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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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Wed Nov 01 2023
Journal Name
Journal Of Ecological Engineering
Product Concentration, Yield Percentage and Productivity of Citric Acid Formation Using Aspergillus Niger Isolated from Palm Dates
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Publication Date
Mon Jun 15 2020
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Biophysics and its scientific data in industrial product design: جاسم خزعل العقيلي -علاء نجم عبود
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  The current research discussed biophysics data as a theoretical and applied knowledge base linking industrial design with the natural sciences at the level of applied strategies through which we can enrich the knowledge base of industrial design. The research focused on two main aspects of the scientific references for biophysics, namely: electromagnetism, and biomechanics. According to the performance and functional applications in designing the functions of industrial products at the electromagnetic level, it was found that remote sensing applications: such as fire sensors that were adopted from the insect (Black Beetle) and that their metaphors enable them to hear fire, and collision sensors, which were adopted from the insect

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Wed Jan 01 2025
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Comparison of the sequences of the viral capsid protein 1 and viral capsid protein 2 encoded genes in symptomatic and asymptomatic cases of canine parvovirus 2 in dogs
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Background and Aim: Canine parvovirus 2 (CPV-2) is a highly contagious virus that infects wild and domestic canines. Despite the use of a routine vaccination protocol, it is endemic in Iraq. The genetic drift of CPV-2 is a major issue worldwide because it abrogates virus control. In Iraq, there is a knowledge gap regarding the genetic sequences of asymptomatic and symptomatic CPV-2 cases. Therefore, this study aimed to perform a genetic analysis of viral capsid protein 1 (VP1) and viral capsid protein 2 (VP2), two major capsid-encoding genes, to demonstrate the possible role of certain mutations in triggering infection. Materials and Methods: Symptomatic and asymptomatic cases (n = 100/each) were tested by a polymerase chain reacti

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Publication Date
Sat Aug 21 2021
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Immunohistochemical Expression of Retinoblastoma Gene Product and p53 Protein in Transitional Cell Carcinoma of the Urinary Bladder and its Relationship to Different Clinicopathological Parameters
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BACKGROUND: Carcinoma of urinary bladder is one of the most common malignancies worldwide and constitutes a major health problem. Multiple risk factors are associated with this tumor and its prognosis will depend on different clinicopathological parameters. Over expression of P53 protein and mutant Rb gene is associated with more aggressive clinical and histopathological features of the tumor such as advanced stage and higher grade. AIM: The immunohistochemical expression of Rb gene and P53 gene will be assessed through their protein products in transitional cell carcinoma (TCC) of the urinary bladder and then will be correlated with other well-known risk factors and prognostic parameters of bladder TCC, such as grading, tumor size, smoking

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Publication Date
Fri Apr 01 2016
Journal Name
Journal Of Economics And Administrative Sciences
Application Tools Lean Six Sigma Definition and measurement phases in new product development. In the Electrical Industries State Company. case Study.
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methodology six sigma Help  to reduce defects by solving problems effectively, and works Lean to reduce losses through the flow of the manufacturing process and when integrating these two methodologies (Lean and six sigma), the methodology of Lean six sigma will form the entrance to the organizers of the optimization process and increase the quality and reduce lead times and costs . by focusing on the needs of the customer. this process uses statistical tools and techniques to analyze and improve processes.

 We have conducted this research in the General Company for Electrical Industries and adopted its product (machine cooling water three taps) as a sample for research. In order to determine t

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Publication Date
Wed Mar 29 2017
Journal Name
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Evaluation of Metformin + Sitagliptin versus Metformin + Glibenclamide on Glycemic Control in Iraqis Type 2 Diabetic Patients
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Combination therapy with a dipeptidyl peptidase–4 inhibitor and metformin or metformin+ glibenclamide results in substantial and additive glucose- lowering effects in Iraqis patients with type 2 diabetes mellitus . This study evaluated the glycemic control by using two groups of  combinations of drugs metformin + glibenclamide and metformin + sitagliptin in Baghdad teaching hospital / medical city. 68 T2DM patients and 34 normal healthy individuals as control group were enrolled in this study and categorized in to two treatment groups. The group 1 (34 patients ) received ( metformin 500 mg three times daily + glibenclamide 5 mg twice daily ) and the group 2 (34 patients) received (metformin 500 mg three times daily + sitaglip

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Synergistic Effects of 2-Deoxy-D-Glucose and Cinnamic Acid with Erlotinib on NSCLC Cell Line
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Background: In spite of all efforts, Non-small cell lung cancer (NSCLC) is a fatal solid tumor with a poor prognosis as of its high metastasis and resistance to present treatments. Tyrosine kinase inhibitors (TKI) such as erlotinib are efficient in treating NSCLC but the emergence of chemoresistance and adverse effects substantially limits their single use. Objective: in this study, the combination treatments of either 2-deoxy-D-glucose (2DG) or cinnamic acid (CINN) with erlotinib (ERL) were tested for their possible synergistic effect on the proliferation and migration capacity of NSCLC cells. Methods: In this study, NSCLC model cell line A549 was used to investigate the effects of single compounds and their combination on cell gro

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Publication Date
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H-Point Standard Addition Method for Simultaneous Determination of Cimetidine and Erythromycin Ethylsuccinate Drugs Using Bromothymol Blue as a Chromogenic Complexing Agent
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The H-Point Standard Addition Method (H-PSAM) has been applied for spectrophotometric simultaneous determination of Cimetidine and Erythromycin ethylsuccinate using Bromothymol Blue (BTB) as a chromogenic complexing agent in a buffer solution at pH 5.5.

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Sun Dec 04 2016
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Type 2 diabetes mellitus (T2DM) is the most frequent endocrinal disease commonly associated with thyroid disorders .The study is conducted at the Specialized Center for Endocrinology and Diabetes in Baghdad ,during December 2014 up to October 2015.This study was done to investigate the prevalence of anti- thyroid peroxidase (Anti-TPO) antibody in patients suffered from type 2 diabetes with thyroid disorders .The study groups included a total number of 80 subjects consisting of 60 type 2 diabetic patients divided into 20 hyperthyroidism subjects (group 1) ,20 hypothyroidism subjects (group 2), 20 euthyroidism subjects (group 3) and 20 healthy controls (group 4) . The fasting blood samples were analyzed for (T3,T4,TSH) by using Vitek Immuno d

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