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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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Mon Mar 07 2022
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Journal Of Educational And Psychological Researches
Google Classroom in Teaching Writing Composition for College Students
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Technology plays a vital role in all walks of life, one of these is Education. Google Classroom is one of the educational tools that are free of cost and recently has gained popularity within a short period in many countries, including Iraq. The primary purpose of this study is to explore the Google Classroom use in EFL learners' composition writing. The sample of the study is EFL Second-year College students from the College of Science for Women /Computer Science Department, which consisted of (35) students who have implemented Google Classroom for at least one semester in their classroom. The students were asked to finish two uncompleted paragraphs that have the only main idea and write a suitable conclusion to each one. The results sh

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Wed Jun 14 2023
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Fractal and its implications for industrial product design
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The current research dealt with the rapid development of industrial product design in recent times, and this development in the field of design led to the emergence of modern trends in many terms and theories to direct greater interest in the cognitive foundations of design and its relationship with the components of other natural sciences, and despite the impressive technological development, nature remains With its content of formative values and structural dimensions, it is the first source of inspiration and the source of all modern mathematical sciences and theories, as God made them tend towards organization to continue to provide us with endless inspiration. Hence, the fractional one, which is an important part of dedicating the d

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Wed Sep 11 2019
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Journal Of Mechanical Engineering Research And Developments
INDUSTRIAL TRACKING CAMERA AND PRODUCT VISION DETECTION SYSTEM
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Wed Nov 29 2023
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H. Pylori and Autoimmune Disorders: Unraveling the Links between Chronic Infection and Immune Dysfunction: Review Paper
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The human stomach is home to the Gram-negative bacterium Helicobacter pylori, which has been connected to several gastrointestinal disorders. There may be a link between H. pylori infection and the start of autoimmune disorders, according to recent research. This review examines the intricate connections between persistent H. pylori infection, immune system dysregulation, and their possible role in initiating autoimmune disorders. The study begins with a summary of H. pylori infection and its prevalence worldwide, emphasizing the mounting data that connects this bacterium to autoimmune disorders. Then, using experimental data from animal models and epidemiological research as support, it undertakes a thorough review of autoimmune di

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Thu Oct 10 2019
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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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Fri Jan 01 2010
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Electrical and Optical Properties of :H Thin Films Prepared by Thermal Evaporation Method
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Thin a-:H films were grown successfully by fabrication of designated ingot followed by evaporation onto glass slides. A range of growth conditions, Ge contents, dopant concentration (Al and As), and substrate temperature, were employed. Stoichiometry of the thin films composition was confirmed using standard surface techniques. The structure of all films was amorphous. Film composition and deposition parameters were investigated for their bearing on film electrical and optical properties. More than one transport mechanism is indicated. It was observed that increasing substrate temperature, Ge contents, and dopant concentration lead to a decrease in the optical energy gap of those films. The role of the deposition conditions on value

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Publication Date
Sun Jan 01 2023
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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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Wed Sep 14 2016
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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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Publication Date
Thu Mar 30 2017
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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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Experimental and Quantum Chemical Studies on the Corrosion Inhibition of Mild Steel By 2-((Thiophen-2-Ylmethylene) Amino)Benzenethio in 1M HCl
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The impact of a Schiff base namely 2-((thiophen-2-ylmethylene)amino)benzenethiol  to corrode mild steel in 1 M HCl  resolved was evaluated using different weight loss technique and scanning electron microscopy (SEM).different weight measurements to expand that the 2-((thiophen-2-ylmethylene) amino) benzenethiol  inhibits  the corrosion of mild steel through adsorbing  of  top for mild steel and block the active locality. The inhibitive impacts of 2-((thiophen-2-ylmethylene)amino)benzenethiol  increase with increasing concentration and decrease with increasing temperature. SEM to checking revealed that the alloy surface was quite unaffected and formed protective film on its surface. The investigated

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