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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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Sun Jun 07 2009
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Mathematical Relationship between Temperature Change and the Changing Consumption of the Product and Kerosene Consumption Forecasting for these years (2005-2015)
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The aim of this study is to construct a Mathematical model connecting the variation between the ambient temperatures and the level of consumption of kerosene in Iraq during the period (1985-1995), and use it to predict the level of this consumption during the years (2005-2015) based on the estimation of the ambient temperatures.

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Publication Date
Fri Oct 30 2020
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Reforming the insurance sector and its role in stimulation gross domestic product in Iraq for the period (2014-2018)
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The main purpose of the research is to demonstrate the importance of the insurance sector in the economy through its role in providing security for all economic sectors and thus stimulating the gross domestic product and reducing dependence on the output of the oil sector, which may expose the Iraqi economy to several problems and imbalances, I have found that there is a great weakness in the role of the insurance sector in Iraq at the level of government, companies and individuals, and the reason for this is the lack of policies supporting the insurance sector and the lack of work in the strategy of economic diversity and the decrease of security awareness by individuals so became Developing the sector to ensure the urgent need

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Publication Date
Sat Dec 01 2018
Journal Name
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"Testing Caldor's Hypothesis to Estimate the Relationship between the Industrial Production and Growth in Gross Domestic Product in Iraq"
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The study aimed to test the hypothesis of Caldor to estimate the relationship between industrial production and GDP growth in Iraq using with Integration Framework  and to determine the causal relationship in the short and long term using the error correction vector model for the period 1990-2016. the results showed a long-term equilibrium relationship between GDP and industrial output, while Ganger causality tests showed a causal relationship in the long run of GDP to output Subliminal thus illustrated the extent of the recession suffered by the industrial sector, which is supposed to be the driving force of the economy and the development and expansion of the productive base of the industry, so this study recommends attent

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Stable isotope composition in precipitation and groundwater of Shwan Sub-Basin, Kirkuk governorate, northeast of Iraq
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Abstract<p>Stable isotope composition of δ2H and δ18O was investigated in the water resources of the Shwan sub-Basin northeast of Iraq. The study objects conceived the possible factors that affect the stable isotopes’ composition in precipitation additionally to achieve information concerning recharge processes and estimate the groundwater recharge sources. In this study, four precipitation samples were collected at the study area for the 2020–2021 hydrological year. Thirty-two groundwater samples and one surface water sample from Lesser Zab River (LZR) were collected during the same period for two sampling seasons. The results of observed meteorological data show a very small amount of pr</p> ... Show More
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Publication Date
Wed Mar 25 2020
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Comparison of Weight, Components and Chemical Composition of Eggs in Guinea Fowl, Turkey, and Domestic Chicken.
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The present study was carried out to compare the physicochemical characteristics of eggs of guinea fowl, turkeys and domestic chickens outdoor reared in traditional farms in Baghdad, Iraq. A total of 166 fresh eggs; 32 eggs from guinea fowls (Numida meleagris), 44 eggs from turkeys (Meleagris gallopavo) and 90 eggs from domestic chickens; were collected. Egg weight, percentage of egg components, chemical composition (protein, lipids, and ash), and lipid profile were determined. Results revealed the significant differences in egg weight among studied birds. The average egg weights for guinea fowl, turkey, and indigenous chicken were 48.51 ± 0.72, 52.15 ± 0.74 and 61.24 ± 0.22 g, respectively. No significant differences were found in egg c

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Tue Jan 01 2019
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Community Composition of Parasitic Nematodes of Cyprinion Macrostomum from North and Mid West Regions In Iraq
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Tue Sep 11 2018
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Synthesis and characterization of ligands derived 2-hydroxy-1- naphthaldehyde and their complexes with divalent metal ions (Mn+2, Fe+2, Ni +2)
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In this work, Schiff base ligands L1: N, N-bis (2-hydroxy-1-naphthaldehyde) hydrazine, L2: N, N-bis (salicylidene) hydrazine, and L3:N –salicylidene- hydrazine were synthesized by condensation reaction. The prepared ligands were reacted with specific divalent metal ions such as (Mn2+, Fe2+, Ni2+) to prepare their complexes. The ligands and complexes were characterized by C.H.N, FT-IR, UV-Vis, solubility, melting point and magnetic susceptibility measurements. The results show that the ligands of complexes (Mn2+, Fe2+) have octahedral geometry while the ligands of complexes (Ni2+) have tetrahedral geometry.

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Publication Date
Wed Apr 01 2020
Journal Name
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Influence of the variation in the Hubbard parameter (<i>U</i>) on activation energies of CeO<sub>2</sub>-catalysed reactions
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Accurate description of thermodynamic, structural, and electronic properties for bulk and surfaces of ceria (CeO2) necessitates the inclusion of the Hubbard parameter (U) in the density functional theory (DFT) calculations to precisely account for the strongly correlated 4f electrons. Such treatment is a daunting task when attempting to draw a potential energy surface for CeO2-catalyzed reaction. This is due to the inconsistent change in thermo-kinetics parameters of the reaction in reference to the variation in the U values. As an illustrative example, we investigate herein the discrepancy in activation and reaction energies for steps underlying the partial and full hydrogenation of acetyl

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Full synchronization of 2$\times$ 2 optocouplers network using LEDs
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The synchronization of a complex network with optoelectronic feedback has been introduced theoretically, with use of 2×2 oscillators network; each oscillator considered is an optocoupler (LED coupled with photo-detector). Fixing the bias current (δ) and increasing the feedback strength (Ԑ) of each oscillator, the dynamical sequence like chaotic and periodic mixed mode oscillations has been observed. Synchronization of unidirectionally coupled of light emitting diodes network has been featured when coupling strength equal to 1.7×10-4. The transition between non-synchronization and synchronization states by means of the spatio-temporal distribution has been investigated.

Publication Date
Thu May 05 2022
Journal Name
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Comparative Study on the Corneal Endothelial Cell Count between Type 2 Diabetic and Non-Diabetic Patients
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Background: Diabetes mellitus is one of the commonest chronic disorders worldwide with a rapid rise in prevalence. In Iraq its prevalence is high especially in elderly age group. Patients with type 2 diabetes mellitus have higher vulnerability for complications, whether microvascular or macrovascular. Ocular complications are common in diabetes mellitus, and comprise diabetic retinopathy, diabetic papillopathy, cataract, glaucoma, dry eye disease and diabetic keratopathy. Diabetic keratopathy involves endothelial and epithelial tissues of the cornea, leading to persistent epithelial defect, corneal erosion, or corneal ulcers.

Aim of the Study: To compare the mean corneal endothelial cell count between patients wi

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