in Iraq. and rank in Middle East. Beside increasing in prevalence- also poor glucose control. Nutrition plays a critical role. This paper narratively review variables that affect  reduce the incidence of T2DM in Iraq and affect nutritional status among Iraqi withT2DM. The factors contribute  to T2DM were high rates of obesity and overweight, as well as levels of body fat indicate a high prevalence of poor glycemic control. Likewise, levels of physical activity are low among older Iraqis.

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Publication Date
Tue Aug 04 2009
Journal Name
Journal Of The College Of Basic Education, Al-mustansiriyah University
cyclic decomposition of SL(2,p) where p=9, 25 and 27
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Publication Date
Thu Sep 15 2022
Journal Name
Bionatura
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 Ba

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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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Publication Date
Mon Apr 01 2019
Journal Name
Biochem. Cell. Arch
Association Of – 1195a/g Single Nucleotide Polymorphism Of Cyclooxygenase-2 Gene With The Severity Of Chronic Periodontitis In An Iraqi Population
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Chronic periodontitis (CP) is an inflammatory disease affecting tooth supporting structures in response to bacterial dental plaque causing irreversible tissue destruction. Cyclooxygenase-2 (COX-2) is an effective mediator in the pathogenesis of periodontitis. Polymorphisms in the COX-2 gene may contribute to its overexpression and increased disease susceptibility. To evaluate the association between -1195 A/G single nucleotide polymorphism (SNP) in the promotor area of the cyclooxygenase-2(COX-2) gene and severity of chronic periodontitis in a sample of Iraqi population. -1195A/ G COX-2 SNP was investigated in 70 chronic periodontitis (CP) cases and 30 healthy controls. CP cases composed of 2 subgroups (35 moderate CP cases and 35 severe CP

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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
Tue Mar 28 2017
Journal Name
Iraqi Journal Of Pharmaceutical Sciences ( P-issn 1683 - 3597 E-issn 2521 - 3512)
The Correlation Between Hyperglycemia and Rheumatoid Factor in Type 2 Diabetic Patients in Al- Risafa Area, Baghdad
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Diabetes mellitus type 2 (T2DM) formerly called non-insulin dependent diabetes mellitus (NIDDM) or adult-onset diabetes is a common disease. Rheumatoid factor is a well-established test used in the diagnosis and follows the prognosis of rheumatoid arthritis (RA). Rheumatoid factor is sometimes found in serum of patients with other diseases including diabetes mellitus (DM), due to the presence of pro-inflammatory cytokines such as TNF- α which play an important role in chronic inflammatory and autoimmune diseases like rheumatoid arthritis (RA). The aim of the study is to investigate the associations between type 2 diabetes mellitus (T2DM) and rheumatoid arthritis (RA) in scope of rheumatoid factor (RF), hyperglycemia a

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