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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
Fri Mar 15 2019
Journal Name
Journal Of Baghdad College Of Dentistry
The effect of 2 different techniques in second stage implant surgery
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Background: Dental implant is one of the most important options for teeth replacement. In two stage implant surgery, a few options could be used for uncovering implants, scalpel and laser are both considered as effective methods for this purpose. The Aim of the study: To compare soft tissue laser and scalpel for exposing implant in 2nd stage surgery in terms of the need for anesthesia, duration of procedure and pain level assessment at day 1 and day 7 post operatively using visual analogue scale . Materials and methods: Ten patients who received bilateral implants participated after healing period completed, gingival depth over each implant was recorded and then implant(s) were exposed by either scalpel or laser with determination for th

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Publication Date
Thu Dec 01 2016
Journal Name
Karbala Journal Of Medicine
Assessment Of Her-2/Neu Gene Amplification Status by Chromogenic in Situ Hybridization in Breast Cancer Patients with Equivocal 2+ Her-2/Neu Immunostaining and Its Relation to The Clinic Pathological Parameters
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background: human epidermal growth factor receptor-2 (her2/neu) is related to growth factor receptors with alkaline kinase activity and it is regarded as important prognostic and therapeutic factor that can depended on in breast cancer therapy. HER2/neu expression by immunohistochemistry (IHC) is submitted to a great in terob server inconsistency. Subsequently additional confirmatory tests for assessment of gene alterations and amplification status are needed for patients with early or metastatic breast cancer. In situ hybridization techniques and specifically Chromogenic in situ hybridization (CISH) was arise as a practical, cost-effective, and alternative to fluorescent in situ hybridization in testing for gene alterationAims of the study

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Publication Date
Wed Oct 17 2018
Journal Name
Journal Of Economics And Administrative Sciences
the role of marketing intelligence in promoting new product policies.a sample survey of workers in a number of mineral water plants in dohuk governorate
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Marketing Intelligence is one of the important methods of collecting information about competitors ' products and changes in customers ' tastes and needs that contribute to determining the policies to be followed in product development.

The problem of research, which seeks to be answered by the extent to which the companies in question have the appropriate and effective mechanisms to develop their products, and the nature of the relationship between the components of marketing intelligence and new product development policies. The importance of research is determined by the importance of obtaining important and necessary information to make the appropriate decision on the development of the new product an

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Publication Date
Wed Jan 01 2025
Journal Name
Veterinary World
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
Mon Mar 15 2021
Journal Name
Al-academy
Icon, Symbol and Values of Functional and Aesthetic Communication in Industrial Product Design: زياد حاتم حربي العامري
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The icon and the symbol represent the constituents of the communication process, through their intellectual and philosophical concepts that have been addressed by the current research that it has touched upon their importance in conveying the design idea for the recipient and showing the specificity of each one of them in the communication process. The research problem has been limited by the following question: what are the communication roles that the symbol and the icon present for the user in designing the industrial product?
The research objective is to reveal the theoretical visualization that describes the icon and the symbol in the industrial product and its importance in the communication process through stating the of simil

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Publication Date
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
Journal Name
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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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Publication Date
Wed Aug 01 2018
Journal Name
Ecotoxicology And Environmental Safety
Biochemical and molecular alterations in freshwater mollusks as biomarkers for petroleum product, domestic heating oil
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Publication Date
Wed Mar 29 2017
Journal Name
Iraqi Journal Of Pharmaceutical Sciences ( P-issn 1683 - 3597 E-issn 2521 - 3512)
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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Publication Date
Fri Nov 03 2023
Journal Name
Iraqi Journal Of Pharmaceutical Sciences( P-issn 1683 - 3597 E-issn 2521 - 3512)
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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