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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 Dec 20 2013
Journal Name
Journal Of The College Of Basic Education
Determination of Some heavy metals in Different vinegar Samples Applied in folk medicine by flame atomic absorption Spectrophotometry
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A study was carried out to analysis of some heavy metals in nine different types of vinegar, belong to Grape, Apple, Synthetic White, Date, Hawthorn, Garlic, Cactus, Pomegranate and Ginger vinegar, which are locally available in Iraqi folk medicine markets. The concentrations of heavy metals in the studied samples including, Cr, Mg, Mn, Zn, Fe, Cd, Ni, Pb and Ag, were determining by using flame atomic absorption spectrophotometry. All data were subjected to statistical analysis by calculating accuracy, precision and correlation coefficient for each concentrations level. The results indicate that Ni was recorded the highest concentration in all studied samples except, Ginger and cactus vinegar, each one receded the highest concentration valu

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Publication Date
Sun Nov 01 2015
Journal Name
Journal Of Natural Sciences Research
Genetic Study for G-Protein Coupled Receptor from Saccharomyces Cerervisiae and From Sera of Patients with Heart Thrombosis
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Aim of the present study is Identification of specific gene for GPCR using specific primers .and identification of difference in PCR analysis in patients with heart thrombosis and compared with healthy, Sequencing of PCR product regarding GPCR compared for all three subject, Identification the similarity of human GPCR with local strain of yeast fifty healthy control and fifty patients with thrombosis which diagnosed medically with cardiac specific troponin t, troponin 1 levels and electro myocardiogram ECG. The aged for all subjects ranged (39-75) years patients were lying in cardiac care unit at Ibn- al- Nafees teaching hospital and Sheikh Zayed teaching hospital. Genomic DNA of whole blood was extracted from buffy coat and cell cu

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Publication Date
Sun Aug 31 2014
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Petroleum system modeling and risk assessments of Ad’daimah oil field: a case study from Mesan Governorate, south Iraq
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Publication Date
Fri Jun 29 2018
Journal Name
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Experimental Investigation of Short Square Normal and Hybrid Fiber Reactive Powder Concrete Columns Subjected to Chloride Solution Attack
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In this research, the structural behavior of reinforced concrete columns made of normal and hybrid reactive powder concrete (hybrid by steel and polypropylene fibers) subjected to chloride salts with concentration was 8341.6 mg/l. The study consists of two parts, the first one is experimental study and the second one is theoretical analysis.  Three main variables were adopted in the experimental program; concrete type, curing type and loading arrangement. Twenty (120x120x1200) mm columns were cast and tested depending on these variables. The samples were reinforced using two different bars; Ø8 for ties and Ø12 with minimum longitudinal reinforcement (0.01Ag). The specimens were divided into two main groups based o

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Publication Date
Sun Dec 01 2013
Journal Name
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Spectrophotometric Determination of Ketotifen Drug in Pure form and Pharmaceutical Preparation Using Bromothymol Blue Via Ion-Pair Formation
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Publication Date
Wed Oct 15 2025
Journal Name
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Marginal leakage of amalgam and modern composite materials related to restorative techniques in class II cavity (Comparative study)
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Background: Restoration of the gingival margin of Class II cavities with composite resin continues to be problematic, especially where no enamel exists for bonding to the gingival margin. The aim of study is to evaluate the marginal leakage at enamel and cementum margin of class II MOD cavities using amalgam restoration and modern composite restorations Filtek™ P90, Filtek™ Z250 XT (Nano Hybrid Universal Restorative) and SDR bulk fill with different restoratives techniques. Materials and method: Eighty sound maxillary first premolar teeth were collected and divided into two main groups, enamel group and cementum group (40 teeth) for each group. The enamel group was prepared with standardized Class II MOD cavity with gingival margin (1 m

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Publication Date
Mon Feb 01 2016
Journal Name
Journal Of Engineering
Removal of Fluoride Ions from Wastewater Using Green and Blue-green Algae Biomass in a Fluidized Bed System
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The removal of fluoride ions from aqueous solution onto algal biomass as biosorbent in batch and continuous fluidized bed systems was studied. Batch system was used to study the effects of process parameters such as, pH (2-3.5), influent fluoride ions concentration (10- 50 mg/l), algal biomass dose (0–1.5 g/ 200 ml solution), to determine the best operating conditions. These conditions were pH=2.5, influent fluoride ions concentration= 10 mg/l, and algal biomass dose=3.5 mg/l. While, in continuous fluidized bed system, different operating conditions were used; flow rate (0.667- 0.800 l/min), bed depth (8-15 cm) corresponded to bed weight of (80- 150 g). The results show that the breakthrough time increases with the inc

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Publication Date
Fri Aug 19 2022
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Application of TOPSIS method for Multi-Criteria Decision Making for poultry fields By using GIS in Hilla district
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Statistical methods and statistical decisions making were used to arrange and analyze the primary data to get norms which are used with Geographic Information Systems (GIS) and spatial analysis programs to identify the animals production and poultry units in strategic nutrition channels, also the priorities of food insecurity through the local production and import when there is no capacity for production. The poultry production is one of the most important commodities that satisfy human body protein requirements, also the most important criteria to measure the development and prosperity of nations. The poultry fields of Babylon Governorate are located in Abi Ghareg and Al_Kifil centers according to many criteria or factors such as the popu

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Tue Jan 29 2019
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Using Quality and Accreditation standard in performance improvement of education institutions: بحث تطبيقي في كلية الهندسة جامعة بغداد
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enjoyed the process of the development of higher education institutions attention of most countries of the world and to reconsider its objectives and programs and administrative and organizational structures, and it was the most important development of the application of Quality Assurance and Accreditation Standards (QAAS) tools, as the aim of these tools to the application of advanced with a far-reaching impact on all of the disciplines in the organization methods education that contribute, and plays a performance audit an important role in verifying the extent to which carried out these institutions activities or programs effectively and efficiently, economic, There are a number of objectives for the search of the most important attem

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Thu Oct 12 2023
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Association of Human Herpesvirus Type 8 (HHV-8) expression in patients with Kaposi’s sarcoma: A clinico-immunohistochemical study
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Abstract Background: Kaposi’s sarcoma (KS) is an angioproliferative neoplastic disorder that occurs in different epidemiological forms. Human Herpesvirus type 8 (HHV-8) is established as a causative agent of KS that has been mentioned in textbooks and literature. In the last two decades, KS cases were up searched through many Iraqi medical researches which have been published, but unfortunately, none of which had confirmed this association. Objectives: To assess the association of latent nuclear antigen-1(LANA-1) of HHV-8 among KS patients with clinicopathological parameters and to evaluate if this procedure is valuable for diagnosing this disease through the first immunohistochemical study in Iraq. Methods: This is a clinico-immunohis

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