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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 Oct 10 2019
Journal Name
Open Access Macedonian Journal Of Medical Sciences
Are Histopathological Changes of H. pylori Infection in Young Dyspeptic Patients Necessitate Endoscopy?
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BACKGROUND: Helicobacter pylori is an important gastrointestinal infective bacteria with many serious complications including gastric erosions and ulceration, duodenal ulcer, gastric carcinoma and MALT gastric lymphoma. The gastric biopsy is commonly performed in H. pylori-positive dyspeptic individuals, and many previous researchers studied the histopathological features of infected gastric biopsies however little previous studies focused on the histopathological findings in young population in comparison to the older one. AIM: To make a focus on the histopathological effects of H. pylori infection in young patients compared with the older one and predicts the need for endoscopy in this population, also to estimates the prevalence of

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Publication Date
Wed Mar 10 2021
Journal Name
Baghdad Science Journal
Determination of chemical composition of local black seeds Nigella sativa L
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Chemical analysis for evaluation of Nigella sativa L. (black cumin) seeds showed a composition of Fat 39% ; Protein 28% ; Carbohydrate 21% ; Moisture 6% and Ash 4.5% . It was found that the black seed contains the following mineral element : Magnesium 0.26 gm /100gm seed ; Calcium 0.25 gm /100gm seed and Iron 25 ?g / gm /100gm seed ; zinc 4.51?g /gm /100gm seed and Copper 3.60 ?g /gm /100gm seed. The analysis also showed that mineral element I. e. ; lead ; Cobalt ; Nickel ; Chrom ; Cadmium and Aresenic are not present . It was found that the fat of the black seed contains the following fatty acids : Myristic 2.8%; Palmtic 16.6%; Stearic 0.8 % ; Oleic 13.79% ; Linoleic 64.2% and Arachidic 1.9% .

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Publication Date
Tue Dec 30 2014
Journal Name
College Of Islamic Sciences
Investigations in the sanctity of divine texts and their composition: (Comparative study between the Quran and the Torah)
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The research deals with an important issue that many people are working on, namely the sanctification of the texts on which the timings of the time and the different conditions of the place took place. Do not live up to the ranks of perfection and perfection, and every effort has explanations according to the mind machine, which is not protected by infallibility from error. The great downfall is to put these intellectual efforts in the Bible without separating them from the Word of God. The situation and the place on the adherents of a religion and mixed with the trick of the average individual only to be subject to the words of the teachers of Sharia and docility.

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Publication Date
Sun Jan 01 2023
Journal Name
Journal Of Interdisciplinary Mathematics
On maps of Γ -period 2 on prime Γ- near-rings
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We present the concept of maps Γ- periodi2 on Γ -near-ring S. Our main goal is to research and explore the presence and mapping traits such as h Γ –hom anti-Γ –hom, Γ –α-derivations of Γ -periodi2 on Γ- near-rings.

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Publication Date
Sat Mar 31 2018
Journal Name
Iraqi Journal Of Chemical And Petroleum Engineering
A Comparison between the Product-Refill and the Equalization Oxygen Pressure Swing Adsorption Processes
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This work presents a design for a pressure swing adsorption process (PSA) to separate oxygen from air with approximately 95% purity, suitable for different numbers of columns and arrangements. The product refill PSA process was found to perform 33% better (weight of zeolite required or productivity) than the pressure equalization process. The design is based on the adsorption equilibrium of a binary mixture of O2 and N2 for two of the most commonly used adsorbents, 5A & 13X, and extension from a single column approach. Zeolite 13X was found to perform 6% better than zeolite 5A. The most effective variables were determined to be the adsorption step time and the operational pressure. Increasing the adsorption step

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Publication Date
Mon Jun 01 2009
Journal Name
Journal Of Economics And Administrative Sciences
The contemporary vision of marketing And its impact in crystallizing the chances of success of the new product
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The current research aims at identifying the new marketing directions that in the picture because if the changes and challenges that face the business nowadays, these effect on the future of the new product.

The problem of the research concentrate on the new marketing activities and how to make it appropriate between the product and the market's need, and to fulfill the needs and desire of the customer and it's importance for achieving the economical goals of the organization for a long relationship with the customer.

The resume of the research is about the impact of nowadays marketing and it's effect on knowing the customer instead of concentrating on the important roll of mark

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Publication Date
Mon Jun 20 2022
Journal Name
Journal Of Positive School Psychology
The Role Of Product Lifecycle Cost Technology And Cleaner Production Strategy In Reducing Costs
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Reducing costs and protecting the environment surrounding economic unity has become the concern of many economic units and shifting their ideas towards preserving resources and protecting the environment by adopting strategies and techniques that take into account when applied reducing production costs and protecting the environment, including these strategies and techniques, the technical costs of the product life cycle and the strategy of cleaner production, as the application of the two concepts in local economic units helps to try to keep up with the countries that work to keep up with the success of their economic units by following the concepts that have been successful in&nbsp; Developed countries by maintaining the sustainabilit

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Publication Date
Wed Dec 15 2021
Journal Name
Al-academy
Simulation of myths in industrial product design "the seven eyes amulet as a model"
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The research is to identify the legend of the seven eyes amulet of Babylonian origin and the representations it carried of the link between the Babylonian past and the Islamic present presented in the design works of the promoted products, preserving its impact in the souls as a way to avoid the act of envy, and from this was the research problem that I want to get answers to, which That is (How was the legend of the seven-eyes amulet represented in the design of industrial products?), making its goal to identify how that legend was represented within the design work of marketed industrial products, and in order to reach the answer, the research presented many concepts starting with the legend in its various forms in industrial products.

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Publication Date
Thu Mar 30 2017
Journal Name
Iraqi Journal Of Pharmaceutical Sciences ( P-issn 1683 - 3597 E-issn 2521 - 3512)
Effect of COX-2 Inhibitors Selectivity on Lipid Profile in Hyperlipidemic and Normolipidemic Type 2 Diabetics
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Development of NSAIDS based on inhibiting cyclooxygenase activity. However, the different physiological consequences arrised by appearance of new drugs with different selectivity to COX-2 enzyme upon their administration with their relevant affects on some cardiovascular risk factors. To study the potential effects of relatively  diclofenac and highly specific  celecoxib COX-2 inhibitors on lipid profile and serum C-reactive protein in type 2 diabetes, whom have hyperlipidemia to be compared by their effects with normolipidemic patients. A total number of 34 type 2 diabetics (14 normolipidemics and 20 hyperlipidemics) treated with either diclofenac 100mg/day or celecoxib 200mg/day for eight weeks. Analysis  of results indi

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Publication Date
Wed Sep 14 2016
Journal Name
Journal Of Baghdad College Of Dentistry
Evaluation of the Effect of Bone Morphogenetic Protein-2 on Stability of Dental Implant
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Background: The healing period for bone–implant contact takes 3–6 months or even longer. Application of Escherichia coli-derived recombinant human bone morphogenetic protein-2 (ErhBMP-2) to implant surfaces has been of great interest on osseointegration due to its osteoinductive potential. The objective of this study was to evaluate the effect of ErhBMP-2 on implant stability. Materials and methods: A total of 48 dental implants were inserted in 15 patients. Twenty four implants coated with 0.5 mg/ml ErhBMP-2 (study group). The other 24 implants were uncoated (control group). Each patient was received at least two dental implants at the same session. Both groups were followed with repeated implant stability measurements by me

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