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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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Wed Aug 09 2023
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Effect of Crude Oil on the Geotechnical Properties of Various Soils and the Developed Remediation Methods
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Crude oil still affects many countries because it is one of the essential fuel sources. It makes life more manageable in modern communities and cannot be overstated because it is easy to use and find. However, the pollution caused by its use in industries such as mining, transportation, and the oil and gas business, especially soil pollution, cannot be ignored. Soil pollution is an issue in most communities because it influences people and ecology. Accidental infusions and spills of ore oils are prevalent occurrences leading to the entire or fractional exchange of the soil pore fluid by oil-contaminated soils that have affected the geotechnical engineering properties. The liquid limitations for polluted soil grades silty loam and sa

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Publication Date
Wed Aug 09 2023
Journal Name
Applied Sciences
Effect of Crude Oil on the Geotechnical Properties of Various Soils and the Developed Remediation Methods
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Crude oil still affects many countries because it is one of the essential fuel sources. It makes life more manageable in modern communities and cannot be overstated because it is easy to use and find. However, the pollution caused by its use in industries such as mining, transportation, and the oil and gas business, especially soil pollution, cannot be ignored. Soil pollution is an issue in most communities because it influences people and ecology. Accidental infusions and spills of ore oils are prevalent occurrences leading to the entire or fractional exchange of the soil pore fluid by oil-contaminated soils that have affected the geotechnical engineering properties. The liquid limitations for polluted soil grades silty loam and sa

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Publication Date
Mon Jul 01 2019
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Plant Archives
Effect of the level of corticosteron hormone in the blood of local Iraqi chicken mothers on the sex ratio of the produced offsprings
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This study was conducted to investigate the relationship between corticosterone hormone in the blood of local Iraqi white chicken mothers and the sexual ratio of the hatching chicks. A field experiment located at the Poultry Research Station, Livestock Department, Agricultural Research Department, Ministry of Agriculture for the period from 16 of September 2018 to 25 of December 2018. One hundred and forty birds of Iraqi local chicken mothers (100 females+ 40 males) at the age of 28 weeks were provided from the poultry research station. The birds were raised in individual cages and distributed sequentially to the cages after the numbering of the females. Data were recorded in three periods, each period was of 28 days, and then the general a

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ASSOCIATION OF NFE2L2 GENE POLYMORPHISM (rs35652124) WITH DEVELOPMENT OF RETINOPATHY IN IRAQI TYPE 2 DIABETIC PATIENTS, IN RELATION TO VASCULAR ENDOTHELIAL GROWTH FACTOR AND ENDOCAN SERUM LEVELS
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Scopus
Publication Date
Mon Jan 01 2018
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J. Of University Of Anbar For Pure Science
Synthesis, spectral Characterization and studies of Some Divalent Metal Ion Complexes with Ligand of [3-(1H-indol- 3-yl)-2-(3-(4-methoxybenzoyl)thiouereido)propanoic acid] (MTP
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In this work, prepared new ligand[3- (1H-indol-3-yl) -2- (3-(4- methoxybenzoyl)thiouereido) propanoic acid](MTP) has been synthesized by reaction of 4-Methoxybenzoyl isothiocyanate with tryptophane(1:1), The ligand was characterized by elemental microanalysis C.H.N.S, FT-IR, UV-Vis and 1H,13C NMR spectra, Some transition metals complexes of this ligand were prepared and characterized by FT-IR, UV-Vis spectra, conductivity measurements, magnetic susceptibility and atomic absorption, From obtained results the molecular formula of all prepared complexes were [M(MTP)2] (M+2 =Mn, Co, Ni, Cu, Zn, Cd and Hg), the proposed geometrical structure for all complexes were tetrahedral except copper complex has a square planer geometry around metallic ion

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Thu Dec 01 2016
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Journal Of Engineering
Numerical and Experimental Investigations of the Effect of PVD and Vacuum Pressure on the Degree of Saturation
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    Soft clays are generally characterized by low shear strength, low permeability and high compressibility. An effective method to accelerate consolidation of such soils is to use vertical drains along with vacuum preloading to encourage radial flow of water.  In this research numerical modeling of prefabricated vertical drains with vacuum pressure was done to investigate the effect of using vertical drains together with vacuum pressure on the degree of saturation of fully and saturated-unsaturated soft soils.  Laboratory experiments were conducted by using a specially-designed large consolidometer cell where a central drain was installed and vacuum pressure was applied. All tests were conducted

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Publication Date
Sat Feb 01 2014
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Journal Of Economics And Administrative Sciences
A reflection of the integration of accounting income and economic value added on the decisions of investors
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           The support qualitative information regards as an additional step in the process of decision-making where the method following by companies to provide information help in the creation of value because it is very important to deliver information to investors about their stratigies and what happen truly inside the companies i.e.  every case relating with the expectations of stockhotslder and the prices of markets depending on those expectation ,and if the matter isn’t that there will be lack of confidence thate couldn’t be backed again. The decisions of the investors effected by security ,economic ,political, psychological, emotional ,and financial factors .

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Publication Date
Wed Nov 14 2018
Journal Name
Iraqi National Journal Of Nursing Specialties
The Effect of Different Concentrations of Gilvest with Water on the Setting Time of Phosphate-bonded investment
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Objective: To identify of the effect of the different concentrations of the special liquid (for mixing the investment, Gilvest)
and mixed with water/powder ratio on setting time of phosphate–bonded investment.
Method and materials: The present study is (60) specimens made from phosphate bonded investment divided into (4)
groups (control and experimental groups), (15) specimens for each group. The Gillmore needle device is used to setting
time of phosphate bonded investment mixed with different concentration of Gilvest and water.
Results: Showed that there is a high significant difference (P<0.01) between each groups in the ANOVA test and a
significant difference (P<0.05) between the group (A) and control group i

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Publication Date
Fri Jul 21 2023
Journal Name
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The Effect of Different Types of Aggregate and Additives on the Properties of Self-Compacting Lightweight Concrete
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The major aim of this research is study the effect of the type of lightweight aggregate (Porcelinite and Thermostone), type and ratio of the pozzolanic material(SF and HRM) and the use of different ratios of w/cm ratio(0.32 and 0.35) on the properties of SCLWC in the fresh and hardened state. SF and HRM are used in three percentage 5%,10%, and 15% as a partial replacement by weight of
cement for all types of SCLWC. The requirements of self-compatibility for SCC are fulfilled by using the high performance superplasticizer (G51) at 1.2liter per 100 kg of cement. The values of air dry density and compressive strength at age of 28 days within the limits of structural lightweight concrete. The air dry density and compressive strength at a

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Crossref
Publication Date
Tue May 28 2024
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Study of the optical properties of aluminum films and the effect of current frequency on plasma parameters
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